Wage Decompositions with Selectivity-Corrected Wage Equations: A Methodological Note

This paper examines the implications of the standard Heckman (Heckit) correction for selectivity bias in wage and earnings functions that are subsequently used in wage decompositions. Even when justified, Heckit selectivity correction introduces some fundamental ambiguities in the context of wage decompositions. The ambiguities arise from group differences in the selection term which consists of a parameter multiplied by the Inverse Mills Ratio (IMR). The parameter is identified as the product of the standard deviation of the errors in the wage equation and the correlation between the wage equation error and the selection equation error. How should group differences in these parameters be interpreted in terms of structural differences and endowment effects? The same issue arises with respect to group differences in the IMR which reflect nonlinear group differences in the determinants of selection and in the probit coefficients.