Discussion Papers In Economics
And Business

Deflation and Downward Nominal Wage Rigidity: Evidence from Japan

Kengo Yasui
Shinji Takenaka
Discussion Paper 05-21

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDeflation and Downward Nominal Wage Rigidity: Evidence from Japan

Kengo Yasui
Shinji Takenaka

Discussion Paper 05-21

July 2005

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDeflation and Downward Nominal Wage Rigidity: Evidence from Japan *Kengo Yasui †Graduate School of Economics, Osaka University, Osaka, Japanyasui@iser.osaka-u.ac.jp
Shinji Takenaka
Graduate School of Economics, Osaka University, Osaka, Japan
stakena@iser.osaka-u.ac.jp

July 2005

Abstract
This study empirically analyzed downward nominal wage rigidity using time-series
cross-industry data from 1981 to 2002, a period which included deflation. We foundthat nominal wages remained rigid to downward pressure by expected deflation andlabor-market tightness. Estimations according to worker age categories revealed
downward wage rigidity with deflationary pressure for most age categories. Wagerigidity during labor-market tightness was greater for younger workers.

JEL Classification Numbers: E24, E31, J30.
Keywords: wage rigidity, nominal wage, deflation, unemployment, Japan*We are especially grateful to Fumio Ohtake for his constructive comments and continuous encouragement.

We thank Hiroyuki Chuma, Souichi Ohta, and Masayuki Takahara for their helpful comments. Of course, weare responsible for any remaining errors. This research was financially supported by a Grant-in-Aid for theJapan Society for the Promotion of Science (JSPS) Fellows provided by the Ministry of Education, Culture,
Sports, Science and Technology, of Japan.
†

Author for correspondence; Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka,

Ibaraki, Osaka 567-0047, Japan1. Introduction

The unemployment rate in Japan has remained high since the late 1990s. One possible
cause may be downward nominal wage rigidity. Downward rigidity, or “stickiness”, can becharacterized by the following: (1) nominal wages respond asymmetrically to upward anddownward pressures, and (2) downward wage adjustments are slower than upward wage
adjustments. Downward rigidity can remarkably obstruct regulating functions in a labor market
through nominal wage adjustments and can keep unemployment rates high. Figure 1 illustrates
the recent sustained deflation in Japan, which should have placed downward pressure on
nominal wages. Such a situation provides important information on the regulating functions of
nominal wages.
Most previous studies on downward nominal wage rigidity have used microdata (e.g.,
McLaughlin, 1994, 1999; Lebow et al., 1995; Card and Hyslop, 1996; Kahn, 1997; Altonji and
Devereux, 1999; and Kuroda and Yamamoto, 2003a, 2003b). Microdata can help explain
downward nominal wage rigidity as related to individual workers. However, such data are
insufficient when discussing downward wage rigidity for the entire labor market. For instance,even if an individual’s nominal wage is downwardly rigid, he or she can be replaced withanother worker of equal ability and lower wage, so that wages are actually downwardly flexible
for the entire labor market. This replacement effect would not necessarily be obvious throughobservations of individual workers. Therefore, we investigated aggregate data to determine thedownward flexibility of wages within the overall labor market.
Two main factors cause nominal wage fluctuations in the labor market: (1) the tightnessof the labor market and (2) variation of the expected inflation rate, as implied by thewage-version Phillips curve. Using this curve as a framework, we analyzed whether nominal
wages have responded sufficiently to pressures presented by the above factors.

1

We also verified differences in downward rigidity across various age categories. In
recent years, Japan has witnessed a disparity in unemployment rates by age. Younger workers
in particular have faced higher unemployment rates. This condition can create serious social
problems (see figure 2) and may relate to downward nominal wage rigidity. Therefore, we
examined the existence of more severe downward rigidity in the young-worker labor market.
This paper is organized as follows: in section 2, we introduce the wage-version Phillips
curve and its relevance to this study; in sections 3, 4, and 5, we present estimation equations, thedata set, and estimation results, respectively. Conclusions are presented in section 6.

2. Wage-Version Philips Curve

2.1. Phillips Curve and Downward Nominal Wage Rigidity
First, we will briefly introduce the Philips curve, which is a key to this study. The
wage-version Philips curve shows the hyperbolic, inverse relationship between theunemployment rate and the rate of nominal wage change. The curve implies that the rate of
nominal wage change increases as the labor market tightens and falls as the labor market
loosens. Therefore, this curve characterizes adjustment mechanisms of the economy-wide labormarket by indicating the trade-off between employment and stable wage changes.
As Friedman (1968) noted, however, the labor market should be adjusted not by
nominal wages, but by the real wages, unless workers have monetary illusions. Anotherviewpoint sees the actual Philips curve as shifting with the expected inflation rate, althoughbasic Philips curve methods ignore expectation effects. In other words, the unemployment rateshould be independent of the long-term rate of nominal wage change, which the expected
inflation rate equates to its actual value. The unemployment rate will then reach a unique value2

determined by the real factors of labor market. This rate is referred to as the natural rate ofunemployment. By contrast, in the short term, when the expected inflation rate differs from theactual rate, the relationship between the unemployment rate and the rate of nominal wagechange will create a downward-sloping curve for each expected inflation rate. This is called theshort-run Philips curve.
Second, the Phillips curve form should be distinguished from a straight line, with thefocus placed on the curve’s non-zero curvature, as well as its negative slope 1 . The Phillips
curve is defined by its appearance, e.g., a steeper slope on the left side of the natural
unemployment rate and a gentler slope on the opposite side. To understand the ramifications of
this shape, suppose that the unemployment rate is greater than its natural value. If the slope on
the right side were nearly equal to that on the left, then the rate of change in the nominal-wage
would be much smaller than what the actual curve indicates. The labor market would then soon
adjust without any wage rigidity, and the unemployment rate would decrease and approach its
natural state. By contrast, downward wage rigidity would cause the wage to behave differently
once the unemployment rate increased beyond its natural value. For every marginal increase in
the unemployment rate, the nominal wage would decrease at a much slower rate, below acertain value. The slope of the Phillips curve would therefore become much gentler, reflecting
this relation. In other words, the wage would reflect the nonlinearity of the changing slopes ofthe left- and right-hand areas bounded by the natural unemployment rate. In summary, thePhillips curve would have non-zero curvature only if the nominal wage bore the downward
rigidity.

2.2. Downward Nominal Wage Rigidity and Recent Deflation in Japan
To our knowledge, only Kimura and Ueda (2001) have analyzed the recent nominal

1

Kurosaka and Hamada (1984) and Genda and Kondo (2003) provided similar explanations of this issue.

3

wage rigidity in Japan using aggregate data from the deflationary periods 2 . They examined thenonlinear relation between the actual rate of change in the nominal wage and the “notional”
rate, derived from the wage-version Phillips curve equation. The nonlinearity was thought toresult from the disparity between the notional and actual nominal wage change rates if actual
rates failed to decrease sufficiently to equal the negative, notional values. Conversely, the actual
rates were assumed to equal the notional rates when both rates were positive and wages weregoing to increase. Consequently, Kimura and Ueda (2001) determined the nominal wage
downward rigidity defined by the above disparity, using time-series cross-industry data from1976 to 1998. By contrast, applying the same method to aggregated time-series data from 1976
through 2000 failed to confirm downward rigidity throughout the period. Integrating thoseresults, they concluded that wages should converge at their equilibrium levels after a time lag,although downward rigidity had been temporarily observed because of labor’s monetaryillusions under unfamiliar zero or negative inflation rates.
However, two problems from this study must still be solved. First, two different sourcesof downward pressure on wages were combined: the expected inflation rate and theunemployment rate. The authors’ conclusions, however, emphasized only the role of the former
factor in the disappearance of wage rigidity in recent years. Although downward pressure
exerted by expected deflation began in the late 1990s, they postulated its prevalence before that
period and paid little attention to how unemployment rates affected nominal wages. That is, thedownward pressure observed from the time-series cross-industry data until the late 1990s
should have come solely from an increase in the unemployment rate. Therefore, it is2

By contrast, many other studies found a nonlinear relation between the labor supply-and-demand situationand the rate of nominal-wage change. These studies, such as one by Nishizaki and Watanabe (2000), useddata from the pre-deflationary period in Japan. However, Nishizaki and Watanabe (2000) has two
shortcomings. First, their initial estimates were apparently biased by sample selection, depending onwhether the value of the consumer price index inflation rate, adopted as the dependent variable, was three
percent or more. Second, subsequent analysis emphasized a slope decrease in linear Phillips curves for a
few consecutive periods as evidence of the nonlinear relation, although those separately estimated curves
could have lacked mutual coincidence and thus give only indirect evidence of nonlinearity over the period.

4

problematic to have concluded that a greater familiarity with zero or negative inflation rates
from 1999 on suddenly enabled the nominal wage to begin adapting flexibly to the expected
deflation. In principle, it seems misleading to have assumed that the expected inflation rate andthe unemployment rate exerted equal influence on the actual nominal wages with regard to
downward rigidity. Our analysis, by contrast, contained no such assumptions.
Second, as Ohtake (2001) pointed out, Kimura and Ueda (2001) failed to consider theeffect of substituting part-time workers earning lower wages for better-paid regular employees,
although that replacement could have hidden persistent rigidity in the nominal wages earned byregular workers after 1999. Since Kimura and Ueda’s macro-level aggregated data averaged theearnings of regular employees and part-time workers, the nominal wage could have appeared
flexible in the economy-wide labor market. The examination of downward rigidity requires
data that identify the wages of only regular employees since 1999.
To solve these problems, we used time-series cross-industry data to examine thebehavior of nominal wages in Japan; similar data were also used by Kimura and Ueda (2001),
but only until 1998, during the period 1981-2002. Our analyses were based primarily on direct
estimations of the Phillips curve. We were able to identify sources of downward nominal wage
rigidity using the estimated relation between each explanatory variable and the rate of change in
the nominal wage. Using this method, nonlinearity of the nominal wage with regard to theunemployment rate, one of the explanatory variables, would prove the non-zero curvature of
the Phillips curve. Similarly, the nonlinearity of nominal wage in regard to the expected
inflation rate would show downward rigidity in the nominal wage with the expectation thatsuch a condition would cause deflationary pressure. Different reactions to inflationary anddeflationary pressure, implied by the above expectation concerning nonlinearity, would suggest
asymmetric shifts of the Phillips curve, depending on whether the directions were upward or
downward.

5Note that our analysis contains no strong assumption regarding the perfect adjustmentof nominal wages faced with upward pressure, as was postulated by Kimura and Ueda (2001).
The estimation, detailed in the next section, had no need for such an assumption because it
tested nonlinear influences directly (i.e., the expected inflation rate and unemployment rate) on
the nominal wage. Note also that the remaining part of this paper adopts the following criterion
for determining the existence of nominal wage rigidity: the response of the nominal wage todownward pressure was significantly smaller than its reaction to the upward pressure. The next
section will describe the specific estimation methods, which were based on the arguments
presented in the first two sections.

3. SpecificationsFirst, we postulated a basic Phillips-curve-type equation (1) with the rate of change in
the nominal wage as the dependent variable. The explanatory variables π te , U t , and y i ,t denotethe expected inflation rate, unemployment rate, and industry-specific shock measured by therate of change in the industrial real GDP, respectively:

wi ,t = α1π e t +β1U t +γyi ,t + ci + ui ,t .

(1)

Kimura and Ueda (2001) also used these specifications to explain the rate of nominal wagechange in the absence of nominal-wage downward rigidity. In the above equation, the expected
inflation coefficient α 1 should be positive, and the unemployment rate coefficient β 1 should be
negative. Furthermore, α 1 is thought to be unity if the nominal wage has no downward rigidity
with deflationary pressure.
6

The sign of the industry-specific shock coefficient γ can be either positive or negative.
That effect is predictable as long as the nominal wage behavior coincides with the real wage
through perfect correspondence with the expected inflation rate. For example, the coefficient
representing the real GDP of each industry, γ, has to be positive when real wages areprocyclical. For counter-cyclical behavior in the real wage, γ should be negative. Literature on
the relationship between the real wage and the business cycle provides insight into the influenceof each industry’s business cycle. An array of related empirical research has found both signs ofthe γ coefficient, and both possible effects have been theoretically supported by many otherstudies 3 .Recent works by Sumner and Silver (1989) and Abraham and Haltiwanger (1995)
pointed out the correspondence between the inflation rate and real-wage responses to thebusiness cycle. That is, when the former moved procyclically, the latter changed
counter-cyclically and vice versa. As indicated in Figure 3, the inflation rate moved
procyclically during the observation period in this study; Therefore, γ was assumed to be
negative as long as α1 equaled unity. However, γ could be positive or negative if α1 differedfrom unity due to nominal wage rigidity.

wi ,t = α1π e t +α2 d tπ e t +β1U t +γyi ,t + ci + ui ,t(2)

Equation (2) also adds an interaction term between the expected inflation π te and thedummy variable d t , which indicates whether the expected inflation rate is below zero. Adding
this variable enabled us to examine the symmetry of the nominal wage response to any
downward or upward pressure by the inflation rate. In other words, downward wage rigidity
would be confirmed if the coefficient α 2 in the interaction between the deflationary dummy

3

Abraham and Haltiwanger (1995) reviewed these studies particularly.

7

d t and the expected inflation π te was estimated to be significantly negative and sufficiently

large in absolute value to eliminate the effect of α 1 . In addition, the unemployment rate
coefficient β 1 was expected to be negative; the industry-specific shock coefficient γ wasdeemed unpredictable using the same argument given in specification (1).

wi ,t = α1π e t +β21+γyi ,t + ci + ui ,tUt(3)

Equation (3) replaced the unemployment rate variable U t with its inverse. If thatspecification had a higher goodness-of-fit index score than that from equation (1), the responseof the nominal wage to the unemployment rate should be regarded as non-linear rather thanlinear. The nonlinearity implies the different slopes of the Phillips curve in the left and rightareas divided by the natural unemployment rate. Further, nonlinearity provides evidence ofwage rigidity against the downward pressure generated by looseness in the economy-wide labormarket, as discussed previously. In addition, stronger nonlinearity should lead to a greater value
for the inverted unemployment rate coefficient β 2 . Using the same argument used for equation(1), α 1 was expected to be positive, and γ estimations were unpredictable a priori.

wi ,t = α1π e t +α2 d tπ e t +β21+γyi ,t + ci + ui ,tUt(4)

Equation (4) addresses not only the symmetry of effects from both positive and negative
expected inflation rates, but also the non-linear influence of the unemployment rate.

8

4. Data and Expected Inflation Rate

Our analyses primarily used industry-specific time-series data concerning changes in
the nominal wage and industry-specific shock measured by the rate of change. Kimura andUeda (2001) used a similar method. Our estimation, based on time-series cross-industry data,also used macroeconomic data on expected inflation and unemployment rates. We usedaveraged wage data and wage data classified into five groups based on worker age: 15-24,
25-34, 35-44, 45-54, and 55 and over 4 . Descriptions of the data sources and variables follow.
First, the nominal wages were evaluated using hourly wages including bonuses
calculated from data on “contractual cash earnings”, “annual special cash earnings”, “annual
number of scheduled hours worked”, and “annual number of overtime worked”. These data
categories were created from the definitions provided in the Basic Survey on Wage Structure or
the so-called The Japanese Wage Census.
Second, based on the static expectation, the inflation rate of each prior year was adopted
as a proxy for the expected inflation, as in Kimura and Ueda (2001). We chose this expectation
based on an examination of adaptive expectation. The “short-cut method” was used to obtain
the worst fitness for models with larger numbers of lagged variables 5 . The best fitness wasmarked only when the one-term lag was thought to have explained the expectation. The results
should justify the use of static expectation and the exclusion of adaptive expectation. Kitamura
et al. (2003) and Genda and Kondo (2003) also noted that adaptive expectation poorly

4
5

See the appendix for details on the data for each age category.
The short-cut method regresses lagged explanatory variables with linearly decreasing weights for longer
time lags and clarifies the optimal number of such variables with regard to the goodness of fit. Specifically,
the weight for the ith term is defined as wi = ( m + 1 − i ) /[m( m + 1) / 2] , where m signifies the maximummdegree of lag. Each explanatory variable has the following weighted average

∑w X
i =1

i

t −i

for a particular m.

The simple regression of Xt using the above regressors indicates the optimal degree of m, introducing themodel with the highest fitness.

9explained the expected inflation rate in their research on a non-accelerating inflation rate ofunemployment (NAIRU) Phillips curve in which the inflation rate was the dependent variable.
The inflation rate was represented by the GDP deflator in the Annual Report on National
Accounts, as used by Kimura and Ueda (2001) 6 .
Third, each annual unemployment rate used here equaled the “ratio of unemployed in
the labor force” as given in the Monthly Report on the Labor Force Survey. The
industry-specific shock was evaluated using the rate of change reported in the “Gross domestic
product classified by economic activities (2001-)” or the “Gross domestic product by kind of
economic activity (1980-2000)” publications in the Annual Report on National Accounts. Data
were collected for 1981 through 2002 for 25 industries 7 . Descriptive statistics are given in the
appendix.

5. Response of the Nominal Wage Rate of Change

5.1. Estimated Results using Averaged Data for all Regular Employees
Using the average wage for all age groups, pooled ordinary least squares (OLS), random
effect (RE), and fixed effect (FE) estimators were obtained from regression equations (1)through (4). The Breusch-Pagan test rejected the null hypothesis of zero variance for fixed
effects for all the equations at the 5% significance level. Consequently, the pooled OLS model
could be rejected for all of the models. The Hausman tests did not reject the null hypothesis(i.e., no correlation between the fixed effect and explanatory variables) for any of the regression
6

The use of the CPI, instead of the GDP deflator, did not affect our conclusions. Since the absolute values of
the CPI during the deflationary period were smaller than those of the GDP deflator, a significant change wasobserved only in the absolute value of the interaction term between the expected inflation and the
deflationary dummy.
7
See the appendix for industry classifications. The study period (1981 to 2002) was limited due to the10equations, even at the 10% significance level. Therefore, the RE model was adopted. Its
estimation results are briefly explained below and summarized in Table 1.
Model (1) produced a positive value for the expected inflation coefficient α1; however,its level differed substantially from unity, indicating that wages did not fully behave as real
wages. The effects of unemployment (β1) and industry-specific shock (γ) were estimated to be
negative. The latter, showing the negative but insignificant influences of industrial GDP, werealso confirmed by specifications (2), (3), and (4).
Second, the interaction term between the deflationary dummy and expected inflation
produced a significantly negative estimated α2 by equation (2). Moreover, the marginal effect of
expected inflation (α1) approached unity more closely than α1 in model (1). The absolute valueof estimated α2 was large enough to eliminate the effect of expected inflation (α1); this result
showed that wages had not responded to deflation pressure. In other words, while positive
inflation was expected, the wages behaved as a real variable to a certain degree in response toreal economic factors. Conversely, wage behavior showed downward rigidity with expected
deflation and therefore played an insufficient role as a labor-market adjustment factor.
Third, the estimation results from models (1) and (3) indicated a higher significance of
β2 in (3) than β1 in (1) and a higher coefficient of determination from (3) than from (1). Model(3) estimated coefficient β2 from the inverse of the unemployment rate as an explanatory
variable, while model (1) evaluated β1 based on the unemployment rate itself. Hence, the wagechange should have reacted non-linearly rather than linearly to the unemployment rate. There
should have been downward rigidity in the nominal wage change with a real factor, i.e., thelabor supply-and-demand situation. The same point can be drawn from comparing the results of(2) and (4). From regression (4), however, the estimated expected inflation coefficient (α1) was
far from unity, and the counterpart of the interaction term (α2) had a smaller absolute value. Thisavailability of real GDP data for each industry at the time of writing.

11

result might reflect a possible correlation between expected inflation and the unemployment
rate (U). Introducing the inverse of the latter could weaken the nonlinear influences of those
two variables.
A main finding was that the nominal wage made no response to deflationary
expectations; such rigidity thereby raised the real wage. In other words, the Phillips curve
shifted upward under such an expectation, although it theoretically should have moved
downward. Now, it can be shown how the unemployment rate would have behaved if nominal
wage adjustment had worked under deflation in the same way it changed under inflation. Thatis, the following simple calculation based on the result of (4) can show the hypothetical value ofU when α2 = 0. We based this simulation on unemployment rates from 1999-2002 because thecalculation requires a one-period lagged variable of expectation. Recall that the consecutive
deflationary period began in 1998 and was indexed by the GDP deflator. The average inflationfrom 1998 to 2001 equaled –1.265%; the coefficient of interaction between the deflationary
dummy and expected inflation (α2) was estimated to be –1.476. Therefore, the Phillips curveshould have, on average, shifted downward by 1.867% (= 1.265–1.476) during the period. Any
downward shift of a negatively sloped Phillips curve would reduce the unemployment if theidentical rate of nominal wage change were then realized. Second, the mean unemployment rate(U) for 1999-2002 was 4.95%, while the estimated coefficient of the inverse of U equaled
24.723. The U* denoted the unemployment rate without wage rigidity. Then, the following
equality could be derived from model (4): (1/4.95) × 24.723 + 1.867 = (1/ U*) × 24.723. The
equation revealed that U* = 3.60%. Since the above procedure was based roughly on thewage-unemployment correlation underpinning the Phillips curve, room was left for
improvement, such as dynamic modeling of the process.

125.2. Estimation Results for Each Age Group
This section examines the estimations for each age group. The Breusch-Pagan and
Hausman tests were applied to equations (1) through (4) for every age category, as in theprevious estimations. The former test rejected the null hypothesis of zero fixed-effect varianceabout all age groups, but model (4) revealed a 5% significance level for the 55-and-over age
category. Nevertheless, the p-value in that exceptional case did not exceed 0.0501. By contrast,
the latter test never rejected the hypothesis that the fixed effect is uncorrelated with the
explanatory variables even at the 10% significance level. The RE estimation was then applied
to every age class; tables 2 through 6 show the outcomes.
The model (2) results for each age category resulted in a significantly negative
coefficient for the interaction between the deflation dummy and expected inflation α2; the wage
showed downward rigidity with deflation. Except for the 25-34 age category, the results also
showed that the influence of expected inflation α1 tended to approach unity much more closelythan the α1 estimated for all age groups. The coefficients for the 45-54 and 55-and-older age
categories were especially close to unity: 0.877 and 0.893, respectively. Testing the null
hypothesis that estimates would equal one revealed p-values of 0.324 and 0.506, respectively.
This result implies that the nominal wage responded somewhat flexibly to expected prices
when positive inflation was predicted. The data were separated by age groups to clarify thetheoretical relationship between the nominal wage and expected inflation for each age group.
By model (4) the coefficient representing the interaction between the deflation dummy
and expected inflation, d t π e t , was significantly negative for all age categories except the
55-and-older category; this indicates downward wage rigidity with deflation. The deflation rate
coefficient α1 was far from unity with weaker non-linearity than that estimated using the
averaged total for all age groups. Here, the insignificant estimate for the 55-and-older category
could indicate flexible adjustment of the nominal wage during the deflationary period, as
13

opposed to the contradictory result obtained by model (2) and described above. Considering
these two opposite effects, no decisive argument can be derived concerning this age group.
The replacement of explanatory variable U, the unemployment rate, with its inverse
value improved the performance of the estimation models. Comparing the R2uared and t-value
on each regressor between the results from models (3) and (1), the estimates using (3) werehigher than those using (1) for most age groups. Similar results were obtained on comparing
specifications (4) and (2). While equations (1) and (2) included the unemployment rate U itself
as an explanatory variable, (3) and (4) used its inverse value. The same findings were obtained
for all age groups. However, for the 55-and-older category, the performance of (3) was poorer
than that of (1); similarly, model (4) performed worse than (2). Therefore, the possibility of
downward rigidity with unemployment rate could almost be ignored for that age category.
Table 7 contrasts the estimated inverse unemployment rate (β2) coefficients for all age
categories. Greater values indicate stronger nonlinearity of the nominal wage with the
unemployment rate. The results from both (3) and (4) show large estimated values for the 15-24
age bracket, but small values for the 35-44 and 45-54 age categories. These results suggest
stronger downward rigidity for workers aged 15 to 24, which can be considered a reason for the
recent rise in unemployment among young workers. The effects of downward rigidity on
unemployment in the 55-and-over category can be regarded as linear, as mentioned above,
although the corresponding estimates were greater than those for the 35-44 and 45-54 age
categories.
Strong wage rigidity for those aged 15-24 was confirmed by the higher inverted
unemployment rate coefficient; this result might be explained by a greater proportion ofworkers in their early 20s, as opposed to those under age 19. In other words, the increasing
sample weight for the early 20s of relatively higher wages could have raised the mean wage forthe 15-24 age groups and caused the mean wage to appear rigid. To examine this possibility, we
14

analyzed younger-worker subcategories as follows. First, the 15-24 age category was divided
into the three age subcategories: 15-16, 17-18, and 19-24 8 . Second, regression analyses for thethree categories were carried out using the processes described above. Model (3) estimated theinverse unemployment rates as 57.759, 28.781, and 41.796, respectively, for each group; model(4) provided estimates of 57.920, 34.397, and 41.839. These estimates were greater than thosefor the same coefficient estimated for groups aged 25 and over (Figure 7). This result proves thestronger downward rigidity for all three under-24 subgroups. Thus, the greater numbers ofworkers in their early 20s in the Japanese labor market is not the reason for the nominal wage
rigidity in the wages of the 15-24 age groups, contrary to the suggested alternative.

6. Conclusions

This study examined downward nominal wage rigidity using data from Japan observed
during a period that included deflationary periods. Estimates were based on time-series
cross-industry data from 1981 to 2002. We found that nominal wages were rigid to downward
pressure by both expected deflation and the unemployment rate. Estimates for each age
category confirmed the existence of downward rigidity to deflationary pressure in all thegroups, although rigidity for the 55-and-older category was ambiguous. Considering thoseeffects, it can be concluded that mild inflation is preferable from the standpoint of labor market
adjustments. Moreover, the nominal wages for workers in younger age categories were found to
be more downwardly rigid to the real pressure of the unemployment rate. Therefore, downward
rigidity likely contributed to rising youth unemployment in recent years. Further study using
dynamic analysis should examine the extent to which downward rigidity has raised the8This classification follows that adopted by the Basic Survey on Wage Structure.

15

unemployment rate.

16

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Ohtake, F., 2001, Prompt Implementation of Active Employment Policy is Necessary(Sekkyokuteki Koyo Seisaku no Jitsugen wo Isoge), Economics, Autumn, Toyo Keizai, pp.
52–58. (in Japanese)
Sumner, S. and S. Silver, 1989, Real Wages, Employment, and the Phillips Curve, Journal of
Political Economy, 97, 706–20.

18

CPI

19
GDP deflater
2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

Figure1 Trends in the Inflation Rate
6%

5%

4%

3%

2%

1%

0%

-1 %

-2 %

-3 %

Figure 2 Trends in the Unemployment Rate by Age Categories
12 %

10 %

8%

6%

4%

2%

15-24

25-34

35-44

20

45-54

55-64

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

0%

Figure 3 Procyclicality of the Inflation Rate
6
54th e in flation rate

3
2
1
0
-2

-1

-1

0

1

2

3

4

5

6

GDP deflator

CPI

-2
-3
the rate of change in real GDP
GDP deflator

CPI

21

7

8

Table 1 Estimation Results using the Average Wage Total for all Age Groups
Expected Inflation

(1)

(2)

(3)

(4)

0.376 ***

0.585 ***

0.115

0.359 ***

(0.109)(0.110)Deflation Dummy*Expected Inflation
Unemployment

Constant
Number of Observations
R2(0.111)-2.004 ***-1.476 ***(0.311)(0.272)-1.364 ***-2.039 ***(0.191)(0.211)

1/Unemployment
Industry-Specific Shock(0.105)21.436 ***24.723 ***(2.017)(2.055)-0.302-0.971-0.946-1.151(1.443)(1.394)(1.370)(1.334)6.604 ***

7.932 ***

-4.797 ***-6.616 ***(0.707)(0.711)(0.617)(0.688)

525

525

525

525

0.360

0.408

0.423

0.454

Note: Standard errors are in parentheses. *** indicates significance at the 1% level, ** indicates significanceat the 5% level, and * indicates significance at the 10% level.

22

Table 2 Estimation Results for the 15–24 Age Category
Expected Inflation

(1)

(2)

(3)

(4)

0.543 ***

0.661 ***

0.193

0.330 **

(0.117)(0.119)(0.124)(0.129)Deflation Dummy*Expected Inflation
Unemployment-1.293 ***-0.967 ***(0.318)(0.282)-0.636 ***-0.879 ***(0.109)(0.123)

1/Unemployment
Industry-Specific Shock
Constant
Number of Observations
R2

41.480 ***46.593 ***(4.802)(4.982)

1.373

0.914

0.493

0.303

(1.453)(1.436)(1.407)(1.394)5.743 ***

6.716 ***

-5.148 ***-6.490 ***(0.769)(0.795)(0.758)(0.846)

525

525

525

525

0.393

0.412

0.434

0.447

Note: Standard errors are in parentheses. *** indicates significance at the 1% level, ** indicates significanceat the 5% level, and * indicates significance at the 10% level.

23

Table 3 Estimation Results for the 25-34 Age Category
Expected Inflation

(1)

(2)

(3)

(4)

0.246 **

0.423 ***

-0.1720.061(0.118)(0.117)(0.115)(0.120)Deflation Dummy*Expected Inflation
Unemployment-2.022 ***-1.452 ***(0.317)(0.270)-1.082 ***-1.643 ***(0.158)(0.176)

1/Unemployment
Industry-Specific Shock
Constant
Number of ObservationsR2

24.944 ***28.192 ***(2.221)(2.247)-0.536-1.401-1.937-2.223(1.476)(1.429)(1.387)(1.352)5.680 ***

6.921 ***

-5.493 ***-7.169 ***(0.684)(0.688)(0.599)(0.661)

525

525

525

525

0.318

0.368

0.402

0.433

Note: Standard errors are in parentheses. *** indicates significance at the 1% level, ** indicates significanceat the 5% level, and * indicates significance at the 10% level.

24

Table 4 Estimation Results for the 35-44 Age Category
Expected Inflation

(1)

(2)

(3)

(4)

0.511 ***

0.740 ***

0.172

0.450 ***

(0.119)(0.122)(0.116)(0.125)

Deflation Dummy*Expected Inflation
Unemployment-2.077 ***-1.599 ***(0.357)(0.308)-1.369 ***-2.301 ***(0.280)(0.315)

1/Unemployment
Industry-Specific Shock
Constant
Number of Observations
R2

13.447 ***15.714 ***(1.554)(1.578)-2.172-2.871 *-2.899 *-3.065 **(1.631)(1.586)(1.555)(1.518)4.992 ***

6.245 ***

-4.246 ***-6.106 ***(0.743)(0.752)(0.671)(0.746)

525

525

525

525

0.268

0.313

0.331

0.364

Note: Standard errors are in parentheses. *** indicates significance at the 1% level, ** indicates significanceat the 5% level, and * indicates significance at the 10% level.

25

Table 5 Estimation Results for the 45-54 Age Category
Expected Inflation

(1)

(2)

(3)

(4)

0.600 ***

0.877 ***

0.417 ***

0.713 ***

(0.120)(0.124)(0.110)(0.124)

Deflation Dummy*Expected Inflation
Unemployment-2.528 ***-1.662 ***(0.408)(0.343)-1.760 ***-2.919 ***(0.273)(0.323)

1/Unemployment
Industry-Specific Shock
Constant
Number of Observations
R2

11.278 ***13.251 ***(1.160)(1.206)0.041-0.617-0.289-0.403(1.760)(1.703)(1.678)(1.643)5.808 ***

7.155 ***

-3.738 ***-5.610 ***(0.672)(0.685)(0.569)(0.678)

525

525

525

525

0.333

0.379

0.390

0.417

Note: Standard errors are in parentheses. *** indicates significance at the 1% level, ** indicates significanceat the 5% level, and * indicates significance at the 10% level.

26

Table 6 Estimation Results for the 55-and-older Age Category
Expected Inflation

(1)

(2)

(3)

(4)

0.669 ***

0.893 ***

0.764 ***

0.914 ***

(0.143)(0.161)(0.134)(0.163)

Deflation Dummy*Expected Inflation
Unemployment-1.392 ***-0.699(0.462)(0.436)-1.440 ***-1.761 ***(0.243)(0.264)

1/Unemployment
Industry-Specific Shock
Constant
Number of ObservationsR2

19.345 ***20.507 ***(3.340)(3.413)-1.483-1.547-0.820-0.758(2.164)(2.148)(2.161)(2.158)8.497 ***

9.124 ***

-2.519 ***-3.195 ***(1.087)(1.099)(0.831)(0.931)

525

525

525

525

0.276

0.288

0.274

0.277

Note: Standard errors are in parentheses. *** indicates significance at the 1% level, ** indicates significanceat the 5% level, and * indicates significance at the 10% level.

27

Table 7 Comparison of the Inverse Unemployment Rate Coefficients by Age Categories as
Determined by Equations (3) and (4)
(3)
(4)

15–24
41.48046.593

25–34
24.94428.19235–44
13.44715.71428

45–54
11.27813.25155-and-older
19.34520.507

Data Appendix
1. Derivation of Average Wage for Each Age Bracket
NIKKEI NEEDS data were available in electronic form and provided the unemployment
rate via a Monthly Report on the Labor Force Survey that included figures classified by five age
brackets: (1) 15-24, (2) 25-34, (3) 35-44, (4) 45-54, and (5) 55 and older. For comparison, theavailable data on nominal wages from the Basic Survey on Wage Structure were averaged for 12
age groups: (1) 17 and younger, (2) 18-19, (3) 20-24, (4) 25-29, (5) 30-34, (6) 35-39, (7) 40-44,(8) 45-49, (9) 50-54, (10) 55-59, (11) 60-64, and (12) 65 and older. To make these two sourcesof data correspond, the mean wages for the former five groups were calculated, as shown in theexample below.
(Example: average wage of the 25-34 age category)

w25−34 =w25− 29 × l 25− 29 + w30−34 × l30−34
l 25− 29 + l 30−34

where wi − j denotes the average wage over the i-j age bracket, and l i − j equals the number ofworkers aged between i and j (i < j).

29

2. Industry Classifications
Following the criteria adopted in Kimura and Ueda (2001), Japanese domestic
industries were categorized according to “major groups” for non-manufacturing and “medium
groups” for manufacturing as given in the Standard Industrial Classification for Japan. Of thecategories, those in both the Basic Survey on Wage Structure and Annual Report on National

Accounts were chosen for our analyses. Those 25 industries were as follows: (1) mining, (2)manufacture of food products and beverages (including tobacco and feed), (3) manufacture of
textile mill products, except apparel and other finished products made from fabrics and similarmaterials, (4) manufacture of pulp, paper, and paper products, (5) manufacture of chemicals andallied products, (6) manufacture of ceramic, stone, and clay products, (7) manufacture of ironand steel, (8) manufacture of non-ferrous metals and products, (9) manufacture of fabricatedmetal products, (10) manufacture of general machinery, (11) manufacture of electricalmachinery, equipment, and supplies, (12) manufacture of transportation equipment, (13)manufacture of precision instruments and machinery, (14) manufacture of apparel and otherfinished products made from fabrics and similar materials, (15) manufacture of lumber andwood products except furniture, (16) manufacture of furniture and fixtures, (17) publishing,printing, and allied industries, (18) manufacture of rubber products, (19) construction, (20)electricity, gas, heat supply, and water, (21) wholesale and retail trade, eating and drinking
establishments, (22) finance and insurance, (23) real estate, (24) transport and communications,and (25) services.

30

3. Descriptive Statistics
Obs.

mean

S.D.

min

max

Rate of change in the nominal wage
(overall)

525

2.664

3.167

-10.566

15.755Rate of change in the nominal wage
(15-24)

525

2.473

3.266

-6.54513.657

Rate of change in the nominal wage
(25-34)

525

2.033

3.114

-6.03513.863Rate of change in the nominal wage
(35-44)

525

2.385

3.347

-8.77016.552Rate of change in the nominal wage
(45-54)

525

2.801

3.809

-15.59322.220Rate of change in the nominal wage
(55 and older)

525

3.433

4.520

-13.887

22.791

Expected inflation rate

21

1.009

1.741

-1.990

4.525

Unemployment rate (overall)

21

3.162

1.017

2.100

5.400

Unemployment rate (15-24)

21

6.047

1.907

4.350

9.925

Unemployment rate (25-34)

21

3.592

1.330

2.333

6.467

Unemployment rate (35-44)

21

2.252

0.751

1.475

4.108

Unemployment rate (45-54)

21

2.053

0.773

1.217

3.967

Unemployment rate (55 and older)

21

3.965

1.027

2.442

5.842

Rate of change in the industrial real
GDP

525

0.018

0.080

-0.1960.535

31