On Finite Sample Distributions of Generalized Classical Linear Identifiability Test Statistics

Abstract

In the estimation of econometric simultaneous equations models, hypothesized necessary conditions for the identifiability of a single equation usually specify the exclusion of a number of variables from the structural equation in question. If the pre-determined variables are completely exogenous, if the disturbances in the equations are jointly normally distributed, and if a moderately high degree of precision can be obtained in reduced-form estimation, then the exact finite sample distribution of the generalized classical linear identifiability test statistic can be closely approximated by Snedecor's F with appropriate degrees of freedom.