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Bayesian Estimation and Comparison of Conditional Moment Models

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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.

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  • Siddhartha Chib & Minchul Shin & Anna Simoni, 2019. "Bayesian Estimation and Comparison of Conditional Moment Models," Working Papers 19-51, Federal Reserve Bank of Philadelphia.
    • Handle: RePEc:fip:fedpwp:19-51
    DOI: https://doi.org/10.21799/frbp.wp.2019.51
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    Cited by:

    1. Chung, Ray S.W. & So, Mike K.P. & Chu, Amanda M.Y. & Chan, Thomas W.C., 2020. "Regularization of Bayesian quasi-likelihoods constructed from complex estimating functions," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    2. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    3. Zhichao Liu & Catherine Forbes & Heather Anderson, 2017. "Robust Bayesian exponentially tilted empirical likelihood method," Monash Econometrics and Business Statistics Working Papers 21/17, Monash University, Department of Econometrics and Business Statistics.
    4. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    Bayesian inference; Bernstein-von Mises theorem; Conditional moment restrictions; Exponentially tilted empirical likelihood; Marginal likelihood; Misspecification; Posterior consistency;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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