A Tiny Example

A three-period consumption-savings model with two regimes:

Working life (ages 25 and 45): The agent chooses whether to work and how much to consume. A simple tax-and-transfer system guarantees a consumption floor. Savings earn interest.
Retirement (age 65): Terminal regime. The agent consumes out of remaining wealth.

This notebook teaches the common GridSearch workflow, not a universal model template. If your own model needs EGM, nested EGM, or declared institutional kinks, start from the matching specialized regime and margin declarations. Make the solver-choice checkpoint before adapting the code below.

Model¶

An agent lives for three periods (ages 25, 45, and 65). In the first two periods (working life), the agent chooses whether to work $d_t \in \{0, 1\}$ and how much to consume $c_t$ . In the final period (retirement), the agent consumes out of remaining wealth.

Working life (ages 25 and 45):

V_t(w_t) = \max_{d_t,\, c_t} \left\{ \frac{c_t^{1-\sigma}}{1-\sigma} - \phi \, d_t + \beta \, V_{t+1}(w_{t+1}) \right\}

(1)

subject to

\begin{align} e_t &= d_t \cdot \bar{w} \\[4pt] \tau(e_t, w_t) &= \begin{cases} \theta\,(e_t - \underline{c}) & \text{if } e_t \geq \underline{c} \\ \min(0,\; w_t + e_t - \underline{c}) & \text{otherwise} \end{cases} \\[4pt] a_t &= w_t + e_t - \tau(e_t, w_t) - c_t \\[4pt] w_{t+1} &= (1 + r)\, a_t \\[4pt] a_t &\geq 0 \end{align}

(2)

where $w_t$ is wealth, $e_t$ earnings, $\bar{w}$ the wage, $\underline{c}$ a consumption floor guaranteed by transfers, $\theta$ the tax rate, and $a_t$ end-of-period wealth. The transfer only kicks in when the agent’s resources ( $w_t + e_t$ ) fall below the consumption floor.

Retirement (age 65, terminal):

V_2(w_2) = \max_{c_2 \leq w_2} \frac{c_2^{1-\sigma}}{1-\sigma}

(3)

from pprint import pprint

import jax.numpy as jnp
import numpy as np
import pandas as pd
import plotly.express as px

from lcm import (
    AgeGrid,
    DeterministicTransition,
    DiscreteGrid,
    LinSpacedGrid,
    LogSpacedGrid,
    Model,
    Regime,
    Transition,
    categorical,
)
from lcm.typing import (
    BoolND,
    ContinuousAction,
    ContinuousState,
    DiscreteAction,
    FloatND,
    ScalarInt,
)

Categorical Variables¶

@categorical(ordered=True)
class LaborSupply:
    do_not_work: ScalarInt
    work: ScalarInt


@categorical(ordered=False)
class RegimeId:
    working_life: ScalarInt
    retirement: ScalarInt

Model Functions¶

# Utility


def utility(
    *,
    consumption: ContinuousAction,
    labor_supply: DiscreteAction,
    disutility_of_work: float,
    risk_aversion: float,
) -> FloatND:
    return consumption ** (1 - risk_aversion) / (
        1 - risk_aversion
    ) - disutility_of_work * (labor_supply == LaborSupply.work)


def utility_retirement(*, wealth: ContinuousState, risk_aversion: float) -> FloatND:
    return wealth ** (1 - risk_aversion) / (1 - risk_aversion)


# Auxiliary functions


def earnings(*, labor_supply: DiscreteAction, wage: float) -> FloatND:
    return jnp.where(labor_supply == LaborSupply.work, wage, 0.0)


def taxes_transfers(
    *,
    earnings: FloatND,
    wealth: ContinuousState,
    consumption_floor: float,
    tax_rate: float,
) -> FloatND:
    return jnp.where(
        earnings >= consumption_floor,
        tax_rate * (earnings - consumption_floor),
        jnp.minimum(0.0, wealth + earnings - consumption_floor),
    )


def end_of_period_wealth(
    *,
    wealth: ContinuousState,
    earnings: FloatND,
    taxes_transfers: FloatND,
    consumption: ContinuousAction,
) -> FloatND:
    return wealth + earnings - taxes_transfers - consumption


# State transition


def next_wealth(
    *, end_of_period_wealth: FloatND, interest_rate: float
) -> ContinuousState:
    return (1 + interest_rate) * end_of_period_wealth


# Constraints


def borrowing_constraint_working(end_of_period_wealth: FloatND) -> BoolND:
    return end_of_period_wealth >= 0


# Regime transition


def next_regime(*, age: float, last_working_age: float) -> ScalarInt:
    return jnp.where(
        age >= last_working_age, RegimeId.retirement, RegimeId.working_life
    )

Regimes and Model¶

age_grid = AgeGrid(start=25, inclusive_stop=65, step="20Y")
retirement_age = age_grid.exact_values[-1]

working_life = Regime(
    states={
        "wealth": LinSpacedGrid(start=0, stop=50, n_points=25),
    },
    state_transitions={
        "wealth": next_wealth,
    },
    actions={
        "labor_supply": DiscreteGrid(category_class=LaborSupply),
        "consumption": LogSpacedGrid(start=4, stop=50, n_points=100),
    },
    functions={
        "utility": utility,
        "earnings": earnings,
        "taxes_transfers": taxes_transfers,
        "end_of_period_wealth": end_of_period_wealth,
    },
    constraints={
        "borrowing_constraint_working": borrowing_constraint_working,
    },
)

retirement = Regime(
    states={
        "wealth": LinSpacedGrid(start=0, stop=50, n_points=25),
    },
    functions={"utility": utility_retirement},
)

# At 25 the graph permits both working life and retirement, and the age-based
# `next_regime` selects one; at 45 retirement is the only edge, and `next_regime`
# returns it there. `retirement` has no outgoing edges, which makes it terminal.
edges = {
    "working_life": Transition(
        targets={"working_life": 25, "retirement": (25, 45)},
        law=DeterministicTransition(func=next_regime),
    )
}

model = Model(
    regimes={
        "working_life": working_life,
        "retirement": retirement,
    },
    ages=age_grid,
    edges=edges,
    initial_nodes=((25, "working_life"),),
    regime_id_class=RegimeId,
    description="A tiny three-period consumption-savings model.",
)

Parameters¶

Use model.get_params_template() to see what parameters the model expects, organized by regime and function. The regime-transition law belongs to the edges, so its parameters sit under the "edges" root, keyed by the source regime.

pprint(dict(model.get_params_template()))

{'edges': {'working_life': {'last_working_age': 'float'}},
 'retirement': {'utility': {'risk_aversion': 'float'}},
 'working_life': {'borrowing_constraint_working': {},
                  'certainty_equivalent': {},
                  'earnings': {'wage': 'float'},
                  'end_of_period_wealth': {},
                  'koopmans_aggregator': {'discount_factor': 'FloatND'},
                  'next_wealth': {'interest_rate': 'float'},
                  'taxes_transfers': {'consumption_floor': 'float',
                                      'tax_rate': 'float'},
                  'utility': {'disutility_of_work': 'float',
                              'risk_aversion': 'float'}}}

Parameters shared across regimes (risk_aversion, discount_factor, interest_rate) can be specified at the model level. Parameters unique to one regime go under the regime name. last_working_age, read by the law next_regime, goes under "edges" and the source regime working_life.

params = {
    "discount_factor": 0.95,
    "risk_aversion": 1.5,
    "interest_rate": 0.03,
    "working_life": {
        "utility": {"disutility_of_work": 1.0},
        "earnings": {"wage": 20.0},
        "taxes_transfers": {"consumption_floor": 2.0, "tax_rate": 0.2},
    },
    "edges": {"working_life": {"last_working_age": age_grid.exact_values[-2]}},
}

Simulate¶

n_agents = 100

initial_df = pd.DataFrame(
    {
        "regime_name": "working_life",
        "age": float(age_grid.exact_values[0]),
        "wealth": np.linspace(1, 20, n_agents),
    }
)

result = model.simulate(
    params=params,
    initial_conditions=initial_df,
    log_level="debug",
)

solve call 5d3391250426 phase public_simulate begin

INFO:lcm:solve call 5d3391250426 phase public_simulate begin

solve call 5d3391250426 phase params_validation begin

INFO:lcm:solve call 5d3391250426 phase params_validation begin

solve call 5d3391250426 phase params_validation end status=ok seconds=0.110484

INFO:lcm:solve call 5d3391250426 phase params_validation end status=ok seconds=0.110484

solve call 5d3391250426 phase simulation_inputs begin

INFO:lcm:solve call 5d3391250426 phase simulation_inputs begin

solve call 5d3391250426 phase simulation_inputs end status=ok seconds=0.404670

INFO:lcm:solve call 5d3391250426 phase simulation_inputs end status=ok seconds=0.404670

solve call 5d3391250426 phase authority_fingerprint begin

INFO:lcm:solve call 5d3391250426 phase authority_fingerprint begin

solve call 5d3391250426 phase authority_fingerprint end status=ok seconds=0.004692

INFO:lcm:solve call 5d3391250426 phase authority_fingerprint end status=ok seconds=0.004692

solve call 5d3391250426 phase solver_param_checks begin

INFO:lcm:solve call 5d3391250426 phase solver_param_checks begin

solve call 5d3391250426 phase solver_param_checks end status=ok seconds=0.000041

INFO:lcm:solve call 5d3391250426 phase solver_param_checks end status=ok seconds=0.000041

solve call 5d3391250426 phase state_action_spaces begin

INFO:lcm:solve call 5d3391250426 phase state_action_spaces begin

solve call 5d3391250426 phase state_action_spaces end status=ok seconds=0.000166

INFO:lcm:solve call 5d3391250426 phase state_action_spaces end status=ok seconds=0.000166

solve call 5d3391250426 phase continuation_templates begin

INFO:lcm:solve call 5d3391250426 phase continuation_templates begin

solve call 5d3391250426 phase continuation_templates end status=ok seconds=0.001071

INFO:lcm:solve call 5d3391250426 phase continuation_templates end status=ok seconds=0.001071

solve call 5d3391250426 phase program_graphs begin

INFO:lcm:solve call 5d3391250426 phase program_graphs begin

solve call 5d3391250426 phase program_graphs end status=ok seconds=0.000624

INFO:lcm:solve call 5d3391250426 phase program_graphs end status=ok seconds=0.000624

solve call 5d3391250426 phase structural_resolution begin

INFO:lcm:solve call 5d3391250426 phase structural_resolution begin

structural blueprint: miss (hits=0, misses=1, entries=1)

DEBUG:lcm:structural blueprint: miss (hits=0, misses=1, entries=1)

solve call 5d3391250426 phase structural_resolution end status=ok seconds=0.034128

INFO:lcm:solve call 5d3391250426 phase structural_resolution end status=ok seconds=0.034128

solve call 5d3391250426 phase residency_inventory begin

INFO:lcm:solve call 5d3391250426 phase residency_inventory begin

solve call 5d3391250426 phase residency_inventory end status=ok seconds=0.000023

INFO:lcm:solve call 5d3391250426 phase residency_inventory end status=ok seconds=0.000023

solve call 5d3391250426 phase compilation_waves begin

INFO:lcm:solve call 5d3391250426 phase compilation_waves begin

candidate evaluation ('working_life', 0, 'main') {'action_product': 64, 'cell': 16}

DEBUG:lcm:candidate evaluation ('working_life', 0, 'main') {'action_product': 64, 'cell': 16}

candidate evaluation ('working_life', 1, 'main') {'action_product': 64, 'cell': 16}

DEBUG:lcm:candidate evaluation ('working_life', 1, 'main') {'action_product': 64, 'cell': 16}

candidate evaluation ('retirement', 1, 'main') {'cell': 16}

DEBUG:lcm:candidate evaluation ('retirement', 1, 'main') {'cell': 16}

candidate evaluation ('retirement', 2, 'main') {'cell': 16}

DEBUG:lcm:candidate evaluation ('retirement', 2, 'main') {'cell': 16}

AOT compilation wave 0: 3 unique lowerings for 4 regime-period-core triples (2 workers)

INFO:lcm:AOT compilation wave 0: 3 unique lowerings for 4 regime-period-core triples (2 workers)

1/3  working_life main (age 25, widths={'action_product': 64, 'cell': 16})

INFO:lcm:1/3  working_life main (age 25, widths={'action_product': 64, 'cell': 16})

  lowering working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  lowering working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...

  lowered in 388.3ms

INFO:lcm:  lowered in 388.3ms

  compiling working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  compiling working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...
2/3  working_life main (age 45, widths={'action_product': 64, 'cell': 16})

INFO:lcm:2/3  working_life main (age 45, widths={'action_product': 64, 'cell': 16})

  lowering working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  lowering working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

  lowered in 306.1ms

INFO:lcm:  lowered in 306.1ms

  compiling working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  compiling working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

3/3  retirement main (age 45, widths={'cell': 16})

INFO:lcm:3/3  retirement main (age 45, widths={'cell': 16})

  lowering retirement main (age 45, widths={'cell': 16}) ...

INFO:lcm:  lowering retirement main (age 45, widths={'cell': 16}) ...

  lowered in 50.8ms

INFO:lcm:  lowered in 50.8ms

  compiled  working_life main (age 25, widths={'action_product': 64, 'cell': 16})  1.0s

INFO:lcm:  compiled  working_life main (age 25, widths={'action_product': 64, 'cell': 16})  1.0s

  compiling retirement main (age 45, widths={'cell': 16}) ...

INFO:lcm:  compiling retirement main (age 45, widths={'cell': 16}) ...

  compiled  retirement main (age 45, widths={'cell': 16})  204.4ms

INFO:lcm:  compiled  retirement main (age 45, widths={'cell': 16})  204.4ms

  compiled  working_life main (age 45, widths={'action_product': 64, 'cell': 16})  930.0ms

INFO:lcm:  compiled  working_life main (age 45, widths={'action_product': 64, 'cell': 16})  930.0ms

AOT compilation wave 0: 3 unique variants compiled, 0 fallback evaluations skipped, 0 fallback requests avoided

INFO:lcm:AOT compilation wave 0: 3 unique variants compiled, 0 fallback evaluations skipped, 0 fallback requests avoided

solve call 5d3391250426 phase compilation_waves end status=ok seconds=1.658820

INFO:lcm:solve call 5d3391250426 phase compilation_waves end status=ok seconds=1.658820

solve call 5d3391250426 phase workspace_selection begin

INFO:lcm:solve call 5d3391250426 phase workspace_selection begin

core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":971,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":0,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":971,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":0,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":867,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":867,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":2,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":2,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

solve call 5d3391250426 phase workspace_selection end status=ok seconds=0.035775

INFO:lcm:solve call 5d3391250426 phase workspace_selection end status=ok seconds=0.035775

Starting solution

INFO:lcm:Starting solution

solve call 5d3391250426 phase backward_induction begin

INFO:lcm:solve call 5d3391250426 phase backward_induction begin

Age 65 (1 regimes):

INFO:lcm:Age 65 (1 regimes):

  finished in 135.5ms

INFO:lcm:  finished in 135.5ms

Age 45 (2 regimes):

INFO:lcm:Age 45 (2 regimes):

  finished in 26.1ms

INFO:lcm:  finished in 26.1ms

Age 25 (1 regimes):

INFO:lcm:Age 25 (1 regimes):

  finished in 4.1ms

INFO:lcm:  finished in 4.1ms

Inf in V_arr for 1 other state(s) for regime 'retirement', period 2 (age 65.0)

WARNING:lcm:Inf in V_arr for 1 other state(s) for regime 'retirement', period 2 (age 65.0)

Inf in V_arr for 1 other state(s) for regime 'retirement', period 1 (age 45.0)

WARNING:lcm:Inf in V_arr for 1 other state(s) for regime 'retirement', period 1 (age 45.0)

  retirement  age 65.0   V min=-inf  max=-0.283  mean=-inf

DEBUG:lcm:  retirement  age 65.0   V min=-inf  max=-0.283  mean=-inf

  working_life  age 45.0   V min=-2.35  max=-0.774  mean=-1.29

DEBUG:lcm:  working_life  age 45.0   V min=-2.35  max=-0.774  mean=-1.29

  retirement  age 45.0   V min=-inf  max=-0.283  mean=-inf

DEBUG:lcm:  retirement  age 45.0   V min=-inf  max=-0.283  mean=-inf

  working_life  age 25.0   V min=-3.42  max=-1.38  mean=-2.15

DEBUG:lcm:  working_life  age 25.0   V min=-3.42  max=-1.38  mean=-2.15

solve call 5d3391250426 phase backward_induction end status=ok seconds=0.190140

INFO:lcm:solve call 5d3391250426 phase backward_induction end status=ok seconds=0.190140

Solution complete  (191.4ms)

INFO:lcm:Solution complete  (191.4ms)

solve call 5d3391250426 phase result_assembly begin

INFO:lcm:solve call 5d3391250426 phase result_assembly begin

solve call 5d3391250426 phase result_assembly end status=ok seconds=0.004145

INFO:lcm:solve call 5d3391250426 phase result_assembly end status=ok seconds=0.004145

solve call 5d3391250426 phase solution_resolution begin

INFO:lcm:solve call 5d3391250426 phase solution_resolution begin

solve call 5d3391250426 phase solution_resolution end status=ok seconds=0.001894

INFO:lcm:solve call 5d3391250426 phase solution_resolution end status=ok seconds=0.001894

solve call 5d3391250426 phase solution_handover begin

INFO:lcm:solve call 5d3391250426 phase solution_handover begin

solve call 5d3391250426 phase solution_handover end status=ok seconds=0.000003

INFO:lcm:solve call 5d3391250426 phase solution_handover end status=ok seconds=0.000003

solve call 5d3391250426 phase chunk_planning begin

INFO:lcm:solve call 5d3391250426 phase chunk_planning begin

solve call 5d3391250426 phase chunk_planning end status=ok seconds=0.000347

INFO:lcm:solve call 5d3391250426 phase chunk_planning end status=ok seconds=0.000347

solve call 5d3391250426 phase simulation_setup begin

INFO:lcm:solve call 5d3391250426 phase simulation_setup begin

Starting simulation

INFO:lcm:Starting simulation

Simulation plan: route=legacy; 1 cpu device(s) (0,); outer chunks=1 (widths=(100,)); unbudgeted.

INFO:lcm:Simulation plan: route=legacy; 1 cpu device(s) (0,); outer chunks=1 (widths=(100,)); unbudgeted.

Simulation plan detail: route=legacy; subject_devices=(cpu) (0,); axis_widths_by_regime=[working_life: {}; retirement: {}]; outer_chunk_count=1; admitted_chunk_widths=(100,); budget_mode=unbudgeted; effective_device_memory_bytes=None; subject_grouping=None.

DEBUG:lcm:Simulation plan detail: route=legacy; subject_devices=(cpu) (0,); axis_widths_by_regime=[working_life: {}; retirement: {}]; outer_chunk_count=1; admitted_chunk_widths=(100,); budget_mode=unbudgeted; effective_device_memory_bytes=None; subject_grouping=None.

solve call 5d3391250426 phase simulation_setup end status=ok seconds=0.262311

INFO:lcm:solve call 5d3391250426 phase simulation_setup end status=ok seconds=0.262311

solve call 5d3391250426 phase simulation_chunk begin

INFO:lcm:solve call 5d3391250426 phase simulation_chunk begin

Age 25 (1 regimes):

INFO:lcm:Age 25 (1 regimes):

solve call 5d3391250426 phase simulation_compilation begin

INFO:lcm:solve call 5d3391250426 phase simulation_compilation begin

solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.601453

INFO:lcm:solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.601453

solve call 5d3391250426 phase simulation_compilation begin

INFO:lcm:solve call 5d3391250426 phase simulation_compilation begin

solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.052402

INFO:lcm:solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.052402

solve call 5d3391250426 phase simulation_compilation begin

INFO:lcm:solve call 5d3391250426 phase simulation_compilation begin

solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.039353

INFO:lcm:solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.039353

Off-grid next states: regime='working_life', target='retirement', period=0, state='wealth', phase='realized', count=0

INFO:lcm:Off-grid next states: regime='working_life', target='retirement', period=0, state='wealth', phase='realized', count=0

Off-grid next states: regime='working_life', target='working_life', period=0, state='wealth', phase='realized', count=0

INFO:lcm:Off-grid next states: regime='working_life', target='working_life', period=0, state='wealth', phase='realized', count=0

  transitions:
  - working_life → working_life = 100

DEBUG:lcm:  transitions:
  - working_life → working_life = 100

  finished in 2.3s

INFO:lcm:  finished in 2.3s

Age 45 (2 regimes):

INFO:lcm:Age 45 (2 regimes):

solve call 5d3391250426 phase simulation_compilation begin

INFO:lcm:solve call 5d3391250426 phase simulation_compilation begin

solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.408189

INFO:lcm:solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.408189

solve call 5d3391250426 phase simulation_compilation begin

INFO:lcm:solve call 5d3391250426 phase simulation_compilation begin

solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.039116

INFO:lcm:solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.039116

Off-grid next states: regime='working_life', target='retirement', period=1, state='wealth', phase='realized', count=0

INFO:lcm:Off-grid next states: regime='working_life', target='retirement', period=1, state='wealth', phase='realized', count=0

solve call 5d3391250426 phase simulation_compilation begin

INFO:lcm:solve call 5d3391250426 phase simulation_compilation begin

solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.043345

INFO:lcm:solve call 5d3391250426 phase simulation_compilation end status=ok seconds=0.043345

  transitions:
  - working_life → retirement = 100

DEBUG:lcm:  transitions:
  - working_life → retirement = 100

  finished in 851.9ms

INFO:lcm:  finished in 851.9ms

Age 65 (1 regimes):

INFO:lcm:Age 65 (1 regimes):

  transitions:
  - retirement → retirement = 100

DEBUG:lcm:  transitions:
  - retirement → retirement = 100

  finished in 60.9ms

INFO:lcm:  finished in 60.9ms

solve call 5d3391250426 phase simulation_chunk end status=ok seconds=3.190706

INFO:lcm:solve call 5d3391250426 phase simulation_chunk end status=ok seconds=3.190706

solve call 5d3391250426 phase simulation_completion begin

INFO:lcm:solve call 5d3391250426 phase simulation_completion begin

Simulation complete  (3.5s)

INFO:lcm:Simulation complete  (3.5s)

solve call 5d3391250426 phase simulation_completion end status=ok seconds=0.000889

INFO:lcm:solve call 5d3391250426 phase simulation_completion end status=ok seconds=0.000889

solve call 5d3391250426 phase simulation_result begin

INFO:lcm:solve call 5d3391250426 phase simulation_result begin

solve call 5d3391250426 phase simulation_result end status=ok seconds=0.005291

INFO:lcm:solve call 5d3391250426 phase simulation_result end status=ok seconds=0.005291

solve call 5d3391250426 phase result_finalization begin

INFO:lcm:solve call 5d3391250426 phase result_finalization begin

solve call 5d3391250426 phase result_finalization end status=ok seconds=0.000007

INFO:lcm:solve call 5d3391250426 phase result_finalization end status=ok seconds=0.000007

solve call 5d3391250426 phase public_simulate end status=ok seconds=5.956747

INFO:lcm:solve call 5d3391250426 phase public_simulate end status=ok seconds=5.956747

df = result.to_dataframe(additional_targets="all")
df["age"] = df["age"].astype(int)
df.loc[df["age"] == retirement_age, "consumption"] = df.loc[
    df["age"] == retirement_age, "wealth"
]
columns = [
    "regime_name",
    "labor_supply",
    "consumption",
    "wealth",
    "earnings",
    "taxes_transfers",
    "end_of_period_wealth",
    "value",
]
df.set_index(["subject_id", "age"])[columns].head(20).style.format(
    precision=1,
    na_rep="",
)

# Classify agents by work pattern across the two working-life periods
first_working_age = age_grid.exact_values[0]
last_working_age = age_grid.exact_values[-2]

df_working = df[df["regime_name"] == "working_life"]
work_by_age = df_working.pivot_table(
    index="subject_id",
    columns="age",
    values="labor_supply",
    aggfunc="first",
)
work_pattern = (
    work_by_age[first_working_age].astype(str)
    + ", "
    + work_by_age[last_working_age].astype(str)
)
assert "work, work" not in work_pattern.to_numpy(), (
    "Plotting assumes that no agent works in both periods of working life."
)

label_map = {
    "work, do_not_work": "low",  # work early, not later
    "do_not_work, work": "medium",  # coast early, work later
    "do_not_work, do_not_work": "high",  # never work
}
groups = work_pattern.map(label_map).rename("initial_wealth")

# Combined descriptives and work decisions table
initial_wealth = df[df["age"] == first_working_age].set_index("subject_id")["wealth"]
group_desc = initial_wealth.groupby(groups).agg(["min", "max"]).round(1)

df_groups = df.copy()
df_groups["initial_wealth"] = df_groups["subject_id"].map(groups)
df_mean = df_groups.groupby(["initial_wealth", "age"], as_index=False).mean(
    numeric_only=True,
)
work_table = df_mean[df_mean["age"] < retirement_age].pivot_table(
    index="initial_wealth",
    columns="age",
    values="earnings",
)
work_table = (work_table > 0).astype(int)
work_table.columns = [f"works {c}" for c in work_table.columns]

summary = pd.concat([group_desc, work_table], axis=1)
summary.index.name = "initial_wealth"
summary.loc[["low", "medium", "high"]].style.format(precision=1, na_rep="")