Consistent Variance of the Laplace Type Estimators: Application to DSGE Models

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