Robust estimation and detection of outliers in simultaneous regression model

The Two Stage Least Squares (2SLS) method is the commonly used method to estimate the parameters of the Simultaneous Equation Regression Model (SEM). This method employs the Ordinary Least Squares (OLS) method twice. Firstly, the endogenous X variable is estimated by the OLS and secondly the parameters of the SEM are again estimated using the OLS. It is now evident that the OLS method is easily affected by outliers. Consequently the 2SLS estimates are less efficient in the presence of outliers. Hence robust estimation methods such as the 2SMM, 2SGM6, 2SMMGM6 and 2SGM6MM are formulated to remedy this problem. These methods employ two robust methods in the first and in the second stages. The findings signify that the 2SGM6MM provides the most efficient results compared to other methods. Since the distributions of the proposed methods are intractable, robust bootstraps methods are developed to estimate the standard errors of the estimates. The findings indicate that the 2SGM6MM bootstraps standard errors of the estimates are the smallest compared to other estimates. The identification of high leverage points (HLPs) is very crucial because it is responsible for the drastic change in the parameter estimates of various regression models. Nonetheless, thus far no research has been done to detect HLPs in SEM. Hence, the Diagnostic Robust Generalized Potential (DRGP), Generalized Potential (GP) and Hat Matrix are incorporated with OLS, MM and the GM6 estimator in the development of diagnostic measures for the identification of HLPs in SEM. The results of the study show that the DRGPSEM based on the GM6 estimator is the most successful method in the detection of HLPs compared to other methods in this study.

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