The Endogenous Grid Method for Epstein-Zin Preferences

TL;DR

This paper introduces a modified endogenous grid method that efficiently handles Epstein-Zin preferences, significantly speeding up dynamic programming without sacrificing accuracy.

Contribution

A power transformation enables EGM to work with Epstein-Zin preferences, eliminating root-finding and vastly improving speed and accuracy over traditional methods.

Findings

Speed gains of 10 to 100 times over value function iteration

Improved accuracy by more than tenfold

EGM avoids speed-accuracy tradeoff faced by VFI and time iteration

Abstract

The endogenous grid method (EGM) accelerates dynamic programming by inverting the Euler equation, but it appears incompatible with Epstein-Zin preferences where the value function enters the Euler equation. This paper shows that a power transformation resolves the difficulty. The resulting algorithm requires no root-finding, achieves speed gains of one to two orders of magnitude over value function iteration, and improves accuracy by more than one order of magnitude. Holding accuracy constant, the speedup is two to three orders of magnitude. VFI and time iteration face a speed-accuracy tradeoff; EGM sidesteps it entirely.