Solving Multi-Dimensional Dynamic Programming Problems Using Stochastic Grids and Nearest-Neighbor Interpolation

Abstract

We propose two modifications to the method of endogenous grid points that greatly decreases the computational time for life cycle models with many exogenous state variables. First, we use simulated stochastic grids on the exogenous state variables. Second, when we interpolate to find the continuation value of the model, we split the interpolation step into two: We use nearest-neighbor interpolation over the exogenous state variables, and multilinear interpolation over the endogenous state variables. We evaluate the numerical accuracy and computational efficiency of the algorithm by solving a standard consumption/savings life-cycle model with an arbitrary number of exogenous state variables. The model with eight exogenous state variables is solved in around eight minutes on a standard desktop computer. We then use a more realistic income process estimated by Guvenen et al (2015) to demonstrate the usefulness of the algorithm. We demonstrate that the consumption dynamics differ compared to agents facing a more traditional income process.