Estimation of Wage Gains and Welfare Gains from Self-Selection Models

In this paper we consider the basic self-selection model for the effects of education, training, unions, and other activities on wages. We show that past models have ignored "heterogeneity of rewards" to the activity--i.e., differences across individuals in the rate of return to the activity--as a source of selection bias. We model such heterogeneity, show how its presence can be tested, and draw out its implications for the wage and welfare gains to the activity. An empirical application provides strong support for such heterogeneity.