where is the child’s educational attainments, is a vector of observed characteristics of the child and his or her family (e.g., age, sex, birth order, and father’s and mother’s education and working status), is a variable of child i’s sibship size, is the family-specific unobserved determinant (e.g., parental preferences or quality of schooling), and
edui Xi
Ni vi
ε
i represents the idiosyncratic shock that is assumed to be independent across other factors.β
The central parameter of interest is , which is viewed as a measure of the trade-off between quantity and quality of children. Early studies primarily found this coefficient to be negative in OLS estimation and therefore inferred that substantial quality improvements can be gained by controlling for family size. However, the regression results are likely to be confounded by the existing observed factors (e.g., parental education) as well as the unobserved determinants (e.g., quality of schooling). The omitted variable formula suggests that the OLS coefficient from the regression is:
cov( , ) cov( , )
Therefore, even if children raised in larger families have less schooling than those in smaller families, the strength of the relationship could be driven by the correlation between sibship size and other observed and unobserved factors, not necessarily the quantity–quality trade-off.
B. Existing Identification Strategy
In light of the potential bias, the existing literature has adopted several methods to uncover the underlying relationship between a child’s education and sibship size. Early studies attempted to account for this potential bias by including more controls, such as parental IQ, and better measures of household income. However, adding more controls cannot rule out the possibility of an association between family size, educational attainment, and something immeasurable, such as housing environment, neighborhood conditions, or quality of schooling. As a result, recent studies have taken different approaches to account for unobserved family heterogeneity. For instance, Guo and VanWey (1999) and Black, Devereux, and Salvanes (2005) include the household’s dummies, i.e., family fixed effects, to control for the unobserved family-level heterogeneity. Angrist, Lavy, and Schlosser (2005), Caceres (2004), and Conley and Glauber (2005) employ exogenous variations in family size, such as multiple births or preferences of a mixed sibling-sex composition, as instruments to investigate the causal effect of family size on a child’s education. Notably, studies using IV estimations or fixed family effects found weaker correlations between family size and a child’s education, many of which turn out to be negligible.
The inconsistency of results between OLS and other estimation methods cast doubts over the link between family size and a child’s outcome. One likely explanation, as pointed out by Phillips (1999), is that sibship size per se does not affect the child’s educational attainments, but the type of resources it dilutes does. Goux and Maurin (2005) extended this line of thought by exploring the impact of a child’s private space, one important kind of resource likely to be affected by additional children, on the child’s schooling. Specifically, they considered the following equation:
i i i i i ,
edu =X
α β
+ N +γ
h + +ν ε
i(3)
where is the average number of rooms per person in the household, used as a proxy for a child’s private space. Notice that equation (3) also includes the sibship size variable to account for the effect caused by family size. Because sibship size and the child’s private space are likely to be endogenous, they employ two instruments, gender of the first two children and of the last two children, respectively, to control for unobserved family heterogeneity. Consistent with previous studies, they found that the coefficient of sibship size becomes insignificant under IV estimation. Interestingly, the coefficient of the average number of rooms per person in IV estimates is significantly negative, suggesting that children in large families perform less well, not because of their family size, but because of the smaller private space available to each child.
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C. Our Identification Strategy
In contrast to Goux and Maurin (2005), our study seeks to identify the effect of a variety of housing variables on a child’s educational outcome, such that:
i i i i i .
edu =X
α β
+ N +Hγ ν
+ +ε
i(4)
The biggest difference between (3) and (4) is that the housing environment is now a vector of multiple variables ( ) instead of a single variable ( ). There are substantial difficulties in using existing identification strategies for this specification. Because these housing variables do not change within a household, including household dummies essentially eliminates the effect of housing environment. Another possible strategy is to find instruments for housing variables, as Goux and Maurin (2005) did for household crowdedness. Nevertheless, controlling for the unobserved heterogeneity in this setting requires us to find many more instruments.
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We take a different approach to identify the causal link. Apart from including a detailed set of important variables of a child’s family background used in previous studies (e.g., a child’s birth order, parental age, work status, and education), we account for unobserved family heterogeneity by adding dummies of the child’s residential neighborhood. Our unique data are derived from the census data
Therefore, we are able to compare a child with his or her peers of the same age in the same very small neighborhood, the lin. Families residing in the same lin tend to share similar housing preferences and parental incomes, as well as earning potentials. Moreover, youths raised in the same lin generally encounter the same neighborhood effect. Furthermore, youths in the same lin typically attend the same elementary or junior high schools, allowing us to control for the quality of compulsory schooling prior to high school or college. In fact, given Taiwan’s current school regulation, it is almost certain that youths in the same lin go to the same school.5,6 Thus, by controlling for neighborhood fixed effects, we account for the neighborhood effect, quality of schooling, and parental incomes and preferences.
Nevertheless, it is still possible that our approach may not fully capture unobserved family heterogeneity. We will discuss this point in the results section.
To be more specific, we estimate the following equation:
i,
i i i i i
edu =X
α β
+ N +γ
H +Area +ε
(5)
where is a dummy equal to one if child i’s highest educational attainment is general high school for teens or general college for young adults, and zero otherwise; is a set of variables on the housing environment, including building age, tenure status, household crowdedness, and residential stability; is a vector of neighborhood dummies to control for unobserved family heterogeneity;
and edui
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Areai
ε
i is an independent error across various individuals. As discussed earlier, we compare youths residing in the same lin. In Taiwan, the lin is the fourth and smallest level of government jurisdiction, following county, town, and village. As such, the estimation includes tens of thousands of area
5 According to Taiwan Compulsory Education Law, students residing in the same “lin” belong to the same public school district and thus are assigned to the same public elementary or junior high school. For instance, the school district for Beitu Elementary School in Taipei includes every Lin of Central and Da-Tong Villages, 1st–9th and 12th Lin of Chang-An, 2nd Lin of Hot-Spring Village, and 1st–10th Lin of Ching-Jiang Village. For details on the regulations, see http://www.tp.edu.tw/neighbor/elementary/e_beitu.jsp.
6 One exception is that children hoping to enroll in better elementary or junior high schools may move their registries to relatives or friends residing in better school districts, but continue to live with their parents. In this case, those children are coded as “other relatives” in the households of friends or relatives in the census. Because our data remove children that coreside with other relatives, we expect this proportion to be small in our sample.
dummies. Because of computational complexity, we focus on the linear probability model instead of nonlinear models. Alternative models (e.g., probit and logit), however, yield similar results.