Robust versus traditional methods for outlier detection in the simultaneous equations model

Abstract

The Simultaneous Equation Model (SEM) is used for modelling real problems aris ing from Econometrics, Finance and other fields (see, for example, Greene [2003], Chen et al. [2007] or Lee et al. [2017]). The model is caracterized by a system of dependent equations whose coefficients can be estimated by methods like the Three Stages Least Squares (3SLS) or the Generalized Method of Moments (GMM). The corresponding estimators have nice properties but, unfortunately, they are not ro bust. Besides, outlier observations are particularly difficult to detect and interpret in the SEM and the use of non-robust estimators in the process reduces the confi dence on potential outlier detection analysis. We present a study that illustrates the use of a robust outlier detection method. The estimation of the coefficients of the model is performed with a robust version of the GMM. Outliers are interpreted and considered as outliers in the residuals, for the response variables, or as outliers in the explanatory variables. Identification of outlying points is based on the distribution of the robust Mahalanobis distances, computed with Minimum Covariance Determinant estimates and using a generalized inverse. The method is compared with outlier detection based on traditional non robust procedures, namely using Mahalanobis distances with the 3SLS, since the latter is a very popular estimator for the SEM parameters. A real data example with Econometric Portuguese data and a simulation study show the advantages of the robust proposal.