Comparing different data descriptors in Indirect Inference tests on DSGE models

•Evaluates the power of Indirect Inference testing in small samples.•Evaluates three different and widely-considered auxiliary models: VAR, Moments and Impulse Response Functions (IRFs).•Finds that VAR and IRFs invariably give similar power.•Finds that Moments gives similar power to the other two for simple macro model but considerably less power for a large macro model.

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.