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

Author(s): Pierpaolo Benigno, Gianluca Benigno and Salvatore Nisticò

Publication Date: January 2011

Keyword(s): second order approximation, stochastic volatility and uncertainty

Programme Area(s): International Macroeconomics

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.

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Bibliographic Reference

Benigno, P, Benigno, G and Nisticò, S. 2011. 'Second Order Approximation of Dynamic Models with Time-Varying Risk'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=8177