Volume 29, Issue 2
The 1.03 million yen ceiling and earnings inequality among married women inJapanYukiko Abe
Graduate School of Economics and Business
Administration, Hokkaido University

Akiko Sato Oishi
Faculty of Law and Economics, Chiba University

Abstract
In this paper, we examine the impact of the `1.03 million yen ceiling,' a means-tested transfer scheme for secondary
earners in Japan, on earnings inequality of married women. We find that the decline in earnings inequality amongmarried women between 1993 and 2003 is attributable to the increase in the number of wives with low earnings andthe decrease in the number of wives with zero earnings.

The analysis in Section 3 uses resampled microdata from the NSFIE made available through the Research Centre for Information and Statisticsof Social Science, Institute of Economic Research, Hitotsubashi University. The resampled microdata cannot be released owing to the terms ofusage of the data. This research was supported by Grants-in-Aid for Scientific Research from the Japan Society for Promotion of Science(Abe, C-17530188 and C-20530188; Oishi, C-19530198) and Health Labour Sciences Research Grant (Oishi). All remaining errors are ourown.
Citation: Yukiko Abe and Akiko Sato Oishi, (2009) ''The 1.03 million yen ceiling and earnings inequality among married women in Japan'',Economics Bulletin, Vol. 29 no.2 pp. 1510-1519.
Submitted: Jun 21 2009. Published: June 28, 2009.

1 Introduction
Income taxes or other government policies sometimes create circumstances wherein
individual earnings tend to concentrate at certain levels (bunching); Saez (2009)lists a number of such examples. In this paper, we focus on one such scheme inJapan: the 1.03 million yen ceiling.
The 1.03 million yen ceiling refers to the tendency that married women in
Japan who work part time set their annual earnings close to 1.03 million yen.
This phenomenon has attracted much attention in the literature (e.g., Nagase &Nawata (2005); Akabayashi (2006); Sakata & McKenzie (2006); Abe (2009a)).
The concentration around this ceiling is owing to the discontinuities in the budget
set, which are created by the income tax set-up, social security system and fringe
benefit arrangements provided by the husband’s employer.1 In spite of much attention, however, the focus of previous studies has almost exclusively been on
behavioral or eﬃciency aspects of the ceiling: the distributional consequences of
the ceiling are not well known.
In this paper we provide a simple decomposition procedure to understandhow the ceiling aﬀects earnings inequality among married women, and apply it
to Japanese microdata. The novel feature of our procedure is that it explicitly
considers the concentration of married women’s earnings around 1.03 million yenand measures its quantitative impacts on earnings inequality.
The 1.03 million yen ceiling is most relevant for married women who workpart time. The number of women working under part-time status increased dramatically in the past two decades.2 The earnings of those workers are generally
lower than those of regular, full-time workers because (1) hourly wages of parttime workers are about 30 percent lower than those of full-time workers and (2)the 1.03 million yen ceiling provides incentives for married women to restrain
their working hours so that their earnings do not exceed the threshold.
Empirical evidence shows that the earnings of married female part-timers areheavily concentrated slightly below 1.03 million yen (Akabayashi (2006); Abe(2009a)). Figure 1 illustrates the pattern of concentration from the microdata of
the National Survey of Family Income and Expenditure (NSFIE).

1

See Nagase & Nawata (2005), Akabayashi (2006), and Abe (2009a) for explanation and evidence.
2
In fact, in Japan, the increase in labor force participation by women was in the form of parttime employment, and not of regular full-time employment (Abe (2009b)).

2

2Earnings decomposition when the ceiling is present

In this section, we explain the framework for earnings decomposition taking into
account the 1.03 million yen ceiling.
Let ȳ be the mean earnings for married women, V(y) be their variance and CV 2
be the square of the coeﬃcient of variation (CV 2 = V(y)/ȳ2 ).
We denote yi as the earnings of individual (wife) i and θ is the threshold value
around which the earnings are concentrated (i.e., 1.03 million yen). For the purpose of our analysis, wives are classified into one of the following four categories
depending on their earnings level (notations in parentheses are the labels for eachgroup): (1) zero earnings (Z), (2) earnings between 0 and θ (I0 ), (3) earnings equalto θ (T ) and (4) earnings over θ (I1 ).
The variance of wives’ earnings, V(y), is decomposed as follows:∑∑∑]
1 [∑(0 − ȳ)2 +(yi − ȳ)2 +(θ − ȳ)2 +(yi − ȳ)2N i∈Zi∈I0i∈Ti∈I1∑∑[1(ȳ)2 +{(yi − y¯0 )2 + (y¯0 − ȳ)2 }=N i∈Zi∈I0∑∑]2{(yi − y¯1 )2 + (y¯1 − ȳ)2 } ,(θ − ȳ) ++V(y) =(1)i∈I1i∈Twhere y¯0 is the mean earnings of wives in group I0 , and y¯1 is the mean earnings ofwives in group I1 .
Dividing V(y) in Eq. (1) by ȳ2 and simplifying yields the following expression
for CV 2 , which is the sum of the between-group term and the within-group term:{ nZ

nI0 (y¯0 − ȳ)2 nθ (θ − ȳ)2 nI1 (y¯1 − ȳ)2 }++NNȳ2N ȳ2Nȳ2{ nI0 V(yi | i ∈ I0 ) nI1 V(yi | i ∈ I1 ) }++.
Nȳ2Nȳ2

CV 2 (y) =+(2)The first line of Eq. (2) is the between-group component; it is the sum of thesquared deviations of the group means from the population mean, weighted by thepopulation share of each group. The second line is the sum of the within-groupvariances for the groups I0 and I1 . Workers in groups I0 and I1 choose working

3hours as an interior solution.3 For non-workers and those with earnings equal toθ, earnings are equal for everyone within the group, and thus, the within-groupvariance is zero.4
The decomposition of Eq. (2) implies the following: (1) a decrease in thenumber of wives with zero earnings (i.e., decrease in nZ /N) reduces CV 2 and (2)CV 2 is the sum of six terms, where each term is the product of the population
share and the square of the deviation of the group mean from ȳ (the within-groupvariance). The decomposition of CV 2 in Eq. (2) is summarized in Table 1.
3 Empirical analysis
The data used for our empirical analysis is the microdata from the NSFIE5 for theyears 1994 and 2004. The NSFIE is a nationally representative survey in Japanthat collects information on household earnings. We apply the above procedure
to wage-salary earnings data for married women. The earnings figures are annual
earnings in the previous year of the survey (1993 and 2003). The sample is restricted to women married to male household-heads aged 25-59 years; the sample
size is 31,166 for 1994 and 24,434 for 2004. The threshold value is set at 0.9
million yen to separate I0 and T , and at 1.3 million yen to separate T and I1 . This
selection is made because women who intend to limit their annual earnings arelikely to keep their earnings between 0.9 and 1.3 million yen.6 The decomposition results are reported in Table 2.
In the 2003 sample, 53 percent of the women had no wage-salary earnings,
16 percent had positive earnings below 0.9 million yen, 11 percent had earnings
around 1.03 million and the remaining 20 percent had earnings over 1.3 million.
The concentration around the threshold (the T group) is remarkable: 23 percent ofmarried women with positive wage-salary earnings are in this very narrow range,
for which the within-group variance (divided by ȳ) is only 0.013 (as compared to3

On the other hand, zero earnings and threshold earnings are corner solutions in the optimization problem for labor supply of married women.
4However, in the empirical analysis below we assume that individuals with earnings around θare in the T category, and as such, the variance of earnings for group T is not zero but is still verysmall.
5The NSFIE has been conducted by the Statistics Bureau, Ministry of Internal Aﬀairs andCommunications for every five years since 1959.
6We choose 1.3 million yen for the upper bound earnings for the T group because dependant
spouse are exempted from paying social security contributions as long as their earnings are below
1.3 million yen. This rule is explained in detail in Akabayashi (2006).

44.73 for the I1 group, which is 342 times larger). The mean is 0.92 million, which
is close to the earnings threshold θ.
In both years, the major components of CV 2 are as follows: (1) the betweengroup component for zero earnings (group Z, row c) that is equal to the population
share of group Z, (2) the between-group component for earnings over θ (group I1 ,row c) and (3) the within-group component for group I1 (row e). The other components are quite small as compared to these three. Of the three components above,the largest is the between-group component for group I1 , which accounts for morethan half of CV 2 . Therefore, the primary source of inequality in married women’searnings is that high earners (wives with earnings above θ; approximately 20 percent of married women) earn much more than the overall average (ȳ). The second
largest source of inequality is the within-group variance for group I1 , which accounts for approximately 30 percent of CV 2 .
The notable changes between 1993 and 2003 are summarized as follows. Inequality in the earnings of married women declined with CV 2 decreasing from
3.42 in 1993 to 3.17 in 2003 (a decline of 0.25). The component that contributed
most to this decline is the fall in the between-group components: the betweengroup component of the Z group fell by 0.055 and that of the I1 group fell by0.208. The contribution of the other components is negligible. In both years, theproportion of high earners (group I1 ) remained the same at approximately 20 percent. On the other hand, the proportion of wives with positive earnings below 1.3
million yen increased by 6 percent and those with zero earnings decreased by 5percent. This shift from zero earnings to low positive earnings reduces the proportion of zero earnings (nZ /N), and increases the mean earnings (ȳ), which is themain source of falling inequality over this period.
Even though the 1.03 million yen ceiling is likely to constrain earnings growth,inequality nonetheless fell between 1993 and 2003. The shift from zero earnings
to low positive earnings is rational in the presence of the ceiling, and that is precisely how the earnings inequality decreased between 1993 and 2003.7 It is worth
noting that the weight of high earners fell during this period. One might havethought that since the ceiling restrains earnings, the disparity between high earners and others would widen. However, this eﬀect was negligible. The result isin line with Cancian & Reed (1998), who report that earnings inequality among
married women fell between 1979 and 1989 in the United States (Cancian & Reed(1998), Table 1).87

It is important to note that we are not making a counterfactual comparison of earnings distribution in the presence and absence of the threshold.
8Reed & Cancian (2001) report that earnings inequality among all women fell continuously

54Conclusion

This paper presents a framework for decomposing the earnings inequality for married women in Japan that explicitly considers the concentration of earnings around1.03 million yen, and applies it to Japanese household data.
We find that earnings inequality of married women in Japan consists of threemajor components: (1) the diﬀerence between the mean earnings of high earners(top 20 percent) and the overall mean, (2) the large within-group variance of highearners and (3) the proportion of wives with zero-earnings (more than 50 percent).
Earnings inequality among married women fell between 1993 and 2003, and thedecline is attributable to the increase in the number of wives with low earnings
and the decrease in the number of wives with zero earnings.
References
Y. Abe (2009a). ‘The Eﬀects of the 1.03 million yen Ceiling in a Dynamic Labor
Supply Model’. Contemporary Economic Policy 27(2):147–163.
Y. Abe (2009b). ‘The Equal Employment Opportunity Law and Labor Force Behavior of Men and Women in Japan’. mimeo, Hokkaido University.
H. Akabayashi (2006). ‘The Labor Supply of Married Women and Spousal Tax
Deduction in Japan A Structural Estimation’. Review of Economics of theHousehold 4(4):349–378.
M. Cancian & D. Reed (1998). ‘Assessing the Eﬀects of Wives’ Earnings on
Family Income Inequality’. Review of Economics and Statistics 80(1):73–79.
N. Nagase & K. Nawata (2005). ‘Changes in Taxes and Social Security System
on Part-time Labor Supply (Part no zeisei, shakai-hoken seido no henkou toroudou kyoukyu heno eikyo)’. Paper presented at the 2005 Fall Meeting of theJapanese Economic Association (in Japanese).
D. Reed & M. Cancian (2001). ‘Sources of Inequality: Measuring the Contributions of Income Sources to Rising Family Income Inequality’. Review ofIncome and Wealth 47(3):321–333.
E. Saez (2009). ‘Do Tax Filers Bunch at Kink Points? Evidence, Elasticity Estimation, and Salience Eﬀects’. mimeo, University of California at Berkeley.
from 1969 to 1999 and attribute this change to the rising labor force participation of women.

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K. Sakata & C. R. McKenzie (2006). ‘The Impact of the Tax Reform in 2004 on
the Female Labour Supply in Japan’. mimeo, Ritsumeikan University.

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Table 1: Decomposition of CV 2
Group
Income range(a) Population(b) Between(c) Total(Between)((a) × (b))(d) Within(e) Total(Within)((a) × (d))

Zyi = 0nZ /N1I00 < yi < θ
nI0 /N(y¯0 − ȳ)2 /ȳ2Tyi = θnθ /N(θ − ȳ)2 /ȳ2I1yi > θ
nI1 /N(y¯1 − ȳ)2 /ȳ2nZ /N-(nI0 /N)(y¯0 − ȳ)2 /ȳ2
V(yi0 )/ȳ2(nθ /N)(θ − ȳ)2 /ȳ2-

(nI1 /N)(y¯1 − ȳ)2 /ȳ2
V(yi1 )/ȳ2-(nI0 /N){V(yi0 )/ȳ2 }-(nI1 /N){V(yi1 )/ȳ2 }Note: yi j ( j = 0, 1) represents the earnings of the i-th individual belonging togroup I j .

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Table 2. Decomposition results for married women's earnings
YearGroup(a) Population(b) Between(c)Total, Between(d) Within(e) Total, Within
CV21993Z
yi=00.5887
10.588700I0
T0<yi≤0.9≤0 9 0.9<y0 9<yi≤1.3≤1 3
0.13480.07510.08310.03980.01120.00300.07120.01650.00960.00123.42242003I1yi>1.3>1 30.20149.25391.86354.69340.9452

Note: Earnings figures are in million yen.
Source: Authors
Authors' calculation from the micro data of the NSFIE (1994 and 2004).

I0ZT
yi=00<yi≤0.9≤0 9 0.9<y0 9<yi≤1.3≤1 3
0.53410.15830.1082
10.12530.02030.53410.01980.002200.0688
0.013800.0109
0.0015
3.1675I1yi>1.3>1 3
0.19958.29931.65554.7302
0.94369

Figure 1.

Earnings distribution of married women working part time,by age groupAge: 40-49

0012

3.2

Age: 50-59

0.1

Fraction.1.2

Age: 30-39

01

2

3

wives' earnings (in million yen)

Source: Figure 2 of Abe (2009a). The sample is from the resampled data of NSFIE(2004).
Note: The figures are drawn from the sample of married women working part time.
Individuals with earnings over 3 million yen are excluded. The proportion of earnings
over 3 million yen is less than 1.4 percent for each of the three age groups. Observations
are weighted by the sampling weight. The number of observations are 1363 for age
30-39, 2136 for age 40-49, and 520 for age 50-59.

10