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 2f05b078ac02 phase public_simulate begin

INFO:lcm:solve call 2f05b078ac02 phase public_simulate begin

solve call 2f05b078ac02 phase params_validation begin

INFO:lcm:solve call 2f05b078ac02 phase params_validation begin

solve call 2f05b078ac02 phase params_validation end status=ok seconds=0.113916

INFO:lcm:solve call 2f05b078ac02 phase params_validation end status=ok seconds=0.113916

solve call 2f05b078ac02 phase simulation_inputs begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_inputs begin

solve call 2f05b078ac02 phase simulation_inputs end status=ok seconds=0.399758

INFO:lcm:solve call 2f05b078ac02 phase simulation_inputs end status=ok seconds=0.399758

solve call 2f05b078ac02 phase authority_fingerprint begin

INFO:lcm:solve call 2f05b078ac02 phase authority_fingerprint begin

solve call 2f05b078ac02 phase authority_fingerprint end status=ok seconds=0.004177

INFO:lcm:solve call 2f05b078ac02 phase authority_fingerprint end status=ok seconds=0.004177

solve call 2f05b078ac02 phase solver_param_checks begin

INFO:lcm:solve call 2f05b078ac02 phase solver_param_checks begin

solve call 2f05b078ac02 phase solver_param_checks end status=ok seconds=0.000048

INFO:lcm:solve call 2f05b078ac02 phase solver_param_checks end status=ok seconds=0.000048

solve call 2f05b078ac02 phase state_action_spaces begin

INFO:lcm:solve call 2f05b078ac02 phase state_action_spaces begin

solve call 2f05b078ac02 phase state_action_spaces end status=ok seconds=0.000209

INFO:lcm:solve call 2f05b078ac02 phase state_action_spaces end status=ok seconds=0.000209

solve call 2f05b078ac02 phase continuation_templates begin

INFO:lcm:solve call 2f05b078ac02 phase continuation_templates begin

solve call 2f05b078ac02 phase continuation_templates end status=ok seconds=0.001120

INFO:lcm:solve call 2f05b078ac02 phase continuation_templates end status=ok seconds=0.001120

solve call 2f05b078ac02 phase program_graphs begin

INFO:lcm:solve call 2f05b078ac02 phase program_graphs begin

solve call 2f05b078ac02 phase program_graphs end status=ok seconds=0.000614

INFO:lcm:solve call 2f05b078ac02 phase program_graphs end status=ok seconds=0.000614

solve call 2f05b078ac02 phase structural_resolution begin

INFO:lcm:solve call 2f05b078ac02 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 2f05b078ac02 phase structural_resolution end status=ok seconds=0.034036

INFO:lcm:solve call 2f05b078ac02 phase structural_resolution end status=ok seconds=0.034036

solve call 2f05b078ac02 phase residency_inventory begin

INFO:lcm:solve call 2f05b078ac02 phase residency_inventory begin

solve call 2f05b078ac02 phase residency_inventory end status=ok seconds=0.000265

INFO:lcm:solve call 2f05b078ac02 phase residency_inventory end status=ok seconds=0.000265

solve call 2f05b078ac02 phase compilation_waves begin

INFO:lcm:solve call 2f05b078ac02 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 384.3ms

INFO:lcm:  lowered in 384.3ms

  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 304.6ms

INFO:lcm:  lowered in 304.6ms

  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 39.3ms

INFO:lcm:  lowered in 39.3ms

  compiled  working_life main (age 25, widths={'action_product': 64, 'cell': 16})  1.1s

INFO:lcm:  compiled  working_life main (age 25, widths={'action_product': 64, 'cell': 16})  1.1s

  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})  182.1ms

INFO:lcm:  compiled  retirement main (age 45, widths={'cell': 16})  182.1ms

  compiled  working_life main (age 45, widths={'action_product': 64, 'cell': 16})  954.9ms

INFO:lcm:  compiled  working_life main (age 45, widths={'action_product': 64, 'cell': 16})  954.9ms

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 2f05b078ac02 phase compilation_waves end status=ok seconds=1.675006

INFO:lcm:solve call 2f05b078ac02 phase compilation_waves end status=ok seconds=1.675006

solve call 2f05b078ac02 phase workspace_selection begin

INFO:lcm:solve call 2f05b078ac02 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 2f05b078ac02 phase workspace_selection end status=ok seconds=0.033395

INFO:lcm:solve call 2f05b078ac02 phase workspace_selection end status=ok seconds=0.033395

Starting solution

INFO:lcm:Starting solution

solve call 2f05b078ac02 phase backward_induction begin

INFO:lcm:solve call 2f05b078ac02 phase backward_induction begin

Age 65 (1 regimes):

INFO:lcm:Age 65 (1 regimes):

  finished in 145.5ms

INFO:lcm:  finished in 145.5ms

Age 45 (2 regimes):

INFO:lcm:Age 45 (2 regimes):

  finished in 27.2ms

INFO:lcm:  finished in 27.2ms

Age 25 (1 regimes):

INFO:lcm:Age 25 (1 regimes):

  finished in 4.6ms

INFO:lcm:  finished in 4.6ms

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 2f05b078ac02 phase backward_induction end status=ok seconds=0.204343

INFO:lcm:solve call 2f05b078ac02 phase backward_induction end status=ok seconds=0.204343

Solution complete  (206.2ms)

INFO:lcm:Solution complete  (206.2ms)

solve call 2f05b078ac02 phase result_assembly begin

INFO:lcm:solve call 2f05b078ac02 phase result_assembly begin

solve call 2f05b078ac02 phase result_assembly end status=ok seconds=0.004358

INFO:lcm:solve call 2f05b078ac02 phase result_assembly end status=ok seconds=0.004358

solve call 2f05b078ac02 phase solution_resolution begin

INFO:lcm:solve call 2f05b078ac02 phase solution_resolution begin

solve call 2f05b078ac02 phase solution_resolution end status=ok seconds=0.001816

INFO:lcm:solve call 2f05b078ac02 phase solution_resolution end status=ok seconds=0.001816

solve call 2f05b078ac02 phase solution_handover begin

INFO:lcm:solve call 2f05b078ac02 phase solution_handover begin

solve call 2f05b078ac02 phase solution_handover end status=ok seconds=0.000004

INFO:lcm:solve call 2f05b078ac02 phase solution_handover end status=ok seconds=0.000004

solve call 2f05b078ac02 phase chunk_planning begin

INFO:lcm:solve call 2f05b078ac02 phase chunk_planning begin

solve call 2f05b078ac02 phase chunk_planning end status=ok seconds=0.000344

INFO:lcm:solve call 2f05b078ac02 phase chunk_planning end status=ok seconds=0.000344

solve call 2f05b078ac02 phase simulation_setup begin

INFO:lcm:solve call 2f05b078ac02 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 2f05b078ac02 phase simulation_setup end status=ok seconds=0.270885

INFO:lcm:solve call 2f05b078ac02 phase simulation_setup end status=ok seconds=0.270885

solve call 2f05b078ac02 phase simulation_chunk begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_chunk begin

Age 25 (1 regimes):

INFO:lcm:Age 25 (1 regimes):

solve call 2f05b078ac02 phase simulation_compilation begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation begin

solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.618325

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.618325

solve call 2f05b078ac02 phase simulation_compilation begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation begin

solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.052660

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.052660

solve call 2f05b078ac02 phase simulation_compilation begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation begin

solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.039055

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.039055

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 2f05b078ac02 phase simulation_compilation begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation begin

solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.404511

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.404511

solve call 2f05b078ac02 phase simulation_compilation begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation begin

solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.039879

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.039879

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 2f05b078ac02 phase simulation_compilation begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation begin

solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.046916

INFO:lcm:solve call 2f05b078ac02 phase simulation_compilation end status=ok seconds=0.046916

  transitions:
  - working_life → retirement = 100

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

  finished in 876.2ms

INFO:lcm:  finished in 876.2ms

Age 65 (1 regimes):

INFO:lcm:Age 65 (1 regimes):

  transitions:
  - retirement → retirement = 100

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

  finished in 69.2ms

INFO:lcm:  finished in 69.2ms

solve call 2f05b078ac02 phase simulation_chunk end status=ok seconds=3.309838

INFO:lcm:solve call 2f05b078ac02 phase simulation_chunk end status=ok seconds=3.309838

solve call 2f05b078ac02 phase simulation_completion begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_completion begin

Simulation complete  (3.6s)

INFO:lcm:Simulation complete  (3.6s)

solve call 2f05b078ac02 phase simulation_completion end status=ok seconds=0.000853

INFO:lcm:solve call 2f05b078ac02 phase simulation_completion end status=ok seconds=0.000853

solve call 2f05b078ac02 phase simulation_result begin

INFO:lcm:solve call 2f05b078ac02 phase simulation_result begin

solve call 2f05b078ac02 phase simulation_result end status=ok seconds=0.006772

INFO:lcm:solve call 2f05b078ac02 phase simulation_result end status=ok seconds=0.006772

solve call 2f05b078ac02 phase result_finalization begin

INFO:lcm:solve call 2f05b078ac02 phase result_finalization begin

solve call 2f05b078ac02 phase result_finalization end status=ok seconds=0.000008

INFO:lcm:solve call 2f05b078ac02 phase result_finalization end status=ok seconds=0.000008

solve call 2f05b078ac02 phase public_simulate end status=ok seconds=6.115185

INFO:lcm:solve call 2f05b078ac02 phase public_simulate end status=ok seconds=6.115185

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="")