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1 New Keynesian Theories of Inflation and Output A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy University of Western Sydney 2012 By Cung Cao
1
New Keynesian Theories of
Inflation and Output
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy
University of Western Sydney
2012
By
Cung Cao
2
Statement of Authentication
The work presented in this thesis is, to the best of my knowledge and belief, my own
and original except as acknowledged in the text. I hereby declare that I have not submitted
this material, either in full or in part, for a degree at this or any other institution.
Signature ...........................................................
Cung Cao
3
Acknowledgements
I would like to thank my supervisors: Professor B. Bhaskara Rao, Professor Steve
Keen and Associate Professor Brian Pinkstone for their patience, guidance and wisdom.
I am very grateful to Professor John Lodewijks, in his capacity as the head of the
school of economics at the University of Western Sydney for his support and valuable
comments on this thesis. I would also like to acknowledge that I received very helpful
comments from two anonymous examiners.
I would like to thank the University of Western Sydney for supporting my research
with a scholarship (UWS Postgraduate Research Award).
Finally, I would like to thank my family and friends for their support.
4
TABLE OF CONTENTS
Abstract
Introduction
7
8
Chapter 1
1.1
1.2
1.3
1.4
New Keynesian Economics: A Review of the Literature
Main Features of New Keynesian Economics
Microeconomic Foundations of Prices Rigidities
Real Rigidities in the Labour Market
Conclusion
12
12
14
19
22
Chapter 2
2.1
2.2
2.3
2.4
2.5
2.6
From Sticky-Prices to Sticky-Information to Sticky-Knowledge
Introduction
The Philips Curve and some Developments
The Sticky-Prices Approach
The Sticky-Information Approach
The Sticky-Knowledge Phillips Curve
Conclusion
23
23
24
28
33
42
51
Chapter 3
3.1
3.2
3.3
3.4
3.5
An Empirical Survey of the New Keynesian Phillips Curve
Introduction
Sticky-Price-Single-Equation Estimations of the NKPC
DSGE Model-Based Estimations of the NKPC
Estimations of the Sticky-Information Phillips Curve (SIPC)
Conclusion
53
53
53
63
65
68
Chapter 4
4.1
4.2
4.3
Proxies for Real Marginal Cost
Introduction
Literature Review
Proxies for Real Marginal Cost
70
70
70
79
5
4.4
4.5
4.6
4.7
4.8
4.9
4.10
Proxies for Inflation Expectations
Data and Estimation Strategy
Empirical Comparisons
Robustness Analysis
An Alternative Instrument Set
Endogeneity of Real Marginal Cost
Conclusion
83
84
85
88
92
94
97
Chapter 5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
Estimations of the Phillips Curve Using Survey Measures of
Inflation Expectations
Introduction
Are Survey Measures of Inflation Expectations Rational?
Data and Estimation Strategy
Tests of Rationality of Survey Measures of Inflation Expectations
Empirical Comparisons Between Job Finding Probability, the
Output Gap and Labour’s Share of Income as Proxy for Real
Marginal Cost
Robustness Analysis
Conclusion
Appendix to Chapter 5
100
100
100
103
105
114
115
116
120
Chapter 6
6.1
6.2
6.3
6.4
6.5
The Flattening of the Phillips Curve
Introduction
The Flattening of the Phillips Curve
Tests for Structural Changes
Competing Explanations
The Labour Market and the Slope of the Phillips Curve
160
160
160
167
170
173
6
6.6
6.7
Conclusion
Appendix to Chapter 6
183
185
Chapter 7
7.1
7.2
7.3
7.4
7.5
7.6
Non-Stationary Inflation and the Phillips Curve
Introduction
Time Series Properties of the Variables in the Phillips Curve
Tests for Cointegration
Does Non-Stationary Inflation Invalidate Previous Research
Findings?
Conclusion
Appendix to Chapter 7
193
193
193
195
196
201
203
Chapter 8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Estimations of the Phillips Curve for Australia with Different
Proxies for Real Marginal Cost
Introduction
The Australian Phillips Curve
The Data
Proxies for Real Marginal Cost
Empirical Comparisons Between Job Finding Probability, the
Output Gap and Labour’s Share of Income as Proxy for Real
Marginal Cost
Robustness Analysis
Conclusion
206
206
207
209
211
212
216
226
Chapter 9 Summary and Conclusions 228
References 234
7
Abstract
This thesis examines two important issues in the empirical literature on the new
Keynesian Phillips curve (NKPC). First, are inflation expectations consistent with rational
expectations? Many researchers find that the old Keynesian Phillips curve with adaptive
expectations fits the data better new Keynesian Phillips curve with rational expectations.
Second, do real marginal costs drive inflation dynamics? Gali and Gertler (1999) argue that
the reason why the NKPC fits the data poorly is because traditional empirical work on the
Phillips curve uses some output gap measures as a proxy for real marginal cost rather than
labour’s share of income. Our results suggest that the pure rational expectations new
Keynesian Phillips curve might be misspecified and that the hybrid new Keynesian Phillips
curve fits the data best. The relative importance of backward-looking inflation expectations
and forward-looking inflation expectations changes over time. Backward-looking inflation
expectations dominate forward-looking inflation expectations independent of which measures
of real marginal cost are used. Furthermore, we have tested the rationality of various survey
measures of inflation expectations; our results indicate that these survey measures of inflation
expectations are biased and inefficient. We have also showed that there are Granger
causalities from the professional forecasters (as represented by the SPF forecasts and the
Greenbook forecasts) to households (as represented by the Michigan forecasts), but no
Granger causality in the opposite direction.
Our empirical results suggest that the probability of finding a job or job finding
probability (JFP) is a better proxy for real marginal cost than the output gap and labour’s
share of income, at the same time JFP provides a direct link between frictions in the labour
market and the Phillips curve relationship. The use of job finding probability as a proxy for
real marginal cost is a novel aspect of this thesis.
We have also examined the flattening of the slope of the reduced-form Phillips curve
for the United States over the last 20 years; this phenomenon is also observed in many other
industrialized countries. We proposed the flattening of the slope of the reduced-form Phillips
curve is caused by deindustrialization and the computer revolution have shifted employment
from the manufacturing sectors to the service sectors; these structural changes in the labour
market have changed jobs’ skill requirements, increasing heterogeneity (real rigidities)
between workers, producing more mismatches in the labour market.
8
Introduction
Although the 1960s and 1970s macroeconomic models of IS-LM1 and the
Expectations-Augmented Phillips curve incorporated adaptive expectations into
macroeconomic analysis, the new classical models incorporated rational expectations.
Rational expectations modelling became a popular modelling technique. However, some
Keynesians, who developed explicit micro-foundations for macroeconomic theories, argued
that such micro-founded models are methodologically superior to ad hoc models based on
empirical considerations. Implicit in this view is that micro-founded models can explain
macro-phenomena better and yield improved and more accurate predictions. These
economists are known as the new Keynesians and can said to be the dominant group of
macroeconomists.
In a way the micro-founded new Keynesian models can also seen as a methodological
attempt to validate Keynesian models in theory also. Consequently, both the new classical
and new Keynesian models use similar optimization techniques and rational expectations.
They differ only in respects of their assumptions about adjustment lags, market imperfections
and imperfections in information. In the new classical models price-quantity adjustments are
fast, markets are perfectly competitive and information is perfect. Therefore, the economy
reaches equilibrium in a short period and fluctuations in output, prices and unemployment are
due to random shocks and short lived. In the Keynesian models price-quantity adjustments
take a long time and therefore the economy will depart from its long run equilibrium for a
number of periods.2 Fluctuations caused by shocks to the system persist and policy is
necessary to move the economy towards its long run equilibrium. These Keynesian objectives
are achieved by the new Keynesians in a number of ways. To limit the scope, this thesis will
examine only new Keynesian models with rational expectations based on sluggish price
adjustments and sluggish adjustment in expectations. It is our contention that that the sticky
information Phillips curve (Mankiw and Reis (2002) and Carroll (2003)), and the hybrid new
1 Rao (2006, p.2) points out that some post Keynesian economists do not consider Hick’s IS-LM model as
Keynesian, but as neoclassical instead. He suggests that “it is perhaps more appropriate to call the textbook
Keynesian models Hicksian rather than Keynesian”.
2 I thank Professor Steve Keen for clarifying that that term Keynesian economics in this thesis refers to the
neoclassical synthesis interpretation of Keynes’ work, this approach is based on the pioneering work of “Hicks
(1937), Modigliani (1944), Klein (1947), Samuelson (1948) and Hansen (1953). The IS-LM model formed the
backbone of theorizing within this approach…Following Modigliani’s contribution; Keynesian economics was
seen to be the economics of wage and price rigidities. The destabilizing impact of unstable expectations was
played down in this approach” (Snowdon and Vane, 2005, p.70-71).
9
Keynesian Phillips curve (Furher (1995) and Gali and Gertler (1999)) can be interpreted as a
class of bounded rationality models of Simon. Simon (1957, 1959, 1979, 1991) believes that
human rationality is limited because agents don’t have all of the knowledge (for example,
about an uncertain future) and the mental capacity to process all relevant information, as a
result, people make choices that are satisfactory – good enough – rather than optimal.
Many new Keynesian economists use a micro-founded Phillips curve and at times a
monetary policy rule such as the Taylor Rule to explain the observed macroeconomic
fluctuations and dynamics. In this framework the key relationship is the Phillips curve. The
success or failure of the new Keynesian macro-model to explain macroeconomic fluctuations
depends mainly on the specification used for the Phillips curve. However, there are some
differences between the new Keynesians on the specification of this important relationship.
This is the subject matter of this thesis. We review the literature justifying different
specifications of the Phillips curve and estimate these specifications with alternative
econometric methods. After examining the pros and cons of these empirical estimates we
draw our conclusions about their relative merits. Our empirical results are based on the US
data. However, towards the end of this thesis we also estimate a Phillips curve with the
Australian data.
Organizational Structure
This thesis consists of nine chapters. Chapter 1 briefly surveys the main developments
in new Keynesian economics. New Keynesians attempt to develop business cycle theories,
which explain prices rigidities and market failures based on rational expectations with micro-
foundations. We will focus on potential causes of real and nominal rigidities and various
structural features of the labour market that could explain involuntary unemployment.
Chapter 2 briefly examines the main developments in the Phillips curve literature and
reviews the debate on its micro-foundations. The micro-foundations based Phillips curve is
known as the new Keynesian Phillips curve (NKPC hereafter).The NKPC literature can be
divided into two categories: models based on sluggish adjustments in prices and sluggish
adjustments of inflation expectations. This has implications for the specification of the
Phillips curve and therefore for the inflation—output dynamics and the effectiveness of
discretionary policies. Proponents of models with sluggish expectations, such as Mankiw and
Reis (2001, 2002), argue that these models can explain stylized facts better than models with
sluggish price adjustments. We will attempt to argue that Mankiw and Reis and other new
10
Keynesians have neglected an earlier rationalization for sluggish adjustments in expectations,
based on the bounded rationality approach of Herbert Simon.
Chapter 3 surveys selected empirical works on the new Keynesian Phillips curve
(NKPC) for the USA. We will focus on recent developments with regard to the abilities of
these models to fit the data, whether labour’s share of output or the output gap is the
appropriate measurement for real marginal cost, the relative importance of forward and
backward-looking expectations and whether these models assume that price adjustments are
sluggish or expectation adjustments are sluggish.
Chapter 4 examines two important issues raised by the work of Gali and
Gertler (1999) and Gali, Gertler and Lopez-Salido (2001, 2005). First, the new Keynesian
Phillips curve (NKPC) needs to take into account labour market frictions. Second, the output
gap (GAP) may not be an appropriate proxy for real economic activity because it assumes
that the labour market clears. In their influential paper, Gali and Gertler (1999) argue that the
reason why the NKPC fits the data poorly is because traditional empirical work on the
Phillips curve uses some output gap measures as a proxy for real marginal cost rather than
labour’s share of income. We will attempt to argue that the probability of finding a job or job
finding probability (JFP) is a better proxy for real marginal cost than GAP and labour’s share
of income, at the same time JFP provides a direct link between frictions in the labour market
and the Phillips curve relationship.
Chapter 5 examines the rationality of the Greenbook, the Survey of Professional
Forecasters (SPF) and the Michigan survey measures of inflation expectations. We will
estimates various specifications of the Phillips curve using survey measures of inflation
expectations as proxy for inflation expectations and examine whether job finding probability
(JFP), the output gap or labour’s share of income is a better proxy for real marginal cost.
Chapter 6 examines the flattening of the slope of the reduced-form Phillips curve for
the United States over the last 20 years; this phenomenon is also observed in many other
industrialized countries. The flattening of the Phillips curve raises two important questions:
What explains the flattening of the Phillips curve? And what are the implications of this
phenomenon for the proper conduct of monetary policy? We will attempt to argue that
increase in specialization of labour and lower and more-stable inflation that led to less-
frequent price adjustment are the causes of the flattening of the Phillips curve in the United
States and other industrialized countries.
11
Chapter 7 argues that the finding that the United States inflation rates are non-
stationary does not necessarily invalidate previous body of empirical research that do not take
into account the non-stationary behaviour of inflation.
Chapter 8 estimates various specifications of the Phillips curve for Australia using
three proxies for real marginal cost: job finding probability (JFP), the output gap and labour’s
share of income as well as survey measures of inflation expectations and mathematical
expectations as proxy for inflation expectations. We will attempt to show that job finding
probability (JFP) is a better proxy for real marginal cost than the output gap or labour’s share
of income. Chapter 9 concludes.
Relationship to Previous Research by the Author
The idea of linking the definitions of information and knowledge, and drawing on the
sticky nature of knowledge to explain frictions in the economy as the result of human
bounded rationality, was previously considered in my Master’s thesis, completed at the
University of New South Wales in 2007 under the title “Asymmetric and Imperfect
Knowledge: A Proposal to Replace Unbounded Rationality with Bounded Rationality”. This
was subsequently published as a book with the same title in 2008 by VDM Verlag Dr.
Muller. In this thesis some of the themes from that earlier work, particularly two chapters
from my Master’s thesis: Asymmetric Knowledge and Unemployment (chapter 2, pp. 30-41)
and Imperfect Knowledge and Economic Fluctuations (chapter 3, pp. 42-68) are elaborated
on and developed in far more detail. Where I draw on that earlier work, the page references
are clearly indicated and those contributions acknowledged in full. The current work builds,
elaborates, extends and develops the earlier contributions. For example, in my Master’s thesis
I suggested that the Mankiw and Reis’ (2002) sticky information Phillips curve can be
considered as way of modelling bounded rationality. In this thesis I suggested that Fuhrer and
Moore (1995) and Gali and Gertler’s (1999) hybrid new Keynesian Phillips curve can also be
considered as a way of modelling bounded rationality. Much of our empirical work in this
thesis is a direct response to Gali and Gertler’s (1999) empirical finding that the reason why
the new Keynesian Phillips curve fits the data poorly is because traditional empirical work on
the Phillips curve uses some output gap measures as a proxy for real marginal cost rather than
labour’s share of income. Another important issue that the work of Gali and Gertler (1999)
raised is the new Keynesian Phillips curve literature needs to take into account labour market
frictions. This motivated us to use job finding probability as a proxy for real marginal cost.
12
CHAPTER 1 New Keynesian Economics: A Review of the Literature
“It is time to put Keynes to rest in the economists’ Hall of Fame, where he certainly
belongs, and to proceed with integrating the most relevant contributions by Keynes
and his early and late followers with other strands of macroeconomic theory”
(Lindbeck, 1998, p.178).
1.1Main Features of New Keynesian Economics
New Keynesian economics is a school of thought in modern macroeconomics that
evolved from the ideas of John Maynard Keynes. New Keynesian economics emerged as a
response to the theoretical challenge of rational expectations and new classical economics in
the 1970s.New Keynesian economics attempts to derive Keynesian propositions with rational
expectations and optimizing behaviours. New Keynesian economics can be considered as
attempts to provide plausible microfoundations to explain wages and prices rigidities in the
old Keynesian spirit.
Mankiw and Romer (1991) define new Keynesian economics with reference to the
following pair of questions (Snowdon and Vane, 2005, p.363, Romer, 1993, p. 20-21):
Question 1 Does the theory violate the classical dichotomy? That is, is money non-neutral?
Question 2 Does the theory assume that real market imperfections in the economy are crucial
for understanding economic fluctuations?
Of the mainstream macroeconomics research programmes only new Keynesians
answer both questions in the affirmative; real business cycle models gave a negative response
to both questions. The primary disagreement between new classical and new Keynesian
economists is over how quickly wages and prices adjust. New classical economics assume
that wages and prices are flexible, therefore markets clear quickly. New Keynesian
economists recognize that accepting that the labour market clears implies there are no
involuntary unemployment and accepting that there are no wages and price rigidities implies
the monetary policy is neutral. Hence, many new Keynesian models attempt to explain wages
and prices stickiness in order to justify the existence of involuntary unemployment and that
monetary disturbances have real effects.
The term new-Keynesian theory was first used by Parkin and Bade in 1982 in their
textbook on modern macroeconomics. However, this line of thought had been conceived in
13
the 1970s during the first phase of the new classical revolution (Snowdon and Vane, 2005,
p.361).The word new rather than neo to describe the recent work in the classical tradition
distinguishes it from what Paul Samuelson in the early postwar period called the neoclassical
synthesis of old-Keynesian macroeconomics and classical microeconomics. In turn, the word
new rather than neo is used for the recent work in the Keynesian tradition, so that it can be
properly juxtaposed to the new-classical approach (Gordon, 1990.p. 1115).
New Keynesian economists are an extremely heterogeneous group partly because
there is no unifying new Keynesian model approximating the behaviour of the economy.
Some of the economists who have made significant contributions to the new Keynesian
literature are: Gregory Mankiw, Lawrence Summers, Olivier Blanchard, Stanley Fischer,
Bruce Greenwald, Edmund Phelps, Joseph Stiglitz, Ben Bernanke, Laurence Ball, George
Akerlof, Janet Yellen, David Romer, Christina Romer, Robert Hall and John Taylor, Dennis
Snower, Assar Lindbeck, Christopher Carroll, Ricardo Reis, Alan Blinder and Guillermo
Calvo. The proximity of US new Keynesians to the east and west coasts inspired Robert Hall
to classify these economists under the general heading of ‘Saltwater’ academic institutions:
Harvard, MIT, Columbia, Princeton, Stanford and Berkeley. By a strange coincidence new
classical economists tend to be associated with ‘Freshwater’ academic institutions: Chicago,
Rochester, Minnesota and Carnegie-Mellon (Snowdon and Vane, 2005, p.362).
Mankiw and Romer (1991) argue that much of new Keynesian economics could be
considered as ‘new monetarist economics’ because of the following two reasons: First, there
is no unified new Keynesian view of the role of fiscal policy although new Keynesians do
give much greater weight to the stabilizing role of monetary policy compared to the old
Keynesian view. Second, new Keynesians do not hold a unified view on the desirability and
feasibility of activist (discretionary) stabilization policy. While most new Keynesians accept
Friedman’s critique relating to the problems that arise from uncertainty, time lags and the
potential for political distortions of policy, they also reject the ‘hard core’ monetarist
argument relating to the need for a strict monetary growth rate rule (Snowdon and Vane,
2005, p.364).
From a modeling perspective, the main difference between new classical and new
Keynesian models is the price-setting behaviour. In contrast to the price takers who inhabit
new classical models, new Keynesian models assume price-making monopolistic, rather than
perfectly competitive, firms. Most new Keynesian models assume that expectations are
formed rationally. However, some prominent new Keynesians (Blinder, 1987; Phelps, 1992)
14
remain critical of the theoretical foundations and question the empirical support for the
rational expectations hypothesis. New Keynesians regard both supply and demand shocks as
potential sources of instability, but, unlike real business cycle theorists when it comes to an
assessment of a market economy’s capacity to absorb such shocks so that equilibrium (full
employment) is maintained. Many new Keynesians (but not all) also share Keynes’s view
that involuntary unemployment is both possible and likely (Snowdon and Vane, 2005,
p.365).In short, new Keynesian economics is characterized by imperfect competition,
incomplete markets, heterogeneous labour, fairness concerns and asymmetric information. A
perceived weakness with new Keynesian school that is often pointed out by its critics is that
there are many different models addressing specific issues, rather than a universal model
approximating the behaviour of the economy, the new Keynesian models appear flexible and
ad hoc to some while realistic to others (Cao, 2008, p.46).
1.2 Microeconomic Foundations of Prices Rigidities
As mentioned previously, one of the inadequacies of the neoclassical synthesis was its
assumption that prices did not adjust immediately to equilibrate supply and demand, so that,
changes in demand have real effects. The natural response to the collapse of the synthesis was
thus to investigate whether imperfect price adjustment could be derived from realistic
assumptions about the microeconomic environment, rather than assumed (Romer, 1993, p.6-
7). New Keynesians attempt to develop business cycle theories, which explain prices
rigidities with rational expectations. Various phenomena were identified as potential causes
of prices rigidities. For convenience we will divide the explanations of rigidities between
those that focus on nominal rigidities and those that focus on real rigidities. A nominal
rigidity occurs if something prevents the nominal price level from adjusting. A real rigidity
occurs if some factor prevents real wages from adjusting or there is stickiness of one wage
relative to another (Snowdon and Vane, 2005, p.365).
Nominal Rigidities
Early new Keynesian models focus on providing possible theoretical explanations for
why nominal adjustment might be incomplete. These models (Fischer (1977) and Phelps and
Taylor (1980)) showed that nominal rigidities were capable of producing real effects in
models that incorporate rational expectations, providing the assumption of continuously
clearing markets was dropped, that is, perfect and instantaneous wage and price flexibility.
15
Following these contributions it became clear to everyone that the rational expectations
hypothesis did not imply the end of Keynesian economics. The crucial feature of new
classical models was shown to be the assumption of continuous market clearing, that is,
perfect and instantaneous wage and price flexibility (Snowdon and Vane, 2005, p.367). There
are two types of nominal rigidities models: staggered wages and prices and menu costs.
Staggered Wages and Prices
The Fischer (1977) and Taylor (1980) models are examples of two early new
Keynesian models that attempt to provide theoretical justifications for nominal wage
rigidities. The Fischer (1977) and the Taylor (1980) models introduce nominal inertia in the
form of long-term wage contracts. That is, not everyone in the economy set new wages and
prices every period, but, adjustment is staggered. In developed economies wages are not
determined in spot markets but tend to be set for an agreed period in the form of an explicit
(or implicit) contract (Snowdon and Vane, 2005, p.367). The Fischer (1977) and the Taylor
(1980) models posit that wages and prices are set by multi-period contracts. In each period,
the contracts governing some predetermined fraction of wages and prices expire and are
renewed. Staggered wages and prices lead to gradual adjustment of the price level to nominal
disturbances. As a result, aggregate demand disturbances leads to monetary non-neutrality,
policy rules can be stabilizing even under rational expectations (Romer, 2001, p.280).
The Fischer (1977) and Taylor (1980) models differ in one important respect, the
Fischer (1977) model assumes prices are predetermined but not fixed (i.e. different prices can
be set in each period). The Taylor (1980) model assumes fixed prices throughout contract. In
the Fischer (1977) and Taylor (1980) models, the timing of price changes is determined
solely by the passage of time, this time dependent approach is an approximation introduced to
slow down the adjustment process. In most cases, firms are free to respond to economic
conditions and developments; therefore state dependent pricing needs to be considered. The
Caplin-Spulber (1987) model emphasizes the importance of endogenous state dependent
pricing. In the Caplin-Spulber (1987) model, price changes are determined endogenously so
that the fraction of prices that changes each period can vary.
Some critics pointed out that the existence of such contracts is not explained from
solid microeconomic principles. In most cases, workers and firms are free to respond to
economic developments. An immediate question that arises from the staggered wages and
prices approach is why are long-term wage agreements formed if they increase
16
macroeconomic instability? Mankiw (1990) points out that staggered wages and prices
models implies that real wages are countercyclical, which is not consistent with empirical
evidence. A monetary expansion increases employment by lowering the real wages. Yet,
empirical evidence suggests that real wages appear to be weakly procyclical. Mankiw notes,
if this were the case then recessions would be “quite popular”. While many people will be
laid off, most people who remain employed will enjoy a higher real wage (Snowdon and
Vane, 2005, p.371). We will re-examine staggered wages and prices models in more details in
chapter 2.
Coordination Failure
Coordination failures can occur when firms strategically set prices based on other
firm’s actions (Cooper and John, 1988). Some new Keynesian economists suggest recessions
are the results of coordination failures. Coordination problems can arise in the setting of
wages and prices because those who set them must anticipate the actions of other wage and
price setters. Union leaders negotiating wages are concerned about the concessions other
unions will win. Firms setting prices are mindful of the prices other firms will charge.
Suppose the economy is made up of two firms. After a fall in the money supply, each
firm must decide whether to cut its price. Each firm wants to maximize its profit, but its profit
depends not only on its pricing decision but also on the decision made by the other firm. If
neither firm cuts its price, the amount of real money (the amount of money divided by the
price level) is low, a recession ensues, and each firm makes a profit of only, for example,
fifteen dollars. If both firms cut their price, real money balances are high, a recession is
avoided, and each firm makes a profit of thirty dollars. Although both firms prefer to avoid a
recession, neither can do so by its own actions. If one firm cuts its price while the other does
not, a recession follows. The firm making the price cut makes only five dollars, while the
other firm makes fifteen dollars. The main point of this example is that each firm’s decision
influences the set of outcomes available to the other firm. When one firm cuts its price, it
improves the opportunities available to the other firm, because the other firm can then avoids
the recession by cutting its price. The inferior outcome, in which each firm makes fifteen
dollars, is an example of a coordination failure. If the two firms could coordinate, they would
both cut their price and reach the preferred outcome. In the real world, unlike in this example,
coordination is often difficult because the number of firms setting prices is large. The moral
of the story is that even though sticky prices are in no one’s interest, prices can be sticky
simply because price setters expect them to be (Mankiw, 2000, p.518-519).
17
Menu Costs
One reason why prices may not adjust immediately to clear when economic
conditions change is because adjusting prices is costly. To change prices firms need to send
out new catalogue, prices lists, or, in the case of a restaurant, print new menus, hence the term
‘menu costs’. These costs cause firms to adjust prices periodically rather than continuously.
In imperfect competition, a firm’s profits will vary differentially with changes in its
own price because its sales will not fall to zero if it marginally increases price. Price
reductions by such a firm will increase sales and raises real income. The stimulus from higher
income, in turn, raises the demand for the products of all firms. In such circumstances any
divergence of price from the optimum will only produce “second-order” reductions of profits.
Hence, the presence of even small costs to price adjustment can generate considerable
aggregate nominal price rigidity and aggregate demand externality. This observation is due to
Akerlof and Yellen (1985a), Mankiw (1985) and Parkin (1986) (Snowdon and Vane, 2005,
p.372).
Some economists are skeptical about whether menu costs can help explain short-run
economic fluctuations. They argue that these small costs are unlikely to help explain
recessions. James Tobin thinks that “Keynes would have laughed at the idea that menu costs
are a big enough resource-using problem to cause the Great Depression or any other
substantial losses of economic activity. It’s not credible” (Snowdon and Vane, 2005, p.156).
Any microeconomic basis for failure of the classical dichotomy (money is non-
neutral) requires some kind of nominal imperfection; otherwise, a purely nominal disturbance
leaves the real equilibrium (or the set of real equilibria) unchanged.' This immediately raises
a difficulty. Individuals are ultimately concerned with real prices and quantities: real wages,
hours of work, real consumption levels, and the like. Nominal magnitudes matter to them
only in ways that are minor and easily overcome. Prices and wages are quoted in nominal
terms, but it costs little to change (or index) them. Individuals are not fully informed about
the aggregate price level or the money supply, but they can obtain quite accurate information
at little cost. Thus, if failure of the classical dichotomy is important to fluctuations in
aggregate activity, it must be that nominal frictions that appear small at the level of individual
households and firms somehow have a large effect on the macro-economy (Romer, 1993, p.
8).
18
Real Rigidities
Romer (1993, p. 10) points out that it is not plausible that adding imperfect
competition and small barriers to price adjustment is enough to provide a microeconomic
basis for the view that aggregate demand shocks are central to economic fluctuations because
of the nature of the labour market. If labor supply is relatively inelastic and if there are no
departures from Walrasian assumptions aside from the presence of small barriers to nominal
adjustment, then the decline in labour input associated with the decline in production leads to
a large fall in the real wage. In this case, marginal cost falls greatly in recessions. As a result,
unless the elasticity of demand also falls sharply, firms' incentives to reduce prices are large.
If labour supply is relatively inelastic, firms' incentives to change their prices in the face of
aggregate demand movements of a few percent swamp any plausible barriers to nominal
adjustment. A great deal of research in new Keynesian economics is concerned with specific
factors that can give rise to real rigidities. Below are four potential sources of real price
rigidity that the new Keynesian literature has identified, of the four, three are briefly
mentioned below and the fourth in more detail in section 1.3.
The first potential source of real price rigidity is external economies of scale arising
from "thick market externalities" (Diamond, 1982). Markets tend to function better during
periods of high economic activity when traders are more active than in times of low
economic activity. It is possible that people are much more willing to participate when
market are more active where a lot of trade is taking place and this leads to strategic
complementary; that is, “the optimal level of activity of one firm depends on the activity of
other firms. If these thick market externalities help to shift the marginal cost curve up in
recessions and down in booms, then this will contribute to real price rigidity” (Snowdon and
Vane, 2005, p.380).
The second line of work considers capital market imperfections (Bernanke and
Gertler, 1989) arising from asymmetric information between lenders and borrowers. That is,
borrowers are much better informed about their business than lenders. “It follows that in a
situation of asymmetric information, internal finance is less expensive than external finance.
Since firms have higher profits and hence more funds available for internal finance in booms
than in recessions, capital market imperfections tend to make the cost of capital
countercyclical; and since capital costs are an important component of overall costs, this acts
to make the cost curve move in a countercyclical direction” (Romer,1993, p. 11-12).
19
The third area of research focuses on the cyclical behavior of demand elasticities in
goods markets. The elasticity of demand might vary in response to aggregate output
movements for a number of reasons. “For example, when aggregate output is high, "thick
market" effects may make it easier for firms to disseminate information and for consumers to
acquire it. This could act to make the elasticity of demand, and hence the marginal revenue
curve more procyclical, and would thus reduce firms' incentives to adjust their prices in
response to aggregate demand movements” (Romer, 1993, p. 12).
1.3 Real Rigidities in the Labour Market
The fourth and most important area of research is real rigidities in the labour market.
Due to its importance and the vast literature relating to this topic, we will consider this topic
under a different sub heading. Nominal rigidities allow fluctuations of aggregate demand to
have real effects and contribute to a non-market-clearing explanation of business cycles.
However, new Keynesian economists are also concerned with explaining the persistently high
levels of unemployment that have been a major feature of the labour markets of the major
industrial countries since the early 1970s. In new classical monetary and real business cycle
models all agents are price takers. Perfect and instantaneous price and wage flexibility
ensures that the labour market always clears at Walrasian market-clearing real wage. In a new
Keynesian world, where price makers predominate, an equilibrium real wage can emerge
which differs from the market-clearing real wage. Models involving real wage rigidity are
capable of generating involuntary unemployment in long-run equilibrium, in contrast to new
classical models where, with everyone on their labour supply function, unemployment in
equilibrium is a voluntary phenomenon (Snowdon and Vane, 2005, p.383).
An important empirical observation that new Keynesian theories of unemployment try
explain why shifts in labour demand appear to lead to large movements in employment and
only small movements in the real wage, that is, the real wage is weakly procyclical. If the
labor market were Walrasian and labour supply inelastic, real wages would be highly
procyclical. If this pattern held in practice, real rigidities elsewhere in the economy would
have to be extremely strong to overcome the large incentive for adjustment created by sharply
procyclical wages. However, although analysts dispute the precise cyclical behavior of real
wages, there is no evidence that they are strongly procyclical (Romer, 1993, p. 12). New
Keynesian explanations of real wage rigidity fall into four main groups: implicit contract
theories, efficiency wage theories, insider–outsider theories and search and matching
theories.
20
Implicit Contracts
The main idea of implicit (unwritten) contract theory is to explain unemployment as a
result of implicit contract between an employer and an employee that specifies how much
labour is supplied and how much wage is paid. Implicit contract can lead to a firm choosing
wage and employment levels off the conventional labour demand curve, potentially helping
us to explain involuntary unemployment. Though originally intended to underpin the
Keynesian nominal wage rigidity assumption, it is now recognized that implicit contracts lead
to real rather than nominal wage rigidities. Important contributions to the implicit contracts
literature include Azariadis, (1975), Bailey (1974) and Gordon (1974) (Romer, 2001, p. 435).
Azariadis, (1975), Bailey (1974) and Gordon (1974) examine the consequences of
optimal labour contracts established between less risk-averse employers and risk-averse
workers. “Employers are less risk averse and have greater access to the capital market than
they do. As a result, employers provide some form of wage and employment insurance as
part of the employment package. To put it another way, a firm which offered such insurance
as part of its employment package would be able to attract workers at a lower (average)wage
than a firm which did not provide such insurance” (Stiglitz, 1984, p. 6).
A major problem with implicit contract models is they fail to explain involuntary
unemployment. “If all states of nature are observable (and verifiable), then the implicit
contract would specify the amount of labour and the wage to be paid in each state. In such
circumstances, though there may be relatively little fluctuations in wage (incomes), the
implicit contract would not give rise to unemployment: the marginal rate of substitution of
each individual between income and leisure would be equal to the marginal rate of
transformation, and there would be no lay-offs” (Stiglitz, 1984, p. 6).
Efficiency Wage Theories
The idea of efficiency wage theories is that the real wage is not only a cost for firms.
In the presence of perfect information and transaction costs, the wage is also an instrument to
recruit, retain and motivate workers. A firm which wants to recruit workers more quickly or
to reduce the number of quits can raise its wage above the wage set by others employers.
Similarly, a firm which cannot observe its employees’ effort may find worthwhile to increase
its wage in order to motivate them. In all of these cases, the wage is for something else that
the allocation of labour on the clearing of the labour market. Efficiency wage models can
21
provide an explanation for involuntary unemployment as well as explaining why real wage is
weakly procyclical (Romer, 2001, p. 415 and Cao, 2008, p. 31).
Stiglitz (1984, pp. 43-49) points out that there are at least five different explanations
for the wage-productive relationship in the efficiency wage literature. The first theory is
based on the hypothesis that individual's productivity depended on their nutrition, which
depended in turn on their pay. This idea was first hypothesized by Leibenstein (1957) and
subsequently analyzed in greater detail by Mirrless (1975) and Stiglitz (1976). This version of
the theory is more relevant in developing countries where food is scarcer. However,
nutritional considerations are less important in more developed countries.
The second version of efficiency wage theory hypothesizes that some firms pay above
the market-clearing wage in order to reduce costly labour turnover. This approach is based on
the pioneering work of Phelps (1970) and Stiglitz (1974, 1982) in the development of
explanations of the natural rate of unemployment and search behaviour. Even in the presence
of unemployment firms are unlikely to lower its wages because unemployed workers might
continue to search for a still better job.
The third version of efficiency wage theory hypothesizes that firms have imperfect
information about the quality of job applicants; firms that pay higher wages in order to obtain
higher quality applicants and any applicant who offers to work for less than the efficiency
wage will be regarded as a potential “lemon” (adverse selection). This approach is based on
the pioneering work of Stiglitz (1976) and Weiss (1980).
The fourth version of efficiency wage theory is based on asymmetric information
concerning the efforts of workers; workers tend to know more about their effort levels than
their employers. This asymmetry creates a principal–agent problem. In order to induce
workers not to shirk, firms thus attempt to raise their wages relative to the market wage by
paying an efficiency wage as an incentive for workers not to shirk. This approach is based on
the work of Shapiro and Stiglitz (1984)
The fifth version of efficiency wage theory hypothesizes that the productivity of
workers depends on whether they believe they are being fairly treated. In a series of papers,
Akerlof (1982, 1984) and Akerlof and Yellen (1987, 1988, 1990) developed models where
fairness act as a deterrent to firms to offer too low wages in the labour market. “The ability of
workers to exercise control over their effort, and their willingness to do so in response to
grievances, underlies the fair wage–effort hypothesis” (Akerlof and Yellen, 1990, p. 262).
22
“Though the five theories differ in a number of important respects, they have a
common mathematical structure”: the net productivity of a worker is a function of the wage
paid by the firm and the unemployment rate (Stiglitz, 1984, p. 48).
Search and Matching Theories
The search and matching theories provide a way of modeling frictional
unemployment in the labour market. This approach considers workers and jobs as highly
heterogeneous. Workers and firms meet in a one-on-one fashion and engage in a costly
process of trying to match up idiosyncratic preferences, skills and needs. Since this process is
not instantaneous, it results in some frictional unemployment.
1.4 Conclusion
The new Keynesian research programme has been driven by the view that the
orthodox Keynesian model lacked coherent microfoundations with respect to wage and price
rigidities. As a result the new Keynesian literature has been, until recently focused on
theoretical developments instead of empirical testing. The main problem with the new
Keynesian research programme is its incoherencies, since there are many alternative models
addressing a specific issue. New Keynesians recognize this problem, with Blanchard (1992)
reflecting that “we have constructed too many monsters with “few interesting results”. The
fascination with constructing a “bewildering array” of theories with their “quasi religious”
adherence to microfoundations has become a disease. Because there are too many reasons for
wage and price inertia, no agreement exists on which source of rigidity is the most important”
(Snowdon and Vane, 2005, p. 429).
23
CHAPTER 2
From Sticky-Prices to Sticky-Information to Sticky-Knowledge
2.1 Introduction
The purpose of this chapter is to argue that inflation expectations are boundedly
rational and to provide the theoretical foundation for our empirical work in the later chapters.
Under rational expectations, the NKPC implies inflation is a purely forward variable;
inflation depends on expectations of future inflation and on current output. No lagged
variables-including lagged inflation-should have an impact on the current level of inflation.
However, contrary to the prediction of rational expectations, many empirical studies on the
new Keynesian Phillips curve find that the old Keynesian Phillips curve with adaptive
expectations fits the data much better than the new Keynesian Phillips curve (Fuhrer and
Moore (1995), Fuhrer (1997), Mankiw (2001) and Rudd and Whelan (2006)).
In order to incorporate bounded rationality into the Phillips curve framework we
utilise two types of models that include lagged inflation as an explanatory variable in the
Phillips curve. The first type is Mankiw and Reis (2001, 2002) sticky-information Phillips
curve and the second type is Fuhrer and Moore (1995) and Gali and Gertler‘s (1999) hybrid
new Keynesian Phillips curve. Without considering bounded rationality, and the relationship
between economists and non-economists, these models cannot provide a plausible rationale
for the inclusion of lagged inflation as an explanatory variable in the Phillips curve. Fuhrer
and Moore (1995) assume that agents are concerned with relative real wages, Gali and
Gertler (1999) assume that only a fraction of agents use rational expectations, while the
remainder use last period’s inflation rate as a simple rule of thumb for forecasting inflation.
Mankiw and Reis (2001, 2002) sticky-information model use epidemiological analogy, and
use deviations of the actual inflation rates from the expected inflation rates to explain the
inflation-output dynamics.
We will attempt to argue that bounded rationality can explain the observation that
lagged inflation plays an important role in empirical inflation regressions as the dissemination
of economic information and knowledge between professional economists and non-
economists. Since economics agents take expectations subject to the information and
knowledge decision-making constraints that confront them, and if the required knowledge is
not common knowledge but professional knowledge, the best ways for non-professionals to
minimize their forecast errors is by employing the services of professionals forecasters or
24
observe how professionals forecasters respond and replicate their actions, rather than making
forecasts without the required knowledge. Since the general public’s inflation expectations
respond to the professional economists’ expectations with time lag, lagged inflation rates are
correlated with the current inflation rate. In the later chapters, we use the NKPC as a
benchmark comparing the empirical results of the old Keynesian Phillips curve and the
hybrid new Keynesian Phillips curve, which represents bounded rationality.
The structure of this chapter is as follows. Section 1 describes some of the early
developments of the Phillips curve and their implications. Section 2 examines sticky-prices
new Keynesian models of Taylor (1979, 1980) and Calvo (1983). While in these models the
price level is sticky, the inflation rate can change quickly because there is no sluggishness in
adjusting inflationary expectations. Although there are different ways of deriving the NKPC,
they all have a common formulation; inflation in the Taylor (1979, 1980) and the Calvo
(1983) models depends on expectations of future inflation and on current output (also see
Roberts (1995)). Section 3 examines sticky-information models of Carroll (2003) and
Mankiw and Reis (2001, 2002), it can be said that these models use expectations based on the
bounded rationality approach of Simon (1979, p. 507). The main difference between these
models and the earlier models of Taylor and Calvo is that while in these models sluggish
adjustments are in the formation of expectations, in the Taylor and Calvo models
sluggishness is due to inertia in price adjustments. Although this difference appears to be
minor, proponents of the sluggish expectations models claim that their models can explain
some observed facts better than the sluggish price adjustment models. Section 4 attempts to
redefine the microfoundations of Mankiw and Reis (2001, 2002) and Carroll’s (2001, 2003)
approach, based on the idea of that knowledge about monetary policy (inflation) is
professional knowledge, the best way for non-economists to minimize their forecast errors is
to listen to the advices of professional economists. Section 5 concludes.
2.2 The Philips Curve and some Developments
The Phillips curve is an empirical relationship first observed by A.W. Phillips in
1958. Phillips documented that there was a relatively stable relationship between wage
inflation and the rates of unemployment in the United Kingdom from 1861 to 1957. The
original Phillips curve was only an empirical phenomenon, lacking theoretical underpinning.
Lipsey (1960) provided the first major theoretical underpinning through the combination of
two postulated relationships: First, a positive linear relationship between the rate of increase
in money wage and excess demand for labour. Second, a negative non-linear relationship
25
between excess demand for labour and unemployment rate. By combining these two
postulated relationships, Lipsey was able to provide the rationale that the rate of change of
money wages depends on the degree of excess demand (or supply) in the labour market as
proxy by the rate of unemployment (Snowdon and Vane, 2005, pp.137-139).
One of the main reasons why the Phillips curve was quickly adopted by the
Keynesians was it provided an explanation of price determination and inflation, which was
missing in the Keynesian macroeconomic literature based on the ISLM model at that time.
Keynesians thought that the price level was fixed and unresponsive to changes in aggregate
demand. Only when full employment is reached will changes in aggregate demand affect the
price level. The Phillips curve allowed the Keynesian theory of output and employment
determination to be linked to a theory of wage and price inflation (Snowdon and Vane, 2005,
p.142). Following Samuelson and Solow’s (1960) influential contribution, the Phillips curve
was interpreted by many Keynesians as the existence of a stable trade-off between inflation
and unemployment. In addition, this trade-off has generally been expressed in terms of price
inflation instead of wage inflation (Snowdon and Vane, 2005, p.144).
In the late 1960s and early 1970s many countries experienced high levels of
unemployment and inflation simultaneously, a phenomenon that theories based on the
Phillips curve could not explain. The idea of a stable relationship between inflation and
unemployment was challenged independently by Milton Friedman (1968) and Edmund
Phelps (1967, 1968) (Snowdon and Vane, 2005, p.144).Friedman’s (1968) and Phelps’ (1967,
1968) ‘natural rate hypothesis’ states that there is a natural rate of unemployment and that
monetary policy cannot keep unemployment below this level indefinitely. Friedman and
Phelps argued that the idea that nominal variables such as money supply or inflation could
permanently affect real variables such as output or unemployment was unreasonable; as in
the long-run, real variables are affected by real forces. Permanent expansionary monetary
policy would eventually change the way wages and prices are set. There is no reason for
workers and firms to settle on different levels of employment and real wage just because
inflation is higher (Romer, 2001, p.245-246).
Subsequently whether there is a permanent output-inflation trade-off became an
important debate in modern macroeconomics. These issues have important implications for
modelling the dynamics of inflation, unemployment and output and the scope for stabilisation
policy. In general, the monetarist and neoclassical models imply that stabilisation policies are
ineffective. On the other hand, the Keynesian and New Keynesian models imply that
26
stabilisation policies are effective and should be implemented. An alternative way of stating
this difference is that while monetarists argue that changes to nominal demand have no real
effects, Keynesians argue that they have significant real effects.
There have been some crucial developments in this debate and one of the most
important developments was due to the Friedman-Phelps argument that the original Phillips
curve has ignored the role of inflation expectations in wage bargains and implies that workers
suffer with money illusion. This is not consistent with the axioms of economics that all agents
are rational.3 Therefore, these authors have developed the expectations augmented Phillips
curve and their theoretical arguments imply that there is no trade-off between inflation and
unemployment in the long run. This in turn validates the monetarist arguments that nominal
demand shocks have no real effects and stabilisation policies will be ineffective in the long
run.
There are two main theories regarding the formulations of expected inflation.
Expectations are adaptive if they are based on past behaviour of inflation; the main problem
with adaptive expectation is the failure of economic agents to use additional information
available to them other than past values of inflation, despite making repeated errors. In
contrast, expectations are rational if they are based on all information available at the time the
expectations are made and not just past information (Snowdon and Vane, 2005, p.227). The
problem with the adaptive expectations formulation employed in many Keynesians and
monetarists in the 1960’s and the 1970’s was that it implies systematic error in forecasting as
it does not take into account of other relevant information.
The Lucas Imperfect – Information Model
The Friedman (1968) and Phelps (1967, 1968) insight was given an explicit rational
expectations foundation by Robert Lucas. Lucas (1972, 1973) and Phelps (1970)
independently developed a monetary theory of the business cycle based on imperfect-
information to producers. The central idea of the Lucas-Phelps model is that when a producer
observes a change in the price of his product, he is not sure if it reflects a change in the
good’s relative price or a change in the aggregate price level, this is sometimes referred to as
3An alternative and simpler explanation is that it is the real wage rate—not the nominal wage rate as in the
original Phillips curve—that should change with the excess demand for labour. Therefore, the Phillips curve is
based on the assumption that workers suffer with money illusion and this is not consistent with rational
behaviour.
27
a “signal extracting problem”. Suppose the price level of the firm’s product rises, the firm
will rationally attribute part of the change to an increase in the price level and part to an
increase in the relative price, and therefore to increase output somewhat. This implies that the
aggregate supply curve is upward sloping (Romer, 2001, p.266). The analysis of producer
behaviour under imperfect information led to what is referred to as the Lucas supply curve,
which is as follows.
* ( [ ])y y b p E p (2.1)
Equation (2.1) states that deviations of output ( )y from its natural level *( )y is an
increasing function of deviations of price ( )p from its expected level ( [ ]).E p The Lucas
supply curve is interpreted by many same as the expectations augmented Phillips curve.
However, while the Phillips curve is a price adjustment equation in a disequilibrium market,
the Lucas supply curve is a quantity response function of firms in the imperfect information
markets. Prices in these markets are determined by the equality of the demand and (Lucas)
supply functions. If we accept the common interpretation that the Lucas supply curve is an
inverted Phillips curve, it may be stated that both relationships imply that if we neglect
disturbances to supply, output is above its natural level only to the extent that inflation (and
hence the price level) is greater than expected (Romer, 2001, p.266-274). In this thesis,
however, we shall use this common interpretation of the Lucas supply curve, albeit with some
reservations.
The Lucas supply curve implies a positive statistical relationship between output and
inflation can arise even though prices adjust instantaneously and markets clear, but there is no
exploitable trade-off between output and inflation because changes in policy affect
expectations, which can change this trade off. In short, if policy makers attempt to take
advantage of this trade off, firms take into account the effects of changed policies on
expectations because these expectations are rational and the relationship breaks down. This
insight is known as the Lucas critique (Romer, 2001, p. 275)
The Lucas Imperfect Information model was very influential and provided important
insights into the effects of monetary policy under rational expectations. However, the model
implies that monetary disturbances should not have any transitory effects on real activity if
the public can observe changes in monetary policy. In real life the money supply is published
regularly and can be observed within a few weeks. Therefore the real effects of variations in
the money supply should last only a few weeks. Yet in empirical studies on the effects of
28
monetary disturbances the real effects seem to persist for many quarters. According to
Woodford (2001, p.4) even after ten quarters from the initial shock, this real effect is still
more than one-third of the size of its peak effect.
2.3 The Sticky-Prices Approach
The First Taylor Model
One of the earliest formulations of the sticky price models is by Taylor (1979). His
staggered-contract model assumes that wage contracts last one year, with half of the contacts
are set in January and half in July. Let tx be the log of the contact wage for periods t and 1t , set at the start of period ,t then the contract wage determination is given by (Roberts, 1995,
pp. 978-979).
1 1 1ˆ ˆ ˆ( )t t t t t tx bx dx by dy (2.2)
where ty is a measure of excess demand in period t , t
is a random shock, and b , d and
are positive parameters. The “hat” over a variable represents its conditional expectation based
on period 1t information. Equation (2.2) states that contract wage in the current period
depends on the contract wage set in the previous period, the contract wage expected to be set
in the next period and a weighted average of excess demand expected during the next two
periods.
In order to derive the implied dynamics of equation (2.2) we need to specify an
aggregate demand equation and a policy rule. Assume that excess demand ( )ty is the
deviation of output from its trend and that the demand for money is given by t t t tm y w v ,
where the variable tm , t
w and tv are the logs of the money supply, the aggregate wage level,
and a shock, all measured as deviations from trend. Note that this money demand equation is
simply the quantity equation with the wage substituted for the price level.
If the policy rule for the money supply is given by t tm gw , then the aggregate demand
equation is given by
(1 )t t ty g w v w v (2.3)
where is a policy parameter indicating the degree of accommodation of aggregate demand
by the policy maker to wage changes. The average wage for two periods is given by
29
10.5( )t t tw x x (2.4)
Workers are assumed to be concerned about real wages and unemployment, therefore the
labour supply curve, stated in terms of unemployment rate, given by (Roberts, 1995, p.979),
is as follows.
1 10
( ) ( )
2 2
t t t t t tt t
p E p RU E RUx c (2.5)
where p is the log of price, RU is the unemployment rate, is a white noise error term, and
0c and are constants. 0 , there is a negatively relationship between the unemployment
rate and real wage.
If firms set prices as a mark-up over costs, the price equation is:
(1 )t t
p w (2.6)
where is the mark-up ratio. For simplicity is assumed to be zero in the following price
equation.
t tp w (2.7)
Equations (2.4), (2.5) and (2.7) can be combined to give:
1 0 1 1 1
1
( )
2( )
t t t t t t t t t
t t t
p E p c RU RU E RU E RU
(2.8)
where t is an expectational error 1( )t t tE p p . Inflation depends on expected inflation and a
moving average of the unemployment rate (Roberts, 1995, p.979). This is the specification
implied for the NKPC and can be estimated with a suitable hypothesis for rational
expectations for inflation so that [ ] 0.E
The Second Taylor Model
In Taylor’s second model of 1980, the expected average real contract wage is
assumed to be increasing in the level of output ( ),ty which is simpler than his assumption in
his first model, and is as follows (Walsh, 2003, pp. 224-225).
30
1
1( )
2t t t t t
x p E p ky (2.9)
If prices are set as a mark-up on the two periods average cost, with the mark-up assumed to
be zero for simplicity, we have the following price equation.
1
1( )
2t t t
p x x (2.10)
Substitution of (2.9) in (2.10) gives:
1 1 1 1
1 1 1
1 1 1( ) ( )
2 2 2
1 = (2 ) ( )
4 2
t t t t t t t t t
t t t t t t t
p p E p ky p E p ky
kp E p p y y
(2.11)
where 1t t t tE p p is an expectational error term. Rearranging (2.11) gives the following.
1 1 1
1 1 1( )
2 2 2t t t t t t t
p p E p k y y (2.12)
Thus in the second Taylor (1980) model inertia in the aggregate price level tp depends on
expectations of future prices and the price level in the previous period. If the inflation rate
1 t t tp p then (2.12) can be rearranged as:
1 12 ( )t t t t tE k y y (2.13)
Inflation depends on expectations of future inflation, current output and output in the
previous period. An important aspect of the Taylor (1979, 1980) models is that “while prices
display inertia, there is no inertia in the rate of inflation” (Walsh, 1998, p.217).
The Calvo Model
In the Calvo (1983) model each period a fraction ( ) of monopolistic competitive
firms update their information on the current state of the economy and compute optimal
prices based on that information. The rest of the firms (1 ) continue to set prices based on
past and outdated information. Calvo’s (1983) model is set in continuous time. We follow
Walsh (1998, pp. 218-220) and Rotemberg (1987) in our exposition of the Calvo model in
discrete time as it allows us to make comparisons easier.
Suppose the representative firm i sets its price using a quadratic loss function that
depends on the difference between its actual price ( )itp and its optimal price *( )tp . The firm
31
sets its prices to minimize the squared deviations of its actual prices from its optimal prices
subject to when the firm will be next be able to adjust.
* 2
0
1( )
2
j
t it j t j
j
E p p (2.14)
Since 1 is the probability of not being able to adjust its price in the next period. The first
order condition for the optimal choice of itp requires that
*
0 0
1 1 0
jjj j
it t t j
j j
p E p
Let t denote the price set at t by all firms adjusting their price.
*
0
1 1 1j j
t t t j
j
E p
(2.15)
The price set by the firm at time t is a weighted average of current and expected future values
of the target*p . This can be rewritten as
*
11 1 1t t t tp E
Assume that the optimal price is given by *
t t tp p y w , the optimal price *p is
assumed to depend on the aggregate price level tp and output t
y as would be the case if
firm face a downward-sloping demand curve, where tw is a random disturbance. With a large
number of firms, a fraction will actually adjust their price each period, and the aggregate
price level can be expressed as 11
t t tp p .
The evolution of t and tp are given by
11 1 1t t t t t tp y w E (2.16)
11
t t tp p (2.17)
Update equation (2.17) by one period and take expectations
1 11
t t t t tE p E p
This can be rewritten as
32
1 1t t t t tE E p
Eliminate 1t tE for equation (2.16), then eliminate t from equation (2.17).
1 1
1 1
1 1
t t t t
t t t t
p p y w
E p p
Rearranging
1
' '
1
1 1
1
t t t t t
t t t t
E y w
E y w
(2.18)
where
'
1 1
1
and
'
1 1
1
t
t
ww
Similar to the Taylor model, inflation in Calvo’s model depends on expectations of
future inflation and on current output. Another important similarity between the two models
is the Phillips curve only have forward-looking expectations, as a result, there is no inertia in
the rate of inflation.
Problems with the Sticky-Prices Approach
Much of the literature on the standard new Keynesian Phillips curve builds on the
pioneering work of Taylor (1979,1980), Rotemberg (1982) and Calvo (1983), and is based on
time-contingent price adjustment. Despite its popularity in the theoretical analysis of
monetary policy, the standard NKPC makes several predictions that are not supported by
empirical evidence. The two main problems with this standard NKPC are that inflation is not
very persistent and that the model predicts credible disinflations can cause booms. These
problems originate from the assumptions that prices are sluggish in the models, but, inflation
expectations can change quickly. Furthermore, empirical studies have shown inflation rates
are highly autocorrelated, this suggests that past inflation rates are important in the
determining the current rate of inflation. Below are various attempts to explain the
persistence of inflation.
Fuhrer and Moore (1995) attempt to explain the persistence of inflation by modelling
wage negotiations in terms of relative wage contracts (i.e. wage indexation) instead of
nominal wage contracts. Gali and Gertler (1999) modify Calvo’s (1983) model by
introducing lagged inflation into the Phillips curve. They also estimate the coefficient of
33
lagged inflation of their hybrid Phillips curve and find that the coefficient of lagged inflation
is generally lower than that of other papers (i.e. Fuhrer, 1997), which suggest that inflation is
predominantly backward-looking. Gali and Gertler (1999) suggest that the output gap is a
poor proxy for real marginal cost. Rudd and Whelan (2006, p.319) find that adding lags to the
standard NKPC improve empirical fit, they suggest that inflation expectations are not fully
rational and that adding lagged inflation term is just addressing the cause of the problem,
which they believe to be deviations from rational expectations (bounded rationality).
In the next section we will examine another approach to explaining the persistence of
inflation by assuming inflation expectations are sluggish rather than assuming price
adjustments are sluggish.
2.4 The Sticky-Information Approach
Mankiw and Reis Model4
The motivation for Mankiw and Reis’ (2002, p. 1295) sticky-information Phillips
curve is to replace the earlier rationalisations of the NKPC based on sticky-prices and they
argue that:
“Compared to the commonly used sticky-price model, this sticky-information model
displays three related properties that are more consistent with accepted views about
the effects of monetary policy. First, disinflations are always contractionary (although
announced disinflations are less contractionary than surprise ones). Second, monetary
policy shocks have their maximum impact on inflation with a substantial delay. Third,
the change in inflation is positively correlated with the level of economic activity”.
Mankiw and Reis note that these problems appear to arise from the same source,
namely that although the price level is sticky in the model, the inflation rate can change
quickly because expectations adjust quickly. The central idea of Mankiw and Reis model is
that information about macroeconomic conditions diffuses slowly through the population.
They argue that this slow diffusion could arise because of either costs of acquiring
information or costs of reoptimizing. To formalize this idea, they assume that in each period a
fraction of the population updates itself on the current state of the economy and computes
optimal prices based on that information. The rest of the population continues to set prices
based on old plans and outdated information. Essentially, the model combines elements of
4 A less detailed version of this model was presented as part of my Master’s thesis (Cao, 2008, pp. 49-53).
34
Calvo’s (1983) model of random adjustment with elements of the Lucas (1972) model of
imperfect information, set in monopolistic competition.
Expectations are formed similar to that of Fischer’s (1977) contracting model with the
current price level formed far in the past, because price setters are setting prices based on old
decisions and old information. This way of modelling expectations yields large differences in
the dynamic pattern of prices and output in response to monetary policy. This can be
modelled as follows. All variables are expressed in log. The optimal price *p of any firm in a
given period is given by:
*
t t tp p y (2.19)
wherety is the output gap and tp is the aggregate price level. The parameter captures the
sensitivity of the optimal relative price to the current output gap. If is small, then each firm
gives more weight to what other firms are charging than to the level of aggregate demand,
therefore a small value of α can be interpreted as a high degree of real rigidity (to use the
terminology of Ball and Romer (1990)) or high degree strategic complementarities (to use the
terminology of Cooper and John (1988)). In the sticky-information model, this real rigidity is
a source of inflation inertia.
In each period, a fraction of firms obtains new information about the state of the
economy and compute a new path of optimal prices. Other firms continue to set prices based
on old plans and outdated information. An assumption is made about information arrival that
is analogous to the adjustment in the Calvo model: Each firm has the same probability of
being one of the firms updating their pricing plans, regardless of how long it has been since
its last update.
A firm that last updated its plans j periods ago sets the price:
*j
t t j tE p (2.20)
The aggregate price level is the average of the prices of all firms in the economy:
0
1j j
t t
j
p
(2.21)
Putting these three equations together yield the following equation for the price level:
0
1
j
t t j t t
j
p E p y
(2.22)
35
This is the short-run Phillips curve, where output is positively associated with surprise
movements in the price level. For convenience, we have included the algebra in the appendix
of Mankiw and Reis (2002, pp. 1320-1321) in the derivation of the sticky-information
Phillips curve.
By taking out the first term and redefining the summation index, this equation can be written
as:
1
1
0
1
j
t t t t j t t
j
p p y E p y
(2.23)
Analogous to equation (2.23), the previous period’s price level can be written as:
1 1 1 1
0
1
j
t t j t t
j
p E p y (2.24)
Subtracting (2.23) from (2.24) by breaking up the sum of tp and 1t
p and rearranging yields
the following equation for the inflation rate:
1
1
0
1
j
t t t t j t t
j
p p y E p y
2
1 21 1 ...t t t t t t t t tp p y E p y E p y
1 1 1 1
0
1
j
t t j t t
j
p E p y
1 1 1 1 2 1 11 ...
t t t t t t tp E p y E p y
1 1 1 1 1
2
2 2 1 1
1
1 1 ...
t t t t t t t t t t t
t t t t t t
p p p y E p y E p y
E p y E p y
Let 1t t tp p and 1t t t
y y y , after rearranging, we obtain
1 1 2
2 2
1 2
1
1 ...
t t t t t t t t t t t
t t t t t t
p p p y E y E y
E p y E p y
1
0
2
1
0
1
1
j
t t t t j t t
j
j
t j t t
j
p y E y
E p y
(2.25)
36
Now equation (2.24) can be rearranged to show that:
1
0
11
j
t t t j t t
j
p y E p y
1
1
0
1
j
t t t t j t t
j
p p y E p y
1
1
0
1
j
t t t t j t t
j
p p y E p y
1
1
0
1
j
t t t t j t t
j
p p y E p y
1
0
1 1 1
j
t t t j t t
j
p y E p y
1
0
11
j
t t t j t t
j
p y E p y
(2.26)
We now use equation (2.27) to substitute for the last term in equation (2.26). After
rearranging, we obtain:
111
j
t t t t j t t t t
j o
p y E y p y
11
1
j
t t t t t t j t t
j o
p y p y E y
11 1j
t t t j t t
j o
y E y
(2.27)
where 1t t ty y y is the growth rate of output. This is the sticky-information Phillips
curve; inflation depends on output, expectations of inflation, and expectations of output
growth.
37
Inflation and Output Dynamics
To complete the model, Mankiw and Reis add an aggregate demand equation
m p y (2.28)
where m is nominal GDP. This equation can be viewed as a quantity theory approach to
aggregate demand, where m can be interpreted as the money supply. Mankiw and Reis also
introduce a backward-looking model:
t t t 1 y (2.29)
This model can be viewed as the sticky-price model together with the assumption of adaptive
expectations:
t t 1 t 1E (2.30)
Three policy experiments were conducted:
E1 – An unexpected fall in the level of aggregate demand by 10% at date 0. Thus,
log(0.9)tm for 0t and 0tm for 0t
E2 – An unexpected drop in the rate of money growth m at date 0, from 2.5 percent per
period to 0 percent. Thus, 0.025(1 )tm t for 1t 0tm for 0t .
E3 – Same as E2 but announced at date 8t .
Results of Monetary Policy Experiments
Experiment 1: A 10% drop in the level of aggregate demand.
All three models predict sudden recessions.
All three models predict the fall in demand on output is close to zero after 16 quarters.
The backward-looking model generates an oscillatory pattern, whereas the other two
models yield monotonic paths.
In the sticky-price model, the greatest impact of the fall in demand on inflation occurs
immediately.
In the sticky-information model, the maximum impact of the fall in demand on
inflation occurs after seven quarters, implying more inflation inertia.
38
Experiment 2: A sudden disinflation.
In the sticky-price model, prices are sticky but inflation exhibits no inertia, therefore
inflation responds instantly to the fall in money growth and output does not change.
Hence, the sticky-price model predicts disinflation is costless.
The sticky-information model predicts a gradual reduction in inflation because some
firms are setting prices based on old information. The economy experiences a
recession with the trough occurring about six quarters after the policy change.
Experiment 3: An anticipated disinflation
The predictions for the backward-looking model are the same as in Experiment 2
because the assumption of adaptive expectations prevents the announcement from
having any effect.
The sticky-price model predicts announced disinflation causes a boom. “When price
setters anticipate a slow-down in money growth, inflation, together with continued
increases in the money supply, leads to rising real money balances and higher output”.
The sticky-information model does not predict booms in response to anticipated
disinflations. In this model, there is no change in output on inflation until the
disinflationary policy of slower money growth begins. An announced disinflation
leads to a quicker inflation response and a smaller output loss than does a sudden
disinflation.
Mankiw and Reis then introduce a first-order autoregressive process for the money
supply t t tm pm and then examine the impulse responses of output and inflation to a
one-standard-deviation (-0.007) contractionary monetary policy shock.
In all three models, output exhibits a hump-shaped response. The backward-looking
model yields oscillatory dynamics, whereas the other two models yield a monotonic
recovery from the recession, with the sticky-price model taking longer to return to 0 .
The impulse responses for inflation to the monetary shock show important differences
between the sticky-price and sticky-information models. In the sticky-price model, the
greatest impart of monetary shock on inflation occurs immediately, whereas the
maximum impact of the monetary shock on inflation in the sticky-information model
occurs after seven quarters.
39
The backward-looking model generates an oscillatory pattern.
Finally, Mankiw and Reis (2002, p.1297) examine whether their model can explain
the acceleration phenomenon documented by many empirical studies, that vigorous economic
activity causes inflation to rise. Their findings as summarized in the paper are:
“The standard sticky-price model is inconsistent with this finding and, in fact, yields a
correlation of the wrong sign. By contrast, the sticky-information model can explain
the widely noted correlation between economic activity and changes in inflation”.
In short, Mankiw and Reis sticky-information Phillips curve resolves three anomalies
in rational expectations staggered price models. Its empirical results matches empirical
evidence better and therefore are more consistent with accepted views of how monetary
policy works, which make it very appealing. However, the idea that information can be sticky
is not very plausible and faces the same criticisms as other imperfect information models.
Mankiw and Reis (2002, p.1317) believe that a better understanding of bounded rationality is
what is required.
“In the end, micro-foundations for the Phillips curve may require a better
understanding of bounded rationality. But until those foundations are established, the
sticky information model as describe here may offer a useful tool for the study of
inflation-output dynamics”.
Problems with the Sticky-Information Approach
The sticky-information Phillips curve successfully addressed three important
empirical anomalies with respect to the standard stick-price Phillips curve and has won the
support of some monetary policy researchers. However, its microfoundations are its major
weaknesses. The idea that inflational information diffuses slowly because of either costs of
acquiring information or costs of reoptimizing is not very satisfactory as the assumption of
imperfect information can be overcome easily. Quite accurate information about movements
in the price level is readily available, in most countries the current money supply is published
regularly and the cost of wage and price adjustment is relatively small. This raises the
question, why self-interested households and firms do not act in a way that brings about more
rapid adjustment?
In the model, the timing of price changes is determined solely by the passage of time,
this time contingent approach is an approximation introduced to slow down the adjustment
40
process without any solid microeconomic foundations. In most cases, firms are free to
respond to economic conditions and developments; therefore state dependent pricing needs to
be considered. In short, Mankiw and Reis’ (2002) sticky-information Phillips curve lacks a
clear and plausible theory of information and knowledge processing by economic agents.
The Carroll Model
Suppose that an individual who is exposing to a disease in a given period has a fixed
probability p of catching the disease. Denote the set of newly infected individuals in period t
as tN and the set of susceptible individuals as ,ts t tN ps . The growth rate of the disease
depends on the fraction of the population already infected and the probability that someone
who is infected will recover. The dynamics of the disease are as follows, in the first period,
proportion p of the population catches the disease, leaving 1 p uninfected. In the second
period, proportion p of these people catch the disease and the new infection rate is 1p p ,
1p p p of the population is now infected. The total proportion infected at the end of t
period is given by
2
0
1 1 ... 1 1t
t s
s
Fraction ill p p p p p p p p p
(2.31)
whose limit as t is 1pp , implying that everyone will eventually become infected
(Carroll, 2001, p.4).
Now consider the dissemination of a piece of information about the latest forecast of
inflation by reading newspaper articles rather than the spread of a disease through a
population. Assume that every inflation article contains a complete forecast of the inflation
rate for all future quarters and readers can recall the entire forecast. Assume that in each
period a fraction of the population read newspaper articles on inflation. The rest of the
population 1 continues to set prices based on the last forecast that they read. Thus, this
framework is similar to the Calvo (1983) model mathematically (Carroll, 2003, p.272).
Let tM be the operator that yields the population-mean value of inflation expectations
at time t and denote the newspaper forecast printed in quarter t for inflation in quarter s tas t s
N .
41
1 1 1 1 2 11 1 ...t t t t t t t tM N N N (2.32)
The derivation of this equation is as follows. In period t a fraction of the population will
have absorbed the current-period newspaper forecast for the next quarter, 1t tN . Fraction
1 of the population retains the views they held in period t−1 of period t+1’s inflation
rate. Those period-t−1 views in turn can be decomposed into a fraction λ of people who
encountered an article in period t – 1 and obtained the newspaper forecast of period t + 1’s
forecast, 1 1t tN , and a fraction 1 who retained their period-t − 2 views about the
inflation forecast in period t + 1. Recursion leads to the remainder of the equation. This
equation is similar to Mankiw and Reis’ equation for inflation expectations. In Mankiw and
Reis’ (2001, 2002) model economic agents compute their own forecasts rather than obtaining
inflation forecasts from reading newspaper.
Carroll then modify equation (2.33) in order to relate the population-mean value of
inflation expectations tM to the Michigan Survey mean value of inflation expectations
over the next year and for newspaper forecast of inflation t tN Carroll uses the mean value
from the survey of Professional Forecasters (SPF) over the next year as a proxy (Carroll,
2003, p.278).
, 4 , 4 1 1, 31t t t t t t t t tM N M (2.33)
Thus, , 4t t tN and 1 1, 3t t tM denote inflation expectations of professional
forecasters and inflation expectations of the general public respectively, the dissemination of
inflational news can be thought of as a disease that spreads slowly across the population,
infecting a fixed proportion of the general public in each period.
Carroll (2003, p.283) estimate equation (2.34) using the Michigan household survey
measure of mean inflation expectation as proxy for 1 1, 3t t tM and the Survey of
Professional Forecaster over the next year as a proxy for, 4t t tN as represented by the
equation below
, 4 1 , 4 2 1 1, 3t t t t t t t t t tM N M (2.34)
42
He estimates the above equation and obtains unrestricted estimates of 1 and 2 as:
1 0.33 and 2 0.66 . He also estimates the above equation and obtains restricted
1 21 estimates of 1 and 2 as 1 0.27 and 2 0.73 .
Carroll also observes that professional forecasters’ expectations and household
expectations are closer on average when there is more news coverage about inflation. This
observation suggests that the absorption rate is not constant over time.
Problems with the Epidemiological Approach
Carroll (2003) derives a model similar to Mankiw and Reis’ (2001) model, but his
model is based on an epidemiological model, where inflation expectations of professional
forecasters slowly spreads person–to–person, similar to the way a disease spreads in the
population. Carroll’s (2003) model is very useful for understanding differences in the lag
structures between sluggish price adjustments models from sluggish expectations models
because of its epidemiological analogy. However, it is also potentially problematic if we take
the epidemiological analogy seriously because of the human intentionality issue, unlike a
passive victim of a disease, people will actively devote more time and mental resources to
learning and thinking about economic matters so that they can respond to economic
developments quicker if they think the potential economic gains are greater than its costs.
This is a crucial factor necessary in order to understand the behaviour of people in economic
crises. Carroll (2003, p.296) also notes that his epidemiological approach lacks a general
explanation of how individuals process information and knowledge.
“Finally, it is clear that in order for this framework to be a complete and general
purpose tool, it will be necessary to develop a theory that explains the variations in the
absorption parameter λ overtime. For present purposes it was enough to show that λ is
related to the intensity of news coverage, but that only pushes the problem one step
back, to the need for a model of the extent of news coverage.”
2.5 The Sticky-Knowledge Phillips Curve
The purpose of the sticky-knowledge Phillips curve is to provide Mankiw and Reis’
(2001, 2002) sticky-information approach and Carroll’s (2003) epidemiological approach
more plausible micro-foundations, by endogenising the notion that inflational knowledge
cannot be obtained easily because of our bounded rationality. We borrowed the name from
Mankiw and Reis’ (2001, 2002) papers, but replace the word information with the word
43
knowledge as our aim is to show that knowledge about inflation is professional knowledge
which cannot be obtained easily (Cao, 2008, p. 49).
�o��ded �atio�alit�
Much of the literature on bounded rationality is a reaction against the restrictive
assumptions of unbounded rationality in neoclassical economics. Economists have long
recognized the importance of bounded rationality as the concept seems so obvious in some
cases and also due to an increasing number of anomalies discovered with respect to the
predictions of rational choice theory in neoclassical economics.
More than fifty years ago Herbert Simon first expressed the idea that individuals are
constrained by limited information and knowledge, limited mental processing ability and
information and knowledge are costly to obtain and to store. As a result, much of economic
behaviour involves search, trial and error processes, with individuals being prepared to settle
for satisfactory outcomes (satisficing procedure) rather than optimal outcomes (Cao, 2008, p.
49).
The main problem with capturing bounded rationality in economic models is how to
formalize it, as much of Simon’s work was conceptual rather than formal (Foss, 2003). The
first problem with modeling bounded rationality is to define it. Simon (1957, p. XXIV)
defined bounded rationality as “intendedly rational, but only limitedly so”, this definition is
vague and therefore open to various interpretations. One common definition of bounded
rationality is all observed deviations from maximizing rationality. The problems with this
definition is that the sets of candidates for boundedly rational behaviour is without bounds
and could also include irrational behaviours, which implies that anything is possible. Perhaps
it is because of this negative perception and the difficulties with formalizing bounded
rationality that many economists do not use the term bounded rationality as a means of
explaining frictions in the economy, instead they attempt to identify various phenomena as
potential causes of frictions: staggered wages and prices, menu costs and transaction costs
(Cao, 2008, p. 80).
In order to operationalize bounded rationality it is necessary to redefine bounded
rationality. By redefining bounded rationality as people are rational, but are constrained by
asymmetric and imperfect knowledge, all irrational choices are excluded. This definition is
also more precise since it identifies the sources of bounded rationality as asymmetric and
imperfect knowledge, that is, bounded rationality is due to both not having the necessary
44
knowledge (imperfect knowledge or uncertainty) and also due to not having the professional
knowledge to understand the new information and knowledge due to human cognitive
limitations (Cao, 2008, p. 82). Furthermore, the term knowledge incorporates the meaning of
the term information. Essentially, information and knowledge are made of the same building
blocks, called data, in the form of knowledge, some of the non-factual data and irrelevant
data have been filtered out, the remaining data are generalized into factual statements, and
these factual statements are then interconnected to form complex technical knowledge, to this
extent knowledge behaves more like a private good, the more complex nature of knowledge
relative to information means that it generates much greater persistence since the time
horizon of knowledge gaps are significantly longer (Cao, 2008, p. 6).
The interactions between economic agents are made necessary because of the
specialization of labour. The reason why the division of labour is necessary is because the
stock of knowledge is so vast that no one has sufficient time or ability to be an expert in
every field of knowledge. A natural way of overcoming human limited capacity to absorb the
vast stock of knowledge is by specialization of labour, because specialization of labour
allows economic agents to maximize their economic outcomes without having to obtain the
required knowledge by exchanging knowledge (Cao, 2008, p. 83).
Traditionally, expected inflation is modeled as the expectations of inflation
conditional upon the information available at time t ,
1 1 1
e
t t t t tE � E (2.35)
where t� represents the informational set at time t , but in many cases, having access to the
information is not enough, knowledge about the subject matter is also needed in order to
understand and to exploit the information for possible economic gains, and in this case the
constraints are about a lack of economic knowledge. Therefore expected inflation should be
modeled as the expectations of inflation conditional upon the information and knowledge
available at time t .
Thus expected inflation should be modeled as:
1 1 1
e
t t t t tE � E (2.36)
where t� represents the knowledge about inflation set at time t .
Whether constraints about the information and knowledge can be overcome easily or
not partly depends on the nature of the subject matter. Essentially it is a question about
45
whether the nature of the subject matter is common knowledge or professional knowledge.
While it is reasonable to assume that the definition of inflation and the actions of the
monetary authorities are common knowledge, the causes, effects, costs and benefits of
inflation are not common knowledge. It takes intensive economic study in order to gain a
good understanding of inflation. The existence of educational institutions teaching economic
courses ranging from elementary level to advanced level suggests that we should think about
economic knowledge as a continuum ranging simple definitions to advanced economic
concepts, it also suggests that certain aspects of economic knowledge can only be obtained
through time consuming formal education and training (Cao, 2008, pp. 53-54).
Bounded rationality implies that the best way for non-economists to minimize their
forecast errors is to listen to the advices of professional economists. Furthermore, bounded
rationality opens up the possibility that when economists have the wrong model of economy,
which in turn causes non-economists to have the wrong model of the economy. This is
evident by the existence of many obsolete economic theories in the history of economic
thought and admissions of influential economists (such as Alan Greenspan recently) that they
had the wrong model of the economy. Thus, when an influential economist such as Alan
Greenspan makes predictions about the economy based on the wrong model of the economy,
he also causes many non-economists to make the wrong predictions about the economy.
Whether a non-economist decides to learn economics and become a professional
economist depends on the potential costs and benefits of his decision. For many non-
economists the costs of learning economics so that they can understand economics as well as
professional economists outweigh the benefits, this is reflect by the relatively small size of
economic profession to the general public as a whole. For these non-economists, the best way
to minimize their forecast errors is to listen to the advices of professional economists. This
implies that the most important cost of price adjustment is the mental cost of obtaining
information and knowledge about economic matters rather than the actual costs of changing
prices (menu costs).
Note that we are not proposing that all economic knowledge is professional
knowledge, but we are proposing that economic knowledge is a continuum ranging from
simple definitions (such as the definition of that inflation) that could be considered as
common knowledge to highly specialize economic concepts, such as financial derivatives,
economic growth and monetary economics. With respect to inflation expectations, it is
reasonable to assume that the definition of inflation and the actions of the monetary
46
authorities are common information or knowledge, but having access to the information is not
enough, specialized knowledge about the subject matter is also needed in order to understand
and to exploit this information for possible economic gains, as a result the causes, effects,
costs and benefits of inflation are not common knowledge, but are professional knowledge,
rather than common knowledge. This is evident by the fact that the economic profession
exists, the reason why the economic professional exists is because economic knowledge is
not easily transferable, much of economic knowledge can only be obtained through time
consuming formal education and training and certain aspects of economic knowledge are
highly specialized as evident by the fact that the economic professional is further divided into
different fields of specialization, such as econometrics, finance, monetary economics...etc.
Thus, our approach to modeling bounded rationality could be considered as a direct
application of Adam Smith’s notion of the division of labour.
One of the main ideas in Adam Smith’s Wealth of Nations is the division of labour
increases productivity, Smith (1776, pp. 4-5) demonstrates the power of the division of labour
by describing the work in a pin factory, Smith estimates that the division of labour in the pin
factory increases productivity between 240 and 4800 folds.
“I have seen a small manufactory of this kind where only ten men were employed,
and where some of them consequently performed two or three distinct operations. But
though they were very poor, and therefore but indifferently accommodated with the
necessary machinery, they could, when they exerted themselves, make among them
about twelve pounds of pins in a day. There are in a pound about four thousand pins
of a middling size. Those ten persons, therefore, could make among them upwards of
forty-eight thousand pins in a day. But if they had all wrought separately and
independently, and without any of them having been educated to this particular
business, they certainly could not each of them have made twenty, perhaps not one
pin a day; that is, certainly, not the two hundred fortieth, perhaps not the four
thousand eight hundredth part of what they are at present capable of performing, in
consequence of a proper division and combination of their different operations”.
The division of labor is such an important characteristic of a modern economy; the
production of complicated products (such as the computer, automobile, television, etc.)
would be unimaginable without the combine efforts of professionals. This is reflected by the
fact that every profession owes its function to the unequal distribution of knowledge between
the profession and its clients and that the more specialization of labour an economy
47
experiences, the greater is the productivity in the economy. This readily observable
phenomenon is one of the most striking differences between a developed and a developing
country.
The reason why the division of labour is necessary is because the stock of knowledge
is so vast that no one has sufficient time or ability to be an expert in every field of knowledge.
A natural way of overcoming human limited capacity to absorb the vast stock of knowledge
is by specialization of labour, because specialization of labour allows economic agents to
maximize their economic outcomes without having to obtain the required knowledge by
exchanging knowledge. If people really have unbounded rationality, then it would be difficult
to explain why the division of labour is necessary (Cao, 2008, pp. 82-83).
The importance of economic knowledge is perhaps most elegantly expressed by
Keynes (1936, p.241).
“The ideas of economists and political philosophers, both when they are right and
when they are wrong, are more powerful than is commonly understood. Indeed the
world is ruled by little else. Practical men, who believe themselves to be quite exempt
from any intellectual influence, are usually the slaves of some defunct economist.
Madmen in authority, who hear voices in the air, are distilling their frenzy from some
academic scribbler of a few years back. I am sure that the power of vested interests is
vastly exaggerated compared with the gradual encroachment of ideas”.
There are at least two readily observable evidence of the importance of economics
generally and of the specialized nature of monetary economics more specifically. First, the
Federal Reserve is an extremely powerful institution and the Chairman of the Federal
Reserve is sometimes described as the second most powerful person in the world by the mass
media, after the president of the United States. If economic knowledge is common knowledge
and people really have unbounded rationality, then it would be difficult to explain why the
Federal Reserve and its chairman are so powerful. Second, the existence of organizations
such as the Council of Economic Advisers, it would be difficult to explain why the President
of the United States needs a Council of Economic Advisers to advise him about economic
matters, if economic knowledge is common knowledge and the President of the United States
has unbounded rationality.
The idea that economic knowledge is specialized knowledge and not common
knowledge in supported by Carroll’s (2001, 2003) (also see Mankiw and Reis (2001, p.28))
48
empirical findings. Carroll compares the inflation expectations from surveys of two groups:
professional forecasters and the general public. He finds the professional forecasters are
better at forecasting inflation than the general public. In addition, he finds that the general
public’s expectations respond to the professionals’ expectations with a lag. Furthermore,
when there are more news stories about inflation; the public’s expectations adjust more
rapidly and are closer on average to the professionals’ expectations (Cao, 2008, p. 54).
The Mankiw and Reis (2001, 2002) model and the Carroll (2001, 2003) model are
similar to the Calvo (1983) model with respect to its assumption that in each period a fraction
of the population obtains new information about the economy regardless of how long it
has been since its last price adjustment, and the rest of the population 1 continues to set
price based on old information. The crucial difference between Calvo’s (1983) sticky-price
approach and Mankiw and Reis’ (2001, 2002) sticky-information approach is the timing of
expectations. In the Calvo (1983) model, current expectations of future economic conditions
play important an important role in determining the inflation rate. In the sticky-information
model the relevant expectations are past expectations of current economic conditions. This
difference yields large differences in the dynamic pattern of prices and output in response to
monetary policy (Mankiw and Reis 2002, p.1300).
Mankiw and Reis (2002, p.1302) find that 0.25 fits the data well (Carroll finds
that 0.27 fits the well), they claim that “[t]his value of means that firms on average
make adjustments once a year”. However, this creates a problem for explaining persistent
inflation because the probabilities of a firm not having the opportunity of adjusting its prices
after four quarters and eight quarters are given by (Cao, 2008, p. 55):
4
4( ) (0.75) 0.3164p E
8
8( ) (0.75) 0.1001p E
This implies that inflation persistence should not last for much more than eight
quarters. This is inconsistent with empirical evidence mentioned in the paper that the
maximum impact of a monetary shock on inflation occurs after 7 quarters and the full life
span of the shock lasts much longer, typically between 15-20 quarters.
In our model represents the flow of inflational knowledge from professional
economists to the general public. The value of is depended on factors such as: the
credibility of the monetary authority, the frequency and availability economic news,
49
effectiveness of communication between economists and non-economists and the potential
economic gains or losses of responding quickly to economic developments.
“The general equation is given by:
2 2
t �t �t , provided that,1
�� (2.37)
where � is the number of periods in the lifespan of the monetary shock.
This general equation is based on the assumption that in each period, an additional
percentage of population acquire inflational knowledge � , therefore the proportion of
population that possesses inflational knowledge after t periods is given by �t , at the same
time the proportion of the population that have not acquired inflational knowledge is given by
1 �t . The flow of inflational knowledge in a particular period is given by the product of
the proportion of the population that have not acquired inflational knowledge 1 �t and the
proportion of the population that possesses inflational knowledge �t .
Thus the Sticky-Knowledge Phillips curve is given by:
1
0
1 1
�
t t t t t t t � t t
�
� E �
(2.38)
where 2 2
t �t �t , when 0.05, 20� � , the time path of t is given by” (Cao, 2008, pp.
55-56):
t 0 1 2 3 4 5 6
0 0.0475 0.0900 0.1275 0.1600 0.1875 0.2100
t 7 8 9 10 11 12 13
0.2275 0.2400 0.2475 0.25 0.2475 0.2400 0.2275
t 14 15 16 17 18 19 20
0.2100 0.1875 0.1600 0.1275 0.0900 0.0475 0
0.16625 4 17 0.20875
50
Under the Carroll (2003) and the Mankiw and Reis (2001, 2002) framework, the
fraction of the population that have adjusted its prices is given by:
112 1
0
1 1 ... 1 1 1 1
ttt t
t
t
�
(2.39)
where t� is the fraction of the population that has adjusted prices, assuming that 0.25 , the
fraction of the population that have adjusted its prices for the first ten quarters are as follows:
1� 2� 3� 4� 5� 6� 7� 8� 9� 10�
0.250 0.4378 0.578 0.684 0.762 0.822 0.867 0.900 0.925 0.944
Under our framework, when 0.05, 20� � , the fraction of the population that have
adjusted its prices is given by t� �t , the fraction of the population that have adjusted its
prices for the first ten quarters are as follows:
1� 2� 3� 4� 5� 6� 7� 8� 9� 10�
0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
The differences in the lag structures between the Carroll (2003) model, Mankiw and
Reis (2001, 2002) model and our model is clear, our approach yields much greater
persistence and hence it provides a better explanation for the empirical observation that the
maximum impact of a monetary shock on inflation occurs after seven quarters and the full
life span of the shock is much longer, typically between 15-20 quarters.
Mankiw and Reis (2002, p.1316) note that the sticky-information model cannot
explain Carroll’s (2001) empirical findings that “professional’s and public’s expectations are
closer on average when there are more news stories about inflation. In addition, when there is
more news stories about inflation, the public’s expectations adjust more rapidly to the
professional’s expectations… it suggests that the rate in information acquisition is not
constant overtime”.
51
Under our formulation represents the flow of inflational knowledge from
professional economists to the general public, the rate of dissemination of inflational
knowledge depends on the credibility of the monetary authority, the frequency, availability
and effectiveness of communication between economists and non-economists. This also
implies that our approach is only an approximation, as there are many factors and shocks
affecting the real economy at the same time, people cannot identify individual shocks and
respond to them separately, it is also possible that they could make more than one price
adjustments in respond to a particular shock, over adjust and under adjust based on their
sources of information.
A simpler way of specifying that inflation expectations are boundedly rational is to
use a hybrid new Keynesian Phillips curve
1 1t t b t � t tmc E . (2.40)
Inflation depends on real marginal cost, expected inflation and lagged inflation. This
specification is popular and a common interpretation of this specification is that only a
fraction � of agents use rational expectations, while the remainder use last period’s inflation
rate as a simple rule of thumb for forecasting inflation (Gali and Gertler, 1999 and Gali,
Gertler and Lopez-Salido, 2005). Fuhrer and Moore (1995) assume that agents are concerned
with relative real wages. Similarly, Christiano, Eichenbaum and Evans (2005) and Smets and
Wouters (2003, 2004) attempt to explain inflation persistence (lagged inflation) by assuming
some form of indexation. However, Walsh (2010, p. 255) points out that are no empirical
evidence to support such indexation price setting behaviour.
Our rationale for the inclusion of lagged inflation in the hybrid new Keynesian
Phillips curve is bounded rationality. Bounded rationality implies that the best way for non-
economists to minimize their forecast errors is to listen to the advices of professional
economists as much of economic knowledge is professional knowledge. Since the general
public’s inflation expectations respond to the professional economists’ expectations with time
lag, lagged inflation rates are correlated with the current inflation rate.
2.6 Conclusion
Our main objective in this chapter was to show that bounded rationality can provide a
theory of information and knowledge processing by economic agents, which emphasizes that
when the nature of the required knowledge is professional economic knowledge, then the best
52
way for non-economists to minimize their forecast errors is to listen to the advices of
economists, as the costs of acquiring this professional knowledge can be very high. Bounded
rationality explains why lagged inflation plays an important role in empirical inflation
regressions as the dissemination of economic information and knowledge between
professional economists and non-economists involves time lags, lagged inflation rates are
correlated with the current inflation rate.
53
CHAPTER 3
An Empirical Survey of the New Keynesian Phillips Curve
3.1 Introduction
The purpose of this chapter is to survey selected empirical works on the new
Keynesian Phillips curve (NKPC) for the USA. We will focus on recent developments with
regard to the abilities of these models to fit the data, whether labour’s share of output or the
output gap is the appropriate measurement for real marginal cost (inflationary pressures), the
relative importance of forward and backward-looking expectations and whether these models
assume that price adjustments are sluggish or expectation adjustments are sluggish. This
chapter consists of four sections. The first section surveys sticky-price-single equation
estimations of the NKPC; the second section surveys dynamic stochastic general equilibrium
(DSGE) sticky-price-model-based estimations of the NKPC, the third section surveys
estimations of the sticky-information Phillips curve and the fourth section concludes.
3.2 Sticky-Price-Single-Equation Estimations of the NKPC
Single-equation estimations of the NKPC are appealing because they do not require us
to make any assumption about other sectors of the economy; hence their findings will still be
valid even if the other sectors of the economy are misspecified. The main disadvantage of
single-equation estimation is its incompleteness, since in the real world different sectors of
the economy are interconnected; taking into account what we know about other sectors of the
economy can help us to make more accurate estimations and gain greater insights (Nason and
Smith, 2008, p. 262).
Calvo’s (1983) formulation of the NKPC has become the workhorse for monetary
policy analysis. However, as mentioned previously, it does not fit the data well. Currently
there is a large body of research on the empirics of the NKPC. This literature originated from
the Gali and Gertler (1999) seminal paper, which focuses on measuring real marginal cost,
explaining the persistence in the rate of inflation and the relative importance of forward and
backward-looking expectations in determining the rates of inflation. We will first examine
the Gali and Gertler (1999) model and then discuss the empirical literature regarding the
issues mentioned above. We will examine the Gali and Gertler (1999) model in more detail
as, much of our empirical work is a direct response to Gali and Gertler’s (1999) empirical
findings.
54
�he �ali a�d �ertler ������ �odel
A Baseline NKPC
Assume that each firm has a fixed probability 1 that it may adjust its price, this
probability is independent of its last adjustment. Hence, is the probability that it keeps its
price unchanged.
The aggregate price level tp is given by
*
1 (1 )t t tp p p (3.1)
where *
tp is the optimal price level and 1tp is the lag of price level tp .
Let �
tmc be the firm’s nominal marginal cost at t and let denote a subjective
discount factor, the optimal reset price is given by
*
0
(1 ) ( ) [ ]� �
t t �
�
p E mc
(3.2)
In setting its price at t , the firm takes into account the expected future path of
marginal cost, subject to the next time it can adjust its price.
Let 1t t tp p denote the inflation rate at t , and tmc the percent deviation of the
firm’s real marginal cost from its steady states value. The equation for inflation is derived by
combining equation (3.1) and equation (3.2).
1[ ]t t t tmc E (3.3)
where(1 )(1 ) depends on the frequency of price adjustment and the subjective
discount factor .Intuitively, because firm’s mark-up price over marginal cost, are forward
looking, and must lock into price for (possibly) multiple periods, they base their pricing
decision on the expected future behaviour of marginal costs.
Iterating equation (3.3) forward yields
0
[ ]�
t t t �
�
E mc
(3.4)
55
The NKPC implies that inflation should equal a discounted stream of expected future
marginal cost.
Gali and Gertler (1999) argue that the reason why the NKPC fits the data poorly is
because traditional empirical work on the Phillips curve uses some output gap measures as
the relevant indicator of real economic activity. In other words, Gali and Gertler (1999)
attribute the poor empirical results of the NKPC to the output gap measure as a poor proxy
for real marginal cost.
To obtain an alterative measure for real marginal cost, Gali and Gertler (1999) note
that with a Cobb-Douglas production function the real marginal cost is given by the real wage
divided by the marginal product of labour (MPL), the marginal product of labour is
proportional to its average product. Thus, real marginal cost can be written as.
t t t t t tt t
t t t t
� P � P � ��� �
�P� � � P�
Hence, real marginal cost is proportional to labour’s share of total income. Expressed
in terms of percent deviations around the steady state, where t� is the labour income share
(equivalent to real unit labour costs). Let lower case letters denote percent deviations from
the steady state, we have t tmc s (also see Walsh, 2010, p.253).
The baseline NKPC with labour income share as a proxy for real marginal cost is given by:
1[ ]t t t ts E (3.5)
where (1 )(1 ) . Since under rational expectations the error in the forecast of 1t is
uncorrelated with information dated t and earlier, it follows from equation (3.5) that
10
t t t t tE s � (3.6)
where t� is a vector of variables dated t and earlier (and, thus, orthogonal to the inflation
surprise in period 1t ). The orthogonality condition given by equation (3.6) then forms the
basis for estimating the model via generalized method of moments (GMM).
56
Gali and Gertler (1999) then estimate the reduced form equation (3.6) using real
marginal cost ts and detrended log GDP as a proxy for the output gap ( )t� . The following
results were obtained:
10.023 0.942 [ ]t t t ts E
(0.012) (0.045)
10.016 0.988 [ ]t t t t
� E
(0.005) (0.030)
The coefficient of the output gap ( )t� has the wrong sign, whereas the coefficient of
real marginal cost ( )t
s has the right sign. Hence, they conclude that real marginal cost is the
relevant real sector driving variable in the NKPC.
Gali and Gertler (1999) then estimate the following structural equations using GMM:
11 1 0t t t t tE s � (3.7)
1
11 1 0t t t t tE s � (3.8)
The structural parameters and were estimated using a nonlinear instrumental
variables estimator. Two alternatives to the benchmark case were considered. In the first
alternative the authors restrict the estimate of the discount factor to unity, and in the
second, nonfarm GDP deflator instead of the overall deflator. Finally, two different
normalizations were used, as given by equations (3.7) and (3.8).
The results are reported in Table 1. The first two columns give the estimates of and
. The third then gives the implied estimate of , the reduced form slope coefficient on real
marginal cost. In general, the structural estimates tell the same overall story as the reduced
form estimates. The implied estimate of is always positive and is highly significant in
every case but one (restricted , normalization (2)). The estimate of in the unrestricted
case is somewhat low, but not unreasonably so, given the sampling uncertainty.
57
Table 3.1: Estimations of the Standard NKPC
GDP deflator (1)
(2)
0.829
(0.013)
0.884 (0.020)
0.926
(0.024)
0.941 (0.018)
0.047
(0.008)
0.021 (0.007)
Restricted
(1) (2)
0.829 (0.016)
0.915 (0.035)
1.000
1.000
0.035 (0.007)
0.007 (0.006)
NFB deflator
(1)
(2)
0.836 (0.015)
0.884 (0.023)
0.957 (0.018)
0.967 (0.016)
0.038 (0.008)
0.018 (0.008)
Notes: This table reports GMM estimates of the structural parameters of equation (3.5).
Rows (1) and (2) correspond to the two specifications of the orthogonal conditions found in equations (3.7) and (3.8) respectively. Estimates are based on quarterly data and cover the
sample period 1960:1-1997:4. Instruments used include four lags of inflation, labour income share, long-short interest rate spread, output gap, wage inflation, and commodity price
inflation. A 12-lag Newey-West estimate of the covariance matrix was used. Standard errors are shown in brackets.
Source: Gali and Gertler (1999, p. 208)
�he ��brid Philips ��r�e
The purpose of Gali and Gertler’s (1999) hybrid Phillips curve is to explain the
persistence nature of inflation. The authors modified the Calvo (1983) model by assuming the
existence of two types of firms. A fraction of firm (1 )w has forward-looking price setting
behaviour, while the remaining firms ( )w have backward-looking rule of thumb based price
setting behaviour, based on the recent history of aggregate price behaviour.
The aggregate price level is given by
*
1 (1 )t t tp p p (3.9)
58
where*
tp is an index for the prices newly set in period t . Let �
tp denote the price set by a
forward-looking firm at t and b
tp the price set by a backward-looking firm. The index for
newly set prices is given by
*
(1 ) � b
t ttp w p wp (3.10)
forward-looking firms behave exactly as in the baseline Calvo (1983) model. Hence, �
tp is
given by
0
(1 ) ( ) [ ]� � �
t t t �
�
p E mc
(3.11)
The rule of thumb that backward-looking firms is assumed to follow has the following
features: First, no persistent deviations between the rule and optimal behaviour. Second, the
price in period t depends only information dated 1t or earlier. Third, Firms are unable to
tell whether their competitors are backward-looking or forward-looking price setters. These
considerations lead to the following rule of thumb:
*
11
b
t ttp p
Intuitively, a backward-looking firm at t sets its price equal to the average price set in
the most recent round of price adjustments, *
1tp , with a correction for inflation.
The hybrid Phillips curve is obtained by combining equations (3.9) – (3.11)
1 1[ ]t t � t t b tmc E (3.12)
where1(1 )(1 )(1 )w , 1
t and [1 (1 )]w
Inflation depends on real marginal cost, expected inflation and lagged inflation, where
is the degree of price stickiness, w is the degree of “backwardness” in price setting, and
is the discount factor. When 0w , all firms are forward looking, the hybrid Phillips curve
converges to the baseline NKPC. When 1 , then 1� b the model take the form of the
hybrid Phillips curve.
Gali and Gertler (1999) then estimate the hybrid Phillips curve using labour’s share of
output as a proxy for real marginal cost.
59
1 1[ ]t t � t b ts E (3.13)
The authors consider three cases: the baseline model, the model with restricted to
unity and the non-farm deflator substituted for the overall GDP deflator. They also use two
alternative specifications of the orthogonal condition, one which does not normalize the
coefficient on inflation to be unity (method 1) and one which does (method 2).
11 1 1 0t t t t tE w s � (3.14)
1 1
11 1 1 0t t t t tE w s � (3.15)
Overall, the authors found the results are consistent with the underlying theory,
implying that expected future marginal costs drive inflation dynamics. With respect to the
relative importance of forward-looking expectations and backward-looking expectations,
their results indicates that forward-looking behaviour is more important that backward-
looking behaviour. Table 2 presents the estimates of equation (3.14).
Table 3.2: Estimations of the Hybrid Phillips Curve
w b �
GDP deflator (1) (2)
0.265
(0.031)
0.486 (0.040)
0.808
(0.015)
0.834 (0.020)
0.885
(0.030)
0.909 (0.031)
0.252
(0.023)
0.378 (0.020)
0.682
(0.020)
0.591 (0.016)
0.037
(0.007)
0.015 (0.004)
Restricted (1)
(2)
0.244
(0.030)
0.522 (0.043)
0.803
(0.017)
0.838 (0.027)
1.000
1.000
0.233
(0.023)
0.383 (0.020)
0.766
(0.015)
0.616 (0.016)
0.027
(0.005)
0.009 (0.003)
NFB deflator (1) (2)
0.077
(0.030)
0.239 (0.043)
0.830
(0.016)
0.866 (0.025)
0.949
(0.019)
0.957 (0.021)
0.085
(0.031)
0.218 (0.031)
0.871
(0.018)
0.755 (0.016)
0.036
(0.008)
0.015 (0.006)
Notes: This table reports GMM estimates of parameters of Eq. (3.14). Rows (1) and (2) correspond to the two
specifications of the orthogonality conditions found in equations (3.15) and (3.16) in the text, respectively.
Estimates are based on quarterly data and cover the sample period 1960:1}1997:4. Instruments used include
60
four lags of inflation, labour income share, long-short interest rate spread, output gap, wage inflation, and
commodity price inflation. A 12-lag Newey-West estimate of the covariance matrix was used. Standard errors
are shown in brackets.
Source: Gali and Gertler (1999, p. 212)
Gali and Gertler (1999) also consider two robustness exercises. The first allows extra
lags of inflation to enter the right hand side of the equation for inflation. The second explores
sub-sample stability. Overall, the broad picture remains unchanged. Marginal costs have a
significant impact on short run inflation dynamics of roughly the same quantitative
magnitudes as suggested by the full sample estimates. Across all specifications forward-
looking behaviour remains dominant. In the estimated hybrid Phillips curve, the weight on
inflation lagged one quarter is generally small. Furthermore, additional lags of inflation
beyond one quarter do not appear to matter much at all. “Taken as a whole, accordingly, the
results suggest that it is worth searching for explanations of inflation inertia beyond the
traditional ones that rely heavily on arbitrary lags” (Gali and Gertler, 1999, p. 219).
Table 3.3: Robustness Analysis
w b �
GDP deflator
0.244
(0.062)
0.860
(0.025)
0.772
(0.054)
0.090
(0.040)
0.231
(0.050)
0.628
(0.033)
0.033
(0.007)
Restricted 0.291
(0.039)
0.787
(0.023)
1.000 -0.025
(0.014)
0.270
(0.028)
0.729
(0.021)
0.029
(0.006)
NFB deflator
0.018
(0.041) 0.922
(0.023) 0.779
(0.050) 0.208
(0.058) 0.019
(0.043) 0.767
(0.046) 0.022
(0.007)
Notes: This table reports GMM estimates of a version of equations (3.14) with three extra lags of inflation added. represents the sum of the coefficients of the extra lags. Using the specification of the orthogonality conditions
found in equation (3.15) in the text. Estimates are based on quarterly data and cover the sample period 1960:1}1997:4. Instruments used include four lags of inflation, labour income share, long-short interest rate spread, output gap, wage inflation, and commodity price inflation. A 12-lag Newey-West estimate of the covariance matrix was used. Standard errors are shown in brackets.
Source: Gali and Gertler (1999, p. 215)
Due to the large body of work on the empirics of the NKPC, it is not possible to list
all the results of this literature. Hence, we will only attempt to review some of the main
contributions and discuss their findings. Besides Gali and Gertler (1999), Gali Gertler and
Lopez-Salido (2001) and Sbordone (2002) have also argued that the standard NKPC is
61
empirically valid, provided that real marginal cost rather than the output gap is used as the
variable driving inflation. Gali, Gertler and Lopez-Salido (2001) confirm Gali and Gertler
(1999) empirical findings for the Euro area and use their empirical result to compare with
those observed in the US. Some of their finding can be summarized as follows: “(a) the NPC
fits Euro area data very well, possibly better than U.S. data, (b) the degree of price stickiness
implied by the estimates is substantial, but in line with survey evidence and U.S. estimates,
(c) inflation dynamics in the Euro area appear to have a stronger forward-looking component
(i.e., less inertia) than in the U.S., (d) labour market frictions, as manifested in the behaviour
of the wage markup, appear to have played a key role in shaping the behaviour of marginal
costs and, consequently, inflation in Europe” (Gali, Gertler and Lopez-Salido, 2001, p.1237).
There are several issues regarding the estimation of the NKPC, below are some of the
discussions regarding these issues:
How do we interpret the empirical success of Gali and Gertler (1999) hybrid Phillips
curve? Do marginal costs drive inflation dynamics? The direct implication of Gali and
Gertler’s approach is the relationship between real marginal cost and the output gap is weak.
“According to New Keynesian models, a simple structural relationship between inflation and
the output gap does not hold in general—it holds only if the labour market is perfectly
competitive. If the labour market is not competitive, labour frictions become crucial, and one
needs to model the “wage markup” produced by monopoly power in labour supply, which
drives a wedge between real marginal cost and the output gap” (Neiss and Nelson, 2005,
p.1020, also see Gali, Gertler and Lopez-Salido 2001, p.1261-1262).Is the labour market
perfectly competitive? If not, what is the nature of the frictions in the labour market?
Gali and Gertler (1999, p. 204) state that “[A] more fundamental issue, we believe, is
that even if the output gap were observable the conditions under which it corresponds to
marginal cost may not be satisfied. Our analysis of the data suggests that movements in our
measure of real marginal cost (described below) tend to lag movements in output, in direct
contrast to the identifying assumptions that imply a co-incident movement. This discrepancy,
we will argue, is one important reason why structural estimations of Phillips curves based on
the output gap have met with limited success, at best.”
However, using labour’s share of output as a proxy for real marginal cost also has its
difficulties. The standard approximation of real marginal cost by real unit labour cost
(labour’s share of output) assumes a constant-returns-to scale production function. Under
62
more realistic assumptions, real unit labour cost needs to be corrected for some factors, such
as: assumptions about technology, non-constant elasticity of factor substitution between
capital and labour, the presence of overhead costs and labour adjustment costs (Guay and
Pelgrim, 2004, p.5, Rotemberg and Woodford (1999)). The key issue is how to distinguish
when the increase in output is cause by technological progress, which does not cause
inflationary pressures and when the increase in output is not caused by technological
progress, which tends to raise nominal marginal costs or inflationary pressures, as workers
demand higher wages in order to supply more labour. The output gap cannot do this because
it assumes the labour market perfectly competitive. Similarly, labour’s share of output cannot
do this because it assumes constant returns to scale. Rudd and Whelan (2007, p. 160) plot the
output gap (based on HP filter) and labour income share (Nonfarm Business Sector) from
1960 to 2005, both measures of real marginal cost raised because it failed to recognise that
the increases in output from 1995 to 2000 were due to internet related technologies allowing
households and businesses to operate more efficiently, which does not cause inflationary
pressures, as reflected by the low rates of unemployment and inflation recorded during the
period.
Is the use of Generalized Method of Moments (GMM) appropriate for estimating the
NKPC? Linde (2005) argues that Full Information Maximum Likelihood (FIML) provide
more efficient parameters than GMM. Gali, Gertler and Lopez-Salido (2005, p. 1107) rebut
claims that their results are the product of specification bias by presenting a series of
robustness tests, including using FIML techniques. The authors point out that estimating the
NKPC using GMM may be sensitive to the choice of instruments. On the other hand,
maximum likelihood estimation may be sensitive to imposing false assumptions about either
the error term (normality of the error term is required) or the overall model structure (in the
case of FIML). They conclude that GMM estimations of the NKPC are informative and valid
(Gali, Gertler and Lopez-Salido 2005, p. 1116).
Are inflation expectations consistent with rational expectations? Most empirical
studies on the hybrid Phillips curve assume that inflation expectations are consistent with
rational expectations. Gali and Gertler’s (1999) hybrid Phillips curve cannot explain the
persistence nature of inflation without adding a lagged inflation term in an ad hoc manner.
Fuhrer and Moore (1995) attempt to explain the persistence of inflation by modelling wage
negotiations in terms of relative wage contracts (i.e. wage indexation) instead of nominal
wage contracts. Rudd and Whelan (2006, p.319) find that adding lags to the standard NKPC
63
improve empirical fit, they suggest that inflation expectations are not fully rational and that
adding lagged inflation term is just addressing the cause of the problem, which they believe
to be deviations from rational expectations (bounded rationality).
3.3 DSGE Model-Based Estimations of the NKPC
More recently, empirical work on the NKPC has relied on dynamic stochastic general
equilibrium (DSGE) models to estimate the parameters of the NKPC. This approach
combines rational expectations with a microeconomic foundation in which a representative
household or firm is assumed to behave optimally, given their objectives and constraints.
This approach is becoming increasingly popular among central banks around the world for
policy analysis.
New Keynesian economists borrow this approach from new classical economists,
which is based on the pioneering work of Kydland and Prescott (1982), designed to study
how real (supply) shocks to the economy might cause business cycle fluctuations under the
assumptions of rational expectations, flexible prices and representative agents. In contrast,
new Keynesian DSGE models typically assume monopolistically competitive firms and
emphasise that prices and wages display rigidities and that this nominal stickiness accounts
for the real effects of monetary policy (Walsh, 2010, p.28).
Our approach to modelling bounded rationality in terms of asymmetric
(heterogeneous agents) and imperfect knowledge (uncertainty) implies that DSGE is not
appropriate for modelling and analysing models based on bounded rationality. Hence, we will
pay less attention to this literature.
Some examples of DSGE-base estimation of the NKPC are Christiano, Eichenbaum,
and Evans (2005), Smets and Wouters (2005), Cho and Moreno (2006), Linde (2005), Salemi
(2006) Andres, Lopez-Salido, and Nelson (2004). In this literature Bayesian and Maximum
Likelihood Estimation (MLE) techniques are often used to estimate the NKPC. Interested
readers can consult Tovar (2009) for more details on the use DSGE models by various central
banks.
A �imple ���E �odel
Our exposition of the structure of a DSGE model follows Cho and Moreno (2006,
p.1463 – 1465). A typical DSGE model consists of three structural equations: an aggregate
64
supply (AS) equation, an aggregate demand (AD) equation and a monetary policy rule
equation. The model assumes that there is no informational difference between the private
sector (firms and households) and the central Bank. The aggregate supply equation is
represented by the NKPC, Cho and Moreno (2006) use a hybrid Phillips curve
1 1 ,(1 )t t t t t A� tE � (3.16)
where t is the inflation rate, t
� is the output gap and ,A� t is the aggregate supply structural
shock or error term.
The aggregate demand equation is represented by the new Keynesian IS equation
1 1 1 ,(1 ) ( )t t t t t t t ��t� E � � r E (3.17)
where t�is the output gap, t
is the inflation rate and ,�� t is the aggregate demand structural
shock or error term. In this specification, the habit formation in the utility function impacts
endogenous persistence to the output gap. The forward-looking parameter depends
inversely on the level of habit persistence. The monetary policy channel in the �� equation is
captured by the contemporaneous output gap dependence on the ex-ante real rate of interest.
To close the model, an interest rates rule that the central bank is assumed to follow in
setting the nominal interest rate
1 1 ,(1 )[ ]t �P t t t t �P tr pr p E � (3.18)
where tr is nominal interest rate, �P is a constant and �P is the monetary policy shock. The
policy rule exhibits interest rate smoothing, placing a weight of p on the past interest rate.
The Fed reacts to high-expected inflation and to deviations of output from its trend. The
parameter measures the long run response of the central bank to expected inflation and the
parameter describes it reaction to output gap fluctuations.
The three structural equations are expressed in matrix form and the rational
expectations equilibrium can be computed numerically using the generalized Schur matrix
decomposition method (QZ). When there are multiple equilibria, recursive method can be
used to solve the system. These structural equations can also be estimated separately using
Full Information Maximum Likelihood (FIML) or Bayesian methods.
65
The main advantage of DSGE-based estimations of the NKPC is it allows us to take
into account what we know about other sectors of the economy, which can provide more
accurate estimations and greater insights. However, in practice this is very difficult to achieve
because DSGE models are difficult to build as we still do not know enough about some
sectors of the economy (i.e. finance) and strong assumptions have to be made, some of these
assumptions are: complete markets, no labour and financial market frictions. In many DSGE
models, Calvo pricing is used to model nominal rigidities, but it is assumed other markets
clear, which tend to lead to unrealistic and internally inconsistent implications. If prices are
sticky, it is unlikely that that the labour and the financial markets will clear.
Some economists have blamed DSGE models for the failure of modern
macroeconomics to anticipate and to make sense of the current financial crisis. Willem Buiter
(2009) has criticized DSGE models for its assumptions of complete and efficient markets.
Robert Solow (2010) was very critical of the DSGE models because of its unrealistic
assumptions and implications.
“[T]he basic story always treats the whole economy as if it were like a person... This
can not be an adequate description of a national economy…An obvious example is
that the DSGE story has no real room for unemployment of the kind we see most of
the time, and especially now…The only way that DSGE and related models can cope
with unemployment is to make it somehow voluntary, a choice of current leisure or a
desire to retain some kind of flexibility for the future or something like that…
DSGE model has nothing useful to say about anti-recession policy because it has built
into its essentially implausible assumptions the “conclusion” that there is nothing for
macroeconomic policy to do”.
3.4 Estimations of the Sticky-Information Phillips Curve (SIPC)
Recall that the sticky-information Phillips Curve is given by:
1
0
(1 ) [ ]1
�
t t t � t t
�
� E �
(3.19)
where 1t t t� � � is the growth rate of the output gap. According to the SIPC, inflation
depends on the current output gap, past expectations of current inflation and the growth rate
of the output gap. The parameter represents the degree of information stickiness. A higher
66
value of implied that more firms are updating their expectation about the state of the
economy. The parameter represents the sensitivity of the optimal relative price to the
output gap. It can be interpreted as the degree of real rigidity as discussed by Ball and Romer
(1990).
An important feature of the SIPC “is that current inflation depends not only on the
current output gap but also on the past expectations of both current inflation and the growth
rate of the current output gap. This feature also makes the empirical estimation of the SIPC
parameters difficult (Kahn and Zhu, 2006, p.196). Perhaps of the difficulties mentioned
above and the lack of interest in the SIPC in comparison to the standard NKPC and the
hybrid NKPC there has been relatively few attempts to estimate the SIPC (Dopke et al., 2008,
p.1514).The most important parameter in the SIPC is , as represents the degree of
information stickiness or the extent of deviations from unbounded rationality more generally.
In the literature on estimating the SIPC, the main objective is to estimate . Once is
estimated, the duration of information update in quarters is given by1
.
Currently there is no consensus with regard to what is the best method to estimate the
SIPC. Some of the methods commonly used to estimate the SIPC are: Full Information
Maximum Likelihood (FIML), Maximum Likelihood Estimation (MLE), Generalize Method
of Moments (GMM), Bayesian, Ordinary Least Square (OLS) and combining Vector
Autoregressive (VAR) and Ordinary Least Square (OLS). See table 4 for details of various
studies surveyed in this chapter. It should also be noted that most of the studies use VAR
models as proxies for inflation and output forecasts. Only two studies (Dopke et al., 2008 and
Coiboin, 2009) use survey-based data as proxy for inflation expectations.
Similarly, there is no consensus on the estimates of . In Mankiw and Reis’ (2002)
original paper, the authors obtain the value of 0.25 by calibration, each period in the
model represents a quarter, the average duration between information updates according to
Mankiw and Reis is given by 1
40.25
quarters. The durations of information updates of the
studies we surveyed in this chapter range from 4 months to 18 months (also see Knotek,
2006, p.40)
Since Mankiw and Reis (2002) proposed the SIPC as a possible replacement to
standard new Keynesian Phillips curve (NKPC), many researchers have attempted to
67
compare the empirical results of the SIPC with the NKPC and in the process these studies
also attempt to estimate the parameter of the SIPC. The general conclusion from this
literature (Arslan, 2010, Korenok 2008, Korenok and Swanson 2007, Dupor et. al. 2009, and
Coibion 2009) is that sticky price firms have a dominant role in comparison the sticky
information firms in explaining the relationship between inflation and the real side of the
economy. Furthermore, many of these studies also conclude sticky information firms should
also be taken into account in modelling firm’s price setting behaviour (Arslan, 2010, p.8).
Table 3.4 - Published SIPC Estimations of
Study Sample Period Average Duration
Between Information
Updates (Months)
Method
Single Equation Estimations
Kahn and Zhu
(2006)
1969.1 – 2000.4 8 VAR and OLS
Carroll (2003) 1981.3 – 2000.2 12 OLS
DSGE Model-Based Estimations
(with assumption of information stickiness only on the part of firms)
Andres et.al. (2005) 1979.3 – 2003.3 18 FIML
Dupor et.al. (2006) 1960.1 – 2005.2 8 VAR and OLS
Kiley (2007) 1965.1 – 2002.4 7 MLE
Kiley (2007) 1983.1 – 2002.4 5 MLE
Korenok (2007) 1983.1 – 2002.1 10 FIML
DSGE Model-Based Estimations
(with assumption of information stickiness imposed on workers and consumers also)
Mankiw and Reis 1954.3 – 2006.1 4 (firms) MLE
68
(2007) 16 (consumers)
16 (workers)
and
Bayes
Mankiw and Reis
(2006)
1954.3 – 2005.3 6 (firms)
9 (consumers)
4 (workers)
Method
of Simulated
Moment
Arslan (2010, p.8) also points out that due to the poor performance of the sticky-
information model, Mankiw and Reis (2007) developed and analysed a general equilibrium
model with sticky information. Mankiw and Reis claim that the poor empirical performance
of the sticky information model arises from a partial equilibrium approach, which only
assumes information stickiness on the part of firms, they argue that information stickiness
should be pervasive across all markets.
3.5 Conclusion
In the empirical literature on the NKPC, two issues dominate this literature. First, are
inflation expectations consistent with rational expectations? Second, do real marginal costs
drive inflation dynamics?
In chapter 2 we attempted to argue that inflations expectations are boundedly rational
and that the persistence nature of inflation is cause by sticky nature of knowledge, which
disseminate slowly after monetary policy shocks. This approach is based on the work of
Mankiw and Reis (2002), Carroll (2003), Roberts (1995, 1997) and Furher and Moore
(1995).
The work of Gertler and Gali (1999) and Gertler, Gali and Lopez-Salido (2001) and
Sbordone (2002) have shown that the output gap is not a good proxy for real marginal cost
(inflationary pressures) because it is likely that the labour market is not competitive. If the
labour market is not competitive, labour frictions become critical, we need to model wage
markup produced by monopoly power in labour supply (Neiss and Nelson, 2005, p.1020).
This implies that we need to consider labour market frictions in modelling the NKPC.
However, using labour’s share of output as a proxy for real marginal cost is also potentially
problematic. The standard approximation of real marginal cost by real unit labour cost
69
(labour’s share of output) assume a constant-returns-to scale production function. Under more
realistic, assumptions, real unit labour cost needs to be corrected for a number of factors, such
as: assumptions about technology, non-constant elasticity of factor substitution between
capital and labour, the presence of overhead costs and labour adjustment costs (Guay and
Pelgrim, 2004, p.5, Rotemberg and Woodford (1999)).
70
CHAPTER 4
Proxies for Real Marginal Cost
4.1 Introduction
The work of Gali and Gertler (1999) and Gali, Gertler and Lopez-Salido (2001, 2005)
have raised two important issues. First, the new Keynesian Phillips curve (NKPC) needs to
take into account labour market frictions. Second, the output gap (GAP) may not be an
appropriate proxy for real economic activity because it assumes that the labour market clears.
Gali and Gertler (1999) argue that the reason why the NKPC fits the data poorly is because
traditional empirical work on the Phillips curve uses some output gap measures as a proxy for
real marginal cost rather than labour’s share of income. Moreover, there is not a single
method of measuring potential output and therefore the GAP. We will attempt to argue that
the probability of finding a job or job finding probability (JFP) is a better proxy for real
marginal cost than GAP and labour’s share of income, at the same time JFP provides a direct
link between frictions in the labour market and the Phillips curve relationship. This chapter is
structure as follows: Section 1 provides a brief literature review of recent debates. Section 2
examines the intuitions behind the use of the output gap, labour’s share of income and job
finding probability as proxies for real marginal cost. Section 3 compares their empirical
appropriateness as proxies for real marginal cost and section 4 concludes.
4.2 Literature Review
In recent years, there has been a trend in modelling inflation dynamics by using Calvo
(1983) pricing in order to motivate a forward-looking inflation equation known as the new
Keynesian Phillips curve (NKPC) of the form
1[ ]t t t tE mc (4.1)
The implication of this model is that inflation should be independent of its own lagged
values. As a result, this specification has often been criticized because it does not fit the data
well; empirical studies have shown that inflation can be predicted well from its own lagged
value. Simple regressions of inflation on its own lags have much higher 2� values than the
NKPC in equation (4.1).
In response to this critique, Gali and Gertler (1999, p.195) have suggested an
alternative to the pure forward-looking model that is intended to better capture observed
71
inflation inertia. This "hybrid" specification modifies the new Keynesian Phillips curve so
that inflation depends on a weighted sum of its lag and its rationally expected future value.
1 1[ ]t b t � t t t tE mc (4.2)
Where the structural parameters of the reduced form coefficients are:
1
1
(1 )(1 )(1 )
[1 (1 )].
�
b
and t is the error term. The coefficients are explicit functions of three model parameters: ,
which measures the degree of price stickiness; , the degree of “backwardness” in price
setting, and the discount factor . Note that when goes to zero, the equation becomes the
pure forward-looking NKPC, with 0b and � .
Gali and Gertler (1999) attribute the poor empirical results of the NKPC to the output
gap measure as a poor proxy for real marginal cost. Gali and Gertler (1999 found “backward-
looking price setting, while statistically significant, is not quantitatively important and that
“the new Keynesian Phillips curve provides a good first approximation to the dynamics of
inflation”. Gali and Gertler’s (1999) work have generated much interest on the empirics of
the hybrid new Keynesian Phillips curve, their empirical findings are accepted by many as a
sensible compromise between the pure rational expectations new Keynesian Phillips curve
with micro-foundations, but does not fit the data well and the old Keynesian Phillips curve,
which lacks strong micro-foundations but fits the data better.
Rudd and Whelan (2005a, 2005b, 2006, 2007) are the leading critics of Gali and
Gertler’s approach, they based their criticisms on their empirical findings that labour share
does not drive inflation dynamics and also question the validity of the assumption of rational
expectations assumed in the hybrid new Keynesian Phillips curve. Furthermore, if
expectations are rational they should be model consistent, but the Gali and Gertler’s
expectations are not model consistent. Below are some of their critiques.
�he Persiste�ce Problem
Under rational model consistent expectations, the closed form of the pure forward-
looking NKPC can be written as (by applying repeated substitution):
72
0
�
t t t �
�
E mc
(4.3)
Symbols used in (3) have the same meaning as in equation (4.2). The main difference
between the Gali and Gertler NKPC in (4.1) and the Rudd and Whelan NKPC in (4.3) is that
while inflationary expectations are model consistent in (4.3), they are not in (4.1). Both the
NKPCs imply inflation is a purely forward variable, current inflation is proportional to the
expected present discounted value of current and future real marginal cost. No lagged
variables-including lagged inflation-should have an impact on the current level of inflation.
The model predicts that current inflation should forecast future movement in real marginal
cost as, for example, a rise in future real marginal cost that can be forecast should
immediately raise current inflation. Rudd and Whelan (2005a) found that the empirical fit of
the NKPC is poor across a wide variety of VAR specifications. In addition, VAR
specifications that include lagged inflation reveal that there is a statistically significant and
economically large role for lagged inflation. This result is obtained whether one uses the
output gap or labour’s share of income as proxy for real marginal cost. The failure of the pure
forward-looking NKPC to account for the empirical importance of lagged inflation is known
as the persistence problem (also see Walsh, 2010, p. 253).
Rudd and Whelan (2005b) augment equation (4.3) with an additional one lag of
inflation in order to test whether the pure NKPC provides a good characterization of the
inflation process, if the pure forward-looking model were correct, coefficients on lagged
inflation should be relatively small. The equation they consider is given by.
1
0
�
t t t � t
�
E mc
(4.4)
Rudd and Whelan (2005b, p. 1167) constructed a proxy for the infinite discounted
sum of the expected future values of the driving variable then estimate equation (4.4) using
GMM. They concluded that “the new-Keynesian pricing model cannot explain the
importance of lagged inflation in standard inflation regressions, and find that forward-looking
terms play a very limited role in explaining inflation dynamics”. If estimates of the closed
form results are significantly different from those obtained from estimating the structural
form, then Gali and Gertler’s (1999) results are likely to be a product of mis-specification.
Gali, Gertler and Lopez-Salido (2005, p.1112) rebut Rudd and Whelan’s (2005b)
criticisms by arguing that the reason they got very different results is because they failed to
73
exploit the connection between the key parameters of the structural form of the hybrid model
given by equation (4.2) and the reduced form parameters of the closed form they estimate. In
particular, the reduced form parameters of the closed form are explicit functions of the
parameters of structural form (4.2), including � and b , the parameters that identify the
relative importance of forward- looking versus backward-looking behaviour. They then
estimate the closed form equation in a way that incorporates the restrictions of the structural
form, the parameter estimates are virtually identical to those obtained in Gali and Gertler’s
(1999) and Gali, Gertler and Lopez-Salido (2001) by estimating the structural form directly.
More specifically, they argue that the parameter on lagged inflation is not the same as b ,
the coefficient on lagged inflation in the baseline hybrid specification (4.2). In other words, it
is not possible to assess the relative importance of forward-versus backward-looking
behaviour from the Rudd and Whelan (2005b) specification and that it is important to
identify the parameters � and b directly.
Rudd and Whelan (2007) summarise their previous empirical findings and also
respond to Gali, Gertler and Lopez-Salido (2005) defence of their previous critiques. Rudd
and Whelan (2007, p. 167) emphasise that the most important test of the NKPC “is whether
there is a statistically significant role for expected future labour shares”. They identify the
source of the disagreements between their empirical findings and that of Gali, Gertler and
Lopez-Salido (2005) is the very different metric for judging the importance of forward-
looking behaviour. Rather than focusing on the role played by expected future labour shares,
they focus on the values of � and b implied by the estimated roots of the closed form
representation. The relationship between the estimated roots of the closed form representation
and the implied values of � and b occurs through a second-order polynomial equation, and
cannot be related to values of � and b directly.
Gali, Gertler and Lopez-Salido (2005, p. 1117) recognise that the hybrid Phillips
curve lacks a “coherent rationale for the role of lagged inflation in the hybrid NKPC”. They
appeal to the work of Christiano, Eichenbaum and Evans (2005) and Smets and Wouters
(2003, 2004) which attempt to explain inflation persistence by assume some form of
indexation. The Fuhrer and Moore (1995) model is perhaps the most well-known model to
explain inflation persistence by introducing indexation. Fuhrer and Moore (1995) assume that
wage negotiations are conducted in terms of the wage relative to an average of real contract
74
wages in effect over the life of the contract. Fuhrer and Moore (1995, p. 130) specification
produce a hybrid Phillips curve of the form
1 1
1ˆ
2t t t t tE � (4.5)
where �̂ is a moving average of current and past output. Inflation depends on its past (and
thus on past output). This specification imparts significant inertia to the inflation rate (as well
as the price level) beyond the inertia in the driving term. One time shocks to output and
inflation will persist. The model also implies that disinflations lead to a decline in output,
which is more consistent with empirical evidence. Fuhrer and Moore (1995) then showed that
their model fits U.S. data better than Taylor’s (1980) model. It is important to point out that
the motivation for the Fuhrer and Moore (1995) model is to explain inflation persistence
which cannot be explained by the forward-looking Taylor staggered contract type models.
Fuhrer (1997, p. 349) tests the empirical significance of expected future prices in forward-
looking contract price specifications and finds that expectations of future prices are
empirically unimportant in explaining price and inflation behaviour.
Roberts (1997, p.174) shows that the Fuhrer and Moore (1995) model is
observationally equivalent to a model with sticky prices and expectations that are imperfectly
rational. That is, we could obtain equation (4.5) based on the assumption that expectations are
an average of rational expectations and a simple extrapolation of last period's inflation rate.
Using survey measures of inflation expectations, Roberts (1997, p. 173) concludes that
“inflation is not sticky and that inflation expectations are less than perfectly rational”. Below
are some selected reduced-form and closed-form GMM estimations of the Phillips curve for
the United States mentioned in the literature review.
75
Table 4.1 Selected Reduced Form GMM Estimations of the Phillips Curve for the United States
General Equation 1 1t t b t � t tmc E
Authors Sample
Period
Proxy for RMC b � Instruments Notes
Gali and Gertler
(1999)
1960q1-
1997q4
Labour’s Share 0.23 - 0.942 Four lags of inflation, labour income share,
long-short interest rate spread, output gap,
wage inflation, and commodity price
inflation.
Coefficient of labour’s share of
income has the correct sign
Gali and Gertler
(1999)
1960q1-
1997q4
Output Gap -0.016 - 0.988 Four lags of inflation, labour income share,
long-short interest rate spread, output gap,
wage inflation, and commodity price
inflation.
Coefficient of the output gap
has the wrong sign
Gali and Gertler
(1999)
1960q1-
1997q4
Labour’s Share 0.037 0.252 0.682 Four lags of inflation, labour income share,
long-short interest rate spread, output gap,
wage inflation, and commodity price
inflation.
Forward expectations dominate
Gali and Gertler
(1999)
1960q1-
1997q4,
Labour’s Share 0.027 0.233 0.766 Four lags of inflation, labour income share,
long-short interest rate spread, output gap,
wage inflation, and commodity price
inflation.
1b �
Forward expectations dominate
Gali, Gertler and
Lopez-Salido
(2001)
1970q1-
1998q2
Labour’s Share 0.250 - 0.924 Four lags of inflation, and two lags of
labour’s share of income, the output gap,
and wage inflation.
Coefficient of labour’s share of
income has the correct sign
Gali, Gertler and
Lopez-Salido
(2001)
1970q1-
1998q2
Labour’s Share 0.291 0.347 0.584 Four lags of inflation, and two lags of
labour’s share of income, the output gap,
and wage inflation.
Forward expectations dominate
76
Gali, Gertler and
Lopez-Salido
(2005)
1960q1–
1997q4
Labour’s Share 0.013 0.349 0.635 Two lags of detrended output, real
marginal costs and wage inflation and four
lags of price inflation.
1b �
Forward expectations dominate
Gali, Gertler and
Lopez-Salido
(2005)
1960q1–
1997q4
Output Gap -0.005 0.325 0.684 Two lags of detrended output, real
marginal costs and wage inflation and four
lags of price inflation.
1b �
Forward expectations dominate
Rudd and Whelan
(2005)
1960q1–
1997q4
Labour’s Share 0.011 0.221 0.764 Four lags of inflation, labour income share,
long-short interest rate spread, output gap,
wage inflation, and commodity price
inflation.
2SLS
Forward expectations dominate
Rudd and Whelan
(2005)
1960q1–
1997q4
Output Gap -0.010 0.188 0.817 Four lags of inflation, labour income share,
long-short interest rate spread, output gap,
wage inflation, and commodity price
inflation.
2SLS
Forward expectations dominate
77
Table 4.2 Selected Closed Form GMM Estimations of the Phillips Curve for the United States
Authors Sample
Period
Proxy for RMC b � Instruments Notes
Gali, Gertler and
Lopez-Salido
(2005)
1960q1–
1997q4
Labour’s Share 0.013 0.374 0.618 Two lags of detrended output, real
marginal costs and wage inflation and four
lags of price inflation.
Forward expectations dominate
Gali, Gertler and
Lopez-Salido
(2005)
1960q1–
1997q4
Output Gap 0.016 0.882 -0.000 Two lags of detrended output, real
marginal costs and wage inflation and four
lags of price inflation.
Backward expectations
dominate
Gali, Gertler and
Lopez-Salido
(2005)
1960q1–
1997q4
Labour’s Share 0.010 0.373 0.627 Two lags of detrended output, real
marginal costs and wage inflation and four
lags of price inflation.
1b �
Forward expectations dominate
Gali, Gertler and
Lopez-Salido
(2005)
1960q1–
1997q4
Output Gap 0.002 0.540 0.460 Two lags of detrended output, real
marginal costs and wage inflation and four
lags of price inflation.
1b �
Backward expectations
dominate
Rudd and Whelan
(2007)
1960q1-
1997q4
Labour’s Share 0.042 0.486 0.473 Two lags of inflation, labour income share,
long-short interest rate spread, output gap,
wage inflation, and commodity price
Backward expectations weakly
dominate
78
inflation.
Rudd and Whelan
(2007)
1960q1-
1997q4
Labour’s Share 0.032 0.440 0.535 Four lags of inflation, two lags each of
inflation, the output gap, the labour income
share, and wage inflation.
Forward expectations weakly
dominate
Rudd and Whelan
(2007)
1960q1-
1997q4
Labour’s Share 0.036 0.452 0.516 Two lags of inflation, and two lags each of
labour’s share of income, the output gap,
and wage inflation.
Forward expectations weakly
dominate
79
4.3 Proxies for Real Marginal Cost
�he ��tp�t �ap
The output gap measures the gap between actual level of output and the potential level
of output that the economy could produce at full employment. The output gap allows us to
measure the size of the deviations of output from potential level of output or trend output
(Dornbush and Fischer, 1994, pp.14-15). The intuition of using the output gap as a measure
of real marginal cost is simple. If the actual level of output exceeds the potential level of
output, then there will be upward inflationary pressures because production costs and labour
costs are higher. Conversely, if the actual level of output is less than the potential level of
output, then there will be downward deflationary pressures because of underemployment of
human resources and machinery. This implies that the output gap and inflation are positively
correlated. As mentioned in chapter 3 the use of the output gap as a proxy for real marginal
cost is potentially problematic because it does not take into account labour market
imperfections and it cannot distinguish when an increase in output is caused by technological
progress, which is less inflationary and when an increase in output is induced say by
monetary policy.
�abo�r�s �hare o� ��come
The logic behind Gali and Gertler’s (1999) is based on the assumption of Cobb-
Douglas production function. Let tA denote technology, t
� capital and t� labour. Then
output t� is given by:
1
t t t t� A � � (4.6)
Real marginal cost is given by the ratio of the real wage rate to the marginal product
of labour (MPL); the marginal product of labour is proportional to its average product. Thus,
real marginal cost is proportional to labour’s share of total income (real unit labour cost). Let
lower case letters denote percent deviations from the steady state t tmc s , where s is the
measure of labour’s share (Walsh, 2010, p. 253). This is valid only when there are constant
returns.
/ /
/t t t t t
t t
t � t t
� P � P � ��� �
�P� � � P� (4.7)
80
As mentioned previously, the approximation of real marginal cost by labour’s share of
income assumes a constant return to scale production function. Under more realistic
conditions, real unit labour cost needs to be corrected for assumptions about technology, non-
constant elasticity of factor substitution between capital and labour, the presence of overhead
costs and labour adjustment costs (Guay and Pelgrim, 2004, p.5).
�ob �i�di�g Probabilit�
The intuition behind the use of job finding probability as a proxy for real marginal
cost is that it directly measures how difficult it is for unemployed people to find jobs, in other
words, the tightness of the labour market. If the labour market is tight, then there will be
upward inflationary pressures because labours costs are higher as workers demand higher
wages in order to supply more labour. Conversely, if the labour market is slack, then there
will be downward deflationary pressures because of underemployment of human resources.
This implies that job finding probability and inflation are positively correlated.
Whether the output gap, labour’s share of output or job finding probability is a better
proxy for real marginal cost is an empirical question. However, theoretically job finding
probability is more appealing because of the following reasons: First, perhaps the most
important aspect about job finding probability is its ability to capture labour market frictions,
as mentioned in the previous chapter, because of our bounded rationality, a lack of
knowledge and skills and the difficulties in overcoming a lack of knowledge and skills are the
main sources of frictions in the labour market. Besides capturing labour market frictions due
to specialization of labour, job finding probability also captures other forms of heterogeneity
in the labour market such as: long-term unemployed, age, sex, race, marital status, levels of
education and geography (Shimer, 2007, p. 4). Second, we do not need to make assumptions
about the type of technology in the production process. In short, job finding probability
overcomes theoretical weaknesses of the output gap and labour’s share of income as proxies
for real marginal cost, at the same time it provides a direct link between labour market’s
frictions and the Phillips curve relationship.
The standard theory of job finding probability describes employers as recruiters of
workers. They expand their efforts until the cost of recruiting a worker exhausts the
employer’s share of the surplus of employing the worker. The employer-equilibrium curve
slopes upward because higher surplus gives employers more incentive to recruit more
81
workers, creating a tighter labour market with a higher job finding probability. For job
seekers, a tighter labour market lowers the surplus. The surplus is the difference between the
present value of a worker’s product and the worker’s opportunity cost. The opportunity cost
in turn, depends on the ease of finding a job – in a tight labour market with a high job-finding
probability, the opportunity cost is higher and the surplus from a job is lower, the job-seeker
equilibrium curve is downward slopping. The equilibrium of the labour market occurs at the
intersection of the employer-equilibrium curve and the job seeker- equilibrium curve (Hall,
2005, p.23-24).
Source: Hall, 2005, p. 23.
The use of job finding probability as a proxy for real marginal cost is not without its
problems, as job finding probability is an unobservable variable, it has to be constructed from
other observable variables. This implies that job finding probability is sensitive to its own
definition as there are various ways of measuring job finding probability. There are at least
three types of job finding probabilities: First, some workers changed jobs without
experiencing unemployment. Second, some people are returning to the labour after being out
of the labour force for various reasons, such as health and child birth. Third, people who are
currently unemployed and wish to find employment (Hall, 2005, p.18).
Intuitively, the job finding probability is the ratio of the flow from other activities into
employment, divided by the number of people who are looking for work. Our objective is to
Employer Equilibrium
Job Seeker Equilibrium
Job Finding Probability
Surplus
82
compute the probability of a job seeker in finding employment without having to be retrained
in order to find employment, it is reasonable that we exclude workers who are currently
employed, but, wish to find other jobs since these job seekers are only a small fraction of the
total number of job seekers, their exclusion should not affect the job finding probability.
Our formulation of job finding probability follows Robert Shimer’s (2005, p.30-31)
formulation, which infers the job finding probability from dynamic behaviour of the
unemployment level and the short-term unemployment level. Let �
t denote the number of
workers unemployed for less than 15 weeks, in month t . Then assuming all unemployed
workers find a job with probability t� in month t and no unemployed workers exit the labour
force, then the number of unemployed workers next month is equal to the number of
unemployed workers this month who failed to find a job, plus the number of newly
unemployed workers.
1 1(1 ) �
t t t t� (4.8)
The job finding probability is given by
1 11�
t tt
t
�
(4.9)
where t� is the job finding probability, t
is the number of unemployed workers, �
t is the
number of short term (less than 15 weeks) unemployed workers and 1t is the number of
unemployed workers next month. We have also considered job finding probability for the
number of workers unemployed for less than five weeks, the results are similar to the results
of job finding probability for the number of workers unemployed for less than 15 weeks. In
order to conserve space we will only report the results of job finding probability for the
number of workers unemployed for less than 15 weeks.
The use of job finding probability as a proxy for real marginal cost is a novel aspect
of this chapter. Previous works on job finding probability such as: Hall (2005), Shimer (2005,
2007), Elsby, Michaels and Solon (2007) and Fujita and Ramey (2007) do not take into
account the connection between specialization of labour as a source of labour market friction
and job finding probability. Cao (2008, pp. 30-41) presents a search and matching model due
to Romer (2001) which is re-interpreted with an emphasis on the role of asymmetric
83
knowledge and the sticky nature of knowledge in the labour market so that the main matching
frictions in the labour market are due to heterogeneous knowledge between unemployed
workers and available jobs. The model proposes that job finding probability should captures
the extent of specialization of labour, informational imperfections about the timing of job
creation in different locations and the slow mobility of the production factors, which lead to
mismatch problems in the labour market, potentially helping us to explain involuntary
unemployment
4.4 Proxies for Inflation Expectations
An important issue in the empirical literature on the NKPC is what should be used as
proxy for inflation expectations because inflation expectations is an unobservable variable,
the choice of data as proxy for inflation expectations has important implications for various
methods of estimation and possibly the validity of the results.
A popular way of dealing with this problem is by using the actual value of inflation
expectations as a proxy for inflation expectations. However, the actual rate of inflation is
correlated with the error term; as a result, instrumental variables are use as proxy for actual
inflation. Suppose that the information used by price setters to forecast inflation 1 |t t t
E � .
As inflation expectations are unobservable, we need to generate econometric forecasts of
inflation expectations by using instrumental variables. Let 1 |t t tE � denote an econometric
forecast that uses some variables, t� to predict next period’s inflation rate 1t
, where t�a
subset of the information available to price setters. To generate our econometric forecast of
inflation expectations we regress actual inflation on our sets of instrumental variables t� .
1 1t t tb� (4.10)
Our forecast is simply the fitted values
1ˆ|t t t tE � b� (4.11)
By construction it is uncorrelated with the error term 1t̂ . According to the law of
iterated expectations, our econometric predictions of price-setters’ inflation expectations are
simply our forecasts.
84
1 1| | |t t t t t t t
E E � � E � (4.12)
Generalized Method of Moments (GMM) is an instrumental variables technique,
which can be used to estimate the Phillips curve (Nason and Smith, 2008).
4.5 Data and Estimation Strategy
Table 4.3 presents the definitions and sources of the data used in this chapter; all
series are quarterly data for the United States and are expressed in log unless stated
otherwise. We use core CPI as our measure of inflation because it is less volatile than other
measures of inflation, since it excludes food and energy. The price of oil is an important
determinant of inflation since oil is needed in the production process as well as in delivering
goods and services, but the price of oil is often determined by external factors such as war. If
we were to use other measures of inflation5 such as the Consumer Price Index (CPI) we may
need to include the price of oil as an explanatory variable as Roberts (1995) did, which would
complicates our attempt to estimate the Phillips curve.
Table 4. 3 Definitions and Sources of Data
Variable Definition Source
t t is measured as4
ln t
t
p
p using core CPI. Core CPI - Consumer
Price Index (All Items Less Food and Energy), Index 1982-1984=100.
Bureau of Labor Statistics (BLS).
dlw Wage Inflation, measured as the log- difference in nonfarm compensation per hour (Nonfarm Business Sector Real Hourly Compensation, Index 1992=100).
Bureau of Labor Statistics (BLS).
j Job Finding Probability. Constructed from the number of unemployed workers, the number of short term (less than 15 weeks) unemployed workers and the number of unemployed workers next month.
Bureau of Labor Statistics (BLS).
y Output Gap (Nonfarm Business Sector Output, Index 2005=100), using the Hodrick-Prescott filter with a smoothing parameter of 1600.
Bureau of Labor Statistics (BLS).
s The Log of Labour’s Share of Income (Nonfarm Business Sector, Index 1992=100).
Bureau of Labor Statistics (BLS).
5 In their influential paper, Gali and Gertler (1999) use the GDP deflator in their analysis.
85
dlppi Commodity Price Inflation. Measured as4
ln t
t
ppi
ppi using
Producer Price Index: Finished goods, Index 1982=100.
research.stlouisfed.org/fred2/categories/31.
sp Long-Short Interest Rate Spread. The Difference Between 10-Year Treasury Constant Maturity Rate and 3-Month Treasury Bill.
Federal Reserve Board (FRB).
Our estimation strategy is simple, we will estimate various specifications of the
Phillips curve and compare the empirical results using the output gap, labour’s share of
income and job finding probability as proxies for real marginal cost and also examine the
relative importance of forward-looking and backward inflation expectations. In particular, we
will estimate the reduced form of the hybrid Phillips curve and use the same instruments as
Gali and Gertler (1999) and Gali, Gertler and Lopez-Salido (2001, 2005), which will allows
us to directly compare our results with their results. We will use GMM to estimate the new
Keynesian Phillips curve and the hybrid new Keynesian Phillips curve.
4.6 Empirical Comparisons
First we estimate the old Keynesian Phillips curve using Ordinary Least Square
(OLS). We will use the results of the old Keynesian Phillips curve, with adaptive
expectations as our benchmark, since rational expectations predicts that modelling the
Phillips curve with rational expectations should fit the data better than modelling the Phillips
curve with adaptive expectations. Rational expectations implies that inflation expectations are
rational, in the sense that they efficiently incorporate all information available at time the
expectations are taken, and not just the past information as implied by adaptive expectations.
The empirical results in this chapter were estimated using Eviews; we used a HAC (Newey
West) weighting matrix, with automatic lags selection based on Schwarz information
criterion. The numbers of lags are presented in the proxy for real marginal cost column.
86
Table 4.4 OLS Estimates of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real Marginal Cost Constant b
Job Finding Probability (1 lag)
-0.015781 0.003178
-4.965459 0.000000
0.024167 0.004485 5.387857
0.0000
0.960334 0.014313 67.09330
0.0000
Output Gap (1 lag)
0.000727 0.000666 1.092342
0.276000
0.001606 0.000309 5.204447
0.000000
0.983034 0.014106 69.68890
0.000000
Labour’s Share of Income ( 1 lag)
-0.148958 0.069784
-2.134567 0.034100
0.032696 0.015218 2.148541 0.032900
0.958852 0.016980 56.46937 0.000000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third
row. Statistical probabilities are shown in the fourth row.
The coefficients of the three proxies of real marginal cost are all statistically
significant at 5% level.
The following estimations below were estimated using Generalized Method of
Moments (GMM). The instrument set t�consists of four lags of inflation, labour income
share, long-short interest rate spread, output gap, wage inflation, and commodity price
inflation. This instrument set is the same as the instrument set used in Gali and Gertler
(1999).
Table 4.5 GMM Estimations of the New Keynesian Phillips Curve
Equation estimated 1t t � t tmc E
Proxy for Real
Marginal Cost
Constant �
Job Finding Probability (2 lags)
0.015362 0.005583 2.751668 0.006500
-0.022438 0.007798
-2.877212 0.004500
1.021599 0.016934 60.32975 0.000000
Output Gap -1.35E-05 -0.000846 1.015788
87
The coefficients of the three proxies for real marginal cost have the wrong signs. The
coefficients of the forward inflation expectations are all statistically significant at 1% level
for the three proxies of real marginal cost.
Table 4.6 GMM Estimations of the Hybrid New Keynesian Phillips Curve
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
�
Job Finding Probability (4 lags)
0.000320 0.000887 0.360837
0.718600
-0.000814 0.001316
-0.618251
0.537200
0.505190 0.015124 33.40395
0.000000
0.502469 0.016508 30.43848
0.000000
Output Gap (4 lags)
-0.000307 7.70E-05
-3.992571 0.000100
-0.000230 0.000108
-2.123102 0.035100
0.463124 0.023645 19.58638 0.000000
0.546278 0.024747 22.07448 0.000000
Labour’s Share of Income (4 lags)
0.019587 0.007891 2.482128
0.013900
-0.004325 0.001728
-2.502913
0.013200
0.503032 0.011162 45.06467
0.000000
0.506640 0.011310 44.79621
0.000000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
The coefficients of the three proxies for real marginal cost have the wrong signs. The
results also indicate that the coefficients of forward-looking and backward-looking inflation
expectations are about the same in magnitude. The results of the new Keynesian Phillips
curve (Table 4.5) and the results of the hybrid new Keynesian Phillips curve above do not
(4 lags)
0.000458 -0.029455 0.976500
0.000398 -2.124386 0.034900
0.010177 99.81653 0.000000
Labour’s Share of Income ( 3 lags)
0.041830 0.042288 0.989172 0.323800
-0.009185 0.009252
-0.992736 0.322100
1.018013 0.013120 77.59343 0.000000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
88
support the notion that labour’s share of income is a better proxy for real marginal cost than
the output gap.
4.7 Robustness Analysis
We consider two robustness exercises. The first robustness exercise examines sub-
sample stability, our sub-samples are the periods from 1961q1 to 1984q4 and the period from
1985q1 to 2010q1, we also wanted to examine the relative importance of forward-looking
and backward-looking inflation expectations during different sub-sample periods. The second
robustness exercise examines an alternative instrument set which includes four lags of
inflation, and two lags of the real marginal cost (labour’s share of income), the output gap,
and wage inflation. This instrument set is the same instrument set used by Gali, Gertler and
Lopez-Salido (2001, p.1250).
��b��ample �tabilit�
Table 4.7 OLS Estimations of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real Marginal Cost Constant b
Job Finding Probability (1 lag)
-0.032716 0.012124 2.698494 0.008300
0.045316 0.015504 2.922914 0.004400
0.977941 0.029517 33.13118 0.000000
Output Gap
(0 lag)
0.001470
0.001110 1.325080 0.188400
0.003650
0.000682 5.354550 0.000000
0.983038
0.027521 35.71904 0.000000
Labour’s Share of Income (1 lag)
-0.250777 0.452849
-0.553776 0.581100
0.054832 0.098119 0.558831 0.577600
0.952926 0.952926 26.53684 0.000000
Note: The above equation was estimated over the 1961q1 to 1984q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
89
The coefficients of job finding probability and the output gap are statistically
significant at 1%. The coefficients of backward inflation expectations are all statistically
significant at 1% level for the three proxies of real marginal cost.
Table 4.8 OLS Estimations of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real Marginal Cost
Constant b
Job Finding Probability (0 lag)
-0.006209 0.001880
-3.302680
0.001300
0.011305 0.002955 3.825133
0.000200
0.936905 0.027062 34.62037
0.000000
Output Gap (0 lag)
0.000400 0.000726 0.550186 0.583400
0.000512 0.000155 3.296777 0.001400
0.975051 0.025195 38.70032 0.000000
Labour’s Share of Income (1 lag)
-0.067951 0.036291
-1.872382
0.064100
0.015004 0.008072 1.858807
0.066100
0.957827 0.037693 25.41106
0.000000
Note: The above equation was estimated over the 1985q1 to 2010q1 period using quarterly data. Standard errors
are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West
procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third
row. Statistical probabilities are shown in the fourth row.
The coefficients of job finding probability and the output gap are statistically
significant at 1%. The coefficients of backward inflation expectations are all statistically
significant at 1% level for the three proxies of real marginal cost.
Table 4.9 GMM Estimations of the New Keynesian Phillips Curve
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost Constant �
Job Finding Probability
(0 lag)
0.046623
0.012950 3.600203 0.000500
-0.060680
0.016323 -3.717485 0.000400
0.986891
0.022455 43.95051 0.000000
Output Gap (0 lag)
-0.001518 0.000805
-0.003944 0.000524
1.021562 0.014999
90
-1.885489 0.062600
-7.521233 0.000000
68.11082 0.000000
Labour’s Share of Income (2 lags)
-0.003542 0.123471
-0.028688 0.977200
0.000633 0.026788 0.023643 0.981200
0.996002 0.019147 52.01755 0.000000
Note: The above equation was estimated over the 1961q1 to 1984q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
The coefficients of forward inflation expectations are all statistically significant at 1%
level for the three proxies of real marginal cost. Compare to the results of the full sample
(Table 4.5), the sign of the coefficient of labour’s share of income is now positive, but not
statistically significant.
Table 4.10 GMM Estimations of the New Keynesian Phillips Curve
Equation estimated 1t t � t t
mc E
Proxy for Real Marginal Cost
Constant �
Job Finding Probability (0 lag)
0.006231 0.001759 3.542796 0.000600
-0.009304 0.002946
-3.157926 0.002100
1.013673 0.025182 40.25423 0.000000
Output Gap
(0 lag)
-4.30E-05
0.000576 -0.074563 0.940700
-0.000685
0.000185 -3.707331 0.000300
1.009096
0.019547 51.62322 0.000000
Labour’s Share of Income (0 lag)
0.050213 0.031874 1.575334 0.118400
-0.010929 0.007040
-1.552461 0.123800
1.001967 0.025855 38.75351 0.000000
Note: The above equation was estimated over the 1985q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
The coefficients of forward inflation expectations are all statistically significant at 1%
level for the three proxies of real marginal cost. The coefficients of the three proxies for real
marginal cost have the wrong signs.
91
Table 4.11 GMM Estimations of the Hybrid New Keynesian Phillips Curve
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b �
Job Finding Probability (0 lag)
-0.004695 0.005252
-0.893996 0.373800
0.005376 0.006682 0.804606 0.423200
0.529394 0.035538 14.89660 0.000000
0.480562 0.035291 13.61731 0.000000
Output Gap (0 lag)
-0.000624 0.000459
-1.358735 0.177700
-0.000432 0.000506
-0.855054 0.394800
0.473848 0.054635
8.672891 0.000000
0.537466 0.058808
9.139401 0.000000
Labour’s Share of Income (0 lag)
-0.002027 0.069795
-0.029039 0.976900
0.000339 0.015115 0.022427 0.982200
0.509036 0.027071 18.80369 0.000000
0.498271 0.027353 18.21653 0.000000
Note: The above equation was estimated over the 1961q1 to 1984q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the
third row. Statistical probabilities are shown in the fourth row.
The coefficient of the output gap has the wrong sign. The coefficients of forward-
looking and backward-looking inflation expectations are about the same in magnitude and are
all statistically significant at 1% level for the three proxies of real marginal cost.
Table 4.12 GMM Estimations of the Hybrid New Keynesian Phillips Curve
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b �
Job Finding Probability (0 lag)
-0.001327 0.001642
-0.808198 0.421000
0.002024 0.002768 0.731028 0.466500
0.617113 0.070008 8.814906 0.000000
0.377764 0.081663 4.625908 0.000000
Output Gap
(0 lag)
-0.000200
0.000266 -0.751322 0.454300
1.59E-05
0.000106 0.149999 0.881100
0.592147
0.073301 8.078313 0.000000
0.413408
0.078263 5.282319 0.000000
Labour’s Share of Income (0 lag)
0.000103 0.022207 0.004629
-3.31E-05 0.004884
-0.006772
0.584653 0.047893 12.20744
0.415958 0.053516 7.772617
92
0.996300 0.994600
0.000000 0.000000
Note: The above equation was estimated over the 1985q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
The coefficient of labour’s share of income has the wrong sign. The coefficients of
backward-looking dominate forward-looking inflation expectations and these coefficients are
all statistically significant at 1% level for the three proxies of real marginal cost.
4.8 An Alternative Instrument Set
Next we consider an alternative instrument set, which includes four lags of inflation,
and two lags of labour’s share of income, the output gap, and wage inflation. This instrument
set is the same instrument set used by Gali, Gertler and Lopez-Salido (2001, p.1250).
Table 4.13GMM Estimations of the New Keynesian Phillips Curve
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost
Constant �
Job Finding Probability (2 lags)
0.009993 0.006261 1.596089 0.112100
-0.014983 0.008902
-1.683073 0.094000
1.014705 0.020232 50.15369 0.000000
Output Gap (2 lags)
0.000307 0.000581 0.527287 0.598600
-0.001803 0.000585
-3.081177 0.002400
0.994676 0.013767 72.25140 0.000000
Labour’s Share of Income (4 lags)
0.033188 0.041725 0.795404 0.427400
-0.007336 0.009133
-0.803214 0.422900
1.023358 0.012638 80.97683 0.000000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
93
The coefficients of forward inflation expectations are all statistically significant at 1%
level for the three proxies of real marginal cost. The coefficients of the three proxies for real
marginal cost have the wrong signs.
Table 4.14 GMM Estimations of the Hybrid New Keynesian Phillips Curve
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b �
Job Finding Probability (4 lags)
0.000374 0.001030 0.363535 0.716600
-0.000916 0.001510
-0.606353 0.545000
0.500503 0.014664 34.13093 0.000000
0.507321 0.015891 31.92607 0.000000
Output Gap (4 lags)
-0.000387 0.000112
-3.467746 0.000700
-0.000507 0.000173
-2.933563 0.003800
0.425374 0.027847
15.27563 0.000000
0.587061 0.029472
19.91934 0.0000
Labour’s Share of Income (4 lags)
0.023085 0.012469 1.851375 0.065700
-0.005089 0.002728
-1.865774 0.063600
0.500347 0.012372 40.44285 0.000000
0.510151 0.012526 40.72825 0.000000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-
West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
The coefficients of the three proxies for real marginal cost have the wrong signs. The
results also indicate that the coefficients of forward-looking and backward-looking inflation
expectations are about the same in magnitude. The results of the new Keynesian Phillips
curve (Table 4.13) and the results of the hybrid new Keynesian Phillips curve above do not
support the notion that labour’s share of income is a better proxy for real marginal cost than
the output gap.
94
4.9 Endogeneity of Real Marginal Cost
One possible explanation for the change in the sign of real marginal cost variable in
the new Keynesian Phillips curve – relative to the results for the old Keynesian Phillips curve
estimated by OLS – is that the real marginal cost variable is treated as endogenous and is
instrumented along with future inflation rather than the real marginal cost variable being
treated as an exogenous variable as in the old Keynesian Phillips curve6. We will now
examine whether treating the real marginal cost as an endogenous variable has a significant
impact on the results. We will estimate the new Keynesian Phillips curve and the hybrid new
Keynesian Phillips curve with and without the three proxies for real marginal cost in the
instrument set t� .
The following new Keynesian Phillips curves below were estimated using
Generalized Method of Moments (GMM). The instrument set t�consists of four lags of
inflation, labour income share, output gap, job finding probability, long-short interest rate
spread, wage inflation, and commodity price inflation.
6I thank an anonymous examiner for raising this issue.
Table 4.15 GMM Estimations of the New Keynesian Phillips Curve
Equation estimated 1t t � t tmc E c
Proxy for Real
Marginal Cost
Constant �
Job Finding Probability (2 lags)
0.011702 0.003948 2.963950
0.0034
-0.017068 0.005546
-3.077624 0.0024
1.015422 0.016166 62.81202
0.0000
Output Gap (2 lags)
0.000473 0.000550 0.859928
0.3909
-0.002090 0.000577
-3.620822
0.0004
0.989877 0.012793 77.37471
0.0000
Labour’s Share of Income (2 lags)
0.055272 0.043535 1.269597
0.2058
-0.012052 0.009498
-1.268995 0.2060
1.005815 0.017031 59.05721
0.0000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the
third row. Statistical probabilities are shown in the fourth row.
95
The following estimations below were estimated using Generalized Method of
Moments (GMM). The instrument set t�consists of four lags of inflation, long-short interest
rate spread, wage inflation, and commodity price inflation.
The coefficients of the three proxies for real marginal cost have the wrong signs for
estimations with and without labour income share, output gap and job finding probability in
the instrument set t�.
The following hybrid new Keynesian Phillips curves below were estimated using
Generalized Method of Moments (GMM). The instrument set t�consists of four lags of
inflation, labour income share, output gap, job finding probability, long-short interest rate
spread, wage inflation, and commodity price inflation.
Table 4.16 GMM Estimations of the New Keynesian Phillips Curve
Equation estimated 1t t � t tmc E c
Proxy for Real Marginal Cost
Constant �
Job Finding Probability
(4 lags)
0.013171 0.005646
2.332921 0.0207
-0.020102 0.007869
-2.554633 0.0114
1.048545 0.015941
65.77513 0.0000
Output Gap (4 lags)
-0.000354 0.000610
-0.581278 0.5617
-0.002134 0.000789
-2.704799 0.0075
1.019004 0.009443 107.9084
0.0000
Labour’s Share of Income (5 lags)
0.245741 0.142306
1.726851 0.0858
-0.053713 0.031053
-1.729710 0.0853
1.047541 0.018617
56.26673 0.0000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
96
Table 4.17 GMM Estimations of the Hybrid New Keynesian Phillips Curve
Equation estimated 1 1t t b t � t tmc E c
Proxy for Real Marginal Cost
Constant b �
Job Finding Probability (4 lags)
0.001102 0.001160 0.949570
0.3435
-0.001933 0.001755
-1.101021 0.2723
0.476079 0.031553 15.08816
0.0000
0.530072 0.032423 16.34876
0.0000
Output Gap (0 lag)
-0.000223 0.000209
-1.064469 0.2885
-0.000128 0.000152
-0.837090 0.4036
0.477196 0.035147 13.57733
0.0000
0.527590 0.036255 14.55231
0.0000
Labour’s Share of Income (0 lag)
0.029483 0.018227 1.617574
0.1074
-0.006479 0.003992
-1.623002 0.1063
0.492714 0.026257 18.76486
0.0000
0.514641 0.025428 20.23899
0.0000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
The following estimations below were estimated using Generalized Method of
Moments (GMM). The instrument set t�consists of four lags of inflation, long-short interest
rate spread, wage inflation, and commodity price inflation.
Table 4.18 GMM Estimations of the Hybrid New Keynesian Phillips Curve
Equation estimated 1 1t t b t � t tmc E c
Proxy for Real Marginal Cost
Constant b
�
Job Finding Probability (4 lags)
0.002133 0.001753
1.216712 0.2252
-0.003478 0.002559
-1.359059 0.1758
0.477907 0.022807
20.95413 0.0000
0.533038 0.025483
20.91758 0.0000
Output Gap (4 lags)
-0.000379 0.000152
-2.495849 0.0134
-0.000410 0.000408
-1.003705 0.3168
0.441995 0.052554 8.410279
0.0000
0.568490 0.055870 10.17520
0.0000
Labour’s Share of Income (4 lags)
0.103708 0.048855
2.122751 0.0351
-0.022720 0.010665
-2.130326 0.0344
0.521114 0.022023
23.66211 0.0000
0.501351 0.024612
20.36992 0.0000
Note: The above equation was estimated over the 1961q1 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. Statistical probabilities are shown in the fourth row.
97
Once again, the coefficients of the three proxies for real marginal cost have the wrong
signs for estimations with and without labour income share, output gap and job finding
probability in the instrument set t� . This brief section suggests that whether we include or
exclude labour income share, output gap and job finding probability from the instrument set
t� , the signs of the real marginal costs variable remain the same.
4.10 Conclusion
Our empirical results are not supportive of Gali and Gertler’s (1999) empirical
findings that labour’s share of income is a better proxy for real marginal cost than the output
gap. Also, our results are not supportive Gali and Gertler’s (1999, p.195) empirical findings
that “[b]ackward-looking price setting, while statistically significant, is not quantitatively
important”. In general, our results indicate that forward-looking and backward-looking
inflation expectations are about the same in magnitude.
Our first robustness exercise examines sub-sample stability of the periods from
1961q1 to 1984q4 and the period from 1985q1 to 2010q1. The results of first robustness
exercise suggest that the second sub-sample period fits the data slightly better overall, this is
as expected since the US economy experienced higher inflation and higher economic
volatility (due to the OPEC oil crisis of 1970’s) during the first sub-sample period, the lower
economic volatility of the second sub-sample period makes forecasting inflation easier
(despite the recent financial crisis), at the same time, it makes lagged inflation more reliable,
since the rates of inflation do not change much quarter to quarter (see table 4.7 and Table
4.8), this is also reflected by our empirical results showing that backward-looking dominate
forward-looking inflation expectations when the hybrid Phillips curve is estimated (see table
4.11and Table 4.12).Our first robustness exercise also indicate that the that the slope of the
reduced form Phillips curve for the United States has flattened over the last 25 years, this is
reflected by the lower values of the coefficients of real marginal cost of the second sub-
sample period relative to the first sub-sample period. We will examine this issue in more
details later. The results of our second robustness exercise are consistent with our initial
results.
Overall our results suggest the old Keynesian Phillips curve with adaptive
expectations fits the data better than the new Keynesian Phillips curve with rational
98
expectations, this result is consistent with some well-known previous work, such as Fuhrer
and Moore (1995) and Mankiw (2001). Rudd and Whelan (2006, p.319) conclude that
“lagged inflation plays an important role in empirical inflation regressions poses a major
challenge to the rational-expectations sticky-price models that underpin the new Keynesian
Phillips curve”. Similarly Mankiw (2001, p.59) made the following concluding remarks in his
survey article, which also reflect our sentiment regarding this matter.
“There is a simple way to reconcile the new Keynesian Phillips curve with the data:
adaptive expectations. In my analysis throughout this paper, I have used the now
standard assumption that expectations are formed rationally. If, instead, the inflation
rate expected in period t for period t + 1 always equals inflation experienced at time t
- 1, then the forward-looking model reduces to the backward-looking model, which
works just fine. Because of this, some people working in this area are now
questioning the assumption of rational expectations. (See, e.g., Roberts, 1997).
Assuming adaptive expectations, however, is far from a satisfying resolution to the
puzzle. The rational-expectations hypothesis has much appeal, for reasons that were
widely discussed in the 1970s. Moreover, the public is not ignorant about monetary
shocks. Central bank actions are widely reported in the news, and they are dissected
by commentators in agonising detail. In light of all this media coverage of monetary
policy, it is odd to assert that expectations about inflation are formed without
incorporating this news. Yet the assumption of adaptive expectations is, in essence,
what the data are crying out for”.
Rudd and Whelan (2007, p.163) note that the hybrid new Keynesian Phillips curve is
considered by many as a sensible compromise between the pure rational expectations new
Keynesian Phillips curve with micro-foundations, but does not fit the data well and the old
Keynesian Phillips curve, which lack strong micro-foundations but fits the data better. Even
if we accept the hybrid new Keynesian Phillips curve as having the right specifications for
the Phillips curve relationship we still need to consider two things: First, why are some price
setters backward-looking and why are some price setters forward looking? What determine
their price setting behaviours? Second, are the fraction of backward-looking firms and the
fraction forward-looking firms constant over time?
99
We have introduced the concept of job finding probability which provides a direct
link between frictions in the labour market and the Phillips curve relationship and used job
finding probability as a proxy for real marginal cost to estimate of various specifications of
the Phillips curve. Our results suggest that job finding probability should be considered as an
alternative proxy for real marginal cost in empirical work on the Phillips curve.
Unfortunately, we have not been able to show conclusively that job finding probability is a
better proxy for real marginal cost than the output gap and labour’s share of income in this
chapter. We will re-examine this issue in the next in the next chapter using survey measures
of inflation expectations as proxy for inflation expectations.
100
CHAPTER 5
Estimations of the New Keynesian Phillips Curve Using Survey Measures of Inflation
Expectations
5.1 Introduction
The purpose of this chapter is to estimate various specifications of the Phillips curve
using survey measures of inflation expectations as proxy for inflation expectations and to
examine whether job finding probability (JFP), the output gap or labour’s share of income is
a better proxy for real marginal cost. We found that the output gap and job finding probability
performed equally well when the old Keynesian Phillips curve is estimated. Labour’s share of
income is the best proxy for real marginal cost when the new Keynesian Phillips curve is
estimated. Job finding probability is marginally a better proxy for real marginal cost than the
output gap and labour’s share of income when the hybrid new Keynesian Phillips curve is
estimated. We also found that backward-looking dominate forward-looking inflation
expectations, independent of which measures of real marginal cost are used and that all of the
survey measures of inflation expectations are biased and inefficient. This chapter is structured
as follows: The first section examines the rationality various survey measures of inflation
expectations. The second section compares the empirical appropriateness of job finding
probability (JFP), the output gap and labour’s share of income as proxies for real marginal
cost. The third section considers two robustness exercises: The first robustness exercise
examines sub-sample stability. The second robustness exercise uses the implicit price deflator
(nonfarm business) instead of core inflation to examine if our initial results are robust. The
fourth section concludes.
5.2 Are Survey Measures of Inflation Expectations Rational?
Since the advent of rational expectations, researchers in monetary policy have
understood that the key to understanding how monetary policy works is to understand how
economic agents form inflation expectations. Furthermore, "[t]here is a growing consensus,
based on both historical analysis and econometric evidence, that monetary policy has strong
effects on real output. There is not, however any consensus about how to explain this fact"
(Ball and Croushore, 2003, p.473).
101
A useful way of testing the rational expectations hypothesis is by directly testing
whether inflation forecasts are rational. Rational expectations predicts that inflation forecasts
should be unbiased, that is, the forecast errors should be zero over time (i.e. no systemic
errors) and inflation forecasts should be efficient, that is, forecasters should use all relevant
information at the time in forming their expectations. In his famous seminal paper on rational
expectations, Muth (1961, p. 316) notes two stylized facts about survey data on expectations.
“Averages of expectations in an industry are more accurate than naive [adaptive]
models and as accurate as elaborate equation system, although there are considerable
cross-sectional differences in opinion.
Reported expectations generally underestimated the extent of changes that actually
take place.”
Muth (1961, p.316) suggested that since expectations are informed predictions of
future events, they “are essentially the same as the predictions of the relevant economic
theory”. For Muth, the assumption that expectations were formed rationally was a natural
extension of the assumptions that firms rationally maximize profits and consumers rationally
maximize their utilities. Rational expectations implies that expectations are rational, in the
sense that they efficiently incorporate all information available at time the expectations are
taken, and not just the past information as implied by adaptive expectations, a popular way of
modelling expectations at the time. Furthermore, Muth thought that rational expectations was
more appealing than alternative theories of how economic agents form expectations was more
realistic, can be applied to all dynamics problems, can be tested and be compared to
alternative theories (Muth, 1961, p.330):
“From a purely theoretical standpoint, there are good reasons for assuming rationality.
First, it is a principle applicable to all dynamic problems (if true). Expectations in
different markets and systems would not have to be treated in completely different
ways. Second, if expectations were not moderately rational there would be
opportunities for economists to make profits in commodity speculation, running a
firm, or selling the information to present owners. Third, rationality is an assumption
that can be modified. Systematic biases, incomplete or incorrect information, poor
memory, etc., can be examined with analytical methods based on rationality. The only
102
real test, however, is whether theories involving rationality explain observed
phenomena any better than alternative theories”.
Muth (1961, p.333) also noted that regression analysis can be used to test the
assumption of rational expectations. “The rational expectation hypothesis states that, in the
aggregate, the expected price is an unbiased predictor of the actual price”.
There is a relatively large literature on survey measures of inflation expectations; a
common conclusion from this literature is that survey measures of inflation expectations are
more accurate than adaptive expectations models, which confirms one of Muth’s (1961)
empirical findings mentioned above. However, most papers that have examined the
rationality of survey measures of inflation expectations have also concluded that inflation
expectations are not perfectly rational, in particular, they seems to indicate survey
participants do not use all relevant information available to them when forecasting inflation
(Roberts, 1997 p. 177). This suggests that we should consider bounded rational expectations
instead of adaptive expectations or pure rational expectations in modelling inflation
expectations.
The use of survey measures of inflation expectations provide data on an otherwise
unobservable variable and also to allow economic researchers to avoid making “strong”
assumptions about human rationality, by letting the data speak instead. The use of survey
measures of inflation expectations have their limitations, two of the main potential problems
are: survey participants may not be representative of the actual population and as there is no
monetary incentive for the survey participants to invest their time and efforts in formulating
their best expectations, the survey results may be poor proxies for the actual expectations of
the population (Roberts, 1995, p. 980). However, the problems with using econometric
forecasts of inflation as a proxy for inflation expectations is that we are implicitly assuming
inflation expectations are rational. If inflation expectations are not fully rational, then using
econometric forecasts of inflation as a proxy for inflation expectations may be less precise
than using survey measures of inflation expectations. Ang, Bekaert and Wei (2007, p. 1163)
examine the predictive power of four alternative methods of forecasting U.S. inflation out-of-
sample: time-series ARIMA models; regressions using real activity measures motivated from
the Phillips curve; term structure models that include linear, non-linear, and arbitrage-free
103
specifications; and survey measures of inflation expectations. They found that survey
measures of inflation expectations are more accurate than other forecasting methods.
5.3 Data and Estimation Strategy
The definitions and sources of the data used in this chapter are presented in the data
appendix at the end of this chapter; all series are quarterly data for the United States. We use
core CPI as our measure of inflation because it is less volatile than other measures of
inflation, since it excludes food and energy. We will examine three well-known surveys of
inflation expectations: the Survey of Professional Forecasters (SPF), which collects inflation
expectations from economists who forecast for a living, the Michigan Survey, which collects
forecasts from consumers and the “Greenbook” forecasts, which are produced by the research
staff at the Board of Governors before each meeting of the Federal Open Market Committee
(FOMC).
�he ��r�e� o� Pro�essio�al �orecasters ��P��
The Survey of Professional Forecasters (SPF) came into existence in the fourth
quarter of 1968 under the management of the American Statistical Association and the
National Bureau of Economic Research, it was known as the ASA/NBER Economic Outlook
Survey. In the first survey participants were asked to forecast 10 variables for the next five
quarters. Among the variables to be forecast each quarter was the rate of change of the GNP
deflator for the current quarter and the next four quarters. Consumer Price Index inflation
forecast were not initiated until the third quarters of 1981. The forecasters in the survey come
predominantly from the business sector, where they make economic forecasts for a living. In
addition to submitting forecasts of inflation, the participants are also asked to assign
probabilities to various inflationary scenarios. This provides researchers an alternative
measure of inflation uncertainty other than the variance of inflation expectations. The
Philadelphia Federal Reserve is currently in charge of this survey, the data is publicly
available at the Philadelphia Federal Reserve’s website (www.phil.frb.org/research-and-
data/real-time-center/survey-of-professional-forecasters/). See Thomas (1999, p.129-130) and
Croushore (1997) for more details. The SPF data provide quarterly forecasts of inflation
expectations for the next four quarters, which we can use to test our model, we will use the
median values instead of the mean values because outliers can sometimes distort the mean
values for estimating various specifications of the Phillips curve. However, for testing the
104
rationality of survey measures of inflation expectations we will use the mean values instead
of the median values because it allows us to make direct comparison with the mean values of
the Michigan survey.
�he ��stit�te o� �ocial �esearch ��ichiga�� ��r�e� o� �o�seholds
The Survey Research Center at the University of Michigan started collecting forecasts
of numerous macroeconomic variables, including the inflation rate over the next year in terms
of the “things you buy” via the telephone interview in 1948. The respondents are randomly
selected from a sample size of a minimum of 500 households. Prior to the second quarter of
1966, respondents were simply asked: “Do you think prices will go up in the next year, or go
down, or stay the same?” From the second quarter of 1966 through the third quarter of 1977,
respondents who indicated they expected prices to increase were asked to indicate a range in
which they expected prices to rise. After the third quarter of 1977, respondents were simply
asked to supply their expected rate of inflation. Another important change is the frequency of
the survey, before 1959, the Michigan Survey was conducted 2-3 times annually. From 1959
through the end of 1977, the survey was conducted quarterly. Since the beginning of 1978, it
has been conducted monthly. The historical series for the mean CPI inflation forecasts and its
variance are publicly available through the website of the Institute of Social Research’s
Survey of Consumer Attitudes at (www.sca.isr.umich.edu).
�he �ree�boo� �orecasts
The Federal Reserve forecasts are contained in the "Green Book" prepared by the staff
of the Board of Governors before each meeting of the Federal Open Market Committee
(FOMC).The data set includes the projections of real output growth and inflation. These
projections are made available to the public after a lag of five years. The historical series for
real output growth and inflation are publicly available through the website of the Philadelphia
Fed's (www.philadelphiafed.org/research-and-data/real-time-center/greenbook-data/) (See
Romer and Romer (2000, p. 431)).
Our estimation strategy is to estimate various specifications of the Phillips curve using survey
measures of inflation expectations as proxy for expected inflation and to compare the
empirical results of using the output gap, labour’s share of income and job finding probability
105
as proxy for real marginal cost. We will also examine the relative importance of forward-
looking and backward-looking inflation expectations.
5.4 Tests of Rationality of Survey Measures of Inflation Expectations
For inflation expectations to be rational they should exhibit two main predictions of
rational expectations. First, they should be unbiased, that is survey participants should
forecast inflation correctly on average. Second, inflation expectations should be efficient, that
is survey participants should use all relevant information available to them when forecasting
inflation. We have also included an adaptive model as a simple test of the rationality various
surveys. The adaptive forecast is simply the most recent 12-month rate of core CPI inflation
known to the agent at the time the forecast is made. The adaptive forecast is purely
backward-looking. A failure of survey respondents to outperform the adaptive forecasts
would suggest that they fail to effectively take into account the past rate of actual inflation in
their forecast future inflation.
We first report various forecasting evaluation statistics and briefly compare the
performances of various survey measures of inflation expectations. The summary statistics
include the mean absolute error (MAE), the root mean squared error (RMSE) and Theil
Inequality Coefficient (U). The forecast error for any period is defined as the forecast
inflation rate minus the actual inflation rate. Thus, a positive mean error indicates that agents,
on average, overestimate inflation. A negative mean error indicates a propensity to
underestimate inflation. The mean absolute error (MAE) is a measure of accuracy of
forecasts. The root mean square error (RMSE) is an alternative measure of accuracy. The
RMSE has the effect of magnifying the effect of large forecast errors, as opposed to the MAE
(Thomas, 1999, p.132). Theil Inequality Coefficient (U) provides a measure of how well a
time series of estimated values compares to a corresponding time series of observed values.
The Theil inequality coefficient always lies between zero and one, where zero indicates a
perfect fit. The MAE, the RMSE and Theil Inequality Coefficient (U) are given by:
1
1 �
tt
�AE e�
(5.1)
106
1/22
1
1 �
tt
���E e�
(5.2)
1
22
1/2 1/22 2
1 1
1
/ /
t t
� �
t tt t
� ��
�
� � � �
(5.3)
Table 5.1 Inflation Forecasts Evaluation Statistics for the Survey of Professional Forecasters (SPF),
Michigan, and the Greenbook Forecasts.
Survey Sample Period MAE RMSE U
Michigan 4t tE 1981Q3 2004Q4 0.005894 0.007655 0.097822
SPF 4t tE 1981Q3 2004Q4 0.004463 0.006044 0.086748
Greenbook 4t tE 1981Q3 2004Q4 0.004707 0.006571 0.083753
Adaptive 4t tE 1981Q3 2004Q4 0.007653 0.009892 0.128964
In terms of accuracy, if one uses the RMSE (or the MAE) as the criterion for evaluate
the surveys’ results, the rankings from best to worst are: SFP, Greenbook, Michigan and
Adaptive. If one uses Theil Inequality Coefficient (U), the rankings from best to worst are:
Greenbook, SFP, Michigan and Adaptive. All survey measures of inflation expectations are
more accurate than the adaptive expectations model, this result is consistent with Muth’s
(1961, p. 316) empirical finding and other previous research.
�ests �or the E�iste�ce o� As�mmetric ���ormatio�
Are economists better at forecasting inflation than the general public? To answer this
question, we run the following “horserace” regressions to test for the forecasting power of the
Michigan, the Survey of Professional Forecasters and the Greenbook forecasts using Romer
and Romer’s (2000) framework.
107
Table 5.2: Tests for the Existence of Asymmetric Information Between the Michigan, SPF and The Greenbook
Forecasts
, 4 1 2 , 4 3 , 4 4 , 4General Equation :t t t t t t t t
�� �P� �ich
Equation
1
2
3
4
2�
1
0.007789 0.002722
2.861425 0.005300
0.005888 0.001296 4.544154 0.000000
0.002202 0.001618 1.360916 0.177100
-5.14E-05 0.001308 -0.039271 0.968800
0.768795
2
0.002693 0.002746 0.980552 0.329500
0.007492 0.001244 6.022518
0.000000
0.000622 0.001439 0.432032
0.666800
0.713280
3
0.007722 0.002125
3.634131 0.000500
0.005882 0.001280 4.595538
0.000000
0.002168 0.001355 1.600341 0.113100
0.768790
4
0.000340 0.002488 0.136613 0.891600
0.006761 0.001031 6.554926 0.000000
0.003228 0.001163 2.775185 0.006700
0.856206
Notes: t is the actual inflation rate at time t. , 4t t�ich is the period-t mean of the Michigan survey measure of
household expectations for inflation over the next year. , 4t t�P� is the period-t mean of the Survey of
Professional Forecasters’ forecasts of the inflation rate over the next year. , 4t t
�� is the Greenbook forecast of
the inflation rate over the next year. All equations were estimated (OLS) over the 1981q3 to 2004q4 period.
Our results show that the Greenbook forecasts of inflation has more predictive power
than the SPF forecasts and the Michigan forecasts; this is consistent with Romer and Romer
(2000) empirical finding. Both the Greenbook forecasts and the SPF forecasts have more
predictive power than the Michigan forecasts, providing support for the hypothesis that
economists are better at forecasting inflation than the general public. Note that the first
regression’s results indicate that the Michigan forecasts contain no information that is not
also included in the Greenbook forecasts and the SPF forecasts; this is consistent with
Carroll’s (2003) empirical finding. The results also implies that Michigan forecasts and the
SPF forecasts are prima facie irrational since the information that forecasters of the
Greenbook forecasts possessed that allowed them to make superior forecasts were in
principle also available to households and forecasters of the SPF. The findings that the
108
Greenbook forecasts of inflation have more predictive power than the SPF forecasts and the
Michigan forecasts do not imply that the Greenbook forecasts are fully rational.
�ests �or ��biased�ess
The test for unbiasedness is usually conducted by running the following regression:
�
t t te (5.4)
where t is the actual inflation rate at time t, �
t is the inflation expectations from the survey
at time t and te is the error term. Inflation expectations are unbiased if =0 and = 1.Note
that inflation rates were converted to percentages.
Table 5.3 Tests for Unbiasedness of the Survey of Professional Forecasters (SPF), Michigan, and the Greenbook
forecasts.
Equation Estimated �
t t te
Survey Sample Period 2� 2
o�or�
SPF 1t tE 981Q3 2010Q1
-0.286400
0.146800 -1.950993 0.053600
1.103100
0.042800 25.793870 0.000000
0.855916 6.534639
(0.03810)
Greenbook 1t tE 1974Q2 2004Q4
0.435100 0.127700 3.406809 0.000900
1.055800 0.027000
39.129390 0.000000
0.926760
104.271400 ( 0.00000)
Michigan 4t tE 1981Q3 2010Q1
-0.886700
0.277200 -3.198671 0.001800
0.986400
0.061900 15.922160 0.000000
0.691691 125.953800
(0.00000)
SPF 4t tE 1981Q3 2010Q1
0.306300 0.164400 1.862752 0.065200
0.805300 0.044800
17.988780 0.000000
0.748033 65.224080 (0.00000)
Greenbook 4t tE 1974Q3 2004Q4
0.117100
0.205000 0.571358 0.568800
1.150800
0.046000 25.043340 0.000000
0.840519 64.676310
(0.00000)
Note: The above equations were estimated using Ordinary Least Square (OLS). Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row. Chi-squared statistics of null
hypothesis that 0 1a�d and its p-values (in parentheses) are shown in the last column.
109
The results for each forecast are presented in the table above, along with the
coefficient of determination ( 2� ), and the chi-square statistics associated with the null
hypothesis of unbiasedness ( 0 1a�d ). The chi-square statistic indicates that
unbiasedness can be rejected at 5 % level for all of the forecasts.
�ests �or E��icie�c�
The tests for efficiency determine whether forecasters use all of the information
available to them when making inflation forecasts, the tests for efficiency are usually
conducted by regressing the forecast error ( te ) on the variables in the information set ( t�),
either individually or jointly.
t t te � � (5.5)
where te is the forecast error, t�is the information set and t�is the disturbance term. Inflation
expectations are said to be efficient if the forecast error is uncorrelated with the forecast error,
implying that the coefficient should equal zero.
A distinction is commonly made between weak-form and strong-form efficiency.
Weak-form efficiency implies that forecasters have adequately considered all the information
contained in past rates of inflation. Strong-form efficiency implies that forecasters use the
most up-to-date information when making inflation forecasts (Thomas, 1999, p.136). We will
conduct a series of weak-form efficiency tests; our information set consists of one lag of each
of the following variables: inflation ( 1t ), unemployment ( 1t� ), wage inflation ( 1t��� ),
the output gap ( 1t�AP ), monetary aggregate ( 12t� ), and the federal funds rate ( 1t�� ),
these variables were chosen because we thought that they would be useful in forecasting
inflation. Below are the results for the tests of efficiency for the Survey of Professional
Forecasters (SPF), Michigan, and the Greenbook forecasts.
110
Table 5.4 Tests of Efficiency of the Survey of Professional Forecasters (SPF) Forecasts 1t tE
Equation Estimated t t te � �
Independent
Variable t-statistic P-value
t-statistic
P-value 2�
1t -0.004085 -3.639949 0.0004 0.122446 4.040799 0.0001 0.127237
1t� -0.003507 -1.675827 0.0966 0.000572 1.728953 0.0866 0.025996
1t��� -0.001146 -1.891848 0.0611 0.104011 3.319114 0.0012 0.089553
1t�AP -4.04E-05 -0.077857 0.9381 -0.000527 -1.336743 0.1840 0.015704
12t� -0.001486 -0.981666 0.3284 0.000452 1.044991 0.2983 0.009656
1t�� -0.001505 -1.457455 0.1478 0.000270 1.681775 0.0954 0.024631
Note: The above equations were estimated using Ordinary Least Square (OLS) over the 1981q3- 2010q1 period.
Table 5.5 Tests of Efficiency of the Greenbook Forecasts 1t tE
Equation Estimated t t te � �
Independent
Variable t-statistic P-value
t-statistic
P-value 2�
1t -0.002953 -2.25761 0.0258 0.062332 2.593196 0.0107 0.052650
1t� 0.001024 0.338315 0.7357 -0.000161 -0.346670 0.7294 0.000992
1t��� -0.000104 -0.128460 0.8980 0.009746 0.224076 0.8231 0.000415
1t�AP 3.41E-05 0.051457 0.9590 0.000353 0.559947 0.5766 0.002585
22t� 0.000499 0.291010 0.7717 -0.000224 -0.486099 0.6281 0.002590
1t�� -0.001878 -1.320126 0.1893 0.000274 1.487138 0.1396 0.017949
Note: The above equations were estimated using Ordinary Least Square (OLS) over the 1974q2- 2004q4 period.
111
Table 5.6 Tests of Efficiency of the Michigan Forecasts 4t tE
Equation Estimated t t te � �
Independent
Variable t-statistic P-value
t-statistic
P-value 2�
1t -0.008282 -4.939615 0.0000 0.244630 5.518118 0.0000 0.212267
1t� 0.001275 0.371605 0.7109 -0.000208 -0.383310 0.7022 0.001299
1t��� 0.000176 0.171661 0.8640 -0.016053 -0.302053 0.7632 0.000807
1t�AP 0.000145 0.179034 0.8582 0.001943 3.141920 0.0021 0.0021
22t� -0.010730 -5.001132 0.0000 0.003194 5.215018 0.0000 0.195382
1t�� -0.006621 -4.491612 0.0000 0.001167 5.231059 0.0000 0.194950
Note: The above equations were estimated using Ordinary Least Square (OLS) over the 1981q3- 2010q1 period.
Table 5.7 Tests of Efficiency of the Survey of Professional Forecasters (SPF) Forecasts 4t tE
Equation Estimated t t te � �
Independent Variable
t-statistic P-value
t-statistic
P-value 2
�
1t -0.005419 -3.869040 0.0002 0.171365 4.146658 0.0001 0.136256
1t� 0.005859 2.747850 0.0070 -0.000964 -2.834523 0.0055 0.068651
1t��� 0.000335 0.507258 0.6130 -0.029821 -0.884268 0.3785 0.007123
1t�AP 0.000103 0.208985 0.8349 0.001789 4.774618 0.0000 0.172970
22t� -0.005153 -3.016292 0.0032 0.001619 3.165806 0.0020 0.084205
1t�� -0.002641 -2.355927 0.0203 0.000497 2.666986 0.0088 0.061258
Note: The above equations were estimated using Ordinary Least Square (OLS) over the 1981q3- 2010q1 period.
112
The results of the weak-form tests for efficiency presented in the five tables above
indicate that some of the survey respondents of all of the forecasts failed to take into account
all of the information available to them when making inflation forecasts. All of the forecasts
have at least one of the variables in the informational set significantly (5% level) correlated
with the forecast errors.
Another useful way of testing whether past inflationary information are useful in
determining the current rate of inflation can be econometrically tested by implementing a
Granger causality test between the actual inflation rate t and the survey measures of inflation
expectations for over the next year, 4t t�ich . For example, the Michigan survey asks survey
respondents: “During the next 12 months, do you think that prices in general will go up, or go
down, or stay where they are now?” The pure rational expectations model predicts that the
Michigan survey measure of households’ expectations for inflation over the next year should
Granger-cause the actual inflation rate because future expectations matter. However, the pure
rational expectations model also predicts the past actual inflation rates should not Granger-
Table 5.8 Tests of Efficiency of the Greenbook Forecasts 4t tE
Equation Estimated t t te � �
Independent
Variable t-statistic P-value
t-statistic
P-value 2�
1t -0.005188 -2.746995 0.0069 0.110702 3.155469 0.0020 0.077212
1t� 0.012422 2.914982 0.0043 -0.001949 -2.987471 0.0034 0.069767
1t��� 0.001683 1.437479 0.1532 -0.152797 -2.430521 0.0166 0.047295
1t�AP 0.000220 0.232157 0.8168 0.002266 2.526663 0.0128 0.050916
22t
� 0.004850 2.201318 0.0302 -0.001992 -3.363245 0.0011 0.110559
1t�� -0.001572 -0.756678 0.4507 0.000231 0.854260 0.3947 0.006095
Note: The above equations were estimated using Ordinary Least Square (OLS) over the 1974q2- 2004q4 period.
113
cause future inflation expectations because only significantly new information moves
markets, not something that people know already.
Table 5.9 Granger Causality Tests Between Actual Inflation Rates and the Michigan, Survey of
Professional Forecasters and Greenbook Forecasts
Null Hypothesis: F-value P-value
t does not Granger Cause, 4t t�ich 2.18718 0.0772
, 4t t�ich does not Granger Cause t
6.94944 7.E-05
t does not Granger Cause, 4t t�P� 3.77585 0.0072
, 4t t�P� does not Granger Cause t 11.4558 2.E-07
t does not Granger Cause, 4t t�� 5.96114 0.0003
, 4t t�� does not Granger Cause t 8.96415 4.E-06
Notes: t is the actual inflation rate at time t.
, 4t t�ich is the period-t mean of the Michigan survey
measure of household expectations for inflation over the next year. , 4t t�P� is the period-t mean of the
Survey of Professional Forecasters forecasts of the inflation rate over the next year. , 4t t�� is the
Greenbook forecasts of the inflation rate over the next year. All Granger causality tests were conducted over the 1981q3 to 2004q4 period with 4 lags.
The results of these Granger causality tests suggests that some of the survey
respondents in the Michigan survey, the Survey of Professional Forecasters and the
Greenbook forecasts formulate their inflation expectations by taking into account past actual
inflation rates. This also provides statistical evidence that survey measures of inflation
expectations are not perfectly rational.
Finally we test if households minimize their forecast errors by listening professional
forecasters’ forecasts of inflation; we have implemented Granger causality tests between the
Michigan forecasts, the SPF forecasts and the Greenbook forecasts. Rational expectations
predicts that economic agents form their own expectations. However, bounded rational
expectations predicts that the professional forecasts should Granger-cause the household
forecasts but there should be no Granger causality in the opposite direction, because
households minimize their forecast errors by listening professional forecasters’ forecasts of
inflation, The results of our Granger causality tests below confirm that there are Granger
causalities from the professional forecasts (as represented by the SPF forecasts)to household
114
forecasts (as represented by the Michigan forecasts), but no Granger causality in the opposite
direction. This is consistent with Carroll’s (2003, p.282) empirical finding. Our results below
show that the Greenbook forecasts do not Granger-cause the Michigan forecasts, but the
Michigan forecasts Granger-cause the Greenbook forecasts, this could be because the
Greenbook forecasts are only made available to the public after a lag of five years.
Table 5.10 Granger Causality Tests Between the Michigan, Survey of Professional Forecasters and
Greenbook Forecasts
Null Hypothesis: F-value P-value
, 4t t�� does not Granger Cause
, 4t t�ich 1.28381 0.2644
, 4t t�ich does not Granger Cause
, 4t t�� 3.65798 0.0012
, 4t t�P� does not Granger Cause
, 4t t�ich 2.24814 0.0339
, 4t t�ich does not Granger Cause
, 4t t�P� 1.63175 0.1318
, 4t t�P� does not Granger Cause
, 4t t�� 4.32158 0.0003
, 4t t�� does not Granger Cause
, 4t t�P� 2.05337 0.0526
Notes:, 4t t
�ich is the period-t mean of the Michigan survey measure of household expectations for
inflation over the next year. , 4t t�P� is the period-t mean of the Survey of Professional Forecasters
forecasts of the inflation rate over the next year. , 4t t�� is the Greenbook forecasts of the inflation rate
over the next year. All Granger causality tests were conducted over the 1981q3 to 2004q4 period with 8
lags.
5.5 Empirical Comparisons Between Job Finding Probability, the Output Gap and
Labour’s Share of Income as Proxy for Real Marginal Cost
We estimated different Phillips Curve specifications (old Keynesian Phillips curve,
new Keynesian Phillips curve, and hybrid new Keynesian Phillips curve ) with three different
proxies for real marginal cost (job finding probability, the output gap and labour’s share of
income). We used the results of the old Keynesian Phillips curve, with adaptive expectations
as our benchmark, since rational expectations predicts that modelling the Phillips curve with
rational expectations should fit the data better than modelling the Phillips curve with adaptive
expectations. Rational expectations implies that inflation expectations are rational, in the
sense that they efficiently incorporate all information available at time the expectations are
taken, and not just the past information as implied by adaptive expectations. The results of
these estimations are presented in the appendix of this chapter.
115
We found that the output gap and job finding probability performed equally well
when the old Keynesian Phillips curve is estimated. Labour’s share of income is the best
proxy for real marginal cost when the new Keynesian Phillips curve is estimated. Job finding
probability is marginally a better proxy for real marginal cost than the output gap and
labour’s share of income when the hybrid new Keynesian Phillips curve is estimated. In
general, when the hybrid new Keynesian Phillips curve is estimated with job finding
probability as the proxy for real marginal cost, the 2
� values are marginally higher, the
coefficients of job finding probability tend to have the right sign and are statistically
significant.
5.6 Robustness Analysis
We consider two robustness exercises. The first robustness exercise examines sub-
sample stability, our first sub-sample is the period from 1974q1 to 1982q4; this period was
chosen because of the high level of inflation the US economy experienced. Our second sub-
sample is the period from 1987q1 to 2006q4, this sub-sample period is also referred to as the
Great Moderation; this period was chosen because of the lower level of inflation and lower
economic volatility the US economy experienced. Our objective is to examine if the results of
our estimations are robust during a period of higher inflation and higher economic volatility
and a period of lower inflation and lower economic volatility. Since the SPF forecasts are not
available before 1981q3, we will not examine the SPF forecasts in this robustness exercise.
Also, due to the Greenbook forecasts only available up to 2004q4 for the second sub-sample
period, we can only examine the Greenbook forecasts from 1987q1 2004q4.We will also
examine the relative importance of forward-looking and backward-looking inflation
expectations during the two sub-sample periods. The second robustness exercise examines an
alternative measurement of inflation; we will use the implicit price deflator (nonfarm
business) instead of core inflation to examine if our results are robust. The results of these
robustness exercises are presented in the appendix of this chapter.
We found that the job finding probability is clearly the best proxy for real marginal
cost in the first sub-sample period (1974q1 - 1982q4); which is characterized by higher level
of inflation and economic volatility, the reason why job finding probability is better than the
output gap and labour’s share of income as proxy for real marginal cost in the first sub-
sample period is not clear and warrants further investigation. The results of the second sub-
116
sample period (1987q1 - 2006q4) are broadly consistent with the results of the full sample,
but, with higher 2
� values, indicating that these models fit the data better. This is as expected
since the lower economic volatility make forecasting inflation easier, at the same time, it
makes lagged inflation more reliable, since the rates of inflation do not change much quarter
to quarter. The results of our second robustness exercise are consistence with our initial
results.
With respect to the relative importance of forward-looking and backward-looking
inflation expectations, our results indicate that the backward-looking inflation expectations
dominate forward-looking inflation expectations. Note that weights of forward-looking and
backward-looking inflation expectations are similar independent of which measures of real
marginal cost are used. Our results indicate the old Keynesian Phillips curve with adaptive
expectations fits the data better than the new Keynesian Phillips curve with rational
expectations and when the hybrid new Keynesian Phillips curves are estimated, the
coefficients of backward-looking inflation expectations dominate the coefficients forward-
looking inflation expectations, these results are independent of which measures of real
marginal cost are used. Note that the SPF forecasts and the Greenbook forecasts are produced
by professional economists, they have been shown to be more accurate and more “rational”
than the Michigan forecasts, which is produced by non professional economists. The
coefficients of the backward-looking inflation expectations terms of the hybrid new
Keynesian Phillips curve when the Michigan forecasts are used as proxy for expected
inflation expectations, the coefficients of the backward-looking inflation expectations term
tend to be larger, suggesting that survey respondents in the Michigan forecasts are more
backward-looking (or less forward-looking).
5.7 Conclusion
We began this chapter by comparing the predictive power of the three survey
measures of inflation expectations, our results indicate that the Greenbook forecasts has more
predictive power than the SPF forecasts and the Michigan forecasts; this is consistent with
Romer and Romer (2000) empirical finding. We then test the rationality of these survey
measures of inflation expectations; our results indicate that all of the survey measures of
inflation expectations are biased and inefficient. We have also showed that there are Granger
causalities from the professional forecasters (as represented by the SPF forecasts) to
117
households (as represented by the Michigan forecasts), but no Granger causality in the
opposite direction. Many empirical studies that have examined the rationality of survey
measures of inflation expectations have also concluded that inflation expectations are not
perfectly rational (Bryan and Gavin, 1986). Croushore (1998) shows that some of the
empirical work in the 1980’s that concluded that survey measures of inflation expectations
were not rational, were later found to be better when the sample periods were updated to
include more recent data . “However, there remain some problems in the forecasts. It appears
to be possible to improve inflation forecasts over some sample periods using bias regressions,
and the forecasts don’t pass all tests for optimality” Croushore (1998, p.2). Roberts (1997 p.
177) found that survey participants do not use all relevant information available to them when
forecasting inflation.
The main purpose of this chapter is to estimate various specifications of the Phillips
curve using survey measures of inflation expectations as proxy for inflation expectations and
to examine whether job finding probability (JFP), the output gap or labour’s share of income
is a better proxy for real marginal cost. In general, we found that the output gap and job
finding probability performed equally well when the old Keynesian Phillips curve is
estimated. Labour’s share of income is the best proxy for real marginal cost when the new
Keynesian Phillips curve is estimated. Job finding probability is marginally a better proxy for
real marginal cost than the output gap and labour’s share of income when the hybrid new
Keynesian Phillips curve is estimated. We also found that the old Keynesian Phillips curve
with adaptive expectations fits the data better than the new Keynesian Phillips curve with
rational expectations. Overall our results suggest the hybrid new Keynesian Phillips curve fits
the data best.
The finding that the old Keynesian Phillips curve with adaptive expectations fits the
data much better than the new Keynesian Phillips curve when estimated with survey
measures of inflation expectations as proxy for inflation expectations suggests that lagged
inflation plays an important role in inflation dynamics beyond that could be explained by less
than fully rational survey measures of inflation expectations. This result is consistent with
Adam and Padula (2003, p.2) empirical finding that estimating the new Keynesian Phillips
curve with survey based data fit the data well but lagged inflation “enters the price equation
significantly suggesting that there is a role for lagged inflation beyond that of capturing non-
rationalities in expectations”. Rudd and Whelan (2006, p.318) argue that “the observation
118
that lagged inflation plays an important role in empirical inflation regressions poses a major
challenge to the rational expectations sticky price models that underpin the new Keynesian
Phillips curve. Indeed, it has now become relatively well accepted that purely forward-
looking models of inflation cannot account for the degree of inflation inertia that we actually
observe in the data, and that this failure significantly reduces these models' usefulness in
assessing practical policy questions”.
Our results also suggest that the pure rational expectations new Keynesian Phillips
curve might be misspecified. Even if we accept the hybrid new Keynesian Phillips curve as
having the right specifications for the Phillips curve relationship, our results suggest that
backward inflation expectations strongly dominate forward-looking inflation expectations.
Furthermore, we need to be able to explain why are some price setters backward-looking and
why are some price setters forward-looking and also are the fractions of backward-looking
agents and the fractions forward-looking agents constant over time? Recall that bounded
rationality implies that the best way for non-economists to minimize their forecast errors is to
listen to the advices of professional economists as the costs of acquiring this professional
knowledge can be very high. This proposition is supported by Carroll’s (2003) empirical
findings that professional economists are better at forecasting inflation than the general
public. In addition, he finds that the general public’s inflation expectations respond to the
professional economists’ expectations with a lag. The way that professional economists help
the general public to overcome their lack of inflation knowledge is by giving their
professional advices via the mass media, economic education and private consulting. In real
life this is what financial and economic advisors do; they examine their clients’ economic
situations and give them the economic implications of the policy change regarding their
economic situations. Since the general public’s inflation expectations respond to the
professional economists’ expectations with time lag, lagged inflation rates are correlated with
the current inflation rates. In short, bounded rationality explains why lagged inflation plays
an important role in empirical inflation regressions as the dissemination of economic
information and knowledge between professional economists and non-economists involves
time lags, since the general public’s inflation expectations respond to the professional
economists’ expectations with time lags, lagged inflation rates are correlated with the current
inflation rate.
119
With respect to whether the fractions of backward-looking agents and the fractions
forward-looking agents are constant over time, our results indicate that during a period of
lower inflation and lower economic volatility (The Great Moderation), backward-looking
inflation expectations are more significant, this implies that the fractions of backward-looking
agents and the fractions forward-looking agents are not constant over time.
120
5.8 Appendix to Chapter 5 Empirical �es�lts o� �ompariso�s �etwee� �ob �i�di�g Probabilit�� the ��tp�t �ap a�d
�abo�r�s �hare o� ��come as Pro�� �or �eal �argi�al �ost
The tables 5.11 through to 5.22 below present the results of estimations of different
Phillips curve specifications with three different proxies for real marginal cost.
Table 5.11 Estimations (OLS) of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real Marginal Cost
Constant b
2
�
Job Finding Probability
-0.90021 0.3571 -2.521
0.013
1.6695 0.5982 2.791
0.006
0.90884 0.03133 29.010
0.000
0.9493
Output Gap
0.13540 0.7682E-01
1.763 0.081
0.10751 0.5042E-01
2.132 0.035
0.94287000 0.2487E-01
37.910 0.000
0.9516
Labour’s Share of Income
-2.4288 8.051
-0.3017 0.763
0.57051 1.762
0.3238 0.747
0.92336000 0.3419E-01
27.000 0.000
0.9441
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The old Keynesian Phillips curve with adaptive expectations produces relatively high
2
� values for the three proxies of real marginal cost. The coefficients of job finding
probability and the output gap are statistically significant at 5%.
121
Table 5.12Estimations of the New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for Inflation
Expectations
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-0.18072 0.6958
-0.2597 0.796
-0.50394 0.1109
-0.4542 0.651
1.1912 0.1356 8.788 0.000
0.8405
Output Gap
-0.53713 0.3300 -1.628 0.106
-0.16185 0.4468E-01
-3.623 0.000
1.1907 0.1066 11.17 0.000
0.8575
Labour’s Share of Income
-24.172 16.61
-1.455 0.148
5.2070 3.654 1.425 0.157
1.1046 0.1546 7.143 0.000
0.8450
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the SPF over the next quarter
forecasts as proxy for inflation expectations produce lower 2
� values for the three proxies of
real marginal costs than the old Keynesian Phillips curve with adaptive expectations; this is
contrary to the prediction of rational expectations. The coefficients of the job finding
probability and the output gap have the wrong signs.
122
Table 5.13Estimations of the New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for Inflation
Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-1.3640 0.7104 -1.920 0.057
0.98699 1.088
0.9071 0.366
1.1695 0.1298 9.010 0.000
0.8656
Output Gap
-0.75166 0.3552 -2.116 0.037
-0.14329E-01 0.4579E-01
-0.3129 0.755
1.1875 0.1171 10.14 0.000
0.8640
Labour’s Share of Income
-8.2423 14.73
-0.5597 0.577
1.6482 3.266
0.5047 0.615
1.1637 0.1453 8.011 0.000
0.8643
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the SPF over the next year forecasts
as proxy for inflation expectations produce lower 2
� values for the three proxies of real
marginal costs than the old Keynesian Phillips curve with adaptive expectations; this is
contrary to the prediction of rational expectations. The coefficient of the output gap has the
wrong sign.
123
Table 5.14Estimations of the Hybrid New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for
Inflation Expectations
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-0.67370 0.3829
-1.760 0.081
0.86478 0.5801
1.491 0.139
0.72404 0.5715E-01
12.67 0.000
0.29425 0.8741E-01
3.366 0.001
0.9588
Output Gap
-0.11756 0.1125 -1.045 0.298
0.51032E-01 0.4347E-01
1.174 0.243
0.75328 0.4549E-01
16.56 0.000
0.27584 0.7083E-01
3.894 0.000
0.9589
Labour’s Share of Income
4.3829 8.444
0.5190 0.605
-0.99645 1.873
-0.5321 0.596
0.71864 0.5205E-01
13.81 0.000
0.33511 0.9408E-01
3.562 0.001
0.9577
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the SPF over the next
quarter forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 1% level. The coefficient of labour’s share of income has the wrong sign.
124
Table 5.15 Estimations of the Hybrid New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for
Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-0.97281 0.4157
-2.340 0.021
1.3213 0.6217
2.125 0.036
0.72687 0.4346E-01
16.73 0.000
0.27049 0.6044E-01
4.475 0.000
0.9557
Output Gap
-0.13674 0.1093 -1.251 0.213
0.86312E-01 0.4338E-01
1.990 0.049
0.76456 0.4074E-01
18.77 0.000
0.25507 0.5391E-01
4.732 0.000
0.9572
Labour’s Share of Income
5.3353 10.55
0.5057 0.614
-1.2089 2.329
-0.5191 0.605
0.72507 0.3820E-01
18.98 0.000
0.31613 0.7048E-01
4.485 0.000
0.9527
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the SPF over the next year
forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 1% level. The coefficient of labour’s share of income has the wrong sign. The
coefficients of the job finding probability and the output gap are statistically significant at 5%
level.
125
Table 5.16 Estimations (OLS) of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real Marginal Cost
Constant b
2
�
Job Finding
Probability
-3.5216
1.241 -2.837 0.005
5.2585
1.833 2.869 0.005
0.95013
0.2729E-01 34.81 0.000
0.9616
Output Gap
0.70129E-01 0.9745E-01
0.7197 0.473
0.24143 0.6808E-01
3.546 0.001
0.98510 0.2365E-01
41.65 0.000
0.9593
Labour’s Share of Income
-36.390 48.09
-0.7566 0.451
7.9514 10.48
0.7584 0.450
0.93879 0.5224E-01
17.97 0.000
0.9519
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The old Keynesian Phillips curve estimated over the 1974q2 to 2004q4 period with
adaptive expectations produces relatively high 2
� values for the three proxies of real
marginal cost. The coefficients of job finding probability and the output gap are statistically
significant at 1%. Note that the coefficients of backward-looking inflation expectations for
the 1974q2 to 2004q4 sample period are higher than the coefficients of backward-looking
inflation expectations for the 1981q3 to 2010q1 sample period (Table 5.11).
126
Table 5.17 Estimations of the New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for
Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
0.84573 2.577
0.3281 0.743
-2.1696 3.608
-0.6013 0.549
1.0569 0.9453E-01
11.18 0.000
0.7682
Output Gap
-0.90670 0.4560 -1.988 0.049
-0.49821 0.1717 -2.901 0.004
1.0884 0.8535E-01
12.75 0.000
0.8025
Labour’s Share of Income
-197.83 43.52
-4.545 0.000
43.033 9.528 4.516 0.000
0.81440 0.9169E-01
8.882 0.000
0.8238
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated using the Michigan forecasts for over the
next year forecasts as proxy for inflation expectations produces lower 2
� values for the three
proxies of real marginal costs than the old Keynesian Phillips curve with adaptive
expectations; this is contrary to the prediction of rational expectations. The coefficients of the
job finding probability and the output gap have the wrong signs.
127
Table 5.18 Estimations of the Hybrid New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for
Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-2.3250 0.6693
-3.474 0.001
2.9067 0.9967
2.916 0.004
0.80304 0.3276E-01
24.52 0.000
0.22863 0.4083E-01
5.600 0.000
0.9716
Output Gap
-0.36784 0.1110 -3.315 0.001
0.82765E-01 0.5870E-01
1.410 0.161
0.80978 0.3122E-01
25.94 0.000
0.24478 0.4779E-01
5.122 0.000
0.9696
Labour’s Share of Income
-28.422 23.82
-1.193 0.235
6.1060 5.197
1.175 0.242
0.75575 0.2849E-01
26.53 0.000
0.27491 0.4626E-01
5.943 0.000
0.9697
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Michigan forecasts for
over the next year forecasts as proxy for inflation expectations produces higher2
� values
than the old Keynesian Phillips curve for the three proxies of real marginal costs; all
coefficients of backward-looking and forward-looking inflation expectations terms are
statistically significant at 1% level. The coefficient of the job finding probability is
statistically significant at 1% level.
128
Table 5.19 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
1.1429 0.9266
1.233 0.220
-0.93049 1.364
-0.6824 0.496
1.0555 0.4546E-01
23.22 0.000
0.9069
Output Gap
0.45049 0.1684
2.674 0.009
-0.21414 0.9120E-01
-2.348 0.021
1.0580 0.4015E-01
26.35 0.000
0.9136
Labour’s Share of Income
-91.500 22.53
-4.061 0.000
20.053 4.910
4.084 0.000
0.94134 0.4507E-01
20.88 0.000
0.9172
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated using the Greenbook forecasts for over
the next quarter forecasts as proxy for inflation expectations produces lower 2
� values for
the three proxies of real marginal costs than the old Keynesian Phillips curve with adaptive
expectations; this is contrary to the prediction of rational expectations. The coefficients of the
job finding probability and the output gap have the wrong signs. The coefficient of the
labour’s share of income is statistically significant at 1% level.
129
Table 5.20 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
2.3297 1.458
1.598 0.113
-3.1288 2.181
-1.435 0.154
1.2009 0.8667E-01
13.86 0.000
0.8529
Output Gap
0.14698E-01 0.2752
0.5341E-01 0.957
-0.45746 0.1474 -3.103 0.002
1.2132 0.7958E-01
15.24 0.000
0.8801
Labour’s Share of Income
-142.34 35.08
-4.057 0.000
31.082 7.645
4.066 0.000
0.98505 0.7244E-01
13.60 0.000
0.8771
Note: The above equations were estimated (OLS) over the1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated using the Greenbook forecasts for over
the next year forecasts as proxy for inflation expectations produces lower 2
� values for the
three proxies of real marginal costs than the old Keynesian Phillips curve with adaptive
expectations; this is contrary to the prediction of rational expectations. The coefficients of the
job finding probability and the output gap have the wrong signs. The coefficient of the
labour’s share of income is statistically significant at 1% level.
130
Table 5.21 Estimations of the New Hybrid Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-1.9662 0.7249
-2.712 0.008
2.9786 1.005
2.965 0.004
0.69105 0.6066E-01
11.39 0.000
0.32199 0.6597E-01
4.881 0.000
0.9721
Output Gap
0.68736E-01 0.7220E-01
0.9520 0.343
0.99664E-01 0.5053E-01
1.972 0.051
0.69529 0.6364E-01
10.93 0.000
0.33932 0.7606E-01
4.461 0.000
0.9703
Labour’s Share of Income
-25.919 25.31
-1.024 0.308
5.6673 5.510
1.028 0.306
0.62632 0.5586E-01
11.21 0.000
0.38414 0.7380E-01
5.205 0.000
0.9698
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Greenbook forecasts for
over the next quarter as proxy for inflation expectations produces higher2
� values than the
old Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 1% level. The coefficient of the job finding probability is statistically significant
at 1% level.
131
Table 5.22 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-2.0383 0.9923
-2.054 0.042
2.8926 1.409
2.052 0.042
0.77132 0.3946E-01
19.55 0.000
0.27214 0.4988E-01
5.456 0.000
0.9692
Output Gap
-0.75618E-01 0.8197E-01
-0.9225 0.358
0.72941E-01 0.6174E-01
1.181 0.240
0.76903 0.4331E-01
17.76 0.000
0.30054 0.6930E-01
4.337 0.000
0.9671
Labour’s Share of Income
-30.370 29.28
-1.037 0.302
6.6019 6.379
1.035 0.303
0.70496 0.4054E-01
17.39 0.000
0.34148 0.5873E-01
5.815 0.000
0.9676
Note: The above equations were estimated (OLS) over the1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Greenbook forecasts for
over the next year as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 1% level. The coefficient of the job finding probability is statistically significant
at 5% level.
132
Empirical �es�lts o� �ob�st�ess A�al�sis
The tables 5.23 through to 5.36 below present the results of the first robustness exercise,
which examines sub-sample stability. The first sub-sample is the period from 1974q1 to
1982q4. The second sub-sample is the period from 1987q1 to 2006q4 (the Great Moderation).
��b��ample �tabilit�
Table 5.23OLS Estimations of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real
Marginal Cost
Constant b
2
�
Job Finding Probability
-9.1970 0.9116 -10.09 0.000
13.471 1.305 10.32 0.000
0.92133 0.3361E-01
27.41 0.000
0.8820
Output Gap
0.90798 0.5307
1.711 0.096
0.40839 0.7107E-01
5.746 0.000
0.90085 0.5267E-01
17.10 0.000
0.8183
Labour’s Share of Income
-69.141 91.92
-0.7522 0.457
15.244 19.97
0.7632 0.451
0.82988 0.6253E-01
13.27 0.000
0.7656
Note: The above equations were estimated (OLS) over the 1974q1 to 1982q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth
row.
The old Keynesian Phillips curve estimated over the 1974q1 to 1982q4 period yields
lower 2� values for the three proxies of real marginal cost than that of the full sample. The
coefficients of job finding probability and the output gap are statistically significant at 1%.
The coefficients of backward-looking inflation expectations are all statistically significant at
1% level for the three proxies of real marginal cost.
133
Table 5.24 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
7.1262 2.107
3.381 0.002
-10.181 3.188
-3.194 0.003
1.1697 0.8879E-01
13.17 0.000
0.6228
Output Gap
-0.60256 0.5922 -1.017
0.316-0
-0.53130 0.1873 -2.836
0.008
1.1942 0.6584E-01
18.14 0.000
0.6558
Labour’s Share of Income
-62.352 80.38
-0.7757 0.443
13.752 17.36
0.7924 0.434
0.94715 0.7250E-01
13.06 0.000
0.5772
Note: The above equations were estimated (OLS) over the1974q1 to 1982q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated over the 1974q1 to 1982q4 period using
the Greenbook forecasts over the next quarter as proxy for inflation expectations yields lower
2
� values than the old Keynesian Phillips curve for the three proxies of real marginal cost.
The coefficients of the job finding probability and the output gap have the wrong signs.
134
Table 5.25 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
4.3087 2.346 1.837 0.075
-1.2107 4.677
-0.2589 0.797
0.75397 0.1998 3.774 0.001
0.4005
Output Gap
2.4356 1.899
1.282 0.209
-0.44986 0.2065
-2.179 0.037
0.89546 0.2693
3.325 0.002
0.4626
Labour’s Share of Income
-217.81 53.65
-4.060 0.000
47.788 11.48 4.163 0.000
0.75740 0.1302 5.818 0.000
0.5457
Note: The above equations were estimated (OLS) over the1974q1 to 1982q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated over the 1974q1 to 1982q4 period using
the Greenbook forecasts over the next year as proxy for inflation expectations yields lower2
�
values than the old Keynesian Phillips curve for the three proxies of real marginal cost. The
coefficients of the job finding probability and the output gap have the wrong signs. The
coefficient of the labour’s share of income is statistically significant at 1% level.
135
Table 5.26Estimations of the New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
13.545 5.123 2.644 0.012
-15.926 9.576
-1.663 0.106
0.78237 0.3016 2.594 0.014
0.2354
Output Gap
2.1274 1.687 1.261
0.216
-0.65700 0.2389 -2.750
0.010
0.73806 0.2200 3.355
0.002
0.2536
Labour’s Share of Income
-138.25 104.6
-1.321 0.196
30.960 22.46 1.378 0.177
0.39170 0.2017 1.942 0.061
0.2196
Note: The above equations were estimated (OLS) over the1974q1 to 1982q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation
using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated over the 1974q1 to 1982q4 period using
the Michigan forecasts over the next year as proxy for inflation expectations yields lower2
�
values for the three proxies of real marginal costs than the old Keynesian Phillips curve with
adaptive expectations. The coefficients of the job finding probability and the output gap have
the wrong signs.
136
Table 5.27 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-7.0671 2.344
-3.015 0.005
9.7277 3.675
2.647 0.013
0.81508 0.1228
6.639 0.000
0.20246 0.1768
1.145 0.261
0.8858
Output Gap
-0.56200 0.4040 -1.391 0.174
0.80401E-01 0.1083 0.7427 0.463
0.66879 0.7127E-01
9.384 0.000
0.45279 0.1006
4.502 0.000
0.8577
Labour’s Share of Income
-29.640 41.36
-0.7167 0.479
6.2846 9.012
0.6974 0.491
0.63082 0.6130E-01
10.29 0.000
0.49169 0.1023
4.807 0.000
0.8587
Note: The above equations were estimated (OLS) over the 1974q1 to 1982q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the Greenbook over the next
quarter forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs. All of the coefficients of
backward-looking inflation expectations terms are statistically significant at 1% level. The
coefficients of forward-looking inflation expectations term of job finding probability is not
statistically significant. The coefficient of the job finding probability is statistically
significant at 5% level.
137
Table 5.28 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-8.4009 1.223
-6.872 0.000
12.132 1.734 6.997 0.000
0.87378 0.5749E-01
15.20 0.000
0.89843E-01 0.4874E-01
1.843 0.075
0.8819
Output Gap
0.60303 0.6683 0.9024
0.374
0.28534 0.1019
2.801 0.009
0.82106 0.8315E-01
9.874 0.000
0.14666 0.8270E-01
1.773 0.086
0.8198
Labour’s Share of
Income
-106.62
54.52 -1.956 0.059
23.169
11.92 1.944 0.061
0.64856
0.6993E-01 9.274 0.000
0.35628
0.1046 3.406 0.002
0.8332
Note: The above equations were estimated (OLS) over the 1974q1 to 1982q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the Greenbook over the next
year forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs. All of the coefficients of
backward-looking inflation expectations terms are statistically significant at 1% level. All of
the coefficients of forward-looking inflation expectations terms are statistically significant at
10% level. The coefficients of the three proxies of real marginal costs are statistically
significant at 10% level.
138
Table 5.29 Estimations of the Hybrid New Keynesian Phillips Curve Using Michigan Forecasts as Proxy for
Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-9.1338 2.838
-3.219 0.003
13.358 4.745
2.815 0.008
0.92017 0.6077E-01
15.14 0.000
0.35093E-02 0.1239
0.2832E-01 0.978
0.8783
Output Gap
-0.55418 0.3025 -1.832 0.076
0.10583 0.1411 0.7502
0.459
0.82396 0.4474E-01
18.42 0.000
0.25061 0.6758E-01
3.708 0.001
0.8420
Labour’s Share of Income
-30.865 49.93
-0.6181 0.541
6.5323 10.91
0.5985 0.554
0.79301 0.3006E-01
26.38 0.000
0.28856 0.7147E-01
4.037 0.000
0.8425
Note: The above equations were estimated (OLS) over the1974q1 to 1982q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Michigan forecasts for
over the next year forecasts as proxy for inflation expectations produces higher2
� values
than the old Keynesian Phillips curve for the three proxies of real marginal costs. All of the
coefficients of backward-looking inflation expectations terms are statistically significant at
1% level. The coefficients of forward-looking inflation expectations term of job finding
probability is not statistically significant. The coefficient of the job finding probability is
statistically significant at 1% level.
139
�he �reat �oderatio�
Table 5.30 Estimations (OLS) of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real Marginal Cost
Constant b
2
�
Job Finding Probability
-0.89751 0.3207 -2.798 0.006
1.5098E-01 0.5216 2.895 0.005
0.94147 0.3078E-01
30.59 0.000
0.9697
Output Gap
0.44668E-01 0.6058E-01
0.7374 0.463
0.81754E-01
0.1819E-01 4.496 0.000
0.97971
0.2063E-01 47.49 0.000
0.9707
Labour’s Share of Income
-1.6295 8.498
-0.1917 0.848
0.36689 1.854
0.1979 0.844
0.97609 0.3000E-01
32.53 0.000
0.9646
Note: The above equations were estimated (OLS) over the 1987q1 to 2006q4 period using quarterly data.
Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The old Keynesian Phillips curve estimated over the 1987q1 to 2006q4 period yields
higher 2
� values for the three proxies of real marginal cost than that of the full sample. The
coefficients of job finding probability and the output gap are statistically significant at 1%.
The coefficients of backward-looking inflation expectations are all statistically significant at
1% level for the three proxies of real marginal cost.
140
Table 5.31 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-0.25644 0.8122
-0.3157 0.753
1.6247 1.318 1.233 0.222
0.86613 0.7102E-01
12.20 0.000
0.7965
Output Gap
0.74171 0.8656E-01
8.568 0.000
-0.57198E-01 0.6223E-01
-0.9192 0.361
0.92263 0.5341E-01
17.27 0.000
0.7933
Labour’s Share of Income
-70.407 26.41
-2.666 0.010
15.523 5.766 2.692 0.009
0.81769 0.6203E-01
13.18 0.000
0.8333
Note: The above equations were estimated (OLS) over the1987q1 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the Greenbook over the next quarter
forecasts as proxy for inflation expectations produces lower2
� values than the old Keynesian
Phillips curve for the three proxies of real marginal costs. All coefficients of forward-looking
inflation expectations terms are statistically significant at 1% level. The coefficient of the
output gap has the wrong sign. The coefficient of the labour’s share of income is statistically
significant at 1% level.
141
Table 5.32 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
1.0455 1.246
0.8389 0.404
-0.44519 1.876
-0.2373 0.813
0.94312 .1099 8.584 0.000
0.7485
Output Gap
0.64884 0.2094
3.099 0.003
-0.14482 0.1216 -1.191 0.238
0.97200 0.1019
9.543 0.000
0.7641
Labour’s Share of Income
-69.048 32.03
-2.156 0.035
15.229 6.995 2.177 0.033
0.82802 0.9198E-01
9.002 0.000
0.7884
Note: The above equations were estimated (OLS) over the1987q1 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the Greenbook over the next year
forecasts as proxy for inflation expectations produces lower 2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs. All coefficients of
forward-looking inflation expectations terms are statistically significant at 1% level. The
coefficients of job finding probability and the output gap have the wrong signs.
142
Table 5.33 Estimations of the New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for
Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-3.8983 1.776
-2.195 0.031
5.5517 3.020 1.838 0.070
0.77766 0.1651 4.710 0.000
0.5655
Output Gap
-0.91889 0.6308 -1.457 0.149
-0.19608 0.1245 -1.575 0.119
1.0159 0.1884 5.393 0.000
0.5209
Labour’s Share of Income
-114.54 28.83
-3.973 0.000
24.863 6.282 3.958 0.000
0.83989 0.8889E-01
9.448 0.000
0.6934
Note: The above equations were estimated (OLS) over the 1987q1 to 2006q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated using the Michigan forecasts for over the
next year forecasts as proxy for inflation expectations produces lower 2
� values for the three
proxies of real marginal costs than the old Keynesian Phillips curve with adaptive
expectations. The coefficient of the output gap has the wrong signs. The coefficient of the
labours share of income is statistically significant at 1% level.
143
Table 5.34 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-0.89015 0.2870
-3.101 0.003
1.4532 0.4456
3.262 0.002
0.92071 0.4056E-01
22.70 0.000
0.34947E-01 0.3136E-01
1.114 0.269
0.9725
Output Gap
0.45681E-01 0.6947E-01
0.6576 0.513
0.82916E-01 0.2223E-01
3.731 0.000
0.96972 0.3619E-01
26.80 0.000
0.12435E-01 0.3196E-01
0.3891 0.698
0.9729
Labour’s Share of Income
-13.750 8.865
-1.551 0.126
3.0116 1.931 1.560 0.123
0.88753 0.5109E-01
17.37 0.000
0.86709E-01 0.3967E-01
2.186 0.032
0.9691
Note: The above equations were estimated (OLS) over the 1987q1 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the Greenbook over the next
quarter forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking inflation expectations terms are statistically significant at 1% level. The
coefficients of job finding probability and the output gap are statistically significant at 1%.
144
Table 5.35 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-0.58137 0.2394
-2.429 0.018
0.94430 0.3191
2.959 0.004
0.87069 0.4028E-01
21.61 0.000
0.11820 0.4137E-01
2.857 0.006
0.9753
Output Gap
0.30306E-01 0.5850E-01
0.5181 0.606
0.55550E-01 0.1496E-01
3.714 0.000
0.89258 0.3705E-01
24.09 0.000
0.11439 0.4028E-01
2.840 0.006
0.9757
Labour’s Share of Income
-12.549 8.072
-1.555 0.125
2.7442 1.756 1.562 0.123
0.83808 0.2711E-01
30.92 0.000
0.16204 0.3944E-01
4.108 0.000
0.9748
Note: The above equations were estimated (OLS) over the 1987q1 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the Greenbook over the next
year forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 1% level. The coefficients of the job finding probability and the output gap are
statistically significant at 1% level.
145
Table 5.36 Estimations of the Hybrid New Keynesian Phillips Curve Using Michigan Survey Data
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-1.0802 0.1862 -5.802 0.000
1.3105 0.2718
4.822 0.000
0.88114 0.2793E-01
31.54 0.000
0.13101 0.3668E-01
3.572 0.001
0.9750
Output Gap
-0.19964 0.1094 -1.824
0.072
0.53172E-01 0.1282E-01
4.149
0.000
0.92766 0.2969E-01
31.25
0.000
0.10435 0.4686E-01
2.227
0.029
0.9733
Labour’s Share of Income
-11.706 5.357
-2.185 0.032
2.4879E-01 1.168E-01
2.130 0.036
0.87171 0.3146E-01
27.71 0.000
0.16642 0.4432E-01
3.75 0.000
0.9725
Note: The above equations were estimated (OLS) over the1987q1 to 2006q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Michigan forecasts for
over the next year forecasts as proxy for inflation expectations produces higher2
� values
than the old Keynesian Phillips curve for the three proxies of real marginal costs; all
coefficients of backward-looking and forward-looking inflation expectations terms are
statistically significant at 5% level. The coefficients of the three proxies of real marginal
costs are statistically significant at 5% level.
146
Empirical �es�lts o� Estimatio�s �si�g a� Alter�ati�e �eas�reme�t o� ���latio�
The tables 5.37 through to 5.48 present the results of estimations using the implicit
price deflator (nonfarm business) instead of core inflation to examine if our initial results are
robust.
Table 5.37 Estimations (OLS) of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real
Marginal Cost
Constant b
2
�
Job Finding Probability
-0.79996 0.3320 -2.410 0.018
1.4562 0.5016 2.903 0.004
0.89091 0.2472E-01
36.05 0.000
0.9355
Output Gap
0.15697 0.6290E-01
2.496
0.014
0.76709E-01 0.4196E-01
1.828
0.070
0.90923 0.2224E-01
40.89
0.000
0.9351
Labour’s Share of Income
-4.4032E-01 10.05
-0.4381 0.662
0.99905 2.192
0.4558 0.649
0.89443 0.2750E-01
32.53 0.000
0.9306
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth
row.
The old Keynesian Phillips curve with adaptive expectations produces relatively high
2
� values for the three proxies of real marginal cost. The coefficients of job finding
probability and the output gap are statistically significant at 10% level.
147
Table 5.38 Estimations of the New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for Inflation
Expectations
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
0.72396 0.8639 0.8380
0.404
-2.2285 1.469
-1.517 0.132
0.99381 0.1958 5.075 0.000
0.6637
Output Gap
-0.66386 0.6564 -1.011 0.314
-0.99283E-01 0.9992E-01
-0.9936 0.323
0.94899 0.1893 5.014 0.000
0.6613
Labour’s Share of Income
32.448 27.11 1.197 0.234
-7.2730 5.917
-1.229 0.222
1.0468 0.1943 5.389 0.000
0.6650
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the SPF over the next quarter
forecasts as proxy for inflation expectations produce lower 2
� values for the three proxies of
real marginal costs than the old Keynesian Phillips curve with adaptive expectations; this is
contrary to the prediction of rational expectations. The coefficients of the three proxies of real
marginal costs have the wrong signs.
148
Table 5.39 Estimations of the New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for Inflation
Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-0.30281 0.9855
-0.3073 0.759
-0.57171 1.447
-0.3951 0.693
0.90486 0.2271 3.985 0.000
0.5945
Output Gap
-0.65848 0.7706
-0.8545 0.395
0.15174E-01 0.9576E-01
0.1585 0.874
0.89490 0.2186 4.094 0.000
0.5939
Labour’s Share of Income
35.253 34.46 1.023 0.308
-7.9034E-01 7.533E-01
-1.049 0.296
1.0126 0.2244 4.512 0.000
0.6066
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the SPF over the next year forecasts
as proxy for inflation expectations produce lower 2
� values for the three proxies of real
marginal costs than the old Keynesian Phillips curve with adaptive expectations; this is
contrary to the prediction of rational expectations. The coefficients job finding probability
and labour’s share of income have the wrong signs.
149
Table 5.40 Estimations of the Hybrid New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for
Inflation Expectations
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-0.61389 0.3104
-1.978 0.050
0.87521 0.4656
1.880 0.063
0.81854 0.4894E-01
16.73 0.000
0.12114 0.7519E-01
1.611 0.110
0.9383
Output Gap
-0.60344E-01 0.1575
-0.3832 0.702
0.57245E-01 0.3763E-01
1.521 0.131
0.82285 0.4330E-01
19.01 0.000
0.13327 0.6712E-01
1.985 0.050
0.9393
Labour’s Share of Income
10.007 12.32
0.8124 0.418
-2.2213 2.700
-0.8228 0.412
0.79558 0.4913E-01
16.19 0.000
0.19588 0.7990E-01
2.451 0.016
0.9379
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the SPF over the next
quarter forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs. The coefficient of
labour’s share of income has the wrong sign.
150
Table 5.41 Estimations of the Hybrid New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for
Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-0.77548 0.3286
-2.360 0.020
1.2947 0.4476
2.893 0.005
0.86440 0.4247E-01
20.36 0.000
0.44284E-01 0.6102E-01
0.7257 0.470
0.9355
Output Gap
0.11407E-01 0.1555
0.7336E-01 0.942
0.75185E-01 0.3751E-01
2.004 0.047
0.86021 0.3735E-01
23.03 0.000
0.77942E-01 0.5875E-01
1.327 0.187
0.9364
Labour’s Share of Income
3.6779 12.86
0.2860 0.775
-0.80677 2.821
-0.2860 0.775
0.84806 0.4707E-01
18.02 0.000
0.96774E-01 0.7715E-01
1.254 0.212
0.9319
Note: The above equations were estimated (OLS) over the 1981q3 to 2010q1 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the SPF over the next year
forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs. The coefficient of
labour’s share of income has the wrong sign. The coefficients of the job finding probability
and the output gap are statistically significant at 5% level.
151
Table 5.42 Estimations (OLS) of the Old Keynesian Phillips Curve
Equation estimated 1t t b tmc
Proxy for Real Marginal Cost
Constant b
2
�
Job Finding
Probability
-3.0893
1.489 -2.075 0.040
4.5594
2.121 2.150 0.034
0.95337
0.2374E-01 40.16 0.000
0.9644
Output Gap
0.59032E-01 0.8672E-01
0.6807 0.497
0.22085 0.6437E-01
3.431 0.001
0.98255 0.2425E-01
40.51 0.000
0.9634
Labour’s Share of Income
-22.588 47.48
-0.4758 0.635
4.9322 10.34
0.4772 0.634
0.95295 0.4716E-01
20.21 0.000
0.9576
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The old Keynesian Phillips curve estimated over the 1974q2 to 2004q4 period with
adaptive expectations produces relatively high 2
� values for the three proxies of real
marginal cost. The coefficients of job finding probability and the output gap are statistically
significant at 5% level. All of the coefficients of backward-looking inflation expectations are
statistically significant at 1% level. Note that the coefficients of backward-looking inflation
expectations for the 1974q2 to 2004q4 sample period are higher than the coefficients of
backward-looking inflation expectations for the 1981q3 to 2010q1 sample period (Table
5.37).
152
Table 5.43 Estimations of the New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for
Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
1.2358 2.214
0.5581 0.578
-4.7410 2.952
-1.606 0.111
1.1525 0.1142
10.09 0.000
0.7541
Output Gap
-2.3248 0.4281 -5.430 0.000
-0.68779 0.2795 -2.461 0.015
1.1768 0.9162E-01
12.84 0.000
0.8063
Labour’s Share of Income
-158.70 55.13
-2.879 0.005
34.216 12.06
2.838 0.005
0.92667 0.1182
7.842 0.000
0.7785
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated using the Michigan over the next year
forecasts as proxy for inflation expectations produces lower 2
� values for the three proxies
of real marginal costs than the old Keynesian Phillips curve with adaptive expectations. The
coefficients of the job finding probability and the output gap have the wrong signs. The
coefficient of labour’s share of income is statistically significant at 1% level.
153
Table 5.44 Estimations of the Hybrid New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
--1.9186 1.133
-1.693 0.093
1.9550 1.577 1.239 0.218
0.81612 0.3619E-01
22.55 0.000
0.23437 0.3450E-01
6.794 0.000
0.9736
Output Gap
0.61739 0.1549 -3.986 0.000
0.37931E-01 0.5797E-01
0.6544 0.514
0.81448 0.2812E-01
28.96 0.000
0.25327 0.3721E-01
6.807 0.000
0.9726
Labour’s Share of Income
-3.3333E-01 28.75
-0.1159 0.908
0.58242 6.251
0.9317E-01 0.926
0.80061 0.2867E-01
27.92 0.000
0.26887 0.3507E-01
7.667 0.000
0.9725
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Michigan over the next
year forecasts as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 1% level.
154
Table 5.45 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 1t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
1.1924 1.755
0.6794 0.498
-2.6219 2.447
-1.072 0.286
1.1067 0.1047
10.57 0.000
0.8348
Output Gap
-0.68728 0.3417 -2.012 0.046
-0.36900 0.2099 -1.758 0.081
1.1018 0.9363E-01
11.77 0.000
0.8503
Labour’s Share of Income
-61.120 46.75
-1.307 0.194
13.195 10.15
1.300 0.196
1.0136 0.9089E-01
11.15 0.000
0.8365
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated using the Greenbook over the next
quarter forecasts as proxy for inflation expectations produces lower 2
� values for the three
proxies of real marginal costs than the old Keynesian Phillips curve with adaptive
expectations. The coefficients of the job finding probability and the output gap have the
wrong signs.
155
Table 5.46 Estimations of the New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for
Inflation Expectations
Equation estimated 4t t � t tmc E
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
2.1790 2.104
1.036 0.302
-4.3958 3.058
-1.438 0.153
1.2280 0.1134
10.83 0.000
0.7496
Output Gap
-1.0583 0.3933 -2.691 0.008
-0.61298 0.2730 -2.246 0.027
1.2421 0.1118 11.11 0.000
0.7911
Labour’s Share of Income
-132.63 64.14
-2.068 0.041
28.748 13.95
2.061 0.041
1.0109 0.8547E-01
11.83 0.000
0.7641
Note: The above equations were estimated (OLS) over the1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated using the Greenbook over the next year
forecasts as proxy for inflation expectations produces lower 2
� values for the three proxies
of real marginal costs than the old Keynesian Phillips curve with adaptive expectations. The
coefficients of the job finding probability and the output gap have the wrong signs. The
coefficient of the labour’s share of income is statistically significant at 5% level.
156
Table 5.47 Estimations of the New Hybrid Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 1t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-2.4188 1.362
-1.775 0.078
3.3510 1.885
1.778 0.078
0.84936 0.4674E-01
18.17 0.000
0.14525 0.4793E-01
3.030 0.003
0.9666
Output Gap
-0.10554 0.1387
-0.7611 0.448
0.14756 0.5718E-01
2.58 0.011
0.86942 0.4782E-01
18.18 0.000
0.14636 0.5922E-01
2.471 0.015
0.9655
Labour’s Share of Income
-3.2015 39.27
-0.8152E-01 0.935
0.65865 8.541
0.7712E-01 0.939
0.81077 0.4904E-01
16.53 0.000
0.21300 0.5032E-01
4.233 0.000
0.9633
Note: The above equations were estimated (OLS) over the 1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Greenbook over the
next quarter forecasts as proxy for inflation expectations produces higher2
� values than the
old Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 5% level. The coefficients of the job finding probability and the output gap are
statistically significant at 10% level.
157
Table 5.48 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 4t t b t � t tmc E
Proxy for Real Marginal Cost
Constant b
� 2
�
Job Finding Probability
-2.4961 1.585
-1.575 0.118
3.4635 2.285
1.516 0.132
0.88991 0.5133E-01
17.34 0.000
0.11103 0.6232E-01
1.782 0.077
0.9656
Output Gap
-0.98867E-01 0.1109
-0.8917 0.374
0.15332 0.6377E-01
2.404 0.018
0.91363 0.5238E-01
17.44 0.000
0.10763 0.5469E-01
1.968 0.051
0.9644
Labour’s Share of Income
-7.4557 42.01
-0.1775 0.859
1.5786 9.146
0.1726 0.863
0.85486 0.4410E-01
19.38 0.000
0.18252 0.5828E-01
3.132 0.002
0.9624
Note: The above equations were estimated (OLS) over the1974q2 to 2004q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure with 12 lags. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated using the Greenbook forecasts for
over the next year as proxy for inflation expectations produces higher2
� values than the old
Keynesian Phillips curve for the three proxies of real marginal costs. All coefficients of
backward-looking and forward-looking inflation expectation terms are statistically significant
at 10% level. The coefficient of the output gap is statistically significant at 5% level.
158
Table 5.49 Definitions and Sources of Data
Variable Definition Source
dlp t is measured as 100
4ln t
t
p
p using core CPI.
Consumer Price Index (All Items Less Food and Energy), Index 1982-1984=100. Source:
Bureau of Labor Statistics (BLS).
u Unemployment Rate (in %). Bureau of Labor Statistics
(BLS).
jfp Job Finding Probability. Constructed from the number of unemployed workers, the number of short term (15 weeks) unemployed workers and the
number of unemployed workers next month.
Bureau of Labor Statistics (BLS).
gap Output Gap (Nonfarm Business Sector Output, Index 2005=100), using the Hodrick-Prescott filter
with a smoothing parameter of 1600.
Bureau of Labor Statistics (BLS).
s Labour’s Share of Income (Nonfarm Business Sector, Index 1992=100).
Bureau of Labor Statistics (BLS).
p Implicit Price Deflator of Nonfarm Business Sector Output, Index 1992=100.
Bureau of Labor Statistics (BLS).
S1 Represents the median forecasts of the SPF for the first quarter after the current quarter.
www.philadelphiafed.org/.../survey-of-professional-
forecasters/
S4 Represents the median forecasts of the SPF for the
fourth quarter after the current quarter.
www.philadelphiafed.org/..
./survey-of-professional-forecasters/
MI Represents the mean forecasts of the Michigan Survey for the fourth quarter after the current quarter.
www.src.isr.umich.edu/
DLW Wage Inflation, measured as the log- difference in nonfarm compensation per hour (Nonfarm Business Sector Real Hourly Compensation, Index 1992=100).
Bureau of Labor Statistics (BLS).
FF Federal Funds Rates (in %). Federal Reserve Board (FRB).
DLPPI Measured as4
ln t
t
ppi
ppi using Producer Price Index:
Finished goods (Index 1982 = 100).
http://research.stlouisfed.or
g/fred2/categories/
159
SP Long-Short Interest Rate Spread. The difference
between 10-Year Treasury Constant Maturity Rate and 3-Month Treasury Bill.
Federal Reserve Board
(FRB).
G1 Greenbook forecasts for the GNP/GDP price level
for the first quarter after the current quarter.
http://www.philadelphiafed
.org/research-and-data/real-time-center/greenbook-
data/
G4 Greenbook forecasts for the GNP/GDP price level for the fourth quarter after the current quarter.
http://www.philadelphiafed.org/research-and-data/real-time-center/greenbook-data/
M1 Represents the mean forecasts of the SPF for the first quarter after the current quarter.
www.philadelphiafed.org/.../survey-of-professional-forecasters/
M4 Represents the mean forecasts of the SPF for the
fourth quarter after the current quarter.
www.philadelphiafed.org/..
./survey-of-professional-forecasters/
M2 M2 consists of M1 plus: (1) savings deposits
(which include money market deposit accounts, or MMDAs); (2) small-denomination time deposits
(time deposits in amounts of less than $100,000); and (3) balances in retail money market mutual funds(MMMFs). Seasonally adjusted M2 is computed by summing savings deposits, small-denomination time deposits, and retail MMMFs, each seasonally adjusted separately, and adding this result to seasonally adjusted M1.
http://research.stlouisfed.or
g/fred2/series/M2SL?cid=29
160
CHAPTER 6
The Flattening of the Phillips Curve
6.1 Introduction
In recent years, a number of empirical studies such as: Roberts (2006), Ihrig et al
(2007), Mishkin (2007), Kuttner and Robinson (2006), Binyamini and Razin (2007) and
Beaudry and Doyle (2000) report that the slope of the reduced form Phillips curve for the
United States has become much smaller over the last 20 years, this phenomenon is also
observed in many other industrialized countries. The flattening of the Phillips curve raises
two important questions: What explains the flattening of the Phillips curve? And what are the
implications of this phenomenon for the proper conduct of monetary policy? We will attempt
to argue that increase in specialization of labour is also a possible cause of the flattening of
the Phillips curve. This chapter is structured as follows: The first section presents empirical
evidence of the flattening of the Phillips curve and tests for structural changes. The second
section examines competing explanations for the flattening of the Phillips curve. The third
section proposes that increase in specialization of labour is a possible cause of the flattening
of the Phillips curve. The fourth concludes.
6.2 The Flattening of the Phillips Curve
As a starting point, we estimate the hybrid new Keynesian of the Phillips curve using
the Michigan forecasts, the Survey of Professional Forecasters (SPF) forecasts and the
Greenbook forecasts as proxies for inflation expectations. We also consider job finding
probability, the output gap and labour’s share of income as proxy for real marginal cost.
Table 6.1, 6.2 and 6.6 present the results of estimations of the hybrid new Keynesian Phillips
curve using the Michigan forecasts as proxy for inflation expectations. Table 6.4, 6.5 and 6.6
present the results of estimations of the hybrid new Keynesian Phillips curve using the SPF
forecasts as proxy for inflation expectations. Table 6.7, 6.8 and 6.9 present the results of
estimations of the hybrid new Keynesian Phillips curve using the Greenbook forecasts as
proxy for inflation expectations and are presented in the appendix of this chapter. The results
from the nine tables mentioned above show that the slopes of the reduced form new
Keynesian of the Phillips curve are much smaller over the past 20 years. Besides the
flattening of the Phillips curve over the past 20 years, we have also noted the following
interesting empirical findings:
161
1. The relative importance of backward-looking inflation expectations and forward-
looking inflation expectations changes over time. Backward-looking inflation
expectations dominate forward-looking inflation expectations independent of which
measures of real marginal cost and survey measures of inflation expectations are used.
This is consistent with our previous empirical finding in chapter 5.
2. The signs and magnitudes of the slope of the reduced form Phillips curve depend on
which measure of inflation expectations are used and which measures of real marginal
cost are used.
3. The recent financial crisis does not seem to have affected the slopes of the reduced
form hybrid new Keynesian Phillips curve. We have estimated the hybrid new
Keynesian Phillips curve for the sub-sample periods from 2000q1 to 2006q4 and for
Phillips curve from 2007q1 to 2010q1; it appears that the slopes and the R square
values have not changed much. Note that the second sub-sample period is relatively
short, we need to be careful about drawing any conclusion from this sub-sample
period.
4. The R square values of the hybrid new Keynesian Phillips curve estimated for the
sub-sample period from 2000q1 to 2010q1 are lower than that of the previous two
decades, this suggests the inflation process has become more difficult to forecast; this
is consistent with Stock and Watson’s (2007) empirical finding. Our results also
indicate that backward-looking inflation expectations have become less significant
(less persistent), but forward-looking inflation expectations have not become more
significant. This is an empirical result that needs further investigation and is beyond
the scope of this chapter.
5. Job finding probability is marginally a better proxy for real marginal cost than the
output gap and labour’s share of income when the hybrid new Keynesian Phillips
curve is estimated.
162
Table 6.1 Estimations of the Hybrid New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for Inflation Expectations and with Job Finding Probability as Proxy for Real Marginal Cost
Equation estimated 1 4t t b t � t tmc E
Sample Period Constant b
�
2�
1961q1 to 1969q4 0.7324 1.0898
0.672072 0.5065
-1.7030 1.6959
-1.004176 0.3231
0.875677 0.056137 15.59903
0.0000
0.3201 0.0953
3.358082 0.0021
0.975927
1970q1 to 1979q4 -5.4480 01.7670
-3.083139 0.0039
6.1728 2.2321
2.765412 0.0089
0.963073 0.059258 16.25229
0.0000
0.1552 0.0513
3.028107 0.0045
0.939176
1980q1 to 1989q4 -2.1894 1.3108
-1.670199 0.1036
2.3562 1.8619
1.265521 0.2138
0.679871 0.067757 10.03389
0.0000
0.4042 0.0919
4.398224 0.0001
0.962117
1990q1 to 1999q4 -1.6932 0.4029
-4.203029 0.0002
1.8194 0.5452
3.337395 0.0020
0.888320 0.034310 25.89078
0.0000
0.1857 0.0481
3.860308 0.0005
0.976544
2000q1 to 2010q1 -0.56.79 0.23.50
-2.416087 0.0207
1.40.14 0.39.20
3.574975 0.0010
0.726571 0.084294 8.619477
0.0000
0.0660 0.0355
1.859752 0.0709
0.831325
2000q1 to 2006q4 -1.0343 0.4113
-2.515061 0.0190
1.7780 0.7686
2.313405 0.0296
0.791480 0.094251 8.397576
0.0000
0.0887 0.0527
1.682290 0.1055
0.872219
2007q1 to 2010q1 0.0547 0.3114
0.175809 0.8643
2.8782 0.9946
2.893945 0.0178
0.028622 0.286442 0.099922
0.9226
0.0678 0.0548
1.238698 0.2468
0.851044
1961q1 to 2010q1 -1.5105
0.2702 -5.591050
0.0000
1.7251
0.3894 4.430226
0.0000
0.825487
0.019734 41.83093
0.0000
0.2076
0.0239 8.677273
0.0000
0.972790
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
163
Table 6.2 Estimations of the Hybrid New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for Inflation Expectations and the Output Gap as Proxy for Real Marginal Cost
Equation estimated 1 4t t b t � t tmc E
Sample Period Constant b
� 2�
1961q1 to 1969q4 -0.3028 0.1560
-1.940742 0.0614
0.1081 0.1414
0.764274 0.4505
0.867623 0.055281 15.69486
0.0000
0.2311 0.0743
3.110024 0.0040
0.975603
1970q1 to 1979q4 -0.6466 0.3619
-1.786353 0.0825
-2.24E-03 0.1416
-0.015813 0.9875
0.865678 0.073526 11.77383
0.0000
0.2289 0.0711
3.220710 0.0027
0.926255
1980q1 to 1989q4 -0.5066 0.2586
-1.958888 0.0579
0.1437 0.1017
1.412175 0.1665
0.717845 0.078596 9.133376
0.0000
0.3656 0.1022
3.578252 0.0010
0.962509
1990q1 to 1999q4 -0.4421 0.1545
-2.860961 0.0070
0.0859 0.0404
2.126728 0.0404
0.936668 0.041097 22.79184
0.0000
0.1548 0.0534
2.897211 0.0064
0.972714
2000q1 to 2010q1 0.2949 0.2639
1.117640 0.2709
0.0510 0.0230
2.212613 0.0332
0.826179 0.082434 10.02235
0.0000
0.0173 0.0481
0.359302 0.7214
0.799580
2000q1 to 2006q4 0.1463 0.3145
0.465322 0.6459
0.0723 0.0348
2.074563 0.0489
0.878681 0.079012 11.12087
0.0000
0.0395 0.0669
0.589926 0.5608
0.867488
2007q1 to 2010q1 0.4750 0.5964
0.796543 0.4462
0.0382 0.0371
1.031261 0.3293
0.604170 0.235073 2.570141
0.0302
0.0702 0.0819
0.857030 0.4137
0.742824
1961q1 to 2010q1 -0.3230 0.0790
-4.086299 0.0001
0.0502 0.0310
1.620371 0.1068
0.838952 0.022926 36.59331
0.0000
0.2078 0.0278
7.482747 0.0000
0.970413
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
164
Table 6.3 Estimations of the Hybrid New Keynesian Phillips Curve Using the Michigan Forecasts as Proxy for Inflation Expectations and Labour’s Share of Income as Proxy for Real Marginal Cost
Equation estimated 1 4t t b t � t tmc E
Sample Period Constant b
� 2�
1961q1 to 1969q4 -25.7121 16.2363
-1.583614 0.1234
5.4684 3.5010
1.561944 0.1285
0.813181 0.061512 13.21982
0.00
0.3180 0.0785
4.051476 0.0003
0.976957
1970q1 to 1979q4 -95.3349 30.3329
-3.142954 0.0033
20.4567 6.5528
3.121829 0.0035
0.917265 0.049508 18.52743
0.0000
0.1873 0.0449
4.172137 0.0002
0.941966
1980q1 to 1989q4 17.0309 42.2774
0.402837 0.6895
-3.8240 9.1890
-0.416154 0.6798
0.677648 0.087130 7.777452
0.0000
0.4319 0.0924
4.674714 0.0000
0.960621
1990q1 to 1999q4 -31.5177 15.8656
-1.986546 0.0546
6.7774 3.4594
1.959120 0.0579
0.822137 0.053711 15.30683
0.0000
0.2263 0.0570
3.969309 0.0003
0.972245
2000q1 to 2010q1 -10.9254 5.0170
-2.177669 0.0359
2.3859 1.1017
2.165686 0.0369
0.817009 0.084407
9.679430 0.0000
0.1088 0.0405
2.688118 0.0107
0.798592
2000q1 to 2006q4 -3.7563 8.0900
-0.464321 0.6466
0.7592 1.7570
0.432083 0.6695
0.913242 0.086649 10.53956
0.0000
0.1412 0.0598
2.362489 0.0266
0.844931
2007q1 to 2010q1 -54.2659 20.4386
-2.655071 0.0263
12.3023 4.6306
2.656745 0.0262
-0.025774 0.325685
-0.079138 0.9387
0.1213 0.0542
2.235827 0.0522
0.838831
1961q1 to 2010q1 -17.8503 5.7445
-3.107405 0.0022
3.8133 1.2522
3.045337 0.0027
0.799602 0.021580 37.05279
0.0000
0.2326 0.0240
9.675960 0.0000
0.971390
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
165
Table 6.4 Estimations of the Hybrid New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for Inflation Expectations and with Job Finding Probability as Proxy for Real Marginal Cost
Equation estimated 1 4t t b t � t tmc E
Sample Period Constant b
� 2�
1981q3 to 1989q4 -3.0028 1.4088
-2.131445 0.0414
2.7582 1.8217
1.514075 0.1405
0.652109 0.098482 6.621616
0.0000
0.5434 0.1890
2.874334 0.0074
0.914300
1990q1 to 1999q4 -1.9944 0.4292
-4.646381 0.0000
2.1641 0.5509
3.928378 0.0004
0.814391 0.048324 16.85286
0.0000
0.3115 0.0791
3.939720 0.0004
0.976826
2000q1 to 2010q1 -0.7216 0.3412
-2.114571 0.0413
1.0758 0.5179
2.077150 0.0448
0.664258 0.100573 6.604770
0.0000
0.3140 0.2504
1.253853 0.2178
0.823075
2000q1 to 2006q4 -1.2325 0.4536
-2.717258 0.0120
1.3680 0.9230
1.482069 0.1513
0.675889 0.104628 6.459951
0.0000
0.4305 0.2851
1.510211 0.1440
0.869548
2007q1 to 2010q1 -0.2957 0.7022
-0.421083
0.6836
3.2137 0.9993
3.215809 0.0106
-0.164088 0.391832
-0.418770
0.6852
0.3756 0.5380
0.698182 0.5027
0.834607
1981q3 to 2010q1 -0.5904 0.1933
-3.054384 0.0029
0.7757 0.3171
2.446020 0.0161
0.775954 0.042863 18.10310
0.0000
0.2237 0.0461
4.854514 0.0000
0.963904
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
166
Table 6.5 Estimations of the Hybrid New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for Inflation Expectations and the Output Gap as Proxy for Real Marginal Cost
Equation estimated 1 4t t b t � t tmc E
Sample Period Constant b
� 2�
1981q3 to 1989q4 -0.9182 0.5280
-1.739173 0.0923
0.2758 0.0999
2.762122 0.0097
0.799240 0.110072 7.261072
0.0000
0.3712 0.1894
1.960555 0.0593
0.926455
1990q1 to 1999q4 -0.4214 0.1713
-2.459413 0.0189
0.0919 0.0416
2.208255 0.0337
0.903203 0.057779 15.63208
0.0000
0.2107 0.0895
2.354100 0.0241
0.970841
2000q1 to 2010q1 -0.4110 0.3972
-1.034748 0.3075
0.0380 0.0192
1.976669 0.0556
0.681112 0.101147 6.733852
0.0000
0.4628 0.2147
2.155235 0.0377
0.821313
2000q1 to 2006q4 -0.4471 0.4653
-0.960826 0.3462
0.0613 0.0288
2.130960 0.0435
0.744609 0.102484 7.265629
0.0000
0.4266 0.2486
1.716395 0.0990
0.880264
2007q1 to 2010q1 0.8138 1.1800
0.689636
0.5078
0.0566 0.0358
1.582904
0.1479
0.627154 0.394539 1.589590
0.1464
-0.0505 0.7729
-0.065371 0.9493
0.721967
1981q3 to 2010q1 -0.1211 0.0703
-1.722091 0.0881
0.0403 0.0164
2.452957 0.0158
0.805069 0.042399 18.98776
0.0000
0.2151 0.0465
4.622393 0.0000
0.963915
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
167
Table 6.6 Estimations of the Hybrid New Keynesian Phillips Curve Using the SPF Forecasts as Proxy for Inflation Expectations and Labour’s Share of Income as Proxy for Real Marginal Cost
Equation estimated 1 4t t b t � t tmc E
Sample Period Constant b
� 2�
1981q3 to 1989q4 56.7864 45.4168
1.250338 0.2208
-12.5568 9.8595
-1.273570 0.2126
0.728683 0.128769 5.658845
0.0000
0.4989 0.1997
2.497595 0.0182
0.912483
1990q1 to 1999q4 -32.9549 17.0106
-1.937311 0.0606
7.0883 3.7057
1.912805 0.0638
0.751092 0.075714 9.920127
0.0000
0.3411 0.0993
3.434469 0.0015
0.969946
2000q1 to 2010q1 -0.4755 5.1272
-0.092751 0.9266
-0.0782 1.1696
-0.066877 0.9470
0.670644 0.106370 6.304825
0.0000
0.6534 0.2297
2.844938 0.0072
0.802468
2000q1 to 2006q4 7.1594 6.8504
1.045113 0.3064
-1.8025 1.5176
-1.187757 0.2466
0.708663 0.106361 6.662810
0.0000
0.7390 0.2324
3.179431 0.0040
0.865514
2007q1 to 2010q1 -63.2481 23.8872
-2.647780
0.0266
14.1322 5.3664
2.633443
0.0272
-0.446487 0.528591
-0.844674
0.4202
0.9198 0.6147
1.496290 0.1688
0.799252
1981q3 to 2010q1 -4.8228 4.5227
-1.066361 0.2888
1.0292 0.9958
1.033516 0.3038
0.785246 0.044091 17.80958
0.0000
0.2269 0.0475
4.780299 0.0000
0.962199
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
6.3 Tests for Structural Changes
��a�dt�A�drews �rea�poi�t �est �or ����ow� �tr�ct�ral �rea�poi�ts
We will now formally test for structural changes. Our first objective is to determine
when the structural changes took place and attempt to explain the breakpoints. We use the
Quandt-Andrews breakpoint test for one or more unknown structural breakpoints (trimming
15 percent of the data). The Quandt-Andrews test performed a Chow breakpoint test at every
observation between two dates. The point in the series with the highest Likelihood Ratio F-
statistic and the Wald F-statistic determines the breakpoint.
168
Table 6.7 Quandt-Andrews Unknown Breakpoint Tests
Proxy for Real Marginal Cost Maximum LR F-statistic (1975Q3) Maximum Wald F-statistic (1975Q3)
Output Gap 1.320277 0.0443
9.108471 0.0011
Job Finding Probability 4.707637
0.0184
18.83055
0.0184
Labour’s Share of Income 5.195267 0.0084
20.78107 0.0084
Note: The above Quandt-Andrews unknown breakpoint tests were conducted over the 1961q1 to 2010q1 period using quarterly data. The maximum LR F-statistics and maximum Wald F-statistics are associated with the null hypothesis of no breakpoints within 15% trimmed data. P-values are shown in the second row.
The Quandt-Andrews breakpoint tests indicate that a structural break occurred in
1975q3. It is interesting that three proxies for real marginal cost suggest the same break point
date. Fig. 6.3 plots the unemployment rates (percentages) and the average duration of
unemployment (weeks) over the 1948M02 to 2010M08 period. Note that the average
duration of unemployment series is trending upward while the unemployment rate series is
relatively flat and this phenomenon started at about 1975q3. It is also interesting that the
Quandt-Andrews breakpoint tests did not detect the 1973 oil crisis and the 1979 change in
policy at the Federal Reserve, which helped to end the stagflation crisis of the 1970s.
�how �est �or �tr�ct�ral �rea�s
We will now use the Chow tests for structural breaks to confirm the results from the
Quandt-Andrews tests. The results of the Chow breakpoint tests below (Table 6.8) support
the Quandt-Andrews tests that a structural break occurred in 1975q3.
Table 6.8 Chow Breakpoint Tests:1975Q3
Proxy for Real Marginal Cost F-Statistic Log Likelihood Ratio Wald Statistic
Output Gap 6.895918 0.0000
26.83380 0.0000
27.58367 0.0000
Job Finding Probability 4.707637 0.0012
18.70974 0.0009
18.83055 0.0008
Labour’s Share of Income 5.195267 0.0005
20.54947 0.0004
20.78107 0.0003
Note: The above Chow Breakpoint Tests were conducted over the 1961q1 to 2010q1 period using quarterly
data. The F-statistics, Log likelihood ratio and Wald statistics are associated with the null hypothesis of no break at specified breakpoint (1975Q3). P-values are shown in the second row.
169
�ests �or �tr�ct�ral �ha�ges i� the ��brid �ew �e��esia� Phillips ��r�e �si�g ��mm�
�ariable
The Quandt-Andrews and Chow tests suggest that there was a structural change in
1975q3. However, these tests do not tell us whether the difference in the two regressions was
because of differences in the intercept terms or the slope coefficients or both. An alternative
to the Chow test is to use dummy variable. The source of difference, if any, can be identified
by pooling all the observations and running the regression below. Note that is the
differential intercept, it enables us to distinguish between the intercepts of the two periods. is the differential slope coefficient, it enables us to differentiate between slope coefficients of
the two periods (Gujarati, 2003, pp.307-310).
1 4t t t b t � t t t tc � mc E �mc (6.1)
where:
t Core Inflation
tmc Real Marginal Cost
4t tE Expected Inflation (proxies by the Michigan survey of inflation expectations)
D = 1 for observations from 1975q4-2010q1
D = 0 for observations from 1961q1–1975q3
Table 6.9 Tests for Structural Changes in the Hybrid New Keynesian Phillips Curve Using Dummy Variable
Equation estimated 1 4t t b t � t t tc � mc E �mc
Proxy for Real Marginal Cost
� b �
2
�
Job Finding Probability
-0.667989 0.453953
-1.471494 0.1428
-0.353221 0.513545
-0.687809 0.4924
1.021034 0.941100
1.084937 0.2793
0.825411 0.020627
40.01557 0.0000
0.213947 0.024863
8.605054 0.0000
0.709169 1.114729
0.636181 0.5254
0.972412
Output Gap
-0.221846 0.087909
-2.523578 0.0124
-0.178901 0.066875
-2.675144 0.0081
-0.067068 0.087806
-0.763819 0.4459
0.825851 0.024831 33.25921
0.0000
0.224169 0.029025 7.723267
0.0000
0.125140 0.087694 1.427014
0.1552
0.971839
Labour’s Share of Income
-36.75893 16.79266
27.47709 17.79136
7.907594 3.633986
0.814302 0.022694
0.225078 0.024436
-5.967277 3.849310
0.971994
170
-2.188988 0.0298
1.544406 0.1242
2.176011 0.0308
35.88178 0.0000
9.211059 0.0000
-1.550220 0.1228
Note: The above equations were estimated (OLS) over the1961q2 2010q1period using quarterly data. Standard
errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The Michigan survey of inflation expectations was used as proxy for expected inflation.
The differential intercept coefficient is statistically insignificant for job finding
probability and labour’s share of income but is significant for the output gap; we can accept
the hypothesis that the two regressions have the same intercept for job finding probability and
labour’s share of income but not for the output gap before and after the break date (1975q3).
The differential slope coefficient b is statistically insignificant for all three proxies for real
marginal cost; we can accept the hypothesis that the two regressions have the same slope
before and after the break date (1975q3).
We have also tested for structural changes in the hybrid new Keynesian Phillips curve
using dummy variables7 that correspond to each decade from 1961q1 to 2010q1. In general,
when labour’s share of income is used as proxy for real marginal cost, the intercepts and the
slopes of the hybrid new Keynesian Phillips curve are different for the 1970s and 1980s.
When the output gap is used as proxy for real marginal cost, the intercept of the hybrid new
Keynesian Phillips curve is different for the 1970s, the slope of the hybrid new Keynesian
Phillips curve is different for the 1980s. When job finding probability is used as proxy for
real marginal cost, the differential intercept coefficient and differential slope coefficient are
statistically insignificant in all five decades. The results of this exercise are presented in the
appendix of this chapter.
6.4 Competing Explanations
In recent years, a number of empirical studies such as: Roberts (2006), Williams
(2006), Ihrig, Kamin, Linder and Marquez (2007), Mishkin (2007), Kuttner and Robinson
(2006), Binyamini and Razin (2007) and Beaudry and Doyle (2000) report that the slope of
the reduced form Phillips curve for the United States has flattened over the last 20 years, this
phenomenon is also observed in many other industrialized countries. However, there is no
consensus regarding what explains this phenomenon, many of the proposed explanations can
be broadly categorized as: globalization and improvements in the conduct of monetary
policy.
7I thank an anonymous examiner for suggesting the use of dummy variables to test for structural changes.
171
�lobalisatio� a�d ���latio�
The dramatic decline in the slope of the reduced form Phillips curve for the United
States (and in other industrialized countries) over the last 20 years is one of the most
remarkable developments in the nature of the inflation process. To what extent has
globalisation affected the nature of the inflation process? There is a rapidly growing body of
empirical literature examining this question.
Globalisation is generally referred to the integration of national economies into the
international economy through the increase in openness to trade, immigration and the spread
of scientific ideas and technology. Below are some of the channels that globalisation may
have affected the nature of the inflation process, providing potential explanations for the
flattening of the short-run trade-off between inflation and the domestic output gap (real
marginal cost). First, the increased trade associated with globalisation reduces importance of
domestic gaps and increased the importance of the rest of the world demand and supply
(global gaps) in explaining inflation dynamics of individual countries because import prices
become more important in domestic inflation. Borio and Filardo (2006) find empirical
evidence for this proposition across a range of countries. However, Ihrig et al (2007) and Ball
(2006) find only weak evidence that import prices affect domestic inflation.
Second, increase in competition among workers in the labour market due to
migration and out sourcing to China and India implies that wages are likely to be less
sensitive to the state of the business cycle. Workers are less likely to demand higher wages
when unemployment falls, reducing the effect of higher economic activity on the marginal
cost of labour. Third, increase in competition between domestic firms and a foreign firm in
the product market make domestic firms less able to raise their prices when domestic demand
increases, if foreign firms do not. This implies that the domestic output gap becomes less
important in determining domestic inflation. Iakova (2006) of the IMF and Borio and Filardo
(2006) argues that globalisation, in the form of increased openness to trade is the cause of
flattening of the Phillips curve, but other authors such as Ihrig et al (2007), Kohn (2006) and
Ball (2006) find little evidence of the increase in importance of the foreign or global output
gap relative to the domestic output gap. Rogoff (2003, 2006) argues that globalization should
make the Phillips curve steeper, rather than flatter. This is because increase in competition
makes wages and prices more flexible, it also encourages businesses to revise their prices
more frequently, which tend make the Phillips curve steeper. Contrary to Rogoff’s argument,
172
Iakova (2006) of the IMF argues that that globalization flattens the Phillips curve because
increases in competition make it hard for firms to raise prices.
Since Borio and Filardo (2006) find strong empirical evidence supporting the
argument that globalisation reduces importance of domestic gaps and increased the
importance of the rest of the world demand and supply (global output gaps) in explaining
inflation dynamics and the paper has received widespread attention, we will briefly review
this paper.
Borio and Filardo (2006) augment a mainstream model of inflation to include the
foreign or global output gaps
1 1
� � �
t t t t tc �ap �ap (6.2)
where t is the inflation rate, � is the underlying inflation rate trend (used largely as a proxy
for slowly changing inflation expectations),��ap is the domestic output gap and is a
random error. ��ap is the global output gap or a global measure of economic slack.
Borio and Filardo (2006, p.32) examines 17 industrialized countries for the period
1985-2005, their results show in 16 out of 17 countries examined, the global gaps have larger
effects on inflation than the domestic gaps. With respect to the United States, the domestic
output gap is negative and statistically insignificant.
Ball (2006, p.6) questions the logic of this argument. “In mainstream theories, output
affects inflation because it affects firms’ marginal costs. Rises in marginal cost are passed
through into higher prices. Marginal costs for a country’s firms depend on their own output
levels, not foreign output... Higher domestic output still raises marginal cost and hence prices.
For globalization to dampen this effect, it would have to somehow cause countercyclical
movements in mark-ups. I don’t see a reason to expect this outcome”.
Ihrig et al (2006) argue that Borio and Filardo (2006) results are not robust. Ihrig et al
(2006, p.13) change the country weights used by Borio and Filardo (2006) to construct the
global output gaps, their results show that global gaps do not have larger effects on inflation
than the domestic gaps.
“We find the coefficient on the foreign output gap to be positive and significant in
only five of the 14 industrial economies considered. This discrepancy reflects the fact
that our estimates of the foreign output gap for each individual country differ from the
Borio-Filardo estimates”.
173
�mpro�eme�ts i� the �o�d�ct o� �o�etar� Polic�
A complementary explanation for the flattening of the reduced form Phillips curve is
improvements in the conduct of monetary policy. Roberts (2006, p. 195) argues that changes
in monetary policy can provide an explanation for the reduction in the slope of the reduced-
form Phillips curve and for a large portion of the reduction in the volatility of output gap.
Since the early 1980s the monetary authorities in the U.S. have been more aggressive against
increases in inflation, generating greater monetary policy credibility, which help to anchor
inflation expectations. Ball, Mankiw, and Romer (1988) argue that more-stable inflation may
lead less-frequent wage and price adjustments, which also reduce in the slope of the reduced-
form hybrid new Keynesian Phillips curve.
While it is possible that more-stable inflation may lead less-frequent wage and price
adjustments, which flattens the Phillips curve. It is unlikely that this is sufficient to explain
the flattening of the Phillips curve; this is because higher domestic output raises marginal cost
and hence prices, when a firm decides to keep prices unchanged, it would be very costly for
the firm that is making this decision.
6.5 The Labour Market and the Slope of the Phillips Curve
In this section we will attempt to argue that part of the reason why the slope of the
reduced form Phillips curve for the United States has flattened over the last 20 years is
because of increase in specialization of labour. As the rationale behind each of these
arguments are very different, we can not think of a direct way of testing which argument is
correct, it is very plausible that all of the three arguments mentioned above are partly
responsible for causing of the flattening of the Phillips curve. In addition, our task is further
complicated by the fact the signs and magnitudes of the slope of the reduced form Phillips
curve depend on which measure of inflation expectations are used and which measures of real
marginal cost are used.
Our argument that the increase in specialization of labour as a possible cause for the
flattening of the reduced form Phillips curve is based on the observations that the average
duration of unemployment has been increasing since 1970 and the probability of finding a job
after 15 weeks of unemployment has been decreasing since 1970, this about the same time
that deindustrialization started in the United States.
174
Fig. 6.1Average duration of unemployment, monthly data from 1948M01 to 2010M08.
Fig. 6.2 The probability of finding a job after 15 weeks of unemployment, quarterly data from 1961q1 to 2010q1.
Deindustrialization refers to the decrease in the output of manufactured goods and
employment in the manufacturing sectors and the increase in the output of services and
employment in the service sectors. There is a large body of literature on the costs and benefits
of deindustrialization and its implications for international trade which we will not discuss
5
10
15
20
25
30
35
40
194
8 -
M01
195
0 -
M07
195
3 -
M01
195
5 -
M07
195
8 -
M01
196
0 -
M07
196
3 -
M01
196
5 -
M07
196
8 -
M01
197
0 -
M07
197
3 -
M01
197
5 -
M07
197
8 -
M01
198
0 -
M07
198
3 -
M01
198
5 -
M07
198
8 -
M01
199
0 -
M07
199
3 -
M01
199
5 -
M07
199
8 -
M01
200
0 -
M07
200
3 -
M01
200
5 -
M07
200
8 -
M01
201
0 -
M07
Average Weeks Unemployed
.3
.4
.5
.6
.7
.8
.9
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Job Finding Probability (JFP)
175
here, as it is beyond the scope of this chapter. Our main interest in the process of
deindustrialization is the changes in the skills and knowledge of workers that are required
when employment shift from the manufacturing sectors to the service sectors that
deindustrialization embodied. According to the Bureau of Labour Statistics (BLS)
(http://www.bls.gov/spotlight/2008/around_the_world/). “In the United States, the share of
employment in services increased from about 60 percent in 1965 to 79 percent in 2005. In
contrast, the share of U.S. employment in manufacturing decreased from 27 percent to about
12 percent. This employment shift from manufacturing to services seen in the United States is
also seen in countries around the world”.
Our hypothesis is the shift in employment from the manufacturing sectors to the
service sectors and the changes in skills and knowledge that is associated with this change
increase the number of mismatches between unemployed workers and vacancies, increasing
the level of real rigidities in the labour market, reducing the inflation-output tradeoffs and
reducing the slope of the Phillips curve, in other words inflation is less responsive to changes
in real marginal cost.
Cao (2008, pp. 30-41) presents a search and matching model due to Romer (2001)
which is re-interpreted with an emphasis on the role of asymmetric knowledge and the sticky
nature of knowledge as the main source of frictions in the labour market. In this model i
k
represents the probability of an unemployed worker finding another job without having to be
retrained because of heterogeneity between workers and jobs’ skill requirements. As an
aggregate variable, K captures the extent of specialization of labour, which leads to
mismatch problems in the labour market, potentially helping us to explaining involuntary
unemployment. In addition some frictions are also generated by informational imperfections
about the timing of job creation in different locations and by the slow mobility of the
production factors. Empirical studies have shown that jobs destruction appears to be much
more variable than job creation. That is, the fall in employment in recessions stem mainly
from increases in the loss of existing jobs and only to a small extent from decreases in the
creation of new jobs, ((Blanchard and Diamond, 1990; Davis and Haltiwager,
1990,1992,1999)). The dynamics of the economy is such that there is a high turnover of jobs.
In US manufacturing, at least 10% of existing jobs disappearing each year (Davis and
Haltiwager, 1990, 1992, quoted in Romer (2001, p.452)). The high turnover of jobs and the
cyclical variations in turnover implies some unemployed workers will not be able to find
employment in the same profession. These unemployed workers will have to be retrained in
176
order to find employment in another profession and since much of professional knowledge
cannot be transferred easily, the process of education and training can be very lengthy,
typically, from one to three years as indicated by the durations of vocational and university
courses. Unemployed workers that have difficulties in changing to another profession will
suffer long-term unemployment; in addition their existing skills and knowledge may decay or
become obsolete. Furthermore, unemployment is complicated by the effects of aging on
learning, as people become older, their ability to absorb new knowledge decreases and also
differences in natural abilities, which make acquiring certain skills and knowledge difficult
(Cao, 2008, pp. 33-34).
One of the most significant changes in the labour market in the last forty years that
could provide further support for the notion that increases in specialization of labour is the
use of computer technology in the workplace and in the production process; computer
technology has created entirely new products and services, altering the way firms producing
existing products, the way that it communicates with its staff and customers. These changes
require workers to upgrade their skills and knowledge and to acquire new skills and
knowledge. As a consequence of these changes, the skills and knowledge of workers are
much more diverse than before the computer revolution. The increase in heterogeneity
between workers will inevitably leads to more mismatches in the labour market, this change
is capture by Job Finding Probability (JFP), the plot of JFP over time shows that the
probability of an unemployed worker finding another job after fifteen weeks of
unemployment has decrease over the past forty years, suggest the real rigidities in the labour
market has increased in the past forty years.
Since our results from Table 1-Table 6 and Table 9-Table11 indicate that job finding
probability is marginally a better proxy for real marginal cost than the output gap and
labour’s share of income when the hybrid new Keynesian Phillips curve is estimated, this
result is robust independent of which survey measures of inflation expectations are used. We
will briefly return to this issue by examining the correlations of the three proxies for real
marginal cost with inflation and unemployment. The results shown in the table below indicate
potential problems with using the output gap and labour’s share of income as proxy for real
marginal cost. Note that the correlation between core CPI and the output gap (-0.007891) has
the wrong sign and the correlation between unemployment and labour’s share of income
(-0.012243) has the correct sign but it is very weak. In contrast, job finding probability’s
correlations with the output gap and labour’s share of income are relative strong.
177
Table 6.10 Correlation Matrix of Three Proxies for Real Marginal Cost with Inflation and Unemployment
Core CPI
Job Finding
Probability Output Gap
Labour’s Share of
Income Unemployment
Core CPI 1.000000 0.282482 -0.007891 0.483455 0.333555
Job Finding Probability 0.282482 1.000000 0.489600 0.626852 -0.644585
Output Gap -0.007891 0.489600 1.000000 0.002727 -0.583569
Labour’s Share of Income 0.483455 0.626852 0.002727 1.000000 -0.012243
Unemployment 0.333555 -0.644585 -0.583569 -0.012243 1.000000
Note: The correlation matrix was computed using quarterly data from 1961q1 to 2010q1.
A useful way to picture the changes in the labour market in the past forty years is to
plot the unemployment rates and the average duration of unemployment over time. Both the
unemployment rates and the average duration of unemployment are counter cyclical and
should rise and fall over the business cycle together. Fig. 6.1 plots the unemployment rates
(percentages) and the average duration of unemployment (weeks) over the 1948M02 to
2010M08 period. As expected both the unemployment rates and the average duration of
unemployment are counter cyclical, they rise and fall over the business cycle together.
178
Fig. 6.3 Changes in the unemployment rates and average duration of unemployment over time, monthly data from1948M01 to 2010M08.
Fig. 7.4 The difference between the average duration of unemployment series and the unemployment rate series, monthly data from1948M01 to 2010M08.
In principle, when the unemployment rates are high, it is more difficult for
unemployed workers to find jobs; as a result the corresponding average durations of
unemployment are higher. This pattern can be observed in Fig. 6.3, it also appears the
0
4
8
12
16
20
24
28
32
36
50 55 60 65 70 75 80 85 90 95 00 05 10
Unemployment RateAverage Weeks Unemployed
0
4
8
12
16
20
24
28
50 55 60 65 70 75 80 85 90 95 00 05 10
Average Weeks Unemployed - Unemployment Rate
179
unemployment rate series leads the average duration of unemployment series by about a year.
The most puzzling aspect about Fig. 6.3 is that the average duration of unemployment series
is that it is trending upward while the unemployment rate series is relatively flat.
Alternatively, if the unemployment rates are not increasing over time, then why is it taking
longer for unemployed workers to find jobs? Fig. 6.4 is the difference between the average
duration of unemployment series and the unemployment rate series. There is no structural
relationship between the two series as the average duration of unemployment series is
measured in weeks and the unemployment rate series is measured in percentages. Our
objective is to examine the increases in the average duration of unemployment over time
taking on to account changes in the rates of unemployment over time. Fig. 6.4 shows the
differences between the series have increased over time; note the every consecutive peak is
higher than the previous peaks since 1970. It is also interesting to note that the plot of the
probability of an unemployed worker finding another job after fifteen weeks of
unemployment (Fig. 6.5) has decrease over the past forty years.
Fig. 6.5 The probability of finding a job after 15 weeks of unemployment (JFP), monthly data from 1948M01 to 2010M08.
Table 6.8 below presents the correlations between the unemployment rates (U), job
finding probability (JFP) and the average duration of unemployment (ADU) over time, our
objective is to examine changes in the labour market from 1948M02 to 2010M08. Note that
.1
.2
.3
.4
.5
.6
.7
50 55 60 65 70 75 80 85 90 95 00 05 10
Job Finding Probability (JFP)
180
job finding probability is highly correlated with the unemployment rates, in all of the sub-
sample periods except for the 1990M01-1999M12 sub-sample period the, job finding
probability and the unemployment rates are strongly (negatively) correlated, the correlation
between job finding probability and the unemployment rates for the full sample period is (-
0.725110) considerably smaller than that of the five sub-sample periods presented below, the
reason why the full sample period is considerably smaller is because of the 1990M01-
1999M12 sub-sample period (-0.551872) is not as strongly correlated .
Table 6.11 Correlations between the Unemployment Rates (U), Job Finding Probability (JFP) and the Average Duration of Unemployment (ADU) Over Time.
1948m02-1959m12 U JFP ADU
U 1.000000 -0.904210 0.655632
JFP -0.904210 1.000000 -0.719688
ADU 0.655632 -0.719688 1.000000
1960m01-1969m12 U JFP ADU
U 1.000000 -0.950548 0.913184
JFP -0.950548 1.000000 -0.914924
ADU 0.913184 -0.914924 1.000000
1970m01-1979m12 U JFP ADU
U 1.000000 -0.939867 0.827902
JFP -0.939867 1.000000 -0.818318
ADU 0.827902 -0.818318 1.000000
1980m01-1989m12 U JFP ADU
U 1.000000 -0.945308 0.658850
JFP -0.945308 1.000000 -0.692156
ADU 0.658850 -0.692156 1.000000
1990m01-1999m12 U JFP ADU
U 1.000000 -0.551872 0.456313
JFP -0.551872 1.000000 -0.831802
ADU 0.456313 -0.831802 1.000000
2000m01-2010m08 U JFP ADU
U 1.000000 -0.933880 0.889543
JFP -0.933880 1.000000 -0.877470
181
ADU 0.889543 -0.877470 1.000000
1948M02-2010M08 U JFP ADU
U 1.000000 -0.725110 0.639816
JFP -0.725110 1.000000 -0.874810
ADU 0.639816 -0.874810 1.000000
Note: Monthly Data from 1948M01 to 2010M08.
�������������������������������k�������������i��i��������������i����i��i�������������
The Phillips curve relationship predicts that inflation rises when the labour market
tightens, this relationship appears to have broken down in the 1990s (Brayton, Roberts, and
Williams, 1999) due to the information technology revolution, which allows goods and
services to be produced more cheaply, dramatically increasing economic productivity,
producing a deflationary environment. The three graphs below show what happened to the
labour market and the Phillips curve relationship during the economic expansion of the1990s.
Fig. 6.6 shows that the unemployment rate fell while core inflation (Fig. 6.7) and labour’s
share of income (Fig. 6.8) fell in the 1990s. These empirical data are at odds with the Phillips
curve relationship. Our results also show (Table 6.8) that in the last decade (2000M01-
2010M08) the Phillips curve relationship appears to resume its normal pattern.
Fig. 7.6 Unemployment rate, quarterly data from 1961q1 to 2010q1.
3
4
5
6
7
8
9
10
11
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Unemployment
182
Fig. 6.7 Core CPI, quarterly data from 1961q1 to 2010q1.
Fig. 6.8 Labour’s share of income, quarterly data from 1961q1 to 2010q1.
.00
.02
.04
.06
.08
.10
.12
.14
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Core CPI
4.48
4.52
4.56
4.60
4.64
4.68
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Labour's Share of Income
183
6.6 Conclusion
We have presented evidence of the flattening of the Phillips curve using job finding
probability, the output gap and labour’s share of income as proxies for real marginal cost.
Our results confirmed previous of empirical studies that the slope Phillips curve for the
United States has become much smaller over the past 20 years.
We have also examined some of the competing explanations given for why this has
occurred. Currently, there is no consensus regarding what explains this phenomenon, many of
the proposed explanations can be broadly categorized as: globalization and improvements in
the conduct of monetary policy. We believe that structural changes in the labour market in the
past forty years can partly account for this phenomenon. Our view is that deindustrialization
and the computer revolution have shifted employment from the manufacturing sectors to the
service sectors; these structural changes in the labour market have changed jobs’ skill
requirements, increasing heterogeneity (real rigidities) between workers, producing more
mismatches in the labour market. Increase in the division of labour implies that it would take
longer for unemployed workers to be retrained in order to find employment in another
profession and since much of professional knowledge cannot be transferred easily, the
process of education and training can be very lengthy, this is reflected by the fact that the
average duration of unemployment has been increasing since 1970 and the probability of
finding a job after 15 weeks of unemployment has been decreasing since 1970, this about the
same time that deindustrialization started in the United States. In other words, inflation is less
responsive to changes in real marginal cost, because of increase in the level of real rigidities
in the labour market, reducing the inflation-output tradeoffs and reducing the slope of the
reduced form Phillips curve.
The findings that inflation has become less responsive to real marginal cost is
generally interpreted as a positive output / unemployment gap would be less inflationary, but,
the cost of reducing inflation would be greater (Mishkin 2007. p.5).
“The finding that inflation is less responsive to the unemployment gap, suggests that
fluctuations in resource utilization will have smaller implications for inflation than
used to be the case. From the point of view of policymakers, this development is a
two-edged sword: On the plus side, it implies that an overheating economy will tend
to generate a smaller increase in inflation. On the negative side, however, a flatter
Phillips curve also implies that a given increase in inflation will be more costly to
wring out of the system”.
184
The stylized fact that inflation has become less responsive to the output /
unemployment gap can lead to inappropriate policy recommendations. For example, the
above interpretations suggest that policymakers could respond less to shocks as inflation is
likely to remain at a low level. Similarly, policymakers may think that reducing inflation is
very costly because it causes extended periods of high unemployment. However, if the
monetary authorities were to become complacent about high inflation then inflation
expectations would raise as the monetary authorities’ credibility erode. This is because the
actual causes of the flattening of the Phillips curve are structural changes in the labour market
have changed jobs’ skill requirements, increasing heterogeneity between workers, producing
more mismatches in the labour market. The policy recommendations of our approach are
monetary authorities should continue to be aggressive against high inflation and try to reduce
unemployment by focusing on providing more flexible education and retraining to
unemployed workers in order to reduce the number of mismatches in the labour market.
185
6.7 Appendix to Chapter 6
Table 6.12 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for Inflation Expectations and with Job Finding Probability as Proxy for Real Marginal Cost
Equation estimated 1 4� � � � � � ��� �
Sample Period Constant �
� 2�
1974q2 to 1979q4 -0.3478 2.1697
-4.769196 0.0001
16.2519 3.4424
4.721147 0.0001
0.964604 0.081229 11.87507
0.0000
-0.1885 0.1585
-1.189475 0.2489
0.902782
1980q1 to 1989q4 -2.5445 1.2766
-1.993109 0.0539
2.8166 1.8007
1.564171 0.1265
0.688868 0.063846 10.78946
0.0000
0.4637 0.1015
4.569802 0.0001
0.963142
1990q1 to 1999q4 -0.9249
0.4397 -2.103604
0.0425
1.1904
0.6466 1.840892
0.0739
0.900403
0.042131 21.37166
0.0000
0.1440
0.0594 2.424464
0.0205
0.971489
2000q1 to 2004q4 -0.7239 0.4996
-1.449069 0.1666
1.4699 1.1635
1.263371 0.2246
0.715507 0.095620 7.482806
0.0000
0.2156 0.2362
0.912973 0.3748
0.912290
1974q2 to 2004q4 -2.0383
0.6129 -3.325868
0.0012
2.8926
0.9034 3.201940
0.0018
0.771316
0.036179 21.31939
0.0000
0.2721
0.0490 5.556442
0.0000
0.969977
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
186
Table 6.13 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for Inflation Expectations and the Output Gap as Proxy for Real Marginal Cost
Equation estimated 1 4� � � � � � ��� �
Sample Period Constant �
� 2�
1974q2 to 1979q4 -0.8595 1.3413
-0.640745 0.5293
-0.0255 0.2563
-0.099624 0.9217
0.792699 0.139144 5.696983
0.0000
0.4065 0.2578
1.576962 0.1313
0.788844
1980q1 to 1989q4 -0.5286 0.2683
-1.970005 0.0566
0.1063 0.1104
0.962960 0.3420
0.715227 0.082524 8.666881
0.0000
0.4327 0.1266
3.417682 0.0016
0.961625
1990q1 to 1999q4 -0.1764 0.1052
-1.677867 0.1020
0.0785 0.0424
1.851448 0.0723
0.926440 0.047156 19.64633
0.0000
0.1491 0.0584
2.555005 0.0150
0.971517
2000q1 to 2004q4 0.0653 0.2098
0.311427 0.7595
0.0645 0.0349
1.849142 0.0830
0.804781 0.096216 8.364295
0.0000
0.2432 0.1775
1.369877 0.1896
0.920525
1974q2 to 2004q4 -0.0756 0.0936
-0.807661 0.4209
0.0729 0.0525
1.389478 0.1673
0.769025 0.043109 17.83888
0.0000
0.3005 0.0554
5.426263 0.0000
0.967911
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
187
Table 6.14 Estimations of the Hybrid New Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy for Inflation Expectations and Labour’s Share of Income as Proxy for Real Marginal Cost
Equation estimated 1 4� � � � � � ��� �
Sample Period Constant �
�
2�
1974q2 to 1979q4 -196.1680 41.8839
-4.683617 0.0002
42.5845 9.1274
4.665557 0.0002
0.785903 0.074050 10.61317
0.0000
0.1821 0.1112
1.637214 0.1180
0.901538
1980q1 to 1989q4 -33.4202 46.2144
-0.723156 0.4743
7.1305 10.0367
0.710441 0.4820
0.611338 0.097587 6.264552
0.0000
0.5489 0.1152
4.763130 0.0000
0.961181
1990q1 to 1999q4 -28.3498 15.9048
-1.782465 0.0831
6.1664 3.4763
1.773820 0.0846
0.812334 0.057643 14.09257
0.0000
0.2237 0.0596
3.751342 0.0006
0.971313
2000q1 to 2004q4 13.9816 14.2646
0.980160 0.3416
-3.1186 3.1502
-0.989981 0.3369
0.780649 0.104514
7.469341 0.0000
0.5417 0.1719
3.151705 0.0062
0.909108
1974q2 to 2004q4 -30.3699 15.3652
-1.976539 0.0504
6.6019 3.3508
1.970267 0.0511
0.704955 0.038422 18.34751
0.0000
0.3415 0.0444
7.697371 0.0000
0.968420
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
188
Table 6.15 Tests for Structural Changes in the Hybrid New Keynesian Phillips Curve Using Dummy Variable
Equation estimated 1 1 4 1� � � � � � � �� � �� � ���
Proxy for Real Marginal Cost
� � �
2�
Job Finding Probability
-0.956100 0.203693
-4.693825 0.0000
0.241879 0.599811 0.403258
0.6872
1.508475 0.553349 2.726084
0.0070
0.829779 0.020103 41.27724
0.0000
0.214447 0.025289 8.479782
0.0000
-0.370907 1.223745
-0.303092 0.7622
0.972400
Output Gap
-0.423949 0.086889
-4.879195 0.0000
0.222078 0.085807 2.588108
0.0104
0.041591 0.030803 1.350214
0.1786
0.841395 0.022626 37.18675
0.0000
0.218488 0.027642 7.904101
0.0000
0.123182 0.201625 0.610949
0.5420
0.971607
Labour’s Share of Income
-12.71181 6.540321
-1.943606 0.0534
-6.548806 23.64840
-0.276924 0.7821
2.677197 1.429767 1.872471
0.0627
0.809474 0.022222 36.42745
0.0000
0.238260 0.024299 9.805554
0.0000
1.453413 5.121363 0.283794
0.7769
0.971861
Note: The above equations were estimated (OLS) over the1961q1 2010q1period using quarterly data. Standard
errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The Michigan survey of inflation expectations was used as proxy for expected inflation. 1
1� for
observations from 1961q1-1969q4. 1
0� for observations from 1970q1-2010q1.
189
Table 6.16 Tests for Structural Changes in the Hybrid New Keynesian Phillips Curve Using Dummy Variable
Equation estimated 2 1 4 2� � � � � � � �� � �� � � ��
Proxy for Real Marginal Cost
� � �
2�
Job Finding Probability
-1.029293 0.187037
-5.503145 0.0000
-0.097921 0.748133
-0.130887 0.8960
1.707787 0.430574 3.966306
0.0001
0.829194 0.022707 36.51741
0.0000
0.219421 0.028016 7.831925
0.0000
-0.005353 1.661376
-0.003222 0.9974
0.972517
Output Gap
-0.359523 0.087330
-4.116822 0.0001
-0.040215 0.091712
-0.438493 0.6615
0.056735 0.031936 1.776528
0.0772
0.826212 0.025676 32.17855
0.0000
0.228649 0.033625 6.799955
0.0000
-0.085229 0.078177
-1.090214 0.2770
0.970616
Labour’s Share of Income
-13.38052 6.219169
-2.151496 0.0327
-63.08480 23.28421
-2.709339 0.0074
2.838875 1.353643 2.097211
0.0373
0.820246 0.022817 35.94898
0.0000
0.222489 0.026595 8.365964
0.0000
13.61638 5.034599 2.704560
0.0075
0.972664
Note: The above equations were estimated (OLS) over the1961q1 2010q1period using quarterly data. Standard
errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The Michigan survey of inflation expectations was used as proxy for expected inflation. 2
1� for
observations from 1970q1-1979q4. 2
0� for observations from 1961q1-1969q4, 1980q1-2010q1.
190
Table 6.17 Tests for Structural Changes in the Hybrid New Keynesian Phillips Curve Using Dummy Variable
Equation estimated 3 1 4 3� � � � � � � �� � �� � ���
Proxy for Real Marginal Cost
� � �
2�
Job Finding Probability
-0.908526 0.175804
-5.167825 0.0000
-1.041934 0.683685
-1.523997 0.1292
1.464979 0.422976 3.463500
0.0007
0.836745 0.021996 38.04109
0.0000
0.205395 0.024559 8.363477
0.0000
2.446806 1.610797 1.519003
0.1304
0.972668
Output Gap
-0.334938 0.077657
-4.313035 0.0000
-0.048341 0.083994
-0.575524 0.5656
0.012863 0.032817 0.391972
0.6955
0.848895 0.024459 34.70676
0.0000
0.204064 0.027805 7.339038
0.0000
0.229085 0.069776 3.283130
0.0012
0.972033
Labour’s Share of Income
-19.44300 5.718131
-3.400236 0.0008
54.55742 21.73017 2.510676
0.0129
4.152396 1.246158 3.332158
0.0010
0.822545 0.023981 34.30004
0.0000
0.222929 0.024313 9.169288
0.0000
-11.82353 4.706097
-2.512385 0.0128
0.972338
Note: The above equations were estimated (OLS) over the1961q1 2010q1period using quarterly data. Standard
errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The Michigan survey of inflation expectations was used as proxy for expected inflation. 3 1� for
observations from 1980q1-1989q4. 3 0� for observations from 1961q1-1979q4, 1990q1-2010q1.
191
Table 6.18 Tests for Structural Changes in the Hybrid New Keynesian Phillips Curve Using Dummy Variable
Equation estimated 4 1 4 4� � � � � � � �� � �� � � ��
Proxy for Real Marginal Cost
� � �
2�
Job Finding Probability
-0.978865 0.182752
-5.356244 0.0000
-0.138367 0.713775
-0.193853 0.8465
1.629931 0.426163 3.824664
0.0002
0.828715 0.020061 41.31037
0.0000
0.210848 0.024309 8.673796
0.0000
0.399928 1.813380 0.220543
0.8257
0.972349
Output Gap
-0.314476 0.084674
-3.713978 0.0003
-0.023036 0.079905
-0.288295 0.7734
0.050917 0.032560 1.563818
0.1195
0.838875 0.023075 36.35360
0.0000
0.207027 0.028088 7.370592
0.0000
-0.010487 0.098100
-0.106902 0.9150
0.970426
Labour’s Share of Income
-17.29987 5.893691
-2.935321 0.0037
-19.93698 27.63748
-0.721375 0.4716
3.693002 1.283754 2.876722
0.0045
0.798081 0.021769 36.66195
0.0000
0.234441 0.024379 9.616683
0.0000
4.338571 6.012074 0.721643
0.4714
0.971470
Note: The above equations were estimated (OLS) over the1961q1 2010q1period using quarterly data. Standard
errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The Michigan survey of inflation expectations was used as proxy for expected inflation. 4 1� for
observations from 1990q1-1999q4. 4 0� for observations from 1961q1-1989q4, 2000q1-2010q1.
192
Table 6.19 Tests for Structural Changes in the Hybrid New Keynesian Phillips Curve Using Dummy Variable
Equation estimated 5 1 4 5� � � � � � � �� � �� � � ��
Proxy for Real Marginal Cost
� � �
2�
Job Finding Probability
-1.113176 0.256053
-4.347440 0.0000
0.258833 0.422148 0.613134
0.5405
1.926565 0.571570 3.370655
0.0009
0.835026 0.022030 37.90374
0.0000
0.205547 0.025007 8.219701
0.0000
-0.569215 1.116865
-0.509654 0.6109
0.972410
Output Gap
-0.252029 0.085363
-2.952446 0.0036
-0.117601 0.082191
-1.430833 0.1541
0.117646 0.047118 2.496855
0.0134
0.846135 0.025423 33.28247
0.0000
0.191797 0.029344 6.536083
0.0000
-0.115548 0.057688
-2.002967 0.0466
0.971401
Labour’s Share of Income
-19.13433 9.518616
-2.010201 0.0458
3.758474 13.54201 0.277542
0.7817
4.093617 2.069095 1.978457
0.0493
0.798684 0.021914 36.44677
0.0000
0.231792 0.024417 9.493055
0.0000
-0.821853 2.949270
-0.278663 0.7808
0.971406
Note: The above equations were estimated (OLS) over the1961q1 2010q1period using quarterly data. Standard
errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The Michigan survey of inflation expectations was used as proxy for expected inflation. 5 1� for
observations from2000q1-2010q1. 5 0� for observations from 1961q1-1999q4.
193
CHAPTER 7
Non-Stationary Inflation and the Phillips Curve
7.1 Introduction
This chapter argues that the finding that the United States inflation rates are non-
stationary8 does not necessarily invalidate a previous body of empirical research that did not
take into account the non-stationary behaviour of inflation. This chapter is structured as
follows: The first section examines if inflation and various proxies for real marginal cost and
various survey measures of inflation expectations are non-stationary. The second section
examines if inflation is cointergrated with these variables. The third section examines if
cointergration between inflation and various proxies for real marginal cost and inflation and
various survey measures of inflation expectations lead to spurious regression problems. The
fourth section concludes.
7.2 Time Series Properties of the Variables in the Phillips Curve
The standard new Keynesian Phillips curve builds on the pioneering work of Taylor
(1979, 1980), Rotemberg (1982) and Calvo (1983) has the form:
1[ ]� � � �� �� (7.1)
Inflation depends on expectations of future inflation and on real marginal cost. The
implication of this model is that inflation should be independent of its own lagged values.
This specification has often been criticized because it does not fit the data well; empirical
studies have shown that inflation can be predicted well from its own lagged value. Simple
regressions of inflation on its own lags have much higher 2� values than the NKPC in
equation (7.1). Furthermore, the coefficient of real marginal cost traditionally represented by
the output gap often has the wrong sign or is not statistically significant.
Before we formally test to see if various variables in the Phillips curve are non-
stationary we should anticipate what we expect to find. Economic theory suggests that
expected inflations should be able to track actual inflation “fairly closely” and the two
variables should have similar statistical properties, that is, if inflation is non-stationary then
we should expect survey measures of inflation expectations to be non-stationary. If actual
inflation and expected inflations are non-stationary, then we should expect that that the two
variables are cointergrated because there should be a long-run relationship between the two
variables. These predictions are made based on the assumption that survey measures of
8I thank an anonymous examiner for raising this point.
194
inflation expectations are “reasonably” accurate. In chapter 5 (section 5.2) of this thesis we
examined if survey measures of inflation expectations are consistent with predictions of
rational expectations. In general we found that all of the survey measures of inflation are not
perfectly rational.
Empirical evidence suggests that there is a relationship between inflation and real
marginal cost in the short-run but not in the long-run. Empirical studies show that vigorous
economic activities tend to cause inflation to rise; this is known as the acceleration
phenomenon. However, there is no relationship between inflation and real marginal cost in
the long-run. That is, there in no positive relationship between inflation and economic growth
in the long-run. Thus, if inflation and real marginal cost are non-stationary, the two variables
should not be cointergrated, as cointergration implies that there is a long-run relationship
between the two variables.
We use core CPI as our measure of inflation. We considered three proxies for real
marginal cost: output gap (GAP), labour’s share of income (LS) and job finding probability
(JFP) (see section 5.3 of this thesis). We have also used three survey measures of inflation
expectations so proxies for expected inflation: the Survey of Professional Forecasters (SPF),
which collects inflation expectations from economists who forecast for a living, the Michigan
Survey, which collects forecasts from consumers and the “Greenbook” forecasts, which are
produced by the research staff at the Board of Governors before each meeting of the Federal
Open Market Committee (FOMC). For more details about the three survey measures of
inflation expectations above, please refer to section 5.3 of this thesis and the data appendix at
the end of this chapter.
First we examine if inflation and various proxies for real marginal cost and survey
measures of inflation expectations are non-stationary. The results of the Augmented Dickey-
Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root
tests are reported in Table 7.1 below. All of the variables tested are first-order integrated I
(1), except for the output gap, which is stationary9.
9Culver and Papell (1997) using panel data unit root tests find that inflation is stationary.
195
Table 7.1 Unit Root Tests
Variable Sample Period ADF PP KPSS
� 1961Q1 - 2010Q1 -1.217887 -2.199186 0.478868**
� 1961Q1 - 2010Q1 -6.579304*** -8.207592*** 0.135901
��� 1961Q1 - 2010Q1 -6.282778*** -4.462408*** 0.019618
��� 1961Q1 - 2010Q1 -10.19951*** -10.28453*** 0.023994
��� 1961Q1 - 2010Q1 -1.333538 -1.181570 1.066906***
��� 1961Q1 - 2010Q1 -7.209865*** -12.97946*** 0.200256
�� 1961Q1 - 2010Q1 -0.690982 -0.632463 1.271203
�� 1961Q1 - 2010Q1 -15.30225*** -15.28659*** 0.161550
��������K 1983Q3 - 2004Q4 -1.605328 -1.290914 1.188939***
��������K 1983Q3 - 2004Q4 -11.10034*** -11.81995*** 0.187039
��� 1983Q3 - 2004Q4 -1.305676 -1.127290 1.101983***
��� 1983Q3 - 2004Q4 -11.47386*** -11.59578*** 0.047702
�������� 1983Q3 - 2004Q4 -2.951347** -2.729120* 0.964585***
�������� 1983Q3 - 2004Q4 -12.24768*** -12.79873*** 0.050326
Notes: *** Significant at 1%; **Significant at 5%; * Significant at 10%. The lags in ADF are selected with
Schwartz Information Criterion. The PP and the KPSS test statistics were computed using Newey-West
automatic bandwidth selection. The null hypothesis in the ADF and the PP tests are that the variables are non-
stationary and are reversed in the KPSS tests.
7.3 Tests for Cointegration
Table 7.2 presents the results of the Engle-Granger two step tests for cointegration.
The first step of this test involves running a regression of inflation on each variable, saving
the residuals. The second step tests the residuals to determine if it is stationary. The two
series are said to be cointegrated if the residual is itself stationary. The results of the
Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-
Shin (KPSS) unit root tests of various residual series are reported below. Inflation is
cointegrated with LS, GREENBOOK, SPF and MICHIGAN but not with JFP.
196
Table 7.2 Engle-Granger (EG) tests for Cointegration
���i����� Sample Period ��� PP K���
and �
��� 1961Q1 - 2010Q1 -2.506601 -2.372774 0.350030***
and LS� 1961Q1 - 2010Q1 -2.813170*** -3.024395** 0.249968
and GREENBOOK�
1983Q3 - 2004Q4 -4.148931*** -4.168483*** 0.249539
and SPF� 1983Q3 - 2004Q4 -3.186576** -4.133009*** 0.110301
and MICHIGAN�
1983Q3 - 2004Q4 -3.684830*** -3.714469*** 0.609870**
Notes: *** Significant at 1%; **Significant at 5%; * Significant at 10%. The lags in ADF are selected with
Schwartz Information Criterion. The PP and the KPSS test statistics were computed using Newey-West
automatic bandwidth selection. The null hypothesis in the ADF and the PP tests are that the variables are non-
stationary and are reversed in the KPSS tests.
As expected we found that actual inflation and the three survey measures of inflation
expectations are cointergrated, implying that there is a long-run relationship between actual
inflation and expected inflation. Our results also show that labour’s share of income and job
finding probability are first-order integrated I (1) and actual inflation is cointergrated with
labour’s share of income but not job finding probability. This implies that there is a long-run
relationship between actual inflation and job labour’s share of income, but there is no long-
run relationship between actual inflation and job finding probability. The finding that actual
inflation is cointergrated with labour’s share of income is not consistent with economic
theory and empirical evidence on monetary policy which suggest that there in no positive
relationship between inflation and economic growth in the long-run. This leads us to question
whether labour’s share of income is an appropriate proxy for real marginal cost.
7.4 Does Non-Stationary Inflation Invalidate Previous Research Findings?
Many empirical studies on the NKPC simply assume that inflation is stationary. Does
the finding that inflation is non-stationary invalidate previous research findings? The answer
to this question essentially depends on whether the cointergration between actual inflation
and expected inflation leads to spurious regression problem. A spurious regression refer to a
regression that seem to give a good fit and statistically significant relationship between
variables, but this relationship does not really exist. This problem was first recognized by
Yule in 1926. Hendry (1980) provides an example of spurious regression involving inflation;
197
he shows that cumulative rainfall in the UK provided an excellent statistical explanation of
inflation.
Granger and Newbold (1974, p.111) began their paper by observing that many
econometric studies tend to have very high 2� and very low Durbin-Watson (DW) statistics
(residuals are autocorrelated). They wanted to determine what could be inferred from these
regression results.
“It is very common to see reported in applied econometric literature time series
regression equations with an apparently high degree of fit, as measured by the
coefficient of multiple correlation 2� or the corrected coefficient
2� , but with an
extremely low value for the Durbin-Watson statistic. We find it very curious that
whereas virtually every textbook on econometric methodology contains explicit
warnings of the dangers of autocorrelated errors, this phenomenon crops up so
frequently in well-respected applied work. Numerous examples could be cited, but
doubtless the reader has met sufficient cases to accept our point. It would, for
example, be easy to quote published equations for which 2� = 0.997 and the Durbin-
Watson statistic (d) is 0.53. The most extreme example we have met is an equation for
which 2� = 0.99 and d = 0.093”.
Granger and Newbold (1974) then showed that the regression of two generated
random walks series can generate spurious regression results with very high 2� and very low
Durbin-Watson (DW) statistics. Granger and Newbold (1974, p.117) suggested that the DW
statistics could be used to identify spurious regressions, they argued that a low DW statistic is
a strong indication that the model is misspecified.
“It has been well known for some time now that if one performs a regression and
finds the residual series is strongly autocorrelated, then there are serious problems in
interpreting the coefficients of the equation. Despite this, many papers still appear
with equations having such symptoms and these equations are presented as though
they have some worth. It is possible that earlier warnings have been stated
insufficiently strongly. From our own studies we would conclude that if a regression
equation relating economic variables is found to have strongly autocorrelated
residuals, equivalent to a low Durbin-Watson value, the only conclusion that can be
reached is that the equation is mis-specified, whatever the value of 2� observed”.
198
Much of the empirical studies on the NKPC that do not take into account the time
series properties of inflation. However, the mains problems that applied macroeconomists
face regarding the NKPC are the opposite to the problems of spurious regressions (the model
fits the data but the theory doesn’t make sense). To many applied macroeconomists the
NKPC makes sense (has strong microfoundations and is consistent with the assumption of
rational expectations) but it does not fit the data well enough; the real marginal cost variable
often has the wrong sign or is not statistically significant (note that the coefficient of the
output gap has the wrong sign (-0.017298) below. Backward-looking inflation expectations
tend to dominate forward-looking inflation expectations. Furthermore, tests the rationality of
various survey measures of inflation expectations often indicates that survey measures of
inflation expectations are biased and inefficient (see chapter 5). Table 7.3 below presents the
results of the regressions of core inflation and various proxies for real marginal cost; note that
the 2� values are very low; there are no indications of spurious regression between core
inflation and various proxies for real marginal cost.
Table 7.3 Estimations of Core Inflation and Various Proxies for Real Marginal Cost
Equation Estimated � ��� �
Proxy for Real Marginal Cost
c 2�
Output Gap
4.001954 0.178681
22.39724 0.0000
-0.017298 0.156975
-0.110196 0.9124
0.000062
Job Finding Probability
1.185544 0.981961 1.207322
0.2288
6.766642 2.321302 2.915020
0.0040
0.041757
Labour’s Share of Income
-194.1364 25.69185
-7.556341 0.0000
43.00261 5.575876 7.712261
0.0000
0.233728
Note: The above equations were estimated (OLS) over the 1961q1 to 2010q1 period using quarterly
data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
Table 7.4 below presents the results of the regressions of core inflation and various
proxies for expected inflation. This table is the same as table 6.3, the results of our test for
unbiasedness in chapter 5. Note that the 2� values are reasonably high, but not as high as
(i.e. 0.99) some of the examples given by Granger and Newbold (1974, p.111) mentioned
199
above. The chi-square statistics are associated with the test for unbiasedness ( 0 1��� ).
Our results show that unbiasedness is rejected for all survey measures of inflation
expectations.
Table 7.4 Estimations of Core Inflation and Various Proxies for Expected Inflation
Equation Estimated �
� � ��
Survey Sample Period 2� 2
�����
SPF 1� �� 981Q3 2010Q1
-0.286400 0.146800
-1.950993 0.053600
1.103100 0.042800
25.793870 0.000000
0.855916 6.534639 (0.03810)
Greenbook 1� �� 1974Q2 2004Q4
0.435100 0.127700 3.406809 0.000900
1.055800 0.027000
39.129390 0.000000
0.926760
104.271400 ( 0.00000)
Michigan 4� �� 1981Q3 2010Q1
-0.886700 0.277200
-3.198671 0.001800
0.986400 0.061900
15.922160 0.000000
0.691691 125.953800 (0.00000)
SPF 4� �� 1981Q3 2010Q1
0.306300 0.164400 1.862752 0.065200
0.805300 0.044800
17.988780 0.000000
0.748033 65.224080 (0.00000)
Greenbook 4� �� 1974Q3 2004Q4
0.117100 0.205000 0.571358 0.568800
1.150800 0.046000
25.043340 0.000000
0.840519 64.676310 (0.00000)
Note: The above equations were estimated using Ordinary Least Square (OLS). Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row. Chi-squared statistics of null
hypothesis that 0 1��� and its p-values (in parentheses) are shown in the last column.
Table 7.5 below presents the hybrid new Keynesian Phillips curve estimated using
the Greenbook forecasts for over the next year as proxy for inflation expectations produces
relatively high 2� values; all coefficients of backward-looking and forward-looking inflation
expectations terms are statistically significant at 1% level. Durbin-Watson (DW) test
statistics in the second last column indicate that the residuals are not autocorrelated.
However, it is well known that if there are lagged dependent variables DW test statistics are
biased and therefore not valid. A more general test is the Breusch-Godfrey LM test which can
be used if there are lagged dependent variables. Note that the DW test and the LM test do not
200
directly test for spurious regressions; they test for autocorrelated in the residuals which
indicate if the equation is mis-specified. The LM tests indicate that the hybrid new Keynesian
Phillips curve is correctly specified, which implies that it is unlikely that there is spurious
regression problems in the hybrid new Keynesian Phillips curve.
Table 7.5 Estimations of the New Hybrid Keynesian Phillips Curve Using the Greenbook Forecasts as Proxy
for Inflation Expectations
Equation estimated 1 1� � � � � � ��� �
Proxy for Real Marginal Cost
Constant �
� 2� DW LM
Job Finding Probability
-0.176181 0.192467
-0.915379 0.3627
0.696364 0.537414 1.295767
0.1987
0.818194 0.035900 22.79122
0.0000
0.175051 0.036245 4.829656
0.0000
0.966453 1.732890 1.525448 (0.4664)
Output Gap
0.073622
0.070396 1.045828
0.2987
0.042883
0.026428 1.622649
0.1085
0.832989
0.036606 22.75522
0.0000
0.167755
0.036815 4.556729
0.0000
0.966831 1.765637 1.148143
(0.5632)
Labour’s Share of Income
-15.76281 8.293264
-1.900677 0.0609
3.455126 1.811325 1.907514
0.0600
0.792443 0.038237 20.72435
0.0000
0.192746 0.034035 5.663135
0.0000
0.967221 1.765039 1.260767 (0.5324)
Note: The above equations were estimated (OLS) over the 1983q3 to 2004q4 period using quarterly data.
Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row. Durbin-Watson (DW) test statistics are presented in the second last column. The Breusch-Godfrey LM test statistics associated with null hypothesis that there is no serial correlation and its p-values (in parentheses) are shown in the last column.
If there is spurious regression problem in the hybrid new Keynesian Phillips curve,
then the source of the problem is most likely to be due to the expected inflation variable,
because actual inflation and expected inflation are cointergrated. If that is the case, then
estimations of the hybrid new Keynesian Phillips curve should show very high 2� values, the
residuals are autocorrelated and the expected inflation variable should be highly statistical
significant. Our results shows that the 2� values are relatively high, but this is because
lagged inflation is highly correlated with actual inflation, note that backward-looking
inflation expectations dominate forward-looking inflation expectations independent of which
measures of real marginal cost are used. Furthermore, The LM test statistics in the last
201
column indicate that the residuals are not autocorrelated. In short, these results suggest that
spurious regression is not a problem in the hybrid new Keynesian Phillips curve.
In a paper on spurious regression called “Econometrics – Alchemy or Science?”
David Hendry (1980, p.390) warns of the flaws of regression analysis.
“Econometricians have their Philosophers’ Stone; it is called regression analysis and
is used for transforming data into “significant” results! Deception is easily practised
from false recipes intended to simulate useful findings and these are derogatively
referred to by the profession as “nonsense regressions”.
We have considered David Hendry’s (1980, p.390) warning of the flaws of regression
analysis. We are confident that the variables in the hybrid new Keynesian Phillips curve are
not “nonsense variables”. As mentioned in chapter 1, the main objectives of new Keynesian
economics are to derive Keynesian propositions with rational expectations and optimizing
behaviours, not just producing models that fit the data. The problem is the new Keynesian
Phillips curve is it does not includes lagged inflation as an explanatory variable; the NKPC
implies inflation is a purely forward variable; current inflation is proportional to real marginal
cost and expected inflation. It has been well known for some time now that lagged inflation
plays an important role in empirical inflation regressions; simple regressions of inflation on
its own lags have much higher 2� values than the NKPC. This has led some economists to
question the validity of the assumption of rational expectations and to provide a plausible
rationale for the inclusion of lagged inflation as an explanatory variable in the Phillips curve.
7.5 Conclusion
We have examined time series properties for the main variables (real marginal cost
and expected inflation) of the new Keynesian Phillips curve and its relationships with
inflation. We found that all of the variables tested are first-order integrated I (1), except for
the output gap, which is stationary. Our cointegration tests show that actual inflation and the
three survey measures of inflation expectations are cointergrated and inflation is
cointergrated with labour’s share of income. We follow Granger and Newbold’s (1974,
p.117) suggestion and tested the hybrid new Keynesian Phillips for autocorrelation in the
residuals as a mean for identifying spurious regression problems. Our tests (LM) for
autocorrelation in the residuals suggest that the hybrid new Keynesian Phillips curve is
202
correctly specified, implying that it is unlikely that there is spurious regression problems in
the hybrid new Keynesian Phillips curve.
The finding that the inflation rates are non-stationary does not invalidate previous
body of empirical research, but instead it complements previous studies. It has been well
known for sometime now that inflation is persistence (see chapter 2). The persistence of
inflation is a central concern to macroeconomists and central bankers and it has implications
for the specifications of the Phillips curve and the conduct of monetary policy. If there a unit
root in inflation, then it is implies that the pure forward-looking New Keynesian Phillips
curve is likely to be mispecified. Indeed, much of the New Keynesian Phillips curve literature
in recent years is about the inability of the pure forward-looking New Keynesian Phillips
curve to generate sufficient persistence in inflation. This has motivated some economists to
incorporate backward-looking inflation expectations term in the New Keynesian Phillips (see
chapter 2). From a central banker’s perspective the persistence of inflation implies that
disinflation is contractionary. Furthermore, the finding that actual inflation and the three
survey measures of inflation expectations are cointergrated implies that there is a long-run
relationship between actual inflation and expected inflation, which is consistent with the
notion that people’s future expectations matter. This implies that the old Keynesian Phillips
curve is likely to be mispecified as it does not include expected inflation as an explanatory
variable.
203
7.6 Appendix to Chapter 7 Table 7.5 Definitions and Sources of Data
Variable Definition Source
� Inflation is measured as 1004
ln �
�
�
� using core
CPI. Consumer Price Index (All Items Less Food and Energy), Index 1982-1984=100. Source:
Bureau of Labor Statistics (BLS).
JFP Job Finding Probability. Constructed from the number of unemployed workers, the number of short term (5 weeks) unemployed workers and the number of unemployed workers next month using Shimer’s (2005) formulation.
Bureau of Labor Statistics (BLS).
GAP Output Gap (Nonfarm Business Sector Output, Index
2005=100), using the Hodrick-Prescott filter with a smoothing parameter of 1600.
Bureau of Labor Statistics
(BLS).
LS Labour’s Share of Income (Nonfarm Business Sector, Index 1992=100).
Bureau of Labor Statistics (BLS).
MICHIGAN Represents the mean forecasts of the Michigan Survey for the fourth quarter after the current quarter.
www.src.isr.umich.edu/
G1 Greenbook forecasts for the GNP/GDP price level for the first quarter after the current quarter.
http://www.philadelphiafed.org/research-and-data/real-time-center/greenbook-data/
GREENBOOK Greenbook forecasts for the GNP/GDP price level for the fourth quarter after the current quarter.
http://www.philadelphiafed.org/research-and-data/real-time-center/greenbook-data/
M1 Represents the mean forecasts of the SPF for the first quarter after the current quarter.
www.philadelphiafed.org/.../survey-of-professional-forecasters/
SFP Represents the mean forecasts of the SPF for the fourth quarter after the current quarter.
www.philadelphiafed.org/.../survey-of-professional-forecasters/
S1 Represents the median forecasts of the SPF for the first quarter after the current quarter.
www.philadelphiafed.org/.../survey-of-professional-forecasters/
S4 Represents the median forecasts of the SPF for the fourth quarter after the current quarter.
www.philadelphiafed.org/.../survey-of-professional-forecasters/
� �
204
�����������i����������i��������i����������������i���������
Fig. 7.1 core CPI, output gap (GAP), labour’s share of income (LS) and job finding
probability (JFP), quarterly data from 1961q1 to 2010q1.
-4
-2
0
2
4
65 70 75 80 85 90 95 00 05 10
GAP
.1
.2
.3
.4
.5
.6
65 70 75 80 85 90 95 00 05 10
JFP
4.48
4.52
4.56
4.60
4.64
4.68
65 70 75 80 85 90 95 00 05 10
LS
0
2
4
6
8
10
12
14
65 70 75 80 85 90 95 00 05 10
CORE CPI
205
�����������i����������i��������i����������������������i���
Fig. 7.2 core CPI, the “Greenbook” forecasts, the Survey of Professional Forecasters (SPF)
and the “Michigan” Survey, quarterly data from 1983q3 to 2004q4.
1
2
3
4
5
6
84 86 88 90 92 94 96 98 00 02 04
CORE CPI
0
1
2
3
4
5
6
84 86 88 90 92 94 96 98 00 02 04
GREENBOOK
1
2
3
4
5
6
84 86 88 90 92 94 96 98 00 02 04
SPF
1
2
3
4
5
6
84 86 88 90 92 94 96 98 00 02 04
MICHIGAN
206
CHAPTER 8
Estimations of the Phillips Curve for Australia with Different Proxies for Real Marginal
Cost
8.1 Introduction
In their influential paper, Gali and Gertler (1999) argue that the reason why the new
Keynesian Phillips curve (NKPC) fits the data poorly is because traditional empirical work
on the Phillips curve uses some output gap measures as a proxy for real marginal cost rather
than labour’s share of income. Gali and Gertler (1999) also raise two related issues: First, the
NKPC needs to take into account labour market frictions. Second, the output gap may not be
an appropriate proxy for real economic activity because it assumes that the labour market
clears. The main purpose of this chapter is to address the two issues raised by Gali and
Gertler (1999) mentioned above by using job finding probability (JFP) as proxy for real
marginal cost. We re-examined Gali and Gertler (1999) empirical results by estimating
various specifications of the Phillips curve for Australia using three proxies for real marginal
cost: job finding probability (JFP), the output gap and labour’s share of income. We found
that the three as proxies for real marginal cost performed equally well when the old
Keynesian Phillips curve is estimated. Labour’s share of income is the best proxy for real
marginal cost when the new Keynesian Phillips curve is estimated. Job finding probability is
marginally a better proxy for real marginal cost than the output gap and labour’s share of
income when the hybrid new Keynesian Phillips curve is estimated. We also found that
backward inflation expectations looking dominate forward-looking inflation expectations
independent of which measures of real marginal cost are used.
This chapter is structured as follows: The first section briefly review the Australian
new Keynesian Phillips curve literature. The second section compares the empirical
appropriateness of job finding probability (JFP), the output gap and labour’s share of income
as proxies for real marginal cost. The third section considers three robustness exercises: The
first robustness exercise examines sub-sample stability. The second robustness exercise uses
the Consumer Price Index instead of the Reserve Bank of Australia’s analytical measures of
consumer price inflation to examine if our initial results are robust. The third robustness
exercise estimates the new Keynesian Phillips curve and the hybrid new Keynesian Phillips
curve using GMM. The fourth section concludes.
207
8.2 The Australian Phillips Curve
The first Australian Phillips Curve was estimated by A.W. Phillips in 1959, during
Phillips’ sabbatical year in Australia at the University of Melbourne. The equation Phillips
estimated related wage inflation to unemployment; this specification influenced many early
studies of the Australian Phillips curve. Gruen, Pagan and Thompson (1999, pp.9-10) provide
a summary of these works. The emergence of the new Keynesian economics, which
emphasises the importance of microeconomic foundations to the Phillips curve, incorporated
rational expectations to the Phillips curve theoretic (Fischer (1977), Taylor (1979, 1980) and
Calvo (1983)). More recent studies of the Australian Phillips Curve tend to relate price
inflation to the output gap and inflation expectations. In addition, empirical studies on the
Australian Phillips curve tend to focus on backward-looking inflation expectations, as it fits
the data better than the pure forward-looking new Keynesian Phillips curve. Gali and
Gertler’s (1999) hybrid specification is also popular. In an open economy setting, price
inflation is determined by a weighted average of domestic and imported inflation, with the
latter equal to the change in real import prices and the former determined as per the standard
closed economy NKPC (Norman and Richards, 2010, p.4). Since Australia is a small open
economy, import prices could be an important determinant of domestic consumer price level,
as a result some empirical studies on the Australian Phillips curve include import prices as an
explanatory variable (See Gruen, Pagan and Thompson, 1999).
Some researchers (Debelle and Vickery 1998, p.386) have attempted to allow for
shifts in the non-accelerating inflation rate of unemployment (NAIRU) over time. Gregory
(1986) and Simes and Richardson (1987) allow for a time trend in their specification,
although it is not apparent whether this is necessarily capturing the shifts in the NAIRU. The
Treasury model (TRYM) allows for a once-off level shift in the NAIRU in 1974
(Commonwealth Treasury 1996). Debelle and Vickery (1998, p.384) compare the actual rates
of unemployment in Australia and the United States and argue that the assumption of a
constant NAIRU over the sample period may be appropriate in the United States, but not for
Australia. Gruen, Pagan and Thompson (1999, pp.236-237) discuss various ways to allow the
NAIRU to shift over time, a once-off level shift in the NAIRU is absorbed into the intercept,
“presenting the possibility of using statistical procedures to determine the number and
location of breaks in that coefficient. Once located, any shifts in the NAIRU could be
captured by a series of dummy variables”. Traditionally Australian studies have “not treated
208
breaks in the NAIRU in such a formal manner. Instead, breaks in the NAIRU have been
imposed after an inspection of the history of the unemployment rate; the logic being that,
within a few years of a shock to the NAIRU, the unemployment rate adjusts to this new
equilibrium level in most macroeconomic models in use in Australia”. More recently some
researchers treat the NAIRU as a unit-root process. For example Debelle and Vickery (1998)
used a Phillips curve framework to estimate the NAIRU as a unit-root process using the
Kalman filter. Gruen, Pagan and Thompson (1999, p.236) plotted the unemployment rate
over the sample period (1965-1997) and examine the peaks and troughs, the plot reveals quite
clearly the shift in the NAIRU, although estimates of it tend to have been fairly stable since
the early 1980s. Such an outcome is consistent with estimates of the Phillips curve made in
previous research in Australia, which had the NAIRU creeping up as data from the early
1970s was included. Moreover, the unemployment rate rose sharply in the mid 1970s and has
never returned to its pre-1973 level.
Another feature of the Australian Phillips curve literature is the inclusion of the speed
limit effects; this refers to the view that rapid reductions in the unemployment rate are
associated with increased inflationary pressure. Debelle and Vickery (1998, p.393) attempt to
capture the speed limit effects by introducing an unemployment change variable in their non-
linear and linear Phillips curve specifications. They also tested for speed-limit effects, but
generally found them to be of the wrong sign (also see Gruen, Pagan and Thompson, 1999,
p.237).
Some studies on the Australian Phillips curve use mark-up pricing, that is, firms raise
their mark-up over marginal cost when demand for their products is high. In these models,
“inflation is determined by current and lagged growth in unit labour costs and import prices,
based on the theory that firms set their prices as a mark-up on costs, as in the NKPC.
However, there has previously been little explicit allowance for forward-looking behaviour
by firms in such models, and the presence of nominal rigidities has only been included
implicitly by allowing for lags of input costs’ (Norman and Richards, 2010, pp.5-6).More
recently, some researchers such as Jaaskela and Nimark (2008) and Buncic and Melecky
(2007) have also started to estimate the new Keynesian Phillips curve using dynamic
stochastic general equilibrium (DSGE) framework.
209
Two different measures of inflation expectation are used in the Australian Phillips
curve literature: an estimate derived from bond-market yields, and the Melbourne Institute10
measure of consumer inflation expectations. Debelle and Vickery (1998, p.389) derived a
measure of inflation expectations from bond yield data, this measure of inflation expectations
is computed from bond-market yields by subtracting a measure of the equilibrium world real
interest rate from the 10-year bond yield. The series for the world real interest rate is based on
empirical work that relates the equilibrium world real interest rate to movements in the stock
of world government debt. The Melbourne Institute measure of consumer inflation
expectations started in 1973; the Melbourne Institute of Applied Economic and Social
Research conduct telephone interviews of a minimum of 1200 Australian households on a
regular basis about the outlook for consumer price index (CPI) inflation, among other
variables. The design of this survey of similar to that of the Michigan survey (Thomas and
Grant, 2008, p.239). The Melbourne survey was initially conducted quarterly, since January
1987 it has been conducted on a monthly basis.
8.3 The Data
Table 8.1 presents the definitions and sources of the data used in this chapter; all
series are quarterly data for Australia and are expressed in log unless stated otherwise. We
use Reserve Bank of Australia’s (RBA) analytical measures of consumer price inflation as
our measure of inflation; this series is constructed by the RBA and are provided as a
convenience for researchers. The series excludes interest charges and the tax changes of
1999/2000 and the effect of major health policy changes and some other policy changes.
10 I am grateful to Guy Debelle for providing data on the Melbourne Institute measure of consumer inflation expectations.
210
Table 8.1 Definitions and Sources of Data
Variable Definition Source
� Reserve Bank of Australia (RBA) Analytical Measures of
Consumer Price Inflation. The interest charges and tax
adjustments made for this series are the same as those made in
Heath, Roberts and Bulman (2004). Further adjustments are made
for the impact of major health policy changes, such as the
introduction of Medibank and Medicare and changes to health
insurance rebates; in these quarters CPI inflation rates excluding
hospital and medical services have been used. This series is also
adjusted for the inclusion of the child care tax rebate in the
September 2007 quarter.
Reserve Bank of Australia
�� �� is measured as
4100 ln �
�
�
� using the Consumer Price Index. Reserve Bank of
Australia
J13 Job Finding Probability. Constructed from the number of
unemployed workers, the number of short term (less than 13
weeks) unemployed workers and the number of unemployed
workers next month using Shimer’s (2005) formulation.
Reserve Bank of Australia
J26 Job Finding Probability. Constructed from the number of
unemployed workers, the number of short term (less than 26
weeks) unemployed workers and the number of unemployed
workers next month using Shimer’s (2005) formulation.
Reserve Bank of Australia
G Output Gap. Chain volume measures are referenced to 2008/2009
values. Constructed using the Hodrick-Prescott filter with a
smoothing parameter of 1600.
Australian Bureau
of Statistic, ABS
Cat No 5206.0.
S The log non-farm of Real Unit Labour Cost. Datastream, Series
ID:AUULCNF.G.
MEL Consumers’ inflation expectations are measured by the
Melbourne Institute median expected inflation rate for the year
ahead.
Melbourne Institute Survey of Consumer Inflation
211
U The Unemployment rate is defined as unemployed persons as a
percentage of the labour force.
Australian Bureau
of Statistic, ABS
Cat No 6202.0.
WI Wage Inflation, measured as the log-difference in nonfarm
average weekly earning per wage and salary earner.
Australian Bureau
of Statistic, ABS
Cat No 5206.0.
8.4 Proxies for Real Marginal Cost
We will briefly examine the correlations of the three proxies for real marginal cost
with inflation and unemployment. The results shown in the table below indicate potential
problems with using the output gap and labour’s share of income as proxy for real marginal
cost. Note that the correlation between inflation and the output gap (0.049270) has the correct
sign but it is very weak and the correlation between unemployment and labour’s share of
income (0.379737) has the wrong sign. In contrast, job finding probability’s correlations with
inflation and unemployment have the correct signs and are relative strong.
Table 8.2 Correlation Matrix of Three Proxies for Real Marginal Cost with Inflation and Unemployment
U � S J26 J13 G
U 1.000000 0.044325 0.379737 -0.816829 -0.880445 -0.464241
� 0.044325 1.000000 0.784966 0.233397 0.133099 0.049270
S 0.379737 0.784966 1.000000 -0.125095 -0.238924 -0.056420
J26 -0.816829 0.233397 -0.125095 1.000000 0.887402 0.202941
J13 -0.880445 0.133099 -0.238924 0.887402 1.000000 0.312910
G -0.464241 0.049270 -0.056420 0.202941 0.312910 1.000000
Note: The correlation matrix was computed using quarterly data from 1978q2 to 2011q1
The intuition behind the use of job finding probability as a proxy for real marginal
cost is that it directly measures how difficult it is for unemployed people to find jobs, in other
words, the tightness of the labour market. Our formulation of job finding probability follows
Robert Shimer’s (2005, pp.30-31) formulation, which infers the job finding probability from
dynamic behaviour of the unemployment level and the short-term unemployment level. Let
�
� denote the number of workers unemployed for less than 13 weeks, in month �. Then
212
assuming all unemployed workers find a job with probability �� in month � and no
unemployed workers exit the labour force, then the number of unemployed workers next
month is equal to the number of unemployed workers this month who failed to find a job,
plus the number of newly unemployed workers.
1 1(1 ) �
� � � �� (8.1)
The job finding probability is given by
1 11�
� ��
�
�
(8.2)
where �� is the job finding probability, �
is the number of unemployed workers, �
� is the
number of short term (less than 13 weeks) unemployed workers and 1� is the number of
unemployed workers next month. We have also considered job finding probability for the
number of workers unemployed for less than 26 weeks, the results are similar to the results of
job finding probability for the number of workers unemployed for less than 13 weeks. In
order to conserve space we will only report the results of job finding probability for the
number of workers unemployed for less than 13 weeks.
8.5 Empirical Comparisons Between Job Finding Probability, the Output Gap and
Labour’s Share of Income as Proxy for Real Marginal Cost
First we estimate the old Keynesian Phillips curve using ordinary least square (OLS).
We use the results of the old Keynesian Phillips curve, with adaptive expectations as our
benchmark, since rational expectations predicts that modelling the Phillips curve with rational
expectations should fit the data better than modelling the Phillips curve with adaptive
expectations. Rational expectations implies that inflation expectations are rational, in the
sense that they efficiently incorporate all information available at time the expectations are
taken, and not just the past information as implied by adaptive expectations.
213
Table 8.3 Estimations (OLS) of the Old Keynesian Phillips Curve
Equation estimated 1� � � �� ��
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding
Probability
-0.459447
0.357055 -1.286766
0.2005
1.304261
0.793413 1.643861
0.1026
0.969168
0.019067 50.83011
0.0000
0.952564
Output Gap
0.099302 0.109038 0.910708
0.3641
9.002609 4.441238 2.027050
0.0447
0.972016 0.018863 51.53002
0.0000
0.953065
Labour’s Share of Income
-15.45751 7.548277
-2.047820 0.0426
3.368309 1.634172 2.061171
0.0413
0.924114 0.030086 30.71535
0.0000
0.953115
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The old Keynesian Phillips curve with adaptive expectations produces relatively high
2
� values for the three proxies of real marginal cost. The coefficients of labour’s share of
income and the output gap are statistically significant at 5%.
214
Table 8.4Estimations of the New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as Proxy
for Inflation Expectations
Equation estimated 4� � � � �� �� �
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-0.679956 0.593096
-1.146452 0.2537
1.732442 1.312538 1.319917
0.1892
0.850109 0.028972 29.34243
0.0000
0.870018
Output Gap
-0.001852 0.185389
-0.009990 0.9920
-21.10123 7.289028
-2.894931 0.0045
0.865981 0.028436 30.45381
0.0000
0.876299
Labour’s Share of Income
-48.86822 11.17061
-4.374714 0.0000
10.59658 2.418849 4.380835
0.0000
0.719571 0.040904 17.59157
0.0000
0.885323
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the Melbourne Institute over the
next year forecasts as proxy for inflation expectations produce lower 2
� values for the three
proxies of real marginal costs than the old Keynesian Phillips curve with adaptive
expectations; this is contrary to the prediction of rational expectations. The coefficient of the
output gap has the wrong signs. The coefficient of labour’s share of income is statistically
significant at 1%.
215
Table 8.5 Estimations of the Hybrid New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as
Proxy for Inflation Expectations
Equation estimated 1 4� � � � � � �� �� �
Proxy for Real Marginal Cost
Constant �
� 2
�
Job Finding Probability
-0.579453 0.337386
-1.717477 0.0883
1.292267 0.747001
1.729939 0.0861
0.784305 0.047663
16.45524 0.0000
0.183181 0.043752
4.186854 0.0001
0.957952
Output Gap
-0.018446 0.109167
-0.168965 0.8661
2.964018 4.560054 0.649996
0.5169
0.798480 0.051111 15.62240
0.0000
0.172213 0.047460 3.628579
0.0004
0.957111
Labour’s Share of Income
-12.30245 7.194522
-1.709975 0.0897
2.659315 1.558321 1.706526
0.0903
0.757799 0.050678 14.95337
0.0000
0.174853 0.044055 3.968972
0.0001
0.957926
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The hybrid new Keynesian Phillips curve estimated with the Melbourne Institute over
the next year forecasts as proxy for inflation expectations produces higher2
� values than the
old Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 1% level. The coefficients of labour’s share of income and job finding
probability are statistically significant at 10% level.
216
Table 8.6Estimations of the Hybrid New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as
Proxy for Inflation Expectations and Import Prices
Equation estimated 1 4� � � � � � � i �� �� � �
Proxy for Real Marginal Cost
Constant �
� i 2
�
Job Finding Probability
0.829303 2.530761
0.327689 0.7437
1.110991 0.780807
1.422876 0.1575
0.763984 0.051751
14.76277 0.0000
0.177919 0.046014
3.866587 0.0002
-0.264498 0.524798
-0.503999 0.6152
0.951016
Output Gap
0.810587 2.561734 0.316421
0.7523
4.007614 4.861084 0.824428
0.4114
0.785385 0.056483 13.90490
0.0000
0.163872 0.051591 3.176382
0.0019
-0.161265 0.520222
-0.309993 0.7571
0.950442
Labour’s Share of Income
-14.17423 11.62571
-1.219215 0.2253
2.639065 2.039681 1.293862
0.1983
0.756847 0.052395 14.44495
0.0000
0.186989 0.046061 4.059615
0.0001
0.405037 0.644841 0.628119
0.5312
0.950868
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth.
Some empirical studies on the Australian Phillips curve include import prices as an
explanatory variable because Australia is a small open economy. Our results show that the
coefficients of import prices for the three proxies of real marginal cost are not statistically
significant at 10% level.
8.6 Robustness Analysis
We consider three robustness exercises. The first robustness exercise examines sub-
sample stability. Our sub-samples are the periods from 1978q2 to 1989q4, 1990q1 to 1999q4,
2000q1 to 2011q1, 2000q1 to 2006q4, and the full sample period from 2007q1 to 2011q1, we
also wanted to examine the relative importance of forward-looking and backward-looking
inflation expectations during different sub-sample periods. The second robustness exercise
examines an alternative measurement of inflation; we use the Consumer Price Index without
various adjustments instead of the Reserve Bank of Australia’s analytical measures of
consumer price inflation to examine if our initial results are robust. The third robustness
exercise examines the new Keynesian Phillips curve and the hybrid new Keynesian Phillips
curve using generalized method of moments (GMM).
217
���������������i�i���
Table 8.7 Estimations of the Hybrid New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as Proxy for Inflation Expectations and with Job Finding Probability as Proxy for Real Marginal Cost
Equation estimated 1 4� � � � � � �� �� �
Sample Period
Constant �
� 2�
1978q2 1989q4
-4.708178 2.853552
-1.649936 0.1062
2.691179 1.998028 1.346918
0.1851
0.806498 0.081540 9.890783
0.0000
0.526017 0.341630 1.539728
0.1310
0.804760
1990q1 1999q4
-0.677981 0.710182
-0.954658 0.3461
3.063017 2.203650 1.389975
0.1731
0.698001 0.104732 6.664659
0.0000
0.098734 0.079702 1.238797
0.2234
0.865889
2000q1 2011q1
-0.466626 0.683634
-0.682568 0.4987
-0.125831 1.461144
-0.086118 0.9318
0.625670 0.089823 6.965551
0.0000
0.487346 0.096679 5.040873
0.0000
0.697525
2000q1 2006q4
-0.242455 0.870985
-0.278369 0.7831
1.011801 1.604427 0.630631
0.5342
0.559283 0.138210 4.046608
0.0005
0.320595 0.121242 2.644249
0.0142
0.539944
2007q1 2011q1
-1.130187
1.758870 -0.642564
0.5317
0.012232
3.775292 0.003240
0.9975
0.641273
0.146816 4.367878
0.0008
0.618311
0.165920 3.726574
0.0025
0.782993
1978q2 2011q1
-0.579453 0.337386
-1.717477 0.0883
1.292267 0.747001 1.729939
0.0861
0.784305 0.047663 16.45524
0.0000
0.183181 0.043752 4.186854
0.0001
0.958915
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second
row. t-ratios are shown in the third row. P-values are shown in the fourth row.
218
Table 8.8Estimations of the Hybrid New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as Proxy for Inflation Expectations and with the Output Gap as Proxy for Real Marginal Cost
Equation estimated 1 4� � � � � � �� �� �
Sample Period Constant �
� 2�
1978q2 1989q4
-5.273633 3.023747
-1.744072 0.0883
-3.633520 8.026664
-0.452681 0.6531
0.773890 0.102137
7.576944 0.0000
0.735091 0.358841
2.048513 0.0466
0.797488
1990q1 1999q4
0.317591 0.195020 1.628506
0.1121
16.00744 7.645109 2.093815
0.0434
0.742614 0.094246 7.879504
0.0000
0.110505 0.076995 1.435216
0.1599
0.874032
2000q1 2011q1
-0.742800 0.387006
-1.919347 0.0619
-13.26340 8.866891
-1.495834 0.1424
0.620650 0.084710 7.326737
0.0000
0.554550 0.101872 5.443593
0.0000
0.713126
2000q1 2006q4
0.115124 0.465561 0.247280
0.8068
-22.50437 9.665426
-2.328337 0.0286
0.502162 0.128433 3.909901
0.0007
0.396273 0.113274 3.498351
0.0018
0.618496
2007q1 2011q1
-1.287856 0.714850
-1.801575 0.0948
-8.349816 17.29328
-0.482836 0.6372
0.644525 0.130391 4.943007
0.0003
0.667930 0.188156 3.549878
0.0036
0.786816
1978q2 2011q1
-0.018446 0.109167
-0.168965 0.8661
2.964018 4.560054 0.649996
0.5169
0.798480 0.051111 15.62240
0.0000
0.172213 0.047460 3.628579
0.0004
0.958093
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
219
Table 8.9Estimations of the Hybrid New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as Proxy for Inflation Expectations and with Labour’s Share of Income as Proxy for Real Marginal Cost
Equation estimated 1 4� � � � � � �� �� �
Sample Period Constant �
� 2�
1978q2 1989q4
-40.12865 13.98731
-2.868934 0.0064
7.588507 2.955107
2.567929 0.0138
0.689750 0.088684
7.777569 0.0000
0.688373 0.308184
2.233643 0.0308
0.823578
1990q1 1999q4
101.1636 47.61433 2.124646
0.0406
-21.56458 10.17674
-2.119008 0.0411
0.743480 0.094101 7.900883
0.0000
0.157967 0.080445 1.963671
0.0573
0.874362
2000q1 2011q1
-3.010206 13.73513
-0.219161 0.8276
0.535932 2.950664 0.181631
0.8568
0.626498 0.088255 7.098706
0.0000
0.486031 0.093222 5.213690
0.0000
0.697714
2000q1 2006q4
1.434286 19.97793 0.071794
0.9434
-0.263992 4.281935
-0.061653 0.9514
0.561872 0.140619 3.995716
0.0005
0.329237 0.121644 2.706564
0.0123
0.532395
2007q1 2011q1
58.61725 38.64506
1.516811 0.1532
-12.97918 8.394807
-1.546096 0.1461
0.585384 0.126100
4.642213 0.0005
0.702859 0.156188
4.500073 0.0006
0.816698
1978q2 2011q1
-12.30245 7.194522
-1.709975 0.0897
2.659315 1.558321 1.706526
0.0903
0.757799 0.050678 14.95337
0.0000
0.174853 0.044055 3.968972
0.0001
0.958890
Note: The above equations were estimated (OLS) using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The results of the first robustness exercise presented above show that the slopes of the
reduced form hybrid new Keynesian of the Phillips curve are much smaller over the past 10
years when Job finding probability and labour’s share of income are used as proxies for real
marginal cost. The relative importance of backward-looking inflation expectations and
forward-looking inflation expectations changes over time. Backward-looking inflation
expectations dominate forward-looking inflation expectations independent of which measures
of real marginal cost are used. The signs and magnitudes of the slope of the reduced form
Phillips curve depend on which sample periods and which measures of real marginal cost are
220
used. We have also estimated the hybrid new Keynesian Phillips curve for the sub-sample
periods from 2000q1 to 2006q4 and for Phillips curve from 2007q1 to 2011q1; it appears that
the R square values have increase after the recent financial crisis, this is an unexpected
finding as one would expect the R square values to be lower because of greater uncertainty
making modelling inflation more difficult. Note that the second sub-sample period is
relatively short, we need to be careful about drawing any conclusion from this sub-sample
period. Based on the signs and magnitudes of the slope of the reduced form hybrid new
Keynesian Phillips curve and the R square values, job finding probability is marginally a
better proxy for real marginal cost than the output gap and labour’s share of income.
�����������i������������������������i���
Our alternative measurement of inflation is defined as 4
100 ln �
�
�
� using the
Consumer Price Index.
Table 8.10 Estimations (OLS) of the Old Keynesian Phillips Curve
Equation estimated 1� � � �� � �� �
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-0.429111 0.461204
-0.930416 0.3539
1.414127 1.051544 1.344810
0.1810
0.951376 0.024576 38.71185
0.0000
0.923402
Output Gap
0.172161 0.131469 1.309515
0.1927
18.31982 5.653663 3.240345
0.0015
0.955182 0.023353 40.90206
0.0000
0.928175
Labour’s Share of Income
-12.34342 8.663796
-1.424712
0.1567
2.700852 1.870684 1.443778
0.1512
0.924219 0.033495 27.59309
0.0000
0.923564
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The old Keynesian Phillips curve with adaptive expectations produces relatively high
2
� values for the three proxies of real marginal cost. The coefficient the output gap is
statistically significant at 5% level.
221
Table 8.11Estimations of the New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as Proxy
for Inflation Expectations
Equation estimated 4� � � � �� � �� � �
Proxy for Real Marginal Cost
Constant �
2
�
Job Finding Probability
-2.462800 0.792281
-3.108493 0.0023
5.759913 1.753339 3.285110
0.0013
0.811392 0.038702 20.96517
0.0000
0.780717
Output Gap
-0.009672
0.264052 -0.036627
0.9708
-4.738918
10.38184 -0.456462
0.6488
0.826613
0.040502 20.40943
0.0000
0.762755
Labour’s Share of Income
-21.83081 16.42578
-1.329058 0.1862
4.728792 3.556787 1.329512
0.1860
0.763962 0.060148 12.70146
0.0000
0.765584
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth row.
The new Keynesian Phillips curve estimated with the Melbourne Institute over the
next year forecasts as proxy for inflation expectations produce lower 2
� values for the three
proxies of real marginal costs than the old Keynesian Phillips curve with adaptive
expectations. The coefficient of the output gap has the wrong signs. The coefficient of job
finding probability is statistically significant at 1%.
222
Table 8.12Estimations of the Hybrid New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as
Proxy for Inflation Expectations
Equation estimated 1 4� � � � � � �� � �� � � �
Proxy for Real Marginal Cost
Constant �
� 2
�
Job Finding Probability
-0.859847 0.459842
-1.869876 0.0638
1.949057 1.021128 1.908730
0.0585
0.803893 0.048672 16.51647
0.0000
0.156935 0.045301 3.464245
0.0007
0.929421
Output Gap
0.018597 0.142337 0.130657
0.8963
14.86716 5.703635 2.606612
0.0102
0.848956 0.047757 17.77647
0.0000
0.115480 0.045573 2.533948
0.0125
0.931071
Labour’s Share of
Income
-1.976673
9.213157 -0.214549
0.8305
0.422531
1.995041 0.211791
0.8326
0.823580
0.048468 16.99239
0.0000
0.139579
0.049699 2.808460
0.0058
0.927438
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth
row.
The hybrid new Keynesian Phillips curve estimated with the Melbourne Institute over
the next year forecasts as proxy for inflation expectations produces higher2
� values than the
old Keynesian Phillips curve for the three proxies of real marginal costs; all coefficients of
backward-looking and forward-looking inflation expectations terms are statistically
significant at 5% level. The coefficients of job finding probability and the output gap are
statistically significant at 10% level.
223
Table 8.13Estimations of the Hybrid New Keynesian Phillips Curve Using the Melbourne Institute Forecasts as
Proxy for Inflation Expectations and Import Prices
Equation estimated 1 4� � � � � � � i �� � �� � � � �
Proxy for Real Marginal Cost
Constant �
� i 2
�
Job Finding Probability
-2.353473 3.435977
-0.684950 0.4948
1.768276 1.127836 1.567849
0.1197
0.802454 0.051679 15.52778
0.0000
0.168657 0.058474 2.884326
0.0047
0.323399 0.713645 0.453166
0.6513
0.914070
Output Gap
-0.556915 3.484136
-0.159843 0.8733
16.00409 6.378317 2.509140
0.0135
0.851438 0.051237 16.61778
0.0000
0.113686 0.061167 1.858605
0.0657
0.120946 0.708082 0.170808
0.8647
0.916811
Labour’s Share of
Income
-12.49728
16.65533 -0.750347
0.4546
1.730821
2.899248 0.596990
0.5517
0.815350
0.051488 15.83568
0.0000
0.167681
0.059053 2.839506
0.0054
0.916059
0.916825 0.999165
0.3198
0.912491
Note: The above equations were estimated (OLS) over the 1978q2 to 2011q1 period using quarterly data. Standard errors are shown in the second row. t-ratios are shown in the third row. P-values are shown in the fourth.
The coefficients of import prices for the three proxies of real marginal cost are not
statistically significant at 10% level. Overall, the results of the second robustness exercise are
consistence with our initial results.
�������i���i����
The third robustness exercise examines the new Keynesian Phillips curve and the
hybrid new Keynesian Phillips curve using generalized method of moments (GMM). Our
instrument set includes four lags of inflation, and two lags of labour’s share of income, the
output gap, and wage inflation. This instrument set is similar to the instrument set used by
Gali, Gertler and Lopez-Salido (2001, pp.1250).
224
Table 8.14Estimations of the New Keynesian Phillips Curve Using GMM
Equation estimated 1� � � � �� �� �
Proxy for Real Marginal Cost Constant �
Job Finding Probability
(0 lag)
0.258398 0.813895
0.317483 0.7514
-0.918891 1.961624
-0.468434 0.6403
1.029047 0.024012
42.85530 0.0000
Output Gap
(0 lag)
-0.145283 0.090825
-1.599603 0.1122
-8.740759 3.609836
-2.421373 0.0169
1.033213 0.021201 48.73337
0.0000
Labour’s Share of Income
(0 lag)
3.379606 18.84963 0.179293
0.8580
-0.760041 4.076105
-0.186463 0.8524
1.037690 0.059096 17.55944
0.0000
Note: The above equations were estimated (GMM) over the 1978q2 to 2010q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. P-values are shown in the fourth row.
The coefficients of the three proxies of real marginal costs have the wrong signs.
225
Table 8.15Estimations of the Hybrid New Keynesian Phillips Curve Using GMM
Equation estimated 1 1� � � � � � �� �� �
Proxy for Real Marginal Cost Constant �
�
Job Finding Probability
(0 lag)
-1.316378 0.751750
-1.751085 0.0823
3.230459 1.811231
1.783571 0.0769
0.822034 0.145614
5.645282 0.0000
0.143031 0.160206
0.892794 0.3737
Output Gap
(0 lag)
0.050436 0.080780 0.624362
0.5335
4.338309 5.650586 0.767763
0.4441
0.835471 0.178450 4.681819
0.0000
0.147834 0.192835 0.766635
0.4447
Labour’s Share of Income
(0 lag)
29.78048 11.80209 2.523323
0.0129
-6.441849 2.554895
-2.521375 0.0129
0.772400 0.105537 7.318748
0.0000
0.309637 0.111652 2.773241
0.0064
Note: The above equations were estimated (GMM) over the 1978q2 to 2010q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. P-values are shown in the fourth row.
All coefficients of backward-looking inflation expectations terms are statistically
significant at 1% level. The coefficient of job finding probability and labour’s share of
income are statistically significant at 10% level, but, the coefficient of labour’s share of
income has the wrong sign.
226
Table 8.16Estimations of the Hybrid New Keynesian Phillips Curve with Import Prices Using GMM
Equation estimated 1 4� � � � � � � i� �� � �
Proxy for Real Marginal
Cost
Constant �
� i
Job Finding Probability
(0 lag)
-7.390669 3.210472
-2.302050 0.0232
1.159493 2.394049 0.484323
0.6291
0.665970 0.154447 4.311970
0.0000
0.397966 0.193388 2.057859
0.0419
1.407405 0.782713 1.798111
0.0748
Output Gap
(0 lag)
-7.485784
2.138261 -3.500875
0.0007
2.563460
5.670240 0.452090
0.6521
0.680922
0.144977 4.696769
0.0000
0.389738
0.161011 2.420578
0.0171
1.530445
0.436871 3.503196
0.0007
Labour’s Share of Income
(0 lag)
-28.14116 32.69093
-0.860825 0.3912
3.704099 5.887508
0.629146 0.5305
0.589698 0.085813
6.871904 0.0000
0.484261 0.088335
5.482083 0.0000
2.243139 1.185721
1.891794 0.0611
Note: The above equations were estimated (GMM) over the 1978q2 to 2010q4 period using quarterly data. Standard errors are shown in the second row; errors are corrected for heteroskedasticity and autocorrelation using Newey-West procedure, with automatic lags selection based on Schwarz information criterion. t-ratios are shown in the third row. P-values are shown in the fourth row.
The coefficients of import prices for the three proxies of real marginal cost are
statistically significant at 10% level. The coefficients of the three proxies for real marginal
costs are not statistically significant at 10% level. All coefficients of backward-looking and
forward-looking inflation expectations terms are statistically significant at 5% level.
8.7 Conclusion
We have introduced and applied job finding probability to estimate the Australian
Phillips curve, which provides a direct link between frictions in the labour market and the
Phillips curve relationship. Our results suggest that job finding probability should be
considered as an alternative proxy for real marginal cost in empirical work on the Phillips
curve, particularly when the hybrid new Keynesian Phillips curve is estimated.
In general, our empirical results are not supportive of Gali and Gertler’s (1999)
empirical findings that labour’s share of income is a better proxy for real marginal cost than
the output gap. Also, our results are not supportive of Gali and Gertler’s (1999, p.195)
empirical findings that “[b]ackward-looking price setting, while statistically significant, is not
227
quantitatively important”. Our results suggest the old Keynesian Phillips curve with adaptive
expectations fits the data better than the new Keynesian Phillips curve with rational
expectations; this result is consistent with many previous studies on the Australian Phillips
curve, as well as some well known studies on the American Phillips curve, such as Fuhrer
and Moore (1995) and Mankiw (2001). Bounded rationality can explain the observation that
lagged inflation plays an important role in empirical inflation regressions as the dissemination
of economic information and knowledge between professional economists and non-
economists involves time lags, since the general public’s inflation expectations respond to the
professional economists’ expectations with time lags, lagged inflation rates are correlated
with the current inflation rate. Overall, our results using Australian data are broadly
consistent with our results using American data from previous chapters.
The results of the first robustness exercise indicate that the relative importance of
backward-looking inflation expectations and forward-looking inflation expectations changes
over time. Backward-looking inflation expectations dominate forward-looking inflation
expectations independent of which measures of real marginal cost are used. The signs and
magnitudes of the slope of the reduced form Phillips curve depend on which sample periods
and which measures of real marginal cost are used.
The second robustness exercise examines an alternative measurement of inflation; we
use the Consumer Price Index without various adjustments instead of the Reserve Bank of
Australia’s analytical measures of consumer price inflation series to examine if our initial
results are robust. The results of the second robustness exercise are broadly consistent with
our initial results.
The third robustness exercise examines the new Keynesian Phillips curve and the
hybrid new Keynesian Phillips curve using generalized method of moments (GMM).The
coefficients of the three proxies of real marginal costs output gap have the wrong signs. The
coefficients of import prices for the three proxies of real marginal cost are not statistically
significant when the Melbourne Institute forecasts are used as proxy for inflation
expectations. However, when mathematical expectations (GMM) are used as proxy for
inflation expectations import prices are statistically significant for the three proxies of real
marginal cost.
228
CHAPTER 9
Summary and Conclusions
We have examined two important issues in the empirical literature on the NKPC.
First, are inflation expectations consistent with rational expectations? Many researchers find
that the old Keynesian Phillips curve with adaptive expectations fits the data better new
Keynesian Phillips curve with rational expectations. Rudd and Whelan (2006, p.319)
conclude that “lagged inflation plays an important role in empirical inflation regressions
poses a major challenge to the rational-expectations sticky-price models that underpin the
new Keynesian Phillips curve”. In general, our empirical results using American data and
Australian data are not supportive of Gali and Gertler’s (1999) empirical findings that
labour’s share of income is a better proxy for real marginal cost than the output gap. Also,
our results are not supportive Gali and Gertler’s (1999, p.195) empirical findings that
“[b]ackward-looking price setting, while statistically significant, is not quantitatively
important”. Our results suggest the old Keynesian Phillips curve with adaptive expectations
fits the data better than the new Keynesian Phillips curve with rational expectations and that
the relative importance of backward-looking inflation expectations and forward-looking
inflation expectations changes over time. Backward-looking inflation expectations dominate
forward-looking inflation expectations independent of which measures of real marginal cost
are used. Furthermore, we have tested the rationality of survey measures of inflation
expectations in chapter 5; our results indicate that all of the survey measures of inflation
expectations are biased and inefficient. We have also showed that there are Granger
causalities from the professional forecasters (as represented by the SPF forecasts) to
households (as represented by the Michigan forecasts), but no Granger causality in the
opposite direction. Second, do real marginal costs drive inflation dynamics? Gali and Gertler
(1999) argue that the reason why the NKPC fits the data poorly is because traditional
empirical work on the Phillips curve uses some output gap measures as a proxy for real
marginal cost rather than labour’s share of income. In general, our results suggest that job
finding probability (JFP) is marginally a better proxy for real marginal cost than the output
gap and labour’s share of income when the hybrid new Keynesian Phillips curve is estimated.
Our results from chapters 4 and chapter 5 suggest that the pure rational expectations
new Keynesian Phillips curve might be misspecified and that the hybrid new Keynesian
Phillips curve fits the data best. If we accept the hybrid new Keynesian Phillips curve as
229
having the right specifications for the Phillips curve relationship, we need to be able to
explain why are some price setters backward-looking and why are some price setters
forward-looking and also are the fractions of backward-looking agents and the fractions
forward-looking agents constant over time? Bounded rationality implies that the best way for
non-economists to minimize their forecast errors is to listen to the advices of professional
economists as much of economic knowledge is professional knowledge. The way that
professional economists help the general public to overcome their lack of inflational
knowledge is by giving their professional advices via the mass media, economic education
and private consulting. Since the general public’s inflation expectations respond to the
professional economists’ expectations with time lag, lagged inflation rates are correlated with
the current inflation rate. In short, bounded rationality explains why lagged inflation plays an
important role in empirical inflation regressions as the dissemination of economic
information and knowledge between professional economists and non-economists involves
time lags, since the general public’s inflation expectations respond to the professional
economists’ expectations with time lags, lagged inflation rates are correlated with the current
inflation rate.
In chapter 6 we presented evidence of the flattening of the Phillips curve and
examined some of the competing explanations given for why this has occurred. We proposed
that structural changes in the labour market in the past forty years can partly account for this
phenomenon. Our view is that deindustrialization and the computer revolution have shifted
employment from the manufacturing sectors to the service sectors; these structural changes in
the labour market have changed jobs’ skill requirements, increasing heterogeneity (real
rigidities) between workers, producing more mismatches in the labour market, this is
reflected by the fact that the average duration of unemployment has been increasing since
1970 and the probability of finding a job after 15 weeks of unemployment has been
decreasing since 1970, this about the same time that deindustrialization started in the United
States. In other words, inflation is less responsive to changes in real marginal cost, because of
increase in the level of real rigidities in the labour market, reducing the inflation-output
tradeoffs and reducing the slope of the reduced form Phillips curve.
In Chapter 7 we argued that the finding that the United States inflation rates are non-
stationary does not necessarily invalidate a previous body of empirical research that did not
230
take into account the non-stationary behaviour of inflation, but instead it complements
previous studies.
In Chapter 8 we estimated various specifications of the Phillips curve for Australia
using job finding probability (JFP), the output gap and labour’s share of income as well as
survey measures of inflation expectations and mathematical expectations as proxy for
inflation expectations. In general, our results suggest that job finding probability should be
considered as an alternative proxy for real marginal cost in empirical work on the Phillips
curve, particularly when the hybrid new Keynesian Phillips curve is estimated. Also, our
results are not supportive Gali and Gertler’s (1999, p.195) empirical findings that
“[b]ackward-looking price setting, while statistically significant, is not quantitatively
important”. Our results suggest the old Keynesian Phillips curve with adaptive expectations
fits the data better than the new Keynesian Phillips curve with rational expectations; this
result is consistent with many previous studies on the Australian Phillips curve. Overall, our
results using Australian data are broadly consistent with our results using American data.
An important implication of our approach is that economists’ inflation expectations
are more important than households’ inflation expectations for macroeconomic outcomes;
this may sound obvious since it is a direct application of Adam Smith’s notion of the division
of labour. However, it also implies that when there are serious problems with the economy,
economists and their theories are likely to play some role in this process. Bounded rationality
opens up the possibility that when economists have the wrong model of economy, it causes
non-economists to have the wrong model of the economy. This is evident by the existence of
many obsolete economic theories in the history of economic thought and admissions of
influential economists (such as Alan Greenspan recently) that they had the wrong model of
the economy.
When people do not have sufficient knowledge about the nature of the problem, they
often seek the advices of those that they believe know more than them. This behaviour is
highly rational and is an important feature of the economy, in an uncertain environment,
when an “expert” claims or gives the impression that he knows what will happen in the
future, then it is rational for those whose don’t know what will happen due to their lack of
understanding about a particular subject (asymmetric knowledge) to base their opinions and
expectations on the opinions and expectations of the experts in that particular field of
knowledge, such as those of professional economists or rating agencies (Note that, the
231
recently appointed prime ministers of Italy (Mario Monti) and Greece (Lucas Papademos) are
economic professors).
By redefining bounded rationality in terms of asymmetric and imperfect knowledge it
implies that knowledge about the subject matter is also needed in order to understand and to
exploit the information for possible economic gains and by drawing on the sticky nature of
knowledge, it is possible to explain short-run monetary non-neutrality and other real rigidities
in the economy as a result of knowledge lags rather than informational lags, which makes it
much more plausible. From a business cycle perspective bounded rationality opens up the
possibility that when economists have the wrong model of economy, it causes non-
economists to have the wrong model of the economy, which may exacerbate economic crisis.
In Mankiw and Reis (2002) and in Carroll’s (2003) models, the authors assumed that
professional economists do not suffer from sticky information. Similarly, in our model, we
also assumed that professional economists do not suffer from sticky knowledge. However, by
redefining bounded rationality in terms of asymmetric and imperfect knowledge we have
explicitly acknowledged that economists do not have perfect foresight. Under bounded
rational expectations economists are the first to adjust their inflation expectations because
they know more about the economy than non-economists; this action does not imply that
economists have perfect foresights.
In the real world, the interactions between economists and non-economists go
something like this. Both non-economists and economists know that economists do not have
perfect foresight. This is reflected by the large number of jokes about economic predictions.
Part of the reasons why economists make forecast errors is simple, economists are asked to
make predictions about the future, both economists and non-economists know that the future
cannot be predicted with certainty. Despite the fact that non-economists know that
economists often make forecast errors, economists are better at making economic forecasts
than non-economists because they know more about economics. This is reflected by the fact
the economics as a profession exist, the reason why the economics profession exist (or any
other profession) is because of the unequal distribution of knowledge between the profession
and its clients. This is further complicated by the fact that economics is characterized by
many competing of schools of thought and that predictions of economists cannot be verified
accurately because other factors may influence the outcome that economists could justify that
they have no way of knowing, as economists often qualify their predictions with the clause
232
"ceteris paribus" . Some non-economists may choose to learn economics so that they don’t
have to rely on economists’ forecasts, learning economics will allow non-economists to
respond to economic news quicker, it does not allow non-economists to make predictions as
accurately as economists until they have invested as much time and efforts as a professional
economist in studying about economics.
Whether a non-economist decides to learn economics and become a professional
economist depends on the potential costs and benefits of his decision. For many non-
economists the costs of learning economics so that they could make economic forecasts as
accurately as profession economists outweigh the benefits, this is reflect by the relatively
small size of economic profession to the general public as a whole. For these non-economists,
the best way to minimize their forecast errors is by employing the services of professional
economists or observe how professional economists respond and replicate their actions, rather
than making economic forecast themselves without the requires economic knowledge. Given
that economics is characterized by many competing of schools of thought and that predictions
of economists cannot be verified accurately, it is likely that non-economists take into account
the uncertain nature of economic forecasts mentioned previously, that is, they take
economists’ advices but, with a grain of salt. As a result they take a wait and see approach to
updating their expectations of inflation, in other words, they make many incremental
adjustments in respond to economic developments as reported by the media during the life
span of a monetary policy shock. Furthermore, how quickly people respond to economic
developments also depends on the potential economic gains or losses of responding quickly.
When the monetary policy shock occurs and the government has good credibility the
potential economic gains or losses are small, as the general public believes that the
government’s policy will have a positive outcome. However, when the government is
perceived as incompetent, and its policy is viewed as not credible, this is likely to have a
negative outcome. The economic gains or losses of responding to economic development
quickly are very high as an economic recession happens much quicker than an economic
expansion. People will devote more time and mental resources to learning and thinking about
economic matters so that they can respond to economic developments quicker.
233
REFERENCES
Adam, K. and M. Padula (2003), “Inflation Dynamics and Subjective Expectations in the
United States”, ��������������������k����ki������������i��, No. 222.
Akelof, G.A. and J.E. Stiglitz (1969), “Capital, Wages and Structural Unemployment”,
������i���������, 79: 269-81.
Akerlof, G. A. and J. L. Yellen (1985), “A Near-Rational Model of the Business Cycle with
Wage and Price Inertia”, ���������������������������i��, 100: 823-838
Akerlof, G. A. and J. L. Yellen (1985), “Can Small Deviations from Rationality Make
Significant Differences to Economic Equilibria?”,�����i����������i�����i��, 75(4): 708-721.
Akerlof, G. and H. Miyazaki. (1980), “The Implicit Contract Theory of Unemployment Meets
the Wage Bill Argument”, ���i������������i������i��, 47: 321-338.
Akerlof, G.A. (1984), “Gift Exchange and Efficiency Wage Theory: Four Views”, ����i����
������i�����i��, 74: 79-83
Akerlof, G.A. and J. L. Yellen (1987), “Rational Models of Irrational Behavior”, ����i����
������i�����i��, 77: 137-142.
Akerlof, G.A. and J. L. Yellen (1988), “Fairness and Unemployment”, ����i����������i��
���i��, 78: 44-49.
Akerlof, G.A. and J. L. Yellen (1990), “The Fair Wage-Effort Hypothesis and Unemployment”,
���������������������������i��, 105: 255-283.
Akerlof, G.A. and J. L. Yellen, (eds) (1986), ���i�i����������������������������������k��,
Cambridge, Cambridge University Press.
Akerlof, G.A., W.T. Dickens, and G.L. Perry, (1996), “The Macroeconomics of Low Inflation”,
����ki��������������������i�����i�i��, 1: 1-76.
Akerlof, George (1970), “The Market for Lemons: Quality Uncertainty and The Market
Mechanism”, ���������������������������i��, 98: 488-500.
Akerlof, George and Janet, Yellen (1983), “The Macroeconomic Consequences of Near
Rational Rule of Thumb Behavior”, �i���, U.C. Berkeley.
Andres, J., J. D. Lopez-Salido, and E. Nelson (2005), “Sticky Price Models and the Natural
234
Rate Hypothesis”, ��������������������������i��, 52(5): 1025-1053.
Andrews, D. (1993), “Tests for Parameter Instability and Structural Change with Unknown
Change Point: A Corrigendum”, ���������i��, 71 (1): 395-397.
Ang Andrew, Geert Bekaert, and Min Wei, (2005), “Do Macro Variables, Asset Markets, or
Surveys Forecast Inflation Better?”, ��������ki������������i����No. 11538.
Arnold, Lutz (2002), ���i�����������������, New York, Oxford University Press.
Arslan, M.M. (2008), “Dynamics of the Sticky Information and Sticky Price Models in a New
Keynesian DSGE Framework”, ������i��������i��, 25: 1276-1294.
Azariadis, C. (1975), “Implicit Contracts and Underemployment Equilibria”, �����������
���i�i�����������, 83: 1183-1202.
Bailey, M.N. (1974), “Wages and Unemployment under Uncertain Demand”, ���i������
������i������i��, 41: 37-50.
Ball, L., (1994), “Credible Disinflations with Staggered Price Setting”, ����i����������i��
���i��� 84: 282-289.
Ball, L., N.G. Mankiw, R. Reis (2004), “Monetary Policy for Inattentive Economies”, ��������
������������������i��� 52: 703-725.
Ball, Laurence (1994), “Credible Disinflation with Staggered Price-Setting”, ����i����
������i�����i��� 84(1): 282-289.
Ball, Laurence and David Romer (1990), “Real Rigidities and the Non-Neutrality of Money”,
���i������������i������i��, 57: 183-203.
Ball, Laurence, and Mankiw, N. Gregory (1994), "A Sticky-Price Manifesto", ������i��
����������������������������i�����i��, 41: 127- 151.
Ball, Laurence, N. Gregory Mankiw, and David Romer (1988), "The New Keynesian
Economics and the Output-Inflation Trade-off", ����ki��������������������i�����i�i��, 1: 1-
65.
Barro, R.J. (1974), “Are Government Bonds Net Wealth?”, ��������������i�i�����������,
82(6): 1095-1117.�
235
Barro, R.J. (1977), “Unanticipated Money Growth and Unemployment in the United States”,
����i����������i�����i��, 67 (2): 101-115.
Bils, M., Klenow, P.J. (2004), “Some Evidence on the Importance of Sticky Prices”, �����������
���i�i�����������, 112: 947-985.
Blanchard, O.J. (1992), “For a Return to Pragmatism”, in M. Belongia and M. Garfinkel (eds),
�������i�����������������i���������i�����, London, Kluwer Academic Publishers.
Blanchard, O.J. (1997a), �����������i��, New Jersey, Prentice-Hall.
Blanchard, O.J. (1997b), “Is There a Core of Usable Macroeconomics?”, ����i����������i��
���i��, 2: 244-246.
Blanchard, O.J. and Fischer, S. (1989), �����������������������i��, Cambridge, MA: MIT
Press.
Blanchard, O.J. and Kiyotaki, N. (1987), “Monopolistic Competition and the Effects of
Aggregate Demand”, ����i����������i�����i��, 77: 647-666.
Blanchard, Olivier and Peter Diamond (1990), “The Cyclical Behavior of The Gross Flows of
U.S. Workers”, ����ki�������������������i�����i�i��, 2: 85-155.
Blanchard, Olivier and Peter Diamond (1992), “The Flow Approach to Labour Markets”, ����
����i����������i�����i��, 82: 354-359.
Blinder, A.S. (1997a), “Is There a Core of Practical Macroeconomics That We Should All
Believe?”, ����i����������i�����i��, 87(2): 240 - 243.
Blinder, A.S. (1997b), “What Central Bankers Can Learn from Academics and Vice Versa”,
�����������������i����������i���, 11(2): 3-19.
Blinder, A.S. (1998), �����������ki���i������������������i��, Cambridge, MA: MIT Press.
Blinder, Alan (1988), “The Challenge of High Unemployment”, ��������i����������i��
���i��, 78(2): 1-15.
Borland, Jeff (1996), “Job Creation and Job Destruction in Manufacturing Industry in
Australia”, ����������i��������, 72: 46-62.
Bowlus, Audra (1995), “Matching Workers and Jobs: Cyclical Fluctuations in Match Quality”,
�����������������������i��, 13(2): 335-350.
236
Brayton, Flint, John M. Roberts, and John C. Williams, “What's Happened to the Phillips
Curve?” (1999), ����� ���ki��� ������ ���� �����. Available at SSRN:
http://ssrn.com/abstract=190852 or http://dx.doi.org/10.2139/ssrn.190852.
Brissimis, Sophocles N., and Nicholas S. Magginas, (2008), “Inflation Forecasts and the New
Keynesian Phillips Curve”, ��������i���������������������������ki��, 4 (June): 1-22.
Buiter, Willem (2009), "The Unfortunate Uselessness of Most ‘State of the Art’ Academic
Monetary Economics", ft.com/maverecon, Financial Times,
http://blogs.ft.com/maverecon/2009/03/the-unfortunate-uselessness-of-most-state-of-the-art-
academic-monetary-economics/
Buncic, D. and M. Melecky (2008), “An Estimated New Keynesian Policy Model for
Australia”, ����������i��������, 84: 1-16.
Calvo, G. (1983), “Staggered Prices in a Utility-Maximizing Framework”, ��������������������
������i����12: 383-398.
Cao, Cung (2008), ��������i����������������K������������������������������������������
���i����i����i��������������i����i��, Germany, VDM Verlag Dr. Muller.
Caplin, Andrew S., and Daniel F. Spulber (1987). "Menu Costs and the Neutrality of Money”,
���������������������������i��, 102(4): 703-726.
Carroll, Christopher (2001), “The Epidemiology of Macroeconomic Expectations”, �����
���ki������������i��, No. 8695.
Carroll, Christopher (2003), “Macroeconomic Expectations of Household and Professional
Forecasters”, �������������������������������i��, 118 (1): 269-298
Challen, D., W., and A. J. Hagger (1975), “Another Look at Australia’s Inflation-
Unemployment Trade-offs”, �������i���������i��������, 14: 137-153.
Chen-Yu Leu, S., and J. Sheen (2006), “Asymmetric Monetary Policy in Australia”, ����
������i��������, 82: 85-96.
Cho, Seonghoon, and Antonio Moreno (2006), “A Small-Sample Study of the New Keynesian
Macro Model”, ����������������������i���������ki��, 39: 471-507.
Christiano, L.J., M. Eichenbaum, C.L. Evans (2005), “Nominal Rigidities and the Dynamic
237
Effects of a Shock to Monetary Policy”, ��������������i�i�����������, 113(1): 1-45.
Christiano, Lawrence, Martin Eichenbaum, and Charles Evans, (1999), “Monetary Policy
Shocks: What Have We Learned And To What End?”, �������k���������������i��, J.B.
Taylor and Michael Woodford, eds. (Amsterdam, The Netherlands), 65-148.
Clarida, Richard, Mark Gertler, and Jordi Gali, (1999), "The Science of Monetary Policy: A
New Keynesian Perspective”, �����������������i���i��������, 37: 1661-1707.
Coibion, O. (2010), “Testing the Sticky Information Phillips Curve”, �������i������������i���
��������i��i����92: 87-101.
Commonwealth Treasury (1996), “User’s Guide to the TRYM Model of the Australian
Economy”, CPN Printing, Canberra.
Conlisk, John (1996), “Why Bounded Rationality?”, �����������������i���i��������, 34: 669-
700.
Croushore, Dean (1998), “Evaluating Inflation Forecasts”, �������������������k����
��i�������i�����ki������������������.
Croushore, Dean and Tom, Stark (2001), "A Real-Time Data Set for Macroeconomists",
��������������������i��� 105: 111-130.
Culver, S.E and D.H. Papell (1997), “Is There a Unit Root in the Inflation Rate?”, J����������
����i������������i��, 12: 435-444.
Darby, Michael, John Haltiwanger, and Mark Plant (1985), “Unemployment Rate Dynamics
and Persistent Unemployment Under Rational Expectations”, ����i����������i�����i��,
75(4): 614-637.
Darby, Michael, John Haltiwanger, and Mark Plant (1986), “The Ins and Outs of employment:
The Ins Win”, ��������ki������������i����No. 1997�
Davis, S.J., R.J. Faberman and J. Haltiwanger (2006), “The Flow Approach to Labor Markets:
New Data Sources and Micro-Macro Links”, ��������ki������������i��, No. 12167.
Davis, Steven and John, Haltiwanger (1999), “On the Driving Forces Behind Cyclical
Movements in Employment and Job Reallocation”, ����i����������i�����i��� 89: 1234-
1258.
238
Davis, Steven, and John Haltiwanger (1990), “Gross Job Creation and Destruction:
Microeconomic Evidence and Macroeconomic Implications”, ����������������i���������,
ed. by Olivier Blanchard, and Stanley Fischer, MIT Press.
Davis, Steven, and John Haltiwanger (1992), “Gross Job Creation, Gross Job Destruction, and
Employment Reallocation”, ���������������������������i��, 107(3): 818-863.
Davis, Steven, Jason Faberman and John Haltiwanger (2005), “The Flow Approach to Labor
Markets: New Data Sources, Micro-Macro Links and the Recent Downturn”, �����i�����i���
������ No. 1639.
de Brouwer G., and N. Ericsson (1995), “Modeling Inflation in Australia”, �������������
�i�����i��������, No. 9510.
Debelle, G., J. Vickery (1998), “Is the Phillips Curve a Curve? Some Evidence and Implications
for Australia”, ������i��������, 74 (227): 384-398.
Diamond, Peter A. (1982), “Aggregate Demand Management in Search Equilibrium”, ��������
������i�i�����������, ���(5): 881-894.
Dixon, Huw and Neil, Rankin (1994), "Imperfect Competition and Macroeconomics: A
Survey", �������������i��������, 46: 171-199.
Dixon, Huw and Neil, Rankin (1995), �������������������i�����������������k��������
���i���������i������, New York, Cambridge University Press.
Dopke, J., J. Dovern, U. Fritsche, and J. Slacalek (2005), “European Inflation Expectations
Dynamics", ������������������k��i�����i������������i����, Economics Studies No. 37.
Dornbusch, Rudiger and Stanley, Fischer (1994), �����������i����Sixth Edition, New York,
McGraw- Hill.
Dufour, Jean-Marie, Lynda Khalaf, Maral Kichian (2006), “Inflation Dynamics and the New
Keynesian Phillips Curve: An Identification-Robust Econometric Analysis”, �����������
������i�������i��������������, 30: 1707-1727.
Dupor, B., T. Kitamura, T. Tsuruga (2010), “Integrating Sticky Prices and Sticky Information”,
�������i������������i�����������i��i��� 92: 657-669.
Dupor, Bill and Takayuki, Tsuruga, (2005), “Sticky Information: The Impact of Different
Information Updating Assumptions”, ����������������������i����������ki��� 37(6): 1143-
239
1152.
Dwyer J., and K., Leong (2001), “Changes in the Determinants of Inflation in Australia”, ����
����������i�����i��������, No. 02.
Elsby, Michael W., Ryan Michaels, and Gary Solon (2007), “The Ins and Outs of Cyclical
Unemployment”, ��������ki������������i����No. 12853.
Engle, R. and C.W.J. Granger, (1987), “Co-integration and Error Correction: Representation,
Estimation and Testing”, ���������i��, 55 (2): 251-276.
Fischer, Stanley (1977), “Long-Term Contracts, Rational Expectations, and the Optimal Money
Supply Rule”, ��������������i�i�����������, 85: 191- 205.
Foote, Christopher (1998), “Trend Employment Growth and the Bunching of Job Creation and
Destruction”, �������������������������������i��, 113(3): 809-834.
Foss, Nicolai (2003), “Bounded Rationality in Economics of Organization: Much Cited and
Little Used”, �����������������i������������, 24: 245-264.
Foster, Lucia, John Haltiwanger and Namsuk Kim (2006), “Gross Job Flows for the U.S.
Manufacturing Sector: Measurement from the Longitudinal Research Database”,
http://econweb.umd.edu/~haltiwan/download/gflows_112906.pdf.
Frank, Robert (1997), �i���������i������������i��, Third Edition, New York, McGraw Hill.
Friedman, M. (1957), ������������������������i��������i����Princeton, Princeton University
Press.
Friedman, Milton (1968), "The Role of Monetary Policy”, ����i����������i�����i��, 58(1):
1-17.
Fuhrer, J.C., G. Moore (1995), “Inflation Persistence”, �������������������������������i��,
110: 127-159.
Fuhrer, Jeffrey C. (1997), “The (Un)Importance of Forward-Looking Behavior in Price
Specifications”, ����������������������i���������ki��� 29: 338-350.
Gali, J. and M. Gertler (1999), “Inflation Dynamics: A Structural Econometric Analysis”,
��������������������������i��, 44: 195-222.
Galı, J., M. Gertler, D. Lopez-Salido (2001), “European Inflation Dynamics”, ���������
240
������i�����i��, 45 (7): 1237-1270.
Galı, J., M. Gertler, D. Lopez-Salido (2003), “Erratum to European Inflation Dynamics”,
���������������i�����i��, 47 (4): 759-760.
Galı, J., M. Gertler, D. Lopez-Salido (2005), “Robustness of the Estimates of the Hybrid new
Keynesian Phillips Curve”, ��������������������������i��, 52: 1107-1118.
Golosov, M., R.E. Lucas Jr. (2007), “Menu Costs and Phillips Curves”, ��������������i�i����
�������� 115 (2): 171-199.
Gordon, D.F. (1974), “A Neoclassical Theory of Keynesian Unemployment”, ������i��
����i��, 12: 431-459
Granger, C. W. J. and P. Newbold (1974), "Spurious Regressions in Econometrics", �����������
������������������i��, 2: 111-120.
Gregory, R.G. (1986), “Wages Policy and Unemployment in Australia”, ������i��, 53 (210)
Supplement: S53-S74.
Gruen D., A., Pagan and C., Thompson (1999), “The Phillips Curve in Australia”, �����������
���������������i��, 44(2): 223-258.
Gujarati, D. (2003),” ���i�����������i��”, 4th edition, New York: McGraw-Hill.
Hagger. A.J. (1978), “Inflation”, in F.,H., Gruen (ed.), ������������������i���������i����
Sydney, Allen & Unwin, 133-186.
Haley, J. (1990), “Theoretical Foundations of Sticky Wages”, �����������������i���������, 4:
115-155.
Hall, R. (2005), “Employment Fluctuations with Equilibrium Wage Stickiness”, ����i����
������i�����i��, 95: 50-65.�
Hall, Robert (1972), “Turnover in the Labor Force”, ����ki��������������������i�����i�i��, 3:
709-756.
Hall, Robert (1988), “Fluctuation in Equilibrium Unemployment”, ��������i����������i��
���i��, 78(2): 269-275.
Hall, Robert (1999), “The Concentration of Job Destruction”, ��������ki������������i��, No.
7025.
241
Hall, Robert E (2005), “Job Loss, Job Finding, and Unemployment in the U.S. Economy over
the Past Fifty Years”, ����������������i���������, 20: 101-137.
Hashimoto, H. (1981), “Firm-Specific Human Capital as a Shared Investment”, ����i����
������i�����i��, 71: 475-482.
Hausman, Daniel (1994), ������i�����������������i����������������, Second Edition, New
York, Cambridge University Press.
Heertje, Arnold (1995), ������k��������������������i��, �olume Two, �rookfield, US,
Edward Elgar.
Hendry, D.F., (1980), “Econometrics: Alchemy or Science�”, ������i��, 47: 387-406.
Hornstein, Andreas (2007), “Evolving Inflation Dynamics and the New Keynesian Phillips
Curve”, �������������������k�����i�������������i������������ 93: 317-39.
Ireland, P.N. (2001) “Sticky Price Models of the �usiness Cycle: Specification and Stability”,
��������������������������i��� 47(1): 3-18.
J��skel� J., and K., Nimark (2008), “A Medium-Scale �pen Economy Model of Australia”,
��������������i�����i��������, No. 07.
Jondeau, E., H. Le �ihan (2005), “Testing for the New Keynesian Phillips Curve, Additional
International Evidence”, ������i��������i��, 22: 521-550.
Jonson, P., K. Mahar, G. Thompson (1973), “Earnings and Award Wages in Australia”, ��������
���k�����������i������������i�����i����������� (revised).
Jonson, P., Mahar, K., Thompson, G., (1974), “Earnings and Award Wages in Australia”,
�������i���������i��������� 13 (22): 80-98.
Kahneman, Daniel and �ernon Smith (2002), “Foundation of �ehavioral and E�perimental
Economics”, http:��www.nobelprize.org�nobel�prizes�economics�laureates�2002�advanced-
economicsciences2002.pdf
Kahneman, Daniel, and Amos, Tversky (1979), “Prospect Theory: An Analysis of Decision
Under Risk”, ���������i��, 47: 263-292.
Katz, L.F. (1986), “Efficiency Wage Theories: A Partial Evaluation”, ����������������i���
������, 1: 235-276.
242
Katz, L.F. (1988), “Some Recent Developments in Labour Economics and Their Implications
for Macroeconomics”, ����������������������i����������ki��, 20(3):507-522.
Khan, H., �. �hu (2006), “Estimates of the Sticky-Information Phillips Curve for the United
States”, ����������������������i���������ki��, 38: 195-207.
Khan, Hashmat and �henhua, �hu (2002), “Estimates of the Sticky-Information Phillips Curve
for the United States, Canada, and the United Kingdom”, ���k��������������ki��������� No.
19.
Kiley, M. (2007), “A �uantitative Comparison of Sticky Price and Sticky Information Models
of Price Setting”, ����������������������i����������ki��, 39: 102-125.
Klenow, P. J. and J. L. Willis, (2007), “Sticky Information and Sticky Prices”, �����������
���������������i��, 54(S1): 79-99.
Knotek, E. (2006), “A Tale of Two Rigidities Sticky Prices in a Sticky Information
Environment”,��������������������k����K�������i��, Research Working Paper No. 15.
Korenok, �. (2008), “Empirical Comparison of Sticky Price and Sticky Information Models”,
����������������������i�, 30: 906-927.
Korenok, �., N. Swanson (2007), “How Sticky is Sticky Enough� A Distributional and Impulse
Response Analysis of new Keynesian DSGE Models”, ����������������������i���������ki��,
39: 1481-1508.
Kuhn, Thomas (1970), �������������������i���i�i���������i��, Chicago, University of Chicago
Press.
Kurmann, Andre (2005), “�uantifying the Uncertainty about a Forward-Looking, New
Keynesian Pricing Model”, ��������������������������i��, 52: 1119-1134.
Kuttner, K. and T. Robinson (2010), “Understanding the Flattening Phillips Curve”, ����������
����i���������������������i��������i�����, 21(2): 110-125.
Kydland, F.E. and E.C. Prescott (1977), “Rules Rather Than Discretion: The Inconsistency of
�ptimal Plans”, ��������������i�i�����������, 85(3): 473-492.
Kydland, F.E. and E.C. Prescott (1982), “Time to �uild and Aggregate Fluctuations”,
���������i��, 50(6): 1345-1370.
243
Lacker Jeffrey M., and John A. Weinberg (200), “Inflation and Unemployment: A Layperson�s
Guide to the Phillips Curve”, �������������������k�����i�������������i�����������, 93: 201-
227.
Leeper E., C. Sims, and T. �ha (1996), “What Does Monetary Policy Do�”, ����ki�����������
���������i�����i�i��, 2: 1-78.
Lelbensteir, J. (1957), ������i�����k�������������������i��������, New York, Wiley.
Lindbeck, A. and D.J. Snower (1985), “E�planations of Unemployment”, ����������i������
������i�����i��, 28(2): 34-59.
Lindbeck, A. and D.J. Snower (1986), “Wage Setting, Unemployment, and Insider-�utsider
Relations”, ����i����������i�����i��, 76(2): 235-239.
Lindbeck, A. and D.J. Snower (1988a), “Cooperation, Harassment and Involuntary
Unemployment: An Insider-�utsider Approach”, ����i����������i�����i��, 78(1): 167-188.
Lindbeck, A. and D.J. Snower (1988b), �������i��������i�����������������������������
������������, Cambridge, MA: MIT Press.
Lind�, Jesper (2005), “Estimating the New-Keynesian Phillips Curves: A Full Information
Ma�imum Likelihood Approach”, ��������������������������i��, 52(6): 1135-1149.
Lipsey, R.G. (1960), “The Relationship �etween Unemployment and the Rate of Change of
Money Wage Rates in the U.K. 1862-1957: A Further Analysis”, ������i��, 17: 1-31.
Lucas, Robert (1972), “E�pectations and Neutrality of Money”, �����������������i��������, 4:
103-124.
Lucas, Robert (1973), “Some International Evidence on �utput-Inflation Trade-offs”, ����i����
������i�����i��, 63: 326-334.
Lucas, Robert E. (1976), “Econometric Policy Evaluation: A Critique”, ������i������������
��������������i����������i�����i��� 1: 19-46.
Mankiw, Gregory (1985), “Small Menu Costs and Large �usiness Cycles: A Macroeconomic
Model of Monopoly”, ���������������������������i��, 100: 529-539.
Mankiw, Gregory (1988), “Recent Developments in Macroeconomics: A �ery �uick Refresher
Course”, ����������������������i���������ki��, 20: 436-458.
244
Mankiw, Gregory and Ricardo Reis (2001), “Sticky Information �ersus Sticky Prices. A
Proposal to Replace the New Keynesian Phillips Curve”, ��������ki������������i��, No.
8290.
Mankiw, Gregory and Ricardo Reis (2002), “Sticky Information �ersus Sticky Prices: A
Proposal to Replace The New Keynesian Philips Curve”, �������������������������������i��,
117(4): 1295-1328.
Mankiw, N. Gregory (2006), "The Macroeconomist as Scientist and Engineer", ���������������
������i����������i���, 20(4): 29-46.
Mankiw, N. Gregory, and Ricardo Reis (2006), “Pervasive Stickiness”, ����i����������i��
���i��, 96(2): 164-169.
Mankiw, N. Gregory, Ricardo Reis, and Justin Wolfers (2003), “Disagreement About Inflation
E�pectations”, ��������ki������������i����No. 9796.
Mankiw, N.G. (1992), “The Reincarnation of Keynesian Economics”, ���������������i��
���i��, 36(2-3): 559-565.�
Mankiw, N.G. (2001), “The Ine�orable and Mysterious Trade-off �etween Inflation and
Unemployment”,�����������i���������, 111: 45-61.
Mankiw, N.G. and D. Romer (eds) (1991), ����K�����i���������i��, Cambridge, MA: MIT
Press.
Mankiw N.G., R. Reis (2007), “Sticky Information in General Equilibrium”, ���������������
���������������i�������i��i��, 5: 603-613.
Mavroeidis, S. (2005), “Identification Issues in Forward-Looking Models Estimated by GMM,
with an Application to the Phillips Curve”, ����������������������i����������ki��� 37(3): 421-
448.
McDonald, J. (1975), “Wages and prices in Australia: �n the Short and Long-Run Trade-offs
�etween Inflation and Unemployment”, �������i���������i��������� 14 (25): 154-170.
Mirrlees, J. (1975), “A Pure Theory of Underdeveloped Economies”, ���i��������i��
��������������������ed. L.A. Reynolds, New Haven, Yale University Press.
Mortensen, Dale and Christopher A. Pissarides (1994), “Job Creation and Job Destruction in the
245
Theory of Unemployment”, ���i������������i������i��, 61(3): 397-415.
Nason, James, and Gregor Smith (2008), “The New Keynesian Phillips Curve: Lessons From
Single-Equation Econometric Estimation”, ������i������������ �olume 94, No. 4, �on-line�
�September 5, 2009� available from:
http:��www.richmondfed.org�publications�research�economic�quarterly�2008�fall�pdf�nason�sm
ith.pdf
Nason, James, and Gregor Smith (2008), “Identifying the New Keynesian Phillips Curve”,
���������������i������������i����23: 525-551.
Neiss, Katharine S., and Edward Nelson (2005), “Inflation Dynamics, Marginal Cost, and the
�utput Gap: Evidence from Three Countries”, ����������������������i���������ki��, 37
(December): 1019-1045.
Nelson, C.R. and C.I. Plosser (1982), “Trends and Random Walks in Macroeconomic Time
Series: Some Evidence and Implications”, ��������������������������i��, 10: 139-162.
Nevile, J. (1977), “Domestic and �verseas Influences on Inflation in Australia”, �������i���
������i����������16(28): 121-129.
Nevile, J. (1975), “A Comment on Short-Run and Long-Run Trade-offs �etween Inflation and
Unemployment In Australia”, �������i���������i��������� 14 (24): 132-136.
Norman, R., and A. Richards (2010), “Modelling Inflation in Australia”, �������������
�i�����i��������� No. 03.
�rmerod, Paul (1994), �������������������i��, London, Faber and Faber.
Parkin, M. (1973), “The Short-Run and Long-Run Trade-offs between Inflation and
Unemployment in Australia”, �������i���������i����������12 (21): 127-144.
Parkin, M. (1986), “The �utput-Inflation Trade-off When Prices Are Costly to Change”,
��������������i�i�����������, 94: 200-224.
Parkin, M. and R. �ade (1982), ������������������i��, ��ford, Philip Allan.
Pennant-Rea, Rupert and Clive Crook (1986), ����������i����������i��, New York, Pelican
�ooks.
246
Perry, L., (1980), “A Note on Phillips and Phillips Curve Economics”, ������i��������, 56
(152): 87-90.
Phelps, E.S. (1967), “Philips Curves, E�pectations of Inflation and �ptimal Unemployment
�ver Time”, ������i��, 34: 254-281.
Phelps, E.S. (1970), �i����������i���������i����������������������������i���������, New
York, Norton.�
Phelps, E.S. (1990), ����������������������������i���������, ��ford, ��ford University
Press.
Phelps, E.S. (1992), “E�pectations in Macroeconomics and the Rational E�pectations Debate”,
in A. �ercelli and N. Dimitri (eds), �����������i��������������������������������i��, ��ford,
��ford University Press.
Phelps, Edmund (1967), “Phillips Curves, E�pectations of Inflation and �ptimal
Unemployment �ver Time”, ������i��, 2(3): 22-44.
Phelps, Edmund (1968), "Money-Wage Dynamics and Labor Market Equilibrium”, �����������
���i�i�����������, 76 (4): 678-711.
Phelps, Edmund (1970), “Introduction”, In Edmund Phelps et al., �i���������i���������i����
������������������������i���������, New York, Norton.
Pissarides, Christopher (1985), “Short-Run Dynamics of Unemployment, �acancies and Real
Wages”, ����i����������i������i��, 75: 676-690.
Polanyi, Michael (1958), ���������K��������, Chicago, Chicago University Press.
Porter, Michael (1990), ����������i�i�������������������i���, New York, Macmillan.
�uandt, R. (1960), “Tests of the Hypothesis That a Linear Regression System �beys Two
Separate Regimes”, �������������������i��������i��i���������i��i��, 55 (290): 324-330.
Rabanal, Pau and Juan F. Rubio-Ramırez (2005), “Comparing New Keynesian Models of the
�usiness Cycle: A �ayesian Approach”, ��������������������������i����52: 1151-1166.
Rao, �. �haskara (1977), “An Analysis of the Short and Long-Run Trade-offs between
Unemployment and Inflation and Estimates of the Equilibrium Steady State Unemployment
Rate in Australia”, �������i���������i��������, 16: 273-284.
247
Rao, �. �haskara (1992), “A Model of Income, Unemployment and Inflation for the USA”,
����i���������i��, 24(6): 597-605.
Rao, �. �haskara and Tamazian, Artur (2008), “A Model �f Growth and Finance: FIML
Estimates for India”, http:��mpra.ub.uni-muenchen.de�8763�
Reis, Ricardo (2005), “Inattentive Producers”, ���i������������i������i��� 73: 793-821.
Richard, Curtin (1996), “Procedure to Estimate Price E�pectations”, mimeo, University of
Michigan Survey Research Center.
Roberts, J.M. (1998), “Inflation E�pectations and the Transmission of Monetary Policy”,
���ki��������, Federal Reserve �oard.
Roberts, J.M. (1995), “New Keynesian Economics and the Phillips Curve”, ������������������
����i����������ki��, 27(4): 975-984.
Roberts, J.M. (2001), “How Well Does the New Keynesian Sticky-Price Model Fit the Data�”
�i����������������i����i�����i������i����No. 13, Federal Reserve �oard.
Romer, Christina and David Romer (2000), “Federal Reserve Information and the �ehavior of
Interest Rates”, ��������i����������i�����i��, 90(3): 429-457.
Romer, David (2001), ��������������������i��, New York, McGraw Hill.
Rotemberg, J.J., M. Woodford (1997), “An �ptimization-�ased Econometric Framework for
the Evaluation of Monetary Policy”, In: �ernanke, �.S., Rotemberg, J.J. (Eds.), �����
�����������i���������, Cambridge, MIT Press.
Rotemberg, Julio (1982), “Sticky Prices in the United States", ��������������i�i�����������,
90(6): 1187-1211.
Rotemberg, Julio (1987), “The New Keynesian Microfoundations", ������i���������������
������i����������������������i���������, edited by Stanley Fischer, 69-104.
Rudd, Jeremy, and Karl Whelan (2005a), “Does Labor�s Share Drive Inflation�”, �����������
�����������i���������ki��, 37: 297-312.
Rudd, Jeremy, and Karl Whelan (2005b), “New Tests of the New Keynesian Phillips Curve”,
��������������������������i��� 52 (September): 1167-1181.
248
Rudd, Jeremy, and Karl Whelan (2006), “Can Rational E�pectations Sticky-Price Models
E�plain Inflation Dynamics�”, ����i����������i����i��,96 (March): 303-320.
Rudd, Jeremy, and Karl Whelan (2007), “Modelling Inflation Dynamics: A Critical Review of
Recent Research”, ����������������������i����������ki��, 39: 155-170.
Russell, �. and A. �anerjee (2006), “The Long-run Phillips Curve and Non-stationary
Inflation”, �����������i����i�������i����, Working Papers EC� 2006�16.
Salemi, Michael K. (2006), “Econometric Policy Evaluation and Inverse Control”, �����������
�����������i����������ki����38: 1737-1764.
Salop, S.C. (1973), “Wage Differentials in a Dynamic Theory of the Firm”, �����������
������i��������, 6:321-344.
Salop, Steven (1979), “A Model of the Natural Rate of Unemployment”, ����i����������i��
���i��, 69: 117-125.
Samuelson, P.A. and R.M. Solow (1960), “Analytical Aspects of Anti-Inflationary Policy”,
����i����������i�����i��, 49: 177-194.
Sargent, T.J. and N. Wallace (1975), “Rational E�pectations, the �ptimal Monetary Instrument
and the �ptimal Money Supply Rule”, ��������������i�i�����������, 83: 241-254.
Sargent, T.J. and N. Wallace (1976), “Rational E�pectations and the Theory of Economic
Policy”, ��������������������������i��, 2: 169-183.
Sbordone, A. (2002), “Prices and Unit Labor Costs: a New Test of Price Stickiness”, �����������
���������������i��� 49 (2): 235-456.
Sbordone, Argia M (2005), “Do E�pected Marginal Costs Drive Inflation Dynamics�”, ��������
������������������i��, 52: 1183-1197.
Shimer, R. (2005), “The Cyclical �ehaviour of Equilibrium Unemployment and �acancies”,
����i����������i�����i��, 95(1): 25-49.
Shimer, Robert (1998), “Why is the U.S. Unemployment Rate So Much Lower�”,
http:��www.princeton.edu��shimer
Shimer, Robert (2007), “Mismatch”, ��������i����������i�����i��, 97(4): 1074-1101.
Shimer, Robert (2007), “Reassessing the Ins and �uts of Unemployment”,
249
http:��robert.shimer.googlepages.com�reassess-print.pdf
Shimer, Robert and Ivan Werning (2007), “Reservation Wages and Unemployment Insurance”,
�������������������������������i��, 122(3): 1145-1185.
Simes, R. and C. Richardson (1987), “Wage Determination in Australia”, ������i��������, 63(181): 144-155.
Simon, Herbert (1957), ������������������i����������i����, New York, John Wiley and Sons.
Simon, Herbert (1959), “Theories of Decision Making in Economics and �ehavioral Science”,
����i����������i�����i��, 49: 253-283.
Simon, Herbert (1979), “Rationality Decision Making in �usiness �rganizations”, ����i����
������i�����i��, 69: 493-513.
Simon, Herbert (1991), “�rganizations and Markets”, �����������������i����������i���, 5: 25-
44.
Sims, C. (2003), “Implications of Rational Inattention”, ��������������������������i��, 50:
665-690.
Smets, F., R. Wouters (2003), “An Estimated Stochastic General Equilibrium Model of the
Euro Area”, ������������������������������i�������i��i��� 1(5): 1123-1175.
Snowdon, �rian and Howard, �ane, ������������������i�� (2005), MA (USA), Edward
Elgar.
Solow, R.M. (1979), “Another Possible Source of Wage Stickiness”, �������� ���
�����������i��, 1:79-82.
Solow, R.M. (1990), ��������������k�����������i�������i���i��, ��ford, �asil �lackwell.
Solow, R.M. (1997), “Is There a Core of Usable Macroeconomics That We Should All �elieve
In�”, ����i����������i�����i��, 87(2): 230-232.
Solow, Robert (1981), “�n Theories of Unemployment”, ����i����������i�����i��, 91: 848-
866
Solow, Robert (2010), “�uilding a Science of Economics for the Real World”, Prepared
Statement of Robert Solow, Professor Emeritus, MIT, to the House Committee on Science and
Technology, Subcommittee on Investigations and �versight.
250
Stiglitz, J.E. (1976), “The Efficiency Wage Hypothesis, Surplus Labor and The Distribution of
Income in L.D.C.�s”, �������������i��������, 28: 185-207.
Stiglitz, J.E. (1982), “The Wage-Productivity Hypothesis: Its Economic Consequences and
Policy Implications”, Paper presented at the New York Meetings of the American Economic
Association. Also in M.J. �oskin, ed., ��������������������i������i���i�����, ��ford, �asil
�lackwell, 1987, pp. 130-165.
Stiglitz, J.E. (1984), “Theories of Wage Rigidity” ��������ki������������i��, No. 1142.
Stiglitz, J.E. (1997), “Reflections on the Natural Rate Hypothesis”, �����������������i��
��������i���, 11(1): 3-10.
Stiglitz, J.E. (1976), “Prices and �ueues as Screening Devices in Competitive Markets”, �����
�����i������������������, Stanford University.
Stiglitz, Joseph (2000), “The Contributions of the Economic of Information to Twentieth
Century Economics”, ���������������������������i��, 115: 1441-1478.
Stiglitz. J.E. and A. Weiss (1983), “Incentive Effects of Terminations: Applications to the
Credit and Labor Markets”, ����i����������i�����i��, 73: 912-927.
Stock, James H., and Mark W. Watson (2007), “Why Has U.S. Inflation �ecome Harder to
Forecast�”, ����������������������i���������ki��� 39: 3-34.
Stone, A., T. Wheatley and L. Wilkinson (2005), “A Small Model of the Australian
Macroeconomy”, �����������k�����������i���i�����i��������, No. 11.
Summers, Lawrence (1986), “Why Is the Unemployment Rate So �ery High Near Full
Employment�”, ����ki��������������������i�����i�i��, 2: 339-383.
Summers, Lawrence, Charles Holt, Robert Hall, Martin �ailey, and Kim Clark (1979), “Labor
Market Dynamics and Unemployment: A Reconsideration”, ����ki��������������������i��
���i�i��, 1: 13-72.
Svensson, Lars (1997), “Inflation Forecast Targeting: Implementing and Monitoring Inflation
Targets”, ���������������i�����i��, 410: 1111-1146.
Taylor, John (1979), “Staggered Wage Setting in a Macro Model”, ����i����������i�����i��,
69(2): 108-113.
251
Taylor, John (1980), "Aggregate Dynamics and Staggered Contracts", ��������������i�i����
�������, 88(1): 1-23.
Thurow, L.C. (1983), ���������������������������������������i��, New York, Random
House.
Tisdell, Clem (1996), �����������i����i�������������i��������i��, MA (USA), Edward
Elgar.
Tovar, Camilo (2008), “DSGE Models and Central �anks”, ���k�������������i�����������������
���ki������������.
Trabandt, M. (2006), “Sticky Information vs. Sticky Prices: A Horse Race in a DSGE
Framework”, ���ki��������, Humboldt University.
Weiss, A. (1991), ���i�i������������������������������������������������������i�����i��,
��ford, Clarendon Press.�
Weiss, Andrew (1980), “Job �ueues and Layoffs in Labor Markets with Fle�ible Wages”
��������������i�i������������ 88: 526-538.
Woodford, M. (2003), ���������������i������������i�������������������������������i��,
Princeton, Princeton University Press.
Woodford, Michael (2001), “Imperfect Common Knowledge and the Effects of Monetary
Policy”, ��������ki������������i��, No. 8673.
Woodford, Michael (2008), "Convergence in Macroeconomics: Elements of a New Synthesis",
Annual Meeting of the American Economics Association,
http:��www.columbia.edu��mw2230�Convergence�AEJ.pdf
Yellen, J. (1984), “Efficiency Wage Models of Unemployment”, ����i����������i�����i��,
74: 200-205
Yule, G.U. (1926), "Why Do We Sometimes Get Nonsense Correlations between Time Series�
A Study in Sampling and the Nature of Time Series", �������������������������i��i�������i���
89: 1-64.
�hang, Chengsi, Denise �sborn, and Dong Heon Kim (2008), “The New Keynesian Phillips
Curve: From Sticky Inflation to Sticky Prices”, ����������������������i���������ki��, 40: 667-
699.
