The effects of using different distributions to parameterize the prior beliefs in a Bayesian analysis of vector autoregressions are studied. The wellknown Minnesota prior of Litterman as well as four less restrictive distributions are considered. TWO of these prior distributions are new to vector autoregressive models. When the forecasting performance of the different parameterizations of the prior beliefs are compared it is found that the prior distributions that allow for dependencies between the equations of the VAR give rise to better forecasts. KEY WORDS Diffuse prior ENC prior Normal-Diffuse prior Normal-Wishart prior Minnesota prior Monte Carlo integration Multivariate time series
The use of Vector Autoregressive (VAR) models in applied economics has increased significantly following the criticism of the Cowles Commission approach to the modelling of systems of simultaneous equations (see, for example, Sims, 1980). There has been a shift from the modelling of economic systems with structural equations towards modelling the joint timeseries behaviour of the variables. The frequent use of VARs for modelling the time-series behaviour can partly be explained by their relative ease of use as compared to the richer class of vector ARMA models. The main advantage of VAR models lies in the identification stage, especially if all variables are taken to enter with identical lags. The estimation problem is also particularly simple in the case of identical lags. In the classical analysis, OLS is efficient under the usual assumptions and the Bayesian case is also considerably more straightforward.
The main disadvantage of the VAR models is the large number of parameters that need to be estimated. With the sample sizes common in economics the classical estimation procedures often run into degrees-of-freedom problems. In a Bayesian framework, on the other hand, sharp posteriors can often be obtained even with relatively uninformative prior distributions.