Working Paper: CEPR ID: DP8177
Authors: Gianluca Benigno; Pierpaolo Benigno; Salvatore Nistic
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.
Keywords: Second Order Approximation; Stochastic Volatility; Uncertainty
JEL Codes: C63
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| first-order approximation (C60) | conditionally linear model (C20) |
| first-order approximation (C60) | endogenous variables (C29) |
| second-order approximation (C69) | time-varying volatility (C22) |
| second-order approximation (C69) | endogenous variables (C29) |
| first-order approximation (C60) | time-varying risk premia (C22) |
| standard linear approximations (C60) | constant risk premia (G19) |