Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects

Abstract This study proposes an econometric framework to interpret and empirically decompose the difference between instrumental variables (IV) and ordinary least squares (OLS) estimates given by a linear regression model when the true causal effects of the treatment are nonlinear in treatment levels and heterogeneous across covariates. I show that the IV-OLS coefficient gap consists of three estimable components: the difference in weights on the covariates, the difference in weights on the treatment levels, and the difference in identified marginal effects that arises from endogeneity bias. Applications of this framework to return-to-schooling estimates demonstrate the empirical relevance of this distinction in properly interpreting the IV-OLS gap.