Comparison of misspecified calibrated models: The minimum distance approach

This paper proposes several testing procedures for comparison of misspecified calibrated models. The proposed tests are of the Vuong-type (Vuong, 1989, Rivers and Vuong, 2002). In our framework, the econometrician selects values for model's parameters in order to match some characteristics of data with those implied by the theoretical model. We assume that all competing models are misspecified, and suggest a test for the null hypothesis that they provide equivalent fit to data characteristics, against the alternative that one of the models is a better approximation. We consider both nested and non-nested cases. We also relax the dependence of models' ranking on the choice of a weight matrix by suggesting averaged and sup-norm procedures. The methods are illustrated by comparing the cash-in-advance and portfolio adjustment cost models in their ability to match the impulse responses of output and inflation to money growth shocks.