MARCO CONCEPTUAL

The equations estimated for Table 1.2 control for mother's ability and family income, so the impact of maternal schooling can move through both initial endowment channel and efficiency of investment. To isolate the efficiency component, I now try to control for the the other two channels: income and initial endowment. That is, instead of controlling for the mother's corrected ASVAB score, I attempt to control for the child's cognitive ability.

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That is, I use to replace in equation (15), so that it can be written as equation (15)' as follows:

( ) ₍ ( _{) ( )}) ( ) (15)’

From equation (15)', we can see the first term, when is a constant rather than a function of , will be a constant too and thus the marginal efficiency effect will be 0. Table 1.8 presents the results when the child's cognitive ability is included. The subsample will be smaller here, reduced to 2306 observations. In the specification (2) in Table 1.8A, where the linear probability models are estimated, without income and child's cognition controls, the marginal effect of maternal schooling is 2.5 percentage points. When income is controlled for, the maternal schooling impact decreased to 2 points in specification (3). When child's cognitive ability is controlled for in specification (4), however, the maternal schooling effect does not go away, indicating that when the two channels- income and initial endowment- are controlled for, maternal schooling remains significant, indicating the existence of an efficiency channel according to the theory. In specification (5), where both mother's cognitive and child's cognitive abilities are controlled for, however, mother's cognitive ability is not significant and the coefficient of child's cognitive ability is similar to the one in specification (4). Therefore, the mother's initial endowment appears to have a direct impact on the child's initial endowment formation, but does not have a direct effect on child's college attendance. I also conduct a similar regression as in Table 1.2 on this subsample in specification (1), and found that the marginal maternal education has a slightly greater impact than in specification (4). This is reasonable, considering that the maternal schooling effect in specification (1) is transmitted through both channels of investment efficiency and child's

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endowment, while the effect in specification (4) is transmitted only through the channel of investment efficiency. In specifications (6) and (7), I generated interaction terms with income or with child's PIAT scores. It is found that the maternal schooling impact does not differ in different families with different income levels, but there is evidence that the maternal schooling transmitted through efficiency has a lower impact on smarter children. Table 1.8B presents the probit estimation results for this sample and the maternal schooling impact is slightly greater than with the linear estimates. Similar to the linear models, adding additional controls of income and child's PIAT scores does not erase all of the maternal schooling effect on child's college attendance outcome. However, with the probit there is evidence that maternal schooling plays a bigger role in lower income families and for children with lower cognitive ability.17 The positive effect of maternal schooling suggests an efficiency channel when family income and child’s cognitive ability are controlled for. However, the negative interaction between family income and maternal schooling shows that better educated mothers do not have a higher marginal effect of income, which does not support the efficiency channel hypothesis. The idea that mother’s education enhances the efficiency of human capital investment is thus not clearly supported in the data.18

I have also explored the effects of changing the set of instrumental variables to examine the robustness of the endogeneity results. Table 1.9 shows new results for the linear probability model with different instrumental variables. With only mother's family

17 _{The models are also estimated with IV and the results are also similar to the previous} studies: when family income is included, maternal schooling does not appear to be an endogenous variable. Therefore, I only report non-IV estimates.

18 _{One explanation for the contradiction is that some educational transmission channels} are not fully considered and controlled for in the model, for example, mother’s preference to child’s schooling and family culture.

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background used as instruments, the results do not differ much from the estimates in Table 1.3. When family income is controlled for, we again cannot reject the null hypothesis that maternal schooling is exogenous. The joint significance of all instruments in this case, however, is larger than in Table 1.4, which is reasonable considering only family background variables show significance in Table 1.3. I next keep the family background but change the location-related instruments to be measured in the county where the mother turns age 17. The results are still similar. Location-related instruments are not significant in the first stage and the maternal schooling effect remains similar as in the other IV estimations. I also want to examine the results if non family background variables are used as the only instrumental variables. The results are presented in the last three columns using the location-related instruments measured in the county where the mother is 14. The coefficient for maternal schooling does not change much, but the standard errors are so large that the significance of the coefficients is removed. The tests of endogeneity are also small and one cannot reject the null hypothesis that mother's education is exogenous in this case. The F-stat also plummets, indicating that the location variables are weak instruments and the estimates are problematic. This is not surprising considering the low significance of these location variables estimates in the first stage in Table 1.3.

In earlier estimations, mother's education is measured in the target year. However, this measure might be different from the education attained when the child is born and the maternal schooling begins to take effect. Therefore, I also changed the mother's schooling-years measure to when the child is born, and the results are reported in Table 1.10. The estimates are slightly greater than the results in Table 1.2, both in the linear

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probability and probit probability models. However, when mother's cognitive ability and family income are controlled for, the estimate of maternal schooling coefficient is very close to the results in Table 1.2. The interaction effect between maternal schooling and family income has a negative coefficient and significant at the 10 percent level in linear probability estimations, and at the 5 percent level in probit estimations.