ESRI Research Note No.51

Business cycle asymmetry:
Evidence from Japan’s decade-long deflation
Satoshi Urasawa
March 2020

Economic and Social Research InstituteCabinet Office
Tokyo, JapanThe views expressed in “ESRI Research Note” are those of the authors and not those of
the Economic and Social Research Institute, the Cabinet Office, or the Government of Japan.
(Contact us: https://form.cao.go.jp/esri/en_opinion-0002.html)

ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"

Business cycle asymmetry:
Evidence from Japan’s decade-long deflation
Satoshi Urasawa†

Abstract
This paper empirically examines the asymmetric behavior of macroeconomic timeseries under different economic regimes, focusing especially on whether the economy isin a deflationary or non-deflationary regime, using a threshold vector autoregression
model (TVAR).
The results provide evidence in favor of asymmetric spillover effects from demand
shocks on economic variables such as wages and consumption. In contrast to thenon-deflationary period, during the deflationary period demand shocks are not clearlytransmitted to the economy overall due mainly to the rigidity of nominal wages. The
findings highlight that the state of the economy also matters when we consider thenature of the business cycle.
JEL Code: E32
Keywords: Business cycle asymmetry, deflation, Japanese economy†Economic and Social Research Institute, Cabinet Office

Any views expressed herein are those of the author and not of the Cabinet Office. Any remaining errors are my own.

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ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"

1. Introduction
Understanding the mechanisms underlying business cycles, one of the key concepts
in macroeconomics, is important not only from an academic but also from a
policy-making perspective in order to gauge the overall state of the economy and todevise effective economic policies. At the same time, however, these mechanisms maychange depending on the state of the economy. In fact, it is well-known that businesscycle characteristics– that is, the links between dynamics in the economy as a whole andindividual macroeconomic time series–are nonlinear over phases of the business cycle,
resulting in business cycle asymmetries.
Economic theory and empirical analysis suggest several conditions under which thenonlinear relationships between macroeconomic time series can explain the asymmetricnature of business cycles. One of the most prominent examples is nominal rigidity inprices and wages, a key feature of many macroeconomic models, which becomes more
pronounced in periods of low inflation.
Given that Japan experienced decades of deflation, the question naturally arises
whether this deflation has given rise to business cycle asymmetries – that is, whether
propagation mechanisms differ in the deflationary and the non-deflationary regime. In
other words, is there a change in dynamic links when the economy changes from an
inflationary to a deflationary regime? This study empirically examines the asymmetricbehavior of macroeconomic time series under different economic regimes, focusing
especially on whether the economy is in a deflationary or non-deflationary regime,
using a threshold vector autoregression (TVAR) model.
2. Asymmetric behavior of macroeconomic time series
Before exploring the TVAR model, the study starts by considering the dynamic
cross-correlations obtained from a linear VAR model that assumes that both deflationary
and non-deflationary periods are known in order to examine how the relationships
among macroeconomic time series differed between the two periods, while identifying
in which areas differences in business cycle characteristics can or cannot be observed. If
the regime is known, the TVAR model reduces to an ordinary least squares (OLS)
model for two distinct observation periods; in contrast, if the regime is unknown, it
needs to be identified endogenously through the joint estimation of the optimal
parameters using a Grid search (as will be done in the next section).
Data description and statistics
For the purpose of the analysis here, the study separates the observation period from2

ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"

1980 to 2016 into deflationary and non-deflationary periods based on the official
assessment of the Japanese government. Specifically, Japan experienced deflation from
1999Q4 to 2006Q2 and from 2009Q4 to 2013Q3, and for convenience these two
periods together are referred to as the “deflationary period,” while the rest of theobservation period is referred to as the “non-deflationary period.” Figure 1 shows thedevelopments in Japan’s inflation rate, with the areas in grey depicting the deflationary
period. During the deflationary period, prices fell by around 0.6 percent a year on
average.
In order to examine differences in the relationships among macroeconomic timeseries under the different economic regimes, dynamic cross-correlation analysis
examining up to six orders of cross-correlation of a series (𝑥𝑥𝑡𝑡 )with real GDP (𝑔𝑔𝑔𝑔𝑔𝑔𝑡𝑡+𝑘𝑘 ,where k represents the k quarter lag or lead of real GDP) is employed. The
cross-correlation of each series with real GDP measures the strength of its correlation
with real output (a proxy of the business cycle), and it is assumed that series 𝑥𝑥𝑡𝑡 isprocyclical if its cross-correlation is positive and countercyclicalif its cross-correlationis negative; moreover, series 𝑥𝑥𝑡𝑡 is said to lag real GDP if its maximum correlation lags
real GDP observations. Turning to the data used for the analysis, various quarterly
macroeconomic time series spanning a wide range of fields, including consumption andinvestment, wages, deflators and prices, and financial market indicators, will be
examined.
Differences in the relationships among macroeconomic time series
Table 1 shows the dynamic cross-correlations (with the 95percent confidence
interval)in the deflationary period and the non-deflationary period to investigate thebehavior of macroeconomic time series during each of the periods and compare them.
Looking at the direction and strength of the correlation, as well as whether a variableleads or lags the economy, particularly notable differences can be observed in relation to
wages and prices: 1- Starting with wages, the correlation with output is lower in the deflationary than
the non-deflationary period, particularly in the case of nominal wages.
1The business cycle characteristics in the non-deflationary period here are essentially in line with those reported in

Urasawa (2018), which examined the stylized facts of Japanese business cycles. The stylized facts observed in
Urasawa (2018) can be summarized as follows: Consumption and investment are contemporaneously procyclical,
while the unemployment rate is countercyclical and strongly correlated with output; furthermore, it lags the economy.
Employment is procyclical and lags fluctuations in output, reflecting the traditional pattern of labor input adjustment
in Japan whereby in the early stages of an upswing or downswing, it is not the number of employees but hours
worked that are adjusted. Wages and inflation are basically procyclical and lag fluctuations in output. Finally, stock
prices are procyclical with a lead, while the effective exchange rate is counter-cyclical with a lag, that is, there is anegative correlation between an appreciation of the yen and output.

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ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"-

Specifically, the correlation coefficient for the wage index is 0.49 for the
non-deflationary period but only 0.16 for the deflationary period (which is below
the 95 percent confidence interval of the correlation coefficient obtained for the
non-deflationary period). Similarly, the correlation coefficient for compensation of
employees is 0.52 for the non-deflationary period but only 0.11 for the
deflationary period. These results suggest that wages in the deflationary regime
are more rigid than in the non-deflationary regime in the sense that they no longer
relate to developments in the economy overall.
Turning to prices, the correlation of inflation with output disappears in the
deflationary period, which is consistent with the finding of a flattening in theslope of the Phillips curve during the deflationary period. Specifically, while thecorrelation coefficient for the GDP deflator is 0.24 for the non-deflationary period,
it is –0.10 (below the 95 percent confidence interval of the correlation coefficientobtained for the non-deflationary period) for the deflationary period, while thecorresponding values for the consumer price index are 0.46 and almost zero.

In sum, the results indicate a decreased responsiveness of wages and prices toeconomic activity, which points to differences in the propagation mechanisms in theeconomy in a deflationary and a non-deflationary regime. To further examine thereasons for these differences, the next section presents additional analyses based on a
TVAR model, focusing on spillover effects on the demand side of the economy throughwages and consumption (the consumption channel). 2
3. Analysis of business cycle asymmetries using a TVAR model
To examine the business cycle asymmetries in more detail, this section presents theestimation of a TVAR model, which does not require any prior assumptions about
different regimes. Since TVAR models, originally developed by Tong (1978) and Tsay
(1998), allow the behavior of time series to depend on the state of the system, they
provide a useful and flexible tool to capture possible non-linearities and asymmetric
reactions to shocks.
Structure of the two-regime model
Consider the following TVAR (p) model with two regimes (𝑗𝑗 = 1,2) and a pth orderlag, assuming that there is an observable threshold variable 𝑞𝑞𝑡𝑡 , belonging to y, which is2

To examine the propagation mechanisms on the supply side of the economy through wages and the number ofworkers, the unemployment rate is used an alternative variable. However, no difference can be observed between two
regimes.

4

ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"a (𝑘𝑘 × 1) vector consisting of k observed variables:𝑝𝑝

𝑦𝑦𝑡𝑡 = ∑𝑖𝑖=1 𝐴𝐴𝑗𝑗,𝑖𝑖 𝑦𝑦𝑡𝑡−𝑖𝑖 + 𝜀𝜀𝑡𝑡,𝑗𝑗

where 𝑗𝑗 = 1 (deflationary regime) if 𝑞𝑞𝑡𝑡−𝑑𝑑 < 𝛾𝛾 and 𝑗𝑗 = 2 (non-deflationary regime)otherwise; 𝛾𝛾 is the value of the threshold; d is the lag of the threshold variable relevant
for regime changes; 𝐴𝐴𝑗𝑗,𝑖𝑖 is the matrix of coefficients of regime j and lag i. Each regime
can be characterized by a variance-covariance matrix ∑𝑗𝑗 .

Note that the model is linear within each regime, while changes in the parametersacross regimes account for non-linearities. The TVAR model can be estimated using
OLS conditional on the threshold variable, 𝑞𝑞𝑡𝑡−𝑑𝑑 , the number of regimes, and the orderp. Given the linearity of the model within each regime, using conditional least squares(for all possible threshold values) under the assumption of a given number of regimes,
the model is estimated by minimizing the sum of squares of the residuals.
Data and settings
The TVAR model used in this study is based on four time series consisting of real
GDP (GDP), nominal wages (NWG), nominal private consumption (NPC), and theconsumer price index (CPI). 3 For the estimation, data from 1980Q1 to 2016Q3 is
employed using log differences. Structural shocks are identified through are cursive
approach assuming that the time ordering of variables is GDP, NWG, NPC, and CPI. In
the estimation, the threshold variable is assumed to be the first lag of CPI, and thethreshold 𝛾𝛾 is assumed to be an unknown parameter.
Employing this approach, the differences in propagation mechanisms between the
deflationary and the non-deflationary regime are examined, focusing on nominal rigidity.
Specifically, how the response of wages, consumption, and the CPI to a structural shockin GDP (demand shock) differs between the two regimes is examined. The model allows
two ways in which the propagation of structural shocks can differ; that is, in the waythat shocks are propagated contemporaneously via differences in the covariancematrices for disturbances, and in the way they are propagated dynamically via
differences in lag polynomials.
Estimation results
Figure 2 shows the estimation results of the TVAR model and a linear VAR model of
3To avoid an implausible number of regime switches over time, the average of four subsequent quarters of the series

in log differences is used.

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ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"

the cumulative impulse responses of GDP, NWG, NCP, and CPI to a structural shock toeach of these variables. For the TVAR model, the figure shows the cumulative impulse
responses in both the deflationary regime, defined as periods with an inflation rate
below the threshold value of 0.06, and the non-deflationary regime, defined as periods
with inflation above the threshold value. For the linear VAR model, the results for theentire period (1980Q1 to 2016Q3) are shown.
The estimation results suggest the following. The initial response of GDP to ademand shock (structural shock to GDP)differs substantially between the two regimes,
with the simultaneous correlation of a demand shock dropping from 1.2 in the
non-deflationary regime to 0.7 in the deflationary regime. In addition, subsequent
responses are also weaker, resulting in flatter impulse responses in the deflationary
regime (below the 95 percent confidence interval obtained from the linear VAR model);in contrast, in the non-deflationary period, impulse responses display a strong andpersistent reaction of output to a demand shock.
This is also true for the responses of NWG, NCP, and CPI to a demand shock,indicating a weaker response to economic activity in the deflationary regime, which isconsistent with the result in the previous section that the correlation between output andboth wages and prices was substantially lower in the deflationary period.
A likely reason for the weaker response of consumption and prices is the weaker
response of wages; in contrast, the responses of NCP and CPI to own shocks are thesame in the two regimes (within the 95 percent confidence interval obtained from thelinear VAR model).This implies that nominal wages appear to be downwardly and even
upwardly rigid in the deflationary regime, so that they do not respond to demand shocks,
resulting in weaker spillover effects on the economy through the consumption channel.
4. Conclusion
Aggregate output, as measured by real GDP, fluctuates as a result of various shocks tothe economy as well as the way that such shocks are transmitted to the economy.
Although business cycle characteristics to some extent can be regarded as universal andconstant over time, they can change depending on the state of the economy. Against thisbackground, this study estimated a TVAR model to quantify the differences inpropagation mechanisms in the Japanese economy in a deflationary and anon-deflationary regime, providing evidence in favor of asymmetric spillover effects
from demand shocks on economic variables such as wages and consumption.
References
6

ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"Tong, H., 1978. On a Threshold Model. C.H. Chen (Ed.), Pattern Recognition and
Signal Processing, Sijthoff & Noordhoff, Amsterdam.
Tsay, S., 1998. Testing and Modeling Multivariate Threshold Models. Journal of theAmerican Statistical Association 93, 1188–1202.
Urasawa, S., 2018. Structural Change and Business Cycles in Japan: Revisiting the
Stylized Facts. Journal of the Business Cycle Research 14(2), 243–281.

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ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"

Figure 1: Developments in Japan’s inflation rate and wage growth(%)

Consumer price index (excl. fresh food and energy)
4-month-moving-average
Compensation of employees

1.5

0

-1.5

1985

1990

1995

2000

2005

2010

2015

Notes: The thick solid line shows the 4-month-moving-average of the log difference of the CPI, while the broken line shows the log
difference of the CPI. The CPI figures exclude the direct effects of the consumption tax hikes in1989, 1997, and 2014. The thin solidline shows the 4-month-moving-average of the log difference of the Compensation of employees. Shaded areas represent
deflationary periods as identified by the Cabinet Office.

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ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"

Figure 2: Impulse responses of GDP, wages, consumption, and CPI to a shock toeach of these variables: TVAR model and linear VAR model
GDP response to GDP shock

3.0

NWG response to GDP shock

3.0

3.0

NPC response to GDP shock

2.5

CPI response to GDP shock

2.5

2.5

2.5

2.0

2.0

2.0

2.0

1.5

1.5

1.5

1.5

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

-0.5

1.0

Linear VAR (w/ 95% CI)
Non-deflationary regime
Deflationary regime

0.5
0.0

5

10

GDP response to NWG shock

5

5

10

NWG response to NWG shock

NPC response to NWG shock

1.5

2.0

1.0

1.5

1.5

1.5

0.5

1.0

1.0

1.0

0.0

0.5

0.5

0.5

-0.5

5

10

GDP response to NPC shock

0.0

0.0

5

0.0

0.0

0.0

-0.5

5

10

-0.5

-0.5

5

NPC response to CPI shock

1.0

1.0

0.5

0.5

0.5

0.5

0.0

0.0

0.0

0.0

5

10

-0.5

5

10

-0.5

5

10

1.0

-0.5

10

10

CPI response to CPI shock

-0.5
5

10

CPI response to NPC shock

NPC response to NPC shock

0.5

NWG response to CPI shock

GDP response to CPI shock

5

0.5

0.0

1.0

0.0

0.5

0.5

10

NWG response to NPC shock

10

1.0

1.0

5

5

10

10

CPI response to NWG shock

2.0

1.0

1.0

-0.5

2.0

5

10

5

10

Notes: The panels show the cumulative impulse responses obtained with the TVAR model for the deflationary period (thick brokenline) and the non-deflationary period (thick solid line), together with the results of the linear VAR model (thin line) with the 95
percent confidence interval (indicated by the thin broken lines).

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ESRI Research Note No.51"Business cycle asymmetry:
Evidence from Japan’s decade-long deflation"

Table 1: Dynamic cross-correlations: deflationary and non-deflationary period
Deflationary period
Macroeconomic time series

Non-deflationary period

Maximum correlation with GDP (Corr[xt, gdpt+k]) Maximum correlation with GDP (Corr[xt, gdpt+k])lag
k<095% C.I.

k=0

lead
k>0

95% C.I.

lag
k<0

k=0

GDP components (real) and employment
Private consumption
Private residential investment
Private non-resid. investment
Government consumption
Public investment
Exports
Imports0.74 0.62
0.12 -0.17
0.26 0.18
0.10 -0.20
0.15 -0.11
0.66 0.49
0.48 0.37

0.86
0.40
0.34
0.41
0.41
0.83
0.59

k=0
k=0
k=1
k=0
k=0
k=0
k=-1

0.71 0.63
0.23 0.06
0.56 0.42
0.22 0.04
0.14 -0.06
0.50 0.36
0.36 0.20

0.80
0.41
0.69
0.41
0.33
0.65
0.52

k=0
k=0
k=0
k=0
k=0
k=0
k=0

Employees
Average hours worked (total)
Unemployment rate
Effective job-openings-to-applicants ratio
Labor productivity

0.36 0.25 0.47
0.44 0.34 0.54
-0.43 -0.55 -0.31
0.46 0.34 0.59
0.95 0.92 0.98

k=-1
k=0
k=2
k=-1
k=0

0.41 0.34 0.47
0.26 0.10 0.41
-0.46 -0.54 -0.38
0.53 0.46 0.60
0.96 0.95 0.97

k=-2
k=0
k=-1
k=-1
k=0

Wages
Wage index (total cash earnings, nominal)
Wage index (total cash earnings, real)Compensation of employees (nominal)
Labor share

0.16 0.07 0.24
0.24 0.15 0.34
0.11 0.03 0.19
-0.73 -0.87 -0.60

k=-1
k=1
k=1
k=0

0.49 0.43 0.55
0.33 0.25 0.41
0.52 0.48 0.57
-0.69 -0.76 -0.63

k=-1
k=-1
k=-1
k=0

Deflators and prices
GDP deflator
Consumer price index
CPI (excl. fresh food)
CPI (excl. fresh food and energy)-0.10 -0.18 -0.03
0.07 0.00 0.13
-0.08 -0.38 0.23
-0.09 -0.17 -0.01

k=1
k=-1
k=0
k=1

0.24
0.46
0.44
0.30

0.19
0.39
0.37
0.21

0.29
0.53
0.50
0.40

k=-1
k=-2
k=-2
k=-1

Interest rates and stock prices
Call rate (collateralized overnight)
Newly issued government bonds (10-year)
Stock prices-0.26 -0.34 -0.18
0.16 0.09 0.23
0.13 -0.18 0.44

k=3
k=2
k=0

0.29
0.42
0.28

0.22
0.34
0.23

0.35
0.49
0.34

k=-1
k=-1
k=1

Money and exchange rate
Money stock (M2, nominal)
Monetary base (nominal)
Effective exchange rate

-0.07 -0.37 0.24
-0.21 -0.31 -0.10
0.17 0.09 0.25

k=0
k=-1
k=-1

0.47 0.39 0.54
-0.08 -0.27 0.11
-0.21 -0.40 -0.03

k=1
k=0
k=0

lead
k>0

Notes: The table reports the maximum value of six orders of cross-correlation of each series with real GDP in the deflationary
period and the non-deflationary period with the 95percent confidence interval.

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