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Robust Bayesian Analysis for Econometrics

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Abstract

We review the literature on robust Bayesian analysis as a tool for global sensitivity analysis and for statistical decision-making under ambiguity. We discuss the methods proposed in the literature, including the different ways of constructing the set of priors that are the key input of the robust Bayesian analysis. We consider both a general set-up for Bayesian statistical decisions and inference and the special case of set-identified structural models. We provide new results that can be used to derive and compute the set of posterior moments for sensitivity analysis and to compute the optimal statistical decision under multiple priors. The paper ends with a self-contained discussion of three different approaches to robust Bayesian inference for set-identified structural vector autoregressions, including details about numerical implementation and an empirical illustration.

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  • Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Robust Bayesian Analysis for Econometrics," Working Paper Series WP-2021-11, Federal Reserve Bank of Chicago.
  • Handle: RePEc:fip:fedhwp:93001
    DOI: 10.21033/wp-2021-11
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    1. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    2. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    3. Stéphane Bonhomme & Martin Weidner, 2018. "Minimizing sensitivity to model misspecification," CeMMAP working papers CWP59/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    5. 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.
    6. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2020. "On the Informativeness of Descriptive Statistics for Structural Estimates," Econometrica, Econometric Society, vol. 88(6), pages 2231-2258, November.
    7. Arias, Jonas E. & Caldara, Dario & Rubio-Ramírez, Juan F., 2019. "The systematic component of monetary policy in SVARs: An agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 1-13.
    8. Christiane Baumeister & James D. Hamilton, 2015. "Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information," Econometrica, Econometric Society, vol. 83(5), pages 1963-1999, September.
    9. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2017. "Measuring the Sensitivity of Parameter Estimates to Estimation Moments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1553-1592.
    10. Jonas E. Arias & Juan F. Rubio‐Ramírez & Daniel F. Waggoner, 2018. "Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications," Econometrica, Econometric Society, vol. 86(2), pages 685-720, March.
    11. Edward Barankin, 1960. "Sufficient parameters: Solution of the minimal dimensionality problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 12(2), pages 91-118, June.
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    Cited by:

    1. Timothy Christensen & Hyungsik Roger Moon & Frank Schorfheide, 2022. "Optimal Decision Rules when Payoffs are Partially Identified," Papers 2204.11748, arXiv.org, revised May 2023.
    2. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Oct 2024.

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    More about this item

    Keywords

    ambiguity; Bayesian robustness; statistical decision theory; identifying restrictions; multiple priors; structural vector autoregressions;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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