Iterative Instrumental Variables Method and Estimation of a Large Simultaneous System

Abstract

The estimation method proposed here offers a way to achieve consistent estimates of simultaneous systems for which the number of observations falls short of the number of predetermined variables in the system as a whole. This method, called the iterative instrumental variables (IIV) method, can be described as iterative use of the instrumental variable interpretation of the 2SLS as given by Klein. A discussion is presented on convergence of the iterative procedure and the asymptotic properties of the IIV method. The special case of the OLS start of the iterative procedure is carefully examined. It is argued that the IIV and the 2SLS methods yield estimators with the same asymptotic distribution. An analysis of the asymptotic covariance matrix of the structural coefficients is presented and compared with that given by Basmann for the 2SLS method. Finally, we analyze the results of a test application of the IIV method to an undersized simultaneous system.