The small sample properties of Indirect Inference in testing and estimating DSGE models

Indirect inference testing can be carried out with a variety of auxiliary models. Asymptotically these different models make no difference. However, the small sample properties can differ. We explore small sample power and estimation bias both with different variable combinations and descriptive models (Vector Auto Regressions, Impulse Response Functions or Moments) in the auxiliary model. We find that both power and bias are similar when the number of variables used is the same. Raising the number of variables lowers the bias but may also raise the power unacceptably because it lowers the chances of finding a tractable model to pass the test.