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 IV OLS estimates given by a linear regression model when true causal effects of treatment are nonlinear in levels heterogeneous across covariates. I show that IV–OLS coefficient gap consists three estimable components: weights on covariates, levels, identified marginal arises from endogeneity bias. Applications this return-to-schooling demonstrate empirical relevance distinction properly interpreting gap.