We study identiﬁcation and estimation of the average treatment effect in a correlated random coefficients model that allows for ﬁrst stage heterogeneity and binary instruments. The model also allows for multiple endogenous variables and interactions between endogenous variables and covariates. Our identiﬁcation 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 identiﬁcation 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 ﬁnite-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 ﬁnd substantial heterogeneity in ﬁrst stage instrument effects as well as heterogeneity in treatment effects that is consistent with household sorting.
Instrumental variables estimation of a generalized correlated random coefficients model
8 January 2014
Working Paper (CWP02/14)