Simultaneous Least Squares: A Distribution Free Method of Equation System Structure Estimation

Abstract

A METHOD of structure estimation is here developed which separates the regular from the random component of structure by minimizing the vector distance between the observed data and the corresponding values computed from the systematic structure of a complete model treated as a whole. The method is, accordingly, the simultaneous equation counterpart of single equation least squares. It too is distribution free. The sample error variance-covariance matrix is constructed. Its elements are zero for an infinitely large sample. This, plus the hypothesis that only true structure could produce the above minimum vector distance, suggests consistency. The method is tested on a model with known structure, which generated its own data and moments. The estimates are equal to the true values. The method is also tested on a model with unknown structure, using actual data. The results are compared with estimates by other well-known methods. Further research on the relative efficiency of estimation methods is suggested.