  When recruiting job candidates, employers rarely observe their underlying
skill level directly. Instead, they must administer a series of interviews
and/or collate other noisy signals in order to estimate the worker's skill.
Traditional economics papers address screening models where employers access
worker skill via a single noisy signal. In this paper, we extend this
theoretical analysis to a multi-test setting, considering both Bernoulli and
Gaussian models. We analyze the optimal employer policy both when the employer
sets a fixed number of tests per candidate and when the employer can set a
dynamic policy, assigning further tests adaptively based on results from the
previous tests. To start, we characterize the optimal policy when employees
constitute a single group, demonstrating some interesting trade-offs.
Subsequently, we address the multi-group setting, demonstrating that when the
noise levels vary across groups, a fundamental impossibility emerges whereby we
cannot administer the same number of tests, subject candidates to the same
decision rule, and yet realize the same outcomes in both groups.
