Data and Statistical Approach

III. Data and Statistical Approach

In this analysis, we use the 1990 Census 5 percent PUMS. The unit of analysis is the first-born or second-born boy older than four and younger than 18. Our sibship size instrument—the sibling sex composition of the first two children—requires that we locate households where all currently residing children are the biological chil- dren of the householder and where the householder does not have other children living elsewhere. To make this assumption more reasonable, we limit the sample according to six household composition constraints: 1 parents in the household are married; 2 there are at least two children residing; 3 there are no children residing who are not the biological child of the head of household; 4 there are the same number of children currently residing as the primary female adult has ever given birth to; 5 there are no subfamilies residing in the unit; and, 6 there are no twins in the household. These deci- sions limit the generalizability of our findings, but they are necessary to produce a clean instrument. We would ideally like to have retrospective educational attainment data, but the Census provides us only with educational measures for children currently coresiding in the household. Given this limitation, we examine two measures: boys’ probability of attending a religious or secular private school and boys’ probability of having been held back a grade in school. While it certainly may be the case that a particular pri- vate school represents a worse educational alternative than a particular public school, privately schooled children typically receive more resources than publicly schooled children. For example, in 1990, the average pupil-to-teacher ratio in U.S. elementary and secondary public schools was 17.2 and it was 14.7 in private schools National Center for Educational Statistics 2001. Smaller class sizes also have been linked to enhanced test performances and increased probability of taking college-entrance exams, especially among minority students Krueger and Whitmore 2001. 2 These racial differences in class size effects may translate into race heterogeneous treatment effects of sibship size on parental investment in private schooling. Our second outcome measure is a very conservative estimate of the probability that a child is held back a grade in school. We ascertain grade retention by comparing a child’s age to the highest grade that he or she has completed. Because birthday cut- offs may result in children starting late, we use a two-year conservative estimate. For example, a seven year-old must not have completed kindergarten in order to be clas- sified as being held back. One complication to this measure stems from the Census collapsing Grades 7–10 into one category which results in an underestimation of the proportion that we deem age inappropriate for their level of schooling. It therefore comes as no surprise to find that the mean percent of eldest two children that we clas- sify as being held back from 0.3 percent to 0.5 percent depending on racial-ethnic group is much smaller than the 11.1 percent of U.S. adults held back in 1992 reported by the National Center for Educational Statistics 1997, and the 15 percent of chil- dren held back that Oreopoulos, Page, and Stevens 2004 estimate using the 1980 Census. Conley and Glauber 725 2. There is some debate on this see Hanushek 1999. A recent study by Currie and Yelowitz 2000 examining the effect of public hous- ing on children’s likelihood of being held back a grade among other outcomes using the 1990 Census reports a larger percentage of children held back than we do. We attribute differences between our sample means and Currie and Yelowitz’s sample means to their reliance on two datasets, the March Current Population Survey CPS and the Census, and a two-sample IV approach. They do not report using as strict a set of Census data sample constraints that we use to produce a valid instrument dis- cussed above and without these constraints, they report higher percentages of chil- dren that are held back a grade in school. We also include in our analyses control variables for parental average years of schooling, parental average age, nativity status, and the age and sex of children. Age is measured through 13 dummy variables for each age from five to 17. Descriptive sta- tistics for all variables used in the analysis are presented in Table 1 and most variables display mean values similar to other nationally representative reports. Our parameter estimates apply to families who go on to have an additional child because the eldest two children are of the same sex. This is the strict local average The Journal of Human Resources 726 Table 1 Sample Means for Boys, by Race standard deviations All Races White Black Hispanic Asian n = n = n = n = n = 445,610 354,399 25,508 48,553 38,471 Private school attendance 0.130 0.139 0.075 0.098 0.096 0.337 0.346 0.263 0.297 0.294 Held back in school 0.004 0.003 0.005 0.005 0.005 0.061 0.058 0.072 0.070 0.067 Three or more children 0.485 0.461 0.554 0.622 0.586 0.500 0.498 0.497 0.485 0.493 Same sex first-born children 0.520 0.522 0.511 0.518 0.517 0.500 0.500 0.500 0.500 0.500 Parental education 11.163 11.498 10.500 8.927 9.601 2.805 2.504 2.418 3.575 3.907 Non-native born 0.122 0.039 0.096 0.529 0.677 0.327 0.194 0.294 0.499 0.468 Parental age 36.631 36.718 35.707 35.730 36.780 5.129 5.001 5.438 5.460 5.701 Age of child 9.796 9.788 9.896 9.730 9.858 3.300 3.298 3.304 3.302 3.317 Age difference of children 3.089 3.064 3.520 3.050 3.030 1.808 1.744 2.250 1.945 1.921 Notes: Estimates are for boys aged 5 to 17 who reside in nuclear families as described in text; Asian includes all individuals in the 1990 Census 5 percent PUMS “Other” category. treatment effect LATE and it does not tell us anything about families that have one or two children or have three children where the eldest two are of mixed sex. Our approach also does not tell us anything about the effect of having ten children as opposed to nine. Even to interpret this estimate as unbiased locally, we must make a couple of assumptions. First, we must assume that assignment to the treatment group same sex or the control group mixed sex is really random. This is a reasonable assumption given that there are no systematic differences in the likelihood of having two boys, two girls, or a mixed-sex pair across the population Bennett 1980. Further, we must also assume monotonicity—that for no subgroup does having same sex children make them less likely—on average—to have additional children. 3 We also must assume that sibling sex mix affects our educational measures only through an increase in sibship size. If, for example, there were significant returns to scale for same sex children, then IV estimates might be biased Rosenzweig and Wolpin 2000. The evidence on sex composition’s direct effects is mixed see, for example, Powell and Steelman 1990; Butcher and Case 1994; Kaestner 1997; Hauser and Kuo 1998; Conley 2000; Dahl and Moretti 2004. We limit our presentation of analyses to boys only as some recent research indicates that sex composition may directly affect girls but not boys Butcher and Case 1994. And more importantly, we find that sibship size has stronger and more consistent effects on boys than on girls. Our analysis proceeds as follows. We report first stage results in Table 2, and we use these predicted values—from ordinary least squares OLS regressions including all other variables—in the second stage. Linear probability models are reported in both stages, since Heckman and Macurdy 1985 argue that this is the ideal specifi- cation when faced with a set of simultaneous equations where the instrument, the variable being instrumented, and the dependent measures are dichotomous. The first stage equation predicting the likelihood of three or more children is as follows: 1 MORETWO = β + β 1 SAMESEX + β 2 X + ν where MORETWO is a dummy variable equal to one if a family has three or more children residing at home subject to the sample constraints discussed above, SAME- SEX is a dummy variable equal to one if the eldest two children are of the same sex, and X is a vector of control variables. The second stage uses the predicated probabilities from the first stage to estimate the likelihood of private school attendance and the likelihood of being held back a grade in school. The second stage equation is as follows: 2 OUTCOME = γ + γ 1 MORETWO + γ 2 X + ε where OUTCOME is a dummy variable equal to one if a child has been held back a grade in school or attends a private school and MORETWO is the first stage predicted probability. Standard errors in the second stage are adjusted to account for our use of a predicted probability. Conley and Glauber 727 3. We also restricted the analyses to a sample of children from families with only two or three siblings due to possible concerns about the dilution of the LATE by families who continue to have children beyond the experimentally induced third. Results are largely unchanged and are available from the authors upon request.

IV. Results