Silviase/jgov_v1.4_full_ann huggingface dataset:
ital status, educational background, and employment status. The analysis sample includes 259,756 males and 267,838 females. For junior high school graduates, high school graduates, 9 and 12 years of education are assigned, respectively. Fourteen years of education is assigned for junior college or technical college graduates, and 16 years of education is assigned for 4-year college graduates or graduate school graduates. The survey records the annual earnings in ranges. These ranges are transformed into a continuous variable by using the center value for each range. For the highest range, more than 150 thousand yen, 150 thousand is assigned.

The means of the variables by birth year - birth month appear in the Figures. The number of observations reported in Figure 1 indicates that observations are more likely to be taken from winter months (i.e., between January and March) than summer months (i.e., between June and August). This seasonal pattern of births is observed among elder generations, because farmers tend to deliver their babies during the agricultural off-season. These figures imply that birth month might carry information about parental occupation and other socio-economic background characteristics. In particular, those born in the winter might be more likely to have a farm background.

Figure 3 shows the month-to-month variation in the eventual years of education. Given the possibility that summer- and winter-born individuals have different socioeconomic backgrounds, it is not surprising to find fewer years of education among the winter-born than the summer-born, as reported in Figure 3. Thus, to identify the relative age effect on educational attainment,
It is important to focus on the discontinuity of educational attainment between the March-born and the April-born because the discontinuity at this point is arguably created by the cut-off date of primary school admission, which consistently has been April 1 in Japan since 1947. The only sharp gap in educational attainment is found between March and April, as expected. After adjusting for the difference in the eventual years of education across school cohort groups, there is about a 0.14-year gap between the March-born and the April-born.

Figure 4 indicates that there is virtually no annual income gap between March-born and April-born males. In contrast, there is a sharp annual-earnings gap between these two groups. However, once the windows of comparisons are widened to two months before and after the cut-off point, the February+March born and the April+May born do not seem to have a gap in annual income. Figure 5 indicates the employment rate is virtually continuous between March-born and April-born. No gap in the employment rate assures the validity of taking a look at the earnings of the working population because we do not have to worry about sample-selection bias. Figure 5 indicates a fairly continuous marriage rate across birth months.

Because our sample is household-based, we can identify the father’s education, given co-residence with father. Figure 6 plots the father’s years of education by the birth month of his children as a proxy of socio-economic status. For both males and females, those born in August had fathers with more years of education. This is probably because those who were born in
August were less likely to have a non-farm background. It should, however, be noted that these figures are calculated given co-residence with father and thus issues of sample-selection should be kept in mind.

## 4 Estimation Results

### 4.1 The Discontinuity of Variables by Birth Month

Tables 1 and 2 report the formal test of the differences in individual characteristics by birth month. All the specifications include school-cohort dummy variables to capture the time-series changes in years of education, annual income, employment rate, etc. These analyses indicate that the gap in the years of education between March-born and April-born individuals is statistically significant.

The regression results for years of education indicate a discontinuity between the March-born and the April-born, probably because of the relative age effect. It is then interesting to examine at which margin of the years of education the discontinuity between the March-born and the April-born occurs. Identifying the margin of treatment is important to interpret the results on earnings because the local, average treatment effect interpretation of the IV estimator by Imbens and [1994] and Angrist et al. [1996] offers a unified theme for interpreting the results of birth month on education and earnings. The margin of the treatment is identified by running the following
regression for s=12, 14, and 16:

$$ 1(S\geq s)=z\beta+s c h o o l c o h o r t d u m m i e s+u, $$

where $ 1(\cdot) $ is an indicator function and z is a set of birth-month dummy variables. The results of the regression appear in Table 3. The results indicate that being born in April instead of March uniformly increased the probability of finishing high school $ (s = 12) $ , finishing junior college or technical college $ (s = 14) $ , and finishing 4-year college $ (s = 16) $ by 2 percentage points for males and by 1 percentage point for females.

In contrast to the results for education, there was no statistically significant gap between the March-born and the April-born in terms of annual earnings, the employment rate, or the marriage rate, as reported in Tables 1 and 2.

Column (2) of Tables 1 and 2 reports the regression result of the employment status on dummy variables for the birth months, using the male sample. The dependent variable is the dummy variable that indicates being employed and having valid annual earnings information. The result shows that none of the coefficients for the dummy variables is statistically significant. These results suggest that there is no variation in the employment rate induced by differences in birth month. Confirming no systematic selection into employment depending on birth month, we can interpret the regression result of the log annual income on the birth months dummy variables without worrying about sample-selection bias.
The regression result for the log annual income among males is reported in Column (3) of Table 1. The result for males indicates that there is no gap in the log annual earnings between the March-born and the April-born. Regardless of the fact that the April-born had 0.14 year more education than the April-born, the April-born earned as much as the March-born. This implies that having greater educational attainment induced by the relative age effect does not induce an increase of earnings. Those who were born in April did better in terms of educational attainment due to their subtle advantage, but the greater amount of education induced by this advantage was not rewarded in the labor market. It is worth noting that those who were born in August and September earned about two percent more than the April-born. This is probably because those who were born in August or September were likely to have an urban background and higher socioeconomic status.

The regression result for the log annual income among females, which is reported in Column (3) of Table 2 contrasts with the result for males: The April-born earned 2 percent more than the March-born. This might suggest a positive return to an additional year of education induced by the relative age effect; however, we should notice that the May-born also earned 2 percent less than April-born. Thus, if the comparison windows are extended for two months, as we will see, there was no significant gap between the February+March-born and the April+May-born.

In term of father’s years of education, there was no statistically significant
difference between the March- and the April-born among males, as reported in Column (5) of Table 1. However, among females, the March-born had fathers with significantly more education than the April-born, as reported in Column (5) of Table 2. The fact that March-born females had fathers with more education might cause the downward bias in the estimate of the relative age effect. This is because the gap in years of education due to the relative age effect was partly canceled by the better family background of March-born females. To address this potential problem, the regression model with father's educational background as an additional covariate is estimated in a later section.

### 4.2 The Implied Return to Education

Based on the findings reported so far, it is interesting to discuss the return to additional years of education induced by the relative age effect. To implement this exercise, the analysis sample is basically restricted to the March-born and the April-born because previous results suggested a difference in the socio-economic background between those who were born in winter and summer. The March-born and the April-born presumably shared the same socio-economic background, but the age at school entry was discontinuously different. The continuous socio-economic background between the March-born and the April-born was evidenced by such continuous background variables as marriage rate and father's education, as far as the male sample is concerned. The discontinuity in years of education was arguably
created by the cut-off day of school admission. Thus this research is based on a regression discontinuity design.

The concept of the local average treatment effect by Imbens and [1994] and Angrist et al. [1996] offers a unified theme for interpreting the two regressions of education on birth month and annual earnings on birth month. The IV estimate

$$ \beta^{LATE}=\frac{E[\ln(inc)|april,school cohort]-E[\ln(inc)|march,school cohort]}{E[educ|april,school cohort]-E[educ|march,school cohort]} $$

identifies the return to an additional year of education induced by the relative age effect.

To implement this identification, the analysis sample is restricted to the March- and April-born, and a dummy variable that indicates April born, april, is created. Using the first-stage regression model:

$$ educ=\gamma a p r i l+s c h o o l c o h o r t d u m m i e s+u $$

and the reduced form regression model:

$$ \ln(i n c)=\delta a p r i l+s c h o o l c o h o r t d u m m i e s+v, $$

we can show that

$$ \beta^{L A T E}=\frac{\delta}{\gamma}, $$

under the assumptions $ E[u|april, school cohort] = E[v|april, school cohort] = 0 $ . The actual estimation of $ \beta^{LATE} $ is made by using the standard IV procedure of regressing $ \ln(inc) $ on educ and age and city dummies using april
as an IV for educ, but the estimate should not be interpreted as the return to education in the usual sense. Instead, $ \beta^{LATE} $ estimates the return to an additional year of education induced by the relative age effect.

Table 4 reports the estimation results based on the male sample. Table 4 Column (1) reports the return to education estimated by OLS in the usual sense, just for reference. Table 4 Column (2) reports the result of the first-stage regression. It indicates that the April-born had 0.14 year more education than the March-born. Table 4 Column (3) reports the estimation result for the reduced-form equation. As found in the previous section, those who were born in April did not earn more than those who were born in March. The result in Column (4) combines the results of Columns (2) and (3), and the estimated return to an additional year of education induced by the relative age effect is 0.04, but statistically insignificant. The advantage of being born in April is that it makes people stay in school longer, but this additional year of education is not rewarded in the labor market.

Table 5 reports the estimation results based on the female sample. The return to education estimated by OLS is reported in Column (1), just for reference. Column (2) reports the first-stage regression result, which indicates that the April-born had 0.07 year more education than the March-born. The reduced-form estimation result reported in Column (3) indicates that the April-born earned about 2 percent more than the March-born. Combining the results of Columns (2) and (3) together, the LATE estimate reported in Column (4) indicates that an additional year of education due to the relative
age effect reaped a 19-percent return in the labor market. The advantage of being born in April is that it makes people stay longer in school, and the effect of this additional year of education is not washed out in the labor market.

Before concluding that there is a positive return to education due to the relative age effect among females, extra attention should be paid to the fact that there was a positive spike in the average annual income of April-born women, as shown in Figure 4. This positive spike could have been created by sampling error due to the relatively small sample size of 23,000 observations of the April-born. If the relative age effect is the true mechanism that increases the annual income of April-born females, it should equally raise the annual income of May-born females, though presumably to a smaller degree. By the same token, if the relative age effect is disadvantageous for the March-born, the same should apply to the February-born. To increase the efficiency of the estimation, the same estimation is repeated, using the sample that consists of those who were born between February and May. Instead of comparing the education and annual income of the March-born and the April-born, the (February + March)-born and the (April + May)-born are now compared. In other words, we extend the sample window for both the control and treatment groups to increase the estimation’s efficiency.

The results of the estimation using the February-May-born as a sample appear in Tables 6 and 7. The results for males reported in Table 6 are almost identical to those obtained from the March-April sample reported in Table 4.
This arguably assures the appropriateness of using the February-March born sample to identify the relative age effect. The results for the female sample reported in Table 7 are almost identical to those based on the March-April sample reported in Table 5, except for the annual income regression. The (April+May)-born earned 1 percent more than the (February+March)-born, but this difference is not statistically significant. The implied return to an additional year of education induced by the relative age effect was 10 percent, but this is not statistically significant.

All in all, the analysis suggests that those who were born early in a school cohort had more years of education. In particular, among males, those who were born in April had 0.14 year more education than those who were born in March. The corresponding number for females is 0.07 year. The college-attendance rate was 2 percentage points and 1 percentage point higher for males and females, respectively. These effects are not negligible, considering that the average college attendance rate was 27 percent for males and 9 percent for females in the analysis sample.

Regardless of the significant, relative age effect in terms of education, a robust relative age effect is not found for annual income. This implies that the additional year of education induced by the relative age effect did not lead to a higher income in the labor market. In other words, March-born people earned more than April-born people, given the same amount of education.
## 5 Discussion

### 5.1 Birth months and socio-economic background

As we have seen, there used to be a seasonal pattern of birth months during the 1950s and 60s. This seasonal pattern of birth months likely occurred because agricultural households were more likely to have babies in the agricultural off-season, which is winter. Thus the month of birth may be correlated with the family's socio-economic background. Although there is no a priori reason to doubt the difference in socio-economic family background between the March-born and the April-born, it is a useful exercise to examine the relative age effect while controlling for family background.

Father’s education is used as a proxy for socio-economic family background. Among the people who lived with their fathers in the same household, fathers’ years of education are identified. Categorical dummy variables for the father’s years of education are created, and these variables are included in both the education and income equations.

The results of the estimation with the dummy variables for father’s years of education appear in Table 8 for males and Table 9 for females. The results for males are almost identical to the estimation results without father’s years of education that appeared in Table 4.

The difference in the results for females is notable. After controlling for father’s years of education, the April-born had 0.17 year more education. This result contrasts with the result obtained without controlling for father’s
years of education, which was 0.07, as reported in Table 5. The change in the result comes from the fact that March-born females tended to have fathers with more education, as evidenced in Figure 7. The difference in the coefficients comes from the fact that April-born people had more education than March-born people, regardless of whether they had fathers with shorter years of education.

We should be careful, however, that these results are obtained for individuals who lived with their fathers. The decision of co-residence is presumably endogenous, and this estimation might suffer from sample-selection bias. What we should take from these tables is that the results without father’s years of education do not suffer from obvious omitted variable bias due to omitted family background variables.

The other way to examine the differences in socio-economic background that could be correlated with the month of birth is to divide the analysis sample into periods. The seasonality of the birth-month distribution is most notable in the period between 1945 and 1954. This seasonality almost disappeared after 1965. Thus, if there is a correlation between the month of birth and socio-economic status, the correlation should be stronger for the period between 1945 and 1955. If the correlated, socio-economic background creates a gap between the March-born and the April-born in terms of educational and labor market outcomes, we should find a gap for the people who were born during the period between 1945 and 1954 rather than for the people who were born between 1965 and 1974.
The results of the regression applied for the divided sample appear in Tables 10 and 11. For males, the results are fairly stable over the sample period, except that the gap in the years of education between the March-born and the April-born is larger for those who were born between 1945 and 1954.

The results for females reported in Table 11 are also fairly stable over the sample period. Although the size of the coefficients fluctuates, what is important is that we confirm the gap in educational attainment between the March-born and the April-born, even among the birth cohort of 1965-1974 for which the seasonal variation of the birth-month distribution is not present.

### 5.2 Absolute age effect or relative age effect?

The discussion so far assumes that the gap in educational attainment between the March-born and the April-born is due to the relative age effect. However, previous studies have tended to ask about the optimal school-starting age (Fertig and Kluve [2005] and Datar [2005]). Their implicit presumption is that the effect of age at school entry on educational attainment is due to differences in the degrees of children's physical and mental development. Fredriksson and Ockert [2005] go a step further and ask whether the effect of age at school entry on educational outcomes is due to the absolute age or relative age of a subject within his/her school cohort. They regressed test scores on the absolute and relative measures of age at school entry. They found a large coefficient for absolute age and a small coefficient for relative age and thus dismissed the relative age effect. However, the birth-month
distribution within a school cohort does not seem to vary much over time and their test for the relative age effect might not have sufficient power.

To separately identify the absolute and relative age effect, I exploit the sudden drop of birth cohort size in 1966 due to the superstition of the Fire-Horse (Hinoeuma) year. The Fire-Horse year comes every 60 years according to the Chinese zodiac calendar. Japanese people share a superstition that women born in this year are hot-tempered and unmarriageable. Due to this superstition, people try to avoid having babies in this specific year and the number of births drops by 25 percent compared with adjacent years. $ ^{5} $

We can confirm that the number of observations who were born in 1966 is about 25 percent smaller in our analysis sample, as shown in Figure 8. Careful examination of this figure suggests an interesting variation in the number of observations by birth month. The number of observations jumped at the beginning of year 1967 because “the Hinoeuma sanction” was lifted. Due to this huge swing in the population size from one month to the next, there are many people who were born between January and March in the school cohort starting in April 1966. Thus, if the relative age effect is in motion, the gap in the years of education between the April-born and the March-born should be smaller for this school cohort because the March-born
in this school cohort was not as handicapped as those in other school cohorts. By the same token, those who were born in March 1966 should be the most seriously handicapped because their relative age position in the same school cohort is behind that of other students.

The prediction from the relative age effect hypothesis is tested by running a regression of outcome variables on the April-born dummy and the interaction terms of the 1965 school cohort $ \times $ April-born dummy and the 1966 school cohort $ \times $ April-born dummy, using the sample that consists of observations of the March- and April-born. The relative age hypothesis predicts a positive coefficient for the first interaction and a negative coefficient for the second interaction. The sample is restricted to the school cohort of the 1960s.

The results of the regression are reported in Table 12. For males, The April-born had 0.18 year more education than the March-born in the usual years. However, for the 1966 school cohort, the April-born had 0.04 year less education than the March-born, as evidenced by the negative coefficient for the interaction term of 1966 school cohort $ \times $ April-born dummy variable. Although the coefficient for the interaction term is not statistically significant, the size of coefficient is suggestive for the relative age effect. The school cohort of 1965 does not seem to be different from other school cohorts in the 1960s. The school cohort around 1966 does not seem to be different in terms of its income structure.

For females, the coefficient for the interaction term of the April dummy