Robust Hausman Pretest for Panel Data Model in the Presence of Heteroscedasticity and Influential Observations

DOI: https://doi.org/10.33003/jobasr-2023-v1i1-19

Muhammad Sani.

Shamsuddeen Suleiman.

Mustapha Isyaku.

Abstract
The classical Hausman pretest (HT) is used to specified the right model between random and fixed effect panel data models. However, in the presence of heteroscedastic error variances and influential observations (IOs) in the data set, it may not correctly identify the right model. Therefore, this motivated us to proposed a new method termed Robust Hausman Test (RHTFIID) which employed residuals from weighted least square (WLS) instead of OLS in the construction of heteroscedasticity consistent covariance matrix (HCCM) estimator. The weighting method is based on an efficient High Leverage Points (HLPs) detection method called Fast Improvised Influential Distance (FIID) which down weight only vertical outliers and bad HLPs. The good HLPs were allowed in the estimation as they might contribute to the precision of the estimate. The result indicates that the new proposed RHTFIID outperformed the existing classical Hausman pretest by identifying the right model with and without heteroscedasticity and influential observations.
References
Baltagi, B. (2008). Econometric analysis of panel data, John Wiley & Sons. Baltagi B.H. (2005). The Econometrics of Panel Data. John Wiley & Sons, New York. Balestra P. and Nerlove M. (1966) Pooling cross-section and time series data in the estimation of a dynamic model: the demand for natural gas. Econometrica 34: 585-612 Choulakian, V., Lockhart, R. A., and Stephens, M. A. (1994). Cramér‐von Mises statistics for discrete distributions. Canadian Journal of Statistics, 22(1), 125- 137. Greene, W. (2008) Econometric Analysis; New York: Pearson Grunfeld Y. (1958) The Determinants of Corporate Investment. Unpublished Ph.D. dissertation, Department of Economics, University of Chicago Habshah Midi, Muhammad Sani Shelan Saied Ismaeel (2021) Fast Improvised Influential Distance for the Identification of Influential Observations in Multiple Linear Regression. Sains Malaysiana, 50 (7) (2021): 2085-2094 http://doi.org/10.17576/jsm-2021-5007-22 Hausman J.A. (1978) Specification tests in econometrics, Econometrica 46, 1251–1271 Hsiao C. (2003) Analysis of Panel Data, 2nd edition. Cambridge University Press. Lima, V.M.C., Souza, T,C., Cribari-Neto, F. and Fernandes, G.B. (2009). Heteroskedasticity- robust inference in linear regressions. Communications in Statistics-Simulation and Computation 39: 194-206 Maronna, R. A., et al. (2006). "Wiley Series in Probability and Statistics." Robust Statistics: Theory and Methods: 404-414 Muhammad Sani, Habshah Midi & Jayanthi Arasan (2019) Robust Parameter Estimation for Fixed Effect Panel Data Model in the Presence of Heteroscedasticity and High Leverage Points, ASM Science. Journal 12, Special Issue 1, 2019 for IQRAC2018, 227-238 Muhammad Sani, Shamsuddeen Suleiman & Baoku Ismail G (2020) Robust Parameter Estimation for Random Effect Panel Data Model In The Presence Of Heteroscedasticity And Influential Observations, FUDMA journal of sciences, 4(4): 561- 569, ISSN; 2645 – 2944 Muhammad S., Habshah M. & Babangida I.B. (2019) Robust White’s Test For Heteroscedasticity Detection In Linear Regression FUDMA journal of sciences, 3(2): 173- 178, ISSN; 2645 – 2944 Mundlak Y. (1961) Empirical production function free of management bias, Journal of Farm Economics43, 44–56 Rahman, M., Pearson, L. M., and Heien, H. C. (2006). A modified anderson-darling test for uniformity. Bulletin of the Malaysian Mathematical Sciences Society, 29(1). Richard, A. J., and Dean, W. W. (2002). Applied multivariate statistical analysis. London: Prenticee Hall, 265 Wallace, T.D. and Hussain A. (1969). The use of error components models in combining cross-section and timeseries data, Econometrica37, 55–72 Wooldridge, J.M., (2002) Econometric Analysis of Cross Section and Panel Data. MIT Press, Cambridge, London.
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