Higher-order statistics for DSGE models
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Date
2016
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Abstract
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: Smets and Wouters
(AER, 586-606, 97, 2007) (first-order approximation), An and Schorfheide (Econom.
Rev., 113-172, 26, 2007) (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.
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Keywords
higher-order statistics, GMM, pruning, polyspectra, cumulants