Two Stage Least Absolute Deviations Estimators

Abstract

In this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model. A class of estimators called two stage least absolute deviations estimators is defined, their asymptotic properties are derived, and the problem of finding the optimal member of the class is considered. IN THIS PAPER WE APPLY the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model. We define a class of estimators called two stage least absolute deviations estimators (2SLAD) and derive their asymptotic properties. They are so named as their relationship to the two stage least squares estimator (2SLS) is analogous to the relationship of the least absolute deviations estimator (LAD) to the least squares estimator (LS) in the standard regression model. The LAD estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized. In this paper we show that the advantage of 2SLAD over 2SLS in the simultaneous equations model can be as great as that of LAD over LS in the standard regression model, if 2SLAD is properly defined. This last clause is very important, since the results of this paper indicate that the LAD analogue of 2SLS that has been considered before in the literature is not an appropriate method.