DP2022-32

Cyclical Activity and Inflation underSecular Stagnation: Empirical Evidence
Using Data on Japanʼs Lost Decades
Masahiko SHIBAMOTO

July 4, 2022

Cyclical Activity and Inﬂation under Secular Stagnation:
Empirical Evidence Using Data on Japan’s Lost Decades∗
Masahiko Shibamoto†
July 4, 2022

Abstract
This paper disputes the suspicions about the existence and stability of the trade-oﬀ between
nominal inﬂation and the real economy when missing deﬂation and reinﬂation under secularstagnation by providing empirical evidence of the stability of this short-run trade-oﬀ. To thisend, we construct a simple measure of demand-pull pressures, namely the cyclical activity
index, using time-series data for a period that includes Japan’s secular stagnation. We thenquantitatively examine the relationship between inﬂation and the measured cyclical activity.
The empirical results support that the cyclical activity index has a stable and economicallymeaningful relationship with short-term inﬂation.
JEL Classiﬁcation: E31; E32.
Keywords: Inﬂation; Cyclical activity; Phillips curve; Economic slack; Secular stagnation;
Japan.

∗

This study received ﬁnancial support from the Japan Society for the Promotion of Science (JSPS KAKENHI
Grant Number 20H05633 and 21K01579).
†
Correspondence to: Masahiko Shibamoto, Research Institute for Economics and Business Administration(RIEB) and Center for Computational Social Science (CCSS), Kobe University, 2–1, Rokkodai, Nada, Kobe,
657–8501, Japan. E–mail: shibamoto@rieb.kobe-u.ac.jp.

1

Introduction

A short-run trade-oﬀ between nominal inﬂation and the real economy is one of the criticalbuilding blocks for understanding business cycles and macroeconomic policy. Since the seminal
papers of Fisher (1926) and Phillips (1958), the Phillips curve has been the primary tool thatboth academics and policymakers rely upon to understand this trade-oﬀ. Standard economics
textbooks, such as Mankiw (2019), describe the trade-oﬀ from the aggregate supply relationship,that is, inﬂation accelerates when the economy is in a boom and decelerates when it is in a slump.
The central banks in many countries discuss their judgments about the current and future stateof inﬂation and the approaches to achieving the policy goal of macroeconomic and inﬂation
stability in terms of the Phillips curve.
The signiﬁcance of the Phillips curve often exposes it to controversy over its empiricalregularity and reliability as a tool for policymaking. The dispute is particularly vigorous when
the actual evolution of inﬂation diverges from the negative relationship with labor market
slack.1 Concerning inﬂation and the real economy during the prolonged stagnation following
the global ﬁnancial crisis, there are many skeptical views about the stability of the Phillips curve
slope, which represents the sensitivity of inﬂation to the demand-pull pressure. For example,
in response to stable inﬂation with a surge and decline in unemployment, Simon et al. (2013),
Blanchard et al. (2015), Hooper et al. (2020), and Del Negro et al. (2020) point out that thePhillips curve would be either irrelevant or be been ﬂattening out in recent years in the U.S.
and other advanced economies.2 This assertion can have a signiﬁcant implication for a central
bank’s policy management to achieve macroeconomic stability. If the Phillips curve were to
become irrelevant or ﬂatter, it would justify a more aggressive focus of the central bank on
employment and the real economy without paying less attention to inﬂation. Although they
are by no means advocating that central banks can manage their policies without considering
inﬂation, Simon et al. (2013), Blanchard et al. (2015), Hooper et al. (2020), and Hazell et al.
1

In response to the high inﬂation period that occurred in the 1970s, Friedman (1968) and Phelps (1968)
propose a modiﬁcation of the Phillips curve to an inﬂation-expectation augmented one. They argue that thePhillips curve relationship is only valid in the short term, considering inﬂation expectations. Since then, thestandard approach has been to understand inﬂation based on a triangle model of inﬂation, under which inﬂation
is determined by expected inﬂation, demand-pull pressures such as the output gap and labor-market slack, andcost-push shocks. For details on the triangle model of inﬂation, see Gordon (1997) and the references therein.
2
Some studies argue that the role of the Phillips curve slope has been limited since before the Great Moderationand the global ﬁnancial crisis. Atkeson and Ohanian. (2001) argue that Phillips curve-based models are not enoughfor practically forecasting inﬂation. Hazell et al. (forthcoming) estimate the slope of the Phillips curve for the
cross-section of U.S. states and argue that its slope was already small as of the early 1980s and there is limited
evidence of its structural change.

1(forthcoming) emphasize the importance of inﬂation expectations being well anchored by policy
management rather than the trade-oﬀ between inﬂation and the real economy to achieve pricestability.3
These facts and discussions are not new in Japan but have plagued the Japanese economy
for many years. Figure 1 shows the unemployment rate and 12-month rate of inﬂation in Japan.
On the one hand, while it began to rise after the collapse of asset prices in the early 1990s,
Japanese unemployment rose at a growing pace from early 1997 through the mid-2000s. On theother hand, unemployment had been declining steadily for about a decade since the beginningof the 2010s. The labor market slack signiﬁcantly changed during that period. As a deviationfrom the full employment level, the unemployment gap was high between the early 1997 andthe end of the 2000s, with a maximum above 2%.4 Then, the unemployment gap shrank in the2010s, showing that the labor market has been relatively tight since 2015, at less than −0.5%
at its tightest. Nevertheless, neither did severe deﬂation occur in the late 1990s and early 2000s
nor did robust inﬂation in the 2010s. In practice, Japan’s inﬂation has remained stable at alow level of around 0% since the mid-1990s, although there were some temporary rises andfalls. As shown in Figure 2, one can see that the unemployment gap and the 12-month rateof inﬂation since 1997 have been far from what could be explained by the relationships prior
to that time. These facts have long raised suspicions among both academics and policymakers
about the existence and stability of the trade-oﬀ under Japan’s secular stagnation. 5 Althoughmany previous studies tackle the Japanese inﬂation experience over secular stagnation, such as
De Veirman (2009), Fuhrer et al. (2012), Okimoto (2019), and Hoshi and Kashyap (2021), mostof them presume that the Phillips curve is ﬂattening under secular stagnation and explore thecauses behind it.6
Although the correlation between inﬂation and economic slack has weakened, this does not
3
In practice, policymakers account for policy operations and their relevance in a manner consistent with theacademic discussions. For example, Powell (2018) addresses risk factors in achieving inﬂation stability, following
his view that the Phillips curve is ﬂattening under inﬂation expectations suﬃciently anchored by monetary policy.
4
The Japan Institute for Labour Policy and Training names the unemployment gap “deﬁcient-demand unemployment” and publishes its estimated values. It deﬁnes equilibrium as the condition in which unemployed andvacant positions exist equally and measures the equilibrium unemployment rate considering the actual unemployment and vacancy rates, given the estimated Beveridge curve relationship.
5
For example, in an early study, Nishizaki and Watanabe (2000) estimated the nonlinear short-run Phillips
curve using Japanese data and concluded that the short-run Phillips curve becomes ﬂatter as inﬂation approaches
zero.
6
See Hoshi and Kashyap (2021) for a literature review on the price and wage Phillips curve during secularstagnation in Japan. De Veirman (2009), Fuhrer et al. (2012), and Okimoto (2019) argue that the output-inﬂation
trade-oﬀ has been limited in Japan since the late 1990s based on their empirical results.

2

Figure 1: Unemployment and inﬂation in Japan
Notes: The sample period is from February 1983 to December 2021. The upper panel shows the actual andequilibrium unemployment rates. The equilibrium unemployment rate is constructed by the Japan Institute forLabour Policy and Training. The lower panel shows the 12-month inﬂation rate. HCPI: consumer price index(CPI), all items (headline CPI). CPIxF: CPI, all items excluding fresh foods. CPIxFE: CPI, all items excluding
food and energy. The shaded areas show periods of recession in Japan, as deﬁned by the Cabinet Oﬃce.

3

Figure 2: Missing deﬂation and reinﬂation since 1997 in Japan: Scatter plot of the unemployment gap and inﬂation
Notes: The horizontal axis plots the unemployment gap (percent), as the diﬀerence between the actual unemployment rate and the equilibrium unemployment rate constructed by the Japan Institute for Labour Policy
and Training. The vertical axis plots the 12-month rate of CPIxF inﬂation (percent). The blue and red circles
indicate scatter plots using subsamples from February 1983 to April 1997 and from May 1997 to December 2021,
respectively. The blue solid line indicates the ﬁtted values for the inﬂation regression on the constant and theunemployment gap based on an ordinary least squares estimation using subsamples from February 1983 to April
1997. CPIxF: Consumer price index, all items excluding fresh foods.

4necessarily suggest that the short-run trade-oﬀ causality has disappeared or become limited.
While both academics and policymakers commonly accept the slope of the Phillips curve to
be characterizing the extent of a trade-oﬀ between inﬂation and demand-pull pressure at thebusiness cycle frequency, empirical studies usually evaluate the relationship between inﬂationand economic slack. Economic slack can include a stochastic trend, reﬂecting the prolonged
stagnation in developed countries after the global ﬁnancial crisis and that in Japan since thelate 1990s. Even if a stochastic trend shifts the long-run level of economic slack, it will notaﬀect inﬂation without being reﬂected in demand pressure. In this case, we should regard thechange in stochastic trend as a persistent shift in the short-run trade-oﬀ rather than a change
alongside it. Such factors inﬂuence inﬂation in a way that looks like oﬀsetting the inﬂuenceof economic slack along the short-run trade-oﬀ. Consequently, when analyzing the relationshipbetween economic slack and inﬂation during the secular stagnation period, there is the potential
issue that the short-run trade-oﬀ would be spuriously overseen even if it exists.
This study thus re-examines the existence and stability of the short-run trade-oﬀ during
secular stagnation. To this end, we construct a simple measure of the demand-pull pressure as
a composite index of indicators summarizing the labor market and economic activity at businesscycle frequencies, namely the cyclical activity index, for approximately 40 years since the early
1980s in Japan. Subsequently, we quantitatively examine the relationship between inﬂation andmeasured cyclical activity, including the possibility of a structural change in this relationshipunder secular stagnation.
This paper contributes to the literature by providing new empirical evidence and presenting
the standard but essential perspective regarding inﬂation and the real economy during secularstagnation. The empirical results support that the cyclical activity index has an economicallymeaningful relationship with short-term inﬂation. Quantitatively, a one-unit increase in thecyclical activity index corresponding to a 1% in unemployment decelerates CPI inﬂation byapproximately 2% in the case of Japan’s secular stagnation. Further, the relationship is stablethroughout the sample period, both before and during secular stagnation. Our ﬁnding suggeststhat the short-run trade-oﬀ is well-functioning, even under secular stagnation, but can be masked
by underlying a stochastic trend in the economic slack. This implies that policymakers shouldmake their policies conditional on this trade-oﬀ to achieve macroeconomic stability during
secular stagnation, even if neither severe deﬂation nor robust inﬂation occur in practice.

5

The rest of this paper is organized as follows. Section 2 explains the econometric methodology used for measuring the cyclical activity index and estimating the short-run Phillips curve.
Section 3 presents the empirical results of applying our empirical framework. Section 4 concludes the paper. The Appendix provides detailed deﬁnitions of the variables with data sources
and additional analyses.

2

Econometric methodology

2.1

Empirical model

We begin by specifying the short-run Phillips curve, which describes the relationship between
inﬂation and economic activity at business cycle frequencies. Assume variable πt represents
the inﬂation for month t. Following the literature, such as Gordon (2013), Ball and Mazumder(2011), Stock and Watson (1999, 2009, 2020), we consider the following linear regression modelfor the short-run Phillips curve:π̃t = α + β x̃t + ϵπt ,(1)where π̃t represents the short-term inﬂation, which captures the change in inﬂation over thecourse of the business cycle, x̃t represents the unobservable measure of cyclical activity in theeconomy at month t, and ϵπt , with a mean of zero and a variance of σϵ2 , represents the deviation
component from the short-run Phillips curve.
Following Stock and Watson (2020), we use a one-sided ﬁlter to eliminate the long-run
trend and a high-frequency noise underlying the macroeconomic variables. Particularly, in caseof inﬂation, we apply the monthly observation of inﬂation, πt , to the following year-over-yearchange ﬁlter that concentrates the gains at business cycle frequencies:π̃t ≡ b(L)πt ,(2)where b(L) = (1 − L12 )(1 + L + L2 + · · · + L11 )/12. That is, π̃t is a year-over-year change in the
12-month moving average inﬂation for month t.
Next, we consider the model under which we extract a cyclical component of x̃t as a common
factor from a variety of variables in the labor market and from real economic activity. Assumeỹt is a K × 1 vector consisting of observed ﬁltered activity measures. The observed variables, ỹt ,6are presumed to be related to a common factor, x̃t , through the following observation equation:′ỹt = λ1 + λx x̃t + ξt ,(3)

where ξt is a K × 1 vector of mean-zero idiosyncratic components. λ1 and λx are K × 1 vectorsof intercept and slope coeﬃcients, respectively. Assuming the ﬁrst variable in ỹt is ﬁltered
unemployment ũt , we restrict the ﬁrst element in the slope coeﬃcient vector λx to be equal to
one in the factor model (3). Under this restriction, a one-unit increase in common factor x̃tcorresponds to a one-percent increase in ﬁltered unemployment.
We construct the composite index of ﬁltered activity measures as common factor x̃t thatsatisﬁes factor model (3). Speciﬁcally, we adopt the principal component approach to estimate
the unobserved composite index. We ﬁrst calculate the ﬁrst principal component, pct , using
standardized ﬁltered activity measures. Then, we consider the following regression to scale andsign the factor to ﬁltered unemployment, ũt :ũt = γ1 + γpc pct + vt ,(4)

where γ1 and γpc are the intercept and slope coeﬃcient, respectively, and vt is an error term.
Given the estimate of γpc , we compute the composite index as x̃t = γ̂pc pct . We refer to thecomposite index of x̃t as the cyclical activity index.

2.2

Data

As the measure of inﬂation, we consider πt = 1200 log(Pt /Pt−1 ), where Pt is the monthly priceindex. We use the consumer price index (CPI) for all items less fresh food (CPIxF) as thebenchmark proxy of Pt . As alternative price indexes, we also use the CPI for all items (headline
CPI, HCPI) and the CPI for all items less fresh food and energy (CPIxFE). Additionally, we
consider the wage inﬂation to be calculated using the hourly wage (Wage/h) as a proxy of Pt .
To construct a vector ỹt consisting of the year-over-year change ﬁltered measures, we use
six time series of the labor market and three time series of real economic activity. The six labor
variables are unemployment rate, employment-population ratio, vacancy ratio, job opening
ratio, unemployment insurance beneﬁciaries, and overtime worked hour index. The three realvariables are the 3-month lag of the industrial production index, the 3-month lag of the capital
7

utilization index, and the tertiary industry activity index. 7 See the Appendix for more detailed
information on these variables.
Our dataset covers the period from February 1983 to December 2021. The sample starts
with the trough of the ninth business cycle, as deﬁned by the Cabinet Oﬃce. We omitted theperiods when inﬂation in the Japanese economy was relatively high due to the high economic
growth in the postwar period and the oil shocks of the 1970s.

3

Empirical results

3.1

Measuring cyclical activity index

We measure the cyclical activity index in four steps. In step 1, we construct a dataset on timeseries, {y1 , · · · , yT }, consisting of six labor market variables and three real economic variables.
Then, in step 2, we apply the series to the year-over-year-change ﬁlter ỹt ≡ b(L)yt , that is, we
calculate a year-over-year change in their 12-month moving average at month t. In step 3, we
calculate the ﬁrst principal component using standardized ﬁltered measures with zero mean andunit variance. In step 4, we regress equation (4) and scale and sign the principal component toﬁltered unemployment. Consequently, the cyclical activity index is a composite index, that is,a weighted average of the year-over-year change in the 12-month moving average of real activity
measures.
Table 1 shows the empirical results for factor model (3) by ordinary least squares (OLS)
regression. The composite index explains much of the variation in ﬁltered measures in the table. 8
We ﬁnd that the composite index explains around 68% of the variation in unemployment overthe business cycle frequency. This result suggests that the composite index, which summarizes
common features of the labor market and economic activity, adequately captures the businesscycle ﬂuctuations in unemployment. In the following analysis, we consider the composite index
as a measure of cyclical activity.
Next, we document the time series of cyclical activity. Speciﬁcally, we compare the measured
cyclical activity index with labor market slack.
7

Preliminary analysis conﬁrms that three-month lags have stronger correlations with the other variables thanthe contemporaneous values of industrial production and the capacity utilization indices. This result is consistent
with the stylized fact that labor market variables, including the unemployment rate, are lagging indicators in thebusiness cycle.
8
The employment-population ratio and tertiary industry activity are explained to a lesser degree, given thelarge share explained by the idiosyncratic components.

8

Table 1: OLS estimation results for the factor model
Regressand

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Estimates of
λ1
0.02(0.03)
λx
1(0.09)

0.15(0.06)-0.82(0.14)

0.03(0.02)-0.97(0.07)

0.01(0.01)-0.54(0.05)-0.01(0.01)
0.38(0.02)

0.00(0.00)-0.18(0.02)

0.01(0.00)-0.19(0.02)-0.01(0.00)-0.21(0.02)

0.03(0.01)-0.11(0.02)

R2

0.30

0.80

0.87

0.78

0.69

0.82

0.79

0.34

0.68

[1] Unemployment (%, MA(12), yoy)[2] Employment/population (%, MA(12), yoy)[3] Vacancy (%, MA(12), yoy)[4] Job opening/applicant (ratio, MA(12), yoy)
[5] Unemployment insurance beneﬁciaries (log, MA(12),yoy)[6] Overtime worked hour (log, MA(12), yoy)[7] Industrial product (lagged 3-month, log, MA(12), yoy)[8] Capital utilization (lagged 3-month, log, MA(12), yoy)
[9] Tertiary industry activity (log, MA(12),yoy)Notes: This table shows the ordinary least squares (OLS) results of the year-over-year change ﬁltered indicator
described in the upper header on the composite index of indicators and constant term in equation (3). We obtainthe composite index by scaling and signing the ﬁrst principal component calculated using the nine standardized
indicators to the year-over-year change ﬁltered unemployment. The numbers between parentheses are Newey andWest (1987) heteroskedasticity and autocorrelation robust standard errors for least squares with a 12-month lag
truncation. The sample period is from February 1983 to December 2021.

9For comparison with the cyclical activity index, we consider two proxies typically used aslabor market slack. First, we use the unemployment gap, calculated as the diﬀerence between
the actual and equilibrium unemployment rates presented in Section 1. Second, following Stockand Watson (1999), we measure detrended unemployment as the deviation of the actual unemployment rate from the trend estimates based on the one-sided version of the Hodrick–Prescott(HP) ﬁlter. We use a value of the HP smoothing parameter for monthly unemployment series
equal to 6400 × 34 adjusted by multiplying the parameter of 6400 applied to quarterly data by
Gordon (2013) with the fourth power of the frequency observation ratio proposed by Ravn andUhlig (2002).9
Figure 3 shows the measured cyclical activity index and the labor market slack from February
1983 to December 2021 in Japan. The thick solid line in the ﬁgure represents the monthly
time series of a calculated cyclical activity index. The thin solid and dotted lines indicate themeasures of the unemployment gap and detrended unemployment, respectively.
By comparing the cyclical activity index with the unemployment gap and detrended unemployment, we can visually conﬁrm its two distinctive properties. First, the cyclical activity
index correlates highly with detrended unemployment but less so with the unemployment gap.
The former is an entirely natural and expected feature. The cyclical activity index is intended
to measure the degree of temporary stagnation or overheating in the labor market and thereal economy. However, the cyclical activity index can be inherently diﬀerent from the unemployment gap, thus aiming to measure the diﬀerence between the unemployment measured inreal-time and the equilibrium level representing the full utilization of productive resources.
Second, while the cyclical activity index behaved similar to the unemployment gap and detrended unemployment before the secular stagnation period, it behaved diﬀerently during thesecular stagnation since the mid-1990s. As mentioned in the introduction, the unemployment
gap has behaved quite diﬀerently before and during the secular stagnation. Namely, it expanded
persistently from the mid-1990s to the mid-2000s, then declined persistently until just before theglobal ﬁnancial crisis. Subsequently, it rose sharply again during the global ﬁnancial crisis andhas been shrinking slowly since then.10 While not as large as the unemployment gap, detrended
9

Gordon (2013) shows that the reason for not choosing the typical HP quarterly parameter of 1600 is that thetrend would be extremely variable in response to actual movements, which would be at odds with the estimates of
the time-varying non-increasing inﬂation rate of unemployment (NAIRU) by Staiger et al. (2001). Shimer (2005)
and Miyamoto (2011) employ a value of the parameter of 10 5 , which yields a smoother trend when extracting
business-cycle-frequency ﬂuctuations in quarterly unemployment.
10This may partly reﬂect structural factors such as the increasing mobility of the Japanese labor market since10Figure 3: Cyclical activity, unemployment gap, and detrended unemployment
Notes: The sample period is from February 1983 to December 2021. Cyclical activity is the composite index of
the year-over-year-change ﬁltered indicators of the labor market and economic activity from factor model (3).
The unemployment gap is the diﬀerence between the actual unemployment rate and the equilibrium unemployment rate constructed by the Japan Institute for Labour Policy and Training. HP ﬁltered unemployment isthe diﬀerence between the actual unemployment rate and the smoothed series by the one-sided HP ﬁlter withsmoothing parameter 6400 × 34 . The shaded areas show periods of recession in Japan, as deﬁned by the Cabinet
Oﬃce.

11

unemployment also shows periods of persistent movement during the secular stagnation. In
particular, detrended unemployment has ﬂuctuated more during secular stagnation. For example, it has slowly declined from its peak in the late 1990s to a maximum of approximately −1%
in 2005. On the other hand, there does not appear to be any structural change in the timeseries of the cyclical activity index before and during the secular stagnation. Speciﬁcally, thecyclical activity index tended to rise sharply during recessions and decline moderately during
expansions throughout the sample period.
We can re-aﬃrm the properties of the cyclical activity index from the descriptive statistics.
Table 2 reports the Pearson correlation coeﬃcients of the cyclical activity index with the unemployment gap or the detrended unemployment from February 1983 to December 2021 andby subsamples from February 1983 to April 1997 and from May 1997 to December 2021. The
table shows that the correlation between the cyclical activity and detrended unemployment isrelatively high, with a coeﬃcient of approximately 0.8, whether over the entire sample periodor subsample periods. By contrast, the correlation between cyclical activity and the unemployment gap is moderate, with a coeﬃcient of approximately 0.4. Table 3 reports the standard
deviation of the cyclical activity index, unemployment gap, and detrended unemployment for
the entire sample period and by subsamples. The table shows that the variances of the cyclicalactivity index do not diﬀer much regardless whether it is in a secular stagnation period, witha standard deviation of approximately 0.3.11 By contrast, the variances of the unemployment
gap and detrended unemployment are higher during the secular stagnation period, with thestandard deviation of the unemployment gap being around 2.6 times higher than before thestagnation period and the standard deviation of the detrended unemployment being around 1.7
times higher. Note that the standard deviations of the unemployment gap and detrended unemployment before the stagnation are comparable to that of the cyclical activity index, mirroring
the fact that the cyclical activity index exhibited a similar behavior to the unemployment gap
and the detrended unemployment over this period.

the late 1990s.
11
The variances of the cyclical activity index are relatively small compared to similar measures in the U.S.
For example, the standard deviation of the U.S. unemployment gap, measured by unemployment minus CBO’s
current estimate of the natural rate of unemployment from the ﬁrst quarter of 1983 to the ﬁrst quarter of 2019,is approximately 1.5.

12

Table 2: Correlation of the cyclical activity index with the unemployment gap or detrended
unemployment
Cyc-A
Full sample:1983m2–2021m12
Subsample:1983m2–1997m4
1997m5–2021m12

Gap-U
HP-U
Gap-U
HP-U
Gap-U
HP-U

0.39
0.78
0.37
0.82
0.40
0.81

Notes: This table reports the Pearson’s correlation coeﬃcients of the cyclical activity index (Cyc-A) with the
unemployment gap (Gap-U) or the HP ﬁltered unemployment (HP-U) over the sample period from February 1983
to December 2021 and by subsamples from February 1983 to April 1997 and from May 1997 to December 2021.
We obtain Cyc-A by scaling and signing the ﬁrst principal component calculated using the nine standardized
indicators to the year-over-year change in ﬁltered unemployment. Gap-U is the diﬀerence between the actual
unemployment rate and the equilibrium unemployment rate constructed by the Japan Institute for Labour Policy
and Training. HP-U is the diﬀerence between the actual unemployment rate and the smoothed series by the
one-sided HP ﬁlter with smoothing parameter 6400 × 34 .

Table 3: Standard deviations of cyclical activity index, unemployment gap, and detrended
unemployment

Full sample:1983m2–2021m12
Subsample:1983m2–1997m4
1997m5–2021m12

Cyc-A

Gap-U

HP-U

0.28
0.25
0.30

0.59
0.26
0.69

0.38
0.24
0.43

Notes: This table shows the standard deviation of the cyclical activity index (Cyc-A), unemployment gap (GapU), and HP ﬁltered unemployment (HP-U) over the sample period from February 1983 to December 2021 and by
subsamples from February 1983 to April 1997 and May 1997 to December 2021. We obtain the cyclical activity
index by scaling and signing the ﬁrst principal component calculated using the nine standardized indicators to
the year-over-year change in ﬁltered unemployment. The unemployment gap is the diﬀerence between the actual
unemployment rate and the equilibrium unemployment rate constructed by the Japan Institute for Labour
Policy and Training. HP ﬁltered unemployment is the diﬀerence between the actual unemployment rate and thesmoothed series by the one-sided HP ﬁlter with smoothing parameter 6400 × 34 .

13

3.2

Estimating short-run Phillips curve

Table 4 provides the results of the short-run Phillips curve (1) estimated by OLS. It also reports
the results for the sup-Wald test proposed by Andrews (1993) and Hansen (1996) based on the
hypothesis that the slope coeﬃcient in the regression is stable over the sample period. The
ﬁrst column shows the estimated slopes of the curve using the cyclical activity index. The
second and third columns show the result when using the unemployment gap and HP ﬁltered
unemployment, respectively, as a regressor in equation (1). The upper panel shows the results
for the entire sample period, from February 1983 to December 2021. The lower panel shows theresults in two subsample periods, February 1983–April 1997 and May 1997–December 2021.
The cyclical activity index has an economically meaningful relationship with short-term
inﬂation. As shown in Table 4, a one-unit increase in cyclical activity index corresponding
to a 1% increase in unemployment decelerates CPI inﬂation by approximately 1.74%, whichis statistically signiﬁcant at the 1% level. The estimated slope of the Phillips curve −1.74
is relatively steep compared with previous studies in the U.S., such as Ball and Mazumder(2011).12
We also ﬁnd that the short-run Phillips curve relationship is stable over time, including
before and during the secular stagnation period. As shown in Table 4, the sup-Wald test statistic
is 1.72, which indicates that conventional signiﬁcance levels do not reject the null hypothesisof the structural stability of the slope coeﬃcient in the regression against the alternative ofstructural shift at an unknown point in time. The test result suggests that the Phillips curve
regression using the cyclical activity index is stable throughout the sample period. Furthermore,even when we run Phillips curve regressions for separate subsample periods before and during thesecular stagnation period, there is no signiﬁcant quantitative diﬀerence between the estimatesof the slope coeﬃcient. The estimate is −1.95 for the subsample before the secular stagnation
period from February 1983 to April 1997 and −1.70 for the subsample during the secularstagnation period from May 1997 to December 2021. Figure 4 shows the scatter plot of thecyclical activity index and the year-over-year change in the 12-month rate of CPIxF inﬂation,
which graphically conﬁrms the stability of the short-run Phillips curve relationship over the
sample period.
Ball and Mazumder (2011) report the estimated slope of the Phillips curve to be around −0.5. This result
may reﬂect the relatively rigid labor market in Japan and the fact that unemployment ﬂuctuates less than in the
U.S.
12

14

Table 4: OLS estimation results for the short-run Phillips curve
Regressand
Regressor
Full sample: 1983m2–2021m12
Estimate of βAdjusted R2
sup-Wald
Subsample: 1983m2–1997m4
Estimate of βAdjusted R2
1997m5–2021m12
Estimate of βAdjusted R2

Year-over-year change in 12-month rate of inﬂation (%)
CPIxF
CPIxF
CPIxF
Cyc-A

Gap-U

HP-U

-1.74
(0.37)
0.27
1.72[0.86]-0.33(0.25)
0.04
19.00[0.00]-1.20(0.34)
0.24
8.93[0.04]-1.95(0.42)
0.33-1.76(0.56)
0.30-1.98(0.39)
0.32-1.70(0.50)
0.27-0.29(0.28)
0.04-1.07(0.43)
0.22

Notes: This table shows the OLS regression results of the year-over-year change in inﬂation for the constantterm and the independent variable, that is, the cyclical economic activity measure (Cyc-A), unemployment gap(Gap-U), or HP ﬁltered unemployment (HP-U). We obtain the cyclical activity index by scaling and signing theﬁrst principal component, calculated using the nine standardized indicators to the year-over-year change ﬁltered
unemployment. The unemployment gap is represented by the diﬀerence between the actual unemployment rate
and the equilibrium unemployment rate constructed by the Japan Institute for Labour Policy and Training. HP
ﬁltered unemployment is the diﬀerence between the actual unemployment rate and the smoothed series by the
one-sided HP ﬁlter with smoothing parameter 6400 × 34 . The numbers between parentheses are Newey and West
(1987) heteroskedasticity and autocorrelation robust (HAR) standard errors for least squares with a 12-month lag
truncation. The estimated constant term and its standard error are not reported. sup-Wald represents a HAR
F statistic with the null hypothesis that the regression model is stable throughout the sample period and thealternative hypothesis that there is a structural break in coeﬃcient β at an unknown point in time. The numbers
between brackets are the p-values for test statistic sup-Wald, computed using the critical values proposed byAndrews (1993) and Hansen (1996). CPIxF: consumer price index, all items excluding fresh foods.

15

Figure 4: Scatter plot of the cyclical activity and short-term inﬂation
Notes: The horizontal axis plots the cyclical activity index, which is the composite index of the year-over-yearchange ﬁltered indicators of the labor market and economic activity from factor model (3). The vertical axis plots
the year-over-year change in the 12-month rate of CPIxF inﬂation (percent). CPIxF: consumer price index, allitems excluding fresh foods. The blue and red circles indicate scatter plots using the subsamples from February
1983 to April 1997 and from May 1997 to December 2021, respectively. The dashed line indicates the ﬁtted
value for the regression of the change in inﬂation on constant and the cyclical unemployment based on the OLS
estimation using the sample from February 1983 to December 2021. The blue and red solid lines indicate theﬁtted values for the regression using the subsamples from February 1983 to April 1997 and from May 1997 to
December 2021, respectively.

16

The above results of the Phillips curve regression using the cyclical activity index diﬀer
from the ones using the unemployment gap or the detrended unemployment often employed asa measure of labor market slack. As in the second column of Table 4, the relationship between
the unemployment gap and inﬂation appears to have disappeared; the empirical results thus
support the possibility of a structural change in the relationship, and the negative coeﬃcientestimate on the unemployment gap during the secular stagnation period is statistically insignificant. Regarding the results of the regression using detrended unemployment, as shown in thethird column of Table 4, the slope of the detrended unemployment appears to be ﬂattening,although the relationship with inﬂation is fairly statistically supported. In particular, the results support the possibility of a structural change in the relationship, with the estimate of
the slope of detrended unemployment becoming smaller in the absolute sense during a secularstagnation period. These results suggest that monitoring the unemployment gap or detrended
unemployment as demand-pull pressures on inﬂation could be misunderstood as the trade-oﬀ
between inﬂation and the real economy having disappeared or becoming limited.
We argue that it is critical to adequately identify demand-pull pressures to quantitatively
understand the short-run trade-oﬀ between nominal inﬂation and the real economy, especiallyduring the secular stagnation period. Of particular signiﬁcance is the extraction of cyclical activity measures as demand-pull pressures for eliminating stochastic trends that cause persistent
shifts in the Phillips curve, in addition to removing idiosyncratic elements among the various
economic activity variables. As mentioned in the previous subsection, during Japan’s secularstagnation period, the labor market slack has changed dramatically and persistently over a longtime. This fact suggests there exists a stochastic trend that is not directly reﬂected in thecyclical demand-pull pressure but is included in the time-series evolution of labor market slack.
If the stochastic trend is positively correlated with the deviation from the short-run Phillips
curve, ϵπt , in equation (1) (i.e., if the labor market tightens (slackens), but inﬂation (deﬂation)
does not occur), it can produce an upward endogenous bias in the estimated coeﬃcient on theslope of the Phillips curve as if the short-run trade-oﬀ as a causal relationship would be deador have ﬂattened. In other words, the short-run trade-oﬀ can be masked by a stochastic trend
underlying labor market slack during the secular stagnation.
In estimating a model of short-run Phillips curves with labor market slack, a straightforward
solution to obtain an unbiased estimator of the coeﬃcient of the slope of the Phillips curve is to17

run a regression with the demand-pull pressure as an instrumental variable (IV) for the labormarket slack. Therefore, we conduct an exercise using the cyclical activity index as an IV for
the unemployment gap in a short-run Phillips curve regression for the period including andduring secular stagnation.
The cyclical activity index works well to solve the endogenous bias problem in estimating theshort-run Phillips curve using the unemployment gap. Table 5 shows the IV regression results of
the year-over-year change in CPIxF inﬂation on the constant term and the unemployment gap
using as instruments the cyclical activity index and a constant. The IV estimate of coeﬃcientβ is statistically negative both over the entire sample period or the secular stagnation period.
There is a less signiﬁcant quantitative diﬀerence in the estimated slopes of −2.15 for the entire
sample and −1.86 for the secular stagnation sample. The estimated slope is comparable withthe one before secular stagnation shown in Figure 2 and Table 4. The instrument is robust,with ﬁrst-stage F -statistics of 15.58 and 23.72 for the entire sample and sample of the secularstagnation period, respectively.13 Furthermore, the Hausman test statistics are 6.04 and 4.61 forthe entire sample and sample of secular stagnation period, respectively. This result statisticallysupports a serious upward endogenous bias in the estimated coeﬃcient on the slope of the shortrun Phillips curve using the unemployment gap for the period including and during the secularstagnation by OLS regression.
Finally, we discuss the implications from a summary of Japan’s 40-year experience withinﬂation and labor market slack based on our empirical results for the short-run Phillips curve.
Figure 5 shows the relationship between short-term inﬂation and the unemployment gap. As
shown in the scatter plots of × and the solid line in the ﬁgure, the slope of the short-run Phillips
curve was stable for around 40 years. However, the Phillips curve shifted to the right in thelate 1990s and 2000s, as seen in the scatter plots of the blue circles for the February 1983
to April 1997 sample and the purple circles for the May 1997 to December 2012 sample. Itthen shifted to the left in the 2010s, as shown by the scatter plots of the light red circles forthe sample from January 2013 to December 2021. As a result of these long-term shifts in thePhillips curve during the secular stagnation period, a trade-oﬀ between nominal inﬂation andthe real economy simply appears to have spuriously disappeared or been limited, as indicated13

To ensure that a weak instrument problem is not present, Stock et al. (2002) and Stock and Yogo (2005)
recommend a rule of thumb that requires the F -statistic from the ﬁrst-stage regression of the two-stage leastsquares to exceed 10.

18

Table 5: IV estimation results for the short-run Phillips curve using the unemployment gap
Regressand
Regressor
SampleEstimate of βWald F
HausmanYear-over-year change in 12-month rate of inﬂation (%)
CPIxF
CPIxF
Gap-U
Gap-U
1983m2–2021m12
1997m5–2021m12-2.15(0.78)
15.58
6.04[0.01]-1.86(0.78)
23.72
4.61[0.03]

Notes: This table shows the IV regression results of the year-over-year change in CPIxF inﬂation on the constantterm and the unemployment gap (Gap-U). We use the cyclical activity index as an instrument for the unemployment gap in the IV regression. The unemployment gap is the diﬀerence between the actual and the equilibrium
unemployment rates constructed by the Japan Institute for Labour Policy and Training. We obtain the cyclicalactivity index by scaling and signing the ﬁrst principal component, calculated using the nine standardized indicators to the year-over-year change ﬁltered unemployment. The numbers between parentheses are Newey and West
(1987) heteroskedasticity and autocorrelation robust (HAR) standard errors for least squares with a 12-monthlag truncation. The estimated constant term and its standard error are not reported. Wald F indicates the HAR
F -statistic under the null hypothesis that the coeﬃcients from the ﬁrst-stage regression of the unemployment gap
on the instrument and a constant are both equal to zero. Hausman indicates the HAR statistic on the Hausman(1978) test under the null hypothesis that the OLS and IV estimators of β are consistent, but the OLS estimate
is eﬃcient. The numbers between brackets are p-values for the Hausman test. CPIxF: consumer price index, allitems excluding fresh foods.

19

by the dotted line. Instead, as long as a stable trade-oﬀ relationship exists, it is not surprising if
demand-pull inﬂation occurs at any time. This summary implies that policymakers should maketheir policies conditional on the trade-oﬀ to achieve the policy goal of macroeconomic stability
during periods of secular stagnation, even if neither severe deﬂation nor robust inﬂation still
occur in practice.

Figure 5: Scatter plot of the unemployment gap and short-term inﬂation
Notes: The horizontal axis plots the unemployment gap (percent), as the diﬀerence between the actual and theequilibrium unemployment rates constructed by the Japan Institute for Labour Policy and Training. The verticalaxis plots the year-over-year change in the 12-month rate of CPIxF inﬂation (percent). The blue, purple, andlight red circles indicate scatter plots over the subsamples from February 1983 to April 1997, from May 1997
to December 2012, and from January 2013 to December 2021, respectively. ×s indicate scatter plots replacing
the unemployment gap with the ﬁtted values for its regression on the constant and the cyclical activity index.
The dashed line indicates the ﬁtted value for the regression of the year-over-year change in the 12-month rate of
CPIxF inﬂation on the constant and the unemployment gap based on the ordinary least squares estimation using
the sample from February 1983 to December 2021 (slope: −0.33). The solid black line indicates the ﬁtted values
for the regression of the year-over-year change in the 12-month inﬂation rate on constant and the unemployment
gap based on the IV estimation (slope: −2.15). We use the cyclical activity index as an instrument for theunemployment gap in the IV regression. CPIxF: consumer price index, all items excluding fresh foods.

20

4Concluding remarks

The principal argument of this paper is that there is the potential peril that the existence ofa trade-oﬀ between nominal inﬂation and the real economy would be overseen during secularstagnation. This study empirically examines whether the trade-oﬀ is well-functioning undersecular stagnation. A pivotal issue in quantifying this trade-oﬀ is how to measure demand-pullpressures. By constructing the cyclical activity index as a proxy of demand-pull pressures,
we ﬁnd a stable causal relationship between cyclical activity and inﬂation even during Japan’ssecular stagnation, when the correlation between economic slack and inﬂation weakened. Ourﬁnding suggests that the demand-pull pressures on deﬂation and reinﬂation would be spuriously
missing during secular stagnation, as a result the short-run trade-oﬀ is masked by a persistentand stochastic trend underlying the economic slack as shifting factors in the Phillips curve suchas structural changes in the labor market. It also implies the need for policymakers to keep
the short-run trade-oﬀ in mind when making judgments about the underlying state of inﬂation,even under secular stagnation.
There are several limitations and restrictions of the empirical analysis in this study, leavingroom for future research in several directions. The ﬁrst is ascertaining whether analogous
mechanisms can be found in other advanced countries. As mentioned in the introduction, it iswell known that missing deﬂation and reinﬂation were observed in many advanced economies
during the long period of stagnation after the global ﬁnancial crisis. In some of these countries,
high inﬂation was registered after mid-2021 when the COVID-19 crisis had settled down. One
reason may be that the central banks have failed to manage inﬂation expectations in 2021,
although, as previous studies such as Simon et al. (2013), Blanchard et al. (2015), Hooper et al.
(2020), and Hazell et al. (forthcoming) have pointed out, it has been successful in hitherto
anchoring them adequately. Alternatively, as in the ﬁndings of this study, the trade-oﬀ maywell have existed but simply been masked by the presence of stochastic trends during secularstagnation in other countries. If so, it would not be shocking that high inﬂation occurred,given the sudden increase in demand-pull pressures after the COVID-19 crisis. International
comparisons such as constructing a cyclical activity index and examining the stability of theslope of the Phillips curve in other countries are thus crucial in future works.
The second is examining the role of the shift factors in the Phillips curve. This study
focuses on quantifying the extent of the short-run trade-oﬀ. Therefore, by constructing a cyclical21

activity index for economic activity, we remove the stochastic trend included in the real economy.
Additionally, we remove the stochastic trend included in inﬂation expectations by measuring
short-term inﬂation at business cycle frequency. However, the shifting factors of the Phillips
curve associated with changes in stochastic trends can play an essential role in the businesscycle and inﬂation dynamics, as well as the developments along the Phillips curve. 14
In particular, it is essential to examine the structural and stochastic change in long-run
trends underlying the real economy, including the labor market, to understand the businesscycle under secular stagnation. Our results suggest the possibility that the stochastic trends
contained in economic slack have been dominant in the dynamics of inﬂation and the real
economy during Japan’s secular stagnation. One of the major future research topics is thus
clarifying the factors that cause long-term shifts in the Phillips curve due to such stochastic
trends.15
It is also a research challenge to examine inﬂation dynamics and business cycles by explicitly
addressing the role of inﬂation expectations. Stock and Watson (2007), Watson (2014), andfollow-up studies point out that the anchoring of inﬂation expectations may have contributed
to the declines in real activity and inﬂation volatility in various advanced countries since the1980s. Furthermore, the decline in inﬂation expectations due to less aggressive monetary policy
management, which is pointed out by several papers such as Bernanke (2000), Jinushi et al.
(2000), Kuttner (2014), and Shibamoto et al. (forthcoming), may pose a severe problem during
Japan’s secular stagnation.16 Although beyond the scope of this study, such challenges are
14

Several papers have pointed out that large output shocks can aﬀect long-run growth and the business cycle.
For example, Cerra and Saxena (2008), using panel data for many countries, including advanced, emerging, anddeveloping countries, empirically shows that huge output loss due to ﬁnancial and political crises tends to cause
a persistent decline in growth along with recessions. Further, Shibamoto and Miyao (2008) argue that shifts inboth aggregate demand and supply curves lead to signiﬁcant and permanent eﬀects on output and limited eﬀects
on prices after the signiﬁcant output loss due to the collapse of the asset price bubble in Japan during the early
1990s.
15
Hoshi and Kashyap (2021), after reviewing previous studies, focus on three reasons why wage inﬂation has notbeen responsive to economic slack in Japan. The ﬁrst is an explanation based on a dual labor market; given thediﬀerence in wages paid to regular and non-regular workers, the composition of regular and non-regular workers
has been changing in the macroeconomy since the late 1990s. The second is due to downward wage rigidity;ﬁrms are more likely to face frictions of being less likely to lower wages when the economy is sluggish, making
them reluctant to raise wages even if the economy tightens later in a year. The third is due to the supply side ofthe labor market; as the population ages, more older workers remain in the labor market as non-regular workers.
Consequently, the traditional practice of on-the-job training for employees has dwindled and the supply of highly
skilled workers who are relatively well-paid has declined.
16
Bernanke (2000) shows that money growth was weak in the ﬁrst half of the 1990s despite the considerable
reduction in the broader nominal interest rates. Jinushi et al. (2000) show that the Japanese monetary policy
actions during the ﬁrst half of the 1990s were delayed compared with the “good” Taylor-style policy rule, which
they estimated over the pre-bubble period from 1975 to 1985. Kuttner (2014) shows that these actions were
not as decisive as the measures taken by the Federal Reserve during the recessions beginning in 2000 and 2007.
Shibamoto et al. (forthcoming)’s counterfactual simulation results suggest that the Bank of Japan’s reluctance22

worthy of consideration in future research.

A

Appendix

A.1

Variable deﬁnitions• HCPI: consumer price index, all items (2020 = 100), consumption-tax-adjusted for theperiod from April 1997 to March 1998 and from April 2014 to March 2015, retrieved from
the Ministry of Internal Aﬀairs and Communications in Japan and calculated backward
for the period before December 1989 using the monthly change in the index by adding 1.2
in March 1989 to eliminate the inﬂuence of the consumption tax from April 1989.
• CPIxF: consumer price index, all items excluding fresh foods (2020 = 100), consumptiontax-adjusted for the period from April 1997 to March 1998 and from April 2014 to March
2015, retrieved from the Ministry of Internal Aﬀairs and Communications in Japan andcalculated backward for the period before December 1989 using the monthly change in
the index by adding 1.2 in March 1989 to eliminate the inﬂuence of the consumption tax
from April 1989.
• CPIxFE: consumer price index, all items excluding food and energy (2020 = 100), consumptiontax-adjusted for the period from April 1997 to March 1998 and from April 2014 to March
2015, retrieved from the Ministry of Internal Aﬀairs and Communications in Japan, calculated backward for the period before December 1989 using the monthly change in theindex by adding 1.2 in March 1989 to eliminate the inﬂuence of the consumption tax from
April 1989.
• Wage/h: hourly wage, cash earnings over hours worked, yen. Cash earnings, total-all industries (5 persons or more), yen, retrieved from NIKKEI NEEDS FINANCIAL QUEST.
Hours worked, total-all industries (5 persons or more), hour, retrieved from NIKKEINEEDS FINANCIAL QUEST, retrieved from NIKKEI NEEDS FINANCIAL QUEST.

• Unemployment: unemployment over labor force ratio, percent, retrieved from NIKKEINEEDS FINANCIAL QUEST.
to cut policy interest rates in response to the post-bubble downturn signiﬁcantly contributed to the long-lastingrecession in the 1990s.

23• Equilibrium unemployment: quarterly series of equilibrium unemployment rate constructedby the Japan Institute for Labour Policy and Training, percent, retrieved from Japan Institute for Labour Policy and Training. Interpolated (using linear interpolation under theconstraint that the average of three monthly observations within a quarter must equal thequarterly series) to obtain monthly observations.
• Cyc-A: cyclical activity index described in the text.
• Gap-U: actual unemployment minus equilibrium unemployment.
• HP-U: actual unemployment minus the smoothed series by the one-sided Hodrick–Prescottﬁlter with smoothing parameter 6400 × 34 .
• Employment/population: total employed person over population ratio, percent. Total employed person, 10,000 persons, seasonally adjusted series, retrieved from NIKKEI NEEDSFINANCIAL QUEST. Population: estimated population at the beginning of the month,

10,000 persons, retrieved from NIKKEI NEEDS FINANCIAL QUEST.
• Vacancy: (Number of eﬀective job openings minus number of job oﬀerings) over labor force
ratio, percent. Number of eﬀective job openings, thousands persons, seasonally adjusted
series, retrieved from NIKKEI NEEDS FINANCIAL QUEST. Number of job oﬀerings, thousands persons, retrieved from NIKKEI NEEDS FINANCIAL QUEST, seasonally adjusted
series obtained using the Census X-12. Labor force, 10,000 persons, seasonally adjusted
series, retrieved from NIKKEI NEEDS FINANCIAL QUEST, divided by 10.
• Job opening/applicant: eﬀective job oﬀer ratio, multiplier, seasonally adjusted series,
retrieved from NIKKEI NEEDS FINANCIAL QUEST.
• Unemployment insurance beneﬁciaries: actual number of employment insurance beneﬁciaries, thousands persons, retrieved from NIKKEI NEEDS FINANCIAL QUEST, seasonallyadjusted series obtained using Census X-12, taking the logarithm.
• Overtime worked hour: index of nonscheduled hours worked, all industry (30 persons ormore), seasonally adjusted series (2020 = 100), retrieved from NIKKEI NEEDS FINANCIAL
QUEST, taking the logarithm.

24• Industrial product: index of industrial production, mining and manufacturing, seasonallyadjusted series (2015 = 100), retrieved from NIKKEI NEEDS FINANCIAL QUEST, taking
the logarithm.
• Capital utilization: index of capital utilization, manufacturing, seasonally adjusted series(2015 = 100), retrieved from NIKKEI NEEDS FINANCIAL QUEST, taking the logarithm.
• Tertiary industry activity: index of tertiary industry activity, seasonally adjusted series(2015 = 100), retrieved from NIKKEI NEEDS FINANCIAL QUEST, taking the logarithm.

A.2

Additional analyses

A.2.1

Preliminary analyses on the cyclical activity measures

First, we present the contemporaneous relationships among the year-over-year change ﬁlteredactivity measures over the sample period. Table A1 reports the Pearson correlation coeﬃcients
between two ﬁltered measures. From the table, the ﬁltered measures are highly correlated.
In particular, unemployment is strongly intercorrelated with unemployment insurance beneﬁciaries and has a strong negative correlation with the employment/population ratio, vacancy,
job opening/applicant ratio, overtime worked hours, industrial product, capital utilization, andtertiary industry activity. This result suggests there exist common components characterizing
the labor market and economic activity at business cycle frequencies.
Figure A1 plots the nine year-over-year change ﬁltered and standardized indicators of thelabor market and economic activity. To simplify the comparison of time-series trends among
the indicators in the ﬁgure, the employment/population, vacancy, job opening, overtime worked
hours, industrial product (lagged 3 months), capacity utilization (lagged 3 months), and tertiaryindustry activity are multiplied by −1, so they co-vary positively with the unemployment.
Additionally, the ﬁltered indicators are standardized to have zero mean and unit variance.
As shown in the ﬁgure, most indicators are highly correlated with unemployment. In particular, the ﬁltered unemployment and other ﬁltered indicators show a surge during recessions.

A.2.2

Estimating short-run Phillips curve for alternative inﬂations

We examine the slope of the Phillips curve for diﬀerent inﬂation measures and their stability.
Table A2 reports the OLS regression results of the short-run Phillips curve (1) for alternative25

Figure A1: Year-over-year change ﬁltered indicators of the labor market and economic activity
Notes: The sample period is from February 1983 to December 2021. The year-over-year change ﬁltered indicators
are listed in the legend. The ﬁltered indicators are standardized to have zero mean and unit variance. The
employment/population, vacancy, job opening, overtime worked hours, industrial product (lagged 3 months),
capacity utilization (lagged 3 months), and tertiary industry activity are multiplied by −1, so they co-vary
positively with unemployment.

26

Table A1: Correlations among year-over-year change ﬁltered indicators

[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

-0.67
-0.71
-0.78
0.81
-0.49
-0.65
-0.65
-0.28

0.34
0.50
-0.35
0.18
0.47
0.38
0.40

0.93
-0.76
0.80
0.70
0.73
0.49

-0.82
0.76
0.73
0.72
0.56

-0.69
-0.76
-0.78
-0.37

0.76
0.80
0.47

0.95
0.57

0.38

[1] Unemployment (%, MA(12), yoy)[2] Employment/population (%, MA(12), yoy)[3] Vacancy (%, MA(12), yoy)[4] Job opening/applicant (ratio, MA(12), yoy)
[5] Unemployment insurance beneﬁciaries (log, MA(12),yoy)[6] Overtime worked hour (log, MA(12), yoy)[7] Industrial product (lagged 3 months, log, MA(12), yoy)[8] Capital utilization (lagged 3 months, log, MA(12), yoy)
[9] Tertiary industry activity (log, MA(12),yoy)Notes: This table reports the Pearson’s correlation coeﬃcients between two indicators. The sample period isfrom February 1983 to December 2021.

inﬂations. The ﬁrst three columns on the left-hand side of the table are the OLS regression
results of the short-run Phillips curve (1) for the HCPI inﬂation, CPIxFE inﬂation, and Wage/h
inﬂation, respectively, using the cyclical activity index as the regressor. The three columns on
the middle and right-hand side of the table show the results for the alternative inﬂations using
the unemployment gap and detrended unemployment, respectively, as the regressors.
We conﬁrm the robustness of the quantitative assessment of the short-run trade-oﬀ in thebenchmark model for alternative inﬂations. In particular, it is robust for other inﬂations and(1) the cyclical activity index has an economically meaningful relationship with the short-term
inﬂation, (2) the short-run Phillips curve using the cyclical activity index is stable over time,and (3) these results are diﬀerent from the results using the unemployment gap or detrended
unemployment.
Note that there are slight diﬀerences in the estimates of the slope of the Phillips curve
depending on the inﬂation measure used. In particular, the slope of the Phillips curve for
CPIxFE inﬂation is relatively ﬂat compared to HCPI or CPIxF inﬂation. By contrast, theslope of the Phillips curve for Wage/h inﬂation is relatively steep. This result reﬂects that27

the sensitivity of a demand-pull pressure varies by CPI items and that the sensitivity of thedemand-pull pressure concerning wages is relatively high compared to prices.

28

29
-1.71
(0.45)
0.24-2.05(0.61)
0.21-1.78(0.34)
0.22
2.63[0.63]

Cyc-A

-1.25
(0.26)
0.32-1.67(0.34)
0.38-1.34(0.20)
0.33
6.33[0.14]

Cyc-A

-2.96
(0.60)
0.10-4.18(1.27)
0.13-3.27(0.58)
0.11
3.87[0.40]

Cyc-A

-0.26
(0.27)
0.03-1.71(0.80)
0.16-0.31(0.26)
0.03
12.79[0.01]

Gap-U

-0.22
(0.18)
0.05-1.42(0.42)
0.30-0.25(0.16)
0.05
25.12[0.00]

Gap-U

-0.43
(0.33)
0.01-1.97(1.56)
0.03-0.49(0.34)
0.01
10.17[0.02]

Gap-U

Year-over-year change in 12-month rate of inﬂation (%)
HCPI CPIxFE Wage/h HCPI CPIxFE Wage/h-1.02(0.41)
0.17-2.14(0.56)
0.21-1.18(0.33)
0.17
12.05[0.01]

HP-U

HCPI

-0.79
(0.23)
0.26-1.61(0.39)
0.33-0.91(0.20)
0.27
9.94[0.03]HP-U

CPIxFE-1.38(0.56)
0.04-3.23(1.20)
0.07-1.62(0.51)
0.05
6.81[0.11]

HP-U

Wage/h(headline CPI). CPIxFE: CPI, all items excluding food and energy. Wage/h: hourly wage.

between brackets are the p-values for test statistic sup-Wald computed using the critical values proposed by Andrews (1993) and Hansen (1996). HCPI: CPI, all items

model is stable throughout the sample period and the alternative hypothesis that there is a structural break in coeﬃcient β at an unknown point in time. The numbers

truncation. The estimated constant term and its standard error are not reported. sup-Wald represents a HAR F statistic with the null hypothesis that the regression

numbers between parentheses are Newey and West (1987) heteroskedasticity and autocorrelation robust (HAR) standard errors for least squares with a 12-month lag

unemployment is the diﬀerence between the actual unemployment rate and the smoothed series by the one-sided HP ﬁlter with smoothing parameter 6400 × 34 . The

diﬀerence between the actual unemployment rate and the equilibrium unemployment rate constructed by the Japan Institute for Labour Policy and Training. HP ﬁlteredﬁrst principal component calculated using the nine standardized indicators to the year-over-year change ﬁltered unemployment. The unemployment gap represent thecyclical activity index (Cyc-A), unemployment gap (Gap-U), or HP ﬁltered unemployment (HP-U). We obtain the cyclical activity index by scaling and signing theNotes: This table shows the ordinary least squares regression results of the year-over-year change in inﬂation on constant term and the independent variable, that is,

Adjusted R2

1997m5–2021m12
Estimate of βAdjusted R2

Subsample: 1983m2–1997m4
Estimate of βAdjusted R2
sup-Wald

Full sample: 1983m2–2021m12
Estimate of βRegressor

Regressand

Table A2: Estimation results for the short-run Phillips curve for alternative inﬂations

The results for the slope of the Phillips curve using the unemployment gap are also robust.
Table A3 shows the IV regression results of the short-run Phillips curve using the unemployment
gap for alternative inﬂations. We can conﬁrm the benchmark result is robust for alternative
inﬂations and that the cyclical activity index works well to solve the endogenous bias problem.
Table A3: IV estimation results for the short-run Phillips curve for alternative inﬂations using
the unemployment gap
Regressand
Regressor
SampleEstimate of β
HausmanYear-over-year change in 12-month rate of inﬂation (%)
HCPI CPIxFE Wage/h HCPI CPIxFE Wage/h
Gap-U Gap-U
Gap-U Gap-U Gap-U
Gap-U
1983m2–2021m12
1997m5–2021m12-2.20(0.80)
6.30[0.01]-1.66(0.65)
4.96[0.03]-4.04(1.80)
4.04[0.04]-1.87(0.77)
4.97[0.03]-1.37(0.59)
4.24[0.04]-3.24(1.56)
3.40[0.07]

Notes: This table shows the IV regression results of the year-over-year change in CPIxF inﬂation on constant term
and the unemployment gap (Gap-U). We use the cyclical activity index as an instrument for the unemployment
gap in the IV regression. The unemployment gap represents the diﬀerence between the actual unemployment rate
and the equilibrium unemployment rate constructed by the Japan Institute for Labour Policy and Training. We
obtain the cyclical activity index by scaling and signing the ﬁrst principal component calculated using the ninestandardized indicators to the year-over-year change ﬁltered unemployment. The numbers between parentheses
are Newey and West (1987) heteroskedasticity and autocorrelation robust (HAR) standard errors for least squares
with a 12-month lag truncation. The estimated constant term and its standard error are not reported. Hausman
indicates the HAR statistic on the Hausman (1978) test under the null hypothesis that the OLS and IV estimatorsof β are consistent, but the OLS estimate is eﬃcient. The numbers between brackets are p-values for the Hausman
test. HCPI: CPI, all items (headline CPI). CPIxFE: CPI, all items excluding food and energy. Wage/h: hourly
wage.

30

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