International Journal of Systems Science and Applied Mathematics

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Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach

Received: Jun. 05, 2018    Accepted: Jun. 25, 2018    Published: Jul. 25, 2018
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Abstract

This paper considers panel data models when the errors are first-order serially correlated as well as with stochastic regression parameters. The generalized least squares (GLS) estimators for these models have been derived and examined in this paper. Moreover, an alternative estimator for GLS estimators in small samples has been proposed, this estimator is called simple mean group (SMG). The efficiency comparisons for GLS and SMG estimators have been carried out. The Monte Carlo studies indicate that SMG estimator is more reliable in most situations than the GLS estimators, especially when the model includes one or more non-stochastic parameter.

DOI 10.11648/j.ijssam.20180302.14
Published in International Journal of Systems Science and Applied Mathematics ( Volume 3, Issue 2, March 2018 )
Page(s) 37-51
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

First-Order Serial Correlation, Mixed-Stochastic Parameter Regression, Negative Variances, Pooled Least Squares, Simple Mean Group, Swamy’s Test

References
[1] Dielman, T. E. (1983). Pooled cross-sectional and time series data: a survey of current statistical methodology. The American Statistician 37 (2):111-122.
[2] Dielman, T. E. (1989). Pooled Cross-Sectional and Time Series Data Analysis. New York: Marcel Dekker.
[3] Livingston, M., Erickson, K., Mishra, A. (2010). Standard and Bayesian random coefficient model estimation of US Corn–Soybean farmer risk attitudes. In Ball, V. E., Fanfani, R., Gutierrez, L., eds. The Economic Impact of Public Support to Agriculture. Springer New York.
[4] Alcacer, J., Chung, W., Hawk, A., Pacheco-de-Almeida, G. (2013). Applying random coefficient models to strategy research: testing for firm heterogeneity, predicting firm-specific coefficients, and estimating Strategy Trade-Offs. Working Paper, No. 14-022. Harvard Business School Strategy Unit.
[5] Swamy, P. A. V. B. (1970). Efficient inference in a random coefficient regression model. Econometrica 38:311-323.
[6] Swamy, P. A. V. B. (1973). Criteria, constraints, and multicollinearity in random coefficient regression model. Annals of Economic and Social Measurement 2 (4):429-450.
[7] Swamy, P. A. V. B. (1974). Linear models with random coefficients. In: Zarembka, P., ed. Frontiers in Econometrics. New York: Academic Press.
[8] Rao, U. G. (1982). A note on the unbiasedness of Swamy's estimator for the random coefficient regression model. Journal of econometrics 18 (3):395-401.‏
[9] Dielman, T. E. (1992). Misspecification in random coefficient regression models: a Monte Carlo simulation. Statistical Papers 33 (1):241-260.‏
[10] Dielman, T. E. (1992). Small sample properties of random coefficient regression estimators: A Monte Carlo simulation. Communications in Statistics-Simulation and Computation 21 (1):103-132.‏
[11] Beck, N., Katz, J. N. (2007). Random coefficient models for time-series–cross-section data: Monte Carlo experiments. Political Analysis 15 (2):182-195.‏
[12] Youssef, A. H., Abonazel, M. R. (2009). A comparative study for estimation parameters in panel data model. Working paper, No. 49713. University Library of Munich, Germany.
[13] Mousa, A., Youssef, A. H., Abonazel, M. R. (2011). A Monte Carlo study for Swamy’s estimate of random coefficient panel data model. Working paper, No. 49768. University Library of Munich, Germany.
[14] Poi, B. P. (2003). From the help desk: Swamy’s random-coefficients model. The Stata Journal 3 (3):302-308.‏
[15] Abonazel, M. R. (2009). Some Properties of Random Coefficients Regression Estimators. MSc thesis. Institute of Statistical Studies and Research. Cairo University.
[16] Abonazel, M. R. (2016). Generalized random coefficient estimators of panel data models: Asymptotic and small sample properties. American Journal of Applied Mathematics and Statistics 4 (2): 46-58.
[17] Abonazel, M. R. (2017). Generalized estimators of stationary random-coefficients panel data models: Asymptotic and small sample properties, Revstat Statistical Journal (in press). Available at: https://www.ine.pt/revstat/pdf/GENERALIZEDESTIMATORSOFSTATIONARY.pdf
[18] Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Heidelberg, New York, Dordrecht, London: springer.‏
[19] Anh, V. V., Chelliah, T. (1999). Estimated generalized least squares for random coefficient regression models. Scandinavian journal of statistics 26 (1):31-46.‏
[20] Murtazashvili, I. and Wooldridge, J. M. (2008). Fixed effects instrumental variables estimation in correlated random coefficient panel data models. Journal of Econometrics 142:539-552.
[21] Hsiao, C., Pesaran, M. H. (2008). Random coefficient models. In: Matyas, L., Sevestre, P., eds. The Econometrics of Panel Data. Vol. 46. Berlin: Springer Berlin Heidelberg.
[22] Boot, J. C., Frankfurter, G. M. (1972). The dynamics of corporate debt management, decision rules, and some empirical evidence. Journal of Financial and Quantitative Analysis 7 (04):1957-1965.
[23] Feige, E. L., Swamy, P. A. V. B. (1974). A random coefficient model of the demand for liquid assets. Journal of Money, Credit and Banking 6 (2):241-252.
[24] Boness, A. J., Frankfurter, G. M. (1977). Evidence of Non-Homogeneity of capital costs within “risk-classes”. The Journal of Finance 32 (3):775-787.
[25] Westerlund, J., Narayan, P. (2015). A random coefficient approach to the predictability of stock returns in panels. Journal of Financial Econometrics 13 (3):605-664.
[26] Srivastava, V. K., Giles, D. E. A. (1987). Seemingly Unrelated Regression Equations Models: Estimation and Inference. New York: Marcel Dekker.
[27] Swamy, P. A. V. B. (1971). Statistical Inference in Random Coefficient Regression Models. New York: Springer-Verlag.
[28] Judge, G. G., Griffiths, W. E., Hill, R. C., Lütkepohl, H., Lee, T. C. (1985). The Theory and Practice of Econometrics, 2nd ed. New York: Wiley.
[29] Hsiao, C. (2014). Analysis of Panel Data. 3rd ed. Cambridge: Cambridge University Press.
[30] Rosenberg, B. (1973). A survey of stochastic parameter regression. Annals of Economic and Social Measurement 2: 381-397.
[31] Pesaran, M.H., Smith, R. (1995). Estimation of long-run relationships from dynamic heterogeneous panels. Journal of Econometrics 68:79-114.
[32] Baltagi, B. H. (2013). Econometric Analysis of Panel Data. 5th ed. Chichester: John Wiley and Sons.
[33] Abonazel, M. R. (2014). Some Estimation Methods for Dynamic Panel Data Models. PhD thesis. Institute of Statistical Studies and Research. Cairo University.
[34] Youssef, A. H., El-sheikh, A. A., Abonazel, M. R. (2014). Improving the efficiency of GMM estimators for dynamic panel models. Far East Journal of Theoretical Statistics 47:171–189.
[35] Youssef, A. H., El-sheikh, A. A., Abonazel, M. R. (2014). New GMM estimators for dynamic panel data models. International Journal of Innovative Research in Science, Engineering and Technology 3:16414–16425.
[36] Youssef, A. H., Abonazel, M. R. (2017). Alternative GMM estimators for first-order autoregressive panel model: an improving efficiency approach. Communications in Statistics-Simulation and Computation 46 (4): 3112–3128.
[37] Abonazel, M. R. (2018). A practical guide for creating Monte Carlo simulation studies using R. International Journal of Mathematics and Computational Science 4 (1), 18-33.
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    Mohamed Reda Abonazel. (2018). Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach. International Journal of Systems Science and Applied Mathematics, 3(2), 37-51. https://doi.org/10.11648/j.ijssam.20180302.14

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    ACS Style

    Mohamed Reda Abonazel. Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach. Int. J. Syst. Sci. Appl. Math. 2018, 3(2), 37-51. doi: 10.11648/j.ijssam.20180302.14

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    AMA Style

    Mohamed Reda Abonazel. Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach. Int J Syst Sci Appl Math. 2018;3(2):37-51. doi: 10.11648/j.ijssam.20180302.14

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  • @article{10.11648/j.ijssam.20180302.14,
      author = {Mohamed Reda Abonazel},
      title = {Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach},
      journal = {International Journal of Systems Science and Applied Mathematics},
      volume = {3},
      number = {2},
      pages = {37-51},
      doi = {10.11648/j.ijssam.20180302.14},
      url = {https://doi.org/10.11648/j.ijssam.20180302.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijssam.20180302.14},
      abstract = {This paper considers panel data models when the errors are first-order serially correlated as well as with stochastic regression parameters. The generalized least squares (GLS) estimators for these models have been derived and examined in this paper. Moreover, an alternative estimator for GLS estimators in small samples has been proposed, this estimator is called simple mean group (SMG). The efficiency comparisons for GLS and SMG estimators have been carried out. The Monte Carlo studies indicate that SMG estimator is more reliable in most situations than the GLS estimators, especially when the model includes one or more non-stochastic parameter.},
     year = {2018}
    }
    

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    T1  - Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach
    AU  - Mohamed Reda Abonazel
    Y1  - 2018/07/25
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    JF  - International Journal of Systems Science and Applied Mathematics
    JO  - International Journal of Systems Science and Applied Mathematics
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    AB  - This paper considers panel data models when the errors are first-order serially correlated as well as with stochastic regression parameters. The generalized least squares (GLS) estimators for these models have been derived and examined in this paper. Moreover, an alternative estimator for GLS estimators in small samples has been proposed, this estimator is called simple mean group (SMG). The efficiency comparisons for GLS and SMG estimators have been carried out. The Monte Carlo studies indicate that SMG estimator is more reliable in most situations than the GLS estimators, especially when the model includes one or more non-stochastic parameter.
    VL  - 3
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Author Information
  • Department of Applied Statistics and Econometrics, Institute of Statistical Studies and Research, Cairo University, Cairo, Egypt

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