Pre-Estimation Checks

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 action, state, next-state transition tensors internally.

Canonical Simulation Checks

The machine-readable results file records these pre-estimation checks. See the simulation study page for the generator script and results file.

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 can collapse the action-specific payoff differences. 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.