The Endogenous Grid Method for Epstein-Zin Preferences¶

Solving consumption-savings problems with recursive utility

Alan Lujan

Krieger School of Arts and Sciences, Johns Hopkins University, Washington, DC 20036, USA; Econ-ARK

Corresponding author: alujan@jhu.edu

Highlights¶

• Power transformation $W = V^{1-\rho}$ extends EGM to Epstein-Zin preferences

• Algorithm eliminates root-finding while tracking policy and value

• Speed gains of 50-100x over VFI/TI; 150-630x at equal accuracy

• Accuracy improves by over one order of magnitude versus VFI and TI

• Method generalizes to risk-sensitive preferences and limiting cases

Keywords¶

Endogenous grid method; Epstein-Zin preferences; Recursive utility; Dynamic programming; Consumption-savings

JEL Classification: C61, C63, D15

Requirements¶

• Python >= 3.12

• JAX, NumPy, SciPy, Numba, QuantEcon, Matplotlib

Install dependencies with:

uv sync

Reproducibility¶

Code to reproduce all results is available at https://github.com/econ-ark/ezegm.

To run the benchmarks:

cd code
uv run python benchmark_paper.py

Repository Structure¶

ezegm/
+-- code/                    # Implementation and benchmarks
|   +-- ez_egm.py           # Main EGM algorithm for Epstein-Zin
|   +-- benchmark_paper.py  # Reproduce all paper results
|   +-- ...
+-- content/
|   +-- figures/            # Generated figures
|   +-- references.bib      # Bibliography
|   +-- paper/              # Paper source (MyST Markdown)
|   |   +-- ezegm.md        # Main paper
|   |   +-- ezegm_appendix.md   # Online appendix
|   |   +-- ezegm_full.md   # Combined (includes paper + appendix)
|   +-- exports/            # Build artifacts (PDFs)
|       +-- ezegm.pdf       # Paper PDF
|       +-- ezegm_appendix.pdf  # Appendix PDF
|       +-- ezegm_full.pdf  # Full PDF
+-- myst.yml                # MyST configuration

Citation¶

If you use this code, please cite:

@article{lujan2026egm,
  title={The Endogenous Grid Method for Epstein-Zin Preferences},
  author={Lujan, Alan},
  year={2026},
  doi={10.5281/zenodo.18176984},
  url={https://github.com/econ-ark/ezegm}
}

License¶

• Content: CC-BY-4.0

• Code: MIT

(c) 2026 Alan Lujan

Funding¶

This work was supported by the Alfred P. Sloan Foundation [G-2025-79177].

Declaration of Generative AI and AI-Assisted Technologies in the Manuscript Preparation Process¶

During the preparation of this work the author used Claude (Anthropic) to assist with code development and manuscript editing. After using this tool, the author reviewed and edited the content as needed and takes full responsibility for the content of the published article.