Sensitivity Analysis for Unobserved Confounder: An introduction

Abstract

　Sensitivity analysis is a thought experiment typically performed as one of the robustness checks in statistical analysis. It relaxes one of the assumptions necessary to estimate the unbiased estimator. Especially, sensitivity analysis for unobserved confounder slightly relaxes the ignorability assumption. While ignorability usually requires that the independence between potential outcomes and the treatment assignment conditional on observed covariates, this sensitivity analysis posits ignorability holds only after conditioning on both observed and unobserved confounders. Then, the treatment effects are estimated under the influence of an unobserved confounder with various strengths. If these estimated treatment effects still reveal the substantively same results as the original estimates, researchers might conclude that the original estimates are robust against the presence of an unobserved confounder. In this paper, I introduce the three major classes of sensitivity analyses with the examples drawn from political economic literature.