We present several Markov chain Monte Carlo simulation methods that ha
ve been widely used in recent years in econometrics and statistics, Am
ong 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 expla
nation of applications to important models that are studied in econome
trics, We include a discussion of some implementation issues, the use
of the methods in connection with the EM algorithm, and how the method
s can be helpful in model specification questions, Many of the applica
tions of these methods are of particular interest to Bayesians, but we
also point out ways in which frequentist statisticians may find the t
echniques useful.