Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects
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This study proposes an econometric framework to interpret and empirically decompose the difference between IV and OLS estimates given by the linear regression equation 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 associated with endogeneity bias. Applications of this framework to return-to-schooling estimates demonstrate the empirical relevance of this distinction in properly interpreting the IV-OLS coefficient gap.
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