Business cycle accounting for the Japanese economy

RIETI Discussion Paper Series 05-E-023

Business cycle accounting for the Japanese economy*

Keiichiro Kobayashi† and Masaru Inaba‡

October 11, 2006 (First draft: May 30, 2005)

Abstract
We conducted business cycle accounting (BCA) using the method
developed by Chari, Kehoe, and McGrattan (2002a) on data from the
1980s--1990s in Japan and from the interwar period in Japan and the United
States. The contribution of this paper is twofold. First, we find that labor
wedges may have been a major contributor to the decade-long recession in
the 1990s in Japan. Assuming exogenous variations in the share of labor, we
find that the deterioration in the labor wedge started around 1990, which
coincides with the onset of the recession. Second, we performed an
alternative BCA exercise using the capital wedge instead of the investment
wedge to check the robustness of BCA implications for financial frictions.
The accounting results with the capital wedge imply that financial frictions
may have had a large depressive effect during the 1930s in the United States.
This implication is the opposite of that from the original BCA findings.

Keywords: Business cycle accounting; Japanese economy; capital wedge;
Great Depression.
JEL Classifications: E32; E37; O47.

* We thank Ken Ariga, Richard Anton Braun, Shin-ichi Fukuda, Fumio
Hayashi, Charles Y. Horioka, Tomoyuki Nakajima, Tetsuji Okazaki, Hak K.
Pyo, Hajime Takata, Tsutomu Watanabe, Noriyuki Yanagawa, Masaru
Yoshitomi, the anonymous referee, and seminar participants at RIETI,
University of Tokyo, the CIRJE-TCER 7th Macro Conference, KIER, the
2006 Annual Meeting of SED (Vancover), and the 2006 NBER Japan Project
Meeting for their helpful comments. All remaining errors are ours. The views
expressed herein are those of the authors and not necessarily those of the
Research Institute of Economy, Trade and Industry.
† Research Institute of Economy, Trade and Industry, e-mail: kobayashi-keiichiro@rieti.go.jp
‡ Graduate School of Economics, University of Tokyo

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Business cycle accounting for the Japanese economy∗
Keiichiro Kobayashi†and Masaru Inaba‡
Revised on October 11, 2006 (Final draft: March 30, 2006; First: May 30, 2005)
Abstract
We conducted business cycle accounting (BCA) using the method developed by
Chari, Kehoe, and McGrattan (2002a) on data from the 1980s—1990s in Japan and
from the interwar period in Japan and the United States. The contribution of this
paper is twofold. First, we find that labor wedges may have been a major contributor
to the decade-long recession in the 1990s in Japan. Assuming exogenous variations in
the share of labor, we find that the deterioration in the labor wedge started around
1990, which coincides with the onset of the recession. Second, we performed an
alternative BCA exercise using the capital wedge instead of the investment wedge
to check the robustness of BCA implications for financial frictions. The accounting
results with the capital wedge imply that financial frictions may have had a large
depressive effect during the 1930s in the United States. This implication is the
opposite of that from the original BCA findings.
Keywords: Business cycle accounting; Japanese economy; capital wedge; Great
Depression.
∗We thank Ken Ariga, Richard Anton Braun, Shin-ichi Fukuda, Fumio Hayashi, Charles Y. Ho-
rioka, Tomoyuki Nakajima, Tetsuji Okazaki, Hak K. Pyo, Hajime Takata, Tsutomu Watanabe, Noriyuki
Yanagawa, Masaru Yoshitomi, the anonymous referee, and seminar participants at RIETI, University of
Tokyo, the CIRJE-TCER 7th Macro Conference, KIER, the 2006 Annual Meeting of SED (Vancover),
and the 2006 NBER Japan Project Meeting for their helpful comments. All remaining errors are ours.
The views expressed herein are those of the authors and not necessarily those of the Research Institute
of Economy, Trade and Industry.
†The Research Institute of Economy, Trade and Industry. E-mail: kobayashi-keiichiro@rieti.go.jp
‡Graduate School of Economics, University of Tokyo
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JEL Classifications: E32; E37; O47.
1
Introduction
A popular analytical framework for business cycle research, which was pioneered by Kyd-
land and Prescott (1982), is to quantitatively model the economy as a dynamic general
equilibrium. The standard method in this literature is to model market distortions and
shocks in a neoclassical growth model, calibrate parameters, and simulate the equilibrium
outcome by numerical calculations. The performance of a dynamic equilibrium model is
judged by the closeness of the simulated outcome to the actual data.
Recently, a “dual” method for the above standard approach was proposed and applied
in an analysis of the Great Depression by Mulligan (2002) and Chari, Kehoe, and Mc-
Grattan (2002a, 2004). In the dual method, it is assumed that the economy is described
as a standard neoclassical growth model with time-varying productivity, labor taxes,
investment taxes, and government consumption. These wedges, called efficiency, labor,
investment, and government wedges, are measured so that the outcome of the model is
exactly equal to the actual data. Therefore, in this dual approach the distortions are
measured so that the model replicates the data exactly. In the standard approach, by
contrast, the researcher predetermines plausible distortions and simulates the outcome,
which is usually different from the actual data.
The dual approach, which was named “business cycle accounting (BCA)” by Chari
et al., has several useful features. First, the calculations are quite easy to make, since the
wedges are directly calculated from the equilibrium conditions, which necessitate data
for only one or two consecutive years and few assumptions on the future equilibrium path
(see also the propositions in Mulligan [2002]). Second, BCA is a useful method for guiding
researchers in developing relevant models. This is because, as Chari et al. (2004) show,
a large class of quantitative business cycle models is equivalent to a prototype growth
model with wedges. Since the BCA procedure shows which wedges are most crucial in
actual business fluctuations, researchers can judge their business cycle models by whether
they can reproduce relevant wedges.
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The BCA method seems to provide particularly useful insight into the recent recession
in Japan. In the policy and academic debate over the persistent recession in Japan during
the 1990s, people have proposed different causes of the recession: for example, insufficient
fiscal stimulation, financial frictions caused by the severe nonperforming loan problem,
deflation caused by a contractionary monetary policy, and productivity declines caused
by structural problems. When we try to infer which is the most promising among these
explanations, it is useful to see which wedges are the main contributors to the recession
by applying BCA.
For this paper, we conducted business cycle accounting using data from the 1980s—
1990s, and the 1920s in Japan. Since in both periods the Japanese economy suffered from
deflationary recessions subsequent to asset-price collapses, BCA results for both periods
are useful to infer the causes of the recent recession in Japan. Interesting implications
are given by comparing our results with other explanations, especially those of Hayashi
and Prescott (2002). Hayashi and Prescott show that time-varying productivity, i.e.,
the efficiency wedge, can explain most of the output fluctuations during the 1990s. Our
results show that the labor wedge may have been even more crucial in producing the
recession. The BCA exercise shows that the labor wedge began to deteriorate in the early
1980s. We elaborate on the implications of this result and show that the deterioration
in the 1980s may be a misspecification of a technological change in which the aggregate
labor share changes: A modified BCA exercise in which we assume variable labor share
shows that the labor wedge began to deteriorate in the early 1990s, when the asset-price
bubble burst. We also examine why the labor wedge continued to deteriorate: While the
deterioration during the early 1990s may be explained by sticky wages and a deflationary
shock, the deterioration from 1995 onward points to other factors; one candidate may
be that the continuation of asset-price declines worsened the labor wedge by making
collateral constraints more severe.
We also conducted a different version of the BCA method, which is basically the
same as the dual method proposed by Mulligan (2002). In the original business cycle
accounting proposed by Chari et al. (2002a), friction in financial markets is assumed
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to manifest itself as the investment wedge, which is an imaginary tax on investment.
Mulligan (2002) introduces the capital wedge, which is an imaginary tax on dividends
from capital holdings. In order to justify the assumption that financial friction may
manifest itself as a capital wedge in the Mulligan-type BCA, we show that a model with
financial frictions proposed by Carlstrom and Fuerst (1998) is equivalent to the prototype
growth model with a capital wedge. We then examine whether different versions of
BCA produce different implications for the role of financial frictions using the data
from the 1980s—1990s in Japan and from the Great Depression in the United States.
The accounting results show that the capital wedge might have had a large depressive
economic effect in the latter case. This result is the opposite of the BCA result for the
Great Depression by Chari et al. They suggest that models of financial frictions are not
a promising explanation for the Great Depression, since their BCA result shows that the
investment wedge had no depressing effect. Our results with the capital wedge imply
that financial frictions may have had considerable effects in the Great Depression in the
United States, and that models with financial frictions may capture an important aspect
of reality.
This paper is not the first to apply the BCA method to the Japanese economy.
Chakraborty (2004) conducted BCA for the 1980s and the 1990s in Japan, and she
found that the investment wedge played a major role in the performance of the Japanese
economy in the 1990s. This result is somewhat different from our result in Section
3.1, which is that the investment wedge did not have a crucial effect. This difference
between her results and ours seems to be caused by a combination of differences in
data constructions, data sources, and simulation methods: For example, government
investment and net exports are categorized differently; The steady state values of wedges
are assumed to be those in 1980 in her simulation, while they are assumed to be the
values in 2003 in ours; and she simulates a log-linearlized model, while we simulate a full
nonlinear model without linearizing it.
The organization of the paper is as follows. Section 2 describes the general method
of business cycle accounting, which is basically the same as that in Chari et al. (2002a,
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2004) but includes a simplification, i.e., an assumption of perfect foresight, and some
modifications in exposition. Section 3 reports the BCA results for the 1980s—1990s and
the 1920s in Japan. Section 4 describes the new method of BCA with the capital wedge
and presents the results of the new BCA for the Great Depression in the United States.
Section 5 provides some concluding remarks.
2
Framework of business cycle accounting
In this section we briefly describe the method of BCA, following Chari, Kehoe, and
McGrattan (2004).
2.1
Prototype growth model
In the BCA framework, it is assumed that an economy is described as the following
standard neoclassical growth model with time-varying wedges: the efficiency wedge At,
the labor wedge 1 − τlt, the investment wedge 1/(1 + τxt), and the government wedge gt.
The representative consumer solves
∞
max E0[XβtU(ct,lt)Nt]
ct,kt+1,lt
t=0
subject to
ct + (1 + τxt) ½Nt+1kt+1
N
− kt¾ = (1 − τlt)wtlt + rtkt + Tt,
t
where ct denotes consumption, lt labor, kt capital stock, wt the wage rate, rt the rental
rate on capital, Nt population, β the discount factor, and Tt lump-sum taxes. All quan-
tities written in lower case letters denote per-capita quantities. The functional form of
the utility function is given by U (c, l) = ln c + φ ln(1 − l), where the unit of labor is set
so that the total time endowment for one year is normalized to one. The firm solves
max AtγtF (kt, lt) − {rt + (1 + τxt)δ}kt − wtlt,
where δ is the depreciation rate of capital and γt is the long-term trend rate of technical
progress, which is assumed to be a constant. The functional form of the production
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function is given by F (k, l) = kαl1−α. The resource constraint is
ct + xt + gt = yt,
(1)
where xt is investment and yt is per-capita output. The law of motion for capital stock
is
Nt+1 kt+1 = (1
N
− δ)kt + xt.
(2)
t
The equilibrium is summarized by the resource constraint (1), the law of motion for
capital (2), the production function,
yt = AtγtF (kt, lt),
(3)
and the first-order conditions,
U
− lt = (1
U
− τlt)AtγtFlt,
(4)
ct
(1 + τxt)Uct = βEtUct+1{At+1γt+1Fkt+1 + (1 + τxt+1)(1 − δ)},
(5)
where Uct, Ult, Flt and Fkt denote the derivatives of the utility function and the produc-
tion function with respect to their arguments.
Chari, Kehoe, and McGrattan (2004) show that various quantitative business cycle
models are equivalent to the above prototype economy with wedges: A model with
input-financing frictions is equivalent to the prototype growth model with an efficiency
wedge; a sticky-wage economy or one with powerful labor unions is equivalent to the
prototype economy with labor wedges; and an economy with financial friction of the
type proposed by Carlstrom and Fuerst (1997) is equivalent to the prototype economy
with an investment wedge.
2.2
Accounting procedure
The values for the parameters of preferences and technology are given in a standard way,
as in quantitative business cycle literature. Then we calculate wedges from the data using
equilibrium conditions (1), (3), (4), and (5). We then feed the values of the measured
wedges back into the prototype growth model, one at a time and in combinations, to
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assess what portion of the output movements can be attributed to each wedge separately
and in combinations. By construction, all four wedges account for all of the observed
movements in output. In this sense, this procedure proposed by Chari et al. (2002a,
2004) is an accounting procedure.
An important simplification in this paper from the original version by Chari et al.
(2004) is that we assume perfect foresight in the prototype economy so that all wedges
are given deterministically from (1), (3), (4), and
(1 + τxt)Uct = βUct+1{At+1γt+1Fkt+1 + (1 + τxt+1)(1 − δ)},
(6)
instead of (5). The assumption of perfect foresight enables us to avoid complicated
arguments and calculations concerning the stochastic process of wedges, which Chari et
al. (2004) discuss in detail. Since the perfect foresight version in Chari et al. (2002a)
provides identical implications for the Great Depression as the stochastic version in Chari
et al. (2004), we adopt this simplification in this paper.
Measuring realized wedges
We take the government wedge gt directly from the
data. To obtain the values of the other wedges, we use the data for yt, lt, xt, gt, and Nt,
together with a series on kt constructed from xt by (2). The efficiency wedge and the
labor wedge are directly calculated from (3) and (4).
To solve (6), we need to posit a strict assumption on the values of the wedges for
the time period after the target period of business cycle accounting. Denoting the target
period of BCA by t = 0, 1, 2, · ·· , T, we assume that At = A∗ = AT, gt/yt = (g/y)∗ =
gT /yT , and τlt = τ ∗ = τ
l
lT for t ≥ T + 1. The growth rate of the population is assumed
to be constant for t ≥ T + 1. We also assume that τxt is an unknown constant τ∗x for
t ≥ T. Under these assumptions, given that kT+1 is constructed from the data xt (t ≤ T),
we pick a value for τ ∗x and calculate the equilibrium path of {ct, kt} (t ≥ T + 1) which
converges to the balanced growth path with constant wedges. Since the equilibrium path
of ct (and kt) is uniquely determined for a given value of τ ∗x, we can choose the “true”
value of τ ∗x such that τxT = τxT+1 = τ ∗x and the initial consumption cT+1(τ ∗x) satisfy
(6) at t = T , given cT and kT +1. Once τ ∗x = τxT is determined by this method, τxt for
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t = 0, 1, 2, · · · , T − 1, are obtained by solving (6) backward.
Decomposition
To see the effect of the measured wedges on movements in macroe-
conomic variables from the initial date t = 0, we decompose the movements as follows.
Define st = (At, τlt, τxt, (gt/yt)). First, we construct the benchmark equilibrium by solv-
ing the prototype model with constant wedges. The values of the benchmark wedges are
determined as the initial values at t = 0, or the averages of the values of the wedges for
some period prior to the target period. Therefore, we solve the model assuming that
st is a constant vector for 0 ≤ t ≤ T and st = s∗ = (A∗, τ∗, τ∗
l
x , (g/y)∗) for t ≥ T + 1.
The derived sequences: ybt, cbt, xbt, and lbt are taken as the benchmark case. In order
to determine the effect of one wedge, we solve the prototype model, given that the one
wedge takes the measured value and the other wedges stay at the benchmark values.
We then compare the derived sequences of macroeconomic variables with those of the
benchmark case. For example, to see the effect of the efficiency wedge, we solve the
model, given that st = (At, τl−, τx−, (g−/y−)) for 0 ≤ t ≤ T, where τl−, τx−, (g−/y−) are
the benchmark wedges, and st = s∗ for t ≥ T + 1. If the derived output is below the
benchmark, we say that the efficiency wedge had a depressing effect.
A similar method is used to determine the effect of two wedges in combination: We
solve the prototype model, given that the two wedges take the measured values and the
other wedges stay at the benchmark values.
One caveat for our decomposition procedure is that we assume in all cases that st = s∗
for t ≥ T + 1. This is because we want to compare equilibrium paths which converge to
the same balanced growth path with the same wedges. Since we measured the realized
wedges under the assumption that st = (AT , τlT , τxT , (gT /yT )) for t ≥ T +1, we continue
to posit the same assumption in the decomposition.1 In addition to the main exercise, we
1 An alternative method may be to assume that wedges go back to the initial values at t = T + 1, and
to assume st = (A0, τl0, τx0, g0) for t ≥ T + 1 for all cases. There are, however, two difficulties with this
method. In conducting BCA for business fluctuations in one decade, it may not be plausible to assume
that people will believe that the wedges for the next year will jump back to their initial values of ten
years ago. A second problem is that the value of the investment wedge for t ≥ T + 1: τ∗x, which is the
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also conduct the BCA exercises with different assumptions on the values of st (t ≥ T +1)
to check the robustness of the BCA results, and report the results in the next section.
3
BCA for Japan
Japan experienced persistent deflationary recessions subsequent to asset-price collapses
during the 1990s and the 1920s. In the late 1980s the Japanese economy experienced an
unprecedented stock market and real estate boom, which came to be called the “bubble
economy.” At the beginning of the 1990s, both stock and land prices collapsed, leav-
ing huge amounts of nonperforming loans. Soon afterward, a persistent recession took
hold, leading to nationwide bank panics in 1997—99, and to subsequent deflation. This
deflation continues in 2005. After World War I, on the other hand, Japan experienced
an investment boom in military and heavy industries, and the stock market collapsed in
1920. A deflationary recession continued during the 1920s, and led to the first nation-
wide bank panics in Japanese history in 1927. A deflationary policy in 1929—1931 aimed
at restoring a fixed exchange rate worsened the recession, which forced Japan to leave
the gold standard again in December 1931. In the early 1930s the Japanese economy
staged a strong recovery, which is said to have been enabled by the expansionary fiscal
and monetary policies introduced in 1932.
3.1
The 1980s—1990s
The target period of our first accounting exercise is 1981—2003. We constructed the
data set following the method of Hayashi and Prescott (2002). The data set is provided
in a data appendix (Kobayashi and Inaba [2005]). We assume that β = 0.98. We set
α = 0.372 and δ = 0.0846, which are the averages during 1984—89.2 We also set gn = 0,
and gz = 0.0206, where gn is the population growth rate for t ≥ 2004, and (1+gz)1−α = γ.
The trend rate of technical progress (1 + gz) was set as the average during 1981—2003.
solution to (6) under the assumption that the other wedges take the initial values, may not coincide with
τx0.
2We set these values following Hayashi and Prescott for convenience of comparison.
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