Model comparisons in unstable environments

The goal of this paper is to develop formal tests to evaluate the relative in-sample per- formance of two competing, misspecified, non-nested models in the presence of possible data instability. Compared to previous approaches to model selection, which are based on measures of global performance, we focus on the local relative performance of the models. We propose three tests that are based on different measures of local performance and that correspond to different null and alternative hypotheses. The empirical application provides insights into the time variation in the performance of a representative DSGE model of the European economy relative to that of VARs.