Silviase/jgov_v1.4_full_ann huggingface dataset:
#### 3.4. Other Datasets

For the IV—the ratio of the first-year graduate enrollment capacity to the number of fourth-year undergraduate students—data for the graduate school capacity are obtained from the Zenkoku Daigaku Ichiran, 1972-2012 (List of Universities in Japan, 1972-2012). The number of fourth-year undergraduate students is obtained from the Basic Survey of Schools (BSS). The List of Universities in Japan and the BSS are exhaustive surveys respectively covering all universities and all schools, including graduate schools, in Japan.

### 4. Estimation Method

For the analysis, Mincer’s human capital earnings function (see Mincer, 1974) is estimated for workers with a bachelor’s degree:

$$ \ln W_{it}=\alpha+\beta G_{i}+\gamma_{1}E_{it}+\gamma_{2}E_{it}^{2}+\zeta X_{it}+\epsilon_{it} $$

where $ W_{it} $ is the wage of individual i at time t, $ G_{i} $ is a dummy variable indicating whether individual i has a master's degree, $ E_{it} $ represents individual i's work experience, which is measured in terms of years since graduation, and $ X_{it} $ is a vector of other control variables such as year dummies and five-year birth cohort dummies. $ ^{12} $ The subject of individuals' undergraduate degree and type of university (private or public) are included in $ X_{it} $ . The coefficient of main interest is that on the master's dummy, $ G_{i} $ , and the null hypothesis $ H_{0}:\beta=0 $ is tested.

For the baseline estimation, Equation (1) is estimated using OLS focusing on individuals working full-time. Taking sample selection bias into account, Equation (1) is also estimated using the Heckman two-step estimation method. The dependent variable of the selection equation is a dummy variable indicating that the individual is working full-time. In addition to the independent
variables in Equation (1), the selection equation includes the number of children under the age of four, children aged four to six, and children aged seven to eighteen in order for the exclusion restriction to be satisfied. While the parametric Heckman two-step estimation procedure does not require an exclusion restriction, many empirical researchers do not rely on identification using only parametric assumptions. Therefore, the number of children of different ages is added to the selection equation based on the assumption that the number of children of different ages determines labor force participation but does not directly affect the wage. $ ^{13} $ $ ^{14} $

Since the large majority of those who obtain a master's degree in Japan do so immediately after completing their undergraduate studies, the master's dummy $ G_{i} $ is constant over time for most individuals. Therefore, it is not possible to eliminate the effect of unobserved ability by including individual fixed effects in the regression model. Consequently, in order to account for the self-selection bias, the IV described above is used. Specifically, the variable is calculated as follows. Let $ \tau_{i} $ be the year in which individual i completed their undergraduate studies, $ \phi_{i} $ be the type of university (private or public) where individual i completed their undergraduate studies, and $ \mu_{i} $ be individual i's subject of study. The IV $ Z_{i} $ is defined as follows:

$$ \mathrm{Z}_{\mathrm{i}}=\frac{G r a d u a t e\;e n r o l l e m t\;c a p a c i t y\;o f\;t y p e\;\phi_{i}\;u n i v e r s i t y\;i n\;s u b j e c t\;\mu_{i}\;a t\;\tau_{i}+1}{N u m b e r\;o f\;f o u r t h-y e a r\;u n d e r g r a d u a t e\;s t u d e n t s\;i n\;t y p e\;\phi_{i}\;u n i v e r s i t y\;s t u d y i n g\;s u b j e c t\mu_{i}\;a t\;\tau_{i}}. $$

$ Z_{i} $ can be interpreted as a measure of the difficulty of being admitted to a master's program in subject $ \mu_{i} $ in a type $ \phi_{i} $ university at time $ \tau_{i} $ . Thus, $ Z_{i} $ affects an individual i's decision of

studying for a master's degree, but the graduate enrollment capacity is determined by universities.
Consequently, $ Z_{i} $ is not correlated with individuals' unobserved ability. Moreover, it is unlikely that graduate schools expand or contract capacity in response to labor market conditions. $ ^{15} $ Therefore, self-selection bias due to graduate enrollment in response to the business cycle can be eliminated using $ Z_{i} $ as an instrument. $ ^{16} $

### 5. Estimation Results

## Estimation Results of Wage Regressions

Let us perform the analysis by running a regression excluding the subject that individuals studied and the type of university they attended and compare the results with those obtained by Morikawa (2015). The results are presented in the first three columns in Table 5 and reveal that male workers with a master’s degree earn 26.4% more than male workers with only a bachelor’s degree, and that female workers with a master’s degree earn 26.9% more than female workers with only a bachelor’s degree. Although the sample size of the JPSC data is much smaller than that of the ESS data, the estimates of the postgraduate wage premium are very close to the estimation results reported by Morikawa (2015). Moreover, the postgraduate wage premiums are very similar for male and female workers, which is also in line with the results obtained by Morikawa (2015).

The last three columns in Table 5 present the estimation results when the subject of undergraduate study and type of university are included. As mentioned above, omitting these variables potentially exaggerates the postgraduate wage premium, so it is expected that including them will reduce the coefficient on the graduate dummy. However, as can be seen in Table 5, the coefficient estimates continue to be positive and significant, although their size shrinks to some
extent. Specifically, for males, the estimated postgraduate wage premium drops from 26.4% to 24.9%, while for females, it falls from 26.9% to 23.6%. These results indicate that omitting the subject individuals studied for their undergraduate degree and the type of university they attended results in an overestimation, but these variables explain only a small fraction of the postgraduate wage premium.

Next, Table 6 presents the results of the Heckman two-step estimation. They indicate that the number of children influences the labor force participation decision of women, and that the estimates of the postgraduate wage premium increase by one to three percentage points. The OLS estimates underestimate the effect of postgraduate education, because the opportunity cost of quitting their job to raise a child is lower for those without a master's degree, and they are therefore more likely to quit.

Finally, in order to eliminate the ability bias, the IV is used. To assess the validity of the IV, the master's dummy is regressed on the instrument. The estimation result, shown in Table 7, indicates that the IV is closely related to whether individuals have obtained a master's degree. $ ^{17} $ The results of the IV estimation, presented in Table 8, $ ^{18} $ reveal that none of the estimated coefficients are significant and are even negative in the regressions for the entire sample and for male workers. $ ^{19} $

How can the IV estimation result be interpreted? The IV estimation relies on the reaction of the average wage to changes in the measure of the difficulty of entering a master’s program. However, the share of workers with a graduate degree is at most 10% in Japan. It is therefore possible that even if the return to graduate education is positive, the estimates are not significant.
because of the sample size and the scarcity of “treated” individuals.

In order to check if insignificant estimation results are caused by the small sample, we run the same regression by using the WPS data. Table 9 shows OLS estimates with the WPS data. The estimates of postgraduate education premium are smaller than those obtained from regression with JPSC data, but not too different from the estimates reported by Morikawa (2015). $ ^{20} $ The estimation result of the first stage regression for IV regression is presented in Table 10. The value of F-statistic is 81.35, which is so large that we do not have to worry about the weak instrument problem. Table 11 shows the estimation results of IV regression. The estimates of the effect of postgraduate education are negative, and not significant for all samples and male samples.

## Estimation Results of Job Satisfaction Regressions

The negative and insignificant estimates are obtained even for the regression with the WPS data, which contains more than 1,000 individuals with a postgraduate degree. Thus, insignificant estimates may not be caused by a small sample. It is possible, as previous studies such as Taubman and Wales (1973) and Hussey (2012) suggest, that the postgraduate wage premium to a considerable extent reflects signaling/screening effects rather than higher productivity through graduate education. In that case, it is possible that the average wage remains constant when the share of workers with a master’s degree increases without a significant increase in workers’ productivity.

Another possibility is that there are non-pecuniary returns to postgraduate education. Under Japan’s typical employment system, many job seekers do not know what kind of job they will have until they are employed. For instance, it is common in Japan for someone interested in working as a salesman to be forced to work at the personnel division or accounting division.
However, new graduates are likely to be hired as an engineer and work at the research and development section if they have a master's degree. To check if this is true, we define job satisfaction variable $ S_{it} $ , which takes on the value of one if an individual is satisfied with the current job and zero otherwise. The WPS 2006, 2010, and 2012 data contains a question about the job satisfaction, and an individual is considered satisfied if they report “very satisfied” or “satisfied” with his/her current job. $ ^{21} $ Table 12 shows the estimation results of the job satisfaction regression with the IV. $ ^{22} $ The coefficient on the master’s dummy is positive and significant for males. Therefore, it can be conjectured that earning a master’s degree can help job seekers to find a job, which is not high paying but more desirable than the jobs they could get without a master’s degree.

### 6. Conclusion

This paper attempted to estimate the returns to graduate education in Japan using data from the JPSC. Unlike previous studies using the ESS data, the present study controls for the subject that individuals studied for their undergraduate degree and the type of university they attended, and employs an IV to deal with the endogeneity of postgraduate schooling. The estimation results of the OLS regression without the undergraduate subject and type of university are close to estimates of the postgraduate wage premiums obtained by Morikawa (2015). Moreover, also in line with Morikawa's (2015) results, the postgraduate wage premium was found to be very similar for male and female workers. Next, controlling for the undergraduate subject and type of university (private or public), the postgraduate education wage premium shrinks to a certain extent but
continues to remain positive and significant. The results thus confirm that the estimates of the postgraduate wage premium presented in previous studies are likely biased upward due to omitted variables, but also indicate that the subject studied and the type of university attended (private or public) explain only a small portion of the postgraduate wage premium. The estimation results based on the Heckman two-step estimation method indicate that the estimated postgraduate wage premium is biased downward due to sample selection. Taking the labor force participation decision into consideration, the estimates of the postgraduate wage premium increase by one to three percentage points. On average, the estimated postgraduate wage premium ranges from 23-27% and is statistically significant. However, when the IV is used, the estimated effect of postgraduate education is not statistically significant.

If the IV used in this study is valid and the sample size is not too small, the estimation results indicate that graduate education did not have a sizable impact on the wages of those whose graduate enrollment decision was potentially affected by the change in graduate enrollment capacity. The estimation results of the job satisfaction regression with the same IV, on the other hand, indicate that male workers with a master's degree are more likely to be satisfied with their current job. These results suggest that those who obtained a master's degree owing to the expansion of graduate education may not enjoy higher pay than those without a master's degree, but they receive non-pecuniary benefits from the job which they could not get without a master's degree.
## References

Ashenfelter, O. and J. D. Mooney (1968) “Graduate education, ability, and earnings,” Review of Economics and Statistics, 50, 78-86.

Bedard, K. and D. A. Herman (2008) “Who goes to graduate/professional school? The importance of economic fluctuations, undergraduate field, and ability,” Economics of Education Review, 27, 197-210.

Bunkyo-Kyokai (various issues): A list of universities in Japan (Zenkoku Daigaku Ichiran), Bunkyo-Kyokai.

Card, D. (1999) “The causal effect of education on earnings,” Handbook of Labor Economics, 3, 1801-1863.

Deere, D. R. and J. Vesovic (2006) “Educational wage premiums and the US income distribution: A survey,” Handbook of the Economics of Education, 1, 255-306.

Hamaaki, J., M. Hori, S. Maeda, and K. Murata (2013) "How does the first job matter for an individual's career life in Japan?" Journal of the Japanese and International Economies, 29, 154-169.

Hussey, A. (2012) “Human capital augmentation versus the signaling value of MBA education,” Economics of Education Review, 31, 442-451.

Jaeger, D. A. and M. E. Page (1996) “Degrees matter: New evidence on sheepskin Effects in the returns to education,” Review of Economics and Statistics, 733-740.

Johnson, M. T. (2013) “The impact of business cycle fluctuations on graduate school enrollment,” Economics of Education Review, 34, 122-134.

Kakizawa, H., T. Hirano, H. Matsushige, I. Yamasaki, and T. Inui (2014) “The postgraduate wage premium: estimating the age-wage profiles using 2007 employment status survey (in Japanese),” Discussion paper, ESRI Discussion Paper series, No.310.
Morikawa, M. (2015) “Postgraduate education and labor market outcomes: an empirical analysis using micro data from Japan,” Industrial Relations: A Journal of Economy and Society, 54, 499-520.

Shimizu, R. and Y. Higuchi (2009) “The value of MBA education in the Japanese labor market,” Japanese Economy, 36, 61-104.

Song, M., P. F. Orazem, and D. Wohlgemuth (2008) “The role of mathematical and verbal skills on the returns to graduate and professional education,” Economics of Education Review, 27, 664-675.

Taubman, P. J. and T. J. Wales (1973) “Higher education, mental ability, and screening,” Journal of Political Economy, 28-55.

Walker, I. and Y. Zhu (2011) “Differences by degree: Evidence of the net financial rates of return to undergraduate study for England and Wales,” Economics of Education Review, 30, 1177-1186.
Figure 1: Graduate enrollment by undergraduate major and school type Data source: Basic Survey of Schools

Figure 2: Growth rate of graduate enrollment by undergraduate major and school type Data source: Basic Survey of Schools
Table 1: Summary statistics (JPSC)

All (college graduates)	Postgraduates
All	Male	Female	All	Male	Female
Number of observations	8,287	6,362	1,925	379	284	95
Mean of age	37.0	38.5	31.2	36.3	38.1	30.6
Mean of wages	588.6	636.9	406.0	679.8	739.1	492.9
Std. dev. of wages	259.3	261.9	141.8	281.5	272.8	221.1

Table 2: Number of observations by undergraduate major and school type (public/private) (JPSC)

Public school	Private school
All	Male	Female	All	Male	Female
Natural sciences (B.S.)	200	167	33	126	100	26
Humanities and social sciences (B.A.)	1	0	1	52	17	35
Total	201	167	34	178	117	61

Table 3: Summary Statistics (WPS)

All (college graduates)	Postgraduates
All	Male	Female	All	Male	Female
Number of observations	10,577	8,603	1,974	1408	1,257	151
Mean of age	40.2	41.3	35.3	38.8	39.2	36.0
Mean of wages	639.0	683.3	446.2	702.5	722.5	535.5
Std. dev. of wages	309.7	314.9	190.0	321.0	326.1	210.5

Table 4: Number of observations by undergraduate major and school type (public/private) (WPS)

All	Male	Female
Natural sciences (B.S.)	1,152	1,062	90
Humanities and social sciences (B.A.)	256	195	61
Total	1,408	1,257	151
Table 5: OLS estimation results (JPSC)

All	Male	Female	All	Male	Female
Master's dummy	0.275*** (0.017)	0.264*** (0.020)	0.269*** (0.030)	0.236*** (0.018)	0.249*** (0.021)	0.236*** (0.031)
Humanities and social sciences, public university	0.122*** (0.010)	0.136*** (0.012)	0.123*** (0.016)
Natural sciences, public university	0.114*** (0.012)	0.066*** (0.013)	0.182*** (0.029)
Natural sciences, private university	0.070*** (0.009)	0.041*** (0.010)	0.029 (0.023)
Experience	0.064*** (0.003)	0.053*** (0.004)	0.052*** (0.005)	0.064*** (0.003)	0.054*** (0.004)	0.055*** (0.005)
Experience squared	-0.001*** (0.000)	-0.001*** (0.000)	-0.001*** (0.000)	-0.001*** (0.000)	-0.001*** (0.000)	-0.001*** (0.000)
Unemployment rate	-0.011* (0.006)	-0.004 (0.008)	-0.033*** (0.009)	-0.007 (0.006)	-0.004 (0.008)	-0.022*** (0.009)
Constant	5.737*** (0.057)	5.824*** (0.069)	5.950*** (0.093)	5.661*** (0.057)	5.775*** (0.068)	5.871*** (0.091)
Observations	8287	6362	1925	8287	6362	1925
Adjusted R²	0.375	0.246	0.282	0.390	0.262	0.314

Notes: Standard errors in parentheses. Year dummies and birth year cohort dummies are included as control variables but not shown for brevity. Experience is defined as the number of years since completing undergraduate or graduate education. The baseline is the humanities and social science majors at private schools.

$ ^{*} $ p < 0.10, $ ^{**} $ p < 0.05, $ ^{***} $ p < 0.01
Table 6: Heckman two-step estimation results (JPSC)

All	Male	Female	All	Male	Female
log wage
Master's dummy	0.240***
(0.031)	0.304***
(0.045)	0.297***
(0.034)	0.214***
(0.024)	0.254***
(0.025)	0.247***
(0.033)
Humanities and social sciences, public university	0.106***
(0.015)	0.144***
(0.029)	0.125***
(0.016)
Natural sciences, public university	0.085***
(0.024)	0.074***
(0.029)	0.196***
(0.032)
Natural sciences, private university	0.056***
(0.013)	0.046**
(0.019)	0.030
(0.023)
Experience	0.058***
(0.006)	0.055***
(0.005)	0.056***
(0.006)	0.058***
(0.005)	0.055***
(0.004)	0.057***
(0.005)
Experience squared	-0.001***
(0.000)	-0.001***
(0.000)	-0.001***
(0.000)	-0.001***
(0.000)	-0.001***
(0.000)	-0.001***
(0.000)
Unemployment rate	-0.010
(0.007)	-0.008
(0.010)	-0.035***
(0.009)	-0.006
(0.006)	-0.005
(0.008)	-0.023***
(0.009)
Constant	5.753***
(0.104)	5.744***
(0.124)	5.760***
(0.102)	5.672***
(0.105)	5.728***
(0.107)	5.629***
(0.101)
Full-time work dummy
Master's dummy	0.554***
(0.100)	0.410***
(0.125)	0.689***
(0.171)	0.371***
(0.105)	0.244*
(0.130)	0.599***
(0.181)
Humanities and social sciences, public university	0.245***
(0.049)	0.438***
(0.071)	0.214***
(0.078)
Natural sciences, public university	0.504***
(0.071)	0.409***
(0.079)	0.769***
(0.199)
Natural sciences, private university	0.193***
(0.045)	0.236***
(0.053)	0.011
(0.107)
Experience	0.091***
(0.014)	0.016
(0.021)	0.130***
(0.024)	0.091***
(0.014)	0.021
(0.021)	0.134***
(0.024)
Experience squared	-0.001***
(0.000)	0.000
(0.000)	-0.002**
(0.001)	-0.001***
(0.000)	0.001
(0.000)	-0.002**
(0.001)
Unemployment rate	-0.020
(0.028)	-0.035
(0.043)	-0.054
(0.041)	-0.013
(0.029)	-0.032
(0.044)	-0.048
(0.041)
Number of children aged 1 to 3	0.072*
(0.038)	0.008
(0.043)	-0.689***
(0.148)	0.064*
(0.038)	0.013
(0.043)	-0.717***
(0.149)
Number of children aged 4 to 6	0.051
(0.038)	0.069
(0.042)	-0.567***
(0.153)	0.051
(0.039)	0.077*
(0.043)	-0.596***
(0.155)
Number of children aged 7 to 18	-0.058**
(0.025)	-0.010
(0.028)	-0.615***
(0.088)	-0.057**
(0.025)	-0.003
(0.029)	-0.636***
(0.090)
Constant	0.433
(0.316)	1.483***
(0.498)	0.410
(0.456)	0.272
(0.320)	1.266**
(0.503)	0.269
(0.462)
lambda	-0.216
(0.153)	0.391
(0.366)	0.107*
(0.055)	-0.204
(0.141)	0.075
(0.236)	0.054
(0.054)
Observations	9596	7095	2501	9596	7095	2501

Notes: See the footnotes for Table 5.
Table 7: The effect of graduate school capacity on master’s dummy (JPSC)

Master's dummy
Graduate enrollment capacity/number of fourth year undergraduates	0.916***
(0.145)
Humanities and social sciences, public university	-0.082***
(0.012)
Natural sciences, public university	-0.030
(0.038)
Natural sciences, private university	0.043***
(0.007)
Experience	-0.025***
(0.002)
Experience squared	0.000**
(0.000)
Unemployment rate	-0.008**
(0.004)
Constant	0.497***
(0.034)
Observations	8287
Adjusted $ R^{2} $	0.166

Notes: See the footnotes for Table 5.
Table 8: IV estimation results (JPSC)

All	Male	Female
Master's dummy	-0.093(0.266)	-0.434(0.291)	5.448(10.747)
Humanities and social sciences, public university	0.117***(0.011)	0.128***(0.013)	0.296(0.361)
Natural sciences, public university	0.180***(0.055)	0.197***(0.057)	-1.190(2.831)
Natural sciences, private university	0.092***(0.021)	0.083***(0.021)	-0.577(1.253)
Experience	0.056***(0.008)	0.036***(0.009)	0.223(0.348)
Experience squared	-0.001***(0.000)	-0.001***(0.000)	-0.000(0.001)
Unemployment rate	-0.009(0.007)	-0.010(0.009)	-0.010(0.043)
Constant	5.832***(0.150)	6.126***(0.167)	-0.193(11.268)
Observations	8287	6362	1925
Adjusted R²	0.366	0.135	-

Notes: See the footnotes for Table 5.
Table 9: OLS estimation results (WPS)

All	Male	Female	All	Male	Female
Master's dummy	0.156*** (0.010)	0.129*** (0.010)	0.170*** (0.025)
M.A. in Humanities and social sciences	0.141*** (0.022)	0.149*** (0.024)	0.124*** (0.039)
M.A. in Natural Science	0.129*** (0.012)	0.114*** (0.012)	0.165*** (0.035)
Natural sciences	0.050*** (0.007)	0.020** (0.008)	0.054*** (0.017)
Experience	0.005*** (0.001)	0.005*** (0.001)	0.003 (0.003)	0.004*** (0.001)	0.005*** (0.001)	0.003 (0.003)
Experience squared	-0.000** (0.000)	-0.000*** (0.000)	0.000*** (0.000)	-0.000* (0.000)	-0.000*** (0.000)	0.000*** (0.000)
UnempRate	0.003 (0.007)	-0.013 (0.008)	0.001 (0.015)	0.003 (0.007)	-0.012 (0.008)	-0.001 (0.015)
Constant	28.702*** (9.474)	23.550** (9.378)	-1.769 (16.182)	28.754*** (9.453)	23.833** (9.376)	-2.150 (16.134)
Observations	9975	8014	1961	9975	8014	1961
Adjusted R²	0.364	0.339	0.317	0.367	0.340	0.322

Notes: Standard errors in parentheses. Year dummies and birth year cohort dummies are included as control variables but not shown for brevity. Experience is defined as the number of years since completing undergraduate or graduate education. The baseline is the Humanities and Social Science majors.

$ ^{*} $ p < 0.10, $ ^{**} $ p < 0.05, $ ^{***} $ p < 0.01
Table 10: The effect of graduate school capacity on master’s dummy (WPS)

Master's dummy
Graduate enrollment capacity/number of fourth year undergraduates	1.336 $ ^{***} $
(0.143)
Natural sciences	0.076 $ ^{***} $
(0.019)
Experience	-0.004 $ ^{***} $
(0.001)
Experience squared	0.000
(0.000)
UnempRate	-0.012
(0.007)
Constant	13.361
(9.256)
Observations	9975
Adjusted $ R^{2} $	0.145

Notes: See the footnotes for Table 9.