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On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests

Author

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  • Pierre Perron

    () (Boston University)

  • Yohei Yamamoto

    () (Boston University)

Abstract

Elliott and Müller (2006) considered the problem of testing for general types of parameter variations, including infrequent breaks. They developed a framework that yields optimal tests, in the sense that they nearly attain some local Gaussian power envelop. The main ingredient in their setup is that the variance of the process generating the changes in the parameters must go to zero at a fast rate. They recommended the so-called qLˆL test, a partial sums type test based on the residuals obtained from the restricted model. We show that for breaks that are very small, its power is indeed higher than other tests, including the popular sup-Wald test. However, the differences are very minor. When the magnitude of change is moderate to large, the power of the test is very low in the context of a regression with lagged dependent variables or when a correction is applied to account for serial correlation in the errors. In many cases, the power goes to zero as the magnitude of change increases. The power of the sup-Wald test does not show this non-monotonicity and its power is far superior to the qLˆL test when the break is not very small. We claim that the optimality of the qLˆL test does not come from the properties of the test statistics but the criterion adopted, which is not useful to analyze structural change tests. Instead, we use the concept of the relative approximate Bahadur slopes to assess the relative efficiency of two tests. When doing so, it is shown that the sup-Wald test indeed dominates the qLˆL test and, in many cases, the latter has zero relative asymptotic efficiency.

Suggested Citation

  • Pierre Perron & Yohei Yamamoto, 2008. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Boston University - Department of Economics - Working Papers Series wp2008-006, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2008-006
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    References listed on IDEAS

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    Cited by:

    1. repec:eee:econom:v:204:y:2018:i:1:p:66-85 is not listed on IDEAS
    2. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    3. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    4. 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.
    5. HORIE, Tetsushi & YAMAMOTO, Yohei, 2016. "Testing for Speculative Bubbles in Large-Dimensional Financial Panel Data Sets," Discussion Papers 2016-04, Graduate School of Economics, Hitotsubashi University.
    6. Seongyeon Chang & Pierre Perron, 2013. "A Comparison of Alternative Methods to Construct to Confidence Intervals for the Estimate of a Break Date in Linear Regression Models," Boston University - Department of Economics - Working Papers Series 2013-023, Boston University - Department of Economics.
    7. 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.
    8. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    9. YAMAZAKI, Daisuke & KUROZUMI, Eiji, 2014. "Improving the Finite Sample Performance of Tests for a Shift in Mean," Discussion Papers 2014-16, Graduate School of Economics, Hitotsubashi University.

    More about this item

    Keywords

    structural change; local asymptotics; Bahadur efficiency; hypothesis testing; parameter variations;

    JEL classification:

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

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