polyspectra

Closed-form expressions for unconditional moments, cumulants and polyspectra of order higher than two are derived for non-Gaussian or nonlinear (pruned) solutions to DSGE models. Apart from the existence of moments and white noise property no distributional assumptions are needed. The accuracy and utility of the formulas for computing skewness and kurtosis are demonstrated by three prominent models, the baseline medium-sized New Keynesian model used for empirical analysis (first-order approximation), a small-scale monetary business cycle model (second-order approximation) and the neoclassical growth model (third-order approximation). Both the Gaussian as well as Student’s t-distribution are considered as the underlying stochastic processes. Lastly, the efficiency gain of including higher-order statistics is demonstrated by the estimation of a RBC model within a Generalized Method of Moments framework.

This thesis adds to the literature on the local identification of nonlinear and non-Gaussian DSGE models. It gives applied researchers a strategy to detect identification problems and means to avoid them in practice. A comprehensive review of existing methods for linearized DSGE models is provided and extended to include restrictions from higher-order moments, cumulants and polyspectra. Another approach, established in this thesis, is to consider higher-order approximations. Formal rank criteria for a local identification of the deep parameters of nonlinear or non-Gaussian DSGE models, using the pruned state-space system are derived. The procedures can be implemented prior to estimating the nonlinear model. In this way, the identifiability of the Kim (2003) and the An and Schorfheide (2007) model are demonstrated, when solved by a second-order approximation.

This 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.