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

The predictive likelihood is of particular relevance in a Bayesian setting when the purpose is to rank models in a forecast comparison exercise. This paper discusses how the pre-dictive likelihood can be estimated for any subset of the observable variables in linear Gaussian state-space models with Bayesian methods, and proposes to utilize a missing observations consistent Kalman filter in the process of achieving this objective. As an empirical application, we analyze euro area data and compare the density forecast performance of a DSGE model to DSGE-VARs, a BVAR, and a multivariate random walk model.