# Pre-Estimation Checks

Read this page before fitting MPEC. The same structural checks as NFXP matter,
plus the constrained optimizer must be able to enforce the Bellman equations.

MPEC can show estimation risk for reasons that are visible before optimization
starts. Run these checks before treating a result as structural evidence.

| Check | Why it matters |
| --- | --- |
| Feature rank | Rank below the number of parameters means theta is not identified. |
| Feature condition number | A high condition number signals unstable estimates. |
| Transition row sums | Each transition row must be a valid probability distribution. |
| State coverage | Unobserved states produce weak or degenerate likelihood regions. |
| Action support | Rare actions make their payoff weakly identified. |
| Reward normalization | Reward level and scale need a valid anchor. |
| Bellman constraint size | Too many value variables can make the constrained problem impractical. |
| Transition orientation | MPEC expects transition tensors in action, state, next-state order. |

## Canonical Simulation Checks

The results file records these pre-estimation checks.
See the [simulation study page](validation.md) for the generator script and
detailed results.

| Check | Value | Status |
| --- | ---: | --- |
| Feature rank | 4 / 4 | pass |
| Feature condition number | 4.512 | pass |
| Transition row error | 2.42e-8 | pass |
| Observed states | 21 / 21 | pass |
| State-action coverage | 1.000 | pass |
| Action shares | 0.345, 0.330, 0.325 | pass |
| Minimum action share | 0.325 | pass |
| Exit and absorbing anchor | true | pass |

The canonical cell is intentionally small enough that the value-function
constraint is inspectable, while still requiring recovery of reward, policy,
value, Q, and counterfactual oracle objects.

## Common Risk Patterns

Feature matrices with copied state-only features across actions have zero
immediate payoff contrasts. Action-dependent transitions can still make them
choice-relevant through continuation values. Data with almost no replacement
choices can fit in-sample behavior while leaving replacement cost weakly
identified. Very large state spaces create many value-function variables and
can make the constrained optimizer unstable. Transition matrices with wrong
orientation can produce plausible arrays and wrong economics.