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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.
Narita, Yusuke, "(Non)Randomization: A Theory of Quasi-Experimental Evaluation of School Quality" (2016). Cowles Foundation Discussion Papers. 2518.