Monte Carlo Estimation of Heteroscedasticity and Periodicity Effects in a Panel Data Regression Model
This research attempts to investigate the effects of heteroscedasticity and periodicity in a Panel Data Regression Model (PDRM) by extending previous works on balanced panel data estimation within the context of fitting PDRM for Banks audit fee. The estimation of such model was achieved through the derivation of Joint Lagrange Multiplier (LM) test for homoscedasticity and zero-serial correlation, a conditional LM test for zero serial correlation given heteroscedasticity of varying degrees as well as conditional LM test for homoscedasticity given first order positive serial correlation via a two-way error component model. Monte Carlo simulations were carried out for 81 different variations, of which its design assumed a uniform distribution under a linear heteroscedasticity function. Each of the variation was iterated 1000 times and the assessment of the three estimators considered are based on Variance, Absolute bias (ABIAS), Mean square error (MSE) and the Root Mean Square (RMSE) of parameters estimates. Eighteen different models at different specified conditions were fitted, and the best-fitted model is that of within estimator when heteroscedasticity is severe at either zero or positive serial correlation value. LM test results showed that the tests have good size and power as all the three tests are significant at 5% for the specified linear form of heteroscedasticity function which established the facts that Banks operations are severely heteroscedastic in nature with little or no periodicity effects.
[1] P. Mazodier and A. Trognon, Heteroskedasticity and stratification in error Components Models, Annales de L’INSEE, 1978, vol. 30-31, pp. 451-482.
[2] C. R. Rao, R. A. Wayne and I. K. Hogdson, The Theory of Least Squares when the Parameters are Stochastic and its Application to the Analysis of Growth Curves. 1981, Biometrika, vol. 52, pp. 447-58.
[3] J. R. Magnus, Multivariate Error Components Analysis of Linear and Non Linear Regression Models by Maximum Likelihood, 1982, Journal of Economerics, 1982, vol. 19, pp. 239-285.
[4] V. A. Hajivassiliou and D. McFadden, “The Method of Simulated Scores for the Estimation of LDV Models,” Econometrica, 1998, vol.66, pp. 863–896.
[5] B. H. Baltagi, An Alternative Heteroscedastic Error Component Model. Econometric Theory, 1988, vol.4, pp. 349-350.
[6] B. H. Baltagi and J. M. Griffin, A generalized Error Component Model with Heteroscedastic Disturbances, International Economic Review, 1988, 29, 745-753.
[7] W. C. Randolph, A transformation for Heteroscedastic Error Components Regression Models. Economic Letters, 1988
[8] T. J. Wansbeek, GMM Estimation in Panel data models with Measurement Error. Journal of Econometrics, 1989, vol. 104 (2001), pp. 259-268.
[9] Q. Li and T. Stegnos, An Adaptive Estimation in the Panel Data Error Component Model with Heteroscedasticity of unknown form. International Economic Review, 1994, vol 35, pp. 981-1000.
[10] B. Lejeune, A Full Heteroscedasticity One-way Error Component Model: Pseudo Maximum Likelihood Estimation and Specification Testing, Theoretical Contributions and Empirical Applications. Elsivier Science, Amsterdam, 1996, pp. 31-66.
[11] A. Holy and L. Gardiol, “A Score Test for Individual heteroscedasticity in a One Way Error Components Model. In: Kirshnakumar, J., Ronchetti, E. (Eds.). Panel Data Econometrics: Future Directions, Elsevier Amsterdam, 2000, pp. 199-211 (Chapter. 10).
[12] N. Roy, Is Adaptive Estimation Useful for Panel Models with Heteroscedasticity in the Individual Specific Error Component? Some Monte Carlo Evidence. Econometric Review, 2002, vol. 21, pp. 189-203.
[13] R. L. Phillips, “Estimation of a Stratified Error Components Model”. International Economic Review, 2003, vol. 44, pp. 501-521.
[14] B. H. Baltagi, G. Bresson and A. Pirotte, Joint LM Test for Homoscedasticity in a One-way Error Component Model. Journal of Econometrics, 2006, vol. 134, pp. 401-417.
[15] J. Hyppolite, Alternative Approaches for Econometric Modeling of Panel Data using Mixture Distributions, Journal of Statistical Distributions and Applications, 2017, vol. 4 (9), pp. 1-34.
[16] N. O. Adeboye and D. A. Agunbiade, Estimating the Heterogeneity Effects in a Panel Data Regression Model. Annals of Computer Science Series, 2017, vol. 15 (1), pp. 149-158.
[17] L. Lillard and J. Willis, “What Do We Really Know about Wages? The Importance of Nonreporting and Census Imputation,” Journal of Political Economy, 1978, vol 94, pp.489–506.
[18] A. Bhargava, L. Franzini and W. Narendranathan, Serial correlation and the fixed effects Model. Review of Economic Studies, 1982, vol. 49, pp. 533-549.
[19] S. P. Burke, L. G. Godfrey and A. R. Termayne, Testing AR(1) Against MA(1) Disturbances In The Linear Regression Model: An Alternative Procedure. Review of Economic Studies, 1990, vol.57, pp. 135-145.
[20] B. H. Baltagi and Q. Li, Testing AR(1) against MA(1) Disturbances in an Error Component Model. Journal of Econometrics, 1995, vol. 68, pp. 133-151.
[21] B. H. Baltagi, B. C. Jung and S. H. Song, Testing for Heteroskedasticity and Serial Correlation in a Random Effects Panel Data Model. Journal of Econometrics, 2010, vol. 154 (2), pp. 122-124.
[22] S. O. Olofin, E. Kouassi and A. A. Salisu, Testing for heteroscedasticity and serial Correlation in a Two-way Error Component Model. Unpublished Ph.D. thesis, University of Ibadan, Nigeria. p., 2010.
[23] M. K. Garba, B. A. Oyejola and B. A. Yahya, Investigations of Certain Estimators for Modelling Panel Data under Violations of Some Basic Assumptions. Journal of Mathematical Theory and Modelling, 2013, vol. 3 (10), pp. 1-8.
[24] E. Kouassi, M. Mougoue, J. Sango, J. M. Bosson Brou, M. O. Claude and A. A. Salisu, Testing for Heteroscedasticity and Spatial Correlation in a Two-way Random Effects Model, Computational Statistics and Data Analysis, 2014, vol. 70, pp. 153-171.
[25] T. S. Breusch and A. R. Pagan, The Lagrange Multiplier Test and its Applications to Model Specification in Economics. The review of economic studies, 1980, vol. 47(1), pp. 239-253.
[26] T. J. Wansbeek and A. Kapteyn, A Simple Way to Obtain the Spectral Decomposition of Variance Components Models for Balanced Data. Communication in Statistics, 1982, A11, 2105-2112.
[27] J. M. Wooldridge, Introductory Econometrics: A Modern Approach. South-Western Publishing Co, 5th Edition, p. 450.
[1] P. Mazodier and A. Trognon, Heteroskedasticity and stratification in error Components Models, Annales de L’INSEE, 1978, vol. 30-31, pp. 451-482.
[2] C. R. Rao, R. A. Wayne and I. K. Hogdson, The Theory of Least Squares when the Parameters are Stochastic and its Application to the Analysis of Growth Curves. 1981, Biometrika, vol. 52, pp. 447-58.
[3] J. R. Magnus, Multivariate Error Components Analysis of Linear and Non Linear Regression Models by Maximum Likelihood, 1982, Journal of Economerics, 1982, vol. 19, pp. 239-285.
[4] V. A. Hajivassiliou and D. McFadden, “The Method of Simulated Scores for the Estimation of LDV Models,” Econometrica, 1998, vol.66, pp. 863–896.
[5] B. H. Baltagi, An Alternative Heteroscedastic Error Component Model. Econometric Theory, 1988, vol.4, pp. 349-350.
[6] B. H. Baltagi and J. M. Griffin, A generalized Error Component Model with Heteroscedastic Disturbances, International Economic Review, 1988, 29, 745-753.
[7] W. C. Randolph, A transformation for Heteroscedastic Error Components Regression Models. Economic Letters, 1988
[8] T. J. Wansbeek, GMM Estimation in Panel data models with Measurement Error. Journal of Econometrics, 1989, vol. 104 (2001), pp. 259-268.
[9] Q. Li and T. Stegnos, An Adaptive Estimation in the Panel Data Error Component Model with Heteroscedasticity of unknown form. International Economic Review, 1994, vol 35, pp. 981-1000.
[10] B. Lejeune, A Full Heteroscedasticity One-way Error Component Model: Pseudo Maximum Likelihood Estimation and Specification Testing, Theoretical Contributions and Empirical Applications. Elsivier Science, Amsterdam, 1996, pp. 31-66.
[11] A. Holy and L. Gardiol, “A Score Test for Individual heteroscedasticity in a One Way Error Components Model. In: Kirshnakumar, J., Ronchetti, E. (Eds.). Panel Data Econometrics: Future Directions, Elsevier Amsterdam, 2000, pp. 199-211 (Chapter. 10).
[12] N. Roy, Is Adaptive Estimation Useful for Panel Models with Heteroscedasticity in the Individual Specific Error Component? Some Monte Carlo Evidence. Econometric Review, 2002, vol. 21, pp. 189-203.
[13] R. L. Phillips, “Estimation of a Stratified Error Components Model”. International Economic Review, 2003, vol. 44, pp. 501-521.
[14] B. H. Baltagi, G. Bresson and A. Pirotte, Joint LM Test for Homoscedasticity in a One-way Error Component Model. Journal of Econometrics, 2006, vol. 134, pp. 401-417.
[15] J. Hyppolite, Alternative Approaches for Econometric Modeling of Panel Data using Mixture Distributions, Journal of Statistical Distributions and Applications, 2017, vol. 4 (9), pp. 1-34.
[16] N. O. Adeboye and D. A. Agunbiade, Estimating the Heterogeneity Effects in a Panel Data Regression Model. Annals of Computer Science Series, 2017, vol. 15 (1), pp. 149-158.
[17] L. Lillard and J. Willis, “What Do We Really Know about Wages? The Importance of Nonreporting and Census Imputation,” Journal of Political Economy, 1978, vol 94, pp.489–506.
[18] A. Bhargava, L. Franzini and W. Narendranathan, Serial correlation and the fixed effects Model. Review of Economic Studies, 1982, vol. 49, pp. 533-549.
[19] S. P. Burke, L. G. Godfrey and A. R. Termayne, Testing AR(1) Against MA(1) Disturbances In The Linear Regression Model: An Alternative Procedure. Review of Economic Studies, 1990, vol.57, pp. 135-145.
[20] B. H. Baltagi and Q. Li, Testing AR(1) against MA(1) Disturbances in an Error Component Model. Journal of Econometrics, 1995, vol. 68, pp. 133-151.
[21] B. H. Baltagi, B. C. Jung and S. H. Song, Testing for Heteroskedasticity and Serial Correlation in a Random Effects Panel Data Model. Journal of Econometrics, 2010, vol. 154 (2), pp. 122-124.
[22] S. O. Olofin, E. Kouassi and A. A. Salisu, Testing for heteroscedasticity and serial Correlation in a Two-way Error Component Model. Unpublished Ph.D. thesis, University of Ibadan, Nigeria. p., 2010.
[23] M. K. Garba, B. A. Oyejola and B. A. Yahya, Investigations of Certain Estimators for Modelling Panel Data under Violations of Some Basic Assumptions. Journal of Mathematical Theory and Modelling, 2013, vol. 3 (10), pp. 1-8.
[24] E. Kouassi, M. Mougoue, J. Sango, J. M. Bosson Brou, M. O. Claude and A. A. Salisu, Testing for Heteroscedasticity and Spatial Correlation in a Two-way Random Effects Model, Computational Statistics and Data Analysis, 2014, vol. 70, pp. 153-171.
[25] T. S. Breusch and A. R. Pagan, The Lagrange Multiplier Test and its Applications to Model Specification in Economics. The review of economic studies, 1980, vol. 47(1), pp. 239-253.
[26] T. J. Wansbeek and A. Kapteyn, A Simple Way to Obtain the Spectral Decomposition of Variance Components Models for Balanced Data. Communication in Statistics, 1982, A11, 2105-2112.
[27] J. M. Wooldridge, Introductory Econometrics: A Modern Approach. South-Western Publishing Co, 5th Edition, p. 450.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:78919", author = "Nureni O. Adeboye and Dawud A. Agunbiade", title = "Monte Carlo Estimation of Heteroscedasticity and Periodicity Effects in a Panel Data Regression Model ", abstract = "This research attempts to investigate the effects of heteroscedasticity and periodicity in a Panel Data Regression Model (PDRM) by extending previous works on balanced panel data estimation within the context of fitting PDRM for Banks audit fee. The estimation of such model was achieved through the derivation of Joint Lagrange Multiplier (LM) test for homoscedasticity and zero-serial correlation, a conditional LM test for zero serial correlation given heteroscedasticity of varying degrees as well as conditional LM test for homoscedasticity given first order positive serial correlation via a two-way error component model. Monte Carlo simulations were carried out for 81 different variations, of which its design assumed a uniform distribution under a linear heteroscedasticity function. Each of the variation was iterated 1000 times and the assessment of the three estimators considered are based on Variance, Absolute bias (ABIAS), Mean square error (MSE) and the Root Mean Square (RMSE) of parameters estimates. Eighteen different models at different specified conditions were fitted, and the best-fitted model is that of within estimator when heteroscedasticity is severe at either zero or positive serial correlation value. LM test results showed that the tests have good size and power as all the three tests are significant at 5% for the specified linear form of heteroscedasticity function which established the facts that Banks operations are severely heteroscedastic in nature with little or no periodicity effects.
", keywords = "Audit fee, heteroscedasticity, Lagrange multiplier test, periodicity.", volume = "13", number = "6", pages = "157-10", }
