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The effect of recursive detrending on panel unit root tests

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  • Westerlund, Joakim

Abstract

This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.

Suggested Citation

  • Westerlund, Joakim, 2015. "The effect of recursive detrending on panel unit root tests," Journal of Econometrics, Elsevier, vol. 185(2), pages 453-467.
  • Handle: RePEc:eee:econom:v:185:y:2015:i:2:p:453-467
    DOI: 10.1016/j.jeconom.2014.06.015
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    References listed on IDEAS

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    Cited by:

    1. Herwartz, Helmut & Maxand, Simone & Walle, Yabibal M., 2017. "Heteroskedasticity-robust unit root testing for trending panels," Center for European, Governance and Economic Development Research Discussion Papers 314, University of Goettingen, Department of Economics.
    2. repec:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0784-5 is not listed on IDEAS
    3. Westerlund, Joakim & Narayan, Paresh, 2016. "Testing for predictability in panels of any time series dimension," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1162-1177.
    4. repec:nea:journl:y:2017:i:35:p:71-102 is not listed on IDEAS
    5. Skrobotov, Anton & Turuntseva, Marina, 2017. "Testing the Hypothesis of a Unit Root for Independent Panels," Working Papers 021707, Russian Presidential Academy of National Economy and Public Administration.

    More about this item

    Keywords

    Unit root test; Panel data; Deterministic trend; Polynomial trend function; Recursive detrending;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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