# Quick Start

This page shows the constrained-program API. Read the returned constraint
violation together with the estimates, because MPEC's structural interpretation
requires the Bellman constraint to be satisfied.

The public MPEC surface is the full estimator API. Create an estimator,
call `estimate`, and read the returned summary object.

```python
from econirl.environments.rust_bus import RustBusEnvironment
from econirl.estimation.mpec import MPECEstimator, MPECConfig
from econirl.preferences.linear import LinearUtility
from econirl.simulation import simulate_panel

env = RustBusEnvironment(
    operating_cost=0.01,
    replacement_cost=2.0,
    num_mileage_bins=20,
    discount_factor=0.99,
    seed=42,
)
panel = simulate_panel(env, n_individuals=100, n_periods=50, seed=123)
utility = LinearUtility.from_environment(env)

model = MPECEstimator(config=MPECConfig(solver="sqp"), verbose=False)
summary = model.estimate(
    panel=panel,
    utility=utility,
    problem=env.problem_spec,
    transitions=env.transition_matrices,
)

print([float(x) for x in summary.parameters])
print([float(x) for x in summary.standard_errors])
print(summary.policy.shape)
print(summary.metadata["final_constraint_violation"])
```

Output

```text
[0.017559314146637917, 2.244328022003174]
[0.003141143824905157, 0.07669873535633087]
(20, 2)
9.265894274079756e-09
```

After fitting, the summary provides structural parameters, standard errors, a policy,
a value function, a likelihood, and constrained-optimizer diagnostics.

| Attribute | Meaning |
| --- | --- |
| `parameters` | Estimated structural reward parameters. |
| `standard_errors` | Standard errors for the structural parameters. |
| `policy` | Estimated action probabilities by state. |
| `value_function` | Estimated value function by state. |
| `log_likelihood` | Maximized constrained choice log likelihood. |
| `metadata` | Solver status and Bellman constraint diagnostics. |

## Counterfactual Example

MPEC does not currently expose the same one-call dataframe wrapper
`counterfactual` method as NFXP and CCP. The counterfactual evidence is
therefore produced through the simulation harness, which re-solves
oracle Type A, Type B, and Type C counterfactuals against the recovered
structural object.

See [Counterfactuals](counterfactuals.md) for the reported counterfactual
cases and [Simulation Study](validation.md) for the generator and results file
links.

## Full Estimator API

Use `econirl.estimation.mpec.MPECEstimator` when you need direct control over
panel objects, utility objects, transition tensors, constrained optimizer
options, Bellman constraint tolerance, or diagnostic metadata.