Bayesian and Frequentist Inference in Partially Identified Models
A large sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by a finite-dimensional reduced form parameter vector. It is used to analyze the differences between frequentist confidence sets and Bayesian credible sets in partially identified models. A key difference is that frequentist set estimates extend beyond the boundaries of the identified set (conditional on the estimated reduced form parameter), whereas Bayesian credible sets can asymptotically be located in the interior of the identified set. Our asymptotic approximations are illustrated in the context of simple moment inequality models and a numerical illustration for a two-player entry game is provided.
We thank seminar participants at the 2007 NASM, the 2008 SETA, Boston College, Johns Hopkins, Ohio State, Rice, UC Davis, UC Irvine, UCLA, and Vanderbilt for helpful comments. Moon gratefully acknowledges financial support from the USC Faculty Development Award. Schorfheide gratefully acknowledges financial support from the Alfred P. Sloan Foundation and the National Science Foundation under Grant SES 0617803. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.
Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, 03. citation courtesy of