Comparison of Misspecified Calibrated Models: The Minimum Distance Approach

This paper presents 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, an econometrician selects values
for the parameters in order to match some characteristics of the 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 all
considered models provide equivalent fit to the data characteristics,
against the alternative that one of the models is a better approximation. We
consider both nested and non-nested cases. Our discussion includes the
situation when parameters are estimated to match one set of moments and the
model is evaluated by its ability to match another. We also relax the
dependence of ranking of the models on the choice of weight matrix by
suggesting averaged and sup procedures. The proposed method is applied
to comparison of cash-in-advance and portfolio adjustment cost models.