College Education and Wages in the U.K.: Estimating Conditional Average Structural Functions in Nonadditive Models with Binary Endogenous Variables

We propose and implement an estimator for identifiable features of correlated random coefficient models with binary endogenous variables and nonadditive errors in the outcome equation. It is suitable, e.g., for estimation of the average returns to college education when they are heterogeneous across individuals and correlated with the schooling choice. The estimated features are of central interest to economists and are directly linked to the marginal and average treatment effect in policy evaluation. They are identified under assumptions weaker than typical exclusion restrictions used in the context of classical instrumental variables analysis. In our application for the U.K., we relate levels of expected wages to unobserved ability, measured ability, family background, type of secondary school, and the decision whether to attend college.