Silviase/jgov_v1.4_full_ann huggingface dataset:
### 1. Introduction

The number of graduate students in Japan has increased substantially over the past few decades. Figure 1, which presents the number of students enrolled in master’s programs in private and public universities, illustrates this trend: graduate enrollment followed a steady upward trend from the 1970s until the first decade of the 21st century, although this trend has declined to a certain extent in recent years (reflecting overall population trends). If graduate education imparts useful skills and knowledge to students and increases their productivity, the increase in the number of graduate students should boost technological development and guide economic growth. The question then is about the extent by which graduate education raises workers’ human capital stock. In order to address this question, this paper attempts to estimate the returns to graduate education in Japan, taking into account the endogeneity of graduate schooling.

Recent studies by Morikawa (2015) and Kakizawa et al. (2014) reveal that the postgraduate wage premium in Japan is positive, significant, and comparable to that in the United States. The study by Morikawa (2015) was the first attempt to estimate the postgraduate wage premium for the nationally representative sample in Japan, $ ^{1} $ and the estimation results indicate that the expansion of graduate education in Japan could affect the wages of workers with a postgraduate degree. However, these studies did not control for the undergraduate majors of the workers and for whether they attended a private or public university. Moreover, they also do not take potential self-selection bias due to the business cycle into consideration. $ ^{2} $

As highlighted in the education literature on the effect of higher education on wages, it is important not to ignore the possible self-selection bias arising from the association between schooling decisions and unobserved ability: students with higher ability are more likely to go to
university and find a high-paying job after they graduate, not only because of what they learned at university, but also because of their inherent ability. Although previous studies on returns to post-secondary education in the U.S. have shown that the ability bias is small, there are at least three major reasons why self-selection biases may cause a serious upward bias in the estimates of the returns to graduate education in Japan. First, as seen in Figure 1, the majority of Japanese graduate students major in science and engineering subjects at public universities, and admission to such subjects at public universities is considerably more selective than admission to humanities and social science subjects at private universities, for instance. Therefore, unless information about individuals' undergraduate subjects and type of university (private or public) is taken into consideration, ordinary least squares (OLS) estimates of the postgraduate wage premium may reflect differences in the inherent abilities of individuals with different majors and from different types of university. Second, the percentage of undergraduate students who continue to graduate study is higher in top universities, and it is possible that the returns to graduate education are higher for those who graduated from a top university. Unless information about a university's ranking or a direct measure of individuals' academic ability such as test scores is taken into consideration, the potential upward bias due to selection reflecting unobserved ability remains even if the undergraduate subjects and type of university are controlled for. Third, students completing their undergraduate studies during a recession have an incentive to pursue graduate education in the hope that the recession will be over by the time they graduate and that they will thus have more chances of getting a high-paying job as their first job, since not finding a first job immediately after graduation in Japan puts job seekers at a disadvantage and tends to have a lingering negative effect on career prospects (see, e.g., Hamaaki et al., 2013). Therefore, those who can afford to go to graduate school are more likely to find a high-paying job, and the wage differentials between graduates and non-graduates may reflect individuals'
financial backgrounds. In order to deal with these potential sources of bias, this study uses data from the Japanese Panel Survey of Consumers (JPSC) provided by the Institute for Research on Household Economics and the Working Person Survey (WPS) provided by the Recruit Works Institute to estimate the effect of earning a master’s degree on wages.

The JPSC has the advantage that it covers a longer period (20 years) than other panel data in Japan and provides more detailed information than surveys published by the government. Utilizing the extensive information provided by the JPSC, the analysis controls for workers' undergraduate major and type of university (private or public) to mitigate the ability bias. Furthermore, in order to deal with any self-selection bias that cannot be eliminated by the control variables and the Heckman two-step estimation procedure, the ratio of the number of student places (capacity) available at graduate schools across Japan to the number of fourth-year undergraduate students for each undergraduate subject and type of university is used as an instrumental variable (IV). The estimated coefficient can be regarded as the local average treatment effect for those whose graduate enrollment decision was potentially affected by the change in graduate enrollment capacity. $ ^{3} $ Although they are only a subgroup of the whole population, the estimate of the effect of postgraduate education on them has significant meaning from a policy analysis point of view, because this motivates the Japanese government to encourage universities to expand/contract the graduate enrollment capacity.

This paper is the first to present estimates of the effect of graduate education in Japan that carefully take the self-selection bias into consideration. $ ^{4} $ The estimation results suggest that the postgraduate wage premium continues to remain positive and significant even if workers’
undergraduate major and type of university (private or public) are controlled for. Using OLS, the estimated postgraduate wage premium for male workers is 25.0%, while it is 26.4% using the Heckman two-step estimation. The corresponding figures for female workers are 23.7% and 24.7%. However, the IV estimation results reveal that the estimated postgraduate wage premium is not statistically significant.

The biggest concern about our IV estimation result is that the estimate of the effect of earning a master's degree is not significant because of the scarcity of the sample with a postgraduate degree. To overcome this problem, this study uses the WPS data, which contains information about more than one thousand individuals with a postgraduate degree. The OLS estimation results reveal that the estimates of postgraduate wage premium using the WPS data is positive, significant, and not too far from those obtained from the OLS regression with JPSC data and those from previous literature. Similarly, the first-stage regression for the IV regression with the WPS data also gives an F-statistic high enough not to worry about the weak instrument problem. The estimates of the effects of postgraduate education on wages by using the IV, however, were not significant and even negative.

The results of log wage regression with the IV indicate that the estimates of the postgraduate wage premium in the OLS regression may simply reflect sorting based on unobserved ability or screening/signaling effects rather than higher worker productivity due to postgraduate education. However, another possibility needs to be accounted for—students obtain a postgraduate degree in pursuit of the job’s non-pecuniary benefits. In order to check if this association is true, we regress the job satisfaction indicator using the same IV. The estimate of the effect of earning a master’s degree is positive and significant for male workers, which indicates that Japanese males pursue a graduate degree not for higher wages, but for the non-pecuniary aspects of the job.
The remainder of this paper is organized as follows. Section 2 provides some background about the current study and discusses the related literature. Section 3 describes the dataset used for the estimation. The estimation method and procedure are presented in Section 4, while Section 5 presents and discusses the estimation results. Section 6 describes the conclusions.

### 2. Background and Related Literature

Numerous studies have discussed the effect of post-secondary education on wages using U.S. data, and some of these include analyses of the effects of postgraduate education. Although there are debates about whether the postgraduate wage premium is attributable to enhanced productivity or signaling/screening effect, most of these studies report positive and significant wage premiums for graduates. For example, early studies in the field such as Ashenfelter and Mooney (1968) and Taubman and Wales (1973) suggest that postgraduate education has a positive effect on wages, although Taubman and Wales (1973) suspect that to a certain extent, the wage premium can be attributed to screening effects. Estimating the so-called sheepskin effect of diplomas using data from the 1991 and 1992 March Current Population Survey, Jaeger and Page (1996) find that white workers with a master's degree earn 5-16% more than those with only a bachelor's degree, even if they have the same years of schooling. Deere and Vesovic (2006) report that the wage gap between those with a graduate degree and those with only an undergraduate degree corresponds to 10.5-42.0% of the average wage of high school graduates. One of the few studies outside the United States is by Walker and Zhu (2011), who estimate a standard wage function for workers in the United Kingdom using data from the Labour Force Survey. They find that workers with a postgraduate degree in science, technology, engineering, or mathematics earn 6.6-16.6% more than those without a postgraduate degree.

All of the above-mentioned studies are similar in that they do not take the endogeneity
of schooling into account; that is, the fact that the link between wages and education potentially reflects confounding factors such as self-selection and unobserved ability. However, there is a growing body of literature that explicitly considers such potential endogeneity. A comprehensive survey of such studies focusing on undergraduate education is provided by Card (1999), suggesting that there is indeed evidence of an upward ability bias, but the bias is so small that it can be offset by downward bias due to measurement errors in schooling variables. On the other hand, Song et al. (2008), examining the postgraduate wage premium, find evidence of a substantial downward bias due to sorting effects, reflecting the fact that students with a higher quantitative graduate records exam (GRE) score are less likely to go to graduate school. While Song et al. (2008) use tuition fees as an IV to deal with the endogeneity of graduate schooling, Hussey (2012) uses the panel data of MBA holders to eliminate the ability bias. The majority of MBA holders in the U.S. have work experience before earning an MBA, and Hussey (2012) estimates a fixed effect model using panel data that contains information on wages before and after individuals obtained an MBA in order to eliminate the upward bias due to unobserved ability, which is assumed not to change over time.

There are very few studies on the postgraduate wage premium in Japan. One of the few exceptions is the study by Shimizu and Higuchi (2009), who examine the effect of obtaining an MBA degree on wages using a dataset from a survey they conducted of MBA degree holders in Japan, in which they asked respondents about their work experience and wage before and after obtaining the MBA and about their current wage. They find that workers who obtained an MBA degree overseas experienced a positive and significant wage increase, while those with a domestic MBA degree did not. The estimation results provided by Shimizu and Higuchi (2009) cast doubt on the effectiveness of MBA postgraduate education in Japan. As mentioned in the previous section, however, the majority of those holding a postgraduate degree are science/engineering
majors, and the MBA holders are an exception in Japan.

The study by Morikawa (2015) was the first attempt to estimate postgraduate wage premiums regardless of individuals' majors. Using cross section data from the Employment Status Survey (ESS), which is a nationally representative survey, the study by Morikawa (2015) found that workers with a graduate degree earn 15-30% more than those with only a bachelor's degree. Similarly, Kakizawa et. al. (2014) estimated a wage function and found that the internal rate of return to earning a master's degree is around 11-12%. Morikawa (2015) and Kakizawa et. al. (2014) use the Heckman's two-step estimation method in order to deal with the bias arising from the selection into the labor market, but none of the studies on the postgraduate wage premium in Japan take the endogeneity of graduate schooling into account.

As outlined earlier, there are at least three major reasons why it is important to consider possible self-selection biases when assessing the effect of postgraduate education on wages in Japan. These reasons are grounded in certain idiosyncrasies of Japan's education system and labor market practices, and it is useful to consider these in greater detail. The first reason is that the majority of graduate students in Japan are science or engineering majors at public universities and the fact that admission to science and engineering courses at public universities is highly selective. In general, prospective students in Japan have to take entrance examinations for admission to colleges or universities, with public universities requiring applicants to take the National Center Test for University Admission in addition to the university's own entrance examination. Public universities examine examinees in four to six subjects, and those applying for a course in science or engineering have to choose mathematics as one of their exam subjects. On the other hand, private universities require examinees to take only the university's examination in two to four subjects. The stricter entrance requirements for science and engineering degrees at public universities mean that students majoring in these subjects are more likely to have higher ability.
than other students do. Omitting individuals’ subject and type of university can cause a positive bias when estimating the postgraduate wage premium, since most of those with a graduate degree are science/engineering graduates.

Second, even if workers' undergraduate subject and type of university (private or public) are controlled for, it is possible that an ability bias remains. The reason is that the probability that a student will progress to study for a graduate degree appears to be associated with the selectivity or quality of the university attended and his/her own ability. For example, while around 85% of students completing an undergraduate degree in the science and engineering departments at the University of Tokyo and Kyoto University in 2011 enrolled in a graduate degree, the corresponding figure for public universities as a whole is only approximately 50%. Moreover, science and engineering students in Japan typically belong to a research group (called "laboratory") organized by their advisor, and whether students enroll in a graduate program often depends on their relationship with their advisor. It is possible that professors encourage students with superior ability to enroll in a graduate program, which can result in a positive correlation between graduate schooling and unobserved ability. Thus, workers with a graduate degree are likely to have higher academic ability than those with only a bachelor's degree, but test scores to control for academic ability, such as GRE or SAT scores in the U.S., are not available in Japan.

Third, in addition to these ability biases, there may be another type of self-selection bias linked to the timing of entry into the labor market. Figure 3 shows annual growth rates of graduate enrollment from 1972 to 2012. Graduate enrollment increased rapidly following the 1973 oil crisis, in 1990-1993 in the wake of collapse of the bubble economy, and in 2010 following the collapse of Lehman Brothers $ ^{5} $ that triggered the global financial crisis. The pattern suggests that a considerable
numbers of students decided to enroll in graduate school instead of finding a job during a recession. $ ^{6} $ College students in Japan have an incentive to postpone their entry into the labor market during recession, because those who fail to obtain a job, or a good job, immediately after graduation in Japan's highly standardized recruitment process are at a disadvantage compared to fresh graduates in subsequent years following the recession. Hamaaki et. al. (2013), for example, have shown that in Japan, the first job has a significant lingering effect on future wages, and it takes ten years for the effect of the first job to disappear. Students, therefore, have a strong incentive to avoid graduating during a recession and to go to graduate school instead in order to postpone leaving university. Given that attending graduate school involves substantial costs, if those who are able to attend graduate school to avoid entering the job market during a recession subsequently find higher-paying jobs than those who were not able to attend graduate school, then the difference in wages between those with and without a graduate degree may reflect not only the human capital accumulated through graduate education but also differences in students' financial means reflecting, e.g., their family's wealth.

For the reasons mentioned above, the analysis in this study uses an IV to deal with the endogeneity of graduate schooling. The instrument used is the number of student places (capacity) available at graduate schools across Japan divided by the number of fourth-year undergraduate students for each undergraduate subject and type of university. The rationale for using graduate enrollment capacity as the instrument variable is as follows. The increase in the number of graduate students during the observation period increased in line with the expansion of university capacity for graduate study, and unless the distribution of students' ability and preferences for graduate education has changed substantially, the expansion of graduate enrollment capacity has made it easier for undergraduate students to proceed to graduate study. Therefore, the change in
graduate enrollment capacity affects the decision of college students to go to graduate school but is not correlated with individuals’ unobserved abilities. $ ^{7} $

### 3. Data

As mentioned earlier, the two major preceding studies on the returns to graduate education in Japan by Morikawa (2015) and Kakizawa et al. (2014) employ the ESS data. The ESS is a nationally representative survey consisting of a very large sample. However, the ESS data do not contain information on the subject of workers' undergraduate degree or the type of university (private or public) that they attended, and, as highlighted, omitting these variables can potentially cause serious upward bias. Consequently, this study employs data from the Japanese Panel Study of Consumption (JPSC), even though the sample size is considerably smaller than that of the ESS.

#### 3.1. Japanese Panel Study of Consumer

The JPSC is one of a very limited number of panels available in Japan and offers a host of advantages, including the fact that it is the longest panel of its kind, spanning a period of 20 years. The survey is conducted by the Institute for Research on Household Economics (IRHE) and started in 1992 with 1,500 women aged between 24 and 34. Of the initial sample, 1,002 women were married, while 498 were unmarried. The IRHE added 500 women aged 24 to 27 in 1997, 1,000 women aged 24 to 29 in 2003, and 500 women aged 24 to 28 in 2008. Although the sample size of the JPSC is smaller than that of the ESS, the JPSC data provides more detailed information about the households, including the undergraduate subjects and type of university (private or public) of the respondents and their husbands. Since this paper focuses on the effect of earning a
master’s degree, the analysis focuses on those who have at least a bachelor's degree. $ ^{8} $

In the JPSC data, 53% of individuals with a master’s degree had obtained a bachelor’s degree in science or engineering from a public university, while 29% majored in science or engineering at a private school. Thus, more than 80% of those with a master’s degree majored in science or engineering.

The analysis below will focus on those with a degree in science, engineering, agriculture, the humanities, social sciences, $ ^{9} $ or education. Those with a degree in medical, pharmaceutical, dental, or veterinary science are excluded, since these degrees require six years of undergraduate study and those intending to obtain a graduate degree in these fields directly enroll in a Ph.D. program after completing their undergraduate degree.

Summary statistics of the sample are provided in Table 1. Since the present study focuses on the postgraduate wage premium, those who do not work and those who work part-time are also excluded. Based on these selection criteria, the sample contains 6,362 observations for men and 1,925 observations for women. $ ^{10} $ Since the sample size is not that large, those with a degree in science, engineering, and agriculture are aggregated into those holding a degree in natural sciences, and those with a degree in the humanities, social sciences, and education are aggregated into those with a degree in humanities and social sciences. Table 2 presents the number of observations for those with a master's degree by degree subject and type of university.
#### 3.2. Working Person Survey

The sample size of the JPSC data is not very large, and single male individuals are not included. The IV regression relies on the response of the average wage to the change in the difficulty of entrance to graduate schools, but only a few percentage of workers are interested in undertaking graduate education in Japan. Thus the sample size can affect the estimation result significantly. In order to deal with this problem, we employ the data from Working Person Survey conducted by the Recruit Works Institute.

The WPS is a biannual cross-sectional survey on workers in Japan, starting in 2000. Around 10,000 workers are interviewed at each survey, but information on the year of graduation is available only for the 2006, 2010, 2012, and 2014 data. The WPS data contains information on the undergraduate subjects, but the type of university that workers graduated from are not available. $ ^{11} $

Summary statistics of the sample are presented in Table 3, and the sample size by major in Table 4. As the table reveals, the sample size is not very different from the JPSC data, but the number of observations with a master’s degree is more than three times as large as that of the JPSC.

Unlike the JPSC data, the WPS data lacks information about the type of universities individuals graduated from which can be an important variable to mitigate the ability bias, but the WPS data contains a significantly greater number of individuals with a master’s degree than the JPSC data. Moreover, unlike the JPSC data, the WPS data contains single males. In summary, the WPS data has an advantage over the JPSC data in terms of the sample size and sample coverage, while the JPSC data has richer information on individuals’ education than the WPS data.