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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. 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.
  2. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  3. Hadri, Kaddour & Kurozumi, Eiji, 2008. "A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence," CCES Discussion Paper Series 7, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
  4. 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.
  5. Jushan Bai & Serena Ng, 2001. "A Panic Attack on Unit Roots and Cointegration," Economics Working Paper Archive 469, The Johns Hopkins University,Department of Economics.
  6. Eiji Kurozumi & Shinya Tanaka, 2009. "Reducing the Size Distortion of the KPSS Test," Global COE Hi-Stat Discussion Paper Series gd09-085, Institute of Economic Research, Hitotsubashi University.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, vol. 115(1), pages 75-89, July.
  14. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  15. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  16. 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.
  17. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
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