If a child had PIAT scores in both 1986 and 1988, as would occur if the child had reached age five by 1986, the 1986 score, at the younger age, was used.
The PIAT and PPVT scores are age-standardized against a population norm of 100 with standard deviations based on historical population data.(6) Based on the mean scores, there is a tendency for first-born children to outperform their second-born siblings in all three tests.
In the PIAT sample, of the 404 mothers, 40 increased schooling by one year, 15 by two years, and two by three years.
Table 3 reports the effects of the two schooling variables, attainment at birth and enrollment in the first three years of the child's life, on PIAT and PPVT test scores for alternative assumptions about the covariance structure of endowments and inputs, the endowment variances, the ratios of the endowment variances to total test score variances, and the correlations between the idiosyncratic errors for the math and reading test scores.(7) Tables 4 and 5, discussed below, report the other production function parameters and endowment-input correlations, respectively.
We began with the assumption that the math and reading PIAT scores measure different human capital attributes.
Adding these inputs reduces the impact of both schooling attainment at birth and post-birth enrollment on the PIAT and PPVT scores, but the magnitudes of the reductions are small in all cases.
Unlike the GLS results for the PIAT scores with AFQT used as a proxy for the endowment of the mother, controlling "perfectly" for the mother-specific endowment by using only within-mother variation actually increases, by 61 percent, the schooling attainment coefficient relative to that obtained using GLS without the AFQT control in Column 2, while leaving the school enrollment effect at the same level, although with reduced precision.
Chi-square tests of that restriction for both the PIAT system and for the PPVT, reported in Table 3, reject the GLS specification.
Based on the within-mother specification, the common mother-specific endowment accounts for 30 percent of the PIAT math score variance, 32 percent of the PIAT reading score variance, and 35 percent of PPVT variance, based on the respective predicted total test score variances of first-born children.
Among the prenatal behaviors, smoking more than one pack a day reduces the PIAT scores by four points and the PPVT by almost three points, although for the PPVT the standard error is as large as the coefficient.
The effect is also quite small quantitatively, the largest estimates implying a one point increase in the PIAT scores for each one pound increase in birthweight.
Although the PIAT scores decline with maternal work (within-mother) the PPVT score is estimated to increase.