Counterfactual Analysis under Partial Identification Using Locally Robust Refinement
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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.
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