Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2012, Volume 80, Issue 2

Bayesian and Frequentist Inference in Partially Identified Models

https://doi.org/10.3982/ECTA8360
p. 755-782

Hyungsik Roger Moon, Frank Schorfheide

A large‐sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by an identifiable finite‐dimensional reduced‐form parameter vector. It is used to analyze the differences between Bayesian credible sets and frequentist confidence sets. We define a plug‐in estimator of the identified set and show that asymptotically Bayesian highest‐posterior‐density sets exclude parts of the estimated identified set, whereas it is well known that frequentist confidence sets extend beyond the boundaries of the estimated identified set. We recommend reporting estimates of the identified set and information about the conditional prior along with Bayesian credible sets. A numerical illustration for a two‐player entry game is provided.


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Supplemental Material

Supplement to "Bayesian and Frequentist Inference in Partially Identified Models"

This supplement contains proofs and derivations for results presented in the paper.

Supplement to "Bayesian and Frequentist Inference in Partially Identified Models"

The replication files for the results presented in section 4.

Supplement to "Bayesian and Frequentist Inference in Partially Identified Models"

The replication files for the results presented in section 2.