Relaxing Instrument Exogeneity with Common Confounders

TL;DR

This paper introduces a new identification method for causal inference that relaxes traditional instrument exogeneity assumptions by conditioning on unobserved confounders with relevant proxies, enabling more flexible and robust estimation.

Contribution

It proposes a novel approach to relax instrument exogeneity assumptions using proxies for unobserved confounders, with point identification and robust estimation techniques.

Findings

Successfully applied to NLS97 data to distinguish ability bias from selection bias.

Provides doubly robust and Neyman orthogonal moments for low-dimensional parameter estimation.

Achieves identification under less restrictive assumptions than traditional IV methods.

Abstract

Instruments can be used to identify causal effects in the presence of unobserved confounding, under the famous relevance and exogeneity (unconfoundedness and exclusion) assumptions. As exogeneity is difficult to justify and to some degree untestable, it often invites criticism in applications. Hoping to alleviate this problem, we propose a novel identification approach, which relaxes traditional IV exogeneity to exogeneity conditional on some unobserved common confounders. We assume there exist some relevant proxies for the unobserved common confounders. Unlike typical proxies, our proxies can have a direct effect on the endogenous regressor and the outcome. We provide point identification results with a linearly separable outcome model in the disturbance, and alternatively with strict monotonicity in the first stage. General doubly robust and Neyman orthogonal moments are derived consecutively to enable the straightforward root-n estimation of low-dimensional parameters despite the high-dimensionality of nuisances, themselves non-uniquely defined by Fredholm integral equations. Using this novel method with NLS97 data, we separate ability bias from general selection bias in the economic returns to education problem.