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Linear Regression Limit Theory for Nonstationary Panel Data

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  • Peter C. B. Phillips
  • Hyungsik R. Moon

Abstract

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section and time series observations. The limit theory allows for both sequential limits and joins limits, and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and near-homogeneous cointegration. The paper explores the existence of long-run average relations between integrated panel vectors. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied.

Suggested Citation

  • Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    • Handle: RePEc:ecm:emetrp:v:67:y:1999:i:5:p:1057-1112
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    References listed on IDEAS

    as
    1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    2. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(1), pages 95-131, April.
    3. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    5. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    6. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    7. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    8. 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.
    9. Uhlig, Harald, 1994. "On Jeffreys Prior when Using the Exact Likelihood Function," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 633-644, August.
    10. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    11. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    12. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(3), pages 528-533, December.
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