This note points out that the proof of Theorem 1, the main theorem, in Ergin (2002) needs two corrections. We provide two counterexamples to Ergin's proof, and then, show that the theorem holds as it is by providing an alternative proof

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...

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...

Centralized matching markets are designed assuming that participants make well-informed choices upfront. However, this paper uses data from NYC's school choice system to show that families' choices change after the initial match as they learn about schools. I develop an empirical model of...