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 Ch ao and Phillips (1998, CP), Geweke (1996), Kleibergen and van Dijk (1998, KVD), and Zellner (1998). Amongst the Sample theory methods, OLS, 2SLS, LIML, Fuller's modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist, Imben s 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 availabi lity 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 endogeneity is not weak and $\rho$$w_{12}>0$, where $\rho$ is the correlation coefficient between the structural and reduced form errors, and $w_{12}$ is the covariance between the unrestricted reduced form errors, BMOM outp erforms all other estimators by a wide margin. When the endogeneity is not weak and $\beta \rho <0$ ($\beta$ being the structural parameter), KVD approach seems to work very well. Surprisingly, the performance of JIVE was disappointing in all our experim ents.
