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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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File URL: http://econ-wpseries.com/2011/201107-2.pdf
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Bibliographic Info

Paper provided by University of Sydney, School of Economics in its series Working Papers with number 2011-07.

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Date of creation: Aug 2011
Date of revision: Feb 2014
Handle: RePEc:syd:wpaper:2123/7761

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Related research

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

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References

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  1. Bai, Jushan & Lumsdaine, Robin L & Stock, James H, 1998. "Testing for and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 395-432, July.
  2. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. 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.
  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. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  6. 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.).
  7. Zhongjun Qu & Pierre Perron, 2005. "Estimating and testing structural changes in multivariate regressions," Boston University - Department of Economics - Working Papers Series WP2005-012, Boston University - Department of Economics.
  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. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  11. Cochrane, John H, 1994. "Permanent and Transitory Components of GNP and Stock Prices," The Quarterly Journal of Economics, MIT Press, vol. 109(1), pages 241-65, February.
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Cited by:
  1. Donayre, Luiggi & Eo, Yunjong & Morley, James, 2014. "Improving Likelihood-Ratio-Based Confidence Intervals for Threshold Parameters in Finite Samples," Working Papers 2014-04, University of Sydney, School of Economics.

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