The Sequential Endogenous Grid Method
The Sequential Endogenous Grid Method
Heterogeneous-agent models with multiple decisions face a computational dilemma. Joint optimization over all choices is slow; strong separability restrictions speed computation but rule out economically interesting interactions. I introduce Sequential EGM (EGM$^n$), which eases this tension by decomposing the problem into sequential stages so that each stage can exploit the Endogenous Grid Method’s closed-form inversion, chaining speed gains across decisions wherever separable utility or an invertible transition permits it. The resulting curvilinear grids require interpolation that respects their structure, so I develop ENGINE (ENdogenous Grid INterpolation and Extrapolation), which exploits the index structure inherited from exogenous grids, with no construction step and no triangulation. In the canonical liquid-illiquid household block, EGM$^n$ solves an order of magnitude faster than the nested method in serial and $3.7$ to $7.9$ times faster at sixteen threads. Replacing existing curvilinear interpolation with ENGINE cuts full-solve time $2.8$- to $4.5$-fold at matched accuracy.
Reproduction
reproduce.shregenerates every table, figure and quoted reading of the paper and online appendix intocontent/figures/, one command per row of the exhibit table incode/README.md.reproduce_min.shruns the test suite and builds the website with every example notebook executed, in a few minutes.
Both scripts install the locked environment with uv sync --locked first.
Reference
Lujan, Alan. “The Sequential Endogenous Grid Method.” Working paper. See CITATION.cff.
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Abstract
Heterogeneous-agent models with multiple decisions face a computational dilemma. Joint optimization over all choices is slow; strong separability restrictions speed computation but rule out economically interesting interactions. I introduce Sequential EGM (EGM^n), which eases this tension by decomposing the problem into sequential stages so that each stage can exploit the Endogenous Grid Method’s closed-form inversion, chaining speed gains across decisions wherever separable utility or an invertible transition permits it. The resulting curvilinear grids require interpolation that respects their structure, so I develop ENGINE (ENdogenous Grid INterpolation and Extrapolation), which exploits the index structure inherited from exogenous grids, with no construction step and no triangulation. In the canonical liquid-illiquid household block, EGM^n solves an order of magnitude faster than the nested method in serial and 3.7 to 7.9 times faster at sixteen threads. Replacing existing curvilinear interpolation with ENGINE cuts full-solve time 2.8- to 4.5-fold at matched accuracy.
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Metadata
| Key | Value |
|---|---|
| abstract | Heterogeneous-agent models with multiple decisions face a computational dilemma. Joint optimization over all choices is slow; strong separability restrictions speed computation but rule out economically interesting interactions. I introduce Sequential EGM (EGM^n), which eases this tension by decomposing the problem into sequential stages so that each stage can exploit the Endogenous Grid Method’s closed-form inversion, chaining speed gains across decisions wherever separable utility or an invertible transition permits it. The resulting curvilinear grids require interpolation that respects their structure, so I develop ENGINE (ENdogenous Grid INterpolation and Extrapolation), which exploits the index structure inherited from exogenous grids, with no construction step and no triangulation. In the canonical liquid-illiquid household block, EGM^n solves an order of magnitude faster than the nested method in serial and 3.7 to 7.9 times faster at sixteen threads. Replacing existing curvilinear interpolation with ENGINE cuts full-solve time 2.8- to 4.5-fold at matched accuracy. |
| authors | {"affiliation"=>"Johns Hopkins University", "city"=>"Washington", "email"=>"alujan@jhu.edu", "family-names"=>"Lujan", "given-names"=>"Alan", "orcid"=>"0000-0002-5289-7054", "region"=>"DC", "website"=>"https://advanced.jhu.edu/directory/alan-lujan/"} |
| cff-version | 1.2.0 |
| contact | {"affiliation"=>"Johns Hopkins University", "city"=>"Washington", "email"=>"alujan@jhu.edu", "family-names"=>"Lujan", "given-names"=>"Alan", "orcid"=>"0000-0002-5289-7054", "region"=>"DC", "website"=>"https://advanced.jhu.edu/directory/alan-lujan/"} |
| date-released | 2026-10-10 |
| github_repo_url | https://github.com/alanlujan91/SequentialEGM |
| keywords | endogenous grid method dynamic programming interpolation computational economics |
| license | CC-BY-NC-ND-4.0 |
| license-url | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| message | Please cite the following works when using this project. |
| notebooks | code/examples/example_ConsumptionLabor.md code/examples/example_TwoAssetHousehold.md code/examples/example_HealthInvestment.md code/examples/example_ENGINEInterpolation.md |
| remark-name | SequentialEGM |
| remark-version | 1.0 |
| repository | https://github.com/alanlujan91/sequential_egm |
| tags | REMARK Notebook |
| tier | |
| date |