Bus Engine Example

Important Links

This example uses the bundled bus engine replacement dataset to load the panel, estimate the costs, inspect uncertainty, and run a counterfactual.

from econirl.datasets import load_rust_bus, rust_bus_reward_spec
from econirl import NFXP

df = load_rust_bus()

model = NFXP(n_states=90, discount=0.9999, utility=rust_bus_reward_spec(90))
model.fit(df, state="mileage_bin", action="replaced", id="bus_id")

for name in model.params_:
    print(f"{name}: estimate={model.params_[name]:.6f}, se={model.se_[name]:.6f}")

Result

operating_cost: estimate=0.001003, se=0.000389
replacement_cost: estimate=3.072264, se=0.073965

Estimation

rust_bus_reward_spec estimates two parameters: the operating cost slope over mileage states (operating_cost) and the flat replacement cost (replacement_cost).

Parameter	Estimate	Standard error	95 percent interval
Operating cost	0.0010	0.0004	[0.0002, 0.0018]
Replacement cost	3.0723	0.0740	[2.9273, 3.2172]

The positive operating-cost estimate means keeping an engine becomes less attractive as mileage rises. The fitted policy gives the replacement probability at each mileage state:

states = [0, 10, 50, 89]
for state, probabilities in zip(states, model.predict_proba(states)):
    print(
        f"{state:2d}: keep={probabilities[0]:.6f}, "
        f"replace={probabilities[1]:.6f}"
    )

Result

keep=0.955734, replace=0.044266
keep=0.947597, replace=0.052403
keep=0.913667, replace=0.086333
keep=0.884130, replace=0.115870

Inference

The standard errors use the robust sandwich covariance estimate. On these data, the operating-cost estimate has a p-value of 0.010 and the replacement-cost estimate has a p-value below 0.001. The Simulation Study checks repeated-sample interval coverage on 1,000 independently simulated panels.

Counterfactual

Increasing the fitted replacement cost by 50 percent lowers the long-run replacement rate from 5.3 percent to 2.2 percent. Mean long-run mileage rises from 10.5 to 20.6 states. Under this counterfactual, buses run longer before engine replacement.

cf = model.counterfactual(
    replacement_cost=model.params_["replacement_cost"] * 1.5
)
print(
    f"replacement_cost: {model.params_['replacement_cost']:.6f}"
    f" -> {cf.params['replacement_cost']:.6f}"
)
print(
    f"P(replace | state=50): {model.predict_proba([50])[0, 1]:.6f}"
    f" -> {cf.policy[50, 1]:.6f}"
)

Result

replacement_cost: 3.072264 -> 4.608396
P(replace | state=50): 0.086333 -> 0.042539

This worked example uses the bundled data. The Rust replication reproduces the published table, while the bus engine simulation study compares NFXP with other estimators.