Second-Order Approximation of Dynamic Models with Time-Varying Risk
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.
Financial support from and ERC Starting Independent Grant is gratefully acknowledged. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Benigno, Gianluca & Benigno, Pierpaolo & NisticÃ², Salvatore, 2013. "Second-order approximation of dynamic models with time-varying risk," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1231-1247. citation courtesy of