DP10999 Exact Present Solution with Consistent Future Approximation: A Gridless Algorithm to Solve Stochastic Dynamic Models

Author(s): Wouter Den Haan, Michal L. Kobielarz, Pontus Rendahl
Publication Date: December 2015
Keyword(s): risky steady state, solution methods
JEL(s): C63, E10, E23, F41
Programme Areas: Monetary Economics and Fluctuations
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=10999

This paper proposes an algorithm that finds model solutions at a particular point in the state space by solving a simple system of equations. The key step is to characterize future behavior with a Taylor series expansion of the current period's behavior around the contemporaneous values for the state variables. Since current decisions are solved from the original model equations, the solution incorporates nonlinearities and uncertainty. The algorithm is used to solve the model considered in Coeurdacier, Rey, and Winant (2011), which is a challenging model because it has no steady state and uncertainty is necessary to keep the model well behaved. We show that our algorithm can generate accurate solutions even when the model series are quite volatile. The solutions generated by the risky-steady-state algorithm proposed in Coeurdacier, Rey, and Winant (2011), in contrast, is shown to be not accurate.