Relaxing Instrument Exogeneity with Common Confounders
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.