Identification of DSGE Models - the Effect of Higher-Order Approximation and Pruning

Several formal methods have been proposed to check local identification in linearized DSGE models using rank criteria. Recently there has been huge progress in the estimation of non-linear DSGE models, yet formal identification criteria are missing. The contribution of the paper is threefold: First, we extend the existent methods to higher-order approximations and establish rank criteria for local identification given the pruned state-space representation. It is shown that this may improve overall identification of a DSGE model via imposing additional restrictions on the moments and spectrum. Second, we derive analytical derivatives of the reduced-form matrices, unconditional moments and spectral density for the pruned state-space system. Third, using a second-order approximation, we are able to identify previously non-identifiable parameters: namely the parameters governing the investment adjustment costs in the Kim (2003) model and all parameters in the An and Schorfheide (2007) model, including the coeffcients of the Taylor-rule.