Asymptotic Relative Efficiency Analysis of Certain Tests of Independence in Structural Systems

A new test of independence between the explanatory endogenous variables and the disturbance in a structural equation is proposed. The test was motivated by suspected inadequacies in the Revankar-Hartley test (RHT) in the case of an overidentified equation. The "asymptotic relative efficiency" criterion was utilized. The null hypothesis considered is that the explanatory endogenous variables in a structural equation are independent of the disturbance in that equation. The relative efficiencies of some tests are evaluated analytically in the context of a conventional but otherwsise arbitrary structural equation.