The Bell Curve: Intelligence and Class Structure in American Life - Richard J. Herrnstein, Charles Murray (1996)

Appendix 6. Regression Analyses from Chapter 14

This appendix presents the regression analyses underlying the presentation in Chapter 14.

The results in Chapter 14 and in this appendix are based on separate regressions for each of the three ethnic groups in question (black, Latino, and white). This procedure was chosen in preference to a single regression entering ethnicity as a nominal variable so that the relationships would not be constrained to a single slope. The regressions used the entire NLSY sample, with exclusions as noted for specific analyses, applying 1990 sample weights.

LOGISTIC REGRESSIONS

All the indicators in Chapter 14 except for those involving income are binary variables, and the mode of analysis is logistic regression. The interpretation of logistic regressions is discussed in Appendix 4.

The data tables use short labels for the indicators. The full description of each indicator and associated characteristics of the analysis are shown in Table 1.

Table 2 first summarizes the results, by ethnic group, for four sets of regressions: when age (zAge) is the only independent variable, when age and IQ (zAFQT) are independent variables, when age and parental SES (zSES) are independent variables, and when all three are entered as independent variables. Three basic questions are then examined:

1. How much do ethnic differences change when IQ is taken into account?

2. How much do ethnic differences change when parental SES is taken into account?

3. What are the comparative roles of IQ and parental SES?

Table 1 Description of Indicators Used for Logistic Regression Analyses in Chapter 14

Because zAge, zAFQT, and zSES are all expressed as standard scores with mean of zero and standard deviation of 1, the intercept for the equation (abbreviated Int. in the tables) represents the expected value when those variables are set at their respective means. The coefficients for zAFQT and zSES are given so that you may examine the slopes associated with them.

The summary columns (Table 3) show the computed probabilities of the dependent variable when the independent variables are set at their means.

Income Analyses

Following the tables showing the logistic regressions, we present the detailed results of the ordinary least squares regressions used to estimate differences in income by ethnicity (Table 4). Because education is such an important causal factor in income, we show analyses in which years of education (as of the 1990 interview) replaces IQ as an independent variable.

The first set of models shows the parameters for wages of full-time, year-round workers by ethnic group. The sample for this analysis consisted of all persons in the NLSY who reported working for fifty-two weeks in 1989, had a reported wage greater than 0 (a handful of apparently self-employed persons who reported working fifty-two weeks reported no income), had an identified occupation, and had valid scores for IQ, parental SES, and educational level as of 1990. The second set of models shows the parameters for total family income from all sources. The sample for this analysis includes all persons with valid scores on the independent variables, excluding only those who reported being out of the labor force in 1989 or 1990 because of enrollment in school.

Table 5 shows the results when IQ, parental SES, and education are all entered as independent variables. Education is expressed as the highest degree attained as of 1990 (no high school diploma, high school diploma, associate degree, bachelor’s degree, professional degree).

Table 6 shows the analysis of wages by ethnicity and occupational grouping based on the subjects occupation in the 1990 interview (the variable labeled “Occ90”), using the 1970 U.S. Census Occupational Classification System. The software used for these analyses, JMP 3.0, treats nominal variables differently from the convention in many other regression packages. See the introduction to Appendix 4 for details and an example.

Table 5 Income Analyses in Chapter 14 (in 1990 dollars), by Degree Attained

Sample sizes for the different occupations analyzed in Table 6 below are as follow:

Because of the small numbers of farmworkers, that category is omitted from the table. Note, however, that farmworkers were included in the actual regression equation; hence the coefficients for the nominal occupation categories will not sum to zero.