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 is that it retains the versatility of the value function iteration approach and also achieves a high degree of accuracy without resorting to the very computationally burdensome task of calculating a very fine grid. There are two innovations, the first is not to discretise the state space but effectively to allow the states to take any value on the real line by using two different third order interpolation algorithms: bicubic spline for extrapolation and interpolation on the edge of the grid and the faster cubic convolution interpolation 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 consumption 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 relation to those already in the literature. We shall argue that value function iteration approach is probably the most flexible and robust way to solve these 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.