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Asymptotically Ump Panel Unit Root Tests—The Effect Of Heterogeneity In The Alternatives

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  • Gaia Becheri, I.
  • Drost, Feike C.
  • Akker, Ramon van den

Abstract

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

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  • Gaia Becheri, I. & Drost, Feike C. & Akker, Ramon van den, 2015. "Asymptotically Ump Panel Unit Root Tests—The Effect Of Heterogeneity In The Alternatives," Econometric Theory, Cambridge University Press, vol. 31(3), pages 539-559, June.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:03:p:539-559_00
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    Cited by:

    1. Samuel Brien & Michael Jansson & Morten Ørregaard Nielsen, 2022. "Nearly Efficient Likelihood Ratio Tests of a Unit Root in an Autoregressive Model of Arbitrary Order," Working Paper 1429, Economics Department, Queen's University.
    2. Norkutė, Milda & Westerlund, Joakim, 2021. "The factor analytical approach in near unit root interactive effects panels," Journal of Econometrics, Elsevier, vol. 221(2), pages 569-590.
    3. 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.
    4. Westerlund, Joakim & Larsson, Rolf, 2015. "New tools for understanding the local asymptotic power of panel unit root tests," Journal of Econometrics, Elsevier, vol. 188(1), pages 59-93.
    5. Becheri, I. Gaia & Drost, Feike C. & van den Akker, Ramon & Wichert, Oliver, 2016. "The power envelope of panel unit root tests in case stationary alternatives offset explosive ones," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 1-8.

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