Structural identification of simultaneous equation system
by
Alexander Gorobets
Sevastopol state technical university

The model to be considered is a system of m nonlinear simultaneous equations F(Y, X, Ai) = U, where F is the true but unknown vector of models, Y is the m x n - matrix of endogenous variables (n is a total number of observations), X is a k x n - matrix of predetermined variables, Ai is a vector of unknown parameters in i-th structural equation(i=1..m), and U is a m x n matrix of disturbances with zero mean and covariance matrix S. We have a large number of similar models which are nested one in other. These models differ with each other not only the number of variables but they can have the different number of equation also. The main problem is selection the optimal structure of simultaneous equation system which minimize the expected error of prediction of endogenous variables. The objective of the research is to present the method of selection of the optimal structure of the functions F and to investigate two criteria that assures one quality in the selection strategy, such as the average of the mean square error of prediction (AMSEP). The next two criteria are proposed: Cr=n*ln(trR)+2*Epi and Crn=n*ln(detR)+2*Epi , where tr is the trace of matrix, det is the determinant of matrix, R is the matrix of resudials for all equations, where elements of main diagonal are RSSi - resudial sum of squares for each equation and the rest elements are covariances between resudials of equations, pi is the number of parameters in i-th equation (E is the symbol of sum). Monte-Carlo methods with the use of computer simulations have given concrete results for identification and selection of the optimal model, depending on a large number of parameters. Proposed method has been used for selecting the optimal structure of Sevastopol region economics and good results were received in the conditions of the limited sample of observations.

Date received: February 16, 2000