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What happens when employers would like to screen their employees but only observe a subset of output? We specify a model in which heterogeneous employees respond by producing more of the observed output at the expense of the unobserved output. Though this substitution distorts output in the short-term, we derive three sufficient conditions under which the heterogenous response improves screening efficiency: 1) all employees place similar value on staying in their current role; 2) the employees' utility functions satisfy a variation of the traditional single-crossing condition; 3) employer and worker preferences over output are similar. We then assess these predictions empirically by studying a change to teacher tenure policy in New York City, which increased the role that a single measure — test score value-added — played in tenure decisions. We show that in response to the policy teachers increased test score value-added and decreased output that did not enter the tenure decision. The increase in test score value-added was largest for the teachers with more ability to improve students' untargeted outcomes, increasing their likelihood of getting tenure. We find that the endogenous response to the policy announcement reduced the screening efficiency gap — defined as the reduction of screening efficiency stemming from the partial observability of output — by 28%, effectively shifting some of the cost of partial observability from the post-tenure period to the pre-tenure period.

There is an emerging consensus that teachers impact multiple student outcomes, but it remains unclear how to summarize these multiple dimensions of teacher effectiveness into simple metrics that can be used for research or personnel decisions. Here, we discuss the implications of estimating teacher effects in a multidimensional empirical Bayes framework and illustrate how to appropriately use these noisy estimates to assess the dimensionality and predictive power of the true teacher effects. Empirically, our principal components analysis indicates that the multiple dimensions can be efficiently summarized by a small number of measures; for example, one dimension explains over half the variation in the teacher effects on all the dimensions we observe. Summary measures based on the first principal component lead to similar rankings of teachers as summary measures weighting short-term effects by their prediction of long-term outcomes. We conclude by discussing the practical implications of using summary measures of effectiveness and, specifically, how to ensure that the policy implementation is fair when different sets of measures are observed for different teachers.