El IEDMT EN LAS COMUNIDADES AUTONOMAS CARACTERISTICAS

On average, a twin birth increases family size by about 0.65 to 0.85 persons. Table 2.3 documents the first stage of the twins instrument by census year, age group, and parity sample. Each cell corresponds to the coefficient α1 from regression (29). These

coefficients are somewhat larger than Angrist et al. (2010) but are similar to Black et al. (2005, 2010) and Caceres-Delpiano (2006). While not perfectly monotonic, the largest estimates tend to be found among the biggest households. This is reasonable since having a twin birth when the family is already large is more likely to push parents beyond their optimal number of children. The t-statistic in each first stage is always well over 10, alleviating concerns of weak instruments.

Figures 2.2 and 2.3 provide graphical comparisons of the OLS and 2SLS estimates by age group, census year, and parity sample. To facilitate the presentation of my findings, I focus on the 2+ and 3+ samples. These groups are usually relevant to the majority of families having at least two children.16 _{Tables A.19, A.20 and A.21}

in Appendix A.9 provide the estimates for all parities and years for the 7-13, 14-

16_{Among all households with at least two native-born white children, 25.7, 35.9, 37.7, 40.4 and}

46.6 percent have two children in the years 1850, 1910, 1920, 1930 and 1940 respectively. The corresponding percentages of those with three children are: 21.3, 24.5, 24.9, 25.0 and 24.9. The corresponding percentages of those with four children are: 17.2, 16.1, 15.8, 14.9 and 13.2.

15 and 16-17 year olds respectively. The results with the higher order parities are often qualitatively similar. Most of the differences arise in the 4+ rather than the 5+ or 6+ samples.17 In Figures 2.2 and 2.3, the solid circle markers represent the OLS coefficients, controlling for individual and household characteristics as well as a full vector of county dummies. The open circle markers are the corresponding 2SLS estimates. 95 percent confidence intervals are displayed for the latter, based on standard errors clustered at the household level.18 _{Given the very large sample sizes}

of the full counts, the standard errors for the OLS results are close to zero, and the confidence intervals are thus not visible.

I discuss the results for younger and older children separately, beginning with those aged 7-13. In contrast with the usual motivation of papers studying family size effects, a positive correlation between family size and school attendance is typically observed in the OLS results, as shown in Figures 2.2A and 2.3A. The 2SLS point estimates, on the other hand, usually reverse the sign and exhibit a negative relationship instead. Put differently, the OLS results are biased upwards. Instrumenting family size using twin births, I find that having an additional sibling reduces the likelihood of attending school by less than 1 percentage point to slightly over 3 percentage points depending on the census year and parity sample. These effects are largest in 1850 and diminish

17_{The different parity samples need not yield exactly the same estimates since each group comprises}

children from different households. More important is whether family size effects can be found across the various parities. If so, that would suggest a more general and widespread impact of family size on schooling.

18_{Since the complete counts represent the population universe, one might wonder whether standard}

errors are still relevant. I argue that standard errors should still be provided for two reasons. First, there are missing observations for some variables so the final data used will not be perfectly complete. Second, Abadie et al. (2014) posit that there is still uncertainty in the treatment effects estimated from complete populations, as the observational data only reveal the outcomes for a given time and place, but not the counterfactuals under various treatment intensities. They suggest that the appropriate standard errors to use are randomized standard errors, which are generally even smaller than robust standard errors. In this chapter, I use standard errors clustered at the household level as conservative estimates. Other papers utilizing the universe of observations (or close to) also provide standard errors. See Autor et al. (2015); Black et al. (2005); Cai et al. (2016); Chetty et al. (2014); Gillitzer and Wang (2016); and Mogstad and Wiswall (2016).

in magnitude by the 20th century.19 _{A potential explanation for the smaller effects of}

family size in the later decades is the rise of compulsory school attendance and child labor laws, which could have limited the margin for parents to tradeoff family size and human capital investment in children. However, this may not have been the most important factor since the laws themselves had limited impact on school attendance (Clay et al. 2016; Goldin and Katz 2008).20 In all cases, the impact of family size is small relative to the share of 7-13 year olds attending school. 70.8 and 71.9 percent of 7-13 year olds attended school in 1850 for the 2+ and 3+ samples respectively. The corresponding rates were even higher in 1940 at 94.1 and 94.3 percent. Interestingly, the decline in the 2SLS family size effects coincides with a decrease in the magnitude of the OLS coefficients. This indicates a reduction in upward bias, which is reasonable since the higher rates of school attendance by the 20th century imply that there is much less variation in schooling to be explained in the first place.

Among the older 14-15 and 16-17 year olds, causal family size effects are ob- served from 1920 onwards but are unlikely to have been present during the preceding decades. Consider first the period from 1920 to 1940 – OLS estimates are negative and these negative effects typically survive instrumenting with twins, as illustrated in Figures 2.2B, 2.2C, 2.3B and 2.3C. The 2SLS results suggest that having an addi- tional sibling reduces the likelihood of attending school by around 1 to 2 percentage points, with slightly more negative coefficients for the 16-17 year olds. These 2SLS estimates are usually greater in magnitude compared to those for the 7-13 year olds in the corresponding periods. Tables A.20 and A.21 of Appendix A.9 show that while the coefficients display some variation in magnitude and statistical significance when

19_{Statistical significance during the later decades also varies by parity sample, but for each of the}

five parities, at least two decades in the 1900s have sufficient precision to reject the null of no family size effects at the 5 percent level.

20_{In any case, as alluded to in an earlier footnote, inter-temporal inferences should be treated}

higher order parity samples are used, much of these differences are concentrated in the 4+ sample.

The findings for the 14-15 and 16-17 year olds before 1920 are less clear. Here, the 2SLS coefficients are almost never significant at the 5 percent level. The 1850 estimates also exhibit substantial variation in magnitude and direction across parity samples – such inconsistencies suggest that there was unlikely to have been much negative effect during the 19th century. Interpreting 1910 is more tricky as the point estimates can be similar to the later decades depending on the parity sample, but with less precision. One cannot determine if 1910 is an anomaly since complete counts data for the preceding decades are not available.21 _{1910 aside, the contrasting family}

size effects between the 19th and 20th centuries for older children may have to do with the supply of schools. The analysis thus far has focused on the demand for schooling – whether families want to send their children to school. Absent from this setting are supply-side constraints. Households will not be able to send their children to school if there are insufficient places at schools to begin with. This explanation fits the historical context as 1850 belonged to the era of the common school movement, which focused on basic levels of education. It was not until the first half of the 20th century that schools for older children increased dramatically to characterize the phenomenon that came to be known as the high school movement. Family size effects on older children are thus more likely to be observed in the later periods, when school supply limitations do not restrict schooling decisions that parents make for their children. In addition, the high school movement is typically dated to have only begun in 1910 (Goldin and Katz 2008), which could potentially account for the lack of significant family size effects in 1910 itself.

A valid conceptual concern is whether the twins instrument produces consistent

21_{The 1900 IPUMS complete counts have not yet been released at the time of writing, the 1890}

census was destroyed in a fire, and the 1880 IPUMS full counts data lack the school attendance variable.

estimates of the family size effect. Specifically, mothers of twins may be negatively selected, which could create the illusion of an inverse relationship between family size and schooling. While this is difficult to verify historically, the contemporary literature offers some guidance. Bhalotra and Clarke (2016) use data across 72 countries to show that mothers are positively selected into twinning in terms of health and health-related behaviors. Suppose that a positive correlation between health, wealth and education holds, then any bias in my estimates will be upwards. Put differently, the true family size effect may well be larger in magnitude than the above estimates suggest, but the negative direction per se is likely to be correct.22