Markov Chain Monte Carlo Simulation Methods in Econometrics

We present several Markov chain Monte Carlo simulation methods that have
been widely used in recent years in econometrics and statistics. Among these
is the Gibbs sampler, which has been of particular interest to econometricians.
Although the paper summarizes some of the relevant theoretical literature, its
emphasis is on the presentation and explanation of applications to important
models that are studied in econometrics. We include a discussion of some implementation
issues, the use of the methods in connection with the EM algorithm,
and how the methods can be helpful in model specification questions. Many
of the applications of these methods are of particular interest to Bayesians, but
we also point out ways in which frequentist statisticians may find the techniques
useful.

1. INTRODUCTION
In this paper we explain Markov chain Monte Carlo (MCMC) methods in
some detail and illustrate their application to problems in econometrics.
These procedures, which enable the simulation of a large set of multivariate
density functions, have greatly expanded the domain of Bayesian statistics
and appear to be applicable to many complex parametric econometric models.
Our purpose is to explain how these methods work both in theory and
in practical applications. Because many problems in Bayesian statistics (such
as the computation of posterior moments and marginal density functions)
can be solved by simulating the posterior distribution, we emphasize Bayesian
applications, but these tools are also valuable in frequentist inference,
where they can be used to explore the likelihood surface and to find modal
estimates or maximum likelihood estimates with diffuse priors.