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 characterizing the sensitivity of counterfactuals with respect to parametric assumptions about the distribution of latent variables in a class of structural models. In particular, we show how to characterize the smallest and largest values of the counterfactual as the distribution of latent variables spans nonparametric neighborhoods of a researcher's parametric specification while other "structural" features of the model are maintained. Our procedure replaces the infinite-dimensional optimization with respect to the distribution by a finite-dimensional convex program and is therefore computationally simple to implement. We develop a novel MPEC implementation of our procedure to further simplify computation in models featuring endogenous parameters defined by equilibrium constraints. Our procedure recovers sharp bounds on the nonparametrically identified set of counterfactuals over large neighborhoods and has connections with local approaches to sensitivity analysis over small neighborhoods. We propose plug-in estimators of the smallest and largest counterfactuals and two procedures for inference. We illustrate the broad applicability of our procedure with empirical applications to matching models and dynamic discrete choice.
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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
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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
procedure replaces the infinite-dimensional optimization with respect to the distribution by a finite-dimensional convex program and is therefore computationally simple to implement. We develop a novel MPEC implementation of our procedure to further simplify computation in models featuring endogenous parameters defined by equilibrium constraints. Our procedure recovers sharp bounds on the nonparametrically
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(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
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of the smallest and largest counterfactuals and two procedures for inference. We illustrate the broad applicability of our procedure with empirical applications to matching models