Consumption-saving regimes and margins

EGM-family solvers need economic role names that a general DAG cannot infer. Specialized regimes own those names; solver objects own only numerical configuration.

Import these declarations from lcm or lcm.consumption_savings_regime. Import every solver from lcm.solvers.

LiquidMargin¶

import lcm

liquid = lcm.LiquidMargin(
    state="wealth",
    action="consumption",
    resources="wealth",
    post_decision_state="savings",
)

Fields:

• state: the liquid continuous state;

• action: the continuous action paid from resources;

• resources: the liquid state itself, a named resources function, or NetOfAdjustmentCost;

• post_decision_state: the named post-decision liquid state.

When resources are exactly the state, name that state directly. Do not create an identity function merely to rename it.

NetOfAdjustmentCost(output, before_cost, cost) asks pylcm to compose output = before_cost - cost. This keeps the accounting relation explicit without an extra wrapper whose only job is subtraction.

ConsumptionSavingsRegime¶

ConsumptionSavingsRegime(liquid=..., solver=...) accepts GridSearch or a one-margin solver: EGM, DCEGM, or NBEGM. It otherwise carries the same economic slots as Regime.

The declaration is useful even while validating against grid search: the economic role names remain attached to the model while the numerical method changes.

OuterContinuousMargin¶

outer = lcm.OuterContinuousMargin(
    state="durable",
    action="next_durable",
    post_decision_state="durable_after_choice",
    no_adjustment=lcm.outer_unchanged,
    adjustment_cost=None,
)

adjustment_cost declares how the keeper and adjuster branches combine at this margin. None means adjusting is free at the margin and the branches combine by the deterministic maximum; UniformObservedFixedCost(...) declares an i.i.d. uniform cost observed before the branch choice and integrates it analytically. See Outer search and branch aggregation.

no_adjustment is either a named DAG function or the outer_unchanged sentinel when the outer stock literally remains unchanged. Use the sentinel instead of an identity helper.

NestedConsumptionSavingsRegime¶

NestedConsumptionSavingsRegime(liquid=..., outer_continuous=..., solver=...) accepts GridSearch or a two-margin solver: NEGM or NNBEGM.

The inner liquid and outer roles must be distinct and resolve in the assembled regime. Nested EGM represents a conditional one-dimensional liquid problem around an outer search; it does not infer or solve a general coupled two-dimensional Euler system.

Post-decision lower bounds¶

post_decision_lower_bound(margin=liquid, lower=0.0) returns an ordinary constraint callable for

It also retains the relationship to the margin. An EGM solver can prove the restriction from the matching savings grid and rejects a different lower endpoint during model construction. Grid search and simulation simply evaluate the callable.

Use this form for a borrowing limit on the declared post-decision state. Use a general structured Condition for other retained comparisons and an ordinary callable when no solver needs their named structure.

Method background: The endogenous-grid method and Nested endogenous-grid methods.