Frequentist evaluation of small DSGE models

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.