Fiducial Approximations to Posterior Distributions

In this paper we consider the ducial argument of Fisher from the point of view of constructing e cient approximations of (or importance distributions to) posterior distributions in econometric models with intractable likelihood functions. The importance or proposal distributions are used along with MCMC methods for Bayesian inference. We propose several variations which are tested in arti cial and actual data, including the simultaneous equations model with weak instruments and multivariate stochastic volatility models. We routinely fi nd that versions of fiducial distributions provide reasonable approximations to posterior distributions and when they do not, we propose efficient techniques to improve dramatically the quality of approximation using MCMC techniques