Relaxing Instrument Exclusion with Common Confounders
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Instruments can be used to identify causal effects in the presence of unobserved confounding, under the famous relevance and exclusion assumptions. As exclusion 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 exclusion to exclusion 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. Using this novel method with NLS97 data, we demonstrate the insignificant role of ability bias compared to general selection bias in the economic returns to education problem. Beyond economics, the approach is just as relevant in health treatment evaluation with an unobserved underlying health status, or a psychological study where character traits are unobserved common confounders.
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