Estimation of Nonlinear DSGE Models Through Laplace Based Solutions

Elnura Baiaman Kyzy and Roberto Leon-Gonzalez
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Elnura Baiaman Kyzy: Hitotsubashi Institute for Advanced Study (HIAS), Hitotsubashi University, Tokyo, Japan

No 24-06, GRIPS Discussion Papers from National Graduate Institute for Policy Studies

Abstract: This paper proposes a novel Laplace based solution to nonlinear DSGE models that has a closed form likelihood. We implicitly use a nonlinear approximation to the policy function that is invertible with respect to the shocks, implying that in the approximation the shocks can be recovered uniquely from some of the control variables. Using perturbation methods and a Lagrange inversion formula we are able to calculate the derivatives of the likelihood and construct the Laplace based solution. In contrast with previous likelihood-based approaches, the method used here requires neither the introduction of linear shocks nor simulation to evaluate the likelihood. Using US data we estimate linear and nonlinear variants of a well-known neoclassical growth model with and without time-varying variances. We find that a nonlinear heteroscedastic model has a much better empirical performance. Furthermore, our models allow us to ascertain that the monetary policy shock causes 95% of the time changes in economic uncertainty.

Keywords: Economic Uncertainty; Time-Varying Volatility; Risk-Premium; Higher-Order Approximation (search for similar items in EconPapers)
Pages: 49 pages
Date: 2024-07
New Economics Papers: this item is included in nep-dge
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https://grips.repo.nii.ac.jp/record/2000100/files/DP24-6.pdf (application/pdf)

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Working Paper: Estimation of Nonlinear DSGE Models Through Laplace Based Solutions (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:ngi:dpaper:24-06

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