3.1 OLS results

Some observations consist of siblings from the same household; therefore, we correct the standard errors with the assumption that observations are clustered at the household level in all the estimations below. The effects of sibling number on individual migration decisions are reported in Table 2. Columns 1 and 2 present the effects of being the only child (singleton) on migration decisions; singletons are significantly less willing to migrate out of their city and province. In columns 3 and 4, we report the effects of number of siblings on migration decisions. For individuals with one or more sibling, the probability of migrating out of the home city and province increases by about 2%, relative to those without siblings. In a traditional East Asian society with a strong son-preference, the effects of having sisters could differ from those of having brothers. Therefore, we estimate the effects of number of brothers and number of sisters separately. The results in columns 5 and 6 suggest that the number of brothers has a stronger effect on migration decisions than the number of sisters. Coefficients of the control variables in Table 2 show that migration decisions are more strongly correlated with individual characteristics than those of parents. In general, well-educated children with greater earning potential are more likely to migrate out of their homes. Female children have greater likelihood to migrate than their male counterpart, this perhaps because that, in Chinese culture, boys are more responsible for supporting their parents, whereas girls normally leave their parents' family and join their husbands' one after the marriage.

Table 2. The effects of singleton, number of siblings, number of sisters, and number of brothers on migration decisions

Note: The reported standard errors are clustered at the household level, we also cluster standard errors at the community level, and the significance of variables remain. ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively.

In the above analysis, we assume a linear relationship between sibling number and migration decision and estimate the average effects. To allow maximum flexibility in this relationship, we transform the variables related to sibship size into a set of dummy variables and re-estimate equation (1). From Table 3, we observe a trend of increasing marginal effects of sibship size on migration. For example (see column 1), compared with singletons, the probability of an individual with one sibling migrating out of his/her city increases by about 15%; the probability increases by 3.6% to 18.6% when an individual has two siblings, but marginal effects are negligible after two siblings. A similar pattern is observed if we separate sibship size into number of sisters and number of brothers.

Table 3. The effects of number of siblings, number of sisters and number of brothers on children's migration decisions

Note: The reported standard errors are clustered at the household level, we also cluster standard errors at the community level, and the significance of variables remain. ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively. Other control variables include: Age, Age2, gender, children's education levels, children's birth Hukou status. The parent's information includes their age, marriage status, income, and education levels. Children's birth provinces are also controlled.

To see whether there are heterogeneous effects of sibship size on migration decisions, we conduct subgroup analyses and report the results in Table 4. First, we make between-gender comparisons of the effects of sibship size on migration decisions. Columns 1 and 2 show that for singletons, being female has a much stronger negative impact on migration than being male. Nonetheless, having siblings could significantly stimulate female's probability of inter-city and inter-provincial migration, particular for female who have brothers. We also conduct the analyses by children's birth Hukou status and their education level. Columns 3–6 show that the effects of sibling number on migration decisions are slightly stronger for children birth with an urban Hukou and high-education levels. Over all, we observe a positive effect of sibling number on migration.

Table 4. Effects of singleton, number of siblings, number of sisters, and number of brothers on migration decisions, by subgroup

Note: The reported standard errors are clustered at the household level, we also cluster standard errors at the community level, and the significance of variables remain. ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively. Other control variables include: Age, Age2, gender, children's education levels, children's birth Hukou status. The parent's information includes their age, marriage status, income, and education levels. Children's birth provinces are also controlled.

3.2 Endogeneity of sibship size, and a propensity score matching method with tests of hidden bias

In the literature on effects of sibship size on children's accumulation of human capital, a foremost concern is the potential endogeneity issue of sibling number. Both quantity and quality of children could be chosen by parents. If this is true, an observed quantity–quality trade-off could be spurious due to unobserved household characteristics and parental preferences. Whether an explanatory variable suffers from endogeneity is crucially related to the nature of the dependent variable. The two most important causes of endogeneity are reverse causality and omitted variables. The dependent variable in our analysis is individual migration decision, which occurs many years later than parental decisions about fertility. While there is a potential effect of sibling number on migration decisions, there might not be an effect from the other direction. Regarding the omitted variable issue, one concern is that that some parental characteristics could be correlated with both fertility decisions and children's migration decisions. To formally address this concern, we first employ a propensity score matching method with tests of hidden bias and then use an IV approach as a robustness check.

We follow Rosenbaum and Rubin (Reference Rosenbaum and Rubin1985) to perform a matching approach to evaluate the causal effects of sibling number on children's migration decisions. In practical terms, estimating the effects of sibling number (with singletons as the reference group) is equivalent to measuring the effects of singletons (with children with siblings as the reference group). Since about 5.7% of children in our sample are singletons, and matching a small sample from a large population facilitates a better matching balance, we consider singletons as the treatment group whereas children with siblings are in the control group. The identified average treatment effect on the treated (ATT) implies how less likely a singleton tends to migrate compared with a child with siblings?

Children are distinguished by whether they are the only child (P = 1/0), where 1 indicates that the child is a singleton and 0 indicates the child with siblings; Y ¹ denotes the migration outcome conditional on a singleton (P = 1), and Y ⁰ denotes the migration outcome conditional on a child with siblings (P = 0). The ATT is defined as:

(2)$${\rm ATT} = E\lsqb {Y^1{\rm \vert} P = 1} \rsqb - E\lsqb {Y^0{\rm \vert} P = 1} \rsqb $$

Empirical data for E[Y ¹|P = 1] are available for singletons, but the migration outcomes of their counterfactual state (if they have siblings), E[Y ⁰|P = 1], are unavailable. We assume that given a set of observable covariates of children (X) and their parents (Z), potential outcomes are independent of whether the child is a singleton, and the mean of potential migration outcomes is the same for singletons and children with siblings after adjustments for observable differences [Lechner (Reference Lechner2002); Imbens (Reference Imbens2004)]. Thus, we use matched children with siblings to measure how the singletons would have made migration decisions had they had siblings. Conditional on the matching estimators of observable covariates from both children (X) and their parents (Z) in equation (1), the ATT is calculated by comparing the mean probability of migration between treated singletons and controlled children with siblings:

(3)$${\rm ATT} = \displaystyle{1 \over N}\mathop \sum \limits_i \left[ {\lsqb {Y_i^1 {\rm \vert} P = 1,X} \rsqb - \mathop \sum \limits_j \omega \lpar {i,j} \rpar \; \lsqb {Y_j^0 {\rm \vert} P = 0,X} \rsqb } \right]$$

where N is the number of matches; $Y_i^1$ and $Y_j^0$ are outcome variables measuring the migration outcomes of singletons and children with siblings, respectively; and ω(i, j) is the weight of a child with siblings (j) matched to a singleton child (i). Matching covariates are control variables of both children (X) and their parents (Z) in our linear probability model. We separately match singletons with children with a given number of siblings to reflect the relative effects of different sibling numbers. Mating variables are control variables from both children (X) and their parents (Z) in our linear probability model. The ATT outcome variables are presented in Table 5.Footnote ⁴

Table 5. ATT of outcome variables and sensitivity analysis

Note: ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively.

The matching approach is based on the assumption of conditional independence or unconfoundedness. Nonetheless, if there are unobserved variables that simultaneously affect assignment into treatment and the outcome variable, a hidden bias might arise to which matching estimators are not robust. Following Rosenbaum (Reference Rosenbaum2002), we apply a bounding approach to determine how strongly an unmeasured variable may influence the selection process. Sensitivity analysis of hidden bias is also presented in Table 5. For example, when the critical value of hidden bias (Γ) equals 1.75–1.80, if children with the same covariates differ in their odds of being a singleton vs. a non-singleton by a factor of 75%–80%, the significance of singleton effects on outcome variables may be questionable.

The ATT estimates from each matching group in Table 5 uniformly indicate that singletons are less likely to migrate out of the city or province compared with their counterfactual state (having siblings), reflecting the positive effects of sibship size on migration decisions. In addition, as sibling number increases, the magnitude of the estimated ATT increases. These results are consistent with the linear probability model (section 3.1) that having more siblings increases the probability of migration.

3.3 IV approach as a robustness check

The results in Table 5 indicate that omitted variables do not pose a serious threat to our analysis. As a further check on the assumption of unconfoundedness, we use variability in the strictness of the one-child policy across locations and over time to construct an IV and re-estimate the main equations. This is a commonly used approach in recent literature [e.g., Ebenstein (Reference Ebenstein2010); Li and Wu (Reference Li and Wu2017); Wei et al. (Reference Wei, Zhang and Liu2017); Zhong (Reference Zhong2017)]. China's one-child policy was implemented from 1979 until 2015. This policy significantly reduced the average number of children per family. As a result, the fertility rate dropped from about six in the 1960s to less than two in the 1990s. Meanwhile, the strictness with which the one-child policy was implemented varied across provinces and over time and had a significant influence on individual fertility decisions. Penalties for above-quota births usually included a large fine, denial of household registration, and demotion or dismissal from work for parents employed in the state sector. Fines were heavy and varied dramatically across provinces and over time. For example, for an above-quota birth, Liaoning province fined parents 10% of their income for 14 years, while Guangxi province collected a one-time penalty equivalent to about 5 years of household annual income [Li and Wu (Reference Li and Wu2017)].

Using data from Ebenstein (Reference Ebenstein2010), we construct an IV “Fine,” which equals the ratio of the fine to family annual income for above-quota births from 1979 to 2000.Footnote ⁵ This variable varies over time and across provinces. For people born before 1979, the variable equals zero. We then match this variable with the CHARLS data according to birth year and province of each child. On the one hand, “Fine” is considered as the financial cost of a child imposed by the government; the demand for children should decrease as the fine increases. On the other hand, “Fine” reflects the rigidity of each province in implementing the one-child policy, which largely depended on incentives of government officials in charge of the local Population and Family Planning Commission in the 1980s and 1990s and is not directly correlated with an individual's current migration decision.

The results of the IV estimation are reported in Table 6. In the first column, the coefficient of “Fine” in the first-stage regression is statistically significant and shows a negative impact on sibling number. The first stage F-statistic is 174.52, which is above the conventional criteria of 10, indicating that “Fine” is a strong instrument for number of siblings. The Anderson–Rubin weak identification test is equal to 4.19, with a p-value of 0.04, suggesting that the endogenous regressor is not under-identified and the instrument variable is valid.

Table 6. Two-stage least squares IV estimation

Note: “Fine” is used as the instrument for the number of siblings. The Anderson–Rubin weak identification test is equal to 4.19, with a p-value of 0.04, suggesting that the endogenous regressor is not under-identified and the instrument variable is valid. The reported standard errors are clustered at the household level, we also cluster standard errors at the community level, and the significance of variables remain. ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively.

Since we have only one IV, we only estimate the effects of sibling number on migration decisions. Columns 2–3 show qualitatively similar conclusions that having more siblings significantly increases an individual's probability of migration.

3.4 Additional robustness checks

As shown in the top panel of Table 7, introduction of the one-child policy at the end of the 1970s produced a radical change in family structure in China. One concern is that the effect of being a singleton differs for cohorts before and after introduction of the one-child policy. Therefore, we estimate equation (1) separately for individuals born before and after 1978. Results in the bottom panel of Table 7 support our conclusion, i.e., being a singleton affects migration decisions of both the younger and older generations. However, the negative effects of being a singleton on migration are stronger for those born before 1978, possibly because parents are older and more likely to need family support.

Table 7. Sub-sample analysis, born before and after 1978

Note: The reported standard errors are clustered at the household level, we also cluster standard errors at the community level, and the significance of variables remain. ***, **, *: Statistically significant at the 1%, 5%, and 10% level, respectively. In view of space, results for the other control variables are not reported.

Another concern might be an omitted variable bias caused by the omission of birth order. This is, if parents have some preference for children based on their birth parity, the effect of sibship size may mask this preference (due to the co-movement of birth order and sibship size). In other words, if for some reasons Chinese parents prefer to have their first child close to them, and dispatch higher parity children as migrants instead, a spurious positive correlation may emerge between sibship size and emigration, since higher parities are only found in larger families. As a sensitivity test, in our regression we add a dummy variable that equals to one if the observation is the first child in his or her family, and report the results in Table 8. Although the magnitude of the coefficients of our variables of interest are smaller, we still could reach similar conclusions.

Table 8. When birth order is introduced for children with siblings

Note: The reported standard errors are clustered at the household level, we also cluster standard errors at the community level, and the significance of variables remain. ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively. In view of space, results for the other control variables are not reported.

Furthermore, the effects of sibship size on migration decisions might be different across age groups. Children may migrate out more easily when their parents are relatively young, and have to stay home to provide support to their parents when they get older. To test this hypothesis, we run the regressions separately for the following four age groups: between 20 and 25, between 25 and 30, between 30 and 35, between 35 and 40. Results in Table 9 provide supporting evidence for this hypothesis.

Table 9. The effects of singleton and number of siblings on migration decisions among different age groups

Note: The reported standard errors are clustered at the household level, we also cluster standard errors at the community level, and the significance of variables remain. ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively. In view of space, results for the other control variables are not reported.

Finally, the estimated effects might be different between rural and urban areas. Therefore, we conduct sub-group analysis according to parents' Hukou status. In China, people with rural Hukou normally live in rural areas and participate in certain agricultural related work. Regression results in Table 10 show that for those children who have at least one parent with rural Hukou, and those whose parents both have urban Hukou, the estimated effects do not have systematic difference.

Table 10. The effects of sibship size on migration decisions among when group children by their parents' Hukou status

Note: The reported standard errors are clustered at the household level. ***, **, *: Statistically significant at the 1%, 5%, and 10% levels, respectively. In view of space, results for the other control variables are not reported.