Counterfactuals

Important Links

• NFXP Overview

• Quick Start

• Simulation Study

• Bus Engine Example

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.

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

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:

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

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 for the corresponding estimation and inference results.