pylcm exposes one broad solver and a family of structural specializations.
The map¶
| Economic problem | Solver | Continuous maximization |
|---|---|---|
| General discrete-continuous regime | GridSearch | Full action-grid product |
| Smooth one-margin consumption-saving problem | EGM | One Euler inversion |
| One liquid margin with general resources or optional discrete choice | DCEGM | Euler inversion over supported branches, then upper envelope |
| Liquid inner margin plus finite outer margin | NEGM | DCEGM conditional on each outer candidate |
| One liquid margin with declared non-convex budget structure | NBEGM | EGM per smooth run/case, then branch-aware envelope |
| Nested outer margin with declared inner budget structure | NNBEGM | NBEGM conditional on outer candidates |
The table is not a ranking. Each row solves a different declared problem class.
EGM-family glossary¶
| Acronym | Problem shape | Required regime | Main algorithmic device |
|---|---|---|---|
EGM | Smooth one-margin consumption-saving | ConsumptionSavingsRegime | Euler inversion on a savings grid |
DCEGM | One liquid margin with a general resources node or competing branches | ConsumptionSavingsRegime | EGM by branch plus an upper envelope |
NBEGM | One liquid margin with declared non-convex budget structure | ConsumptionSavingsRegime | EGM by smooth run/case plus a topology-aware envelope |
NEGM | DCEGM liquid problem conditional on a finite outer choice | NestedConsumptionSavingsRegime | Complete inner DCEGM solves followed by an outer maximum |
NNBEGM | NBEGM liquid problem inside an outer choice | NestedConsumptionSavingsRegime | Complete inner NBEGM solves plus configurable outer search/aggregation |
Grid search is the baseline¶
If there are nodes for continuous action , grid search evaluates a candidate count proportional to
at every state cell. This is expensive as action dimensions accumulate, but it makes few structural assumptions. Dense candidates also map naturally to accelerators and can be chunked to control memory. Grid search is exact relative to its action grids, not to the underlying continuous choice set.
EGM replaces search with inversion¶
For a smooth liquid margin, EGM chooses an exogenous post-decision savings grid and inverts the Euler equation for consumption. That changes the dominant candidate growth from a current-state-by-action grid to a savings-grid construction plus interpolation. The gain comes from amortizing one inversion over current liquid states.
The gain disappears if the Euler right-hand side still varies arbitrarily with the current liquid state after conditioning on the solver’s rows. Declared intervals can sometimes recover amortization; otherwise grid search may be the better representation.
Envelopes recover non-concave choices¶
A discrete choice or a non-convex budget can produce several candidate value branches.
DCEGM also supplies the general resources route when plain EGM is too narrow. When a
discrete choice or non-convex schedule produces several branches, DCEGM and NBEGM
construct them and take an upper envelope. Envelope configuration affects accuracy,
topology handling, memory, and accelerator suitability; it is not cosmetic
post-processing.
Nesting avoids a coupled two-dimensional inversion¶
NEGM and NNBEGM condition the liquid solve on candidates for an outer durable or
illiquid post-decision state. They do not solve a genuinely coupled two-dimensional
first-order-condition system. The outer candidate count therefore multiplies the cost of
the complete inner solve, and batching or adaptive search can matter as much as the
inner algorithm.
Read the detailed method pages:
For exact constructors and prerequisites, see Solvers and capabilities.
Related pages¶
Guide: Choosing a solver and Authoring for EGM-family solvers
Methods: The endogenous-grid method, Nested endogenous-grid methods, and Declared non-convex budgets
Examples: Curated examples
Reference: Solvers and capabilities