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A Simple Panel Unit Root Test in the Presence of Cross Section Dependence

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  • Pesaran, M.H.

Abstract

A number of panel unit root tests that allow for cross section dependence have been proposed in the literature, notably by Bai and Ng (2002), Moon and Perron (2003) and Phillips and Sul (2002) who use orthogonalization type procedures to asymptotically eliminate the cross dependence of the series. In this paper we propose a simple alternative test where the standard DF (or ADF) regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series. A truncated version of the CADF statistics is also considered. New asymptotic results are obtained both for the individual CADF statistics and their simple averages. It is shown that the CADFi statistics are asymptotically similar and do not depend on the factor loadings under joint asymptotics where N (cross section dimension) and T (time series dimension) ? 8, such that N/T? k, where k is a fixed finite non-zero constant. But they are asymptotically correlated due to their dependence on the common factor. Despite this of the proposed tests are investigated by Monte Carlo experiments for a variety of models. It is shown that the cross sectionally augmented panel unit root tests have satisfactory size and power even for relatively small values of N and T. This is particularly true of cross sectionally augmented and truncated versions of the simple average t-test of Im, Pesaran and Shin, and Choi’s inverse normal combination test.

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Bibliographic Info

Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0346.

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Length: 72
Date of creation: Oct 2003
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Handle: RePEc:cam:camdae:0346

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Keywords: panel unit root tests; cross-section dependence; heterogeneous dynamic panels; finite sample properties;

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  1. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 8633, Universite de Montreal, Departement de sciences economiques.
  2. Im, K.S. & Pesaran, M.H., 2003. "On The Panel Unit Root Tests Using Nonlinear Instrumental Variables," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0347, Faculty of Economics, University of Cambridge.
  3. Pesaran, M. Hashem, 2004. "General Diagnostic Tests for Cross Section Dependence in Panels," IZA Discussion Papers 1240, Institute for the Study of Labor (IZA).
  4. Yongcheol Shin & Andy Snell, 2006. "Mean group tests for stationarity in heterogeneous panels," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 9(1), pages 123-158, 03.
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  7. Jushan Bai & Serena Ng, 2001. "A Panic Attack on Unit Roots and Cointegration," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 469, The Johns Hopkins University,Department of Economics.
  8. Yoosoon Chang, 2000. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1251, Cowles Foundation for Research in Economics, Yale University.
  9. Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics, Boston College Department of Economics 300., Boston College Department of Economics.
  10. MOON, Hyungsik Roger & PERRON, Benoit., 2002. "Testing for a Unit Root in Panels with Dynamic Factors," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2002-18, Universite de Montreal, Departement de sciences economiques.
  11. Levin, Andrew & Lin, Chien-Fu & James Chu, Chia-Shang, 2002. "Unit root tests in panel data: asymptotic and finite-sample properties," Journal of Econometrics, Elsevier, Elsevier, vol. 108(1), pages 1-24, May.
  12. Badi H. Baltagi & Chihwa Kao, 2000. "Nonstationary Panels, Cointegration in Panels and Dynamic Panels: A Survey," Center for Policy Research Working Papers, Center for Policy Research, Maxwell School, Syracuse University 16, Center for Policy Research, Maxwell School, Syracuse University.
  13. Meghir, Costas & Pistaferri, Luigi, 2002. "Income Variance Dynamics and Heterogeneity," CEPR Discussion Papers, C.E.P.R. Discussion Papers 3632, C.E.P.R. Discussion Papers.
  14. Pesaran, H.M., 2003. "Estimation and Inference in Large Heterogeneous Panels with Cross Section Dependence," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0305, Faculty of Economics, University of Cambridge.
  15. Leybourne, S J, 1995. "Testing for Unit Roots Using Forward and Reverse Dickey-Fuller Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(4), pages 559-71, November.
  16. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 942, Cowles Foundation for Research in Economics, Yale University.
  17. Timothy K. Chue & In Choi, 2007. "Subsampling hypothesis tests for nonstationary panels with applications to exchange rates and stock prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 22(2), pages 233-264.
  18. Harris, David & Leybourne, Stephen & McCabe, Brendan, 2005. "Panel Stationarity Tests for Purchasing Power Parity With Cross-Sectional Dependence," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 23, pages 395-409, October.
  19. Peter C.B.Phillips & Donggyu Sul, 2002. "Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1362, Cowles Foundation for Research in Economics, Yale University.
  20. David Bowman, 1999. "Efficient tests for autoregressive unit roots in panel data," International Finance Discussion Papers, Board of Governors of the Federal Reserve System (U.S.) 646, Board of Governors of the Federal Reserve System (U.S.).
  21. Harvey, A. & Bates, D., 2003. "Multivariate Unit Root Tests and Testing for Convergence," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0301, Faculty of Economics, University of Cambridge.
  22. Kaddour Hadri, 1999. "Testing For Stationarity In Heterogeneous Panel Data," Research Papers, University of Liverpool Management School 1999_04, University of Liverpool Management School.
  23. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, Elsevier, vol. 20(2), pages 249-272, April.
  24. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, Elsevier, vol. 115(1), pages 53-74, July.
  25. Maddala, G S & Wu, Shaowen, 1999. " A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 631-52, Special I.
  26. George Kapetanios, 2007. "Dynamic factor extraction of cross-sectional dependence in panel unit root tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 22(2), pages 313-338.
  27. Peter C.B. Phillips, 1995. "Unit Root Tests," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1104, Cowles Foundation for Research in Economics, Yale University.
  28. O'Connell, Paul G. J., 1998. "The overvaluation of purchasing power parity," Journal of International Economics, Elsevier, Elsevier, vol. 44(1), pages 1-19, February.
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