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Generalized Bayes in Conditional Moment Restriction Models

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  • Sid Kankanala

Abstract

This paper develops a generalized (quasi-) Bayes framework for conditional moment restriction models, where the parameter of interest is a nonparametric structural function of endogenous variables. We establish contraction rates for a class of Gaussian process priors and provide conditions under which a Bernstein-von Mises theorem holds for the quasi-Bayes posterior. Consequently, we show that optimally weighted quasi-Bayes credible sets achieve exact asymptotic frequentist coverage, extending classical results for parametric GMM models. As an application, we estimate firm-level production functions using Chilean plant-level data. Simulations illustrate the favorable performance of generalized Bayes estimators relative to common alternatives.

Suggested Citation

  • Sid Kankanala, 2025. "Generalized Bayes in Conditional Moment Restriction Models," Papers 2510.01036, arXiv.org.
    • Handle: RePEc:arx:papers:2510.01036
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    File URL: https://arxiv.org/pdf/2510.01036
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    References listed on IDEAS

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    1. 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.
    2. Chen, Xiaohong & Pouzo, Demian & Powell, James L., 2019. "Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions," Journal of Econometrics, Elsevier, vol. 213(1), pages 30-53.
    3. Giovanni Compiani, 2022. "Market counterfactuals and the specification of multiproduct demand: A nonparametric approach," Quantitative Economics, Econometric Society, vol. 13(2), pages 545-591, May.
    4. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    5. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, July.
    6. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    7. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    8. Xiaohong Chen & Timothy Christensen & Sid Kankanala, 2025. "Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 92(1), pages 162-196.
    9. Andres Santos, 2012. "Inference in Nonparametric Instrumental Variables With Partial Identification," Econometrica, Econometric Society, vol. 80(1), pages 213-275, January.
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    Cited by:

    1. Desmond Fairall & Thomas Glinnan, 2026. "Quasi-Bayesian Hierarchical Models," Papers 2606.31930, arXiv.org.

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