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.sh regenerates every table, figure and quoted reading of the paper and online appendix into content/figures/, one command per row of the exhibit table in code/README.md.
• reproduce_min.sh runs 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.