Second-Order Approximation of Dynamic Models with Time-Varying Risk

25 Pages Posted: 27 Dec 2010 Last revised: 14 Jun 2023

See all articles by Gianluca Benigno

Gianluca Benigno

Federal Reserve Bank of New York; London School of Economics & Political Science (LSE) - Department of Economics

Pierpaolo Benigno

University of Bern - Department of Economics

Salvatore Nisticò

Sapienza University - Department of Social Science and Economics

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Date Written: December 2010

Abstract

This paper provides first and second-order approximation methods for the solution of non-linear dynamic stochastic models in which the exogenous state variables follow conditionally-linear stochastic processes displaying time-varying risk. The first-order approximation is consistent with a conditionally-linear model in which risk is still time-varying but has no distinct role -- separated from the primitive stochastic disturbances -- in influencing the endogenous variables. The second-order approximation of the solution, instead, is sufficient to get this role. Moreover, risk premia, evaluated using only a first-order approximation of the solution, will be also time varying.

Suggested Citation

Benigno, Gianluca and Benigno, Gianluca and Benigno, Pierpaolo and Nisticò, Salvatore, Second-Order Approximation of Dynamic Models with Time-Varying Risk (December 2010). NBER Working Paper No. w16633, Available at SSRN: https://ssrn.com/abstract=1730580

Gianluca Benigno (Contact Author)

Federal Reserve Bank of New York ( email )

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London School of Economics & Political Science (LSE) - Department of Economics

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Pierpaolo Benigno

University of Bern - Department of Economics ( email )

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Salvatore Nisticò

Sapienza University - Department of Social Science and Economics ( email )

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Rome, 00185
Italy

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