  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.
