Marginalized Predictive Likelihood Comparisons of Linear Gaussian State-Space Models with Applications to DSGE, DSGE-VAR, and VAR Models

Summary: In a Bayesian setting, the predictive likelihood is of particular relevance when the objective is to rank models in a forecast comparison exercise. We discuss how the predictive likelihood can be estimated, by means of marginalization, for any subset of the observable variables in linear Gaussian state-space models and propose to utilize a missing observations consistent Kalman filter for that purpose. Based on this convenient and simple approach, we analyze euro area data and compare the density forecast performance of a DSGE model to a DSGE-VAR, a large BVAR, and a multivariate random walk model over the forecast sample 1999Q1–2011Q4. While the BVAR generally provides superior density forecasts, its performance deteriorates substantially with the onset of the Great Recession. This is particularly notable for longer-horizon real GDP forecasts, where the DSGE and DSGE-VAR models with stronger economic foundations perform better. In fact, for longer horizons the ranking of models changes over the forecast sample when the focus is on a subset of variables comprising real GDP growth, GDP deflator inflation, and the nominal interest rate