Coefficient estimation of simultaneous equations in the case of stochasticity of exogenous variables

Abstract

The paper deals with the question of obtaining such an estimate of the parameters of the model of simultaneous equations, which would have better statistical properties in comparison with the estimates of both the usual method of least squares and two-, three-step methods of least squares, as well as the method of fixed point and other methods of evaluating the coefficients of the equations considered in the system simultaneously. The main drawback of methods based on minimization of the sum of squares of deviations of real observations from some theoretical dependence is that the sum of squares of errors that correlate with the values of variables included in the expression for these errors is minimized. A violation of the basic assumption of least-squares methods about the independence of predetermined variables and errors leads to the fact that least-squares estimation methods in this case lose their best properties: unbiasedness, efficiency, and consistency. The paper proves the theorem about the efficiency of estimates obtained using two-step least squares methods and that of estimates obtained using the method of factorization of simultaneous equations.