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 two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and a generalized method of moments (GMM) (or the estimating equation) estimator. Tables and figures 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 micro-econometric models with many instruments or many weak instruments in the terminology of recent econometric literatures. We give a new result on the asymptotic optimality of the LIML estimator when the number of instruments is large.