Structural models that admit multiple reduced forms, such as game-theoretic models with multiple equilibria, pose challenges in practice, especially when parameters are set-identified and the identified set is large. In such cases, researchers often choose to focus on a particular subset of equilibria for counterfactual analysis, but this choice can be hard to justify. This paper proposes a refinement criterion for the identified set. Our criterion chooses a subset such that counterfactual predictions of outcomes are most stable against local perturbations of the reduced forms (e.g. the equilibrium selection rule). Our refinement has multiple appealing features, including an intuitive characterization, lower computational cost, and stable predictions. Focusing on moment inequality models, we propose bootstrap inference on the refinement and provide generic conditions under which the inference is uniformly asymptotically valid. We present and discuss results from our Monte Carlo study and an empirical application based on a model with top-coded data.
Structural models that admit multiple reduced forms, such as game-theoretic models with multiple equilibria, pose challenges in practice, especially when parameters are set-identified and the identified set is large. In such cases, researchers often choose to focus on a particular subset of equilibria for counterfactual analysis, but this choice can be hard to justify. This paper shows that some parameter values can be more ``desirable'' than others for counterfactual analysis, even if they are empirically equivalent given the data. In particular, within the identified set, some counterfactual predictions can exhibit more robustness than others, against local perturbations of the reduced forms (e.g. the equilibrium selection rule). We provide a representation of this subset which can be used to simplify the implementation. We illustrate our message using moment inequality models, and provide an empirical application based on a model with top-coded data.
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proposes a refinement criterion for the identified set. Our criterion chooses a subset such that counterfactual predictions of outcomes are most stable
shows that some parameter values can be more ``desirable'' than others for counterfactual analysis, even if they are empirically equivalent given the data. In particular, within the identified set, some counterfactual predictions can exhibit more robustness than others,
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Our refinement has multiple appealing features, including an intuitive characterization, lower computational cost, and stable predictions. Focusing on moment inequality models, we propose bootstrap inference on the refinement and provide generic conditions under which the inference is uniformly asymptotically valid. We present and discuss results from our Monte Carlo study and
We provide a representation of this subset which can be used to simplify the implementation. We illustrate our message using moment inequality models, and provide