Estimation of a DSGE model under VAR expectations

The bad time series performances of dynamic stochastic general equilibrium (DSGE) models currently used in monetary policy, can be ascribed to the tight nature of the crossequation restrictions these models impose on vector autoregressions (VAR) for the data under the rational expectations (RE) hypothesis. Part of these restrictions involve constraints on the VAR dynamics, and are typically at odds with the data. We argue that a way to circumvent this issue is to resort to an expectations generating mechanism based on the idea that boundedly rational agents do not know the true model solution, and form their forecasts using more lags than predicted by the theoretical model. The paper proposes a novel approach for estimating and testing small-scale New Keynesian monetary DSGE models under ‘VAR expectations’. If properly embodied in the system, ‘VAR expectations’ allow to rule out that part of the restrictions that affect the lag order of the VAR without relaxing the other set of restrictions. After discussing solution properties and the conditions ensuring generic local identifiability of the structural parameters, the paper puts forth a likelihoodbased approach for estimating and testing the DSGE model through Newton-like methods. The analysis is generalized to the case where some of the variables in the system can be approximated as highly persistent nonstationary processes. We investigate the properties of the suggested estimation and testing method through Monte Carlo experiments.