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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.

Suggested Citation

  • 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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    1. Chang-Jin Kim & James Morley & Jeremy Piger, 2008. "Bayesian counterfactual analysis of the sources of the great moderation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(2), pages 173-191.
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    6. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    7. 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.
    8. Yohei Yamamoto, 2018. "A modified confidence set for the structural break date in linear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 37(9), pages 974-999, October.
    9. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
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    11. John H. Cochrane, 1994. "Permanent and Transitory Components of GNP and Stock Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 109(1), pages 241-265.
    12. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    13. 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.
    14. Karl Whelan, 2000. "A guide to the use of chain aggregated NIPA data," Finance and Economics Discussion Series 2000-35, Board of Governors of the Federal Reserve System (U.S.).
    15. 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.
    16. Eiji Kurozumi & Yohei Yamamoto, 2015. "Confidence sets for the break date based on optimal tests," Econometrics Journal, Royal Economic Society, vol. 18(3), pages 412-435, October.
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    Citations

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    Cited by:

    1. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    2. Eo, Yunjong & Morley, James, 2017. "Why has the U.S. economy stagnated since the Great Recession?," Working Papers 2017-14, University of Sydney, School of Economics.
    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. 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.
    5. repec:taf:emetrv:v:36:y:2017:i:6-9:p:667-698 is not listed on IDEAS
    6. 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.
    7. 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.
    8. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    9. repec:exl:29stat:v:19:y:2018:i:1:p:7-23 is not listed on IDEAS
    10. repec:gam:jecnmx:v:6:y:2018:i:2:p:27-:d:148392 is not listed on IDEAS

    More about this item

    Keywords

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

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