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Structural models that admit multiple reduced forms, such as game-theoreticmodels with multiple equilibria, pose challenges in practice, especially whenparameters are set-identified and the identified set is large. In such cases,researchers often choose to focus on a particular subset of equilibria forcounterfactual analysis, but this choice can be hard to justify. This papershows that some parameter values can be more "desirable" than others forcounterfactual analysis, even if they are empirically equivalent given thedata. In particular, within the identified set, some counterfactual predictionscan exhibit more robustness than others, against local perturbations of thereduced forms (e.g. the equilibrium selection rule). We provide arepresentation of this subset which can be used to simplify the implementation.We illustrate our message using moment inequality models, and provide anempirical application based on a model with top-coded data.

Counterfactual Analysis under Partial Identification Using Locally Robust Refinement