Nominal GDP Targeting, Real Economic Activity and Inflation Stabilization in A New Keynesian Framework Huiying Chen Department of Economics, University of Central Oklahoma Abstract This paper examines the performance of a nominal GDP growth targeting (NGDP-GT) rule versus a Taylor rule in a New Keynesian model. Compared to the Taylor rule, the targeting of the growth rate of nominal GDP leads to the avoidance of nearly half of the fluctuations in output, consumption, and inflation when an economy is hit by a total factor productivity shock. The NGDP-GT regime produces one third less fluctuation in output and consumption when the economy is subject to a markup shock. Remarkably, NGDP-GT does not cause inflation instability; in fact, it generates only half of the volatility in inflation compared to the Taylor rule. Involving a more appealing combination of output and inflation to absorb shocks, the NGDP-GT is a demonstrable and system- atic improvement. NGDP-GT can better address the dual mandate of the Fed- eral Reserve. Another advantage of NGDP-GT is the increasing prominence of smoothing fluctuations of real economic aggregates as the target of GDP growth increases within a plausible range. Moreover, the NGDP-GT rule outperforms strict inflation targeting and a strong response to inflation rule in stabilizing la- bor (subject to a markup shock), output, consumption, real wage and the real marginal cost. Key words: Nominal GDP Targeting; Inflation Targeting; Taylor Rule; Stabi- lization; Fluctuations; Shocks. JEL Classification: E31; E52; E58; E50 1
Transcript
Nominal GDP Targeting, Real Economic Activity and Inflation
Stabilization in A New Keynesian Framework
Huiying Chen
Department of Economics, University of Central Oklahoma
Abstract
This paper examines the performance of a nominal GDP growth targeting(NGDP-GT) rule versus a Taylor rule in a New Keynesian model. Compared tothe Taylor rule, the targeting of the growth rate of nominal GDP leads to theavoidance of nearly half of the fluctuations in output, consumption, and inflationwhen an economy is hit by a total factor productivity shock. The NGDP-GTregime produces one third less fluctuation in output and consumption when theeconomy is subject to a markup shock. Remarkably, NGDP-GT does not causeinflation instability; in fact, it generates only half of the volatility in inflationcompared to the Taylor rule. Involving a more appealing combination of outputand inflation to absorb shocks, the NGDP-GT is a demonstrable and system-atic improvement. NGDP-GT can better address the dual mandate of the Fed-eral Reserve. Another advantage of NGDP-GT is the increasing prominence ofsmoothing fluctuations of real economic aggregates as the target of GDP growthincreases within a plausible range. Moreover, the NGDP-GT rule outperformsstrict inflation targeting and a strong response to inflation rule in stabilizing la-bor (subject to a markup shock), output, consumption, real wage and the realmarginal cost.
Key words: Nominal GDP Targeting; Inflation Targeting; Taylor Rule; Stabi-lization; Fluctuations; Shocks.JEL Classification: E31; E52; E58; E50
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1 Introduction
Prior to the frequent federal funds rate hikes in the recent two years, the economic
crisis of 2007 to 2009 and the nominal interest rate at the zero lower-bound (ZLB)
revived economists’ interest in the targeting of nominal GDP (or nominal income)
as an attractive monetary policy option. Before 2008, the Taylor rule had kept its
prevalence of nearly two decades by virtue of being both relatively simple to compute
and practically implementable by the Federal Reserve while having great effectiveness
in preventing the recurrence of high inflation. As pointed out by Sumner (2014), if the
Great Moderation had continued, there would be few reasons to abandon the Taylor
rule. The current study is motivated by the ineffectiveness of the Taylor rule due to
the ZLB in recent years and its congenital defects in requiring the measurement of
real economic activity and core inflation, and by the discussion about nominal GDP
targeting.
This paper evaluates a nominal GDP growth rate targeting (NGDP-GT) rule and
a Taylor rule within a calibrated New Keynesian framework. For empirically plausible
sizes of total factor productivity (TFP) shocks, the NGDP-GT regime can significantly
improve economic performance in comparison to the Taylor rule regime. Relative to
the Taylor rule, the NGDP-GT rule leads to a reduction of deviations by 40% or
more in output, inflation, consumption, real wage, real marginal cost and interest
rate when a negative TFP shock impacts the economy. When a negative markup
shock hits the economy, anywhere from a third to a half of all variation in output,
inflation, labor, consumption, real wage, real marginal cost and interest rate can be
avoided by targeting the NGDP growth rate. In addition, I found that the standard-
deviation-ratios of key variables between the Taylor rule and NGDP-GT rule increase
along with the NGDP growth rate, which reveals that when the NGDP growth rate
2
increases within a plausible range the NGDP-GT rule further outperforms the Taylor
rule. Moreover, even though policy arrangements cannot be explicitly ranked when
nesting inflation targeting (IT) and strong response to inflation (IR)-type rules into
the pool, countries that implement strict IT and IR rules are expected to experience
smoother labor (in a markup shock case), output, consumption, real wage, and interest
rate paths. These countries are expected also to recover faster in recessions when they
instead pursue nominal GDP targeting.
The baseline setup of this paper is characterized by three sectors of the econ-
omy: households, monopolistically-competitive firms that face adjustment costs, and
a monetary authority. The private-sector equilibrium is constituted by optimal paths
of consumption, labor, real wage, real marginal cost, output, and inflation. For the
NGDP-GT rule, I keep the growth rate of nominal output between two consecutive
periods constant. In the benchmark model, the growth rate of NGDP is set to the U.S.
historical level. The paper then shows results that are robust to various nominal GDP
growth rates and to different magnitudes of shocks.
This paper contributes to the literature on NGDP targeting in the following as-
pects. First, the stability of an NGDP targeting rule is verified, and there is an
exploration of the mechanism that contributes to that stability. There is also a quan-
titative demonstration to what extent this rule can smooth out fluctuations of the
economy in comparison with the Taylor rule within a New Keynesian DSGE frame-
work. McCallum (1987), McCallum (1989), and Hall & Mankiw (1994) found that
this policy rule provides policy makers operability and robustness due to its favorable
performance across a range of models. In response to the ’Ball-Svensson’ instability
conclusion of Ball (1997) and Svensson (1997), McCallum (1997) utilizes a model in-
volving forward-looking rational expectations and alternative analysis of supply-side
specifications where he ultimately shows that the result of Ball (1997) and Svensson
3
(1997) is fragile. To examine these two competing results, Dennis (2001) considers
the general case where inflation expectations are a mixture of backward-looking and
forward-looking terms, which nests those of Ball (1997) and McCallum (1997) as spe-
cial cases. This general case yielded the result that nominal GDP growth targeting did
not lead to instability. In a recent paper, Henderson & Kim (2005) designs a model
that features optimization and monopolistic competition in both product and labor
markets where one-period nominal contracts signed before shocks are known. Quali-
tatively, nominal-income-growth targeting turned out to dominate inflation targeting
for plausible parameter values In a more recent literature, Garín et al. (2016)finds that
nominal GDP targeting is associated with smaller welfare losses compared to a Taylor
rule regime.
A second finding of this article is that the NGDP growth rate matters to the
relative performance of NGDP-GT. Standard deviation ratios of key variables between
the Taylor rule and NGDP-GT regimes turn out to have a positive linear relationship
with the NGDP growth rate, implying that an increase in GDP growth rate within a
plausible range strengthens the comparative advantages of NGDP-GT rule.
Third, when the economy is mainly subject to shocks that do not necessarily involve
monetary policy trade-offs for society, NGDP-GT is also relatively more effective in
stabilizing output, consumption, labor, and wage, which differs from Jensen (2002).
Jensen (2002)evaluates NGDP-GT versus IT and concludes that when the economy
is mainly subject to shocks that do not involve monetary policy trade-offs for society,
nominal income growth targeting is not preferred.
Finally, a conclusion can be drawn that nominal output targeting minimizes vari-
ance of all key economic indicators, such as real output, consumption, inflation, labor
and real wage, thereby minimizing the variance of the combination of real output and
price level; this is in line with the conclusions of Meade (1978), Tobin (1980) and Bean
4
(1983).
The rest of this paper is organized in the following structure: Section 3 outlines
the model and defines the private-sector equilibrium. Section 4 provides a description
of the policy rules. Section 5 presents the calibration of the model. Section 6 shows
the main results of this paper. Section 7 presents some robustness analysis. Section 8
concludes.
2 The Model
The economy is composed of three sectors: a continuum of infinitely-lived households
who derive utilities from consumption and leisure, monopolistically-competitive firms
that hire labor as the only input to produce differentiated products and face an ad-
justment cost for changing prices, and the monetary authority. The paper assumes an
efficient labor market.
2.1 Households
The representative household seeks to maximize the objective function:
E0
∞∑t=0
βtU(ct,lt)(1)
where β ∈ (0, 1) is the subjective discount factor, E0 is the mathematical expectation
operator conditional on information available in period 0. ct is the composite con-
sumption index, and lt is labor. The period utility function U(ct,lt) is assumed to be
continuous and twice differentiable, satisfying the usual properties: ∂U(·)∂c2 6 0, ∂U(·)
∂l< 0,
and ∂U(·)∂l2
6 0.
As standard in NK models, consumption ct is a Dixit-Stiglitz aggregator of differ-
5
entiated products cj,t, supplied by monopolistically-competitive firms:
ct =(� 1
0c
εt−1εt
j,t dj,t
))εt
εt−1
(2)
where εt measures the elasticity of substitution between two varieties of final goods.
The elasticity of substitution is set to be time-varying to allow for exogenous cost-push
shocks. All else equal, an increase in εt leads to a fall in the desired markup, and hence
to less inflationary pressure in equilibrium. The paper allows for markup shocks (i.e.
variations in εt) to avoid the ’Divine Coincidence’ result. In what follows, the study
also considers a constant elasticity of substitution, which is the case with TFP shocks
only.
The solution to the household’s problem of maximizing the consumption bundle ct
for any given level of expenditures yields the set of demand equations:
cj,t =(Pj,tpt
)−εt
ct, (3)
where Pt =(� 1
0P1−εtj,t dj
) εtεt−1 is the Dixit-Stiglitz price index that results from cost
minimization.
Maximization is subject to the sequence of the budget constraints:
ct + Bt
Pt= Rt−1Bt−1
Pt+ Wtlt
Pt+ Trt
Pt+ Πt
Pt(4)
where Bt represents the quantity of one-period nominally riskless bond that is pur-
chased in period t and matures in period t+ 1. Each bond pays one unit of money at
maturity. Rt is the nominal gross policy (or market) interest rate. Wt denotes nominal
wage, and wt denotes the real wage expressed as Wt
Pt. Trt is the net nominal transfers,
and Πt stands for nominal profits from the ownership of firms. Household’s choices of
6
ct, lt and Bt yield the following optimality conditions:
−Ul,tUc,t
= wt (5)
and
Uc,t = βRtEt
(Uc,t+1
πt+1
)(6)
where πt = Pt
Pt−1is the gross inflation rate, and Uc,t and Ul,t are respectively the marginal
utility of consumption and labor. Equation (1.5) describes the labor supply decisions,
and Equation (1.6) describes the optimal consumption decisions, which is the standard
Euler equation in consumption.
2.2 Firms
There is a continuum of identical monopolistically-competitive firms indexed by j ∈
[0, 1]. Each firm j hires labor as the only input and produces a differentiated product
yj,t using the identical technology:
yj,t = ztlj,t (7)
where zt represents the level of aggregate productivity, assumed to be common to all
firms, and to evolve exogenously over time. lj,t is the labor hired by firm j at time
t. First consider the cost minimization problem of firm j, min wtlj,t s.t. yj,t = ztlj,t,
where by symmetry, it implies
mct = wtzt
(8)
where mct is the Lagrange multiplier on the output constraint (7) and also the real
7
marginal cost of production. Equation (1.8) is the labor demand function.
The pricing of a firm is subject to a quadratic adjustment cost as in Rotemberg
(1982),
φ
2
(Pj,tPj,t−1
− π)2
yt (9)
where φ > 0 determines the degree of price rigidity, and π is the gross steady-state
inflation rate.
The problem for firm j is then to choose its price to maximize the expected present
discounted stream of profits:
E0∑∞t=0
βtUc,t
Uc,0
{(Pj,t
Pt−mcj,t)yj,t − φ
2 ( Pj,t
Pj,t−1− π)2yt
}(10)
subject to the downward-sloping demand curve that firm j faces:
yj,t =(Pj,tPt
)yt (11)
where βtUc,t
Uc,0is the stochastic discount factor.
Firms can change their prices in each period, subject to the adjustment cost. There-
fore, all the firms face the same problem, and thus will choose the same price and
produce the same quantity. In other words, Pj,t = Pt and yj,t = yt for any j. Hence,
the first-order condition for a symmetric equilibrium
1− φ(πt − π)πt + βφEt
[Uc,t+1
Uc,t(πt+1 − π)πt+1
yt+1
yt
]= εt(1−mct) (12)
is the Rotemberg version of the non-linear Phillips curve showing that current inflation
is a function of future expected inflation, the real marginal cost, and the level of output.
At steady state, this equation collapses to the familiar condition, mc = ε−1ε
which is
8
the inverse of the steady state gross price markup.
Since all firms will employ the same amount of labor, the aggregate production
function is simply given by:
yt = ztlt (13)
2.3 Market Clearing
In equilibrium, the aggregate resource constraint is given by:
yt = ct + φ
2 (πt − π)2yt (14)
2.4 The Private Sector Equilibrium
Given the exogenous process of zt and εt the private sector equilibrium is a state-
contingent sequence of allocations of {ct, lt, wt,mct, yt, πt}that satisfies the equilibrium
conditions of (5)-(6), (8) and (12)-(14) .
3 Policy Regimes
Given the model described above, I examine the performance of two simple policy rules
in the benchmark analysis. One rule targets the growth rate of nominal output and
the other resorts to the nominal interest rate as the instrument to respond to changes
of the economy (Taylor rule). Next, I discuss these two policy rules and analyze their
performances following a negative TFP shock and a negative markup shock with the
exogenous processes of zt and εt.
9
3.1 Nominal GDP Growth Targeting Rule
McCallum (1998), Orphanides (1999), and Trehan (1999) suggest that monetary pol-
icy should focus on nominal output growth because such a strategy does not rely on
uncertain estimates of the level of the output gap. Rudebusch (2002)admits that it
automatically takes into account movements in both prices and real output and can
serve as a long-run nominal anchor for monetary policy. Such a target linked to a
weighted average of inflation and employment will better address the Fed’s dual man-
date, according toSumner (2014). In the debate on nominal income level targeting
versus growth rate targeting, Billi (2015) provides evidence that in the presence of
persistent supply and demand shocks, nominal GDP level targeting (NGDP-LT) is
not preferable. During ZLB episodes, NGDP-LT leads to larger fluctuations in eco-
nomic activity. Therefore, the paper mainly focuses on the growth-rate targeting. In
the NGDP-GT regime, policymakers observe and respond only to the variations of
nominal GDP growth rate.
Nominal GDP growth assumes that the monetary authority commits to a certain
growth rate of nominal GDP. Letting Yt being nominal output, this rule reads:
YtYt−1
= k (15)
where k is the growth rate of NGDP. Equation (1.15) can be rewritten as:
ytyt−1
πt = k (16)
The regime of NGDP-GT implies a positive steady state inflation (or zero inflation
when k is set to 1). In particular, π = k at steady state.
10
3.2 The Taylor Rule
Following Faia (2008), a standard nonlinear version of the Taylor rule without labor
market inefficiency is an interest rate reaction function of this form:
log(Rt
R
)= ρrlog
(Rt−1
R
)+ (1− ρr)[ρπlog
(πtπ
)+ ρylog
(yty
)] (17)
where R and y represent the steady-state values of nominal gross interest rate and real
output, ρr denotes the smoothing coefficient of the interest rate, and ρπ and ρy are
respectively the coefficients of inflation and output. In line with the literature, the
interest rate responds to the deviations of inflation and output from their targets (or
steady-state values).
Different from most of the literature about the Taylor Rule, the paper does not
presume a zero (net) inflation steady state. For the purpose of consistency, the value
of π in the Taylor rule anchors at the value of π in the NGDP-GT rule, which also equals
to k. These identical steady-state inflation settings under the two policy frameworks
ensure that the steady-state values under both rules are the same. Any differences
between the rules will not result from the different steady states, which allows for
direct comparisons and contrasts between the policies to be made. For the benchmark
analyses, π in the benchmark analysis is set to 1.016 in the two regimes described
above. Other values are considered in the robustness tests.
4 Calibration
4.1 Functional Forms
Assume the following period utility function:
11
U(ct, lt) = c1−σt
1− σ − χl1+θt
1 + θ(18)
where σ is the curvature parameter, which represents households’ risk aversion. χ is
the scaling parameter and θ is the inverse of the intertemporal elasticity of substitution
(IES) for labor supply.
Total factor productivity and the elasticity of substitution are governed by the
following AR(1) process:
log(zt) = (1− ρz)log(µz) + ρzlog(zt−1) + vt (19)
log(εt) = (1− ρε)log(µε) + ρεlog(εt−1) + ut (20)
with ρz and ρε being the AR(1) coefficients of these processes, µz and µε, deterministic
steady state value of zt and εt respectively, being normalized to 1 and 6, the innovation
terms vt ∼ N(0, σ2z) and ut ∼ N(0, σ2
ε ). In the benchmark model, σz is set to 0.048 and
σε is set to 0.380 to generate a 0.015 standard deviation in output under the Taylor
rule.
4.2 Parameterization
Table 1 lists the baseline parameter values. These parameters are set to widely accepted
values based on US data. Assuming a time unit of one quarter, the discount factor β
is set to 0.99, implying a 4% annual interest rate. The risk aversion parameter sv is
set to 1.5. The scaling parameter χ is set to 12.792, so that the deterministic steady-
state value of l is 0.21, implying an average workweek of 35 hours in line with the
empirical average of weekly hours per worker over the period of 1964:Q1-2014:Q1, as
12
in Abo-Zaid (2015). The underling theory introduced in Faia & Monacelli (2007) and
Abo-Zaid (2015) implies the adjustment cost parameter φ = λ(λ−1)(ε−1)λ−β(λ−1) , with λ being
the quarterly price duration. Following Christiano et al. (2005) and Abo-Zaid (2015),
I set the price duration to 2.5 quarters. The deterministic steady-state value of εt is
set to 6, so that the net steady-state markup is 20%, consistent with the literature.
In the benchmark calibration, I assume the monetary authority targets the nominal
GDP growth rate k at 1.016 based on the historical quarterly GDP growth rate over
the period of 1947:Q1-2015:Q1. Moreover, other values of k are used in Section 6. The
value of R can be easily obtained from the consumption Euler equation: R = π/β.
The steady-state output level y is determined by the aggregate production function.
Values of ρr, ρπ and ρy are set following Faia (2008).
5 Quantitative Results
This section presents the numerical results regarding the two policy rules when the
economy is hit by a TFP shock and a markup shock. A general approach to policy
evaluation is to check the ability of the policy to smooth output, consumption, infla-
tion, labor and other important aggregates paths around the potential levels. This
smoothing can be achieved by producing the least fluctuations in these important eco-
nomic indicators. Tables 2 and 3 and Figures 1 and 2 provide the dynamic results of
these two policy regimes with respect to a negative TFP shock and markup shock.
5.1 Moment Conditions
Tables 2 and 3 report the results of the first and second moments of the economic
indicators following shocks of the same magnitude. Compared to the Taylor rule, the
prevention of swings in NGDP growth vastly helps prevent deviations of economic
13
aggregates from their trend path. The variables under the NGDP-GT render to be
substantially less volatile than under the Taylor rule. The standard deviations of
output, consumption, and inflation under the NGDP-GT are 60%, 60%, and 40%,
respectively, of the ones under the Taylor rule when the economy is hit by a negative
TFP shock. The Taylor rule also brings about at least 50% more fluctuations in real
wage and approximately 25%r more fluctuations in real marginal cost. Remarkably,
the interest rate appears to be sluggish under the NGDP-GT regime. Following an
exogenous markup shock, the Taylor rule still produces more than 40%, 40%, and
110% of fluctuations than the other regime, sequentially, on output, consumption, and
inflation, and about 42% more deviations on labor, real wage, and real marginal cost.
The interest rate also repeats its performance from the TFP shock scenario.
The effect of NGDP-GT on real economic activity and inflation stabilizing is sur-
prising to what economic intuition would suggest when the economy is subject to
supply shocks. The above numbers and the nature of the two policy rules reflect the
mechanism that makes the NGDP-GT rule a ’systematic improvement’. The Taylor
rule turns out to be rather aggressive in manipulating the interest rate to stabilize in-
flation; it places a larger weight on the deviation of inflation from its target. Through
the policy instrument of interest rates, the Taylor rule allows for variations in output
as well as other economic aggregates to absorb any shocks in order to keep inflation
under control. However, this forms an unstable environment for inflation and leads
to inflation’s “surprising” instability relative to the NGDP-GT rule: generating 60%
more fluctuations. In contrast, NGDP-GT does not cause inflation instability, but in
fact produces considerably low standard deviations. In fact, the NGDP-GT allows out-
put and inflation to share the shock burden, which results in mild variations in these
two variables. Furthermore, with the absence of an active interest rate as the transi-
tory channel, dramatic variations in other key economic aggregates are also effectively
14
avoided.
An interesting point is labor’s performance following a productivity shock. The
negative correlation of labor with output shown in Table 2 and the behavior of labor
following TFP shocks in the impulse responses under the NGDP-GT rule in this paper
is consistent with the theoretical indication of Gali (1999) in his class of models with
imperfect competition, sticky prices, and variable effort. The combination of price
stickiness and demand constraints leads firms, in the short run, to contract labor in
the presence of a positive TFP shock and to expand labor in the face of a negative
TFP shock.
5.2 Impulse Responses
The impulse responses enable us to observe the short-run behavior of some key variables
following a negative TFP shock and a negative markup shock in order to gain some
insights about the mechanisms of the model. Since the paper considers each scenario
separately and there is no asymmetry in the model, the responses to positive shocks
are not shown, as they are just mirror images of the results to negative shocks. Figure
1 presents the response of the economy to a shock to productivity. Figure 2 displays
the behavior of the key variables following a negative markup shock.
In general, a negative TFP or markup shock decreases the aggregate supply as well
as output, leading to higher inflation that, in turn, drives up the nominal interest rate.
A negative TFP shock also reduces the demand for labor, causing a decline in the labor
and wages.
Figure 1 shows that under a Taylor rule, a negative TFP shock greatly undermines
output, consumption and the real wage, and produces more inflation, albeit associated
with a soaring nominal interest rate, which as a consequence, further discourages con-
sumption and output. When shocked with the same magnitudes under NGDP-GT,
15
the above variables become inertial around the steady-state values with the assistance
of the systematic stability of NGDP-GT.
The responses to an exogenous markup shock essentially replicate the results of a
TFP shock with some differences in the behavior of labor. A markup shock directly
affects the marginal cost and inflation. The markup shock in Figure 2 causes a rise
in inflation, in line with the standard result in the NK model with ad-hoc cost push
shocks. This shock also leads to the drops in output, consumption, labor and wage as
in the case of the TFP shock. Figure 2 provides the solid evidence that even after the
introduction of an exogenous process to generate a trade-off between stabilizing output
and stabilizing inflation, the performances of the key economic indicators under the
NGDP-GT rule landslide those under the Taylor rule.
One side effect of policy rules, according to Hall & Mankiw (1994), is that it may
bring high volatility to other variables when keeping one variable under tight control.
The NGDP-GT rule, however, does not rely solely on the interest rate as an instrument.
With the economy anchored at a constant NGDP growth rate, the monetary authority
will respond accordingly once the actual growth rate deviates from the target. Target-
ing the growth rate assists in finding the point where the relative levels of output and
inflation lead to lower volatility of the economy. One of the advantages of NGDP-GT is
that maintaining output stability also serves as maintaining inflation stability1, which
does not compromise to the introduction of a trade-off between inflation stability and
output stability. These prove that NGDP-GT significantly outperforms the Taylor rule
in stabilizing the key economic aggregates, and could effectively prevent the economy
from stumbling into severe recessions when negative supply shocks hit the economy.1This could also be observed through log-linearization of the policy equation (1.16) in period t and
t+1: logyt+1− logyt+ logπt+1 = k, logyt− logyt−1 + logπt = k. By reorgamizing these two equations,we can derive log[ gyt+1
gyt] + log[πt+1
πt] = 0, where gyt+1 = log(yt+1/yt).
16
6 Robustness Analysis
Sensitivity analysis takes the form of varying one parameter relative to the baseline.
This section shows the relative volatility changes under the two policy regimes with
deviations to the baselines of structural parameters.
6.1 Changing the Target Rate
Figure 3 shows the results when NGDP growth rate varies between 0% and 8% (net
annual rate) following the productivity shock. The ratios presented are between the
standard deviations under the Taylor rule and those under the NGDP-GT rule for
corresponding variables following a negative TFP shock.
The results for k < 1, which indicates a negative GDP growth rate, are not consid-
ered. From this robust test, two conclusions are drawn. First, the main claim of this
paper, that NGDP-GT outperforms the Taylor rule in stabilizing the economy, is ro-
bust to different targeting rates. Second, the volatility ratios, as shown in Figure 3, are
increasing for all variables in the value of k, a prominent advantage of the NGDP-GT
rule in better smoothing economic fluctuations with a higher k.
The test results have similarities when the economy is hit by a markup shock relative
to the results following a TFP shock, as shown in Figure 4, with a 0% to 8% net annual
GDP growth.
6.2 Elasticity between the Shock and Output Deviation
If the two types of shocks generate more volatility under the Taylor rule, then the
increased volatility can be taken as a strong indication that the Taylor rule regime is
more sensitive to shocks. Accordingly, this implies that in order to achieve a specific
level of output deviation, the Taylor rule regime would only require a smaller σz relative
17
to the other rule. Consistent with the literature, I set a standard deviation of output
at 0.015.
As shown in Table 4, compared to the Taylor rule, it takes 1.65 times the size of
the TFP shock, and 1.4 times the magnitude of the markup shock for the NGDP rule
at any given k; to achieve the same output deviation (0.015), which again highlights
the advantage of NGDP growth targeting. Meanwhile, the advantage can be tested
by going one step further. By deriving the different values of σz for various k (or
π) to generate a 0.015 deviation of output under the Taylor rule, I list the standard
deviations of the six variables under two policy scenarios for each derived σz. Results
inform no significant difference from those of the benchmark model.
6.3 Changing Magnitudes of Shocks
In this experiment, I increase the shock size to observe the nature of the NGDP-GT
rule with respect to stability. Figures 5 and 6 show the results when the magnitude
of the shock is twice that of the benchmark value. I found no significant changes in
the relative performance between these two policy rules from the benchmark model.
Furthermore, the NGDP-GT regime becomes much more favorable as the magnitude
of the shocks (σz = 0.096 and σε = 0.761) are twice the value of the magnitudes of the
two shocks required separately to generate a 0.015 output deviation under the Taylor
rule in the benchmark model.
6.4 A Strict Inflation Targeting Rule and A Strong Inflation
Response Rule
Besides Taylor type rules and NGDP-GT rules, strict inflation targeting (IT) rules and
strong inflation response (IR) rules also receive much attention. There are about 28
18
countries, including the United Kingdom, Canada, Australia, New Zealand, Sweden,
Brazil, Norway, and other countries, that are using inflation targeting through fixing
the consumer price index (CPI) as their monetary policy goal, as in Jahan (2012). In
this subsection, I add these two inflation-type-rules into the pool- a strict IT rule and
a strong IR rule to examine the relative performance of NGDP-GT rule among a wider
range of regimes.
As in Svensson (1999), the monetary authority is assumed to have perfect control
over the inflation rate. It sets the inflation rate in each period. For simplicity purposes,
I assume the inflation rate is set at its steady-state value π at any period t. Inflation
targeting can be written
πt = π (21)
Following Faia (2008), a strong IR rule can be expressed as Equation (1.17) by
setting ρπ = 5, and ρy = 0.
Since variables under the strong IR rule behave similar to their performance under
the IT rule, this paper mainly presents the impulse responses of the IT rule, the Taylor
rule, and the NGDP-GT rule. Tables 5 and 6, and Figures 7 and 8 show the dynamic
results of these three policy regimes following a negative TFP shock and a negative
markup shock.
In both scenarios, the NGDP-GT rule is still preferable in stabilizing output, con-
sumption, wage, interest rate and labor (only in the case of the markup shock). The
relative performance of the NGDP-GT rule is more favorable compared to the IT rule
in the case of a markup shock. In addition, it still holds for the above variables that
the volatility ratios of the economic aggregates are increasing in the value of k. The
economic intuition of the above results is quite straightforward. Following a supply
19
shock, we either allow output or inflation or a combination of the two to absorb the
shock, which implies variations on output, inflation, or both. When keeping inflation
under control to allow output to fluctuate, which is the cases of IT rule and the Taylor
rule; it generates deviations in output and other important economic aggregates. When
keeping NGDP under control to allow output and inflation to share the shock burden,
it brings moderate variations in both variables and prevents other economic indica-
tors from fluctuating dramatically through the interest rate channel. However, due to
the nature of the IT rule, inflation keeps constant in both scenarios. Thus, policy ar-
rangements cannot be explicitly ranked according to the first order solution. Further,
welfare analysis will solve this question. Nevertheless, countries that implement strict
IT rules are expected to experience smoother paths of output, consumption, labor (only
in the case of the markup shock), and real wage, and recover faster in recessions when
switching to the nominal GDP targeting.
7 Conclusion
In this paper, I examine the performance of a nominal GDP targeting (NGDP-GT)
rule and a Taylor rule in a simple New Keynesian DSGE model. Results show that
the primary benefits of the NGDP-GT are lower volatilities in the output, inflation,
labor, and other important economic aggregates following a TFP shock. The NGDP-
GT framework reduces fluctuations in output and inflation by 40% or more in contrast
to the Taylor rule regime. Furthermore, implementing the NGDP-GT rule following a
markup shock reduces output volatility by one third and inflation by one half. More-
over, as the nominal output growth rate is set at a higher level within a plausible range,
the NGDP-GT regime further outperforms the Taylor rule. These results are robust
to introducing different magnitudes of shocks and various target rates.
20
In a larger set of policy rules that includes strict inflation targeting and a strong
response to inflation rules, the NGDP-GT rule appears to have more advantages in sta-
bilizing output, consumption, wage and labor, but it is subject to further confirmation
whether this rule is the most efficacious.
This study stays within the domain of comparing alternative policy rules. This
paper did not discuss the conduction of the rule. As the implementation of the NGDP-
GT does not rely on the nominal interest rate as the sole instrument, alternative
monetary instruments that follow the NGDP-GT could replace the nominal interest
rate, a very meaningful and attractive difference during zero-lower-bound episodes.
21
Appendix
Table 1: Values of the Parameters
Parameter Description Value
β Households’ discount factor 0.990σ Risk aversion 1.500χ Scaling parameter 12.792θ Inverse of IES 0.250φ Price adjustment cost parameter 18.473µz Mean of productivity index 1.000µε Mean of elasticity of substitution between goods 6.000k Nominal GDP growth rate(gross) 1.016R Steady-state gross interest rate 1.026π Steady-state gross inflation 1.016y Steady-state output 0.210ρr Smoothing coefficient of the interest rate 0.900ρπ Coefficients of inflation in Taylor Rule 1.500ρy Coefficients of output in Inflation Targeting 0.125ρz AR(1) coefficient of TFP 0.950ρε AR(1) coefficient of MKP 0.900σz Standard deviation of the innovation term in TFP 0.048σε Standard deviation of the innovation term in MKP 0.380
22
Table 2: Moment Conditions under the two regimes following a TFP shock
Policies Moments y c π R l w mc
TR
x 0.2214 0.2214 1.0016 1.0133 0.2105 0.9020 0.8584
Note: x represents the variable mean, std(x) is the standard deviation of a variable, autocorr(x)stands for autocorrelation, and corr(x, y) is the correlations between a variable and y.
23
Table 3: Moment Conditions under the two regimes following a markup shock
Policies Moments y c π R l w mc
TR
x 0.2162 0.2162 1.0081 1.0195 0.2162 0.8762 0.8762
Figure 1: Impulse Responses to a negative TFP shock
27
Figure 2: Impulse Responses to a markup shock
28
Figure 3: The relative volatilities of variables between the Taylor rule and the NGDP-GT rule for k ∈[1.0000,1.0194] following a TFP shock.
Figure 4: The relative volatilities of output, inflation and labor between the Taylorrule and the NGDP-GT rule for k ∈ [1.0000, 1.0194] following a markup shock.
29
Figure 5: Impulse Responses to σz = 0.096
30
Figure 6: Impulse Responses to σε = 0.761
31
Figure 7: Impulse Responses to a negative TFP shock
32
Figure 8: Impulse Responses to a negative markup shock
33
References
Abo-Zaid, S. (2015), ‘Optimal long-run inflation with occasionally-binding financial
constraints.’, European Economic Review 75, 18–42.
Ball, L. (1997), ‘Efficient rules for monetary policy.’, National Bureau of Economic
Research Working Paper (5952).
Bean, C. (1983), ‘Targeting nominal income: An appraisal.’, The Economic Journal
93(372), 806–819.
Billi, R. (2015), ‘A note on nominal gdp targeting and the zero lower bound.’, Sveriges
Riksbank Working Paper (270).
Christiano, L., Eichenbaum, M. & Evans, C. (2005), ‘Nominal rigidities and the dy-
namic effects of shock to monetary policy.’, Journal of Political Economy 113(1), 1–
45.
Dennis, R. (2001), ‘Inflation expectations and the stability properties of nominal gdp
targeting.’, The Economic Journal 111(468), 103–113.
Faia, E. (2008), ‘Optimal monetary policy rules with labor market frictions.’, Journal
of Economic Dynamics & Control 32(5), 1600–1621.
Faia, E. & Monacelli, T. (2007), ‘Optimal interest rate rules, asset prices, and credit
frictions.’, Journal of Economic Dynamics & Control 31, 3228–3254.
Gali, J. (1999), ‘Technology, employment, and the business cycle: Do technology shocks
explain aggregate fluctuations.’, American Economic review 89(1), 249–271.
Garín, J., Lester, R. & Sims, E. (2016), ‘On the desirability of nominal gdp targeting’,
Journal of Economic Dynamics and Control 69, 21–44.
34
Hall, R. & Mankiw, G. (1994), Nominal income targeting., in ‘Monetary policy’, Uni-
versity of Chicago Press, pp. 71–93.
Henderson, D. & Kim, J. (2005), ‘Inflation targeting and nominal-income-growth tar-
geting: When and why are they suboptimal?’, Journal of Monetary Economics
52(8), 1463–1495.
Jahan, S. (2012), ‘Inflation targeting: holding the line.’, Finance & Development, www.
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