The marginal likelihood of Structural Time Series Models , with application to the US and the euro area NAIRU ∗

We propose a new result that simplifies the evaluation of the marginal likelihood in Gaussian Structural Time Series (STS) models. For this we exploit the statistical properties of STS models and a theorem in Dickey (1968) to obtain the likelihood marginally to all variance parameters. Our strategy applies under inverted gamma-2 prior distributions for the structural shocks variances. In general, we show that marginalizing with respect to variance parameters greatly improves the accuracy of the Laplace method. Moreover, in some empirically relevant cases such as the local level and the local linear trend, it yields the marginal likelihood by single or double integration over a finite support. We use our methodology to weight models for the NAIRU in the US and in the euro area. * The ideas expressed here are those of the authors and do not necessarily reflect the positions of the European Commission. Thanks are due to Daniel Grenouilleau, Martin Hradisky, and Werner Roeger for useful discussions.