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Linear Regression Limit Theory for Nonstationary Panel Data

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This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section (n) and time series (T) observations. The limit theory allows for both sequential limits, wherein T -> infinity followed by n -> infinity, and joint limits where T, n -> infinity simultaneously; 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 when there is no individual time series cointegration and when there is heterogeneous cointegration. These relations are parametrized in terms of the matrix regression coefficient of the long-run average covariance matrix. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied. The limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population.

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  • 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.
  • Handle: RePEc:cwl:cwldpp:1222
    Note: CFP 986.
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    1. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    2. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    3. 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.
    4. 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.
    5. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    11. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    12. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
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