Age Adjustment of Racial Income Differences: A Research Note

Abstract

The contention that failure to control for age leads to an understatement of black-white income differentials is shown to be inaccurate for those aged 25-64. The importance of the issue of racial inequality in the United States has led social scientists to undertake a number of studies concerning income differences between blacks and whites (Cherlin and Hodge, 1973, in press; Duncan, 1969; Farley and Hermalin, 1972; Freeman, 1973; Hauser and Featherman, 1974; Jencks et al., 1972; Siegal, 1965; Wattenberg and Scammon, 1973). A research note which appeared in this journal (Tucker, 1969) contended that such studies of racial income inequality must control for age distributions of white and nonwhite populations or else such studies will the actual relative disadvantage of the Negro. We will present evidence that age distributions can be safely ignored in at least one common type of comparison: income differences between white and nonwhite males aged 25-64. Tucker (1969) presented a table, reproduced here as Table 1, of incomes and income differences drawn from the 1960 Census of Population (Bureau of the Census, 1963a). This table refers to white and nonwhite median incomes within categories of educational attainment for males aged 25 and over with an income in 1959. The author calculated a standardized nonwhite median income, which adjusts the nonwhite median to what it would be if nonwhites had the same age distribution as whites and if nonwhite median incomes within each age and educational category remained the same. The fourth column of Table 1 shows that the use of these agestandardized median incomes increases the differences between white and nonwhite incomes for those with low educational attainments. The author concluded that comparisons which do not adjust for age distributions understate white-nonwhite income differences. One immediate problem with this study is the author's use of median, rather than mean, income. The standardization procedure was based upon a weighted sum of category medians, the weights being proportional to the percentage of the standardizing population in each category. This procedure would have been well-defined mathematically if category means had been used (they were unavailable), but there is no straightforward mathematical rationale for the procedure if category medians are used. Our calculations, however, indicate that the error involved in using categ*The calculations reported herein were supported by a grant from the Russell Sage Foundation. The support of the Foundation is gratefully acknowedged, as is that of our colleague, Ricardo Klorman. 194 This content downloaded from 157.55.39.208 on Fri, 14 Oct 2016 04:18:07 UTC All use subject to http://about.jstor.org/terms Income Differences I 195 TABLE I. White, Nonwhite and Standardized Nonwhite Median Income by Educational Level for Males with Income in 1959, Age 25 and Over* Standardized Differences Between Median Income of Nonwhite Real Nonwhite and Median Standardized Nonwhite Years of School Completed White Nonwhite Income Median Income No years of school completed $1,437 $1,053 $ 929 $124 Elementary I to4 years 1,816 1,554 1,321 233 5 to 7 years 3,243 2,358 2,080 278 8 years 3,988 2,911 2,667 244 High School I to 3 years 5,010 3,270 3,235 35 4 years 5,532 3,741 3,756 -15 College I to 3 years 6,102 4,039 4,010 49 4 years 7,540 4,447 4,466 -19 5 years or more 8,089 5,464 5,508 -44 *From Tucker (1969), Table 3. Source: Bureau of the Census (1963a). TABLE 2. Nonwhite and Standardized Nonwhite Median Income by Educational Level for Males Age 25 to 64 with Income in 1959. Standardized Differences Between Nonwhite Nonwhite Nonwhite and Median Median Standardized Nonwhite Years of School Completed Income Income Median Income No years of school completed $1,531 $1,510 $ 21 Elementary I to 4 years 1,846 1,823 23 5 to 7 years 2,548 2,533 15 8 years 3,089 3,094 -5 High School I to 3 years 3,336 3,379 -43 4 years 3,811. 3,862 -51 College I to 3 years 4,106 4,153 -47 4 years 4,557 4,582 -25 5 years or more 5,423 5,496 -73 Source: Bureau of the Census (1963a). This content downloaded from 157.55.39.208 on Fri, 14 Oct 2016 04:18:07 UTC All use subject to http://about.jstor.org/terms