Assessing Sensitivity to Unconfoundedness: Estimation and Inference

TL;DR

This paper develops methods to assess how sensitive treatment effect estimates are to violations of the unconfoundedness assumption, providing bounds and confidence bands under relaxations that account for unobserved confounding.

Contribution

It introduces a framework for quantifying robustness of treatment effects using sensitivity parameters and constructs confidence bands for bounds, with practical implementation in Stata.

Findings

Bounds on treatment effects vary with sensitivity parameter c

Confidence bands are constructed using a non-standard bootstrap method

Application to National Supported Work Demonstration illustrates the approach

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.