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Cointegration versus Spurious Regression in Heterogeneous Panels

  • Giovanni Urga
  • Lorenzo Trapani

We consider the issue of cross sectional aggregation in nonstationary, heterogeneous panels where each unit cointegrates. We first derive the asymptotic properties of the aggregate estimate, and a necessary and sufficient condition for cointegration to hold in the aggregate relationship. We also develop an estimation and testing framework to verify whether the condition is met. Secondly, we analyze the case when cointegration doesn't carry through the aggregation process, investigating whether a mild violation can still lead to an aggregate estimator that summarizes the micro relationships reasonably well. We derive the asymptotic measure of the degree of non cointegration of the aggregated estimate and we provide estimation and testing procedures. A Monte Carlo exercise evaluates the small sample properties of the estimator.

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 266.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:266
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  1. Granger, C. W. J., 1993. "Implications of seeing economic variables through an aggregation window," Ricerche Economiche, Elsevier, vol. 47(3), pages 269-279, September.
  2. Gonzalo, Jesus, 1993. "Cointegration and aggregation," Ricerche Economiche, Elsevier, vol. 47(3), pages 281-291, September.
  3. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  4. Harris, David, 1997. "Principal Components Analysis of Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 13(04), pages 529-557, August.
  5. Snell, Andy, 1998. "Testing for r versus r-1 cointegrating vectors," Journal of Econometrics, Elsevier, vol. 88(1), pages 151-191, November.
  6. Hall, Stephen & Lazarova, Stepana & Urga, Giovanni, 1999. " A Principal Components Analysis of Common Stochastic Trends in Heterogeneous Panel Data: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 749-67, Special I.
  7. Ghose, Devajyoti, 1995. "Linear aggregation in cointegrated systems," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1011-1032.
  8. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation for Research in Economics, Yale University.
  9. Pesaran, M. Hashem & Smith, Ron, 1995. "Estimating long-run relationships from dynamic heterogeneous panels," Journal of Econometrics, Elsevier, vol. 68(1), pages 79-113, July.
  10. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230.
  11. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  12. Clive W. J. Granger, 1988. "Aggregation of time series variables-a survey," Discussion Paper / Institute for Empirical Macroeconomics 1, Federal Reserve Bank of Minneapolis.
  13. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  14. Lazarov , tep na & Trapani, Lorenzo & Urga, Giovanni, 2007. "Common Stochastic Trends And Aggregation In Heterogeneous Panels," Econometric Theory, Cambridge University Press, vol. 23(01), pages 89-105, February.
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