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

29 Pages Posted: 6 Mar 2017

See all articles by Jakob Almerud

Jakob Almerud

Stockholm University

Anders Eskil Österling

Stockholm University, Students

Date Written: March 3, 2017

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.

Keywords: Computational economic model, life-cycle model, endogenous grid method, stochastic grid, exogenous state variable

JEL Classification: C61, C63, D91

Suggested Citation

Almerud, Jakob and Österling, Anders Eskil, Solving Multi-Dimensional Dynamic Programming Problems Using Stochastic Grids and Nearest-Neighbor Interpolation (March 3, 2017). Available at SSRN: https://ssrn.com/abstract=2926954 or http://dx.doi.org/10.2139/ssrn.2926954

Jakob Almerud

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Anders Eskil Österling (Contact Author)

Stockholm University, Students ( email )

Stockholm
Sweden

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