Indirect inference and small sample bias - some recent results

Macroeconomic researchers use a variety of estimators to parameterise their models empirically. One such is FIML; another is a form of indirect inference we term "informal" under which data features are "targeted" by the model -i.e. parameters are chosen so that model-simulated features replicate the data features closely. In this paper we show, based on Monte Carlo experiments, that in the small samples prevalent in macro data, both these methods produce high bias, while formal indirect inference, in which the joint probability of the data- generated auxiliary model is maximised under the model simulated distribution, produces low bias. We also show that FII gets this low bias from its high power in rejecting misspecified models, which comes in turn from the fact that this distribution is restricted by the modelspecified parameters, so sharply distinguishing it from rival misspecified models.