We modify the basic self-selection model for the effects of education, training, unions, and other activities on wages, by including "heterogeneity of rewards" to the activity -i.e., differences across individuals in the rate of return to the activity. We show that such heterogeneity creates a new form of selection bias. We provide tests for its presence and we draw out its implications for the wage and welfare gains to the activity. An empirical application provides strong support for such heterogeneity in one particular training program.
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