Equilibrium Failure Rates in Tests of Endogenous Competence

Rational individuals who obtain a premium by passing an imprecise test change their choice of costly competence when the pass threshold varies. At given premium that reaction prevents variation of the failure rate completely if the marginal cost of competence is constant, only partially if it is increasing. The offsetting effect of endogenous competence is stronger when the pass premium varies in the same direction as the threshold, as it plausibly does when in equilibrium it depends on the expected competence differential between otherwise unobservably heterogeneous individuals who pass and fail. Failure rates remain very similar as different thresholds elicit different endogenous competence, and depend much more strongly on the test's precision: the outcome of a frequently failed test must be very random from the point of view of those who take it.