Race and Human Capital: Comment
质疑Smith关于种族教育差距扩大的结论，指出其基于普查数据的方法存在谬误，并利用1890年起的人口普查入学率数据重新估算，发现种族教育差距实际上在缩小。
According to human capital theory, changes in the racial schooling gap are a key factor in the historical evolution of blackwhite male income ratios. In a recent paper in this Review (1984), James Smith points out a basic paradox in the human capital explanation. Race differences in years of schooling have diminished sharply and continuously for male cohorts born in the twentieth century. Black-white male income ratios, however, rose only slightly in the aggregate before 1960. After 1960, the ratios increased appreciably. Smith resolves the paradox by constructing new estimates of the racial schooling gap for cohorts stretching back to the Civil War, based on retrospective educational attainment data from the 1940 and subsequent censuses. Race differences in years of schooling widened among males born from 1886 to 1910. Additionally, the quality of black schooling fell relative to the quality of white schooling. Since these cohorts dominate the census occupation and income statistics until 1960, Smith claims the relative constancy of black-white income ratios until 1960 is consistent with the human capital model. This comment challenges one of Smith's conclusions. The increase in the racial schooling gap is shown to be spurious. Scholars often interpret census attainment data as a measure of years of schooling, but the data refer to highest grade completed. Historically, the average black pupil took longer than a single school year to complete a grade. Retention alone would not bias the census attainment data. Most blacks born in the late nineteenth century, however, were educated in ungraded schools. For them, census attainment data measure years of schooling, not grades. The shift from ungraded to graded schools took place throughout the period of educational retrogression identified by Smith. It is the change from years to grades that causes black schooling levels to appear to lag behind white schooling levels. Consistent data show a continuously decreasing racial schooling gap. Whatever the merit of Smith's explanation, it cannot rest on census attainment data. Beginning in 1890, the U.S. Bureau of the Census reported school attendance rates for narrow age groups (for example, ages 5 to 9).1 I use these data to construct new estimates of average years of schooling in the following manner. Let p(j) = proportion of children of age j at school, a(e) = minimum age at entering school, and a(L) = maximum age at leaving school. I assume that a(e) = 5 and a(L) = 20, since attendance rates before age 5 or after age 20 were negligible for the period. Because data are unavailable for single years of age, I also assume the agespecific attendance rates are equal to the average attendance rate for the relevant age 2 j-a(L) group. The sum Ej=a(e)P(j) estimates average years of schooling.3 Empirically, the number of students who skip a grade is less than the number who fail the grade. Hence average years of schooling should exceed average highest grade completed. Table 1 presents the cohort-specific estimates of years of schooling. According to my calculations, the racial schooling gap fell from 3.8 years among 1886-90 cohorts to 2.5 years among 1906-10 cohorts. According