Selection Bias and the Decomposition of Wage Differentials

The major contribution of this paper is finding a new and general approach to decomposing log-wage differentials when selection effects are present. We divide the observed log-wage differentials between two groups into 1) differentials in predicted log-wages computed using observed individual characteristics and consistent coefficients while assuming both groups' stochastic component (unobserved individual characteristics) of log-wages to have the same mean zero, and 2) differentials caused by differences in unobserved individual characteristics (selection effects). We compute the average of the selection effects by taking sample average of the residuals of log-wages (observed log-wages minus predicted log-wages) without relying on the analytical formula(e) for computing the selection effects. Blinder-Oaxaca type decomposition can be applied for the differentials in predicted log-wages in order to find the effects of differences in observed individual characteristics and the effects of differences in coefficients. We call this approach a ``generalized selection bias (GSB) approach.'' Our approach can be implemented with any kind estimation method as long as we can obtain consistent coefficients for the log-wage equation. We illustrate our approach by applying it to the racial wage differentials among women using data from the current population survey.