Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods

This paper investigates extensions of the method of endogenous grid-points (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 (EXGM), (ii) the pure method of endogenous grid-points (ENDGM) and (iii) a hybrid method (HEGM). ENDGM comes along with Delaunay interpolation on irregular grids. Comparison of methods is done by evaluating speed and accuracy. We find that HEGM and ENDGM both dominate EXGM. The choice between HEGM and ENDGM depends on the number of dimensions and the number of grid-points in each dimension. With less than 150 grid-points in each dimension ENDGM is faster than HEGM, and vice versa. For a standard choice of 20 to 40 grid-points in each dimension, ENDGM is 1:6 to 1:8 times faster than HEGM.