Targeting moments for calibration compared with indirect inference

A common practice in estimating parameters in DSGE models is to Önd a set that when simulated gets close to an average of certain data moments; the modelís simulated performance for other moments is then compared to the data for these as an informal test of the model. We call this procedure informal Indirect Inference, III. By contrast what we call Formal Indirect Inference, FII, chooses a set of moments as the auxiliary model and computes the Wald statistic for the joint distribution of these moments according to the structural DSGE model; it tests the model according to the probability of obtaining the data moments. The FII estimator then chooses structural parameters that maximise this probability. We show in this note via Monte Carlo experiments that the FII estimator has low bias in small samples, whereas the III estimator has much higher bias. It follows that models estimated by III will typically also be rejected by formal indirect inference tests.