Counterfactual Sensitivity and Robustness

Abstract

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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• $f$-divergence Inequalities
• Monte Carlo Confidence Sets for Identified Sets
• Counterfactual Sensitivity and Robustness
• Optimal transportation and the falsifiability of incompletely specified economic models
• Sensitivity Analysis using Approximate Moment Condition Models
• Set Identification in Models with Multiple Equilibria
• Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

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• Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments
• Robust decision-making under risk and ambiguity