Counterfactual Decomposition of Changes in Wage Distributions via Quantile Regression with Endogenous Regressors

Counterfactual decomposition allows the researcher to analyze the changes in wage distributions by discriminating between the e¤ect of changes in the population characteristics and the e¤ect of changes in returns to these characteristics. In this paper we propose to apply this methodology by recovering the conditional distribution via a set of quantile regressions. Additionally, we also propose estimators for counterfactual distributions that correct for the endogeneity of the schooling decisions in the wage equation using a control function approach. We apply this metholodogy to analyze the changes in wage distribution that took place in the United States between 1983 and 1993 by extending the work in Machado and Mata (2005) and Melly (2005) in order to allow for endogenous schooling. For comparative purposes, we perform the analysis …rst assuming that education is exogenous and then assuming that is endogenous. In the endogenous model, we consider as instrumental variables proximity to college for di¤erente parental backgrounds, avearage-state tuituion fees and parental education. Our method allow us to obtain the counterfactual distribution that would have prevailed in the unobservables a¤ecting schooling and earnings were distributed as in a previous period of time. The overall changes attributed to changes in the unobservables o¤set those changes attributed to schooling. The major di¤erences among the results under endogeneity and exogeneity are found in the decomposition of the changes attributed to changes in the median returns of the individual characteristics. J.E.L. Classi…cation Numbers: C14, C81, D63.