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Bayesian Estimation and Comparison of Conditional Moment Models

Siddhartha Chib, Minchul Shin and Anna Simoni

No 19-51, Working Papers from Federal Reserve Bank of Philadelphia

Abstract: We provide a Bayesian analysis of models in which the unknown distribution of the outcomes is speci?ed up to a set of conditional moment restrictions. This analysis is based on the nonparametric exponentially tilted empirical likelihood (ETEL) function, which is constructed to satisfy a sequence of unconditional moments, obtained from the conditional moments by an increasing (in sample size) vector of approximating functions (such as tensor splines based on the splines of each conditioning variable). The posterior distribution is shown to satisfy the Bernstein-von Mises theorem, subject to a growth rate condition on the number of approximating functions, even under misspeci?cation of the conditional moments. A large-sample theory for comparing different conditional moment models is also developed. The central result is that the marginal likelihood criterion selects the model that is less misspeci?ed, that is, the model that is closer to the unknown true distribution in terms of the Kullback-Leibler divergence. Several examples are provided to illustrate the framework and results.

Keywords: Misspecification; Bernstein-von Mises theorem; Conditional moment restrictions; Exponentially tilted empirical likelihood; Bayesian inference; Marginal likelihood; Posterior consistency (search for similar items in EconPapers)
JEL-codes: C13 C11 C14 C52 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2019-12-09, Revised 2019-12-09
New Economics Papers: this item is included in nep-ecm and nep-ore
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DOI: 10.21799/frbp.wp.2019.51

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Handle: RePEc:fip:fedpwp:19-51