Generalized selection bias and the decomposition of wage differentials

The major contribution of this paper is ending a new and flexible way to measure the effects of selection on log-wages. In this context, we offer a general approach to performing decomposition analysis when selection effects are present. We call the difference between unconditional and conditional expectations of the log-wages a generalized selection bias (GSB) when the two expectations are measured using the estimates from the joint estimation of the whole model (log-wages and selection equations) by the MLE method. The unconditional and conditional expectations are, respectively, the deterministic component of log-wages, and the deterministic component plus the conditional expectation of the stochastic component of log-wages, where the deterministic component is computed using the estimates from the joint estimation. That is, the GSB is the expectation of the residuals estimated from the joint estimation. It is appropriate to apply the Blinder-Oaxaca decomposition method to the wage differentials adjusted for the GSB. The GSB approach to decomposition analysis is not only easy to implement and flexible enough to apply to virtually any kind of selection issue, but also efficient because it uses full information. We illustrate the GSB approach by applying it to the racial wage differentials among women using data from the Current Population Survey. We discuss the possibility of using semiparametric or Bayesian sampling method for the joint estimation and related modifications of decomposition analysis.