Estimation of an overidentified equation in an econometric model by the method of generalized least squares

Abstract

As a mathematical preliminary we first prove by construction in Section III, that there always exists a matrix B of the form mxn and of rank r, which has the shortest Euclidean distance from a given matrix A of the form m×n and of rank greater than or equal to r. B may be called the rank r nearest Euclidean neighbour of the matrix A. This result becomes handy in Section IV where we show how to estimate the coefficiants of an overidentified equation of an econometric model, by the model of generalized least squares. Linear estimation appropriate for a multivariate linear model is first used to estimate the coefficients of the matrix A of an econometic model in its reduced form Next, these estimators are used to derive the estimators of the coefficients of the overidentified equation together with improved estimtators of the coefficients of the matrix A. Although presented in the context of econometrics, the statistical model and the estimation procedure will fit in in other areas of research as well.