Research Article Open Access

Bayesian Estimation of Simultaneous Equation Models with Outliers and Multicollinearity Problem

Abstract

Outliers and multicollinearity are problems in the analysis of Simultaneous Equation Model (SEM). They can lead to bias or inefficiency of estimators. This study employed a Bayesian technique for estimation of SEM that is characterized with both multicollinearity and outliers. Monte Carlo experiment was applied while the data sets with specified outliers and multicollinearity were simulated for the SEM. The estimates of Bayesian and classical methods namely; two Stage Least Squares (2SLS), Three Stage Least Squares (3SLS), and Ordinary Least Squares (OLS) in simultaneous equation model were then compared. The criteria used for comparison were the Mean Square Error (MSE) and Absolute Bias (AB). The Bayesian method of estimation outperformed other classical methods followed by two stage least squares, three stage least squares, and limited information maximum likelihood in terms of MSE and AB. However, the classical method has the same performance with Bayesian method when there are no outliers and multicollinearity in the simultaneous equation model. Hence, Bayesian method of estimation is preferred than classical method when there is problem of outlier and multicollinearity in a just identified simultaneous equation model. Mathematical subject classification: 62C10, 62CO7.

Oluwadare O Ojo*, Oluwaseun A Adesina

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