The missing "one-offs": the hidden supply of high-achieving, low-income students.

Hoxby, Caroline ; Avery, Christopher

IV. C. College Enrollment and Progress toward a Degree

In this subsection, we demonstrate that, conditional on applying to a specific college, high- and low-income students thereafter behave similarly. There is no statistically significant difference in their probability of enrolling or in their progress toward a degree.

To find the first of these results, we estimate a conditional logit model in which the binary outcome is 1 for the college in which the student initially enrolled and zero for all others. Importantly, we limit the student's choice set to the colleges to which he or she applied. So that the student's enrollment decision is compared to those of students who applied to the same college, we include a fixed effect for each college. We also include interactions between these fixed effects and an indicator for a student's having high or low income. We then test whether each college's high-income or low-income interaction is statistically significantly different from zero. Thus, we test, specifically, whether high- and low-income students who apply to the same college are differentially likely to enroll in it.

We also estimate a variant of this model in which we include an indicator variable for each number of colleges to which the student applied: 1 college, 2 colleges, and so on up to 20 or more colleges. This variant tests whether a high- and a low-income student who apply to the same college and the same number of colleges are differentially likely to enroll in the college in question.

Because so few high-income students apply to nonselective and low-selectivity colleges, many of the high-income x college interactions are dropped by the regression. Therefore, the effect of income on enrolling in such colleges, conditional on having applied, is not identified.

Note that the tests subsume colleges' admissions decisions. That is, if we find that high- and low-income students are equally likely to enroll in a college, conditional on having applied to it and to the same number of colleges, they must be getting treated similarly in the admissions process. Otherwise, they would enroll differentially simply because they had been admitted differentially. (27) Moreover, if we find that high- and low-income students are equally likely to enroll in a college, conditional on having applied to it (regardless of the number of colleges to which they applied), not only must they be treated similarly in the admissions process, but they must also typically apply to the same number of colleges. (28)

Table 5 shows the results from these estimations. The table is organized by colleges' median test scores, with more selective colleges closer to the top. We find that only very small shares of low- and high-income enrollment probabilities (conditional on applying) are statistically significantly different from one another at the 5 percent level. For instance, low-income enrollment probabilities differ from high-income enrollment probabilities in only 4 percent of the colleges that have median scores at the 90th percentile or above. This is about what one would expect from a test at the 5 percent level. The remaining rows of the table contain similar results, all suggesting that low- and high-income students do not enroll differentially, conditional on applying. The results are very similar when the estimation includes an indicator for each number of colleges to which a student applies.

Our test for differential progress toward a degree, conditional on the school at which a student initially enrolled, is constructed in an analogous way. The dependent variable is now the percentage of coursework toward a 4-year degree that the student appears to have completed as of June 2012. (29) A student who is making on-time progress should have completed 100 percent of his or her coursework by then. We estimate a fixed effect for every college so that students are compared to others who enrolled in the same school. We interact the fixed effects with high- and low-income indicators, and we test whether these interactions are statistically significantly different. Again, the effects for nonselective and low-selectivity colleges are not identified because so few high-income students enroll in them.

The left-hand column of table 6, which is organized in much the same way as table 5, shows the results from this estimation. For selective colleges, we find that only very small shares of colleges have statistically significant differences between the progress of their low- and of their high-income students. For instance, low-income students' progress toward a degree differs from high-income students' progress toward a degree at only 5 percent of the colleges that have median scores at the 90th percentile or above. This is what one would expect from a test at the 5 percent level.

The right-hand column of table 6 reports results of reestimating the model excluding low-income students who attend selective and magnet high schools. The reestimation addresses the possibility that achievement-typical students perform well in college because, although poor, they attended high schools that offer unusually strong preparation. (This is true of some but not most achievement-typical students, as shown below.) We obtain very similar results.

There are two key takeaways from this subsection. First, the application stage is where interesting differences appear in the behavior of high-income high achievers and low-income high achievers. If they apply to the same colleges, their educational paths are similar afterward. Thus, interventions that could make low-income high achievers' college careers look more like those of their high-income counterparts must, as a logical matter, be focused on the application stage or preparation for it. Second, the data do not suggest that low-income students who currently fail to apply to selective colleges and therefore fail to attend one would be rejected or would perform badly if they were admitted and enrolled. Of course, we cannot say that they would do just as well as the low-income students who do apply. One would need to induce low-income students to apply to substantially more selective schools and then estimate causal effects to make such a claim. We do not attempt to do that in this paper. (30) However, we are certainly not struck by evidence that low-income students have poor outcomes when they apply to selective schools.

V. Factors That Predict a Student's Being Achievement-Typical or Income-Typical

In this section, we use simple descriptive statistics to identify some factors that predict whether a low-income student is achievement-typical or income-typical. Our goal in this section is to characterize the two types of low-income students sufficiently well that we can build hypotheses about why they apply to colleges so differently.

Ex ante, our hypotheses fall into three broad categories:

(i) Despite the fact that both income-typical and achievement-typical students have estimated family incomes in the bottom quartile, income-typical students are actually socioeconomically disadvantaged compared to achievement-typical students when we examine their backgrounds more carefully. Given their greater disadvantage, they cannot be expected to behave similarly.

(ii) Income-typical students are likely to be poorly informed about college compared to achievement-typical students.

(iii) Income-typical students are making rational, well-informed choices about college. Their utility from attending nonselective or less selective colleges exceeds the utility they would derive from attending more selective colleges.

We can look for evidence of hypotheses in categories (i) and (ii). The hypothesis in category (iii) is inherently untestable, so it is effectively the residual explanation if there is no evidence for other hypotheses. Note that if hypothesis (iii) is the true one, students need not get more utility from attending a nonselective college because it is a good academic match for them. A student might attend a school that is obviously a poor academic match because it enables him or her, say, to look after his or her family. The student might derive sufficient utility from doing this so that his or her college choice is utility maximizing. Cultural and social factors that deter students from applying would also fall under hypothesis (iii). For instance, a student might feel that he or she would enjoy a better social life if he or she attended school with people from a very similar background.

Table 7 reports statistics on several characteristics of the families of high-achieving students that might reveal that income-typical students are truly socioeconomically disadvantaged relative to achievement-typical students. These statistics tend to go the wrong way for hypotheses of type (i). Income-typical students have slightly higher estimated family income than achievement-typical students do. Their (admittedly very flawed) reports of parents' education suggest that income-typical students' parents might have 0.7 years more of education than those of achievement-typical students. Achievement-typical students are more likely to be black or Hispanic, so they are presumably more, not less, likely to have experienced discrimination or to expect to experience it in college.

Table 8 reports statistics on several neighborhood factors that are useful for assessing hypotheses of both types (i) and (ii). A person's neighbors reveal something about his or her own socioeconomic disadvantage, but they also reveal something about the information he or she is likely to encounter. The statistics show that income-typical and achievement-typical students live in Census block groups with very similar average family income. However, achievement-typical students' block groups are less white, and more black, Hispanic, and Asian than those of income-typical students. Achievement-typical students also have more baccalaureate degree holders in their block groups, both in absolute number (207 versus 144) and as a share of adults (22.0 percent versus 16.8 percent). This last fact suggests that income-typical students may be less likely to get advice about college from a neighbor with a degree.

Table 9 compares the geography of income-typical and achievement-typical students, and the contrast is striking. Sixty-five percent of achievement-typical students live in the main city of an urban area, whereas only 30 percent of income-typical students do. Even within main city residents, achievement-typical students are much more likely to live in a large urban area (one with population greater than 250,000). Indeed, 70 percent of the achievement-typical students come from just 15 metropolitan areas (out of 334 nationwide): San Francisco, Oakland, Los Angeles, San Diego, Dallas, Houston, Chicago, Cleveland, Pittsburgh, Portland (Maine), Boston, Providence, New York, Philadelphia, and Baltimore. (31)

Only 21 percent of achievement-typical students live in a nonurban area (not necessarily rural, but a town rather than an urban-area suburb). By contrast, 47 percent of income-typical students live in a nonurban area. Put another way, income-typical students tend to be the high achievers who live in counties that have a large number of high achievers per 17-year-old (figure 7) but not a large number of achievers in absolute terms (figure 6).

Using administrative data from the U.S. Department of Education, table 10 compares the high schools attended by income-typical and achievement typical students. These statistics should help us to assess these students' academic disadvantages and the amount of college-related information they might obtain at school. Achievement-typical students are considerably more likely to attend a school that is classified as a magnet school or an independent (as opposed to religious) private school. These statistics certainly understate the extent to which the achievement-typical students attend high schools that admit students on the basis of exams or grades. Chester Finn and Jessica Hockett (2012) find that only a small share of such high schools are classified as magnet schools. (32) Spending per pupil at achievement-typical students' public schools is higher, but since facilities and staff costs are often higher in the urban areas where they tend to live, it is unclear whether the higher spending actually gives them an advantage. Pupil-teacher and pupil-counselor ratios are fairly similar for achievement-typical and income-typical students: 18.3 versus 17.2, and 328 versus 305.

Using survey data from the Schools and Staffing Surveys from 1987 to 2007 and data on previous cohorts from the College Board and ACT, table 11 compares college-related factors at the high schools attended by achievement-typical and income-typical students. (33) The first striking statistic in the table is what a tiny share of low-income students' teachers graduated from colleges that would be peer or safety colleges for high-achieving students. Only 1.1 percent of income-typical students' teachers attended peer colleges, and only 5.0 percent attended safety colleges. The shares are larger for achievement-typical students teachers, but still not large: 2.9 percent from peer colleges and 7.5 percent from safety colleges. Even high-income students do not encounter many teachers with degrees from very selective colleges.

Income-typical students attend high schools where just 1.6 students in a typical previous cohort applied to one of the 10 most selective colleges in the United States. (34) In contrast, 7.6 students applied to these colleges in a typical previous cohort of achievement-typical students' schools. Thus, compared to an income-typical student, an achievement-typical student would be much more likely to vicariously experience the process of applying to a very selective college, through an upperclassman. In addition, only 3.8 percent (including the student) of the average income-typical student's high school class, compared with 11.2 percent of the average achievement-typical student's class, are high achievers themselves. Since income-typical students' high schools are, on average, less than two-thirds the size of achievement-typical students' high schools, these low percentages translate into very little school-based contact with other high achievers. The low percentages also suggest that their counselors are unaccustomed to advising students who have opportunities to attend selective colleges.

Of course, one might gather and advise a critical mass of high achievers outside of the high school setting, but the bottom rows of table 11 show that even this is difficult for income-typical students. The radius needed to gather 50 high achievers is 37.3 miles for the average income-typical student, but only 12.2 miles for the average achievement-typical student. Since a college access program cannot expect to get participation from every qualified student in the area it covers, the radii shown suggest that most income-typical students cannot be reached by programs that require a critical mass of high achievers to operate at efficient scale.

VI. Thought Experiments: Interventions That Might Inform Income-Typical Students

In this section we consider a few interventions that might affect how informed income-typical students are about their college-going opportunities. We do this because, as shown in the previous section, the data evince no support for hypothesis i (that income-typical students are actually more disadvantaged than achievement-typical ones) so that we are left with hypotheses ii (students are poorly informed) and iii (students are well informed and utility-maximizing). One way to assess hypothesis ii is to consider what information actually reaches or could reach income-typical students. After all, they are low-income high achievers who are apparently desirable applicants. Why should they not, for instance, become informed by their counselors or by traditional college recruitment methods?

VI.A. Traditional Interventions

Colleges often send admissions staff to high schools to recruit high-achieving students. Therefore, consider a thought experiment in which any student who attends a high school that contains at least 20 high-achieving students will have contact with some college admissions staff. (We chose a cutoff of 20 because it is expensive in time and money for admissions staff to visit high schools in which they cannot fill at least a classroom with potential applicants.) If this experiment occurred, 92 percent of high-income high achievers and 66 percent of achievement-typical students would have contact with admissions staff, but only 17 percent of income-typical students would have such contact.

Of course, admissions staff can hold evening or weekend events that students from multiple high schools can attend. Thus, we should also consider what would happen if admissions staff visited every location in the United States where they could gather at least 20 high-achieving students from a 10-mile radius. Such visits would ensure that 94 percent of high-income high achievers and 73 percent of achievement-typical students could meet with admissions staff. But such visits would allow only 21 percent of income-typical students to meet admissions staff.

Clearly, admissions staff visiting students is unlikely to be an effective method of informing income-typical students. What about students visiting colleges? As another thought experiment, consider what would happen if every high-achieving student visited colleges if he or she could reach five peer colleges by traveling 2,000 miles or less. Then 75 percent of high-income high achievers and 71 percent of achievement-typical students would do a college "tour." Only 22 percent of income-typical students would.

In fact, remembering that 70 percent of achievement-typical students are drawn from only 15 urban areas, we note that many of these students need not travel out of town at all to visit one or more selective colleges. Without needing anything other than a subway pass, a New York City student could easily visit Columbia University, Barnard College, New York University, Cooper Union, and at least six other colleges ranked at least "very competitive" by Barron's. A student living in Boston, Chicago, Los Angeles, Philadelphia, or the San Francisco Bay area would also be spoiled for choice. Even a student from Portland, Maine--an area that might have seemed out of place on our list of 15 urban areas--has Bates, Bowdoin, Colby, and Dartmouth (all very selective institutions) within a modest radius. In fact, we know from colleges' own published materials and communications with their authors that many colleges make great efforts to seek out low-income students from their metropolitan areas. These strategies, although probably successful, fall somewhat under the heading of "searching under the lamppost." That is, many colleges look for low-income students where the college is instead of looking for low-income students where the students are.

We have already seen that income-typical students are very unlikely to encounter a teacher, counselor, or neighbor who attended a selective college himself or herself. Furthermore, income-typical students' counselors (each of whom typically manages a roster of hundreds of students) cannot be expected to develop expertise about very selective colleges, given the rarity with which they are called upon to advise high achievers. Indeed, at College Board sessions attended by the authors, several counselors reported that when the rare student in their school was qualified to attend very selective colleges, they told him to guide himself or herself by gathering information on the Internet because they themselves lacked expertise. This is despite the fact that counselors who attend College Board sessions are probably more sophisticated and informed than the average counselor.

The logic that makes admissions staff visits ineffective with income-typical students works similarly for after-school or weekend college mentoring programs: programs with sustainable costs are unlikely to reach income-typical students. Of course, college mentoring programs do exist in areas where income-typical students live, but the typical program focuses on motivating students merely to attend college--not on the decisions faced by high-achieving students with many college opportunities. The typical program also does not provide much advice on negotiating the multilayered application process that very selective colleges use.

What about mailing brochures with a specialized letter to students who live in ZIP codes where most families are poor? This strategy might work in the very largest urban areas, particularly if they are densely populated, but it cannot work well outside them. The United States Postal Service defines ZIP codes with the goal of making mail delivery efficient, not with the goal of identifying families with similar incomes. In a place like Manhattan, a ZIP code might be physically small enough to contain families with fairly uniform socioeconomics. In smaller cities and rural areas, though, the typical ZIP code contains families with diverse incomes, ensuring that mail campaigns targeted to high-poverty ZIP codes systematically fail to reach most low-income students.

VI.B. Novel Interventions

What, then, are some interventions that might inform income-typical students about college and that might overcome the challenge of serving high achievers who are geographically dispersed? First, a college has many more alumni than admissions staff, and alumni are much more broadly distributed geographically than admissions staff. For instance, the anonymous private, very selective university studied by Jonathan Meer and Harvey Rosen (2012) has at least one alumnus or alumna in nearly every U.S. county. (35) Presumably, colleges could give their alumni the names of local students who appear on the search lists of students who are likely qualified for admission. Such alumni-based information interventions could potentially overcome the lack of geographic concentration among income-typical students. The main challenges for such interventions would seem to be the need to coordinate and inform alumni. It would be problematic, for instance, if alumni knew very little about their college's current curriculum or financial aid policies.

Income-typical students are intelligent and able to absorb written material. Thus, other interventions that might affect them would be purely informational ones, whether distributed by mail, online, or through social media. To be effective, however, such interventions must be much better targeted to low-income students than a campaign based on ZIP codes. Also, they cannot simply replicate the content that students already receive in the form of numerous college brochures. The two most obvious deficiencies of these brochures are that they are generic rather than customized to a student's situation (for instance, the student's family finances), and that they have a boosterism that may make it difficult for students to derive information from them. Taking these points to heart, we test several interventions in Hoxby and Sarah Turner (2013) that have the potential to identify causal effects of giving low-income students information about their college-going opportunities.

VI.C. Recruiting Athletes versus Recruiting Low-Income High Achievers

Colleges seem able to identify and recruit students who are top athletes. (36) Should they therefore be able to identify and recruit the vast majority of low-income high achievers? Our analysis suggests that not only is the answer no, but that athletes are the exception that proves the rule.

Regardless of how dispersed they are, it is easy for colleges to identify top athletes. Any top athlete who participates in an individual sport can be easily found on lists of state finalists, often as early as the 10th grade. Most recruited athletes who play team sports also generate statistics (such as rushing yards) that are readily available, or play for a team that participates in state competitions. Even athletes who play only a team sport and whose home team is mediocre can be readily identified by the coaches of the top state teams with whom they compete: "John Smith from High School X is a great running back, even though his team has a mediocre record." (37)

Our conversations with college athletic directors suggest that they use simple, traditional recruiting methods to find athletes. The same methods would not work with low-income high achievers. Again, we emphasize that the data and analytics used in this paper are not available to colleges.

VII. Conclusions

We have demonstrated that the majority of high-achieving, low-income students do not apply to any selective colleges despite apparently being well qualified for admission. These income-typical students exhibit behavior that is typical of students of their income rather than typical of students of their achievement. There are, however, high-achieving, low-income students who apply to college in much the same way as their high-income counterparts. These achievement-typical students also enroll and persist in college like their high-income counterparts.

There are several plausible explanations for income-typical students' behavior:

(i) they cannot afford to attend peer institutions;

(ii) they are actually more disadvantaged than achievement-typical students and therefore behave differently;

(iii) they would fail to be admitted to peer institutions or would fail to thrive at them, were they to apply;

(iv) they are poorly informed about their college-going opportunities;

(v) they have cultural, social, or family issues that make them unwilling to apply to peer institutions, even if they are confident of being admitted and succeeding academically.

We believe we have eliminated explanations (i) and (ii). What is especially striking is that income-typical students pay more to attend less selective colleges than they would pay to attend peer institutions. Our evidence also does not support explanation (iii) since we find that--if they apply--low-income high achievers enroll and persist at the same rates as high-income students with the same test scores. Nevertheless, we cannot definitively test explanation (iii) in this paper. We are mainly left with explanations (iv) and (v), both of which are compatible with the fact that income-typical students are fairly isolated. Hoxby and Turner (2013) rigorously test explanations (iii) and (iv), leaving (v) as the residual explanation.

In this paper we have demonstrated that achievement-typical students not only come disproportionately from the central cities of large urban areas but are likely to attend selective, magnet, or other feeder high schools. A majority of achievement-typical students are drawn from only 15 urban areas, each of which has at least one and often several selective colleges. We show that traditional recruiting methods are likely to work better in large, dense urban areas and in the immediate vicinity of the college itself. Probably unintentionally, colleges end up looking for low-income students where the college is, instead of looking for low-income students where the students are. Thus, they recruit the low-income students "under the lamppost" but fail to identify the vast majority of others. We speculate that admissions staff believe that the supply of low-income high achievers is inelastic for two reasons. Many of these students are not on the radar screen because they do not apply. Also, staff spend much of their time informing students who attend high schools that are already so "tapped out" that their efforts merely shift students among colleges but fail to expand the number of low-income, high-achieving applicants.

Even if we knew for certain that income-typical students behaved as they do because they are poorly informed (as opposed to being deterred by cultural factors), we would not attribute blame to colleges, counselors, or the students themselves. Income-typical students are insufficiently geographically concentrated to be reached, cost-effectively, by traditional methods of informing students about their college opportunities. Their high school counselors cannot be expected to develop expertise about selective colleges when doing so is rarely relevant to their duties, which require them to advise hundreds of students on myriad issues. Low-income high achievers are not necessarily less enterprising than their high-income counterparts; they simply do not have parents or counselors who ensure that they know something about peer institutions.

Our results suggest that interventions likely to affect low-income high achievers' college-going behavior will be ones that do not depend, for their efficacy, on the students being concentrated in a limited number of schools or small geographic areas.

ACKNOWLEDGMENTS For inspiration, generous help with data, and numerous useful suggestions, we thank the College Board and ACT. These two organizations' dedication to providing students with well-informed college application advice is the reason that this research exists. We have been especially helped by Connie Betterton, Michael Matthews, Anne Sturvenant, Ryan Williams, and Robert Ziomek. For important comments and suggestions we thank Sarah Turner, Amanda Pallais, Eric Bettinger, Scott Carrell, Charles Clotfelter, Susan Dynarski, Bridget Long, Parag Pathak, Bruce Sacerdote, Douglas Staiger, Jacob Vigdor, and the editors.

References

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Avery, Christopher, and Sarah Turner. 2009. "Aid and Application Awareness." Harvard Kennedy School and University of Virginia.

Avery, Christopher, Mark Glickman, Caroline Hoxby, and Andrew Metrick. 2013. "A Revealed Preference Ranking of American Colleges and Universities." Quarterly Journal of Economics. 128 (1): 425-467.

Avery, Christopher, Caroline Hoxby, Clement Jackson, Kaitlin Burek, Glenn Pope, and Mridula Raman. 2006. "Cost Should Be No Barrier: An Evaluation of the First Year of Harvard's Financial Aid Initiative." Working Paper no. 12029. Cambridge, Mass.: National Bureau of Economic Research.

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Hoxby, Caroline, and Sarah Turner. 2013. "Expanding College Opportunities for Low-Income, High-Achieving Students." SIEPR Discussion Paper no. 12014. Stanford, Calif.: Stanford Institute for Economic Policy Research.

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Comments and Discussion

COMMENT BY AMANDA PALLAIS

This paper by Caroline Hoxby and Christopher Avery provides a comprehensive analysis of the differences in college application patterns between high-achieving students of differing family incomes. It finds that high-achieving, low-income students apply to substantially different sets of colleges than do their higher-income peers. Over half of the low-income group send SAT or ACT test scores to at least one nonselective college and do not send scores to any college with a median test score within 15 percentiles of their own score. Only 8 percent send scores to a portfolio containing at least one "match" college, one "safety" college, and no nonselective college.

This paper is not the first to note that low-income students apply to different sets of colleges than high-income students (see, for example, Spies 2001, Bowen and others 2005, and Pallais and Turner 2006). However, it is distinguished by its comprehensiveness and the sheer amount of data that allow the authors to fully characterize the application choices of high-achieving students. The paper starts with data on everyone in the high school class of 2008 who took either the ACT or the SAT I. Then it links these students to the colleges they sent scores to, to data on their high schools, and to data on their census block and zip code, as well as to information on whether and where they ultimately enrolled in college and whether they had completed a 4-year degree by 2012.

After showing the differences in application patterns between high- and low-income high achievers, the paper considers the characteristics both of those low-income students whose application behavior is similar to high-income students' (what the authors call "achievement-typical" students) and of those who do not apply to selective institutions ("income-typical" students). Achievement-typical students are more likely to come from schools and neighborhoods where they could more easily obtain information about colleges (for example, because they are more likely to have teachers who attended selective colleges and friends from earlier cohorts who applied to selective colleges). The paper suggests that many low-income, high-achieving students would actually benefit from attending selective colleges but do not apply, because unlike high-income students, they do not have specific relevant information (for example, about the range of colleges available, colleges' true costs, or the relevant benefits of attending specific colleges).

A closely related explanation for low-income high achievers' distinct application choices is that applying to college or for financial aid is prohibitively difficult for some. For example, they may be less likely to have parents or guidance counselors who can assist them with the application process. This explanation also implies that low-income high-achievers might benefit from attending selective colleges but are failing to apply. However, if the applications themselves are preventing these students from attending selective colleges, simply providing more information without also assisting them in filling out the applications (or simplifying the application process) will not be effective. In the rest of this comment, I summarize some of the existing literature on these two explanations as they relate to low-income students in general, not just high-achievers. (1) This relatively new literature provides many examples in which giving high school students information about colleges or assistance with completing applications affects whether and where students attend college.

A recent paper by Hoxby and Sarah Turner (2013) presents the results of a randomized experiment with several different treatments. In one treatment, they sent high-achieving, low-income students information on colleges' actual net cost. (2) They found that this induced students to apply to more colleges and raised the likelihood both of their applying to a selective college and of their being admitted. (The point estimate also implies that this intervention increased the probability that students attended a selective college, but it is not statistically significant.) Another randomized treatment sent students information about suggested application strategies, college graduation rates, and application deadlines. Additionally, it sent students a copy of the Common Application (a standardized application used by many colleges), perhaps making it easier to apply. This treatment also induced students to send more applications and led to their being admitted to more-selective colleges. As a result of this treatment, students attended more-selective colleges.

Hoxby and Turner (2013) also provide evidence that application fees present a barrier to attending selective colleges for high-achieving, low-income students. Although low-income students can obtain fee waivers, the process requires additional paperwork. Randomly selected students in another treatment received fee waiver coupons in the mail and information on where the coupons could be used. Low-income students in this treatment also sent more applications, were admitted to more-selective colleges, and attended more-selective colleges than a randomly selected control group.

Eric Bettinger and others (2012) provide evidence that another aspect of the college application process, the Free Application for Federal Student Aid (FAFSA), is a barrier to low-income students attending college in general. In this project, H&R Block completed the FAFSA for randomly selected students. These students were significantly more likely to attend college than a control group. In contrast, students who received individualized financial aid information and were encouraged to complete the FAFSA on their own were not more likely to attend college than the control group.

Pallais (2012) shows that a small decrease in the cost of sending standardized test scores to colleges can induce low-income students to attend more-selective colleges. Before the fall of 1997, ACT allowed students to send three score reports to colleges for free and charged $6 for each additional score report. Thereafter ACT allowed students to send four score reports for free, with the same marginal cost for additional reports. Before the change, 82 percent of students sent exactly three score reports, while only 3 percent sent four. Afterward, only 10 percent of students sent three score reports, while 74 percent sent four. Both high- and low-income students sent more score reports as a result of the cost change, widened the range of colleges they sent scores to, and sent score reports both to more-selective and to less selective colleges than they would have otherwise. However, only low-income students ended up actually attending more-selective colleges as a result. It could have been the actual decrease in the cost of the fourth score report that led students to change their behavior: perhaps the $6 was a financial barrier to applying to colleges for low-income students. Alternatively, students could have viewed the number of free score reports as information about the optimal number of score reports to send, interpreting the provision of three (or four) free score reports as reflecting ACT's informed judgment that sending three (or four) score reports was optimal.

Sarena Goodman (2012) and George Bulman (2013) show that inducing students to take a college entrance exam changes their college matriculation outcomes. Goodman (2012) analyzes the effect of mandates in some states that require all high school juniors to take the ACT. She finds that these mandates increased the number of students who took the ACT and did so disproportionately for low-income students. The mandates did not change the overall college attendance rate in these states but did substantially increase the number of students attending selective colleges (which are much more likely to require standardized test scores). Bulman (2013) examines the effect of opening an SAT testing center at a student's own high school. Having such a testing center allows students to take the SAT at their own high school rather than travel to other local schools. He finds that opening such a center increased the probability that a given student took the SAT and the probability that he or she attended a selective college. Both these effects were larger for students attending schools in low-income areas.

Finally, Scott Carrell and Bruce Sacerdote (2012) show that helping high school students navigate the college application process can induce these students to attend college. Their paper presents the results of a randomized intervention targeted at high school students in the winter of their senior year. Eligible students were identified by their guidance counselors as those who were "on the margin" of applying to college: they had expressed interest in applying to college but had made little or no progress in applying. Treated students were chosen at random from this pool. They had their application fees, SAT fees, and ACT fees paid for them and received in-person mentoring by a Dartmouth student. Dartmouth students also helped the students sign up for the SAT or the ACT if they had not already done so, complete essays, complete and file applications, request transcripts and recommendation letters, and start the FAFSA. The mentors sometimes also provided advice on how many and which colleges the students should apply to. Finally, students in the treatment group received $100 for completing their applications. This intervention substantially increased 4-year college going among female students, but not among men. (3) The intervention also seemed to have larger effects at more-disadvantaged high schools.

An important question is whether inducing low-income students to attend college and to attend more-selective colleges actually benefits them. It is hard to answer this question fully without knowing more about students' utility functions or the information they have when making college decisions. However, Hoxby and Avery's paper provides evidence that low-income students actually pay less on average to attend very selective colleges than they would to attend less selective colleges. Moreover, research suggests that low-income students receive particularly high returns from attending college in general (Card 1995) and from attending more-selective colleges (Dale and Krueger 2002, Saavedra 2008). Hoxby and Avery show that low-income students who attend highly selective colleges have graduation rates similar to those of high-income students attending these colleges; thus, low-income students appear to be successful in these selective colleges. Of the studies described above, those that followed the students who were induced by the interventions to attend college or to attend more-selective colleges (Hoxby and Turner 2013, Bettinger and others 2012, Sacerdote and Carrell 2012, and Bulman 2013) all find that these students have high persistence in college. Thus, it seems likely that many low-income students who do not already do so would benefit from attending college and attending more-selective colleges.

REFERENCES FOR THE PALLAIS COMMENT

Bettinger, Eric P., Bridget Terry Long, Philip Oreopoulos, and Lisa Sanbonmatsu. 2012. "The Role of Application Assistance and Information in College Decisions: Results from the H&R Block FAFSA Experiment." Quarterly Journal of Economics 1277, no. 3: 1205-42.

Bowen, William G., Martin A. Kurzweil, and Eugene M. Tobin. 2005. Equity and Excellence in American Higher Education. University of Virginia Press.

Bulman, George. 2013. "The Effect of Access to College Assessments on Enrollment and Attainment." Working paper. Stanford University.

Card, D. 1995. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling." In Aspects of Labour Market Behavior: Essays in Honour of John Vanderkamp, edited by L. N. Christofides, E. K. Grant, and R. Swidinsky. University of Toronto Press.

Carrell, Scott E., and Bruce Sacerdote. 2012. "Late Interventions Matter Too: The Case of College Coaching in New Hampshire." Working Paper no. 19031. Cambridge, Mass.: National Bureau of Economic Research.

Dale, Stacy Berg, and Alan B. Krueger. 2002. "Estimating the Payoff to Attending a More Selective College: An Application of Selection on Observables and Unobservables." Quarterly Journal of Economics 117, no. 4: 1491-1527.

Ellwood, D. T., and T. J. Kane. 2000. "Who Is Getting a College Education: Family Background and the Growing Gaps in Enrollment." In Securing the Future: Investing in Children from Birth to College, edited by Sheldon Danziger and Jane Waldfogel. New York: Russell Sage Foundation.

Goodman, Sarena. 2012. "Learning from the Test: Raising Selective College Enrollment by Providing Information." Working paper. Columbia University and University of California, Berkeley.

Hoxby, Caroline M., and Sarah Turner. 2013 "Expanding College Opportunities for High-Achieving, Low Income Students." SIEPR Discussion Paper no. 12-014. Stanford Institute for Economic Policy Research.

Pallais, Amanda. 2011. "Essays in Labor Economics." Ph.D. dissertation. Massachusetts Institute of Technology.

--. 2012. "Small Differences That Matter: Mistakes in Applying to College." Working paper. Harvard University.

Pallais, Amanda, and Sarah Turner. 2006. "Opportunities for Low Income Students at Top Colleges and Universities: Policy Initiatives and the Distribution of Students." National Tax Journal 59, no. 2: 357-86.

Saavedra, Juan E. 2008. "The Returns to College Quality: A Regression Discontinuity Analysis." Working paper. Harvard University.

Spies, Richard R. 2001. "The Effect of Rising Costs on College Choice: The Fourth and Final in a Series of Studies on This Subject." Princeton University Research Report Series no. 117. Princeton University.

(1.) Throughout the ability distribution, low-income students apply to less selective colleges than their higher-income peers (Pallais 2011) and, conditional on high school performance, are less likely to attend any college (for example, Ellwood and Kane 2000). However, the application barriers that high-achieving students face may be different from those faced by lower-achieving students.

(2.) As the paper documents, students' net cost of attendance after financial aid often differs substantially from colleges' sticker prices, particularly at selective colleges.

(3.) It was not only the $100 payment that increased college going: students receiving the whole intervention experienced large increases in college going relative to a randomly selected group who received only the $100 incentive.

COMMENT BY PARAG A. PATHAK

This paper by Caroline Hoxby and Christopher Avery provides convincing evidence of the following fact: a large number of high-achieving, low-income students systematically do not apply to selective colleges or universities. The authors identify two major classes of low-income college applicants. "Income-typical" applicants apply to schools in much the same pattern as do other students in their local area and to no schools whose median scores are similar to their own. "Achievement-typical" applicants apply to schools in much the same pattern as do high-income high achievers, who are mostly from urban areas or have exposure to selective colleges. One noteworthy feature of the low-income, high achieving students in their sample is that most are not underrepresented minorities. The paper nicely illustrates the importance of descriptive empirical work and the value of a nationally representative data set.

There are some important parallels between this paper and existing work on selective K-12 institutions in the United States. Atila Abdulkadiroglu, Joshua Angrist, and Pathak (2012) study exam high schools, including Boston Latin School and New York City's Stuyvesant High School and Bronx High School of Science. In both Boston and New York, roughly two-thirds of exam school students are eligible for a free or subsidized lunch, an indicator of poverty. Moreover, students enrolled in an exam school are between 1.3 and 1.5 standard deviations ahead of their public school peers on baseline standardized tests. Thus, they are low-income high achievers, but they are a few years away from applying to college.

The barriers to application for these schools seem, if anything, lower than the barriers faced by low-income, high-achieving students when they apply to college. For instance, the schools in both cities have long histories, they are widely known, and admission requires completing a common application on a standardized timeline. To gauge the extent to which applicants do not apply to a selective exam school in Boston for seventh grade, I estimate linear probability models of application and offers for students, controlling for their baseline test scores and demographics. By comparing the offer probability with the application probability, it is possible to measure the extent to which students who seem likely to obtain an offer at a school are likely to apply.

My table 1 reports the estimates by decile of predicted offer. An important fact shown in the table is that a large fraction of students who would almost certainly be offered admission to one of Boston's exam schools do not apply. Only 75.8 percent of students in the top decile submit an application, even though applicants in this group would be very likely to obtain an offer given their baseline test scores and demographics. That is, for this highest achieving, mostly low-income population, there is roughly a one-quarter gap in the fraction of students who apply to an exam school among those who are most likely to be given an offer. Seen in this light, it is perhaps no longer that surprising that for the more complicated process of applying to a selective college or university, many students who would almost surely be admitted do not apply.

Given the fact that Hoxby and Avery uncover, a natural question is whether it reflects a market failure, which would rationalize some form of policy intervention. There are many aspects to this question, and in what follows I will only touch on a few. First, this paper and other work by Hoxby (2009) provides evidence that more selective colleges provide more student-oriented resources than less selective colleges, a trend that has increased dramatically in the last two decades (see, for example, figure 2 in Hoxby 2009). This fact, together with the likely scenario that attendance at a selective college will cost low-income students less, because of the college's own financial aid and other scholarship opportunities, seems to suggest that applicants are making suboptimal decisions. Moreover, the evidence that Hoxby and Avery marshal about the tendency of achievement-typical students to come from major urban areas or magnet or independent private schools seems to imply that the income-typical applicants lack adequate information about college, so that reducing application costs (broadly defined) seems likely to boost demand from this population.

There has been progress in making it easier for students to exercise their choice options for K-12 education. In districts that allow a choice of schools to attend, through either open enrollment plans or charters, there has been a recent push toward standard application timelines and common, online application systems. Cities like Denver and New Orleans have recently adopted single-offer coordinated charter and district school admissions schemes, and new assignment mechanisms that make it safe for participants to rank schools truthfully have become increasingly widespread (see, for example, Abdulkadiroglu, Pathak, and Roth 2009, Pathak 2011, Pathak and Sonmez 2008, 2013). The goal of these reforms is to increase access to high-quality educational options for students. Unlike college admissions, many of these reforms involve changes within existing centralized institutions. However, it seems that decision aids, informational cues, and further guidance would be beneficial in either a decentralized college admissions system or a centralized assignment mechanism.

Second, a perhaps more difficult issue for policy is related to the fact that college admissions is an assignment market. It is possible that low-income, high-achieving students benefit from selective colleges and universities. However, if there are slot constraints at schools, reforms in favor of low-income students would involve a reallocation between these students and other students. Therefore, it seems especially important to investigate whether low-income students benefit more or less from selective education than other students. This may be so either because their fallback options are not as good, or because a selective school education creates social externalities.

Relatively few studies address these questions. Mark Hoekstra (2009) documents earnings effects from attending a flagship state university. Stacy Dale and Alan Krueger (2002, 2011) present "selection-adjusted" evidence on the returns to selective education and find some effects of attending a selective college for students from disadvantaged family backgrounds (as measured by parental education or income). However, identifying the causal effect of selective colleges is a challenging issue. In particular, it seems hard to describe a data generating process under which all selection bias operates through the set of schools one applies to, as in Dale and Krueger's research design. Perhaps just as important, if it were possible to encourage low-income high-achievers to attend selective schools, the relevant margin is probably the switch from a local community college to a lower-end selective college, which may not be the effect identified by Dale and Krueger. On the other hand, the evidence from selective secondary schools seems to point to little benefit to selective education (Bui and others 2011, Abdulkadiroglu and others 2012, Clark 2010). Without a doubt, additional research is needed to measure the benefits of selective education. The additional work by Hoxby and Turner (2013), foreshadowed in this paper, will likely provide valuable evidence on this challenging empirical question.

Finally, the stylized facts documented by Hoxby and Avery indicate another rationale for intervention, one related to issues of equity. Of course, whether equity should be seen as a rationale for policy intervention depends on the objective functions of colleges, and of society more generally. These points are being brought forward in recent policy debates. For example, a possible response to court challenges of affirmative action is the adoption of broader income-based criteria. Here again an important precedent at the K-12 level seems worth noting. The 2007 Supreme Court ruling in Parents Involved in Community Schools v. Seattle School District No. 1 has been widely seen as outlawing the use of racial preferences in K-12 school admissions. A number of districts throughout the country are experimenting with a redefinition of diversity. For instance, Chicago Public Schools has established a "tier system" for its nine selective high schools. Each census tract in Chicago is given a socioeconomic status score based on median family income, educational attainment, the percentage of single-parent households, the percentage of residents who are homeowners, the percentage that speak a language other than English, and average school performance. At each selective school, 30 percent of seats are reserved to be assigned on the basis of admissions test scores only, and the remaining 70 percent are assigned according to admission test scores within tier. It seems a good bet that school systems will continue to experiment with like-minded policies that seek to redefine diversity for higher education. If so, an encouraging aspect of Hoxby and Avery's finding is that low-income, high-achieving students are plentiful, and if Hoxby and Avery can find them, others might be able to as well.

REFERENCES FOR THE PATHAK COMMENT

Abdulkadiroglu, Atila, Parag A. Pathak, and Alvin E. Roth. 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match." American Economic Review 99, no. 5: 1954-78.

Abdulkadiroglu, Atila, Joshua D. Angrist, and Parag A. Pathak. 2012. "The Elite Illusion: Achievement Effects at Boston and New York Exam Schools." IZA Discussion Paper no. 6790. Bonn, Germany: Institute for the Study of Labor. (Also forthcoming in Econometrica.)

Bui, Sa A., Steven G. Craig, and Scott A. Imberman. 2011. "Is Gifted Education a Bright Idea? Assessing the Impact of Gifted and Talented Programs on Achievement." Working Paper no. 17089. Cambridge, Mass.: National Bureau of Economic Research (May).

Clark, Damon. 2010. "Selective Schools and Academic Achievement." B.E. Journal of Economic Analysis and Policy: Advances 10, no. 1: article 9.

Dale, Stacy Berg, and Alan B. Krueger. 2002. "Estimating the Payoff of Attending a More Selective College: An Application of Selection on Observables and Unobservables." Quarterly Journal of Economics 107, no. 4:1491-1527.

--.2011. "Estimating the Return to College Selectivity over the Career Using Administrative Earnings Data." Working Paper no. 17159. Cambridge, Mass.: National Bureau of Economic Research (June).

Hoekstra, Mark. 2009. "The Effect of Attending the Flagship State University on Earnings: A Discontinuity-Based Approach." Review of Economics and Statistics 91, no. 4: 717-24.

Hoxby, Caroline. 2009. "The Changing Selectivity of American Colleges." Journal of Economic Perspectives 23, no. 4:95-118.

Hoxby, Caroline, and Sarah Turner. 2013. "Expanding Opportunities for High-Achieving, Low Income Students." SIEPR Discussion Paper no. 12-014. Stanford Institute for Economic Policy Research.

Pathak, Parag A. 2011. "The Mechanism Design Approach to Student Assignment." Annual Review of Economics 3:513-36.

Pathak, Parag A., and Tayfun Sonmez. 2008. "Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism." American Economic Review 98, no. 4: 1636-52.

--. 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation." American Economic Review 103, no. 1: 80-106.

Table 1. Probability of Sixth-Graders Applying to a Boston Exam
School, by Decile of Predicted Probability of Receiving an Offer

            Predicted probability
Decile   p of receiving an offer (a)   Probability p of applying

1                   0.021                        0.085
2                   0.042                        0.111
3                   0.068                        0.141
4                   0.105                        0.178
5                   0.160                        0.226
6                   0.237                        0.286
7                   0.357                        0.361
8                   0.520                        0.460
9                   0.726                        0.583
10                  0.927                        0.758

Source: Author's calculations using data from Abdulkadiroglu,
Angrist, and Pathak (2012).

(a.) Predictions are based on baseline test scores and the following:
interactions of application year x baseline decile for both math and
English; race: sex; and whether the student is eligible for the free
school lunch program. Students classified as having limited English
proficiency or as in special education are excluded.

GENERAL DISCUSSION

Donald Kohn wondered what incentives selective colleges have to find and admit high-performing low-income students. Noting that most available diversity statistics measure racial and ethnic diversity and not income diversity, Kohn speculated that admissions officers have less of an incentive to search out high-performing, low-income students who are not members of historically disfavored racial and ethnic groups. He also asked, given the recent drop in male college application and completion rates, whether the missing high-performing, low-income students were predominantly male.

Justin Wolfers mentioned that he had written an op-ed with Betsey Stevenson describing Hoxby and Avery's results, which had led the president of the University of Michigan to inquire about the results and how the university might utilize them. That indicated that at least one selective university was interested in improving its recruitment of high-performing low-income students.

Benjamin Friedman observed that the geographic distribution of the "missing" high-performing, low-income students in the authors' data appeared to be correlated with current political patterns in the United States: relatively larger numbers of such students tend to be found in the "red" (Republican-leaning) states. He thought this correlation might offer some clues for understanding why these students were "missing."

Robert Gordon questioned the assumption in the discussion thus far that improving the situation of high-performing, low-income students would yield a net gain to society. A student who is admitted to and attends Harvard instead of a Chicago community college almost surely reaps a lifetime benefit, but that student displaces another student from attending Harvard, who then attends a slightly less prestigious school. That displaced student in turn displaces another student at that school, and so on. The sum of these displaced students' lost utilities, Gordon argued, should be taken into account in any net social welfare calculation. Gordon further noted that the shares of black and Hispanic students among the population of high-performing, low-income students are lower than their shares in the overall population.

Raquel Fernandez wondered how much additional financial aid is being allocated to high-performing, low-income students and what that might imply for colleges' incentive to admit them. She also asked whether it would it be possible for a high school student's performance information to be automatically made available to selective colleges when the student takes a standardized test.

Citing his own experience as a parent of high school students, Michael Klein proposed that the largest component of the cost of applying to any given college might be the cost of making a campus visit. He wondered how many students attend a college that they had not first visited, and how many high-performing, low-income students are prevented from attending colleges appropriate to their ability by the cost of visiting.

Betsey Stevenson suggested that family issues may help explain why some high-performing, low-income students do not go to the most competitive colleges. For instance, firstborn children might have responsibilities for younger siblings that prevent them from going away to college. In terms of the things over which colleges have more influence, she argued that it might be the perceived, not the actual, cost of a selective college that is deterring applications: many low-income applicants might be poorly informed about the true cost of attending college.

Gary Burtless cited a possible adverse consequence of increasing the number of high-performing, low-income applicants to elite colleges. He recalled reviewing a recent book by Charles Murray that showed that in the 1940s, students at elite universities scored only slightly better, on average, on standardized tests than students at a cross section of Pennsylvania universities. Given that elite universities now accept high-performing students almost exclusively, the distribution of high-performing, low-income students by selectivity of their college is roughly the same today in as the 1940s, but the distribution of other high-performing students has become significantly more concentrated. If that trend were to continue so that all high-performing students ended up attending elite colleges, it would contribute to what Murray saw as an increasing divide between the elite and the rest in society. Supporting Burtless's point, Gordon noted that until roughly 1960, the majority of Harvard students were from college preparatory schools, but from then on more public high school graduates than college prep graduates attended.

Alexandre Mas observed that colleges generally do a better job of recruiting high-achieving athletes than of recruiting high academic achievers. Could colleges use their athletic recruitment policies as a model for recruiting more high-performing, low-income students? Laurence Ball added that it was absurd to imagine that there are students capable of playing intercollegiate basketball at UCLA or Duke but not applying there and ending up at local community colleges instead.

Ricardo Reis asked how the authors reconciled their finding of large benefits from attending an elite college with those of other studies, such as by Parag Pathak, that find little value added from attending an elite high school. Reis noted that students can apply to elite schools at any of three different levels: high school, undergraduate, or graduate school. But the differences in family income among attendees of elite high schools are less pronounced than those for attendees of undergraduate colleges, and applicants to graduate schools are less tied to their city or state of origin. This suggested to Reis that, of the three levels, only for undergraduate college is geography the binding constraint on elite school attendance for high-performing low-income students.

Willaim Brainard agreed with Stevenson that students face important information constraints in deciding which college to apply to. Even many Yale faculty members and administrators, he reported, cannot accurately state the current cost of a year's tuition at Yale. Brainard suspected that many high-performing students do not apply to elite colleges because they think, mistakenly, that they have a negligible chance of being admitted, or if admitted, being able to afford the cost.

Bradford DeLong observed that the number of undergraduate students at Harvard has roughly tripled since the end of the 19th century, from about 500 then to about 1,600 currently. But the number of qualified individuals who might want to attend Harvard has increased by a factor of at least 10 over the same period. The result has been a substantial increase in selectivity, which means that a student's best strategy is to submit many applications and hope for a good draw from what has become largely a random selection process.

David Romer noted that many colleges like to have students from all 50 states. He wondered how well these colleges do at finding high-achieving students from small states who do not attend high schools with large numbers of high achievers.

Responding to the discussion, Caroline Hoxby remarked that selective colleges today are quite eager to diversify their student bodies by recruiting more low-income students--so eager that some, regrettably, have been willing to lower their admission standards to do so. These colleges would much prefer to find low-income students who meet their standards and can do the academic work, because such students are less likely to fail to keep up or to become segregated in the easier majors. The problem, Hoxby said, is not in locating high achievers and sending them information: colleges can easily buy lists of high-scoring students from the College Board and ACT; indeed, college applicants today are inundated with brochures, catalogs, application forms, and the like--to say nothing of the vast amount of information now available through the Internet. Part of the problem is that most students have great difficulty navigating this sea of information without help from more knowledgeable people, and such people tend to be scarce in the homes, schools, and neighborhoods of low-income students.

Once a high-achieving, low-income student has applied to a selective college, Hoxby continued, the college will likely make every effort to recruit him or her--offering all-expense-paid visits, for example, or even sending admissions staff to the student's home. But many high-achieving, low-income students, precisely because they lack adequate guidance about the opportunities available to them, never apply. Hence they remain invisible to the selective colleges that are so assiduously looking for them.

Hoxby also addressed the question of whether admitting more low-income students to highly selective colleges simply displaces other students to slightly less selective colleges, thus negating any net social gain. She noted that before the financial crisis, several of the nation's most selective colleges, including Harvard and Stanford, had made plans to expand their freshman classes. Princeton actually did so. In principle, then, the displacement problem could--and may yet--be avoided. A concern, however, has been that higher-income students would end up taking most of the new slots. Thus, the paper's finding that many more low-income high achievers are out there than had been widely believed should encourage these schools to proceed with their expansions.

More broadly, Hoxby thought it a mistake to view college admissions as a zero-sum game in which selective colleges have a fixed quantity of resources to allocate among a fixed number of successful applicants. That might be the case in the short run, she said, but the long run presents a very different picture. Selective colleges seldom recoup their operational costs from tuition and other upfront revenue--even most of their higher-income students pay no more than about half the true cost of their education. Rather, the books for a given graduating class balance only decades later, as donations from successful--and grateful--alumni flow in. Hoxby added that although in the short run a college might lose more, because of financial aid, on its low-income students than on the average student, often it is the low-income students, mindful of the enormous difference the college has made in their lives, who become the most loyal and generous alumni.

Finally, Hoxby argued that although streamlining the college application process was surely part of the solution, it might inadvisable if by "streamlining" one means reducing the amount of information collected. After all, the aid package that a low-income applicant to a highly selective college receives can be worth nearly half a million dollars. Just as a bank considering a $500,000 small business loan will require extensive information about the borrower's business plan, so it is only reasonable for a college to scrutinize each financial aid applicant carefully, to decide whether he or she is a good investment.

Christopher Avery added, replying to Donald Kohn, that colleges are in fact facing strong pressure to admit more low-income students. One source of that pressure, he said, was the increasing availability of rankings of colleges by their percentage of students who are eligible for Pell grants.

Replying to a point in Amanda Pallais's comment, Avery agreed that it was important for low-income high achievers to apply to many selective colleges rather than a few, because although the average aid package at such colleges is generous, the distribution of aid offers is fairly wide. He also agreed with Pallais that even though the cost of applying to a college is typically negligible relative to the potential long-run benefits of attending, it nevertheless seems to be a behavioral sticking point for many students. That underlined for him the importance of fee waivers for low-income applicants.

CAROLINE HOXBY

Stanford University

CHRISTOPHER AVERY

Harvard Kennedy School

(1.) Hereafter, "low-income" and "high-income" mean, respectively, the bottom and top quartiles of the income distribution of families with a child who is a high school senior. "High-achieving" refers to a student who scores at or above the 90th percentile on the ACT comprehensive or the SAT I (math and verbal) and who has a high school grade point average of A- or above. This is approximately 4 percent of U.S. high school students. When we say "selective college" in a generic way, we refer to colleges and universities that are in the categories from "Very Competitive Plus" to "Most Competitive" in Barron's Profiles of American Colleges. There were 236 such colleges in the 2008 edition. Together, these colleges have enrollments equal to 2.8 times the number of students who scored at or above the 90th percentile on the ACT or the SAT I. Later in the paper, we are much more specific about colleges' selectivity: we define schools that are "reach," "peer," and "safety" for an individual student, based on a comparison between that student's college aptitude test scores and the median aptitude test scores of students enrolled at the school.

(2.) Note that such a student's out-of-pocket costs (including loans), in absolute terms, peak at private colleges of middling to low selectivity. This is because these colleges have little in the way of endowment with which to subsidize low-income students and receive no funding from their state government (as public colleges do) with which to subsidize students. Moreover, the most selective colleges spend substantially more on each student's education than is paid by even those students who receive no financial aid (Hoxby, 2009). Thus, when a low-income student attends a very selective college, he or she gets not only financial aid but also the subsidy received by every student there.

(3.) In order to guarantee low-income students that they are at no disadvantage in admissions, many colleges maintain "Chinese Walls" between their admissions and financial aid offices. Consequently, many schools can only precisely identify low-income students once they have been admitted. However, admissions officers target recruiting by analyzing applicants' essays, their teachers' letters of recommendation, their parents' education, and their attendance at an "underresourced" high school.

(4.) Even highly endowed colleges cannot afford to have their admissions staff personally visit many more than 100 high schools a year, and there were more than 20,000 public and more than 8,000 private high schools nationwide in the school year relevant to our study.

(5.) Colleges routinely purchase "search files" from the College Board and ACT that contain names and addresses of students whose test scores fall in certain ranges (and who agree to be "searched"). The colleges can then purchase marketing information on which ZIP codes have low median incomes. The materials they send to students in such ZIP codes typically include, in addition to their usual brochures, a letter describing their financial aid and other programs that support low-income students.

(6.) These schools are informally known as "feeders." Feeder schools are often selective schools (schools that admit students on the basis of exams or similar criteria), magnet schools, or schools that enroll a subpopulation of low-income students despite having most of their students drawn from high-income, highly educated families.

(7.) Since the vast majority of college mentoring programs rely on students to self-select into their activities, it is unclear whether they identify students who would otherwise be unknown to colleges or merely serve as a channel for students to identify themselves as good college prospects.

(8.) This practice is controversial. Since the organization may merely be moving low-income students to colleges that pay from colleges that do not, some admissions staff suspect that poaching (not expansion of the pool of low-income applicants) is the reason that the organization can fulfill the guarantees. They suspect that some very selective colleges are able to look good at the expense of others, with little net change in the lives of low-income students. Another controversial aspect is that low-income students who allow themselves to be funneled by the organization do not get to consider the full range of admissions offers they could obtain.

(9.) In this paragraph, we draw upon personal communications between the authors and many college admissions staff, including those who attend the conferences of the College Board, the Consortium for Financing Higher Education, and the Association of Black Admissions and Financial Aid Officers of the Ivy League and Sister Schools (ABAFAOILSS).

(10.) Much of the data we use are available only to researchers. Moreover, the analytics involved are far beyond the capacity of the institutional research groups of even the best endowed colleges. We have worked for almost a decade to build the database and analysis that support this paper.

(11.) The cutoff is 1300 for combined mathematics and verbal ("Critical Reading") scores on the SAT. The cutoff is 29 for the ACT composite score.

(12.) We also considered excluding students who had taken no subject tests, since some selective colleges require them. (Subject tests include SAT II tests, Advanced Placement tests, and International Baccalaureate tests.) However, we dropped this criterion for a few reasons. First, many selective colleges do not require subject tests or make admissions offers conditional on a student taking subject tests and passing them. Second, among SAT I takers, few students were excluded by this criterion. Third, ACT comprehensive takers usually take subject tests offered by the College Board or International Baccalaureate. When we attempt to match students between these data sources, errors occur so that at least some of the exclusions are false.

We match students between the ACT comprehensive and the SAT I to ensure that we do not double-count high-achieving students. However, this match is easier than matching the ACT comprehensive takers to College Board subject tests, which students often take as sophomores or juniors in high school.

(13.) Approximately 2,400,000 students per cohort take a College Board test, and approximately 933,000 students per cohort take the ACT.

(14.) Since we require microdata to create the relevant distribution, our source for this information is the American Community Survey 2008.

(15.) We obtain these numbers by counting the number of high achievers whose estimated family income puts them in the bottom quartile of family income. We subtract a number corresponding to our false positive rate and add a number corresponding to our false negative rate. There are two reasons why this procedure gives us a range rather than an exact number. First, many high achievers appear in both the College Board and ACT data. We cannot definitively eliminate all of the duplicates because their names, addresses, and birthdates often do not exactly match in the two data sets. Eliminating all possible duplicates pushes us toward the lower bound. Second, although our false positive rate is robust to the aid data we use, our false negative rate is not. This is because the false negatives are low-income students who come from block groups where only a small percentage of families have low incomes. Our aid data from such block groups are fairly sparse, and we are therefore not confident about whether we can extrapolate the false negative rate to areas that appear similar but where we have never observed a false negative. Extrapolating pushes us toward the upper bound.

(16.) We do not attempt to correct these data for biases because we do not have verified data on parents' education that we could use to estimate the errors accurately. This is in contrast to family incomes, where we do have a source of verified data (the CSS Profile).

(17.) "Underrepresented minority" is the term of art in college admissions. Notably, it excludes Asians.

(18.) That is, the size and scope of municipalities, school districts, and other jurisdictions are far less consistent than those of counties.

(19.) Experts also advise students to look at the high school grade point average that is typical of a college's students. However, such grade-based categories are not terribly relevant to high-achieving students because selective colleges vary so much more on the basis of college aptitude test scores than on the basis of high school grades.

(20.) State flagship universities are something of a special case. On the one hand, they vary widely in selectivity. On the other hand, even flagships with low overall selectivity can create opportunities (formal or informal) for their highest-aptitude students to get an education oriented to students with their level of achievement. These opportunities may include research jobs and taking courses primarily intended for doctoral students.

(21.) As noted above, a student may often apply to a nonselective college without sending scores, although a good number of students send scores to them for apparently no reason (the first few sends are free) or for placement purposes (that is, to avoid being placed in lower-level or even remedial courses). If we match students to their enrollment records in the National Student Clearinghouse, we can add to their set of applications any nonselective school in which they enrolled without sending scores. This does not change the figures much, although it does systemically raise the bar for nonselective applications. We do add applications in this way for the analysis in the second half of this section, but it makes too little difference here to be worthwhile, especially as we would then have to show figures for a sample of the students, rather than the population of them.

(22.) For instance, consider a student whose own scores put him or her at the 94th percentile. In order to apply to a reach school, he or she would need to apply to a school whose median student scored at the 99th percentile. There are no such schools--or at least no schools that admit to having such a high median score.

(23.) We do not treat the sending of no scores as equivalent to applying to no selective institution. The reason is that a student may send no scores because he or she takes both the SAT and the ACT and prefers to send the scores from only one of the two tests. Since we cannot definitively match students across the two data sources (see note 15), we cannot assume that no-score-sending corresponds to no selective applications.

(24.) We considered estimating a rank-ordered logit model (Beggs, Cardell, and Hausman 1981), on the assumption that the order in which the student sent scores to colleges indicates the rank order of his or her preference among them. (All colleges to which no application is sent are assumed to generate net utility below the bottom-ranked college.) If we do this, the rank-ordered logit generates fairly similar results, in part because many students do not send scores to more than a few colleges. However, the order of score sending might be a poor proxy for some students' preference orderings because they choose a first batch of colleges to receive their scores before they know what those scores are. Once they learn their scores, they choose a second batch of colleges to receive their scores. At application time, they presumably prefer the second batch to the first.

(25.) That is, we do not assume that the response of a student to mismatch is symmetric around his or her own test score. A student may only slightly like being at a reach school, for instance, but strongly dislike being at a safety school.

(26.) In Avery and Hoxby (2004), we found much smaller differences in the behavior of low- and high-income students, but all the students we sampled attended high schools that were at least somewhat reliable feeders. As we will show, the low-income students we sampled were thus very disproportionately what we call "achievement-typical" students who do behave fairly similarly to high-income students.

(27.) We can interact additional student characteristics that might affect admission for instance, race and ethnicity--with colleges' fixed effects. This effectively "soaks up" each college's preferential admissions standards. However, such a specification does not change the estimated coefficients of interest to a noticeable extent, and it makes interpretation slightly harder.

(28.) This is a somewhat subtle test of whether the achievement-typical students have total application portfolios like those of high-income high achievers.

(29.) We do not consider progress toward a 2-year degree because virtually none of the high-achieving students reported that a 2-year degree was their educational goal in the descriptive questionnaires that accompany the ACT and SAT I tests.

(30.) Hoxby and Turner (2013) implement exactly the causal test needed by inducing income-typical students to apply to substantially more selective institutions. That study finds no evidence that the students thus induced fail to be admitted at normal rates, fail to attain normal grades, or fail to persist at normal levels.

(31.) There were 334 metropolitan statistical areas and primary metropolitan statistical areas in the 2000 Census of Population.

(32.) Finn and Hockett found most of the selective high schools in their study by word of mouth and by contacting all high schools that were so dissimilar to other schools in their district that they seemed likely to practice selective admissions. Interestingly, many school districts deemphasize the existence of their selective high schools, which can be controversial. This perhaps explains why there was no reasonably accurate list of them before Finn and Hockett (2012).

(33.) We use all of the Schools and Staffing surveys in an attempt to pick up as many high schools as possible, but we nevertheless end up with teacher data for only 34 percent of the high-achieving students we study. We use the survey weights to create statistics that should be nationally representative. For the statistics based on previous cohorts, we use the actual previous cohorts from the College Board but must assume that our one previous cohort from the ACT was representative of the whole previous decade.

(34.) Arguably, focusing on these colleges overstates the extent of previous cohorts' sophistication about college applications. These colleges are the most likely to show up in odd strategies like applying to one nonselective institution and to Harvard.

(35.) Meet and Rosen generously computed the relevant statistics for us.

(36.) Many readers of previous drafts have asked us to compare athletes and low-income high achievers, which we are glad to do because the comparison is telling. However, there is no evidence that colleges actually identify and recruit most students who have the potential to perform very well in college sports. Our readers tend to assume that this is true, but colleges might, in fact, neglect to recruit many talented athletes.

(37.) Of course, colleges will likely not identify a student who is a potentially top athlete but only in a team sport and who plays on a weak team that competes only with other weak teams. But arguably that student cannot develop his or her potential in any case.

Table 1. College Costs and Resources, by Selectivity of College (a)

Dollars per year

                      Out-of-pocket     Comprehensive       Average
                     cost for student     cost (cost     instructional
                     at 20th %ile of        before        expenditure
Selectivity           family income     financial aid)    per student

Most competitive          6,754             45,540          27,001
Highly
  competitive plus        13,755            38,603          13,732
Highly competitive        17,437            35,811          12,163
Very competitive
  plus                    15,977            31,591           9,605
Very competitive          23,813            29,173           8,300
Competitive plus          23,552            27,436           6,970
Competitive               19,400            24,166           6,542
Less competitive          26,335            26,262           5,359
Some or no
  selectivity,
  4-year                  18,981            16,638           5,119
Private 2-year            14,852            17,822           6,796
Public 2-year             7,573             10,543           4,991
For-profit 2-year         18,486            21,456           3,257

Sources: Barron's Profiles of American Colleges and authors'
calculations using the colleges' own net cost calculators and data
from the Integrated Postsecondary Education Data System (IPEDS),
National Center for Education Statistics.

(a.) All costs include tuition and room and board. Out-of-pocket
costs include loans. At the very competitive level and above, the net
cost data were gathered by the authors for the 2009-10 school year.
For all other institutions, net cost estimates are based on the
institution's published net cost calculator for the year closest to
2009-10, but never later than 2011-12. These published net costs are
then reduced to approximate 2009-10 levels using the institution's
own figures for room and board and tuition net of aid, from WEDS, for
the relevant years. Instructional expenditure data are from IPEDS.

Table 2. College Assessment Results of High-Achieving Students, by
Family Income (a)

                  Average SAT or ACT percentile score
Income quartile      among high-achieving students

First (bottom)                    94.1
Second                            94.3
Third                             94.8
Fourth                            95.7

Source: Authors' calculations using data from the ACT, the College
Board, WEDS, and other sources described in the text (hereafter
referred to as the "combined data set").

(a.) High-achieving students are students in 12th grade who have an
ACT comprehensive or SAT I (math plus verbal) score at or above the
90th percentile and a high school grade point average of A- or above.

Table 3. Conditional Logit Regressions Explaining High-Achieving
Students' College Applications (a)

                                              Low-income   High-income
Factor                                         students     students

College is a peer school (b)                  1.015        76.214 ***
College is a safety school (c)                3.009 ***    14.895 ***
College is nonselective                       0.748 ***     1.6e-9 ***
Tuition before discount (thousands of
  dollars)                                    0.865 ***     1.176 ***
Average tuition discount (percent)            1.091 **      0.925 **
Could live at family home (college is <10
  miles away)                                 4.942 ***     0.810 ***
Could go home often (college is <120 miles
  away)                                       1.556 ***     1.185 ***
Distance in miles to college                  0.996         0.998
Square of (distance in miles/1,000)           1.056 **      1.283 ***
College is in-state                           2.595 ***     1.206 ***
College is private                            0.838 ***     1.002
College is for-profit                         0.834 ***     0.012 ***
Highest degree offered is 2-year              0.925 **      0.009 ***
College is a university                       0.997         0.567 ***
College is a liberal arts college             0.717 ***     0.973 *

Source: Authors' regressions using the combined data set described in
the text.

(a.) Results of a conditional logit estimation in which the dependent
variable is an indicator equal to 1 if a high-achieving student
applies to the college and zero otherwise. Coefficients are expressed
as odds ratios, so that a coefficient greater than 1 means that an
increase in the covariate is associated with an increase in the
probability that the student applies to a college with the indicated
factor, all other covariates held constant. High-achieving students
are defined as in table 2. Low- and high-income students are those
from families in the bottom and top quartiles of the family income
distribution, respectively. Asterisks indicate statistical
significance at the * 10 percent, ** 5 percent, or *** 1 percent
level.

(b.) The absolute value of the difference between the college's
median test score and the student's own is within 5 percentiles.

(c.) The college's median score is 5 to 15 percentiles below the
student's own

Table 4. Conditional Logit Regressions Explaining Income-Typical and
Achievement-Typical Students' College Applications (a)

                                 Low-income students

                                Income-     Achievement-   High-income
Factor                        typical (b)   typical (c)     students

College is a peer school      7.21e-8 ***   87.808 ***     76.214 ***
College is a safety school    2.142 ***     19.817 ***     14.895 ***
College is nonselective       0.795 ***      1.04e-8 ***    1.6e-9 ***
Tuition before discount
  (thousands of dollars)      0.973 ***      1.004          1.176 ***
Average tuition discount
  (percent)                   1.000          1.020 *        0.925 **
Could live at family home
  (college is <10 miles
  away)                       5.140 ***      1.477 ***      0.810 ***
Could go home often
  (college is <120 miles
  away)                       1.972 ***      1.436 ***      1.185 ***
Distance in miles to
  college                     0.999          0.999          0.998
Square of (distance in
  miles/1,000)                1.042 *        1.448 ***      1.283 ***
College is in-state           4.891 ***      7.455 ***      1.206 ***
College is private            0.662 ***      0.296 ***      1.002
College is for-profit         0.806 ***      0.001 ***      0.012 ***
Highest degree offered is
  2-year                      0.855 ***      0.016 ***      0.009 ***
College is a university       0.956 **       0.861 ***      0.567 ***
College is a liberal arts
  college                     0.515 ***      0.167 ***      0.973 *

Source: Authors' regressions using the combined data set described in
the text.

(a.) Results of a conditional logit regression in which the dependent
variable is an indicator equal to I if a high-achieving student
applies to the college and zero otherwise. Coefficients are expressed
as odds ratios, so that a coefficient greater than 1 means that an
increase in the covariate is associated with an increase in the
probability that the student applies to a college with the indicated
characteristic, all other covariates held constant. The coefficients
for high-income students are repeated from table 3 for ease of
comparison. High-achieving students are defined as in table 2.
Low-and high-income students are those from families in the bottom
and top quartiles of the family income distribution, respectively.
Asterisks indicate statistical significance at the * 10 percent,
** 5 percent, or *** 1 percent level.

(b.) Those who apply to no school whose median score is within 15
percentiles of their own and apply to at least one nonselective
school.

(c.) Those who apply to at least one peer college, at least one
safety college with a median score not more than 15 percentiles lower
than their own, and no nonselective colleges.

Table 5. Estimates Showing Whether High-Achieving, Low-and High-
Income Applicants Have Different Probabilities of Enrolling in
Selective Colleges (a)
                                     Percent of colleges where low-
                                        and high-income students'
                                       probabilities of enrolling
                                    (conditional on application) are
                                      statistically significantly
                                    different at the 5 percent level

                                                            Base
                                                       specification
                                                       plus indicator
                                                       variables for
                                                         number of
                                         Base           applications
College's median test score        specification (b)      sent (c)

[greater than or equal to] 90th
  percentile                               4                 5
[greater than or equal to] 80th
  but <90th percentile                     5                 5
[greater than or equal to] 70th
  but <80th percentile                     4                 5
[greater than or equal to] 60th
  but <70th percentile                     3                 4
[greater than or equal to] 50th
  but <60th percentile                     6                 5
<50th but college is selective             Not identified (d)
College is nonselective                    Not identified

Source: Authors' calculations using the combined data set described
in the text.

(a.) Results of a conditional logit estimation in which the dependent
variable is an indicator equal to I if a high-achieving student
enrolls in a particular postsecondary institution and zero otherwise.
Each student's choice set is the set of colleges to which he or she
applied. High-achieving students are defined as in table 2. Low- and
high-income students are those from families in the bottom and top
quartiles of the family income distribution, respectively.

(b.) The only independent variables are indicators for each college
interacted with an indicator for whether the student is high- or
low-income.

(c.) Indicator variables for whether the student applied to 1
college, 2 colleges, and so on up to 20 or more colleges are added to
the specification in the previous column.

(d.) Results are not identified for low-selectivity and nonselective
colleges because too few high-income students apply to such colleges.

Table 6. Estimates of Whether Low-and High-Income Students Have
Different Probabilities of Persisting at a Selective College,
Conditional on Having Enrolled (a)

                                      Percent of colleges where
                                   low- and high-income students'
                                   shares of credits earned toward
                                      a degree (conditional on
                                    enrollment) are statistically
                                  significantly different at the 5
                                            percent level

                                                        Excluding
                                                      students from
                                                      selective and
                                                       magnet high
                                        Base           schools (c)
College's median test score       specification (b)

[greater than or equal to] 90th
  percentile                              5                 4
[greater than or equal to] 80th
  but <90th percentile                    4                 5
[greater than or equal to] 70th
  but <80th percentile                    4                 5
[greater than or equal to] 60th
  but <70th percentile                    5                 5
[greater than or equal to] 50th
  but <60th percentile                    4                 4
<50th but college is selective           Not identified (d)
College is nonselective                  Not identified

Source: Authors' calculations using the combined data set described
in the text.

(a.) Results of an ordinary least squares regression in which the
dependent variable is the share of credits toward a baccalaureate
degree earned by a student by June 2012. Students who do not enroll
in a postsec ondary institution are not included in the regression.
High-achieving students are defined as in table 2. Low- and
high-income students are those from families in the bottom and top
quartiles of the family income distribution, respectively.

(b.) The only independent variables are indicators for each college
interacted with an indicator for whether the student is high- or
low-income.

(c.) Same specification as in the previous column, but students who
attended high schools classified as magnet schools or that select
incoming students on the basis of test scores or grades are excluded.

(d.) Results are not identified for low-selectivity and nonselective
colleges because too few high-income students apply to such colleges.

Table 7. Socioeconomic Characteristics of High-Achieving Students (a)

                                                 Low-income students

                                 High-income   Achievement-    Income
Characteristic                    students       typical      typical

Annual family income
  (dollars) (b)                  157,569       30,475         32,418
Parents' education (years) (c)        18.7         16.0           16.7
Race or ethnicity (d)
    (percent of total)
  White                               74.8         45.1           79.5
  Black                                2.1          5.2            2.9
  Hispanic                             5.6         12.6            6.0
  Asian                               20.5         31.8            7.3

Source: Authors' calculations using the combined data set described
in the text.

(a.) High-achieving students are defined as in table 2. Low- and
high-income students are those from families in the bottom and top
quartiles of the family income distribution, respectively.
Achievement-typical and income-typical students are defined as in
table 4.

(b.) Estimated as described in section II.

(c.) Highest level of education attained by either parent, as
reported by the student. Such self-reporting of parental education is
unreliable because students may be more likely not to report if their
parents' educational attainment is low.

(d.) Self-reported.

Table 8. Socioeconomic Characteristics of the Neighborhoods of
High-Achieving Students (a)

                                                 Low-income students

                                 High-income   Achievement-    Income
Characteristic (b)                students       typical      typical

Annual family income (dollars)   123,684       32,142         31,767
Adjusted gross income
  (dollars) (c)                  121,448           41.358     37,652
Residents with a B.A. degree
  Number                             863          207
  Percent of all adults               66.7         22.0           16.8
Race or ethnicity (percent of
    total)
  White                               86.7         58.2           77.1
  Black                                2.6         12.8           10.1
  Hispanic                             4.1         16.9            8.7
  Asian                                9.2          8.5            2.2

Source: Authors' calculations using the combined data set described
in the text.

(a.) High-achieving students are defined as in table 2. Low- and
high-income students are those from families in the bottom and top
quartiles of the family income distribution, respectively.
Achievement-typical and income-typical students are defined as in
table 4.

(b.) Neighborhoods are census block groups except where noted
otherwise.

(c.) Neighborhood is the ZIP code.

Table 9. Types of Communities Where High-Achieving Students
Reside (a)

Percent

                                                Low-income    students
                                 High-income   Achievement-    Income
Community type                    students       typical      typical

Main city, urban area with
  population > 250,000               17             26            8
Main city, urban area with
  population 100,000-250,000         14             21           13
Main city, urban area with
  population < 100,000               48             18            9
Suburb, urban area with
  population > 250,000                8              9            9
Suburb, urban area with
  population 100,000-250,000          0              2            2
Suburb, urban area with
  population < 100,000                0              4           12
Town, near an urban area              0              5           12
Town, far from an urban area          5              7           13
Rural, near an urban area             6              4           10
Rural, far from an urban area         0              5           10

Source: Authors' calculations using the combined data set described
in the text.

(a.) High-achieving students are defined as in table 2. Low- and
high-income students are those from families in the bottom and top
quartiles of the family income distribution, respectively.
Achievement-typical and income-typical students are defined as in
table 4.

Table 10. Characteristics of High Schools Attended by High-Achieving
Students (a)

                                                 Low-income students

                                 High-income   Achievement-    Income
Characteristic                    students       typical      typical

Number of students per cohort       333           330            241
Type of school (percent of
    total)
  Regular public school              66            73             86
  Magnet school                       4            11              0
  Independent private school         16             7              3
  Catholic or other religious
    school                           15             9             11
Spending per pupil (dollars;
  public schools only)           15,558        12,975         10,701
Pupil-teacher ratio                  16.8          18.3           17.2
Pupil-counselor ratio (public
  schools only)                     307           328            305

Source: Authors' calculations using the combined data set described
in the text.

(a.) High-achieving students are defined as in table 2. Low- and
high-income students are those from families in the bottom and top
quartiles of the family income distribution, respectively.
Achievement-typical and income-typical students are defined as in
table 4.

Table 11. College-Related Characteristics of High Schools Attended
by High-Achieving Students (a)

                                                 Low-income students

                                  High-income   Achievement-   Income
Characteristic                     students       typical      typical

Percent of teachers who
  graduated from a peer
  college (b)                         8.9            2.9         1.1
Percent of teachers who
  graduated from a safety
  college (c)                        14.4            7.5         5.0
Number in a typical previous
  cohort who applied to top 10
  U.S. colleges (d)                  12.9            7.6         1.6
Number in a typical previous
  cohort who were admitted to
  a top 10 U.S. college (d)          12.3            7.4         1.5
Number in a typical previous
  cohort who enrolled at a top
  10 U.S. college (d)                12.3            7.4         1.5
Percent of cohort who are high
  achievers                          17.1           11.2         3.8
Radius to gather 20 high
  achievers (miles)                   2.6            7.7        19.3
Radius to gather 50 high
  achievers (miles)                   4.1           12.2        37.3

Source: Authors' calculations using the combined data set described
in the text.

(a.) High-achieving students are defined as in table 2. Low- and
high-income students are those from families in the bottom and top
quartiles of the family income distribution, respectively.
Achievement-typical and income-typical students are defined as in
table 4.

(b.) A peer college is one where the college's median test score is
within 5 percentiles of the score of the average high achiever
attending the high school.

(c.) A safety college is one where the college's median test score is
between 5 and 15 percentiles below that of the average high achiever
attending the high school.

(d.) Average over the last 10 years.

Figure 2. High-Achieving Students, by Family Income Quartile (a)

1st quartile      (17.0%)
2nd quartile      (22.0%)
3rd quartile      (27.0%)
4th quartile      (34.0%)

Source: 2008 American Community Survey and authors' calculations
using the combined data set described in the text.

(a.) High-achieving students are defined as in table 2.

Note: Table made from pie chart.

Figure 3. High-Achieving Students, by Parents'
Educational Attainment (a)

High school diploma             3.2%
Some college or trade school    7.4%
Associate's degree              4.2%
Bachelor's degree              27.9%
Some graduate school            6.0%
Graduate degree                50.7%
Grades 8 or below               0.2%
Grades 9-11                     0.4%

Source: Authors' calculations using the combined data
set described in the text.

(a.) Parents' educational attainment is the highest level
attained by either parent. Percentages are of those
high-achieving students (defined as in table 2) who took
a College Board test and answered the question
about parents' education (61 percent of high achievers
declined to answer; the ACT questionnaire does not include
a similar question).

Note: Table made from pie chart.

Figure 4. High-Achieving Students, by Race and Ethnicity (a)

Mixed                  2.6%
Native American        0.4%
Asian                 15.0%
Black, non-Hispanic    1.5%
Hispanic               4.7
White, non-Hispanic   75.8%

Source: Authors' calculations using the combined data
set described in the text.

a. Percentages are of those high-achieving students
(defined as in table 2) who took an ACT or a College
Board test and answered the question about their race
or ethnicity (2.1 percent of high achievers declined to
answer).

Note: Table made from pie chart.

Figure 5. High-Achieving, Low-Income Students,
by Race and Ethnicity (a)

Mixed                    1.4%
Native American          0.7%
Asian                   15.2%
Black, non-Hispanic      5.7%
Hispanic                 7.6%
White, non-Hispanic     69.4%

Source: Authors' calculations using the combined data
set described in the text.

a. Percentages are of those high-achieving students
(defined as in table 2) from bottom-quartile-income
families who took an ACT or a College Board test and
answered the question about  their race or ethnicity
(2.1 percent of all high achievers declined to answer).

Note: Table made from pie chart.