Cross Equation Effects of Misspecification: A partial estimation approach to DSGE Models

Fully specified DSGE models are increasingly successful in explaining observed macroeconomic data. Thinking about the specification of a certain equation in a DSGE approach has the drawback of imposing many implicit priors on the specification of the remaining equations. Mis-specifications in one block can have effects on the structural parameter estimates of the remaining equations. One resort from this problem is to use a VAR as an auxiliary model and to impose the structural equations stepwise on the unrestricted VAR. In a linear framework, we can interpret the unrestricted equations as an approximation of the solution process of the structural model. Once the model contains unobservable variables the solution process does not have a finite VAR representation anymore and the VAR approximation to the solution process is misspecified. The method of indirect inference allows to correct for mis-specification in the auxiliary model. The approach is illustrated with the example of the basic New Keynesian Phillips Curve and an extended version containing unobservable variables. In a Monte Carlo exercise the estimation properties of Kalman filter based maximum likelihood and indirect inference are evaluated for both models