Robust estimation methods for fixed effect panel data model having block-concentrated outliers

The Ordinary Least Squares (OLS) is the commonly used method to estimate the parameters of fixed effect panel data model. However, the method is tremendously affected by the presence of outliers. In addressing the problem, we proposed new and improved robust estimators to provide resilient estimates against the most critical outlying values known as block high leverage points (HLPs). Firstly, we proposed robust panel data transformation to be performed around the MM-estimate of location as an alternative to the non-robust centering by the mean. Two robust Within Group estimators known as Robust Within Group MM (RWMM) and Robust Within Group GM (RWGM) are also proposed to be simulated under the MM-centering. Results of simulation study and real data identify RWMM and RWGM to provide more resistant and efficient estimates under MM-centering compare to the existing estimation based on median centering. Not much research has been done on method of detecting HLPs for panel data. Hence, we have proposed Robust Diagnostic-F (RDF) to remedy the problem of masking and swamping in detecting HLPs. Simulation works and numerical examples prove that the newly proposed RDF outperforms existing methods with the lowest rates of swamping. The existing RWGM estimator has shortcoming whereby it is based on Robust Mahalanobis Distance (RMD) based on Minimum Volume Ellipsoid (MVE) which is prone to suffer from swamping effect. To rectify this problem, the RWGM with RDF and RWGM with DRGP are developed by integrating the RDF and existing Diagnostic Robust Generalized Potential (DRGP); respectively, into the algorithm of GM-estimator. Results indicate that the performance of RWGM(RDF) estimator which uses RDF as part of its weighting scheme surpasses other methods under study. To date no work has been focused on robust bootstrapping methods for fixed effect panel data model. Thus, bootstrapping methods known as Diagnostic Bootstrap (Boot-D) and Weighted Bootstrap with RDF (Boot RDF) are also developed to provide resistance bootstrap estimates against block HLPs. In Boot-D, a diagnostic measure is introduced to eliminate any outlier from the sampling plan whereas new re-sampling with probabilities is derived in Boot RDF. In the study, Boot RDF is found to provide robust and superior performance as confirmed by the numerical examples and simulation results. This research also addresses the combined problem of HLPs and heteroskedastic errors for fixed effect panel data model. A two-step robust estimator called Two Step Heteroskedasticity-Outlier (TSHO) is proposed and successfully dampens both problems. This study is considered to be among the first to solve simultaneous problems of heteroskedastic and non-normal errors for panel data. Empirical evidence via simulation experiments and numerical data show TSHO to be persistent under zero or high level of contamination. Standard errors of the beta estimates are also corrected by the newly proposed heteroskedasticity- and outlier- robust standard error or HORSE estimator. Two types of robust weights are introduced in HORSE to protect against large residuals caused by block HLPs and also heteroskedasticity. In the events, simulation results indicate the lowering level of biasness by HORSE. This leads to the final conclusion that HORSE is able to produce less bias standard errors due to the robust weighting schemes introduced in its algorithm.

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