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Asymptotic properties of Bayesian inference in linear regression with a structural break

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  • Shimizu, Kenichi
Abstract
This paper studies large sample properties of a Bayesian approach to inference about slope parameters γ in linear regression models with a structural break. In contrast to the conventional approach to inference about γ that does not take into account the uncertainty of the unknown break date, the Bayesian approach that we consider incorporates such uncertainty. Our main theoretical contribution is a Bernstein–von Mises type theorem (Bayesian asymptotic normality) for γ under a wide class of priors, which essentially indicates an asymptotic equivalence between the conventional frequentist and Bayesian inference. Consequently, a frequentist researcher could look at credible intervals of γ to check robustness with respect to the uncertainty of the break date. Simulation studies show that the conventional confidence intervals of γ tend to undercover in finite samples whereas the credible intervals offer more reasonable coverages in general. As the sample size increases, the two methods coincide, as predicted from our theoretical conclusion. Using data from Paye and Timmermann (2006) on stock return prediction, we illustrate that the traditional confidence intervals on γ might underrepresent the true sampling uncertainty.

Suggested Citation

  • Shimizu, Kenichi, 2023. "Asymptotic properties of Bayesian inference in linear regression with a structural break," Journal of Econometrics, Elsevier, vol. 235(1), pages 202-219.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:1:p:202-219
    DOI: 10.1016/j.jeconom.2022.03.006
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    1. Casini, Alessandro & Perron, Pierre, 2022. "Generalized Laplace Inference In Multiple Change-Points Models," Econometric Theory, Cambridge University Press, vol. 38(1), pages 35-65, February.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
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    6. Casini, Alessandro & Perron, Pierre, 2021. "Continuous record Laplace-based inference about the break date in structural change models," Journal of Econometrics, Elsevier, vol. 224(1), pages 3-21.
    7. Hong, Han & Preston, Bruce, 2012. "Bayesian averaging, prediction and nonnested model selection," Journal of Econometrics, Elsevier, vol. 167(2), pages 358-369.
    8. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    9. Paye, Bradley S. & Timmermann, Allan, 2006. "Instability of return prediction models," Journal of Empirical Finance, Elsevier, vol. 13(3), pages 274-315, June.
    10. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    11. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
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    Cited by:

    1. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.

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