As JonahSinick notes, many high school students and their parents believe this both by stated and revealed preference, and I think they are correct although the magnitude of the effect is hard to pin down. If nothing else, however, if you greatly surpass the academic standards of a college, they will give you merit scholarships in order to get you to pick their college, and the amounts here can be very large especially if the alternative was being forced to borrow money at interest! Thus, signaling is at a minimum a paying job.
As JonahSinick notes, many high school students and their parents believe this both by stated and revealed preference, and I think they are correct although the magnitude of the effect is hard to pin down. If nothing else, however, if you greatly surpass the academic standards of a college, they will give you merit scholarships in order to get you to pick their college, and the amounts here can be very large especially if the alternative was being forced to borrow money at interest! Thus, signaling is at a minimum a paying job.