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Asymptotic Properties of Estimators for the Linear Panel Regression Model with Individual Effects and Serially Correlated Errors: The Case of Stationary and Non-Stationary Regressors and Residuals



This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares, fixed effects, first-difference, and generalized least squares (GLS) estimators when both T and n are large. We show that all the estimators have asymptotic normal distributions and have different convergence rates dependent on the non-stationarity of the regressors and the remainder disturbances. We show using Monte Carlo experiments that the loss in efficiency of the OLS, FE and FD estimators relative to true GLS can be substantial.

Suggested Citation

  • Badi H. Baltagi & Chihwa Kao & Long Liu, 2007. "Asymptotic Properties of Estimators for the Linear Panel Regression Model with Individual Effects and Serially Correlated Errors: The Case of Stationary and Non-Stationary Regressors and Residuals," Center for Policy Research Working Papers 93, Center for Policy Research, Maxwell School, Syracuse University.
  • Handle: RePEc:max:cprwps:93

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    References listed on IDEAS

    1. repec:adr:anecst:y:1997:i:48:p:04 is not listed on IDEAS
    2. Breitung, Jörg & Pesaran, Mohammad Hashem, 2005. "Unit roots and cointegration in panels," Discussion Paper Series 1: Economic Studies 2005,42, Deutsche Bundesbank.
    3. Maeshiro, Asatoshi, 1976. "Autoregressive Transformation, Trended Independent Variables and Autocorrelated Disturbance Terms," The Review of Economics and Statistics, MIT Press, vol. 58(4), pages 497-500, November.
    4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    5. 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.
    6. Chi-Young Choi; Ling Hu; Masao Ogaki, 2004. "A Spurious Regression Approach to Estimating Structural Parameters," Econometric Society 2004 Far Eastern Meetings 555, Econometric Society.
    7. Choi, In, 2002. "Instrumental variables estimation of a nearly nonstationary, heterogeneous error component model," Journal of Econometrics, Elsevier, vol. 109(1), pages 1-32, July.
    8. 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.
    9. Baltagi, Badi H. & Li, Qi, 1991. "A transformation that will circumvent the problem of autocorrelation in an error-component model," Journal of Econometrics, Elsevier, vol. 48(3), pages 385-393, June.
    10. Boozer, Michael A., 1997. "Econometric Analysis of Panel Data Badi H. Baltagi Wiley, 1995," Econometric Theory, Cambridge University Press, vol. 13(05), pages 747-754, October.
    11. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    12. Sentana, Enrique, 1997. "Estimation of a Triangular, Seemingly Unrelated, Regression System by OLS," Econometric Theory, Cambridge University Press, vol. 13(03), pages 463-463, June.
    13. Park, Rolla Edward & Mitchell, Bridger M., 1980. "Estimating the autocorrelated error model with trended data," Journal of Econometrics, Elsevier, vol. 13(2), pages 185-201, June.
    14. 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.
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    Cited by:

    1. Mahir Binici & Yin-Wong Cheung & Kon S. Lai, 2011. "Trade Openness, Market Competition, and Inflation: Some Sectoral Evidence from OECD Countries," CESifo Working Paper Series 3690, CESifo Group Munich.
    2. Yin-Wong Cheung & Xingwang Qian, 2009. "The Empirics of China's Outward Direct Investment," CESifo Working Paper Series 2621, CESifo Group Munich.

    More about this item


    Panel data; OLS; Fixed-effects; First-difference; GLS.;

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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