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A Modified Confidence Set for the Structural Break Date in Linear Regression Models

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  • Yamamoto, Yohei

Abstract

Elliott and Müller (2007) (EM) provides a method to construct a confidence set for the structural break date by inverting a locally best test statistic. Previous studies show that the EM method produces a set with an accurate coverage ratio even for a small break, however, the set is often overly lengthy. This study proposes a simple modification to rehabilitate their method. Following the literature, we provide an asymptotic justification for the modified method under a nonlocal asymptotic framework. A Monte Carlo simulation shows that like the original method, the modified method exhibits a coverage ratio that is very close to the nominal level. More importantly, it achieves a much shorter confidence set. Hence, when the break is small, the modified method serves as a better alternative to Bai's (1997) confidence set. We apply these methods to a small level shift in post-1980s Japanese inflation data.

Suggested Citation

  • 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.
  • Handle: RePEc:hit:econdp:2014-08
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    File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/26678/3/070econDP14-08.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. 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.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    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 953-966, July.
    6. Pierre Perron & Yohei Yamamoto, 2016. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 782-844, May.
    7. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    8. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 10372, University Library of Munich, Germany.
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    Cited by:

    1. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.
    2. Skrobotov Anton & Eiji Kurozumi, 2016. "Confidence Sets for the Break Date in Cointegrating Regressions," Working Papers wpaper-2016-268, Gaidar Institute for Economic Policy, revised 2016.
    3. 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.
    4. KUROZUMI, Eiji, 2017. "Confidence Sets for the Date of a Mean Shift at the End of a Sample," Discussion Papers 2017-06, Graduate School of Economics, Hitotsubashi University.

    More about this item

    Keywords

    coverage ratio; nonlocal asymptotics; heteroskedasticity and autocorrelation consistent covariance; condence set;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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