Impulse Response Functions in Generalized Bayesian Autoregressive Models

Vector autoregressions (VAR) are extensively used to model economic time series. The large number of parameters is the main diicult with VAR models, however. To overcome this, Litterman (1986) suggests to use a Bayesian strategy to estimate the VAR, equation by equation, where, a priori, the lags have decreasing importance (known as Litterman Prior). In this paper, a VAR model is analyzed through a Bayesian multivariate regression, with time varying parameter, i.e. a multivariate Bayesian dynamic linear model. In this case correlation between the VAR equations is allowed, as suggested by Kadiyala and Karlsson (1993). This methodology was applied to some Brazilian economic variables, as a bivariate VAR, (Lima, Migon and Lopes (1993)). The main interest remains in studying the impulse response functions sensitivity of Bayesian VAR modeling to the hyperparam-eters choice of the Litterman Prior. Conndence interval to these functions, extreme non-linear functions of the VAR parameters, are given.