Introduction

Many econometric models are based on sets of simultaneous structural equations. Although there are methods for estimating the parameters of the entire system, procedures for single equations are relevant, because often only one in a small number of equations is of interest and because such procedures are much easier to carry out than full-system methods. Recently, the properties of these single-equation methods have been investigated extensively. The purpose of this chapter is to review some of these studies. Because this chapter is limited, we shall focus our attention on the two-stage least-squares (TSLS) estimator and the limited-information maximum-likelihood (LIML) estimator, which is also known as the least-variance-ratio estimator. Much of the work reported here has involved my associates Takamitsu Sawa, Naoto Kunitomo, and Kimio Morimune. The emphasis is on comparison of the TSLS and LIML estimators based on finite-sample distributions. We shall also comment on the higher-order efficiency of the LIML estimator and some improvements.