DP8177 Second Order Approximation of Dynamic Models with Time-Varying Risk
| 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.