FIGURE E-1 The supply of teachers: no licensing test.


T0=number of individuals who would choose the teaching occupation at wage W0;

E0=number of individuals in group C who would choose the teaching occupation at wage W0.

may do with varying success. To capture the imperfect nature of tests, let mI and mC be the proportions of incompetent and competent individuals, respectively, who are classified as incompetent.3 Thus, if the test could discriminate perfectly, mI would be one (all those from group I would be determined to be incompetent) and mC would be zero (none of those from group C would be determined to be incompetent). It is reasonable to assume that mI exceeds mC for current licensing tests, although the extent to which this is true is unknown and may differ among both the type of skills that are tested (basic skills, subject matter knowledge, pedagogical content knowledge) and among different tests of the same skills.

Further, assume that a cost must be incurred to take the test, including both a monetary cost, which is the same for both groups, and a cost in terms of the effort involved in preparing for the test, which may differ between the two groups.4 These costs are denoted by tI and tC. Although stronger than necessary,


The proportion of those who are not competent but who are classified as competent, 1−mI, is the type 1 error of the test and mC is the type 2 error.


The monetary cost may, in fact, be higher for group I if those individuals take the test more times (in order to pass it) than group C. In addition, the cost of failure is increased by specialized coursework required for licensure in teaching. To the extent that these education courses have a lower

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