Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo

Abstract

textabstractMonte Carlo (MC) is used to draw parameter values from a distribution defined on the structural parameter space of an equation system. Making use of the prior density, the likelihood, and Bayes' Theorem it is possible to estimate posterior moments of both structural and reduced form parameters. The MC method allows a rather liberal choice of prior distributions. The number of elementary operations to be preformed need not be an explosive function of the number of parameters involved. The method overcomes some existing difficulties of applying Bayesian methods to medium size models. The method is applied to a small scale macro model. The prior information used stems from considerations regarding short and long run behavior of the model and form extraneous observations on empirical long term ratios of economic variables. Likelihood contours for several parameter combinations are plotted, and some marginal posterior densities are assessed by MC.