Assessing Sensitivity to Unconfoundedness: Estimation and Inference

Abstract

This article provides a set of methods for quantifying the robustness of treatment effects estimated using the unconfoundedness assumption. Specifically, we estimate and do inference on bounds for 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 nonstandard 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 the National Supported Work Demonstration program. We implement these methods in the companion Stata module tesensitivity for easy use in practice.

Keywords:

• Causal inference
• Partial identification
• Sensitivity analysis
• Treatment effects

Supplementary Materials

The supplementary materials contain files to replicate the empirical results and thirteen appendices to accompany the main text. These appendices provide supporting theoretical results and discussions, more details on the formal asymptotic results, simulation studies, and proofs for all results.

Acknowledgments

This article was presented at the 2018 Western Economic Association International Conference, the 2019 Stata Conference Chicago, the 2020 World Congress of the Econometric Society, the DC-MD-VA Econometrics Workshop 2020, the University of Southern California, the University of Toronto, the 2020 SEA Conference, and the 2021 IAAE Conference. We thank participants at those seminars and conferences, as well as Karim Chalak, Toru Kitagawa, and John Pepper. We thank Paul Diegert for excellent research assistance. The accompanying Stata module tesensitivity is available on the SSC—type ssc install tesensitivity from within Stata—or via Github at https://github.com/mattmasten/tesensitivity.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Masten thanks the National Science Foundation for research support under grant no. 1943138.