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Bayesian inference for partially identified smooth convex models

Author

Listed:
  • Yuan Liao
  • Anna Simoni

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique)

Abstract
This paper proposes novel Bayesian procedures for partially identified models when the identified set is convex with a smooth boundary, whose support function is locally smooth with respect to the data distribution. Using the posterior of the identified set, we construct Bayesian credible sets for the identified set, the partially identified parameter and their scalar transformations. These constructions, based on the support function, benefit from several computationally attractive algorithms when the identified set is convex, and are proved to have valid large sample frequentist coverages. These results are based on a local linear expansion of the support function of the identified set. We provide primitive conditions to verify such an expansion.
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Suggested Citation

  • Yuan Liao & Anna Simoni, 2019. "Bayesian inference for partially identified smooth convex models," Post-Print hal-03089881, HAL.
    • Handle: RePEc:hal:journl:hal-03089881
    DOI: 10.1016/j.jeconom.2019.03.001
    Note: View the original document on HAL open archive server: https://hal.science/hal-03089881v1
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    Cited by:

    1. Siddhartha Chib & Minchul Shin & Anna Simoni, 2022. "Bayesian estimation and comparison of conditional moment models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 740-764, July.
    2. Jean-Pierre Florens & Anna Simoni, 2021. "Revisiting Identification Concepts in Bayesian Analysis," Annals of Economics and Statistics, GENES, issue 144, pages 1-38.
    3. Brendan Kline & Elie Tamer, 2024. "Counterfactual Analysis in Empirical Games," Papers 2410.12731, arXiv.org.
    4. Alvarez, Luis Antonio, 2023. "Approximate Bayesian Computation for Partially Identified Models," MPRA Paper 117339, University Library of Munich, Germany.
    5. Liu, Xiaobin & Li, Yong & Yu, Jun & Zeng, Tao, 2022. "Posterior-based Wald-type statistics for hypothesis testing," Journal of Econometrics, Elsevier, vol. 230(1), pages 83-113.
    6. Emanuele Bacchiocchi & Toru Kitagawa, 2020. "Locally- but not globally-identified SVARs," CeMMAP working papers CWP40/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    8. Kline, Brendan, 2024. "Classical p-values and the Bayesian posterior probability that the hypothesis is approximately true," Journal of Econometrics, Elsevier, vol. 240(1).

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • 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

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