Instrumental variables estimation of a generalized correlated random coefficients model

We study identiï¬cation and estimation of the average treatment effect in a correlated random coefficients model that allows for ï¬rst stage heterogeneity and binary instruments. The model also allows for multiple endogenous variables and interactions between endogenous variables and covariates. Our identiï¬cation approach is based on averaging the coefficients obtained from a collection of ordinary linear regressions that condition on different realizations of a control function. This identiï¬cation strategy suggests a transparent and computationally straightforward estimator of a trimmed average treatment effect constructed as the average of kernel-weighted linear regres-sions. We develop this estimator and establish its √n–consistency and asymptotic normality. Monte Carlo simulations show excellent ï¬nite-sample performance that is comparable in precision to the standard two-stage least squares estimator. We apply our results to analyze the effect of air pollution on house prices, and ï¬nd substantial heterogeneity in ï¬rst stage instrument effects as well as heterogeneity in treatment effects that is consistent with household sorting.