Assessing Sensitivity to Unconfoundedness: Estimation and Inference

Abstract: This paper provides a set of methods for quantifying the robustness of treatment effects estimated using the unconfoundedness assumption (also known as selection on observables or conditional independence). Specifically, we estimate and do inference on bounds on various treatment effect parameters, like the average treatment effect (ATE) and the average effect of treatment on the treated (ATT), under nonparametric relaxations of the unconfoundedness assumption indexed by a scalar sensitivity parameter c. These relaxations allow for limited selection on unobservables, depending on the value of c. For large enough c, these bounds equal the no assumptions bounds. Using a non-standard bootstrap method, we show how to construct confidence bands for these bound functions which are uniform over all values of c. We illustrate these methods with an empirical application to effects of the National Supported Work Demonstration program. We implement these methods in a companion Stata module for easy use in practice.