Competitive screening and information transmission

We consider a simple model of the competitive screening of students by schools and colleges. Students apply to schools which then perform costly screening procedures of the applicants to select those with high ability. Students who receive more than one offer may choose among those. Colleges select students and can observe the school which they attended. We show a channel through which students' preferences affect schools' screening decisions and outcomes: as schools increase the screening for high-ability students, a greater proportion of them is identified as such by multiple schools and are able to select one among them to attend. Schools' marginal gains from screening therefore depend on other schools' screenings and students' preferences. By focusing on the schools' screening choices (instead of the students' application decisions), we show how the competition for students between schools and colleges affect outcomes and students' welfare. We also show that, simply by observing which school a candidate attended, colleges can "free-ride" on the information produced by a fierce competition between schools for those students. Finally, we show that although colleges make full use of the information contained in the school a student attended, the extent to which students can improve the college that they are matched to by going to a (less desired) high-ranked school is fairly limited.