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

TL;DR

This paper develops an econometric framework to decompose the difference between IV and OLS estimates into interpretable components, accounting for nonlinear and heterogeneous effects, with applications to return-to-schooling data.

Contribution

It introduces a novel empirical decomposition method for the IV-OLS gap that considers nonlinearities and heterogeneity in treatment effects.

Findings

The IV-OLS gap can be decomposed into three estimable components.

Application to return-to-schooling shows the importance of the decomposition.

Highlights the role of heterogeneity and nonlinearity in causal inference.

Abstract

This study proposes an econometric framework to interpret and empirically decompose the difference between IV and 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.