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Covariate Unit Root Test for Cross-Sectionally Dependent Panel Data

  • Eiji Kurozumi
  • Daisuke Yamazaki
  • Kaddour Hadri

This paper proposes the use of covariate unit root tests and the exploitation of the information on the cross-sectional dependence when the panel data null hypothesis of a unit root is rejected or when N is relatively small in order to help the interpretation of the test results. In particular, it investigates the optimal point optimal covariate unit root test by Juhl and Xiao (2003), which is based on the theory by Hansen (1995) and Elliott and Jansson (2003). We first compare the asymptotic power function of the covariate test with those of panel unit root tests and show that the covariate unit root test can be potentially more powerful than panel unit root tests when the cross-sectional dimension is not so large. We also suggest several methods to choose appropriate covariates. The Monte Carlo simulations show that some of our methods work fairly well compared with the simple method of using only one covariate. Using our methods, we investigate the Prebish-Singer hypothesis for nine commodity prices and find that this hypothesis holds except for the price of petroleum. We also examine the PPP hypothesis employing eight real exchange rates of developed economies relative to the US dollar.

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File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd12-256.pdf
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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd12-256.

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Date of creation: Nov 2012
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Handle: RePEc:hst:ghsdps:gd12-256
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  1. Pesaran, M.H., 2003. "A Simple Panel Unit Root Test in the Presence of Cross Section Dependence," Cambridge Working Papers in Economics 0346, Faculty of Economics, University of Cambridge.
  2. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  3. S. de Silva & K. Hadri & A. R. Tremayne, 2009. "Panel unit root tests in the presence of cross-sectional dependence: finite sample performance and an application," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 340-366, 07.
  4. Kaddour Hadri & Eiji Kurozumi, 2008. "A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence," Global COE Hi-Stat Discussion Paper Series gd08-016, Institute of Economic Research, Hitotsubashi University.
  5. 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.
  6. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  7. 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.
  8. Jushan Bai & Serena Ng, 2001. "A PANIC Attack on Unit Roots and Cointegration," Boston College Working Papers in Economics 519, Boston College Department of Economics.
  9. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  10. Elliott, Graham & Jansson, Michael, 2002. "Testing for Unit Roots with Stationary Covariates," University of California at San Diego, Economics Working Paper Series qt4v35s2gv, Department of Economics, UC San Diego.
  11. Hadri, Kaddour & Kurozumi, Eiji, 2012. "A simple panel stationarity test in the presence of serial correlation and a common factor," Economics Letters, Elsevier, vol. 115(1), pages 31-34.
  12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  13. 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, vol. 23, pages 395-409, October.
  14. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April.
  15. Eiji Kurozumi & Shinya Tanaka, 2010. "Reducing the size distortion of the KPSS test," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 415-426, November.
  16. Chang, Yoosoon, 2002. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," Working Papers 2000-08, Rice University, Department of Economics.
  17. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  18. 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.
  19. Elliott, Graham & Pesavento, Elena, 2006. "On the Failure of Purchasing Power Parity for Bilateral Exchange Rates after 1973," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(6), pages 1405-1430, September.
  20. Juhl, Ted & Xiao, Zhijie, 2003. "Power Functions And Envelopes For Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(02), pages 240-253, April.
  21. Jomana Amara & David Papell, 2006. "Testing for Purchasing Power Parity using stationary covariates," Applied Financial Economics, Taylor & Francis Journals, vol. 16(1-2), pages 29-39.
  22. Christopoulos, Dimitris K. & León-Ledesma, Miguel A., 2008. "Time-series output convergence tests and stationary covariates," Economics Letters, Elsevier, vol. 101(3), pages 297-299, December.
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