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ESTIMATING THE PAYOEF TO ATTENDING A MORE SELECTIVE COLLEGE: AN APPLICATION OF SELECTION ON OBSERVABLES AND UNOBSERVABLES^'^ STACY BERG DALE AND AI.AN B . KRUEGER Estimates of the effect of college selectivity on earnings may be biased because elite colleges admit students, in part, based on characteristics that are related to future earnings. We matched students who applied to, and were ac- cepted by, similar colleges to try to eliminate this bias. Using the College and Beyond data set and National Longitudinal Survey of the High School Class of 1972, we find that students who attended more selective colleges earned about the same as students of se<!mingly comparable ability who attended less selective schools. Children from low-income families, however, earned more if they at- tended selective colleges. A burgeoning literature has addressed the question, "Does the 'quality' of the college that students attend influence their subsequent earnings?"^ Obtaining accurate estimates of the pay- off to attending a highly selective undergraduate institution is of obvious importance to the parents of prospective students who foot the tuition bills, and to the students themselves. In addition, because college selectivity is typically measured by the average characteristics (e.g., average SAT score) of classmates, the litera- ture is closely connected to theoretical and empirical studies of peer group effects on individual behavior. And with higher edu- cation making up 40 percent of total educational expenditures in the United States (see U. S. Department of Education [1997, Table 33]), understanding the impact of selective colleges on students' labor market outcomes is central for understanding the role of human capital.^ * We thank Orley Ashenfelter, Marianne Bertrand, William Bowen, David Breneman, David Card, James Heckman, Bo Honore, Thomas Kane, Lawrence Katz, Deborah Peikes, .Michael Rothschild, Sarah Turner, colleagues at the Mel- lon Foundation, and three anonymous referees for helpful discussions. We alone are responsible for any errors in computation or interpretation that may remain despite their helpful advice. This paper makes use of the College and Beyond (C&B) database. The C&B database is a "restricted access database." Researchers who are interested in asing the database may apply to the Andrew W. Mellon Foundation for access. 1. The modem literature began with papers by Hunt [1963], Solmon 11973], Wales [1973], Solmon and Wachtel [1975], and Wise [1975], and has undergone a recent renaissance, witfi papers by Brewer and Ehrenberg [1996], Behrman et al. [1996[, Daniel Black, and Smith [1997], Kane (1998). and others. See Brewer and Ehrenberg [1996, Tabtij 1[ for an excellent summary of the literature. 2. This fif^re ignores any earnings students forgo while attending school, which wtiuld increase tbe relative cost of higher education. © 2002 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, November 2002 1491

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Page 1: ESTIMATING THE PAYOEF TO ATTENDING A MOREfaculty.smu.edu/millimet/classes/eco7321/papers/dale krueger.pdf · ESTIMATING THE PAYOEF TO ATTENDING A MORE SELECTIVE COLLEGE: AN APPLICATION

ESTIMATING THE PAYOEF TO ATTENDING A MORESELECTIVE COLLEGE: AN APPLICATION OF

SELECTION ON OBSERVABLES AND UNOBSERVABLES '

STACY BERG DALE AND AI.AN B. KRUEGER

Estimates of the effect of college selectivity on earnings may be biasedbecause elite colleges admit students, in part, based on characteristics that arerelated to future earnings. We matched students who applied to, and were ac-cepted by, similar colleges to try to eliminate this bias. Using the College andBeyond data set and National Longitudinal Survey of the High School Class of1972, we find that students who attended more selective colleges earned about thesame as students of se<!mingly comparable ability who attended less selectiveschools. Children from low-income families, however, earned more if they at-tended selective colleges.

A burgeoning literature has addressed the question, "Doesthe 'quality' of the college that students attend influence theirsubsequent earnings?"^ Obtaining accurate estimates of the pay-off to attending a highly selective undergraduate institution is ofobvious importance to the parents of prospective students whofoot the tuition bills, and to the students themselves. In addition,because college selectivity is typically measured by the averagecharacteristics (e.g., average SAT score) of classmates, the litera-ture is closely connected to theoretical and empirical studies ofpeer group effects on individual behavior. And with higher edu-cation making up 40 percent of total educational expenditures inthe United States (see U. S. Department of Education [1997,Table 33]), understanding the impact of selective colleges onstudents' labor market outcomes is central for understanding therole of human capital.^

* We thank Orley Ashenfelter, Marianne Bertrand, William Bowen, DavidBreneman, David Card, James Heckman, Bo Honore, Thomas Kane, LawrenceKatz, Deborah Peikes, .Michael Rothschild, Sarah Turner, colleagues at the Mel-lon Foundation, and three anonymous referees for helpful discussions. We aloneare responsible for any errors in computation or interpretation that may remaindespite their helpful advice. This paper makes use of the College and Beyond(C&B) database. The C&B database is a "restricted access database." Researcherswho are interested in asing the database may apply to the Andrew W. MellonFoundation for access.

1. The modem literature began with papers by Hunt [1963], Solmon 11973],Wales [1973], Solmon and Wachtel [1975], and Wise [1975], and has undergone arecent renaissance, witfi papers by Brewer and Ehrenberg [1996], Behrman et al.[1996[, Daniel Black, and Smith [1997], Kane (1998). and others. See Brewer andEhrenberg [1996, Tabtij 1[ for an excellent summary of the literature.

2. This fif^re ignores any earnings students forgo while attending school,which wtiuld increase tbe relative cost of higher education.

© 2002 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnology.The Quarterly Journal of Economics, November 2002

1491

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1492 QUARTERLY JOURNAL OF ECONOMICS

Past Studies have found that students who attended collegeswith higher average SAT scores or higher tuition tend to havehigher earnings when they are observed in the labor market.Attending a college with a 100 point higher average SAT isassociated with 3 to 7 percent higher earnings later in life (see,e.g., Kane [1998]). As Kane notes, an obvious concern with thisconclusion is that students who attend more elite colleges mayhave greater earnings capacity regardless of where they attendschool. Indeed, the very attributes that lead admissions commit-tees to select certain applicants for admission may also be re-warded in the labor market. Most past studies have used Ordi-nary Least Squares (OLS) regression analysis to attempt tocontrol for differences in student attributes that are correlatedwith earnings and college qualities. But college admissions deci-sions are based in part on student characteristics that are unob-served by researchers and therefore not held constant in theestimated wage equations; if these unobserved characteristics arepositively correlated with wages, then OLS estimates will over-state the payoff to attending a selective school. Only three previ-ous papers that we are aware of have attempted to adjust forselection on unobserved variables in estimating the payoff toattending an elite college. Brewer, Eide, and Ehrenberg [19991use a parametric utility maximizing framework to model stu-dents' choice of schools, under the assumption that all studentscan attend any school they desire. Behrman, Rosenzweig, andTaubman [1996] utilize data on female twins to difference outcommon unobserved effects, and Behrman et al. [19961 use familyvariables to instrument for college choice. Our paper comple-ments these previous approaches.

This paper employs two new approaches to adjust for non-random selection of students on the part of elite colleges. In oneapproach, we only compare college selectivity and earningsamong students who were accepted and rejected by a comparableset of colleges, and are comparable in terms of observable vari-ables. In the second approach, we hold constant the average SATscore of the schools to which each student applied, as well as theaverage SAT score of the school the student actually attended, thestudent's own SAT score, and other variables. The second ap-proach is nested in the first estimator. Conditions under whichthese estimators provide unbiased estimates of the payoff tocollege quality are discussed in the next section. In short, ifadmission to a college is based on a set of variables that are

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ATTENDING A MORE SELECTIVE COLLEGE 1493

observed by tbe admissions committee and later by tbe econome-trician (e.g., student SAT), and anotber set of variables tbat isobserved by tbe admissions committee (e.g., an assessment ofstudent motivation) but not by the econometrician, and if botbsets of variables influence earnings, tben looking within matchedsets of students who were accepted and rejected by the samegroups of colleges can help overcome selection bias.

Bamow, Goldberger, and Cain [1981] point out that, "Unbi-asedness is attainable when the variables that determined theassignment rule are known, quantified, and included in the [re-gressionl equation." Our first estimator extends their concept of"selection on the observables" to "selection on the observables andunobservables," since information on the unobservables can beinferred from the outcomes of independent admission decisions bythe schools the stitdent applied to. The general idea of usinginformation refiected in the outcome of independent screens tocontrol ibr selection bias may have applications to other estima-tion problems, such as estimating wage differentials associatedwith working in different industries or sizes of firms (wherehiring decisions during the Job search process provide screens)and racial differences in mortgage defaults (where denials oracceptances of applications for loans provide screens).^

We provide selection-corrected estimates of the payoff toschool quality using two data sets: the College and Beyond Sur-vey, which was collected by the Andrew W. Mellon Foundationand analyzed extensively in Bowen and Bok [1998], and theNational Longitudinal Survey of the High School Class of 1972(NLS-72). Two indirect indicators of college quality are used:college selectivity, as measured by a school's average SAT score,and net tuition. Our primary finding is that the monetary returnto attending a college with a higher average SAT score fallsconsiderably once we adjust for selection on the part ofthe col-lege. Nonetheless, we still find a substantial payoff to attendingschools with higher net tuition.

Although most of the previous literature has implicitly as-sumed that the returns to attending a selective school are homo-geneous across students, an important issue in interpreting ourfindings is that there may be heterogeneous returns to students

3. Braun and Szatrowski [19841 use a related idea to evaluate law schoolgrades across institutions by comparing the performance of students who wereaccepted at a common net of law schools but attended different schools.

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1494 QUARTERLY JOURNAL OF ECONOMICS

for attending the same school. Some students may benefit morefrom attending a highly selective (or unselective) school thanothers. For example, a student intent on becoming an engineer islikely to have at least as high earnings by attending Pennsylva-nia State University as Williams College, since Williams does nothave an engineering major. In this situation, if students areaware of their own potential returns from each school to whichthey are admitted, they could be expected to sort into schoolsbased on their expected utility from attending that school, as inthe Roy model of occupational choice. In other words, the studentswho chose to go to less selective schools may do so because theyhave higher returns from attending those schools (or becausethere are nonpecuniary benefits from attending those schools);however, the average students might not have a higher returnfrom attending a less selective school over a more selective one.Nonetheless, contrary to the previous literature, this interpreta-tion implies that attending a more selective school is not theincome-maximizing choice for all students. Instead, studentswould maximize their returns by attending the school that offersthe best fit for their particular abilities and desired future field ofemployment.

I. A STYLIZED MODEL OF COLLEGE ADMISSIONS,ATTENDANCE, AND EARNINGS

For most students, college attendance involves three sequen-tial choices. First, a student decides which set of colleges to applyto for admission. Second, colleges independently decide whetherto admit or reject the student. Third, the student and her parentsdecide which college the student will attend from the subset ofcolleges that admitted her. To start, we consider a highly stylizedmodel of both admissions and the labor market as a benchmarkfor analysis. We discuss departures from these simplif3dng as-sumptions later on.

Assume that colleges determine admissions decisions byweighing various attributes of students. A National Associationfor College Admission Counseling [1998] survey, for example,finds that admissions officers consider many factors when select-ing students, including the students' high school grades and testscores, and factors such as their essays, guidance counselor andteacher recommendations, community service, and extracurricu-lar activities. Next, we assume that each college uses a threshold

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ATTENDING A MORE SELECTIVE COLLEGE 1495

to make admissions decisions. An applicant who possesses char-acteristics that place him or her above the threshold is accepted;if not, he or she is rejected. Additionally, idiosyncratic luck mayenter into the admission decision.

The characteristics that the admissions committee ohservesand bases admission decisions on can be partitioned into two setsof variables: a set that is subsequently observed by researchersand a set that is unobserved by researchers. The observable set ofcharacteristics includes factors like the student's SAT score andbigh school grade point average (GPA), while the unobservableset includes factors like assessments of the student's motivation,ambition, and maturity as refiected in her essay, college inter-view, and letters of recommendation. For simplicity, assume thatX^ is a scalar variable representing the observable characteristicsthe admissions committee uses and X2 is an unobservable (to theeconometrician) variable that also enters into the admissionsdecisions.^ We assume that each college, denoted j , uses thefollowing rule to admit or reject applicant i\

(1) iiZ,j = 71X1, + 72 21 + e,j > Cj then admit to college^'

otherwise reject applicant at college J,

where Z^^j is the latent quality of the student as judged by theadmissions committee, e, represents the idiosyncratic views ofcolleger's admission committee, -y and 72 are the weights placedon student characteristics in admission decisions, and Cj is thecutoff quality level the college uses for admission.'' The term e^jrepresents luck and idiosyncratic factors that affect admissiondecisions but are imrelated to earnings. We assume that e^ isindependent across colleges. By definition, more selective collegeshave higher values of C .

Now suppose that the equation linking income to the stu-dents' attributes is

(2) In W, = Po + PiSAT,* + PaXi, + p^^ , +

where SATj.-,.- is the average SAT score of matriculants at thecollege student i attended, X^ andX^ are the characteristics used

4. In terms of the previously defined sets of variables, one could think of A*!and X.^ as a linear combination of the variables in each set, where the weightswere selected to give X, and Jf the coefficients in equation (1).

5. We ignore the possibility of wait listing the student.

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1496 QUARTERLY JOURNAL OF ECONOMICS

by the admission committee to determine admission, and t, is anidiosyncratic error term that is uncorrelated with the other vari-ables on the right-hand side of (2). Since individual SAT scoresare a common X^ variable, SATj^, can be thought of as the meanof Zj taken over students who attend collegey^*'. The parameter|3i, which may or may not equal zero, represents the monetarypayoff to attending a more selective college. This coefficient wouldbe greater than zero if peer groups have a positive effect onearnings potential, for example.

In practice, researchers have been forced to estimate a wageequation that omits X2:

(3) In W,. = Pi + ^[SATj, + ^!JCu + «,.

Even if students randomly select the college they attend from theset of colleges that admitted them, estimation of (3) will yieldbiased and inconsistent estimates of p, and p - Most importantlyfor our purposes, if students choose their school randomly fromtheir set of options, the payofTto attending a selective school willbe biased upward because students with higher values of theomitted variable, Xg, are more likely to be admitted to, andtherefore attend, highly selective schools. Since the labor marketrewards X^, and school-average SAT and X2 are positively corre-lated, the coefficient on school-average SAT will be biased up-ward. The coefficient onXj can be positively or negatively biased,depending on the relationship between X^ and X2. Also noticethat the greater the correlation between Xi and X2, the lesser thebias in p^.

Formally, the coefficient on school-average SAT score is bi-ased upward in this situation because £{ln W,|S'Ar M.,Xi;) = Po +^,SATj. + P2^i,- + £{«,|Xi,-,-yiXi, + y-z^-zi + e,j. > Cj.). Theexpected value of the error term iUj) is higher for students whowere admitted to, and therefore more likely to attend, moreselective schools.^

If, conditional on gaining admission, students choose to at-tend scbools for reasons that are Independent of X2 and E, thenstudents who were accepted and rejected by the same set ofschools would have the same expected value of «,. Consequently,our proposed solution to the school selection problem is to includean unrestricted set of dummy variables indicating groups of stu-

6. A classic reference on selection bias is Heckman [1979].

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ATTENDING A MORE SELECTIVE COLLEGE 1497

dents who received the same admissions decisions (i.e., the samecombination of acceptances and rejections) from the same set ofcolleges. Including these dummy variables absorbs the condi-tional expectation of the error term if students randomly chooseto attend a school from the set of schools that admitted them.Moreover, even if college matriculation decisions (conditional onacceptance) are related to X^, controlling for dummies indicatingwhether students were accepted and rejected by the same set ofschools absorbs some of the effect of the unobserved X. .

To see why controlling for dummies indicating acceptanceand rejection at a common set of schools partially controls for theeffect ofXa, consider two colleges that a subset of students ap-plied to with admission thresholds C^ < C2. College 2 is moreselective than college 1. Ifthe selection rule in equation (1) did notdepend on a random factor, then it would be unambiguous thatstudents who were admitted to college 1 and rejected by college 2possessed characteristics such that Cj < "ViX, + 72^2 " "2- '^C-i approaches C2, the (weighted) sum of the students' observedand unobserved characteristics becomes uniquely identified byobservations on acceptance and rejection decisions.^ Because X^is included in the wage equation, the omitted variables bias wouldbe removed if (71X1 + 7^X2) were held constant. If enough acceptand reject decisions over a fine enough range of college selectivitylevels are observed, then students with a similar history of ac-ceptances and rejections will possess essentially the same aver-age value of the observed and unobserved traits used by collegesto make admission decisions. Thus, even if matriculation deci-sions are dependent on X^, we can at least partially control for X2by grouping together students who were admitted to and rejectedby tbe same set of colleges and including dummy variables indi-cating each of these groups in the wage regression. Notice that toapply this estimator, it is necessary for students to be accepted bya diverse set of schools and for some of tbose students to attendthe less selective colleges and others the more selective collegesfrom their menu of choices.

If the admission rule used by colleges depended only on Xj,and if A'l were included in the wage equation, we would have acase of "selection on the observables" (see Barnow, Cain, and

7. Dcile and Krueger |1999] provide a set of simulations to illustrate theseresults. The fact that idiosyncratic factors affect colleges' admissions decisionsthrough c,, complicates but does not distort this result.

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1498 QUARTERLY JOURNAL OF ECONOMICS

Goldberger [1981]). In this case, however, we have "selection onthe observables and unobservables" since X.^i and e, are alsoinputs into admissions decisions. Nonetheless, we can control forthe bias due to selective admissions by controlling for the schoolsat which students were admitted.

In reality, all students do not apply to the same set of col-leges, and it is probably unreasonable to model students as ran-domly selecting the school they attend from the ones that ac-cepted them, A complete model of the two-sided selection thattakes place between students and colleges is beyond the scope ofthe current paper, but it should be stressed that our selectioncorrection still provides an unbiased estimate of Pi if students'school enrollment decisions are a function of Xi or any variableoutside the model.

The critical assumption is that students' enrollment deci-sions are uncorrelated with the error term of equation (2) andXa.If the decision rule students use to choose the college they attendfrom their set of options is related to their value ofX^, then thebias in the within-matched-applicant model depends on the coef-ficient from a hypothetical regression of the average SAT score ofthe school the student attends on X2, conditional on X^ anddummies indicating acceptance and rejection from the same set ofschools. It is possible that selection bias could be exacerbated bycontrolling for such matched-applicant effects. Griliches [1979]makes this point in reference to twins models of earnings andeducation. In the current context, however, if students apply to afine enough range of colleges, the accept/reject dummies wouldcontrol for X2, and the within-matched-applicant estimateswould be unbiased even if college choice on the part of studentsdepended in part on X2.

Also notice that it is possible that the effect of attending ahighly selective school varies across individuals. If this is thecase, equation (2) should be altered to give an "i" subscript on thecoefficient on SAT. Students in this instance would be expected tosort among selective and less selective colleges based on theirpotential returns there, assuming that they have an idea of theirown personalized value of p^,. In such a situation, our estimate ofthe return to attending a selective school can be biased upward ordownward, and it would not be appropriate to interpret our esti-mate of Pi as a causal effect for the average student.

Another factor that would be expected to infiuence studentmatriculation decisions is financial aid. By definition, merit aid is

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I ATTENDING A MORE SELECTIVE COLLEGE 1499

related to the school's assessment of the student's potential. Paststudies have found that students are more likely to matriculate toschools that provide them with more generous financial aid pack-ages (see, e.g., van der Klaauw [1997]}. If more selective collegesprovide more merit aid, the estimated effect of attending an elitecollege will be biased upward because relatively more studentswith higher values of X2 will matriculate at elite colleges, evenconditional on the outcomes of the applications to other colleges.The relationship between aid and school selectivity is likely to bequite complicated, however. Breneman [1994, Chapter 3], forexample, finds that the middle ranked liberal arts colleges pro-vide more financial aid than the highest ranked and lowestranked liberal arts colleges. If students with higher valuesof X2 are more likely to attend less selective colleges because offinancial aid, the selectivity bias could be negative instead ofpositive.

Finally, an alternative though related approach to modelingunobserved student selection is to assume that students areknowledgeable about their academic potential, and reveal theirpotential ability by the choice of schools they apply to. Indeed,students may bave a better sense of their potential ability thancollege admissions committees. To cite one prominent example,Steven Spielberg w,as rejected by both tbe University of SouthernCalifornia and the University of California Los Angeles filmschools, and attended California State Long Beach [Grover 1998].It is plausible tbat students with greater observed and unob-served ability are more likely to apply to more selective colleges.In this situation, the error term in equation (3) could be modeledas a function of the average SAT score (denoted AVG) of theschools to which the student applied: u, = TQ + TJAVG, + Ui. IfUj is uncorrelated with tbe SAT score of the school the studentattended, we can solve the selection problem by including AVG intbe wage equation. We call tbis approacb tbe "self-revelation"model because individuals reveal their unobserved quality bytheir college application behavior. When we implement this ap-proach, we include dummy variables indicating the number ofschools tbe students applied to (in addition to the average SATscore of the scbools), because the number of applications a stu-dent submits may also reveal unobserved student traits, such astheir ambition and patience. Notice that the average SAT score ofthe schools tbe student applied to, and the number of applicationsthey submitted, would be absorbed by including unrestricted

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1500 QUARTERLY JOURNAL OF ECONOMICS

dummies indicating students who were accepted and rejected bythe same sets of schools; therefore, the self-revelation model isnested in our first model.

It is useful to illustrate the difference between the matchedapplicant model and the self-revelation models with an example.In the matched-applicant model, we compare two students whowere each accepted by both a highly selective college, such as theUniversity of Pennsylvania, and a moderately selective college,such as Pennsylvania State University, but one student chose toattend Penn and the other Penn State. It is possible that thereason the student chose to attend Penn State over Penn (or viceversa) is also related to that student's earnings potential: thosewho chose to attend a less selective school from their options mayhave greater or lower earnings potential. In this case, estimatesfrom the matched-applicant model would be biased upward ordownward, depending on whether more talented students choseto matriculate to more or less selective colleges conditional ontheir options. In the self-revelation model, we compare two stu-dents who applied to—but were not necessarily accepted by—both Penn and Penn State. In this case, the student who attendedPenn State is likely to have been rejected hy Penn; as a result, thestudent who attended Penn State is likely to he less promising (asjudged by the admissions committee) than the one who attendedthe University of Pennsylvania. If it is generally true that stu-dents with higher unobserved ability are more likely to be ac-cepted by (and therefore more likely to attend) the more selectiveschools, the self-revelation model is likely to overstate the returnto school selectivity.

II. DATA AND COMPARISON TO PREVIOUS LITERATURE

The College and Beyond (C&B) Survey is described in detailin Bowen and Bok [1998, Appendix A]. The starting point for thedatabase was the institutional records of students who enrolled in(but did not necessarily graduate from) one of 34 colleges in 1951,1976, and 1989. These institutional records were linked to asurvey administered by Mathematica Policy Research, Inc. forthe Andrew W. Mellon Foundation in 1995-1997 and to filesprovided by the College Entrance Examination Board (CEEB)and the Higher Education Research Institute (HERD at the Uni-versity of California, Los Angeles. We focus here on the 1976entering cohort. While survey data are available for 23,572 stu-

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ATTENDING A MORE SELECTIVE COLLEGE 1501

dents from this eohort, we exclude students from four historicallyblack colleges and universities. For most of our analysis we re-strict the sample to full-time workers, defined as those who re-sponded "yes" to the C&B survey question, "Were you workingfull-time for pay or profit during all of 1995?" The 30 colleges anduniversities in our sample, as well as their average SAT scoresand tuition, are listed in Appendix 1. Our final sample consists of14,238 full-time, full-year workers.

The C&B institutional file consists of information drawnfrom students' applications and transcripts, including variablessueh as students' GPA, major, and SAT scores. These data werecollected for all matriculants at the C&B private schools; for thefour public universities, however, data were collected for a sub-sample of students, consisting of all minority students, all varsityletter-winners, all students with combined SAT scores of 1,350and above, and a random sample of all other students. We con-structed weights that equaled the inverse probability of beingsampled from each ofthe C&B schools. Thus, our weighted esti-mates are representative of the population of students who at-tend the colleges and universities included in the C&B survey.

The C&B institutional data were linked to files provided byHERI and CEEB. The CEEB file contains information from theStudent Descriptive Questionnaire (SDQ), whieh students fill outwhen they take the SAT exam. We use students' responses to theSDQ to determine their high school class rank and parentalincome. The file that HERI provided is based on data from aquestionnaire administered to college freshman by the Coopera-tive Institutional Research Program (CIRP). We use this file tosupplement C&B data on parental occupation and edueation.

Finally, the C&B survey data consist of the responses to aquestionnaire that most respondents completed by mail in 1996,although those who did not respond to two different mailingswere surveyed over the phone. The survey response rate wasapproximately 80 percent. The survey data include informationon 1995 annual earnings, occupation, demographics, education,civic activities, and satisfaction.^ Importantly for our purposes.

8. The C&B survey asked respondents to report their 1995 pretax annualearnings in one of the following ten intervals; less than $1,000; $1,000-$9,999; $10,000-$19,999; $20,000-$29,999; $30,000-$49,999; $50,000-$74,999;$75,000-$100,000; $100,000-$149,999; $150,000-$199,999; and more than$200,000. We converted the lowest nine earnings categories to a cardinal scale byassigning values equal to the midpoint of each range, and then calculated the

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1502 QUARTERLY JOURNAL OF ECONOMICS

early in the questionnaire respondents were asked, "In roughorder of preference, please list the other schools you seriouslyconsidered."^ Respondents were then asked whether they appliedto, and were accepted by, each of the schools they listed.^" Bylinking the school identifiers to a file provided by HERI, wedetermined the average SAT score of each school that each stu-dent applied to. This information enabled us to form groups ofstudents who applied to a similar set of schools and received the,same admissions decisions (i.e., the same combination of accep-tances and rejections). Because there were so many colleges towhich students applied, we considered schools equivalent if theiraverage SAT score fell into the same 25 point interval. For exam-ple, if two schools had an average SAT score between 1200 and1225, we assumed they used the same admissions cutoff. Then weformed groups of students who applied to, and were accepted andrejected by, "equivalent" schools.'^ To probe the robustness of ourfindings, however, we also present results in which students werematched on the basis of the actual schools they applied to, and onthe basis of the colleges' Barron's selectivity rating.

Table I illustrates how we would construct five groups ofmatched applicants for fifteen hypothetical students. Students Aand B applied to the exact same three schools and were acceptedand rejected by the same schools, so they were paired together.The four schools to which students C, D, and E applied weresufficiently close in terms of average SAT scores that they were

natural log of earnings. For workers in the topcoded category, we used the 1990Census {after adjustiug the Census data to 1995 dollars) to calculate mean logearnings for college graduates age 36-38 who earned more than $200,000 peryear. The value we assigned for the topcode may be somewhat too low, becauseuicome data from the 1990 Census were also topcoded (values of greater than$400,000 on the 1990 Census were recoded as the state median of all valuesexceeding $400,0001 and because students who attended C&B schools may havehigher earnings than the population of all college graduates.

9. Students who responded to the C&B pilot survey were not asked thisquestion, and therefore are excluded from our analysis.

10. Students could have responded that they couldn't recall applying or beingaccepted, as well as yes or no. They were asked to list three colleges other than theone they attended that they seriously considered. In addition, prior to the questionon schools the student seriously considered, respondents were asked "which schooldid you most want to attend, that is, what was your flrst choice school?" If thatschool was different from the school the student attended, there was a follow-upquestion that asked whether the student applied to their first-choice school, andwhether they were accepted there. Consequently, information was collected on amaximum of four colleges to which the student could have applied, in addition tothe college the student attended.

11. Students who applied to only one school were not included in thesematches.

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ATTENDING A MORE SELECTIVE COLLEGE 1503

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1504 QUARTERLY JOURNAL OF ECONOMICS

975950 1050 1150 1250

Range of Average SAT Scores of Schools Applied To and Attended

FIGURE IRange of Schools Applied to and Attended by Most Common Sets

of Matched ApplicantsEach bar represents the range of the average SAT scorea of the schools that a

given set of matched applicants applied to; the shaded area represents the rangeof schools that students in each set attended. Only matched sets that representfifteen or more students are shown. A total of 3,038 students are represented onthe graph.

considered to use the same admission standards; because thesestudents received the same admissions decisions from compara-ble schools, they were categorized as matched applicants. Stu-dents were not matched if they applied to only one school (stu-dents F and G), or if no other student applied to a set of schoolswith similar SAT scores (student O). Five dummy variables wouldhe created indicating each of the matched sets.

Figure I illustrates the college application and attendancepatterns of the most common sets of matched applicants (i.e.,those sets that include at least fifteen students) in the C&B dataset. The length of the bars indicates the range of schools to which

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ATTENDING A MORE SELECTIVE COLLEGE 1505

each set of matched students applied, and the shaded area of eachbar represents the range of schools that each set of studentsactually attended. The average range of school-average SATscores of all students who were accepted by at least two schoolswas 145 points, approximately equal to the spread between Tuftsand Yale. If students applied to only a narrow range of schools,then measurement error in the classification of school selectivitywiU be exacerbated in the matched-applicant models. In subsec-tion IILB we present some estimates of the likely impact of thispotential bias.

Table II provid(;s weighted and unweighted means and stan-dard deviations for individuals who were employed full-time in1995. Everyone in the sample attended a C&B school as a fresh-man but did not necessarily graduate from the school (or from anyschool). Nearly 70 percent of students listed at least one otherschool they applied to in addition to the school they attended.Among students who were accepted by more than one school, 62percent chose to attend the most selective school to which theywere admitted. We were able to match 44 percent of the studentswith at least one other student in the sample on the basis of theschools that they were accepted and rejected by. Summary sta-tistics are also reported for the subsample of matched applicants.It is clear that the schools in the C&B sample are very selective.The students' average SAT score (Math plus Verbal) exceeds1,100. Over 40 percent of the sample graduated in the top 10percent of their high school class. The mean annual earnings in1995 for full-time, full-year workers was $84,219, which is higheven for college graduates.

Because the C&B data set represents a restricted sample ofelite schools and is not nationa]]y representative, we comparedthe payoff to attending a more selective school in the C&B sampleto corresponding OLS estimates from national samples. When wereplicated the wage regressions based on the High School andBeyond Survey in Kane 11998] and the National LongitudinalSurvey of Youth in Daniel, Black, and Smith 11997], we foundthat OLS estimates of the return to college selectivity based onthe C&B survey were not significantly distinguishable from,though slightly higher than, those from these nationally repre-sentative data sets (see Dale and Krueger [1999]). In the nextsection we examine whether estimates of this type are con-founded by unobserved student attributes.

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1506 QUARTERLY JOURNAL OF ECONOMICS

TABLE IIMEANS AND STANDARD DEVIATIONS OF THE C&B DATA SET

Variable

Log{ earnings!,\n[iual earnings

(1995 dollars)FemaleBlackHispaniciVsian()ther racePredicted log (parental

income}Own SAT/100School average SAT/100Net tuition (1976 dollars)Log(net tuition)High school top 10 percentHigh school rank mi.ssingCCollege athleteAverage SAT/100 of

schools applied toOne additional applicationTwo additional

applicationsThree additional

applicationsFour additional

applicationsUndergraduate percentile

rank in classAttained advanced degreeGraduated from collegePublic collegePrivate collegeLiberal arts collegeN

Unweighted

Full sample

Mean

11.121

86,7680.3910.0590.0160.0270.003

9.99911.82011.949

27337.7810.4270.3600.100

11.6780.222

0.230

0.176

0.047

50.7030.5650.8460.2820,5400.178

14,238

Standarddeviation

0.757

62.5040.4880.2350.1240.1620.0f)9

0.3541.6610.9281077

0.5910.4950.4800.300

0.9280.416

0.421

0.380

0.211

28.4730.4960.3610.4500.4980.382

Weighted*

Full sample

Mean

11.096

84,2190.3920.0500.0130.0230.003

9.98411.67211.655

24547.6470.4180.3560.078

11.5130,225

0.214

0.156

0.040

50.7910.5420,8390.4130.4420.145

14,238

Standarddeviation

0.747

60,8410.4880.2180.1150.1500.059

0.3531.6340.9431145

0.6220.4930.4790.268

0.9400.417

0.410

0.363

0.196

28.2670.4980.3670.4920.4970.353

Matched applicants

Mean

11.148

88,2760.3850.0500,0140.0270.003

9.99711.87511.812

26517.7490.4270.3550.085

11.6010,490

0.366

0.134

0.011

51.6660.5730.8620.3290.5230.1486,335

Standarddeviation

0.737

62,5980.4870,2190.1170.1630.057

0.3491.6320.9431094

0.5820.4950.4780.279

0.9910.500

0.482

0.340

0.104

28.2680.4950.3450.4700.5000.355

^ Means are weighted tii make the sample representative of the population of student.s at thp C&Binstitutions.

III. THE EFFECT OF COLLEGE SELECTIVITY AND OTHERCHARACTERISTICS ON EARNINGS

Table III presents our main set of log earnings regressions.We limit the sample to full-time, full-year workers, and estimate

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ATTENDING A MORE SELECTIVE COLLEGE 1507

TABLE IIILOG EARNINGS RKGRE.SSIONS USING COLLEGK AND BEYOND SIIRVEY,

SAMPLE OF MALE AND FEMALE FULL-TIME WORKERS

1

Variable

School-average SATscore/100

Predicted logi parentalincome)

Own SAT score/100

Femalo

Black

Hispanic

Asian

Dther/missinj! race

High school top 10percent

High school rankmissing

Athlete

Average SAT score/100 of schoolsapplied to

One additionalapplication

Two additionalapplicatioiis

Three additionalapplications

Four additionalapplications

Adjusted R^N

Basic model:no selection

controls

Fullsample

1

0,076(0.016)

0,187(0.024)

0.018(0,006)-0,403(0,015)

0,023(0.035)

0.015(0.052)

0.173(0.036:-0.18e(0,119

0,061(0.018'

0,001(0.0241

0.102(0.0251

0.10714.238

Etestrictedsample

2

0.082(0.014)

0.190(0.033)

0,006(0,007)-0,410(0,018)• 0.026(0,053)

0.070(0,076)

0.245(0.054)-0.048(0,143)

0,091(0,022)

0.040(0.026)

0.088(0,030)

0.1106.335

Matched-applicant

model

Similar school-SAT matcheti'

3

0,016(0,022)

0.163(0.033)-0,011(0,007)- 0,39510,024)

0.057(0,053)

0.020(0,099)

0.241(0.064)

0.060(0,180)

0.079(0.026)

0,016(0.0381

0.104(0,0391

0.1126.335

Model

Alternativematched-applicant

models

Exact school-SAT matches*'

4

-0.106(0.0361

0.232(0.079)

0.003(0.0141-0.476(0.049)-0.028(0.049)-0.248(0,206)

0.368(0.141)-0,072(0,083)

0.091(0.032)

0.029(0,066)

0,169(0,096)

0.1422,3,30

Barron'smatches*"*

5

0.00410.016)

0.154(0.028)-0.005(0.0051- 0.400(0,017)-0.057(0.039)

0,036(0.066)

0.163(0.049)-0,050(0,134)

0.079(0.024)

0.025(0.027)

0,09310.033)

0.1069,202

Self-revelation

model

6

-0,001(0.0181

0.161(0.025)

0.009(0.006)-0,396(0.014)-0.034(0.035)

0,007(0.0531

0,155(0.037)-0.192(0.116)

0.063(0.019)-0.009(0.022)

0.094(0.024)

0,090(0.013)

0.064(0,011)

0.074(0.022)

0.112(0.028)

0.085(0.027)

0.11314,238

Each liquation also includi s a constant term. Standard errors are in parentheses and are robust tocorrelated errors among studerts who atti'nded the samo institution.

Equations are estimated by WLS and are weighted to make the sample representative of the populationof students at the C&B institutions.

* Applicants are matched liy the average SAT score (within 25 point intervals) of each school at whichthey were accepted or rejected. This modelinciudes 1,232 dummy variahies representing each set of matchedapplicants,

'*• Applicants are matched by the average SAT score of each school at which they were accepted orrejected. This model includes 654 dummy variables representing each set of matched applicants.

*'* Applicants are matched by the Barron's category of each school at which they were accepted orrejected. This model includes 350 dummy variahles representing each spt of matched applicants.

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1508 QUARTERLY JOURNAL OF ECONOMICS

separate Weighted Least Squares (WLS) regressions for a pooledsample of men and women. ^ The reported standard errors arerobust to correlation in the errors among students who attendedthe same college. With the exception of a dummy variable indi-cating whether the student participated on a varsity athleticteam, the explanatory variables are all determined prior to thetime the student entered college. Most ofthe covariates are fairlystandard, although an explanation of "predicted log parental in-come" is necessary. Parental income was missing for many indi-viduals in the sample. Consequently, we predicted income by first! egressing log parental income on mother's and father's educationand occupation for the subset of students with available familyincome data, and then multiplied the coefficients from this re-gression by the values of these explanatory variables for everystudent in the sample to derive the regressor used in Table III.

The basic model, reported in the first column of Table III, iscomparable to the models estimated in much of the previousliterature in that no attempt is made to adjust for selectiveadmissions beyond controlling for variables such as the student'sown SAT score and high school rank. This model indicates thatstudents who attended a school with a 100 point higher averageSAT score earned about 7.6 percent higher earnings in 1995,holding constant their own SAT score, race, gender, parentalincome, athletic status, and high school rank.

Column 2 also presents results of the basic model, but re-stricts the sample to those who are included in the "matched-applicants" subsample. As mentioned earlier, we formed groupsof matched applicants by treating schools with average SATscores in the same 25 point range as equally selective. We wereable to match only 6,335 students with at least one other studentwho applied to, and was accepted and rejected by, an equivalentset of institutions. As shown in column 2 of Table III, when weestimate the basic model using this subsample of matched appli-cants, we obtain results very similar to those from the full sam-ple. When we include dummies indicating the sets of matchedapplicants in column 3, however, the effect of school-average SATis slightly negative and statistically indistinguishable from zero.Although the standard error doubles when we look within

12. The sample of women vi-as too small to draw precise estimates from, butthe results were qualitatively similar. The results for men were also similar andmore precisely estimated (see Dale and Krueger [1999]).

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ATTENDING A MORE SELECTIVE COLLEGE 1509

matched sets of students, we can reject an effect of around 3percent higher earnings for a 100 point increase in the school-average SAT score; that is, we can reject an effect size that is atthe low end of the range found in the previous literature.

Column 4 of Table III presents results from an alternativeversion of the matched-applicant model that uses exact matches-thai is, students who applied to and were accepted or rejected byexactly the same schools. When we estimate a fixed effects modelfor the 2,330 students we could exactly match with other stu-dents, the relationship between school-average SAT score andearnings is negative and statistically significant. Thus, the crudernature of the previous matches does not appear to be responsiblefor our results.

To increase the sample and improve the precision of theestimates, we also used the selectivity categories from the 1978edition of Barron's Guide as an alternative way to match stu-dents. Barron's is a well-known and widely used measure ofschool selectivity. Specifically, we classified the schools studentsapplied to according to the following Barron's ratings: (1) MostCompetitive, (2) Highly Competitive, (3) Very Competitive, and(4) a composite category that included Competitive, Less Competi-tive, and Non-Competitive. Then we grouped students togetherwho applied to and were accepted by a set of colleges that wereequivalent in term.s of the colleges' Barron's ratings. This gener-ated a sample of 9,202 matched applicants. As shown in Column5 of Table III, when we estimated a fixed effects model for thissample the coefficient on the school-average SAT score was 0.004,with a standard error of 0.016. In short, the effect of school-SATscore was not significantly greater than zero in any version of thematched-applicant model that we estimated.

Results of the "'self-revelation" model are shown in column 6of Table III. This model includes the average SAT score of theschools to which students applied and dummy variables indicat-ing the number of schools to which students applied to control forselection bias. The effect of the school-average SAT score in thesemodels is close to zero and more precisely estimated than in thematched-applicant models.''^ Because the self-revelation model is

13. Because the C&B earnings data are topcoded, we also estimated Tobitmodels. Results from these models were qualitatively similar to our WLS results.When we estimated a Tobit model without selection controls (similar to our basicmodel), the coefficient (standard error) on school SAT score was .083 (.008); thecoefficient on school-SAT score falls to -.005 (.012) if we also control for thevariables in our self-revelation model.

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1510 QUARTERLY JOURNAL OF ECONOMICS

TABLE IVTHE EFFECT OF SCHOOL-AVERAGE SAT SCORE ON EARNiNCiS IN MODKIS

THAT USE ALTERNATIVE SELECTION CONTROLS, C&B SAMPLE

OF MALE AND FEMALE FULL-TIME WORKERS

Parameter estimates

Type of selection control

(1) None (basic model)

(2) Average SAT score/100 of schoolsapplied to iself-revelation model)

(3) Average SAT score/100 of schoolsaccepted by

(4) Highest SAT score/100 of schoolsaccepted by

(5) Highest SAT score/100 of allschools applied to

(6) Highest SAT score/100 of schoolsapplied to but not attended

(7) Average SAT score/100 of schoolsrejected by

(8) Highest SAT sccre/100 of schoolsaccepted by not attended

Each model also includes the same control variables as the iioIf-revelation mcxiel shown in column 3 ofTable III. Standard errors are in parentheses and are robust to correlated errors among students whoattended the same institution.

Equations are estimated by WLS and an' weighted to make the sample representative of the populationol' students at the C&B institutions.

The first data column presents the coefficient on the average SAT score at the school the studentattended; the second data column presents the coefficient on the selection control described in the left marginof the table.

likely to undercorrect for omitted variahle bias, the fact that theresults of this model are so similar to the matched-applicantmodels is reassuring.

Table IV presents parameter estimates from models that aresimilar to the self-revelation model, but use alternative selectioncontrols in place of the average SAT score of the schools to whichthe student applied.'^ For example, the third row reports esti-

School-averageSAT score

0.076(0.016)

-0.001(0.018)

-0.001(0.021)

-0.007(0.018)0.010

(0.015)0.042

(0.013)0.052

(0.015)0.039

(0.014)

Selectioncontrol

.

0.09010.013)0.084

(0.017)0.091

(0.021)0.075

(0.013)0.051

(0.006)0.072

(0.012)0.049

(0.010)

N

14,238

14,238

14,238

14,238

14.238

9,358

3,805

8,257

14. Each of these models also includes dummy variables representing thenumber of colleges the student applied to, because the numher of applications astudent submits may reveal his unohserved ability. However, even if we excludethe application dummies from tbe self-revelation model, the return to collegeaverage SAT-score is not significantly different from zero; in this model, thecoefficient (standard error) on school-SAT score is .017 (.017).

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ATTENDING A MORE SELECTIVE COLLEGE 1511

mates from a model that controls for the average SAT score of theschools at which the student was accepted. The results of thismodel are similar to those in the self-revelation model in row 2, inthat the effect on earnings of the average SAT score of the schoolthe student attended is indistinguishable from zero. We alsoobtain similar results when we control for the highest school-average SAT score among the colleges that accepted the student(row 4) or the highest school-average SAT score among the col-leges to which the student applied (row 5). Moreover, we consis-tently find that the average SAT score of the schools the studentapplied to, but either was rejected by or chose not to attend, hasa large effect on earnings. For example, results from the model inrow 7 show that a 100 point increase in the highest school-average SAT score among the colleges at which the student wasrejected is associated with a 7 percent increase in earnings. Theseresults raise serious doubt about a causal interpretation of theeffect of attending a school with a higher average SAT score inregressions that do not control for selection.'^

It is possible that, among students with similar applicationpattems, those who attended more selective colleges are alsomore likely to enter occupations with higher nonpecuniary re-turns but lower salaries (such as academia). A systematic rela-tionship between college choice and occupational choice couldpossibly explain why we do not find a financial return to schoolselectivity. To explore this hypothesis further, we added twentydummy variables representing the students' occupation in 1995to each of our models. The coefficient (and standard error) onschool average-SAT score was a robust .065 (.012) in the basicmodel, but fell to -.016 (.023) in the matched-applicant modeland .010 (.012) in the self-revelation model. Thus, in the selec-tion-adjusted models, the effect of school selectivity is indistin-guishable from zero even if we control for occupation. Similarresults hold if we control for students' occupational aspirations at

15. Because the C&B survey asks students about their college applicationbehavior retrospectively, it is possible that students who had higher earningslater on were more likely to remember applying to elite schools, and less appre-hensive about reporting that they were rejected. This type of memory bias wouldcause the coefficient on the selection control to be biased upward and the coeffi-cient on school SAT score to be biased downward. Unlike the C&B survey, tbeNLS-72 survey asks students about their college applications within a year of thestudents' senior year in high school. Thus, our NLS-72 estimates (see subsectionIII.C) should not suffer from retrospective memory bias.

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1512 QUARTERLY JOURNAL OF ECONOMICS

the time they were freshmen, as opposed to their actual occupa-tion twenty years later.

Another explanation for the lack of return to school selectiv-ity is that students who attend more selective colleges tend to bel'anked lower in their graduating class than they would have beenif they had attended a less selective school because of greatercompetition, and this effect may not be taken into full account bythe labor market. To explore this possibility, we used college GPApercentile rank as the dependent variable and estimated themodels in Table III. In all these models, students who attended acollege with a 100 point higher average SAT score tended to beranked 5 to 8 percentile ranks lower in their class, other thingsbeing equal. The improvement in class rank among students whochoose to attend a less selective college may partly explain whythese students do not incur lower earnings. Employers and grad-uate schools may value their higher class rank by enough to offsetany other effect of attending a less selective college on earn-ings. If we add class rank to the wage regressions in Table III, wefind that students who graduate 7 percentile ranks higher intheir class earn about 3 percent higher earnings, which maylargely offset any advantage of attending an elite college onearnings.

A. Student Matriculation

A key assumption of our matched-applicants models is thatthe school students choose to attend from the set of colleges towhich they were admitted is unrelated to X2, their unobservedabilities. To explore the plausibility of this assumption., we testedwhether students' observed characteristics predict whether theychoose to attend the most selective college to which they wereadmitted for the set of students who were admitted to more thanone college. Specifically, we regressed a binary variable indicatingwhether the student attended the most selective school to whichhe or she was admitted on several explanatory variables. Asshown in column 1 of Table V, within matched-applicant groups,parental income and high school class rank were not related toattending the most selective school. Students with higher SATscores, however, were significantly more likely to attend the mostselective college to which they were admitted. Similar resultshold for the self-revelation model in column 2. These resultssuggest that students' choice of college may, in part, be nonran-

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ATTENDING A MORE SELECTIVE COLLEGE 1513

TABLE VLINEAR REGRESSIONS PEEDICTING WHETHER STUDENT ATTENDED MOST SELECTIVECOI,I.EC:K FOR C&B SAMPLE OF STUDENTS ADMITTED TO MORE THAN ONE SCHOOL

Predicted log (parental income)

Own SAT score/100

Female

Black

Hispanic

Asian

Other/missing race

High school top 10 percent

High school rank missing

Athlete

Average SAT score/100 of schoolsapplied to

One additional application

Two additional applications

Three additional applications

N

Parameter estimates

Matched-applicantmodel*

-0.024(0.026)

0.020(0.005)

0.034(0.014)

0.056(0.026)-0.019(0.064)

0.019(0.026)-0.095(0.093)-0.014(0.021)-0.035(0.036)

0.056(0.023)

5536

Self-revelationmodel

-0.037(0.030)

0.021(0.007)

0.033(0.028)-0.005(0.037)

0.042(0.074)

0.074(0.050)

0.010(0.081)-0.020(0.028)-0.040(0.058)

0.059(0.045)-0.122(0.040)

0.149(0.037)

0.076(0.033)

0.020(0.038)

8257

Only stiidentH who were accepted by more than one school are included in the sample.Each equation also includes a constant lurra. Standard errors are in parentheses, and are robust to

correlated crrorB among students who attended the same institution.Equations are estimated by WLS; weighUs are designed to make tbe sample representative of the

population of students at the t'&B institutions,* Applicants are matched by the average SAT score Iwithin 25 point intervals) of each school at which

thty were accepted and rejecled. Model includes 1.079 dummy variables indicating each set of matchedappli cunts.

dom, as students with higher values of an ohserved measure ofability choose to attend more selective schools. If students withhigher values of unobserved ability also choose to attend more

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1514 QUARTERLY JOURNAL OF ECONOMICS

seleetive schools, then our estimates of the return to school qual-ity will be biased upward. It is possible, however, that the sortingon unobserved abilities is in a different direetion.

As mentioned, results of the self-revelation model areless likely to be contaminated by nonrandom student matricu-lation decisions: among students who applied to the same arrayof colleges, many attended less seleetive colleges not becausethey chose to, but because they were rejected by more selec-tive colleges. By comparing students who were accepted to moreselective colleges with those who were rejected by them, theself-revelation model is likely to undercontrol for unobservedstudent characteristics; therefore, our already-negligible esti-mate of the return to school-average SAT score is likely to hebiased upward.

B. Likely Effects of Measurement Error

As is well-known, attenuation bias due to classical measure-ment error in an explanatory variable is exacerbated in fixedeffects models (e.g., Griliches [1986]). Average SAT scores forsome colleges as recorded in the HERI data are measured witherror, since the data are self-reported hy colleges, and collegeshave an incentive to misrepresent their data. The correlation(weighted by number of students) between the sehool-averageSAT score as measured by HERI data and the school averagecalculated from the students in the C&B database for 30 schoolsis .95. This correlation provides a rough estimate of the reliabilityof the SAT data, which we denote X.

As a benchmark, it is useful to consider the likely attenuationbias in the school SAT coefficient in the OLS regression in eolumn1 of Table III. The additional attenuation bias in the matched-applicant and self-revelation models relative to the OLS model isrelevant here. If the school-average SAT score is the only variablemeasured with error, and the errors are white noise, the propor-tional attenuation bias in the school-average SAT coefficient for alarge sample is given h y \ ' = {\ - i?^)/(l - R'^), where i?^ is thecoefficient of determination from a regression of the school SATscore on the other variables in the regression equation. In theOLS model in column 1, the attenuation bias is estimated to equal5 percent. Relative to the OLS model, the estimated attenuationbias is 31 percent in the matehed-applicant model and 8 percent

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I ATTENDING A MORE SELECTIVE COLLEGE 1515

in the self-revelation model.^^ Although the attenuation bias isnontrivial, even wiith this amount of measurement error it islikely that sizable effects would be detected. Moreover, one wouldnot expect attenuation bias to cause the estimate to becomenegative, as was found in Table IIL

Measurement error in the school-average SAT score wouldalso generate measurement error in the matched-applicant dum-mies because they were both constructed from the HERI data. Ifwe use the College and Beyond database to calculate tbe averageSAT score of the school a student attended, and use the HERIdata to group matched applicants, the estimated effect of theschool-average SAT score is even more negative.

Probably a more important issue is whether the school-aver-age SAT score is an adequate measure of school selectivity. Webave focused on this measure because it is a widely used indicatorof school selectivity in past studies. Moreover, college guidebooksprominently feature this measure of school selectivity. One jus-tification for using the school-average SAT score is that it isrelated to the average quality of the potential peer group at theschool. Nevertheless, it may be a poor proxy of school quality. Forthis reason, we also examined the effect of Barron's college rat-ings. Given the sin:iilarity of the results for the two measures, andthe contrast between our results and the previous literaturewhich only partially adjusts for student characteristics, we thinkthe findings for the school-average SAT score are of interest.

C. Results for National Longitudinal Survey of the High SchoolClass of 1972

To explore the robustness of our results in a nationally rep-resentative data set, we analyzed data from the National Longi-tudinal Study of the High School Class of 1972 (NLS-72). Werestrict the NLS-72 sample to those students who started at afour-year college or university in October of 1972, and we use1985 annual earnings data from the fifth follow-up survey. In1985 the NLS-72 respondents were about six years younger thanthe C&B respondents were in 1995 (typically 31 versus 37). In thefirst follow-up survey, the NLS-72 asked students questionsabout other schools to which they may have applied in a fashion

16. The R^ from a regression of school SAT on the other variables in themodel in the matched-applicant model is .86, and in the self-revelation model it is.64.

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1516 QUARTERLY JOURNAL OF ECONOMICS

similar to the C&B survey." The NLS-72 also contains detailedinformation ahout students' academic and family backgrounds,allowing us to construct most ofthe same variables used in Table\\l}^ The NLS-72 survey did not, however, collect information onrespondents' full-year work status in 1985. We include in thesample all NLS-72 respondents (regardless of how much theyworked) whose annual earnings exceeded $5,000.

The means and standard deviations for the NLS-72 sample,as well as regression estimates, are reported in Table VL Becausethe NLS-72 sample is relatively small (2127 workers), we couldnot estimate the matched-applicant model; however, we wereable to estimate tbe basic regression model and self-revelationmodel. The basic model witbout application controls, in column 2,indicates that a 100 point increase in the school-average SATscore is associated with approximately 5.1 percent higher annualearnings. However, the self-revelation model reported in column3 suggests that the effect of school-average SAT score is close tozero, although the standard error of .023 makes it difficult todraw a precise inference. The school SAT score estimates basedon the comparable C&B sample are similar; the coefficient (stan-dard error) on school-average SAT score was .074 (.014) in thebasic model and -.006 (.015) in the self-revelation model usingthe C&B sample and imposing similar sample restrictions (in1995 dollars). These results suggest that our findings in Table IIIare not unique to the schools covered by the C&B survey.

To further compare our results with the previous literature,we also estimated these same models using the Barron 's Guide toconstruct our measure of school quality. Following Brewer, Eide,and Ehrenberg [1999], we classified schools into the following sixcategories; Top private; Middle Private; Bottom Private; Top Pub-lic; Middle Public; and Bottom Public, wbere the "Top" categoryincludes schools with Barron's ratings of "Most Competitive" and"Highly Competitive," the "Middle" category includes those with"Very Competitive" and "Competitive" ratings, and the "Low"

17. Specifically, respondents were asked on the NLS-72 first follow-up survey(in 1973), "When you first applied, what was the name and address ofthe FIRSTscliool or college of your choice? Were you accepted for admission at that school?"These questions were repeated for the respondents' second and third choiceschools. We matched the responses to these questions to the HERI file to deter-mine the average SAT score in 1973 ofthe schools that students applied to.

18. We have parental income data for most ofthe NLS-72 sample, allowing usto control for actual, rather than predicted, parental income. We do not include adummy variable for athletes because NLS-72 does not identify varsity letterwinners.

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ATTENDING A MORE SELECTIVE COLLEGE 1517

TABLE VIMEANS, STANDARD DEVIATIONS, AND LOG EARNINGS REGRESSIONS

FOR NLS-72 POOLED SAMPLE OF MALE AND FEMALE WORKERS

Variable Name

School-average SAT scorc/lOO

\t tended top private school

Attended middle private school

\ t tended low private school

i\ttended top public school

Attended middle puhlic school

Loglparental .ncomol

Own SAT score/100

Female

1Black

Hispanic

Asian

Other/missinf; race

High school tup 10 percent

High school rank missing

Average SAT score/lOO of schools(ipplifd til

On« additUmEil application

Two additional applications

Throe addilional applications

Adjusted /(^N"-value for jdint significance of

school-type dummies

Variablemeans

1 standarddeviation)

1

9.94311-1811

0.04610.2101

0.21010,4081

0.07110.2571

0.00910.0941

0.43210.4951

9.45510-6151

9.75512.0571

0.39810.4891

0.06010.2381

0.01610.1241

0.01010.0991

0.02310.1511

0.20110.401!

0.19310.3941

9.99611.1141

0.24610.4311

0.202[0.4021

0.00810.0891

_2,127

Selectivity measure:achool SAT score

Parameter estimates

Basic model:no selection

controls

2

0.051(0.010)

0.081(0.018>

0.022(0.006 i-0.384(0.022 i

0.065(OO47i

0.096(0.0841-0.175i0.10.'l)-0.525(0.069)

0.055(0.029)

0.039(0,027)

0.1992.127

Self-revelation

model

3

0.013(0.023)

0.074(0.018)

0.020(0.006)-0.384(0,022)

0.053(0,047)

0,085(0,084)-0.16710,1031-0.503(0.069)

0,063(0.030:

0.040(0,027)

0.Q34(0,025)

0,026(0.025)

0.107(0.028)

0.01010,115)

0.2052,127

Selectivity measure:Barren's ratings

Parameter e

Basic model:no selection

controls

4

0.151(0.056)

0.023(0.033)

0.032(0.044)

0.218(0.112)

0.044(0.0281

0,093(0.018)

0.02910,006)- 0,384(0,022)

0-049(0.047)

0.096(0.084)-0 .166(0.103)-0 .485(0.0701

0,055(0.0301

0.026(0.028)

0.1982,127

0.06

sti mates

Self-revelation

model

•>

0.01810-066)-0 .04710-035)

0.000(0.044)

0.09610.115)-0.00710,029)

0,075(D.0I8)

0.021(0.006)-0 ,38310.022)

0.057(0.048)

0.089(0.084)-0 .17010.103)

0.48410.070)

0.060(0,0301

0.03610.028)

0.050(0.014)

0.027(0.025)

0.108(0-028)

0.008(0,115)

8.78810.193)0.2048

2,127

0,59

Each equation also includ.^s a constant term Standard errors are in parentheses. Equations areestimated by WLS, using the fiflh follow-up sample weight. Respondents earning over $5,000 in 1985 areincluded, regardloss of full-limt work status. The mean of the dependent variable is 10,087; the standarddfviution is .525. The tategories T o p private" and "Top puhlic" include schools with a "Most Competitive' or"Highly Competitive" Barron'a rating, "Middle private" and "Middle Puhlic" include achooln with a "VeryCompetitive" or "Competitive" Barron's rating, and "Low private" and "Low puhlic" include schools with a"Less Competitive" or "Non-Competitive" rating, "Attended low public" is the omitted category.

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1518 QUARTERLY JOURNAL OF ECONOMICS

category includes those with "Less Competitive" and "Non-Com-petitive" ratings. Similar to Brewer, Eide, and Ehrenberg, we findthat there is a large return to attending a Top Private collegerelative to a Bottom Puhlic college if we estimate our basic model.However, if we estimate the selection adjusted models, the returnto attending a Top Private falls considerably. For example, thedifferential between the Top Private and Bottom Public schools,with standard errors in parentheses, was .151 (.056) in the basicmodel and -.018 (.066) in the self-revelation model (shown incolumns 4 and 5 of Table VI). Likewise, while the Barron's dum-mies are jointly significant at the 10 percent level in the basicmodel (p = .06), they are insignificant in the self-revelation model(p = .59). Thus, our findings for the school-average SAT scoresappear to be robust when other measures of school selectivity areused.

D. Interactions between School-Average SAT and ParentalIncome

Table VII reports another set of estimates ofthe three modelsusing the C&B data set (basic, matched-applicant, and self-reve-lation model) augmented to include an interaction betweenscbool-average SAT and predicted log parental income. In all themodels we estimated, the coefficient on the interaction betweenparental income and school-average SAT is negative, indicating ahigher payoff to attending a more selective college for childrenfrom lower income households. The interaction term is statisti-cally significant and generally has a sizable magnitude. For ex-ample, based on the self-revelation model in column 3 of TableVII, the gain from attending a college with a 200 point higheraverage SAT score for a family whose predicted log income is inthe bottom decile is 8 percent, versus virtually nil for a familywith mean income.

E. The Effect of Other College Characteristics on Earnings

Although the average SAT score of the school a studentattends does not have a robust effect on earnings once selectionon unobservables is taken into account, we do find that the schoola student attends is systematically related to his or her subse-quent earnings. In particular, if we include 30 unrestricteddummy variables indicating school of attendance instead of theaverage SAT score in the models in Table III, we reject the nullhypothesis that schools are unrelated to earnings at the .01 level.

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ATTENDING A MORE SELECTIVE COLLEGE 1519

TABLE VIILofj EARNINGS REGRESSION ALLOWING THE EFFECT OF SCHOOL-AVERAGE

SAT TO VARY WITH PARENTAL INCOME, C&B SAMPLE

OF MALE AND FEMALE FULL-TIME WORKERS

I Parameter estimates

Variable

School-average SAT score/100

Predicted log(parfntal income)

Predicted log of parental income * schoolSAT score/100

Own SAT score/lOO

High school top 10 percent

High school rank missing

Athlete

Average SAT Score/lOO of schools applied to

One additional application

Two additional applications

Three additional applications

Four additional applications

Adjusted R'^NTab:EfFect of a 200 point increase in school

average SAT score for a person withpredicted parental income:

in the bottom 10 percent of the C&B sampleat the 50th percentile of the C&B samplein the top 10 percent of the C&B sample

Each eqaation indudes dummy variables indicating lemalf!, black. Hispanic, Asian, and other rate andalso includes a constanL term, .'itandsrd errors are in parentheses and are robust to correlattd errora amongstudents wbo attended the same instltuLiun.

Equations are estimated by WLS and are weigbted to make the sample representative of the populationof students at the C&B institu .ions.

' Applicants are matched by the average SAT Kcore (within 25 point intervalKl of each school at whichthey were accepted or rejected. This model includes 1,232 dummy variables representing each set of matchedapplicants.

Basic model:no selection

controls

1

0.701(0.185)

0.915(0.212)-0.063(0.019)

0.018(0.006)

0.062(0.019)

0.005(0.024)

0.104(0.025)

0.10814,238

Matched-applicantmodel"'

2

0.537(0-224)

0.819(0.247)-0.056(0-023)-0.011(0.007)

0.080(0.026)

0,018(0.038)

0.105(0.040)

0.1126,335

Self-revelation

model

3

0.581(0-180)

0,839(0-204)-0.058(0.018)

0.009(0.006)

0,064(0.020)-0,005(0.022)

0.095(0.025)

0.089(0.013)

0.062(0.011)

0.073(0.021)

0.110(0.028)

0.085(0.027)

0.11414,238

0-240.1440.098

0,041-0.045-0.085

0-081-0.008-0.051

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1520 QUARTERLY JOURNAL OF ECONOMICS

Thus, something about schools appears to influence earnings. Apossible reason for the insignificance of school-average SAT in theselection-adjusted models is that the average SAT score is a crudemeasure of the quality of one's peer group. Since, to some extent,all schools enroll a heterogeneous group of students, it is possiblefor students to seek out the type of peer group they desire if theyhad attended any of the schools that admitted them. An ablestudent who attends a lower tier school can find able students tostudy with, and, alas, a weak student who attends an elite schoolean find other weak students to not study with. What character-istics of schools matter, if not selectivity?

Table VIII presents models in which the logarithm of collegetuition costs net of average student aid is the school qualityindicator. ^ These models indicate that students who attendhigher tuition schools earn more after entering the lahor market.Notice also that the coefficient on the interaction term for paren-tal income and tuition (shown in columns 2, 4, and 6) is negative,indicating that there is a higher payoff to attending a moreexpensive school for children from low-income families. The mag-nitude of the coefficient on tuition falls in the models that adjustfor school selection, but remains sizable. ^* For example, the co-eificient of .058 in column 5 implies an internal real rate of returnof approximately 15 percent for a person who begins work afterattending college for four years, then earns mean 1995 incomethroughout his career, and retires 44 years later.^^ The coefficientin column 3 implies an internal real rate of return of 13 percent.A caveat to this result, however, is that students who attendhigher cost schools may have higher family wealth (despite ourattempt to control for family income), so tuition may in part pickup the effect of family background on earnings.

Although the implied internal rates of return to investing ina more expensive college in Table VIII are high, one should

19. Net tuition for 1970 and 1980 was calculated by subtracting the averageaid awarded to undergraduates from the sticker price tuition, as reported in theeleventh and twelfth edition.s of Am.erican Universities and Colleges. Then the1976 net tuition was interpolated from the 1970 and 1980 net tuition, assumingan exponential rate of growth.

20. If we control for both net tuition and school SAT score in the sameregression, the effect of net tuition is even larger. For example, the coefficient(standard error) on tuition from the matched-applicant model is ,096 (,017);however, the coefficient on school SAT score from this model is negative andsignificant,

21. This rate of return would fall to 13 percent if we assumed that the personspent 1.5 years in graduate school (the average time spent in graduate school forthe C&B sample) immediately after college.

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ATTENDING A MORE SELECTIVE COLLEGE 1521

TABLE VIIILOG EARNINGS REGRRSSTONS USING NET TUITION AS SCHOOL QUALITY INDICATOR,

C&B MALE AND FEMALE FULL-TIME WORKERS

Variable

Log(net tuition)

Pradicted loglparental income)

Loginet tuition) * predicted log(parental income}

Own SAT score/100

1Female

Black

Hispanic

Asian

Other/missing race

High schoo! top 10 percent

High school rank missing

Athlete

Average SAT score/100 of schoolsapplied to

One additional application

Two additional application^i

Three additional applications

Four additronal applitations

Adjusted H'^N

Basic models:no selection

controls

1

0.125(0.021)

0.175(0.024)

0.022(0.006)-0.396(0.012)-0.005(0.031)

0.017(0.050)

0.178(0.033)-0.171(0.120)

0.073(0.021)

0.008(0.0231

0.10610.0271

0.11014,238

2

0.711(0.288)

0.626(0.215)-0.059(0.029)

0.022(0.006)-0.395(0.012)-0.005(0.031)

0.011(0.050)

0.176(0.033)-0.171(0.120)

0.074(0.021)

0.009(0.023)

0.107(0.027)

0.11014,238

Parameter estimates

Matched-applicantmodels*

3

0.052(0.022)

0.159(0.032)

-0.012(0.0071-0.396(0.0241-0.060(0.052)

0.012(0.100)

0.237(0.064)

0.067(0.180)

0.083(0.026)

0.020(0.039)

0.102i 0.040)

0.1126,335

4

0,877(0,390)

0.800(0.300)-0.083(0,040)-0.012(0.007)-0.395(0.023)-0.062(0.052)

0.007(0.101)

0.236(0.064)

0.058(0.179>

0.084(0.026»

0.02210.039)

0.101(0.040)

0.1126,335

Self-revelation

models

5

0.058(0.0181

0.156(0.0241

0.009(0.006)-0.396(0.013)-0.039(0.034)-0.006(0.052)

0.152(0.036)

0.188(0.117)

0.067(0,021)-0.006(0.022)

0.090(0.024)

0.067(0.012)

0.052(0.0091

0.057(0.019)

0.095(0.0241

0.071(0.027)

0.11514,238

6

0.727(0.283)

0.67110,219)-0.067(0.029)

0.008(0.006)-0.395(0.013)-0,040(0.035)-0.013(0.053)

0.149(0.036)-0.188(0.117)

0.067(0.021)-0.004(0.022)

0.091(0,024)

0.068(0.012)

0.051(0.009)

0.057(0.018)

0.095(0,024)

0.072(0,027)

0.11514,236

Each equation also includi!S a constant term. Standard errors are in parentheses, and are robust tocorrelated errors among students who attended the same institution.

Equations are estimated bj' WLS, and are weighted to make the .'sample representative ofthe populationof students at the C&B institui.ions. Net tuition is average tuition minua average aid (see t«xt),

* Applicants are matched hy the average SAT score (within 25 point intervals! of each school at whichthey were accepted or rejected. This model includes 1,232 dummy variables representing each set of matchedapplicants.

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1522 QUARTERLY JOURNAL OF ECONOMICS

recognize that the average cost of tuition has roughly douhled inreal terms since the late 1970s, and the payoff to educationincreased in general since the late 1970s. The implicit internalreal rate of return for the estimate in column 5 of Table VIII fallsto 8 percent if tuition costs are douhled. Indeed, the supernormalreturn to investing in high-tuition education in the 1970s mayexplain why it was possible for colleges to raise tuition so much inthe 1980s and 1990s.

College tuition may have a significant effect on subsequentearnings because schools with higher tuition provide their stu-dents with more, or higher quality, resources. We next summa-rize estimates of the effect of expenditures per student on subse-quent earnings. Interestingly, the correlation between tuitionand total expenditures per student in our sample of schools is lessthan .30, so differences in tuition result from factors in addition tospending per student, such as the value of the school's endow-ment and public support. One should also recognize limitations ofour measures of expenditures per students: (1) undergraduateand graduate student expenditures are combined; (2) there areinherent difficulties classifying instructional and noninstruc-tional spending; and (3) expenditures are lumpy over time.

To directly explore the effect of school spending, we includedeither the log of total expenditures per student (undergraduateand graduate), or the log of instructional expenditures per stu-dent, in place of tuition in the earnings equation.^^ Both mea-sures of expenditures per pupil had a statistically significant andlarge impact on earnings in the basic model. When we estimatedthe matched-applicant model and the self-revelation model, theeffect of expenditures per pupil was smaller and less preciselyestimated. Although the effect of expenditures per pupil wasstatistically insignificant, the coefficient was positive in all butone of the models and implied substantial internal rates of returnto school spending, similar in magnitude to those for tuition.^^These results provide mixed evidence on the effect of expendi-tures per student on students' subsequent income, perhaps be-cause spending per student is poorly measured.

22. We use 1976 expenditure data from the Integrated Postaecondary Edu-cation Data System (IPEDS) Survey.

23. The coefficient (and standard error) on log instructional expenditures perstudent if this variable was included instead of tuition in column 1, 3, and 5 ofTable VTII were .114 (.057); .086 (.084); and .024 (.057). The correspondingcoefficients for log total expenditures per student were .102 (.067); -.004 (.077);and .008 (.067).

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ATTENDING A MORE SELECTIVE COLLEGE 1523

IV. CONCLUSION

The colleges that students attend are affected by selectionon the part of the schools that students apply to, and by selec-tion on the part of the students and their families from themenu of feasible options. A major concern with past estimatesof the payoff to attending an elite college is that more selec-tive schools tend to accept students with higher earnings ca-pacity. This pape]' adjusts for selection on the part of schoolshy comparing earnings and other outcomes among studentswho applied to, and were accepted and rejected by, a comparableset of institutions. Although our selection correction has manydesirable features, a complete analysis of school selection alsowould model students' choice of colleges. Nonetheless, since col-lege admission decisions are made by professional administratorswho have much more information at their disposal than research-ers who later analyze student outcomes, we suspect that ourselection correction addresses a major cause of bias in past wageequations.

After we adjust for students' unobserved characteristics,our findings lead us to question the view that school selectivity,as measured by the average SAT score of the freshmen whoattend a college, is an important determinant of students' sub-sequent incomes. Students who attended more selective col-leges do not eai'n more than other students who were ac-cepted and rejected by comparable schools but attended lessselective colleges. Additional evidence of omitted variable biasdue to the collej e application and admissions process comesfrom the fact that the average SAT score of schools that astudent applied to but was rejected from has a stronger ef-fect on the student's subsequent earnings than the averageSAT score of the school the student actually attended. Fur-thermore, we find that students with higher SAT scores aremore likely to attend the most selective college from their set ofoptions, suggesting that students who attend the more selectiveschools may have higher unobserved ability. These results areconsistent with the conclusion of Hunt's [1963, p. 56] seminalresearch: "The C student from Princeton earns more than the Astudent from Podunk not mainly because he has the prestige of aPrinceton degree;, but merely because be is abler. The goldentouch is possessed not by the Ivy League College, but by itsstudents."

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1524 QUARTERLY JOURNAL OF ECONOMICS

It is possible, however, that attending a highly selectivesehool helps some students and hurts others. If this were the ease,and students were aware of it, then the students who chose toattend a less selective school even though they were admitted toa more selective one might be the students with attributes thatlead them to benefit more from attending a less selective sehool.If this type of matching is important, then it is important forfamilies to consider the fit between the particular attributes oftheir children and the school they attend. Moreover, if matchingbetween the student's matriculation decisions and the potentialpayoff for that student from attending a particular (selective)college does take place, our estimates should not be interpreted ascausal. But our results would still suggest tbat there is not a"one-size-fits-all" ranking of sehools, in which students are al-ways better off in terms of their expected future earnings byattending the most selective school that admits them.

This sentiment was expressed clearly by Stephen R. Lewis,Jr., president of Carleton College, who responded to the U.S.News & World Report college rankings (which ranked his schoolsixth among liberal arts colleges) by saying, "The question shouldnot be, what are the best eolleges? The real question should be,best for whom?"^"

We do find that students who attend colleges with higheraverage tuition costs tend to earn higher income years later, afteradjusting for student characteristics. This finding is not surpris-ing given that one would expeet students to receive a pecuniary ornonpecuniary benefit from higher tuition costs. Moreover, ourfindings for expenditures per student closely match those fortuition, although the effect of expenditures is less precisely mea-sured. Because tuition and expenditures per student are posi-tively correlated, these results suggest that tuition matters be-cause higher cost schools devote more resources to studentinstruction. The internal real rate of return on college tuition forstudents who attended college in the late 1970s was high, in theneighborhood of 13 to 15 percent. But college tuition costs haverisen considerably since the 1970s, driving the internal rate ofreturn to a more normal level.

Finally, we find that the returns to school eharaeteristies suehas average SAT score or tuition are greatest for students from more

24. Quoted in Alex Kuczynski, " 'Best' List For Colleges By U. S. News IsUnder Fire," The New York Times, August 20, 2001, p. CI.

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ATTENDING A MORE SELECTIVE COLLEGE 1525

disadvantaged backgrounds. School admissions and financial aidpolicies that have as a goal attracting qualified students from moredisadvantaged family backgrounds may raise national income, asthese students app(3ar to benefit most from attending a more elitecollege. Ellwood and Kane's [1998] recent finding that college enroll-ment hardly increased for children from low-income families in the1980s is troubling in this regard.

APPENDIX 1: SCHOOL-A'^RAGE SAT SCORE AND NET TUITION OF C&B INSTITUTIONS

Institution

Barnard CollegeBryn Mawr CollegeColumbia UniversityDenison UniversityDuke UniversityEmory UniversityGeorgetown UniversityHamilton CollegeKenyon CollegeMiami University (Ohio)Northwestern UniversityOberlin (joilegePennsylvania State UniversityPrinceton UniversityRice UniversitySmith CollegeStanford UniversitySwarthmore CollegeTufts UniversityTulane UniversityUniversity of Michigan (Ann Arbor)University of North Carolina (Chapel Hill)University of Notre DameUniversity of PennsylvaniaVanderbilt UniversityWashington UniversityWellesley CollegeWesleyan UniversityWilliams CollegeYale University

School-averageSAT score in 1978

121013701330102012261150122512461155107312401227103813081316121012701340120010801110108012001280116211801220126012551360

1976Net tuition ($)

353031713591325430523237330435293329130436763441106236131753353936583122385332691517541

32163266315532453312336835413744

The sclIool-average SAT scores were obtained from HERI, and pertain to freshmen. Net tuition for 1970and 1980 «'as calculated by subtracting the average aid awarded to undergraduates from the sticker pricetuition, aa ]-eport«d in the eleventh and twelfth editions of American Universities and Colleges. The 197S nettuition was interpolated from the 1370 and 1980 net tuition, assuming an exponential rat4.> of growth.

MATHEMATICA POLICY RESEARCH, INC

PRINCETON UNIVERSITY

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