One of the leading methods of estimating the structural parameters of DSGE models is the VAR-based impulse response matching estimator. The existing asymptotic theory for this estimator does not cover situations in which the number of impulse response parameters exceeds the number of VAR model...

We show that in weakly identified models (1) the posterior mode will not be a consistent estimator of the true parameter vector, (2) the posterior distribution will not be Gaussian even asymptotically, and (3) Bayesian credible sets and frequentist confidence sets will not coincide...