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Posterior consistency of nonparametric conditional moment restricted models

Author

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  • Liao, Yuan
  • Jiang, Wenxin

Abstract

This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g0. We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior with nonshrinking variance. In addition, g0 is allowed to be only partially identified in the frequentist sense, and the parameter space does not need to be compact. The posterior is regularized using a slowly growing sieve dimension, and it is shown that the posterior converges to any small neighborhood of the identified region. We then apply our results to the nonparametric instrumental regression model. Finally, the posterior consistency using a random sieve dimension parameter is studied.

Suggested Citation

  • Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:38700
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    File URL: https://mpra.ub.uni-muenchen.de/38700/1/MPRA_paper_38700.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
    2. Florens, Jean-Pierre & Simoni, Anna, 2016. "Regularizing Priors For Linear Inverse Problems," Econometric Theory, Cambridge University Press, vol. 32(01), pages 71-121, February.
    3. Xiaohong Chen & Yin Jia Jeff Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: A Gentle Guide," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 259-290, October.
    4. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    5. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    6. Manuel Wiesenfarth & Carlos Matías Hisgen & Thomas Kneib & Carmen Cadarso-Suarez, 2014. "Bayesian Nonparametric Instrumental Variables Regression Based on Penalized Splines and Dirichlet Process Mixtures," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 468-482, July.
    7. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
    8. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Instrumental Variable Estimation with Many Weak Instruments," Discussion Paper Series DP2018-14, Research Institute for Economics & Business Administration, Kobe University.
    9. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation," Cowles Foundation Discussion Papers 1923R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.

    More about this item

    Keywords

    Identified region; limited information likelihood; sieve approximation; nonparametric instrumental variable; ill-posed problem; partial identification; Bayesian inference; shrinkage prior; regularization;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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