Solving SDGE Models: Approximation About The Stochastic Steady State

Recently, there has been many applications of perturbation methods for solving stochastic dynamic general equilibrium models. However, in standard applications of the perturbation method, the Taylor expansion is always computed around the deterministic steady state. Because of nonlinearities, the center of the ergodic distribution of the endogenous variables can be away from the deterministic steady state, making it not the best point around which to take the approximation. In this paper, we advocate the computation of the approximation around the stochastic steady state. We define the stochastic steady state as the point of the state space where, in absence of shocks in that period, agents would choose to remain although that there are taking into account future volatility. The paper suggests a simple and practical way of calculating the approximation at the stochastic steady state. The proposed method, instead of doing one big leap toward uncertainty, makes a few smaller steps adding a new portion of uncertainity in each. Each step corresponds to a problem of finding an approximation of the decision rule with smaller shocks than in the original problem; hence the method is practical, since it allows using an existing implementation of perturbation method. The paper provides results on a few example models using a framework of Dynare++.