| This study deals with estimation of limited information simultaneous equations models in the presence of weak instruments. There are five Chapters. Chapter 1 is an overview of the issues considered, and outlines the major results. Chapter 2 is concerned with the finite sample properties of classical LIML and 2SLS estimators. I explored the consequences of viewing LIML as an iterated Aitken estimator. I derive a simple expression for the difference between 2SLS and LIML in finite samples.;In Chapter 3, I compare Zellner's (1998) extended MELO (ZEM) and Bayesian Method of Moments (BMOM) estimators with a number of other estimators in simultaneous equations models with weak instruments. Among them, I consider recent Bayesian approaches developed by Chao and Phillips (1998, CP), Kleibergen and van Dijk (1998, KVD), and Geweke (1996). Since the posterior densities and their conditionals in CP and KVD are non-standard, we propose a "Gibbs within M-H" algorithm, which only requires the availability of the conditional densities from the candidate generating density. These conditional densities are used in a Gibbs sampler (GS) to simulate the candidate generating density, whose drawings, after convergence, are then weighted to generate drawings from the target density in a Metropolis-Hastings (M-H) algorithm.;In Chapter 4, I try to evaluate numerically the quality of the Laplace's method by comparing it to the marginal posterior density obtained through the "GS-within-MH" algorithm.;Since Zellner's BMOM estimators exhibit exceptional performance for a wide range of model specification even in the presence of weak instruments, and it has the same form as that of Nagar's (1962) double K-class estimator, it is important to reexamine the properties of the double K-class estimator. Dwivedi and Srivastava (1984, DS) derived the first two moments of double K-class estimators as continuous functions of the two characterizing scalars k1 , and k2 and provided guidelines for empirical work based on some limited Monte Carlo study. In Chapter 5, I show that the empirical guidelines provided by DS are not entirely valid since they did not explore the whole range of the relevant parameter space in their numerical evaluations. (Abstract shortened by UMI.). |
