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Testing for Breaks in Coefficients and Error Variance: Simulations and Applications

Author

Listed:
  • Jing Zhou

    (BlackRock, Inc.)

  • Pierre Perron

    (Boston University)

Abstract

In a companion paper, Perron and Zhou (2008) provided a comprehensive treatment of the problem of testing jointly for structural change in both the regression coefficients and the variance of the errors in a single equation regression model involving stationary regressors, allowing the break dates for the two components to be different or overlap. The aim of this paper is twofold. First, we present detailed simulation analyses to document various issues related to their procedures: a) the inadequacy of the two step procedures that are commonly applied; b) which particular version of the necessary correction factor exhibits better finite sample properties; c) whether applying a correction that is valid under more general conditions than necessary is detrimental to the size and power of the tests; d) the finite sample size and power of the various tests proposed; e) the performance of the sequential method in determining the number and types of breaks present. Second, we apply their testing procedures to various macroeconomic time series studied by Stock and Watson (2002). Our results reinforce the prevalence of change in mean, persistence and variance of the shocks to these series, and the fact that for most of them an important reduction in variance occurred during the 1980s. In many cases, however, the so-called “great moderation” should instead be viewed as a “great reversion”.

Suggested Citation

  • Jing Zhou & Pierre Perron, 2008. "Testing for Breaks in Coefficients and Error Variance: Simulations and Applications," Boston University - Department of Economics - Working Papers Series wp2008-010, Boston University - Department of Economics.
    • Handle: RePEc:bos:wpaper:wp2008-010
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    References listed on IDEAS

    as
    1. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, August.
    2. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.
    3. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230, National Bureau of Economic Research, Inc.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    5. Olivier Blanchard & John Simon, 2001. "The Long and Large Decline in U.S. Output Volatility," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 32(1), pages 135-174.
    6. Corbae,Dean & Durlauf,Steven N. & Hansen,Bruce E. (ed.), 2006. "Econometric Theory and Practice," Cambridge Books, Cambridge University Press, number 9780521807234.
    7. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(3), pages 809-822, June.
    8. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    9. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    10. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    11. Jushan Bai & Pierre Perron, 2003. "Critical values for multiple structural change tests," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 72-78, June.
    12. 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.
    13. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, vol. 102(2), pages 78-82, February.
    14. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    15. Chang-Jin Kim & Charles R. Nelson, 1999. "Has The U.S. Economy Become More Stable? A Bayesian Approach Based On A Markov-Switching Model Of The Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 608-616, November.
    16. Herrera, Ana Maria & Pesavento, Elena, 2005. "The Decline in U.S. Output Volatility: Structural Changes and Inventory Investment," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 462-472, October.
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    Cited by:

    1. María Dolores Gadea & Ana Gómez-Loscos & Antonio Montañés, 2016. "Oil Price and Economic Growth: A Long Story?," Econometrics, MDPI, vol. 4(4), pages 1-28, October.
    2. Amélie Charles & Olivier Darné & Laurent Ferrara, 2018. "Does The Great Recession Imply The End Of The Great Moderation? International Evidence," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 745-760, April.
    3. Amélie Charles & Olivier Darné & Laurent Ferrara, 2018. "Does The Great Recession Imply The End Of The Great Moderation? International Evidence," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 745-760, April.
    4. Soo-Bin Jeong & Bong-Hwan Kim & Tae-Hwan Kim & Hyung-Ho Moon, 2017. "Unit Root Tests In The Presence Of Multiple Breaks In Variance," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 62(02), pages 345-361, June.
    5. Loredana Ureche-Rangau & Franck Speeg, 2011. "A simple method for variance shift detection at unknown time points," Economics Bulletin, AccessEcon, vol. 31(3), pages 2204-2218.

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    More about this item

    Keywords

    Change-point; Variance shift; Conditional heteroskedasticity; Likelihood ratio tests; the “Great moderation.”;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

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