Birth control, family size and educational stratification: Evidence from the Han and ethnic minorities in China ☆

This paper investigates the unexpected impact that enforcing birth control policies in China has upon the educational stratification between the Han majority, the policy target group, and ethnic minorities, a partially excluded group. Exploring county-level variation in the value of fines levied for unsanctioned births, we find that a stricter enforcement of the birth control policy leads to a larger educational gap between ethnic minorities and the Han majority in both rural and urban areas. More specifically, we find that higher fines lead to a larger improvement in the educational attainment of the Han majority and that this is principally due to the greater effect of these fines upon the reduction of family size and the subsequent concentration of family resources (among this population). Our findings indicate that the birth control policy has substantially contributed to the rising Han-minority educational gap in China.


Introduction
Ethnic minorities are often among society's most disadvantaged groups and this makes them more vulnerable to poverty in developing countries.While China has experienced dramatic economic growth in the last few decades, the welfare of ethnic minorities (i.e.non-Han Chinese) has lagged behind that of the Han majority.The Hanminority educational gap has been attributed as the main contributor to ethnic minorities' disadvantages in social welfare dimensions such as occupation, health, income and poverty. 1 As such, it is important to understand the forces driving the Han-minority educational gap; previous studies have identified these, among other factors, as differences in geographic location and socioeconomic background (Hannum, 2002)  and in school quality (Yang et al., 2015).
In this paper, we test if the enforcement of the one-child policy leads to unexpected educational stratification between the Han majority and ethnic minorities.This policy mainly targets the Han majority, who constitute approximately 91% of the population of China.According to the quantity and quality tradeoff (Q-Q tradeoff) model (See, e.g., Becker  & Lewis, 1973), a reduction in family size would induce Han households to invest more in human capital for each child, resulting in an enlarged Han-minority educational gap.
The Han-minority educational gap may also be influenced by possible educational impacts of the one-child policy for ethnic minorities.Conceptually, these impacts could operate through at least the following two channels.On the one hand, the one-child policy did place fertility restrictions on ethnic minorities, though in a less restrictive way than for the Han majority.The reduction in family size could induce more human capital investment per child for ethnic minorities.On the other hand, the improved education of the Han majority as predicted by the Q-Q tradeoff model could indirectly affect ethnic minority children of the same age cohort.This indirect effect may go either of two ways: while smarter and healthier peers might help minority children achieve a better school performance (e.g.Burke & Sass, 2013; Ding & Lehrer, 2007), the competitive level of these same peers could mean that ethnic minority children are less likely to be selected in the post-compulsory school admission process.The net impact of population control policy on ethnic minorities' educational attainment is therefore theoretically uncertain.
This paper explores county-level variation in the policy enforcement, i.e. the value of fines levied for unsanctioned births, to evaluate how the implementation of the one-child policy affects educational stratification.The monetary penalty for those who violate this policy has been commonly used in the literature as a source of exogenous shock to fertility in China (Ebenstein, 2011; Liu, 2014; McElroy & Yang, 2000).In our empirical estimation, in addition to the value of fines, we include its interaction with an ethnic minority dummy as a regressor to capture the contribution of the value of the fine on the Han-minority educational gap.We evaluate the educational impact of fines for rural and urban households separately given the slightly different birth control policies faced by these two groups.
One concern in identifying the impact of local variation in fines on education is the existence of confounding factors that could affect the local stringency of the birth control policy and education outcomes simultaneously.First of all, areas with higher birth rates may need stricter birth control policies to meet the population control goal set by the central government, while higher birth rates also reduce average educational attainments of children given fixed educational resources.Second, a richer county has both the budget to devote more resources to education and the need to implement a stricter birth control policy as economic development induces migration inflow.Third, communities with stronger preference for child quality might simultaneously tolerate higher fines and invest more in children's education.If left unaccounted for, these factors can lead to biased estimation results.To address these problems, we control for county-level birth rate, development level and educational resources in the analysis.The local variation in fines is arguably exogenous, conditional on these county characteristics.
Using household-level data, we show that a harsher monetary penalty for violating the birth control policy leads to a larger Han-minority educational gap.In particular, we find that a 10% increase in the value of fines increases the Han-minority high school enrollment gap by 1.1 and 1.4 percentage points for rural and urban samples respectively.Our results indicate that one standard deviation increase in the amount of the fine leads to an increase of 7.1 and 10.8 percentage points, for rural and urban children respectively, in the Han-minority high school enrollment rate gap.These documented effects of one standard deviation increase in the fine are substantial considering that the overall increase in the Hanminority gap was 12 percentage points for cohorts from 1970-1983.Our results are robust to the alternative measure of educational attainment using normalized years of schooling.To the best of our knowledge, we are the first in the literature to provide empirical evidence on birth control policy's contribution to the Han-minority educational gap in China.
The larger Han-minority education gap in areas where fines are higher is likely a result of improved educational attainments for the Han majority.Consistent with the prediction of the quantity and quality tradeoff model, we find higher fines simultaneously reduce family size and increase high school enrollment rates for the Han majority.These results hold for both the rural and urban samples.In addition, we find a lower level of high school enrollment rates for urban ethnic minorities in areas of high fines, which further contributes to the Han-majority educational gap for urban children.As the amount of the fine has no observable impact on the family size of urban ethnic minorities, this negative education effect is unlikely to be operating through concentrations / dilutions of household educational resources associated with family size changes.Instead, our finding is consistent with the presumption that the improved educational attainment for the Han majority in areas of high fines intensifies competition in the school admission process for urban ethnic minorities residing in the same county.
Our study contributes to the literature on the consequences of family planning policies in China.Most empirical studies on this issue have focused on the Han majority and have often used the one-child policy to test the existence of tradeoffs between child quantity and quality within a family.For instance, Li, Zhang, and Zhu (2008), Rosenzweig and Zhang   (2009) and Liu (2014) found a negative relationship between family size and educational and health outcomes.In contrast, Qian (2009) failed to find such evidence using the relaxation of the one-child policy.While most of these papers have recognized the difference in birth control policies between the Han majority and ethnic minorities, and have often controlled for ethnicity in their regression analyses, none of them have acknowledged and evaluated the policy's impact on educational disadvantages of ethnic minorities.We contribute to this literature by being the first to show the unexpected impact of the one-child policy on educational stratification between the Han majority, the target group of the policy, and ethnic minorities, a partially excluded group.
This paper has important policy implications for contemporary China.Recognizing the fast-changing demographic structure and a rapidly aging population, China is relaxing its one-child policy for the Han majority.The "selective two-child policy" was implemented countrywide in 2013, allowing a couple to have two children if either the husband or the wife was from a one-child family.In 2015, China further relaxed its fertility restriction by the implementation of the "universal two-child policy."This new policy allowed all couples to have two children.How would this series of relaxations of the birth control policy affect the educational gap and relative welfare of the ethnic minorities versus the Han majority?If the initial differential application of this policy led to an increase in the Han-minority educational gap, would a more relaxed application, or even removal, potentially reduce this gap?Understanding the initial impact of the birth control policy helps predict possible changes in educational attainment and is crucial at this reform stage.
The rest of this paper is organized as follows.In Section 2, we outline the institutional background of birth control policies and the education system in China.Section 3 describes data used in this study and Section discusses our main empirical strategy.Estimation results and discussion on the underlying mechanisms are presented in Section 5. Section concludes.

Institutional background
In this section, we first outline the history of Chinese birth control policies as well as the different population policies applied to the Han majority and ethnic minorities.We then briefly describe the education system in China, with a special focus on the school admission procedure for post-compulsory education.

Population control in China
Recognizing the incompatibility between unchecked population growth and economic development, the central government in China enacted a series of population control policies starting from early-1970s (Wang, 2012).In July 1971, China launched a family planning campaign promoting the policy "Later (later marriage), Longer (longer interval between births) and Fewer (fewer children)" with education programs and free distribution of contraceptives to married couples (Liu, 2014; McElroy & Yang, 2000; Wang, 2012).This policy required parents to have an interval of at least four years between the birth of each child and recommended a family size of two children for urban households and three children for rural households.
To further curb the rapid population growth in China, a stricter policy, commonly known as the one-child policy, was introduced in the Fifth National People's Congress in 1979 and was enacted in 1980.Both rural and urban married couples were forced to practice birth control and were mandated to have one child per family.In addition to frequent campaigns on abortion and sterilization, this policy was further enforced with the provision of incentives for compliance.One-child families were rewarded better housing and cash subsidies, while non-compliant families were mainly punished via fines, which were significantly larger than the amount of subsidy for one-child families (Wang, 2012).According to Short and Fengying (1998), the median fine value amounted Y. Pan and Y. Liu  to 50% of the median annual household income in early 1990s.In addition, violation of the policy prevented parents from officially registering their "out-of-plan" children, and unregistered children were given inferior health and educational services (Short & Fengying, 1998).The relentless enforcement of the one-child policy caused rebellion in the early stages of its implementation, especially in rural areas (Davin,  1985).Due to the widespread resistance from peasants, the policy was relaxed in 1984, allowing rural households to have a second child if the first born was a girl.As shown in Fig. 1, despite this mild relaxation, family planning policies in China have successfully reduced birth rates since early 1970s.
The one-child policy mainly targeted the Han majority, with ethnic minorities facing a more relaxed birth control policy.Prior to the onechild policy, ethnic minorities were exempt from all family planning policies (Chang, Lee, McKibben, Poston, & Walther, 2005).In September 1980, the Communist Party of China Central Committee issued an open letter mandating the members of Communist party and Communist Youth League to have one child per couple while allowing more flexible birth control regulations for ethnic minorities.Ethnic minorities' partial exclusion from the birth control policy was made clearer by the Communist Party of China Central Committee in Document 7 on April 13, 1984.In general, most ethnic minorities were allowed to have two children with certain minorities/regions having three (Banister, 1991), and the only exception was the Zhuang ethnic minority. 2Given the higher fertility rate of ethnic minority women 3 compared with the Han majority and the overall fertility rate of 5.47 in 1970 (The World Bank, 2016), 4 the relaxed fertility restriction was likely to be binding for ethnic minorities.The more lenient birth control rule was implemented to prevent marginalization of the minorities and to protect the historically disadvantaged groups.As the result of the less restrictive family planning policies for ethnic minorities, their share in the population has increased since early 1970s, as shown in Fig. 2.
The one-child policy has been strictly enforced until recently, when the Chinese government launched a series of reforms to rebalance the demographic structure of Chinese society in the face of rapid population aging.In 2011, a few trial regions started to implement the "selective two-child policy," which allowed a couple to have two children if either the husband or the wife was a "single child."This policy reform was then applied throughout the country in 2013 as part of the "Communist Party of China Central Committee on deepening reform of overall number of major issues," approved by the Third Plenary Session of the 18th Central Committee of the Communist Party of China.Two years later, The National People's Congress passed the population and family planning law amendment on December 27, 2015, leading to the implementation of the "universal two-child policy."This new policy further allowed all couples to have two children and marked the official end of the onechild policy.

The education system in China
Education in China is run by the government and schools at all levels are public.Every Chinese citizen is required to attend nine years of compulsory education, including six years of primary education and three years of junior secondary education (middle school).The costs of compulsory education are mainly borne by the government.Upper secondary (high school) and tertiary education were also heavily subsidized until 1994, when China launched a reform of the education system that obliged households to share part of the educational costs (Pan, 2016).
The transition from middle school to high school is via an annual high school entrance exam.Upon graduation from middle school, students take a three-day entrance exam covering six subject areas including Chinese, mathematics, English, physics, chemistry, and politics (Ding & Lehrer, 2007), and admission depends solely on the exam score.The exact contents of the exam and the scoring system vary by county and applications and admissions are generally conducted within each county.High school admission was competitive in the 1980s and 1990s with admission rates ranging between 38.0% to 51.5%. 5 While being admitted to high school is becoming easier nowadays due to high school expansion, there is still severe competition to gain admittance into the top high schools, which better prepare students for the more competitive college entrance exam.
The Chinese government has made a number of policies in favor of  2 Zhuang is the largest ethnic minority group in China and has faced the same birth control policies as the Han majority.As the data do not allow us to identify whether a ethnic minority child belongs to the Zhuang ethnic minority group or not, we are not able to investigate the impact of the one-child policy on the educational gap between the Han majority and non-Zhuang minorities.
We therefore focus on how the one-child policy affects the average Hanminority educational gap.We will demonstrate that our results are robust to the exclusion of Guangxi province, where most Zhuang ethnic minorities reside. 3The higher fertility rate was due to the birth-encouragement population policy implemented between 1950s and 1970s among minority regions to feed manpower needs (Heberer, 1989). 4The total fertility rate is defined as the number of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with current age-specific fertility rates.
Y. Pan and Y. Liu ethnic minority students to promote their educational achievement.Such preferential policies are mostly in the form of lower admission standards.In practice, the central government has given some flexibility to the provincial governments when it comes to implementing the preferential admission policies for high school and college admissions. 6sually, ethnic minority students receive five additional (bonus) points on their high school entrance exam.
Regardless of the preferential treatment in admission to high schools, the high school enrollment rate has long been lower for ethnic minorities than for the Han majority, and the gap in enrollment rates has widened over time (Fig. 3).Previous studies have attributed the Han-monirity educational gap to differences in geographic location, socioeconomic background and school quality.In the following sections, we will test whether preferential family planning policies in China, which are expected to affect the family size of the Han majority and of ethnic minorities differently, also contribute to the educational stratification.

Data
Data used in this paper are extracted from the China Health and Nutrition Survey (CHNS).The first round of the CHNS panel took place in 1989 and surveyed around 3,800 households drawn by a random cluster process from eight provinces. 7Follow-up surveys were carried out in 1991, 1993, 1997, 2000, 2004, 2006, 2009 and 2011.While the CHNS sample is not representative of the overall population, it covers less developed (Guizhou and Guangxi), medium developed (Liaoning, Henan, Hubei, and Hunan), and developed coastal provinces (Jiangsu and Shandong) in China.These provinces vary substantially in many aspects, such as their geography, demographic composition, economic conditions and health conditions.
We restrict our study sample only to children who were fully subject to the one-child restriction (or a corresponding relaxed restriction for ethnic minorities) announced in 1980.In particular, we exclude households with the oldest child born before 1976, four years prior to the enactment of the one-child policy.Prior to the launch of the one-child policy, couples were required to have an interval of at least four years between the birth of each child.For couples who had their first child in 1976 or later, their eligibility to have a second child would be revoked due to the implementation of the one-child policy in 1980.In contrast, the fertility rate of couples who had their first child earlier than 1976 was not fully constrained by the one-child policy, as they were eligible to have a second child in the gap period occurring between the first child reached age four and 1980.
We then collapse the panel data into a cross-sectional dataset on educational attainment for all remaining children.We construct children's education measure using information reported in the 2011 survey whenever possible.For children who did not participate in this last round of survey due to community and household attrition and replacement, we base our education measure on information reported in the most recent survey they participated in.
As attending primary and middle school is mandatory for every Chinese citizen, we focus on individuals' high school enrollment in the main analysis.For the purpose of the analysis, we exclude individuals younger than 15 when they were surveyed the last time, which is the common age to finish compulsory education and to be admitted to high school.We further exclude seven individuals without any formal education, most of whom are either physically or mentally disabled. 8The resulting sample consists of 2767 individuals born between 1976 and 1995, among which 13 percent are ethnic minorities.The share of ethnic minority children in our estimation sample is comparable to the minority population share calculated using the 2000 population census (Fig. 2).
As a robustness check, we also use normalized years of schooling as an alternative measure of educational attainment.As many children were still in school by the last round of the survey, the conventional "years of schooling" measure would underestimate the educational attainment of these children.To address this issue, we normalize the years of schooling by the mean schooling of children at the same age (following Rosenzweig & Wolpin, 1980).Note that the normalized years of schooling may not be as good a measure for education as high school enrollment given variations in school starting age across regions and widespread grade retention. 9he stringency of the local (county level) birth control policy is measured by the amount of fines imposed by the government for unsanctioned births.We choose this measure for the following reasons.First, the imposition of a fine is the primary and most commonly used sanction for violations of the one-child policy (Short & Fengying, 1998).Moreover, counties with higher fines are also more likely to reward one-child families with cash subsidies, which is another common practice in policy implementation. 10This positive correlation indicates that rewards are used in conjunction with, rather than as alternatives to, fines to ensure compliance to the one-child policy.Therefore, the amount of fines is a reasonably good measure of the local policy enforcement.
The information on fines was collected from the person responsible for family planning in each town/village in the survey rounds of 1989, 1991,  and 1993.The question of the amount of the fine was then dropped from the surveys thereafter.Following Liu (2014), we take the average of fines across these three years to measure the level of punishment in sample towns / villages.While this measure may not fully capture the absolute level of punishment at birth for children in our sample, it reflects the 8 Disabled children do not count towards the birth quota. 9According to the Educational Statistics Yearbook of China, the grade retention rate in 1990 was 6.1% and 2.2% for primary and middle schools respectively. 10The level of fine does not correlate with the level of subsidy or the adoption of other less common forms of penalties such as the loss of job or work unit bonus (Appendix Table A1).
Y. Pan and Y. Liu  relative level of punishment across counties, which we assume to be stable over time. 11Since the local family planning policy, including the amount of the fine, is determined at the county level, we also take the average amount of fines within each county, and use it as a measure of the stringency of birth control policy in the regression analysis to reduce measurement error.Another important reason for focusing on the impact of county-level fines on education is that both educational resources and the level of competitiveness in school admission standards vary across counties.In China, most children receive compulsory and high school education in their county of residence.High school entrance exam and admission are also organized at the county level.The educational spillover effect from the Han majority to ethnic minorities, if there is any, is therefore expected to take place within each county.We construct a rich set of individual and county level controls.The number of siblings for each individual is mainly constructed using the birth history information of ever married women.We exclude children who died before the age of five (less than 3% of all children ever born), because early deceased children would not compete with their siblings for family educational resources. 12For individuals whose information is missing from the CHNS survey of ever married women (about 16%), we use the CHNS family member relation file, which reports relations between all members residing in the same household at the time of the survey, to calculate their number of siblings.Other individual level control variables include gender, years of schooling of both parents and household income.Given that the CHNS sample counties' identity is not revealed to the public, we are unable to merge county-level information from other sources to the study sample.Instead, we construct county-level controls by taking the within-county average of the following variables across all sample villages: birth rate, distance to provincial capital, stable electricity supply and the number of high schools per thousand population.
Table 1 shows summary statistics for the estimation sample.Given that the enforcement of the one-child policy differs between rural and urban households, we report mean individual characteristics for rural and urban Hukou holders separately. 13Note that rural individuals can change their Hukou status to urban if they attend occupational high school or college.As such, we categorize individuals as rural or urban according to their Hukou status prior to their enrollment in high school, utilizing the panel nature of the CHNS data.On average, rural individuals have 1.45 siblings whereas urban individuals have 0.63.This difference confirms the relaxed birth control policies for rural households.While 84% of urban individuals pursued high school education after finishing compulsory schooling, only 44% of rural children did so.The average normalized years of schooling for the urban sample is 1.13, which is 21% higher than that for the rural sample (0.94).At the county level, the fines for unsanctioned births account for a substantial 44% of average urban annual household income.This fraction is even higher for rural households, reaching 61% of average rural annual household income.
Our study sample shows substantial differences in family size and education between the Han majority and ethnic minorities.On average, ethnic minority children have 1.36 siblings, while Han majority children have 1.15.The larger family size for ethnic minorities is consistent with the more relaxed birth control policies implemented towards them.The Han-minority education gap documented in Fig. 3 also exists in the sample.While 59% of Han majority children attended high school, only 42% did so among ethnic minority children.

Empirical strategy
We explore variations in the local level of policy enforcement to empirically assess how family size and education are differentially affected by the one-child policy for the Han majority and ethnic minorities.We use the amount of the fine for unsanctioned births to measure the stringency of the one-child policy.A higher fine is expected to lower the likelihood for a given household to have two or more children, and thus is more effective in restricting fertility.This measure has been widely used in the literature as an exogenous variation to identify the impact of the one-child policy.For example, the amount of the fine for violating the one-child policy have been used by Liu (2014) as an instrument for fertility to test the Q-Q tradeoff and by Huang, Lei, and Sun (2015) to examine the contribution of the birth control policy in China to the gender gap in educational attainment.
One challenge in identifying the impact of local variation in fines on education is that there may exist other confounding factors that affect the local stringency of the birth control policy and education outcomes simultaneously.For instance, areas with higher birth rates initially may need stricter birth control policies to meet the population control goal set by the central government. 14With limited educational resources, higher birth rates also reduce average educational attainments, and when not controlled for, can bias the ordinary least squares (OLS) estimation results.To solve this problem, we include county-level birth rate in 1979, the year before the implementation of the one-child policy, in the empirical analysis.
Moreover, a richer county has both the budget to devote more resources to education and the need to implement a stricter birth control policy as economic development induces migration inflow, creating a spurious positive effect.To address this issue, we include two countylevel variables to control for local development levels: the stable coverage of electricity and the distance to the provincial capital.Note: Normalized years of schooling is calculated by taking the ratio of individuals' years of schooling to the mean schooling of children of the same age.
11 Using the province-year level fine data reported by Ebenstein (2010), we find the relative level of financial penalty for violating the one-child policy is stable over time.In particular, the correlation between provincial fines levied in 1979 and 2000 is 0.54. 12Early deceased children do not count towards the fertility quota.If a single child dies, his/her parents are allowed to have a second child. 13According to the household registration system (also known as the Hukou system), every Chinese citizen was categorized as rural or urban at birth according to their parents' Hukou status.See Pan (2017) for details of the Hukou inheritance rule. 14According to the President Hua Guofeng's speech in the Fifth National People's Congress, the initial target of the birth control was to reduce population growth rate to 0.5%.

Y. Pan and Y. Liu
Third, communities with stronger preference for child quality might resist less of the birth control policy and tolerate higher fines.Parents in these communities also tend to invest more in children's education.This positive association, however, cannot be interpreted as the impact of birth control on education.As the data do not have direct measure of preferences, we use county-level educational infrastructure measured by the number of high schools per thousand population as a proxy for local preference for education in the analysis.
We assume local variation in fines is exogenous conditional on these county characteristics.To support this assumption, we show in a placebo test that the level of fine does not affect the educational attainment of older children who were born before the enactment of the one-child policy. 15This finding indicates that within-county educational differences between the majority and minority are not correlated with fines before the introduction of the one-child policy.
While many rural and urban households reside in the same county and face the same local policies, their fertility decisions are expected to respond differently to monetary penalty for violating the one-child policy.On the one hand, in the absence of any birth restrictions, urban households tend to be richer and their fertility rate is generally lower than that of their rural counterparts.The one-child policy is therefore more likely to be binding for rural households.On the other hand, the one-child policy is more consistently and successfully implemented for urban households, with rural households allowed to have a second child if the first born is a girl.This policy difference could also lead to different fertility responses between rural and urban households to local level of fines for unsanctioned birth.Therefore, we estimate the following equation for rural and urban samples, separately using the constructed cross-sectional individual-level data: where Y itcp is either a family size or educational outcome variable of individual i, born in year t living in county c of province p, F cp is the (demeaned) logarithm of the county-level fines for unsanctioned births, and E itcp is an ethnicity dummy variable that equals one if individual i, born in year t living in county c of province p, is ethnic minority and zero otherwise.X itcp is a vector of individual characteristics including gender, schoolings of both parents and logarithm of household income. 16Z cp s are county-level controls discussed above that may simultaneously affect the amount of fines and education.We also control for countylevel average adult high school enrollment rates of Han and ethnic minorities. 17We further include birth year fixed effects, γ t , and a set of province dummies, ϕ p , to control for general time trends and possible regional differences in educational attainment.We cluster the standard error at the county level.
As the Han majority constitute the default group in our regression by construction, the impact of the stringency of birth control policy on their outcome measures is captured by β 1 .The coefficient on the interaction term of fines and ethnic minority dummy, β 2 , captures the differential impacts of birth control policy for the Han majority and ethnic minor-ities.The sum of β 1 and β 2 is the net effect of the one-child policy for ethnic minorities.This regression specification enables us to examine the impact of birth control policy in China on both ethnic minorities' relative level of educational attainment, e.g. the Han-minority educational gap, and their absolute level of educational attainment.
For Eq. ( 1) to successfully estimate the impact of the enforcement of the one-child policy, we need to assume that, for both family size and education, the time trend across age cohorts is the same for all provinces.This assumption may or may not be true in our case.Some provinces could have built more schools over the years, resulting in a steeper increase in educational attainment than other provinces.To address this issue, we further estimate the following equation: where the term ϕ p × t controls for province-specific time trends.All other notations remain the same.

Empirical results
In this section, we first show the effectiveness of fines for unsanctioned births in limiting family size, and analyze the impact of fines on the Han-minority educational gap for the rural subsample.We then move on to analyze such effects for the urban subsample, and discuss differences between rural and urban findings.

Fines, family size and education for rural children
The estimation results reported in Table 2 show a larger monetary penalty is more successful in reducing rural fertility.As presented in Column 1, a 10% increase in the amount of the fine significantly decreases the number of siblings by 0.053 for the Han majority.As shown in Row 2, this effect is much smaller (reduced by 0.031) for ethnic minorities.Combining these two effects, a 10% increase in the amount of the fine reduces the number of siblings by 0.022 for ethnic minorities, which is statistically significant at the 10% level.These results are robust to controlling for province-specific time trends, as shown in Column 2 of Table 2.
Our result that the financial penalty for violation of the one-child policy effectively reduces the number of siblings for Chinese children is consistent with findings from previous studies that examined the impact of the fines for violating the one-child policy on fertility.For example, McElroy and Yang (2000) found that a 10% rise in fines reduced total birth per woman by 0.03.Liu (2014) also reported that a 10% increase in fines led to 0.04 decrease in fertility.Our estimated impacts are similar in magnitude to their findings.
In addition, our results show that higher fines provoke a sharp decline Note: County level clustered standard errors are in the parentheses.β 1 and β 2 capture the effect of fines for Han majority and the additional effect on ethnic minority.Significance level: 1%***, 5%**, 10%*.
impact of fines on high school enrollment rates of these older cohorts are much smaller than estimates obtained using the main estimation sample and are not statistically different from zero.Detailed estimation results are reported in Appendix Table A2. 16Taking the logarithm transformation reduces possible biases due to measurement errors.As a result, 27 children with negative household income are dropped in the empirical analysis.Results are quantitatively similar when we do not control for household income and include these 27 children in the estimation sample. 17Adults are defined as those born in 1950s, the common age range of parents of the studied cohorts.
Y. Pan and Y. Liu  in fertility among rural ethnic minorities.The Chinese government made tremendous effort to promote the one-child policy and imposed severe punishment for non-compliance.Even though the enforcement of such a birth constraint was relatively weaker for ethnic minorities, as documented in Chang et al. (2005) and Zhang (2001), the population growth was successfully controlled in dense minority regions through local officials' persuasion.Our results confirm that the relaxed birth control policy remains effective in limiting the family size of ethnic minorities.Next, we examine if the level of fines has influences on rural education stratification.As shown in Table 3 Row 2, a 10% rise in the fine increases the gap in high school enrollment, our main educational measure, between the Han majority and ethnic minorities by 1.05 percentage points. 18This effect is both statistically and economically significant.As shown in Column 2, our finding is robust to controlling for province-specific time trends.Results are similar when we estimate using normalized years of schooling as an alternative measure of education (Columns 3 and 4).
The larger Han-minority education gap in areas where fines are higher is likely a result of improved educational attainment for the Han majority.As shown in Table 3 Row 1, a 10% increase in the fine leads to a statistically significant increase in high school enrollment rates by 0.87 percentage points for rural Han.This positive impact of fines on the education of the Han majority is consistent with the quantity and quality tradeoff documented in the literature (See, e.g.Li et al., 2008; Liu, 2014;  Rosenzweig & Zhang, 2009).Note that our results do not necessarily contradict those found by Liu (2014), who used the same data and identification strategy but only found a weak Q-Q tradeoff in terms of educational attainment for the rural Han majority.While Liu (2014) measured educational attainment using middle school graduation rate and school enrollment rate for compulsory education age children, we focus on high school enrollment, a measure that is more likely to be affected by the reductions in family sizes given the sharply increased tuition rate for post-compulsory education in 1990s.
Education of rural ethnic minorities does not vary with the level of fines, therefore does not contribute to the intensified Han-minority educational stratification areas of high fines.Based on the regression specification, the overall impact of fine on ethnic minorities is calculated as the sum of the impact on the Han majority and the impact on the Hanminority gap.For rural households, a 10% higher fine significantly increases the high school enrollment rate for the Han majority, but its additional impact for ethnic minorities is negative.The net effect is slightly negative (0.18 percentage points), but is statistically insignificant (P-value = 0.628).Although stricter birth control policies reduce family size for rural ethnic minorities as shown previously, these changes do not appear to be large enough to lead to educational changes.We also verify in Appendix Table A4 that these rural results are robust to the exclusion of the Guangxi province in which most Zhuang ethnic minorities reside, who have faced the same fertility restrictions as the Han majority.
In sum, our findings provide valuable insights in understanding why ethnic minorities' are experiencing increasingly lower educational attainment than the Han majority.As shown in Fig. 3, while the high school enrollment rates of the Han majority have increased sharply since 1970s, the increase in the high school enrollment rates of ethnic minorities is much slower.The Han-minority high school enrollment rate gap increased from percentage points for the 1970 birth cohort (before any birth control policy) to 16 percentage points for the 1983 birth cohort (before the policy relaxation for rural households).Our results indicate that one standard deviation increase in the amount of the fine, which is an increase of around 68% from the sample mean based on Table 1, leads to an increase of 7.1 percentage points in the rural Han-minority high school enrollment rate gap.These documented effects of one standard deviation increase in the fine are substantial considering that the overall increase in the Han-minority gap was percentage points for cohorts from 1970-1983. 19

Fines, family size and education for urban children
Similar to their rural counterpart, a harsher monetary penalty for unsanctioned birth is more effective in limiting family sizes for urban Han households.As shown in Table 4 Column 1, a 10% increase in the amount of the fine significantly reduces the number of siblings of urban Han majority by 0.024.Compared with the Han majority, a 10% increase in the amount of the fine has a much more limited impact for urban ethnic minorities: the impact is reduced by a significant 0.019, leading to a small combined effect that is not statistically different from zero.
The finding that the amount of the fine only has insignificant impact on the fertility of urban ethnic minorities is in contrast with the rural results.One plausible explanation for this difference is that urban households tend to be richer with a lower fertility rate even without any birth restrictions.The relaxed birth restriction might therefore not be binding for many urban minority households.In this case, birth control policies are unlikely to cause concentrations (or dilutions) of educational resources for these households.
Results on urban education stratification reported in Table 5 are generally similar to those of their rural counterparts.As shown in Row 2, a 10% rise  Note: County level clustered standard errors are in the parentheses.β 1 and β 2 capture the effect of fines for Han majority and the additional effect on ethnic minority.Significance level: 1%***, 5%**, 10%*. 18Coefficients on control variables are reported in Appendix Table A3. 19Unfortunately, we are unable to calculate the Han-minority high school enrollment gap for children originally holding urban and rural Hukou separately, because the 2000 census only collected the Hukou status at the time of the survey, which might have been changed by individuals' enrollment in high school.
Y. Pan and Y. Liu  in fines enlarges the Han-minority high school enrollment gap by 1.44 percentage points for urban individuals.Our results indicate that one standard deviation increase in the amount of the fine, which is an increase of around 75% from the sample mean based on Table 1, leads to an increase of 10.8 percentage points in the urban Han-minority high school enrollment rate gap.
Again, the improved education for the Han majority contributes to the larger Han-minority education gap in areas of high fines, but to a lesser extent than for the rural subsample.In particular, a 10% increase in the fine leads to a statistically significant increase in high school enrollment rates by 0.47 percentage points for the urban Han majority.This effect is still positive but no longer statistically significant for normalized years of schooling.Our results are consistent with those found by Li et al. (2008) and Luo (2016), who have shown that the quantity and quality tradeoff is more evident in rural China.
Unlike its muted effect for rural ethnic minorities, a higher monetary penalty for violation of the one-child policy lowers the educational attainment of ethnic minorities, which further contributes largely to the Hanminority education gap in areas of high fines.The effect size is substantial: a 10% higher fine significantly lowers the high school enrollment rate for ethnic minorities by 0.97 percentage points. 20This education effect is not operating through resource dilution associated with fertility changes as we have shown that the amount of the fine has no observable impact on the family size of urban ethnic minorities.
Several channels may enable the negative impact of higher fines upon education for urban ethnic minorities.One potential explanation for ethnic minorities' lower educational attainment in areas where fines are higher is the increased sex ratio as a result of the birth control policy combined with son preference.Even though we controlled for individuals' gender in our estimations, ethnic minorities' competition for school admission would more often be with Han boys, who might be more competitive than girls.To test if our findings are driven by the increased sex ratio, we calculate a county-level fraction of males for our sample and add it to our regression as a robustness check.The negative impact of the amount of the fine on urban ethnic minorities' education remains the same. 21Our findings are therefore not likely to be mainly driven by the increased sex ratio.
Another possible channel is the spillover effect from the increased educational attainment of the Han majority (both rural and urban) residing in the same county.While a positive spillover effect from the Han majority to ethnic minorities is possible when these minorities benefit directly from having better school peers, the negative impact we find can potentially be explained by increased competition intensity in high school admissions process.To investigate if this is the case, we split the sample by the scarcity of high school education resources, measured by the local number of high schools per thousand population, and re-estimate the impact of fines on education of urban ethnic minorities.Counties with relatively fewer numbers of high schools are expected to have higher levels of competition in the school admission process.As shown in Table A5, a higher fine has a much larger negative effect on high school enrollment of ethnic minorities residing in counties with scarcer high school education resources.These findings provide suggestive evidence that the one-child policy may harm the educational attainment of the partially excluded ethnic minorities via increased competition for educational resources.

Conclusion
This paper provides evidence that the one-child policy that mainly targets the Han majority contributes unexpectedly to the educational disadvantaged of ethnic minorities in China.We use the amount of the fine for unsanctioned births to measure the enforcement of the one-child policy and show that a more stringent enforcement of the birth control policy leads to a larger Hanminority education gap in both rural and urban areas.The main factor leading to this enlarged gap is the improved educational attainment of the Han majority.As their family size is reduced sharply by the one-child policy, households invest more in human capital for each child.
In order to rebalance the demographic structure of society in the face of rapid population aging, the Chinese government launched a series of reforms, including the "selective two-child policy," which allowed a couple to have two children if either husband or wife was a "single child," and the "universal two-child policy," which further allowed all couples to have two children.Recognizing the unexpected initial impact of the one-child policy on the Han-majority education gap is important for projecting the overall policy impact of more relaxed policies.Even though the new policies mean that ethnic minorities are no longer allowed to have more children than the Han majority, they do offer these minorities the opportunity to make gains in the area of education.

Appendix Table 5
Impact of fines for unsanctioned births on urban education.

Fig. 1 .
Fig. 1.Birth rate by year of birth.Notes: Figure is prepared with data drawn from the China Statistical Yearbook 1990.The birth rate is measured as the total number of live births per 1000 population in a year.

Fig. 2 .
Fig. 2. Minority population share by year of birth.Notes: Figure is prepared with data drawn from the Fifth National Population Census of China in 2000.

Fig. 3 .
Fig. 3. High school enrollment gap between Han majority and ethnic minorities.Notes: Figure is prepared with data drawn from the Fifth National Population Census of China in 2000.We exclude younger cohorts (i.e.those born after 1983) who might still be in middle school by the time of the census.

Table 1
Summary statistics.

Table 2
Impact of fines for unsanctioned births on number of siblings for rural children.

Table 3
Impact of fines for unsanctioned births on rural education.Fine is measured in logarithms.County level clustered standard errors are in the parentheses.Normalized years of schooling is calculated by taking the ratio of individuals' years of schooling to the mean schooling of children at the same age.β 1 and β 2 capture the effect of fines for Han majority and the additional effect on ethnic minority.Significance level: 1%***, 5%**, 10%*.

Table 4
Impact of fines for unsanctioned births on number of siblings for urban children.
Fine is measured in logarithms.County level clustered standard errors are in the parentheses.Normalized years of schooling is calculated by taking the ratio of individuals' years of schooling to the mean schooling of children at the same age.β 1 and β 2 capture the effect of fines for Han majority and the additional effect on ethnic minority.Significance level: 1%***, 5%**, 10%*.
20Again, our urban results are robust to the exclusion of the Guangxi province in which most Zhuang ethnic minorities reside (Appendix TableA4).21Theestimate(P-value)for high school enrollment and normalized years of schooling are − 0.087 (0.059) and − 0.073 (0.056) respectively.Y.Pan and Y. Liu

Table A1
Correlation between fines for unsanctioned births and other forms of policy enforcement practices.Note: Significance level: 1%***, 5%**, 10%*.Impact of fines for unsanctioned births on high school enrollment of older children.

Table A3
Impact of fines for unsanctioned births on rural and urban high school enrollment.

Table A5
Impact of fines for unsanctioned births on urban high school enrollment by local high school resources.Low or high level of local high school resources is categorized according to whether the local number of high schools per 1000 population is below or above the sample median.Significance level: 1%***, 5%**, 10%*.