Identification of DSGE models : a comparison of methods and the effect of second order approximation

Several formal methods have been proposed to check identification in DSGE models via (i) the autocovariogram (Iskrev 2010), (ii) the spectral density (Komunjer and Ng 2011; Qu and Tkachenko 2012), or (iii) Bayesian indicators (Koop et al 2012). Even though all methods seem similar, there has been no study of the advantages and drawbacks of implementing the different methods. The contribution of this paper is threefold: First, we derive all criteria in the same framework following Schmitt-Groh and Uribe (2004). While Iskrev (2010) already uses analytical derivatives, Komunjer and Ng (2011) and Qu and Tkachenko (2012) rely on numerical methods. For a rigorous comparison we thus show how to implement analytical derivatives into all criteria. We argue in favor of using analytical derivatives, whenever feasible, due to its robustness and greater speed than relying on numerical procedures. Second, we apply all methods on DSGE models that are known to have lack of identification. Our findings suggest that most of the times the methods come to the same conclusion, however, the issue of numerical errors due to nonlinearities and very large matrices may lead to unreliable or contradictory conclusions. The example models show that by evaluating different criteria we also gain inside into the dynamic structure of the DSGE model. We argue that in order to thoroughly analyze identification, one has to be aware of the advantages and drawbacks of the different methods. Third, we extend the methods to higher approximations given the pruned-state-space representation studied by Andreasen, Fern ndez-Villaverde and Rubio Ram rez (2014). It is argued that this can improve overall identification of a DSGE model via imposing additional restrictions on the mean and variance. In this way we are able to identify previously unidentified models.