A Study of College Attendance in the 1980S

A Study of College Attendance in the 1980s

Michael Aron Badain

Submitted to the Department of Economics of AmherstCollege

in partial fulfillment of the requirements for the degree of

Bachelor of Arts with Honors

Professor Steven Rivkin, Faculty Advisor

Professors Dan Barbezat and Jessica Reyes, Readers

April 23, 2008

Acknowledgements

I owe a large debt of gratitude to Professor Steve Rivkin, who consistently provided me with useful and thoughtful feedback, reading drafts and helping me refine my ideas into something that was usable. Without his advice and encouragement, this thesis would have been pretty bad.

Beyond that, I wish to thank everyone who deserves thanks for putting up with me in one way or another and making my life better as I worked on completing my thesis.

Table of Contents

Chapter 1: Introduction……………………………………………………..1

Chapter 2: Literature Review………………………………………………2

Section 1: Students’ Responsiveness to Cost…………………………2

Section 2: Perception and Knowledge………………………………..2

Chapter 3: Theory…………………………………………………………..7

Section 1: The Becker Investment Model……………………………7

Section 2: The Model In Terms of College Attendance……………..10

Chapter 4: Empirics………………………………………………………...15

Section 1: Data………………………………………………………..15

Section 2: Describing the Gap………………………………………...18

Section 3: Actual and Perceived Costs as a Factor……………………20

Section 4: Psychic Costs……………………………………………….25

Section 5: Opportunity Costs…………………………………………..28

Section 6: Parent Education……………………………………………29

Section 7: A Complete Model………………………………………….35

Section 8: Studying Gender Gaps Within Race………………………...38

Chapter 5: Conclusion…………………………………………………………44

Works Cited…………………………………………………………………….47

Chapter 1: Introduction

A recent article in the New York Times titled “The (Yes) Low Cost of Higher Ed” discusses all of the ways in which elite private schools are lowering costs for students from low or middle income backgrounds, and how these schools, which have a disproportionately high number of students from wealthy backgrounds,hope to enroll more low income students with these policies. The implicit assumption behind this, of course, is that tuition cost is what prevents low-income students from going to these colleges. Of course, it’s not only in the elite colleges that lowincome students are underrepresented; almost any study about family income and educational attainment will reach the conclusion that low income students will attend college at a much lower rate than will high income students, even if you control for ability. Basic economic intuition tells us that this is an unusual situation. If students are rational, utility-maximizing actors who will undertake any investment whose net present value is positive, then for students of roughly equal ability, their expected return to college attendance should be similar, and thus they should attend college at similar proportions. If anything, the low income student should be more likely to attend college, since programs such as Pell grants (which award up to $5000 to low-income students) and specific college financial aid programs are likely to lower the cost of college for the low income student (the new programs elite colleges are introducing hope to implement further cuts of the cost for low and mid SES students. Yet the question must be asked, will this work? Not just at increasing the economic diversity at elite colleges, but if every college in the nation cut its tuition, would college enrollment skyrocket as a result?

Obviously, trying to come up with a model which analyzes all factors that affect a student’s decision to attend college is an untenable goal. This paper will work through a model of college attendance by focusing on students’ perception and attitude, with an emphasis on costs. If students from poor backgrounds perceive the cost of college to be high, or if they were unaware of the financing options available to them, they might hear the price of college years before they graduate, instinctively assume that they had no way of paying for it, and then never investigate college as a serious option. Attitudes toward college may be related to perception; a student who views college as unimportant may perceive a college education to not be worth that much in future earnings. Quantifying the return to college is difficult; I personally have no idea how much I will earn for the rest of my life, nor could I guess how much I would earn had I entered the work force straight from high school. I entered college because that is what was expected of me, and because I knew that all of the high-paying jobs required a college degree. I wondered if students who choose not to go to college are aware of the value of a college degree and choose not to pursue it for whatever reason, or if they simply do not view a college degree as very important. I hope to use this focus on knowledge to partially explain the gaps in college attendance between income classes. Using a longitudinal survey which gathers data from a large number of students over many years, this paper will provide a look at the college attendance gap while focusing in on key factors.

Chapter 2: Literature Review

The following is a summary of some of the papers that I have read that try to explain how certain factors affect college attendance.

Section 1: Students’ Responsiveness to Cost

It seems that cost would be a major factor in a student’s decision whether to go to college (this intuition will be further developed in both the theory and empirics sections). The empirical findings in the literature, however, are mixed in their conclusions. Leslie and Brinkman (1987) conducted a meta-analysis of roughly 30 studies that tried to measure student responsiveness to tuition changes. They concluded that the consensus is that a $100 increase in tuition (in 1982 dollars) would decrease enrollment by about .75%. McPherson and Shapiro (1991) perform a typical study of response of students to changes in the net cost[1] of attending college and find that while increases in the net cost have a significant negative effect on enrollment for students from low-income families, students from high-income families are not very responsive to changes in price. On the other hand, a number of are unable to provide evidence for the hypothesis that a lower price of college will lead to more students attending. Hansen (1983) and Kane (1995) both conclude that the introduction of the Pell Grant, a grant specifically for low-income students to help pay for their college education, had no significant effect on college attendance. Another paper by Kane (2003) found that “during the period of expansion of Pell grants, enrollment rates of low-income youths did not increase disproportionately.” Kane argued that family education has a great effect on the student’s decision to go to college, more so than the grants do. Heckman and Cameron (1999) study the HOPE scholarship program, whose goal was to induce more low-income students to attend college, and conclude that at least 91% of the grants go to students who would enter college in absence of the program.

Ellwood and Kane (2000) offer a simple yet convincing argument for why students from wealthier backgrounds are more likely to attend college: parental gifts. Many upper-class students have parents who are willing to make significant contributions to the student’s education, whereas students from low-income families frequently do not have such parental contributions. The result is that, even after factoring in aid packages, low-income students face a higher cost of going to college. However, gifts also capture immeasurable characteristics like the parent places on college, so their results might really find that a combination of gifts and parental influences are important.

In the theory section, I assume that a student is not credit constrained—a student is said to be credit constrained if he did not go to college only because he could not raise the funds to pay the tuition. The literature generally supports this assumption; Carneiro and Heckman (2002) argue that at most, 8% of American youths are subject to short-term credit constraints, and the number is most likely even lower than that. Carneiro and Heckman end up arguing that if there is indeed a credit constraint, it comes early in life—that is, families aren’t able to invest in their child’s education at a young age, and that inability to invest in the child’s education harms the child’s educational development, which is more significant than any constraint in financing education later in life. Stinebrickner and Stinebrickner(2007) collect a detailed longitudinal data set specifically designed to directly study credit constraints (although their study was about college drop-outs, not those who chose not to attend college in the first place) and find that “the large majority of attrition of students from low income families should be primarily attributed to reasons other than credit constraints.”

There is no unanimous agreement, however, that credit constraints to not exist in financing college education. Ellwood and Kane (2000) carefully present an argument which disagrees with Heckman’s methodology in his assessment of credit constraints. Overall, though, the consensus appears to be that credit constraints are not a significant problem, and my theory section will assume that students can easily borrow funds.

Section 2: Perception and Knowledge

Avery and Hoxby (2004) study a randomly selected group of high achieving high school seniors, and show that perception of a financial aid offer can distort a student’s decision-making process. Students are more likely to attend a school if it offers aid in the form of a “scholarship” as opposed to a “grant”, even though the two serve identical economic purposes. They are also more likely to attend a school that offers them a front-loaded grant than one that offers a similarly sized grant spread out over the four years. Avery and Hoxby estimate that roughly one third of students are making “wrong” decisions that reduce their own lifetime present value.

One of the major problems with the current American financial aid system currently cited by many authors is its complexity. Dynarski and Scott-Clayton (2006) argue that the low-income families find it difficultto fill out forms like the FAFSA. It’s not a trivial form to fill out—two summers ago, I volunteered at a college preparation tutoring program for low-income high school students. One of the activities was a workshop for parents, led by a guidance counselor, on how to fill out the FAFSA. The fact that such a workshop was necessary speaks volumes about the complexity of the financial aid process. If the form were simpler to fill out and produced a clear estimate of the size of the aid package a student could expect to receive, students could know the true cost of college earlier and make decisions accordingly. Avery and Hoxby (2004) agree that the complexity of forms is an issue; they cite the results of a survey in which many parents complained that the complex forms were making college for their child less likely.

In a study of NYULawSchool, Field (2006) presents an argument that people are adverse to debt itself. She studied the decisions of admitted students who were randomly assigned either a partial tuition waiver or a no-interest loan of equivalent value. Thus any significant difference in the actions of the students should be caused by what she describes as “the psychic costs of debt.” She notes that students who received the tuition waivers were significantly (at the 10% level) more likely to enroll in NYU. Her paper implies one of two things: either people are indeed debt averse and their decisions in this study reflect that debt aversion, or that the complexities in financial aid never really end—perhaps students didn’t fully understand the terms of the NYU loan aid packages.

This paper tries to expand the universe of theories about the college attendance gap by examining the decision to attend college as a long-term process. Many of the aforementioned studies either look at students who had already applied to college, or just looked at the students in the year they were applying to college. But if the decision to attend college is made over a period of many years, it makes sense to look at a longitudinal study and see how factors from different points in a student’s life may influence his decision. By focusing in on cost, knowledge, and attitudes, I hope to add a new understanding to the research on what factors affect which groups of people in their decision whether or not to attend college.

Chapter 3: Theory

This paper will examine specific factors that influence college attendance, focusing on the effects of knowledge and attitudes. People go to college to increase their potential earnings; the average college graduate makes than the average high school dropout. But do some people choose to be high school dropouts or merely high school graduates? The theoretical aspect of this paper hopes to suggest some answers to this question and to lay the framework to analyze the determinants of college attendance. This section will first present a general theory of investment in human capital developed by Becker (1975) and then discuss how the theory relates specifically to the decision to attend college and how certain factors should affect a student’s decision whether to go.

Section 1: The Becker Investment Model

Assuming that the typical high school student is a rational actor (an assumption that anyone who deals with teenagers may be tempted to laugh at), he looks to maximize his total utility U, where U=f(C1,C2,…Cn), with each Ci representing consumption in a distinct period of the actor’s life and each period i is of equal length, for simplicity’s sake. In each period, consumption is produced by goods consumed and leisure time. Mathematically, we can write Ci = gi(xi, tci) where xi represents the goods consumed in period i and tci represents the leisure time of period i. Therefore, utility itself is constrained by lifetime earnings and total time.

Leisure is constrained by total time in life. Any period i has length t, and time can be spent in three ways: consuming, investing in human capital (tei), or working (twi), and tci + tei +twi = t. Since t is a constant, every minute spent working is a minute spent not investing, so δtwi/δtei = -1. Goods expenditures are constrained because the present value of a person’s lifetime expenditures must be equal to the present value of his lifetime earnings. Since money can be spent on either consumption goods or investing in human capital and money will be earned only through working, the following equation must hold:

where vi represents wealth not earned through wages (gifts), and r is the market interest rate. This equation can be improved by recognizing that wi is not exogenous; it is affected by the worker’s human capital, which can vary based on xei and tei. We can describe the person’s human capital production function as a function Ω which can vary from person to person, and Ω=g(xei,tei). Investing in human capital in period i changes the level of human capital stock, called Ei. If we set wi = Ei*pi, where pi is the payment per unit of human capital in period i, then the above equation can be rewritten as

If going to college is solely an investment (an assumption which will be relaxed later), then the investment will be made provided that it increases the constrained utility.

To solve for the utility-maximizing solution, we first look to the case in which xei, xci, tci, twi, and tei all have positive values; that is, given that the student chooses to allocate some resources to each of the 5 states, how much should he invest in human capital?To answer this, we look to solve for the utility-maximizing value of tei. In his discussion of finding the solution, Becker makes the simplifying assumption that the human capital production function depends only on tei. From the utility equation, we face the constrained optimization problem to solve

We find that since at the optimal point, δU/δtei must equal 0, then the investment in human capital is a good investment up until period i in which

This convoluted-looking equation is simple and intuitive at its core—it looks at the tradeoff between work and school. It states that if λ is not 0, then the present value of the earnings forgone in period i by going to school must equal the present value of the increased earnings from going to school in period i. The earnings are increased by the student’s human capital production function (as reflected by the δEj/δtei term), the market price of human capital, and the amount of time a person would be willing to work. Willingness to work refers to both the willingness to work long hours in a given period (which would increase twj at the expense of tcj) and willingness to work for many years (which would increase the value of n in the above summation). The value of the foregone earnings is influenced by the market price of capital, the student’s stock of human capital without the investment. Both values are affected by the market interest rate.

The simplifying assumption that the human production function only depends on the time investedis an assumption that is largely unsatisfactory. With this assumption, the theory doesn’t explain why anyone would choose to spend the extra money to go to a private college. Of course, it is complicated to introduce xeiinto the equation—if it weren’t, Becker probably would not have made the simplifying assumption. Instead of focusing on the complicated math involved with including an xeifactor, I will analyze the importance of xei to the extent that a higher investment cost increases the probability of a “corner solution”—that is, a high cost of investment means that this student would likely choose to not go at all. Becker’s model mainly focuses on the case in which a person has decided to invest a nonzero amount in education, and it overlooks the importance of tuition and fees in making that original decision to attend college at all. I am interested in examining the initial decision whether students will enter work or school. Before the student has decided to sink money into the investment, he will ask himself whether the investment,when made optimally, will raise utility. If the investment will raise his wage slightly, but costs a lot to undertake, the student will rationally choose not to make the investment in the first place, as it would have a negative net present value. When the cost of the investment rises, the probability of the investment having a positive net present value falls. Thus, the cost of the investment does need to be accounted for.