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.

Information based inference in models with set-valued predictions and misspecification

“…3 Christensen and Connault (2023) provide tools for the related but distinct question of characterizing the sensitivity of counterfactuals to the distributional assumptions imposed on the latent variables of the model. They allow such distributions to span a nonparametric neighborhood of the parametric specification, and eliminate the infinite-dimensional nuisance parameter via a convex program of fixed dimension.…”