Chapter 1: Introduction - Amherst College
A Study of College Attendance in the 1980s
Michael Aron Badain
Submitted to the Department of Economics of Amherst College
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 low income 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 difficult to 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 NYU Law School, 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 invested is 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 xei into 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 xei factor, 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.
Section 2: The Model In Terms of College Attendance
This section will point explicitly to some factors that may affect college attendance, according to the theory from Section 1. I will make hypotheses how these factors would affect college attendance, and in Chapter 5 test said hypotheses. The income constraint assumes that a person would be borrowing at the market rate throughout his lifetime. However, this assumption does not always hold. Many loans for college are made at a below-market interest rate, and thus would allow a student to borrow more cheaply. Such loans, however, depend on availability. If these loans are not available, on the other hand, a student would face a severe credit constraint and might face a very high interest rate to pay back the loans, due to the student’s lack of a credit history, or loans might not even be available at all. As I mentioned in the literature review, there is a general but not universal agreement that students are usually able to secure loans. Students from a high-income background are more likely to receive gifts or subsidized loans from parents, which would lower their effective cost of college and make them more likely to go.
The decision to invest in human capital depends on the information held by the student; information (or lack thereof) about the return to college and the cost of college can play a large role. The framework above assumed that the student would know a lot about his future. However, at the time of making the decision whether or not to invest more in human capital, it’s quite possible that a teenager would not have anything that resembled perfect information. Indeed, the information that a student has may vary wildly by his background. A student whose parents have a high-paying job, for example, may have been taught from a young age that only college-educated people can get high-paying jobs. A student who grows up in a community where most adults are college educated would be more likely to understand college’s value.
Furthermore, a student may not have complete information about his skills and his ability to produce human capital. Cunha and Heckman (2007) help us formalize this portion of the informational problem by noting the importance of the distinction between ex ante information and ex post information in the decision making process. They theorize that students may not know all of the information about themselves that would be relevant to their human capital production function. After all, some students who are at the bottom of the class, especially at less-selective universities, decide to abandon their studies and drop out of college. These students probably did not know at the time of deciding to go to college that they would end up dropping out and not being able to handle the academic challenges posed by college. This would make college seem like a lottery; students may view it as a matter of chance whether they have the skills necessary to succeed in college. The expected probability of successfully completing college is important because it would influence the perceived profitability of the investment. And because ex ante, a student might not know about all of the factors that would impact his earnings, the uncertainty could cause a student to make a decision that would be viewed ex post as the wrong one.
The risk of failure at college may not be equally distributed across income classes. Students from a low-income background are more likely to experience this failure than are students from a high-income background, and are thus more exposed to the risk of failure. Carneiro and Heckman (2002), as I mentioned earlier, offer the hypothesis that since “better resources in a child’s formative years are associated with higher quality of education and better environments that foster cognitive and noncognitive skill,” it follows that lower-income students would go to college less than would higher-income students because they have less developed skills in certain areas. Heckman argues that in general, students from low-income backgrounds would have a worse human capital production function than would students from high-income backgrounds. Consequently, a student from a low-income background would be more likely to fail to accumulate significant human capital at college, even if the student invested the same amount of xei and tei as a high-income student.
The costs of investment in college are worth examining in greater detail. In-state university tuition will vary from state to state, as different states subsidize their state university system to different degrees. xei is not always equal to the published tuition, though. At all postsecondary institutions, there is a nominal tuition, or “sticker price,” which is the maximum fee that a school will charge for its services (tuition and, in some cases, room and board). Yet this sticker price can be lowered through the financial aid process. Financial aid is available from a variety of sources. The federal government offers grants and low-interest loans to low-income students. Furthermore, students may be offered work-study funds, in which they are guaranteed a job while a student. Schools may also offer financial aid directly to the student; they can offer to lower the price to entice the student to attend. Different schools offer different levels of financial aid. For example, Amherst and other elite private schools have led the movement to replace loans with grants. Other, more financially-strapped schools tend to charge a lower sticker price but are less generous with their financial aid.
Because a high school senior would have to estimate both the benefits and the costs of attending college before making his decision, his estimate of the costs should play a large role in his determination of the wisdom of making the investment. If a student were unaware of the actual tuition charged by the college, he might estimate the cost of college to be too high. This would raise the necessary return to the investment in order to make it one with a positive net present value, and therefore he may not go to college even if it would have been advantageous for him to go had he known the true costs. The student might also accurately understand the price of college, but be unaware of the existence of financial aid or the availability of loans and financing methods. Such a student would inaccurately view himself to be credit constrained. The flow of information is quite important, and information about financial aid can be transmitted a host of different ways. A guidance counselor may be a great source of wisdom to explain financial aid to students. Having an older sibling who has either applied for aid or knows people who have could help students learn about aid. Parents who had gone to college would probably be more familiar with financial aid availability. Students who do not learn about financial aid, however, may not consider college as a viable option, due to the high sticker price of many colleges.
The issue of cost is cannot simply be measured by money and time. There is also a psychic cost involved with attending college which was not accounted for by the Becker model which. If a student really dislikes school and finds it difficult, he would probably be more likely to enter the workforce sooner. A student who really struggles with school might spend longer on the homework, which would increase tei and therefore decrease tci, which lowers the student’s utility. But even if it doesn’t take the student more time to complete the work, the unpleasantness of school work could take a psychic toll on the student and make him unhappy. If the psychic cost were large enough, the student might avoid the cost entirely by not going to college. The consumption value of education is also a factor. If a student enjoys learning and it increases his utility to be in school (perhaps he views learning as leisure time), the higher utility experienced while in school needs to be factored in when tabulating the benefits of college. A student may choose a private college over a significantly cheaper state college not only because he believes that the private college will give him significantly better productivity and make him more attractive to employers, but also because he believes the private college would be a better environment to grow as a person and enhance his utility.
Chapter 4: Empirics
Section 1: Data
This chapter investigates some issues mentioned in the theory section and examines whether the hypotheses from the theory section do indeed show up in data. In order to complete this investigation, I used data from the 1980 High School and Beyond Series. This survey, commissioned by the National Center for Education Statistics, is a longitudinal survey which was administered every two years, starting in 1980 when the cohort was in tenth grade. I was interested in examining students who decided to go to college directly from high school, and so I looked at the first three surveys. The 1980 survey (“Base Year Survey”) was administered to students in 1015 schools throughout the nation. The questions mainly focused on individual and family background, high school experiences, work experiences, and plans for the future. Students were also required to take a timed cognitive (achievement) test, which included math and reading sections.
In 1982, the students were again administered a survey (“First Follow-up Survey”). Surveys were given in all of the schools at which the Base Year Survey was administered. Over 96% of students who had been surveyed for the original survey and had not changed schools participated in the First Follow-up Survey. For students who had left their original school—high school drop-outs, transfers, and early graduates— they were located, telephoned, and offered monetary incentives to participate. 89% of the school-leavers participated in the First Follow-up Survey.
For the 1984 survey (“Second Follow-up Survey”), students were mailed questionnaires and a check for five dollars as an incentive to complete the survey. Students who did not respond were sent postcards and telephone calls reminding them to finish and return their surveys, and those who did not mail in the surveys were either administered surveys over the phone or in person by field workers. Overall, 92% of the people who were mailed surveys ended up responding. Therefore, attrition was relatively minimal, which is an important part of any successful longitudinal survey.
I supplemented the survey with outside data I was interested in including in my model but was not provided by the High School and Beyond survey. These outside data allowed me to assign to each school the 1980 in-state university tuition and the local junior college’s tuition. I also obtained the labor force participation rate of high school graduates of each gender and race for each county—this way, given the information about the student’s gender, race, and school location, I could come up with a probability that the student would be able to find a job as a high school graduate. Last, I obtained the percent of students, broken down by gender and race, from the county who were college graduates, according to 1980 U.S. census data. This allowed me to proxy for the overall cultural view toward school that the student grew up with.
The other main manipulation to the data I made was to only look at people who, in the tenth grade survey answered that they were interested in going to college. Since I am interested in looking at what factors either discourage or encourage college attainment, I made the decision early in the process to eliminate people from the data who did not view college as something they were interested in pursuing. I realize now that this may bias some of my estimations, since some students may have decided not to go to college because of factors I am examining in my data, and thus an endogenous selection problem may occur. However, I think that people who did not view college as an option were more likely to have immeasurable factors influencing their decision to not go. I also dropped from the survey the small percentage of students who answered Asian or “other” to their race; both of these groups represented less than 3% of the sample, and since much of my empirical section investigates race-related results, obtaining meaningful and significant results from them would be difficult.
Most of the regressions are self-explanatory, but a couple of terms I use would benefit from a little explanation. Many regressions use as the dependent variable whether the student went to college. To determine whether a student went to college, I looked at the student’s response to the question, “What kind of school was the first school you attended after high school?” The available responses to the question were vocational, community college, college or university, other, or none. I created a dummy called college attendance which equaled one if and only if a student answered that he[2] attended college or university. Unless stated otherwise, all regressions involving binary dependent variables like college attendance are logistic regressions. Since the dependent variable in such regressions can only be 0 or 1, the error term is not normally distributed and thus OLS cannot be used since its underlying assumptions are not met. In results tables for these regressions, I will present the marginal effects at the means of the independent variables as calculated by STATA; for dummy variables, these effects show what happens when the dummy goes from 0 to 1. Also, if a student either skipped a question or filled in multiple answers to a question, I considered there to be no data for that entry (this is why different regressions could have a substantially different number of observations). This could bias the estimates if certain types of students tended to skip certain questions, and there is evidence to make me believe this might be the case. For example, there seems to be a reluctance of students to admit their family income is low. One question asked students to estimate their family’s income, divided into thirds.[3] 35% of students described themselves as in the middle third, and 27% believed they were in the top 3rd, yet only 17.3% admitted to being in the bottom third of income; 20% did not respond. Even though anonymity was guaranteed, reluctance about giving certain answers may have existed.
Section 2: Describing the Gap
|Table 2.1: College Attendance by Demographic Group |
| |QUARTILE[4] | | |
| |
|Variable |Marginal Effects |z | |8325 Observations |
|Quartile 1 |-0.18542 |-11.4 | | |
|Quartile 2 |DROPPED (BASE CASE) | | |
|Quartile 3 |0.17427 |11.39 | | |
|Quartile 4 |0.27218 |18.83 | | |
Since college attendance looks higher as income rises, I wanted to quantify the gap between income classes to see how big it is. I regressed college attendance upon income class while controlling for test score and the results are presented in Table 2.3. Clearly, test scores do not explain why low income students go to school much less than high-income students do; in fact, a low-income student is nearly 12% less likely to go to college than a high-income student with the same test score.
|Table 2.3: College Attendance By Income |
|(Controlling for Test Score) |
|Variable |Marginal Effects |z | |5946 Observations |
|Low Income |-0.1192 |-6.00 | | |
|Middle Income |-0.09385 |-6.17 | | |
|High Income |DROPPED (BASE CASE) | | |
It seemed that for any given race and income class, females appeared to go to college more than males did. So to test whether this was a significant difference, for each race, I regressed college attendance upon gender (omitting female as the base case) and composite score, and looked whether there were significant differences. Table 2.4 shows within each race the marginal effects of being male.
|Table 2.4: College Attendance By Gender |
|(Effects of Being Male) |
|Race |Marginal Effects |z | |7428 Observations |
|Black |-0.124 |-4.05 | | |
|White |-0.0113 |-0.74 | | |
|Hispanic |-0.1278 |-4.78 | | |
As you can see, while all three signs are negative, white does not possess
a significant difference between the two genders, whereas for blacks and Hispanics, females are indeed significantly more likely to attend college. Further, at the 1% level, the gender gap between Hispanics is significantly greater than the gender gap between whites. None of these regressions explain anything, of course—they merely set the foundation for exploring these key differences. The next sections will test some of the hypotheses set forward in the theory chapter, and after that I will return to discussing gaps between race and gender.
Section 3: Actual and Perceived Tuition Costs As a Factor
A rise in the cost of college should, according to the theory, increase the probability that attending college would be an investment with negative net present value. Thus, I would expect a higher college tuition to cause less college attendance. I would also expect a different responsiveness to tuition among the achievement groups. For a talented, high-achieving student, tuition costs would be unlikely to be high enough to make him decide that investing in college is not worth it. Similarly, for a student who struggles to produce human capital and does poorly in school, even a free college may not be a good investment for this student, since college may only increase his wages slightly and he would have to forgo years of salary while in school. I expect the middle quartiles (2nd and 3rd) to be most responsive to tuition because these quartiles should contain most of the students who are on the margin between going and not going to college. In fact, for all regressions in this paper where students are grouped by quartile, the middle quartiles should be the most responsive because they contain the marginal decision-makers. I also expected students from high-income backgrounds to be less responsive to changes in tuition than students from low-income backgrounds; students from high income backgrounds frequently have all or some of their tuition subsidized by their parents, which means they would care less about the tuition cost. As I mentioned in the literature review, there are papers which suggest that the entirety of the college attainment gap is due to parental gifts. I also mentioned in the theory section that risk of failure could play a role; if college is viewed as a risky investment, and if students from low-income backgrounds viewed college as a more risky investment due to the higher probability of failure, then they would be more worried about the cost and having to repay the debt incurred from the failed investment of going to college.
For these regressions, I used robust standard errors and clustered by state, since tuition does not vary within state. I regressed college attendance upon both college tuition and junior college tuition for each income and achievement group. I included junior college because I was curious to see if a student would attend college because of a high cost of in-state tuition. I report the marginal effects in Table 3.1, with the z-value in
|Table 3.1: University Tuition's Effect on College Attendance |
| |QUARTILE | |6299 Observations |
| |1 |2 |3 |4 | |TOTAL |
|Low Income |-.0002 (-0.02) |-.0119 (1.30) |-.0052 (-0.58) |.0195 (2.22) | |.0019 (0.46) |
|Mid Income |-.0124 (-1.62) |-.0067 (-1.35) |-.0068 (-1.48) |-.0002 (-0.03) | |-.0054 (-2.16) |
|High Income |-.0170 (-1.84) |-.0003 (-0.07) |-.0004 (-0.08) |.0093 (1.71) | |.0018 (0.65) |
| | | | | | | |
|TOTAL |-.0085 (-2.07) |-.0019 (-0.66) |-.0032 (-1.14) |.0091 (3.21) | | |
parenthesis. [5] The results were surprising, particularly the significant positive sign on the marginal effects for the highest-achieving quartile. While I had expected them to be the least responsive to changes in tuition, I was surprised to find a highly significant positive marginal effect. I was also surprised to find a significant negative effect of tuition on low achievers; I did not expect them to care much about tuition costs. The fact that they do, however, suggests some low-achieving students view college as a marginal investment. I found no significant difference between tuition’s middle achievers and low achievers when I tested for their equality. I was surprised that low-income students did not seem to be very affected by changes in tuition (perhaps since they receive the most amount of financial aid as a group and thus may not have to pay full tuition anyway). The finding that tuition has a significant negative marginal effect for middle-income students agrees with the prediction I had made. I also tested in Table 3.2 to see whether the middle-income and high-income students could be equally affected by changes in tuition, and found that at the 5% level, we can reject this hypothesis, though we cannot make the conclusion that the middle income and low income marginal effects are different.
|Table 3.2 a) |Table 3.2b) | |
|Testing Middle Income = High Income | |Testing Middle Income = Low Income |
|Chi2( 1) |= |3.73 | |Chi2( 1) |=|2.24 |
|Prob > chi2 |= |0.0533 | |Prob > chi2 |=|0.1343 |
Lastly, although I did not put it in the table, the junior college tuition variable had a marginal effect which was always positive and usually significant for the different income/achievement groups. This relationship indicates that students will also consider the price of alternative investments in human capital when considering college attendance.
Another area that I was really interested in looking at is the perceived cost of college. In 10th grade, the students were asked to estimate the cost of both in-state university tuition and junior college tuition.[6] I thought it could be useful to see what role estimated costs play in college attendance. Since the student will undertake the investment if its net present value is positive, students whose estimate of tuition is below the actual cost of college should be more likely to attend college than students whose estimate is greater than the actual cost of college. Even though they could become aware of the true price before going to college, a high cost estimate could cause students to not apply at all and avoid the costs (both monetary and psychic) of filling out applications, paying application fees, and obtaining teacher recommendations. Also, if a student in 10th grade believed college was too expensive, he might avoid the psychic cost of working hard in high school, a decision which could not be reversed if he later found out that college wasn’t that expensive. I realized that including students who knew the cost of in-state tuition would leave the regression vulnerable to an endogenous variable problem—a student might know the in-state university cost of tuition because he is planning on going to college—so I excluded such students from the regression. Each entry in Table 3.3 shows the marginal benefit of thinking college is too cheap over thinking that it is too expensive, with the z-statistic again in parenthesis.
|Table 3.3: Effects of Thinking College is Too Cheap |
| |QUARTILE | |5148 Observations |
| |1 |2 |3 |4 | |TOTAL |
|Low Income |-.0651 (-0.46) |-.0265 (-0.13) |.1212 (0.65) |.0635 (0.50) | |.0239 (0.32) |
|Middle Income |-.0348 (-0.30) |.0430 (0.43) |.1293 (1.50) |.0059 (0.07) | |.0287 (0.65) |
|High Income |.0873 (0.50) |.0741 (0.74) |-.0602(0.54) |.0817 (0.71) | |.0536 (0.96) |
| | | | | | | |
|TOTAL |-.0967 (-1.42) |.0853 (1.37) | .0876 (1.47) |.0320 (0.60) | | |
When I tested, there was no significant difference between income groups. This surprised me because if students from high-income backgrounds have their tuition subsidized, they should not care about the perceived tuition either, so I would have expected a larger gap between high-income and other groups. It did seem, however, that students in the middle quartiles (who I theorized would be on the margin) were most affected by perceived costs. So I ran a new regression, restricted to students in the 2nd and 3rd quartiles, looking if among these students estimating university to be cheap had a significant effect on college attendance. At the 5% significance level, I concluded that it did.
|Table 3.4: Effects of Thinking College is Cheap for Middle-Achieving Students |
| |Marginal Effects |Z |3407 Observations | | |
|Thinks University Cheap |0.09081 |2.12 | | | | |
I also tested (but did not include in a table) whether the effect of thinking college is cheap on the new middle combined group was significantly greater than that on either the lowest or highest quartile; I found no significant difference between the middle and the highest quartile, but it was significant at 5% on the lowest quartile.
Section 4: Psychic Costs
As I mentioned in the theory section, the Becker model fails to adequately account for non-monetary costs of college. A student may really dislike school and incur immense psychic costs from attending four more years of schooling. These preferences may not be adequately measured by test scores. To investigate the role of psychic costs, I looked at the students’ answers to the question, “Would you describe your most recent job experience as more enjoyable than school?” I omitted from this regression students who responded that they had not held a job; after all, these students would probably have grown up in a family believes children should focus on school. Such students are more likely to not have a job because they plan on going to college.
|Table 4.1: Marginal Effects of Liking School More than Work |
| |Marginal Effect |Z |5295 Observations |
|Likes School Better |0.1049552 |7.69 | |
Table 4.1 shows that as I had expected, there was a large and significant relationship between preferring school and going to college; a student who likes school is over 10% more likely to continue to college. However, I worried that this relationship might only exist because students who like school better tend to be good at school, and thus this regression would suffer from omitted variable bias. To make sure this was not the driving force behind the relationship, I performed the regression again, but this time controlling for composite test score in Table 4.2. The relevant results were as I had expected—the marginal effect went down in magnitude slightly, but still remained highly significant.
|Table 4.2: Marginal Effects of Liking School More than Work, Controlling for Test Score |
| |Marginal Effect |Z |4960 Observations |
|Likes School Better |0.103139 |6.73 | |
I was curious to see how these effects differed by income and achievement. Once again, I would expect the middle-achieving students to be at the margin, and thus exhibit the greatest responsiveness to psychic costs. A high-achieving student, even if he disliked school, would stand to gain sufficiently much from attending college that he would be more likely to go even if he disliked it strongly, and a low-achieving student may not gain much out of school even if he loved it. Table 4.3 shows the results broken down by quartile and income class.
|Table 4.3: Marginal Effects of Liking School More than Work |
| |QUARTILE | |4328 Observations |
| |1 |2 |3 |4 | |TOTAL |
|Low Income | .1652 (1.58) |.2064 (2.59) |.1720 (2.14) |.2472 (3.81) | |.1734 (4.39) |
|Mid Income |.0643 (0.85) |.0600 (1.28) |.0967 (2.34) |.0668 (1.52) | |.0829 (3.68) |
|High Income |.0607 (0.70) |.1394 (2.84) | .1628 (3.78) |.1174 (2.60) |.1419 (5.96) |
| | | | | | | |
|TOTAL |.0305 (0.69) | .1180 (4.09) | .1104 (4.16) |.1136 (4.33) | | |
As predicted, the marginal effects on the lowest achieving group are generally not significant, whereas the middle quartiles do show a significant relationship. When I tested differences between income groups, I was unable to conclude at the 5% significance level that the three income classes did not all have the same marginal effects on college attendance. I tested in Table 4.4 whether there was a significant difference between quartiles 1 and 2, since their marginal effects that look pretty far apart, but found no significant difference.
|Table 4.4: Testing Quartile 1 = Quartile 2 |
|chi2( 1) |= |2.03 |
|Prob > chi2 |= |0.154 |
I was surprised that the influence of liking school seems to be similar for high- and middle-achieving students. Of course, these regressions don’t conclusively prove there is no difference between the upper and middle quartiles. But if the gap were indeed as small it appears, it may indicate that psychic costs to attending college can be extremely high compared to possible differences in human production function. Under this interpretation, the difference in return to college between a middle-achieving and high-achieving student may appear small to high school students, whereas the psychic toll of going to college for anybody when one prefers to work would be quite large. Whatever the cause, if test scores are an adequate measure of the capacity to absorb human capital, these regressions show that the enjoyment of the learning experience does play a significant role in an educational attainment decision.
Last, I was curious to see if there was a difference within achievement groups of their work-school preference. If some groups tended to like school much more than others, this could explain different college attainment between groups, even if members of different groups respond similarly to liking school. I had anticipated that students who score poorly on achievement tests generally would like work more than school, since they would be more likely to struggle in school. Low income students also tend to go to schools with less physical infrastructure and less talented teachers, which makes me predict that low-income students would more frequently prefer work. Table 4.5 shows that this does not appear to be the case. There are no substantial differences in school
|Table 4.5: School Enjoyment by Income Group and Quartile |
| |QUARTILE | | |
| |
| |QUARTILE |4232 |Observations |
| |1 |2 |3 |4 | |TOTAL |
|Low Income |.6502 (0.69) |.2183 (0.26) |.1691 (0.25) |1.137 (1.26) |.4126 (0.99) |
|Mid Income | 1.407 (2.00) | 1.058 (1.97) |.4677 (0.79) |-.0649 (-0.16) | .2782 (1.08) |
|High Income |-.1637 (-0.16) |-.4739 (-0.68) |-.2902 (-0.38) |.1141 (0.15) |-.6075 (-1.63) |
| | | | | | |
|TOTAL |.6081 (1.47) |.6147 (1.89) |.0124 (0.04) |-.2895 (-0.96) |
effect of high income is surprising; one possible explanation for why students from high income families do not seem at all affected by changes in the labor market is that their family might have connections to get them a good job regardless of the general conditions. Also, students from a high income family could rely on their family’s wealth if they did not immediately find a job. As Table 5.2 shows, students from a high-income background are significantly less responsive to unemployment conditions than students from middle- or low-income backgrounds.
|Table 5.2a) | |Table 5.2b) |
|Testing Middle Income = High Income |Testing Low Income = High Income |
|Chi2( 1) |= |3.34 | |Chi2( 1) |= |3.83 |
|Prob > chi2 |= |0.063 | |Prob > chi2 |= |0.0503 |
It is worthwhile to mention that when the job market is depressed enough, students actually face a tradeoff between investing in human capital and leisure time, rather than investing and working. Though my theory section does not investigate the decision between investing in capital and in leisure time, this may be a decision that some students face who are deciding what to do upon graduation.
Section 6: Parent Education
To examine whether parental education plays a role in college attendance, I looked at the highest level of education that a student’s parent had attained.[8] I then regressed college attendance on each level of parental education, grouped by achievement quartiles. Table 6.1 shows that as the parent’s levels of education rises, so does the probability of the student attending college. I performed some F-tests, which I did not include to save room, and found that for each quartile, the marginal effects of parent college graduate is significantly greater than that of students whose parents are high school dropouts. Clearly, parents who went to college improve their child’s chances of going to college.
|Table 6.1: Effects of Parent Education on College Attendance |
| |QUARTILE |8273 Observations |
| |1 |2 |3 |4 |TOTAL |
|Unknown Parent Ed. |-.229 (-7.12) |.047 (1.16) |.205 (5.31) |.218 (5.95) |-.035 (-1.84) |
|Parents HS Dropouts |-.184 (-4.72) |.027 (0.64) |.100 (2.13) |.197 (4.76) |-.053 (-2.51) |
|Parents HS Grads |-.160 (-5.11) |DROPPED |.175 (5.95) |.081 (8.69) |DROPPED |
| | |(Base case) | | |(Base case) |
|Parents Some College |-.028 (-0.82) |.077 (2.49) |.241 (8.83) |.328 (13.59) |.100 (6.59) |
|Parents College Grads |.077 (1.86) |.248 (8.40) |.381 (17.23) |.465 (26.56) |.292 (20.07) |
This section will look at the possible effects that parental education has on transferring knowledge about college to their children, since I was most interested in looking at the roles of knowledge and attitudes in the college attendance process. Clearly, parents serve more of a purpose than transmitting information, and this section takes a narrow view which will not capture all, or even most, of the effects parents have on their children. That said, having a well-educated parent could encourage a student to go to college in a few ways. A parent who went to college is more likely to be familiar with the existence of college aid. Second, this parent would also be able to communicate to the student the value of a college degree. Third, this parent is likely to place a more value on education, and thus may pass on an enjoyment of learning to his children.
To test if a student with a college educated parent enjoys learning, I return to the question which asked students if they liked school more than their most recent job, again omitting students who had held no job. I regressed liking school on the parental education levels. The results, presented in Table 6.2, show nothing conclusive—most parent education groups have negative but insignificant marginal effects, while one group has a positive marginal effect when compared to parent college graduates.
|Table 6.2: Effects of Parent Education on Liking School |
|Highest Parent Ed. Level |Marginal Effects |z |5271 Observations |
|Unknown Parent Education |-0.01133 |-0.45 | |
|Parents HS Dropouts |0.050156 |1.84 | |
|Parents HS Grads |-0.03963 |-2.1 | |
|Parents Some College |-0.01682 |-0.89 | |
|Parents College Grads |DROPPED (BASE CASE) |
I also ran this regression within each income class, and found no significant results for any group. To simplify the regression, I regressed liking school better upon the parent college graduate variable to see if I could definitively say that students with college graduate parents like school more than students without college graduate parents. Table 6.3 shows that I found a positive but insignificant marginal effect, which is what I expected based on the results from the above regression.
|Table 6.3: Effects of Parent College Grad. on Liking School |
| |Marginal Effects |z |5101 Observations |
|Parent College Grad |0.01266 |0.79 | |
Related to this, which I thought would be worth investigating, is whether students who have parents who are college graduates tend to work less. I anticipate that parents who value education would be more likely to tell their children to focus on school and not work. To investigate this, I regressed not holding a high school job on the different parent education levels, and present the results in Table 6.4. Students with college graduate parents do not always work less than other groups; they work more than some groups but less than others. When I ran a regression like in Table 6.3, to just compare students with college graduate parents to those without, the marginal effect of having a college graduate parent was positive but not significant. Thus, there is no conclusive evidence that college graduate parents create children which enjoy learning more or place more value on education.
|Table 6.4: Effects of Parent Education on Student Not Working |
| |Marginal Effects |z |8273 Observations |
|Unknown Parent Education |0.0693218 |3.53 | |
|Parents HS Dropouts |0.071 |3.28 | |
|Parents HS Grads |-0.043 |-3.11 | |
|Parents Some College |-0.029 |-2.11 | |
|Parents College Grads |DROPPED (BASE CASE) | |
Next, I decided to examine the second proposition—that a college educated parent would be better at explaining to her child the importance of a college education in finding a job. The best question in the survey I could find to test this theory was the question in the First Follow-up Survey, “If you were to go to college, how important of a factor is a school’s job or employment placement record?” Students either answered not important, somewhat important, or very important. I predicted that students who knew more about college’s effects on earnings would be more likely to try to maximize that effect. Since students whose parents are college graduates should better understand the earnings effect, I predicted that when I regressed viewing job placement as very important upon parent education levels, the marginal effect of college graduate parents should be positive. Table 6.5 shows that the result I got was not what I expected.
|Table 6.5: Effects of Parent Education on Viewing Job Placement As Important |
|Highest Parent Ed. Level |Marginal Effects |z |6459 Observations |
|Unknown Parent Education |0.05243 |2.33 | |
|Parents HS Dropouts |0.122291 |4.97 | |
|Parents HS Grads |0.078333 |4.54 | |
|Parents Some College |0.045174 |2.66 | |
|Parents College Grads |DROPPED (BASE CASE) |
Every group was significantly more likely to view job placement more important than were students with college graduate parents. I also ran this regression separately for each income group, and found no big differences from the regression when it did not distinguish between income levels. Furthermore, when I ran this regression separately for each achievement group, the results from Table 6.5 generally held, though there was no significance for most of the variables, probably due to the smaller sample size. These results could mean a few things. It could be that college parents explain to their children that college is important, but this doesn’t necessarily translate into the student picking a school based on job placement. It could mean that students with college graduate parents more likely to care about other factors in a college, such as what academic programs the school has which can better fulfill the student’s needs and desires. Alternatively, students with parents who went to college may believe that although going to college is important, almost any college they look at can help them find a good job.
The third proposition that I wish to examine is that a parent with a college education would be more familiar with the financial aid process, and would pass that knowledge onto his child. In the First Follow-up Survey, students were asked a series of questions about whether they were eligible for a series of financial aid packages (Pell grants, student loans, etc.) I created a dummy variable (which I will refer to as “aid eligibility”) which was equal to 1 if the student knew that he was eligible for at least one of those packages and 0 otherwise. Knowing about aid can have a huge influence on the decision to go to college, as aid lowers real costs. If parents who had gone to college are more familiar with the aid process and pass this familiarity on to their children, then we would expect a positive relationship between parents attending college and a student knowing about aid. I did not want to merely regress aid knowledge on parent education level, though, because it would not let me conclude that parent education causally increases aid knowledge. Because students who have already decided to go to college should know more about aid, I would expect student knowledge of aid to rise as parent education rises even if parent college attendance did not cause aid knowledge and other forces caused the correlation between parent education and college attendance. Therefore, a regression of aid knowledge on parent education level would not be a valid one to determine causal effect. To account for this problem, I regressed aid knowledge on parental education given that the student chose not to go to college. After all, even if the student chose not to go to college, the hypothesis suggests that he would be more likely to know about financial aid if his parents went to college. I only did this regression for low- and middle-income classes, because high-income students would likely not be eligible for financial aid, so I would not get any useful results. There were categories about financial aid on the questionnaire that most low- and middle-income students should have been able to respond affirmatively to.
|Table 6.6: Aid Knowledge by Parent Education |
| | | |2160 Observations |
| |Low Income | |Middle Income |TOTAL |
|Unknown Parent Education |-.0825071 (-0.87) |-.182964 (-2.16) |-.0718948 (-0.43) |
|Parents HS Dropouts |-.0172797 (-0.19) |-.2015441 (-2.37) |.0610269 (0.36) |
|Parents HS Grads |-.0569075 (-0.66) |-.1779042 (-2.21) |-.0339548 (-0.24) |
|Parents Some College |.012245 (0.14) |-.1735936 (-2.14) |.0495605 (0.33) |
|Parents College Grads |DROPPED (Base case) |-.1601143 (-1.87) |DROPPED (Base case) |
For both middle income and low-income students, the marginal effects of parent college graduate are slightly higher than most of the other marginal effects of that income class. There are no significant differences within income classes or in the “Total” table. However, I realized that parents who had some college education should also be familiar with financial aid, so I created a variable for if a student’s parent had entered college. I regressed aid knowledge upon the entered college variable (omitting students who had gone to college and students from high income backgrounds). Table 6.7 shows that there is a positive correlation but it is insignificant.
|Table 6.7: Effects of Parent Attending College on Student Knowing Financial Aid |
| |Marginal Effects |z |2330 Observations |
|Parent Attended College |0.01378 |0.65 | |
This section shows a couple of important things about parental education in this section. Clearly, it is an important factor; students with parents who went to college are more likely to go to college themselves, regardless of race, family income, or student achievement level. None of the three hypotheses I offered to explain the importance were born out by the data; in fact, the significant conclusion I was able to draw is that students who have parents who graduated from college are not as interested in job placement when choosing their own college.
Section 7: A Complete Model
I now want to put all of these effects together into a more complete model to see the results of all the major factors I mentioned put together. After controlling for region, community type, and the peer college attendance variable I mentioned in the data section. I put the factors I mentioned in previous sections into the model and did two regressions. The first regression found marginal effects of the factors for all students; the second computed them for students only in the second and third quartiles, because I expected these students to be most likely to be on the margin in their college attendance decision, and thus the model would be most illuminating if we looked at the way factors affected them.[9] I reported in Table 7.1 how key factors fared. In summary, most of the signs on variables are as I had expected them to be, particularly in the regression on middle-
|Table 7.1: Big Model, No School Fixed Effects |
|Variable |Total | |Middle Quartiles |
|Unknown Parent Education |-0.0166438 (-0.51) |.0193245 (0.50) |
|Parents High School Dropouts |.0196608 (0.57) | |-.0404419 (-1.00) |
|Parents HS Grads |DROPPED (Base Case) |
|Parents Some College or Voc. School |.0822906 (3.74) | |.061764 (2.33) |
|Parents College Grads |.2220209 (10.02) | |.2163487 (7.91) |
|Low Income |-.1130045 (-4.36) | |-.1272209 (-4.26) |
|Middle Income |-.0731242 (-3.84) | |-.0700928 (-3.13) |
|High Income |DROPPED (Base Case) |
|University Tuition |.0010657 (0.35) | |-.000161 (-0.05) |
|Junior College Tuition |-.0021857 (-0.40) | |-.0001152 (-0.02) |
|Unemployment Rate |.2445221 (0.92) | |.4497786 (1.37) |
|College Attendance |.179609 (1.45) | |.302965 (2.05) |
|Prefers School to Working |.1164901 (6.20) | |.1230089 (5.45) |
|Never Worked |.1575341 (6.90) | |.1572108 (5.61) |
|Black Male |DROPPED (Base Case) |
|Black Female |.1732439 (3.77) | |.1186039 (1.99) |
|White Male |-.0961149 (-2.08) | |-.1355308 (-2.57) |
|White Female |-.0777675 (-1.74) | |-.1106375 (-2.12) |
|Hispanic Male |-.1370678 (-2.90) | |-.1536818 (-3.00) |
|Hispanic Female |-.0261895 (-0.55) | |-.0372859 (-0.67) |
achieving students, though few marginal effects are significant. The marginal effects of income are still both significant and large; the marginal effect of low-income is essentially the same as it was in Table 2.3, though the marginal effect of middle income is a little lower. These factors that I added did not fully explain why there is a difference in college attendance between income groups, though the movement toward zero of the middle income marginal effect suggests I might have explained some of it. There are also still large differences between demographic groups which were not explained away. Parental education remained significant in both regressions, which suggests its influence is quite important.
Clearly, there are some influences that I had not been able to measure. To try to get at some of those influences, Table 7.2 shows the results of a regression which controlled for school-fixed effects. This sort of regression should control for unobserved school quality, community factors, and other unobserved variables which may differ by school. I dropped from the regression the variables which would not change within school (college tuition, region, community type, etc.) For school-fixed effects this regression, I did not use a logistic regression model; I instead used a linear model for convenience’s sake. However, the difference should not greatly change any results. The marginal effects of income are still significant, and barely fell at all from the non-fixed effects regression, suggesting that school quality is not necessarily the reason for the college attainment gap (though school quality may very well be associated with factors which affect college attendance). Attitudes toward school’s enjoyment are still very significant. Parental education still retains its significance, though its effect is lower.
I can’t test whether this is a significant difference, of course, because the school-fixed
|Table 7.2: Big Model, School-Fixed Effects |
|Variable | |Total | |Middle Quartiles |
|Unknown Parent Education | |-.0176397 (-0.71) |.0203832 (0.52) |
|Parents High School Dropouts | |.0224447 (0.83) |-.0151719 (-0.36) |
|Parents HS Grads | |DROPPED (Base Case) |
|Parents Some College or Voc. School | |.0561323 (3.14) | .0540153 (2.02) |
|Parents College Grads | |.1542402 (8.04) |.1633039 (5.69) |
|Low Income | |-.0738869 (-3.45) |-.1198883 (-3.58) |
|Middle Income | |-.0442972 (-2.89) |-.0677212 (-2.96) |
|High Income | |DROPPED (Base Case) |
|Unemployment Rate | |.3862642 (1.58) |.7670135 (1.73) |
|Prefers School to Working | |.0879899 (5.84) |.1113878 (4.81) |
|Never Worked | |.0957923 (5.06) |.1126723 (3.91) |
|Black Male | |DROPPED (Base Case) |
|Black Female | |.1283679 (3.02) |.0401795 (0.56) |
|White Male | |-.0162101 (-0.36) |-.0568836 (-0.75) |
|White Female | | .030014 (0.73) |.0079727 (0.11) |
|Hispanic Male | |-.067803 (-1.63) |-.0755379 (-1.09) |
|Hispanic Female | | .0363676 (0.87) |.0010846 (0.02) |
effect regression was a separate regression from the non-fixed effect. We also see in school-fixed effects a wide variety of marginal effects of race variables, but this effect is not nearly as pronounced in the middle quartiles. I want to investigate these differences in the race variables in the next section.
Section 8: Studying Gender Gaps within Race
The biggest thing that jumped out at me from the above regressions is the fact that for blacks and Hispanics, there is a significant difference in college attainment between males and females; females go to college at a significantly higher rate. This is surprising; if the different attendance rates were due to unobserved family or community factors, one would expect that the impact would be equal for males and females, since gender is a randomly distributed variable within the family. The fact that gender gaps do occur merits a close look, and this section will hope to come up with some explanation for those gaps in collegiate enrollment.
I first chose to examine the gap in enrollment in college between Hispanic males and Hispanic females. To examine more closely the differences in college enrollments, I ran a single regression on Hispanic males and Hispanic females, interacting each variable with gender dummies. The advantage of running it as a single regression, of course, is that I would be able to test for significant differences between genders. I did not interact the variables with score quartile dummies, though, because I was worried there would be too few observations for each quartile to conclude anything meaningful and significant.
What appear to be some important differences between these two groups? For one, the fact that the marginal effect of low income for males is negative and significant, whereas the marginal effect of females is slightly positive is clearly important. I tested to
|Table 8.1: Gender Effects on Hispanics |532 Observations |
| |MALE | |FEMALE |
|Variable |Marginal Effects |z | |Marginal Effects |z |
|Unknown Parent Ed. |-0.0749 |-0.58 | |-0.0895 |-0.77 |
|Parent HS Dropout |0.0047 |0.04 | |-0.0205 |-0.21 |
|Parent HS Grad |DROPPED (Base case) | |DROPPED (Base Case) |
|Parent Some College |0.0173 |0.17 | |0.0652 |0.72 |
|Parents College Grads |0.1744 |1.59 | |0.1211 |1.15 |
|Low Income |-0.1903 |-2.24 | |0.0880 |0.9 |
|Middle Income |-0.0695 |-0.86 | |0.0678 |0.83 |
|High Income |DROPPED (Base case) | |DROPPED (Base case) |
|Composite Score |0.0000 |4.59 | |0.0000 |6.04 |
|Unemployment Rate |0.4977 |0.9 | |0.3091 |0.4 |
|Prefers School to Work |-0.0151 |-0.16 | |-0.1192 |-1.64 |
|Prefers Work to School |-0.0040 |-0.04 | |-0.1517 |-2.11 |
|Never Worked |DROPPED (Base case) | |DROPPED (Base case) |
|University Tuition |-0.0147 |-1.27 | |0.0083 |0.89 |
|Junior College Tuition |0.0060 |0.54 | |0.0164 |1.63 |
|Job Placement Importance |0.0880 |1.11 | |0.0507 |0.72 |
|Thinks Univ Cheap |0.1561 |0.91 | |0.0522 |0.34 |
|Thinks Univ Expensive |-0.1139 |-1.12 | |-0.0614 |-0.68 |
|Being Female |N/A | |-0.0100 |-0.02 |
see whether the marginal effects of poor or middle income could be equal between the two groups, and the results are shown in Table 8.2. These results are really interesting; at the 5% significance level, low-income females are more likely to attend college than low-income males. This result does not hold in middle- or high-income cases, though. Therefore, we can determine that some of the gender gap for Hispanics comes from different behavior among only low-income students with similar other characteristics.
|Table 8.2 |
|Testing Low Income Female = | |Testing Middle Income Female = Middle Income Male |
|Low Income Male | | |
|chi2( 1) |= |4.19 | |chi2( 1) |= |1.4 |
|Prob > chi2 |= |0.0407 | |Prob > chi2 |= |0.2365 |
It also seemed like the males were more concerned with the short-term monetary costs than females were; high university tuition appears likely to decrease off male college attendance more than it does female college attendance. I tested to see if the difference was significant; it was not, as Table 8.3 shows.
|Table 8.3:Testing Equal Reaction to University Tuition |
|chi2( 1) |= |2.39 |
|Prob > chi2 |= |0.1221 |
Males also seem to care more about the perceived cost of going to college. Table 8.4 shows that for males, those who estimated college as cheaper than it actually was went to college at a significantly higher rate than those who estimated it as too expensive; this effect was not significant in females.
|Table 8.4: Testing Equality Between University Cost Estimates |
|Male | |Female |
|chi2( 1) |= |3.35 | |chi2( 1) |= |0.69 |
|Prob > chi2 |= |0.0674 | |Prob > chi2 |= |0.4045 |
Parent education effects looked fairly similar between genders; no level of parent education was significantly different for males and females. Males also seemed to worry more about job market factors—they seemed more responsive to changes in the unemployment rate, though this difference was not significant when I tested it. The other interesting result I see is that for females, those who did not work appear to be significantly more likely to go to college than those who did. This effect does not appear in males at all; the male student who never worked is estimated to be only 0.4% more likely to attend college than a similar student who prefers work to school .
I looked to see whether the college enrollment gap could be explained by differences in the genders themselves. If males and females possessed different characteristics which would impact their college attendance, this could also tell us something about why the gap exists. For example, if females Hispanics were simply better students or smarter than their male counterparts, this could account for the gap we saw earlier. This was not the case; the average Hispanic female score was well below the average Hispanic male score, and there were more Hispanic females than males in lower quartiles but more males than females in higher score quartiles. The distribution of parent education levels was about the same for both genders. I then proceeded to look at if there were large differences in attitudes towards school between females and males; there were none. Among females who had held a job, 37% said that their most recent work was more enjoyable than school; among males that number rose slightly to 41%. Females were, however, more likely to not hold a job in high school; 33% of Hispanic females did not work in high school, whereas only 25% of males held no job. This is an important contribution to understanding the college gap, especially when we remember that females who didn’t work tend to go to college significantly more than those who didn’t. This attitude toward jobs may in part come from the fact that Hispanics, particularly low-income Hispanics, may include lots of immigrants bringing their own cultural norms which we might not see in whites or blacks. Last, I ran a school-fixed effects regression but found nothing significant and interesting that was different from the above regressions.
To summarize the difference in college attendance between Hispanic males and females, it seems to boil down to two main points. One is the emphasis on short-term costs; it appears that Hispanic males may have a higher internal discount rate. I base this conclusion on their greater responsiveness to university tuition (both actual and perceived), unemployment rate, and family income. The other main point is that there female seem to concentrate on their schoolwork more than their male counterparts; females tend to work less and among those who don’t work, there is a higher college attendance probability.
I was then interested to compare the experiences of Hispanic males and females to those of black males and females. Like Hispanics, black females went to college at a significantly higher rate, yet they had consistently lower test scores. I performed the
same regression as I did for the Hispanic section with the black population. The results, are below in Table 8.4.
|Table 8.4: Gender Effects on Blacks |336 Observations |
| |MALE | |FEMALE |
|Variable |Marginal Effects |z | |Marginal Effects |z |
|Unknown Parent Ed. |-0.2121 |-1.11 | |-0.0895 |-0.77 |
|Parent HS Dropout |-0.1956 |-0.94 | |-0.0100 |-0.05 |
|Parent HS Grad |DROPPED (BASE CASE) | |DROPPED (BASE CASE) |
|Parent Some College |-0.1374 |-1.01 | |0.0827 |0.78 |
|Parents College Grads |0.0010 |0.01 | |0.0830 |0.71 |
|Low Income |-0.1432 |-0.97 | |-0.2123 |-1.66 |
|Middle Income |0.0031 |0.03 | |-0.2012 |-1.73 |
|High Income |DROPPED (BASE CASE) | |DROPPED (BASE CASE) |
|Composite Score |0.00001 |4.57 | |0.00001 |4.02 |
|Unemployment Rate |-0.4609 |-0.48 | |-0.7276 |-0.77 |
|Prefers School to Work |-0.0330 |-0.31 | |0.0088 |0.09 |
|Prefers Work to School |-0.2144 |-1.59 | |-0.0576 |-0.5 |
|Never Worked |DROPPED (BASE CASE) |DROPPED (BASE CASE) |
|University Tuition |0.0266 |1.68 | |0.0075 |0.6 |
|Junior College Tuition |-0.0035 |-0.25 | |-0.0202 |-1.14 |
|Job Placement Importance |0.0628 |0.68 | |0.2060 |2.78 |
|Thinks Univ Cheap |-0.1231 |-0.55 | |-0.0519 |-0.23 |
|Thinks Univ Expensive |-0.1550 |-1.16 | |-0.0473 |-0.38 |
|Being Female |N/A | |0.4778 |0.71 |
In contrast to Hispanics, black females have the large negative (but not significant) marginal effects of lower income. I tested in Table 8.6 whether these differences are significant between black males and black females, and found they are not. It seems like this regression does not explain the causes of the gender gap as well as the Hispanic regression did; the dummy on being for blacks was not significant, but the marginal effect was estimated to be a lot larger. Neither group has the signs I expected on university tuition or junior college tuition, which is interesting, though no significant conclusions may be drawn.
|Table 8.6 |
|Testing Low Income Female = | |Testing Middle Income Female = Middle Income Male |
|Low Income Male | | |
|chi2( 1) |= |4.19 | |chi2( 1) |= |1.4 |
|Prob > chi2 |= |0.0407 | |Prob > chi2 |= |0.2365 |
It seems that females viewed college as more of a necessity to increase their earnings. I base this hypothesis off of two results. First of all, the marginal effects of being female and not liking school was a lot smaller in magnitude than the marginal effects of being male and not liking school, though this was not a significant difference, as Table 8.7 shows.
|Table 8.7: Testing Equal Gender Reaction to Preferring Work |
|chi2( 1) |= |0.76 |
|Prob > chi2 |= |0.3840 |
Second, the marginal effects of females viewing job placement as highly important was significant, while it wasn’t for males. This may mean that females who were worried about finding jobs went to college, whereas males who worried about finding jobs did not view college as necessary. There was not a significant difference between the two marginal effects, however, so I don’t want to read too much into this difference. I cannot conclude that there is a difference between how black males and black females understand the economic return to college, but the data suggest that this might be something worth looking into in greater depth. I looked to see whether there were large differences in attitude toward school, but there weren’t; both males and females had about the same percentage of students who hadn’t worked, and were within a couple of percentage points in their preference of school/work.
Chapter 5: Conclusion
Studying the college attendance decision of teenagers, as the empirical section has shown, is complicated, to say the least. Some predictions were verified, while others were not. Overall, it does seem that middle-achieving students are more responsive to factors the theory section suggested would be important—we see this in their propensity to not go to college in the wake of high tuition, their tendency to go to college when they estimate college to be cheap, their increased frequency to go to college when they enjoy school, and their responsiveness to the unemployment rate were all generally as I predicted. The results on high-achieving students were a little more ambiguous—they did not behave the way I predicted in reacting to university tuition or unemployment rates.
The section on differences within race showed that gender appears to affect different races differently. For whites, there was no significant difference in college attendance between genders, suggesting that most factors I mentioned affect white males and white females equally. For Hispanics, males and females appear to react to poverty quite differently—females from low-income backgrounds showed a significantly higher propensity to go to college than did their male counterparts. Males seemed to be much more attuned to short-term factors than females did—they appeared to shy away from college when faced with a higher tuition rate, higher expected tuition rate, or a better job market. None of these results were significant, again, but there does appear to be a trend which is worth looking into. For blacks, the picture came out a little more murky—the regression did not seem to explain away the gender gap entirely, but it’s interesting that we did not see the same income-effect difference between males and females that we saw for Hispanics. Nonetheless, again the data seemed to indicate that females viewed school as more of a long-term investment which was necessary to make to ensure higher future earnings. Last, it’s interesting to remember that there was no such gap in college attendance between white males and females. This means that the differences between male and female college attainment in certain demographics aren’t necessarily the result of different job markets and career paths the genders would face.
Future research on this topic could be done in a variety of ways. First and foremost, I’m curious how this analysis would turn out had this analysis been done 20 years later—students in this survey were making their decisions whether to attend college before I was born. I frequently hear about how college degrees are becoming more and more necessary to compete in today’s workplace, and would be curious to see if the college attainment gap has narrowed as degrees become more important. Second, I was originally interested in learning how the most recent trends in financial aid would affect college attendance. Harvard’s policy that all families who earn under $180,000 pay only 10% of their annual earnings and Amherst’s policy to replacing loans with grants seemed interesting, but I wondered if these policies would be taking away students from (cheaper) state schools, encourage students who would not normally apply to college to enroll, or merely give students who would already attend those colleges a lower debt burden upon graduation. It’s too early to tell right now what effect these policies have had. My analysis suggests that high-achieving students from all income classes are not affected by tuition costs, and so the new policies we keep hearing about might not do much to decrease the overall college attainment gap, unless these policies put pressure on other, less selective institutes to also offer more aid and lower their prices. If this were the case, then the new financial aid policies of recent years would have a trickle-down effect that may actually increase overall college attendance among students who are at the margin of deciding whether to go to college. There may never be a consensus on what role tuition costs play in the college decision process, or a widely accepted explanation for why there are such different attendance rates among different groups with similar test scores. Nonetheless, it appears from my research that while lowering prices will help increase college attendance, family and community factors will also remain important.
Works Cited
Avery, C., C. M. Hoxby, et al. (2004). Do and Should Financial Aid Packages Affect Students' College Choices? College choices: The economics of where to go, when to go, and how to pay for it, NBER Conference Report series. Chicago and London: University of Chicago Press: 239-299.
Becker, Gary S. and Gilbert R. Ghez. The Allocation of Time and Goods over the Life Cycle. New York: National Bureau of Economic Research: Columbia University Press: 1975.
Brinkman, P.T and L. L. Leslie. "Student Price Response in Higher Education: The Student Demand Studies." Journal of Higher Education, March/April l987, Vol. 58, No. 2, pp. l8l-204.
Cameron, S. and J.J. Heckman (1999). "Can Tuition Policy Combat Rising Wage Inequality?" Financing College Tuition: Government Policies and Educational Priorities. Washington: American Enterprise Institute Press.
Carneiro, P. and J. J. Heckman (2002). "The Evidence on Credit Constraints in Post-secondary Schooling." Economic Journal 112(482): 705-734.
Cunha, F. and J.J. Heckman (2007). "Identifying and Estimating the Distributions of Ex Post and Ex Ante Returns to Schooling." Labour Economics, December 2007, Vol. 14, iss. 6, pp. 870-93
Dynarski, S. M. and J. E. Scott-Clayton (2006). "The Cost of Complexity in Federal Student Aid: Lessons from Optimal Tax Theory and Behavioral Economics," National Bureau of Economic Research, Inc, NBER Working Papers: 12227.
Ellwood, D. T., T. J. Kane, et al. (2000). Who Is Getting a College Education? Family Background and the Growing Gaps in Enrollment. Securing the future: Investing in children from birth to college, Ford Foundation Series on Asset Building. New York: Russell Sage Foundation: 283-324.
Field, E. (2006). "Educational Debt Burden and Career Choice: Evidence from a Financial Aid Experiment at NYU Law School," National Bureau of Economic Research, Inc, NBER Working Papers: 12282.
Kane, T. J., C. R. Belfield, et al. (2003). College Entry by Blacks since 1970: The Role of College Costs, Family Background, and the Returns to Education. The economics of higher education, Elgar Reference Collection. International Library of Critical Writings in Economics, vol. 165. Cheltenham, U.K. and Northampton, Mass.: Elgar: 253-286.
Kane, T. J. (1995). "Rising Public College Tuition and College Entry: How Well Do Public Subsidies Promote Access to College?" National Bureau of Economic Research, Inc, NBER Working Papers: 5164.
Leonhardt, David. "The (Yes) Low Cost of Higher Ed." New York Times 20 April 2008.
McPherson, M. S. and M. O. Schapiro (1991). "Does Student Aid Affect College Enrollment? New Evidence on a Persistent Controversy." American Economic Review 81(1): 309-318.
Stinebrickner, T. R. and Ralph Stinebrickner (2007). "The Effect of Credit Constraints on the College Drop-out Decision: A Direct Approach Using a New Panel Study." National Bureau of Economic Research, Inc, NBER Working Papers: 13340.
-----------------------
[1] Net cost is defined as tuition minus financial aid; that is, how much the student actually will pay
[2] Throughout this paper, I will use “he” to refer to a single student; this is simply a stylistic decision and should not be interpreted to mean that I am only looking at male students
[3] The question asked if the student’s family income was below $15,000, between $15,000 and $30,000, or above $30,000. The question also stated that each income class represented an “equal group” of American families.
[4] To determine quartiles of achievement groups, I combined the reading score and math score of the student on the standardized test the student took, and then separated that composite score into quartiles. Quartile 1 represents the lowest score quartile, and Quartile 4 represents the highest.
[5] Since this format of table appears repeatedly throughout the paper, I thought it would be useful to briefly explain how I do such tables. First of all, z-values will be in parentheses for all tables like this. Second of all, this table actually shows the results of three regressions. The first regression gave me the results in the middle of the table; marginal effects are from quartile interacted with income level multiplied by tuition. The model for this regression is wenttocollegeually shows the results of three regressions. The first regression gave me the results in the middle of the table; marginal effects are from quartile interacted with income level multiplied by tuition. The model for this regression is wenttocollege = β1*university tuition*low income*quartile 1 + β2*university tuition*low income*quartile 2 +… + β13*low income*quartile 2 +… . For the “Total” categories, however, I did these a separate regression; for example, the marginal effects in the Income Totals come from a regression where I interacted income dummies with tuition, but not quartiles. Similarly, the totals for quartile come from tuition interacted with the score quartile dummy. The fact that there are multiple regressions contained in one table explains why in some tables, there are multiple “Base Cases.”
[6] Specifically, students were asked to estimate “Schooling costs at a state 4-year college or university”. They were given six different price ranges and asked to pick one. If the student picked the price range which contained the actual in-state tuition, I considered him to have known the cost of in-state tuition. The question about junior college tuition was similarly worded and posed.
[7] Numbers in table represent percent of respondents in the group who had worked and preferred school to their most recent job
[8] If both parents’ education were reported by the student, I set parent education to be the higher level of the two. If one was unknown or blank and one was reported, I set parent education level to be the reported level. If both were unknown or blank, I said parent education level was unknown.
[9]The regression for all students also included a composite score variable in it, to make sure no other estimates were biased by achievement-related effects.
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