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Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods

Alexander Ludwig and Matthias Schön
University of Cologne, Working Paper Series in Economics No. 65, 2014

JEL codes: C63, E21

Keywords: dynamic models, numerical solution, endogenous gridpoints method, delaunay interpolation

This paper investigates extensions of the method of endogenous gridpoints (ENDGM) introduced by Carroll (2006) to higher dimensions with more than one continuous endogenous state variable. We compare three different categories of algorithms: (i) the conventional method with exogenous grids (EXOGM), (ii) the pure method of endogenous gridpoints (ENDGM) and (iii) a hybrid method (HYBGM). ENDGM comes along with Delaunay interpolation on irregular grids. Comparison of methods is done by evaluating speed and accuracy. We and that HYBGM and ENDGM both dominate EXOGM. In an infinite horizon model, ENDGM also always dominates HYBGM. In a finite horizon model, the choice between HYBGM and ENDGM depends on the number of gridpoints in each dimension. With less than 150 gridpoints in each dimension ENDGM is faster than HYBGM, and vice versa. For a standard choice of 25 to 50 gridpoints in each dimension, ENDGM is 1:4 to 1:7 times faster than HYBGM in the finite horizon version and 2:4 to 2:5 times faster in the infinite horizon version of the model.

Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods