This paper deals with Dynamic Stochastic General Equilibrium (DSGE) models
under a multivariate student-$t$ distribution for the structural shocks.
Based on the solution algorithm of Klein (2000) and the gamma-normal
representation of the t-distribution, the TaRB-MH algorithm of Chib and
Ramamurthy (2010) is used to estimate the model. A technique for estimating
the marginal likelihood of the DSGE student-t model is also provided. The
methodologies are illustrated first with simulated data and then with the
DSGE model of Ireland (2004) where the results support the t-error
model in relation to the Gaussian model.