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The Empirical Content of the Roy Model

James J. Heckman
Bo E. Honore

Abstract

This paper clarifies and extends the classical Roy model of self selection and earnings inequality. The original Roy model, based on the assumption that log skills are normally distributed, is shown to imply that pursuit of comparative advantage in a free market reduces earnings inequality compared to the earnings distribution that would result if workers were randomly assigned to sectors. Aggregate log earnings are right skewed even if one sectoral distribution is left skewed. Most major implications of the log normal Roy model survive if differences in skills are log concave. However few implications of the model survive if skills are generated from more general distributions. We consider the identifiability of the Roy model from data on earnings distributions. The normal theory version is identifiable without regressors or exclusion restrictions. Sectoral distributions can be identified knowing only the aggregate earnings distribution. For general skill distributions, the model is not identified and has no empirical content. With sufficient price variation, the model can be identified from multimarket data. Cross-sectional variation in regressors can substitute for price variation in restoring empirical content to the Roy model.