PERTANIKA JOURNAL OF SCIENCE AND TECHNOLOGY

Most robust estimation methods for panel data regression models do not consider the panel data structure consisting of several cross-sections and time-series units. This robust method, which does not consider the panel data structure, can completely remove all observations from a cross-section unit in trimming outlier observations. However, it can cause biased estimation results for the cross-section unit. This study determines the robust estimate for the unbalanced panel data regression model using Groupwise Principal Sensitivity Components (GPSC) by considering grouped structure data. The results were compared with Within-Group (WG) estimation and other robust estimation methods, namely Within- Group estimation with median centering (Median WG), Within-Group Least Trimmed Squares (WG-LTS), and Within Generalized M (WGM) estimators. Comparisons were made based on the Mean Squares Error (MSE) value. In this study, we applied the proposed method to the unemployed and the Gross Regional Domestic Product (GRDP) data at constant prices in Kalimantan, Indonesia. The analysis showed that GPSC was the best method with the smallest MSE value. Therefore, we can consider implementing and developing the GPSC method to detect and determine the robust estimates for the unbalanced panel data regression model because it fits the panel data structure.

• Agostinelli, C., & Markatou M. (1998). A one-step robust estimator for regression based on the weighted likelihood reweighting scheme. Statistics & Probability Letters, 37(4), 341-350. https://doi.org/10.1016/S0167-7152(97)00136-3

• Aquaro, M., & Čížek, P. (2013). One-step robust estimation of fixed-effects panel data models. Computational Statistics and Data Analysis, 57, 536-548. https://doi.org/10.1016/j.csda.2012.07.003

• Bakar, N. M. A., & Midi, H. (2015). Robust centering in the fixed effect panel data model. Pakistan Journal of Statistics, 31(1), 33-48.

• Baltagi, B. H. (2005). Econometric Analysis of Panel Data (3rd Ed.). John Wiley & Sons Inc.

• Beyaztas, B. H., & Bandyopadhyay, S. (2020). Robust estimation for linear panel data models. Statistics in Medicine, 39(29), 4421-4438. https://doi.org/10.1002/sim.8732

• Bramati, M. C., & Croux C. (2007). Robust estimators for the fixed effects panel data model. Econometrics Journal, 10, 521-540. https://doi.org/10.1111/j.1368-423X.2007.00220.x

• Gujarati, D. (2004). Basic Econometrics (4th Ed.). McGraw-Hill Companies, Inc.

• Hsiao, C. (2003). Analysis of Panel Data (2nd Ed.). Cambridge University Press.

• Hubert, M., & Rousseeuw, P. J. (1997). Robust regression with both continuous and binary regressors. Journal of Statistical Planning and Inference, 57(1), 153-163. https://doi.org/10.1016/S0378-3758(96)00041-9

• Markatou, M., Basu, A., & Lindsay, B. G. (1998). Weighted likelihood equations with bootstrap root search. Journal of the American Statistical Association, 93(442), 740-750. https://doi.org/10.2307/2670124

• Maroona, R. A., & Yohai, V. J. (2000). Robust regression with both continuous and categorical predictors. Journal of Statistical Planning and Inference, 89(1-2), 197-214. https://doi.org/10.1016/S0378-3758(99)00208-6

• Midi, H., & Muhammad, S. (2018). Robust estimation for fixed and random effects panel data models with different centering methods. Journal of Engineering and Applied Sciences, 13(17), 7156-7161.

• Okun, A. M. (1962). Potential GNP, its measurement and significance. https://milescorak.files.wordpress.com/2016/01/okun-potential-gnp-its-measurement-and-significance-p0190.pdf

• Pena, D., & Ruiz-Castillo, J. (1998). The estimation of food expenditures from household budget data in the presence of bulk purchases. Journal of Business & Economic Statistics, 16(3), 292-303. http://dx.doi.org/10.1080/07350015.1998.10524768

• Pena, D., & Yohai, V. J. (1995). The detection of influence subsets in linear regression by using an influence matrix. Journal of the Royal Statistical Society, 57(1), 145-156.

• Pena, D., & Yohai, V. J. (1999). A fast procedure for outlier diagnostics in large regression problems. Journal of the American Statistical Association, 94(446), 434-445. https://doi.org/10.2307/2670164

• Perez, B., Molina, I., & Pena, D. (2013). Outlier detection and robust estimation in linear regression models with fixed group effects. Journal of Statistical Computation and Simulation, 84(12), 2652-2669. https://doi.org/10.1080/00949655.2013.811669

• Víšek, J. Á. (2015). Estimating the model with fixed and random effects by a robust method. Methodology and Computing in Applied Probability, 17, 999-1014. https://doi.org/10.1007/s11009-014-9432-5

• Wagenvoort, R., & Waldmann, R. (2002). On B-robust instrumental variable estimation of the linear model with panel data. Journal of Econometrics, 106(2), 297-324. https://doi.org/10.1016/S0304-4076(01)00102-6