The Effect of China’s One Child Policy on Sex Selection, Family Size, and the School Enrolment of Daughters
The Effect of China’s One Child Policy on Sex Selection, Family Size, and the School Enrolment of Daughters
Abstract and Keywords
A large economics literature provides evidence that parents trade-off the quantity of children with the quality of children, which implies that child ‘quality’ declines as family size increases. Child psychologists argue that increases in the number of children can increase the child quality because it provides children with opportunities to teach and learn from each other. Alternatively, there may simply be economies of scale in childcare costs for items such as clothes and textbooks such that an additional child lowers the marginal cost of quality for all children. Both China and India have experimented with different family planning policies to limit family size. This study addresses the effect of family size by examining the impact of increasing the number of children from one to two on school enrolment in rural China. To establish causality, the author exploits region and birth year variation in relaxations of the one child policy.
The effect of family size on child ‘quality’ is a question of longstanding interest to economists. The effect is a priori ambiguous.1 On the one hand, a large literature in economics provides evidence that parents trade off the quantity of children with the quality of children, which implies that the quality of children declines as family size increases (e.g. Becker and Lewis 1973; Becker and Tomes 1976).2 On the other hand, child psychologists such as Iacovou (2001) and Zajonc and Markus (1975) emphasize social interaction and learning-by-doing. They argue that increases in the number of children can increase the quality of children because it provides children opportunities to teach and learn from each other.3 Alternatively, there may simply be economies of scale in the costs of childcare for items such as clothes (p.297) and textbooks such that an additional child lowers the marginal cost of quality for all children. In the rural Chinese context, this can be seen in Table 1A in Qian (2017), which shows that average per child expenditures on household chores and childcare for rural Chinese households decrease significantly with the number of children.
For policy makers in developing countries today, understanding this relationship is especially relevant as many governments have attempted to curb population growth as a way of increasing average human capital investment. Both China and India, the world’s two most populous countries, have experimented with different family planning policies to limit family size. This study addresses the effect of family size by examining the impact of increasing the number of children from one to two on school enrolment in rural China. To establish causality, I exploit region and birth year variation in relaxations of the One Child Policy (OCP).
There are two main difficulties. First, there is the possibility of parental heterogeneity. For example, if parents who value education more also prefer to have fewer children, then the correlation between quantity and quality will overestimate potentially negative effects of family size. Endogeneity may also arise from the quality of the first child. For example, if parents are more likely to have a second child when the first child is of high quality, the correlational evidence will under-estimate the potentially negative effects of family size. To address these issues, past studies have carefully constructed strategies that exploit the exogenous variation in family size caused by multiple births or the sex composition of the first two children (Angrist et al. 2010; Black et al. 2006; Conley 2004; Lee 2004; Rosenzweig and Wolpin 1980; Rosenzweig and Zhang 2009).4 While previous works provide important evidence, the strategies they employ cannot be applied to all contexts. Specifically, the estimates from using the sibling sex composition instrument is most suitable for studying the effect of increasing the number of children from two to three, and cannot be an excludable instrument if parents practise sex selection. Estimates from using the twins instrument can lack external validity to non-twin children.
The principal contribution of this chapter is to address these problems and estimate the effect of increasing the number of children from one to two. I exploit regional and time variation in the relaxations of China’s OCP.
(p.298) I use the relaxation that allowed families to have a second child if the first child is a girl to instrument for the family size of first-parity children born before the relaxation was announced. Three facts are exploited: first, an individual is only affected by the relaxation if she is born in a relaxed area; second, among first-born children born in relaxed areas, only girls are affected; and third, a girl is more likely to gain a sibling due to the relaxation if she is younger at the time of the policy announcement. The instrument for family size is the triple interaction term of an individual’s sex, date of birth, and region of birth. The interaction between whether a girl was born in a relaxed area and her birth year estimates the effect of the relaxation on family size. The additional comparison with boys controls for region-specific changes in school provision (and other cohort changes) that affected boys and girls similarly. This strategy differs from previous methods in that it essentially compares one-child households with two-child households. Interpreting the two-stage least squares (2SLS) estimates as causal assumes that absent the introduction of the relaxation, the difference between households with first-born daughters and those with sons would have moved along parallel trends for villages that received the relaxation and villages that did not. This is the standard parallel trends assumption applied to a triple-difference setting. I do not take this assumption as given and will carefully consider and provide evidence against potential caveats in the robustness section.
The ordinary least squares (OLS) estimates show that for households with three or fewer children, the number of siblings is negatively correlated with school enrolment. However, for households with two or fewer children, having a younger sibling is positively correlated with the school enrolment of the eldest child. This is consistent with the descriptive evidence that shows that only children are, on average, less likely to be enrolled in school relative to children from two-child families, who are, on average, more likely to be enrolled in school relative to children from three-child families.
The 2SLS results show that for households with two or fewer children, an additional child significantly increases the school enrolment of first children by up to 16 percentage points. The fact that the 2SLS estimate is larger in magnitude than the OLS estimate is consistent with the existence of parental heterogeneity in preferences for education and quality.
The main results show that there is a significant one-child disadvantage for the eldest child, which is consistent with the belief that children benefit from teaching younger siblings, and also with the possibility that there may be economies of scale in raising children. They do not unambiguously reject the Beckerian quantity–quality tradeoff model since that model makes predictions about the average outcomes of children, and I can only examine the outcomes for the eldest child. However, for quantity to have no average effect on quality given my findings for the eldest child, there would have to (p.299) be inequality across children, which would also be inconsistent with a simple Beckerian case.
In addition to the main results, we attempt to investigate the mechanisms underlying them. First, I investigate the hypothesis that the positive effect of an additional child is driven by economies of scale in childrearing costs. Under the assumption that there are larger economies of scale regarding school for children of the same sex (e.g. children can more easily share clothes if they are the same sex), I explore this hypothesis by examining whether the benefit of the second child is larger when the two children are the same sex. The results show that the benefits of a second child are almost entirely seen by households where the two children are of the same sex. This is consistent with the presence of economies of scale.
Second, I examine the hypothesis that the benefit of an additional child is driven by an increase in permanent income. For example, if adult children provide parents with income, then an additional child will increase the permanent income of the household. If parents can borrow against their children’s future income, this could increase investment in schooling. Under the assumption that parents expect sons to earn more than daughters, I test this hypothesis by investigating if the benefits of a second child are larger when the second child is a boy. The results show the opposite pattern: the benefits are larger when the second child is a girl. Therefore, our results do not seem to be driven by increases in permanent income, which is perhaps not surprising since households in rural China are generally believed to be credit constrained. Note that because the sex of the second child is not random due to sex selection, these results should be interpreted very cautiously as only suggestive evidence.
Finally, I investigate the possibility that the main results occur due to binding income constraints. If the financial costs imposed by an additional child outweigh schooling costs, then parents may increase their labour supply in the labour market and substitute public schools for self-provided childcare. The data limit the extent to which I can investigate this hypothesis. I examine the effect of an additional child on the mother’s labour supply and school delay. The results are suggestive, but imprecisely estimated. They suggest that an additional child causes mothers to be more likely to enter the labour force and causes the elder child to enter school at a younger age. These results are consistent with the hypothesis that income demand caused by the additional child causes mothers to work and the first child to begin school. Interestingly, they suggest the possibility that public schools are being used as a form of low-cost childcare. This is important because it implies that classic frameworks for understanding the relationship between family size and children’s schooling may be inadequate for contexts where schooling costs are low and can be used as a form of subsidized childcare by parents.
(p.300) This study makes several contributions. First, it adds to the existing literature on the effects of family size. The results from this literature have been mixed.5 Most of these studies have focused on the effect of additional children conditional on there already being two children. I add to these studies by being the first to provide evidence for the one-child disadvantage (at least for the eldest child), which suggests that the effect of family size may be non-monotonic across family size. The finding that additional children benefit the schooling outcomes of the eldest child is similar to Angrist et al.’s (2010) finding for Israel. The implication that the effects of family size may differ across birth orders supports the findings of Black et al. (2006) for Norway.
Second, this study provides an evaluation of the effects of the OCP, one of the most restrictive and large-scale family planning policies ever undertaken. While demographers and sociologists have conducted many descriptive studies of the policy’s impact on fertility and sex ratios, the lack of local enforcement data has heretofore prevented an examination of the causal effect of the OCP on child outcomes. The findings indicate that the OCP decreased female survival by up to ten percentage points, and the relaxation was successful in reducing the sex selection to pre-OCP levels. Interestingly, the results also show that the previous rule on four-year birth spacing was well enforced, a fact that has received little attention in policy debates or academic studies. In rigorously evaluating the effects of the OCP, the first stage of this chapter is closely related to a recent study by Ebenstein (2010), which uses Chinese Census data to show that regional sex ratios are closely linked to the level of fines for violating the OCP. More generally, this study adds to the large literature on the effects of family-planning-policy-induced fertility. Recent examples from the Chinese context include Dasgupta et al. (2011), who study the effect of reduced fertility on the marriage market. Similarly, Banerjee et al. (2014) examine the effect of reduced fertility on savings in urban China. Since family-planning policies both reduced fertility and exacerbated the boy-biased sex imbalance in China, my work is also related to a recent study on savings by Wei and Zhang (2011).
Finally, the suggestive results on mothers’ labour supply add to studies on the relationship between subsidized childcare and mothers’ labour supply. For a recent example, see Baker et al.’s (2008) study of Quebec, where they find (p.301) that universal childcare significantly increases maternal labour supply. In a developing context, a recent study by Schlosser (2011) finds that subsidized pre-school increases the labour supply of Arab mothers in Israel.6
The chapter is organized as follows. Section 2 discusses family-planning policies and education in rural China. Section 3 describes the data. Section 4 presents the empirical strategy. Section 5 presents the empirical results. Section 6 offers concluding remarks.
2.1. Family Planning Policies
In the 1970s, after two decades of explicitly encouraging population growth, policy makers in China enacted a series of measures to curb population growth. The policies applied to individuals of Han ethnicity, who make up 92 per cent of China’s population. Beginning around 1972, the policy ‘Later [age], longer [the spacing of births], fewer [number of children]’ offered economic incentives to parents who spaced the birth of their children at least four years apart. The OCP was formally announced in 1979. Actual implementation began in certain regions as early as 1978, and enforcement gradually tightened across the country until it was firmly in place in 1980 (Banister 1987; Croll et al. 1985).7 Second births became forbidden except under extenuating circumstances. Local cadres were given economic incentives to suppress fertility rates. In the early 1980s, parts of the country were swept by campaigns of forced abortion and sterilization and reports of female infanticide became widespread (Banister 1987; Greenlaugh 1986).
Local governments began issuing permits for a second child as early as 1982. However, permits for a second child were not widespread until the Central Party Committee issued ‘Document No. 7’ on 13 April 1984. The two main purposes of the document were to: (1) curb female infanticide, forced abortion, and forced sterilization; and (2) devolve responsibility from the central government to the local and provincial government so that local conditions could be better addressed. In other words, it allowed for regional variation in family-planning policies. The document allowed for second births for rural couples with ‘practical’ difficulties, and strictly prohibited coercive methods.8 The main relaxation following Document No. 7 is called the ‘1-son-2-child’ (p.302) rule. It allowed rural couples to have a second child if the first child was a girl (Greenlaugh 1986). The explicit purpose of this relaxation was to decrease female infanticide of the first-born child.
White (1992) found that 5 per cent of rural households were allotted second child permits in 1982. These permits were generally granted to regions with extremely high levels of infanticide. After Document No. 7, the permits expanded to 10 per cent of the rural population in 1984, 20 per cent in 1985, and 50 per cent by 1986.
Document No. 7 made provincial governments responsible for both maintaining low fertility rates and reducing infanticide. While the exact process of granting permits is unclear, I use county-level data on family-planning policy to show in the next section that the probability of a county obtaining the 1-son-2-child relaxation is positively correlated with the rate of pre-relaxation sex selection, and both are positively correlated with distance from the provincial capital. These facts most likely reflect that in order to maintain low aggregate fertility rates and reduce excess female mortality (EFM), provincial governments granted relaxations to regions that were distant from the administrative capital and where EFM was more prevalent. The higher prevalence of sex selection in rural areas can be due to both more boy-preference in distant rural areas and the fact that geographic distance increases the provincial government’s logistical difficulty in preventing EFM.9 Issues of identification that arise from the correlation of obtaining a relaxation and sex selection will be addressed explicitly in the section on robustness.
2.2. Rural Education
Rural primary schools are exclusively provided by the state in the period of this study. Relative to other developing countries, the cost of schools was very low. Nevertheless, during the time period of this study, there was much inequality in provision across regions—both across provinces and across counties within a province. This was a result of fiscal reforms that occurred during the early 1980s. The fiscal system reduced subsidies from rich regions to poor regions. The system of ‘eating from separate pots’ (fen zao chi fan) devolved expenditure responsibilities from the central and provincial governments onto local governments in order to give the latter stronger incentives to generate revenue. The ratio of the per capita schooling expenditure in the highest-spending province to the lowest-spending province doubled in one decade. Many rural schools were closed; rural enrolment rates dropped (p.303) dramatically and did not recover until the mid-to-late 1990s (Hannum and Park 2002). Using spending data from Gansu Province, they found that per capita school expenditure was positively correlated with income and that significant variation in school quality existed across counties. They found little variation within counties, suggesting that studies examining education outcomes should focus on variation at the county level. Hannum (2002) showed that the difference in school provision between rich and poor areas was much greater for middle schools and high schools than for primary schools. This is consistent with the China Health and Nutritional Survey (CHNS) data used in this study, where primary school enrolment remained stable while middle school and high school dropout rates increased for poor areas (Hannum and Park 2002).
The CHNS data show that counties with some relaxation and counties with no relaxation had similar geographic access to schooling in 1989. However, the data do not reveal the quality of schooling or the changes in school availability during the early 1980s. Because relaxed areas tend to be more rural, it is likely that the quality of schools declined in relaxed areas during the same time that the 1-son-2-child relaxation took effect. To control for this, I will compare outcomes for girls to boys within counties. The strategy is robust as long as the changes in school quality and the economic conditions that determine school quality in relaxed areas have the same impact on boys and girls.
This chapter matches the 1 per cent sample of the 1990 Population Census with the 1989 CHNS at the county level. The 1990 Population Census contains fifty-two variables, including birth year, region of residence, whether an individual currently lives in his/her region of birth, sex, and relationship to the head of the household. The data allow children to be linked to parents. Thus, family size and birth order of children within a household can be calculated. Because the identification is partially derived from the region of birth, the sample is restricted to individuals who reported living in their birth place in 1990. The CHNS uses a random cluster process to draw a sample of approximately 3,800 households with a total of 16,000 individuals in eight provinces that vary substantially in geography, economic development, public resources, and health indicators. Most importantly, the survey provides detailed village- and township-level information on family-planning policy enforcement. Since ethnic minorities were exempt from all family-planning policies, I restrict the analysis to four provinces that are mostly composed of individuals of Han ethnicity. The matched dataset contains twenty-one (p.304) counties in four provinces.10 These provinces are in the middle and upper ranges of gross domestic product (GDP) and GDP growth during this period. The CHNS data are aggregated to the county level in order to be matched to the 1990 Census. Since the policy data are at the village and township levels, the aggregated dataset reports the percentage of the population in each county that is exposed to the relaxation.
For the analysis of family size and education, the sample is restricted to first-born children in cohorts born during 1962–81. The reference group in the regression analysis is comprised of individuals born during 1962–72. Those born after 1981 are excluded because, after the relaxation, parents who preferred larger families may have chosen to keep girls in order to have a second child. Consequently, the 2SLS estimate, if it does not exclude those born after 1981, will be biased by parental preferences and will show that girls with larger family sizes are better-off.
Table 1a in Qian (2017) shows the time and money allocated for household chores according to the number of children in the household. It shows that as family size increases, parents allocate less time to household chores and less money to food. Interestingly, even time allocated to childcare declines with the number of children. This is important for understanding our results later. Panels A and B in Table 1b in Qian (2017) show that among first-born children, girls, on average, have more siblings, more educated parents, and higher school enrolment. Panels C and D show that only-children are more likely to be male, have more educated parents, and are more likely to be enrolled in school. This is consistent with the identified concern that parents with more education may prefer to have fewer children and value education more.
To use individuals in counties without relaxations as a control group for individuals in counties with relaxations, I would like the two groups to have similar characteristics in every respect other than the relaxation. Table 1c in Qian (2017) compares first-born children born in counties with no relaxation and first-born children born in counties with some relaxation. It shows that the two types of counties have similar demographic characteristics. Each has approximately 55 per cent males among the first-born children. Family size and sex composition of siblings are similar. Children born in relaxed areas have slightly more educated parents. School enrolment in both counties with and counties without relaxations are approximately 50 per cent. Panel B shows that in counties with some relaxations, 38 per cent of first-born children are born in villages or townships with the relaxation. Counties with relaxations are further away from urban municipalities.
(p.305) The treatment group comprises children who are 9–14 years old in 1990. In principle, they should be enrolled in primary school or junior high school. The control group comprises children who, in principle, should be in high school. The descriptive statistics show that children in counties with the relaxation must, on average, travel further to attend primary school. This biases against my finding a positive effect of the relaxation on school enrolment. The distances to middle schools and high schools are very similar between counties with and without the relaxation.
One potential concern with Chinese data on children is the fear that parents will misreport the number of children in order to evade the OCP. Past studies have compared hospital birth records and Population Census data to show that misreporting is typically a problem for children under two years old and the data for older children are typically accurate (Zeng et al. 1993). Since I use data from 1990 to study children born close before and after 1976 (who were around 14 years old by the time the data were collected), misreporting should not affect my study.
4. Empirical Strategy
Figure 14.1 plots the total number of children against the birth year of the first-born child. It shows that children born in more recent years have smaller family sizes. This reflects both the fact that parents of young children may not have finished having children and a decrease in family size over time. To reveal the commonly seen OLS evidence for the quantity–quality tradeoff, I regress a dummy variable for school enrolment on dummy variables for the number of children in a household. Children from one-child households are the reference group. Figure 14.2a plots the coefficients. It shows that family size is negatively correlated with school enrolment regardless of whether county-fixed effects are controlled for. However, this confounds the family size effect with several factors: (1) younger children are more likely to be in school; (2) younger children will have fewer siblings because their parents may not have finished having children; and (3) quantity and quality may be jointly determined by parental preferences. Controlling for birth years addresses the first two problems and causes the relationship between family size and school enrolment to become non-monotonic. Figure 14.2b plots the coefficients for family size when controlling for birth year fixed effects.11 Relative to the reference group of children from one-child families, children from two-child (p.306) (p.307) families have higher school enrolment. However, the correlation between enrolment and family size is negative for households with 2–5 children.
The main second-stage equation will control for birth county and birth year fixed effects. It can be written as:
School enrolment for individual i, born in county c, birth year t, is a function of sibsitc, the number of siblings he or she has; Xict, individual characteristics; the interaction term between urbanc, distance to urban area, and dl, a variable indicating whether an individual was born in year l; γt, birth year fixed effects; and ψc, county fixed effects.
This faces the problem that the number of children and investment in these children are jointly determined by parents. Hence, if parents who value education also prefer smaller households, then OLS will overestimate the negative effect of an additional sibling on schooling. I address this by exploiting plausibly exogenous variation in family size caused by relaxations in the OCP. Sex, date, and region of birth jointly determine an individual’s exposure to the 1-son-2-child relaxation. The relaxation allowed parents to have a second child only if the first-born child was a girl. Therefore, family size (p.308) should be positively correlated with being a girl. Since parents are more likely to have a second child if the first girl was younger when the relaxation was announced, family size should be negatively correlated with the age of the first girl. The interaction between whether a girl was born in a relaxed area and her age estimates the effect of the relaxation on family size. The additional comparison with boys controls for changes in policies such as education provision that affected both boys and girls similarly. The instrument for family size is therefore the triple interaction of an individual’s sex, year of birth, and region of birth. Only the combination of the three is exogenous. The exclusion restriction for the instrument is that it must be correlated with family size and only affect school enrolment via the family size channel.
To understand the identification strategy, I first estimate the effect of the policy on family size for boys and girls separately. If the policy were fully enforced, it should increase the number of siblings for first-born girls who the OCP prevented from having younger siblings. The relaxation should have no effect on the family size of boys. I estimate the following equation separately for samples of first-born boys and girls born during 1962–81:
The number of siblings for individual i, born in county c, birth year t, is a function of: the interaction term of relaxc, the extent of relaxation in county c and dil, a dummy indicating whether the individual was born in year l; γt, birth year fixed effects and ψc, county-fixed effects. The reference group comprises individuals born during 1962–72. It and all of its interaction terms are dropped. For all regressions, standard errors are clustered at the county level.
Then, to assess the statistical difference of the effect on boys and girls, I pool the data to estimate the first-stage equation with the triple interaction terms on the right-hand side (RHS):
The number of siblings for individual i, born in county c, birth year t, is a function of: the triple interaction term of relaxc, the extent of relaxation in county c, girlitc, a variable indicating whether a child is a girl and dil, a dummy variable indicating whether the individual was born in year l; the interaction term of relaxc and dil; the interaction term between girlitc, and dil; the interaction term between relaxc and girlitc; girlitc; γt, birth year fixed effects; and ψc, county-fixed effects. As before, the reference group of cohorts born in 1962–72 (p.309) and all its interactions are dropped. βl is the difference in the effect of being born in a relaxed area on family size between girls and boys born in year l. The estimates should be zero for earlier cohorts who were not affected by the OCP and relaxation and positive for later affected cohorts. βl is the effect of being born in a relaxed county on family size for an individual born in year l.
Like simple differences-in-differences estimators, cohort-invariant differences across regions are differenced out by the comparison across cohorts. Changes across cohorts which affect different regions similarly are differenced out by the comparison across regions. The triple difference adds the advantage that cohort-varying differences that affect boys and girls similarly across regions are also differenced out by the comparison between girls and boys within each cohort and region. The exclusion restriction is only violated if a change with differential impacts on areas with and without the relaxation and on boys and girls occurs at the same time the relaxation took effect. In other words, the 2SLS estimate will be biased only if there is a sex-specific change at the time of the relaxation in relaxed regions. For example, if local governments of relaxed regions implemented a programme encouraging girls to attend school when the relaxation was enacted, then the 2SLS will confound the effects of this programme with the effects of family size. There is little reason to think that such a change occurred. The main concern with this strategy arises from the fact that the relaxations were introduced to curb sex selection. If the relaxation is strongly correlated with the extent of sex selection for OCP cohorts, two potential problems will arise. First, unobserved factors correlated with sex selection may affect education investment differentially for boys and girls. This will bias the estimates if the factors driving sex selection are time varying.12 Second, there might be selection bias regarding the parents who choose to keep girls in relaxed regions. The main concern is that parents of girls in relaxed regions could have different unobservable characteristics from parents of girls in regions without the relaxation in such a way that would bias the 2SLS estimates upwards. For example, parents of girls in relaxed regions may, on average, have a higher consumption value for all things related to children, such as education relative to parents of girls in non-relaxed regions. Then, the 2SLS estimate will overestimate the true effect of family size on school enrolment. I investigate this by first examining the (p.310) effect of the relaxation on the fraction of males by birth year using the following equation:
The probability of being male for individual i, born in county c, birth year t is a function of: the interaction terms between relaxc, and birth year dummy variables, dil; birth county fixed effects, ψc; and birth year fixed effects, γt. βl is the correlation between being born in a relaxed county and the sex ratios of your cohort for each birth year l.
Then, to estimate the magnitude of the effect of the relaxation on sex ratios, I estimate the following equation using the sample of first-born children:
The probability of being male for individual i, born in county c, birth year t is a function of: the interaction term between relaxc and postil, a variable indicating the individual’s cohort group; ψc, county-fixed effects and γt, cohort-group-fixed effect. In the section on robustness, I will use the estimate of δl to compute bounds for the main results. The children are divided into three groups according to birth cohort.
The reference group comprises individuals not affected by the OCP and the relaxation (born before 1978). The second group comprises children born after the OCP but before the relaxation (1978–81). The third group comprises children born after the relaxation (1982–89). is the effect of the OCP on sex selection in relaxed areas relative to areas without the relaxation. For robustness, I use it to calculate the extent to which the main results can be driven by selection under certain assumptions.
5. Empirical Results
5.1. The Correlation Between Family Size and Schooling
Panels A and B of Table 2 in Qian (2017) show the estimates from equation (1). All regressions control for the full set of double interaction terms from equation (3).13 Panel A shows that among households with three or fewer children, an additional sibling is negatively correlated with the school enrolment of the first child by 1.1 percentage points. However, since the 2SLS will reveal the effect of increasing the number of children from one to two, the (p.311) relevant OLS comparison should be on a sample of individuals with one or no sibling. Panel B shows that in this restricted sample, an additional sibling is positively correlated with the school enrolment of the eldest child by approximately 1.5 percentage points. Estimates in both cases are statistically significant at the 1 per cent significance level and robust to controls.
Note that the number of observations change slightly across the different estimates of the analysis because the control variables are not always available for the full sample. In this chapter, I present results using the largest possible sample. All of the results are nearly identical when the estimates are repeated on a restricted sample where all controls are available for all observations. These results are not reported for brevity and are available upon request.
5.2. The Effect of the 1-Son-2-Child Relaxation on Family Size
I first estimate equation (2) on separate samples for boys and girls. The estimates are shown in Table 3, columns (1) and (2), in Qian (2017). The estimates for girls are statistically significant at the 1 per cent level for individuals born in 1976 and later. This is consistent with the fact that before the OCP was introduced in 1979–80, there was a four-year birth spacing law. Hence, the OCP was binding for cohorts born four years before its introduction. The estimates for boys are statistically insignificant. The coefficients are plotted in Figure 14.3a. It shows that family size for boys and girls were similar for cohorts born 1973 and 1976, after which the family size for girls increased and the family size for boys remained the same.
The estimated coefficients for the triple interaction terms from equation (3) are shown in Table 3, column (5), in Qian (2017). They are statistically significant at the 5 per cent level for the individuals born 1977–81. Figure 14.3b plots the coefficients for the triple interaction term. It shows that the boy–girl difference in the effect of being born in a relaxed area on family size is zero for unaffected cohorts and positive for the affected cohorts. On average, the relaxation increased family size of first-born girls by approximately 0.25 children. The discrete change in the effect of the triple interaction term between individuals born before 1976 and those born afterwards is consistent with the claim that the OCP was binding for cohorts born four years prior to its enactment. This is evidence for the effective enforcement of the previous four-year birth spacing.
5.3. The Effect of the 1-Son-2-Child Relaxation on Enrolment
I first estimate the effect of the relaxation on enrolment separately for boys and girls using an equation identical to equation (2), but replacing the dependent variable with enrolment, the outcome of interest. The reference (p.312) group comprises individuals born during 1962–72. The coefficients for girls and boys are shown in Table 3, columns (3) and (4), in Qian (2017). The estimates are statistically significant for girls. Figure 14.4a plots the estimates for boys and girls. The plot of the reduced form shows that girls affected by the relaxation (born 1976 and after) had higher education enrolment than boys, whereas girls unaffected by the relaxation (born before 1976) had lower school enrolment rates than boys.
The estimates in Figure 14.4a show that, relative to areas without the relaxation, enrolment for both boys and girls decreased after primary school. This is consistent with the hypothesis that school provision and quality in relaxed regions relative to regions without the relaxation declined during this period. I control for this by comparing the effect of the relaxation on enrolment for boys with the effect of the relaxation on enrolment for girls. I estimate an equation similar to equation (3), with school enrolment as the dependent variable. The reference group comprises individuals born during 1962–72. The coefficients are shown in Table 3, column (6), in Qian (2017). The estimates show that for older cohorts not affected by the relaxation, individuals born in (p.313) relaxed areas had on average 1–17 per cent less school enrolment than areas without the relaxation. However, for cohorts affected by the relaxation, individuals born in relaxed areas were on average enrolled in school 5 per cent more than individuals born in areas without the relaxation. The estimates are statistically significant at the 1 per cent level. Figure 14.4b plots the triple difference reduced form estimates. It shows that school enrolment in relaxed areas was higher for girls of the affected cohort than for boys. Note that the year-by-year first stage and reduced form estimates use the full sample. Estimates for a sample restricted to households with three or fewer children are presented in Table B2 in Qian (2017) (see Appendix 2).
5.4. The Effect of Family Size on Enrolment
Table 2 panel C in Qian (2017) shows the 2SLS estimates for households with three or fewer children. It shows that for a sample where 49 per cent of (p.314) (p.315) individuals were enrolled in school, an additional sibling increased enrolment of first children by approximately 14–16 percentage points. The estimates are statistically significant at the 1 per cent level. Panel D restricts the sample to households with two or fewer children. The estimates show that for a sample where 54 per cent of individuals were enrolled in school, an additional sibling increased enrolment of first children by approximately 12 percentage points. The estimates are mostly statistically significant at the 10 per cent level.
The main results show that eldest children with younger siblings are more likely to be enrolled in school than those without younger siblings. I consider and provide evidence against the concern that the instrument affects the school enrolment of the first child through channels other than family size (i.e. the exclusion restriction is violated). They are not presented here because of space constraints. Please see in Qian (2017).
A second child can increase school enrolment of first children for several reasons. I consider some of the most obvious hypotheses. First, there could be economies of scale in schooling costs. These could include costs related to textbooks, school fees, clothes, or food for school. Unfortunately, the data do not allow me to examine these costs directly. Second, I explore the hypothesis that a second child increases school enrolment of the first through permanent income channels. I provide suggestive evidence against these alternatives. Because of space constraints, please see Qian (2017).
Finally, I explore the possibility that having a second child increases the enrolment of first children by increasing the demand on cash income. I find evidence consistent with the hypothesis that parents view schools as an alternative source of childcare for the first child and send her to school while the mother enters the labour force. Please see Qian (2017).
This chapter estimates the effect of family size on school enrolment of first-born children. It resolves the problem of joint determination by exploiting the plausibly exogenous variation in family size caused by relaxations in the OCP. The results show that both the OCP and the previous four-year birth spacing policy were well enforced, and that the 1-son-2-child relaxation increased family size for girls born in relaxed areas. Then, it uses the variation (p.316) in family size caused by this relaxation to show evidence that a second child increased school enrolment of the first child. The empirical results provide empirical evidence for a novel insight about first-born children, who have thus far been the focus of most existing empirical studies of quantity/quality. They show clearly that first-born children benefit from having a younger sibling.
It is beyond the scope of this chapter to provide conclusive evidence on the mechanisms driving the main effects. The empirical findings suggest that economies of scale in schooling and increased income demand from an additional child could play important roles. Interpreting these results outside of the context of rural China requires caution. This is especially true if parents in these other contexts do not have access to inexpensive public schooling or good labour market opportunities.
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(1) In the labour and household economics literature that we discuss later, quality typically refers to education or health, among other attributes.
(2) The textbook quantity–quality tradeoff argues that as women’s wages rise, the cost of having children increases, and hence, parents will have fewer children. These models assume that parents equalize investment across children. Thus, reducing the number of children will naturally increase the average quality of children. The classic quality–quality model does not allow for differences across children.
(3) Iacovou (2001), a child psychologist, argues that the disadvantage could be because children benefit from social interactions with other children. Using detailed data on time-use of children in the UK, she finds that the one-child disadvantage decreases with the amount of time a child spends playing with other children after school. In the learning-by-doing discussed by Zajonc and Markus (1975), older children are predicted to benefit more from having additional siblings than the youngest child because it is assumed that children teach younger children and benefit especially from teaching.
(4) The sibling sex composition methodology argues that parents prefer children of mixed sex. Therefore, they are more likely to have a third child if the first two are of the same sex. The twins methodology argues that the occurrence of twins (before the introduction of fertility treatments) is uncorrelated to individual characteristics. Hence, twinning is a plausibly exogenous source of variation for family size. Both methodologies examine the effect of an additional sibling for families with at least two children. Angrist et al. (2006) used both techniques and found that the results are similar.
(5) On the one hand, studies have found family size to have no effect or even a positive effect on child outcomes in Israel (Angrist et al. 2006), Korea (Lee 2004), the United States (Kessler 1991), China (Guo and VanWey 1999), and Africa (Gomes 1984). On the other hand, the effect of family size on education has been found to be negative in India (Rosenzweig and Wolpin 1980), France (Goux and Maurin 2003), the United States (Berhman et. al. 1989; Conley 2004; Stafford 1987), and China (Rosenzweig and Zhang 2009). The studies described here all focus on cross-sectional evidence. Alternatively, Bleakely and Lange (2005) examine time-series evidence in the American South. They find that increased schooling causes a decrease in fertility. See Schultz (2005) for a detailed critique of the empirical literature.
(6) Blau and Currie (2006) provides an overview of this literature.
(7) Past studies generally consider the OCP to have only affected the family size of cohorts born after 1979–80. However, this chapter will show that because of the previous four-year birth spacing rule, the OCP affected cohorts born in 1976 and after.
(8) Practical difficulties included households where a parent or first-born child was handicapped, or if a parent was engaged in a dangerous industry (e.g. mining).
(9) Levels of income between counties with some relaxation and counties with no relaxation are comparable in the CHNS data. This is consistent with the findings of Qian’s (2008) study of rural China, which found that total household income had no effect on sex selection.
(10) Liaoning, Jiangsu, Shandong, and Henan.
(12) For example, Qian (2008) finds that increasing relative adult male wages increases sex selection and that increasing relative adult male wages decreases girls’ schooling relative to that of boys. This would cause a downward bias in the 2SLS estimates.
The CHNS does not have accurate data on individual income within the household since much rural production is conducted at the household level and income cannot be accurately assigned to individual members. Consequently, I cannot directly examine the role of relative earnings in this study.
(13) he double interactions include the interaction term of relaxc and dil; the interaction term of girlitc and dil; the interaction term of relaxc and girli; and girlitc. The reference group comprises cohorts born during 1962–72. The dummy variable for the reference cohort and all its interactions are dropped.