This paper develops a method that uses a likelihood approach to directly compare two or more non-nested dynamic, stochastic general equilibrium (DSGE) models. It is shown how DSGE models can be compared across the whole sample and how this measure can be decomposed across individual observations thus allowing models to be compared across any sub-sample of the data. The method is applied to the problem of determining whether the technology shock process in a standard Real Business Cycle model should consist of permanent or temporary, albeit persistent, shocks. Overall, a permanent shock model has a better prediction performance than the temporary shock model. However, the model with the temporary shock performs much better for the part of the sample that includes the most of the 1980's and the 1990's.