Comparing different data descriptors in indirect inference tests on DSGE models

Indirect inference testing can be carried out with a variety of auxiliary models. Asymptotically these different models make no difference. However, in small samples power can differ. We explore small sample power with three different auxiliary models: a VAR, average Impulse Response Functions and Moments. The latter corresponds to the Simulated Moments Method. We find that in a small macro model there is no difference in power. But in a large complex macro model the power with Moments rises more slowly with increasing misspecification than with the other two which remain similar.