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Residual based tests for cointegration in dependent panels

  • Chang, Yoosoon
  • Nguyen, Chi Mai

In the paper, we propose residual based tests for cointegration in general panels with cross-sectional dependency, endogeneity and various heterogeneities. The residuals are obtained from the usual least squares estimation of the postulated cointegrating relationships from each individual unit, and the nonlinear IV panel unit root testing procedure is applied to the panels of the fitted residuals using as instruments the nonlinear transformations of the adaptively fitted lagged residuals. The t-ratio, based on the nonlinear IV estimator, is then constructed to test for unit root in the fitted residuals for each cross-section. We show that such nonlinear IV t-ratios are asymptotically normal and cross-sectionally independent under the null hypothesis of no cointegration. The average or the minimum of the IVt-ratios can, therefore, be used to test for the null of a fully non-cointegrated panel against the alternative of a mixed panel, i.e., a panel with only some cointegrated units. We also consider the maximum of the IV t-ratios to test for a mixed panel against a fully cointegrated panel. The critical values of the minimum, maximum as well as the average tests are easily obtained from the standard normal distribution function. Our simulation results indicate that the residual based tests for cointegration perform quite well in finite samples.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304407611002132
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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 167 (2012)
Issue (Month): 2 ()
Pages: 504-520

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Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:504-520
DOI: 10.1016/j.jeconom.2011.09.032
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Yoosoon Chang, 2000. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Econometric Society World Congress 2000 Contributed Papers 1585, Econometric Society.
  2. Chang, Yoosoon, 2002. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," Working Papers 2000-08, Rice University, Department of Economics.
  3. 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.
  4. Anindya Banerjee & Josep Lluis Carrion-i-Silvestre, 2011. "Cointegration in Panel Data with Breaks and Cross-section Dependence," Discussion Papers 11-25, Department of Economics, University of Birmingham.
  5. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Nonstationary Panel Data Analysis: An Overview of Some Recent Developments," Cowles Foundation Discussion Papers 1221, Cowles Foundation for Research in Economics, Yale University.
  6. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  7. 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.
  8. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  9. Pedroni, Peter, 2004. "Panel Cointegration: Asymptotic And Finite Sample Properties Of Pooled Time Series Tests With An Application To The Ppp Hypothesis," Econometric Theory, Cambridge University Press, vol. 20(03), pages 597-625, June.
  10. Joakim Westerlund, 2005. "New Simple Tests for Panel Cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 297-316.
  11. Christian Gengenbach & Franz C. Palm & Jean-Pierre Urbain, 2006. "Cointegration Testing in Panels with Common Factors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 683-719, December.
  12. Jan J.J. Groen & Frank R. Kleibergen, 1999. "Likelihood-Based Cointegration Analysis in Panels of Vector Error Correction Models," Tinbergen Institute Discussion Papers 99-055/4, Tinbergen Institute.
  13. 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.
  14. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  15. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
  16. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
  17. Christoph Hanck, 2009. "Cross-sectional correlation robust tests for panel cointegration," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(7), pages 817-833.
  18. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  19. Joakim Westerlund & David L. Edgerton, 2008. "A Simple Test for Cointegration in Dependent Panels with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 665-704, October.
  20. 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.
  21. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
  22. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  23. Kao, Chihwa, 1999. "Spurious regression and residual-based tests for cointegration in panel data," Journal of Econometrics, Elsevier, vol. 90(1), pages 1-44, May.
  24. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
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