ECONOMETRICS: Counterfactual Predictive Distributions in Games; Professor Elie Tamer (Harvard University)

Abstract

We construct  predictive distributions for counterfactual analysis in  models involving incompleteness (e.g., multiple equilibria and/or mixed strategies) or partial identification  or both. We accommodate a range of outcomes of interest, including behavioral outcomes and welfare outcomes. The approach allows for any manipulation of the environment to generate the counterfactual analysis, including changes to the utility functions, changes to the distribution of the determinants of utility, changes to the number of decision makers, changes to the solution concept, and more.  We take a Bayesian approach to summarizing the statistical uncertainty. We show that our counterfactual predictive distributions are consistent if the posterior distribution for the underlying model parameter is consistent. This required the derivation of formal new {\it continuous mapping theorem} like results in general spaces specially tailored to handle correspondences in a Bayesian setup where set consistency is clearly defined. In that way, our results can be flexibly used to conduct a counterfactual analysis after a preliminary step of identifying/estimating the utility parameters, from the previous literature. Our proof strategy is sufficiently general that it could be easily adapted to similar settings where a partially identified parameter is mapped to some other object of interest.