Bank of Japan Working Paper Series

Flattening of the Wage Phillips Curveand Downward Nominal Wage Rigidity:
The Japanese Experience in the 2010s

Wataru Hirata*
wataru.hirata@boj.or.jp

Toshitaka Maruyama*
toshitaka.maruyama@boj.or.jp

Tomohide Mineyama*
tomohide.mineyama@boj.or.jp

No.20-E-4
July 2020

Bank of Japan
2-1-1 Nihonbashi-Hongokucho, Chuo-ku, Tokyo 103-0021, Japan* Monetary Affairs Department

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Flattening of the Wage Phillips Curve and Downward Nominal Wage
Rigidity: The Japanese Experience in the 2010s*
Wataru Hirata,† Toshitaka Maruyama,‡ and Tomohide Mineyama§
July 2020

Abstract
In this paper, we examine from both a theoretical and an empirical perspective the validity of the
hypothesis that downward nominal wage rigidity (DNWR) induced upward rigidity in wage setting,thereby contributing to the flattening of the wage Phillips curve. We focus in particular on Japanese
regular workers, those workers who are characteristically employed on long-term contracts. Our
theoretical study, which incorporates long-term employment contracts, indicates that DNWR induces
upward wage rigidity through the following two channels: first, due to the lack of sufficient downward
wage adjustments during economic downturns, firms may become reluctant to increase wages in
economic recovery phases; second, firms contain wage increases even in economic expansion phases
as they take into account the risk of pay cuts in the future. The strength of the latter channel largely
depends on expected economic growth and its uncertainty. As a result, the wage Phillips curve
becomes flatter than would be the case without DNWR. In line with the theoretical result, ourempirical study using the panel data of Japanese regular workers reveals that the slower growth ofmonthly earnings, which excludes bonuses but includes overtime pay, for workers who display astrong degree of DNWR pushed down the growth of monthly earnings at the aggregate level by 0.4
percentage points per year (a range of 0.2 to 0.6 percentage points, given uncertainty regarding theidentification of DNWR) between 2010-17. In particular, the channel arising from future pay cut risks
became relatively stronger in the late 2010s, when labor market conditions became markedly tighter.
JEL Classification: E24; E31; J30
Keywords: Wage Phillips curve; Downward nominal wage rigidity; Long-term employment contracts*

The data used for this analysis, Japan Household Panel Survey (JHPS/KHPS), was provided by the Panel Data
Research Center at Keio University. The authors are grateful to Kazuhiro Hiraki, Tomiyuki Kitamura, IchiroMuto, Kenji Nishizaki, and Masaki Tanaka for their helpful comments and discussions. Any remaining errors are
the sole responsibility of the authors. The views expressed in this paper are those of the authors and do notnecessarily reflect the official views of the Bank of Japan.
†

Monetary Affairs Department, Bank of Japan(E-mail: wataru.hirata@boj.or.jp)‡

Monetary Affairs Department, Bank of Japan(E-mail: toshitaka.maruyama@boj.or.jp)§

Monetary Affairs Department, Bank of Japan(E-mail: tomohide.mineyama@boj.or.jp)1

1

Introduction

Nominal wage growth in advanced economies remained moderate throughout the2010s, relative to improvements in labor market conditions. The growth of scheduled cash earnings for regular workers in Japan, who correspond to full-time employees in Panel (A) of Figure 1, was modest during the long-lasting improvement oflabor market conditions in the 2010s, and the wage Phillips curve during the period
appears to have flattened compared with previous periods, as Bank of Japan (2017)indicates (Panel (B) of Figure 1).
There has been active debate on the causes of the flattening of the wage Phillips
curve in recent years, with various hypotheses proposed.1

Among others, cen-tral bankers have pointed to the importance of downward nominal wage rigidity(DNWR). For example, former Chair of the Board of Governors of the Federal
Reserve System Janet Yellen pointed to the “pent-up wage deflation” mechanism:
firms could not cut wages due to the presence of DNWR during the global financial
crisis (GFC) in the late 2000s, and they became reluctant to increase wages in thesubsequent economic recovery phase (Yellen 2014). Moreover, as Kuroda (2019)argued, firms may prioritize the stability of long-term employment over immediate
wage increases so as to avoid the risk of pay cuts in the future. Japanese regular
workers, who are characteristically subject to long-term employment practices, seemto be particularly affected by these factors.
In this paper, we examine from both a theoretical and an empirical perspective
1

For example, in the U.S., Elsby et al. (2015) pointed out the possibility that a broad measure of labor market slack, e.g., the number of discouraged workers, has remained persistent since
the global financial crisis, while Krueger et al. (2014) mentioned that long-term unemployment,
which increased during the same period, could have rendered wage growth sluggish. In addition,
Acemoglu and Restrepo (2018) argued that recent advances in automation technologies have substituted in part for human labor, which may put downward pressure on wages. Regarding theJapanese economy, while some types of wages, such as the hourly scheduled cash earnings forpart-time employees, as shown in Figure 1, and bonuses for regular workers, rose more clearly than
the scheduled cash earnings for regular workers, it is argued that their growth was still contained
compared with the tightening of labor market conditions and the improvement in corporate profits.
In this respect, Genda (2017) investigated the causes of the slow wage growth in the 2010s fromvarious perspectives, including expansion of the non-regular labor market and sector-specific wage
systems. In addition, Bank of Japan (2018) and Ozaki and Genda (2019) investigated other factors
such as the wage-elastic labor supply of the peripheral labor force in the non-regular labor market
and the asymmetric adjustment of bonuses.

2the validity of the hypothesis that DNWR induced upward rigidity and contributed
to the flattening of the wage Phillips curve, paying particular attention to Japanese
regular workers. We focus on the following two channels through which DNWR
leads to upward rigidity. First, due to the lack of sufficient downward wage adjustments during economic downturns, firms may become reluctant to increase wages in
economic recovery phases (the backward-looking channel of DNWR). Second, witha tendency to place priority on the stability of long-term employment over wage
increases, firms may contain wage increases in economic expansion phases as theytake into account the risk of pay cuts in the future (the forward-looking channel of
DNWR).
This paper’s analyses and findings are summarized as follows. In our theoreticalanalysis, we explore how DNWR affects the wage Phillips curve under long-term employment. We indeed find that, in the presence of DNWR, the wage Phillips curve
becomes flatter than would be the case without DNWR through the backwardand forward-looking channels mentioned above. Moreover, as labor market conditions improve, the forward-looking channel comes to be more significant than the
backward-looking channel, and the degree of economic significance of the forwardlooking channel depends considerably on factors such as expected growth and its
uncertainty.
Our empirical analysis investigates whether each channel of DNWR implied byour theoretical analysis affected Japanese regular workers, using Japanese individual
workers’ panel data in the Japan Household Panel Survey (JHPS/KHPS) compiledby the Panel Data Research Center at Keio University. We find that the growthrate of monthly earnings2 for workers who displayed a strong degree of DNWR was
significantly lower than that for workers who displayed a low degree of DNWR amid
the improvement in labor market conditions during 2010 to 2017. The estimate
implies that the slower growth of monthly earnings for workers who displayed astrong degree of DNWR pushed down the growth of monthly earnings for regular
workers at the aggregate level by 0.4 percentage points per year (a range of 0.2 to2Monthly earnings in this paper exclude bonuses but include overtime pay.

3

0.6 percentage points, given uncertainty regarding the identification of DNWR) on
average. We also find that, consistent with the predictions of our theoretical model,
both the backward- and forward-looking channels of DNWR contributed to theseresults. Moreover, the latter channel became relatively stronger in the late 2010s,
when a tightening of labor market conditions became notable.
Previous studies on the relationship between DNWR and the wage Phillips curve
have been conducted mainly from a theoretical perspective. Building upon studies
that focused on the role of DNWR in economic downturns, such as Akerlof et al.
(1996) and Benigno and Ricci (2011), more recent studies have investigated theconsequences of DNWR in economic recovery and expansion phases. For instance,
Daly and Hobijn (2014) and Iwasaki et al. (2018) demonstrated that DNWR bends
the wage Phillips curve: nominal wage growth remains slow in the early stage of
economic recovery. Our theoretical analysis elaborates on these previous studies bydecomposing the causes due to which DNWR leads to upward rigidity, and thereby
flattens the wage Phillips curve, into the backward- and forward-looking channels
of DNWR. This enables us to investigate the determinants of these channels andto uncover their relative importance in each stage of a business cycle. Our analysis
indicates that the slope of the wage Phillips curve is endogenously determined byvarious factors that affect each channel of DNWR.
On the other hand, there are few studies that have assessed empirically the
hypothesis that DNWR contributes to the flattening of the wage Phillips curve by
inducing upward rigidity.3 One exception is Yamamoto and Kuroda (2016), whoanalyzed a Japanese firm survey. They reported that the firms that had not cut thescheduled earnings in the past were more reluctant to increase the scheduled earnings
and bonuses during the economic expansion of 2014 to 2015. In our empiricalanalysis, we employ a longer series of individual workers’ panel data (until 2017)
to investigate the validity of both the backward- and forward-looking channels as acause of the modest wage growth in spite of the long-lasting improvement in labor3
In recent years, several studies, such as Pischke (2018) and Born et al. (2019), empiricallyinvestigated the effects of DNWR on the dynamics of other variables than wages. To our knowledge,
this paper is the first attempt to explicitly study its impacts on the wage Phillips curve.

4

market conditions in the 2010s.
There is a wealth of studies on the existence and degree of DNWR, from a numberof perspectives. For example, Kim and Ruge-Murcia (2009) and Iwasaki et al. (2018)assessed the degree of DNWR, while it is consistent with developments in othermacroeconomic variables, by estimating a general equilibrium model according to
the aggregate data. In addition, a number of studies, mainly in Europe and the U.S.,
have been conducted using micro data on individual workers’ wage adjustments sincearound the 1990s. Dickens et al. (2007) conducted a comprehensive analysis of 16
countries in Europe and the U.S., and reported the existence of DNWR, though
its degree differs substantially across countries. Recent studies in particular, suchas Fallick et al. (2020) for the U.S. and Branten et al. (2018) for Europe, haveshown that DNWR remained to a considerable degree even in the severe economic
downturn after the GFC. In the case of Japan, with the enhancement of micro
data since the 2000s, there has been a growing empirical literature on this topic,
which has analyzed the data mainly until the early 2000s. For example, Kuroda
and Yamamoto (2003, 2005), Yamamoto (2007), and Kambayashi (2011) studied
the degree of DNWR by assessing the shape of wage-growth distribution. Somestudies have argued that DNWR, measured by the total annual earnings of full-time
employees (mainly represented by regular workers) in the Japanese labor market,
was observed from 1992 to 1997, but disappeared after the Japanese financial crisisof 1998 (Kuroda and Yamamoto 2005). However, looking at each employment status
and salary item, other studies have reported that the scheduled monthly earningsof regular workers display strong DNWR even from an international perspective(Yamamoto 2007). Given these previous studies and the observed fact that thegrowth of scheduled cash earnings remained modest mainly for regular workers in
the 2010s, our analysis focuses on the earnings of regular workers that are assumed
to be subject to strong DNWR.
The remainder of this paper is organized as follows. Section 2 develops a theoretical model that embeds long-term employment contracts and DNWR, and investigates the implications of DNWR for the wage Phillips curve, with particular focus
5

on the upward rigidity induced by DNWR. Section 3 then examines empirically theeffects of DNWR with respect to Japanese regular workers using Japanese household
panel data. Section 4 concludes.

2

Theoretical study

In this section, we build a model for wage setting that incorporates long-term employment contracts and DNWR. Our model extends that of Elsby (2009) in thefollowing two aspects. First, while Elsby (2009) treated hours worked as fixed, weallow for time-variations in hours worked, thereby enabling consideration of a situation in which both wages and hours worked are endogenously determined. Second,
we take into account the dynamics of aggregate wages and hours worked by introducing an aggregate exogenous shock, while Elsby (2009) focused on a stationary
environment in which all aggregate variables are constant. These extensions enable
us to investigate the effects of DNWR on the wage Phillips curve. Then, we derive
the model’s predictions that will be examined in the empirical study in Section 3.

2.1

A stylized model with DNWR

Wage setting of individual workers
To describe the typical employment practice for Japanese regular workers, we
assume that a representative firm makes a long-term employment contract witheach of the individual workers. As we will describe shortly, the firm sets individual
workers’ wages taking into account the fact that workers’ labor intensity depends
on the wages paid to them. Note that labor intensity captures workers’ morale andlabor productivity is positively associated with labor intensity. We follow Elsby(2009) in assuming labor intensity z(·) is given byz

Wit Wit,Pt Wit−1= ln(b) + ln

Wit
Pt




+ c ln

Wit
Wit−1


1{Wit /Wit−1 <1} ,(1)where Wit is the nominal wage for worker i ∈ [0, 1] and Pt is the price level.

61{Wit /Wit−1 <1} is an indicator function that takes one if nominal wage decreases fromthe previous period (Wit < Wit−1 ) and zero otherwise. b > 0 in the first term of theright-hand side of (1) captures the baseline level of labor intensity. In the second
term, we assume that a higher real wage leads to higher labor intensity, as in theefficiency wage theory (see, for example, Solow 1979). In the third term, moreover,
we assume that a decline in nominal wages lowers labor intensity. The assumption
reflects the empirical fact that nominal wage reductions have a negative impact onworkers’ morale (see, for example, Kahneman et al. 1986 and Bewley 1999, andKawaguchi and Ohtake 2007 for the Japanese economy). c > 0 governs the impact
of nominal wage decreases on labor intensity. Note that the third term depends
on the size of nominal wage decrease rates ln (Wit /Wit−1 ), implying the negative
effect on labor intensity is larger for a larger declining rate in nominal wage. The
asymmetric cost induced by nominal wage decreases is the source of DNWR in ourmodel.
The firm maximizes the expected present discounted value of future profits generated by the long-term contract. The value function for each worker-firm pair isgiven by


α
 
Wit
Wit WitWit,
Hit − δmax {Hit − H̃, 0}
Hit −V (Wit−1 , Ait ) = max Ait z
Wit ,Hit
Pt Wit−1
Pt
Pt+ βEt [V (Wit , Ait+1 )],s.t. H ≤ Hit ≤ H,

(2)
(3)

where Hit is hours worked and Ait is exogenous productivity of worker i. Labor
intensity z(·) is given by (1). Notice that the value function depends on the previous
period’s nominal wage, as nominal wage decreases reduce output by lowering labor
intensity. The first term in the right-hand side of (2) represents the output producedby labor input in the current period, and 0 < α < 1 is the degree of decreasing
results to scale for labor input, while the second term is the worker’s base pay, andthe third term is overtime pay. The last term is the expected present discounted
7

value of future profits. 0 < β < 1 is the discount factor for future profits, which
captures time preference and the probability of the contract being extended. For
example, β is equal to zero for a spot contract, whereas β gets close to one for along-term employment contract.
One difference between our model and that of Elsby (2009) is that we endogenize
hours worked, and therefore the firm chooses both nominal wages and labor input
to maximize the present discounted value. In line with Japanese legislation andemployment practice, we incorporate the overtime premium δ > 0 and lower andupper bounds of hours worked, denoted by H and H, respectively.
Another difference from Elsby (2009) is the presence of an aggregate shock. We
assume that exogenous productivity Ait consists of the aggregate component Aaggtand idiosyncratic component Aid
it , each of which follows
ln Ait = ln Aagg
+ ln Aid
t
it ,

(4)

agg
ln Aagg= (1 − ρagg )g + ρagg ln Aagg
, agg∼ N (0, (σ agg )2 ),(5)ttt−1 + t


id 2
id
ρid ln Aid
with probability 1 − γ
idit ∼ N (0, (σ ) )it−1 + it ,id,
ln Ait = ln Aidwithprobability
γ
it−1

(6)
where ρagg and σ agg are the AR(1) coefficient and the standard deviation of innovations for the aggregate component, and ρid and σ id are those for the idiosyncraticcomponent. We assume that the aggregate component follows an AR(1) processwith deterministic trend g. While Elsby (2009) considered a stationary environment, we allow for time-variations of aggregate productivity, so aggregate wages
and hours worked fluctuate accordingly. The idiosyncratic component follows an
AR(1) process with a new innovation with probability 1 − γ, otherwise remaining
at the previous period’s level. The infrequent productivity shocks capture kurtosisof the wage-growth distribution observed in the data—a large spike at zero wagegrowth while fat-tailed distribution—. Similar specifications are often used in theliterature to describe the dynamics of individual productivity of workers and firms8(e.g., Kaplan et al. 2018, Vavra 2014). For descriptive purposes, we refer to Ait as
a labor demand shock in the sense that a rise (decline) in Ait increases (decreases)
marginal products of labor input leading to higher (lower) labor demand.
Aggregate dynamics in the labor market
The aggregate nominal wages Wt and hours worked Ht are defined below.4
Z 1
Wt =

Wit di,(7)

Hit di.

(8)

0

Z 1
Ht =
0

It should be noted that although we do not explicitly describe households’ behavior,
the model setting can be interpreted as assuming that households supply labor andearn wages based on the wages and hours worked determined by the firm, and thatthey consume so that the goods market clears. The aggregate nominal wage growthrate is given by πtw = ln(Wt /Wt−1 ). We assume the inflation rate πt is constant overtime (π):
πt ≡ ln

Pt
Pt−1


= π.

(9)

In this regard, our model describes a partial equilibrium in which labor market
outcomes, such as individual workers’ wages, are determined given an inflation rate.
However, compared with a fully specified non-linear dynamic general equilibrium
model, it provides a parsimonious framework to study labor market dynamics inthe presence of aggregate shocks. In addition, the setting of our model is consistent
with our empirical study in the next section, in which we assess individual wage
determination given macroeconomic conditions.5
4

Consistent with our empirical study in the next section, we define aggregate nominal wages as
the average of individual workers’ wages. We confirm that our result does not change much when
we consider an alternative definition
under which the aggregate wages are Rcalculated by dividing
R1
1
the aggregate labor income ( 0 Wit Hit di) by the aggregate hours worked ( 0 Hit di).
5

A potential extension is to accommodate the interaction between wages and prices by introducing nominal price rigidity. However, the implications of DNWR—the focus of this paper—would
remain unchanged under variable inflation rates, at least qualitatively. As reference, Kim and

9

2.2

Numerical analysis

Numerical method and calibration
The wage setting of individual workers described in the previous subsection includes nonlinearity arising from DNWR. Hence, an approximation of wage setting
using, for example, the perturbation method is not applicable. We solve for theindividual wage function f by using the value function iteration method.
Wit = f (Ait , Wit−1 ).

(10)

In this baseline case, f (·) depends on the previous period’s wage level Wit−1 due to
DNWR in addition to exogenous productivity Ait .
To decompose two channels through which DNWR induces upward rigidity, we
consider the wages, Wit∗ , that exclude the effects of the past wages as below.
Wit∗ = f (Ait , W ),(11)

where f (·) is identical to that in (10) while W takes a sufficiently low value. In thisalternative case, while DNWR does not bind in the current period since the previous
period’s wage is assumed to be sufficiently low, DNWR is still relevant because it
may bind in the future, depending on the wage chosen in the current period.
Moreover, for comparison purposes, we also define the wages, Wit∗∗ , that realize
when nominal wages are flexible :Wit∗∗ = g(Ait ),(12)

where g(·) is obtained by setting c = 0 in (2). In this case, the current wages do notdepend on the previous period’s wage Wit−1 as DNWR does not exist.
Using these wage functions, we conduct a stochastic simulation of the calibrated
model to generate the series of wages and hours worked for individual workers.
Ruge-Murcia (2009) and Iwasaki et al. (2018) investigated the interaction between wages andprices using a general equilibrium model with DNWR and nominal price rigidity.

10Aggregate variables are obtained by integrating them across workers. Given thatthe main focus of this analysis is on deriving qualitative predictions that will betested in the light of the data in Section 3, we calibrate the model by assigningplausible parameter values that are broadly consistent with salient features of theJapanese labor market up until the 2010s.
The calibrated parameter values are listed in Table 1. The model’s frequency isannual. The discount factor β is set to 0.95 (5% annual rate). The value reflects
the subjective discount factor, which is calibrated to an annual rate of around 2% in
previous studies, and the separation rate for regular workers, which is around 3% peryear according to the JHPS/KHPS (described shortly). Regarding the parameters
for labor intensity, the baseline level of labor intensity b is normalized to b = exp(1)so that the real wage in the steady state is equal to one. The degree of DNWR c is set
to c = 1.00 so that the relationship between the hours worked and the wage growthwhen DNWR is present in the model is broadly consistent with the data. The degreeof decreasing returns to scale α is set to 0.66 in line with the conventional value
in the macroeconomic literature. The parameters for hours worked are calibrated
according to the related legal system and employment practice.6 Specifically, theupper bound of hours worked is set to H/H ss = 1.30 according to the difference
between the limit of overtime work determined in the Japanese Labor Standards
Act and the average hours worked in the data, which corresponds to H ss in themodel. The lower bound of hours worked is set to H/H ss = 0.85 based on thestandard scheduled hours worked in practice. The presence of the lower bound ofhours worked implies that, under long-term employment practices, layoffs are notreadily implemented for regular workers even in economic downturns. The overtime
premium δ is set to 0.25 as the Japanese Labor Standards Act requires a premiumof more than 25% for overtime work. We assume that statutory working hours H̃
are equal to the average hours worked in the data, i.e., H̃/H ss = 1.00. The inflation
rate π is set to an annual rate of 2%. The trend productivity growth rate in the6Note, however, that the calibration for hours worked is subject to a considerable margin oferror as, within the law, they may differ across firms.

11baseline calibration is set to 0%, while we examines the cases in which the valuechanges in the later part of this subsection. As for exogenous productivity, we set
ρagg = 0.70, σ agg = 0.015, ρid = 0.70, σ id = 0.15, and γ = 0.5 according to themoments of nominal wage growth, such as standard deviation, in the aggregate andindividual data.
Implications for individual wage setting
Panel (A) of Figure 2 shows the wage functions for individual workers in thecalibrated model. The figure indicates two channels through which DNWR induces
upward rigidity in wage setting. The first is the mechanism arising from insufficient
wage adjustment in the past (the backward-looking channel of DNWR). In the blue
region in the figure (Wit > Wit∗ ), the previous period’s wage remains at a highlevel—workers receive higher wages than implied by their labor productivity—. In
that case, the firm does not increase wages even if labor demand rises, as long as
the insufficient downward wage adjustment in the past remains. The other is themechanism arising from pay cut risks in the future (the forward-looking channel
of DNWR). In the red region in the figure (Wit < Wit∗∗ ), the firm internalizes thefact that DNWR will be more likely to bind in the future once they increase wages,
resulting in lower wage growth than under flexible wages. This is the case even whenstrong labor demand offsets the insufficient wage adjustments in the past.
Panel (B) of Figure 2 compares the cross-sectional wage-growth distribution
obtained in the stochastic simulation with and without DNWR. When DNWR ispresent, the share of workers who receive positive wage growth decreases, as does theshare of those who receive negative wage growth, because DNWR induces upward
rigidity. Consequently, the share of workers who receive wage freezes increases,
rendering the distribution less dispersed than under flexible wages.
Implications for wage Phillips curve
One notable feature of our model is that, unlike Elsby (2009)’s framework, we canderive the wage Phillips curve as aggregate wages and hours worked fluctuate upon12

aggregate shocks. Panel (A) of Figure 3 displays the wage Phillips curve, obtained
as the quadratic fitted curve of the relationship between aggregate nominal wage
growth and hours worked in the stochastic simulation. The wage Phillips curve
suggests a positive association between hours worked and nominal wage growth at
the aggregate level. More importantly, the cases with and without DNWR shownin the figure indicate that the wage Phillips curve becomes flatter in the presence of
DNWR.
It is worth mentioning that the wage Phillips curve becomes flatter for all regionsof hours worked when DNWR is present. This is because DNWR endogenously induces upward rigidity when labor demand increases, in addition to preventing wage
declines when labor demand decreases. The endogenous upward rigidity arises fromthe two channels described above: the backward- and forward-looking channels of
DNWR. To see the effect of each channel in more detail, Panel (B) of Figure 3 decomposes the causes of the flattening of the wage Phillips curve into the two channels. The figure indicates that both channels contribute to the flattening at eachlevel of labor demand. It is also worth mentioning that the forward-looking channel becomes more significant than the backward-looking channel as hours worked
increases. Intuitively, as labor demand increases, the insufficient wage adjustmentin the past gradually diminishes.7 On the other hand, the firm still contains wage
increases because they become more cautious about the risk that labor demand will
begin to decrease at some point in the future and they will thereby be constrainedby DNWR.
Determinants of the forward-looking channel of DNWR
The forward-looking channel of DNWR arises because of the firm’s desire to
avoid the risk of being unable to cut nominal wages in the future, which leads tolower labor intensity. Thus, the channel becomes particularly significant when suchrisk grows. This would be the case, for example, when expected growth decreases
7

The backward-looking channel diminishes but does not disappear, even at high levels of labordemand. This is because some workers remain subject to insufficient wage adjustments due toidiosyncratic labor demand shocks at the individual level.

13

or uncertainty regarding economic growth increases.
To examine this point, we extend the model so that the trend productivity growthrate g and the standard deviation of labor demand shock σ approximately follow
AR(1) processes, and we then compute the generalized impulse responses (GIR)to these shocks.8 Note that g acts as the expected growth rate of the economy
while σ represents uncertainty in our model. Figure 4 shows the GIR of aggregate
variables upon each shock. The figure displays three cases: the baseline case with
DNWR; the case with only the forward-looking channel of DNWR (corresponding
to wage function (11)); and the case without DNWR (flexible wages). As for the
responses to a decline in expected growth, the case with only the forward-looking
channel of DNWR exhibits a deeper decline in nominal wage growth than under
flexible wages.9 When it comes to the responses to a rise in uncertainty, nominal
wage growth sharply decreases on impact in the case with only the forward-looking
channel of DNWR.10
The results in this section imply that, even when labor demand increases in
economic expansion phases, if economic growth stays at a low level or uncertainty
regarding future economic growth increases, nominal wage growth may remain modest as DNWR flattens the wage Phillips curve.
8

For simplicity, we assume that the trend productivity growth rate may take two values: gt ={gh , gl } with gh > gl . The transition probabilities between the two values are given by phl and plh .
Likewise, the standard deviation of labor demand shock is discretized as σts = {σhs , σls } with σhs > σls
for s ∈ {agg, id}. We assume that the standard deviation for the aggregate and idiosyncraticcomponents of productivity stays in the same regime. We set phl = plh = 0.2. In Figure 4, we
compute the GIR to a decline in expected growth by 1 percentage point, i.e., gh = 0.01, gl = 0.00,
and that to a rise in uncertainty by 1 percentage point for aggregate component and 10 percentage
points for idiosyncratic one, i.e., σhagg = 0.02, σlagg = 0.01, σhid = 0.20, and σlid = 0.10. Notice thatthough each variable is discretized with two values the GIR takes a smooth path because it is theconditional expectation upon an initial shock.
9
In the case with full DNWR, the decline in nominal wage growth is smaller than under flexible
wages, as DNWR prevents wage decreases upon the shock for a considerable share of workers.
10Note that under flexible wages the aggregate wage growth remains unaffected by changes in
uncertainty because wages can be adjusted both upwardly and downwardly by necessary amounts
when productivity shocks occur.

14

3

Empirical study

The theoretical study in Section 2 indicates that DNWR induces upward rigidity, leading to lower nominal wage growth during economic recovery and expansion
phases compared with that under flexible wages. In this section, we examine empirically the theoretical predictions using Japanese household panel data.

3.1

Data

JHPS/KHPS
In our empirical study, we use individual data from the Japan Household Panel
Survey (JHPS/KHPS) compiled by the Panel Data Research Center at Keio University. The JHPS/KHPS tracks the employment status and consumption expenditure,etc., of the same individuals over time. The subjects surveyed are chosen in orderto reflect the population composition of the Japanese economy. The spouse of eachsubject also receives the questionnaire, answering separately regarding their own
employment status.
We restrict our sample to workers who are below 59 years old and who haveworked for the same company for two consecutive years. The sample excludes individuals not under employment contract with a company, such as the self-employed,
freelancers, workers at a family business, and consigned workers. In addition, we
exclude worker-year pairs in which the workers have changed jobs, and we limit oursample to full-time/regular workers whose pay-period is monthly, because we are interested in regular workers under long-term employment contracts. We also confine
our sample to workers who worked every month in each survey year so as to exclude
the potential effects on wage dynamics of absence from work or unemployment. As
a result, our final sample, including spouses, contains approximately 3,300 workers
as of the 2018 survey. Our measures of wage are monthly earnings and bonuses.
Monthly earning excludes bonuses but includes overtime pay. The sample covers
the years from 2003 to 2017 (from the 2004 to 2018 surveys).

15Descriptive statistics
Table 2 reports the descriptive statistics of key variables in our sample.11 To
begin with, Table 2-1 compares characteristics of our sample with the Employment
Status Survey (ESS), a representative survey for employment status in Japan. The
table shows that our sample characteristics are consistent with those of the regular
employees in the ESS in terms of gender, educational background, and employment
status, including industry and firm size. Table 2-2 compares the descriptive statistics of wages in our sample with the Basic Survey on Wage Structure (BSWS), a
representative wage survey in Japan. This table shows that the average monthly
earnings, bonuses, and hours of paid work per week in our sample are close to thoseof full-time workers in the BSWS.12 Moreover, Panel (A) of Figure 5 shows thatthe average wage of our sample fluctuates in line with the aggregate statistics derived from the BSWS and the Monthly Labour Survey. These facts confirm that
our empirical study using the JHPS/KHPS provides an accurate representation ofJapanese regular workers.

3.2

Empirical strategy

Differences-in-Differences
Our empirical study first assesses whether individual wages for regular workers in
the JHPS/KHPS displayed DNWR during the GFC that occurred in the late 2000s.
We then use the Differences-in-Differences (DID) to examine if the wage growth of
the workers who displayed a strong degree of DNWR was lower during the recovery
and tightening phases in the 2010s than that of workers whose wages can be flexibly
adjusted. We also test the validity of the backward- and forward-looking channels
of DNWR, which are implied by our theoretical model, by exploiting relevant information on each worker, as described shortly. Our baseline regression equation is11

See Higuchi (2005) for a descriptions of the entire sample of the JHPS/KHPS.

12

Strictly speaking, the average level of bonuses is somewhat lower in our sample. This may
reflect the fact that the special cash earnings in the BSWS include temporary earnings paid toworkers other than bonuses. In addition, the average age and tenure in our sample are slightly
higher, partly because the JHPS/KHPS covers only workers aged 20 years or above.

16

given by∆Wit = c + βXit Yit + γ 0 Zit + µi + λt + it ,(13)

where ∆Wit on the left-hand side of (13) denotes the year-on-year rate of wage
growth of worker i in year t. On the right-hand side, Xit is a measure of the degreeof DNWR for each worker, which we will describe shortly. Yit is a measure of labormarket conditions. c is a constant, and it is an error term. As an example ofidentification, suppose that Xit is a dummy variable that takes one for workers who
display a strong degree of DNWR, and zero otherwise. Also, let Yit be a measureof the aggregate labor market conditions under the assumption that each worker
faces the same labor demand. In this case, the coefficient β represents the difference
between the two groups of workers (Xit = 0 or 1) in the sensitivity of wage growthwith respect to changes in aggregate labor market conditions—the restraining effectof DNWR on wage growth under improving labor market conditions—. Note that
individual factors and factors common across workers are captured by µi and λt , andobservable characteristics are contained in the vector of controls Zit . The advantageof the DID is that we can estimate the effect of interest controlling these various
factors.13
Classification of workers
To implement the above empirical strategy, we need to distinguish the degreeof DNWR for each worker. Many existing studies claimed the existence of DNWR
based on the observation that there is a spike at zero in the cross-sectional wagegrowth distribution and that the distribution exhibits much fewer incidences ofwage decrease than increase. However, as Kuroda and Yamamoto (2003, 2005)
and Barattieri et al. (2014) pointed out, it may not be appropriate to judge thedegree of DNWR only from the unconditional wage-growth distribution, given that13

In the DID specification here, determinants of wage growth other than DNWR are capturedby these controls and others. That is, our empirical study does not exclude other hypotheses
regarding the slower wage growth in the 2010s.

17

wage settings are state-dependent: there would be little incentive to cut wages
even without DNWR when the inflation rate is high on average or the economy isbooming.
To overcome this challenge in measuring the degree of DNWR from the data, wedefine workers who displayed a strong degree of DNWR as those who did not receive
any wage decreases during the GFC (2008 and 2009), when most firms experienced
a sharp drop in sales—the source of wage disbursements—amid the severe economic
downturn. The premise of this classification method is that the GFC that occurred
when inflation in Japan was low can be thought of as a large negative labor demand shock that imposed downward pressure on wages for a wide range of workers,
therefore the lack of wage decreases during the period implies some sort of friction
in wage adjustments. Note, Branten et al. (2018) and Fallick et al. (2020) also used
information on wage changes during the GFC to evaluate the degree of DNWR. A
similar method is used by Yamamoto and Kuroda (2016) for the Japanese economy.
Based on this method, the share of workers who displayed a strong degree of
DNWR is around one third of the sample during the GFC.14 While the fraction islower than the average share of workers without wage decreases for a given year
during our sample period (around 70%), it implies the presence of some sort offriction in downward wage adjustments for Japanese regular workers. However, there
is uncertainty around the identification of DNWR. In the second half of Section 3.3,
we conduct a robustness check with respect to the classification of workers who havea strong degree of DNWR.
In addition, when examining the backward- and forward-looking channels of
DNWR in Section 3.4, it is necessary to identify the workers who are prone to beaffected by each channel. We do so by comparing actual wages and potential wages
for workers who displayed a strong degree of DNWR, where the latter is estimated14

Studies based on this method would be conservative in their estimate of the effects of DNWR
for the following two reasons. First, the monthly earnings in the JHPS/KHPS include overtime
pay as well as base pay. Given that a decline in hours worked in economic downturns leads to adecrease in monthly earnings even when the base pay remains unchanged, our classification may
understate the degree of DNWR embedded in the base pay. Second, there may be measurement
errors in the classification. In the regression analysis, the presence of measurement errors generates
attenuation bias.

18

from various factors, such as tenure and educational background.15 For example,
suppose that a worker’s actual wage is above their potential wage. We then consider
that this worker has inherited the insufficient wage adjustment from the past, henceclassifying the worker as one who is prone to be affected by the backward-looking
channel of DNWR. On the other hand, if the worker’s actual wage is lower than theirpotential wage, we consider that the worker exhibits no wage adjustment pressure
inherited from the past. Then, we classify the worker as one who is prone to beaffected by the forward-looking channel of DNWR.16

3.3

Overall effects of DNWR on wage growth rate

This section examines the overall effect of DNWR on wage growth of regular workers
after the GFC, regardless of its channels. To examine the effect, we first divide thesample period during and after the GFC into three phases based on labor market
conditions: the deterioration phase during 2008–2009, the recovery phase in 2010–2012, and the tightening phase during 2013–2017 (Panel (B) of Figure 5). We thenexamine how much the wage growth of the workers who displayed a strong degree of
DNWR was lower (or higher) than that of the workers who displayed a low degreeof DNWR in each phase. The estimation equation is given by∆Wit = c + β1 Xi D08−09 + β2 Xi D10−12 + β3 Xi D13−17 + γ 0 Zit + µi + λt + it , (14)where Xi is a DNWR dummy equal to one if the worker did not receive any wage
decreases during the GFC (2008 and 2009), and zero otherwise. D08−09 , D10−12 and15

More specifically, we extend the Mincer wage equation (Mincer 1974) to include aggregate
labor market conditions as well as individual workers’ characteristics such as tenure and educational
background. The estimated potential wages can be interpreted as the average wage level determinedby worker characteristics as the wage adjustment proceeds in the medium- and long-run. In thatsense, they correspond approximately to the flexible wages in our theoretical model. The details
are presented in Appendix A.
16
This classification is conducted in each year by comparing the level of actual wages and potential wages in the previous year. Consequently, a worker who was subject to the backward-looking
channel at some point in time may later switch to one who is subject to the forward-looking
channel.

19D13−17 are time dummies equal to one if the period is 2008–2009, 2010–2012 and2013–2017 respectively, and zero otherwise. Zit is a vector of control variables displaying each worker’s characteristics such as tenure and educational background.17µi is a random effect for each worker.18 λt is a time fixed effect. We estimate (14)for the period 2004–2017.
Empirical result
Table 3 reports the estimation result. Looking at the result of the monthly
earnings, both β2 and β3 are negative and they are statistically significant. This
result, consistent with the predictions of our theoretical model, shows that the wage
growth of workers with a strong degree of DNWR was significantly lower than thatof workers with a low degree of DNWR during the recovery and tightening phases
after the GFC.
β1 is positive, but this is by the definition of DNWR dummy: we define theworkers who displayed a strong degree of DNWR as those who did not receive any
wage decreases during the GFC. Regarding bonuses, β2 and β3 are negative, but
not statistically significant. These results show that while DNWR induced upward
rigidity for monthly earnings including base pay, DNWR did not induce upward
rigidity for bonuses. This result may be partly due to the limited number of workers
without any bonus decrease during the GFC, which would make it difficult to infer
17
Control variables include interaction term of industry dummy and year dummy (industry
consists of manufacturing, wholesale and retail, construction, medical services and welfare, andother non-manufacturing), tenure, age category dummy (24 years old or less, 25–29 years old,
30–34 years old, 35–39 years old, 40–44 years old, 45–49 years old, 50–54 years old, and 55–59
years old), title dummy, labor union dummy, firm size dummy (1–29 workers, 30–99 workers, 100–499 workers, 500 workers or more, and government), gender dummy, dummy for type of school
last attended (junior high school, high school, junior college or technical school, university, andgraduate school), region dummy (Hokkaido, Tohoku, Kanto, Chubu, Kinki, Chugoku, Shikoku, andKyusyu), occupation dummy (service worker, manager, specialized or technical worker, clerical
worker, salesperson, agriculture, forestry, fishery and mine worker, and others), CPI by region,
hours of paid work per week in the previous year (only in the estimate regarding monthly earnings).
18

The JHPS/KHPS includes workers added to the sample after 2008. If we used an individual
fixed effect instead of a random effect, both the fixed effect and the DNWR dummy would beconstant over time for these samples of workers, hampering the identification of each effect. This
leads us to employ the random effect model. Note instead that we control for the characteristics
of each worker that are constant over time by Zit , the vector of control variables.

20

the precise effect of DNWR on bonuses. Based on these results, we hereafter focus
on the monthly earnings for which DNWR is considered to induce a large degree of
upward rigidity.
Calculation of the effect on wage growth at the aggregate level
Next, we calculate the effect of DNWR on the wage growth of regular workers
at the aggregate level. For the calculation, it is necessary to take into account theshare of workers who displayed a strong degree of DNWR in our sample, in addition
to the effect of DNWR on the wage growth of each worker, shown in Table 3. In
this respect, as noted in Section 3.2, the share of workers who displayed a strong
degree of DNWR is around one third of the sample during the GFC.19 Based on thisinformation, we calculate the effect of DNWR on the wage growth of regular workers
at the aggregate level during the recovery and tightening phases of labor market
conditions after 2010, as shown in Panel (A) of Figure 6. This figure shows that theslower wage growth of the workers who displayed a strong degree of DNWR pushed
down the growth rate of monthly earnings at the aggregate level by 0.4 percentage
points per annum during both 2010–2012 and 2013–2017. During the recovery andtightening phases, DNWR of regular workers induced upward rigidity, which can beconsidered a non-negligible cause of the flattening of the wage Phillips curve in the2010s. In Section 3.4, we will look at the channel behind this.
Robustness check
The above results may be driven by our assumptions regarding the identification of workers who displayed a strong degree of DNWR. To assess the robustnessof the results, we employ two alternative criteria for identifying DNWR for eachworker. First, workers who displayed a strong degree of DNWR are defined asworkers without any wage decreases in the last three years. This can be regarded
as a looser criterion than our baseline, because we consider the economic recovery
19

We confirm that, among the workers whose wage growth can be observed both during and after
the GFC, the workers who displayed a strong degree of DNWR constantly accounts for around one
third after 2010.

21

and expansion phases in addition to the downturn when identifying DNWR. Second,
as a stricter criterion, we define workers who displayed a strong degree of DNWR
as those whose actual wage growth exceeded their potential wage growth during
the GFC. Since Japanese regular workers receive periodic pay raises, which reflect
their tenure, etc., the potential wage growth of some workers could be positive evenduring economic downturns such as the GFC.
Table 4 reports the estimation results of the effect of DNWR based on these
two alternative criteria.20 The estimation results show that DNWR pushed down
significantly the growth of monthly earnings amid the labor market improvement in
the 2010s, even when we use alternative criteria for measuring the degree of DNWR.
The effect of DNWR on wage growth at the aggregate level under the alternative
criteria is shown in Panel (B) of Figure 6. The figure shows that the impacts ofdownward pressure due to DNWR were around 0.6 percentage points under thelooser criterion and around 0.2 percentage points under the stricter criterion. Theseestimates are statistically significant. The calculated effect under the looser criterion
is larger than that in the baseline, because the estimated coefficient on the effect of
DNWR is larger. Under the stricter criterion, while the estimated coefficients areabout the same as the baseline, the share of workers who displayed a strong degreeof DNWR becomes smaller than that in the baseline. As a result, the calculated
effect under the stricter criterion is smaller. From these findings, the conclusion that
DNWR of regular workers induced upward rigidity, thereby functioning as a factor
for the flattening of the wage Phillips curve amid the improvement of labor market
conditions, is robust as a means of measuring DNWR.21
20

In the estimation based on the looser criterion, we focus on the coefficient of interaction termof the DNWR dummy and the time dummy that displays the period when the unemployment rate
declined (Yt ). Note that, since this DNWR dummy can vary over time, we can use an individual
fixed effect for this specification. As such, we exclude from the control variables those variables
that represent time-invariant characteristics of each worker, and add the individual fixed effect andthe DNWR dummy to the control variables. The equation in the stricter criterion is the same as
the baseline estimation. We estimate both equations for the period 2004–2017, which is the sameas the baseline model.
21

Note that in the baseline specification, we regard workers added to the sample after 2009 asworkers who displayed a low degree of DNWR (Xi =0) during the GFC, since there is no informationon their wage adjustments during the GFC. To assess the robustness of our result regarding thisassumption, Appendix B calculates their degree of DNWR based on the information on their wage

22

3.4

Estimation results on the two channels

Examination of the backward-looking channel
We examine whether the backward-looking channel did indeed work as a background to the upward rigidity induced by DNWR. More specifically, we focus on theworkers who displayed a strong degree of DNWR during the GFC and who inherited the insufficient wage adjustment as identified by their actual wage being higher
than their potential. We examine if, as predicted by our theory, the wage growthof this type of worker was lower than that of workers with a low degree of DNWR
in the recovery and tightening phases of labor market conditions in the 2010s. The
equation is given by∆Wit = c + β4 Xi Gapit−1 1{Gapit−1 ≥0} D10−17 + γ 0 Zit + µi + λt + it ,(15)

where Gapit−1 is the deviation rate of the actual wage from the potential wage in theprevious year. Gapit−1 1{Gapit−1 ≥0} is a variable which is positive if the deviation rate
is positive and zero otherwise. D10−17 is equal to one during 2010–2017, and zerootherwise. µi is a fixed effect for each worker.22 The definitions of other variables
are the same as those in the baseline estimation.23 We estimate the equation forthe period 2008–2017, in order to focus on the effect of the GFC. If the backwardlooking channel had worked, we would have observed that the wage growth rate of
the workers who are prone to be affected by the backward-looking channel (Xi = 1
and Gapit−1 ≥ 0) was lower than that of workers whose wage was flexible in the
improvement phases of the labor market conditions (D10−17 = 1). That is, we expect
change after the GFC, and we reestimate the baseline equation (14) using the revised information
on DNWR for these workers. Our estimates show that the result is also robust to the treatment
of DNWR for workers added to the sample after 2009.
22

Xi Gapit−1 1{Gapit−1 ≥0} in (15) can vary over time hence is not treated as a fixed effect. Therefore, we employ a fixed effect model to estimate (15).
23

We add Xi D08−09 , Xi Gapit−1 and Xi |Gapit−1 |1{Gapit−1 <0} D10−17 to the control variables in(14), because we have to control how much the wage growth of workers who displayed a strong
degree of DNWR was lower than that of other workers in the sample during the GFC, and how
much that of workers with a strong degree of DNWR and without insufficient wage adjustmentin the past was lower than workers with a low degree of DNWR. The time-invariant variables are
excluded from the control variables because they are included in the fixed effect.

23

that β4 takes a negative value.
Table 5 shows the estimation result on monthly earnings. β4 is negative andstatistically significant. This implies that in regard to the workers who are prone
to be affected by the backward-looking channel, the channel actually worked in therecovery phase and tightening phase of labor market conditions in the 2010s.
The effect of this channel on wage growth at the aggregate level depends on
the proportion of workers who are prone to the backward-looking channel. Figure
7 shows the distributions of the deviation rate of actual wage from potential wage
after the GFC, shown separately for workers with a strong or low degree of DNWR.
During 2008–2009, the deviation rate of workers with a strong degree of DNWR isbiased toward positive territory. This implies that there were many workers with astrong degree of DNWR who received insufficient wage adjustment during the GFC,
causing depressed wage growth in the subsequent recovery phase. In the figure, you
can also find that the skew of the distribution diminished during 2013–2017. Thissuggests that the effect of the backward-looking channel gradually diminished aslabor market conditions continued to improve after the GFC.
Examination of the forward-looking channel
Finally, we examine whether the forward-looking channel did indeed work after
the GFC. In this study, we focus on the workers who displayed a strong degree of
DNWR during the GFC, but who received a lower wage than their potential at somepoint in the subsequent years. We then estimate whether, as our theoretical study
predicted, (a) the lower expected growth in the industry to which the workers belong,and (b) the higher uncertainty regarding growth in that industry, are associated withthe lower wage growth for these workers, compared with workers who displayed alow degree of DNWR. The estimation equation is given by∆Wit = c + β5 Xi |Gapit−1 |1{Gapit−1 <0} Y1tj + β6 Xi |Gapit−1 |1{Gapit−1 <0} Y2tj
+ γ 0 Zit + µi + λt + it ,

(16)

24

where |Gapit−1 |1{Gapit−1 <0} is a variable which takes the absolute value of the deviation rate of actual wage from its potential only when the deviation rate in theprevious year was negative, and zero otherwise. Y1tj is the index of expected growthby industry and Y2tj is the uncertainty index by industry. The definitions of othervariables are the same as those in (14).24 We estimate the equation for the period 2008–2017. If the forward-looking channel had worked, the wage growth of theworkers who are prone to be affected by the forward-looking channel (Xi = 1 and
Gapit−1 < 0) would have been lower when expected growth (Y1tj ) declines. Therefore, β5 is expected to be positive. Moreover, if the forward-looking channel had
worked, their wage growth would have been lower, when the uncertainty increases,
therefore β6 is expected to be negative.
We generate the series of the index of expected growth and its uncertainty as
follows: the index of expected growth is the profit forecast of firms taken fromthe Short-Term Economic Survey of Enterprises in Japan (TANKAN), which is a
representative survey of firms in Japan. We use the survey results from March 2003
to December 2018, and we remove the short- to medium-term cycle components (5years or less) of the profit forecasts using the band pass filter of Christiano andFitzgerald (2003). The value in each year is the average of the trend component
among those of the March, June, September and December surveys. We calculate
the indexes for the following five industries: manufacturing, wholesale and retail,construction, medical services and welfare, and other non-manufacturing. As forthe uncertainty index, we employ the historical standard deviation of daily stock
returns for the five industries derived from TOPIX-17.
Table 6 reports the estimation result on monthly earnings. As expected, β5 issignificantly positive and β6 is significantly negative. This implies that as expected
We add Xi D08−09 , Xi Gapit−1 , Xi Gapit−1 1{Gapit−1 ≥0} Y1tj , Xi Gapit−1 1{Gapit−1 ≥0} Y2tj ,Gapit−1 Y1tj , Gapit−1 Y2tj to the control variables used in (14). This is because we aim to control the following: how much the wage growth of workers with a strong degree of DNWR was
lower than that of the other workers during the GFC, how much the wage growth of the workers
with a strong degree of DNWR and with the insufficient wage adjustment was contained by eachindex, and the effect of each index on the wage growth through the deviation rate. In addition,
we exclude time-invariant variables of each worker from the control variables, as we employ a fixed
effect for each worker.
24

25

growth declines or its uncertainty increases, the wage increase of workers who areprone to be affected by the forward-looking channel is contained. It is worth notingthat in Figure 8, we can observe periods when the index of expected growth was
sluggish and when the uncertainty index heightened after 2010.25 These results
suggest that there were workers whose wage increase was contained by the forwardlooking channel amid the improvement in labor market conditions after the GFC.
The effect of the forward-looking channel on wage growth at the aggregate levelseems to have become more significant over time, since the share of workers overpaid
has decreased during the same period and that of workers underpaid has increased,
as shown in Figure 7. These results provide the empirical ground for the viewthat firms prioritized the stability of long-term employment over immediate wage
increases, since firms were not confident about future growth due to pesistent low
growth in the past.

4

Conclusion

Among a number of hypotheses, some economists and central bankers have pointed
to the significance of the upward wage rigidity induced by DNWR, when interpretingthe flattening of the wage Phillips curve. In this paper, we pay particular attention
to Japanese regular workers, characterized by their long-term employment contracts,
and we examine the validity of the hypothesis that DNWR has contributed to theflattening of the wage Phillips curve from both a theoretical and an empirical perspective.
Our theoretical study, which incorporates long-term employment contracts, suggests that DNWR induces upward wage rigidity, contributing to the flattening of
the wage Phillips curve through the following two channels: the mechanism arising from insufficient wage adjustment in the past (the backward-looking channel of
DNWR), and the mechanism arising from pay cut risks in the future (the forward25

Figure 8 (Reference) shows that the similar tendencies are observed in the alternative indexesof expected growth and uncertainty.

26

looking channel of DNWR). In addition, declines in expected growth and increases
in the uncertainty around economic growth strengthen upward rigidity because they
increase the risk of future pay cuts.
In line with the theoretical result, our empirical study using the panel data ofJapanese regular workers reveals that the slower wage growth of the workers who
displayed a strong degree of DNWR pushed down the growth of monthly earnings
at the aggregate level by 0.4 percentage points per year (a range of 0.2 to 0.6
percentage points, given uncertainty regarding the identification of DNWR) during
the years between 2010–2017. We confirm that both the backward- and forwardlooking channels of DNWR contributed to this result. Moreover, the latter channel
became relatively stronger in the late 2010s, when a tightening of labor market
conditions became notable.
Finally, we suggest two future research topics relevant to our study. First, there
remains more room to study the relationship between wage setting and macroeconomic performance. From a theoretical perspective, our model can be extended toincorporate the interaction between wages and prices, and to incorporate monetary
policy. From an empirical perspective, assessing the impact of shifts in labor market
trends, due for example to population aging, and of fluctuations in the natural rateof unemployment in Japan would enrich our empirical analysis. Second, our findings
relate to developments of Japan’s labor market in the 2010s, with our conclusions
and the implications of this paper being also based on those observations. To investigate forthcoming labor market fluctuations in the 2020s, following the outbreakof COVID-19, further study is warranted, based on relevant data as they become
available. That is, the outbreak could affect wages not only through labor demand
shocks at the aggregate level, as examined in this paper, but also through labor force
reallocation pressures as they appear heterogeneously among individual industries
or regions.26 It will also be important to assess the long-term consequences as well
26

Barrero et al. (2020), who examined a U.S. firm survey conducted in April 2020, argued that theoutbreak of COVID-19 would lead to a large-scale reallocation in the labor market, since the firms
surveyed anticipated job creation to meet new types of demand while mentioning the necessity ofmassive layoff of the current workforce. For the Japanese economy, Kikuchi et al. (2020) uncovered
substantial heterogeneity in the impact of the outbreak of COVID-19 across various characteristics

27

as the immediate effects of the labor policy introduced following these shocks. Analysis around these points remains future work awaiting the accumulation of sufficientdata.

such as industry and employment status.

28

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31

Ozaki, T., Genda, Y., 2019. Chingin josho ga yokusei sareru mekanizumu (Mechanism of containing wage growth). Bank of Japan Working Paper Series, No.19-J-6(in Japanese).
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Yamamoto, I., 2007. Nominal wage flexibility after the lost decade in Japan. Mitabusiness review 50, 1–14 (in Japanese).
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wage flexibility? Evidence from panel data analysis of Japanese firms. RIETI
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Economic Symposium, Jackson Hole, Wyoming, August 22, 2014.

32

Appendix A

Estimation of potential wage

When estimating potential wage, we consider the factors of industry and aggregate
economy, based on the Mincer wage equation (Mincer 1974), where the potential
wage is estimated from the characteristics of workers such as tenure, etc. The
estimated potential wage can be interpreted as the average wage level determinedby their characteristics as the wage adjustment proceeds in the medium and longterm.27 The equation is given by
ln Wit = c + γZit + αYt + µi + it ,(17)

where ln Wit is natural log of the wage level. Zit is a vector of variables for characteristics of each worker. More specifically, as the characteristics, we consider tenure,square of tenure, age category dummy, title dummy, labor union dummy, firm size
dummy, occupation dummy, labor productivity by industry, and CPI by region.28
These variables and specifications are based for the most part on previous studies
such as Kawaguchi (2011). We add unemployment rate (Yt ) to capture the effect ofaggregate labor market conditions on the wage. µi is a fixed effect for each worker.
We estimate the equation for the period 2003–2017.
Appendix Table 1 reports the estimation result. The coefficient of tenure ispositive and that of square of tenure is negative. This is consistent with previous
studies on the Mincer wage equation in Japan such as Kawaguchi (2011) and Kimura
et al. (2019). Moreover, that of the unemployment rate whose sign is reversed is
positive, showing that the aggregate labor market conditions had a significant effect.
27

To eliminate the influence of DNWR from estimation of potential wage, it is possible to limit
the sample to workers who displayed a low degree of DNWR. However, in that case, we cannot
estimate the potential wage of workers with a strong degree of DNWR, because we cannot obtain
their fixed effects. Therefore, in this paper, we conduct the estimation using the sample including
the workers who displayed a strong degree of DNWR. Note that the estimated coefficients are close
to those when we limit the sample to workers who displayed a low degree of DNWR.
28

The definitions of variables other than labor productivity are the same as those in Footnote 17.
Labor productivity is calculated by dividing real gross domestic product (classified by economic
activities in the National Accounts), by total labor input, which is the number of employed persons(in the Labour Force Survey) multiplied by hours worked per person (in the Monthly Labour
Survey).

33

Appendix B

Robustness check on treatment of the sample

added after 2009
In the JHPS/KHPS, new cohorts were added in 2007, 2009, and 2012 for reasons
such as to compensate for sample loss.29 Regarding the sample added after 2009,
information on wage growth during the GFC (2008 and 2009) is unavailable. In thebaseline estimation, we define the sample added after 2009 as workers who displayed
a low degree of DNWR (DNWR dummy is zero) for convenience. This treatment of
the sample added after 2009 can distort the estimation result.
To check the robustness with regard to the sample added after 2009, we calculate
the degree of DNWR from the available information on their wage, and estimate
the same equation as that in the first half of Section 3.3. More specifically, for the
sample before 2008, we use the DNWR dummy based on pay cuts during the GFC
as in the baseline. For the sample added after 2009, we define the DNWR index as
the period average of the DNWR dummy based on pay cuts in the past three years,
which is used as the alternative dummy.30
Appendix Table 2 reports the estimation result. Both β2 and β3 take similarvalues as those in the first half of Section 3.3, and they are significantly negative.
This implies that the estimation result in the baseline is robust in its treatment of
the sample added after 2009.

29

A new sample was added in 2009 because the former Keio Household Panel Survey (KHPS)
and the former Japan Household Panel Survey (JHPS) from 2009 were integrated.
30This method assumes that average of the DNWR dummy based on pay cuts in the past three
years is an effective alternative variable for the DNWR dummy based on pay cuts during the GFC.
In fact, the two dummies are positively correlated, with the correlation around 0.4 for the sample
that existed before 2008. This supports the validity of the dummy as an alternative variable.

34

Table 1: Calibrated parameters
SymbolParameters

ValuesDiscount factor

0.950

Baseline level of labor intensityexp(1)

Degree of DNWR

1.000

Degree of decreasing returns to scale

0.660

Overtime premium

0.250

Statutory working hours

1.000

Lower bound of hours worked

0.850

Upper bound of hours worked

1.300

Inflation rate

0.020

Trend productivity growth

0.000

AR (1) coefficient for aggregate component of
productivity

0.700

S. D. of innovations for aggregate component

0.015

AR (1) coefficient for idiosyncratic component of
productivity

0.700

S. D. of innovations for idiosyncratic component

0.150

Probability of no innovations to idiosyncratic component

0.500

Table 2-1: Worker's characteristics(A) JHPS/KHPS sample used in the current study (regular workers, 2003-2017)
Share of answers, %Variables
Male
68.0

Female32.0

Junior highschoolHigh School

2.1

43.7

Junior college
or Technicalschool15.5

RegionHokkaido
4.2
Chugoku
5.9

Tohoku6.7
Shikoku
3.1

Kanto
33.5
Kyusyu10.5

Industry

Construction

Manufacturing

Wholesale andRetail

7.6

21.4

12.2

1-29 pers.

30-99 pers.

100-499 pers.

21.9

16.6

22.0

GenderType ofschoollastattended

Firm size

Observation Individual

University

Graduateschool

35.1

3.5

Chubu
19.2

Kinki
16.9

Medicalservices andWelfare12.2
500 pers. or
more
30.5

Other nonmanufacturing

40,856

8,423

37,334

7,628

40,856

8,423

40,856

8,423

40,423

8,345

46.5
Government
8.9(B) Employment Status Survey (average of 2007, 2012, and 2017 surveys)
Share of answers, %Variables
Male
68.6

Female31.4

Junior highschool or
youngerHigh School

Junior college
or TechnicalschoolUniversity

Graduateschool

5.3

38.2

20.1

32.6

3.9

RegionHokkaido
3.9
Chugoku
5.8

Tohoku7.1
Shikoku
2.9

Kanto
35.4
Kyusyu
10.6

Chubu
17.9

Kinki
16.5

Industry

Construction

Manufacturing

Wholesale andRetail

8.5

22.0

13.6

1-29 pers.

30-99 pers.

100-499 pers.

24.3

13.7

17.3

GenderType ofschoollastattended

Firm size

Medicalservices andWelfare12.5
500 pers. or
more
31.3

Other nonmanufacturing
43.4
Government,
etc.
13.4

Notes: 1. The values shown in Panel (B) are those of regular employees. They are weighted by the number of
employees in the 2007, 2012, and 2017 surveys.
Notes: 2. "Government, etc." shown in firm size in Panel (B) includes national university corporations, independentadministrative agencies, and other national and public offices (public schools and public hospitals, etc.), in
addition to government offices.
Sources: Ministry of Internal Affairs and Communications; Panel Data Research Center at Keio University.

Table 2-2: Descriptive statistics of key variables
Basic Survey on
Wage Structure(2003-2017)

JHPS/KHPS sample used in the current study(2003-2017)
Variables
Monthly earnings(ten thous. yen)Monthly earnings(y/y % chg.)
Bonuses (ten thous. yen)
Bonuses (y/y % chg.)
Hours of paid work(hours/week)
Age
Tenure (year)

Mean

Stdev

10th percentile Median 90th percentile Observation Individual

Mean

31.8

14.8

13.7

30.0

50.0

40,004

8,234

2.9

15.1

-14.3

0.0

22.5

28,442

5,800

80.2
4.5

75.7
47.2

0.0
-41.7

61.0
0.0

197.0
50.0

39,55424,484

8,271
5,149

87.7

43.4

15.0

20.0

45.0

60.0

38,532

8,220

44.6

43.7
14.5

9.4
10.8

30
2

44
12

51
31

40,856
37,836

8,423
7,854

41.4
11.9

32.9

Notes: 1. The statistics of the monthly earnings, bonuses and hours of paid work in the JHPS/KHPS sample exclude
samples above the 99th percentile and below the 1st percentile. The calculating growth rates of monthly
earnings and bonuses (y/y % chg.) are based on the trimmed sample in terms of level, and we show thenumbers that further eliminate outliers (those above the 99th percentile and below the 1st percentile).
Notes: 2. The values in the Basic Survey on Wage Structure are those of regular employees. They are weighted by
the number of employees during 2003-2017.
Notes: 3. Monthly earnings in the Basic Survey on Wage Structure is "contractual cash earnings." Bonuses are"special cash earnings."
Notes: 4. Although the growth rates of monthly earnings and bonuses in the Basic Survey on Wage Structure areavailable, they are not necessarily comparable with the mean of the growth rate of each employee's wage in
the JHPS/KHPS, because they are affected by the composition change of workers. Therefore, the table
does not show the number for those items.
Sources: Ministry of Health, Labour and Welfare; Panel Data Research Center at Keio University.

Table 3: Overall effects of DNWR
Dependent variables
Independent variables

𝛽3

𝛽2

𝛽1

DNWR dummy (𝑋𝑖 ) ×Time dummy for 2013-2017 (𝐷13−17 )DNWR dummy (𝑋𝑖 ) ×Time dummy for 2010-2012 (𝐷10−12 )DNWR dummy (𝑋𝑖 ) ×Time dummy for 2008-2009 (𝐷08−09 )Number of individuals
Number of observations
2
R

Monthly earnings(y/y % chg.)

Bonuses(y/y % chg.)-1.122***-0.147(0.3681)(1.4347)-1.277***-2.169(0.3969)(1.4898)

6.176***

18.88***(0.4567)(1.6740)

4,740
22,0380.0203

3,984
18,7950.0267

Notes: 1. *** denotes statistical significance at the 1 percent level. Values in parentheses indicate standard errors,
clustered at worker level.
Notes: 2. In addition to the independent variables shown in the table, we include industry dummy × year dummy,
tenure, age category dummy, title dummy, labor union dummy, firm size dummy, gender dummy,
dummy for type of school last attended, region dummy, occupation dummy, CPI by region, and hours
worked in the previous year (only for the estimation of monthly earnings). We also include a random
effect for each worker.
Notes: 3. Estimation period is from 2004 to 2017.

Table 4: Robustness check(A) Workers who displayed a strong degree of DNWR are those without any pay cutsin the last three years (looser criterion)
Dependent variable
Independent variable
Alternative DNWR dummy (𝑋𝑖𝑡 ) ×
Dummy for labor market conditions (Y𝑡 )Monthly earnings(y/y % chg.)-1.687***(0.6426)

Number of individuals
Number of observations
R2

5,220
24,3970.0159(B) Workers who displayed a strong degree of DNWR are those whose actual wage
growth exceeded their potential wage growth during the GFC (stricter criterion)
Independent variables

Dependent variable Monthly earnings(y/y % chg.)

Alternative DNWR dummy (𝑋𝑖 ) ×Time dummy for 2013-2017 (𝐷13−17 )-1.189**(0.4902)

Alternative DNWR dummy (𝑋𝑖 ) ×Time dummy for 2010-2012 (𝐷10−12 )-1.260***(0.4686)

Alternative DNWR dummy (𝑋𝑖 ) ×Time dummy for 2008-2009 (𝐷08−09 )7.759***(0.5626)

Number of individuals
Number of observations
2
R

4,740
22,0380.0199Notes: 1. *** and ** denote statistical significance at the 1 and 5 percent levels, respectively. Values in parentheses
indicate standard errors, clustered at worker level.
Notes: 2. In Panel (A), in addition to the independent variables shown in the table, we include industry dummy × year
dummy, tenure, age category dummy, title dummy, labor union dummy, firm size dummy, DNWR dummy,
CPI by region and hours worked in the last year. We also include a fixed effect for each worker.
Notes: 3. In Panel (B), in addition to the independent variables shown in the table, we include industry dummy × year
dummy, tenure, age category dummy, title dummy, labor union dummy, firm size dummy, gender dummy,
dummy for type of school last attended, region dummy, occupation dummy, CPI by region, and hours worked
in the previous year. We also include a random effect for each worker.
Notes: 4. Estimation periods for both estimations are from 2004 to 2017.

Table 5: Backward-looking channel
Independent variable
𝛽4

Dependent variable Monthly earnings(y/y % chg.)

DNWR dummy (𝑋𝑖 ) ×
Positive deviation rate from potential wage
(previous year, 𝐺𝑎𝑝𝑖𝑡−1 1{𝐺𝑎𝑝𝑖𝑡−1≥0} ) ×
Dummy for improvement phases (𝐷10−17 )(2010-2017)
Number of individuals
Number of observations
2R-0.379***(0.0892)
4,400
19,3070.0327

Notes: 1. *** denotes statistical significance at the 1 percent level. Values in parentheses indicate standard errors,
clustered at worker level.
Notes: 2. "Positive deviation rate from potential wage" is a variable that takes the deviation rate of the actual wage
from the potential wage in the previous year only if the deviation rate is positive, and zero otherwise.
Notes: 3. In addition to the independent variables shown in the table, we include industry dummy × year dummy,
tenure, age category dummy, title dummy, labor union dummy, firm size dummy, CPI by region, hours
worked in the previous year, DNWR dummy × time dummy for 2008-2009, DNWR dummy × deviation ratefrom potential wage (previous year), and DNWR dummy × negative deviation rate from potential wage
(previous year) × time dummy for 2010-2017. We also include a fixed effect for each worker.
Notes: 4. Estimation period is from 2008 to 2017.

Table 6: Forward-looking channel

Independent variables
𝛽5

𝛽6

Dependent variable Monthly earnings(y/y % chg.)

DNWR dummy (𝑋𝑖 ) ×
Negative deviation rate from potential wage

0.0186*(previous year, absolute value, 𝐺𝑎𝑝𝑖𝑡−1 1{𝐺𝑎𝑝𝑖𝑡−1 <0}) ×𝑗
Expected growth index (by industry) (𝑌1𝑡 )(0.0100)

DNWR dummy (𝑋𝑖 ) ×
Negative deviation rate from potential wage

-0.662***(previous year, absolute value, 𝐺𝑎𝑝𝑖𝑡−1 1{𝐺𝑎𝑝𝑖𝑡−1 <0}) ×𝑗

Uncertainty index (by industry) (𝑌2𝑡 )Number of individuals
Number of observations
R2(0.0555)
4,400
19,307
0.270

Notes: 1. *** and * denote statistical significance at the 1 and 10 percent levels, respectively. Values in parentheses
indicate standard errors, clustered at worker level.
Notes: 2. "Negative deviation rate from potential wage" is a variable that takes the absolute value of the deviation
rate of the actual wage from its potential only if the deviation rate in the previous year wage is negative,and zero otherwise.
Notes: 3. In addition to the independent variables shown in the table, we include industry dummy × year dummy,
tenure, age category dummy, title dummy, labor union dummy, firm size dummy, CPI by region, hours
worked in the previous year, DNWR dummy × time dummy for 2008-2009, DNWR dummy × deviation ratefrom potential wage (previous year), DNWR dummy × positive deviation rate from potential wage
(previous year) × each index, and deviation rate from potential wage (previous year) × each index. We also
include a fixed effect for each worker.
Notes: 4. Estimation period is from 2008 to 2017.

Figure 1: Flattening of wage Phillips curve(A) Modest growth of scheduled cash earnings for regular workers
y/y % chg.

3

Full-time employees
Part-time employees (hourly scheduled cash earnings)
2

1

0

-1
CY 10

11

12

13

14

15

16

17

18

19

(B) Wage Phillips curve
8hourly scheduled cash earnings, y/y % chg.
83/Q1-09/Q4

y = 4.32x + 2.3

6
10/Q1-19/Q4
4

y = 2.44x - 0.1
2

0

-2
-0.8

-0.6

-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
active job openings-to-applicants ratio, period average=0
Notes: 1. The definitions of quarters for hourly cash earnings are Q1 = March-May, Q2 = June-August,Q3 = September-November and Q4 = December-February.
Notes: 2. Figures of the scheduled cash earnings for establishments in Tokyo with 500 or more employees for 2013/Q12019/Q1 are corrected data based on sample observations. The figures from 2019/Q2 onward are for all such
establishments. Figures from 2016/Q1 are based on continuing observations and the figures before 1990/Q4
are for establishments with 30 or more employees.
Source: Ministry of Health, Labour and Welfare.

Figure 2: Wage functions for individual workers andcross-sectional wage-growth distributions in calibrated model(A) Wage functions for individual workers
1.3

wage level in the current period, 𝑊𝑖𝑡

Forward-looking
channel

1.2

wage level in the previous period: 𝑊𝑖𝑡−1
1.1

Backward-looking
channel

1.0

0.9With DNWR (𝑊𝑖𝑡 )Only with forward-looking channel (𝑊𝑖𝑡∗ )0.8
Without DNWR (𝑊𝑖𝑡∗∗ )
0.7
-0.3

-0.15

0
labor demand, ln 𝐴𝑖𝑡(B) Cross-sectional wage-growth distributions(a) With DNWR
probability density

wage growth, y/y% chg.

0.15(b) Without DNWR
probability density

wage growth, y/y% chg.

0.3

Figure 3: Wage Phillips curve in calibrated model(A) Wage Phillips curve obtained in stochastic simulation
wage growth, y/y % chg.

○ With DNWR
＋ Without DNWR

hours worked, average=100(B) Contribution of the two separate channels to flattening of wage Phillips curve
4.5

wage growth, y/y % chg.

Forward-looking
channel

4.0

3.5
3.0

Backward-looking
channel

2.5

2.0
1.5
1.0

0.5
0.0
96

97

98

With DNWR

99
100
101
hours worked, average=100
Only with forward-looking channel

102

103

104

105

Without DNWR

Notes: 1. Panel (A) shows the scatter plot obtained from the stochastic simulation lasting one thousand periods.
sNote: 2. Panel (A) and (B) show the quadratic fitted curves in the stochastic simulation.
sNote: 3. The degree of DNWR, c, is equal to one for "with DNWR," while c is equal to zero for "without DNWR."

Figure 4: Generalized impulse responses in calibrated model(A) Responses of wage growth to an one percentage point decline in expected growth(b) Expected growth(a) Wage growth
0.0

deviation from baseline, % points

0.0

-0.2

-0.2

-0.4

-0.4

-0.6

-0.6

-0.8

-0.8

-1.0

-1.0

-1.2

-1.2

-1.4

-1.4
-1

0
years

1

2

3

4

With DNWR

5

6

deviation from baseline, % points

-1

7

0
years

1

2

Only with forward-looking channel

3

4

5

6

7

Without DNWR(B) Responses of wage growth to a rise in uncertainty(a) Wage growth(b) Uncertainty (aggregate component)
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2

deviation from baseline, % points

1.2

deviation from baseline, % points

1.0

0.8
0.6
0.4
0.2
0.0
-1

0
years

1

2

3

4

5

6

7

-1

0
years

1

2

3

4

5

6

7

Note: Panel (B) shows the responses to a rise in the standard deviation by 1 percentage point for aggregate comoponentof exogenous productivity and 10 percentage points for idiosyncratic one. These shocks are equivalent todoubling the baseline value of each parameter. The details are described in Footnote 8.

Figure 5: Comparison with the statistics on aggregate wage andthree phases of labor market condition after GFC(A) Average monthly earnings: comparison of JHPS/KHPS and official aggregate statistics
105

CY 2007=100
JHPS/KHPS (workers whose pay-period is monthly, aggregate level)
Basic Survey on Wage Structure (full-time employees)

Monthly Labour Survey (full-time employees)

100

95
CY03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

18

(B) Three phases of labor market condition after GFC
1.8

s.a., %

s.a., ratio
Sample periods of
JHPS/KHPS

1.6

6.0

5.0

1.4
1.2

4.0

1.0
3.0

0.8
Active job openings to applicantsratio (left scale)
Unemployment rate (right scale)

0.6
0.4
0.2

Phase 1
2008 - 2009

Phase 2
2010 - 2012

Phase 32013 - 2017

2.0

1.0

0.0
0.0
CY 04
08
10
13
18
Note: Figures for the JHPS/KHPS are the average among the monthly earnings of workers whose pay-period ismonthly. Those for the BSWS are "contractual cash earnings." Those for the Monthly Labour Survey are"contractual cash earnings" and those for establishments in Tokyo with 500 or more employees for 2013-2018
are corrected data based on sample observations. Shaded areas in Panel (A) indicate recession periods.
Sources: Ministry of Health, Labour and Welfare; Ministry of Internal Affairs and Communications;
Panel Data Research Center at Keio University.

Figure 6: Effect on growth of monthly earnings at aggregate level(A) Effect on growth of monthly earnings for regular workers at aggregate level
0.0

effect on y/y % chg., ann. avg., % points-0.2-0.38%P-0.43%P-0.4［ -0.62－-0.13］［ -0.70－-0.17］
-0.6

-0.8
CY

2010-20122013-2017(B) Robustness check0.0

effect on y/y % chg., annual average from 2010-2017, % points

-0.2
-0.4

-0.20%P[ -0.35－-0.04]-0.6-0.40%P-0.8[ -0.65－-0.15]
-1.0
-1.2

-0.58%P[ -1.01－-0.15]-1.4
Under looser criterion

Baseline estimation

Under stricter criterion

Notes: 1. The values shown in Panel (A) = coefficients shown in Table 3 × the share of workers who displayeda strong degree of DNWR in the sample during 2008-2009.
Notes: 2. The values shown in Panel (B) = coefficients of estimation results × the share of workers who displayeda strong degree of DNWR among the sample. When calculating the values, we use the share in the sample
during 2008-2009 in the baseline estimation and the estimation under the "stricter criterion," and use theshare in the sample in each year under the "looser criterion."
Notes: 3. The values shown in Panel (B) are the weighted averages of the effects during 2010-2012 and those during
2013-2017.
Notes: 4. The bars represent the 95 percent confidence intervals of the estimates.

Figure 7: Distribution of deviation rate of actual wage
from potential wage(A) During 2008-2009(Green: workers with a strong degree of DNWR, White: workers with a low degree)
probability density, %deviation rate, %2008-2009

Workers witha strong degree of DNWR

Workers witha low degree of DNWR

Average2.7-0.1

Skewness

0.3

-0.2

(B) During 2013-2017
probability density, %deviation rate, %2013-2017

Workers witha strong degree of DNWR

Workers witha low degree of DNWR

Average0.8-0.1

Skewness

-0.1

-0.1

Figure 8: Indexes used for estimation on forward-looking channel(B) Index of uncertainty(A) Index of expected growth40

y/y % chg.

6s.d. of d/d, %All industry

20
0

4

-20
-40

2
Trend of profit forecast (all industry)-60

Profit forecast

-80
CY 04

Current profit
06

08

10

12

14

16

18

0
CY 04

(Reference) Alternative indexes(A) Annual Survey of Corporate Behavior
3.0

real, ann., %

2.5
2.0

08

10

12

14

16

18

(B) Economic Policy Uncertainty Index
500

Forecast of real growth rate of demand intheir industries for the next five years(manufacturing)06

avg. from 1997 to 2015=100
Japan

400

GlobalSame above (non-manufacturing)
300

1.5
200

1.0

100

0.5

0.0
FY 04

06

08

10

12

14

16

18

0
CY 04

06

08

10

12

14

16

18

Notes: 1. The index shown in Panel (A) is the profit forecast of firms taken from the Short-Term Economic Survey ofEnterprises in Japan. We use the survey results during the March 2003 to December 2018, and we remove thecyclical component (within five years), extracted using the filter by Christiano and Fitzgerald (2003).
The value in each year is the average of the trend component among those of the March, June, September,and December surveys. We calculate the index for the following five industries: manufacturing, wholesale
and retail, construction, medical services and welfare, and other non-manufacturing.
Notes: 2. The index shown in Panel (B) is the historical standard deviation of daily stock returns for the five industries
derived from TOPIX-17.
Notes: 3. The global index shown in Panel (Reference)-(B) is the GDP-weighted average of indexes for 20 countries
based on PPP-adjusted GDP.
Notes: 4. Shaded areas indicate recession periods.
Sources: Bloomberg; Cabinet Office; Economic Uncertainty Index; Bank of Japan.

Appendix Table 1: Estimation result of Mincer wage equation
Dependent variable
Independent variables

Monthly earnings(natural log)

Unemployment rate (reversed-sign, 𝑌𝑡 )0.0199***(0.0028)

Tenure0.0179***(0.0014)Square of tenure-0.000235*** (0.0000)
0.0816***0.146***
0.191***
0.227***
0.254***
0.255***
0.228***(0.0161)(0.0202)(0.0222)(0.0243)(0.0263)(0.0282)(0.0305)

Title dummy (1 = with title)

0.0415***(0.0042)

Labor union dummy (1 = member)

0.0117**(0.0059)

30-99 pers.
100-499 pers.
500 pers. or more
Government

0.00865
0.01660.0235**0.0159(0.0083)(0.0103)(0.0120)(0.0119)

Service worker
Manager
Specialized or technicalworkerClerical worker
Salesperson
Agriculture, forestry,
fishery and mine worker-0.0401***
0.0236***(0.0100)(0.0072)-0.00784(0.0087)-0.0186***-0.0248***(0.0069)(0.0086)-0.0185(0.0590)

Wholesale and retail
Construction
Medical services and welfare
Other non-manufacturing-0.01400.0295-0.0004-0.0116(0.0194)(0.0286)(0.0304)(0.0163)

Labor productivity by industry-0.00009(0.0003)

CPI by region-0.0013(0.0011)Age category dummy(Base = 24 y/o or less）

Firm size dummy(Base = 1-29 pers.)

Occupation dummy(Base = Others)

Industry dummy(Base = Manufacturing)Number of individuals
Number of observations
2R

25-29 y/o30-34 y/o35-39 y/o40-44 y/o45-49 y/o50-54 y/o55-59 y/o

7,294
34,0730.305

Notes: 1. *** and ** denote statistical significance at the 1 and 5 percent levels, respectively. Values in parentheses
indicate standard errors, clustered at worker level.
Notes: 2. In addition to the independent variables shown in the table, we include a fixed effect for each worker.
Notes: 3. Estimation period is from 2003 to 2017.

Appendix Table 2: Robustness check on treatment ofsample added after 2009
Dependent variable
Independent variables
𝛽3

DNWR index (𝑋𝑖 ) ×Time dummy for 2013-2017 (𝐷13−17 )Monthly earnings(y/y % chg.)-1.075***(0.3614)𝛽2

DNWR index (𝑋𝑖 ) ×Time dummy for 2010-2012 (𝐷10−12 )-1.346***(0.3960)𝛽1

DNWR index (𝑋𝑖 ) ×Time dummy for 2008-2009 (𝐷08−09 )6.176***(0.4568)

Number of individuals
Number of observations
2
R

4,740
22,0380.0203

Notes: 1. *** denotes statistical significance at the 1 percent level. Values in parentheses indicate standard errors,
clustered at worker level.
Notes: 2. In addition to the independent variables shown in Table, we include industry dummy ×year dummy,
tenure, age category dummy, title dummy, labor union dummy, firm size dummy, gender dummy,
dummy for type of school last attended, region dummy, occupation dummy, CPI by region, and hours
worked in the last year. We also include a random effect for each worker.
Notes: 3. Estimation period is from 2004 to 2017.
Notes: 4. For the sample before 2008, we use the DNWR dummy based on pay cuts during the GFC as in thebaseline model. For the sample added after 2009, we define the DNWR index as the period average of
DNWR dummy based on pay cuts in the past three years.