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Classical p-values and the Bayesian posterior probability that the hypothesis is approximately true

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  • Kline, Brendan

Abstract

This paper relates p-values for the hypothesis that θ=c to the Bayesian posterior probability that the hypothesis is approximately true, in the sense that θ∈[c−ϵ,c+ϵ] for a selected ϵ>0. In a setup with a continuous prior for θ, the results show that a larger (respectively, smaller) p-value does not necessarily correspond to a higher (respectively, lower) probability that θ is close to c. Therefore, the results suggest caution about common ways of using p-values, specifically the use of small p-values as a key standard in empirical research.

Suggested Citation

  • Kline, Brendan, 2024. "Classical p-values and the Bayesian posterior probability that the hypothesis is approximately true," Journal of Econometrics, Elsevier, vol. 240(1).
    • Handle: RePEc:eee:econom:v:240:y:2024:i:1:s030440762400023x
    DOI: 10.1016/j.jeconom.2024.105677
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    References listed on IDEAS

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    1. Kitagawa, Toru & Montiel Olea, José Luis & Payne, Jonathan & Velez, Amilcar, 2020. "Posterior distribution of nondifferentiable functions," Journal of Econometrics, Elsevier, vol. 217(1), pages 161-175.
    2. Alberto Abadie, 2020. "Statistical Nonsignificance in Empirical Economics," American Economic Review: Insights, American Economic Association, vol. 2(2), pages 193-208, June.
    3. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    4. Siddhartha Chib & Minchul Shin & Anna Simoni, 2018. "Bayesian Estimation and Comparison of Moment Condition Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1656-1668, October.
    5. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    6. Daniel J. Benjamin & James O. Berger & Magnus Johannesson & Brian A. Nosek & E.-J. Wagenmakers & Richard Berk & Kenneth A. Bollen & Björn Brembs & Lawrence Brown & Colin Camerer & David Cesarini & Chr, 2018. "Redefine statistical significance," Nature Human Behaviour, Nature, vol. 2(1), pages 6-10, January.
      • Daniel Benjamin & James Berger & Magnus Johannesson & Brian Nosek & E. Wagenmakers & Richard Berk & Kenneth Bollen & Bjorn Brembs & Lawrence Brown & Colin Camerer & David Cesarini & Christopher Chambe, 2017. "Redefine Statistical Significance," Artefactual Field Experiments 00612, The Field Experiments Website.
    7. Abel Brodeur & Mathias Lé & Marc Sangnier & Yanos Zylberberg, 2016. "Star Wars: The Empirics Strike Back," American Economic Journal: Applied Economics, American Economic Association, vol. 8(1), pages 1-32, January.
    8. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    9. Brendan Kline, 2022. "Bayes Factors Based on p-Values and Sets of Priors With Restricted Strength," The American Statistician, Taylor & Francis Journals, vol. 76(3), pages 203-213, July.
    10. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
    11. Campbell R. Harvey, 2017. "Presidential Address: The Scientific Outlook in Financial Economics," Journal of Finance, American Finance Association, vol. 72(4), pages 1399-1440, August.
    12. Tom E. Hardwicke & Maia Salholz-Hillel & Mario Malički & Dénes Szűcs & Theiss Bendixen & John P. A. Ioannidis, 2023. "Statistical Guidance to Authors at Top-Ranked Journals across Scientific Disciplines," The American Statistician, Taylor & Francis Journals, vol. 77(3), pages 239-247, July.
    13. 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.
    14. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    15. 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.
    16. Leonhard Held & Manuela Ott, 2016. "How the Maximal Evidence of -Values Against Point Null Hypotheses Depends on Sample Size," The American Statistician, Taylor & Francis Journals, vol. 70(4), pages 335-341, October.
    17. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    18. Kim, Jae-Young, 2002. "Limited information likelihood and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 175-193, March.
    19. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    20. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    21. repec:cup:polals:v:26:y:2018:i:01:p:1-2_00 is not listed on IDEAS
    22. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    23. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    24. Gafarov, Bulat & Meier, Matthias & Montiel Olea, José Luis, 2018. "Delta-method inference for a class of set-identified SVARs," Journal of Econometrics, Elsevier, vol. 203(2), pages 316-327.
    25. Valentin Amrhein & Sander Greenland & Blake McShane, 2019. "Scientists rise up against statistical significance," Nature, Nature, vol. 567(7748), pages 305-307, March.
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    More about this item

    Keywords

    Frequentist; Hypothesis; Posterior; Testing;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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