# Counterfactual Analysis under Partial Identification Using Locally Robust Refinement

## TL;DR

This paper introduces a method to identify more robust counterfactual predictions within partially identified models, especially in the presence of multiple equilibria, by focusing on locally robust refinements.

## Contribution

It proposes a new approach to select desirable parameter values for counterfactual analysis that are robust to local perturbations within the identified set.

## Key findings

- Robust counterfactual predictions can be identified within the identified set.
- The method simplifies implementation through a new representation.
- Application to moment inequality models and top-coded data demonstrates practicality.

## Abstract

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.