TESTS OF OVERIDENTIFICATION AND PREDETERMINEDNESS IN SIMULTANEOUS EQUATION MODELS

A set of simultaneous equations that is a part of a larger complete system is considered. One hypothesis concerning this set of equations is that it is overidentified as a block by a block of zero restrictions. Another hypothesis is that a subset of the current endogenous variables is uncorrelated with the disturbances in the set of simultaneous equations ('econometric predeterminedness'). Likelihood ratio, Lagrange multiplier, and Wald tests are derived for the overidentification hypothesis against unrestricted alternatives. for the predeterminedness hypothesis against unrestricted alternatives, and for the predeterminedness hypothesis against overidentified alternatives. The tests are derived on the basis of normality but are asymptotically valid under very general conditions. This study generalizes and unities many test procedures proposed previously. Some new tests are developed.