The ACT has, since 1997, allowed test-takers to send their scores to four, rather than three, institutions for higher learning, at no additional expense.  It takes a NBER working paper to identify the way in which students respond to the incentive.
On average, most students used the extra free report to apply to a more selective school, but others used it to apply to a less selective school with higher admissions rates.
The old heuristic for applying was "long shot, realistic shot, safety." It makes sense for a fourth free submission to be a convex combination of long and realistic shots.
The free score report policy increased the expected earnings of low-income students. Although [Harvard Faculty Research Fellow Amanda] Pallais  did not study the earnings of the low-income students, back-of-the-envelope calculations suggested that sending in a fourth application increased a student’s future earnings by $10,000.

As for why the new policy encouraged students to apply to more schools, Pallais suggests that students “may use simple heuristics in making application decisions.” In other words, students may interpret the number of free test scores as a recommendation for the number of applications to send. A lesson from this study, then, could be that providing students with better information about the college admissions process helps low-income students attend more-selective colleges.
That there's usually an application submission fee probably also matters.  There's thus a nonlinearity in the budget constraint with the fifth application.  If the incentive steers low-income students out of dropout factories, that's normatively redeeming.

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