as not competent (type 2 error). This outcome could arise if the test is inherently imperfect in the sense that there does not exist a passing score for which there are no classification errors or because the test would be perfect at a specific passing score but the passing score is set at too high a level. As with a perfect test, only group C individuals take the test, but unlike the perfect test some of them fail. In this case, the shift (fall) in supply is larger than that depicted in Figure E-4 by the movement from S0 to S1, even when the test is costless. Depending on how big this type 2 error is, the number of competent teachers may fall below the number when there is no licensure test. Even if the result is not that extreme, this restriction on supply leads to an artificially high wage that might not be the most efficient way to spend community resources.

The analysis of passing scores is more complicated when the test is imperfect in the sense of having both type 1 and type 2 errors. Setting a low passing score may increase the proportion of competent teachers only slightly relative to the situation without a test, but it protects against artificially restricting the supply of competent teachers. Setting a high passing score may increase the proportion of competent teachers a great deal but risks reducing significantly the number of competent teachers and artificially increasing the wage. As the prior discussion makes clear, quantitatively assessing the efficacy of licensure testing requires a great deal of information, about not only the accuracy of the test but also the perceived costs to the test takers, alternative market opportunities of potential teachers, and constraints on the tax revenues of municipalities.

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