We compare the finite sample performance of a number of Bayesian and classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider recent Bayesian approaches developed by Chao and Phillips (1998, CP), Geweke (1996), Kleibergen and van Dijk (1998, KVD), and Zellner (1998). Amongst the sampling theory methods, OLS, 2SLS, LIML, Fuller's modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist, Imbens and Krueger (1999) and Blomquist and Dahlberg (1999) are also considered. Since the posterior densities and their conditionals in CP and KVD are non-standard, we propose a "Gibbs within Metropolis-Hastings" algorithm, which only requires the availability of the conditional densities from the candidate generating density. Our results show that in cases with very weak instruments, there is no single estimator that is superior to others in all cases. When endogeneity is weak, Zellner's MELO does the best. When the

We set out a Gibbs sampler for the linear instrumental-variable model with normal errors and normal priors, and we show how to compute the marginal likelihood. 1

Abstract: Wecomparethe¯nitesampleperformanceofanumberofBayesian and classicalprocedures forlimitedinformationsimultaneous equationsmodels with weak instruments by a Monte Carlo study. We consider recent