Two Types of Residuals and the Classical Identifiability Test Statistic

This paper considers the relations between the classical identifiability test statistic and corresponding significance tests of the coefficients of endogenous variables of one equation of a linear interdependent system in the context of Generalized Classical Linear (GCL) estimation. Known theoretical and empirical results are reviewed and synthesized, within the framework of the modern theory of the linear hypothesis, and two theorems are developed. The first provides a link between GCL chi-squared tests and F-tests of Dhrymes (1968). The second provides a decomposition into GCL and chi-square test statistic components. Both theorems provide an explanation of why Monte Carlo results favour F-tests for identifiability.