(Non)Randomization: A Theory of Quasi-Experimental Evaluation of School Quality

Many centralized school admissions systems use lotteries to ration limited seats at oversubscribed schools. The resulting random assignment is used by empirical researchers to identify the effect of entering a school on outcomes like test scores. I first find that the two most popular empirical research designs may not successfully extract a random assignment of applicants to schools. When do the research designs overcome this problem? I show the following main results for a class of data-generating mechanisms containing those used in practice: One research design extracts a random assignment under a mechanism if and practically only if the mechanism is strategy-proof for schools. In contrast, the other research design does not necessarily extract a random assignment under any mechanism.