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Primary Submission Category: Sensitivity Analysis

Assessing Omitted Variable Bias when the Controls are Endogenous

Authors: Matthew Masten, Alexandre Poirier, Paul Diegert,

Presenting Author: Matthew Masten*

Omitted variables are one of the most important threats to the identification of causal effects. Several widely used methods, including Oster (2019) and Cinelli and Hazlett (2020), have been developed to assess the impact of omitted variables on empirical conclusions. These methods all either (1) require assuming that the omitted variables are uncorrelated with the included controls, which is often considered a strong and implausible assumption, or (2) use a method called residualization to avoid this assumption. We first formally prove that the residualization method generally leads to the wrong conclusions about robustness. We then provide a new approach to sensitivity analysis that avoids this critique, allows the omitted variables to be correlated with the included controls, and lets researchers calibrate sensitivity parameters by comparing the magnitude of selection on observables with the magnitude of selection on unobservables as in previous methods. We illustrate our results in an empirical study of the effect of historical American frontier life on modern cultural beliefs. Finally, we implement these methods in the companion Stata module regsensitivity for easy use in practice.