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Weighted Average Estimation in Panel Data

Author

Listed:
  • Ali Mehrabani

    (Southern Illinois University)

  • Aman Ullah

    (Department of Economics, University of California Riverside)

Abstract

Mukhtar M. Ali has made many innovative and influential contributions in different areas of economics, finance, econometrics, and statistics. His contributions include developing econometric models to examine the determinants of the demand for casino gaming, investigating the approximate and exact distribution and moments of various econometric estimators and test statistics, and studying the statistical properties of time series based statistics under stationary and non-stationary processes (for example, see Ali and Thalheimer (1983, 2008), Ali (1977, 1979, 1984, 1989), Ali and Sharma (1993, 1996), Tsui and Ali (1992, 2002), Ali and Giaccotto (1982a, 1982b, 1984), Ali and Tiao (1971), and Ali and Silver (1985, 1989), among others). All of these have made significant impact on the profession and have been instrumental in advancing further research in statistics and econometrics. In this paper, we study the approximate rst two moments of two weighted average estimators of the slope parameters in linear panel data models. The weighted average estimators shrink a generalized least squares estimator towards a restricted generalized least squares estimator, where the restrictions represent possible parameter specifications. The averaging weight is inversely proportional to a weighted quadratic loss function. The approximate bias and second moment matrix of the weighted average estimators using the large-sample approximations are provided. We give the conditions under which the weighted average estimators dominate the generalized least squares estimator on the basis of their mean squared errors.

Suggested Citation

  • Ali Mehrabani & Aman Ullah, 2022. "Weighted Average Estimation in Panel Data," Working Papers 202209, University of California at Riverside, Department of Economics, revised Apr 2022.
    • Handle: RePEc:ucr:wpaper:202209
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    References listed on IDEAS

    as
    1. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    2. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    3. Ali Mehrabani & Aman Ullah, 2020. "Improved Average Estimation in Seemingly Unrelated Regressions," Econometrics, MDPI, vol. 8(2), pages 1-22, April.
    4. Ali, Mukhtar M. & Sharma, Subhash C., 1993. "Robustness to nonnormality of the Durbin-Watson test for autocorrelation," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 117-136.
    5. G. S. Maddala & Hongyi Li & V. K. Srivastava, 2001. "A Comparative Study of Different Shrinkage Estimators for Panel Data Models," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 1-30, May.
    6. Giaccotto, Carmelo & Ali, Mukhtar M, 1982. "Optimum Distribution-Free Tests and Further Evidence of Heteroscedasticity in the Market Model," Journal of Finance, American Finance Association, vol. 37(5), pages 1247-1257, December.
    7. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    8. Jan R. Magnus & Dmitry Danilov, 2004. "Forecast accuracy after pretesting with an application to the stock market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(4), pages 251-274.
    9. Richard Thalheimer & Mukhtar M. Ali, 2008. "The Demand For Casino Gaming With Special Reference To A Smoking Ban," Economic Inquiry, Western Economic Association International, vol. 46(2), pages 273-282, April.
    10. Silver, J. Lew & Ali, Mukhtar M., 1989. "Testing Slutsky symmetry in systems of linear demand equations," Journal of Econometrics, Elsevier, vol. 41(2), pages 251-266, June.
    11. Ali, Mukhtar M. & Giaccotto, Carmelo, 1984. "A study of several new and existing tests for heteroscedasticity in the general linear model," Journal of Econometrics, Elsevier, vol. 26(3), pages 355-373, December.
    12. Jan R. Magnus, 2002. "Estimation of the mean of a univariate normal distribution with known variance," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 225-236, June.
    13. Leeb, Hannes & Pötscher, Benedikt M., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(1), pages 100-142, February.
    14. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Asymptotic approximations; xed-e ects; panel data; random-e ects; Stein-like shrinkage estimator.;
    All these keywords.

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