Researchers frequently make parametric assumptions about the distribution of unobservables when formulating structural models. Such assumptions are typically motived by computational convenience rather than economic theory and are often untestable. Counterfactuals can be particularly sensitive to such assumptions, threatening the credibility of structural modeling exercises. To address this issue, we leverage insights from the literature on ambiguity and model uncertainty to propose a tractable econometric framework for characterizing the sensitivity of counterfactuals with respect to a researcher's assumptions about the distribution of unobservables in a class of structural models. In particular, we show how to construct the smallest and largest values of the counterfactual as the distribution of unobservables spans nonparametric neighborhoods of the researcher's assumed specification while other "structural" features of the model, e.g. equilibrium conditions, are maintained. Our methods are computationally simple to implement, with the nuisance distribution effectively profiled out via a low-dimensional convex program. Our procedure delivers sharp bounds for the identified set of counterfactuals (i.e. without parametric assumptions about the distribution of unobservables) as the neighborhoods become large. Over small neighborhoods, we relate our procedure to a measure of local sensitivity which is further characterized using an influence function representation. We provide a suitable sampling theory for plug-in estimators and apply our procedure to models of strategic interaction and dynamic discrete choice.

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.