A solution method for consumption decisions in a dynamic stochastic general equilibrium model

In this paper we describe a numerical solution of the consumer's life-cycle problem based on value function iteration. The advantage of our approach i s that it retains the versatility of the value function iteration approach and achieves a high degree of accuracy without resorting to the very comput ationally burdensome task of calculating a very fine grid, There are two in novations, the first is not to discretise the state space but effectively t o allow the stares to take any value on the real line by using two differen t third-order interpolation algorithms: bicubic spline for extrapolation an d interpolation on the edge of the grid and the faster cubic convolution in terpolation for inside the grid, The second is to compute a pair of nested grids, one coarse and one fine. The fine grid is used to calculate the cons umption paths of the majority of individuals, and the coarse grid to catch only the few with very high incomes. We shall discuss our approach in relat ion to those already in the literature. We shall argue that value function iteration approach is probably the most flexible and robust way to solve th ese problems. We shall show that our implementation achieves a high degree of accuracy, using a modified den Haan and Marcet simulation accuracy test, without comprising significantly on speed. (C) 2000 Elsevier Science B.V. All rights reserved, JEL classification: C68; D58.