Comparing Indirect Inference and likelihood testing: Asymptotic and small sample results

Indirect Inference has been found to have much greater power than the Likelihood Ratio in small samples for testing DSGE models. We look at asymptotic and large sample properties of these tests to understand why this might be the case. We find that the power of the LR test is undermined when reestimation of the error parameters is permitted; this offsets the effect of the falseness of structural parameters on the overall forecast error. Even when the two tests are done on a like-for-like basis Indirect Inference has more power because it uses the distribution restricted by the DSGE model being tested.