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Higher Education 8 (1979) 21-37 �9 Elsevier Scientific Publishing Company, Amsterdam - Printed in the Netherlands

Q U A L I T Y O F E D U C A T I O N A N D S T U D E N T E A R N I N G S

EDWARD FOSTER Graduate School of Business A dm inistra tion, University of Minnesota, Minneapolis,

MN., U.S.A.

JACK RODGERS Health Resources Administration, Department of Health, Education and Welfare,

Washington, D.C., U.S.A.

ABSTRACT

When a university increases expenditures in an attempt to improve quality, a natural question for social policy is raised: is the improvement worth the cost? One partial measure of "worth" in this context is given by earnings of graduates: will those earnings rise by enough to pay a reasonable return on the investment in higher quality?

The question is hard to answer by statistical means: universities of higher quality have better reputations which allow them to select students who are themselves of higher quality; so in trying to measure the relation between earnings and university quality, quality of the school may be confounded with quality of the students. Recently, how- ever, several large data sets have been made available which give sufficient information on the students' own backgrounds, and on their later earning, that we can hope to dis- entangle the effect on earnings of the school from that of the student himself.

This article summarizes the results of several such studies, including our own work. The verdict to date is that the relation between "quality", however measured, and earn- ings is significant, and that expenditures to improve quality are worth the cost, even when "worth" is measured narrowly as higher earnings for graduates.

I. I n t r o d u c t i o n

Admin i s t r a t o r s o f publ ic universi t ies have a na tura l in teres t in main-

ta ining high educa t iona l qual i ty . Fund ing author i t ies in g o v e r n m e n t have an

equal ly na tura l in teres t in ho ld ing d o w n expenses . This art icle addresses a

ques t ion tha t is cent ra l to the issue o f qua l i ty versus e c o n o m y : m a y e x p e n -

di tures fo r ma in ta in ing or improv ing qua l i ty be jus t i f ied s t r ic t ly in f inancial te rms, by provid ing higher earnings fo r the un ivers i ty ' s graduates?

G r a d u a t e s o f the bes t schools do earn m o r e than o t h e r graduates on the average; b u t t hey are also m o r e able, and they c o m e to the univers i ty f r o m b e t t e r fami ly backgrounds . Does qua l i ty o f the school have an i n d e p e n d e n t

e f fec t on earnings? I f so, and i f the e f fec t is large enough , g o v e r n m e n t m i g h t f ind tha t expend i tu r e s to i m p r o v e qua l i ty o f fe r an a t t rac t ive inves tment . Bu t

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to answer the policy question it is necessary statistically to separate the effect on earnings of school quality from the effect of the student's own ability and background.

Over the past few years new large data sets have become available with enough information about individuals' earnings, schooling, ability and family background to allow one to carry out this statistical dissection. This article summarizes our own research, and work by other economists and socio- logists, with these large data sets for the light it sheds on the policy question. The conclusion reached so far is that universities do provide a satisfactory return to expenditures that improve quality. In this summary we provide only the minimum of technical discussion needed to explain to nonspecialists the approach used and its possible shortcomings. A more detailed report of the new results discussed here (Rodgers, 1977) will appear in the technical literature.

A general warning is in order: the studies referred to here focus on what can be easily measured - on earnings. But none of the authors would claim that what is most easily measured is necessarily most important. Significant benefits to education, and to education of high rather than low quality, may be totally unrelated to jobs or earnings. Disciplines other than economics are better equipped to address that question; for a pessimistic report on psycho- logists' attempt to detect educational benefits of high quality schools, see Jacobson (1976).

II. Does Quality of Education Pay?

SOME CRUDE EVIDENCE

In broad terms, of course quality pays: graduates of good schools earn more money than graduates of weak schools. For example, of a group of Wisconsin male 1957 high school graduates, in 1967 Madison campus gradu- ates were earning $875 more than Milwaukee campus graduates, $1,506 more than graduates of the Wisconsin State Universities, and $2,696 more than graduates of the Wisconsin County Teachers' Colleges (Alwin et al., 1975, p. 123).

Our own work with a national sample of male 1960 high school gradu- ates yields similar results: those who went on to graduate from the Universi- ty of Michigan received average incomes of $15,506 in 1971; Wisconsin graduates received $12,026, and Minnesota graduates received $11,328. These orderings are in agreement with our impression of relative quality. Moreover, if "quality" is measured by expenditures per full time equivalent student, for a group of 12 major universities the rank correlation between quality and alumni earnings is high. Only Stanford, with just five alumni in

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TABLE I

Mean 1971 Income for Project TALENT Respondents From Selected Universities a

Undergraduate university Number of Spending Mean 1971 Income attended respondents rank c income rank d

Chicago 2 2 Indiana b 12 10 Michigan 18 3 Iowa 15 6 Illinois 42 5 Berkeley 16 NA Northwestern 14 4 UCLA 17 NA Purdue 34 7 Ohio State 65 8 Wisconsin 47 9 Stanford 5 1 Michigan State 24 11 Minnesota 45 12 All 14 Universities 356 Sample of 1,195 Colleges 5,922

$24,222 15,926 15,506 14,866 13,701 13,323 13 026 12 934 12313 12 295 12 026 11 594 11 495 11 328 12 681 11 967

1 2 3 4 5

6

7 8 9

10 11 12

a Excludes farmers, teachers, doctors, lawyers, ministers and persons with no serious occupation. Also excludes persons with income below $2,000.

b Excludes one respondent with income over $60,000. c Rank in expenditures per F.T.E. student, 1963-1964 . d Income rank excluding Berkeley and UCLA (because spending rank not available).

the sample, and Indiana, with 12, show earnings out of line with expenditures (see Table I). With these two schools included the rank correlation is 0.42; without them it is 0.95.

THE PROBLEM OF BIAS: GOOD SCHOOLS ATTRACT GOOD STUDENTS

Unfortunately, these figures prove too much. Students are not randomly distributed among schools; the best, the brightest, the most highly moti- vated, and the richest tend to cluster at the best schools. It is not obvious whether the earnings differences shown above are due to the schools, or to the students. The challenge to research in this area is to keep from confound- ing the two, attributing to the school financial returns which are really due to the student 's own ability, to his ambition, or to his family connections.

The problem of confounding the effects of separate, but correlated causes is familiar in all sciences; and the standard method for avoiding it - careful experimental design - is equally familiar. But that method is rarely

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available in the social sciences, and it is not here. The economist must take the students as they distribute themselves among colleges and try to find out enough about them so that by statistical techniques (usually multiple regression) he can isolate the contribution to later earnings made by quality of the school from those that can be explained by background variables about the student, his earlier education, and his family.

III. Summary of Statistical Results

All of the studies we have seen confirm that students who go to under- graduate colleges of higher quality (however measured) earn more money even after controlling, insofar as possible, for background variables. Studies based on the new microdata sets by Alwin et al. (1975), Solmon (1975), Wachtel (1975a and b; 1976) and our own work all give this result; so does earlier work based on less satisfactory data by Weisbrod and Karpoff (1968). Moreover among those who go on to graduate school, those who go to better universities earn more when they later go to work (Solmon, 1975; Wachtel, 1976).

Similar results have also been found on the secondary school level (Welch, 1973; Link et al., 1976; and Wachtel, 1975b and 1976). These studies are in sharp distinction to one earlier influential, and very pessimistic study which had argued-that providing high quality education would not remove black-white earnings differentials (Jencks, et al., 1972); but that study has been questioned on technical grounds (Blaug, 1976).

NEW RESULTS FROM PROJECT "TALENT" DATA [1]

Project TALENT involved sampling 400,000 high school students in 1960, with follow-up surveys to come after one, 5, 11 and 20 years; con- siderable background information was gathered on each student's ability, academic performance, family background, the secondary school in which enrolled and, in the follow-up surveys, postsecondary education, occupation and income. Results reported here are based on a sample of about 12,900 nonblack male 1960 high school seniors who responded to the 1971 survey. The sample was reduced to 6,000 respondents by excluding those who did not attend college and those with certain special occupations (farmers, teachers, doctors, lawyers, clergy, those in military service, students, and persons with no serious occupation or with incomes under $2,000). Of these 6,000, half went to schools for which some of the measures of quality used here were not available. The final sample of 3,000 cannot in any sense be claimed to be representative of the population of all those who attend college, because of the response bias, because of the deliberate exclusion

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of some occupations (discussed further below) and because of the lack of data on some colleges (especially small church-related colleges and com- munity colleges). Nevertheless the persons studied went to hundreds of different undergraduate colleges; many went for less than a year, others went on to complete Ph.D.'s. The sample is a broad, national one and, despite its biases, may be used to supplement information extracted from other samples with quite different biases. Moreover, because of the unique information collected in the Project TALENT survey, some relationships can be explored with more care, and some controls imposed with greater precision, than has ever been possible before.

This study focusses on the quality of undergraduate schooling (even for those who went on to graduate school), and for each individual the last undergraduate institution attended was used as the basis for measuring quality. We used 10 different measures to help define quality:

To characterize the students, SAT (the estimated average SAT scores of entering freshmen, Astin, 1971). To characterize the faculty, FACSAL (Average faculty salary as reported by the AAUP, 1964). To characterize expenditures [2], EXPI (basic expenditures per FTE student), EXP2 (basic instruction, department research and library expenditures per FTE student), EXP3 (basic income per FTE student) and NEXP2 (EXP 1 -EXP2). To measure quality subjectively, GO and GA (index of overall quality and index of academic quality provided by Gourman, 1967), the Astin Intellectualism Index (INT) and Selectivity Index (SEL) provided by Astin (1965). We do not claim that any of these indices, or all of them together, truly

measure "quality" of a university. But they are appropriate proxy variables for the unobservable "quality", for two reasons. First, expenditures, faculty salaries and SAT scores are under administrators' control, and so they provide operational indexes of quality. It is more useful to measure the consequences of paying for better quality teachers, or adopting a higher SAT cutoff for admissions than to measure (e.g.) the consequence of selecting more students who will go on to graduate school or who will be listed in Who's Who 30 years later. Second, we believe that any plausible explanation for an observed rela- tion between these variables descriptive of the school and the earnings of its alumni is most appropriately captured by the (undefined) word "quality": once background variables describing the student are controlled, there is no other reason for us to postulate a relation between (e.g.) faculty salaries and student earnings. However, the results should be interpreted with care. We do not claim to have an unerring indicator of university quality.

The purpose of this study was not simply to seek a relation between earnings and quality, but to construct a statistical test to judge whether or

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not the relation is significant. The method used was to estimate a relation between earnings and college quality, controlling for ability and other back- ground variables. Earnings relations were estimated separately for each of nine quality measures with the results summarized in Table II. Column 1 shows the percent change associated with a one standard deviation increase in each college quality index. Average faculty salary appears to have the largest effect on earnings with a $1,442 increase (one standard deviation) associated with a $262 (2.8 percent) increase in earnings for a typical student.

TABLE II

The Effects of College Quality on Earnings

Quality index used in log earnings function a

Percent change in income from a one standard deviation change in quality index

R 2

with t-test in parentheses b

Gourman Academic

Gourman Nonacademic

Average Faculty Salary

Freshman S.A.T.

Astin Intellectualism Index

Astin Selectivity Index

Basic Expenditures

Instruction, Research and Library

Basic Income

(GA) 1.3 0.1 15 (1.82)

(GN) 1.6 0.115 (2.26)

(FACSAL) 2.8 0.118 (3.84)

(SAT) 2.5 0.116 (3.4o)

(INT) 2.6 0.117 (3.61)

(SEL) 2.3 0.116 (3.04)

(EXP1) 2.1 0.116 (2.83)

(EXP2) 1.6 0.115 (2.21)

(EXP3) 1.6 0.115 (2.23)

aFrom regressions of log 1971 earnings (LEEN) with ability (COO4L), family socio- economic background (P801), dummies for region (South), religion (CATH, JEW), single marital status (NTMEOT), degree level (S1, $2, $3), and college quality. Sample size is 3,079.

b Without college quality R 2 = 0.114.

A measure of the significance of quality in the earnings relation is the contribution of variables summarizing quality to R 2 , the coefficient of deter- ruination, in a regression of earnings on such explanatory variables as level of schooling, ability and family background. (R 2 measures the percentage of total variance in the underlying earnings which can be associated with or

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"explained by" variation in the independent variables of the regression equation.) The appropriate statistical test to determine whether the increase in R 2 occasioned by these quality variables is significant, is the t-test reported in Column 2 of Table II. For this size sample a t-statistic of 1.96 is significant at the 5 percent level. All measures except for the Gourman academic rating (GA) are significant at the 5 percent level, when entered into the earnings relation [ 3 ].

An alternative to entering measures of college quality separately into the earnings relation, is to enter many measures together in an earnings relation. It is possible that a group of quality variables may more accurately reflect the impact of college quality on earnings. Table III shows that the introduction of three measures of quality (SAT, FACSAL, GA) increase SR 2 by about 11 percent and a one standard deviation change in quality would raise earnings by 3.3 percent. The standard F-statistic of 7.0 indicates that the effect is significant at the one percent level. Moving from an under- graduat e school of average quality to one at the upper tail, three standard deviations from the mean, would be associated with about a 10 percent higher income, based on the result from the complete sample, after "con- trolling" for such other factors as student ability, background, and years of schooling., The last lines of Table III indicate that additional measures of quality do not contribute significantly to the relation.

TABLE III

Effects of College Quality Measures in an Earnings Relation a

R 2 with no college variables 0.109 R 2 with three college variables b 0.121 F-test for removal of three 7.017 Percent Change 3.3

in earnings from a one standard deviation change in quality index R 2 with six college variables c 0.122 F-test for removal of last three 0.818 Percent Change 3.5

in earnings from a one standard deviation change in quality index Number or observations 3,181

a Log earnings with ability (COO4L), socioeconomic status (P801), dummies for region, religion and marital status (SOUTH, CATH, JEW, NTMEOT) and college quality variables.

b SAT, FACSAL, GA. c EXP2, NEXP2, SAT, FACSAL, GA, GN.

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A second way to measure the effect of quality is to treat the expendi-

tures associated with higher quality as an investment, student earnings as a return on that investment, and measure the annual rate of return. Table IV shows those results.

TABLE IV

Rate of Return to $1 Invested in Increased Under- graduate Expenditures per F.T.E. Student a

Group b Percent Standard error c

Some college 4.9 9.3 B.A. 5.8 3.9 M.A. 15.1 5.2 Ph.D. 2.2 8.4

a Expenditures measured by basic instruction, depart- ment research and library expenditures per F.T.E. student.

b While some students went on to graduate school, it is the return to investment by the last undergraduate institution which is measured, for all cases.

c The joint test:

F(4, 4257) = 2.7

is statistically significant at the 5 percent level.

The rate of return estimates are both uncertain (as indicated by the high standard errors) and modest, although not as low as they at first appear: they represent real rates o f return with no inflation effect, so that a corre- sponding monetary rate o f return might be 5 or 6 percent higher. This would

mean that the implied monetary rate of return for investment in higher spending on B.A.'s might be 11 percent to 12 percent, comparable to the rate o f return on corporate bonds [4].

Our interpretat ion and evaluation of these results are given below, following discussion of the evidence provided by other studies.

OTHER STUDIES

Wachtel's (1975a, b and 1976) studies complement the results from the TALENT sample, giving alternative measures o f the rate of return to invest- ment in school spending. Wachtel's estimates are higher than those reported above; they may also be better. (The other studies summarized below can be

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interpreted for our purposes as confirming that school quality affects earn- ings, with numerical results much like those reported above.)

Wachtel's studies are all based on a sample of men aged 18-26 in 1943, who volunteered to take Army flight training qualification tests, after first having passed a preliminary screening test that put them roughly into the top half of the population in intelligence.

These men were surveyed in 1955 and 1969, with information elicited on education since 1943, occupation, income, and family status. The sample is unrepresentative because it is truncated in terms of intelligence, and pre- dominantly white; in addition, those who went to college were older than the average student, since for most of them college attendance came after the war.

For our purposes, Wachtel's studies are of particular interest because expenditure per student worked quite well in his sample as a measure of school quality, so that the resulting measures of rate of return to investment in school expenditures have smaller standard errors than those shown above. (Of course, the fact that a particular variable works well in one sample and not in another still leaves us with questions about its relevance for policy purposes.) His work is also of special interest because he measures quality of primary and secondary schooling separately (again by expenditures per pupil), thereby removing the possibility that college quality, correlated with quality of previous schools the student went to, is measuring the combined effect of primary, secondary and college quality.

It is worth commenting on the use of expenditures per student as a measure of educational quality: if all college and university expenditures went to educational purposes, if all expenditures were wisely made, and if all colleges and universities faced the same costs per pupil to achieve any specified quality of schooling, cost and quality would be functionally related and (possibly afler a suitable transformation of the quality scale) perfectly correlated. To the extent that those conditions are violated, cost is an imperfect measure of quality. Unless expenditures per pupil are also correlated with some other, unobserved, variable that is also correlated with income of the college's graduates, then using expenditures per pupil should give an underestimate of the true effect of quality on earnings. Put differently, when expenditures per student are included in a regression to explain the incomes of college graduates, the coefficient shows the effect on the graduates' income of spending more, under the assumption that a college is no wiser or thriftier than average when it spends the extra funds.

Wachtel's figures on rates of return are shown in Table V (taken from Wachtel 1976, Table 4).

These rates of return are real rates, since expenditures and incomes are all converted to a common year's base. An earlier study lumped together all college students and did not separately estimate the return to primary and

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TABLE V

Rates of Return to School Expenditures (EXP)

Schooling 12 years 12-16 years 16 years Over 16 years

Primary and 15% 10% 13% 11% secondary

Undergraduate 19% 10% (negative) Graduate 14%

secondary school quality. It showed an annual rate of return of 17 percent overall (Wachtel 1975a, Table 6-2).

It should be pointed out that these rates of return do not show the overall payoff from an investment in schooling; they show the return to expenses of the school only. A second important component of investment in schooling is the student's own time (he could be working if not in school). Wachtel's estimates show a rate of return to the student's time of 8 percent for undergraduates, and 14 percent for graduate students. (These results differ from those of earlier studies which have typically shown the rate of return declining as years of schooling increase.) The rates of return to direct spending shown in Table V should be interpreted as returns to increased school expenditure, holding years of schooling (and other factors) constant.

Solmon's (1975) study was based on the same file of 1943 flight volunteers as was Wachtel's. Its chief interest from our point of view is to confirm that a wide variety of measures of quality all appear significant in explaining variations in earnings. Gourman's indices of quality provide a significant contribution to R 2, but expenditures (on instruction, department research and library expenses), SAT scores of entering freshmen, and faculty salaries, all "objective" measures of quality, are better (their contributions to R 2 are each higher).

Two other conclusions are worth noting from Solmon's work: first, going to a college of higher quality appears to provide almost as much benefit to weak students as to strong ones. And finally, the quality of school appears to influence mid-career earnings (1969 survey) more than it does early-career earnings ( 1955 survey) [ 5 ].

Alwin et al.'s (1975) study focusses on Wisconsin students and Wisconsin schools. Virtually all 1957 male high school graduates in Wisconsin were surveyed before graduation regarding their college plans, to help in planning for changes in the state's higher education system. Students were questioned about their motivation for college study by asking about parents' and

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teachers' encouragement, about friends' plans and their own plans for college, and about their occupational aspirations; they were asked to specify their parents' levels of education, father's occupation within certain broad classes and father's income. Course grades and ability test scores were also available.

Later, one-third of these same students were surveyed again, to ask where they went to college and for how long; and their earnings in 1965, 1966 and 1967 (note that the latest earnings figures are for only 10 years after high school graduation).

The study reported here shows the effect on R 2 of adding college "quality" to a list of background and ability variables; their result can therefore be compared with that reported in Table II. The chief differences are as follows: results are reported only for the total sample, not separately for B.A.'s, M.A.'s, and so on. Background variables include dummies for the "motivation" questions described above. And quality of schools is measured in a generally less satisfactory way than in ot~r work, by a group of dummy variables that classify colleges as follows: University of Wisconsin, Center System; Wisconsin State Universities; Wisconsin County Teachers' Colleges; Marquette University; prestigious colleges and universities; liberal arts colleges, general; liberal arts colleges, Catholic; universities; technological colleges and institutes, and other colleges. The effect on R 2 of this group of college indicators was much the same as the effect of college quality measures in Table II [61: they increased R 2 from 0.080 to 0.104 (no F-test is reported, but our estimate of F for their data suggests significance at the one percent level).

IV. Evaluation

To summarize, the crudest evidence shows that graduates of better schools get higher salaries than graduates of weaker ones. This can be demon- strated in dollars and cents as in Table I. Once we try to take account of biases in the distribution of students among schools, though, by statistical techniques, dollars-and-cents estimates are harder to come by. All of the studies say that school quality affects income, even after controlling (to the extent possible) for students' ability, the quality of their previous school- ing, family background and motivation. To translate an assertion that the relationship between school quality and earnings exists to a dollars-and-cents estimate, probably the rate of return estimates are the most useful summary figures.

Here we found low numbers, Wachtel found high ones. Some of the discrepancy is probably due to the fact that the TALENT sample has an average age of under 30, Wachtel's has an average age of 47; and as Solmon showed, the returns to quality of school come later in life rather than early.

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We would expect to see more significant returns to quality from the 20-year survey of Project TALENT respondents than after the 11-year survey. In addition, it is simply the case that in the TALENT data, expenditures per student do not serve as a very satisfactory measure of school quality, while in Wachtel's they do. That must account for part of the difference in results. But, finally, we should keep in mind that rates of return from the TALENT data are not as low as they may look to our inflation-distorted eyes. Nine percent rate of return on a U.S. Government bond, when there is 7 percent inflation, gives a real yield of only 2 percent. The real yield for B.A.'s in the TALENT sample is 5.8 percent, which may not be an unacceptably low return for a public investment. (Recall, too, that the sample excludes physi- cians and lawyers; rates of return may be understated as a result.)

The final question we must ask is whether the statistical adjustments do fully correct for the possible biases that concern us, or whether the reported effects of quality, even in these sophisticated studies, might still be an illu- sion based on biases that yet remain. Two possible biases concern us, and there is some comforting (though not finally conclusive) evidence in these studies to suggest that our concerns might be unfounded.

First, there are regional differences in cost of living that probably translate into higher costs of schooling and higher salaries for college gradu- ates who stay to work where they have gone to school. These regional dif- ferences may also be correlated by chance with other measures of school quality simply because of the concentration of good schools on the east coast and in major cities elsewhere. Could part of the measured effect of school quality be spurious for this reason? Three pieces of evidence suggest not: first, the study based on Wisconsin alone should show no such bias, and it exhibits the effect of quality as strongly as the others. Second, Wachtel explicitly introduced state income per capita in his regression to see if primary and secondary school spending were simply a proxy for state income level; he found that the regression coefficient for quality of school- ing was essentially unaffected by that addition (1975b, p. 515). Finally, our own study uses a zero-one variable to identify residents of the southeast; it has little effect on the results.

Our second concern is in regard to the quality of information available on family background, which is measured in most of these studies by parents' education level and little else. It seems likely that some aspects of socio- economic status which may affect later earnings opportunities for the respondents, may be missed. As an example, suppose that the son of a cor- porate board chairman, rather slow and not very industrious, is admitted to Princeton from whence he graduates with little distinction. Ten years later he has a highly paid job with little responsibility in his father's company. If the economist were so unfortunate as to draw this man in his sample, his statistical technique would attribute the good job to the magic of Princeton, not to father's position.

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Several considerations diminish our concern regarding the importance of this problem. First, we could make the same case for the importance of the individual student 's motivation, which seems to be fairly well captured in the study by Alwin et al. and by no one else (recall the questions regard- ing occupational goals, family expectations, friends' college plans and their own intentions with regard to college); ye t their study showed as significant a role for quality of school as did any of the others. Second, Solmon's results suggest that school quality is more important late in life than early; the mechanism of concern to us here should show the reverse - p a r e n t a l contacts may start the fresh graduate out in a favorable position, but are unlikely to be as influential in middle age. Third, to the extent such a mechanism operates it seems unlikely to be important for college dropouts and junior college graduates, or for M.A.'s and Ph.D.'s, ye t all groups show the effect of quality on earnings. Finally, these studies spread across colleges of all levels of quality, for students coming from all socioeconomic b a c k - grounds. The effects we discuss here are likely to operate only at the highest socioeconomic level, not across so wide a spectrum.

Thus, we conclude that quality counts. Of course, this does not mean that it counts because of cognitive skills imparted or knowledge gained. It may just mean that students in good schools learn how to conform to particular social norms, or that employers are prejudiced in favor of good schools. Different studies would be required to show w h y good schools mean higher earnings. It is enough for now to say that they do.

Acknowledgement

We thank Duane Alwin, Lewis Solmon and Paul Wachtel for helpful discussion of their research, and anonymous referees for improvements in the exposition. The National Institute of Education (Grant No. NIE-OEG- 0-72-1569-AMD #1) and the University of Minnesota Graduate School and Computer Center provided financial support.

Technical Appendix

Both theoretical consideration and empirical evidence suggest that earnings after college are a log-linear function of years of schooling (see Mincer, 1974, pages 83-89). The results reported in Section III were based on an equation of the form:

(1) log (Y) = ao + aaS1 + a2S2 + a3Sa + bQ + background variables

34

where:

Y = Annual earnings $1 = Dummy variable for B.A. degree S 2 = Dummy variable for M.A. degree $3 = Dummy variable for Ph.D. degree Q = Measure of college quality

Background variables = Ability, family socioeconomic background, region, religion and marital status.

Ordinary Least Squares (OLS) regressions were estimated for Equation (1)us ing each of the nine quality measures in place of Q with the results reported in Table II. The percent change in earnings from a one standard deviation change in quality (Ay) was computed from:

(2) Ay = bOQ

where:

= OLS estimate of b in Equation (1)

aQ = Standard deviation of the quality variable

An alternative approach to measuring the effect of college quality is to enter many college quality variables into Equation (1) obtaining:

(3) log (Y) = ao + alS1 + a2S2 +aaSa + blQ1 + �9 �9 - + bnQn + background variables

where:

Q1, Q2, Q3, �9 �9 �9 Qn are college quality variables

Table III reports R 2 and F-test results from OLS regressions with more than one college quality variable.

The effect on earnings of a one standard deviation change in quality (Ay) is esti- mated from:

[ 1 (4) A y = ~ b i b ] %. 1 1

where:

/~i, 6/. are estimates of bi, b] = CO V (atQ/) au

In order to compute the rate of return to expenditures per student we estimated the following earnings function:

(5) log (Y) = ao + alS1 + a2S~ + a3S3 + boEo + blE1 + b2E2 + b3E3 + back- ground variables

35

where:

E0 = Expenditures per F.T.E. student for those with some college E 1 = Expenditures per F.T.E. student for those with a B.A. degree E2 = Expenditures per F.T.E. student for those with an M.A. degree E3 = Expenditures per F.T.E. student for those with a Ph.D. degree The rate of return for an additional dollar of expenditures per student can be

estimated from:

bi Yo (6) r i -

S

where:

r i = Rate of return for the i t h degree level b i = Estimate of b i from Equation (5) S = Years in undergraduate college

Yo = Earnings for those who do not attend college

In 1971 dollars, Yo was roughly $6000 in 1960. S is assumed to be 2 for those with some coUege and 4 for those with a college degree (see Rodgers, 1977 pages 29--35 and Wachtel, 1975b, pages 152-156) . This estimate assumes that the return will be constant over the working life, and neglects the (minor) effect on the rate of return of retirement after approximately 45 years.

N o t e s

This section is based on work done by the second author as part of his thesis research, under the direction of John Hause, whose thoughtful suggestions regarding both data and analysis pervade the work. Each of these measures conforms to the definitions provided in U.S. Office of Educa- tion (1968); the figures for individual schools are not provided there, but were made available by Mr. Robert Berls of the Office of Planning, Budgeting and Evaluation, USOE. Someone not familiar with cross-section statistical studies of this kind, but accustomed to regression equations in other contexts, might look scepticaUy at the low R 2 and ask if we really can conclude that the relationship we posit even exists - such regularity as we can discover appears to explain only about 12 percent of the total variation in respondents' earnings. That is to say, factors of individual skill, luck, background, hard work and who knows what else - not included in the regressions reported here - account for 80 percent to 90 percent of the total variation observed. What is important, though, is that the sample sizes are so large (over 1,000 in each case) that the relationship of earnings with school quality, even though it explains only a t iny fraction of the total variation in earnings among individuals, is much too persis- tent to be attributed to chance. Note, too, that we have restricted attention to a fairly homogeneous group: it would be easy to get higher R2's (as some have done) by adding females, persons without college education, persons from certain deviant occupations, and persons with a wider variety of ages. We are explaining 12 percent of the variation in income of 29-year old, nonblack males who attended college, and who do not work in certain unusually highly paid or low-paid occupations.

36

A more adequate measure of the amount of unexplained variation in income is the standard error of the estimate (SEE). The SEE is the variability in the sample after all the included variables are used to explain earnings. In Table II the SEEs are in the range 0 .370-0 .375. This compares favorably with the higher SEEs in the range of 0 .47-0 .49 observed by Paul Wachtel (Wachtel, 1975) and the 0 .45-0 .59 recorded by Jacob Mincer (Mincer, 1974; see Table 3.3). Another, perhaps more interesting, question concerns the relative pay-offs to years compared with quality of college. Our analysis suggests that the rate of return to the last years of the B.A. is 14.7% and to the M.A. 12.0%. These returns are somewhat larger than the 5.8% return to expenditures per F.T.E. student at the B.A. level. The difference raises but does not answer the question: would students be better served by investing in a program to increase retention than by a program to improve quality? To answer that question would require knowing the cost of such a program per student retained to graduation, and in addition would require a measure of earnings for the marginal graduate rather than earnings for the average graduate. We have not discussed an earlier examination of the NBER-Thorndike data by Terence Wales (Wales, 1973). Using only the Gourman index of academic quality, Wales found that earnings of individuals in the top fifth of undergraduate school quality distribu- tion are significantly and substantially higher than earnings of others. One significant piece of negative evidence on the relation between quality and earnings appearing in this study should be mentioned. After measuring the separate effects of ability and background variables, the authors work backwards and ask: how would earnings of each group of schools differ, if we subtracted out the effects at tr ibutable to what the students bring with them? In most cases the resulting "corrected" earnings distribution is in accord with general indicators of quality of the different schools (showing thereby a positive effect of school quality on earnings); but corrected earnings for the graduates of prestigious colleges and universities are below average. This may be due to the early age at which earnings were sampled and to the fact that so many graduates of prestigious schools go on to graduate work.

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