Bias correction methods for dynamic panel data models with fixed effects

  • Authors

    • Mohamed Abonazel Institute of Statistical Studies and Research, Cairo University
    2017-05-24
    https://doi.org/10.14419/ijamr.v6i2.7774
  • Bias-Corrected Estimators, First-Order Autoregressive Panel Model, Generalized Method of Moments Estimators, Kantorovich Inequality, Least Squares Dummy Variable Estimators.
  • Abstract

    This paper considers the estimation methods for dynamic panel data (DPD) models with fixed effects, which suggested in econometric literature, such as least squares (LS) and generalized method of moments (GMM). These methods obtain biased estimators for DPD models. The LS estimator is inconsistent when the time dimension (T) is short regardless of the cross-sectional dimension (N). Although consistent estimates can be obtained by GMM procedures, the inconsistent LS estimator has a relatively low variance and hence can lead to an estimator with lower root mean square error after the bias is removed. Therefore, we discuss in this paper the different methods to correct the bias of LS and GMM estimations. The analytical expressions for the asymptotic biases of the LS and GMM estimators have been presented for large N and finite T. Finally; we display new estimators that presented by Youssef and Abonazel [40] as more efficient estimators than the conventional estimators.

  • References

    1. [1] Abonazel, M. R. (2014). Some estimation methods for dynamic panel data models. PhD thesis. Institute of Statistical Studies and Research. Cairo University.

      [2] Abonazel, M. R. (2015). R-Codes to Calculate GMM Estimations for Dynamic Panel Data Models. Working paper, No. 70627. University Library of Munich, Germany.

      [3] Abonazel, M. R. (2015). How to Create a Monte Carlo Simulation Study using R: with Applications on Econometric Models. Annual Conference on Statistics, Computer Sciences and Operations Research. Institute of Statistical Studies and Research. Cairo University.

      [4] Alonso-Borrego, C., Arellano, M. (1999). Symmetrically normalized instrumental variable estimation using panel data.Journal of Business and Economic Statistics 17:36–49.

      [5] Alvarez, J., Arellano, M. (2003). The time series and cross-section asymptotics of dynamic panel data estimators. Econometrica 71:1121–1159.http://dx.doi.org/10.1111/1468-0262.00441.

      [6] Anderson,T. Hsiao, C. (1981). Estimation of dynamics models with error components. Journal of the American Statistical Association 76:598–606.http://dx.doi.org/10.1080/01621459.1981.10477691.

      [7] Anderson, T., Hsiao, C.(1982). Formulation and estimation of dynamic models using panel data. Journal of Econometrics 18:47–82.http://dx.doi.org/10.1016/0304-4076(82)90095-1.

      [8] Arellano, M., Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58:277–98.http://dx.doi.org/10.2307/2297968.

      [9] Arellano, M., Bover, O. (1995). Another look at the instrumental variable estimation of error-components models. Journal of Econometrics 68:29-51.http://dx.doi.org/10.1016/0304-4076(94)01642-D.

      [10] Baltagi, B. H. (2013). Econometric Analysis of Panel Data. 5th ed. Chichester: John Wiley and Sons.

      [11] Beggs, J., Nerlove, M. (1988). Biases in dynamic models with fixed effects. Economics Letters 26:29–31.http://dx.doi.org/10.1016/0165-1765(88)90046-8.

      [12] Behr, A. (2003). A Comparison of dynamic panel data estimators: Monte Carlo evidence and an application to the investment function. Working paper. Research Centre of Deutsche Bundesbank, Economic Studies with number 2003, 05.

      [13] Bekker, P.A. (1994). Alternative approximations to the distributions of instrumental variable estimators. Econometrica 62:657–681.http://dx.doi.org/10.2307/2951662.

      [14] Blundell, R., Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87:115–143.http://dx.doi.org/10.1016/S0304-4076(98)00009-8.

      [15] Blundell, R., Bond, S. (2000). GMM estimation with persistent panel data: An application to production functions.Econometric Reviews 19:321–340.http://dx.doi.org/10.1080/07474930008800475.

      [16] Bond, S. R. (2002). Dynamic panel data models: A guide to micro data methods and practice. Portuguese Economic Journal 1:141–162. http://dx.doi.org/10.1007/s10258-002-0009-9.

      [17] Bond, S., Hoeffler, A., Temple, J. (2001). GMM estimation of empirical growth models. Working Paper, No. 2001-W21. University of Oxford, Nuffield College, Economics Group.

      [18] Bruno, G.S. (2005). Approximating the bias of the LSDV estimator for dynamic unbalanced panel data models. Economics Letters 87:361–366.http://dx.doi.org/10.1016/j.econlet.2005.01.005.

      [19] Bun, M., Carree, M. (2005). Bias-corrected estimation in dynamic panel data models. Journal of Business and Economic Statistics 23:200–210. http://dx.doi.org/10.1198/073500104000000532.

      [20] Bun, M., Carree, M. (2006). Bias-corrected estimation in dynamic panel data models with heteroscedasticity.Economics Letters92:220–227.http://dx.doi.org/10.1016/j.econlet.2006.02.008.

      [21] Bun, M., Kiviet, J. (2003). On the diminishing returns of higher-order terms in asymptotic expansions of bias. Economics Letters79:145–152.http://dx.doi.org/10.1016/S0165-1765(02)00299-9.

      [22] Chigira, H., Yamamoto, T. (2006). A bias-corrected estimation for dynamic panel models in small samples. Hi-Stat Discussion Paper, No. 177, Hitotsubashi University.

      [23] Hahn, J., Hausman, J. (2002). Notes on bias in estimators for simultaneous equation models.Economics Letters 75:237–241.http://dx.doi.org/10.1016/S0165-1765(01)00602-4.

      [24] Hansen,G.(2001). A bias-corrected least squares estimator of dynamic panel models. AllgemeinesStatistischesArchiv 85:127–140.http://dx.doi.org/10.1007/s101820100054.

      [25] Hayakawa, K. (2007). Small sample bias properties of the system GMM estimator in dynamic panel data models. Economics Letters 95:32–38.http://dx.doi.org/10.1016/j.econlet.2006.09.011.

      [26] Hsiao, C. (2014). Analysis of Panel Data. 3rd ed. Cambridge: Cambridge University Press.http://dx.doi.org/10.1017/CBO9781139839327.

      [27] Kiviet, J.F. (1995). On bias, inconsistency and efficiency of various estimators in dynamic panel data models. Journal of Econometrics 68:53–78. http://dx.doi.org/10.1016/0304-4076(94)01643-E.

      [28] Kiviet, J. F. (2007). On the optimal weighting matrix for the GMM system estimator in dynamic panel data models, Discussion Paper, No. 2007/08. University of Amsterdam.

      [29] Kunitomo, N. (1980). Asymptotic expansions of the distributions of estimators in a linear functional relationship and simultaneous equations. Journal of the American Statistical Association 75:693–700.http://dx.doi.org/10.1080/01621459.1980.10477535.

      [30] Liu, S., Neudecker, H. (1997). Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models. StatisticaNeerlandica51:345–355. http://dx.doi.org/10.1111/1467-9574.00058.

      [31] Lokshin, B. (2008). Monte Carlo comparison of alternative estimators for dynamic panel data models. Applied Economics Letters 15:15–18.http://dx.doi.org/10.1080/13504850600706545.

      [32] Maddala, G.S. (1971). The use of variance components models in pooling cross section and time series data. Econometrica39:341–358.http://dx.doi.org/10.2307/1913349.

      [33] Morimune, K. (1983). Approximate distributions of k-class estimators when the degree of overidentification is large compared with the sample size. Econometrica 51:821–841.http://dx.doi.org/10.2307/1912160.

      [34] Nelson, C., Startz, R. (1990). Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58:967–976.http://dx.doi.org/10.2307/2938359.

      [35] Nelson, C., Startz, R. (1990). The distribution of the instrumental variable estimator and its t ratio when the instrument is a poor one. Journal of Business 63:125–140.http://dx.doi.org/10.1086/296497.

      [36] Nickell, S. (1981). Biases in dynamic models with fixed effects.Econometrica 49:1417–1426.http://dx.doi.org/10.2307/1911408.

      [37] Sevestre, P., Trognon, A. (1985). A note on autoregressive error component models. Journal of Econometrics 28:231–245.http://dx.doi.org/10.1016/0304-4076(85)90122-8.

      [38] Staiger, D., Stock, J. (1997). Instrumental variables regression with weak instruments. Econometrica 65:557–586.http://dx.doi.org/10.2307/2171753.

      [39] Windmeijer, F. (2005). A Finite sample correction for the variance of linear efficient two-step GMM estimatorsâ€. Journal of Econometrics126:25–51.http://dx.doi.org/10.1016/j.jeconom.2004.02.005.

      [40] 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 Computation46:3112:3128.

      http://dx.doi.org/10.1080/03610918.2015.1073307.

      [41] Youssef, A., El-sheikh, A., Abonazel, M. (2014). Improving the efficiency of GMM estimators for dynamic panel models. Far East Journal of Theoretical Statistics47:171–189.

      [42] Youssef, A., El-sheikh, A., Abonazel, M. (2014). New GMM estimators for dynamic panel data models. International Journal of Innovative Research in Science, Engineering and Technology3: 16414–16425.

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  • How to Cite

    Abonazel, M. (2017). Bias correction methods for dynamic panel data models with fixed effects. International Journal of Applied Mathematical Research, 6(2), 58-66. https://doi.org/10.14419/ijamr.v6i2.7774

    Received date: 2017-05-14

    Accepted date: 2017-05-16

    Published date: 2017-05-24