Hoxby focuses much of her discussion on a comparison of more-selective and less-selective institutions. She presents evidence that the more-selective institutions spend more per student, but also have higher value-added per student. Interesting and perhaps disconcerting conclusions follow. She defines selectivity in this way:
"Selectivity is holistic but, roughly speaking, the "most" selective institutions' average student has a combined (math plus verbal) SAT (or translated ACT) score above 1300, the 90th percentile among test-takers. (Since some students do not take the tests, this corresponds to the 96th percentile among all students.) "Highly" or "very" selective institutions have an average student with combined scores above the 75th percentile (about 1170). "Selective" (without a modifier) institutions ask students to submit scores, grades, and other materials and turn down those judged to be inadequately prepared. Schools with combined scores above 1000 (the 47th percentile) are at least modestly selective. Non-selective schools usually only require that a student have a high school diploma or the equivalent and often have average combined scores of 800 (the 15th percentile) or below. The divide between non-selective and modestly selective schools is rough but somewhere between 800 and 1000."In terms of the market for higher education, selective institutions compete with each other, and students applying to these institutions tend to apply outside their home area. Nonselective institutions face less competition, because most of their students are drawn from close to their geographic location.
Hoxby shows that selective colleges and universities spend a lot more per student than nonselective schools. Each dot on the graph represents a college or university. The horizontal axis shows the median SAT score for the school, so less selective schools are on the left and more selective schools are on the right. The vertical axis graphs "instructional resources" with light blue dots and "core student resources"--which also includes other students services and academic support--with the dark blue dots. This who attend a school where the median SAT is above about 1200 get a lot more resources than those whose attend less selective schools.
Indeed, the total education resources spent on students who attend selective colleges over their lifetime shows an even bigger gap, because such students are more likely to complete a four-year degree and to go on to graduate school education.
Not surprisingly, those who attend more selective colleges earn higher wages on average. What is perhaps more interesting is that even after using various methods to adjust for the differing quality of students, the higher selectivity schools also have higher value-added. For example, Hoxby has the data to do comparisons between students with similar test scores who apply to similar places, but end up at institutions with slightly different selectivity, or to compare student with similar test scores, but only some of whom were admitted to a school of greater selectivity. In this figure, the dark-blue dots and the right-hand axis shows the total wage and salary earnings over a lifetime for graduates of schools with different levels of selectivity. The light-blue dots show the value-added of institutions of different selectivity--that is, how much they add to wages after adjusting for the fact that their students had higher test scores in the first place.
There's an important underlying assumption here. For simplicity, Hoxby assumes that the value-added to attending a less-selective college is zero, and then measured the value-added of more-selective colleges relative to less-selective colleges.
Thus, the more selective institutions spend more per student, but also have higher value-added per student. If you take the gains per student and divide by the cost per student, you have a measure of productivity. Hoxby does the calculation, and finds these patterns: Productivity is lower for low-selectivity schools, which mean that although students at these schools have much less spent on their higher education, they have even-lower value-added from that education (that is, even lower wage gains after taking their test scores into account). However, productivity is basically flat for schools ranging from moderately selective to highly selective. In other words, as schools become more selective they spend more on students but also have greater value-added for students (again, after adjusting for the test scores of those students), and these two factors tend to balance out so that productivity of a moderately selective school is pretty much the same as at a highly selective school.
Hoxby points out some interesting and perhaps disconcerting implications that flow from this analysis.
A common reaction that many people have to the first graph shown above is that it seems potentially inefficient that the selective schools spend more per student. Might the funds spent on higher education have a greater social return if, say, funds from Harvard or Stanford were instead spent at a less-selective school? Hoxby's analysis suggests that student with greater readiness for college who attend selective institutions also have higher value-added from a dollar of spending on higher education. From a broad social point of view, it makes economic sense to spend more on those at more-selective institutions.
Hoxby's analysis also suggests that if our social goal is to expand the number of students in college, it makes more sense to focus more heavily on improving K-12 education so that a greater number of students are college-ready, rather than just offering more loans or aid for college students. If improvements in K-12 education led to a substantially higher share of students being college-ready, then it would actually make sense from a social point of view to dramatically expand college spending per student--because students who are more college-ready would be positioned to take greater advantage of what college has to offer. In contrast, providing additinoal financing to send a greater share of students with low test scores to less-selective colleges may not have much social payoff.
However, Hoxby also provides evidence that there is considerable variability in the productivity of less-selective schools. It turns out that the 90th percentile of less selective schools actually has much higher productivity than the selective schools, while the 50th percentile and below of less selective schools have much lower productivity than the selective schools. Identifying the top 10-20% of less-selective institutions can be useful for students, and also for creating competitive pressures that help these schools to expand and put pressure on the less-selective and low-productivity schools to improve.