Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jan, 2023, Volume 91, Issue 1

Counterfactual Sensitivity and Robustness

https://doi.org/10.3982/ECTA17232
p. 263-298

Timothy Christensen, Benjamin Connault

We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite‐dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite‐dimensional convex program. We also develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug‐in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to matching models with transferable utility and dynamic discrete choice models.


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Supplemental Material

Supplement to "Counterfactual Sensitivity and Robustness"

Timothy Christensen and Benjamin Connault

This zip file contains the replication files for the manuscript.

Supplement to "Counterfactual Sensitivity and Robustness"

Timothy Christensen and Benjamin Connault

This supplement presents extensions of our methodology in Appendix A, additional results on nonparametric bounds on counterfactuals in Appendix B, connections with local approaches to sensitivity analysis in Appendix C, additional details on the empirical applications in Appendix D, and proofs of results from the main text in Appendix E.