Test-optional Policies: Overcoming Strategic Behavior and Informational Gaps

Due to the Covid-19 pandemic, more than 500 US-based colleges and universities went "test-optional" for admissions and promised that they would not penalize applicants for not submitting test scores, part of a longer trend to rethink the role of testing in college admissions. However, it remains unclear how (and whether) a college can simultaneously use test scores for those who submit them, while not penalizing those who do not--and what that promise even means. We formalize these questions, and study how a college can overcome two challenges with optional testing: $\textit{strategic applicants}$ (when those with low test scores can pretend to not have taken the test), and $\textit{informational gaps}$ (it has more information on those who submit a test score than those who do not). We find that colleges can indeed do so, if and only if they are able to use information on who has test access and are willing to randomize admissions.