Factor-analysis estimation of simultaneity-error models

Abstract

A traditional economic simultaneous equation system, herein termed a pure-simultaneity model, is remodelled to take into account the observation errors which me often contained in the dependent (or endogenous) and predetermined variables of the system. Such a remodelled system will be called a simultaneity-error model. It is then shown that the simultaneity-error model may be transformed into a restricted factor-analysis model with Its factor loadings matrix partitioned into a non-identity submatrix and an identity submatrix of order equal to the number of common factors Then, under a special assumption that requires the structural parameters in the transformed restricted factor-analysis model to satisfy a dingonality condition, a three-stage iterative estimation method, using the Newton-Kaphson process, is proposed to estimate the parameters of the restricted factor-analysis model. The structural coefficients of the simultaneity-error model are then derived indirectly from the stepwise factor-analysis es...