On the Admissible Transformation View on Identification for a Linear Simultaneous Equation Model

For a linear simultaneous equation model in econometrics, one authoritative definition of identification is Fisher's admissible transformation view. It takes parameter restriction and covariance restriction together into consideration. We show that the covariance restriction on disturbance terms may obstruct the exclusion restriction on variables. The exclusion restriction on variables is necessary for the test of observationally equivalent of equations so that the union identification does not hold true.