CIRJEF399  "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments" 
Author Name  Anderson, T. W., Naoto Kunitomo and Yukitoshi Matsushita 
Date  February 2006 
Full Paper  PDF file@ 
Remarks  Revised version of CIRJEF321 (2005); revised as 2008CF542 and 2008CF577. 
Abstract 
We compare four different estimation methods for a coefficient of a linear structural equation
with instrumental variables. As the classical methods we consider the limited information
maximum likelihood (LIML) estimator and the twostage least squares (TSLS)
estimator, and as the semiparametric estimation methods we consider the maximum empirical
likelihood (MEL) estimator and the generalized method of moments (GMM) (or
the estimating equation) estimator. We prove several theorems on the asymptotic optimality
of the LIML estimator when the number of instruments is large, which are new as
well as old, and we relate them to the results in some recent studies. Tables and figures of
the distribution functions of four estimators are given for enough values of the parameters
to cover most of interest. We have found that the LIML estimator has good performance
when the number of instruments is large, that is, the microeconometric models with many
instruments in the terminology of recent econometric literature.
