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Forecasting with Unbalanced Panel Data

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Abstract
This paper derives the best linear unbiased prediction (BLUP) for an unbalanced panel data model. Starting with a simple error component regression model with unbalanced panel data and random effects, it generalizes the BLUP derived by Taub (1979) to unbalanced panels. Next it derives the BLUP for an unequally spaced panel data model with serial correlation of the AR(1) type in the remainder disturbances considered by Baltagi and Wu (1999). This in turn extends the BLUP for a panel data model with AR(1) type remainder disturbances derived by Baltagi and Li (1992) from the balanced to the unequally spaced panel data case. The derivations are easily implemented and reduce to tractable expressions using an extension of the Fuller and Battese (1974) transformation from the balanced to the unbalanced panel data case.

Suggested Citation

  • Badi Baltagi & Long Liu, 2020. "Forecasting with Unbalanced Panel Data," Center for Policy Research Working Papers 221, Center for Policy Research, Maxwell School, Syracuse University.
    • Handle: RePEc:max:cprwps:221
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    File URL: https://surface.syr.edu/cpr/253/
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    References listed on IDEAS

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Bruno, Giovanni S.F., 2005. "Approximating the bias of the LSDV estimator for dynamic unbalanced panel data models," Economics Letters, Elsevier, vol. 87(3), pages 361-366, June.
    3. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    4. Baltagi, Badi H. & Liu, Long, 2013. "Estimation and prediction in the random effects model with AR(p) remainder disturbances," International Journal of Forecasting, Elsevier, vol. 29(1), pages 100-107.
    5. Badi H. Baltagi & Long Liu, 2013. "Prediction in the Random Effects Model with MA (q) Remainder Disturbances," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(4), pages 333-338, July.
    6. Baltagi, Badi H. & Chang, Young-Jae & Li, Qi, 1992. "Monte Carlo evidence on panel data regressions with AR(1) disturbances and an arbitrary variance on the initial observations," Journal of Econometrics, Elsevier, vol. 52(3), pages 371-380, June.
    7. Wansbeek, Tom & Kapteyn, Arie, 1989. "Estimation of the error-components model with incomplete panels," Journal of Econometrics, Elsevier, vol. 41(3), pages 341-361, July.
    8. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    9. David J. Mckenzie, 2001. "Estimation of AR(1) models with unequally spaced pseudo-panels," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-40.
    10. Fuller, Wayne A. & Battese, George E., 1974. "Estimation of linear models with crossed-error structure," Journal of Econometrics, Elsevier, vol. 2(1), pages 67-78, May.
    11. Daniel L. Millimet & Ian K. McDonough, 2017. "Dynamic Panel Data Models With Irregular Spacing: With an Application to Early Childhood Development," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 725-743, June.
    12. David M. Drukker, 2003. "Testing for serial correlation in linear panel-data models," Stata Journal, StataCorp LP, vol. 3(2), pages 168-177, June.
    13. Galbraith, John W. & Zinde-Walsh, Victoria, 1995. "Transforming the error-components model for estimation with general ARMA disturbances," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 349-355.
    14. Baltagi, Badi H. & Wu, Ping X., 1999. "Unequally Spaced Panel Data Regressions With Ar(1) Disturbances," Econometric Theory, Cambridge University Press, vol. 15(6), pages 814-823, December.
    15. Timmermann, Allan & Zhu, Yinchu, 2019. "Comparing Forecasting Performance with Panel Data," CEPR Discussion Papers 13746, C.E.P.R. Discussion Papers.
    16. Taub, Allan J., 1979. "Prediction in the context of the variance-components model," Journal of Econometrics, Elsevier, vol. 10(1), pages 103-107, April.
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    More about this item

    Keywords

    Forecasting; BLUP; Unbalanced Panel Data; Unequally Spaced Panels; Serial Correlation;
    All these keywords.

    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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