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Likelihood-Ratio-Based Confidence Sets for the Timing of Structural Breaks

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  • Eo, Yunjong
  • Morley, James

Abstract

We propose the use of likelihood-ratio-based confidence sets for the timing of structural breaks in parameters from time series regression models. The confidence sets are valid for the broad setting of a system of multivariate linear regression equations under fairly general assumptions about the error and regressors and allowing for multiple breaks in mean and variance parameters. In our asymptotic analysis, we determine the critical values for a likelihood ratio test of a break date and the expected length of a confidence set constructed by inverting the likelihood ratio test. Notably, the likelihood-ratio-based confidence sets are more precise than other confidence sets considered in the literature. Monte Carlo analysis confirms their greater precision in finite samples, including in terms of maintaining accurate coverage even when the sample size or magnitude of a break is small. An application to postwar U.S. real GDP and consumption leads to a shorter 95% confidence set for the timing of the “Great Moderation” in the mid-1980s than previously found in the literature. Furthermore, when taking cointegration between output and consumption into account, confidence sets for structural break dates become even shorter and suggest a “productivity growth slowdown” in the early 1970s and an additional large, abrupt decline in long-run growth in the mid-1990s.

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  • Eo, Yunjong & Morley, James, 2011. "Likelihood-Ratio-Based Confidence Sets for the Timing of Structural Breaks," Working Papers 2011-07, University of Sydney, School of Economics, revised Feb 2014.
  • Handle: RePEc:syd:wpaper:2123/7761
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    References listed on IDEAS

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    Cited by:

    1. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    2. Yunjong Eo & James Morley, 2022. "Why Has the U.S. Economy Stagnated since the Great Recession?," The Review of Economics and Statistics, MIT Press, vol. 104(2), pages 246-258, May.
    3. Donayre Luiggi & Eo Yunjong & Morley James, 2018. "Improving likelihood-ratio-based confidence intervals for threshold parameters in finite samples," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(1), pages 1-11, February.
    4. 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.
    5. Günes Kamber & Madhusudan Mohanty & James Morley, 2020. "What drives inflation in advanced and emerging market economies?," BIS Papers chapters, in: Bank for International Settlements (ed.), Inflation dynamics in Asia and the Pacific, volume 111, pages 21-36, Bank for International Settlements.
    6. Agiwal Varun & Kumar Jitendra & Shangodoyin Dahud Kehinde, 2018. "A Bayesian Inference Of Multiple Structural Breaks In Mean And Error Variance In Panelar (1) Model," Statistics in Transition New Series, Polish Statistical Association, vol. 19(1), pages 7-23, March.
    7. Benjamin Wong, 2015. "Do Inflation Expectations Propagate the Inflationary Impact of Real Oil Price Shocks?: Evidence from the Michigan Survey," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 47(8), pages 1673-1689, December.
    8. Polbin, Andrey & Fokin, Nikita, 2017. "К Вопросу О Долгосрочной Взаимосвязи Реального Потребления Домохозяйств С Реальным Доходом В Рф [A note on cointegration relationship between real consumption and real income in Russia]," MPRA Paper 82451, University Library of Munich, Germany, revised Nov 2017.
    9. Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2017. "The asymptotic behaviour of the residual sum of squares in models with multiple break points," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 667-698, October.
    10. Varun Agiwal & Jitendra Kumar & Dahud Kehinde Shangodoyin, 2018. "A Bayesian Inference Of Multiple Structural Breaks In Mean And Error Variance In Panel Ar (1) Model," Statistics in Transition New Series, Polish Statistical Association, vol. 19(1), pages 7-23, March.
    11. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    12. 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.
    13. Karsten Schweikert, 2022. "Detecting Multiple Structural Breaks in Systems of Linear Regression Equations with Integrated and Stationary Regressors," Papers 2201.05430, arXiv.org, revised Aug 2023.
    14. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    15. Güneş Kamber & Madhusudan Mohanty & James Morley, 2020. "Have the driving forces of inflation changed in advanced and emerging market economies?," BIS Working Papers 896, Bank for International Settlements.
    16. Harris, David & Kew, Hsein & Taylor, A.M. Robert, 2020. "Level shift estimation in the presence of non-stationary volatility with an application to the unit root testing problem," Journal of Econometrics, Elsevier, vol. 219(2), pages 354-388.
    17. James Morley & Aarti Singh, 2016. "Inventory Shocks and the Great Moderation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(4), pages 699-728, June.
    18. Eiji Kurozumi, 2018. "Confidence Sets for the Date of a Structural Change at the End of a Sample," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 850-862, November.

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    Keywords

    Inverted Likelihood Ratio; Multiple Breaks; System of Equations; Great Moderation; Productivity Growth Slowdown.;
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