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This study proposes an econometric framework to interpret and empiricallydecompose the difference between IV and OLS estimates given by a linearregression model when the true causal effects of the treatment are nonlinear intreatment levels and heterogeneous across covariates. I show that the IV-OLScoefficient gap consists of three estimable components: the difference inweights on the covariates, the difference in weights on the treatment levels,and the difference in identified marginal effects that arises from endogeneitybias. Applications of this framework to return-to-schooling estimatesdemonstrate the empirical relevance of this distinction in properlyinterpreting the IV-OLS gap.

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