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.