Model comparisons in unstable environments

The goal of this paper is to develop formal tests to evaluate the relative in-sample performance of two competing, misspeci…ed 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 di¤erent measures of local performance and that correspond to di¤erent 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. Keywords: Model Selection Tests, Misspeci…cation, Structural Change, Kullback-Leibler Information Criterion Acknowledgments: We are grateful to M. del Negro, F. Smets, R. Wouters, W.B. Wu and Z. Zhao for sharing their codes. We also thank the editor, three anonymous referees, seminar participants at the Empirical Macro Study Group at Duke U., Atlanta Fed, UC Berkeley, UC Davis, U. of Michigan, NYU Stern, Boston U., U. of Montreal, UNC Chapel Hill, U. of Wisconsin, UCI, LSE, UCL, Stanford’s 2006 SITE workshop, the 2006 Cleveland Fed workshop, the 2006 Triangle Econometrics workshop, the Fifth ECB Workshop, the 2006 Cass Business School Conference on Structural Breaks and Persistence, the 2007 NBER Summer Institute, the 2009 NBER-NSF Time Series Conference and the 2012 AEA Meetings for useful comments and suggestions. Support by NSF grants 0647627 and 0647770 is gratefully acknowledged. J.E.L. Codes: C22, C52, C53