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

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Author Info
Pesaran, M.H.

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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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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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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. O'Connell, Paul G. J., 1998. "The overvaluation of purchasing power parity," Journal of International Economics, Elsevier, vol. 44(1), pages 1-19, February. [Downloadable!] (restricted)
  2. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
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  3. Costas Meghir & Luigi Pistaferri, 2004. "Income Variance Dynamics and Heterogeneity," Econometrica, Econometric Society, vol. 72(1), pages 1-32, 01. [Downloadable!] (restricted)
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  4. 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., vol. 22(2), pages 233-264. [Downloadable!]
  5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July. [Downloadable!] (restricted)
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  6. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April. [Downloadable!] (restricted)
  7. David Bowman, 1999. "Efficient tests for autoregressive unit roots in panel data," International Finance Discussion Papers 646, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  8. Hashem Pesaran, M., 2007. "A pair-wise approach to testing for output and growth convergence," Journal of Econometrics, Elsevier, vol. 138(1), pages 312-355, May. [Downloadable!] (restricted)
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  9. Gengenbach,Christian & Palm,Franz & Urbain,Jean-Pierre, 2004. "Panel Unit Root Tests in the Presence of Cross-Sectional Dependencies: Comparison and Implications for Modelling," Research Memoranda 040, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  10. Harvey, A. & Bates, D., 2003. "Multivariate Unit Root Tests and Testing for Convergence," Cambridge Working Papers in Economics 0301, Faculty of Economics, University of Cambridge. [Downloadable!]
  11. Pesaran, H.M., 2003. "Estimation and Inference in Large Heterogeneous Panels with Cross Section Dependence," Cambridge Working Papers in Economics 0305, Faculty of Economics, University of Cambridge. [Downloadable!]
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  12. 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. [Downloadable!] (restricted)
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  13. Pesaran, M.H., 2004. "‘General Diagnostic Tests for Cross Section Dependence in Panels’," Cambridge Working Papers in Economics 0435, Faculty of Economics, University of Cambridge. [Downloadable!]
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  14. Yongcheol Shin & Andy Snell, 2006. "Mean group tests for stationarity in heterogeneous panels," Econometrics Journal, Royal Economic Society, vol. 9(1), pages 123-158, 03. [Downloadable!] (restricted)
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  15. Kaddour Hadri, 2000. "Testing for stationarity in heterogeneous panel data," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 148-161.
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  16. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, 07. [Downloadable!] (restricted)
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  17. MOON, Hyungsik Roger & PERRON, Benoit., 2002. "Testing for a Unit Root in Panels with Dynamic Factors," Cahiers de recherche 2002-18, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  18. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July. [Downloadable!] (restricted)
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  19. Yoosoon Chang, 2000. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Cowles Foundation Discussion Papers 1251, Cowles Foundation, Yale University. [Downloadable!]
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  20. George Kapetanios, 2007. "Dynamic factor extraction of cross-sectional dependence in panel unit root tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 313-338. [Downloadable!]
  21. Im, K.S. & Pesaran, M.H., 2003. "On The Panel Unit Root Tests Using Nonlinear Instrumental Variables," Cambridge Working Papers in Economics 0347, Faculty of Economics, University of Cambridge. [Downloadable!]
  22. Yoosoon Chang, 2000. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," CIRJE F-Series CIRJE-F-85, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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  23. 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.
  24. 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, vol. 108(1), pages 1-24, May. [Downloadable!] (restricted)
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  25. Peter C.B. Phillips, 1995. "Unit Root Tests," Cowles Foundation Discussion Papers 1104, Cowles Foundation, Yale University. [Downloadable!]
  26. 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. [Downloadable!] (restricted)
  27. Yongcheol Shin & Andy Snell, 2004. "Testing for Stationarity in Heterogeneous Panels with Serially Correlated Errors," ESE Discussion Papers 70, Edinburgh School of Economics, University of Edinburgh.
  28. Badi H. Baltagi & Chihwa Kao, 2000. "Nonstationary Panels, Cointegration in Panels and Dynamic Panels: A Survey," Center for Policy Research Working Papers 16, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  29. Peter C.B.Phillips & Donggyu Sul, 2002. "Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence," Cowles Foundation Discussion Papers 1362, Cowles Foundation, Yale University. [Downloadable!]
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