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Bayesian Estimation and Comparison of Conditional Moment Models

Author

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  • Siddhartha Chib
  • Minchul Shin
  • Anna Simoni

    (CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed to satisfy a sequence of unconditional moments based on an increasing (in sample size) vector of approximating functions (such as tensor splines based on the splines of each conditioning variable). For any given sample size, results are robust to the number of expanded moments. We derive Bernstein-von Mises theorems for the behavior of the posterior distribution under both correct and incorrect specification of the conditional moments, subject to growth rate conditions (slower under misspecification) on the number of approximating functions. 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 misspecified. We also introduce sparsity-based model search for high-dimensional conditioning variables, and provide efficient MCMC computations for high-dimensional parameters. Along with clarifying examples, the framework is illustrated with real-data applications to risk-factor determination in finance, and causal inference under conditional ignorability.

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  • Siddhartha Chib & Minchul Shin & Anna Simoni, 2022. "Bayesian Estimation and Comparison of Conditional Moment Models," Post-Print hal-03504122, HAL.
  • Handle: RePEc:hal:journl:hal-03504122
    Note: View the original document on HAL open archive server: https://hal.science/hal-03504122
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    References listed on IDEAS

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    1. Florens, Jean-Pierre & Simoni, Anna, 2016. "Regularizing Priors For Linear Inverse Problems," Econometric Theory, Cambridge University Press, vol. 32(1), pages 71-121, February.
    2. Siddhartha Chib & Minchul Shin & Anna Simoni, 2018. "Bayesian Estimation and Comparison of Moment Condition Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1656-1668, October.
    3. Florens, Jean-Pierre & Simoni, Anna, 2012. "Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior," Journal of Econometrics, Elsevier, vol. 170(2), pages 458-475.
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    5. Jean-Pierre Florens & Anna Simoni, 2021. "Gaussian Processes and Bayesian Moment Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 482-492, March.
    6. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    7. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    8. Siddhartha Chib & Xiaming Zeng, 2020. "Which Factors are Risk Factors in Asset Pricing? A Model Scan Framework," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 771-783, October.
    9. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
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    12. Chib, Siddhartha & Ramamurthy, Srikanth, 2010. "Tailored randomized block MCMC methods with application to DSGE models," Journal of Econometrics, Elsevier, vol. 155(1), pages 19-38, March.
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    14. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
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    19. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.
    20. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    21. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
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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. 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.
    4. 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.

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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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