Equilibrium Self-Selection in Pass-Fail Tests

Whether taking an optional pass-fail test is optimal depends on pass probabilities, which increase in productivity and are each individual's private information, and on the wages earned when passing or failing the test, which are conditional expectations formed about productivity by employers who know its distribution in the population subset that chooses to take the test. This paper models the relevant rational-expectations equilibrium and shows that plausible pass-probability functions imply that as a difficult test becomes more difficult, taking it becomes more appealing for low-productivity individuals who are likely to fail. Along with other features of real-life tests, this rationalizes the very low success rates of some optional admission and publication processes.