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Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency

  • Yoosoon Chang

    (Rice Univerisity and University of Tokyo)

We propose a unit root test for panels with cross-sectional dependency. We allow general dependency structure among the innovations that generate data for each of the cross-sectional units. Each unit may have different sample size, and therefore unbalanced panels are also permitted in our framework. Yet, the test is asymptotically normal, and does not require any tabulation of the critical values. Our test is based on nonlinear IV estimation of the usual ADF type regression for each cross-sectional unit, using as instruments nonlinear transformations of the lagged levels. The actual test statistics is simply defined as a standardized sum of individual IV t-ratios. We show in the paper that such a standardized sum of individual IV t-ratios has limit normal distribution as long as the panels have large individual time series observations and are asymptotically balanced in a very weak sense. We may have the number of cross-sectional units arbitrarily small or large. In particular, the usual sequential asymptotics, upon which most of the available asymptotic theories for panel unit root models heavily rely, are not required. Finite sample performance of our test is examined via a set of simulations, and compared to those of other commonly used panel unit root tests. Our test generally performs better than the existing tests in terms of both finite sample sizes and powers. We apply our nonlinear IV method to test for the purchasing power parity hypothesis in panels.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-85.

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Length: 33 pages
Date of creation: Jul 2000
Date of revision:
Handle: RePEc:tky:fseres:2000cf85
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  1. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
  2. Yoosoon Chang, 2000. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Cowles Foundation Discussion Papers 1251, Cowles Foundation for Research in Economics, Yale University.
  3. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  4. So, Beong Soo & Shin, Dong Wan, 1999. "Recursive mean adjustment in time-series inferences," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 65-73, May.
  5. Jeffrey A. Frankel & Andrew K. Rose, 1995. "A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries," NBER Working Papers 5006, National Bureau of Economic Research, Inc.
  6. Oh, Keun-Yeob, 1996. "Purchasing power parity and unit root tests using panel data," Journal of International Money and Finance, Elsevier, vol. 15(3), pages 405-418, June.
  7. 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.
  8. 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.
  9. MacDonald, Ronald, 1996. "Panel unit root tests and real exchange rates," Economics Letters, Elsevier, vol. 50(1), pages 7-11, January.
  10. Papell, David H., 1997. "Searching for stationarity: Purchasing power parity under the current float," Journal of International Economics, Elsevier, vol. 43(3-4), pages 313-332, November.
  11. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
  12. Phillips, Peter C. B. & Park, Joon Y. & Chang, Yoosoon, 2004. "Nonlinear instrumental variable estimation of an autoregression," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 219-246.
  13. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  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. Yoosoon Chang & Joon Y. Park, 1999. "Nonstationary Index Models," Working Paper Series no7, Institute of Economic Research, Seoul National University.
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