# Counterfactuals

## Important Links

- [NFXP Overview](../nfxp.md)
- [Quick Start](quick_start.md)
- [Simulation Study](validation.md)
- [Bus Engine Example](rust_bus.md)

Counterfactual analysis re-solves the structural model. NFXP estimates reward
parameters in a model that can be solved again after a primitive changes.

NFXP recovers the utility parameters using the same parameterization as the
data-generating process. For a counterfactual, change a parameter, re-solve the
dynamic program once, and read off the new policy and value function.

```python
cf = model.counterfactual(replacement_cost=4.0)

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**

```text
replacement_cost: 3.072264 -> 4.000000
P(replace | state=50): 0.086333 -> 0.055196
```

The environment can change as well. For example, a new maintenance technology
may alter how engines deteriorate:

```python
alternative_transitions = model.transition_tensor_.copy()
alternative_transitions[0] = 0.0

for state in range(model.n_states):
    for increment, probability in enumerate([0.80, 0.15, 0.05]):
        next_state = min(state + increment, model.n_states - 1)
        alternative_transitions[0, state, next_state] += probability

cf_transition = model.counterfactual(transitions=alternative_transitions)

print(
    f"P(replace | state=50): {model.predict_proba([50])[0, 1]:.6f}"
    f" -> {cf_transition.policy[50, 1]:.6f}"
)
```

**Result**

```text
P(replace | state=50): 0.086333 -> 0.088450
```

## Results

The 200-state study evaluates both kinds of change:

| Change | True shift | Policy error | Value loss |
| --- | ---: | ---: | ---: |
| Increase the first reward parameter by 1.0 | 0.0829 | 0.0064 | 0.0030 |
| Slow engine deterioration | 0.0454 | 0.0067 | 0.0018 |

Policy distance ranges from zero to one. Zero means the two policies choose
each action with the same probability in every state. For both changes, the
fitted-model policy is within 0.0067 of the true-parameter policy.

Expected-value loss compares the fitted counterfactual policy with the policy
computed from the true parameters. It is 0.0030 for the reward change and
0.0018 for the transition change. See the
[Simulation Study](validation.md) for the corresponding estimation and
inference results.