This paper exploits China's one‐child policy (OCP) to study the relationship between fertility and educational attainment of the mothers of China's “sibling‐less generation.” I take two difference‐in‐differences approaches to estimate the OCP's effect on women's education: one compares gender difference among the ethnic majority group and the other compares ethnicity differences between ethnic majority women and ethnic minority women. I also explore the heterogeneity of the policy's effects by parent's status at the Communist Party. I find that the OCP has a positive and significant effect on women's education and explains about half of the increase in educational attainment for women born between 1960 and 1980. Their increased educational attainment associates with delayed entry into first marriage, delayed entry to parenthood and increased labor supply. ( JEL I20, J13, J16, J18)

ABBREVIATIONS

CFPS China Family Panel Studies DD Difference‐in‐Differences MCP Members of Communist Party OCP One‐Child Policy

I. INTRODUCTION In the late twentieth century, women's educational attainment increased remarkably relative to men's in both Western and Eastern countries, and China is no exception. Figure 1 shows that the gender gap in years of schooling started narrowing among cohorts born in 1960 and fully closed within 20 years. Studies have explained this trend with growing expectation of employment by young women, increase female labor force participation, and delayed entry to marriage. I exploit China's one‐child policy (OCP) and provide empirical evidence from this large population on how much the family planing policy explains the shrinking gender gap in educational attainment. Figure 1 Open in figure viewer PowerPoint Average Years of Schooling by Gender Note: Individual sample weights provided by CFPS were used in the construction of this figure. It is well documented that changes in women's educational attainment are correlated with trends in fertility and marriage. The causal direction could be two ways. Women who become mothers at an early age tend to have accumulated fewer years of schooling compared to those who delay their entry to parenthood. Marriage delay also enables women to take formal education more seriously and led to changes in their relationship to work (Goldin 2006; Waite and Moore 1978). Women with higher educational attainment also tend to have lower fertility rate and later entry to marriage or parenthood (Isen and Stevenson 2010; Martin 2000). There is also an extensive literature on the relationship of fertility and childcare on women's labor market attachment (Bailey 2006; Buckles 2008; Budig and England 2001; Goldin and Katz 2000; Goldin and Katz 2002; Waldfogel 1997). As a widely influential fertility policy, the OCP not only affected the fertility decision of married couples at childbearing ages, but also affected the fertility expectation and marriage decision of younger generation. Upon observing the OCP implementation, young women would expect their future time cost of childbearing to be exogenously reduced. Their expected labor supply and option value for their future career would be increased, which together lead to an increase in return to schooling. Furthermore, women may delay their entry to parenthood or even to marriage considering the more relaxed timetable for fertility. These forces would lead women to pursue more education. Thus, this paper asks whether women who observed the OCP before dropping out of school changed their educational decisions, and how? I use individual‐level data from the China Family Panel Studies (CFPS) 2010 baseline survey for the empirical analysis. I take two difference‐in‐differences (DD) approaches—one compares gender difference among the ethnic majority group, the other compares ethnicity differences between ethnic majority women and ethnic minority women—to estimate women's educational attainment changes in response to the policy. I find that compared to Han men, Han women's years of schooling increased by 1.28 years, which explains 53.6% of the 2.38 years increase in educational attainment of women born between 1950 and 1980. Compared with non‐Han women, Han women's educational attainment also increased by 1.28 years. I also explore the heterogeneity of the policy's effect by parent's status of Communist Party, which further supports the finding on OCP's positive effect on women. My analysis on women's post‐school outcomes shows that the OCP associates to women's delayed entry into first marriages, delayed entry to parenthood, and increased labor supply. These findings provide supportive evidence for potential mechanisms through which the OCP increased women's educational attainment. The rich literature on the OCP is threefold.1 First, most effort has been made to explore the effects of China's family planning policies (including the most restricted OCP) on fertility (Becker 1991; Lavely and Freedman 1990; Li, Zhang, and Zhu 2005; McElroy and Yang 2000; Wang 2012). Generally speaking, there are two views exist on how the OCP affected fertility: one group find that the OCP had a significant effect on fertility in China, while the other argue that the OCP did not play much of a role than socioeconomic development in China's fertility decline. Second, instead of fertility reduction, there are studies look at the OCP's effect on other outcomes such as sex ratio, gender selection, saving rate, and housing price (Huang, Lei, and Zhao 2016; Li, Yi, and Zhang 2011; Tuljapurkar, Li, and Feldman 1995; Wei and Zhang 2011). Third, many studies have explored the OCP's effects on human capital accumulation of children, the sibling‐less generation (Angrist, Lavy, and Schlosser 2005; Black, Devereux, and Salvanes 2005; Lee 2012; Li, Zhang, and Zhu 2008; Rosenzweig and Zhang 2009). However, the OCP's effect on mothers of the sibling‐less generation has rarely been studied by economists. Compared to the OCP's quality‐quantity tradeoff effects on children, its effect on the mothers is much less straightforward. I contribute to the existing literature by highlighting the OCP's positive externality on women's education, which has been overlooked by researchers. I also add to the literature on relationship between fertility and women's human capital accumulation. A contemporaneous working paper by (Huang, Lei, and Sun 2016) studies the similar issue by estimating the effect of local monetary penalty for one unauthorized birth on girls' high school completion rates. Using geographic variation on fine rate as a measure of the OCP could be problematic because local fines could be targeted due to the local financial situation as well as the local fertility and education. Additionally, monetary penalty is neither the only nor the harshest enforcement of the OCP. Losing track of the other enforcement2 may overestimate the effect of fines on women's educational attainment. By contrast, the approaches in this paper provide estimates which can be interpreted as the effects from the entire policy.

II. HISTORICAL BACKGROUND A. The One‐Child Policy Since China is such a populous country, controlling the population size has been a fundamental policy since the early 1960s. There are three periods in the history of the Chinese family planning policies. Period 1 (1963–1971): the central government first announced a position advocating “birth planning in urban areas and densely populated rural areas.” Although family planning commissions were established during Period 1, this early family planning operation was halted by the Cultural Revolution. Period 2 (1971–1979): a widely spread family planning campaign was successfully carried out, and Chinese people voluntarily3 delayed marriage, lengthened the period during first and second birth, and had fewer children. Period 3 (1979–2015): The OCP was formally conceived in 1979 and rapidly established across the country in 1980 (Banister 1991; Li, Zhang, and Zhu 2005; Wang 2012). The OCP was the strictest family planning policy as it restricted each couple to having only one child, but this strict requirement only applied to the Han, the ethnic majority.4 The policy allowed many exceptions for ethnic minorities.5 An urban non‐Han couple could have two children, and a rural non‐Han couple could have three, or even more, children depending on the population size of the ethnic group (Wang 2012). There are also some exceptions for rural Han couples, considering that most rural families make a living through labor‐intensive agricultural activities. For example, a rural Han couple could apply for a permit to have a second child 4 years after their first birth if the only child is female or disabled. Thus, the intensity of the OCP could be roughly ordered from high to low from urban Han, rural Han, urban non‐Han, and rural non‐Han. The provincial governments gradually issued detailed regulations to guarantee the enforcement. Population and Family Planning Commissions were set up at every level (province, city, county, etc.) to ensure the enforcement of the policy. The OCP was implemented through varies enforcement: monetary penalties on above‐quota birth, denial of public service, required abortion of subsequent pregnancy, and sterilization (Banister 1991; Li and Zhang 2007; McElroy and Yang 2000). Besides the enforcements, the OCP also strongly encouraged people to delay their first birth and lengthen the spacing between two births. In addition, in the following year, 1980, China passed the new marriage law which delayed the lawful ages at first marriage for women from 18 to 20 and for men from 20 to 22.6 This age change may be more important for females and may raise women's expected age of marriage and fertility, and further induce them to obtain more education as they have more time before marriage. The government also encouraged people to comply with the policy by rewarding couples who had only one child with a “one child certificate,” which entitled them to a variety of benefits (Arnold and Zhaoxiang 1986). Meanwhile, the local governments tightened the hukou registration and inspection work and raised awareness of the policy by campaigns and posters. Note that this paper does not intend to capture the total effect of Chinese family planning policies on women's education. As mentioned above, there are several stages of the policies representing different levels of birth control restrictions before the OCP. Those policies likely already have effects on women's education. I only study the OCP's effect, which can be interpreted as the extra effect that the OCP added to the previous policy. Women's Labor Supply Before the OCP China's female labor force participation has been high as well as male labor force participation since Mao‐era. For those who born between 1945 and 1960, most urban women did wage labor in state‐owned factories or other businesses, while rural women were drawn into the people's communes' labor service. Women's wage was an important part of the family income (Selden and Perry 2003). On top of the “traditional” household work they had to do wage work—mostly outside the family or the community of women in which they grew up. Although working women was a norm by then, compared to men, women tended to be employed in low productive job and paid significantly less (Chi and Li 2014).

III. DATA The microdata used for this paper come from the ongoing CFPS,7 a nationally representative, annual longitudinal survey of Chinese communities, families, and individuals. The CFPS is designed to collect individual‐, family‐, and community‐level longitudinal data in contemporary China, which reflect the social and economic transformation of Chinese society and how that affects the economic activities, education outcomes, family relationships, migration, and health status of China's population. I use the cross‐sectional CFPS 2010 baseline survey for this analysis. The data contain a rich set of individual, household, and community information, including demographic, economic, and educational information. The data have clear advantage to study this topic. They provide detailed information on family background that is essential to one's educational resources, for example, number of brothers and sisters, birth order, both parents' level of education, and both parents' political status.8 Additionally, the survey provides birth province, hukou status at age 3 and age 12, which is essential to deal with the potential problem of inter‐province migration. The survey covers most of the administrative regions in China: all municipalities and 21 provincial regions.9 The darker shaded regions in Figure 2 are the provinces and municipalities in which the survey has been conducted. Note that the regions left out10 are very distinct from the others in terms of ethnic composition, language, and lifestyles; therefore, it would be hard to compare the policy's effect in these regions anyways, had the survey covered them. Figure 2 Open in figure viewer PowerPoint CFPS Covers 21 Provinces and 4 Municipalities The sample used in the estimation includes cohorts born between 1950 and 1980. Table 1 presents summary statistics of the sample. Women account for 52.12% of the population and Han account for 91.89% of the population. About 83.83% of the population is rural. The primary variable used to represent educational attainment is years of schooling, constructed by the CFPS. It ranges from 0 to 22. All individuals in this analysis have completed their schooling. Table 1. Descriptive Statistics of CFPS, by Demographic Groups Han Non‐Han Variable Men Women Men Women All Observations 8,597 9,334 747 836 19,514 Education Year of schooling 8.156 (4.081) 6.331 (4.683) 6.226 (4.628) 4.444 (4.745) 7.373 (4.552) ≥Junior high completed 62.04% (0.485) 45.35% (0.498) 42.84% (0.495) 29.67% (0.457) 51.88% (0.500) ≥Senior high completed 25.11% (0.434) 17.61% (0.381) 14.59% (0.353) 10.52% (0.307) 20.47% (0.403) ≥4‐year college completed 2.90% (0.168) 1.80% (0.133) 1.87% (0.136) 1.675% (0.128) 2.28% (0.149) Family # of siblings 3.09 (1.908) 3.256 (1.939) 3.325 (1.842) 3.459 (1.856) 3.195 (1.921) Father's Edu ≥Junior high school 32.5% (0.469) 34.52% (0.475) 32.13% (0.467) 33.97% (0.474) 33.53% (0.472) Mother's Edu ≥Junior high school 18.06% (0.385) 18.63% (0.389) 17.40% (0.379) 20.45% (0.404) 18.42% (0.388) Father: member of Communist 0.169 (0.375) 0.174 (0.379) 0.146 (0.353) 0.141 (0.349) 0.169 (0.375) Mother: member of Communist 0.022 (0.147) 0.025 (0.157) 0.030 (0.170) 0.014 (0.119) 0.024 (0.152) Rural 0.827 (0.378) 0.834 (0.372) 0.923 (0.266) 0.921 (0.270) 0.838 (0.368) Later outcome Labor force participation 0.682 (0.466) 0.511 (0.500) 0.707 (0.456) 0.590 (0.492) 0.600 (0.490) # of birth 1.688 (0.919) 1.810 (0.908) 1.963 (1.037) 2.138 (1.000) 1.776 (0.927) Age at first marriage 24.327 (3.790) 22.399 (3.276) 23.740 (3.950) 21.941 (3.559) 23.274 (3.678) Age at first birth 26.029 (3.804) 24.272 (3.488) 25.848 (3.964) 24.264 (3.850) 25.099 (3.763) On average, cohorts born between 1950 and 1980 have completed 7.37 years of schooling. Men have more years of schooling than women, and Han have more years of schooling compared to non‐Han. Figure 1 shows the increasing trend of years of schooling across cohorts by gender. The graph shows women's average years of schooling have been catching up with men's among the younger cohorts. The gender gap among the 1980 cohorts has narrowed compared with the older cohorts. There is an obvious downturn among cohorts born between the early 1960s and the early 1970s. This unusual decline has been noticed and briefly mentioned in Hannum (1999) and recently studied by Jiang, Kennedy, and Zhong (2018), which finds that the exposure to trade and industrialization explains more than 20% of the decline. Teenagers left school to pursue new low‐skilled job opportunities, although this generation faced nationwide improvements in education quality and the renewed possibility of college attendance.

IV. METHOD This section presents the empirical strategy to identify the effect of the OCP on educational attainment of Han women. I use two standard DD approaches. Specifically, the first DD approach compares Han women relative to Han men, and the second one compares Han women relative to non‐Han women. A. Pre‐ and Post‐Treatment Groups There are two generations compared in this data. The “old generation,” who probably had made their dropout decisions or had already left school when the policy came into play. The policy should have no effect on their educational outcomes. The “young generation” was supposed to be still in school when the policy was implemented. Considering that the policy lowered the expected fertility and reduced childcare time cost, the “young generation” could potentially devote more time to education and career in the future. Intuitively, the “old generation” and the “young generation” are the pre‐ and the post‐treatment group. As the OCP was formally and rapidly conceived in late 1979, I include cohorts born between 1950 and 1980 in my sample. Expanding the range of cohorts would probably overestimate the policy's effect by attributing the contribution of domestic and international social and economic development to the overall education improvement.11 Apparently, the “cut‐off age” for the pre‐ and post‐treatment groups is hard to be defined. Therefore, I show three specifications. For the main specification, I arbitrarily choose a “cut‐off age” that define the pre‐ and post‐treatment groups. I define the 1950–1959 birth cohorts (age 21–30 when the policy was implemented) as the pre‐treatment group because people older than 20 may have already made dropout decisions or most likely finished schooling. The 1960–1980 birth cohorts (age 0–20 when the policy was implemented) are defined as the post‐policy cohorts.12 In this way, a straightforward interpretation of the average treatment of the OCP is provided. Second, with the birth cohorts included in the pre‐treatment group fixed, I show the average treatment effect of different post‐policy groups by changing the birth cohorts in each post‐policy groups. Last, I abandon the arbitrary “cut‐off age” and relax the linearity assumption by estimating a dynamic DD model to show the policy's effect on each birth cohort. I also show results by using a narrower definition of the post‐treatment group: cohorts born in 1960–1970, as a robustness check. B. Han Women versus Han Men 2014 2001 (1) i indexes individuals, s indexes provinces, and c indexes birth cohorts. The dependent variable Edu is years of schooling. I j is a set of birth cohort dummies, Women is a dummy for Han women (relative to Han men), Post is the dummy for the post policy group, Women × Post is an interaction term of Han women and post‐policy cohorts. X is a vector of observable characteristics. ε is the error term. I first take the approach which compares men and women within the ethnic majority group (Han). Compared to women, men are much less likely to change their education decisions due to changes in the expected fertility of their future partners. The opportunity cost of parenthood is also much higher than that of fatherhood, as it is women who give birth, face extra risk of career after maternity leave, and usually spend more time with children (Adda et al.,; Budig; Budig and England). In this sense, men are appropriate controls for women. The regression can be written as follows:whereindexes individuals,indexes provinces, andindexes birth cohorts. The dependent variableis years of schooling.is a set of birth cohort dummies,is a dummy for Han women (relative to Han men),is the dummy for the post policy group,is an interaction term of Han women and post‐policy cohorts.is a vector of observable characteristics.is the error term. The set of demographic characteristics X isc includes a dummy indicating rural residence, a women × rural interaction term, province fixed effects, parents' educational attainment, number of siblings, number of brothers, birth order, and parents' political status. Controlling for rural factors is important to the estimation, because around 84% of the population were rural residents in the 1960s. Educational outcomes of rural residents are significantly lower than their urban counterparts. Also, the traditions of having a big family and son preference have been more deep‐rooted in rural areas relative to urban areas. Thus, the policy's effect on rural women could be different compared to urban women. Additionally, size of the family reflects one's educational resources. Women and men may face different education opportunities based on factors such as number of siblings, number of brothers and birth order in their household, subjected to the son preferences in different areas. Controlling for parents' education might further control for the gender bias. Lastly, based on China's political environment, being a Communist Party member means having responsibility for insuring the policy's implementation. Therefore, if any parent is a Communist Party member, girls may be more likely to be well informed of and understand the OCP. I run regression (1) on a sample including only Han people. The interpretation of regression (1) is straightforward. The coefficient on the interaction term, β 1 , is the coefficient of interest, capturing all variation in education specific to Han women (relative to Han men) who were younger than a certain cut‐off age (i.e., 20) when the policy was implemented. The vector γ j is the set of the cohort fixed effects that represent the policy's nationwide effects on birth cohorts. λ is the time‐invariant gap between Han women and Han men. One thing worth to note is that β 1 may be bias towards zero. With fewer children in the future, men's expected financial support from children would probably decrease. We should not overlook this channel, considering men were the primary providers of the families during this time period. Thus, men's educational attainment could be positively affected by the implementation of the OCP, and my estimate might be biased towards zero. The main threat of this estimation strategy is potential confounding effect from contemporaneous social movements that influenced the education of post‐policy men and women differently, which violates the parallel trend assumption of the DD method. Thus, I take another approach to estimate the OCP's effect on Han women's education. C. Han Women versus Non‐Han Women The second DD approach is free of gender‐specific impacts from contemporaneous movements. As stated above, the “one child” quota constraint is only against Han couples. Non‐Han couples had more relaxed family planning restrictions compared to Han. An urban non‐Han couple could have two children, and a rural non‐Han couple could have three or more depending on population size of that ethnic group. For some minority groups with a small population size, the OCP was further relaxed (Wang 2012). The identification is straightforward: Han women's fertility expectation was largely reduced while non‐Han women's fertility expectation was slightly reduced by the OCP. Thus this approach estimates the differences in the educational attainment between Han women and non‐Han women, for both the post‐policy group and the pre‐policy group. In other words, I estimate the difference of OCP's effects between Han women and non‐Han women. I expect the OCP also had a positive effect on non‐Han women's educational attainment because it also restricted non‐Han's fertility to some extent. Therefore, I expect that this approach underestimates the OCP's effect on Han women's educational attainment and the estimates are biased towards zero. Note that I do not differentiate minority groups and only compares Han to non‐Han. β 2 is the coefficient of interest, which indicates the educational improvements in the post‐policy Han women relative to non‐Han women. Considering that non‐Han women are disproportionately distribute in rural areas and women's opportunities in labor market and in schooling have increased disproportionately in rural areas for younger cohorts, I add a sequence of interaction terms of rural and birth cohorts. (2) Regression for this DD approach can be written as regression (2) . The notations are the same as in regression (1) . Here,is the coefficient of interest, which indicates the educational improvements in the post‐policy Han women relative to non‐Han women. Considering that non‐Han women are disproportionately distribute in rural areas and women's opportunities in labor market and in schooling have increased disproportionately in rural areas for younger cohorts, I add a sequence of interaction terms of rural and birth cohorts. 13

V. OCP'S EFFECT ON EDUCATIONAL ATTAINMENT A. OCP's Effect on Years of Schooling Table 2 summarizes my first set of results, OLS point estimates of β 1 in different specifications of regression (1). In column 1, I report the estimates from the baseline specification including the women dummy, post‐policy dummy, interaction of women and post‐policy, rural dummy, interaction of women and rural, birth year fixed effects, and province fixed effects. Overall, as expected, women had less education compared to men, and rural women had even less. The estimate of interest in column 1 indicates that Han women obtained 1.269 more years of schooling relative to Han men, when exposed to the shock of the OCP. The standard errors in parentheses are clustered at the province‐cohort level. The estimate is statistically significant at 1% level. Table 2. Han Women vs. Han Men Years of Schooling Dependent Var. (1) (2) (3) (4) Women × Policy 1.269*** 1.282*** 1.286*** 1.282*** (0.153) (0.153) (0.153) (0.154) Women −1.055*** −1.044*** −1.089*** −1.096*** (0.152) (0.152) (0.153) (0.154) Policy 4.330*** 4.069*** 3.710*** 3.680*** (0.250) (0.254) (0.263) (0.264) Rural −2.927*** −2.850*** −2.698*** −2.576*** (0.107) (0.107) (0.109) (0.111) Women × Rural −1.969*** −1.964*** −1.940*** −1.931*** (0.133) (0.133) (0.133) (0.132) #Siblings −0.0988*** −0.101*** −0.104*** (0.0254) (0.0253) (0.0251) #Brothers −0.0474 −0.0589** −0.0602** (0.0289) (0.0289) (0.0290) Birthorder 0.0157 0.0450** 0.0511** (0.0229) (0.0229) (0.0227) FatherJuniorHigh 0.950*** 0.907*** (0.0934) (0.0929) FatherSeniorHigh 0.442*** 0.445*** (0.0841) (0.0831) MotherJuniorHigh 1.107*** 1.034*** (0.124) (0.123) MotherSeniorHigh −0.425*** −0.366*** (0.0985) (0.0978) FatherCommunist 0.801*** (0.0766) MotherCommunist 1.195*** (0.198) Constant 9.626*** 9.831*** 9.495*** 9.152*** (0.263) (0.265) (0.270) (0.275) State FE Yes Yes Yes Yes Birth year FE Yes Yes Yes Yes Siblings No Yes Yes Yes Father/mother Edu No No Yes Yes Father/mother Communist No No No Yes N 18,692 18,692 18,692 18,692 For column 2 and later, I add in controls for family characteristics. The results show that more siblings and more brothers in a household lead to less education. Being a younger child in a household will have higher educational attainment. Having a father with junior high school degree or senior high school degree (compared to no junior high school degree) increases women's years of schooling. Having a mother with junior high school degree will increase a women's educational attainment while having a mother with senior high school degree will have the opposite effect. Having either a parent who is a Communist Party member significantly increases Han women's years of schooling. Estimates in columns 1–4 are highly consistent in magnitude and significance. After controlling for all the above family characteristics, the estimate of interest shows the average effect of the OCP on Han women at schooling ages relative to Han men is an increase in years of schooling by 1.282 years. This accounts for 53.6% of education improvement of women born between 1960 and 1980 relative to women born between 1950 and 1959. In Table S3, I show a robustness check to Table 2 with an older treatment cohort, 1960–1970. The coefficients of interest are still showing the same signs and significance, albeit the magnitudes become smaller due to the fact that the post‐treatment group is an older cohort now. One concern of this approach is that potential confounding effects from other policies or contemporaneous social movements. For instance, the world‐wide feminism movements might have spillover to Chinese women. Such potential factors would violate the assumption of the DD method: difference between the treated and untreated group is constant in the absence of treatment. With this concern, I take a second approach which avoids gender‐specific issues. Table 3 presents the results of the second DD approach, which is used to address concerns related to the first approach. Similarly, the estimate in column 1 is from the baseline specification including the Han dummy, policy dummy, the interaction term of the Han and policy dummies, a rural dummy, a rural and Han interaction, birth cohort fixed effects, and province fixed effects. Column 1 shows the OCP increased Han women's years of schooling by 1.415 years compared to non‐Han women. The estimate is statistically significant at 1% level. By adding controls for family characteristics, the point estimate trends down a little. After controlling for all demographic characteristics, educational resources, and parental characteristics, the average effect of the OCP at schooling ages on Han women relative to non‐Han women is an increase in years of schooling by 1.216 years. Table 3. Han Women v.s. nonHan Women Years of Schooling Dependent Var. (1) (2) (3) (4) (5) Han × Policy 1.415*** 1.297*** 1.206*** 1.216*** 1.289*** (0.358) (0.355) (0.353) (0.350) (0.354) Han −0.856 −0.756 −0.708 −0.785 −0.964* (0.526) (0.528) (0.523) (0.511) (0.509) Policy 4.542*** 4.406*** 4.189*** 4.196*** 3.078** (0.466) (0.465) (0.475) (0.477) (1.022) Rural −5.401*** −5.270*** −5.057*** −4.967*** −5.254*** (0.479) (0.480) (0.482) (0.472) (0.863) Han × Rural 0.804* 0.770 0.762 0.806* 0.955** (0.482) (0.482) (0.480) (0.472) (0.469) #Siblings −0.136*** −0.171*** −0.175*** −0.181*** (0.0246) (0.0351) (0.0350) (0.0352) #Brothers 0.0183 0.0176 0.0158 (0.0407) (0.0410) (0.0408) Birthorder 0.0717** 0.0778** 0.0834** (0.0315) (0.0311) (0.0311) FatherJuniorHigh 1.163*** 1.108*** 1.116*** (0.127) (0.126) (0.125) FatherSeniorHigh 0.456*** 0.449*** 0.443*** (0.105) (0.104) (0.104) MotherJuniorHigh 1.357*** 1.262*** 1.335*** (0.168) (0.167) (0.165) MotherSeniorHigh −0.503*** −0.426*** −0.417** (0.129) (0.128) (0.130) FatherCommunist 0.887*** 0.891*** (0.106) (0.105) MotherCommunist 1.247*** 1.289*** (0.269) (0.267) Constant 9.351*** 9.505*** 9.055*** 8.754*** 8.977*** (0.654) (0.647) (0.656) (0.650) (0.931) State FE Yes Yes Yes Yes Yes Birth year FE Yes Yes Yes Yes Yes Siblings No Yes Yes Yes Yes Father/mother Edu No No Yes Yes Yes Father/mother Communist No No No Yes Yes Rural × birth year No No No No Yes N 10,593 10,593 10,593 10,593 10,593 Considering that non‐Han women are disproportionately represented in rural areas and potential contemporaneous policies aimed to improve the under‐developed areas might favor the younger cohorts in rural areas, I include rural by birth cohort fixed effects for the regression in column 5. This should capture most of the potential differential trends between the two post‐policy groups. If there is any other channel favoring non‐Han women differently relative to Han women, the point estimate should be biased towards zero. The result indicates that the OCP increased Han women's years of schooling by 1.289, relative to non‐Han women. Compared these estimates to the ones in Table 2, which is free of ethnicity specific policy impact, they are not statistically different from each other. Thus, we should be confident about the positive effect of the OCP on Han women's education. Similarly, I show a robustness check to Table 3 with the post‐treatment cohort to be those who born in 1960–1970. See Table S4. Both Tables 2 and 3 show the policy's average effects on all birth cohorts younger than 20 in 1980. As discussed in Section A, the cut‐off age, 20, is rather arbitrarily chosen. Are the policy's effects robust across different treated birth cohorts? Which cohorts were impacted the most? I now run regressions with the same specifications in regressions (1) and (2), but with different “cut‐off age” for the post‐policy groups. Table 4 shows this set of results. Columns 1–11 in both panels present estimates of the policy's effect on cohorts born in 1960–1980, 1961–1980, …, 1970–1980 (column 1, column 2, …, column 11), compared to cohorts born in 1950–1959. Policy dummy equals zero for cohorts born between 1950 and 1959, and equals one for cohorts born in 1960–1980 (i.e., age ≤ 20) in column 1 and for cohorts born between 1970 and 1980 (i.e., age ≤ 10) in column 11. In panel A of Table 4, estimates across columns consistently show the positive effect of the OCP on women's education. All estimates are strongly significant at 1% level. The average treatment of the OCP trends up for younger cohorts, but not statistically different from that of the older cohorts. Similarly, panel B in Table 4 shows the same pattern as panel A. Table 4. OCP's Effects on Each Bunching of Cohort (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Treated Cohorts Age ≤ 20 Age ≤ 19 Age ≤ 18 Age ≤ 17 Age ≤ 16 Age ≤ 15 Age ≤ 14 Age ≤ 13 Age ≤ 12 Age ≤ 11 Age ≤ 10 Panel A. Han women vs. Han men Women × Policy 1.282*** 1.319*** 1.359*** 1.436*** 1.458*** 1.515*** 1.500*** 1.490*** 1.524*** 1.561*** 1.605*** (0.154) (0.154) (0.155) (0.153) (0.155) (0.157) (0.157) (0.159) (0.161) (0.166) (0.166) N 18,692 18,216 17,867 17,099 16,208 15,449 14,739 14,024 13,383 12,557 11,900 Panel B. Han women vs. non‐Han women Han × Policy 1.289*** 1.255*** 1.270*** 1.276*** 1.302*** 1.356*** 1.446*** 1.438*** 1.486*** 1.528*** 1.647*** (0.354) (0.355) (0.359) (0.362) (0.364) (0.369) (0.374) (0.380) (0.387) (0.395) (0.404) N 10,593 10,339 10,137 9,693 9,191 8,758 8,371 7,954 7,587 7,129 6,740 The dynamic DD results presented in Figures 3 and 4 illustrate the OCP's effect on each birth cohort and provide more insight into where the policy kicked‐in. Figure 3 shows that the policy has significantly positive and stable effect on cohorts born in 1963 and after. The policy's effect is stronger and more robust for younger cohorts, which mirrors the results in Table 4. The education trend in Figure 4 is more fluctuating and has larger variances compared to Figure 3. This is not surprising: one primary reason is that the sample size of the control group, non‐Han women, is much smaller. Figure 3 Open in figure viewer PowerPoint Dynamic DD between Han Women and Han Men Figure 4 Open in figure viewer PowerPoint Dynamic DD between Han Women and Non‐Han Women Besides exploring the definition of the post‐treatment group and test for their robustness, it is worthwhile to take a closer look at the definition of the pre‐treatment group. My main assumption for the pre‐treatment group is that they may have already made fertility decisions in addition to education decisions. The current pre‐treatment cohorts, 1950–1959, could have legally married and given birth by 1980; actually, about 31% of them have children in 1980. I reestimate the regressions in Tables 2 and 3 by dropping the observations with children in 1980 in the pre‐treatment group. The new results are in Tables S6 and S7. To sum up, these estimates show that the OCP had a positive and significant effect on Han women's years of schooling. By constraining the quota of birth per couple, the OCP reduced the number of births for women who were exposed to the policy. Among those women, cohorts at schooling ages saw the opportunity of pursuing higher education and ended up getting about one more year of schooling on average. B. Why Not Triple‐Diff for Han and Non‐Han Women and Men? One may suggest an alternative approach, a difference‐in‐difference‐in‐differences (triple‐difference) identification, by taking the difference between the difference between Han women and non‐Han women and the difference between Han men and non‐Han men. This approach would compare gender differences in schooling between Han and non‐Han for cohorts that were differently affected by the OCP. Unfortunately, non‐Han men's educational attainment is distinctly different from the other three groups. Figure S1 shows that Han men, Han women, and non‐Han women all have a clear pattern of trending up, although the line of non‐Han women is more scattered due to a relatively smaller sample size. There is no clear pattern for the educational attainment of non‐Han men and no particular change compared the pre‐ and post‐policy cohorts. Thus, applying a triple differences approach would clearly violate parallel trend assumption. C. Heterogeneity by Parent's Membership of Communist Party Based on China's political environment back then and the fact that the policy was first promoted among the members of Communist Party (henceforth MCP) and mainly enforced by them, it is reasonable to believe that MCP had more responsibility to insure the policy's implementation. Therefore, a woman would be more likely to be well informed of and comply with the OCP if her parent was a MCP. (3) Next, I explore the heterogeneous treatment effects of the OCP by parent's membership of Communist Party. This analysis serves the paper in two ways. First, given the results on the OCP's average treatment effect on Han women in Table 2 , this analysis further investigates the heterogeneous treatment effects within Han women, by comparing a Han woman with a MCP parent to Han women with a non‐MCP parent. Second, as noted in the paper, the identification approach in Section B is subject to potential confounding effect from contemporaneous social movements that may influence the education of Han women and Han men differently. Using parent's MCP status as variation in treatment intensity on top of the DD approach in Section B, I show the add‐on effect of the OCP when having a MCP parent. Specifically, I estimate a difference‐in‐difference‐in‐differences (triple‐difference) model shown below. It is worth notice that I conduct this set of analysis on Han nonrural sample only. 14 I do so because I consider rural MCPs and nonrural MCPs are fundamentally different in terms of their response to the OCP. Most rural MCPs were farmers back, while most nonrural MCPs were state‐owned factory workers, government employees and many of them were in administrative positions. One of the punishments for exceeding the birth quota is forced dismissal from government employment, which is considered to be a serious punishment. The coefficient of interest, β 3 , should be interpreted as the difference between the OCP's effects on a Han woman with a MCP parent and the policy's effect on a Han woman with a non‐MCP parent. Table 5 shows the estimation results from seven separate regressions on father's MCP status. The outcome variable in column 1 is years of schooling, the main outcome variable in Tables 2 and 3. The outcome variable in columns 2–8 is, respectively, a dummy variable of years of schooling greater or equal to 6, 7, 8, 9, 10, 11, or 12. The estimates show that, overall, having a MCP father strengthens the OCP's positive effect on a Han women's educational attainment. Specifically, the difference in policy effects between a woman with a MCP father and a woman with a non‐MCP father is most significant around the margin of completing middle school (8 or 9 years of schooling). I also show the results of the same set of regressions with outcome variable as a dummy of either parent being a party member in Table S2. The fraction of MCP among women is too low (see Table 1) so that I skip the analysis with only mother being a MCP. As a robustness check, I replicate Table 5 with an older post‐treatment cohort and the results are in Table S5. Table 5. Party Member Heterogeneity of OCP's Impact on Women's Education (1) (2) (3) (4) (5) (6) (7) (8) Years of Schooling Edu ≥ 6 Edu ≥ 7 Edu ≥ 8 Edu ≥ 9 Edu ≥ 10 Edu ≥ 11 Edu ≥ 12 Father MCP × Women × Policy 0.389 0.00930 0.0710 0.0856* 0.0911* 0.0522 0.0397 0.0482 (0.536) (0.0306) (0.0453) (0.0464) (0.0495) (0.0836) (0.0825) (0.0827) Father MCP 0.792** 0.0172 0.0400 0.0435 0.0397 0.135** 0.119** 0.125** (0.344) (0.0187) (0.0288) (0.0289) (0.0303) (0.0558) (0.0557) (0.0556) Women −0.479** −0.0252* −0.00972 −0.0150 −0.0136 −0.0518* −0.0472* −0.0431 (0.198) (0.0145) (0.0209) (0.0209) (0.0216) (0.0281) (0.0281) (0.0279) Policy 3.946*** 0.0801** 0.190*** 0.202*** 0.223*** 0.439*** 0.443*** 0.450*** (0.575) (0.0359) (0.0461) (0.0491) (0.0527) (0.0685) (0.0686) (0.0682) Father MCP × Women −0.0812 0.00645 −0.0359 −0.0486 −0.0509 −0.00803 0.00732 0.00226 (0.461) (0.0292) (0.0422) (0.0426) (0.0455) (0.0703) (0.0687) (0.0687) Father MCP × Policy −0.171 −0.00947 −0.0203 −0.0250 −0.0200 −0.0460 −0.0362 −0.0490 (0.403) (0.0197) (0.0317) (0.0322) (0.0337) (0.0658) (0.0659) (0.0659) Women × Policy 0.297 0.0106 −0.00970 −0.00390 −0.00244 0.0656* 0.0581 0.0550 (0.252) (0.0163) (0.0244) (0.0248) (0.0256) (0.0369) (0.0371) (0.0369) N 3,184 3,184 3,184 3,184 3,184 3,184 3,184 3,184 D. Compulsory Education and College Reopening China experienced rapid modernization in the 1980s, together with many policy changes. This fact raises concerns on the identification of the OCP's effect in this paper. One specific policy change that might confound the effects of the OCP is the 9‐year compulsory education law, which took affect on July 1, 1986. The law established deadlines and requirements in an effort to attain a universal education for all school aged children. It requires that all children attend school for a minimum of 9 years, equivalent to a junior high school completion. The local roll‐out of the law implementation was based on local educational resources. To take a closer look at on which level of education the policy affected the most, I run linear probability models with same specifications as the main regressions (1) and (2) but replacing the dependent variables as dummy variables of completion of n years of schooling ***(i.e., 1[years of schooling ≥ n]). Panel A in Table 6 shows that the Han women born after 1960 had significantly higher completion of primary school (6 years of schooling), junior high school (7, 8, and 9 years of schooling), and senior high school (10, 11, and 12 years of schooling) compared to Han men. Specifically, an average Han women who was born after 1960 increased her likelihood of 9 years of schooling by 7.46 percentage points. The increase in the probability of finishing years of schooling from 10 to 12 is 3.19–3.49 percentage points. This implies that OCP significantly increased Han women's completion of junior high school and senior high school. If the gender convergence was only a result from the 9‐year compulsory schooling law, we should only expect columns 1–4 to be statistically different from zero; while columns 5–11 to be no different than zero. Oreopoulos's (2006) finding on compulsory schooling laws shows that there is no positive effect of compulsory schooling law on educational attainment beyond the minimum requirement. However, here, the results in columns 5–11 clearly show that Han women experienced an increase in high school completion. The gender convergence in 10–12 years of schooling is evident that the OCP had a positive effect on women's educational attainment. Results in panel B Table 6 show consistent evidence as the results in panel A. The OCP had a positive and significant effect on Han women's high school completion relative to non‐Han women. If the differential improvement in education between Han women and Han men or between Han women and non‐Han women only came from the 9‐year compulsory schooling law, we should not expect to observe any effect on years of schooling beyond junior high. Table 6. OCP's Effect on each Level of Schooling (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Edu ≥ 6 Edu ≥ 7 Edu ≥ 8 Edu ≥ 9 Edu ≥ 10 Edu ≥ 11 Edu ≥ 12 Edu ≥ 13 Edu ≥ 14 Edu ≥ 15 Panel A. Han women vs. Han men Women × Policy 0.154*** 0.0807*** 0.0760*** 0.0746*** 0.0349** 0.0331** 0.0319** −0.000582 −0.000822 −0.000612 (0.0158) (0.0158) (0.0157) (0.0155) (0.0128) (0.0126) (0.0124) (0.00636) (0.00629) (0.00630) N 18,692 18,692 18,692 18,692 18,692 18,692 18,692 18,692 18,692 18,692 Panel B. Han women vs. non‐Han women Han × Policy 0.125** 0.0828** 0.0800** 0.0778** 0.0457* 0.0433* 0.0465** 0.0161 0.0149 0.0160 (0.0383) (0.0330) (0.0324) (0.0323) (0.0241) (0.0240) (0.0236) (0.0102) (0.0101) (0.0102) N 10,593 10,593 10,593 10,593 10,593 10,593 10,593 10,593 10,593 10,593 Another policy change might arguably affect women and men differently in educational attainment is college reopening in late October 1977. In acknowledgment of more than a decade of missed opportunity due to the cultural revolution, candidates ranging in age from 13 to 37 were allowed to take the National Entrance Examination (a.k.a. Gaokao). Let us assume that college reopening had differential treatment effect on each gender or differential treatment effect on each ethnic group. We should be able to see significant estimates with decent magnitude in columns 8–11.15 Instead, we do not observe any increase in Han women's college enrollment or completion relative to Han men or non‐Han women, indicating that college reopening had no effect on Han women relative to Han men (or non‐Han women). Here, I cannot rule out all possible policy changes that might confound the effect of the OCP, but only discuss the most acknowledged and influential ones above. This analysis implies that the OCP had significant contribution to Han women's education improvement.

VI. HYPOTHESIZED MECHANISM Results above shows that OCP explains a large portion of education improvement of women born between 1960 and 1980 compared to women born between 1950 and 1959. This section investigates the policy's effect on women's later outcomes after finishing school and intends to shed light on the potential mechanism of the policy's effects. There are several channels which could increase Han women's educational attainment. The first one is through labor market. Anticipating higher labor supply due to the exogenous reduction of child‐rearing burden, women would invest more in human capital. Women may also expect less financial support from children, regardless of quantity–quality trade‐off. The second channel is through timing of marriage and timing of fertility. Anticipating having fewer children, women may delay their entry to parenthood or even delay their entry to marriage (Buckles 2008). Further, the delay of lawful age at first marriage may have stronger impact on women relative to men and may raise women's expected age of marriage and fertility, then further induce them to obtain more education as they have more time before marriage. Ideally, I would examine the OCP's effect on changes of women's expectation on career, marriage and fertility. Unfortunately, there is no measure of expectation on those aspects in any survey within the same time frame. Instead, I estimate the OCP's effect on later outcomes such as age at first marriage, age at first birth, labor force participation and employment status. If the channel of the OCP affecting women's educational attainment is through changes in expectation of these later outcomes, we should be able to observe the changes in later outcomes reacting to the OCP. Panel A in Table 7 presents the gender differences of the later outcomes within Han. Assuming that men were much less impacted by the OCP due to their small share of child‐raring burden, we should expect Han men had little change in labor force participation and employment status. Column 1 shows that there is no change in the difference of the treated and the control group's labor force participation before and after the policy. This is not surprising: women's labor force participation in China was as high as 73% in 1990, which was much higher than most of other countries in the world. Men's labor force participation was 85% by then; thus, there was not a huge gender difference in LFP in the 1990s China (WorldBank 2018).16 Table 7. OCP's Effects on Women's Post‐School Outcomes (1) (2) (3) (4) Dependent Variable (LFP) (Employment Status) (Age at First Marr) (Age at First Birth) Panel A. Han women vs. Han men Women × Policy 0.0154 0.112*** 0.378** 0.472*** (0.0127) (0.0184) (0.137) (0.142) N 18,651 15,503 17,492 16,992 Panel B. Han women vs. non‐Han women Han × Policy 0.0301 0.00198 0.152 0.976** (0.0363) (0.0432) (0.277) (0.414) N 10,555 8,253 9,944 9,757 Column 2 shows that after the OCP, Han women are more likely to hold a job by 11.2 percentage points compared to Han men. This improvement of women's labor market performance implies raise of working women's human capital. Unfortunately, we do not see the difference between Han and non‐Han women's employment status. Column 3 shows that Han women delay their entry into first marriage by 0.378 years compared to Han men. This supports the hypothesis of delayed entry into first marriage. Furthermore, results in column 4 indicate that Han women significantly delay their entry to parenthood, relative to both Han men and non‐Han women. Specifically, Han women's age at the first birth increased by 0.472 years compared to Han men and increased by 0.976 years compared to non‐Han women. Obviously, delaying entry to parenthood is the primary channel of OCP's effect on non‐Han women. I want to point out a fact that columns 3 and 4 in panel A are not statistically different. This makes sense: Han women and Han men would be identically affected when further delay their entry to the first birth after marriage. Analysis in this section presents changes in Han women's labor force participation, employment status, entry to marriage, and entry to parenthood caused by the OCP. More importantly, it supports the hypothesized mechanism that women increased their education due to the increase in labor force participation, delayed entry to marriage, and delayed entry to parenthood.

VII. CONCLUSION Women's educational attainment has increased tremendously and even exceeded men's all over the world in the late twentieth century. It is beyond the scope that this paper provides an genetic answer to this phenomenon. Instead, I focus on China's case and assess how much China's OCP can explain the shrinking gender gap in educational attainment. I find that the OCP significantly increased Han women's years of schooling by 1.28 years, which explains 53.6% of the increase in women's educational attainment in birth cohorts between 1950 and 1980. This effect is apparently large, but reasonable. Compared to the western countries, China was a relatively closed society and lack of other widely influential gender equality movements back in the 1980s. The OCP is the biggest social movement that fundamentally changed the lives and family structure of the entire generation born in the 1960s. This paper highlights the OCP's positive externality on women's education, which has been overlooked by the literature. It shows that in China, reductions in fertility expectations increase women's educational attainment. As such, it sheds light on one mechanism that appears to underlie the closing of the gender education gap that may be applicable in other countries where the gender education gap has also closed.

1 Recent paper by Zhang ( 2017

2 Other enforcement of the OCP includes but not limited to excluding unauthorized children from public education, discharging parents from social services, compulsory use of abortion and sterilization, and so forth (Banister 1991

3 The campaign was technically voluntary, but it had some coercive elements, although they were significantly less coercive than the OCP (Zhang 2017

4 The 1982 Census of China indicated that 93.3% of Chinese were Han.

5 There is only one ethnic majority in China, Han. The other 55 ethnic groups count as non‐Han.

6 The lawful age at first marriage was 18 for women and 20 for men in the last version of marriage law since 1950.

7 CFPS was launched in 2010 by the Institute of Social Science Survey of Peking University, China. It is funded by the Chinese government through Peking University.

8 The answers for father/mother's level of education include: “Illiterate,” “Primary school,” “Junior high school,” “Senior high school,” “2‐ or 3‐year college,” “4‐year college/Bachelor's degree,” “Master's degree,” and “Doctoral degree.” The answers for father/mother's political status include: “Member of Communist Party,” “Member of Democratic Party,” “Member of Communist Youth League,” and “General public.”

9 The surveyed provincial regions are four municipalities (Beijing, Tianjin, Shanghai, and Chongqing) and 21 provinces (Hebei, Shanxi, Liaoning, Jilin, Heilongjiang, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong, Henan, Hubei, Hunan, Guangdong, Guangxi, Sichuan, Guizhou, Yunnan, Shaanxi, and Gansu).

10 They are two special administrative regions (Hongkong and Mocau), four autonomous regions (Inner Mongolia, Xinjiang, Tibet, and Ningxia), Qinghai province and Hainan province.

11 There are no qualitative changes to the results when expanding the cohorts.

12 In China, the legal marriage age is 20 and above for women and 22 and above for men. In China, legal fertility is constrained by legal marriage. Therefore, we should expect no one in the post‐treatment group to be married or to give birth before 1980.

13 See Figure S2 for the comparison of education trend for rural and non‐rural Han women.

14 The nonrural accounts for about 16.3% of the Han cohorts born in 1950 and 1980.

15 13–16 years of schooling are equivalent to 1–4 years of college education.

16 U.S. female LFP in 1990: 56%; male LFP in 1990: 75%.

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