# Counterfactuals

Read this page as structural re-solving for UFXP. The estimator uses a
different estimating route, but the counterfactual object is the same kind of
linear reward model used by NFXP.

UFXP recovers the utility parameters in the same parameterization as the
data-generating process. Counterfactual analysis therefore works exactly as
it does for NFXP. Change a parameter, re-solve the dynamic program once, and
read off the new policy and value function.

```python
result = model.counterfactual(replacement_cost=15.0)

print(result.params)   # parameters used for the counterfactual solve
print(result.policy)   # choice probabilities under the new world
print(result.value)    # value function under the new world
```

## Counterfactual Families

The simulation study checks recovered counterfactual behavior against exact
oracle objects for three intervention families:

| Family | Intervention | Checked against |
| --- | --- | --- |
| Type A | Reward shift (a payoff component changes). | Oracle policy, value, and welfare regret. |
| Type B | Transition change (the dynamics change). | Oracle policy, value, and welfare regret. |
| Type C | Action removal (one action is penalized away). | Oracle policy, value, and welfare regret. |

## Reported Results

On the canonical synthetic cell the welfare regret of UFXP's counterfactual
policies is below 0.0003 in every family (Type A 0.00016, Type B 0.00030,
Type C 0.00008; see the
[results file](https://github.com/rawatpranjal/EconIRL/blob/main/validation/results/ufxp.json)
and the [Simulation Study](validation.md) page). Because the recovered reward
uses the same linear feature parameterization as the truth, it re-solves
cleanly under all three intervention types.