No. 3/2013: Frequentist evaluation of small DSGE models
Abstract
This paper proposes a new evaluation approach of the class of small-scale `hybrid' New
Keynesian Dynamic Stochastic General Equilibrium (NK-DSGE) models typically used in
monetary policy and business cycle analysis. The novelty of our method is that the empirical
assessment of the NK-DSGE model is based on a conditional sequence of likelihood-based
tests conducted in a Vector Autoregressive (VAR) system in which both the low and high
frequency implications of the model are addressed in a coherent framework. The idea is that
if the low frequency behaviour of the original time series of the model can be approximated
by unit roots, stationarity must be imposed by removing the stochastic trends. This means
that with respect to the original variables, the solution of the NK-DSGE model is a VAR
that embodies a set of recoverable unit roots/cointegration restrictions, in addition to the
cross-equation restrictions implied by the rational expectations hypothesis. The procedure
is based on the sequence `LR1->LR2->LR3', where LR1 is the cointegration rank test, LR2
the cointegration matrix test and LR3 the cross-equation restrictions test: LR2 is computed
conditional on LR1 and LR3 is computed conditional on LR2. The type-I errors of the
three tests are set consistently with a pre-fixed overall nominal significance level and the
NK-DSGE model is not rejected if no rejection occurs. We investigate the empirical size
properties of the proposed testing strategy by a Monte Carlo experiment and illustrate the
usefulness of our approach by estimating a monetary business cycle NK-DSGE model using
U.S. quarterly data.
Keywords: DSGE models, LR test, Maximum Likelihood, New-Keynesian model, VAR
J.E.L. C5, E4, E5.