The potential for efficiency gains in estimation from the use of additional moment restrictions

Abstract

It is frequently assumed that in Generalised Method of Moments estimation the explicit utilization of valid additional moment restrictions will lead to asymptotic efficiency gains. In this paper I develop a general framework for examining the possibility of such efficiency gains. Using this framework, I then consider in more detail the potential for efficiency gains from utilizing a constant conditional disturbance variance restriction when estimating a single equation from a nonlinear Simultaneous Equations Model (SEM) by nonlinear Two Stage Least Squares (2SLS). In general such efficiency gains will arise; however, for a linear SEM with constant disturbance covariances and zero third moments no efficiency gains arise for fairly general instrument sets. This generalises, in certain respects, the usual result that 2SLS is asymptotically efficient for estimating a single equation from a linear SEM with independently identically distributed normal disturbances.