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Nonparametric Bayes subject to overidentified moment conditions

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  • Gallant, A. Ronald

Abstract

Nonparametric Bayesian estimation subject to overidentified moment equations is a challenge because the support of the posterior is a manifold of lower dimension than the number of model parameters. The manifold therefore has Lebesgue measure zero thus inhibiting the use of the most commonly used Bayesian estimation method: MCMC (Markov Chain Monte Carlo). This study proposes an effective MCMC algorithm and algorithms for estimating scale and the normalizing constant. The algorithms are illustrated with two illustrative applications.

Suggested Citation

  • Gallant, A. Ronald, 2022. "Nonparametric Bayes subject to overidentified moment conditions," Journal of Econometrics, Elsevier, vol. 228(1), pages 27-38.
    • Handle: RePEc:eee:econom:v:228:y:2022:i:1:p:27-38
    DOI: 10.1016/j.jeconom.2021.02.005
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    References listed on IDEAS

    as
    1. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    2. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    3. A. Ronald Gallant, 2016. "Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference — Author Response to Comments," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 284-294.
    4. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    5. A. Ronald Gallant, 2020. "Complementary Bayesian method of moments strategies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 422-439, June.
    6. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
    7. A. Ronald Gallant, 2016. "Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 229-247.
    8. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
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    Cited by:

    1. Gallant, A. Ronald, 2023. "Variance–covariance from a metropolis chain on a curved, singular manifold," Journal of Econometrics, Elsevier, vol. 235(2), pages 843-861.

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    More about this item

    Keywords

    Method of moments; Bayesian inference;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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