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Bayesian Likelihoods for Moment Condition Models

Author

Listed:
  • Giuseppe Ragusa

    (Department of Economics, University of California-Irvine)

Abstract

Bayesian inference in moment condition models is difficult to implement. For these models, a posterior distribution cannot be calculated because the likelihood function has not been fully specified. In this paper, we obtain a class of likelihoods by formal Bayesian calculations that take into account the semiparametric nature of the problem. The likelihoods are derived by integrating out the nuisance parameters with respect to a maximum entropy tilted prior on the space of distribution. The result is a unification that uncovers a mapping between priors and likelihood functions. We show that there exist priors such that the likelihoods are closely connected to Generalized Empirical Likelihood (GEL) methods.

Suggested Citation

  • Giuseppe Ragusa, 2007. "Bayesian Likelihoods for Moment Condition Models," Working Papers 060714, University of California-Irvine, Department of Economics.
    • Handle: RePEc:irv:wpaper:060714
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    File URL: https://www.economics.uci.edu/files/docs/workingpapers/2006-07/Ragusa-14.pdf
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    References listed on IDEAS

    as
    1. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    2. Kim, Jae-Young, 2002. "Limited information likelihood and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 175-193, March.
    3. Chamberlain, Gary & Imbens, Guido W, 2003. "Nonparametric Applications of Bayesian Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 12-18, January.
    4. Ghysels, Eric & Hall, Alastair, 2002. "Interview with Christopher A. Sims," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 448-449, October.
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    6. Sung Jae Jun & Tony Lancaster, 2006. "Bayesian quantile regression," CeMMAP working papers CWP05/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Hahn, Jinyong, 1997. "Bayesian Bootstrap of the Quantile Regression Estimator: A Large Sample Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 795-808, November.
    8. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    9. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    10. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 359-383.
    11. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    12. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
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    Citations

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    Cited by:

    1. Jesús Fernández-Villaverde, 2010. "The econometrics of DSGE models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 1(1), pages 3-49, March.
    2. Dante Amengual & Enrique Sentana, 2016. "Comments on: 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 248-252.
    3. Dale Poirier, 2008. "Bayesian Interpretations of Heteroskedastic Consistent Covariance Estimators Using the Informed Bayesian Bootstrap," Working Papers 080905, University of California-Irvine, Department of Economics.
    4. Mr. Alin T Mirestean & Mr. Charalambos G Tsangarides & Huigang Chen, 2009. "Limited Information Bayesian Model Averaging for Dynamic Panels with Short Time Periods," IMF Working Papers 2009/074, International Monetary Fund.
    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. Dale J. Poirier, 2011. "Bayesian Interpretations of Heteroskedastic Consistent Covariance Estimators Using the Informed Bayesian Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 457-468, August.
    7. Huigang Chen & Mr. Alin T Mirestean & Mr. Charalambos G Tsangarides, 2011. "Limited Information Bayesian Model Averaging for Dynamic Panels with An Application to a Trade Gravity Model," IMF Working Papers 2011/230, International Monetary Fund.

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    Keywords

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • 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
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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