Testing Macro Models by Indirect Inference: A Survey for Users

With Monte Carlo experiments on models in widespread use we examine the performance of indirect inference (II) tests of DSGE models in small samples. We compare these tests with ones based on direct inference (using the Likelihood Ratio, LR). We find that both tests have power so that a substantially false model will tend to be rejected by both; but that the power of the II test is substantially greater, both because the LR is applied after re-estimation of the model error processes and because the II test uses the false model’s own restricted distribution for the auxiliary model’s coefficients. This greater power allows users to focus this test more narrowly on features of interest, trading off power against tractability.