Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods

34 Pages Posted: 21 Oct 2014

See all articles by Alexander Ludwig

Alexander Ludwig

Leibniz Institute for Financial Research SAFE; University of Cologne - Faculty of Management, Economics and Social Sciences

Matthias Schoen

University of Cologne

Multiple version iconThere are 2 versions of this paper

Date Written: June 11, 2014

Abstract

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 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, Endogenous Gridpoints Method, Delaunay Interpolation

JEL Classification: C63, E21

Suggested Citation

Ludwig, Alexander and Schoen, Matthias, Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods (June 11, 2014). Max Planck Institute for Social Law and Social Policy Discussion Paper No. 274-13. Available at SSRN: https://ssrn.com/abstract=2512231 or http://dx.doi.org/10.2139/ssrn.2512231

Alexander Ludwig (Contact Author)

Leibniz Institute for Financial Research SAFE ( email )

(http://www.safe-frankfurt.de)
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

University of Cologne - Faculty of Management, Economics and Social Sciences ( email )

Albertus-Magnus-Platz
Cologne, D-50923
Germany

HOME PAGE: http://www.wiso.uni-koeln.de/cmr/alexludwig

Matthias Schoen

University of Cologne ( email )

Albertus-Magnus-Platz
Cologne, 50923
Germany

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
9
Abstract Views
428
PlumX Metrics