Consistent Variance Of The Laplace‐Type Estimators: Application To Dsge Models

The Laplace‐type estimator has become popular in applied macroeconomics, in particular for estimation of dynamic stochastic general equilibrium (DSGE) models. It is often obtained as the mean and variance of a parameter's quasi‐posterior distribution, which is defined using a classical estimation objective. We demonstrate that the objective must be properly scaled; otherwise, arbitrarily small confidence intervals can be obtained if calculated directly from the quasi‐posterior distribution. We estimate a standard DSGE model and find that scaling up the objective may be useful in estimation with problematic parameter identification. It this case, however, it is important to adjust the quasi‐posterior variance to obtain valid confidence intervals.