Dynamic approach to short run economic
fluctuations.
Part 1.
The Phillips Curve & Dynamic Aggregate Supply.
Macroeconomics II
Macroeconomics 2
Dr hab. Joanna Siwińska-Gorzelak
WNE UW
Motivation
• The static AD/SAS model fails to take into account
inflation
• The dynamic model, which we will start to discuss today,
allows to model inflation and dynamic interactions
between consecutive periods
• Today we will develop the dynamic aggregate supply line
(DAS) - the supply side of the DAD/DAS model and the
famous and very closely related Phillips curve
• While later on we will focus only on DAS, it is good to
know the Phillips curve as well
Important
• If you have difficulties with the AD/AS model, please read
chapters 10, 11 and 13 from Mankiw!
Recall the aggregate supply curve (SRAS)
Three broad explanations are offered:
1. The sticky-wage model
2. The imperfect-information model
3. The sticky-price model
All three imply a relationship that can be approximated by a simple formula (but note that the equation can also be more complicated – for example the function can be non-linear :
natural rate
of output
a positive
parameter
the expected
price level
the actual
price level
agg.
output
)( e
ttttPPYY
Recall the aggregate supply curve (SRAS)
Each of the
three models of
agg. supply imply
the relationship
approximated by
the SRAS curve
& the simple
equation. Y
P LRAS
Y
SRAS eP P
eP P
eP P
)( e
ttttPPYY
Deriving the Dynamic Aggregate Supply & the Phillips
curve from aggregate supply
The DAS Curve -
we will use it later!
)()1( e
ttttPPYY
))(/1()2(tt
e
ttYYPP
ttt
e
ttYYPP ))(/1()3(
)ln(]))(/1ln[()ln()ln()4(11 tttt
e
tttYYPPPP
tt
e
ttyy )()5(
We can also use
a more
complicated
equation
Substract Pt-1 from both sides and take logs.
Deriving the Dynamic Aggregate Supply & the
Phillips curve from aggregate supply
tt
e
ttyy )()5(
)()()6(Nttt
uuyy
tNt
e
ttuu )()7(
Okun’s Law
Phillips curve
Okun’s Law
Source: ECB, 2011
The DAS curve and the Phillips Curve – the first
building block of the DAD/DAS model
The DAS curve states that current is related to:
• expected inflation, e.
• Deviations of output from the natural rate
• supply shocks,
The Phillips curve states that current is related to
• expected inflation, e.
• cyclical unemployment: the deviation of the actual rate of
unemployment from the natural rate
• supply shocks,
Intuition of the DAS & Phillips curve: an ongoing, anticipated inflation
in the AS/AD model
Intuition of the DAS & Phillips curve: Unanticipated inflation
in the AD/AS model
The Phillips Curve and SRAS
• DAS curve: Deviations of output from its natural
level are related to unexpected movements in the
inflation rate.
• Phillips curve: Deviations of unemployment from its
natural rate are related to unexpected movements in
the inflation rate.
The second building block of the DAS: adaptive
expectations
• Adaptive expectations: an approach that assumes
people form their expectations of future inflation
based on recently observed inflation.
• A simple example:
Expected inflation = last year’s actual inflation
Then, the DAS becomes
11 tttE
ttttyy
)(
1
The Dynamic Aggregate Supply Curve
DAS slopes upward:
high levels of output are
associated with higher-
than-expected inflation.
This is because of
demand-pull inflation
Yt
πt
DASt
ty
tt
1
ttttyy
)(
1
The Dynamic Aggregate Supply Curve
A change in
previous period’s
inflation shifts the
DAS curve
Yt
π
DASt=1
Y
0t
ttttt
yy 1
0t
Assume
DASt=2
1t
10
The Dynamic Aggregate Supply Curve
An change of the
natural level of output
will shift the DAS curve
Yt
π
DASt=1
1tY
10
tt
0
DASt=2
Assume that
2tY
ttttt
yy 1
The Dynamic Aggregate Supply Curve
A supply shock will
shift the DAS curve
Yt
π
DASt=1
tY
0t
0210
tttand
DASt=2
21
tt
Assume that
ttttt
yy 1
Inflation expectations
• We are assuming a very simple way of expectation
formation; the reality can be much more complex.
• For example, recently some researches talk about
„anchored expectations”, with very interesting implications
for the Phillips Curve
Inflation inertia
In this form, the DAS (and Phillips curve) implies
that inflation has inertia:
• In the absence of supply shocks or deviations of output (and
unemployment) from its natural level, inflation will continue
indefinitely at its current rate.
• Past inflation influences expectations of current inflation, which
in turn influences the wages & prices that people set and
actual inflation.
ttttyy
)(
1
Two causes of rising & falling inflation
• cost-push inflation:
inflation resulting from supply shocks
Adverse supply shocks typically raise production
costs and induce firms to raise prices,
“pushing” inflation up.
• demand-pull inflation:
inflation resulting from demand shocks
Positive shocks to aggregate demand cause
unemployment to fall below its natural rate,
which “pulls” the inflation rate up.
ttttyy
)(
1
The Phillips curve
People adjust their
expectations over
time,
so the tradeoff only
holds in the short run.
u
nu
1
e
2
e
E.g., an increase
in e shifts the short-run P.C.
upward.
In the short
run, policymakers face a
tradeoff between and u.
The sacrifice ratio
• To reduce inflation, policymakers can contract agg.
demand, causing unemployment to rise above the natural
rate.
• The sacrifice ratio measures the percentage of a year’s
real GDP that had to be foregone to reduce inflation
by 1 percentage point.
• Sacrifice ratio = (lost GDP)/(total disinflation)
The natural rate hypothesis
Changes in aggregate demand affect output
and employment only in the short run.
In the long run, the economy returns to
the natural levels of output, employment,
and unemployment
An alternative hypothesis: Hysteresis
• Hysteresis: the long-lasting influence of history on
variables such as the natural rate of unemployment.
• Negative shocks may increase un, so economy may not
fully recover.
Hysteresis: Why negative shocks may increase
the natural rate
• The skills of cyclically unemployed workers may
deteriorate while unemployed, and they may not
find a job when the recession ends.
• Cyclically unemployed workers may lose
their influence on wage-setting;
then, insiders (employed workers)
may bargain for higher wages for themselves.
Result: The cyclically unemployed “outsiders”
may become structurally unemployed when the
recession ends.
„Old-fashioned Phillips curve” ?
• Krugman writes: „For one thing, the “accelerationist”
doctrine that has dominated economic discussion of
inflation and unemployment for 40 years has fallen flat.”
• “Anchored” expectations. Price- and wage-setters now act
as if they expect policymakers to hit their target (say: 2%)
• „Operationally, of course, such a curve looks just like the
old, pre-NAIRU Phillips curves people estimated in the
1960s.”
During the recent crisis…
• “The surprise [about inflation] is that it’s fallen so little,
given the depth and duration of the recent downturn.
Based on the experience of past severe recessions, I
would have expected inflation to fall by twice as much as
it has.” (John Williams, 2010.)
The changing Phillips curve
Source: Paul Krugman,
https://krugman.blogs.nytimes.com/2012/04/08/unemployment-and-
inflation/
The Phillips Curve for France, 1970-2013
Source: László Andor 01 October 2014;
http://voxeu.org/article/re-discovering-phillips-curve
The Phillips Curve for Germany
Source: László Andor 01 October 2014;
http://voxeu.org/article/re-discovering-
phillips-curve
Recently, questions about the PC are being asked…
• „Advanced economies have experienced little decline in inflation since the financial crisis of 2008-2009, calling into question one of the fundamental tenets of many macroeconomic theories: the Phillips curve linking the rate of change in prices to the level of economic activity”
• We nowadays observe relatively major differences in unemployment rates, while inflation remains rather low and stable.
• „The Phillips curve has not become vertical as the monetarists had predicted; it is much closer to being horizontal in recent years.” Paul Krugman
• .
Downward wage & price rigidity?
• Explanations based on recent labor market
developments, such as long-term unemployed having
smaller effects on wages, or downward wage rigidity
preventing wages from falling as much as in prior
downturns
• „It’s an interesting question why, one that has to be
answered in terms of psychology and sociology, but it’s
simply a fact that actual cuts in nominal wages happen
only rarely and under great pressure.” Paul Krugman
On the other hand….
• „Increasing evidence shows that after a flattening
occurred in the immediate aftermath of the global financial
crisis, the relationship between price inflation and
economic slack became stronger in the euro area.”
• Bulligan, Guido and Viviano, Eliana, Has the Wage Phillips Curve Changed in
the Euro Area? (September 22, 2016). Bank of Italy Occasional Paper No.
355.
Summary
We have derived the supply side of the DAD/DAS
model
• The dynamic supply curve states that inflation
depends on • expected inflation
• deviations of output from its natural level
• supply shocks