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Local asymptotic power of the Im-Pesaran-Shin panel unit root test and the impact of initial observations

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  • David Harris
  • David I. Harvey
  • Stephen J. Leybourne
  • Nikoloas D. Sakkas

Abstract

In this note we derive the local asymptotic power function of the standardized averaged Dickey-Fuller panel unit root statistic of Im, Pesaran and Shin (2003, Journal of Econometrics, 115, 53-74), allowing for heterogeneous deterministic intercept terms. We consider the situation where the deviation of the initial observation from the underlying intercept term in each individual time series may not be asymptotically negligible. We find that power decreases monotonically as the absolute values of the initial conditions increase in magnitude, in direct contrast to the univariate case. Finite sample simulations confirm the relevance of this result for practical applications, demonstrating that the power of the test can be very low for values of T and N typically encountered in practice.

Suggested Citation

  • David Harris & David I. Harvey & Stephen J. Leybourne & Nikoloas D. Sakkas, 2008. "Local asymptotic power of the Im-Pesaran-Shin panel unit root test and the impact of initial observations," Discussion Papers 08/02, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:08/02
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    1. Patrick Sevestre & Laszlo Matyas, 2008. "The Econometrics of Panel Data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00279977, HAL.
    2. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    3. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 115(1), pages 53-74, July.
    4. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
    5. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1, April.
    6. David I. Harvey & Stephen J. Leybourne, 2005. "On testing for unit roots and the initial observation," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 97-111, March.
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    Cited by:

    1. Becheri, I.G. & Drost, F.C. & van den Akker, R., 2013. "Asymptotically UMP Panel Unit Root Tests," Discussion Paper 2013-017, Tilburg University, Center for Economic Research.
    2. Valerija Botric, 2013. "Output Convergence between Western Balkans and EU-15," Research in Economics and Business: Central and Eastern Europe, Tallinn School of Economics and Business Administration, Tallinn University of Technology, vol. 5(1).
    3. Pesaran, M. Hashem & Vanessa Smith, L. & Yamagata, Takashi, 2013. "Panel unit root tests in the presence of a multifactor error structure," Journal of Econometrics, Elsevier, vol. 175(2), pages 94-115.
    4. Yiannis Karavias & Elias Tzavalis, 2016. "Local Power of Fixed-T Panel Unit Root Tests With Serially Correlated Errors and Incidental Trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 222-239, March.
    5. Joakim Westerlund & Jörg Breitung, 2013. "Lessons from a Decade of IPS and LLC," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 547-591, August.
    6. Westerlund, Joakim & Larsson, Rolf, 2012. "Testing for a unit root in a random coefficient panel data model," Journal of Econometrics, Elsevier, vol. 167(1), pages 254-273.
    7. Becheri, I.G. & Drost, F.C. & van den Akker, R., 2013. "Asymptotically UMP Panel Unit Root Tests," Other publications TiSEM e34b7d23-8e53-4cea-ba69-5, Tilburg University, School of Economics and Management.
    8. Karavias, Yiannis & Tzavalis, Elias, 2013. "The Power Performance of Fixed-T Panel Unit Root Tests allowing for Structural Breaks," MPRA Paper 46012, University Library of Munich, Germany.
    9. Pedroni, Peter L. & Vogelsang, Timothy J. & Wagner, Martin & Westerlund, Joakim, 2015. "Nonparametric rank tests for non-stationary panels," Journal of Econometrics, Elsevier, vol. 185(2), pages 378-391.
    10. Chingnun Lee & Jyh-Lin Wu & Lixiong Yang, 2016. "A Simple Panel Unit-Root Test with Smooth Breaks in the Presence of a Multifactor Error Structure," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 365-393, June.
    11. Stauskas, Ovidijus, 2019. "On the Limit Theory of Mixed to Unity VARs: Panel Setting With Weakly Dependent Errors," Working Papers 2019:2, Lund University, Department of Economics.
    12. Kajal Lahiri & Zhongwen Liang & Huaming Peng, 2017. "The Local Power of the IPS Test with Both Initial Conditions and Incidental Trends," CESifo Working Paper Series 6313, CESifo.
    13. Yiannis Karavias & Elias Tzavalis, 2012. "The local power of fixed-T panel unit root tests allowing for serially correlated errors," Discussion Papers 12/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    14. Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Marina (Турунцева, Марина), 2017. "Testing the Hypothesis of a Unit Root for Independent Panels [Тестирование Гипотезы О Наличии Единичного Корня Для Независимых Панелей]," Working Papers 021707, Russian Presidential Academy of National Economy and Public Administration.
    15. Westerlund, Joakim, 2015. "The power of PANIC," Journal of Econometrics, Elsevier, vol. 185(2), pages 495-509.

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