Impulse response matching estimators for DSGE models

The existing asymptotic theory for VAR-based impulse response matching estimators of the structural parameters of DSGE models does not cover situations in which the number of impulse responses exceeds the number of VAR model parameters. We establish the consistency of the estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. We also demonstrate that under our assumptions special care is needed to ensure the asymptotic validity of Bayesian methods of inference. Finally, we show how to deal with weak identification both under our assumptions and under standard assumptions.