College Choice in America [Reprint 2014 ed.] 9780674422285, 9780674422278

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College Choice in America

College Choice in America Charles F. Manski

with contributions

/

David A. Wise

by Winship C. Fuller

and Steven F. Venti

Harvard University Press Cambridge, Massachusetts, and London, England 1983

Copyright © 1983 by the President and Fellows of Harvard College All rights reserved Printed in the United States of America Library of Congress Cataloging in Publication Data Manski, Charles F. College choice in America. Bibliography: p. Includes index. 1. College, Choice of. 2. Universities and colleges— United States. I. Wise, David A. II. Title. LB2350.5.M3 1983 378M98 82-12046 ISBN 0-674-14125-3

To Kitty and Madeline

Acknowledgments

This book is the outgrowth of a large research project on the determinants of college choice in the United States. The work was supported by grants from the Exxon Educational Foundation and the National Center for Educational Statistics. In addition we are especially grateful to Robert Meyer, who was a continual source of input to the project, to Sherwin Rosen, who made many helpful suggestions, and to our colleagues who provided comments on various parts of the book: David Ellwood, Jerry Hausman, Robert Klitgaard, Richard Light, David Mundel, Michael Stoto, and Richard Zeckhauser. Special thanks go to Sally Abbott who typed many drafts of the book. As the work evolved, several major parts of it became the responsibility of individual participants in the project. Chapters 1, 2, and 3 were written by Charles Manski and David Wise. Chapters 4 and 8 were written by Steven Venti and David Wise and Chapter 5 by Steven Venti. Chapters 6 and 7 were prepared by Win Fuller, Charles Manski, and David Wise. Some of our findings appear separately in various publications. Versions of the material in Chapters 4 and 8 are presented in David A. Wise and Steven F. Venti, "Test Scores, Educational Opportunities, and Individual Choice," Journal of Public Economics 18 (1982): 35-63; and in David A. Wise and Steven F. Venti, "Individual Attributes and SelfSelection of Higher Education: College Attendance versus College Completion," Journal of Public Economics 19 (1983), forthcoming. Material in Chapter 6 is incorporated in Winship C. Fuller, Charles F. Manski, and David A. Wise, "New Evidence on the Economic Determinants of PostSecondary Schooling Choices," Journal of Human Resources 17 (Fall 1982): 477-495, copyright © 1982 by the Board of Regents of the University of Wisconsin System.

Contents

Introduction

1

1

Overall Findings

4

2

Econometric Modeling of Student Behavior

3

From High School Graduation to School and Work

4 Application and Admission

26

67

5

The Allocation of Discretionary Grant Aid

6

Selecting a Postsecondary School

7

Enrollment Effects of the BEOG Program

8

College Attendance versus College Completion Conclusion

159

Appendixes 164 Notes 200 References 210 Index 215

91

105 118 129

43

College Choice in America

Introduction

Postsecondary schooling is a major prerequisite for many careers and has an important bearing on lifestyles, aspirations, and social status in general. Thus, the determinants of postsecondary education contribute significantly to social and economic outcomes in American society. Some American high school graduates attend no postsecondary school, some go to junior colleges or vocational schools, and others attend four-year colleges and universities. About half of all high school graduates make the transition from full-time high school education to full-time employment by acquiring additional schooling; the other half make the transition without additional schooling. Who obtains higher education? Does low family income prevent some young people from enrolling, or does scholarship aid offset financial need? How important are scholastic aptitude test scores, high school class rank, race, and socioeconomic background in determining college applications and admissions? Do test scores predict success in higher education? In this book, we present an analysis of postsecondary schooling choices with particular emphasis on these major questions. For the sake of completeness and to give a sense of perspective, we shall also present findings concerning the early work experiences of high school graduates. Although we have tried to give a broad view of the determinants of college-going behavior, our work has been motivated in large part by issues of current policy concern. For example, until the early 1970s the federal government provided very little financial aid to students for higher education. The Basic Educational Opportunity Grant (BEOG) Program was introduced in 1973 and by 1980 had become a major source of aid for low- and middle-income students. The program is now being reduced substantially. One of the goals of our research is to estimate the effect of such aid on college attendance. Perhaps the appropriate question now should be: How will reduction in the program affect attendance? 1

2

College Choice in America

Also, considerable recent public discussion has been focused on the role of Scholastic Aptitude Test (SAT) scores in the determination of educational opportunities. Both the extent to which the tests are used and their predictive validity have been criticized. The chapters that follow provide substantial information that should help inform future discussion on this subject. Our analysis is based on data obtained through the National Longitudinal Study (NLS) of the High School Class of 1972. Commissioned by the National Center for Educational Statistics, the study provides a unique source of information on the transition from high school to work or further schooling. Data were obtained on almost 23,000 seniors from over 1,300 high schools, comprising a stratified random sample of all public, private, and church-affiliated schools in the United States. To increase the number of disadvantaged students in the sample, high schools in low-income areas and schools with a high proportion of minority enrollment were sampled at approximately twice the sampling rate used for the other schools. The data were obtained through a series of questionnaires distributed to seniors and to their high schools during the spring of 1972 and through three follow-up surveys, the most recent in October 1976.' We were thus able to track the cohort of graduates of the class of 1972 through an important transitional period in their lives. Postsecondary educational outcomes are the result of a series of decisions made by individuals and by institutions of higher education. Students apply to schools. Admissions and scholarship aid decisions are made by colleges and universities. Students select from the available alternatives. Those who attend either drop out or remain until graduation, largely at their own volition. The core of this book is made up of a set of interrelated behavioral analyses, each focused on a particular aspect of the school attendance process. The reader unfamiliar with recent econometric methods may find portions of our statistical analyses a bit foreign. In order to infer from the NLS data the magnitudes of partial effects (such as the effect of SAT scores on college admissions conditional on students' race or high school class rank) and in order to answer counterfactual questions (for example: How many people who chose not to enroll in college would have successfully graduated if they had enrolled?), we have applied the most appropriate methods at our disposal. Readers will find that they can follow the presentation and discussion of our major findings without completely understanding the methodology. Those who are uninterested in the tech-

Introduction

3

nical aspects of our work can obtain a general knowledge of the approach (described informally in Chapter 2) and then focus on the parts of the later chapters that motivate the research and discuss the findings. It is our hope that the results of the book will be accessible to a wide audience, even though the complexities of the issues we address have required technical analysis.

Overall Findings

A general summary of the results of our study will serve to acquaint readers with the subject, and will also form a comprehensive base from which to approach the detailed analyses that follow. Because Chapters 4 and 8 afford many parallels for comparison, we group together here the results from those chapters. And although institutional aid awards logically precede student selection of a college, we discuss this topic last. All the points mentioned here will subsequently be examined in greater depth. Application and Admission to Four-Year Colleges and Universities Do young men and women go to college largely at the discretion of admission officers, or are attendance decisions largely their own? Admission criteria of colleges and universities often draw public attention, but the choices of individuals are sometimes forgotten. We have found that individual application decisions are much more important than college admission decisions in the determination of attendance. Self-selection is the major determinant of attendance. Approximately 45 percent of 1972 high school graduates did not attend a postsecondary school in the fall of 1972; few, however, would have been unable to gain admission to some fouryear college or university of average quality if they had wished to attend. APPLICATION

Which individual and family background attributes determine application? The likelihood that a person will apply to a four-year college or university increases with high school class rank, SAT scores, parents' education, and, to a lesser extent, parents' income. For example, the probability that a student with a combined SAT score (verbal plus math) one standard deviation above the average score will apply to a four-year 4

Overall Findings

5

Table 1.1

Effect of changes in four variables on the probability of application. Probability of application High Low Difference Specified Change SAT score 1 standard deviation above the mean, versus 1 standard deviation below the mean

.56

.21

.35

High school class rank 1 standard deviation above the mean, versus 1 standard deviation below the mean

.52

.23

.29

Parents' income 1 standard deviation above the mean, versus 1 standard deviation below the mean

.44

.30

.14

Education of mother and father college degree or more, versus education of mother and father less than high school

.52

.23

.29

school is .35 higher than the probability that a student with a score one standard deviation below the mean will apply, assuming that other individual and family background attributes of the two are the same and equal to the average for all youth. That is, the relationship will hold if each has the same high school class rank, the same athletic and leadership experiences in high school, the same proportion of high school classmates attending college, the same family income and comparably educated parents, and the same race and sex, and if each lives in an area with comparable wage and unemployment rates. (In our discussion, "controlling for other variables" and "other things equal" mean that except for the attribute under discussion, the other attributes are the same and equal to their average values in the sample.) Comparable changes for other variables and their effect on the probability of application are shown in Table 1.1. The probability that a person with the average of attributes in our sample will apply to a four-year college is about .40. The probability is .56 for a person with an SAT score one standard deviation above the average (all other attributes average), whereas it is .21 for a person with an SAT score one standard deviation below the average. By these measures, the attributes measured by SAT scores and prior school performance are jointly the most important determinants of college application; but holding constant both SAT score and high school class rank, as well as other variables, high school graduates whose parents are highly educated are much more likely to apply to a college than those whose parents are less well educated. Parents' income is relatively unimportant.

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College Choice in America

Current federal student aid is based largely on family income and is inversely related to income. Scholarship aid in 1972, although much lower on average than BEOG awards, was also based partly on family income. Even in 1972, then, the relatively small estimated effect of parents' income may have been due in part to the counteracting effect of financial aid. Still, these numbers suggest that even if the effect of family income were completely offset by financial aid, family background would continue to exert substantial influence on college application: the college decisions of youth would still be strongly related to the education of their parents, controlling for other attributes. ADMISSION

Are students who apply admitted? Informal observation and recent public discussion suggest that most people view colleges and universities as quite selective. Our results imply the contrary, however: although a few schools reject a large proportion of applicants, most applicants are admitted to their first-choice schools. Moreover, even most high school graduates who don't apply would have a high probability of admission to a college of average quality (that is, a college where the mean SAT score of entering freshmen is equal to the average of these means over all colleges). For example, consider a group of high school graduates all with individual and family background attributes equal to the average, except that they differ in SAT scores and high school class rank. Table 1.2 shows the probabilities of application to a four-year college and probabilities of admission to an average-quality college for students with selected SAT scores and class rank percentiles. People at the twenty-fifth percentile level in class rank and with verbal and math SAT scores totaling a mere Table 1.2 Probabilities of application and admission, given selected SAT scores and class rank percentiles. Class rank percentile Combined SAT score 25 100 Probability of application 700 1,300

.14 .64

.49 .92 Probability of admission to average-quality college

700 1,300

.74 .94

.93 .99

Overall Findings

7

700 have only a .14 probability of applying to a four-year college, but would nonetheless have a .74 probability of admission to an averagequality school, were they to apply. In other words, if a person who does not apply were to apply, he would have a good chance of admission at an average-quality college. A low likelihood of application is thus not simply a reflection of a low likelihood of admission. We have also found that men and women with a low probability of application would have a low probability of obtaining a college degree, were they to attend. That is, youth who don't attend college would be likely to drop out without a degree if they did attend. We believe that this is a more likely explanation of their low probability of application. While public discussion has tended to stress the effect of SAT scores on admission decisions, their relationship to individual application decisions is often overlooked. We have found that high school class rank is just as important as SAT scores in admission decisions, and that these two measures are more strongly related to individual application decisions than to college admission decisions. Both conclusions are supported by the changes in application and admission probabilities at four-year colleges and universities that are associated with two standard deviation shifts in SAT score and high school class rank (holding other variables constant). This is shown in Table 1.3, where the probabilities of admission pertain Table 1.3 Effect of changes in SAT score and class rank on the probabilities of application and admission. Probability of application Probability of admission Specified change

High

Low

Difference

High

Low

Difference

SAT score 1 standard deviation above the mean, versus 1 standard deviation below the mean

.56

.21

.35

.93

.81

.12

High school class rank 1 standard deviation above the mean, versus 1 standard deviation below the mean

.52

.23

.29

.93

.80

.13

8

College Choice in America

Figure 1.1 Probability of admission for an average person at colleges of different quality.

to the likelihood of admission to a college of average quality; the application probabilities are the same as those shown in Table 1.1. By these measures, SAT scores do not, on average, dominate admission decisions. Given their performance in predicting college completion, test scores also are not accorded undue weight relative to high school class rank in admission decisions. Although most people are admitted to their first-choice four-year college or university, this is not to say that most would be admitted to every school. Most would be admitted to a college of average or lower quality; but certainly admission to some schools—relatively few—is very selective. An indication of the selectivity of schools is given in Figure 1.1, which shows, for an applicant with average individual and family background characteristics, the probability of admission to colleges of different quality, as measured by the average SAT score of entering freshmen. Whereas a two-standard-deviation shift in either student SAT score or high school class rank is associated with approximately a .12 change in the probability of admission, a two-standard-deviation shift in the quality of the first-choice college reduces the probability of admission by - . 1 5 , according to our estimates (evaluated at the mean of all individual attributes). 1 In this sense, the most important determinant of admission from

Overall Findings

9

Table 1.4 Race-region effects on the probabilities of application and admission and on college quality. Comparison Black in the White in the Black in the White in the

South South non-South non-South

Probability of application

College quality"

Probability of admission

.78 .33 .78 .32

731 813 895 837

.87 .87 .91 .88

a. As measured by the average SAT score of entering freshmen.

the point of view of the applicant is the quality of the college or university to which application is made. Race has little effect on admission but a substantial effect on application. A comparison of application and admission probabilities by race and region, assuming other individual attributes at their sample means, reveals these findings. (See Table 1.4, which also shows race-region effects on the quality of colleges to which students apply.) There is little difference between the application probabilities of whites by region or of blacks by region. However, whereas a white with average attributes in the non-South would apply to a four-year school with probability .31, the probability that a black with average attributes would apply is much higher, .78, representing a difference of .47. That is, a black student with average attributes is more than twice as likely as a white student with these same attributes to apply to a four-year college or university. It is important to remember that these comparisons are based on similar black and white youth: they control for individual and family background attributes. Not controlling for these attributes, blacks are on average less likely than whites to apply to a four-year college. Holding other attributes constant, there is little difference in admission probabilities by race and region of the college. Apparently, in 1972 affirmative action policies had not led to dissimilar admission chances for like blacks and whites. Affirmative action practices may, however, have had an impact on applications. These results are also consistent with the relatively greater returns to higher education for blacks than for whites. As shown in Table 1.4, blacks in the South go to lower-quality schools than do similar whites in the South, whereas blacks in the non-South go to somewhat higher-quality schools than do whites in the non-South. For example, a black student in the non-South with a given SAT score and

10

College Choice in America

other attributes would be likely to apply to a slightly higher-quality college than would a white student in the non-South with the same SAT score and other attributes. The difference in the quality of schools applied to by blacks and whites in the South is undoubtedly related to the existence of predominantly black schools in the South. Our research indicates greater persistence to graduation of blacks in the South than in the nonSouth—possibly a reflection of the differences in the colleges attended by the two groups. Attendance and Dropout The occupational, monetary, and other societal rewards to higher education are in large part conditional on earning a degree. Therefore, an important measure of successful performance in higher education is whether a degree is obtained. This is not to say that those who attend and fail to obtain a degree have not benefited. Like trial and error in the job market, postsecondary education may for many young people be part of the search process that leads to discovery of what they like and don't like and of which occupations are compatible with their interests and abilities. To this extent, students may derive informational value from attendance, even if they drop out. And, of course, traditional benefits in the form of learning are not entirely lost just because a student drops out before obtaining a degree. Nonetheless, we take successful completion of a degree program to be a major indicator of individual performance in higher education and of potential benefit from college. Are individual college attendance decisions consistent with likely benefits from attendance? We emphasized above that individual application decisions, not admissions decisions, are the most important determinants of college attendance; particularly significant is the relationship between high school class rank, SAT scores, and other individual attributes on the one hand and college applications on the other. Are test scores also accurate predictors of success in college? Given high school class rank, for example, is there further information in the test scores? Critics of the use of test scores in the college attendance process argue that the additional information is minimal. In general, are people who are likely to attend also likely to succeed? What about those who don't attend? Are attendance choices "correct," or would those who choose not to attend be well advised to go to college? We have found that most young people who do not attend college

Overall Findings

11

Table 1.5 Probability of dropout for selected probabilities of application and attendance. Probability of Probability of Dropout Attendance Dropout Application .05 .10 .50 .90

.81 .72 .42 .16

.05 .10 .50 .90

.75 .65 .30 .10

would be very unlikely to obtain degrees if they were to attend. Suppose we consider a group who didn't go to college and ask whether they would have graduated if they had. In most cases the answer would be no. More generally, those who are unlikely to attend would be unlikely to obtain degrees if they were to go to college, while those who are most likely to attend would also be most likely to obtain degrees. For each student in our sample we have estimated the probability of application and attendance as well as the probability of dropping out without a degree, should he attend. For those with a given probability of application, we have calculated the average probability of dropping out. Also, for those with a given probability of attendance we have calculated the average probability of dropping out. Selected values are as shown in Table 1.5. For example, youth with personal and family background attributes associated with only a .05 probability of application would have on average a .81 chance of dropping out without a degree if they attended. On the other hand, youth with a .90 probability of application would have only a .16 probability of dropping out without a degree. Analogous results apply to attendance versus dropout. Given all the attributes that determine attendance, those who are most likely to apply and to attend are also most likely to benefit from college education by obtaining a degree. What is the partial effect of individual attributes? Again, we can discuss this question by asking how the outcomes would change if only one (or two) attributes changed, with all others remaining at the sample means. Table 1.6 gives probabilities of attendance and dropout for selected values of high school class rank and SAT scores, together with the probabilities of application shown in Table 1.2. The data show a positive partial relationship between SAT scores and high school class rank on the one hand and the probabilities of application and attendance on the other. This positive relationship is reflected in an inverse relationship be-

12

College Choice in America

Table 1.6 Probabilities of application, attendance, and dropout for selected class rank percentiles and SAT scores. Class rank percentile Combined SAT score

25

700 1,300

.14 .64

700 1,300

.07 .43

700 1,300

.74 .56

100 Probability of application .49 .92 Probability of attendance .34 .82 Probability of dropout .28 .15

tween these individual attributes and the probability of dropping out. For example, a person with a 700 SAT and at the twenty-fifth high school class rank percentile has only a .07 probability of attendance; but if a person with these attributes were to attend, he would have a very high probability (.74) of dropping out. In contrast, a person with a high class rank and with a 1,300 SAT is very likely to attend college (.82) and would have a low probability of dropping out (.15). A person whose attributes were like the average in our sample has about a .40 probability of application to some college, about a .25 probability of attendance, and about a .50 probability of dropping out. These numbers do not indicate the predictive validity of tests and high school class rank because other variables are held constant, including a measure of the quality of an individual's high school (the percent of the high school's graduates who go to a fouryear college or university). Parents' income and education also affect the probability of dropping out. Compared to the importance of parents' education, parents' income is relatively more important in the probability of dropping out than in the probabilities of application or attendance. The probabilities of these outcomes for selected values of family income and education reveal this pattern (see Table 1.7). The mean 1972 level of parents' yearly income among people in our sample was about $11,000. Whereas the effect on attendance probability of an income increase from $6,000 to $18,000 is less than a third as large as the effect of the specified education increase, the effect of the income increase on dropout probability is larger than the effect of the education increase.

Overall Findings

13

Table 1.7 Probabilities of application, attendance, and dropout for different levels of parents' education and income. Parents' education

Parents' annual income $6,000

$18,000 Probability of application

Less than high school College degree or more

.19

.29

.45

.58 Probability of attendance

Less than high school College degree or more

.11

.17

.33

.43 Probability of dropout

Less than high school College degree or more

.62

.45

.50

.34

We mentioned above that compared to high school class rank, SAT scores, and parents' education, parents' income is a relatively unimportant determinant of application to college and that its effect may be mitigated by scholarship aid awards. The results shown in Table 1.7 raise the possibility that even if aid is large enough to completely offset the effect of parents' income on college attendance, there might still remain an income effect on persistence in four-year colleges and universities. Our analysis does not directly confirm this speculation, but it is of interest because the emphasis in federal student aid allocation tends to be on attendance, evidently with little independent attention given to persistence. Although there is certainly a relationship between family income and educational background on the one hand and college attendance on the other, these numbers show that having well-educated and high-income parents does not in itself assure college attendance; not all youth from higher-income families or with well-educated parents go to college. For example, even youth with college-educated parents and from families with 1972 incomes of at least $18,000 (all other attributes average) had only a .43 chance of attending college in the fall of 1972. Possibly because the benefits they derive from attendance are greater,

14

College Choice in America

young people with higher academic skills as measured by high school class rank and SAT scores are more likely to apply to and attend more expensive colleges, as well as colleges with higher average SAT scores. Indeed, on average, those with low high school class rank and SAT scores would have to be paid in order to be persuaded to attend college. Holding other attributes constant, youth whose parents are more educated and who earn more are also more likely to go to more expensive and higherquality colleges, as measured by average SAT scores. We have discussed relationships between measured attributes of young people and their college choices. But even among people with the same measured attributes (such as SAT score and parents' education), those who choose to attend college are different in expected ways from those who choose not to attend. For example, among people with all measured individual and family background attributes equal to the sample mean, those who attend pay almost $2,000 more than those who don't would like to pay, were they to attend. Those who attend have a .45 probability of dropping out, whereas if those who don't attend were to attend, they would drop out with probability ,55.2 We have found a substantial relationship between measures of academic ability and performance on the one hand and college attendance and completion on the other. To address the question of the predictive validity of SAT scores, however, we need to present the results of a more limited analysis. Studies of the predictive validity of SAT scores almost invariably relate first-year grades in college to SAT scores and high school grades or class rank only, without controlling for other variables. In large part, this is because these measures serve as the major evidence available to admissions officers. So one can think of making predictions based on the same evidence likely to be available to most colleges when they make admission decisions. The contribution of SAT scores to the prediction of college grades is often measured by the increase in the ability to explain college grades when both SAT scores and high school grades (or possibly class rank) are used instead of high school grades alone. For comparability, we have made calculations based only on SAT scores and high school class rank, excluding from the analysis other determinants of college outcomes. Many attributes, such as parents' education, that we have used in our analysis would not always be available to college admissions officers. And even if they were, they might well be considered inappropriate for use in admission decisions. Suppose then that predictions were made solely on the basis of SAT

Overall Findings

15

Table 1.8 Probabilities of application, admission, attendance, and dropout for selected SAT scores and class rank percentiles. Class rank percentile Combined SAT score

25

700 1,300

.14 .82

100 Probability of application .39 .95 Probability of admissiona

700 1,300

.69 .90

700 1,300

.07 .68

700 1,300

.69 .34

.93 .99 Probability of attendance .25 .89 Probability of dropout .37 .10

a. To a college of average quality—that is, with an average SAT of 1,012.

scores and high school class rank, not controlling for other variables except race and region. Probabilities of application, admission, attendance, and dropout for selected values of high school class rank and SAT scores are shown in Table 1.8. The numbers and the associated analysis reveal several findings. First, given high school class rank, there is a very substantial effect of SAT scores on the probability of dropping out of college before obtaining a degree. On average, 200 SAT points are equivalent to approximately 25 class rank percentile points, or one standard deviation in SAT scores is about equivalent to one standard deviation in high school class rank. For example, a person with a 900 SAT score and a high class rank (one-hundredth percentile) is roughly as likely to graduate from college as a person with an SAT score of 1,100 but at the seventy-fifth percentile in high school class rank. Even though the relatively high correlation between SAT scores and high school class rank means that dropout probabilities can be predicted well using only high school class rank, given class rank the difference in dropout probabilities varies greatly with SAT scores. This means that although, on average, colleges could predict reasonably accurately on the basis of class rank alone, these predictions would be far from expected dropout probabilities in some instances. For example, the mean SAT score of people in our sample who are at the seventy-fifth class

16

College Choice in America

rank percentile is approximately 900, and their average dropout probability is about .36. However, a person at the seventy-fifth class rank percentile but with an SAT score of 1,100 would have only a .25 probability of dropping out, whereas a person with an SAT score of 700 would have a .48 probability of dropping out. Without knowledge of the SAT score, the predicted probability would be .36 for both, when in fact the actual probabilities are quite different. In general, individuals with SAT scores very different from the expected SAT score, given high school class rank, would be either substantially disadvantaged or substantially advantaged if admissions were based on class rank alone. Second, the relationship of test scores and high school class rank to the probability of application and attendance is mirrored inversely by their relationship to the probability of dropping out. Third, the probability of admission and the probability of dropping out are strongly and inversely related. A comparison of the weight given to SAT scores and class rank in admission versus the relative importance of these variables in predicting dropout shows slightly less weight in admission than dropout. In admission, 10 SAT points are, on average, given the same weight as 1 class rank percentile point. But 10 SAT points change the probability of dropping out more than does 1 class rank percentile point: in the prediction of dropout, 10 SAT points are equivalent to about 1.4 class rank percentile points. Thus, one might suppose that SAT scores should be given more weight in admission. Given the statistical variance of our estimates, however, we have concluded that if persistence is treated as the criterion for admission, colleges and universities on average do assign weights to SAT scores and high school performance that are approximately commensurate with college persistence predictions. That is, if colleges and universities intended to base admissions on the probability of persistence to a degree, in making admission decisions they would count high school class rank and SAT scores approximately as they now do. We have not found evidence that too much weight is assigned to SAT scores. Although these numbers reveal that individual choices predicted on the basis of SAT scores and high school class rank are quite consistent with the benefits expected from a college degree, the results are in sharp contrast with the recent criticism of the use of SAT scores in the college attendance process. Much of the recent criticism is based on interpretation of the findings of validity studies of SAT tests that emphasize correlations between test scores and/or class rank on the one hand and college grades on the other. Validity studies and the interpretations of their find-

Overall Findings

17

Table 1.9 Race-region effects on the probabilities of attendance and persistence and on college quality. Race and region Black in the South White in the South Black in the non-South White in the non-South

Probability of attendance

College quality

Probability of persistence

.45 .20 .52 .19

794 888 954 921

.68 .42 .49 .48

ings also by implication emphasize the effect of test scores on college admission decisions, while largely ignoring their relationship to student choices; and they ignore student persistence decisions, which may be the single most important indicator of success in college. Furthermore, they are invariably limited to relationships within a single college or university. Both self-selection by students and the decisions of admissions officers tend to minimize the relationship between test scores and performance among students in a single college or university. Finally, returning again to predictions based on the full array of individual attributes and family background characteristics, we have examined the effect of race and region on attendance and dropout, holding all of these other variables at their sample means (see Table 1.9). Differences in the probability of attendance by race and region are analogous to the differences in the probability of application. Here we see, however, that whereas on average blacks in the South attend colleges of lower average quality than the colleges attended by whites in the South, holding other personal attributes constant, blacks are much more likely than whites in the South to persist to a degree; the difference is .26. Such a difference is not observed in the non-South. A plausible explanation is that a large proportion of blacks in the South attend predominantly black schools. We have also found that holding other variables constant, blacks in both the South and non-South who do go to college pay substantially more than whites—$594 more in the South and $655 more in the non-South. Again, this finding would be consistent with the relatively greater return to a college education for blacks than for whites.

Characteristics of Alternatives and Individual Choice Which attributes of postsecondary alternatives determine individuals' choices after high school? How important is scholarship aid versus tuition? How does the academic quality of the school interact with individ-

18

College Choice in America

ual academic ability? We've discussed the relationship between individual attributes and application, admission, attendance, and dropout decisions at four-year colleges; let's now pursue related questions but with a somewhat different focus. Suppose that a high school graduate has applied to and been admitted to one or more colleges or universities. He could also work and not go to school at all, or he could attend a vocational school or a two-year college. Given these available alternatives, how does he weigh characteristics of the alternatives in deciding which alternative to choose? We can think of him as ordering the alternatives by "value" and then selecting the alternative with the highest value to him (the one he likes best), the value of each alternative being a weighted average of the characteristics of that alternative. Which characteristics receive negative weights and which positive? Do young men and women choose the highest-quality school they can get into? Not according to our findings. Individual self-selection, as stated above, plays a dominant role in the determination of college attendance, college quality, and college cost; but we can provide a more stringent characterization of self-selection. If, holding other characteristics like tuition constant, we graph the value of an alternative versus the difference between the average SAT scores of all students who choose that alternative and the SAT score of an individual applicant, we find that the result looks like Figure 1.2. Suppose that a young person could choose among postsecondary Value of the college alternative

-3C

Figure 1.2 Value of the college alternative.

Average SAT at the school, minus individual SAT

Overall Findings

19

school alternatives that were alike in all respects, except that the colleges he was considering differed in quality (average SAT score of entering freshmen). Our findings, as reflected in the graph, say that he would be most likely to choose the college with an average SAT score about 100 points higher than his own. He would be less likely to choose a school with a higher average, and also less likely to choose a school with a lower average. He would be approximately indifferent between a school with an average 300 points above his own and one with an average equal to his own. A student does not necessarily prefer the highest-quality school. Does cost matter? We expect that people would rather pay less than pay more for something, and colleges are no exception. Among colleges with the same (measured) attributes, except that they differ in tuition, the higher-tuition ones are less preferred; those with higher dormitory costs are also less preferred, other things being equal. What about scholarship aid? We might expect that a one-dollar increase in aid would have the same effect on a student's choice as a onedollar decrease in cost. That is, other things equal, if tuition at school A is one dollar more than at school B, but if scholarship aid is one dollar more at school A than at school B, then a student should be indifferent between A and B. In fact, this is essentially what we find at four-year colleges and universities. The negative value associated with high tuition is almost identical to the negative value associated with dormitory cost, and each of these is approximately equal but opposite in sign to the positive value associated with scholarship aid. An increase in tuition at two-year colleges and at vocational-technical schools also reduces the value that individuals associate with those alternatives, and does so by approximately equal amounts. We have not been able to estimate the effect of aid at vocational-technical schools, but at two-year colleges our estimates indicate that a dollar in scholarship aid is worth considerably more than a one-dollar reduction in tuition cost. Because our aid data for two-year colleges were less extensive than our data for four-year colleges and universities, we have less confidence in this result than in the results for four-year colleges. The primary alternative to postsecondary education for most youth is full-time participation in the labor force. If wage rates are high and unemployment rates are low, expected earnings of people in the labor force are higher, and this will tend to increase the advantages of working versus going to school, other things being equal. Our estimates are consistent with this reasoning: the greater the expected forgone earnings while in

20

College Choice in America

school, the less likely a person will be to attend school and the more likely to get a full-time job. Distant schools are less likely to be chosen than near ones, other things equal. We also find a "peer" or high-school quality effect: the larger the proportion of a high school graduate's classmates who go to a four-year college, the more likely it is that he himself will make this choice (controlling for his personal and family background attributes). Similarly, the larger the proportion of his classmates who go to vocational-technical schools, the more likely it is that he, too, will do so. To help to put these findings in perspective let's consider a series of equivalencies—that is, changes in characteristics of alternatives that would leave a student indifferent between them. Consider a student whose family income is $10,000 per year in 1972. All else equal, a $100 per month decrease in tuition at a four-year college is approximately equivalent to: a $100 per month increase in scholarship aid at a four-year college, a $100 per month decrease in dormitory cost at a four-year college, a $250 per month decrease in expected labor force earnings, an increase in the average SAT of the college from 200 points below the student's SAT to an average equal to the student's SAT, a decrease in the average SAT of the school from 350 points above the student's SAT to 100 points above the student's SAT, a 30 point increase in the percent of a student's high school classmates who go to college. Also, a $100 per month decrease in tuition at a four-year college for a student whose family income is $10,000 is approximately equivalent to a $300 per month decrease in tuition at a four-year college for an individual whose family income is $30,000 per year. 3 The Effect of BEOGs on College Enrollment The Basic Educational Opportunity Grant Program was initiated in 1973 and was designed to equalize educational opportunity across income groups. At its inception, almost all of the grants went to low-income students, but subsequent awards have been increasingly extended to middleand higher-income students. This apparently reflects a shift in policy emphasis away from the provision of equal opportunity to low-income youth and toward the easing of the perceived burden of educational expenditures on middle- and upper-income families.

Overall Findings Table 1.10

21

Predicted number of BEOG recipients and sizes of average awards.

Income group Lower (less than $16,900) Middle Upper (more than $21,700) Total

Predicted Number of Predicted Population Predicted BEOG average recipients size enrollment award (in thousands) (in thousands) (in thousands) (in dollars) 1,254 934

590 398

534 265

1,193 879

1,142 3,330

615 1,603

296 1,095

628 964

What has been the effect of the program on the enrollment of lowincome students? Has the extension of awards to higher-income students affected their enrollment patterns? Approximately 40 percent of 1979 awards went to middle- and upperincome students, according to our estimates. 4 Our predicted number of recipients and the average awards by income group are shown in Table 1.10. The awards assume full-year attendance, although in fact many entrants drop out during the course of the year. It is clear that a disproportionately large number of low-income students receive BEOGs: 91 percent, versus only 48 percent of students from upper-income families. And the average award to the low-income group is almost twice the average award to the high-income group. Nonetheless, 40 percent of all BEOG dollars are given to upper- and middle-income youth. But awards to upper- and middle-income youth have very litttle effect on their enrollment patterns, whereas awards to low-income students have a substantial effect on their postsecondary school enrollment. In addition, the awards have virtually no effect on enrollment in four-year colleges for any income group, according to our estimates. The effect of the awards is to increase enrollment by low-income students in two-year colleges and in vocational-technical schools. Predicted enrollments in 1979 by school type and by income group, with and without BEOG awards, are shown in Table 1.11. Total enrollment was 21 percent higher with BEOGs than it would have been without them, according to these estimates: 60 percent higher among low-income students, 12 percent higher among middle-income students, and 3 percent higher among upperincome students. Although for many low-income youth the awards seem

22

College Choice in America

Table 1.11 Predicted enrollments for 1979 by school type and income group, with and without BEOGs (in thousands). Two-year and All schools Four-year schools voc-tech schools Income group Lower (less than $16,900) Middle Upper (more than $21,700) Total

With Without With BEOGs BEOGs BEOGs

Without With Without BEOGs BEOGs BEOGs

590 398

370 354

128 162

137 164

462 236

233 190

615 1,603

600 1,324

377 668

378 679

238 935

222 645

to tip the balance in favor of junior colleges and vocational schools versus full-time employment, they do not greatly affect attendance at four-year colleges and universities. It seems plausible to us that two-year schools, vocational schools, and work are much closer substitutes for one another than four-year college programs are for any of these three. This possibility is commensurate with our finding that 25 percent of men who are full-time students in junior colleges and vocational schools also work full time and that many more work part time, whereas only about 5 percent of men who are full-time students in four-year colleges also work full time. A large fraction of BEOGs go to youth who would attend a postsecondary school without the awards. An approximation of the number of induced enrollments versus the number of awards, by income group, is given in Table 1.12. According to the figures, 41 percent of awards to Table 1.12 Number of induced enrollments versus number of awards for 1979, by income group.

Income group Lower (less than $16,900) Middle Upper (more than $21,700) Total

Predicted number of BEOG recipients (in thousands)

Predicted induced enrollment (in thousands)

Number of awards to youth who do not require inducement (in thousands)

534 265

220 44

314 221

296 1,095

15 279

281 816

Overall Findings

23

low-income students went to youth who without the awards would not have attended a postsecondary school, whereas 59 percent went to youth who would have attended anyway. Of awards to middle-income youth, 83 percent went to people who would have attended anyway, whereas 95 percent of upper-income recipients would have attended without the awards. Thus, for a large fraction of award recipients, especially those from upper- and middle-income families, there is no corresponding enrollment effect. If the goal of the program were to give awards only to people who would not otherwise enroll, the program could not be considered efficient. We draw no conclusions about the desirability of such a goal, however. To the extent that the goal of the program is to defray college expenses for all students, it is more successful. The less liberal 1977-78 version of the BEOG Program concentrated to a much greater extent on youth who would not otherwise have attended. According to our estimates, of the awards in this year 39 percent went to people who would not otherwise have enrolled, whereas in 1979-80 only 25 percent of awards induced enrollment. Thus, the primary federal government student aid program has a significant effect on the enrollment of low-income students in vocational and two-year colleges; however, a substantial proportion of the funds go to upper- and middle-income students whose enrollment patterns are not affected much by the awards, and to youth who without the awards would have enrolled in four-year colleges anyway. College Financial Aid Offers Before the BEOG Program was initiated, most aid was in the form of discretionary awards granted by colleges and universities and other organizations. Such awards are still an important component of total student aid. On what basis is this component of financial assistance disbursed? Whereas the federal government has primarily been concerned with college accessibility for lower-income youth and possibly with subsidizing college education for all youth, institutions may be more inclined to use financial aid to compete for higher-ranked students. We have found that aid offers could play a substantial role in affecting students' choices among schools. How then do colleges and other organizations weigh need against academic merit in the determination of aid offers? Institutional aid offers, in contrast to BEOG awards, give substantial weight to academic merit, but also place noticeable weight on need. Table

24

College Choice in America

Table 1.13

Relation of merit and need to expected aid awards.

Standard deviation increase of two in

Change in expected aid award (in dollars) Four-year college Two-year college

SAT score High school class rank Parents' income Parents' dependents

810 837 —876 262

793 679 —760 290

1.13 shows how an increase of two standard deviations in selected indicators of academic merit and need is related to changes in expected aid awards, if other variables are held constant in each case. The figures suggest that need and academic promise receive about the same weight. However, since SAT scores and high school class rank are positively related, a person with a high SAT score would also be expected to have a high class rank. Thus, both measures together may receive more weight than does need.5 Despite resolutions by the College Scholarship Service and the National Association of Student Financial Aid Administration, it is clear that college discretionary aid is not based solely on need. We find that black youth receive substantially greater aid offers than white youth, holding constant other individual and family background attributes (see Table 1.14). In four-year colleges, blacks in the non-South receive an average of $873 more than whites; blacks in the South receive $576 more than whites ($431 + $145). In two-year colleges the differences are analogous but not as large, probably reflecting lower average awards in two-year than in four-year colleges: blacks receive $492 more than whites in the non-South and $222 more in the South. For each group, awards are lower in the South than elsewhere. The higher aid awards to Table 1.14

Race-region effects on expected aid offers. Change in expected aid award (in dollars) Comparison Four-year colleges Two-year colleges Black in the non-South versus white in the non-South Black in the South versus white in the non-South White in the South versus white in the non-South

873

492

431

-54

-145

-276

Overall Findings

25

blacks may be one of the reasons for the higher attendance rates of black youth, controlling for other individual attributes. Finally, we find that college aid offers give noticeable weight to athletic and leadership abilities. Controlling for other attributes, a leader in high school athletics can, in comparison to other students, expect to receive $488 more at a four-year college and $752 more at a two-year college. A leader in high school government can, in comparison to other students, expect to receive $314 more at a four-year college and $736 more at a two-year college. In summary, college discretionary aid offers are apparently used in large part to compete against other schools for the most sought-after students. Need is only one of many criteria that are given substantial weight in student financial aid awards. In contrast to BEOG awards, then, nongovernment aid is likely to have a relatively small effect on the college attendance rates of low-income versus higher-income youth.

Econometric Modeling of Student Behavior

The postsecondary educational outcomes that we have observed reflect the interaction of a complex set of decisions made by individuals and institutions. Individuals decide whether to apply to college and to which colleges to apply; colleges make admissions decisions and financial aid awards; individuals select from among the college and noncollege alternatives available to them; enrolled students decide whether to drop out of college without a degree or to persist until a degree is obtained. Our study attempts to shed empirical light on the elements of this sequence of decisions. In particular, we estimate relationships that describe: the probability that a student with given academic and other attributes would be admitted to a college of given quality, if he were to apply (Chapter 4), the expected scholarship aid that a student with given attributes would receive, if the student were to attend a college with given tuition and of given quality (Chapter 5), the probability that a student would choose to enroll at a college, if admitted to that institution and to alternative colleges (Chapters 6 and 7), the probability that a student with given attributes would persist through graduation, if he were to enroll as a college freshman (Chapter 8). In theory, the entire college attendance process could be analyzed using a single, large statistical model. In practice, we have found such an approach impractical and have chosen instead to analyze separately each of the major components of the attendance process. Table 2.1 shows the sequence of decisions that we have examined. In this chapter we describe in some detail how we have proceeded and explain how the various pieces of the analysis are related. 26

Econometric Table 2.1

Modeling

of Student Behavior

27

Sequence of decisions affecting postsecondary school choices.

Décision and décision maker

Choice

Alternatives

Décision 1 (student)

Application to college

Yes, no College quality

Décision 2 (institution)

Admission

Yes No

Décision 3 (institution)

Financial aid

Yes, no How much

Décision 4 (student)

School or work

Universities Junior colleges Work etc.

Décision 5 (student)

Persistence in college

Persist to degree Drop out

Modeling the Selection of a Postsecondary School Suppose that a high school graduate knows the postsecondary schooling alternatives available to him. He knows some because he has applied to a college and has been admitted. Other postsecondary alternatives are available to virtually every high school graduate; for example, most twoyear colleges have open admission, and any graduate could enter the labor force. At this point, he must choose from the alternatives available to him. In Table 2.1, this is the fourth of the decisions listed. How can one predict which of the alternatives he will choose? A primary goal of our analysis is to obtain estimates of the effect of policy instruments on postsecondary education and work choices—"policy instruments" being variables like BEOG scholarship aid that can be controlled by government policy. We wish to examine the effect of policy variables while controlling for other variables that we think are important determinants of what people do after graduating from high school. For example, we would like to estimate the effect on college attendance of increased scholarship aid if academic aptitude, family income, high school quality, tuition charges, and other variables are controlled for. A common method of estimating the relationship between an outcome or dependent variable and explanatory or independent variables is regression analysis. The methodology that we use is in many ways analogous to regression analysis; that is, we are basically interested in deter-

28

College Choice in America

mining the effect of explanatory variables on an outcome variable. But the outcome variable we must explain takes the form of a choice from a group of alternatives—for example, a particular four-year college that is chosen from a set of four-year colleges, two-year colleges, types of vocational schools, and kinds of work. The outcome we are dealing with is thus not a continuous variable like annual wage income but is discrete, one of a finite number of possible outcomes. To estimate the effect of explanatory variables on a discrete outcome, we use a model of discrete (or quantal) response, whose purpose and capabilities are analogous to those of regression analysis. Regression analysis allows prediction, for example, of annual wage income, given an individual's personal characteristics; and, if used properly, it allows estimation of the effect of a variable like education on annual income, holding other variables constant. We obtain comparable predictions and derive estimates of the effects of explanatory variables, but we need to interpret them in the context of a discrete outcome variable. Instead of predicting the expected value of an outcome like annual income, we predict the probability that an outcome will be chosen. That is, if a high school graduate has the option of attending a four-year college, a two-year college, a vocational school, or working, we predict the probability that he will choose each of the alternatives. Just as we cannot hope to predict the exact income he might earn in a given year, we cannot hope to predict exactly which alternative he will choose. Our estimates might imply that the probability that he will attend a four-year college is .5, that he will attend a two-year college is .3, that he will attend a vocational school is .1, and that he will choose to work is .1. These probabilities are specific to each individual, depending on his characteristics (like SAT scores) and the attributes (like tuition) of the options available. That is, the probabilities of choosing each of the options are functions of the individual attributes and alternative characteristics, just as annual income is assumed to be a function of individual attributes in regression analysis. And just as we can estimate the effect of education on income using regression analysis, we are able to estimate the effect of a variable like scholarship aid on the probabilities of selecting each of the alternatives. For example, the probability that a particular individual will attend a given four-year college may be .5 when scholarship aid is zero, with the probabilities of choosing each of the other alternatives .3, .1, and .1, respectively. But if scholarship aid is, say, $1,000, the estimated probabilities may be .75, .15, .05, and .05.

Econometric Modeling of Student Behavior

29

Thus, the analysis is not intended to predict the exact choice that a person will make, but to assign a probability to each choice. If an individual faces a set of college alternatives that are very similar, the predicted probabilities of attendance should be about the same for each of them. If an individual has a very high SAT score and comes from a wealthy family, the predicted probability of attending a four-year school may be very large, while the probability of attending a vocational school may be very small. Among all people with these characteristics, a small number are likely to go to vocational schools, even though most of them will attend four-year colleges. Given that the methodology allows us to predict the probability that a particular individual will choose any one of the available alternatives, the model can also predict college-going rates for any proportion of the population. To obtain estimates for a large sample of people, for example, we simply make predictions for each person, add the results, and divide by the number in the sample. This gives us the proportion of the sample who are predicted to choose each alternative. We can also obtain national simulations by choosing a random sample from the population and carrying out the above process. The National Longitudinal Study provides such a sample after weighting observations to take account of the nature of the sampling process used in the survey. That is, the sample needs to be weighted in order to correct for the overrepresentation in the survey of high schools and students from lower socioeconomic areas and groups. This enables us to predict, for example, the effect of alternative scholarship aid programs on college attendance, or, more specifically, the effect on people from families with low incomes. The above discussion of our methodology is based on an assumed relationship between outcomes and explanatory variables. Our estimates are therefore only reliable to the extent that we capture in our model the basic determinants of postsecondary school and work choices. In practice, this requires that the explanatory variables we use adequately reflect the most important influences on school and work choices, and that we adequately capture the range of alternatives available to individuals. We hypothesize that there are five important general factors that determine people's choices after high school. The first is academic aptitude. Some alternatives are simply not available to students with aptitude below certain levels. We also propose that people tend to shy away from alternatives selected by those with average aptitude much higher or lower than their own. The second factor is family income. The idea is that it is

30

College Choice in America

easier for people from wealthy families to finance large expenditures than it is for those from poor families. The third factor is cost and aid. Costs take the form of tuition, room and board, and distance to the alternative. Everything else being equal, we hypothesize that higher-cost alternatives are less likely to be chosen than lower-cost ones. We presume that aid enhances the desirability of an alternative. For example, everything else being equal, an individual is more likely to go to a college that offers a scholarship than one that doesn't. The fourth factor is the "quality" of the high school a person attends and the decisions of his peers. In practice, we have not distinguished between the two. We have measured only the proportion of the students from a person's high school who go to colleges and the proportion going to other schools. We hypothesize that the larger the proportion of a person's peers who go to college, the more likely the person is to attend college. Other indicators of the quality of the high school, such as the levels of education and academic achievement of the faculty, would have been useful to us but were not available. The fifth factor is labor market conditions. We use in this part of our work one variable to reflect labor market opportunities: expected annual income if an individual were to enter the labor force. This variable encompasses both expected wages and expected hours of work (that is, expected unemployment). We presume (and our results confirm) that, all else equal, the higher the expected income from working, the more likely people are to find a full-time job rather than go to school. We distinguish a large range of alternatives, including specific colleges and universities, several types of vocational schools, military service, homemaking, and full-time work. Although the range of alternatives explicitly allowed for is much greater than in other studies of which we are aware, our work is nonetheless limited in some respects. For example, we are not able to distinguish various types of work alternatives, or to take account of educational opportunities in the form of on-the-job training and apprenticeship programs. We feel that this does not detract from the validity of our approach or from our results; but it does imply that the model cannot be used to make fine predictions among work alternatives—a task that is probably better left to a modeling effort with this particular goal in mind. DECISION MODELS

The starting point for econometric analysis of student behavior is the perception that observed patterns of school attendance and labor force participation are the consequence of decisions made by students, by edu-

Econometric Modeling of Student Behavior

31

cational institutions, and by employers. From observations about the schooling and labor force activities of high school graduates, we can make inferences about the decision processes that led to these actions. In particular, we can use such observations to estimate a priori unknown parameters of mathematical models of student behavior. Why do we think it necessary to interpret the NLS survey data through formal behavioral models? Why shouldn't descriptive analysis of these data suffice? First, a high school graduate's observed schooling and labor force activity is the outcome of a complex set of forces and decisions. The student's college application decisions, colleges' subsequent admissions decisions, the availability of school financing, and short- and long-run labor market prospects all play roles. A model explaining postsecondary school activities is a tool that helps one disentangle these various forces. In the absence of models, the information one can extract from the immensely rich NLS data is limited to determining the presence or absence of simple statistical associations. Second, it is our desire to tap the power of models in policy analysis. The reader may wonder how we could reasonably use data relating to the high school class of 1972 to evaluate the BEOG Program many years later; certainly a great deal has changed since the early 1970s. Our response is that behavioral analysis of the activities of the class of 1972 allows us to separate those activity determinants that have changed over time from those that have remained stable. Over the past decade, the socioeconomic and demographic distribution of the population of high school graduates, the number and attributes of the nation's colleges, and the availability of financial aid for school enrollment have all changed. On the other hand, it's reasonable to suppose that the decision processes that students follow in making their activity choices have remained relatively stable: a student with given scholarship aid, ability, socioeconomic background, and college and labor market opportunities would be likely today to select the same kinds of activities as did students with similar characteristics in 1972. We can therefore use the 1972 NLS data to estimate a model that explains behavior conditional on student attributes and opportunities, and can with some confidence apply this model years after the data were collected. We can also apply the estimated model to answer counterfactual questions; for example, we can predict how the graduates of 1972 would have behaved had college opportunities differed from those that actually prevailed.

32

College Choice in America REVEALED PREFERENCES

Precisely what information do the NLS data contain about the decision processes generating postsecondary activities? If we assume that a student chooses the most preferred alternative from the available options, then observations of chosen activities reveal student preferences. In particular, if we imagine a student as (implicitly) assigning a numerical value to each potential activity, then the fact that the student has chosen a particular activity implies that its utility exceeds that of all others that the student could have chosen. For simplicity, let's assume that after high school graduation a student has two alternatives: alternative c, standing for college, and alternative w, standing for work. If we observe that a student (designated I) chooses to go to college, then this implies that Ulc > Ulw, where Ulc and U,w are the utilities that t associates with college and work, respectively. If another student, designated s, goes to work, then Usw > Usc. The NLS data provide a large set of these inequalities, one for each student in the sample. Such inequalities derivable from the NLS data do not in themselves provide sufficient information to allow us to predict how a student not in the sample will select between college and work. To achieve this vital objective, we must combine the NLS sample information with our own prior knowledge of the factors relevant to schooling decisions. For example, we may suppose that the utility of college enrollment to student t depends on his ability, A„ and family income, I,, and also on the quality, Q„ and cost, C„ of his best college opportunity. Similarly, the utility of working may depend on his potential wage, W,. In particular, let us assume that U,c = /M, + p2I, + faQ, + p4C, Ulw = f35W„ where . . . , f>5 are unknown parameters. Given the observation that student t chooses to go to college, and given data on the explanatory variables A, I, Q, C, and W, the revealed preference inequality

provides information about the parameters . . . , /?5. From the set of such inequalities yielded by the NLS sample, we can determine the parameter values. And once the parameters have been determined, we can

Econometric Modeling of Student Behavior

33

predict the schooling/work decisions of students outside the NLS sample. In particular, if r is a 1982 high school graduate with characteristics Ar, Ir, Qr, Cr, and Wr, we would predict that student r will choose to work if f35Wr>/3tAr

+

+ p3Q, + pACr.

THE RANDOM UTILITY MODEL

In reality, the utilities U are undoubtedly more complicated functions than those assumed in the above example. First, the effect of the variables A, I, Q, C, and W on utilities may not be linear. Second, there certainly exist additional utility-relevant factors beyond those specified. To the extent that the form of possible nonlinear effects is known and that the additional utility-relevant factors are observable, we can modify the functions determining utilities accordingly. Inevitably, however, our model for U will not be perfect; some nonlinear effects may be neglected and some utility-relevant factors may be unobserved. In terms of our example, there will exist disturbances elc and elw such that ulc = ptA, + p2i, + ft a + fuc, + elc Ulw = fi5 w, + £m. The disturbances e are, of course, not directly observable. It is clear that if we have no knowledge at all about these factors, we cannot extract useful information from the observed activities of NLS students. On the other hand, we can continue to make revealed preference inferences about behavior if something about the likely pattern of e values across the student population is known. In particular, if the distribution of the disturbances across students is known to have given characteristics, then we can treat the e's as random variables. The above equations for U,c and U,w now define a "random utility model." In a random utility model setting, we cannot use the revealed preference inequalities to deterministically solve for the parameters fi. Instead, we use information on the e distribution to form choice probabilities and then select parameter estimates that make the choice probabilities and the observed choices of NLS students most closely correspond. In particular, the probability that student t is observed to choose school enrollment is the probability that elc and elw are such that PtA,

+

p2I,

+

&Q, + p4C, + elc >/3sW, + elw.

34

College Choice in America

The product of these probabilities across the sample of NLS respondents is the sample likelihood. We use the method of maximum likelihood to estimate the /?'s as well as any unknown parameters characterizing the e distribution.1 The parameters having been estimated, we can use the model to predict the behavior of students outside the NLS sample. These predictions, of course, are now probabilistic rather than deterministic. That is, for a given student r, we may predict that he will choose full-time work with probability Prw and will select schooling with probability Prc = 1 - Prw. Note that we are not here asserting that student behavior is itself probabilistic. It is rather that we, as analysts, can model behavior only imperfectly and express the knowledge we do have through choice probabilities. Some psychological models of decision making do assume that behavior is probabilistic—that is, that no fixed rule can describe decision making. Interestingly, the random utility models we apply can also be derived from an assumption of probabilistic behavior.2 THE CONDITIONAL LOGIT MODEL

The simple example above treats only two alternatives, work and school, whereas each individual typically can choose among many alternatives, including many schooling possibilities. To model empirically student behavior in choosing among multiple alternatives, we assume that each alternative can be characterized by a vector Y whose elements include attributes like tuition cost and the location of the school or workplace. We also measure attributes of individuals, denoted by the vector X, whose elements might include past academic achievement and family income, for example. The choice that a person makes from among available alternatives is assumed to depend both on the characteristics of the alternatives and on the attributes of the individual decision maker as well. Specifically, we suppose that the value of the y'th alternative (characterized by the vector Yj) to the ith decision maker (whose attributes are summarized in X,) is given by U(Yp X,). Again, we think of utility as random, and it is convenient to think of the function U as being composed of two parts: a mean value and a random deviation from this mean. Then we can write U as U(YJy X,) = U(Yj, X,) + e:j, where U is the mean value and e the random term. One may also think of U indicating the average value of alternatives with measured charac-

Econometric Modeling of Student Behavior

35

teristics Yj to the average or representative individual with measured characteristics X? Because all individuals with measured characteristics X'i do not have the same tastes (we observe and measure only some attributes) and because all alternatives with measured characteristics Yj are not really identical (there are unobserved characteristics as well), the value that any given individual i attaches to an alternative j deviates from the average by some amount e^. For convenience, we assume that U(Yp X:) is a linear in-parameters function of individual and alternative characteristics, so that U(Yj, Xi) = Zjj/3 = ZIJU8, + Zy2fl2 + ... + ZijKpK, where ZtJ is a vector of variables, /J a vector of parameters, and K the number of characteristics. The variables Z,y may be simple characteristics of alternatives like cost, or they may be functions of both alternative and individual attributes, such as cost of the alternative divided by family income of the individual. Others may be alternative specific indicators or dummy variables; for example, one of the Zy values may indicate whether a given alternative is or is not a four-year college. Our behavioral assumption is that the yth alternative is chosen by the /th individual if he values that alternative more than any other available—that is, if U(Yj, Xj) is greater than U(Yk, X,) for all k not equal to j. Since U is treated as random, we can write the probability that the j t h alternative is chosen as P,j = P r { Z t f i + ev > Zikp + eik, for all k * /), where k ranges over all alternatives available to individual i. Convenient distributional assumptions on ey lead to the so-called conditional logit functional form given by Pij = ez'//(ez'|/?

+ eZa,i + ... + ez'jl3),

where the /th individual faces J alternatives. Note that the parameterization of choice probabilities using this functional form is in no way dependent on the utility-maximizing paradigm that we outlined. The functions P t j are well-defined probabilities without it. The idea that individuals make the choices that "suit them best," however, provides an intuitively appealing rationalization for the conditional logit form.

36

College Choice in America

In our empirical work reported in Chapter 6, we obtain maximum-likelihood estimates of the elements of the vector /?. Once estimates of fi are determined, the probability of any particular choice for any given individual can be predicted using the conditional logit specification shown in the equation above. In Chapter 7, we make calculations of this kind in order to assess the impact of the BEOG Program on college enrollments. Modeling Application and Admission Decisions In analyzing the student's choice among postsecondary schools, we take as predetermined the set of available alternatives. In large part, however, the choice set is the result of prior student application and college admission decisions. Thus, we take a step backward and ask which college alternatives are likely to be available to a given student. In particular, our study of the attendance process includes an examination of how admission decisions are made. Since we were faced with a budget constraint, our research priorities precluded a detailed examination of application decisions; but it was necessary to develop a simple application model in order to estimate the admission model correctly. Because application and admission logically precede the student's selection of a college, our analysis of these decisions appears first (Chapter 4). A student who has applied to a college is either admitted or not, depending on his attributes and on the attributes of the college. Major determinants, for example, are measures of the academic ability of the student and the academic quality of the college. Given individual attributes and college quality, it would seem easy to use a discrete-choice model to predict whether the student will be admitted. But the situation is more complex than this. Not all students apply to a college; thus, some are never considered for admission. We would like, however, to predict the probability that a student who did not apply to college would have been admitted if he had applied. We need to answer counterfactual questions. The statistical technique that allows us to make such predictions requires that we estimate not only a model of admission conditional on application but also a model explaining application decisions. Moreover, we need to predict the quality of the school to which a student applies. Thus, to predict admission, we have to estimate a system of three equations. In modeling admission, we continue to motivate our analysis by supposing that the decision maker (here the college) makes the choice that is of greatest value to it.

Econometric Modeling of Student Behavior

37

A relatively simple and effective way to model admission decisions is to assume that a college assigns each of its applicants an index of "potential" based on the applicant's combined SAT score, class rank, high school activities, and other attributes. Given application, the college compares the applicant's potential with a threshold level and grants admission if the student passes the threshold. The threshold level depends on the quality of the college, which we measure by the average SAT score of entering freshmen. Just as we cannot predict with certainty the college a student will choose, we cannot predict with certainty whether an applicant will pass the threshold of a given college. However, as in the college selection case, we can use a discrete-choice model to predict the probability of admission, conditional on observed characteristics of the applicant and college. In particular, let Vi} = X f i + e:j be the potential of applicant i as measured by college j, where X, are observed and etJ are unobserved determinants of potential. Let Lj = Qja + Uj be the threshold level for college j, where Qj and Uj are observed and unobserved determinants of this level. Then the probability that applicant i will be admitted to college j is Pr (V,j>LJ) = Pr (X£ + ev>Qja

+ Uj).

A complicating factor in the estimation of this model is that we observe admission decisions only for those students who choose to apply to at least one college. It can be shown that if the unobserved determinants of potential, ejjt are also determinants of application decisions, then proper statistical estimation of the admission model requires that we also estimate a model of application. 3 That is, we need to form the joint likelihood that a student will apply to a college of given quality and, if so, that he will be admitted (see Chapter 4). Because we developed our application model primarily as an auxiliary tool needed in the analysis of admission, we chose to keep it relatively simple. Specifically, the application model predicts the probability that a student with given attributes will apply to college at all, and, when the student does apply, it predicts the quality of the "first-choice" college. The model does not predict the entire portfolio of college applications or characterize the first-choice school other than by its quality. Nonetheless, our empirical results on the determinants of application decisions are of interest in themselves and are reported in Chapter 4. The joint estimation

38

College Choice in America

of application and admission decisions allows direct comparison of the effect that individual attributes have on student application decisions with the effect of these same attributes on college admission decisions. The Allocation of Discretionary Scholarship Aid Financial aid awards affect the net cost of college enrollment and thereby influence students in their selection among postsecondary schools and other opportunities. As an input to our analysis of college selection (see Chapter 6), it was necessary to know, or at least estimate, the financial aid that a student could expect to receive were he to enroll at each of his available alternatives. However, we observe aid only at the college a person attends. We therefore developed a model that would allow us to predict the expected aid that a student with given observable attributes would receive were he to enroll at a college with given observable characteristics. The major component of this aid model is an equation explaining the allocation of discretionary scholarship funds by colleges to their students. Since the process of scholarship allocation is itself of policy interest, we report our findings on a stand-alone basis in Chapter 5. The model of discretionary scholarship aid predicts the expected award, FIJt that student i would receive from college j, were he to enroll there. The magnitude of a scholarship award, if granted, presumably is a function of a student's socioeconomic and demographic status and of the cost of college enrollment, in particular of tuition cost. Together these factors determine a student's "financial need." The award a student receives may also depend on the student's potential as judged by the college—that is, on "merit." These ideas can be effectively embodied in the linear-in-parameter regression model FtJ = Z J i + e,y, where the values represented by Zy are observed determinants of need and merit and e y represents unobserved effects. A model of this type is estimated in Chapter 5. As in the case of the admission model, estimation of the scholarship equation requires attention to the fact that scholarships are observed only for students who actually enroll. To deal with the potential selection bias in the sample of observations, we specify a reduced-form model of enrollment and form the joint likelihood that a given student will enroll in college and receive a given level of scholarship aid. A complication in the specification of the likelihood is that aid must be greater than or equal to zero, and many students receive no aid. To address this complication, the

Econometric Modeling of Student Behavior

39

aid equation follows a Tobit specification which corrects for the pile-up of observations at zero (see Chapter 5). Persistence to College Graduation A substantial proportion of the students who attend college drop out without earning a degree. In principle, whether a student persists to graduation depends on individual attributes and on the characteristics of the college attended; that is, a person may be more likely to drop out of one college than another college. In practice, because the same attributes that influence students' selections among colleges also influence whether they drop out, it is difficult to empirically separate the role of college characteristics from that of individual attributes. We have therefore chosen to model the relationship between individual attributes and persistence without attempting to identify the college effects statistically. Some of the relationship that we find between individual attributes and dropout probabilities may thus partly reflect differences in the characteristics of colleges attended by people with different individual attributes. Nonetheless, we believe that our findings shed considerable light on the relationship between the likelihood of success in college on the one hand and self-selection of higher education on the other. How do we proceed? First, we can only observe whether a person persists if the person first attends a college. This is analogous to the problem of observing admission decisions only for people who apply. The statistical correction required is likewise the same. Estimation of the persistence model requires that we simultaneously estimate an equation explaining college attendance. Jointly with these two, we have also estimated equations explaining the quality and cost of a person's chosen college. Thus, for a given individual, we predict here four outcomes: (1) the probability of college attendance; (2) the quality of the college attended; (3) the cost of the college attended; and (4) the probability of persisting to graduation. Our primary intent is to estimate persistence probabilities. The other outcomes are estimated jointly for statistical reasons. Nevertheless, the information provided by joint estimation is of substantial interest in its own right. For example, we are able to predict the probability that young people with a low likelihood of attendance would drop out if they were to attend. Notice that the attendance outcome discussed here is the net result of several decisions discussed in previous chapters—namely application, admission, aid award, and college selection. Our attendance equation is a

40

College Choice in America

reduced-form expression reflecting the net outcome of these different decisions, all of which are affected by the individual attributes that enter the equation. To motivate our statistical analysis, we suppose that each individual has noncollege opportunities, to which he attaches a value U0. We suppose also that if a person were to attend a college, it would be one of quality Q and cost C. These outcomes, although in large part the result of the individual's decisions, would also be affected by institutional admission and aid awards, which in turn would depend on the attributes of the individual. The individual attends college if the value U! associated with college of quality Q and cost C is greater than U0. In reduced form, both U0 and Ui are functions of individual attributes. In short, we estimate Pr(f/| > U0). TO estimate the probability of persisting in college, we suppose that the valuation of school and nonschool opportunities may change over time, partly as a result of information that people gain in college about their interests and abilities. We let the new valuation of noncollege opportunities be V0 and of college be V{. A person persists if F, is greater than V0. Since we cannot predict persistence with certainty, we estimate Pr( V, > V0). Both the attendance and persistence probabilities are estimated along with college quality and cost, all as a function of individual attributes X. For reasons of computational convenience, we use a probit model rather than a logit model for estimation in this case, as well as in the admission and aid models (see Chapter 8). The general spirit of the approach is the same as that used in Chapter 6, but the specification is chosen to facilitate estimation in this context. The procedure is analogous to that used in Chapters 4 and 5. Summary of the Sequence of Models Figure 2.1 presents in schematic form a summary of the outcomes that we have analyzed and the relationships among them. The four primary outcomes are identified by capital letters; these are the major subjects of the corresponding chapters. Grouped with the admission and persistence models are subsidiary equations that support the analyses in Chapters 4 and 8. These subsidiary equations came to be estimated as part of the statistical approach used to obtain appropriate estimates of the primary relationships. It turns out that these secondary equations, in conjunction with the primary ones, also provide information that contributes importantly to the whole of our work.

Econometric Modeling of Student Behavior 1.

Application | X

2.

College quality | Application,

3.

ADMISSION I Application, Quality,

Chapter 5

4.

AIO | Admission, X

Chapters 6, 7

5.

COLLEGE CHOICE I Admission, Aid, College characteristics, Xi

Chopter 4

41

X X

Attendance | X Quality | Attendance, X Chapter 8

Cost | Attendance,

X

DROPOUT | Attendance, X

Figure 2.1

Outline of estimated relationships.

The aid equation in the figure is specified as conditional on admission. More precisely, what we are after is the aid that a student would receive if he were to attend a given school. Indeed, the information we use is based on aid at schools students attended, and the relationship is estimated in conjunction with an attendance equation such as equation 6. To explain further the notation in Figure 2.1, consider equation 3. Here, we predict the probability of admission for a person with given attributes X in the event the person applies to a college of known quality. The individual attributes X show up in all of the relationships, although the included attributes are not precisely the same in each case. In particular, the elements of X that are incorporated in choice relationship 5 are a small subset of X and are denoted by Xx. The reason that the range of individual attributes appearing in the model of college choice is more limited than in the other models is that the college choice model emphasizes the effect of school characteristics—like tuition, aid, and quality—on the choices that individuals make. To have included a large variety of individual attributes in this context would have greatly complicated the analysis. In contrast, the admission and persistence models are much simpler in their characterization of schools. This allows greater depth in their treatment of individual characteristics. Notice also that equations 6, 7, and 8 reflect the observed "net" out-

42

College Choice in America

comes of all of the preceding behavioral relationships: they indicate for a person with attributes X what attendance, college-quality, and collegecost outcomes result from the individual and institutional decisions denoted by equations 1-5. They represent the reduced form of these behavioral relationships. The deleted attendance equation that accompanies equation 4 can also be thought of in the same way as equation 6. Figure 2.1 indicates the relationships among the analyses in the chapters that follow. Each chapter, however, is written to stand on its own; for example, our analysis of persistence can be read without reference to earlier parts of the book. This should prove helpful to the reader who wishes to focus on particular aspects of our work. The independence of the chapters is gained at the possible expense of some redundancy in exposition, but we trust that the advantages of our approach outweigh this cost.

3

From High School Graduation to School and Work

This chapter presents descriptive statistics on the postsecondary school and early work experiences of the high school class of 1972.1 The data presented reveal the proportion of youth in selected school and labor force categories in the first years after high school graduation and the major characteristics of the school and work experiences of these youth. Although the remainder of the book emphasizes schooling decisions of high school graduates, we thought it important in this chapter to present data on the experiences of out-of-school youth as well, because these experiences describe in part the alternative to schooling. We hope that this will help put in context the remainder of the book. The summary statistics reported below, based on data collected in the National Longitudinal Study, have not been adjusted to reflect population proportions. They are reported for whites and nonwhites separately, however. Both groups probably reflect more people from low-income families than would be found in a random sample from the population. In most instances, the statistics we present are disaggregated by sex and race (white versus nonwhite). The first distinction is made because women are more likely than men to spend a substantial portion of their time as homemakers and therefore are likely on average to exhibit school and work patterns different from men. We break down the statistics by race because much of the recent discussion about youth employment problems has focused on the experience of black youth relative to white youth. It is often asserted that the early school and work experiences of black youth are distinguished from those of white youth in ways that do not distinguish among subgroups of white or among subgroups of nonwhite youth. To facilitate exposition, we present summary tables in the text, with more detailed results given in Appendix A. The major descriptive findings from our analysis of the National Longitudinal Study of the High School Class of 1972 are as follows: 43

44

College Choice in America

1. These graduates by and large seem to have made a rather smooth transition to the labor force and to subsequent schooling, without substantial periods out of school and without work. 2. School and work are joint activities for many young people. Indeed, 25 percent of men in two-year colleges and in vocational-technical schools work full time. Many more work part time. 3. The vast majority of youth who go to postsecondary school enter in the first year after high school and attend only in consecutive years; sequences of alternating school and work are the exception. 4. According to standard definitions, unemployment rates among fulltime students are about twice the rates for nonstudents. A very large proportion of the youth defined as unemployed are full-time students. 5. Unemployment rates based on the National Longitudinal Study are considerably lower and employment rates considerably higher than the official Bureau of Labor Statistics figures based on Current Population Survey (CPS) data. 6. The hourly wage rates of white and nonwhite high school graduates are very close. Although nonwhites on average work fewer weeks per year than whites, by 1976 this difference was not large. 7. Weeks worked during the first year after high school graduation are not strongly related to weeks worked three or four years later; but as young people grow older, there is increasing consistency between weeks worked in one year and weeks worked in the next. 8. Young people who are out of the labor force are apparently not "discouraged" workers, for the most part. The unemployed and the out-of-the-labor force seem to be fairly distinct groups. People in School ENROLLMENT RATES

The percent of young white men that attend a postsecondary school full time is considerably higher than the corresponding percent of nonwhite men and is somewhat higher than the percent ofyoung white women who attend. Nonwhite women are somewhat less likely to be in school than white women, but are more likely to be in school than nonwhite men. In the NLS sample, the percent of youth in school part time did not vary greatly by race and sex. The percents of high school graduates in school, by race and sex, in October 1972 and October 1976 are shown in Table 3.1.

From High School Graduation to School and Work

45

Table 3.1 Percent of young people in school, by race and sex, October 1972 and October 1976. Whites

Nonwhites

Status

1972

1976

1972

1976

Men In school, full time 3 In school, part time Not in school, total

53.6 4.6 42.4

22.1 7.7 70.2

42.3 4.4 53.3

17.7 7.0 75.3

Women In school, full time 3 In school, part time N o t in school, total

51.7 4.0 44.4

13.8 7.4 78.8

47.4 5.1 47.5

16.3 6.7 77.0

a. Includes a small number of people in graduate school in 1976. Source: Appendix A, Tables 1 and 2.

A lower percent of nonwhite youth than white youth were in school; but among youth with comparable scholastic aptitude, high school class rank, and socioeconomic background, nonwhite youth were considerably more likely than white youth to go to a postsecondary school. The relevant numbers are not shown here but are detailed in Chapters 4 and 8. (See also Meyer and Wise 1979.) SCHOOL AND WORK

A large proportion of people who are in school are also working part time and a significant number are working full time. As shown in Table 3.2, about 25 percent of the fall 1972 freshmen in four-year schools worked part time. In two-year and in vocational and technical schools, the percent who worked was generally much higher, ranging as high as 45 percent for white men and women in two-year schools. Many men who were full-time students in two-year and in vocational and technical schools also had full-time jobs; for example, 24 percent of white men and 27 percent of nonwhite men in voc-tech schools. Thus, for many young people, school and work are joint activities. Although there are differences by race and sex in the percents of people who were in school and also working, the differences seem not to follow a general pattern, with the exception that fewer women than men worked full time while going to school full time. Many students were looking for work, with the percent of nonwhites who were looking being more than twice as high as the corresponding

46

College Choice in America

Table 3.2 Percent of people in school full time who are working or looking for work, by type of school and by race and sex, October 1972.a Whites Nonwhites

Type of school

Fulltime work

Parttime work

Looking for work

Fulltime work

Parttime work

Looking for work

24.0 14.2 5.1

31.8 45.2 26.5

7.8 7.3 4.4

26.8 17.0 5.9

29.9 34.4 26.5

12.4 15.2 11.2

8.1 5.8 1.5

26.3 45.2 23.6

8.7 8.7 7.2

15.3 7.0 2.6

16.4 31.4 25.9

19.7 20.2 14.9

Men Voc-tech Two-year Four-year

Women Voc-tech Two-year Four-year

a. The numbers in the rows do not add to 100 because they exclude people out of the labor force and in the military. Source: Appendix A, Tables 3 and 4. (For other years, see Appendix A, Tables 5-12.)

percent of whites. In general, the percents of two-year-college students and voc-tech students looking for work are higher than the corresponding percent of four-year-college students. For other years, the picture is qualitatively similar to that shown in Table 3.2. In October 1976, for example, even more full-time students were also working full time. Data for each October from 1973 through 1976 are contained in Appendix A, Tables 5-12. A sizable proportion of people in school would be classified as unemployed based on official definitions. Of people both in school full time and in the labor force, the percents looking for work are shown in Table 3.3. These unemployment rates are considerably higher than the rates for people out of school, as can be seen from the numbers presented in Table 3.9. For example, only 5.3 percent of the white male NLS respondents who were not in school in October 1972 were unemployed. 2 Only 5 percent of all young white men were looking for work in October 1972, and only 2 percent were both not in school and looking for work. Only 39.1 percent of those looking for work were not in school. For nonwhite men, these figures were 11.6, 5.7, and 49.1 percent respectively. Unemployment rates for the remaining October periods (1973-1976) are similar to those for October 1972 (see Appendix A, Tables 1-10).

From High School Graduation to School and Work

47

Table 3.3 Unemployment percents for people in school full time, by race and sex, October 1972." Type of school

Whites

Nonwhites

Men Voc-tech Two-year Four-year

12.3 10.9 12.2

17.9 22.8 25.7

Women Voc-tech Two-year Four-year

20.2 14.6 22.3

38.3 34.5 34.3

a. Derived from the numbers in Table 3.2.

SCHOOL ATTENDANCE PATTERNS

Most youth who go to school enter in the first year after high school and attend only in consecutive years; sequences of alternating school and work are the exception. Table 3.4 shows the percent of people who followed each possible schooling pattern. For example, the sequence 10101 indicates in school full time in October 1972, October 1974, and October 1976, but not in school full time in October 1973 and October 1975 (0.2 percent of white men followed this sequence). Although there was some movement into and out of school, it was not the norm. Of people who went to school at all, 71 percent began in the first year after high school and attended only in consecutive years. Eighty-five percent of those who attended at all attended during the year immediately after high school. Similar general observations apply to each of the race and sex groups. Among men, however, a larger percent of nonwhites than whites were never in school; the percents for white and nonwhite women are quite close, although a smaller percent of nonwhite than white women went to school for four or five consecutive years, apparently reflecting the smaller percentage of nonwhite women in fouryear colleges. A different perspective on enrollment patterns is provided in Table 3.5, which contains the percents of men attending school in each October from 1972 to 1976, by school category: four-year universities and colleges, two-year junior colleges and community colleges, and vocationaltechnical schools.3 The percentage of men in school fell steadily from 53 percent in 1972 to 40 percent in 1975, the fourth year after graduation. About 28 percent of the sample were still enrolled in school in 1976, 12

Table 3.4 Percent of youth in school full time in each October from 1972 to 1976, by sequence, sex, and race. Percent of total" Men Women Whites Nonwhites Whites Nonwhites Total Breakdown Total Breakdown Total Breakdown Total Breakdown for each for each for each for each for each for each for each for each group Sequenceb group" group group1 group group1 group1 group Mill

12.4

12.4

8.1

8.1

7.2

7.2

6.3

6.3

11110 11101 11011 10111 01111

17.8

13.2 1.3 1.1 1.2 1.0

10.4

6.3 1.2 0.6 1.3 1.0

18.3

14.8 0.9 1.2 0.8 0.6

12.0

8.5 0.9 0.8 1.2 0.6

11100

8.6

3.9 0.6 0.5 0.8 0.5 0.2 1.1 0.6 0.2 0.2

6.8

3.3 0.4 0.5 0.5 0.3 0.1 0.9 0.5 0.1 0.2

7.7

4.3 0.3 0.3 0.7 0.4 0.1 1.0 0.4 0.1 0.1

9.4

4.3 0.4 0.5 1.0 1.0 0.2 0.9 0.7 0.3 0.1

11000 01100 00110 00011 10100 01010 00101 10010 01001 10001

11.8

7.0 0.9 0.5 0.7 1.1 0.1 0.1 0.7 0.1 0.6

12.6

7.3 0.8 0.7 1.0 1.2 0.1 0.1 0.6 0.1 0.7

10.2

6.9 0.5 0.4 0.4 0.8 0.1 0.1 0.4 0.2 0.4

13.0

7.0 0.8 0.6 1.4 1.4 0.3 0.2 0.7 0.2 0.4

10000 01000 00100 00010 00001

14.4

9.2 1.6 1.4 1.0 1.2

18.3

11.2 1.7 1.9 1.5 2.0

16.6

12.3 1.8 0.9 0.7 0.9

21.0

13.2 2.6 1.8 1.6 1.8

00000

34.9

34.9

44.0

44.0

40.1

40.1

38.7

38.7

omo 00111 11010 11001 01101 10110 10011 01011 10101

Sample sized

7,659

1,492

7,863

1,967 a. Percents have been rounded to the nearest tenth. Differences between the sum of the numbers in the groups and group totals are due to rounding. b. The five digits in each sequence number correspond respectively, left to right, to October 1972, October 1973, October 1974, October 1975, and October 1976. A one in any column indicates "in school full time" for that particular month. c. The total is the percent in the group of sequences. d. We were unable to obtain sequences for 1,428 white men, 505 nonwhite men, 1,052 white women, and 392 nonwhite women.

From High School Graduation

to School and Work

49

Table 3.5 Percent of men in school, by type of school, in each October from 1972 to 1976." Type of school Year

Not in school

Total in school

Four-year

Two-year

Voc-Tech

1972 1973 1974 1975 1976

47.18 51.21 57.60 60.43 72.13

52.82 48.79 42.40 39.57 27.87

31.44 29.47 30.68 30.80 20.93

15.33 13.88 7.80 5.78 4.24

6.05 5.45 3.92 2.99 2.71

a. The total sample is 9,087.

percent of this group being graduate and professional school students. The number of four-year-college students was almost constant at 31 percent of the sample from 1972 to 1975. Apparently, the number of college dropouts was roughly offset by delayed entrants and by the transfer of junior-college students into four-year colleges in years three and four. The proportion in junior colleges fell from 15 percent in 1972 to 6 percent in 1975. The percent of men in vocational school declined modestly from 6 percent in 1972 to 3 percent in 1976. Since vocational-technical schools typically have academic programs lasting less than 2 years, this indicates that many of their students are delayed entrants. To analyze further the flows in and out of school, sequences like those in Table 3.4 are presented in Table 3.6 for men, this time grouped by time of entry and number of interruptions. Of men who attended school at all (68 percent of the total), 65 percent entered right after high school and attended without interruption, while another 20 percent delayed entry by one or more years but attended without interruption once entered. In addition to those who delayed entry, a significant number of those who attended interrupted their schooling for one or more years—9 percent for a single year and 6 percent for more than one year. Table 3.7 examines the relationship between delayed entry and school category. "School track" is defined as the type of school first entered by the individual, if the person decides to attend. School track differed from the postsecondary alternative in 1972 to the extent that an individual delayed school attendance. While 45 percent of young men in the vocational-technical track delayed entry by one or more years, 26 percent delayed in the junior-college track. Only 13 percent of the individuals in the four-year-college track delayed entry. In aggregate, of men not in school

50

College Choice in America

Table 3.6 Percent of young men in school, by sequence and group, in each October from 1972 to 1976. Sequence3

Percent of totalb

Group percentb

00000

32.2

32.2

Never in school

10000 11000 11100 11110 11111

6.5 6.5 3.7 11.4 15.7

43.8

Continuous attendance

01000 01100 01110 01111

2.3 1.3 0.9 1.6

6.2

Delayed entry of one year, continuous attendance

00100 00110 00111 00010 00011 00001

1.7 0.8 0.8 1.3 1.2 1.8

7.7

Delayed entry for two or more years, continuous attendance

10100 10110 10111 11010 11101

1.0 0.7 1.0 1.0 1.2

6.3

Single-year interruption

00101 01001 01010 01011 01101 10001 10010 10011 10101 11001

0.2 0.2 0.2 0.2 0.3 0.6 0.5 0.7 0.1 0.8

3.9

Multiple-year interruptions

Group

a. The five digits in each sequence number correspond respectively, left to right, to October 1972, October 1973, October 1974, October 1975, and October 1976. A one in any column indicates "in school full time" for that particular month. b. Percents have been rounded to the nearest tenth. The total sample is 9,087.

From High School Graduation to School and Work Table 3.7 track. 3

51

Percent of young men who delayed entry to postsecondary school, by

Track

Percent of males in track

Percent in school in 1972

Percent not in school in 1972

11.0

55.2 74.2 87.0 0.0

44.8 25.8 13.0 100.0

Voc-Tech Two-year Four-year Never in school

20.7 36.1 32.2

a. Total sample size is 9,087.

in October 1972, about 32 percent eventually attended some type of school. To some extent, the school sequence data may understate the movement in and out of school, since they do not incorporate changes in academic status during the school year. Some evidence for this is provided by examining the percentage of individuals with sequence patterns 11111 and 11110 who did not obtain an academic degree. About 71 percent of the first group and 26 percent of the second group did not obtain a fouryear-college degree. Thus, a substantial number of individuals exhibit much slower academic progress than is commonly assumed. Unobserved movements in and out of school may contribute substantially to slow academic progress. (Even measured years of school may overstate actual school attainment, defined in terms of a measure of academic progress such as accumulated credit hours.) Furthermore, many people who enter postsecondary schools do not obtain a degree. As of October 1976, in addition to the number of students who had been in school for five consecutive October periods without obtaining a degree, many others had dropped out without obtaining a degree. For example, of people who entered four-year colleges and universities in fall 1972, approximately 20 percent had not obtained a B.A. degree by October 1976 and were not in school at that time. People Not in School LABOR FORCE STATUS

Only a small proportion of NLS respondents not in school were looking for work. The unemployment ratios implied by this survey are much lower than the official government unemployment rates based on Current Population Survey data.

52

College Choice in America

Table 3.8 Percent distribution of people not in school, by labor force status and by race and sex, October 1972 and October 1976. Whites Nonwhites Status

1972

1976

1972

1976

Men Working full time Working part time Military Out of labor force Looking for work Total not in school

71.9 9.2 7.7 6.6 4.6 42.4

80.1 4.1 7.4 2.7 5.7 70.2

60.1 11.4 8.8 9.0 10.7 53.3

71.9 5.1 12.1 4.1 6.9 75.3

Women Working full time Working part time Military Out of labor force Homemaker Not homemaker Looking for work Homemaker Not homemaker Total not in school

59.3 13.5 0.4 18.7 9.2 9.5 8.3 1.6 6.7 44.4

61.7 9.7 1.0 22.0 19.8 2.2 5.6 2.8 2.8 78.8

43.8 12.4 0.8 22.5 6.8 15.7 20.5 4.1 16.4 47.5

61.0 7.9 1.4 18.8 15.3 3.5 10.9 5.3 5.6 77.0

Source: Appendix A, Tables 1 and 2. More detail can be found in Appendix A, Tables 1-12.

While the percent of youth not in school rose very substantially between October 1972 and October 1976, the percent of out-of-school youth who were working full time increased significantly, and the percent of out-of-school youth who were working part time or who were out of the labor force fell dramatically (Table 3.8). The percent looking for work also declined for three of the four sex-race groups, the exception being young white men. The percents of both white and nonwhite men working part time had by 1976 fallen to less than half their 1972 levels, as had the percents out of the labor force. The percents of nonwhite men in these categories were in general higher than the percents of white men, but the differences decreased over time. Specifically, in October 1972 the percent of nonwhite men looking for work was more than twice as high as the percent of white men in this category. In 1976 the unemployment rates for white and nonwhite men were quite close—5.7 percent for whites and 6.9 percent for nonwhites.

From High School Graduation to School and Work

53

The percent of women working part time also declined over the period, but not as much as the percent for men. The percent of women who were out of the labor force and not homemakers, however, fell to about onefourth its 1972 level over the four-year period. At the same time, the percent who were homemakers increased by a factor of two. The total number of women out of the labor force did not change greatly over the period, the percent of white women increasing a bit and the percent of nonwhite women decreasing slightly. While a larger percent of women than men were looking for work, a large proportion of the women who were looking also were homemakers. In 1972 the percent of nonwhite women looking for work was about 2.5 times that for white women. By 1976, the racial gap had closed somewhat, but not nearly as dramatically as it had for men. These numbers suggest a rather consistent progression from school to work. On average, nonwhite youth get full-time jobs less quickly than do white youth; but after four years the differences between white and nonwhite youth by these measures are not striking. By October 1976, a little over four years after high school graduation, only 5.8 and 6.9 percent respectively of white and nonwhite men who were not in school were looking for work. Of women not in school, 2.8 percent and 5.6 percent of whites and nonwhites respectively were nonhomemakers looking for work. The percents of all youth, counting those in and out of school, were 5.7 and 7.6 respectively for men and 2.2 and 4.3 respectively for women. Youth unemployment does not appear from these data to be a severe problem for this group of high school graduates. COMPARISON WITH CPS DATA

The unemployment rates implied by the NLS data are considerably lower than the commonly quoted rates based on Current Population Survey data, and the NLS "proportion employed" figures are substantially higher. Traditional labor force statistics for 1972 and 1976 for NLS respondents not in school and not in the military are shown in Table 3.9. Although it is impossible to provide for each year a direct comparison between these numbers and those based on the Current Population Survey, it is possible to do so for 1972. In October 1972 the Census Bureau conducted a special survey of spring 1972 high school graduates. (See U.S. Department of Labor, Bureau of Labor Statistics 1973, p. 27). A comparison of unemployment and other labor force statistics (in percent) for

54

College Choice in America

Table 3.9 Labor force statistics in percent, by race and sex, for people not in school and not in the military, October 1972 and October 1976. Whites Nonwhites Status

"1972

1976

1972

1976

Men Employed In the labor force Unemployed

88.0 92.9 5.3

90.0 97.2 6.5

78.4 90.2 13.0

87.5 95.3 8.1

Women Employed In the labor force Unemployed

73.1 81.3 10.0

72.1 77.8 7.3

56.7 77.3 26.7

69.9 80.9 13.6

Source: Appendix A, Tables 1 and 2.

young men based on the two data sources is presented in Table 3.10, for people not in school. An investigation of the definitions used in the two surveys does not reveal any differences—other than those in the wording of the questions— that would suggest such apparently contradictory results. The fact that the NLS survey is weighted to oversample low-income youth should tend to raise implied unemployment rates, not lower them. The survey respondent, however, who was the individual in the NLS survey, was likely to be the mother or father of the person in the CPS survey. The NLS data were collected through a mailed questionnaire (together with some mail and telephone reminders), whereas the CPS data were obtained by interview with a household member, often the female head. Freeman and Medoff (1979) found that a large portion of the difference between the CPS numbers and those based on the U.S. Department of Labor's National Longitudinal Survey can be attributed to the different respondents.

Table 3.10 Comparison of NLS and CPS employment and labor force statistics for young men, October 1972 (in percent).

Status Employed In the labor force Unemployed

National Longitudinal Study Whites Nonwhites 88.0 92.9 14

78.4 90.2 110

Current Population Survey Whites Nonwhites 81.5 91.6 1_L0

68.0 88.0 22.7

From High School Graduation to School and Work

55

NONWORK AND NOT-1N-SCHOOL SEQUENCES

The statistics reported above do not reveal high rates of unemployment, on average. This, of course, does not preclude the possibility that there are some youth who are chronically unemployed. For a worst-case analysis, we have grouped together the people out of the labor force with those unemployed. We term this a worst-case analysis because data presented below suggest that people out of the labor force should be distinguished from the unemployed; they apparently are not "discouraged" workers. Among these high school graduates, being out of school and chronically unemployed is surely the exception. Table 3.11 details the percent of young people not in school and not working (in either civilian or military jobs) for each possible number and sequence of time periods; these data are analogous to those presented in Table 3.5, but they pertain to periods of unemployment rather than school attendance. Examination of Table 3.11 reveals that 81 percent of young men were never out of school and without work in an October period. (The data pertain to the first full week in October of each year.) Less than one-tenth of one percent were out of school and not working in all five of the periods. For whites and nonwhites together, this represents 5 people out of 9,115. Three-tenths of one percent were in this category in 4 out of the 5 periods, and one-tenth of one percent in 3 out of the 5. Only 14 percent experienced one idle period. More nonwhites than whites were in this status for one, two, three, and four periods; but over 72 percent of nonwhites were never out of school and without work in these October periods. Many more young women than young men were neither in school nor working, presumably because a substantial number of women were homemakers who were not looking for work. Table 3.12 presents the percent of people not in school and unemployed (looking for work) for each possible sequence and number of periods. Eighty-two percent of all women were never in this classification and only 6 percent were so classified in more than one of the five periods. Although somewhat larger percents of nonwhite than white women were out of school and looking for work, only 10 percent were in this classification in more than one of the five periods. WAGE RATES AND OTHER EMPLOYMENT DATA

For white and nonwhite high school graduates, the hourly wage rates and weekly hours worked are very close. If anything, nonwhites tended to earn

56

College Choice in America

Table 3.11 Percent of youth not in school and not working, in each October f r o m 1972 to 1976, by sequence, sex, and race. Percent of total a Men Women Nonwhites Whites Nonwhites Whites

Sequence b

Total Breakdown Total Breakdown Total Breakdown Total Breakdown for each for each for each for each for each for each for each for each group 0 group group 0 group group 0 group group 0 group

11111

0.1

0.1

0.1

0.1

2.4

2.4

3.0

3.0

11110 11101 11011 10111 01111

0.1

0.0 0.0 0.0 0.0 0.1

0.5

0.3 0.1 0.0 0.1 0.4

4.2

0.5 0.3 0.4 0.8 2.2

5.3

1.0 0.7 0.7 0.6 2.3

11100 OHIO 00111 11010 1I00I 01101 10110 10011 01011 10101

0.8

0.1 0.1 0.2 0.0 0.1 0.0 0.0 0.1 0.1 0.1

2.0

0.6 0.1 0.5 0.0 0.3 0.0 0.2 0.3 0.1 0.0

5.5

0.5 0.6 2.3 0.2 0.2 0.5 0.2 0.4 0.4 0.2

8.4

2.0 0.4 2.3 0.4 0.4 0.5 0.8 0.4 0.5 0.7

11000 01100 00110 00011 10100 01010 00101 10010 01001 10001

3.1

0.6 0.0 0.4 0.0 0.3 0.1 0.3 0.1 0.2 0.2

6.3

1.0 1.0 0.9 0.7 0.4 0.1 0.9 0.5 0.4 0.3

9.5

1.0 1.0 1.2 2.8 0.6 0.5 0.9 0.3 0.5 0.7

12.0

2.0 1.6 1.2 2.4 1.0 0.7 1.1 0.5 0.6 0.9

10000 01000 00100 00010 00001

13.2

2.3 1.8 2.5 2.3 3.9

18.6

5.4 2.5 3.9 3.2 3.7

18.5

2.8 2.5 3.3 3.2 6.7

23.0

5.0 4.8 4.8 3.1 5.4

00000

82.7

82.7

72.2

72.2

60.0

60.0

48.4

Sample sized

7,639

1,475

7,847

48.4 1,956

a. Percents have been rounded to the nearest tenth. Differences between the sum of the numbers in the groups and the group totals are due to rounding. b. The five digits in each sequence number correspond respectively, left to right, to October 1972, October 1973, October 1974, October 1975, and October 1976. A one in any column indicates "not in school and not working" for that particular month. c. The total is the percent in the group of sequences. d. We were unable to obtain sequences for 1,448 white men, 522 nonwhite men, 1,068 white women, and 403 nonwhite women.

From High School Graduation to School and Work

57

Table 3.12 Percent of youth not in school and unemployed, in each October from 1972 to 1976, by sequence, sex, and race. Percent of total" Men Women

Sequence b

Whites Nonwhites Whites Nonwhites Total Breakdown Total Breakdown Total Breakdown Total Breakdown for each for each for each for each for each for each for each for each group 0 group group 0 group group 0 group group 0 group

11111

0.0

0.0

0.0

0.0

0.0

0.0

0.2

0.2

11110 11101 11011 10111 01111

0.0

0.0 0.0 0.0 0.0 0.0

0.4

0.2 0.1 0.1 0.0 0.0

0.0

0.0 0.0 0.0 0.0 0.0

0.5

0.1 0.1 0.2 0.0 0.1

11100 omo 00111 11010 11001 01101 10110 10011 01011 10101

0.1

0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.5

0.0 0.0 0.1 0.0 0.0 0.1 0.1 0.1 0.1 0.0

0.3

0.0 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.0

2.4

0.4 0.3 0.2 0.1 0.1 0.3 0.3 0.3 0.3 0.2

11000 01100 00110 00011 10100 01010 00101 10010 01001 10001

1.4

0.2 0.2 0.3 0.3 0.1 0.0 0.2 0.0 0.0 0.1

3.9

0.2 1.0 0.7 0.7 0.3 0.1 0.6 0.2 0.0 0.1

2.2

0.4 0.3 0.3 0.2 0.3 0.1 0.2 0.1 0.1 0.2

7.7

1.6 1.0 0.5 1.3 0.5 0.5 0.5 0.6 0.6 0.5

10000 01000 00100 00010 00001

9.4

1.3 0.8 2.4 1.8 3.1

15.5

3.9 1.5 4.3 2.8 3.0

12.7

2.5 2.1 2.7 1.9 3.5

19.1

4.5 3.7 4.1 2.7 4.1

00000

88.8

88.8

79.8

79.8

85.0

85.0

70.7

70.7

Sample size

d

7,639

1,475

7,847

1,956

a. Percents have been rounded to the nearest tenth. Differences between the sum of the numbers in the groups and group totals are due to rounding. b. The five digits in each sequence number correspond respectively, left to right, to October 1972, October 1973, October 1974, October 1975, and October 1976. A one in any column indicates "not in school and unemployed" for that particular month. c. The total is the percent in the group of sequences. d. We were unable to obtain sequences for 1,448 white men, 522 nonwhite men, 1,068 white women, and 403 nonwhite women.

58

College Choice in America

Table 3.13 Average hourly wage rates, weekly earnings, and weekly hours worked for people working in October, by school status, sex, and race, 1972 and 1976.a Men Item and race

Out of school 1976 1972

Women In school 1972 1976

Out of school 1972 1976

In school 1972 1976

Hourly wage rate (in dollars) Whites Nonwhites

2.72 2.71

4.63 4.37

2.34 2.52

4.04 4.02

2.14 2.54

3.67 3.56

1.96 2.30

3.49 3.53

Weekly earnings (in dollars) Whites Nonwhites

111.08 102.78

197.41 176.50

61.03 69.04

127.21 140.47

78.25 79.94

139.19 134.35

41.99 46.94

97.84 109.31

41.65 39.57

43.22 41.22

26.18 28.23

30.64 33.49

37.33 35.73

37.97 38.22

21.67 21.68

27.64 30.59

Weekly hours worked Whites Nonwhites

a. The data pertain to the first full week in October. Source: Appendix A, Tables 13 and 14.

a bit more per hour than whites. This is true in particular for women in the first years after high school graduation, and for young men who were in school. But because nonwhite men who were out of school worked somewhat fewer hours per week on average than white men, their weekly earnings were somewhat less than the weekly earnings of out-of-school young white men. Average hourly wage rates, weekly earnings, and weekly hours worked for people not in school and for those in school are shown in Table 3.13. They cover all people in the sample who were working in the first full week of October of the year indicated. People working full time or part time are included. Wage rates for white and nonwhite men out of school are virtually identical right after graduation. After four years, whites earned about 6 percent more per hour than nonwhites, presumably due at least in part to the different schooling patterns of the two groups and post-high-school work experience. Nonwhites also worked about 2 hours per week less than whites in each of the time periods and thus had lower weekly earnings—about 8 percent in the first year and 11 percent after four years. On the other hand, nonwhite men who were in school worked 1.5-3 hours per week more than whites, earned somewhat more per hour in all but the

From High School Graduation to School and Work

59

last period, and had higher weekly earnings in each of the periods—between 5 and 19 percent, depending on the period. Young nonwhite women who were out of school earned 19 percent more than out-of-school white women during the first year after graduation, but somewhat less than white women after four years. Similar relationships exist between white and nonwhite women in school, but even in 1976 nonwhite women earned more than white women who were in school. Average annual weeks worked, weeks looking, weeks out of the labor force, and number of employers, by school status, are shown in Table 3.14. Nonwhites worked fewer weeks per year than whites, but the difference declined continuously over the four-year period. White women worked fewer weeks and spent less time looking for work than did white men. Nonwhite women also worked fewer weeks than nonwhite men, but in general spent more weeks looking for work than did their male counterparts. DOES EARLY EXPERIENCE PERSIST?

There is only a weak relationship between weeks worked in the first year or two after graduation from high school and weeks worked two or three years later; but as young people grow older, there is increasing consistency between weeks worked in one year and weeks worked in the next. To describe the observed relationship between weeks worked in the first four years after graduation from high school, we constructed a series of transition matrices. For each year we classified weeks worked into four intervals: 0 to 20, 21 to 40, 41 to 51, and 52. For each pair of years we calculated the transition probabilities of moving from an interval in the earlier year to each of the intervals in the second year. These probabilities are presented in Tables 3.15, 3.16, and 3.17, with the entries shown as percents. For example, in Table 3.15 the matrix headed "1974-75" says that 69 percent of the out-of-school young men who worked 52 weeks in 1974 also worked 52 weeks in 1975; 5 percent worked between 0 and 20 weeks in each of these two years. The rows of numbers below and to the left of each matrix are marginal proportions (percents). In 1974, for example, according to Table 3.15, 49 percent of young men worked 52 weeks. All entries have been rounded to the nearest percent. 4 The transition matrices reveal several phenomena. Looking first at the results for all men (Table 3.15), it can be seen that the upper bound on weeks worked is reflected in the large probabilities of remaining in the

6 a

[n school

a

T3 « aj

c

O jtf u

u 6 o

£

3 O « .M u u * 0 Xu, Zy, Z2j, Zip e,j),

where F*,is the aid offered to student i from college j; Xu, Z ly are needrelated attributes of student i and school j respectively; X2i, Z2J are meritrelated attributes of student / and school j respectively; X3i, Z3y are other relevant student and school attributes; and e,y captures unmeasured attributes of individuals and colleges. For empirical simplicity we have chosen to work with a functional form linear in parameters: 3

(2)

F*j = H (Xkialk + Zkja2k) + e,y k= 1

The Allocation of Discretionary Grant Aid

95

The coefficients should be thought of as weights assigned by aid administrators to individual attributes in the determination of aid offers. If equation (2) is to be interpreted as a behavioral relationship describing aid offers in the population, then two statistical concerns must be addressed before estimating it from the NLS sample. One is that aid offers are recorded only for students that attend college. The other is that aid offers are constrained to be nonnegative. We expect that the decision to attend college will be based in part on the actual aid offer a student receives. As a consequence, individuals with large aid offers or, what is more important, large positive disturbances in the aid equation tend to self-select into our sample of observed aid offers more often than do other students. Thus, E (F*\a = 0, X, Z) < E(F*\a = 1, X, Z), where a = 1 denotes college attendance, a = 0 denotes no attendance, and E( ) denotes the mathematical expectation operator.9 In other words, after controlling for measured characteristics, we expect the aid offers of students attending to exceed those of students who choose not to attend. Failure to account for this phenomenon will lead to biased estimates of the aid-function parameters. This problem can be overcome by estimating an attendance equation jointly with the aid function. 10 We can motivate the attendance equation by supposing that without college education, a high school graduate with attributes X faces opportunities to which he attaches a value U0 dependent on X, such that U0 = Xa0 + e0, where a0 is a vector of parameters and e0 is an error term representing the collective contribution to U0 of unmeasured attributes. Suppose also that the value associated with college attendance is represented by U t , which can be related to individual attributes according to the relationship £/, = Xax + ex. A person is assumed to attend college if t/, is greater than U0. The probability of attendance is given by (3)

P r ( t / , - U0>0) = Pr[*(a, - a0) + (e, - e0) > 0] = Pr(^i = Xfi + e, > 0),

where A, /?, and e are defined by the last equality.11 The second estimation problem involves the lower limit of zero on aid offers. In our case, the lower limit is nontrivial and regression estimation

96

College Choice in America

will yield biased parameter estimates. 12 To overcome this problem, we reinterpret F* as an unobserved "potential" aid offer and define F to be the observed aid offer, where

l0if^0, F= F*) = Pr( £ l < X/3\F*)- ^ 4> (

=

$

Xß + p/a(F* - Xct 1 - Za2)] 7(IV)

1

(F* — Xax — Za2 \

\'ö*(

where (j> is the univariate standard normal density, c.

j

Student attends college and receives no aid:

i

]'

The Allocation of Discretionary Grant Aid

97

p3 = Pr(A > 0, F = 0) = Pr(e, < Xfi and e2 < - Xat - Za2) x r p tK^i+z^)/"] = / 2(£I. e2\ P)de2deu —00 —00 where e2 = e2/a and 2 denotes the standard bivariate normal density. The log-likelihood of the sample is given by: N, N2 Ny L = 2 In/?,, + 2 \np2i + 2 \npih i=l i=l i=i where the summations are over the relevant subsamples of observations. Maximization of L yields estimates of /?, a,, a2, p, and a.13

Data This analysis is based on a random sample of 4,885 NLS respondents. We define discretionary financial aid as the combined support from the sources listed in Table 5.1. We selected these sources for two reasons: they are all cash-grant programs, and the delivery system for each permits some latitude in the disbursing agency's choice of recipient. Within our sample 1,800 students (37 percent) attended either a twoyear or a four-year college in the first year following high school graduation; 1,292 (72 percent) of these students attended four-year colleges. Among students attending four-year colleges, 456 (35 percent) received aid offers. At two-year colleges the corresponding figure was 125 (25 percent). Table 5.1 indicates that the largest source of aid was internal college funds. However, since many types of aid (particularly SEOGs) are externally funded but delivered by colleges, many NLS respondents may be unaware of the true source of their funds. There is also some confusion with respect to the EOG Program category. The NLS questioned students on support from both the BEOG Program and the SEOG Program. A number of students indicated that they were receiving aid from the BEOG Program, despite the fact that it was not funded until the following year. Since the titles are quite similar ("Supplementary" was added to

oc NO

r»

« ¡»

1/1 OO OO

eoS ta o Ö

f» o

2 S œ o U u •ea t>

a ta ot>

3 O CA

È» o oo u

M O

U

'S " jÄ » U

ê JS 1

Lm

*

8

_

Ûû & U

s o

s i«

1

2 1

«S3

S

UJ

o

z

CA e a. o 'cA 13 cA CA U< ta s tfi « t-i i o 60 J2 "o JS « O u CA i û , « U2 " s i> u » S « 3 È 55
100 12. (a - 100) if a > 100

0.00258 0.00305 0.00325 -0.00197

(6.3) (2.7) (2.9) (-4.3)

High school effect (0-100) 13. If college, percent of class at student's high school who go on to college 14. If voc-tech school, percent of high school class who go on to voc-tech school Alternative-decision-maker dummies (0-1) 15. Four-year college, private control 16. Four-year college, student lives at home 17. Two- or four-year college, black student 18. Two-year college 19. Voc-tech school program under a year 20. Voc-tech school program over a year 21. Voc-tech school, industrial trades, male student 22. Work alternative 23. Military alternative 24. Homemaker alternative 25. Part-time school and work alternative

0.0156

(6.2)

0.0214

(4.0)

0.169 -1.03 -0.980 -2.83 -5.01 -4.15 1.23

(0.8) (-5.4) (-5.0) (-14.3) (-16.5) (-14.8) (6.9)

-1.54 -3.15 -3.01 -3.48

(-5.3) (-13.8) (-12.2) (-14.6)

a. When a condition is not satisfied (for example, if the alternative is not a four-year college in variable 1, or a > —100 in variable 9), the variable takes the value zero. Sample size = 4,000. Log-likelihood at maximum = —4,861. Log-likelihood when parameters are set equal to zero = —9,742. b. a = average SAT of people choosing the alternative, minus the student's SAT. The SAT range is 400-1,600.

114

College Choice in America

components should be equal, and also that the effect of cost should be invariant across schooling types. On the other hand, it has on occasion been suggested that students use tuition, and perhaps dormitory cost, as indicators of institutional quality. If so, then the tuition coefficient should be smaller in absolute value than the one relating to scholarships. An opposing argument asserts that colleges tend to reduce scholarship aid to sophomores, juniors, and seniors. Hence, the amount of a freshman award should be devalued in selecting among schools, implying a smaller scholarship coefficient than tuition coefficient. The above hypotheses cannot be separately tested with our data, but we can admit their possible validity by not constraining the various cost coefficients to be equal. What we find is that, with one exception, the estimated coefficients are roughly similar." In particular, the tuition, dormitory-cost, and scholarship parameters associated with four-year colleges are close to one another and close to the tuition estimates for two-year colleges and vocational-technical schools. The anomaly is the two-year college scholarship coefficient, which is much larger in absolute value than any of the others. A convincing structural interpretation of this last finding is not readily available. A type of living cost not directly expressible in dollar terms is the commuting cost a college-going student faces if he lives at home rather than on campus. In our model, this cost is represented by home-to-college straight-line distance. Since commuting expenses are incurred more in time than in money, we chose not to allow the distance variable to interact with family income. For reasons having to do with our placement of local, open enrollment, two-year colleges and technical schools in the choice set, the distance variable is confined to four-year schools in the estimated model. The estimated effect of distance is negative and statistically significant but quite small in magnitude. In fact, under reasonable assumptions about the out-of-pocket costs of commuting, travel speeds, and numbers of trips made per month, the implied value of travel time is under one dollar per hour for all income levels except the highest. So low a value does not seem plausible to us and may point to inadequacies in straight-line distance as a proxy for travel costs.12 FORGONE EARNINGS

As anticipated, increases in expected forgone earnings detract from the desirability of schooling activities or, symmetrically, add to the utility of labor force participation. It is interesting to compare the effects of an extra dollar paid in tuition and an extra dollar forgone in earnings. For a

Selecting a Postsecondary School

115

student with a $10,000 family income (in 1972 dollars), an increase of one dollar per month in tuition at a four-year college lowers the utility of that college relative to the utility of working by .00536 units; for someone with a $30,000 family income, the drop is .00179 units. On the other hand, an increase of one dollar in expected monthly earnings raises the utility of working relative to the utility of the school by .00206 units.13 Thus, the tuition and expected-earnings effects are roughly comparable, the former being larger for most students. P E R F O R M A N C E S T A N D A R D S A N D S T U D E N T ABILITY

In Table 6.1, variables 9-12 constitute the piecewise linear form used to relate individual academic aptitude and school performance standards to utility. Figure 6.1 gives a visual display of the function. We find that for a student with given ability, A, the utility of an alternative first increases fairly linearly with its performance standard, Q, but eventually turns down. To determine the precise location of the optimal standard would require experimentation with alternative breakpoints for the piecewise linear function or, alternatively, use of a function with more kinks. It is, however, clear that the optimum lies somewhere above the student's own ability level. The credentials and human capital arguments that motivated us to propose that increases in Q have two opposing effects on future earning prospects do not necessarily imply that, for given A, utility should first

Utility

- -.325

Figure 6.1 Utility to a student with ability A of an activity with performance standard Q. (The utility scale is normalized so that utility equals zero when Q = A.)

116

College Choice in America

increase and then decrease as a function of Q. The unimodal pattern we detect seems quite plausible, however. This result suggests that in the absence of institutionalized college admission procedures, students seeking postsecondary education would nonetheless self-select into ability-similar groups.14 OTHER VARIABLES

The remaining explanatory variables in the estimated model are a set of "effects" represented in (5) by the parameters y. We find that, all else equal, the probability that a student will go to college or vocational-technical school rises with the percentage of his high school classmates doing likewise. This result may indicate a peer group effect, may be a proxy for high school attributes that influence all students in a school, or may simply reflect a tendency for students in the same high school to have similar unobserved attributes relevant to the postsecondary activity decision. Among the dummy variables 15-25 in Table 6.1, we find that, all else equal, students tend to prefer privately controlled four-year colleges to other postsecondary activities. The negative coefficient on variable 16 is a proxy for the room and board costs of living at home, for which we have no direct measure, and for the nonmonetary differences between living in a dormitory and living with parents. The positive coefficient on variable 21 indicates that, given application and admission, men are more likely to enroll in industrial trades programs than are women.15 Conclusion In the KMM study of college-going behavior, the authors pointed to a number of data and econometric problems which they felt detracted from their empirical results. The present analysis essentially solves all of those problems but also raises some new questions. On the one hand, numerous extensions of applied importance remain. For example, the researcher interested in occupational-choice behavior will want to recognize that educational institutions vary not only in performance standards but in the substance of their programs of study. The educational economist may wish to investigate further the high school effects we have found, to determine whether they represent causal effects or only spurious correlations. In addition to extensions, several questions arising from the temporal context of student decision making could in principle be taken into ac-

Selecting a Postsecondary School

117

count. One problem, conventionally termed "selection bias," is implicit in our modeling of postsecondary choices conditional on the past decisions of students and schools. Our model regards college application sets, institutional admission decisions, and student high school performance as statistically predetermined variables with respect to the postsecondary choice problem. 16 We are well aware that these prior decisions and the unobserved determinants of postsecondary choices may be statistically dependent, thus falsifying the assumption of predetermination. At the same time, we wish to investigate postsecondary behavior without having to model students' entire histories. How the reality of selection bias and the practical requirements of empirical analysis are best balanced is not clear. The dilemma is analogous to that encountered in partial-equilibrium modeling of market operation. That is, where should one draw the system boundaries? A second question concerns the relation between the student's postsecondary choice and his future. One aspect of this question, discussed above, asks how students form expectations about the future consequences—particularly earnings consequences—of their postsecondary decisions. Since expectations are themselves unobserved, our choice model must implicitly incorporate the expectation process. Empirical analysis then constitutes a joint test of the choice model and the model of expectation formation. Another issue regards the structural relation between the students' postsecondary choices and their subsequent career-related decisions. Our model formally views the postsecondary choice in isolation rather than as an element of a plan. It might be argued that the idea of a plan is in the background, that our model can be interpreted as describing the first step in an optimal plan. But substantiation for such an argument is lacking. The above issues notwithstanding, we feel that the analysis in this chapter provides the basis for forecasting applications.

Enrollment Effects of the BEOG Program

The role and scope of federal student financial aid activities have been periodically debated and revised. In the late 1950s a post-sputnik drive to increase the nation's stock of scientific manpower motivated the formation of the National Defense Student Loan Program. In the mid-1960s a desire to equalize educational opportunities across income classes became prominent. The Basic Educational Opportunity Grant Program, initiated in 1973, gave fullest expression to this policy goal. Also recognized in the mid-sixties was the liquidity burden placed on middleincome families as a result of the unwillingness of the private capital markets to finance educational investments. In an effort to induce private-sector lending for educational purposes, the Guaranteed Student Loan (GSL) Program was enacted. During the 1970s, the institutional framework of federal aid policy remained stable.1 On the other hand, the relative magnitudes of the various programs changed and total federal involvement grew. In particular, the B E O G and G S L Programs became dominant aid instruments as, over time, benefits under both programs were extended to higher-income groups.2 This liberalization of eligibility criteria reflected a shift in the emphasis of policy away from the provision of equal opportunity to students from low-income families and toward the easing of the perceived burden of educational expenditures on middle- and upper-income families. Whatever purposes federally sponsored aid "should" serve, policy evaluation is facilitated by knowledge of the impacts that existing programs have. Our intent in this chapter is to contribute to such knowledge by providing an analysis of the effects of the B E O G Program on freshmen enrollments in the 1979-80 academic year. Given conditions paralThe authors of this chapter are Winship C. Fuller, Charles F. Manski, and David A. Wise.

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Enrollment Effects of the BEOG Program

119

leling those of 1979-80 except that no BEOG Program exists, how would the magnitude and mix of enrollments compare to those actually expected?3 In brief, we estimate that in the absence of BEOG awards 17 percent fewer low-income students would enter postsecondary schools, but that the enrollment rates of middle- and upper-income students would be within 5 percent and 1 percent, respectively, of their current levels.4 The persuasive evidence that only the behavior of low-income students is sensitive to the existence of the BEOG Program would be of little policy interest if the receipt of awards were limited to the low-income group. However, we estimate that fully 40 percent of the one billion dollars in BEOG money awarded to freshmen in 1979-80 was received by students in the middle- and upper-income categories. Thus, a very significant fraction of the BEOG budget is spent as a pure subsidy. Our estimates of these and other impacts of the BEOG Program are obtained using our econometric model of student choice among postsecondary school and work activities, described in Chapter 6. Forecasting with the Model PROCEDURE

Our estimated model of college-going behavior may be used to forecast if and how a given student admitted to a given set of colleges would react to changes in the cost of enrollment at those schools. Applied to a sample representative of the national population, predictions of aggregate enrollment impacts can be produced. The forecasts reported in this chapter are obtained by applying the model to the NLS respondents, suitably weighted so as to represent the population of 1979 high school seniors. The need for weighting of the NLS sample arises because the NLS is a stratified sample of seniors in 1972, with overrepresentation of lowincome and minority groups. To use this sample to predict national enrollment patterns in 1979-80, we obtained the most recent data available characterizing the national population of seniors by race, region, community type, parental education, and family income. Respondents in the NLS sample were then weighted so that the distribution of characteristics in the weighted sample matched that of the national population. 5 Aspects of student behavior beyond those described in the model may be affected by the availability of BEOG awards. In particular, the presence or absence of a BEOG Program may influence the set of schools to

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which a student applies. It must be pointed out that in our forecasting procedure, the sets of schools assumed available in 1979-80 are the actual schooling sets of 1972 NLS respondents. Thus, we implicitly ignore any effect of the BEOG Program on application decisions. Likewise, college admission decisions are implicitly assumed to be insensitive to the existence of BEOGs.6 The ultimate effect of BEOG availability on the scholarship that a given student obtains when attending a given school depends on how college financial aid offices, state student assistance programs, and other aid suppliers react to the existence of an award.7 That is, we need to ask to what extent BEOG awards complement or substitute for aid from other sources. In the absence of evidence on this important question, we have generated forecasts under two alternative assumptions. One is that BEOG awards are simply added to aid from other sources. The other is that such awards do not affect aid from state and private sources but substitute for college-given aid. In the former case, an NLS respondent's hypothesized 1979-80 scholarship aid is taken to be his 1972 aid plus any BEOG award for which he is eligible. In the latter case, the net scholarship aid is his aid from state and private sources, plus his 1972 collegegiven award or estimated BEOG award, whichever is larger.8 A PREDICTIVE TEST

Before beginning our analysis of BEOG impacts, we subjected our forecasting approach to a serious test—that is, to an assessment of its predictive ability in a context significantly different from that faced by the 1972 NLS respondents. To do so, we obtained the most recent available national statistics on postsecondary activity choices and on freshman BEOG recipients, these being for the high school class of 1977.9 These data could then be compared with our predictions for the 1977-78 academic year.10 Table 7.1 displays the distribution of activity choices made by the NLS respondents, the actual 1977 national distribution, and our predicted 1977 national distribution. Comparison of columns 2 and 3 shows that our predictions using the estimated coefficients (the unbracketed numbers) are generally quite close to the mark. In particular, we predicted that 49 percent of the student population would enroll as full-time students and that 44 percent would enter the labor force; the actual numbers were 48 percent and 44 percent, respectively." The major discrepancies between predicted and actual levels are overprediction of the fraction of

Enrollment Effects of the BEO G Program Table 7.1

121

Distributions of postsecondary activity choices in 1977. NLS 1972 respondents (1)

Actual 1977 national population 3 (2)

Four-year college

.21

.21

.24 .24

[.25] [.25]

Two-year college

.13

.22

.16 .17

[.12] [.12]

Voc-tech school

.06

.05

.09 .09

[.06] [.06]

Labor force

.51

.44

.44 .43

[.49] [.49]

Other

.08

.08

.07 .07

[.08] [.08]

Activity type

Predicted 1977 national population b (3)

a. The actual 1977 national population of high school seniors included approximately 3.3 million students. b. Unbracketed predictions in column 3 use estimated coefficients. Those in brackets use restricted coefficients in which scholarship parameters are set equal and opposite to estimated tuition parameters. Predictions in the top row within each activity type assume that BEOG awards substitute for college given aid; those in the bottom rows assume complementarity of awards.

vocational-technical enrollees and underprediction of the fraction of students going to two-year colleges. Since two-year colleges and vocationaltechnical schools are often close substitutes, it is not surprising that it is difficult to distinguish student choice between them, using our model. And because they are close substitutes, the difficulty in distinguishing them does not seem particularly troublesome. Indeed, we predicted 25 percent in these two categories together, which was very close to the actual number of 27 percent. That the predictive test performed here constitutes an external rather than an in-sample test of validity should be clear from comparison of columns 1 and 2 of Table 7.1. The distribution of choices made by 1972 NLS respondents was quite different from the 1977 national distribution. Specifically, the fraction of NLS students choosing to enroll in two-year colleges was much smaller and the fraction in the labor force correspondingly much larger than those found in the 1977 national population. We were able to correctly predict both the direction and, accepting the sub-

122 Table 7.2

College Choice in America Distributions of BEOG awards in 1977.a

Income group Lower (less than $16,900) Middle Upper (more than $21,700) Total

Actual number of recipients (1) 615

Actual average award (in dollars) (2)

28

653

10

599

653

978

994

Predicted number of recipients (3)

Predicted average award (in dollars) (4)

546 577 79 80 5 5

[438] [454] [83] [85] [5] [5]

1,201 1,208 776 774 891 895

[1,181] [1,195] [753] [747] [919] [921]

634 668

[526] [544]

1,137 1,143

[1,111] [1,123]

a. Numbers of recipients in columns 1 and 3 are in thousands. Monetary figures are in 1979 dollars. To convert to 1977 dollars (that is, to nominal terms), multiply by .83. See Table 7.1, note b.

stitutability of two-year colleges and vocational-technical schools, the magnitude of these differences, and this gives us confidence in the usefulness of our model for forecasting. Table 7.2 gives the actual BEOG awards made to members of the high school class of 1977 for use in academic year 1977-78, along with our corresponding forecasts. Using the estimated coefficients, we predicted that a total of 634,000 students would receive awards and that the average grant, in 1979 dollars, would be $1,137; the actual numbers were 653,000 and $978, respectively. One reason for a positive differential between predicted and actual awards is that the former quantity assumes yearlong school enrollment by the BEOG recipient, whereas the latter is lessened by mid-year dropouts. That is, we predicted the government's potential BEOG obligation, whereas the Department of Education data reflects realized BEOG payments. Of the awards made, we predicted that 546,000 would go to lowincome students; the actual number was 615,000. Considering that the BEOG Program did not even exist in 1972, these predictions based on the NLS sample seem a remarkably successful external test of our forecasting procedure. In addition to the predictions made using the estimated coefficients, Tables 7.1 and 7.2 include alternate predictions based on the assumption that scholarships have effects that are equal but opposite to tuition effects. The latter predictions were carried out in order to test the reasonableness

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123

of the large two-year scholarship coefficient in the estimated college choice model (see Chapter 6). The result of the test was that the estimated coefficients predicted far better than the restricted ones. In particular, the estimates using restricted coefficients did not pick up the 1972-1977 shift from labor force to two-year college activities and significantly underforecast the number of 1977 BEOG recipients. Evaluation of the BEOG Program PREDICTION

As in the previous six years, the 1979-80 BEOG Program provided awards according to a formula whereby aid increased with school tuition and living expenses, decreased with family income and assets, and was subject to an upper limit. This version of the program was the most liberal to date, incorporating an award ceiling of $1,800 and a family contribution schedule sufficiently flat that a substantial number of upperincome students were eligible for benefits. The 1979-80 formula and our procedure for estimating awards are detailed in Appendix E. An informative assessment of the BEOG Program may be based on Tables 7.3 and 7.4. Table 7.3 gives our predictions for the number of recipients and for average award size in each of three student-income groups. In Table 7.4, the estimated enrollment impacts of the program are presented. Expected enrollments by school type and student-income group are compared with those in the hypothetical situation in which 1979 conditions are preserved except that no BEOG Program exists. The predictions presented in Tables 7.3 and 7.4 are based on the assumption that BEOG awards substitute for aid awarded by colleges. The awards and enrollment predictions made under the alternative assumption of complementarity are quite similar in all regards. For purposes of comparison, the alternative predictions are given in Appendix E. The version of the choice model that underlies Tables 7.3 and 7.4 uses the two-year scholarship coefficient as estimated and, moreover, assumes that the two-year and vocational-technical school coefficients are equal.12 The decision to work primarily with these coefficients rather than with the restricted ones was made following appraisal of the predictive test reported above. A BEOG analysis based on the restricted coefficients is presented in Appendix E. In general, the results are identical in direction to those in Tables 7.3 and 7.4, but the predicted magnitudes of the BEOG impacts are smaller.

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Table 7.3 Predicted distribution of BEOG awards in 1979."

Income group Lower (less than $16,900) Middle Upper (more than $21,700)

Predicted Predicted Population Predicted number of average award size enrollment BEOG recipients (in dollars) (2) (4) (3) (1) 590 534 1,193 1,254

Total

934 1,142

398 615

265 296

879 628

3,330

1,603

1,095

964

a. Numbers are in thousands of students. In column 4, the average is taken over the relevant group of BEOG recipients. This set of predictions uses estimated structural-variable coefficients and adjusted dummy variable coefficients; it assumes that BEOG awards substitute for collegegiven aid.

The version of the choice model used in generating the BEOG predictions in Tables 7.3 and 7.4 and Appendix E differs from the estimated model in one respect. The coefficients of the alternative-specific dummy variables 15-25 (Table 6.1) have been adjusted so as to make our predictions for 1977 more closely match the actual distribution of activity choices than did the predictions reported in Table 7.1. This adjustment of coefficients of variables without structural interpretations sets a baseline

Table 7.4 gram. 3

Predicted distributions of enrollments in 1979 with and without the BEOG Pro-

Income group Lower (less than $16,900) Middle Upper (more than $21,700) Total

Predicted enrollments All schools 4-year schools 2-year schools Voc-tech schools (1) (2) (3) (4) With Without With Without With Without With Without BEOGs BEOGs BEOGs BEOGs BEOGs BEOGs BEOGs BEOGs 590

370

128

137

349

210

113

23

398 615

354 600

162 377

164 378

202 210

168 198

34 28

22 24

1,603

1,324

668

679

761

576

174

69

a. Numbers are in thousands of students. See footnote to Table 7.3.

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125

for the BEOGs analysis and is analogous to the adjustment of constants common in the forecasting application of regression models. Analysis AWARDS

Inspection of Table 7.3 reveals numerically what has often been asserted verbally. In contrast to earlier years, the 1979-80 BEOG Program is in no way exclusively directed toward low-income students. We predicted that only 49 percent of the awards and 60 percent of the budget would go to low-income students in this year. The extent to which this situation differs from that of past years can be seen by reference to Table 7.2. In 1977-78, fully 86 percent of the predicted awards and 90 percent of the actual budget went to the low-income group. It is important to recognize that the relative shift in the emphasis of the BEOG Program to middle- and upper-income students does not mean that low-income ones have suffered in absolute terms. Comparison of Tables 7.2 and 7.3 shows that the number of awards made to the lowincome group and the average award size have remained stable since 1977. What has happened, rather, is that benefits have been extended to the middle- and upper-income groups, thus greatly increasing the total size of the program. ENROLLMENTS

The predictions in Table 7.4 indicate that the BEOG program was responsible for a truly substantial increase (59 percent) in the enrollment rate of low-income students, a moderate increase (12 percent) in middleincome enrollments, and a minor increase (3 percent) in the rate for upper-income students. Overall, we predicted that 1,603,000 of 3,300,000 1979 high school seniors would enroll in full-time postsecondary education in 1979-80. In the absence of the BEOG Program, the corresponding prediction was 1,324,000.13 A closer look at Table 7.4 shows that the BEOG-induced enrollment increases are totally concentrated at two-year and vocational schools. Enrollments at four-year schools appear to be entirely insensitive to BEOG availability. This aspect of the predictions is fairly extreme and therefore deserves discussion. There exists at least one potential explanation arguing that the above finding is artificial. One might assert that the estimated two-year scholar-

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ship coefficient—and hence the imputed vocational school coefficient—is excessively large, thereby making enrollment rates at these schools overly sensitive to BEOG availability. A way to check this argument is provided by our predictions using restricted coefficients, given in Appendix E. This alternate set of predictions of 1979 enrollments is summarized as follows: for all schools 1,602 (with BEOGs) and 1,511 (without BEOGs); for fouryear schools 678 (with BEOGs) and 668 (without BEOGs); for two-year schools 764 (with BEOGs) and 719 (without BEOGs); for vocationaltechnical schools 162 (with BEOGs) and 124 (without BEOGs). These enrollment impacts of the BEOG Program are much smaller than those shown in Table 7.4, but the concentration of these impacts on two-year and vocational school rates persists. Hence, acceptance of the restricted coefficients changes matters only quantitatively, not qualitatively. It seems to us that the predictions reported in Table 7.4 are quite logical. The effect of the BEOG Program may be to induce a substantial number of high school graduates who would otherwise have chosen the labor force, the military, or homemaking to enroll, instead, at two-year colleges and vocational schools. At the same time, enrollments at fouryear schools may be fairly price insensitive, and therefore not affected by BEOG availability.14 A piece of external evidence in support of this hypothesis is that from 1972 to 1977, freshman enrollment rates at four-year colleges remained quite stable, while two-year and vocational school enrollments climbed sharply. Our results indicate that the introduction of the BEOG Program in 1973 is sufficient to explain this increase in its entirety. EFFECTIVENESS OF THE PROGRAM IN STIMULATING ENROLLMENT

Let's assume for the sake of discussion that inducement of enrollment is the only objective of the BEOG Program; that is, subsidization of students is not per se viewed as desirable.15 It follows that an ideal version of the program would be one constructed so as to distinguish between aid applicants who would choose to enroll even in the absence of an award and those who would not. Awards would be made only to members of the latter group, and then only in the minimum amounts needed to induce enrollment. Of course, the ideal program is not feasible in practice. It is inevitable that some BEOG money will take the form of pure subsidies. The question, then, is to determine what fraction of the current BEOG budget subsidizes existing enrollment and what fraction stimulates new enrollment.

Enrollment

Effects of the BEOG Program

127

Table 7.5 Distribution of BEOG awards between induced and existing enrollees.

Income group Lower (less than $16,900) Middle Upper (more than $21,700) Total

Predicted induced enrollments

Number of awards to existing enrollees

534

220

314

265 296

44 15

221 281

1,095

279

816

Predicted number of BEOG recipients

An exact answer requires student-by-student calculations of the minimum award necessary to induce enrollment and therefore cannot be obtained from the aggregated data of Tables 7.3 and 7.4.16 The tables can, however, give a good indication of the degree of subsidization. In particular, they reveal the number of awards constituting 100 percent subsidy— that is, the awards to people who would have enrolled in the absence of the BEOG Program. The relevant calculations are given in Table 7.5. Table 7.5 indicates that 25 percent of all BEOG awards go to induced enrollees and therefore contain at least some inducement component. Disaggregating by income group, we see that this percentage falls sharply as income rises. Forty-one percent of the low-income awards, 17 percent of the middle-income ones, and only 6 percent of the upper-income ones go to induced enrollees. We also compared the overall degree of inducement in the 1979-80 BEOG Program with that of the less liberal 1977-78 version. In the latter case, 39 percent of the awards went to induced enrollees. At the same time, the number of induced enrollees was 246,000, only slightly lower than that of the 1979-80 program. Thus, from the perspective of enrollment stimulation, the 1977 program appears to have been considerably more effective than the 1979 one. Conclusion Overall, we feel that the results presented here should be taken seriously. At the same time, we believe that refinements of the analysis would enhance our understanding of the effects of aid awards. A more complete examination of BEOG impacts would recognize that the availability of

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awards may influence students' college application and high school tracking decisions, as well as institutions' admission, financial aid, and tuition decisions. Our work could be profitably extended to consider enrollment impacts occurring after the year following high school graduation. In addition, analysis of the effect of the BEOG Program on college dropout rates and on the frequency of delayed college entry would be of substantial interest.

8

College Attendance versus College Completion

Although it is common in casual discussion to equate college attendance with a college degree, many who attend colleges and universities don't obtain degrees; they drop out. Which students are likely to persist in college until a degree is obtained? Would those who don't attend obtain degrees if they did? Are admission decisions consistent with expected college performance, as measured by persistence? In this chapter, we shall focus our discussion on the predictive validity of test scores and high school performance. We do this simply because most other discussions of success in college deal in good part with how well past performance in school predicts future performance. In particular, much recent criticism has been leveled against the use of SAT scores in admission decisions. These concerns serve as the point of departure for our analysis. The evidence that we present, however, relates many individual and family background attributes to persistence in college. Most economic studies of college attendance emphasize the returns to higher education as the motivation for an individual's choice to go to college, but they ignore institutional constraints on possible choices. Critics of the use of test scores in the determination of college attendance tend to emphasize the constraints on educational opportunities imposed by test scores and to ignore individual choice. Indeed, SATs have become an integral part of college application and admission procedures. Implicit in much of the recent criticism of them are two assumptions or claims. One is that test scores exert an influence primarily through their use by college admission officials to screen people out, and thus—by way of the constraints that they place on access to higher education—to limit occupational opportunities. The other is that the test scores are poor predictors of who will succeed in college; they thus may not promote optimal inThe authors of this chapter are Steven F. Venti and David A. Wise. 129

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vestment decisions and may unjustly limit the educational opportunities of some youth.1 We shall in this chapter address the second claim by comparing the determinants of college attendance and the determinants of college completion, with special emphasis on the role of test scores. Our findings reported in Chapter 4 addressed the first assumption. We found that test scores (or, more precisely, the attributes measured by them) bear a much stronger relationship to individual college application decisions than to college admission decisions. Most people who don't apply to any college or university would have a high probability of admission at schools of average academic quality, if they were to apply. The evidence in Chapter 4 also suggests that student application decisions do not simply reflect expectations about college admission decisions. But it may be that to the extent that test scores determine individual human capital investment decisions, they do not provide an adequate or appropriate signal to students, and thus in large part may not be contributing to rational individual choice. It could be, for example, that people who don't go to college—presumably in part because of test scores—would have been well advised to obtain higher education. We shall address this latter issue as the first of two interrelated questions posed in this chapter. We ask first whether individual college attendance decisions are consistent with the likelihood that a degree will be obtained. To motivate this question, recall that simple models of investment in higher education suggest that an individual will choose to attend college if the expected net return from college attendance is greater than the return from time spent by the individual in other ways. The return on a college education can be thought of as the product of two components: the probability that a degree will be obtained, times the expected gain in future earnings (and nonmonetary benefits) with a degree. Much has been written about the second component, but little about the first2—a component of crucial importance because the occupational rewards from college education, and probably the earning gains as well, come in large part with the degree. Whatever the determinants of college attendance, for attendance to be "rational" it should be the case that people who are most likely to attend are also the most likely to obtain a degree and that those who are unlikely to attend would be unlikely to obtain a degree if they did attend. Thus, we investigate the relationship of test scores and other individual attributes to college attendance on the one hand, versus the relationship between these attributes and college completion on the other. We judge the extent to which individuals make "correct" college decisions by the relationship between college attendance decisions of

College Attendance versus College Completion

131

youth and the ability of youth to benefit from college—as measured by the likelihood of graduation.3 Within this context, we shall emphasize the relationship of test scores to these outcomes, and stress implicitly their informational value to students. Not only are universities likely to want to admit people who will succeed, but students may be just as likely to use test scores to judge their own chances of success. In addressing these issues, we shall also emphasize student selfselection. Our model allows us not only to consider the extent of selfselection as explained by measured variables, but also to evaluate the extent of self-selection attributable to unmeasured individual attributes (the idea commonly denoted by "self-selection" in a statistical sense). Then we ask a second, related question. To the extent that expected persistence in college is a criterion for admission, what is the information value of test scores to admission officials, and is their use of the scores consistent with this criterion? Posed in this way, the question provides a framework that allows us to compare our results with the claims of critics of the predictive validity of test scores. The question is essentially whether test scores add measurably to the information available to colleges, given a measure of high school performance—which, as reported in Chapter 4, is also an important determinant of college admission decisions. To address these questions, we specify and estimate a mixed "discretecontinuous" utility maximization model that is in general analogous to the profit maximization discrete-continuous production models put forth by Duncan (1980) and McFadden (1979b) and similar to the model set forth in Chapter 4. The model supposes that if an individual were to attend a college or university it would be one of academic quality and cost commensurate with the individual's personal attributes and family background. Individuals are presumed to compare the net value of opportunities with an education from a college of this quality and cost with the value of opportunities without a college education. If the supposed value to him of opportunities with a college education exceeds the value to him of the opportunities without college, he is presumed to attend. If, after matriculation, he concludes that the net value of opportunities without a degree exceeds the value of opportunities with a degree, he drops out. This idea incorporates attendance and dropout associated with searching, evaluating one's abilities and likes, monetary constraints on attendance, and so forth. In short, the procedure jointly estimates four outcomes: the dichotomous college attendance and college dropout (or persistence) outcomes, and the two continuous college quality and college cost decisions.

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College Choice in America

The college quality and cost estimates represent the preferred type of school among those available to the individual if, given his individual attributes and family background, he were to choose among college possibilities. Estimation of the college dropout relationship yields for an individual the probability of dropping out, if given his attributes he were to attend the most preferred of the college alternatives. And, of course, the college attendance equation yields estimates of attendance for an individual with given attributes. For the purposes of our analysis, the model is estimated in reduced form. The most important results are presented in the form of simulations based on the parameter estimates pertaining to the four outcomes. Our estimation procedure has at least two related substantive advantages. One is that it allows explicitly for individual self-selection of higher education. Given measured attributes, people who elect to attend college are likely to have unmeasured attributes that differ systematically from the unmeasured attributes of those who elect not to attend. For example, among people with the same measured attributes, those who attend college are likely on average to have a higher perceived return from school than those who don't attend, and thus will be willing to pay more for a college education. Willis and Rosen (1979) also stress this idea in distinguishing the relationship between unmeasured determinants of college education and unmeasured determinants of success in college versus noncollege occupations. A concomitant advantage of our procedure is that it allows estimation of outcomes for any person in the population, not just those who have elected to attend a particular college. That is, it corrects for self-selection bias and in so doing yields consistent estimates of population parameters. Invariably, previous studies of the relationship between measures of precollege academic ability and college success have been based on relationships between test scores and, say, first-year college grades for people attending a single college or university. Studies of the "validity" of SAT scores have been based on this sort of relationship, with the validity criterion usually taken to be a correlation or multiple correlation coefficient.4 Not only have those studies ignored the important self-selection of college versus no college, but they have ignored as well the individual selection of a particular college from among many possibilities and the admission decisions of colleges. All of these decisions tend, given SAT scores, to allocate people between college and noncollege and among colleges according to individual comparative or competitive advantage. Individuals tend to go where they will "do well," and a given college tends

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133

to select people who will do well at that college. Thus, the relationship between grades and SAT scores at a particular school underestimates the relationship in the population between SAT scores and expected academic performance. In contrast, our analysis allows estimation of the probability that an individual selected at random from the population will drop out of the type of college that individual would be expected to choose, should he attend. Our results indicate that if people with a low probability of attending college were to attend, they would have a high probability of dropping out. Attendance is strongly consistent with the likelihood of benefiting from college by obtaining a degree, and it reflects self-selection explained by measured as well as unmeasured individual attributes. For example, after controlling for family economic and social background characteristics, a range of values for test scores and high school class rank yields estimated attendance probabilities ranging from a low of about zero to a high of about .85, while corresponding dropout probabilities range from about .90 to about .10. And among people with the same measured characteristics, if those who are ex post observed not to go to college were to attend, they would prefer schools of lower quality and cost and would have a higher probability of dropping out than would those who are observed to attend. If attendance and persistence are predicted on the basis of test scores and high school class rank only—without controlling for socioeconomic background and other determinants of persistence, as is the case in most validity studies—the variation in dropout probabilities with test scores is more pronounced. By these measures, test scores provide substantial distinction among individuals in their estimated persistence probabilities. To the extent that individual educational investment decisions are determined by SAT scores, these decisions appear in the aggregate to be strongly related to the estimated likelihood that the investment (college attendance) would be justified ex post. These results are in sharp contrast with many recent interpretations of the findings of validity studies of SAT tests. As mentioned above, these studies emphasize binary or multiple correlations between test scores and/or class rank on the one hand and college grades on the other. They also by implication emphasize the effect of test scores on college admission decisions while largely ignoring their relationship to student choices; and they ignore student persistence decisions, which may be the single most important indicator of success in college. Furthermore, they are invariably limited to relationships within a single college or university.

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College Choice in America

Both self-selection by students and decisions of admission officers tend to minimize the relationship between test scores and performance among students in a single college or university. Our results should not be interpreted to mean that test scores explain a large part of the variation in academic performance among individuals. We show that the effect of test scores on persistence (a "slope parameter") is large, not that the unexplained variation in college performance is small. And our analysis pertains to a national random sample of high school graduates and thus of colleges and universities; our findings may not reflect relationships that exist within a single university or college. In particular, they may be less accurate at the tails of the distributions of individual and college characteristics than around their central tendencies, necessarily more representative of the weight of the data. The Statistical Model We begin once again by supposing that each individual is characterized by a vector of attributes, X, with elements describing the individual's socioeconomic background, academic ability and past performance, and the local labor market conditions. Upon high school graduation but without a college education, given X, the individual is assumed to face a set of opportunities to which he attaches a value U0, which depends on X:

(1)

U0 = Xa0 + e0,

where a 0 is a vector of parameters and e0 is an error term representing the collective contribution to U0 of unmeasured characteristics, including personal tastes. We have assumed that this and other relationships are linear in parameters. If an individual with attributes X were to attend college, we assume that he would prefer—among the possible alternatives—a school of quality (2)

Q = XaQ + eQ.

And given attendance, we assume that the individual would prefer a school with cost given by (3)

C = Xac + ec,

College Attendance versus College Completion

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where ac is a vector of parameters and ec an error term. Indeed, college quality and cost are likely to be determined jointly, and our estimation procedure will allow for that.5 At the time of high school graduation, the individual is also assumed to attach a value U\ to the opportunities he supposes he would have if he were to attend college. The expected net benefit that an individual associates with college attendance is assumed to depend not only on his personal attributes but also on the quality and cost of the most preferred college among those that the individual could attend.6 Thus, t/, is assumed to be given by (4)

Ui = Xai + alQ + SiC+el = X{ax + a, aQ + 5,ac) + (