Robust Two-Stage Least Squares: some Monte Carlo experiments

The Two-Stage Least Squares (2-SLS) is a well known econometric technique used to estimate the parameters of a multi-equation (or simultaneous equations) econometric model when errors across the equations are not correlated and the equation(s) concerned is (are) over-identified or exactly identified. However, in presence of outliers in the data matrix, the classical 2-SLS has a very poor performance. In this study a method has been proposed to conveniently generalize the 2-SLS to the weighted 2-SLS (W2-SLS), which is robust to the effects of outliers and perturbations in the data matrix. Monte Carlo experiments have been conducted to demonstrate the performance of the proposed method. It has been found that robustness of the proposed method is not much destabilized by the magnitude of outliers, but it is sensitive to the number of outliers/perturbations in the data matrix. The breakdown point of the method is quite high, somewhere between 45 to 50 percent of the number of points in the data matrix.