Abstract
Abstract Standard solution methods of DSGE models do not necessarily deliver minimal state space forms. When the ABCD form is non-minimal, the conditions in the literature are not necessary for the existence of a VAR representation of the observables. In this paper we present necessary and sufficient conditions that are valid in general, and hence can be applied to minimal and non-minimal ABCD forms. If the state space form is minimal, our conditions coincide with those in the literature. These results also clarify that it is possible to have unstable eigenvalues together with a (possibly finite) VAR representation of the observables.
Highlights
Economic shocks of DSGE models cannot always be recovered from VARs
Because in current economic practice systems are not always in minimal state space form, in this paper we present alternative orthogonality conditions that are necessary and sufficient and which hold in possibly non-minimal square systems
In square ABCD forms, it is of interest, see e.g. Fernández-Villaverde et al (2007), to characterize situations in which the economic shocks can be recovered from the infinite history of the observable variables, i.e. cases in which yt admits an infinite order VAR representation
Summary
Economic shocks of DSGE models cannot always be recovered from VARs. This situation has been discussed e.g. in Chari et al (2005), Christiano et al (2006), Kapetanios. Because in current economic practice systems are not always in minimal state space form, in this paper we present alternative orthogonality conditions that are necessary and sufficient and which hold in possibly non-minimal square systems This provides a check that does not require to transform the system to minimal ABCD form. Existence of a finite VAR representation should be checked either using the present orthogonality conditions or by first transforming the state space form to a minimal representation and by applying the unimodularity condition to the minimal state space form, see Franchi (2013) for an illustration on the Smets and Wouters (2007) model.
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