Estimates of the Effect of Same Sex Sibling Composition on Sibship Size Instrumental Variables Estimates of Private School Attendance

IV. Results

A. Estimates of the Effect of Same Sex Sibling Composition on Sibship Size

Table 2 presents the first stage estimates of the effect of same sex eldest siblings on the likelihood that the family has three or more children. Estimates are presented sep- arately by race and by parity. As with all of our analyses, we limit the sample to the eldest two boys who are aged 5 to 17 inclusively and we control for nonnative-born, parental educational attainment, parental age, the age of the child, the race of the child in the overall model, and the age difference between the children. Using a narrower age restriction, such as those aged six to 16, does not alter our point estimates. The first stage estimates for all racial groups are positive and statistically signifi- cant. For the sample of White first-born boys, same sex sibling composition increases the likelihood of a third child by 7.1 percentage points. For the sample of Black, Hispanic, and Asian first-born boys, same sex sibling composition increases the like- lihood of a third child by 4.1, 6.0, and 5.0 percentage points, respectively. 4 For the sample of second-born boys, our first stage estimates are roughly similar. The F -statistics from this first stage are all above ten. Our estimate for the entire sample combined is on par with Angrist and Evans’ 1998 finding of a 6.9 percentage point increase in the likelihood that women of all racial groups have a third child if their first two children are of the same sex. 5 The racial differences in probabilities of hav- ing a third child given having two same sex eldest children might be due to cultural differences in the desire for a sex-mix, or due to our imposed sample constraints. The samples for Whites and Asians are more representative of the national population, whereas the samples for Blacks and Hispanics are truncated at the higher end.

B. Instrumental Variables Estimates of Private School Attendance

Tables 3 and 4 present a comparison of IV and OLS results for the probability of pri- vate school attendance for first-born and second-born boys. Ten columns are pre- sented, two for each racial group where the first column within each racial group presents OLS estimates and the second column presents IV estimates. The key inde- pendent measure in the OLS models is an indicator variable of whether a family has three or more children; the key independent measure in the IV models is a variable indicating the first stage predicted probability of having three or more children. Control variables are not shown, but their effects are relatively consistent with other research findings. For example, parents with more education are more likely to send their children to private school. Table 3 presents estimates for first-born boys for all races and then separately by race. The OLS estimate indicates a positive association between increased sibship size The Journal of Human Resources 728 4. When we run the first stage separately by race and by gender mix of the first two children, we find that while Whites have equal propensities to go on to have additional children irrespective of whether the first two are boys or girls, nonwhites are more likely to go on to have three or more children when the first two are girls; this is particularly true for the Asian group. 5. For ease of discussion, we use the term “Asian” throughout the text and tables, although this is based on the “Other” race category from the 1990 U.S. Census. Conle y and Glauber 729 Table 2 Linear Probability OLS Estimates of the Effect of Same Sex First-born Children on the Probability of Three or More Children in the Household, by Race and Birth Order standard errors First-born Boys Predictor All Races White Black Hispanic Asian Same sex first-born children 0.067 0.071 0.041 0.060 0.050 0.001 0.002 0.008 0.006 0.007 Constant 1.321 1.263 1.583 1.569 1.747 0.010 0.011 0.040 0.029 0.032 R 2 0.120 0.104 0.151 0.189 0.203 Number of cases 219,481 176,190 12,232 22,872 17,990 Second-born Boys Predictor All Races White Black Hispanic Asian Same sex first-born children 0.074 0.080 0.052 0.049 0.039 0.002 0.002 0.009 0.007 0.007 Constant 1.443 1.374 1.813 1.768 1.950 0.012 0.014 0.047 0.034 0.036 R 2 0.092 0.074 0.119 0.128 0.163 Number of cases 179,226 144,286 10,074 17,979 14,580 Notes: ρ 0 .01; estimates are for boys aged 5 to 17 who reside in nuclear families as described in text; models include control variables for nativity status, age dif- ference between children, parental age, parental education, child’s race in overall model, and 12 indicator variables for child’s age; Asian includes all individuals in the 1990 Census 5 percent PUMS “Other” category; Huber-White standard errors robust to clustering within families are presented. The Journal of Human Resources 730 Table 3 First Born Boys: Linear Probability OLS and IV Estimates of Three or More Children on the Probability of Private School Attendance standard errors All Races White Black Hispanic Asian Predictor OLS IV OLS IV OLS IV OLS IV OLS IV Three or more 0.026 −0.027 0.034 −0.032 −0.014 −0.037 −0.010 0.011 −0.006 0.039 children 0.002 0.020 0.002 0.022 0.005 0.115 0.004 0.066 0.005 0.088 Constant −0.374 −0.301 −0.374 −0.286 −0.330 −0.293 −0.414 −0.449 −0.304 −0.385 0.007 0.029 0.009 0.030 0.024 0.188 0.020 0.111 0.022 0.162 Number of 219,481 219,481 176,190 176,190 12,232 12,232 22,872 22,872 17,990 17,990 cases Notes: ρ 0 .01; ρ 0.05; estimates are for boys aged 5 to 17 who reside in nuclear families as described in text; models include control variables for nativity sta- tus, age difference between children, parental age, parental education, child’s race in overall models, and 12 indicator variables for child’s age; Asian includes all indi- viduals in the 1990 Census 5 percent PUMS “Other” category; Huber-White standard errors robust to clustering within families are presented. Conle y and Glauber 731 Table 4 Second-Born Boys: Linear Probability OLS and IV Estimates of Three or More Children on the Probability of Private School Attendance standard errors All Races White Black Hispanic Asian Predictor OLS IV OLS IV OLS IV OLS IV OLS IV Three or more 0.027 −0.061 0.036 −0.046 −0.030 −0.121 −0.014 −0.160 −0.006 −0.145 children 0.002 0.021 0.002 0.022 0.005 0.103 0.005 0.090 0.005 0.135 Constant −0.365 −0.232 −0.370 −0.251 −0.274 −0.108 −0.376 −0.110 −0.281 −0.007 0.009 0.032 0.010 0.033 0.028 0.192 0.024 0.165 0.026 0.267 Number of 179,226 179,226 144,286 144,286 10,074 10,074 17,976 17,976 14,580 14,580 cases Notes: ρ 0 .01; ρ 0.05; ρ 0.10; see notes for Table 3. and White boys’ private school attendance but a negative association between increased sibship size and Black, Hispanic, and Asian boys’ private school attendance with the OLS estimate for Asian boys not statistically significant. This unexpected OLS estimate for White boys also appears in Ca´ceres-Delpiano’s 2006 study, as he finds that for all children, family size is positively associated with the probability of private school attendance. This is most likely due to the tendency among larger fami- lies to be more religious and to send their children to religious private schools. However, when we instrument for having three or more children using the sibling sex mix approach, we find no causal effect of increased sibship size on first-born boys’ pri- vate school attendance. These findings are contrasted to those reported in the next table, Table 4, which indicates that for second-born boys increased sibship size induced by same sex sibling composition causes a 6.1 percentage point decrease in the proba- bility of private school attendance for all racial groups. The parameter estimates of the “true” effect of sibship size on second-born boys’ private school attendance are only significant for Whites and Hispanics. Increases in sibship size induced by sibling sex composition reduce White and Hispanic second- born boys’ probabilities of private school attendance, by 4.6 and by 16.0 percentage points, respectively. The point estimates for Black and Asian second-born males are the same sign and of similar magnitudes as for Hispancis, but they are not statistically significant, most likely due to sample sizes that are too small for an IV approach. 6

C. Instrumental Variables Estimates of Grade Repetition