Using occupational preference in estimating market wage discrimination: the case of the gender pay gap

American Journal of Economics and Sociology, The, Jan, 1999 by Eric J. Solberg

Decomposition of a Reduced-form Wage Equation

I

Introduction

Most empirical studies of market wage discrimination based on human-capital wage equations generate an estimate of potential discrimination either from a coefficient on a gender variable or from an unexplained residual component. It is widely recognized that either measure of market discrimination may be biased upwards if relevant exogenous variables are excluded from the set of explanatory variables, and so researchers attempt to include all relevant variables subject only to data limitations and statistical compromises. In many applications, dummy variables for occupational assignment are used as explanatory variables. The inclusion of dummy variables for occupational assignment adds considerably to the explanatory power of wage regressions, as does the inclusion of hours of work (Blau and Ferber, 1987). The measure of discrimination is higher when hours of work is omitted and when occupational controls are excluded. There are two problems with this practice. First, the wage equation can no longer be interpreted as a reduced-form if occupational assignment is endogenous to the wage outcome. Second, the resulting reduction of the measured pay gap cannot be attributed entirely to preferences because occupational assignment may be influenced by hiring discrimination, and so the discriminatory part of the gap is under estimated.

Some recent authors argue that occupational controls should not be included in estimated wage equations because those controls wrongly shrink estimates of the discriminatory gap. Anderson and Shapiro (1996), in a study of the pay gap between black and white women, found that the addition of occupational controls increased the explained part of the gap to 45 percent, compared to about 20 percent without those controls. Using a dichotomous variable as an indicator for having a "high-paying job," they found that 65 to 74 percent of the "occupational" gap is unexplained by differences in the coefficients in a probability equation. As a consequence, they argue that it is better to assume that preference plays no role in the differences in the black/white occupational distribution. That argument is not very compelling - more so perhaps for a study of the racial pay gap, but not at all compelling for a study of the gender pay gap, as is demonstrated in the next section. Kidd and Shannon (1996), in their study of the gender pay gap, argue that occupation should not be treated as a productivity variable because of barriers to job entry. However, while they recognize the different roles that occupational preferences may play apart from differences in productivity and other traits, the data they used to compare the traditional decomposition with the method of Brown, Moon, and Zolath (1980) do not include job preferences.

If occupational assignment is correlated with gender or race, and if this occurs frequently, the difference in pay is likely to show up as a statistically significant difference in earnings in the absence of occupational controls. However, including dummy variables for current occupation may result in an estimate of the discriminatory part of the gap that is biased downwards because current occupational assignment may be influenced by discrimination. Recognizing this, Brown, et al expanded the traditional decomposition of the average wage differential by applying proportions of male and female occupational attainment. (See Kidd and Shannon, 1996, for a comparison.) However, current occupation is almost surely endogenous to the labor supply decision, and so the use of dummy endogenous variables for current occupational assignment is likely to yield biased coefficient estimates when estimated by ordinary least squares. Wage equations that include dummy variables for current occupation are specified incorrectly because they are not true reduced equations of the demand-price of labor services when supply-side variables are included. Wage equations that exclude dummy variables for occupational assignment may suffer from omit- . ted variable bias if they do not include relevant explanatory variables that determine occupational preference. The correct approach when estimating a reduced-form wage equation is to exclude endogenous variables, but the exogenous variables that determine them should be included as explanatory variables.(1)

A more direct approach is to include respondents' expressions of previously stated occupational preference that are exogenous to current labor market outcomes. The idea is that past preferences influence current choices. Preferences may change as a consequence of current labor force experience, but the new preferences will affect future but not current outcomes. In the empirical application that follows, occupational preferences were expressed prior to entering the labor market, and so such predetermined variables must be exogenous to current outcomes. Past occupational preference has been used by Gill (1994), in a study of race discrimination, to estimate that part of the pay gap due to "hiring" discrimination. In a study of the gender pay gap, Solberg (1995) extended Gill's technique in the context of a structural demand-wage equation. To my knowledge, however, my study is the first to include predetermined indicators of occupational preference in the estimation of reduced-form wage equations.