In centralized school admissions systems, rationing at oversubscribed schools often uses lotteries in addition to preferences. This partly random assignment is used by empirical researchers to identify the eﬀect of entering a school on outcomes like test scores. This paper formally studies if the two most popular empirical research designs successfully extract a random assignment. For a class of data-generating mechanisms containing those used in practice, I show: One research design extracts a random assignment under a mechanism if and almost 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. 2517.