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Higher-order statistics for DSGE models

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  • Mutschler, Willi

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: the baseline medium-sized New Keynesian model used for empirical analysis (first-order approximation), a small-scale 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.

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  • Mutschler, Willi, 2018. "Higher-order statistics for DSGE models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 44-56.
    • Handle: RePEc:eee:ecosta:v:6:y:2018:i:c:p:44-56
    DOI: 10.1016/j.ecosta.2016.10.005
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    2. Javed, Farrukh & Loperfido, Nicola & Mazur, Stepan, 2024. "Edgeworth expansions for multivariate random sums," Econometrics and Statistics, Elsevier, vol. 31(C), pages 66-80.
    3. Mutschler, Willi, 2015. "Identification of DSGE models—The effect of higher-order approximation and pruning," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 34-54.
    4. Olatunji Abdul Shobande & Oladimeji Tomiwa Shodipe, 2021. "Monetary Policy Interdependency in Fisher Effect: A Comparative Evidence," Journal of Central Banking Theory and Practice, Central bank of Montenegro, vol. 10(1), pages 203-226.
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      • Stéphane Adjemian & Houtan Bastani & Michel Juillard & Frédéric Karamé & Ferhat Mihoubi & Willi Mutschler & Johannes Pfeifer & Marco Ratto & Sébastien Villemot & Normann Rion, 2023. "Dynare: Reference Manual Version 5," PSE Working Papers hal-04219920, HAL.
      • Stéphane Adjemian & Houtan Bastani & Michel Juillard & Frédéric Karamé & Ferhat Mihoubi & Willi Mutschler & Johannes Pfeifer & Marco Ratto & Sébastien Villemot & Normann Rion, 2023. "Dynare: Reference Manual Version 5," Working Papers hal-04219920, HAL.

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    More about this item

    Keywords

    Higher-order moments; Cumulants; Polyspectra; Nonlinear DSGE; Pruning; GMM;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

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