Before revision:  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).
After revision:  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).