New Keynesian Dynamics in a Low Interest Rate
Environment I
R. Anton Brauna,∗, Lena Mareen Körberbab1000 Peachtree Street, N.E. Atlanta, Georgia 30309
Department of Economics, London School of Economics and Political Science,
Houghton Street, London WC2A 2AE

Abstract
Recent research has found that the dynamic properties of the New Keynesianmodel are unorthodox when the nominal interest rate is zero. Improvements
in technology and reductions in the labor tax rate lower economic activity
and the size of the government purchase output multiplier is very large. This
paper provides evidence that these results are not empirically relevant. We
show that a prototypical New Keynesian model fit to Japanese data exhibits
orthodox dynamics during Japan’s episode with zero interest rates. We thendemonstrate that this specification is more consistent with outcomes in Japan
than alternative specifications that have unorthodox properties.
JEL codes: E3, E5, E6
Keywords: Government purchases, zero nominal interest rates, monetary
policy, liquidity trapI

The views expressed in this paper are our own personal views and not those of theFederal Reserve System. We thank participants at the conference Frontiers in Structural Macroeconomic Modeling, the Deutsche Bundesbank conference Money, Finance andBanking in East Asia, the 2010 DSGE workshop, the 2010 SED meetings, the Taipei International Conference on Growth, Trade and Dynamics and seminar participants at the
Bank of Japan, the Board of Governors, GRIPS, Keio University and Kyoto University
for their comments. We wish to particularly thank an anonymous referee, Yuichiro Waki
and Tsutomu Watanabe.
∗
Corresponding author
Email addresses: r.anton.braun@atl.frb.org (R. Anton Braun),
L.M.Koerber@LSE.ac.uk (Lena Mareen Körber)

Preprint submitted to Journal of Economic Dynamics and Control

June 27, 2011

1. Introduction
Recent research has found that the dynamics of the New Keynesian (NK)model can be quite different when the nominal interest rate is zero. A reduction in the labor tax or an improvement in technology can lower output
and the size of the government purchase multiplier can be much larger thanone. To understand why the dynamics can be so different consider the caseof a positive, transitory shock to technology. If the central bank keeps thenominal interest rate constant output may fall. In the presence of costly
price adjustment of goods the arrival of a positive technology shock today
has a depressing effect on economic activity. Firms experience temporarily
high markups and profits. But, households realize that prices will be lower
tomorrow and choose to defer their consumption and investment activities.
One situation where monetary policy cannot respond to technology, or
any other shocks for that matter, is when the nominal interest rate is constrained by its lower bound of zero. Braun and Waki (2006) find in this situation that output falls in response to a persistent but transitory improvementin technology using a NK model calibrated to Japanese data. Eggertsson(2011) illustrates that a reduction in the labor tax has a depressing effect onhours and output. Christiano et al. (2011) and Woodford (2011) find thatthe size of the government purchases multiplier can be much larger than one.
Taken together these results might lead one to conclude that the propertiesof the NK model are very different when the nominal rate is zero.
Evidence provided in this paper suggests that this focus on the unorthodox properties of the NK model in a liquidity trap is misplaced. We startby documenting a surprising result. When we fit a prototypical NK modelto Japanese data we find that it has completely orthodox properties during
Japan’s episode with zero interest rates which extended from 1999 to 2006. In
our NK model an increase in the labor tax reduces output, an improvementin the state of technology raises output and the government purchase multiplier is less than one in years when the nominal rate is zero.1 We also findspecifications of the NK model that exhibit unorthodox properties. However,these specifications are not empirically relevant in the following sense. Japan
1

The mechanism that delivers orthodox responses here is different from the one discussed in Mertens and Ravn (2010). They produce orthodox results by considering shocks
to expectations that drive the interest rate to zero. Here we limit attention to shocks tofundamentals.

2experienced a large decline in real and nominal economic volatility during
the period of zero nominal interest rates. The specifications with unorthodox properties predict a counterfactual increase in volatility. Our baseline
specification with orthodox properties, in contrast, successfully reproduces
both observations.
The model that we consider is a medium scale New Keynesian modelwith quadratic price adjustment costs as in Rotemberg (1996), labor supply,
capital accumulation and shocks to preferences, technology, taxes, monetary
policy and government purchases. In this setting the duration of the periodof zero interest rates is endogenous as in Braun and Waki (2006) or Erceg
and Lindé (2010).
Research by Braun and Waki (2010) and Braun and Körber (2010) has
found that the common method of solving the NK model by log-linearizing all
equilibrium conditions except the zero bound constraint about a steady statewith stable prices can produce large approximation errors in the aggregate
resource constraint. In this paper we use an extended path solution methodthat avoids this problem.
This solution technique can easily handle models with multiple endogenous state variables and multiple shocks. However, it is difficult to automate
and thus is not easily amenable to estimation which involves solving themodel for many different configurations of the parameters. For this reason
we calibrate the model’s parameters and some of the shocks that cannot bemeasured directly. The resulting specification does a reasonable job of reproducing the paths of real and nominal variables in a sample period that
extends from 1990 to 2007. We then conduct an impulse response analysis
in years before and during the period of zero interest rates. Surprisingly,
our model exhibits orthodox output responses to shocks to technology andthe labor tax. Moreover, the government purchase output multiplier in themodel never exceeds 0.9.
The single most important factor for why our baseline specification produces orthodox results is household expectations about the duration of theperiod of zero interest rates. Our baseline specification sets these expectations in a way that renders them consistent with estimates reported in Ichiue
and Ueno (2007). They use yield curve data to estimate the expected duration of zero interest rates and find that the expected duration of zero interest
rates between 1999 and 2006 was 2.3 years or less. If instead our model iscalibrated so that the number of periods that households expect the interest
rate to be zero is 5 years or longer it also exhibits unorthodox responses.
3Japan’s episode with zero nominal interest rates was a period of tranquility. Japanese output and real marginal cost volatility dropped by about 1/2
and inflation volatility declined by more than 70 percent during the period ofzero nominal interest rates which extended from 1999-2006 when comparedto the years 1988-1998.
We use these facts as a device to assess the relative plausibility of specifications with orthodox properties and specifications with unorthodox properties. Our baseline specification with orthodox properties predicts a large
decline in both real and nominal volatility. The specifications with unorthodox properties, however, all predict counterfactual increases in real and nominal volatility between 1999 and 2006. With a longer expected duration ofzero interest rates, price and markup variability in response to a variety ofshocks are large and this leads these models to predict that the period ofzero interest rates should have been associated with an increase in economic
volatility.
The unorthodox specifications have another troubling property. They
imply that the resource costs of price adjustment are very large and range
from 2.5 to over 7 percent of output. The resource costs of price adjustmentin the baseline specification are much smaller and well less than one percent
of output.
We conclude that Japanese data from 1999-2006 is most consistent witha New Keynesian model that has the following properties:
1. A lower labor tax rate increases output.
2. An improvement in neutral technology increases output.
3. The government purchases multiplier less than one.
The remainder of the paper is organized as follows. Section 2 describes
the economy. Section 3 explains how the model is calibrated and solved.
The results are reported in Section 4 and Section 5 contains our concluding
remarks.
2. Economy
We consider a prototypical New Keynesian economy. The economy ispopulated by a representative household, a representative final good producer, a continuum of intermediate good producing monopolists that facequadratic costs of adjusting prices, a government and a central bank. We
discuss the problems of these various actors in turn.
4

Households
The representative household chooses sequences of consumption {ct }∞t=0
and leisure {1 − ht }∞t=0 to maximize
E0

∞
X
t=0

β

t

t
Y
j=0


dj

(cνt (1 − ht )1−ν )1−σ
1−σ


(1)

where ct is consumption of the composite good and ht is hours worked expressed as a fraction of a time endowment of one. β denotes the discountfactor, ν is the preference weight a household attaches to consumption andσ is related to risk aversion. Finally, dt is a shock to the subjective discountrate with the law of motionln(dt ) = ρd ln(dt−1 ) + d,t(2)

where t is an I.I.D, mean zero Gaussian random variable. The household’s
period t budget constraint is given by
Bt
Bt−1(1 + τc,t )ct + xt += (1 + Rt−1 )
+
Pt
Pt
Z 1
Πt (i)
di + Tt + (1 − τt,K )rt kt−1 + (1 − τt,W )wt ht + τt,K δkt−1
Pt
0

(3)

where Pt is the price level, wt is the wage rate and rt is the real interest rate.
Bt is the household’s holdings of nominal debt at the end of period t, kt−1 isthe level of capital chosen in period t − 1 and xt is investment. Households
hold equal shares in each intermediate goods firm so that Πt (i) is per capita
nominal profits from intermediate firm indexed i. Households pay taxes τc,t ,τt,k and τt,w on consumption, capital income and labour income, and receive
lump-sum transfers of size Tt from the government. Ponzi schemes are ruledout by limiting attention to solutions that satisfy the standard transversality
condition for bonds and capital. Capital is subject to adjustment costs andis accumulated according to

2
φ
xt
kt = (1 − δ)kt−1 + xt −− µk + 1 − δ kt−1
(4)
2 kt−1
where µk is the growth rate of capital in the balanced growth path and δ isthe depreciation rate. Let λc,t and λk,t be the Lagrangian multipliers on the5household’s budget constraint (3) and on the law of motion for capital (4),respectively. The optimal choices of the representative household satisfy
ν(cνt (1 − ht )1−ν )1−σ
= λc,t (1 + τc,t )ct(5)(1 − ν)(cνt (1 − ht )1−ν )1−σ
= λc,t (1 − τw,t )wt
1 − ht(6)

λc,t = λk,t 1 − φxt− µk + 1 − δ
kt−1


(7)

0 = βEt dt+1 λc,t+1 [(1 − τk,t+1 )rt+1 + τk,t+1 δ] − λk,t
"



2 #
xt+1
xt+1 φ xt+1
+βEt dt+1 λk,t+1 1 − δ + φ− µk + 1 − δ−− µk + 1 − δ
kt
kt
2
kt
(8)
−λc,t /Pt + βEt dt+1 λc,t+1 (1 + Rt )/Pt+1 = 0(9)Final Good Firm
Perfectly competitive final good firms use a continuum of intermediate
goods i ∈ [0, 1] to produce a single final good that can be used for consumption and investment. The final good is produced using the following
production technology
Z 1yt (i)

yt =

θ−1
θ

θ
 θ−1

di

(10)

0

The profit maximizing input demands of the final good firm are−θ
pt (i)dyt (i) =
yt
Pt

(11)

where pt (i) denotes the price of the good produced by firm i. It follows thatthe price index Pt is given byZ 1
1/(1−θ)1−θ
Pt =pt (i) di
(12)
0

6

Intermediate Goods Firms
Monopolistically competitive firms indexed by i ∈ [0, 1] produce differentiated, intermediate goods according to the technology
yt (i) = kt−1 (i)α (At ht (i))1−α(13)

We assume that there are permanent shocks, ψA,t and transitory shocks, A,t
to technology. Both ψA,t and A,t are I.I.D, mean zero Gaussian randomvariables. Technology evolves according to
At = ZA,t evA,t
vA,t = ρA vA,t−1 + A,t
ZA,t /ZA,t−1 = µA,t
ln µA,t = ln µA + ψA,t

(14)
(15)
(16)
(17)

Each intermediate firm solves a dynamic profit maximization problem thatcan be broken down into two parts: The choice of the cost minimizing levelof inputs and the choice of the optimal sequence of prices of output. There
are two inputs: labor and capital. Cost minimization implies
rt = αχt kt−1 (i)α−1 (At ht (i))1−α

(18)

(1−α)

(19)

wt = (1 − α)χt At

kt−1 (i)α ht (i)−αrtα wt1−ααα (1−α)1−α A1−αtis real marginal cost.
where χt =Price rigidity is introduced using a convex cost of price adjustment as inRotemberg (1996). Define gross inflation 1 + πt (i) as pt (i)/pt−1 (i). Given the
optimal choice of labor and capital, a typical intermediate goods producerchooses a sequence of prices pt (i) to maximize
∞
X
t=0

β

t

t
Y

h
i
γ
dj λc,t pt (i)yt (i) − Pt sχt yt (i) − Pt (πt (i) − π)2 yt /Pt
2
j=0

(20)

subject to the input demand function (11). We assume a subsidy s = θ/(θ−1)
is in place that corrects the static inefficiency due to monopolistic competition. This subsidy isolates the dynamic distortion caused by the variation in
the markup which is the distortion that monetary policy corrects in the New
Keynesian model. Introducing a subsidy is also very convenient because it
7

allows us to nest a real business cycle model as a special case by setting theadjustment costs on prices to zero.
The first order condition for the firms’ price setting problem reads
βEt

dt+1 λc,t+1 yt+1
γ(πt+1 −π)(1+πt+1 ) = − [1 − θ + θsχt − γ(πt − π)(1 + πt )]
λc,t yt(21)

Aggregate Resource Constraint
The aggregate resource constraint is given byγ
gdpt ≡ gt + ct + xt = yt (1 − (πt − π)2 )2(22)

Observe that there is a distinction in this economy between (gross) production yt and GDPt that stems from the fact that the NIPA accounts do notrecognize the resource costs of price adjustment. This distinction between
the two concepts will provide to be important when considering the zerobound.
Monetary Policy
Parsimonious interest rate targeting rules have been found to be good
empirical specifications of monetary policy by Taylor (1993). The particularTaylor rule considered here is

ρ 
ρ


1 + πt π 1 + Rt−1 R uM,t
− 1, 0(23)e
Rt = max (1 + R)
1+π
1+R
where uM,t is an I.I.D, mean zero Gaussian random variable. One special
feature of this rule is that it output does not enter. We will consider a sample
period during which Japan experienced a long and persistent departure fromits trend growth rate. It is not clear how to define the target level of output
in this situation.2
2

One possibility is to introduce the growth rate of output in the Taylor rule. Results
for that specification are discussed briefly in Section 4.5 below.

8

Fiscal Policy
The fiscal authority finances its expenditures by collecting distortionary
taxes and lump-sum transfers and by issuing nominal bonds. Fiscal policies
satisfy the period budget constraint
Bt
Bt−1+ St =− Tt + τw,t wt ht + τc,t ct + τk,t kt−1 (rt − δ) (24)Pt
Pt
where St is a subsidy to intermediate monopolists.We limit attention to equilibria where the path of the government debt satisfies a transversality condition. Defining bt ≡ BPtt , we can rewrite the government budget constraint as
gt + (1 + Rt−1 )1= bt − Tt + τw,t wt ht + τc,t ct + τk,t kt−1 (rt − δ) (25)
1 + πt
The tax rates on capital, consumption and labor and government purchases
have the following laws of motion
gt + (1 + Rt−1 )bt−1


log

gt
gdpt



τc,t = (1 − ρc )τc + ρc τc,t−1 + c,t

(26)

τk,t = (1 − ρk )τk + ρk τk,t−1 + k,t(27)

τw,t = (1 − ρw )τw + ρw τw,t−1 + w,t




g
gt−1
= (1 − ρg )log
+ ρg log+ w,tgdp
gdpt−1(28)(29)

where the shocks to each variable are I.I.D, mean zero Gaussian random variables. Lump-sum transfers are assumed to adjust to satisfy the government
budget constraint.
Equilibrium
The notion of equilibrium considered here is an imperfectly competitive
general equilibrium in which the markets for the final good, intermediate
goods, labor, capital and government debt clear in each period. The model
developed above admits a symmetric equilibrium and we limit attention tothat equilibrium. We start by defining a perfect foresight equilibrium.
Definition A perfect foresight symmetric monopolistic competitive equilibrium consists of a sequence of allocations {ct , ht , xt , kt , λc,t , λk,t , yt }∞t=0 , a set∞∞of policies {Rt }t=0 , a sequence of prices {rt , wt , χt , πt }t=0 and a finite set of
integers IB that satisfy9• Households’ optimality conditions• Firms’ optimality conditions• Monetary policy rule:– ∀t∈/ IB the zero constraint on interest rates is not binding andthe Central Bank follows the Taylor rule– ∀ t ∈ IB the zero constraint on interest rates is binding and theCentral Bank sets Rt = 0• Aggregate resource constraint and market clearing
given initial conditions (P−1 , R−1 , k0 ), and sequences of shocks to the rules
3
for {At , dt , τk,t , τc,t , τw,t , gt }∞t=0 .
Two points are worth mentioning. First, the definition of equilibrium
is sequential. Second, the definition of equilibrium includes a statement ofspecific intervals where the zero lower bond on the nominal rate is binding.
3. Solution Method and Calibration
3.1. Solution Method
Our choice of solution method is motivated by four considerations. First,
we choose a nonlinear solution method because recent research by Braunand Waki (2010) and Braun and Körber (2010) has found that the common
practice of log-linearizing all of the equilibrium conditions except for the
Taylor rule around a steady state with a stable price level can produce large
approximation errors. For large or persistent shocks, these approximation
errors can result in sign reversals of e.g. the response of hours to a change
in the labor tax rate, upward biases in the size of the government purchases
multiplier and implausibly large implied costs of price adjustment.4
3

Because we assume that the government adjusts lump-sum transfers such that its
budget constraint is satisfied, we omit the government budget constraint from the equilibrium conditions and we omit government bonds and transfers from the list of variables
determined in equilibrium.
4
We will provide an illustration of this final point below.

10

The second motivation for our choice relates to finding the interval when
the nominal interest rate is zero. Braun and Waki (2010) consider the problem of computing an equilibrium for an economy similar to ours in a perfectforesight setting. They limit attention to equilibria of the form where theinterest rate is zero for only one finite and contiguous number of periods.
Even with this restriction they find that there can be multiple equilibria andthey impose two further equilibrium selection devices. First, they impose therestriction that the nominal interest rate in the model hits zero in a specificyear that is dictated by Japanese data. Second, they select the equilibrium
where the nominal interest rate is zero for the shortest interval of time. We
use the same strategy for selecting an equilibrium here.
Third, we want to relax the perfect foresight assumption and allow for
new shocks/news to arrive each period.
Fourth, we want to analyze a medium scale model of the Japanese economy with capital formation and multiple persistent shocks. Global solution
methods used in e.g. Wolman (2005), Adam and Billi (2006) and Nakov(2008) have the attractive property that agents forecasts are probability distributions over future outcomes. Unfortunately, these methods are subject
to a curse of dimensionality that limits their usefulness in settings wheremodels have multiple shocks and endogenous state variables.
These four considerations led us to use an extended path solution method.5
Starting from the initial period, agents solve the set of nonlinear equations
that describe their respective decision rules forward for 100 periods. We assume that our economy is at its steady state in period 101.6 In all future
periods, shocks are set to 0. We then move time forward by one period.
Agents experience a new set of shocks and have a new set of initial conditions. They once again solve forward for 100 periods. This is repeated foreach year from 1988 to 2007.
Because our solution method is sequential, we can limit the problem of
dealing with the zero bound constraint to a small number of periods. It turns
out that prior to 1999, households assign zero probability to the constraint
binding in equilibrium. In these early periods the model can be solved very
quickly. In the periods where households anticipate or experience a binding5

See Heer and Maussner (2008) for a description of the algorithm. They refer to it as
an extended shooting algorithm.
6
We have also experimented with longer transitions and found that our results are
qualitatively very similar.

11constraint we solve the model using guess and verify methods to find theinterval where the (expected) nominal interest rate is zero.
3.2. Calibration of Parameters
Recently, Bayesian MLE estimation has become popular for parameterizing models like ours. Bayesian MLE estimation is very convenient if one
can solve the model using a loglinearized solution technique. However, as
we have already noted above this solution technique can break down when
considering periods where the nominal interest rate is zero.7 One could in
principal estimate the model parameters using an earlier sample period when
the nominal interest rate is positive. However, previous research by e.g. Chenet al. (2006) and Braun et al. (2009) show that Japan was undergoing largetransitional adjustments between 1960 and 1990. This was the period ofJapan’s growth miracle and it is difficult to derive a stationary representation in the presence of large one off transitional dynamics induced by e.g. a
low capital stock. For these reasons we chose to calibrate the parameters of
our economy by matching model variables to calibration targets in Japanesedata between 1981 and 2007.
Table 1 reports the model parameterization. Most of the parameters arecomputed using averages from Japanese data over the sample period 19812007. The data used for calibrating the model is an updated version of thedata employed by Hayashi and Prescott (2002).8 The capital share parameter α is calibrated to match capital’s share of income. The depreciation rate
δ reproduces average depreciation in Japanese data. The steady state nominal rate is the average of the Japanese overnight call-rate. The coefficientsfor the laws of motion of the taxes on consumption, labor and capital are
estimated using Japanese data on average tax rates for these three variables.
The parameters for the law of motion of government’s share of output are
estimated in the same manner.
The preference discount factor β is set to 0.995, a rather high level for amodel in which the length of a period is one year. This choice implies thatthe inflation rate associated with a steady state nominal interest rate of 2.9%
7

One promising alternative strategy is pursued in Adjemian and Juillard (2010). They
estimate a NK model using an extended shooting solution technique and a simulated GMM
estimation strategy.
8
We wish to thank Nao Sudou of the Bank of Japan for providing us with an updated
version of the Hayashi and Prescott (2002) dataset.

12

is zero. We set the curvature parameter in preferences to 2. The weight on
leisure in the utility function, ν, is calibrated to match the average labor
input between 2000 and 2007. We choose this period because prior to 2000,
labor input exhibits a significant downward trend. The resulting value of ν
is 0.27.
Other parameters are set in a more informal way. The parameter controlling the size of adjustment costs on investment is set to 4 which is a bit
larger than the value of 2 used by Braun and Waki (2006).
The average markup is set to 15% as in Braun and Waki (2006). It thenfollows that the value of the subsidy is 1.15. We assume that technology, At ,advances at an average rate of 2% per annum.
The coefficient on inflation, ρπ , and the lagged nominal rate in the Taylor
rule, ρR , are set to 1.7 and 0.4 respectively. The adjustment cost parameter γ
is set to 80.9 These parameter choices imply that the nominal rate increases
on impact by 0.4% in response to a 1% shock to monetary policy. This
response is a bit lower than the response of 0.6% estimated by Sugo andUeda (2006) for the Japanese economy.
Finally, we start simulating the model from 1987. the initial capital stockin our economy is set to match the beginning of period value of the capitalstock in Japanese data in 1987.
3.3. Calibration of Shocks
Japanese data is used to derive sequences of innovations to technology,
government purchases, and capital and labour taxes. However, we calibrate
the innovations to the preference discount factor, consumption tax and monetary policy to reproduce particular targets. We next describe how this isaccomplished.
We started out by simulating our economy using the parameterization
described above setting the shocks on the consumption tax, the preference
discount rate and monetary policy to zero in all periods. That specification
preformed reasonably well in terms of its implications for most real variables.
However, the model did not reproduce a large secular decline in Japaneselabor input after 1987. Between 1987 and 1991, there were some important
9

When log-linearized, introducing nominal rigidities via Rotemberg price adjustment
costs produces a New Keynesian Phillips curve identical to the one obtained from a Calvomodel of nominal rigidities. The Calvo parameter of price stickiness associated with ourparameterization is 0.75.

13

institutional changes in labor market arrangements in Japan. The numberof national holidays were increased and the length of the work week was
reduced. However, labor input continues to decline throughout the 1990s.
Miyazawa (2010) shows that the secular decline in labor input during the
1990s can partially be attributed to a change in the composition of jobs fromfull-time to part-time work. We do not explicitly model these factors here
and instead treat them as altering the labor wedge as in e.g. Kobayashi andInaba (2006).10
Simulation results for this parameterization are reported in Figure 1. Inspection of Figure 1 indicates that the model does a reasonable job of reproducing some of the basic secular movements in the real side of the Japanese
economy. It captures the capital deepening that occurred between 1990 and2007. The model also captures the decline in output and consumption relative to their trends during the 1990s. However, it does not reproduce thesecular decline in labor input after 1991. In addition, the decline in the nominal interest rate and inflation rate is counterfactually small during the 1990s.
The model, most importantly, does not predict a period of zero nominalinterest rates.
Shocks to the preference discount rate play an important role in getting
the interest rate to fall to zero in the work of Eggertsson and Woodford(2003), Taehun et al. (2005) and Christiano et al. (2011). We follow theirapproach and introduce shocks to the preference discount factor as follows:for 1993 to 1995, 2%, 1%, and 1%, respectively and for 1999, 2%. This final
shock makes the zero lower bound bind in 1999. The value of the log discountrate in 1999 implied by the above shocks is 0.044.
Introducing shocks to dt gets the nominal interest rate to hit its lower
bound of zero but these shocks also result in a deterioration in the fit for output and labour input. To counteract the stimulative effect that shocks to thepreference discount rate have on these variables, we introduced simultaneous
variations in the labor wedge by shocking τc,t . With some experimentation
we found that using a fixed factor of 5 works well.
Preference discount rate shocks also produce counterfactually low inflation in the second half of the 1990s. To counteract the deflationary pressure
10

We accomplished this by altering τc,t in the years 1987 to 1991 to reproduce movements
in Japanese labor input during this sub-sample. τc,t also affects the intertemporal firstorder condition. However, in our experience this effect is quantitatively very small.

14

due to these shocks, we introduced negative monetary policy shocks in thelate 1990s. In our economy, a negative shock to monetary policy lowers thenominal interest rate and increases the inflation rate. In other research Sugoand Ueda (2006) have found that negative monetary policy shocks are important for understanding the Japanese economy during this period. The
shocks to monetary policy are -0.5% in the years 1993, 1996 and 1998 and-1% in 1997.
This setting of the three shocks brings the model’s predictions for thenominal interest rate and the inflation rate into reasonably good accord withJapanese data from 1993 to 1999.
Once the nominal interest rate is zero we were left with a question of how
to choose these shocks during the period of zero nominal interest rates. In
our baseline specification, we assume that in each period between 1999 to2005 households expect that the nominal interest rate will be zero for two
years. This assumption is based on evidence reported in Ichiue and Ueno
(2007). They find using an affine model of the yield curve that the maximum
expected duration of zero nominal interest rates during this period was 2.3
years. In 2006, the nominal rate is zero in the current period but agents
expect positive nominal interest rates for 2007 and beyond. Then in 2007
the nominal interest rate turns positive.
Results for the baseline simulation are reported in Figure 2. A comparison of Figure 2 with Figure 1 reveals that the shocks we have added after
1991 achieve the desired goal of gradually lowering the inflation and nominalinterest rate during the second half of the 1990s. Moreover, the level of inflation during the period of zero nominal interest rates is about of the samelevel as we observe in Japanese data. Relative to Figure 1, there is somedeterioration in the fit of the model for real allocations. The baseline economy understates consumption and overstates the extent of capital deepening.
The reason for these changes in the fit of the model for real variables is thepreference shock. On the one hand, an increase in dt brings the nominal rate
down but it also stimulates labor input and output. We compensate for theseeffects by using τc,t to increase the labor wedge. This improves the fit forthese variables but also induces households to consume less and save more.
Overall, the baseline model captures some of the principal features ofJapan’s experience between 1990 and 2007. It provides us with a quantitatively relevant NK framework for analyzing the effects of changes in technology, the labor tax rate and government purchases on output both before andduring Japan’s episode with zero interest rates.
15

4. Results
4.1. Dynamic Responses of the Baseline Specification
This subsection reports one of our principal results. Previous research
has found that the dynamic properties of the NK model are very different
when the nominal interest rate is zero. We now show that a quantitatively
relevant specification calibrated to the Japanese economy exhibits orthodox
responses to labor tax and technology shocks both when the nominal rate
is positive and when it is zero. Moreover, the government purchase output
multiplier is less than one.
Table 2 reports impulse responses for the baseline specification. The firstrow shows the year in which the shocks are perturbed. The second row
reports the number of years that agents expect the nominal interest rate tobe zero. The third row reports the resource costs of price adjustment as apercent of output. The remaining rows report impact responses of output
and the markup to various shocks. Results are reported for permanent andtransitory shocks to technology, shocks to the labor tax rate and shocks togovernment purchases. In all instances, the sign of the shock is positive.
The upper panel of Table 2 reports the percentage change in output
to a 1% impulse in the variable that is shocked for the first three shocks.
For the shock to government purchases though the results are expressed asgovernment purchase multipliers which are defined as the ratio of the change
in output to the change in government purchases. The first column of results
is for shocks that arrive in 1995, which is representative of years in which
the current nominal interest rate is positive and expected nominal interest
rates are positive in all future years. We also report impulse responses forshocks that arrive in 1999 and 2004. These are both years in which thenominal interest rate is zero. In 1999 agents continue to expect the nominalinterest to be zero for two periods after each of the shocks arrives. In 2004,
in contrast, three of the shocks reduce the expected number of periods ofzero nominal interest rates by one period.
Inspection of Table 2 reveals a surprising fact. Output exhibits orthodox responses to technology shocks and labor tax shocks both in 1995, ayear when the nominal rate is positive and in 1999 and 2004, years when
the nominal rate is zero. Output increases when technology improves andoutput falls when the labor tax is increased. Moreover, the government purchase output multiplier is less than one in all periods. In 1995 it is 0.65. It
increases to 0.87 in 1999 but never rises above 0.9 in any period. Although16not reported in Table 2 we wish to point out that private consumption falls
when government purchases are increased in 1995, 1999 or 2004.
The most significant difference between the results for 1995 and the resultsfor 1999 and 2004 relates to the markup response. The markup response toeach of the shocks is about three times larger in the years where the nominalinterest rate is zero.
What is the economic mechanism responsible for the approximately threefold increase in the response of the markup? It is known from previous workby e.g. Khan et al. (2002) that optimal government policy in a model withimperfectly competitive intermediate goods markets is to smooth the dynamic response of the markup to shocks. Schmitt-Grohe and Uribe (2007)
find that a monetary policy that stabilizes the price level is an effective way
to achieve this objective. In the New Keynesian model prices have a close
link to the value of the markup via the New Keynesian Philips curve and stabilizing prices acts to limit the size of the response of the markup to shocks togovernment purchases and other exogenous variables. In practice, a Taylor(1993) rule with a large inflation elasticity is a simple but effective policythat stabilizes prices and the markup. Once the nominal interest rate is zerothough, the Taylor rule is no longer operative and monetary policy ceases tostabilize the response of the markup to shocks. This is the mechanism triggering the larger markup responses in Table 2. However, what is noteworthy
about our results is that the level of markup variability prior to 1999 is verysmall. Thus, increasing its variability by a factor of three only has small
quantitative effects on the dynamic response of the economy to shocks.
On the one hand, the results reported in Table 2 for the period of zerointerest rates are reassuring. They imply that we don’t have to change theway we think about the world when the nominal interest rate is constrainedby its lower bound of zero. On the other hand, our results are surprising inlight of the previous literature. The value of the government purchase output
multiplier reported in Table 2 is less than one. Christiano et al. (2011) and
Woodford (2011), in contrast, find that the government purchases multiplieris much larger than one when the nominal interest rates is zero. In addition,
the sign of the output response to either type of technology shock is positivein Table 2. Braun and Waki (2006) and Christiano et al. (2011) find that
output falls in response to an improvement in technology when the nominalinterest rate is zero. Finally, we find that output (and hours) fall when
the labor tax is increased during the period of zero nominal interest rates.
Eggertsson (2011) finds that hours increase in this situation. We turn now to17

consider some variants of our model that produce these types of unorthodox
responses.
4.2. Unorthodox Responses
The most important reason why the baseline calibration produces orthodox responses is that the shocks to dt are calibrated to deliver an expected
duration of zero interest rates of two years in each year between 1999-2005.
If we increase the expected duration of zero interest rates enough the modelyields specifications that have unorthodox properties. In practice, there are
two patterns of unorthodox results that emerge. Some specifications exhibit
a government purchase output multiplier that is much larger than one but the
response of output to shocks to technology and the labor tax are orthodox. A
second type of specification has the property that the government purchasemultiplier is larger than one and the responses of output to technology andlabor tax shocks are also unorthodox.
We consider two general strategies for increasing the expected duration ofzero interest rates. The first increases the serial correlation coefficient in thelaw of motion for the preference discount factor shifter (dt ) while holding theshocks fixed at their baseline values. The second strategy varies the patternand size of shocks while holding fixed the serial correlation coefficient ρd .
Before discussing the results in Table 3 we wish to remind the reader about
the distinction in our model between (gross) production which we denote byy and output which we denote by gdpt .11 Output (GDP) is defined asγ
gdpt ≡ ct + gt + xt = yt (1 − (πt − π)2 )2The distinction between production and GDP plays an important role in thesubsequent analysis. Any shock that increases the difference between current
and steady state inflation also raises the resource costs of price adjustment.
This, in turn, increases the gap between production and GDP.
Results reported in Table 3 correspond to the same scenario of a shockin 1999 considered in Table 2. Column 1 restates impulse responses for thebaseline specification and also reports the responses of production. Results
11
We use the term GDP because most national accounts data used in economic researchin recent years is based on GDP. Formally, though the measure of output in our dataset
is based on the Hayashi and Prescott (2002) methodology and they use GNP as theirmeasure of output.

18

reported in columns 2 and 3 under the heading High serial correlation discount factor increase the serial correlation coefficient from the baseline valueof 0.9 to respectively 0.94 and 0.95. Consider the results reported in the top
panel of column 2 under the heading impact response of output. Recall that
output is defined as the sum of consumption, investment and government
purchases as in the NIPA accounts. The government purchases multiplieris 1.55. Increasing the serial correlation of the discount factor from 0.9 to
0.94 nearly doubles the size of the government purchase multiplier.12 Noticethat this magnification of the government purchase output multiplier is due
to a longer expected duration of zero interest rates. From row 2 of Table 3
we see that increasing ρd from 0.9 to 0.94 increases the expected durationof zero interest rates from two to six years. A longer expected duration ofzero interest rates produces a larger drop in the markup. The decline in themarkup with ρ = 0.94 is more than twice as large as the baseline. When
the Taylor feedback rule is active it acts to smooth the price and thereby
the markup response. However, when the nominal interest rate is zero anincrease in the expected duration of zero rates means that this mechanism isabsent longer and both prices and the markup respond by more.
Interestingly, the response of production to an increase in government
purchases is much smaller and only about one. Why is the output multiplierso much larger than the production multiplier?
To provide some intuition for this difference in the response of production
and output we totally differentiate the resource constraint with respect to achange in government purchases to get
∂y
∂Ψ
∂gdp
= (1 − Ψ)
−y
∂g
∂g
∂g

(30)

where Ψ denotes the resource cost of price adjustment (time subscripts aresuppressed for ease of exposition). Equation (30) decomposes the GDP response to a government purchase shock into two terms.13 The first term consists of the response of production to a government purchases shock weighted
12

Most of the increase occurs as the discount factor is increased from 0.93 to 0.94. For
instance, if we simulate the model setting ρd = 0.93 instead, the government purchasemultiplier is just above one.
13
Strictly speaking, the GDP response to a transitory government purchase shock,∂gdp/∂g has a third second order term too. However, for small changes the infinitesimals in (30) are a valid approximation.

19

by one minus the resource costs of price adjustment, (1 − Ψ). The second
term is the response of the price adjustment costs to a government purchases
shock weighted by production, y.
Table 4 reports this decomposition for the various specifications of themodel. Inspection of Table 4 reveals that the most important factor is the
response of the resource cost of price adjustment to a change in government
purchases (∂Ψ∂g). A shock to government purchases puts upward pressure
on prices and this lowers the resource costs of price adjustment. When individuals anticipate a longer period of zero interest rates, the price increase islarger and this produces a bigger saving in resources. With less of production taken up by price adjustment, more is available for consumption andinvestment which implies in turn a larger response of GDP. This effect is so
pronounced that consumption now increases with the increase in government
purchases.
Returning to Table 3 we see that the results reported in column 2 havea second notable feature. The response of both output and production to
shocks in either type of technology or the labor tax are orthodox. An improvement in technology increases production and output and a higher labortax lowers both production and output. However, there is also a distinction
between the production and output response for these variables. The reasoning works in an analogous way to the case of a government purchase shock.
Suppose that the labor tax is increased. This shock acts to reduce the costsof price adjustment. When the shock to the discount factor is more persistent
the price level is also lower and the associated savings in price adjustment
costs are larger.
Given the mechanisms we have identified it is not surprising then thata larger increase in ρd can change the sign of the response of output to a
shock in the labor tax. The results reported in column 3 of Table 3, whichset ρd = 0.95, illustrate this point. Now households expect the interest rate
to be zero for seven years when hit with the baseline model shocks. The
government purchase output multiplier is now nearly two. The response of
output to a labor tax shock or a transitory technology shock is unorthodox. output increases when the labor tax is increased and output falls when
the transitory technology shock is increased.14 If one, however, considers
14

We do not report the consumption responses here due to space considerations but wewish to mention that for all simulations we performed consumption moved in the same20

the response of production instead to these same shocks its properties are
orthodox. Production increases by less than one to a one unit increase ingovernment purchases, production increases when technology improves andproduction falls when the labor tax is increased.
A second way to increase the expected duration of zero interest rates
is to keep the model parameters fixed and to increase the size of the shocks
instead. When the shocks to dt are sufficiently large, the model also produces
unorthodox results.
The persistent expectations specification sets the sequence of preference
shocks hitting the economy between 1999 and 2007 so that agents expect zeronominal rates for 5 years as new information arrives in each year between
1999 to 2003. All parameters of the model are held fixed. After 2003, theshocks are adjusted so that agents expect that the nominal rate will become
positive sooner in a way that is consistent with Japan’s experience. The
nominal rate becomes positive in 2007. To implement this scenario, a shockto the preference discount rate of size 3% hits the economy in 1999. From2000 to 2007, the size of preference discount rate shocks ranges between 0.6%
and -0.6%.
Results for the persistent expectations specification are reported in column 4 of Table 3. This choice of shocks induces a much larger response in
the markup as compared to the baseline specification. Notice also that theresource costs are much larger here (2.51% as compared to 0.59% for the baseline). The government purchase GDP multiplier increases to 1.33. However,
the government purchase multiplier for production (0.87) is only moderately
larger than the baseline multiplier (0.78) and less than one.15 The output
response to either a positive transitory technology shock or a high labor tax
rate shock is also smaller in absolute value than the production response but
it still has the conventional sign. Overall, the qualitative properties of theseresults are very similar to the results reported in column 2.
For the large preference shock specification, we assume that the preference
discount shock arriving in 1999 is equal to 3.5% and that the shock to τc is
17.5%. These shocks lead agents to expect that nominal rates will be zero
direction as output when technology or labor taxes were shocked.
15
One way to see the key role played by expectations about the duration of zero interest
rates is to compute the multiplier for another year. In the year 2000 there are no newshocks to dt yet, the government purchase output multiplier is 1.35 which is about thesame as its value of 1.33 in 1999.

21

in each year between 1999 and 2006. After 1999, no other shocks to dt orτc,t arrive. In this specification the equilibrium value of the nominal interest
rate becomes positive in 2007.
We will report two sets of simulations for this specification. They differ inthe treatment of the resource cost of price adjustment. The results reported
in column 6 include the resource costs of price adjustment in the resource
constraint, while the results reported in column 7 omit them. The values ofthe shocks are the same in both columns.
When the resource costs of price adjustment are recognized in the budget
constraint we find that the government purchase output multiplier is 1.70.
The government purchase production multiplier though is less than one. This
specification also produces anomalous output responses to an increase in thelabor tax and an temporary improvement in technology shock. But the
response of output is very muted.
The results in column 7 are meant to provide the reader with an indicationof how the answer changes if one solves the model using a log-linearized solution, centered at a steady state with price stability. Under these assumptions
the resource costs of price adjustment do not appear in the log-linearized resource constraint. The results in column 7 indicate that omitting this termfrom the aggregate resource constraint acts to magnifies all of the responses.
The response of the markup to any shock is now many orders of magnitudelarger than the baseline. This results in a government purchase multiplier of
2 and large and anomalous responses of output to shocks in the labor tax andtransitory technology shocks. Using the equilibrium prices one can computethe “implied” resource costs of price adjustment. They are very large andexceed 18% of output.
4.3. Assessing the Plausibility of Orthodox and Unorthodox Responses
We have seen that by varying the expected duration of zero interest rates
it is possible to produce specifications that have very different dynamic properties. We now propose a strategy for assessing which of these specifications ismost relevant for understanding Japan’s experience with zero interest rates.
One of the messages from Table 3 is that as the expected duration ofzero interest rates is increased, the response of the markup to a variety ofshocks increases. Each of the specifications we have considered has distinct
implications for the volatility of the markup, prices, GDP and other aggregate
variables. What is interesting about Japan is that the period of zero interest
rates was associated with a sharp decline in real and nominal volatility.
22

Table 5 reports relative volatility statistics for Japanese data and alternative specifications of the model. For each variable we report the standard
deviation from 1988 to 1998 relative to the same variable’s standard deviation between 1999 and 2006. A relative volatility statistic of less than one
means that the respective variable was less volatile during the period of zeronominal interest rates.
The first row of Table 5 reports relative volatility statistics for Japanesedata.16 The volatility of GDP and real marginal costs both fall by about half.
The declines in the volatility of consumption and inflation are even more
pronounced. Consumption volatility falls be over 70% and both measuresof inflation volatility (CPI and Consumption deflator) fall by 65%. Labor
input is the only variable for which volatility actually increases during the
1999-2007 sample period.
The baseline specification successfully predicts the qualitative pattern of
declines in nominal and relative volatility observed in Japanese data. It
predicts declines in output, consumption, real marginal costs and inflation.
The baseline specification also, counterfactually, predicts a decline in labor
input volatility. Some of the magnitudes are off but, overall it is our viewthat this parsimonious model of the Japanese economy does a surprisingly
good job of reproducing the evidence of tranquility in Japanese data.
For purposes of comparison we report volatility statistics for other specifications that have orthodox properties. The moderate price adjustment costmodel uses a value of γ = 10.17 This specification also successfully reproduces the evidence of tranquility. With lower adjustment costs, the relative
volatility of inflation increases to 0.27 which brings it closer to the data valueof 0.35. The flexible price specification, reported in row two of Table 5 does
about as well as the moderate price adjustment cost specification for the realvariables but produces too much volatility in the price level.
Consider next the results reported in rows below the baseline specification. These specifications all have unorthodox properties. Observe that both
specifications with higher serial correlation in dt predict that volatility in consumption, real marginal cost and inflation should have increased during the
Following Muto (2009), we calculate real marginal costs as α1 Compensation of employees/(National income - households’ operating surplus). We would like to thank Ichiro Muto
from the Bank of Japan for his helpful comments on the measurement of real marginal
costs.
17
The associated figure under Calvo price adjustment is 0.45
1623

period of zero interest rates. This occurs even though these two specifications
have lower variability in the preference discount shock than the baseline specification between 1999 and 2006 and the same sequences of all other shocks
as the baseline specification (see column 6 in Table 5). The match between
the model and Japanese data is particularly poor when ρd = 0.95. Recall
that this specification has the property that the response of output to labortax and transient technology shocks is unorthodox. Here output volatility
increases and the volatility of real marginal cost more than doubles between
1999 and 2006.
The persistent expectations and large preference shock specifications also
predict that the period of zero interest rates in Japan should have been aperiod of high economic volatility. The increase in volatility is particularly
dramatic in the final row of Table 5 labeled “Large Preference Shock (alt).”
This specification omits the resource costs of price adjustment from the aggregate resource constraint. Recall that this is done to provide an indicationof how the results would change if one log-linearized the model around a
steady-state with zero inflation. The result is a very large increase in realand nominal volatility. Output volatility nearly triples and inflation volatility
more than doubles during the period of zero interest rates.
In addition to the counterfactual implications for volatility there are twoother factors that cast doubt on the empirical relevance of the unorthodox
specifications. First, Ichiue and Ueno (2007) find that the maximum expected
duration of zero interest rates between 1999 and 2007 was not more than 2.3
years. The specifications that produce unorthodox results all require households to expect zero interest rates for a much longer period of time. Second,
all of the specifications that exhibit unorthodox responses have the property
that the resource costs of price adjustment are large during the episode ofzero interest rates. As reported in Table 3, they range from 1.53% of output
for the high serial correlation discount rate specification with ρd = 0.94 toa massive 18.7% of output for the specification where the resource costs areomitted from the aggregate resource constraint. In this final case the resource
costs of price adjustment are “imputed” using the equilibrium value of theprice level. The baseline specification exhibits much more moderate resource
costs of price adjustment. The value of 0.6% lies in the range of estimatesthat emerge from analyzing the costs of adjusting prices from firms. Levy
et al. (1997) find that menu costs constitute 0.7% of revenues in supermarket
chains.

24

4.4. Robustness
In this section, we briefly describe the robustness of our conclusions. As
regards the choice of the shock processes, we wish to first mention that ourassumption that technology follows a unit root process does have an impact
on some of our results. Under our current assumption that shocks to technology are permanent agents best guess of tomorrow’s state of technology
is today’s state of technology plus drift. The past is of no help in forming
expectations about the future. Technology shocks play an important role inthe dynamics of the model and under the assumption of a unit root process
in technology agents never expect the zero lower bound to bind in advanceof 1999. If instead technological progress is deterministic and shocks to technology are serially correlated agents start to predict zero nominal interest
rates several years before the nominal interest rate falls to zero and this acts
to change the dynamics of the model before the nominal interest rate is zero.
The dynamics start to change as soon as agents expect zero nominal rates in
the future. This finding is significant in the sense that it is not necessary forthe nominal interest rate to be zero in order for the dynamics of the model tostart to shift. All that is necessary is that agents expect the nominal interest
rate to be zero at some point in the future.
We have chosen to model quadratic price adjustment costs and not Calvo(1983) style price adjustment. Braun and Waki (2010) compare Calvo andRotemberg models of price adjustment. They find that the increase in
marginal costs associated with a given change in government purchases islarger under Calvo price adjustment. This results in a larger government
purchase multiplier under Calvo price setting. On the basis of this result
it is our conjecture specifications with Calvo price setting will exhibit evenmore excess volatility as compared to the Rotemberg specification we haveconsidered here.
We have also performed other experiments in which we reduced the relative persistence of the shock to government purchases or the shock to thelabor tax rate by lowering the serial correlation coefficient. Changing the parameters in this way reduced the size of the government purchase multiplierand yielded output responses to the labor tax that were always orthodox.
We have also conducted simulations in which we kept the tax rate on
consumption constant.18 This leads to a deterioration in the fit of the model
18

Under this assumption a 3% shock to the discount factor is needed to induce a binding25

for GDP and labor input. However, the magnitudes of the GDP impulse
responses and the government purchase multiplier are very close to thosereported for our baseline specification.
Finally, the qualitative nature of our results is robust to the parameterization of the Taylor rule. We have obtained qualitatively similar results
using Taylor rules that set the coefficient on the lagged value of the nominal
rate to zero, use a different coefficient on inflation or include output growth.
5. Concluding Remarks
In this paper we have conducted a quantitative investigation aimed atassessing the dynamics of the New Keynesian model in a low interest rateenvironment.
We produced a baseline specification that does a reasonable job of reproducing some basic stylized facts from the Japanese economy between 1988
and 2007. An investigation of the dynamic properties of that specification
implies that the response of output to a range of shocks is consistent withstandard theory. Moreover, the size of the government purchase output multiplier is less than one.
We also considered specifications of the model that have larger government purchase multipliers and some which also exhibit unorthodox predictions for the response of output to labor tax and technology shocks. We
found that these specifications are difficult to square with the fact that theperiod of zero interest rates in Japan between 1999 and 2006 was a period of
low economic volatility. All of the specifications predict the opposite shouldhave occurred. The specifications with unorthodox properties also have otherproblems. They predict large resource costs of price adjustment which are
difficult to reconcile with empirical evidence that menu costs are small andthey require that households expect the period of zero interest rates to be
counterfactually long.
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29

Capital−output ratio

Detrended real output

3
0.95
2.5
0.85
2
0.75
1990

1995

2000

2005

1990

Detrended real consumption

1995

2000

2005

2000

2005

2000

2005

Labor input
36

0.55

32

0.45

28
0.35
1990

1995

2000

2005

1990

Nominal interest rate

1995

Marginal costs

10
0.89
5
0.87
0

0.85
1990

1995

2000

2005

2000

2005

1990

1995

Inflation
2
0
−2
1990

1995

Figure 1: Baseline economy no shocks to preferences, τc,t or monetary policy after 199130

Capital−output ratio

Detrended real output

3
0.95
2.5
0.85
2
0.75
1990

1995

2000

2005

1990

Detrended real consumption

1995

2000

2005

2000

2005

2000

2005

Labor input
36

0.55

32

0.45
0.35

28
1990

1995

2002

2005

1990

Nominal interest rate

1995

Marginal costs

10
0.89
5

0.87
0.85

0
1990

1995

2000

2005

2000

2005

1990

1995

Inflation
2
0
−2

1990

1995

Figure 2: Baseline economy all shocks active.

31

Table 1: Model Parameterization

Symbol
Value
α
0.362
δ
0.085
φ
4
β
0.995
ν
0.27
σ
2
γ
80
θ/(θ − 1) 1.15
R
0.029
ρR
0.4
ρπ
1.7
µA
1.02
G/Y
0.19
τw
0.27
τk
0.41
τc
0.05
ρA
0.92
ρG
0.89
ρw
0.9
ρk
0.9
ρc
0.9

Description
Capital share
Depreciation rate
Adjustment costs on capital
Discount factor
Preference consumption share
Preference curvature
Adjustment costs on prices
Steady state gross markup
Steady state nominal rate
Elasticity of the nominal rate with respect to the lagged nominal rate
Elasticity of the nominal rate with respect to inflation
Steady state growth rate of technology
Steady state government share
Steady state labor income tax
Steady state capital tax
Steady state consumption tax
Autocorrelation coefficient of transient technology shocks
Autocorrelation coefficient of government spending
Autocorrelation coefficient of labor income tax
Autocorrelation coefficient of capital income tax
Autocorrelation coefficient of consumption tax

32

Table 2
Impact responses of output and markup baseline specification
Year
1995
1999
Years expected nominal rate is zeronone
1999-2000
Resource costs of price adjustment**
0.22
0.59
Impact response of output (GDP) to a positive shock in:
Neutral technology (transitory)
0.64
0.57
Neutral technology (permanent)
0.62
0.68
Labor tax
-0.62
-0.56
Government purchases
0.65
0.87
Impact response of the markup to a positive shock in:
Neutral technology (transitory)
0.06
0.21
Neutral technology (permanent)
-0.03
-0.14
Labor tax
-0.06
-0.23
Government purchases
-0.20
-0.64
*For this shock the zero bound constraint applies only in 2004**Resource costs of price adjustment are reported in percentage terms of output

33

2004
2004-2005
0.54
0.59
0.71*
-0.57*
0.87*
0.19-0.17*-0.21*-0.57*

34

Years expected nominal rate is zero
1999-2000
1999-2004
1999-2005
Resource costs of price adjustment*
0.59
1.53
3.62
Impact response of output (GDP) to a positive shock in:
Neutral technology (transitory)
0.57
0.08
-0.38
Neutral technology (permanent)
0.68
0.97
1.27
Labor tax
-0.56
-0.08
0.33
Government purchases
0.87
1.55
1.92
Impact response of production to a positive shock in:
Neutral technology (transitory)
0.60
0.39
0.42
Neutral technology (permanent)
0.66
0.79
0.79
Labor tax
-0.59
-0.36
-0.36
Government purchases
0.78
1.03
0.87
Impact response of markup to a positive shock in:
Neutral technology (transitory)
0.21
0.94
1.34
Neutral technology (permanent)
-0.14
-0.60
-0.89
Labor tax
-0.23
-0.96
-1.35
Government purchases
-0.64
-1.79
-2.07
*Resource costs of price adjustment are reported in percentage terms of output.
For the specification without price adjustment costs in the resource constraint, implied resource costs are reported.

Baseline

-0.04
1.15
0.05
1.70
0.60
0.71
-0.58
0.67
0.79
-0.61
-0.86
-1.58

0.29
0.88
-0.28
1.33
0.52
0.73
-0.50
0.87
0.58
-0.42
-0.63
-1.35

1999-2003 1999-2006
2.51
7.08

2.78
-2.00
-2.95
-4.66

-0.39
1.42
0.42
2.02

-0.39
1.42
0.42
2.02

1999-2006
18.70

Baseline Shocks, Baseline Shocks,
Large preferencehigh serial
high serial
Largeshock without
Persistentcorrelation
correlation in
preference price adjustment
Expectations
discount factor discount rate shock
shock
costs in theshock (0.94)(0.95)
resource constraint

Table 3
Impulse responses to shocks that arrive in 1999 for alternative specifications of the modelTable 4
Decomposition of the GDP response to a government purchases shockSpecification
Baseline
Higher discount factor serial correlation (0.94)
Higher discount factor serial correlation (0.95)
Persistent expectations
Large preference shock! GDP /! g

= (1! " ) ! y /! g

- y (! " /! g)

0.87
1.55
1.92
1.33
1.70

= (1 - 0.006) x 0.78
= (1 - 0.015) x 1.03
= (1 - 0.036) x 0.87
= (1 - 0.025) x 0.87
= (1 - 0.071) x 0.67

- 1.02 x ( - 0.09)- 1.03 x ( - 0.52)- 1.03 x ( - 1.05)- 1.00 x ( - 0.46)- 0.99 x ( - 1.03)

35

36

0.52

0.28

Consumption
1.33

Labor
Input
0.51

0.35

Real
Consumption
Marginal
deflator
Cost
0.35

CPI

-

-

Preference
Consumption tax
discount
shock
shock

Model Specifications with Orthodox Properties
0.4
0.69
0.38
0.00
1.02
0.29
0.11
Flexible Price
0.41
0.71
0.44
0.15
0.27
0.25
0.11
Moderate Price adjustment cost
0.50
0.75
0.53
0.21
0.07
0.29
0.14
Baseline
Model Specifications with Unorthodox Properties
0.74
1.05
0.47
1.86
1.09
0.13
0.14
Higher discount factor serial correlation (0.94)
1.40
1.3
0.65
2.25
1.68
0.11
0.14
Higher discount factor serial correlation (0.95)
1.09
1.36
1.14
1.84
0.78
0.62
0.28
Persistent Expectations
2.14
1.87
1.8
3.01
1.47
0.74
0.34
Large Preference Shock
2.84
2.16
5.64
5.56
2.46
0.74
0.34
Large Preference Shock (alt)* All statistics are calculated as the standard deviation of the variable from 1999 to 2006 relative to its standard deviation from 1988 to 1998.
All variables except marginal cost are expressed in terms of log growth rates.
(alt) refers to the specification where the resource costs of price adjustment are omitted from the resource constraint.

Japanese Data

OutputTable 5
Relative standard deviations for Japanese data and alternative specifications of the model*