Iskhakov et al. (2017)

The deterministic retirement model of Iskhakov et al. (2017): a worker chooses consumption and whether to keep working or retire; retirement is absorbing and death arrives deterministically at a known age. Log utility with work disutility and a borrowing constraint.

The paper provides a closed-form solution, which pylcm’s test suite uses as an analytical oracle (tests/data/analytical_solution/). The discrete retirement choice makes the value function non-concave and produces the paper’s signature saw-tooth consumption function — see the discrete-continuous choice explanation for figures and the brute-force vs DC-EGM comparison.

View source on GitHub

DC-EGM usage¶

import jax.numpy as jnp
from lcm_examples.iskhakov_et_al_2017 import get_dcegm_model, get_params

model = get_dcegm_model(n_periods=6)
params = get_params(
    n_periods=6,
    discount_factor=0.98,  # the paper's analytical-solution parametrization
    disutility_of_work=1.0,
    interest_rate=0.0,
    wage=20.0,
)

result = model.simulate(
    params=params,
    initial_conditions={
        "age": jnp.full(100, model.ages.values[0]),
        "wealth": jnp.linspace(1, 100, 100),
        "regime_id": jnp.full(100, model.regime_names_to_ids["working_life"]),
    },
    log_level="warning",
)

df = result.to_dataframe(additional_targets="all")

The non-terminal regimes are ConsumptionSavingsRegime declarations using DCEGM. The solve constructs an off-grid policy, while the standard simulator currently re-decides consumption on the declared action grid. Read the DCEGM simulation contract before comparing solved and simulated actions or taste-shock frequencies.

Grid-search comparison¶

The same economics is available as a labeled grid-search baseline:

from lcm_examples.iskhakov_et_al_2017 import get_model

grid_search_model = get_model(n_periods=6)

Use it for reduced-grid diagnostics; it is not the principal solver path on this page.

Structure¶

• Regimes: working_life (labor supply + consumption), retirement (absorbing, consumption only), dead (terminal).

• States: wealth (linear grid).

• Actions: consumption (continuous), labor supply (work / retire; working_life only).

• Transitions: deterministic — retiring moves the agent to retirement forever; everyone is dead from final_age_alive + 1 on.