EFFICIENCY GAINS OF SYSTEM GMM AND MDE OVER INDIVIDUAL EQUATION ESTIMATION*

Abstract

In the econometric literature it is known that, under certain conditions, estimating a system of equations together is more efficient than estimating each equation separately. This finding has been proved, however, only under the assumption of a known parametric form of heteroskedasticity (including homoskedasticity) or non-random regressors/instru-ments. This note shows that an analogous finding holds for GMM under heteroskedasticity of unknown form and random regressors/instruments. Specifically, I provide a necessary condition for the efficiency gain of the system GMM over the single-equation GMM. An analogous necessary condition for the efficiency gain is also shown to hold for minimum-distance (or X2) estimation (MDE).