Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods

SAFE Working Paper No. 72

37 Pages Posted: 29 Oct 2014 Last revised: 2 May 2016

See all articles by Alexander Ludwig

Alexander Ludwig

Goethe University Frankfurt

Matthias Schoen

University of Cologne

Multiple version iconThere are 2 versions of this paper

Date Written: April 18, 2016


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 by using a specific model with two endogenous state variables. We find 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.

Keywords: Dynamic Models, Numerical Solution, Method of Endogenous Gridpoints, Delaunay Interpolation

JEL Classification: C63, E21

Suggested Citation

Ludwig, Alexander and Schoen, Matthias, Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods (April 18, 2016). SAFE Working Paper No. 72, Available at SSRN: https://ssrn.com/abstract=2515697 or http://dx.doi.org/10.2139/ssrn.2515697

Alexander Ludwig (Contact Author)

Goethe University Frankfurt ( email )

Gr├╝neburgplatz 1
Frankfurt am Main, 60323

Matthias Schoen

University of Cologne ( email )

Cologne, 50923

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