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Asymptotically UMP Panel Unit Root Tests

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  • Becheri, I.G.
  • Drost, F.C.
  • Akker, R. van den

    (Tilburg University, Center for Economic Research)

Abstract

Abstract This paper considers optimal unit root tests for a Gaussian cross-sectionally independent heterogeneous panel with incidental intercepts and heterogeneous alternatives generated by random perturbations. We derive the (asymptotic and local) power envelope for two models: an auxiliary model where both the panel units and the random perturbations are observed, and the second one, the model of main interest, for which only the panel units are observed. We show that both models are Locally Asymptotically Normal (LAN). It turns out that there is an information loss: the power envelope for the auxiliary model is above the envelope for the model of main interest. Equality only holds if the alternatives are homogeneous. Our results exactly identify in which setting the unit root test of Moon, Perron, and Phillips (2007) is asymptotically UMP and, in fact, they show it is not possible to exploit possible heterogeneity in the alternatives, confirming a conjecture of Breitung and Pesaran (2008). Moreover, we propose a new asymptotically optimal test and we extend the results to a model allowing for cross-sectional dependence.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2013-017.

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Date of creation: 2013
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Handle: RePEc:dgr:kubcen:2013017

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Web page: http://center.uvt.nl

Related research

Keywords: panel unit root test; Local Asymptotic Normality; limit experiment; asymptotic power envelope; information loss;

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References

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  1. Moon, H.R.Hyungsik Roger & Perron, Benoit, 2004. "Testing for a unit root in panels with dynamic factors," Journal of Econometrics, Elsevier, vol. 122(1), pages 81-126, September.
  2. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Sakkas, Nikolaos D., 2010. "Local Asymptotic Power Of The Im-Pesaran-Shin Panel Unit Root Test And The Impact Of Initial Observations," Econometric Theory, Cambridge University Press, vol. 26(01), pages 311-324, February.
  3. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2011. "A class of simple distribution-free rank-based unit root tests," Journal of Econometrics, Elsevier, vol. 163(2), pages 200-214, August.
  4. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
  5. Drost, F.C. & Akker, R. van den & Werker, B.J.M., 2009. "The asymptotic structure of nearly unstable non negative integer-valued AR(1) models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3106433, Tilburg University.
  6. Hyungsik Roger Moon & Benoit Perron & Peter C.B. Phillips, 2003. "Incidental Trends and the Power of Panel Unit Root Tests," Cowles Foundation Discussion Papers 1435, Cowles Foundation for Research in Economics, Yale University.
  7. Samarjit Das & Joerg Breitung, 2004. "Panel Unit Root Tests under Cross- sectional Dependence," Econometric Society 2004 North American Summer Meetings 55, Econometric Society.
  8. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, April.
  9. Banerjee, Anindya, 1999. " Panel Data Unit Roots and Cointegration: An Overview," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 607-29, Special I.
  10. Michael Jansson, 2007. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," CREATES Research Papers 2007-12, School of Economics and Management, University of Aarhus.
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