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a b s t r a c tThis paper shows how to check rank criteria for a local identification of nonlinear DSGE models, given higher-order approximations and pruning. This approach imposes additional restrictions on (higher-order) moments and polyspectra, which can be used to identify parameters that are unidentified in a first-order approximation. The identification procedures are demonstrated by means of the Kim (2003) and the An and Schorfheide (2007) models. Both models are identifiable with a second-order approximation. Furthermore, analytical derivatives of unconditional moments, cumulants and corresponding polyspectra up to fourth order are derived for the pruned state-space.

Both the investment adjustment costs parameters in Kim (2003) and the monetary policy rule parameters in An & Schorfheide (2007) are locally not identifiable. We show means to dissolve this theoretical lack of identification by looking at (1) the set of observed variables, (2) functional specifications (level vs. growth costs, output-gap definition), (3) model features (capital utilization, partial inflation indexation), and (4) additional shocks (investment-specific technology, preference). Moreover, we discuss the effect of these changes on the strength of parameter identification from a Bayesian point of view. Our results indicate that researchers should treat parameter identification as a model property, i.e. from a model building perspective.

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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 coefficients of the Taylor-rule.