Author(s):	Pierpaolo Benigno, Gianluca Benigno, Salvatore Nisticò
Publication Date:	January 2011
Keyword(s):	second order approximation, stochastic volatility, uncertainty
JEL(s):	C63
Programme Areas:	International Macroeconomics
Link to this Page:	cepr.org/active/publications/discussion_papers/dp.php?dpno=8177

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.