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Likelihood-Based Confidence Sets for the Timing of Structural Breaks

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  • Yunjong Eo

    () (School of Economics, the University of Sydney)

  • James Morley

    () (School of Economics, the University of New South Wales)

Abstract

We propose the use of likelihood-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 likelihood-based confidence set constructed by inverting the likelihood ratio test. Notably, the likelihood-based confidence set is considerably shorter than for other methods employed in the literature. Monte Carlo analysis confirms better performance than other methods in terms of length and coverage accuracy in finite samples, including when the magnitude of breaks is small. An application to postwar U.S. real GDP and consumption leads to a much tighter 95% confidence set for the timing of the "Great Moderation" in the mid-1980s than previously found. Furthermore, when taking cointegration between output and consumption into account, confidence sets for structural break dates are even more precise and suggest a sudden "productivity growth slowdown" in the early 1970s and an additional large, abrupt decline in long-run growth in the mid-1990s.

Suggested Citation

  • Yunjong Eo & James Morley, 2013. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," Discussion Papers 2013-12, School of Economics, The University of New South Wales.
  • Handle: RePEc:swe:wpaper:2013-12
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2013-12.pdf
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    References listed on IDEAS

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    1. 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.
    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.
    3. Diebold, Francis X. & Chen, Celia, 1996. "Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures," Journal of Econometrics, Elsevier, vol. 70(1), pages 221-241, January.
    4. 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.
    5. Kurozumi, Eiji & Tuvaandorj, Purevdorj, 2011. "Model selection criteria in multivariate models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 164(2), pages 218-238, October.
    6. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages 2-18, September.
    7. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    8. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    9. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    10. 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.
    11. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
    12. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    13. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    14. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
    15. 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.
    16. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    17. Cogley, Timothy, 2005. "How fast can the new economy grow? A Bayesian analysis of the evolution of trend growth," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 179-207, June.
    18. 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.
    19. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    20. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
    21. 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.
    22. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
    23. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
    24. Jushan Bai & Robin L. Lumsdaine & James H. Stock, 1998. "Testing For and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 395-432.
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    Citations

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    Cited by:

    1. Morley, James & Singh, Aarti, 2009. "Inventory Mistakes and the Great Moderation," Working Papers 2009-04, University of Sydney, School of Economics, revised Feb 2015.
    2. Seong Yeon Chang & Pierre Perron, 2013. "A Comparison of Alternative Methods to Construct Confidence Intervals for the Estimate of a Break Date in Linear Regression Models," Boston University - Department of Economics - Working Papers Series wp2015-010, Boston University - Department of Economics, revised 11 Oct 2015.
    3. Yamamoto, Yohei, 2014. "A Modified Confidence Set for the Structural Break Date in Linear Regression Models," Discussion Papers 2014-08, Graduate School of Economics, Hitotsubashi University.
    4. Luo, Sui & Startz, Richard, 2014. "Is it one break or ongoing permanent shocks that explains U.S. real GDP?," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 155-163.
    5. Morley, James & Singh, Aarti, 2009. "Inventory Mistakes and the Great Moderation," Working Papers 2009-04, University of Sydney, School of Economics, revised Oct 2012.

    More about this item

    Keywords

    Inverted Likelihood Ratio Confidence Sets; Multiple Breaks; Great Moderation; Productivity Growth Slowdown;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

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