essay on the determinants and implications of the choice of undergraduate major

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Mark N. Mitchell

2006

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ESSAYS ON THE DETERMINANTS AND IMPLICATIONS OF THE CHOICE OF

UNDERGRADUATE MAJOR

Abstract

by

Mark N. Mitchell

The following series of essays has been assembled to examine the determinants

and implications surrounding the choice of undergraduate major. Other studies have

analyzed various aspects of the decision making process associated with the choice of

college major, however, many questions remain unanswered. These questions include:

1.) How does the probability of receiving a job offer and expected earnings that

incorporate risk affect a student’s choice of major at a selective university? 2.) What are

some of the implications that the choice of major has upon other college decisions such

as borrowing behavior? 3.) What affect does choosing a second major have upon a

student’s earnings? 4.) How do the answers to these questions change when describing

the choices of men and women? These essays are an attempt to address these

shortcomings in previous research in this area.

There have been several studies that model the college student’s choice of major

as a utility maximizing decision that is primarily based upon the relative expected

earnings that are correlated with different majors. One problem with these studies is that



Mark N. Mitchell

few incorporate the fact that students face various forms and degrees of uncertainty and

risk in their choice of major. Motivated by this shortfall, this first essay models a

student’s choice of major as being determined primarily by a student’s relative expected

earnings. Students’ choice of major at a selective university is shown to be positively

correlated to relative expected earnings adjusted for earnings uncertainty or risk.

Students at this selective university are less motivated by another form of uncertainty

inherent in the choice of major, the probability of receiving job offers across majors.

Once a student has chosen a major, this choice may have particular importance inother decisions that a student makes while in college. The second essay takes an

alternative look at the relationship between a student’s choice of major and the amount of

loan debt they choose to accumulate during college. Based on a life-cycle model of

consumption and borrowing, this essay suggests that a student’s choice of major could

influence the level of debt that a student will take on. This study finds that some students

in higher earnings majors do tend to have higher total debt levels. The endogenous

nature of major choice and loan debt is also addressed.

The final essay explores an aspect of the choice of college major that has

previously been ignored. While the earnings implications of a student’s primary major

have been the focus of several empirical studies, little attention has been paid to the

earnings implications of a student’s choice of a second major. This essay empirically

tests whether students from a selective university actually receive some type of monetary

return to investing in a second major. Results show that some students do benefit from

choosing to obtain a second major.



CONTENTS:

ESSAY 1

EXPECTED EARNINGS, EMPLOYMENT, AND THE CHOICE

OF UNDERGRADUATE MAJOR

1.1 INTRODUCTION

Background ……………………………………………….….………..1

Statement of the Problem…………………………………..…………..1

1.2 REVIEW OF THE LITERATURE.………………………….….…………3 Marc Berger (1988)………………………………………………….…4Eric Eide & Geetha Waehrer (1998) ……………………………...…...5Montmarquette, Cannings, Mahseredjian (2002)…….…………….......5

1.3 METHODOLOGY AND DATA

Similarities with Flyer (1997)………………………………………….7

Data Description………………………………………………………..9

Specification of student’s choice of MajorThe effect of expected earnings on Major………………..….....9

Predicting Expected Earnings………………………………………….10

Predicting Probability of Receiving a Job offer……………………….16

Specification of student’s choice of MajorThe effect of Probability of Job offer on Major………….……16

1.4 EMPIRICAL RESULTS

Mixed Conditional Logits

Effect of Expected Earnings no uncertainty ………..…...….…18

Effect of Expected Earnings with uncertainty……………....…19

Effect of Expected Probability of Job offer……….……....…...21

ii



1.5 SUMMARY AND CONCLUSIONS…………………………….....….…23

1.6 APPENDIX 1

Tables……………………………………..……..…………….85

References……………………………………………………..142

iii



ESSAY 2

UNDERGRADUATE CHOICE OF MAJOR AND LOAN DEBT

2.1 INTRODUCTION

Background …………………………………………………………...26Statement of the Problem……………………………………………...28Data …………………………………………………………………...30

2.2 REVIEW OF THE LITERATURE

Monks (1999)…………………………………………………….…....31St. John (1994)………………………………………………………...35Weiler (1994)……………………………………………...………......38

2.3 METHODOLOGY

Life-Cycle and Marginal Utility Theory……………………………....40 Method of Analysis…………………………………………….……...45Instrument Choice…………………………………..............................47


First Approximation: Single equation OLSChoice of Major and Loan debt…….………………………....50

Testing for Exogeneity…………………………………………….….53

Instrumental Variable: (2SPLS)Choice of Major and Loans………………………….…….….54

2.5 SUMMARY AND CONCLUSIONS……………….………………...…..56

2.6 APPENDIX 2…………………………………….…………………...…..97

Tables………………………………………..………………….…..…95References…………………………………………………………....144

iv



ESSAY 3

AN ANALYSIS OF SECOND MAJORS AND EARNINGS

3.1 INTRODUCTION

Background …………………………………………….…………....58

Statement of the Problem…………………………….……………....58

3.2 REVIEW OF THE LITERATURE……………………………………...59

Rumberger & Thomas (1993)………………….………………….…61Hamermesh and Donald (2004) …………………………...………...63

3.3 DATA

Single Selective University…………………………………………..67College and Beyond 1976 Cohort…………………………………....67

3.4 METHODOLOGY

Method of Analysis………………………………………………......68


Log Earnings Regressions

Single University …………………………………...…….…73College and Beyond…………………………………….…...77

3.6 SUMMARY AND CONCLUSIONS……………………….……......…79

3.7 APPENDIX 3

Tables……………………………………………………………....123Educational choice, earnings and happiness……………...……......135References...………………………………………………………..146

v



ACKNOWLEDGEMENTS

The journey I began nine years ago as a freshman at the University of Notre Dame

has been an exceptional one. My time at Our Lady’s University has been filled with

wonderful experiences and people. Therefore, I cannot reflect upon this time without

acknowledging that I did not make it to this point without the help of many individuals. I

stand in great appreciation of their support. I owe a large debt of gratitude to both my parents

for not only instilling in me a genuine work ethic and stressing the value of obtaining an

education but also for sacrificing to ensure that I obtained the best. I also give a special thank

you to my mother whose own academic achievements have provided me with the inspiration

to complete my own doctorate. I could not have asked for better parents or role models, thank

you both. I’d also like to thank my brothers, particularly my little brother Matthew for

always being there when I need you. I thoroughly enjoyed spending part of our Notre Dame

journeys together. My beautiful wife Elyse, who I was blessed to meet at Notre Dame, is

also deserving of my unending thanks. Her constant love, support and encouragement

allowed me to keep my sanity while working on this dissertation even to the detriment of her

own. You are the love of my life and I thank you dearly.

In addition to those mentioned above, I owe a word of thanks to a few other

individuals. Thank you to my dissertation committee, especially to my chair Thomas R.

Swartz, for your guidance in developing this research and my subsequent career path. Any

errors that remain herein are my own. I give a final thanks to Institutional Research at the

university whose students are the focus of this research for allowing me access to their

student database. I also express my gratitude to the Andrew Mellon Foundation for allowing

me access to The College and Beyond database. This research would have not been possible

without your generosity.

vi



ESSAY 1

EXPECTED EARNINGS, EMPLOYMENT, AND THE CHOICE

OF UNDERGRADUATE MAJOR

1.1 Introduction

This essay, which is the first of three essays that examine the choice of

undergraduate college majors, will investigate the importance of two incentives that

impact a student’s choice of major. Previous research has empirically examined the

many incentives economic theory offers as important influences on higher educationdecisions; however, previous research that examines the nature of the relationship

between expected earnings and choice of college major is incomplete. While a few

studies have shown that expected earnings represent a significant influence on higher

educational decision making, one shortcoming of this research has been the inability to

incorporate into the modeling of student choice the idea that a student’s choice of college

major is a decision made under uncertainty and risk. Although there is an established

link between a college student’s expected earnings across all majors and their choice of

major, the absence of uncertainty in models of a college student’s choice of major may

prohibit a more accurate model of how students choose their major from being estimated.

Incorporating the risk that a student faces in their expected earnings allows this study to

more closely model the choice of major as a case of expected utility maximization.

The first question this research will attempt to answer is the extent to which a

student’s choice of major at a selective institution is influenced by their risk adjusted

expected earnings and uncertainty in probabilities of job offers across majors. This essay

will incorporate earnings uncertainty or risk into the student’s utility maximizing decision

1



by allowing a student’s own abilities across majors and the variance in earnings outcomes

represented by a major’s earnings distribution to affect their earnings projections. This

research will also investigate a question not previously addressed by the current body of

literature. A student’s choice of major is a choice made under uncertainty as a student

will only achieve their expected earnings if they receive a job offer. Therefore, this essay

will investigate whether the expected probabilities of getting a job offer across majors

also affects a student’s choice of major. A unique feature of this essay is that the

analysis focuses on the choice of major at a single selective university. Most other

studies in this area have exclusively used the National Longitudinal Surveys of YoungMen, Youth or High School Class of 1972. So while the results from this study are not

generally descriptive of all college graduates, this essay can determine whether the

relationship between expected earnings and choice of major holds for more recent

graduating cohorts from a selective university. The data used is well suited to address

these questions as it provides descriptive information on four years of graduating seniors

in 1997, 1999, 2001 and 2003 at a single selective university which eliminates problems

with comparing major types across different colleges, a problem encountered by previous

studies.

Like many other incentives theorized to influence higher education decisions,

expected earnings have been shown by the previous literature to influence the decisions

of different demographic groups differently. This study will also find whether there are

differences in the way men and women in this dataset respond to expected earnings in

their choice of major. Any analysis of minority or socioeconomic group differences in

choice of major must unfortunately be abbreviated and left for further research due to the

2



small number of minority students and students of socioeconomic disadvantage. In order

to understand whether accounting for risk in expected earnings adds any precision to

modeling student’s choice of major, this study will first estimate a student’s choice major

following the methodology of previous research and then again after incorporating

earnings uncertainty or risk into the model.

1.2 Review of the Literature

The educational choice literature can be split easily into two parts. The first

segment addresses the incentives and costs that influence the demand for education, that

is, the incentives and costs that influence the decision to invest in additional years of

education. This literature rests on the principle that individual educational investment

decisions are rational economic decisions, influenced by the reconciliation of costs—

which include direct costs of a year of education and indirect costs such as wages lost—

and the returns to an extra year of education. Still other incentives have been linked with

this decision, but for the sake of parsimony, they will not be addressed here. The second

segment of the literature that is directly relevant to this research focuses on the qualitative

choices of students selecting into higher education. These decisions include the choice of

what college an individual attends, whether a student will persist in college and finally

what their final field of study will be. The qualitative choice that will be subject to

empirical scrutiny in this essay is the final choice of college major.

Just as the human capital literature assumes that individuals make rational

educational investment decisions by “implicitly calculating whether or not education is

worthwhile, by comparing expected benefits with the expected costs associated with an

3



investment” 1 , the literature on this qualitative choice is rather cohesive in its conclusion

that college students can implicitly calculate their own relative expected returns in each

available major when deciding between the types of education in which they will invest.

Demand in the labor market (Firoito and Dauffenbach 1982), pre-college ability (Turner

and Bowen 1999) and socioeconomic background (Leppel et al 2001, Simpson 2003, and

Strasser et al 2002), as well as the ease of obtaining a high grade point average (Cohen

2005) are among other incentives linked to the individual and aggregate choice of college

major.

Freeman (1971), Koch (1972), Berger (1988), Eide and Waehrer (1998) andMontmarquette, Cannings and Mahseredjian (2002) have all found empirical evidence

that suggests that increases in the expected earnings of a major relative to expected

earnings of other majors, enhances the utility of that major and consequently increases

the probability that individuals will choose that major relative to others.

One of the seminal works in this area was completed by Marc Berger (1988).

Berger’s hypothesis—that individuals will choose a major that maximizes his or her

lifetime expected earnings—is supported by his analysis which examines the choice of

major of students from the National Longitudinal Survey of Young Men who graduated

college from 1962-1977. These young men are shown to choose majors with relatively

higher expected earnings streams. However, Berger finds that these men are also less

influenced by initial expected earnings and influenced to a greater extent by the expected

earnings stream of a major. 2

1 Paulsen p.56-572 Berger’s model assumes that individuals respond to life-cycle earnings expectations. His results

support this assumption as the results are consistent with rational expectations frameworks where studentsdo not form their earnings expectations in a naïve or myopic manner.

4



expected earnings are estimated with more precision than expected earnings predictions

that don’t account for this earnings uncertainty. Montmarquette et al find that increases

in both the predicted probability of finishing a major, the uncertainty adjusted expected

earnings of a major relative to other majors, increases the utility of that major and

consequently increases the probability that the major will be chosen relative to others. It

should be noted that Montmarquette et al run separate regressions for males and females.

They find that the coefficient on the expected earnings variable is smaller for females but

still positive and significant. The different results for men and women in this analysis

would seem to assert that expected earnings have a greater influence on the choice ofmajor for men than women. This result could also be evidence that women are less likely

to choose majors with higher earnings due to anticipated discrimination or the presence

of other negative attributes of jobs with higher expected earnings; or as many argue,

women choose majors that are less likely to atrophy or receive wage penalties from long

absences from the labor market. However, this last argument might not be as convincing

when describing female students graduating from a selective institution. Montmarquette

et al acknowledge that a more complete model of student choice under uncertainty would

incorporate the idea that students don’t know if they will be able to actually obtain their

expected earnings in the major they choose, due to employment uncertainty. This study

will also address employment uncertainty at graduation which may affect students’

choice of major.

6



1.3 Methodology and Data

Most previous research treat expected earnings only as a function of observed

characteristics and treat individuals as predicting these expected earnings with certainty.

Little attention is paid to the various earnings outcomes that a student may face in a

particular major. Expected earnings across majors are in fact risky, being determined by

a student’s abilities as well as the various feasible earnings outcomes within a major.

Therefore, we allow a student’s expected earnings in a major to be affected by both his or

her own abilities as well as the earnings distribution of that major.

In order to develop a model of student choice that integrates students’ own majorspecific abilities, as well as the various earnings outcomes in the earnings distributions of

each major, this study will in part employ a methodology to predict expected earnings

used by Flyer (1997) in his study of occupational choices made under uncertainty. Flyer’s

study assumes that individuals face uncertainty in their own occupational specific

abilities and in the monetary rewards to an occupation. Flyer calculates life-cycle

earnings estimates that reflect occupational specific abilities and various earnings

outcomes of an occupation and investigates how these expected earnings influence a

person’s initial choice of occupation. Flyer finds that these life-cycle earnings

predictions are strongly related to choosing to enter an occupation. He also finds that

because of an individual’s uncertainty in his or her abilities across occupations, increases

in an occupation’s option value of job mobility are strongly related to choosing that

occupation.

Apart from the direct relationship that risk adjusted expected earnings have on the

choice of major, an issue raised by Montmarquette et al, will also be addressed in this

7



essay. While all students form some type of earnings expectations in each major

conditional upon their own abilities and earnings distribution of a major, there is nothing

that guarantees with certainty that a student will receive or “realize” those earnings given

that they could be unemployed when they graduate from college. For this reason there is

also uncertainty in a student’s ability to obtain employment in each major. As uncertain

job prospects surely weigh on the thoughts of both student and parent alike, the effect of

unemployment uncertainty on the choice of major will also be addressed by this study.

This essay is unique as it is the first to empirically test whether the probability of

receiving a job offer may influence a student’s choice of major. Just as a student might be motivated to choose the major in which he or she has the highest relative expected

earnings, the student might also be more likely to choose a major in which he or she has

the highest expected probability of receiving a job offer. For example, based upon an

individual’s own abilities, an individual who majored in philosophy might have a higher

probability of getting a job as a philosopher than they would as an engineer, and for this

reason chose to major in philosophy.

The methodology for establishing the relationship between uncertain expected

earnings and major choice will closely follow previous studies in this area. This research,

however, will be unique in the manner in which expected earnings is calculated. In most

previous studies, predicted earnings are only a function of an individual’s observed

characteristics and are treated as certain. Earnings estimates that account for both major

specific ability and the variance in major specific earnings outcomes as well as students’

predicted probabilities of receiving job offers will be calculated using data from a pooled

cross-section which provides information on the educational records, major choice, test

8



scores, socioeconomic background, tastes and aspirations of 7,448 undergraduates who

graduated in 1997, 1999, 2001 and 2003 from a single selective university; as well from

the College and Beyond 1976 cohort which includes background and 1995 earnings

information for 22,512 graduates from 30 selective colleges and universities.

Since most variables in the dataset from the single university and in the College

and Beyond dataset are easily matched, and since earnings data from the College and

Beyond is more complete, the College and Beyond data will constitute the sample that

will help provide predictions of both major specific productive probabilities and major

specific earnings distributions for the individuals in the single selective universitysample. 3

Specification of the choice of major

Following a special case of the theory of expected utility maximization, expected

earnings maximization, to explain how students choose their college major, we can

empirically test whether expected earnings of a major is correlated with major choice.

Estimation of the following equation will be carried out using a mixed logit specification,

a special case of the conditional logit proposed by McFadden (1974). In this

specification, major choice is an expected utility maximizing decision, where expected

earnings are characteristics of the dependant variables themselves (the choice

alternatives), and all other independent variables are characteristics of the individual

students.

(1). E(U ij ) = α E ij + Z i δ + u ij

3 A student that falls in a specific quartile of a major’s earnings distribution is assumed for the sake of thisstudy to also fall in that same quartile in the distribution of productive ability for those that enter that major. Soestimating an individual’s major specific productive abilities amounts to predicting the probabilities that an individualwill fall in each of the four quartiles of a major’s earnings distribution.

9



E(U ij ) is the expected utility for individual i associated with choosing major j; E ij

is the expected earnings for individual i from choosing major j over the other majors; and

Z i is a vector of student background characteristics including controls for tastes. So the

expected utility for individual i in major j depends upon the expected earnings of major j

and Z i. Individuals choose major j if U ij > U in, for all n ≠ j. McFadden demonstrates

how the logit transformation allows the equation above to be expressed as the log of the

ratio of two probabilities.

(2). ln ( P ij ) = α ( E ij – E in ) + Z ( δ j – δ n)( P in )

This new equation shows that as expected earnings of major j (E ij ) for individual

i increases, the utility of major j increases as does the probability of choosing major j.

This equation demonstrates that the probability of choosing a major should increase as its

expected earnings relative to all other majors increases.

Estimating major specific earnings (E ij ) without uncertainty

Before discussing how this study will incorporate earnings risk into the expected

earnings predictions (E ij ) for each student in each major j, a short description of how the

previous literature chooses to calculate earnings expectations that do not account for any

kind of uncertainty is in order. The way that most of the previous empirical literature

predicts earnings expectations for students is rather straightforward.

Observed earnings of individuals in the dataset are first used to run log earnings

regressions for each major. These major specific earnings regressions are used to

estimate the underlying wage earnings parameters ( βs) for each major. For example the

equation below is estimated for each major j in order to find the vector β j for that major.

10



(3). Log earnings ij = β0 + X ij β 1 j + λ ij β 2 j + εij

However, earnings are only observed for each major for those who have selected

into that major, therefore there is usually a correction made for this implied sample

selection. Given this censored data, most studies proceed with Lee’s (1983) or

Heckman’s (1976) two-stage estimation method for sample selection. A first stage probit

model is used to predict the probability of being in major j and in a second stage the

inverse mills ratio calculated from the first stage is included as a regressor. This two

stage estimation is implemented in order to arrive at consistent estimates of β j. This

selection correction is completed for each major. This essay uses a student’s probablemajor at the beginning of their freshman year as the exclusion restriction for the

estimated equation above.

Once the correction is made for selection into each major, the vector of β j is used

to estimate unconditional earnings for every individual in major j. This is done for each

major so that every individual in the data set will have an expected earnings prediction

for each major based on their own levels of X ij. The student’s choice of major is then

modeled using a conditional logit where the choice of major is based upon a student’s

relative expected earnings across majors. The problem here is that these earnings

expectations are assumed to be taken with certainty. However, the very nature of the

prediction of earnings using this method implies that earnings are predicted with some

level of error. There inherently exists some level of uncertainty in these earnings

projections. This essay will compare this way of calculating expected earnings with the

alternative process described below.

11



Estimating major specific expected earnings (E ij ) with uncertainty

Alternatively, if we assume that earnings predictions are uncertain and are

determined by both a student’s abilities and the distribution of earnings outcomes in a

major, expected earnings for a student I majoring in major j can be represented.

4(4.) E ij = ∑ ∏ ijm L jm ,

m=1

where L jm is the expected value of earnings for individual I who chooses major j and who

has a productivity level that ranks in quartile m among those also graduating in major j.4

The variance and skewness in the distribution of earnings for major j can affect E ij

through the L jm term. The reason that the I subscript is dropped from L jm is because this

study assumes that all students have the same expectations regarding major specific

earnings distributions. ∏ ijm corresponds to the probability that individual I assigns to

their major specific productivity (earnings) being ranked in quartile m among all

graduates in major j. Together, both ∏ ijm and L jm incorporate a student’s uncertainty and

the variance in feasible earnings outcomes represented by a major’s earnings

distribution. 5

Estimating ∏ ijm

In order to predict the probability ( ∏ ijm ), that an individual assigns to the

likelihood of falling into quartile m of major j’ s productive ability distribution, a simple

prediction method is used. Predicted probabilities that an individual falls into the four

quartiles of each major’s earnings distribution can be found by estimating major specific

earnings equations using a two stage Heckman method for sample selection into a major,

4 m = 1 is equal to the highest quartile and m = 4 is equal to the lowest quartile.5 Earnings are incorporated into this model of student choice following Flyer 1997.

12



The data used comes from the College and Beyond 1976 cohort of students, the

majority of whom, graduated in 1980 from a group of colleges and universities of varying

levels of selectivity. In order to arrive at a reasonable approximation of an earnings

estimate L jm for every quartile in every major, major specific earnings regressions must

be estimated using the College and Beyond data. The following equation is estimated by

OLS for each major.

(6). log earnings ij = β 0 + X ij β 1j + λ ij β 2j + εij

Where log earnings ij is the log of 1995 earnings for individuals who graduated in

major j, and X ij is a vector of personal background characteristics for individual i whograduated with major j. λ ij is once again the selection variable that allows the estimation

to produce consistent estimates of β 1j . Once this equation is estimated for everyone in a

particular major, the coefficient vector β j is used to predict an expected earnings in that

major for everyone in the C&B sample. All of these predicted earnings for major j

represent the distribution of earnings for major j.

The midpoint of each quartile in a major’s earnings distribution is used as the

expected earnings (L jm ) for that quartile. The resulting (L jm ) for each quartile in each

major represents a projected earnings estimate for falling into that productivity quartile

15 years after a student’s graduation.

Calculating E ij

“(Under uncertainty) there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for actionand for decision compels us as practical men to do our best to overlook this awkward factand to behave exactly as we should as if we had behind us a good Benthamite calculationof a series of prospective advantages and disadvantages, each multiplied by itsappropriate probability waiting to be summed.” John Maynard Keynes “General Theoryof Employment”, 1937 Quarterly Journal of Economics

14



In order to calculate an expected earnings variable for individual i in major j, we

take the predicted probabilities that individual i will fall in each quartile of the earnings

distribution for major j and multiply them by the earnings that individual i expects to

receive for being in each quartile of major j (L jm ). Summing across these products will

yield an expected earnings variable E ij for individual i in major j that accounts for

uncertainty or risk by incorporating a variance in earnings outcomes and major specific

abilities.

m

(7). E ij = ∑ ∏ ijm L jm ,m=1

Repeating this process will yield expected earnings for individual i in every major

{1…j}. Every individual in this sample will therefore have five expected earnings

variables that are influenced by the distribution of earnings outcomes, one for each

possible major. 6

Estimating Predicted Probability of Employment at Graduation

An additional source of uncertainty in a student’s choice of major can be derived

from the uncertainty a student faces in finding a job upon graduation from college. A

student will only receive expected earnings in her or his chosen field if he or she is able

to obtain employment after graduation. Higher probabilities of getting a job offer in a

major category are likely to increase the utility of that major and consequently, the

probability that major will be chosen. This study will calculate the predicted probability

of getting a job in each major for every student at the single selective university. Each

6 Majors for which expected earnings are calculated include engineering, business, naturalsciences, social sciences, and humanities.

15



student will therefore have five predicted probabilities of receiving a job offer upon

gradation, one for each major. These predicted probabilities will be used in the choice of

major mixed logit estimation in two ways, in an attempt to ascertain whether or not an

increase in the probability of receiving a job offer in a major relative to others affects an

individual’s choice of that major. This predicted probability of a job offer will be used as

a lone independent variable to find its effect independent of earnings and other

exogenous variables and will then added to the mixed logit along the expected earnings

variable calculated above and the remaining control variables to see if predicted

probability of a job offer affects major choice separately from its possible correlationwith expected earnings.

Using actual job offer observations for individuals from the single selective

university, receiving a job offer will be modeled by major specific probit models, with

corrections for sample selection carried out in a two-step Heckman procedure due to

selection into each major category, with freshman major serving as the exclusion

restriction: The equation that will be estimated:

(8). Job offer ij = α 0 + X ij α 1j + λ ij α 2j + u ij

Parameter values from these probit models will be used to calculate a “predicted

probability of getting a job offer” variable for every individual in each major.

Specification of the choice of major: with Predicted Probability of Employment

Under the assumption that an individual maximizes his or her expected utility by

choosing a college major with the highest expected earnings, modeling the expected

utility of choosing major j as depending on the expected earnings in that major relative to

16



other majors and the probability of receiving a job offer in that major relative to other

majors can be illustrated.

(9). E (U ij ) = α E ij + γJij + δ Z i + u ij

E(U ij ) is the expected utility for individual i associated with choosing major j; E ij

is the expected earnings from choosing major j for individual i; J ij is the predicted

probability of receiving a job offer if major j is chosen by individual i; and Z i is a vector

of personal background variables including controls for tastes. Individuals choose major

j if U ij > U in, for all n ≠ j.

Estimation of the equation above will follow a mixed logit specification, a specialcase of the conditional logit framework proposed by McFadden (1974) where regressors

are characteristics of the choice alternatives and a generalized multinomial logit where

regressors are characteristics of the individuals who are doing the choosing. The logit

transformation allows the equation above to be expressed as the log of the ratio of two

probabilities.

(10). ln ( P ij ) = α ( E ij – E in ) + γ (J ij - J in ) + Z i (δ j – δ n)( P in )

Therefore, as expected earnings or probability of job offer of major j increases

relative to all other majors n ≠ j, the utility of major j increases as does the log odds of

choosing major j. This equation demonstrates that the probability of choosing a major

should increase as its expected earnings or probability of receiving a job offer relative to

all other majors increases.

The mixed logit specification indicates that the variables E ij and J ij are a

characteristic of the choice alternatives, which in this case are the alternative majors. The

other right hand side variables Z i are characteristics of the individuals in the sample. The

17



left hand side variable is a dummy variable indicating that a major was chosen. Whether

a major is chosen or not depends upon the relationship between the expected earnings of

that major and the expected earnings of all other majors ( E ij – E in ). Looking at the logit

transformed equation we see that the higher the expected earnings of a major is relative to

the expected earnings of other majors ( E ij – E in ), the higher the probability will be that

major will be chosen relative to other majors.

For instance, if the engineering major was chosen by individual i, then

major engineer =1, major business =0, major nat.science =0, etc. We expect that the choice of an

engineering major (major engineer =1) should correspond to a higher level of expectedearnings for individual i in engineering relative to his/her expected earnings in other

fields n (a higher value of E i engineer – E in). The higher the expected earnings in

engineering relative to the expected earnings of other majors might have led to an

increase in the probability that major engineer =1 (i.e. the probability that engineering is

chosen over other majors). If the expected earnings variable does have a positive and

significant coefficient in the choice of major estimation, then we would expect that this

individual had higher expected earnings in engineering relative to other majors and

therefore chose engineering. This same relationship between expected earnings and

major choice should apply to the choice of all majors, if the expected earnings parameter

has a positive and significant value. The effect of other variables on the choice of major

can be interpreted in the same way as they would be interpreted in a multinomial logit.

1.4 Empirical Results

The results in Table 1A demonstrate the effect of expected earnings on a

student’s choice of college major at a single selective university. Using the previous

18



literature as guide, this expected earnings variable for students at the single university is a

prediction based upon parameter estimates βs from major specific earnings regressions

for students from the College and Beyond sample as well as individual characteristics X i s

from the students at the single selective university. These expected earnings do not

account for various possible earnings outcomes, so this specification closely parallels

most of the previous literature. And as most of the previous literature finds for students

in the National Longitudinal Surveys, expected earnings does have a positive and

significant effect upon choosing a particular major for this sample from a selective

institution as well.

Results from separate regressions for men and women can be seen inTable 1B . The separate regressions for males and females have a full set of controls,

however, only the parameter estimates for the expected earnings variables are shown.

Table 2A displays the effect that expected earnings has on choosing a major for

the full single university sample, when the variance in earnings distributions are allowed

to effect the expected earnings calculation. Results from separate regressions for males

and females can be seen in Table 2B . Just as in the case of expected earnings that did not

account for risk, an increase in the expected earnings of a major relative to the expected

earnings in other majors, increases the probability that major will be chosen.

However, examination of the different estimates for the two expected earnings

variables in Tables 1A and 2A together suggest that adjusting expected earnings for

uncertainty or risk leads to a more accurate explanation of a student’s choice of major.

Not only is the parameter estimate for expected earnings larger but it estimated more

precisely. The parameter estimate for U_EXPECTED EARNINGS is both large and

significant at the 1% level. Other variables which the previous literature found to be

19



important in the choice of college major have also been included in these regressions as

control variables. Table 1A and 2A show the structural parameter estimates for these

other control variables in this mixed logit model. The estimates in Table 1A and 2A for

all variables besides EXPECTED EARNINGS and U_EXPECTED EARNINGS can be

interpreted in relation to the fifth-baseline major, humanities . Using the gender variable

female as an example in Table 2A ; females are significantly less likely to choose

engineering (1) and natural sciences (3) over the baseline major humanties (5) than their

male counterparts. Females in this sample are also significantly more likely to choose

social sciences (4) over humanities (5) than their male counterparts.When the sample is split between men and women, the results show that men

are very strongly motivated by their expected earnings. The results in Table 2B show

that women in this sample are far less motivated by expected earnings in their choice of

major. The expected earnings variable for women has smaller affect on the choice of

major than for men and is significant at the 5% level.

These results for men and women corroborate much of the literature devoted to

the role of expected earnings in a student’s choice of major. While Montmarquette et al

(2002) found that their expected earnings accounting for uncertainty did have a

significantly positive effect on students’ choice of major, they found that for women, the

coefficient on expected earnings that accounted for graduation uncertainty was half the

size of the coefficient for men. Eide and Waherer (1998) found a positive correlation

between expected earnings from a terminal degree and choice of college major for men in

their sample, but found that there was a significant negative correlation between expected

earnings and choice of college major for women in their sample. Reasons for this finding

20



could include the possibility that women choose majors less likely to atrophy, or that the

majors which have the highest expected earnings for women might also have some type

of negative attribute or risk for women that isn’t captured in the expected earnings

variable. If this is the case, expected earnings in these majors are higher than they would

be if these negative attributes were included in the expected earnings prediction. Also, if

preferences play a role in the choice of major, they may play a greater choice for women

than they do for men. Or finally, because occupational segregation might influence

sorting of females to majors dominated by females. These majors typically receive lower

earnings.Table 3A displays the results from the conditional logits using predicted

probability of obtaining a job offer as the only right hand side independent variable for

the full sample, then for only males and only females. An increase in the predicted

probability of obtaining a job offer in a major has a positive effect on choosing that major

relative to others for males while it has negative effect on the same choice for females.

Females seem to be less impacted by employment uncertainty than males. This result

might be derived from females’ increased probability to major in humanities and social

science majors, majors where post graduate plans are more likely to include graduate

school than job searches. This possibility is born out in the means tables following the

next essay.

Results for the full sample that include the predicted probability of a job offer as

well as all other control variables are shown separately for men and women in Table 4A .

Once these controls are added to the model, the predicted probability of getting a job

offer in a major has little power in explaining the choice of college major for both males

21



and females. Keeping in mind that this study predicts the probability of receiving a job

offer by graduation and not in the period shortly following graduation, this insignificant

correlation between probability of receiving a job offer by graduation and major choice

could be due to the fact that predicted probability of receiving a job offer by graduation

might not be as important as receiving a job offer at some point after graduation.

Also, if a student has a high probability of receiving a job offer in a particular

major based on their own abilities, they might also be more likely to be in the upper

quartiles of a major’s earnings distribution and hence to have higher expected earnings.

This means that the probability of receiving a job offer is most likely positively correlatedwith having high earnings expectations in a major or with other control variables

included in the mixed logit since there is no separate effect that the probability of getting

a job offer has on a student’s choice of major in this sample once all controls are added to

the model.

Given the results from previous studies that examined the choices of students

from the National Longitudinal Surveys of Young Men, Youth and High School Class of

1972, the results presented here are not surprising. Students from a selective university

also seem to be very much affected by expected earnings in their choice of major.

Students who have higher expected earnings in one major relative to all others will likely

choose to major in that field. Females are shown to be less influenced by their own

relative expected earnings across fields in their choice of majors. This persistent result

for women is not necessarily confounding due to reasons described above.

The results from previous studies of the choice of college major, all of which

have utilized national survey data on college graduates from a wide range of schools and

22



returns. It has also been shown that different groups of students, particularly males and

females, respond to expected earnings differently.

Based on the results provided in this essay, we can conclude that students do

care about the relative expected earnings they can obtain in different majors. Therefore,

anything that changes an individual’s expected earnings in one major relative to other

majors will likely affect their choice of undergraduate major. This result does have

important implications on how we model and understand student’s college major and

labor supply decision.

If for example, there were a large increase in the earnings (wage) received byengineers in the labor market, we could expect that this would raise the expected earnings

in engineering of students beginning their college studies by various magnitudes,

depending on the student. Based upon each individual’s abilities and the shape of the

engineering earnings distribution, some student’s expected earnings are likely to increase

more than others. However, it could easily be assumed that for a large number of

students, this increase in the engineering wage in the labor market would now make their

expected earnings in engineering higher than their expected earnings in other majors.

Since we have just shown in this essay that students choose majors based upon their

relative remuneration, we would expect that a larger number of students in the aggregate,

will choose engineering as a major.

This type of scenario would give some credence to a cobweb-type model of

labor supply. However, the cobweb model, even in a rational expectations framework

must be based upon earnings expectations for students being predicted rather myopically,

so that changes in expected beginning earnings will influence changes in major choice

24



behavior. This essay has explored the link between expected earnings 15 years after

graduation and choice of major, and finds a significant correlation between the two

variables. Other studies such as Berger (1988) have also shown that expected beginning

earnings influence the choice of major, but as Berger explains, this may only be because

beginning earnings are positively correlated to life-cycle earnings; and it is expected life-

cycle earnings that people respond to in their choice of major, since life-cycle earnings

take into account differing slopes in earnings growth across majors. If Berger is right,

then the cobweb model’s success in predicting the supply of new entrants into a field

might only be because beginning earnings are closely correlated with life-cycle payestimates.

Since neither beginning nor life-cycle expected earnings were used in this

study, the results from this essay do not address whether students are myopic in their

earnings expectations which would support a cobweb model of labor supply, however,

the results herein do establish that the choice of college major is very much linked to

relative expected earnings across majors.

25



incentives, discrimination, cobweb patterns of human capital investment and

occupational shifts. 1

In particular, the one monetary incentive among others which as been proposed to

influence an individual’s utility of choosing a major is student loan debt. In fact, the

literature devoted to studying the relationship between major choice and loan debt

provides the impetus for this essay. The literature hypothesizes that increases in student

loan debt will tend to lead students to choose higher earnings majors. This economic

reasoning assumes that loan debt is exogenously determined and rejects the assumption

that students might be forward thinking beings, who in the process of their educationlearn more of the benefits and costs to their education and consequently might choose

their loan debt based upon the major that they have chosen. Because the previous

literature misses this very probable possibility when they assume that loan debt is

exogenous, there is relatively little literature that examines the impact that a student’s

choice of major might have upon their borrowing behavior. This essay will attempt to

address and fill a gap present in this area of the empirical educational choice literature.

The work included in this paper will empirically test the relationship between a student’s

loan debt and their choice of major at a selective university, in a way that addresses the

1 Choice of major throughout this essay actually refers to the choice of a particular “college” within auniversity. Of course each “college” will represent a specific type or subgroup of individual majors, but the groupingwithin each “college” usually consists of majors that are relatively similar in nature—with the possible exceptions of

social sciences and humanities. Due to the large number of different majors available to students in college, in order tocompare major choices in a clear and more manageable manner, majors are aggregated into several categories. This

procedure is a limitation of many studies in the educational choice li terature, because although majors within eachcategory may be similar, the subject and fields included within a larger category might range widely. For this study,majors are grouped into Engineering, Business, Social Sciences, Humanities, Pre-professional and Architecture. Whilethere might be wide differences in fields—and salaries—within some of these categories, when majors are aggregatedunder these categories there does exist a hierarchy of average salaries between the categories. This result is usefulsince one goal of this essay is to see whether majoring in a category with high average salaries relative to a categorywith lower average salaries has an affect on a student’s loan debt. Since majors are aggregated in this manner,however, we are unable to compare the effects of choosing specific majors within one category relative to specificmajors in another category.

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endogenous nature of loan debt and choice of major that have been up to this point

ignored.

Educational choices, especially those made in higher education, like the choice of

major for example, have immediate implications on a student’s labor market success and

consequently upon their financial abilities to repay debt. With the yearly price tag at

some colleges rising to astronomical heights and at a rate far greater than the average

family’s income is rising, the pursuit of a better understanding of the motivations and

consequences of important educational choices that take place in the presence of

tremendous costs, risks and returns constitutes the primary motivation for this research.Most studies that examine the relationship between loans and the choice of

college major attempt to test the theory that loan debt is a causal determinant of a

student’s choice of major decision. As mentioned above, the problem with modeling

major choice as a function of loan debt arises because of the fact that loan debt is

incorrectly being treated as an exogenous variable. Loan debt, in fact, should not be

assumed exogenous, as a student’s loan debt is not randomly drawn from a hat, but

instead can be influenced by many factors including but not limited to the student’s

choice of major. A brief discussion of the theoretical relationship between major choice

and loan debt explains why loan debt can be considered endogenous within a system of

equations.

Previous studies follow a particular theoretical line of reasoning. If educational

choices are made at the margin and debt load for a student were to rise, the marginal

utility of consumption for that student would be increased during the repayment period

due to the extra income that needs to be devoted to debt repayment rather than

28



consumption, giving a student an incentive to choose a more remunerative major. The

conclusion of this theoretical reasoning is simple. An increased debt load may influence a

student to choose a higher earning major, ceteris paribus.

What the previous literature ignores is the idea generated from a life-cycle

hypothesis perspective. Once this alternative perspective is included into the analysis, the

simultaneous relationship between loans and choice of major, and hence the endogenous

nature of choice of major and loans becomes apparent. According to the life-cycle

hypothesis, during the beginning period of an individual’s life-cycle—in this case during

college—an individual should borrow based on their future expected wealth or incomewhich is of course in turn based on their skills, talents, education, etc. This argument

suggests that a student is able to choose at least a portion of the amount of the debt they

take on based on the expected future income that their specific major will provide them

after graduation. This perspective explains why a student who chooses a high paying

major, ceteris paribus, will be more apt to take on greater debt now to pay for college.

The conclusion of this theoretical reasoning is also fairly simple, the choice of major can

be said to affect the level of debt a student incurs. Therefore, loan debt can reasonably be

assumed to be an endogenous explanatory variable in the equation that explains choice of

major. The life-cycle hypothesis perspective shows that while debt may influence the

choice of major, the choice of major may also affect the level of debt incurred. This

relationship can be demonstrated by a system of simultaneous equations.

1. Major choice i = X i+ Loans i + ε i2. Loans i = X i + Major choice i + u i

If the first equation is estimated using regression analysis without accounting for

the endogenous nature of loans (how previous studies proceed) it is possible that

29



estimates of the effect of loans on choice of major may suffer from simultaneity bias.

Similarly, if the second equation is estimated in an empirical model that does not take

into account the endogenous nature of major choice, the estimate of the effect of a

students choice of major on loan debt may also be biased due to the correlation between

Major choice and the error u i . The empirical research presented here will reconcile

these two perspectives in a way that addresses the possible endogeneity problem. Also,

while all studies attempt to estimate equation 1 above while ignoring the importance of

estimating the second equation, this paper will alternatively attempt to estimate the effect

that major choice has on loans, to find whether choosing a higher earnings major promptsstudents to take on more loan debt, ceteris paribus. A two-stage instrumental variable

estimator will be presented in order to address the possible endogenous nature of major

choice in equation 2 above that will enable consistent estimates of the effect that choice

of major has on loan debt in this simultaneous context.

Data

The data used in this study comes from a pooled cross-section of graduating

seniors from a single selective university in the years 1997, 1999, 2001 and 2003. The

data used includes information on students’ SAT scores, family background, beginning

and final major, total loan debt, activities during college, graduate school plans, a number

of self-evaluated personal characteristics, as well as whether employment has been

secured at the time of graduation and a salary offered. These data will be used in an

attempt to replicate results of previous research, answer the unique questions proposed in

this paper concerning the relationship between choice of major and loan debt and to

30



examine the possibility that choice of college major is endogenous to the equation of

interest (equation 2 above).

2.2 Review of the Literature

In this section, I will briefly review some of the important literature pertaining to

loan debt and higher education choices. While there are a few other studies in this area,

which are tangential to this work, only the studies most closely related to this work are

mentioned here. In addition to literature reviews, replications of the empirical results

from the previous literature have been attempted using the data described directly above.Results of these replications can be found in the tables of Appendix 2.

Replication of Monks (1999): Loan debt and graduate school plans

James Monks (1999) studied the impact of debt on various higher educational

outcomes and concludes that debt is not significantly influential in the educational

outcomes of college students. Theory might suggest that the student with higher debt

will be less likely to attend graduate school because it increases debt repayment and

therefore the student would have a higher marginal utility of consumption once debts

began to be repaid than if that student decided to begin working immediately after

college. He does not find any relationship between debt and graduate school plans or

between debt and changing majors during college from a lower paying field to a higher

paying field; however he does not specifically test whether debt affects the final choice of

major.

In order to determine the applicability of Monks findings to students from the

dataset used in this study, a similar specification has been used to estimate the effect of

31



loan debt upon the choice to attend graduate school: Grad i = β 1 X i+ β 2 Loans i + ε i .

Grad is a dummy variable indicating the student is planning on attending graduate school

within six months of graduation, X i is a vector of background characteristics and Loans i

is the log of total loan debt for individual i . It should also be mentioned that the problem

that arises when estimating the relationship between loans and major choice if the

endogenous nature of loans is not accounted for can also be applied to the estimation of

the effect that loans have on a student’s plans to attend graduate school. That being said,

the estimates using these data, like the estimates produced in Monks’ study may be

biased due to the simultaneous nature of loans and graduate school attendance.Unlike the findings from the Monks study, where Monks found that loans did not

significantly affect graduate school plans, I find a slight correlation between the amount

of student’s loan debt and the decision to attend graduate school for students in this

sample. Probit regression results are presented in Table 1A in Appendix 2 . The choice

to attend graduate school is modeled as a decision based on student ability, parental

background, undergraduate major, and loan debt. The probit is estimated twice, first

following Monk’s specification which uses categorical dummy variables that represent

having various levels of loan debt relative to the baseline of no loan debt and then using

the log of a student’s loan debt to replace these dummies as regressors.

College G.P.A. and major have signs that were expected and that were also found in

Monks’ study. “College GPA” has a positive and significant influence on graduate

school choice. So these results illustrate that controlling for choice of major, higher

ability individuals tend to be the students going on to graduate school. The female

dummy variable has a negative coefficient; however this estimate is not significant. Had

32



it been significant, it would support the actual raw percentages of males and females who

plan on attending graduate school from this sample. 2 For each major category the

percentage of women choosing to attend graduate school is lower than the percentage of

men in each major who plan on attending graduate school except in Humanities.

Students with higher ability (higher SATs) are more likely to attend graduate school and

African Americans are more likely than their white classmates to attend graduate school. 3

A finding not supported by this data is that Asians and Latinos are more likely to attend

graduate school than their white classmates.

While all loan debt levels have a negative relationship with plans of graduateschool attendance relative to having no debt, having loan totals between $1000-$6000

and between $12,000-18,000 significantly decreases the likelihood that a student plans on

attending graduate school relative to students that have no loan debt.

Variables not included in Monks’ analysis but are nevertheless shown to be

significantly related to plans to attend graduate school include a student’s categorical

self-ranking of their individual “drive to achieve”. Having a high “drive to achieve” is

positively correlated with graduate school plans. Also, having parents with the highest

income decreases the likelihood that students from this sample plan on attending graduate

school upon graduation. It is also interesting to point out that the estimate for “Graduated

in 2003” is positively significant . It is entirely plausible that business cycles might play

an important part in students’ graduate school plans since students who graduated in the

2003 class were more likely to attend graduate school than those who graduated in 1997.

2 Means Table: Appendix 2 3 A finding analogous to those found by Rivkin 1995

33



The incoming class of 1997 was ushered into college by an economic expansion

which eventually lasted nearly 10 years. To the extent that graduate school plans are

affected by employment opportunities, the business cycle expansion since 1991 was

likely to cause fewer students to turn to graduate school as an alternative to employment

in the 1997, 1999 and 2001 graduating classes. The class of 2003 entered college in

1999 in the midst of this last expansion. However, the peak in the last business cycle was

pinpointed in March 2001 which was followed by a trough in November 2001. This

downturn in economic activity between March and November of 2001 most likely

influenced many students in the 2003 class to decide to go to graduate school rather thanattempt to enter the workforce when job prospects were bleak.

However, one might think that since the business cycle recovery began in

November of 2001 over a year before the class of 2003 graduated, the short decline in

economic activity would not be enough to influence more students consider applying to

graduate school. The curious thing about the expansion that began in November of 2001

is that it was mainly due to productivity growth, so while real GDP was growing, the

growth was also accompanied by stagnating or falling employment. So even as there was

increasing economic growth by the time the 2003 class neared graduation, employment

prospects might have still been quite low. It is quite possible that for these reasons the

class of 2003 was more likely to have plans to go to graduate school than the class of

1997.

Unlike Monks, however, I do find some evidence that students in this sample

might be influenced by loans in their switching from a lower paying major to a higher

paying major. Table 1D from Appendix 2 shows that log loan debt is positively

34



correlated with switching to a higher paying major. When loan dummies are included as

exogenous regressors, having $6000-$12000 in loan debt relative to having no loans is

significantly related to switching to a higher paying major. African Americans, as well as

females are more likely to switch to a higher paying major than their white and male

counterparts. Students who graduated in 1999 and 2001 are more likely to have switched

to a higher paying major than 1997 graduates. However 2003 graduates are no more

likely than those in 1997 to have switched to a higher paying major. Another sign that

business cycles may play a part in how students choose their majors. 4

Replication of St. John (1994): Loan debt and choosing higher earning majors

A study by Edward P. St. John (1994) attempts to uncover a relationship between

loan debt and choice of a college major, specifically whether higher loan debt influences

students to choose higher earnings majors. St. John does not find within a margin of

error that loans are significantly influential in major choice. This study does suffer

twofold from shortcomings in its methodology. On one hand, St. John uses an ordered

ranking of majors (14 majors) ranked by their average salary as his dependant variable

and regresses this dependant variable on all independent variables including loan debt

using OLS. On the other hand, this study like all others in this literature does not address

the endogenous nature of loan debt. 5 And because St. John uses data on individuals who

graduated college in 1984-85, there also remains a motivation to determine whether there

has been a change in the loan-major choice relationship since the mid- 1980s.

4 Majors in this dataset can be ranked from highest to lowest paying based on actual reported beginningsalaries for students in each major. Majors are ranked from highest to lowest in this order: Engineers, Business,

Natural Sciences, Social Sciences, Humanities, Architects, Pre-professional . See Means Table in Appendix 2 5 The exception is Weiler’s study that examines the effect of loans on the choice to attend graduate school.

35



Following the methodology laid out by St. John (1994) and using more recent

data from a single selective university, I attempt to establish whether loan debt has no

impact on curriculum choice behavior for this group of students as described by St. John.

The estimates from two OLS regressions of the following equation are presented in

Table 2A and Table 2B in Appendix 2: Major ranking i = β 1 X i+ β 2 Loans i + ε i. In

the first regression the dependant variable is an ordered ranking 1-7 of major chosen by

each student. In the second regression, major categories are disaggregated further to

form an ordered ranking 1-14. 6 Tables 2A and 2B reveal the correlation between certain

independent variables and choosing a higher ranked –higher earnings – major.The result of interest that runs contrary to the findings in St. John’s study is the

positive and significant effect that loan debt seems to have on the choice of higher

earnings majors. When the log of loan debt or loan debt dummy variables are used the

correlation between loan debt and higher earnings majors is evident. We can see in

Table 2B that compared to having very low or no loans, total loan debt between $10,000-

$20,000, and $25,000-$30,000 is associated with choosing higher earnings majors. This

impact is significant at the 10% level. When the log of loan debt is used in the estimation

in place of the loan dummies, log loan debt is also found to be correlated with choosing a

higher earnings major. The coefficient for “ladjloan” suggests that for every unit increase

in log loan debt, major ranking (1-14) increases by .0347. This is also equivalent to

saying that if we multiply actual loan debt (not the log transformed version) by 2.72 (the

unit increment of the natural log) then major ranking increases by 1.04 (the exponent of

6 The ranking 1-7 is based on average remuneration of each major grouping. Engineering being the highest,followed by business, natural sciences, social sciences, humanities, with architecture and pre professional majorshaving the lowest average salary upon graduation. The ordered ranking 1-14 followed a similar pattern except somemajor groupings were disaggregated into more specific major qualifications. More comprehensive BLS average salaryfigures were used to determine the relative rankings among these disaggregated majors.

36



mathematically geared. It seems that students who spend the most hours partying during

the week were also the students choosing higher earnings majors. This finding more

appropriately defines students choosing high earning majors within the business college

than students choosing the highest earning engineering majors. Auxiliary regressions do

reveal that high partying habits increase the probability of choosing business majors

while it decreases the likelihood of choosing engineering majors relative to humanities.

Replication of Weiler (1994): Endogenous loan debt and graduate school plans

One study has acknowledged the possible bias that might arise by estimating the

relationship between college debt and higher education choices—specifically collegedebt and graduate study plans—with only a single equation. William C. Weiler (1994)

does not assume—like most other studies—that loan debt is an exogenous determinant of

the choice to attend graduate school. Weiler implements a multi-equation model to test

the effects of debt on the choice to enroll in post-baccalaureate studies. Weiler finds—in

contrast to previous studies—that loan debt significantly reduces the expectation of

enrolling in graduate studies for students based on the High School and Beyond.

I have previously demonstrated through replication of Monk’s study that when

using only a single equation estimation for this sample of students from a selective

university, loan debt negatively influences graduate school plans. However, that finding

may be driven by the possibility of endogenous loan debt. The prospect of this bias

influences Weiler to use a two-stage empirical model to solve the system of equations:

(3). Loan debt = α1 + α2 Grad + α3 X + ε (4). Grad = γ1 + γ2 Loan debt + γ3 X + u

38



Table 3C displays the results from a replication of Weiler’s model using this

sample of university students and implementing a two-stage estimation procedure that

attempts to account for the possible endogenous nature of loans. Tables 3A -3B presents

regression results that attempt to ascertain whether loan debt is indeed endogenous in

equation (4) above through a Durbin-Wu-Hausman exogeneity test. The Durbin-Wu-

Hausman exogeneity test is implemented in this case by saving the residuals from the

instrumenting regression equation (3) and including these residuals in the structural

equation (4). 8 The alternative hypothesis that there is significant difference between OLS

and IV estimates is tested against the null hypothesis that the Cov {Loan debt, u} = 0. Ifthe coefficient on the included residuals is statistically different from zero then we can

reject the null of exogeneity, therefore an IV estimator is needed to provide consistent

estimates of equation (4). In Table 3B we can see that the coefficient for the residuals

from the instrumenting regression are indeed significantly different from zero and so this

replication will proceed using instrumental variables to find the affect of loan debt upon

graduate school plans. The results from the second stage of the instrumental variable

probit are given in Table 3C. One can see that even after accounting for the

contemporaneous correlation between loan debt and the error, loan debt is still

significantly negatively related to planning to attend graduate school. Many other

variables significantly related to graduate school plans can also be found in Table 4C.

Using a two-stage IV estimator similar to that used in Weiler’s study along with

data from a single university, we find that simultaneity bias does not seem to drive the

significant negative coefficients on loan debt. Once the endogeneity problem has been

8 Durbin-Wu-Hausman test first proposed by Durbin (1954) and independently by Wu (1973) and Hausman(1978). It is numerically equivalent to the standard Hausman test.

39



eliminated or lessened, loan debt does appear to impact grad school choices. This result

runs parallel to Weiler’s study of students in the High School and Beyond where loan

debt was found to significantly effect the decision to go to graduate school, at the 10%

significance level. The estimates found by this replication are somewhat more precise as

loan debt had a significant effect on grad school plans, significant at the 5% level.

The remainder of this essay will develop a model of undergraduate choice of

major and loan debt, where the choice of a higher earnings major is suggested to

influence students to choose higher levels of debt. The model will be empirically tested

using data from a group of students in 4 graduating classes, graduating from a singleselective university between 1997 and 2003. This constitutes the first study that attempts

to estimate the effect of undergraduate choice of major on loan debt.

2.3 Methodology

Economic theory provides two distinct theoretical motivations for modeling the

simultaneous relationship between a student’s loan debt and their choice of

undergraduate major. The first theoretical motivation is drawn from the Life-Cycle

Hypothesis of an individual’s consumption behavior. According to the Life-Cycle

hypothesis, an individual will consume more in the present and hence be more apt to

borrow in the present based on increases in their future expected wealth or income. This

future wealth and income will be all but determined by an individual’s skills, talents,

motivation and education. If we can assume that education and specifically choice of

college major choice affects future income and wealth—an assumption consistent with

the finding of many previous studies—and that the Life-Cycle description of an

40



debt from the first stages and saves for retirement. Approaching retirement and then into

post-retirement, income falls below consumption and an individual dissaves or lives off

of savings from the previous periods. This process can be shown in the following

diagram:

Income, Consumption

DebtAccumulation

Dissaving

Savings

YouthYears

RetirementYears

WorkingYears

Consumption

Income

Figure 1

The Life-cycle framework assumes that an individual takes into consideration

future labor income in making consumption decisions in the present, and therefore has a

low discount rate i.e. values future consumption similarly to present consumption. Since

consumption depends on present value of future income, it does not matter that the

increase in income comes in one particular period or another. In valuing current and

future consumption similarly, individuals smooth their consumption, therefore

consumption (and specifically borrowing in the first life-cycle stages) in any period

should rise proportionally due to the increase in expected future income.

42



Since expected future income during the “working years” determines

consumption and borrowing decisions in the “youth years” of the life cycle, an increase

in expected future income should increase consumption –i.e. borrowing- in the early

“youth years”, ceteris paribus . Following the logic of this theory, a student’s choice of

major should influence the amount debt they are willing to undertake during their years

as an undergraduate student.

The alternative theoretical motivation to modeling loan debt and major choice as a

simultaneous system comes from marginal utility theory. Based on this theory,

educational choices such as college major are made at the margin. Consequently, if anindividual’s debt load were to rise, their marginal utility of consumption would be

increased during the repayment period due to loan repayment. This would give a student

an incentive to choose a more remunerative major. 1 An objective of this essay will be

to empirically test the application of the life cycle hypothesis—whether choosing a highly

remunerative major as opposed to a low paying major provides incentives to students to

undertake higher amounts of loan debt.

After laying out these theoretical motivations which highlight the need for an

empirical model that takes into account the possible endogeneity of curriculum choice

and loan debt, the natural progression is to represent a student’s choice of higher earning

majors and loan debt by the system of simultaneous equations shown below.

(6). Major choice i = X i+ Loans i + ε i (7). Loans i = X i + Major choice i + u i

1 While it only implies that the effect which loan debt has on major choice may often reveal itself after astudent has graduated, Appendix 1 shows that there is a definite link that runs between loans and major choice. Inanswer to the question posed at the end of a student’s senior year, “Given your level of debt, would you have chosen adifferent major?” 9% of students who responded to this question replied that they would change their major if theycould. This was an even higher 12% among students who responded and had more than $25,000 in loans.

43



(9). Loans = β1 + β2Major i + β3Xi + ε iL

Major i = α 1 + α2 (β1 + β2Major i + β3Xi + ε iL ) + α3Xi + ε iMMajor i = α 1 + α2 β1 + α2 β2Major i + α2 β3Xi + α2 ε iL + α3Xi + ε iMMajor i - α2 β2Major i = α 1 + α2 β1 + α2 β3Xi + α2 ε iL + α3Xi + ε iM

Major i ( 1- α2 β2 ) = α 1 + α2 β1 + α2 β3Xi + α2 ε iL + α3Xi + ε iM

Major i = α 1 + α2 β1 + α2 β3Xi + α2 ε iL + α3Xi + ε iM

(1- α2 β2 )

A way to circumvent this simultaneous equation bias problem and ensure that the

error term in equation (9) is not contemporaneously correlated with the choice of a higher

earnings major, is offered by an instrumental variable estimator. A two-stage estimation

can be applied in this case to estimate the effect of choosing a higher earnings major onloan debt.

If major choice is found to be endogenous in this system of equations, the

estimation of the system will be carried out in two ways described below. In order to

ensure that estimation of the relationship between major choice and Loan debt (equation

9) are consistent, the system of equations will first be estimated by two stage least

squares. The drawback to using this first approach would naturally be the fact that the

first stage would estimated via a linear probability model with choice of a high earnings

major being the dichotomous dependant variable. The linear probability model used in

the first stage estimation would treat this dichotomous variable as a continuous variable

and thus allow predicted major choice to fall outside the 0, 1 range of the original

dichotomous variable. However, despite its drawbacks, the two stage least squares

estimation procedure should lead to consistent estimates in the second stage regression

above.

45



Two stage Least Squares:

In the first stage, the dichotomous variable Major choice, the choice of the

highest earning major, will be regressed on all exogenous variables (X) in the structural

model (equation 8 above) as well as the variables Z that will serve as instruments for

choosing a higher earnings major, variables which will be uncorrelated with the error

term, ie. Cov (Z, ε iL) = 0.

(10). Major choice= α1 + α2Loans i + α3Xi + α3 Z i + ε iM

The second stage will proceed by replacing major choice with its fitted value*

predicted from the first stage regression. The second stage equation below excludes theinstruments for major choice and is identified. This two-stage process should produce

consistent estimates of the coefficient β2 below.

(11). Log Loans = β1 + β2Major* i + β3Xi + ε iL

Two stage Probit Least Squares:

Estimation of this system of equations above can also be carried out using a

simultaneous equation model that unlike two stage least squares accounts for the

dichotomous nature of the endogenous variable (Major choice) and the continuous nature

of the other endogenous variable (Loans). 11 The estimation will proceed in a similar

fashion as the 2SLS described above, however, the model would allow the first stage to

be estimated by probit and the second by OLS. 12

11 Heckman (1978) and Maddala (1983) present a simultaneous equation model in which one endogenousvariable is dichotomous and the other endogenous variable is continuous. Mroz (1999) also discusses a similar modelwith application to discern marriage effects on wages.

12 The estimation will be carried out using a STATA program developed by Keshk 2003 that implements thetwo stage estimation described in Maddala (1983) . The STATA command provides consistent second stage estimates,correcting biased standard errors.

46



therefore should not be correlated with the error. Consequently, a student’s self-

measured “Mathematical ability” may serve as a suitable instrument for a student

choosing a higher earnings major. An argument against the use of self-measured

mathematical ability would be that as measure of ability, it might be influential on loan

debt apart from its affect on a student’s major choice, or that it might be correlated with

some unobserved ability embodied in the error. Students with higher ability would be

expected to have higher expected future earnings and consequently higher debt. This

would present a problem if a student’s ability is not completely controlled for by SAT

scores and other ability measures in the second stage regression. Considering this possible shortfall, the data present two more options for instruments for the choice of

major.

A student’s probable major at the beginning of his or her freshman year is known

for almost all students in the dataset. Whether or not the student’s probable major in

their freshman year was engineering will be used to instrument for whether a student’s

final major is also high earnings engineering major. A student’s probable major in a

high paying major in their freshman year is obviously highly correlated with the choice of

a high paying final major and is most likely not as effected by a student’s total loan debt

as a student’s final major might be since the probable freshman major is chosen before

the student has incurred any significant debt . In addition to using whether a student

chose engineering as a probable major in their freshman year to instrument for a high

earnings final major, the choice of a second major will also be used to instrument for the

choice of a high earnings final major. Having a second major is highly correlated with

not choosing a higher earnings final major most likely due to the fact that students in

48



lower paying majors in the business, humanties and social sciences are more likely to

take on a second major. There would be no reason to believe that having a second major

would affect loan debt other than through its effect on an individual’s choice of primary

major.

Testing for the exogeneity of Major

Before using these instruments in any two stage IV estimation, the

appropriateness of an IV estimator—i.e. whether major choice should indeed be treated

as endogenous in equation 13 below—will be tested using a Durbin-Wu-Hausman

exogeneity test previously described in the Weiler replication. This test will be

performed to test whether the assumption that the decision to choose a higher earnings

major is exogenous.

Residuals from the instrumenting regression—equation 12 (minus Loans i )

below—are saved and included as regressors in the loan debt equation—equation 13

below—in order to test the null hypothesis of no contemporaneous correlation between

(Major, ε iL ).

(12). Major = α1 + α2Loans i + α3Xi + ε iM(13). Loans = β1 + β2Major i + β3Xi + ε iL + ( β4 ε iM )

Without adding the residuals from equation 12 ( ε iM ) as regressors in equation 4,

equation 4 produces residuals ε iL . The residuals from equation 13, ε iM , are inserted into

equation 4 in order to see if they produce significant coefficients. In order for the

parameter value ( β4 ) for these residuals ( ε iM ) to be significant they must take some

explanatory power away from ε iL . Therefore, if β4 is significantly different than zero, it

is the case that Major and ε iL are correlated and the null of exogeneity of Major must be

49



rejected. Another version of the Hausman test uses the expected value of Major

predicted from the instrumenting equation as a regressor in equation 13 above. The

significance of the coefficient on this predicted Major variable is then used to test the null

hypothesis of exogeneity of Major i in equation 13.


First approximation: Single Equation OLS

In order to establish the link that theory suggests should exist between choosing a

higher earnings major and loan debt, the equation below has been estimated twice usingOLS. The first specification includes dummy variables for the 6 categories of majors

with humanities, the lowest paying major grouping acting as the seventh and baseline

group. 14 The second specification only includes one dummy indicating whether a

student chose to major in the highest paying major—engineering—relative to all other

lower paying majors. A range of other variables in (X i) are used to control for race,

gender, parental income and education, ability of the student, year of graduation, years in

college and financial background.

(14). Log Loans i = β1 + β2Major i + β3Xi + ε iL

Tables 4A and 4B display the results from these first two OLS regressions. After

dropping observations with missing information on loan debt or other explanatory

variables, there were a total of 3,545 observations used in these regressions. The results

represented in Table 4A illustrate the finding that majoring in highest paying engineering

14 Architect students are both included and excluded from these regressions. The exclusion of these studentsdoes however cause the effect of choosing a high earnings major to be stronger. They are excluded due to the nature ofthe architecture program where students are in school for five rather than only four years, spending one year abroad.The relationship between loan debt and major choice for these students is inherently different since these studentsnaturally have the highest loan debt but are in the lowest paying major.

50



same parental income and education; black, latino and multiracial students have

substantially more loan debt upon graduation. This finding may be due to the possibility

that these minority students may not have as much financial support from extended

families that similar white students have.

Parental background variables have expected correlations with debt levels.

Students with either a mother or father with some graduate education or graduate degree

curtail their borrowing behavior relative to students with either a mother or father with

just a high school education. Also, having a mother with some college education or a

college degree relative to having just a high school education also decreases a student’sdebt levels. Having parents with $50,000-$99,999 annual income increases a student’s

loan debt relative to similar students who have a parental income below $30,000.

Students with parents who make $100,000 or above have significantly less loan debt than

similar students with parents who make less than $30,000. Students with a father who

works in a professional occupation –i.e. doctor or Law Occupationyer—have lower loan

debt than students without fathers working in professional occupations. Each of these

results concerning a student’s parental background point to the ability of higher educated

and income earning parents to subsidize their son or daughter’s educational costs. This

“social capital” enables some students to maintain lower debt levels relative to students

with lower parental education and income.

Results from these two first approximation regressions demonstrate the

correlation that exists between major choice and loan debt. While no other studies have

attempted to empirically find this same link, the literature that examines the possible

effect that loan debt has on major choice does not inspect the possible endogenous nature

52



of loan debt. This study will of course address the possibility that the choice of a higher

earnings major is in fact endogenous.

This essay, therefore will not end under the assumption that major choice is an

exogenous choice variable in the equation that determines loan debt, but rather this study

will attempt to ascertain whether instrumental variable estimation is needed to produce

consistent estimates of the impact of choice of major on loan debt. The next section will

describe the results from the Durbin-Wu-Hausman test of the exogeneity of the choice of

major.

Two Stage Least Squares: Testing the exogeneity of the choice of major

Table 5 presents the results from the second stage of the two stage least squares

regression which also includes the Durbin-Wu-Hausman test for exogeneity. This is the

test of significance for the coefficients on the residuals which are taken from the first

stage regression Major = α1 + α2Loans i + α3X i + ε iM and included as regressors in the

second stage regression Loans = β1 + β

2Major

i + β

3X

i + ε

iL+ β

4ε iM .

The test for significance of these residuals ( ε iM ) can be explained simply as

testing the null hypothesis of no contemporaneous correlation between the choice of

Major i and the error ( ε iL) , and consequently whether the ‘endogenous’ regressor’s

effects on the estimates are in fact meaningful.

If the DWH statistic suggests significance of β4 it would necessarily lead to a

rejection of the null hypothesis of the exogeneity of Major and would point to the

necessity of an IV estimator to obtain consistent estimates of Loans = β1 + β2Major i +

β3X i + ε iL. If the DWH test statistic is found to be insignificant, then we cannot reject

53



the null hypothesis that there is no contemporaneous correlation and must conclude that

the choice of Major is indeed exogenous and consequently can conclude that we would

receive no additional benefit from using an IV estimator, since OLS and IV estimates

would be similar.

The test statistic for the included residuals from the first stage instrumenting

regression (0.44478) is indeed insignificant at every level. Therefore, the null hypothesis

that the coefficients for these residuals are significantly different than zero could not be

rejected. That also means that the exogeneity of the choice of major could not be

rejected.15

It can be concluded that unlike the theorized simultaneous relationshipoutlined above might suggest, the choice of a high earnings major in this case is not

endogenous and it may not be necessary to implement an IV estimator to consistently

estimate of the effect that choice of major has on loan debt.

Two stage Probit Least Squares Results

Although tests for exogeneity do not reveal the need to use an IV estimator, the

results from a two stage IV regression of Loans on Major are presented here. In this

regression, a student’s choice of a second major and whether they indicated their

probable major as engineering at the beginning of their freshman year will serve as

instruments.

This specification allows the first stage to be estimated by probit and then the

second stage by ordinary least squares. Table 6 A shows the results from the first stage

instrumenting regression. The two variables we will use as instruments for the choice of

15 The omitted variable version of the Durbin-Wu-Hausman test was implemented using two similarmethods. The first method used the residuals from the first stage regression as the ‘omitted variable’ regressor in thesecond stage and the second used the predicted value of the dependent variable from the first stage as the ‘omittedvariable’ regressor in the second stage. Both methods produced the same results for the exogeneity test.

54



a high earnings major—engineering—are “Freshman Major is Engineer” and “Double

Major” are both shown to be significantly correlated with the choice of a high earnings

major—engineering—at the .01 level. From these reduced-form estimates, predicted

values for the dependant variable, the choice of a high earnings major are obtained for

use in the second stage. In the second stage the ‘endogenous’ variable Major choice is

replaced with its fitted-value, “Instrument for High Earnings Major”. Since standard

errors from this second stage regression will be based upon “Instrument for High

Earnings Major” and not on the appropriate actual choice a student makes, the estimated

standard errors for the second stage will be incorrect. The standard error corrections thatneed to be made are obtained by STATA procedures and are implemented by the cdsimeq

STATA command. 16 Second stage IV estimates with corrected standard errors are

presented in Table 6B. The instrument for choosing a higher earnings major has a

positive and significant coefficient. Even after controlling for the possibility that major

choice is endogenous in the theorized system of equations, choosing a high earnings

engineering major is correlated with taking on higher amounts of loan debt. This study

proposes that the mechanism for this increased loan debt is the higher expected future

earnings that high earnings majors bring. Assuming credit markets allow shifting of

earnings between periods in the life cycle, these higher expected future earnings allow an

individual to consume and borrow more while they are a student. All of the signs on the

remaining explanatory variables obtained from the single equation loan debt regression

are present in the two-stage method. Both females and those planning to go on to

graduate school take on less debt than their counterpart male and non-graduate school

16 The cdsimeq command is explained by Keshk (2003) in CDSIMEQ: a command to implement two-stage probit least squares.

55



students. Black and latino students take on significantly more loan debt than do white

students. The other result that should be noted is that SAT score is still correlated with an

increase in the amount of loans that a student takes on, indicating that student’s abilities

might also influence loan debt through an increase in expected future earnings potential.

2.5 Summary and Conclusions

In all of the previous literature that presents models of the relationship between

choice of college major and loan debt, the level of debt was specified as an exogenous

determinant of the choice of a higher earnings major. The conclusion drawn frommodeling loan debt as a exogenous factor in determining a college major is that a

student’s future plans or income expectations derived from their major do not affect the

amount that they borrow. The argument underlying the specification presented in this

essay is based on the life-cycle hypothesis and makes the claim that debt is not in fact

exogenous and that the choice of a higher earnings major is a determinant of the level of

debt a student incurs. This essay implies that education occurs at distinct stages, where

the student learns more about the costs and payoffs to additional (or specific types of)

education. The choice of major and amount of debt undertaken are both determined

jointly based upon a student’s background, abilities and future earnings expectations.

Therefore, this work attempts to test the importance that a student’s choice of major has

on the loan debt they incur. Not only does this essay propose that choice of major

determines loan debt, but it also does not assume that the choice of a high earnings major

is exogenous.

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The goal of this essay has been to explore more deeply the relationship between

loan debt and an undergraduate student’s major choice. This constitutes the first attempt

to explore whether there is a direct link between the choice of a higher earnings major

and loan debt. A major problem with previous literature derived from its disregard of any

possible endogenous relationship between loan debt and the choice of undergraduate

major. This gap in the previous literature has been addressed in this work by testing the

endogeneity of the choice of major. And while the hypothesis that major choice is

exogenous could not be rejected, an IV estimator was implemented to test the effect of

choosing a higher earnings major on loan debt. Results from this estimation procedure produced similar results to a single equation OLS model. Both regression results, first

from the single equation and then from the two-stage method point to the significance of

the life-cycle hypothesis in the borrowing choices made by students in this sample. Both

the choice of major and SAT score, reasonable proxies for future expected earnings had a

positive correlation with levels of borrowing.

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ESSAY 3

AN ANALYSIS OF SECOND MAJORS AND EARNINGS

3.1 Introduction

The previous two essays have focused on analyzing the relationship between the

choice of college major, the incentives which motivate that choice, as well as some of the

decisions and outcomes that are associated with that choice. These two essays

demonstrate that we can model students as choosing their major based upon their own

uncertain expected earnings and to a lesser extent on their probability of job prospects

across majors. The previous essay also suggests that once a particular major is chosen,

the expected future earnings of that major relative to other majors is correlated with a

student’s borrowing behavior during college. This final essay will not stray too far from

this developing analysis of the choice of college majors. Since the choice of primary

majors seems to be heavily influenced by expected earnings, might there also be an

earnings incentive for a student to choose a secondary major? This is a question that has

been ignored by the current body of literature.

Consequently, this essay will extend some of the well established literature that

estimates the earnings premiums associated with primary majors for college graduates by

attempting to estimate whether there is a premium associated with adding a second major

to a student’s transcript and whether this result holds across all majors and within specific

major categories.

It is easy to find anecdotal evidence of students contemplating the addition of a

second major in the hope of increasing their market value, or as a “backup major” in case

their primary major alone—possibly the major they enjoy—might not readily land them a

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job. It is reasonable to ask, therefore, whether or not a premium exists for students who

choose to invest in a second major. If second majors fail to carry any remunerative value,

we could assume that either second majors hold more of a purely consumption value for

the student as opposed to the evident investment value embodied in a primary major

choice, or that students have acted upon bad market information on how a second major

would affect earnings prospects.

Since the literature is void of studies that analyze the choice of a secondary major,

the following literature review will summarize the findings and concerns addressed by

the previous literature, which investigates the relationship between primary collegemajors and earnings.

3.2 Review of the Literature :

There has been considerable attention paid by the literature to the qualitative

effects that college attendance has on earnings. Of these qualitative effects, college

selectivity, college major and student performance have been the predominant subjects of

study. This area of research is popular among those involved in economic, sociological

and educational research because of the many implications that the choice of a college

major has on labor market outcomes for the general population of college graduates. 1

Studies centering on the choice of college major and earnings have maintained a level of

Highly Popular especially due to continued concern that some groups of students,

specifically women, tend to choose majors with the lowest average earnings. 2 Thus a

large part of the literature attempts to examine of how the choices of college major for

1 Rumberger and Thomas 1993, Eide, 1994, Grogger and Eide, 1995, Weinberger, 1998, Hamermesh andDonald 2004

2 Daymont and Andrisani, 1984

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men and women affect later earnings differences. Other than examining gender wage

differences, tracking earnings differences by major has garnered general appeal because

of the implications that choice of college major might have on upward mobility for low

income students and minorities as well as on the ability to repay student loans. There has

also been a common recurring limitation in the literature that attempts to measure the

effect that educational choices have on earnings. This caveat deals with the fact that

educational choices are not truly exogenous, and modeling them as such fails to

recognize the fact that the apparent relative returns to primary majors and even the

apparent earnings premium that might accompany the choice of a secondary major couldmainly be due to selection into those majors by students with certain levels of unobserved

abilities. While controls for observable ability have been included in all models

estimated in this study, there still exists the possibility that any results that indicate there

are higher returns to double majoring might be driven by positive selection into second

majors based on both observable characteristics and characteristics which are not

observed by the econometrician. Because of this problem, if no appropriate corrections

are made, we are unable to gather what the earnings premium to double majoring might

be if it were possible to have random assignments to secondary majors.

The remainder of this section will focus on the recurring themes found in the

empirical studies that examine the choice of college major and subsequent earnings.

This will provide an entry point for a discussion of the relationship between the choice of

a second college major and earnings. As noted, this is a relationship that has received

little attention in previous empirical studies.

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Rumberger and Thomas (1993) estimate the impact of college major, selectivity

and performance on student’s subsequent earnings. Citing that the majority of the

literature illustrating the significant impact these qualitiative differences have on

student’s salaries had used data on students graduating in the 1970s, 1960s or earlier, this

study set out to find whether these relationships continue to exist for more recent 1987

graduates. They also extend the literature by focusing on gender and racial differences in

the impact of college quality. Rumberger and Thomas also use a statistical technique

Hierarchical Linear Modeling that is more able to properly estimate the effects of

institutional characteristics on a nested sample of students. This modeling attempts toaccount for the nature of their data where observations on students are nested within

many different subsets of college that make up the complete sample. The HLM, with

fixed and random effects, apart from its methodological advantage over OLS, allows the

researchers to examine earnings outcomes at the student level and also allows the effects

of individual level variables on earnings to vary between schools in the dataset.

This study reveals that for students in the Recent Graduate Survey 1987, starting

salaries for females, after controlling for choice of major were about 13% lower than

similar males and 5% lower after controlling for labor market factors. Contrary to the

existing research, which had shown differences in college earnings among racial

categories, Rumberger and Thomas did not find any earning disadvantage for minority

students in their dataset. It should be noted that this study ignores the possible problems

associated with selectivity.

Ignoring selection bias, the authors find that all the variables representing

qualitative differences in a student’s college experience, especially a student’s choice of

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major are significant determinants of earnings. Engineering and health majors enjoyed a

38% and 36% starting salary advantage respectively over the baseline humanities majors.

Science and math majors received a 24% higher salary. Business majors in their sample

received an 18% higher beginning salary while social sciences had an approximate 7%

earnings advantage. These results are consistent with most studies that analyze the

differentials in wages received by college graduates with different majors. The authors

also find that these salary differences among major vary between men and women.

When separate regressions were carried out for males and females, results show that there

are higher earnings advantages among females for majoring in engineering and businessmajors relative to majoring in humanities majors.

Conditional upon the college majors women typically choose, these higher

earnings premiums available to women for majoring in engineering and business could

play a crucial role in determining the overall earnings gap that is present between male

and female college graduates. In fact, Eide 1994, estimated the impact that the increasing

number of women choosing to enter engineering and business majors between the 1970s

and 1980s had upon the shrinking gender wage gap. Eide finds evidence that this

dramatic “skill ugrade” during these decades, especially among women contributed to a

shrinking of the gender wage gap during the 1980s.

Another paper addresses whether between group differences in the quality of or

type of education can account for between group wage differentials that we otherwise

consider to be proof of discrimination. Weinberger, 1998 estimates wage regressions that

account for narrowly defined majors, college performance and college attended, she still

62



finds that white and Latino males earn approximately 10-15% more than comparable

women, Black males, and Asian male graduates.

A study by Hamermesh and Donald, 2004 estimates the effect of curriculum

choice (major) on college graduates’ earnings and attempts to account for two types of

sample selection bias, but not selection bias that arises from selection into college majors.

The Hamermesh and Donald study relies on responses to surveys sent out to a random

selection of graduates from the University of Texas at Austin, who graduated in the last

20 years. Due to the nature of their survey data, the authors present a unique model of

earnings determination that accounts for not one but two sources of sample selectivity.They control for the sample selectivity that occurs when survey respondents choose to

respond to the survey as well as selection into the labor force for those who did respond.

A similar correction for selection into the labor force is made when estimating earnings

equations in this essay, which will model the effect of the choice of a second major on

earnings.

After correcting for this double sample selectivity in their data, but also ignoring

the selection that occurs when students choose their major, a problem which might put an

upward bias on earnings premiums, Hamermesh and Donald find that there are still

differences in the earnings between majors; however, these differences are not extreme

after accounting for ability sorting, high school performance, parental economic status

and various demographic characteristics. Since Hammermesh and Donald do not control

for selection bias stemming from endogenous major choice, the difference between their

estimated conditional earnings differentials between majors and the actual unconditional

differentials that would occur if there were random assignments to majors, corresponds to

63



the extent to which selection effects reflect differences in unobserved characteristics.

The potential problem of not accounting for endogenous major choice may not be too

troubling since many of the studies that do control for selection bias; whether that

selection is into a college type or college major still have found varied premiums to

choosing some college types relative to others and most college majors relative to

humanities. 3

Like the choice of a primary major, a secondary major can be viewed as an

investment that can bring some level of expected return. The problem with most studies

that examine the choice of a primary major is that they do not make the connection andestimate the possible premium associated with investment in a second major.

The remainder of this paper will turn to the possible impact that a student’s choice

of a second major may or may not have on subsequent earnings. There could be

relatively little earnings effect for taking a second major, in which case we expect there is

an essential non-remunerative incentive to taking a second major. The problem with

estimating the effect of double majoring upon earnings is also the same problem apparent

in much of the educational literature that attempts to empirically test the effect that

educational decisions have on earnings.

The problem is that educational choices such as the choice of first or second

majors are treated as exogenous decisions and are added as regressors in log earnings

regressions, when in fact they are not exogenous choices. The argument might also be

made that choice of a second major may have a greater chance of being exogenous, if as

3 Brewer, Ehenberg, Eide (1999), in a study that estimates the effect of college type on earnings controls forselectivity into college type. They use college net costs to identify selection into college type. They find that there arestill earnings differentials associated with attending different types of colleges, but unconditional earnings differentialare smaller. Arciadiano (2003) controls for selection into college type and college major. This has an ambiguouseffect on the earnings premiums associated with certain majors, increasing the premium for some majors and decreasesthe premium to others.

64



systems, finance and accounting; and the lower earnings (or “soft”) business majors of

management and Marketing.

The second part of this empirical analysis is based upon similar data as described

above for the single university, a university that is also sampled by the larger data set .

The College and Beyond data set contains limited information about the post-secondary

records of students enrolling in one of 30 selective colleges and universities in 1976. The

records include information on grade point averages, SAT scores, majors chosen and

family background. These records were also linked with a survey that was completed 16

years after college graduation. This survey gathers information on graduates’ activitiessince graduation through 1995, including their present occupation, income, civic

activities, graduate work and other general information such as individual levels of

satisfaction. Approximately 80 percent responded to the survey. These records were also

linked with student information from the Higher Education Research Institute.

This sample of students includes students from public private and liberal arts

colleges. Data were collected for all 1976 matriculants enrolled in the private colleges

and universities, however a sub-sample of students were taken from the 1976

matriculants of the public colleges. This subsample included all known minority

students, varsity letter winners, those with SAT scores 1350 and above and a random

sample of others. The analysis will follow mainly those who were working full time at

the time the survey was completed. This will restrict the number

of students with available survey information from 22,514 to 16,367.

67



3.4 Methodology

In the first part of the empirical analysis, an OLS earnings function is used to

estimate beginning earnings for all students from the single university with beginning

salary observations. Variables are included that capture and control for ability

differences, family background, and demographic variation. The basic model is

presented below, where X i is a vector of student characteristics described above. M i

includes dummy variables representing a students choice of primary major, and D i

indicates the student chose a second major. λ i is the selection variable that controls for

selection into employment.

(1). log earnings i = α0 + α1 Xi + α2 M i + α3 Di + α4 λ i + ε i

Separate regressions will also be run for males and females. The earnings effect

of taking a second major will also be investigated within the business college, since

business courses and majors are intrinsically geared more toward gaining occupation

specific skills and training. As a result, a second major might more readily be viewed as

an investment in human capital.

Attention will then turn to addressing the problem of sample selection that is

found whenever there is selection into the workforce. The sample of students with

earnings observations is non-random, meaning there is a selection equation that

determines who does and does not enter the workforce. Most estimations require some

correction for this type of censoring due to the fact that the error term in the earnings

regression is correlated with the explanatory variables biasing the estimated coefficients.

If the expected value of the error term can be included in the regression as an explanatory

variable, this bias could be avoided. The first stage selection equation, of the Heckman

68



method, estimates the expected value of the error term. The original wage regression is

estimated including the expected value of the error as a regressor.

Two variables will be used to identify labor force participation in the selection

equation and will not appear in the second stage of the estimation procedure. The

exclusion restriction will be dummy variables indicating whether the student plans on

attending graduate school within six months of graduation and another indicating whether

the student highly values having a family after graduation. The indication of a student

highly valuing having a family is used in place of the usual identifier of labor force

participation—presence of children—since most students did not have children at thetime of graduation. The log earnings regressions for the full sample of students will be

re-estimated using a Heckman two stage procedure to account for the possible sample

selection bias.

If there does appear to be an earnings premium associated with taking a second

major in the context of the single university, the potential for exploring the possibility

that this result extends beyond a single university is presented by the College and Beyond

dataset. Broadening the lens of this study, we may focus on the choice of second majors

at a wider range of 30 selective colleges and universities. Use of this dataset will serve

a two-fold purpose. Not only will the dataset allow this research to extend the

applicability of the results found for the single university in describing a wider population

but it will also allow further investigation into whether unobservable student abilities

might be driving the estimated earnings premium to investing in a second major .

Students in the College and Beyond dataset answered a series of questions which

allow the researcher to better control for both a student’s observable as well as

69



“unobservable” characteristics that might motivate selection. Each student in this dataset

was asked to list his or her top 4 colleges and universities (including the college the

student attended) and to also indicate whether they were accepted or rejected at each of

these institutions.

In their paper “Estimating the Return to Attending a More Selective College: An

Application of Selection on Observables and Unobservables”, Dale and Krueger (1999)

attempt to estimate whether students receive an earnings boost from attending a more

selective school. Dale and Krueger also realize that there exists a selection problem

making the relationship they wish to study more complicated. Discovering that attendinga more selective school is correlated with higher earnings, might be the result of more

“able” students selecting into more selective schools. Therefore, this apparent earnings

premium might be due to higher levels of unobserved ability of students attending more

selective schools and not because a student attended a more selective school.

Dale and Krueger decide to use the screening procedure inherent in the college

admissions process to control for selection of higher ability students into more selective

schools. The logic of their model is rather straightforward. College admissions

committees are often privy to observing what otherwise might be considered

“unobservable ability” in the eyes of the econometrician. Colleges and universities use

this information on unobservable ability along with observable characteristics in the

admissions process to help decide whether or not a student will be accepted into their

institution. 4

Therefore, we assume that students who get accepted and rejected by the same

post-secondary institutions will have similar levels of observed and unobservable

4 Dale and Kruger (1999) present a model of the college selection process on observables and unobservables.

70



abilities. For example, student A and student B are both accepted into schools where the

average SAT score of matriculants is 1300 and are both rejected from schools with

average SAT scores of 1350. These two students are assumed to have similar levels of

observed and unobserved abilities since they were both accepted and rejected from

schools of similar selectivity and similar admissions standards. Dale and Kruger proceed

by categorizing and grouping students who have been accepted and rejected by schools

with similar average SAT scores (i.e. schools of equal selectivity) and include each of

these groups of students (represented by dummy variables) in the log earnings equations

in order to control for unobservable ability. So what Dale and Krueger are in factestimating is whether there is an earnings premium to attending a more selective

institution between students with similar levels of both observable and unobservable

skills. What they find is that once this unobserved ability is controlled for, any earnings

premium that was associated with attending a more selective institution is reduced to

zero. This current research will use this methodology in an attempt to control for any

selection that might be driving the apparent premium to choosing a second major.

The difference between, this study and that of Dale and Kruger is how this study

will group students with similar levels of unobserved ability. Dale and Krueger were

able to group students together who had been accepted and rejected by similar schools.

The College and Beyond Survey only reports school codes and not the specific school

names where the students applied. Using a file provided by the Higher Education

Research Institute, D&K were able to link these codes with the actual names of

institutions where students applied. In this way they were able match the average SAT

score of a school to the institution’s code. Therefore, a student who was accepted by a

71



school with an average SAT score of 1250 and rejected by a school with an average SAT

score of 1350 could be grouped with another student who was accepted and rejected by

two different schools, but schools that had an approximate average SAT score of 1250

and 1350 respectively.

This study will have access to institution codes for each school that the student

was accepted and rejected by, but does not have access to the file that would allow the

matching of these codes to the name of that specific institution. This makes it

impossible to match groups of students together who were accepted and rejected by

institutions with similar average SAT scores since we cannot garner the average SATscore of a school from only its number code.

Because of this deficiency, this study only matches students who were accepted

by the same exact institutions. This can be done by just comparing the institutional codes

for the schools to which each student applied. While this method is a variation of that

used in the Dale and Krueger study and might not be able to fully capture students’

unobserved ability, it is actually fairly successful in matching students, as many students

in this sample applied to many of the same institutions and therefore should still give

some indication of the premium associated with having a double major if it were possible

to have random assignments to second majors. If a student was not matched to a group,

as in the Dale and Krueger study, they are dropped from the analysis. Due to the inability

to match every student to a group, the sample size in the second College and Beyond

specification drops from 16,367 to 8,528. The estimated log earnings equation that

controls for observed and unobserved ability will be: 5

5 The earnings of each survey respondent appear in categorical form. There are 10 earnings categories. Each

student was assigned a specific earnings value using the midpoint value of the earnings range associated with their

72



(2). log earnings 1995 = β0 + β1 X i +β2 d i + β3 ability i + ε i ,

where log earnings is equal to the log of each individuals’ full time 1995 earnings, X i is a

vector of individuals specific variables including G.P.A., SAT scores and demographic

variables. d i is a dummy variable indicating the choice of a second major. Ability i

includes the 196 dummy variables that represent matched groups of students who applied

and were accepted by the same institutions. The model will be estimated both with and

without these dummy variables. Ability i will also include dummy variables indicating

several self revealed evaluations of student’s own abilities.


In the first stage of the empirical analysis, an OLS earnings function was used to

estimate beginning salary for students at a single university that capture demographic

characteristics, ability measures, choice of major and family background. The model is

estimated for several groups of students. First the model was estimated for the whole

sample including both males and females. Next the model was estimated for men and

then separately for women. The coefficients and standard errors from these regressions

can be found in Table 1 in Appendix 3.

In the overall sample, the regression estimates reveal significant differences in

beginning salaries associated with some of the demographic variables that characterize

individual students. These results illustrate no earnings disadvantage for minority

students; however this result could be driven by the lack of minority students in the

category. For example if a respondent indicated their earnings fell in a category ranging from $5,000 to $9,999, thatindividual is assigned an earnings of $7,499. The log of each of these midpoint values represents the individuals log1995 earnings. Dale and Krueger (1999) follow the same strategy in order to estimate OLS log earnings regressions forstudents in the College and Beyond. Ordered Probit models using the income categories as dependent variable

produced coefficients with similar significance and direc tion for the variables of interest (esp. double major)

73



sample. In fact, we can see that after controlling for a wide range of family and college

background factors as well as occupational attachment, Asian students in this sample earn

significantly more, around 11% more than similar white students. This demonstrates

that earnings differentials between college graduates might be somewhat smaller than

between all educational groups and since we are looking at beginning salaries, these

results might not expose any subsequent earnings disadvantage that college minorities

might face.

While many studies show that family background factors influence the length of

schooling or the type of schooling decision more heavily than the earnings of collegegraduates, it seems that some parental characteristics are associated with higher

beginning earnings. Students who have fathers with high and medium education levels

tend to have around a 5% earnings advantage. This effect that father’s education has on

earnings seems to hold only for women. In the separate regression estimated for females,

we can see that father’s education increases beginning earnings where the same result is

not found in the all male specification. This parental impact may point to the possibility

that students with families with different socioeconomic levels might have different

information about the labor market for educated labor enabling some students to find

better paying jobs. 6

As expected, there are glaring earnings differences across primary majors.

Engineering has the highest wage premium over the baseline humanities majors. The

high earning (hard) business majors, including management information systems,

finance, and accounting majors had the next highest beginning salaries compared to

6 Betts (1996) tests whether students with higher socioeconomic levels do have more accurate information onrelative earnings between occupations than students with lower socioeconomic levels. He finds that they do.

74



humanties, followed by natural science majors, social science majors with low earnings

or “soft” business majors having the lowest earnings premium relative to humanities

majors. Pre-professional students naturally have 18% lower beginning earnings than

humanities majors as many pre-professional students would not be expected to be fully

attached to the labor force.

An interesting finding that parallels many other studies that estimate the wage

premiums associated with different majors, is illustrated in the separate regressions for

men and women. Similar to results found by Rumberger and Thomas (1993) women

have a higher earnings advantage for majoring in engineering and high earning businessmajors relative to humanities majors than men do. It should be noted that these

differentials showing earnings advantages for particular major categories relative to all

humanities say nothing in particular about the relative premiums to individual majors

within these broad categories.

One must also keep in mind that these wage differentials are conditional earnings

differentials, meaning that they are conditional upon individuals selecting into certain

majors. Also these estimates illustrate earnings differences for beginning salaries and

don’t speak to the possible differences in earnings growth between majors.

The main variable of concern in this study is the choice of a second major. For

the whole sample, Table 1 demonstrates that there is a 3% earnings premium associated

with choosing a second major, however, this variable is only found to be significant for

women in separate earnings regressions. It seems that it is mainly women in this sample

who benefit from an earnings advantage to taking a second major. The inclusion of the

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female*double major interaction term provides more evidence that female second majors

do have significantly different earnings.

While Table 1 illustrates the likelihood that double majoring across all primary

majors holds some investment return for females, Table 2 reveals how double majoring

effects earnings within the college of business. One could assume that there might be a

higher investment quality to taking a second major within a college that provides

relatively more fields geared toward occupational training. Similar results are found

within the business college; however, there is an even higher premium to a second major

within the business school. Once again, however, only female business students receive a6% higher beginning wages than female business students without a second major.

Tables 3A and 3B present the results from the Heckman two stage corrections for

sample selection, which attempt to control sample selection bias that might be present

due to individual selection into employment. Selection into the labor market is identified

by two variables. The standard identifier of labor force participation is presence of

children, however since at the time of graduation most individuals in this dataset are

without children, a substitute for presence of children was used. Students are asked the

importance they place on raising a family after graduation. Giving a high import to

raising a family as well as having plans to attend graduate school will be used to identify

selection into the labor force. Both of these variables are strongly positively related to

entering into the sample of students with wages. The results from the second stage of the

Heckman procedures do not differ greatly from the uncorrected results in Table 1 and

Table 2. It still appears that only females receive an earnings premium to a second major

at this selective university. But why might second majors act as human capital which

76



earns a return for women and not for men? Second majors might possibly act as an

ability signal for female graduates at this institution or maybe these results might be

explained simply by the type of second majors women are choosing. A explanation of

these results is likely related to the different types of primary majors males and females

choose. On one hand, since women are more likely to choose their primary majors based

upon their preferences rather than their earnings prospects (see essay 1), they tend to

choose primary majors in the lower paying humanities and social sciences. These same

female students might feel some type of pressure from those financing their education to

take a remunerative second major. Males on the other hand are more likely to choosemore remunerative primary majors and therefore might choose a secondary major based

upon their preferences—likes and dislikes—rather than upon which second major will

provide them the greatest return. In this way, differences in the choice of primary major

between men and women might produce the positive earnings benefit associated with

second majors for women in this sample.

Whether earnings premiums connected to a second major are received by males or

females, the possibility still exists that these estimated earnings premiums associated with

choosing a second major are driven by selection bias. The attempt to correct the problem

that endogenous choice of a second major and unobserved ability might create has led to

a model that attempts to partially control for unobserved ability in earnings regressions

estimated for students in the College and Beyond dataset. The estimates from two

specifications, one that does not control for unobserved ability and a second that includes

students self-revealed ability rankings as well as the 196 dummy variables representing

groups of students with similar levels of unobserved ability, are shown in Table 4 and

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Table 5 respectively. Controlling for some level of unobserved ability decreased the

earnings premiums associated with choosing engineering, business, natural sciences,

social sciences and other majors relative to humanities. This result would reinforce the

idea that conditional earnings differentials between majors given by conventional OLS

regressions might overstate earnings differentials between majors. One more result

regarding the choice of a primary major that should be noted is the apparent difference in

earnings growth that takes place between majors. When earnings models were estimated

for the single university, there existed a significantly greater beginning earnings premium

associated with choosing engineering. The College and Beyond data has earningsobservations for 15 years after graduation as opposed to beginning earnings and we see

that after controlling for observed and unobserved ability, the highest earnings premium

is now associated with choosing a business major. This indicates that while business

majors might begin with lower relative salaries than engineers, the growth in their

relative earnings profile is steeper than the earnings profile for engineers.

The result of primary interest in this section, however, is the effect that

controlling for unobserved ability has upon the estimated coefficient for double majors.

The results illustrated in Table 5 show that there most likely is some amount of selection

into second majors taking place as controlling for selection into a double major decreases

the earnings premium to taking a second major. This would indicate that there is positive

selection into second majors, where students with higher levels of unobserved abilities

tend to be the students who take a second major. The earnings premium decreases from

4.5% to 3.8% between the two specifications.

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Students with higher unobserved ability in the College and Beyond tended to

choose a second major, and one can see that if this higher unobserved ability also

increases earnings and is not controlled for in the earnings equation, the coefficient for

double majoring will be biased upward. When we do not control for this positive

selection into secondary majors as is the case for the regression producing Table 4 , the

effect of double majoring is higher than what we would see in an experiment where a

student were randomly assigned a second major. But even after controlling for selection

there appears to be an earnings premium associated with a second major.

Other background and schooling variables also play a part in determiningearnings for students in this dataset. Having a father with higher education, attending a

catholic high school relative to a public secondary school, and attending a private

university relative to a public university were associated with an increase in individual

earnings 15 years after graduation, controlling for other background characteristics

including occupation. As expected, obtaining an advanced degree also positively affects

earnings over a decade following graduation.

3.6 Summary and Conclusions

In this essay, estimates have been presented that demonstrate the effect of

choosing a secondary major upon subsequent earnings. Unlike previous studies which

focus on earnings premiums across primary majors, this study used data from both a

single university as well as data from several colleges and universities to study earnings

premiums associated with choosing a secondary major both across all majors and within

a specific college. Also, this study allows for the possibility that students may

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systematically choose a secondary major based upon unobservable abilities. It does not

seem that the positive wage premium associated with choosing a second major is greatly

lowered by correcting for selection bias. However, correcting for selectivity provides

evidence that there might be some amount of positive selection into second majors. After

controlling for selection on observables and unobservables, the earnings impact of having

a second major falls slightly. Also, the second major earnings advantage for students in

the single university of around 3.5% was very close to the selection corrected premium of

3.8% for the College and Beyond. The difference between the two datasets rests

primarily on which gender receives the earnings advantage. For the single university, wefind that women rather than men receive an earnings premium to secondary majors, while

in the College and Beyond, the opposite is true. With approximately 41% of students

from the single university selecting second majors and slightly over half of those students

being female, the choice of a second major is potentially an important decision for many

students. This study also finds that there continues to be varied earnings premiums to

most primary majors especially to engineering and business majors relative to humanities

majors. Earnings premiums in these majors also appear to be larger for females than they

are for male students, leaving the opportunity open for continued minimizing of gender

earnings differentials. 7 Findings also suggest that there are most likely different growth

rates in earnings between majors as some majors have lower beginning earnings

premiums but have higher earnings premiums later in the working period. 8

These results that extend and support much of the previous research on higher

education choices and their effect on post graduate outcomes are of particular importance

7 See Eide (1994)8 Berger finds this is true for individuals in the National Longitudinal Survey of Young Men.

80



especially since these choices can vary widely based on gender and socioeconomic status.

As college costs and returns continue to rise, these choices continue to have the potential

to minimize or exacerbate economic differences between student groups.

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SUMMARY AND CONCLUSIONS

The preceding essays have attempted to shed some additional light on a student’s choice

of an undergraduate major. For many students, the choice of major is an important decision

which will have a significant impact upon other higher education decisions as well as on their

later life outcomes; therefore, defining the incentives that determine this choice can be helpful in

discussing why there are different educational and economic outcomes for particular groups of

students.

The first essay attempts to model a student’s choice of primary major in a unique way by

allowing earnings expectations to be determined by various earnings outcomes within a major

and finds that like other groups of students in nationally representative datasets, students from a

selective university also choose their major based upon relative expected returns in each major,

and choose the major that would give them the highest expected returns. Expected earnings,

however, seem to be a more important to the decisions of men than women in this dataset. Little

evidence is found that suggests that students in an environment of uncertainty choose a major

based upon relative probabilities of obtaining a job offer across majors.

Based on these findings we can conclude that increasing the number of individuals

entering a particular field might be achieved by enhancing the monetary returns of that field. Of

course this inference would be truer for men than it is for women. Additional study could focus

on how expected earnings affect the choice of field differently for other minority groups. This

essay did not specifically conclude whether a change in expected beginning earnings or lifetime

earnings would be the most appropriate to affect choice of major or field as the choice of major

was based upon expected earnings 15 years after graduation .

The choice of primary major itself is hypothesized to impact other decisions students

make during college. Therefore, the second essay of this paper focuses on one of the implications

of a student’s choice of major. In the second essay we find that the choice of the highest earning

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majors increases the magnitude of a student’s debt burden. Not only was a student’s major found

to affect the amount that a student chooses to borrow, but we can see that student’s abilities as

measured by their SAT scores also affect borrowing behavior. Consequently, the expected future

earnings of a major and individual ability levels are linked to the amount that a student will

borrow as suggested by the life-cycle hypothesis. Based on the results presented here, we can

also see that students incurring the most debt will also be the students who will be more able

handle their larger debt upon graduation. We also conclude that these results are not driven by

the proposed endogenous nature of the choice of major. The relationship between loans and

choice of major is an interesting one and merits additional study since both the costs of higher

education and also the aid from colleges and universities continue to rise.

The third and final essay fills a void in the choice of major literature by estimating the

premium to investing in a secondary major for students at a selective university and also for

students from a wider range of 30 selective institutions. Estimating the effect of second majors

on log earnings while controlling for selection into secondary majors, evidence is found to

suggest that students from a single selective university who invest in a second major do earn an

earnings premium of about 3.5%. This premium is even greater within the college of business.

However, this positive earnings premium only exists for female graduates in this sample. For the

sample of students from the wider range of colleges and universities, there also exists an earnings

premium of 3.8% that is associated with taking a second major, however, in the College and

Beyond this positive earnings premium was present for only men.

There is also something to be said about controlling for selection into secondary majors.

The College and Beyond dataset allows for a unique way to control for some amount of the

possible selection into second majors that might occur. For the sample of 30 selective institutions

in the College and Beyond, we find that there is apparently a least a small amount of positive

selection into secondary majors, and once selection is controlled for there is a smaller premium to

having a second major than previously estimated. It could be assumed that most individuals

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choosing second majors have higher levels of some unobserved ability that is positively

correlated with earnings and without controlling for this unobserved ability, the premium to

taking a second major is pushed upward.

Results from this third essay give evidence that there is some investment value to

choosing a second major. There do appear to be remunerative reasons for students to choose

second majors. It seems to be reasonable way for students to slightly increase their realized

earnings.

In conclusion, these essays set out to answer four specific questions: 1.) How do

expected earnings affect a student’s choice of major for students from a selective university? 2.)

What are some of the implications that the choice of major has upon other college decisions such

as borrowing behavior? 3.) What affect does choosing a second major have upon a student’s

earnings? 4.) How do the answers to these questions change when describing the choices of men

and women? These three essays do find that there are both strong incentives and implications of

student’s choice of both primary and secondary majors. Expected earnings incorporating

earnings risk significantly affect choice of major; the choice of major and ability are shown to be

significantly correlated with loan debt and there appears to be a monetary remuneration to taking

a second major.

Further research might focus on extending these results that describe qualitative higher

educational choices to the greater population of college undergraduates beyond graduates of

selective colleges and universities. Additional research might be well advised to extend the

analysis in these essays by studying the differences in qualitative educational choices made by

different socioeconomic and demographic groups so that we may better understand the labor

supply, borrowing decisions and earnings outcomes for diverse groups of college graduates.

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1.6 Appendix 1

TABLE 1A:

Conditional (Mixed) Logit:

Estimating the Impact of Expected Earnings on the Choice of CollegeMajor for the Single Selective University

1997, 1999, 2001 and 2003 cohorts

Dependant Variable: Choice of Major

Full Sample

ESTIMATE STD.ERROR

ESTIMATE STD.ERROR

EXPECTEDEARNINGS

.00000921** .00000367 Multiracial 1/5 0.0427 0.3557

Female 1/5 -1.6275** 0.12458 Multiracial 2/5 -0.3865 0.3023Female 2/5 -0.74311** 0.08433 Multiracial 3/5 -0.6564 0.4174Female 3/5 -0.30421** 0.10736 Multiracial 4/5 -0.6688 0.3604Female 4/5 0.1824 0.0984 Unknown Race

1/50.1474 0.6227

Mother Education:College and Above1/5

-0.1885 0.1219 Unknown Race2/5

-0.3570 0.5658


-0.2435** 0.0939 Unknown Race3/5

0.3295 0.6104


-0.1948 0.1193 Unknown Race4/5

0.0322 0.5808


0.0519 0.1004 ParentalIncome 50-100K 1/5

-0.1845 0.1498

FatherEducation:College

and Above 1/5

-0.1897 0.1226 ParentalIncome 50-

100K 2/5

0.3311** 0.1144

Father Education:College and Above2/5

-0.3585** 0.0966 ParentalIncome 50-100K 3/5

-0.1227 0.1446


-0.0364 0.1214 ParentalIncome 50-100K 4/5

0.1240 0.1233

85




-0.2899** 0.1052 ParentalIncome over100K 1/5

0.2264 0.1441

Black 1/5 -0.3113 0.5500 ParentalIncome over

100K 2/5

0.0246 0.1174

Black 2/5 0.7840* 0.3518 ParentalIncome over100K 3/5

0.1010 0.1436

Black 3/5 -0.2806 0.5135 ParentalIncome over100K 4/5

0.0106 0.1262

Black 4/5 0.6030 0.3771 Father isProfessional1/5

-0.5455** 0.1807

Asian 1/5 0.5193 0.2941 Father is

Professional2/5

-0.2491* 0.1270

Asian 2/5 0.3935 0.2443 Father isProfessional3/5

-0.1891 0.1609

Asian 3/5 0.5833* 0.2795 Father isProfessional4/5

-0.0875 0.1345

Asian 4/5 -0.1942 0.2915 SAT /100 1/5 0.0163 0.0105

Latino 1/5 0.1644 0.2317 SAT /100 2/5 0.0769** 0.0089

Latino 2/5 0.2661 0.1827 SAT /100 3/5 -0.0196 0.0107

Latino 3/5 -0.1890 0.2574 SAT /100 4/5 -0.0107 0.0106

Latino 4/5 0.2977 0.1930

86



87

TABLE 1B:

Conditional (Mixed) Logit: Results of separate mixed logits for males and females

Estimating the Impact of Expected Earnings on the Choice of CollegeMajor for the Single Selective University

1997, 1999, 2001 and 2003 cohorts

ESTIMATE STD. ERRORMales:

EXPECTEDEARNINGS

0.0000152 ** 0.0000048282

Females:EXPECTEDEARNINGS

-0.0000067791 0.00000599054

Significance:

Bold = significantly different from zero at the 10% levelBold* = significantly different from zero at the 5% level Bold ** = significantly different from zero at the 1% level



88

TABLE 2A:

Conditional (Mixed) Logit: Full Sample

Estimating the Impact of Risk Adjusted Expected Earnings on the Choice of CollegeMajor for the Single Selective University

1997, 1999, 2001 and 2003 cohorts

ESTIMATE STD.ERROR

ESTIMATE STD.ERROR

U_EXPECTED

EARNINGS

.0000459** .00000677 Multiracial

1/5

0.0049 0.3562

Female 1/5 -1.70327** 0.12122 Multiracial2/5

-0.6015* 0.3047

Female 2/5 -0.03386 0.13137 Multiracial3/5

-0.6780 0.4159

Female 3/5 -0.3908** 0.10779 Multiracial4/5

-0.7043* 0.3606

Female 4/5 0.39191** 0.10175 UnknownRace 1/5

0.1520 0.6227

MotherEducation:College andAbove 1/5

-0.1726 0.1216 UnknownRace 2/5

-0.3087 0.5663


-0.0992 0.0962 UnknownRace 3/5

0.3357 0.6103


-0.1228 0.1189 UnknownRace 4/5

0.0257 0.5808



-0.1903 0.1504

FatherEducation:College andAbove 1/5


0.2639* 0.1151



89


-0.3782** 0.0961 ParentalIncome 50-100K 3/5

-0.1224 0.1453

Father

Education:College andAbove 3/5

-0.0262 0.1213 Parental

Income 50-100K 4/5

0.1103 0.1235


-0.3036** 0.1048 ParentalIncomeover 100K1/5

0.2213 0.1446

Black 1/5 -0.2675 0.5503 ParentalIncomeover 100K2/5

-0.0138 0.1179

Black 2/5 0.6290 0.3538 ParentalIncomeover 100K3/5

0.1013 0.1442

Black 3/5 -0.1450 0.5126 ParentalIncomeover 100K4/5

0.0001 0.1264

Black 4/5 0.5459 0.3774 Father isProfessional1/5

-0.5456** 0.1806


-0.2674* 0.1274


-0.1865 0.1608

Asian 3/5 0.6610* 0.2796 Father isProfessional4/5

-0.0977 0.1345

Asian 4/5 -0.2659 0.2891 SAT/1001/5

-0.0181 0.0118

Latino 1/5 0.0436 0.2323 SAT/1002/5

-0.0459* 0.0191

Latino 2/5 0.0805 0.1852 SAT/1003/5

-0.0244* 0.0108

Latino 3/5 -0.2094 0.2555 SAT/1004/5

-0.0574** 0.0128

Latino 4/5 0.3475 0.1933



90

TABLE 2B:

Conditional (Mixed) Logit: Results from separate mixed logits for males and females

Estimating the impact of Risk Adjusted Expected Earnings on the Choice of CollegeMajor for the Single Selective University

1997, 1999, 2001 and 2003 cohorts

ESTIMATE STD. ERRORMales:

U_EXPECTEDEARNINGS

0.0000557** 0.000009

Females:

U_EXPECTEDEARNINGS

0.0000186* 0.00000948



91

TABLE 3A:

Conditional (Mixed) Logit

Estimating the Impact of the Predicted Probability of Receiving Job Offer on the Choiceof College Major for the Single Selective University1997, 1999, 2001 and 2003 cohorts

Probability of Receiving a Job Offer is the only independent variable

ESTIMATE STD.ERROR

Full Sample :

Predicted Probability ofReceiving Job Offer

0.02704

0.09667

Males :


1.30941**

0.14874

Females :


-1.00785**

0.13099



92

TABLE 4A:

Conditional (Mixed) Logit:

Estimating the Impact of the Predicted Probability of Receiving Job Offer on the Choice

of College Major for the Single Selective University

1997, 1999, 2001 and 2003 cohorts

All Controls

Males Females

ESTIMATE STD.ERROR ESTIMATE STD.ERROR PROBJOB -0.29518 0.327617 PROBJOB 0.291036 0.38585MotherEducationCollege andAbove 1/5

-0.12286 0.157468 MotherEducationCollege andAbove 1/5

-0.18085 0.223039

MotherEducationCollege andAbove 2/5


-0.25636 0.134197



-0.28832 0.162058


0.032672 0.163589 MotherEducationCollege andAbove 4/5

0.030606 0.139143

FatherEducationCollege andAbove 1/5

0.083463 0.156214 FatherEducationCollege andAbove 1/5

-0.67015** 0.218915


-0.29248* 0.138643 FatherEducationCollege andAbove 2/5

-0.42557** 0.138079


0.087401 0.182101 FatherEducationCollege andAbove 3/5

-0.13079 0.170944



93


-0.18748 0.165825 FatherEducationCollege andAbove 4/5

-0.304* 0.139321

Black 1/5 -0.10529 0.638962 Black 1/5 -14.3583 887.6594

Black 2/5 0.534541 0.518019 Black 2/5 0.950181* 0.496095

Black 3/5 -0.87311 0.888238 Black 3/5 0.322548 0.733261

Black 4/5 0.428625 0.583048 Black 4/5 0.69312 0.510563

Asian 1/5 0.497099 0.402941 Asian 1/5 0.680807 0.486174

Asian 2/5 0.319002 0.358281 Asian 2/5 0.573311 0.335015

Asian 3/5 0.593185 0.440299 Asian 3/5 0.634177 0.390491

Asian 4/5 0.067902 0.435 Asian 4/5 -0.1486 0.386503

Latino 1/5 0.007405 0.31018 Latino 1/5 -0.08952 0.45561

Latino 2/5 -0.05263 0.279596 Latino 2/5 0.52622 0.275074

Latino 3/5 -0.44543 0.381882 Latino 3/5 -0.12603 0.353962

Latino 4/5 0.058342 0.325334 Latino 4/5 0.458926 0.301524

Multicultural1/5

0.129137 0.474689 Multicultural1/5

-0.37358 0.648638

Multicultural2/5

-0.29095 0.468186 Multicultural2/5

-0.39725 0.408714

Multicultural3/5

-0.26278 0.627013 Multicultural3/5

-0.82005 0.579908

Multicultural4/5

-1.2535 0.796099 Multicultural4/5

-0.55644 0.416851

Unknown

Race 1/5

0.176487 0.679139 Unknown

Race 1/5

-14.1746 1681.736

UnknownRace 2/5

-0.51531 0.681318 UnknownRace 2/5

0.007754 1.01453

UnknownRace 3/5

0.232874 0.772362 UnknownRace 3/5

0.690047 1.008966

UnknownRace 4/5

-0.19569 0.770388 UnknownRace 4/5

0.361579 0.921614

Parental -0.177 0.196676 Parental -0.03609 0.258944



94

Income 50-100K 1/5

Income 50-100K 1/5

ParentalIncome 50-100K 2/5

0.447544** 0.169398 ParentalIncome 50-100K 2/5

0.159619 0.159038



-0.04721 0.190671



0.133192 0.159769

Parentalincome over100K 1/5

0.118056 0.186102 Parentalincome over100K 1/5

0.245453 0.255417

Parental

income over100K 2/5

-0.1463 0.168864 Parental

income over100K 2/5

0.161462 0.165691


0.050443 0.213484 Parentalincome over100K 3/5

0.100906 0.1972


-0.26078 0.197675 Parentalincome over100K 4/5

0.227157 0.166343

Father isProfessional1/5

-0.55936** 0.230426 Father isProfessional1/5

-0.60926 0.359707


-0.30276 0.188568 Father isProfessional2/5

-0.29415 0.188734


-0.47577 0.256117 Father isProfessional3/5

-0.15108 0.217415


0.061324 0.21374 Father isProfessional4/5

-0.1869 0.184003

SAT/100 1/5 0.037607* 0.017725 SAT/100 1/5 -0.03896 0.023616

SAT/100 2/5 0.047112** 0.017951 SAT/100 2/5 0.003379 0.019061

SAT/100 3/5 -0.00965 0.019629 SAT/100 3/5 -0.0334 0.018821

SAT/100 4/5 0.006458 0.018252 SAT/100 4/5 -0.00361 0.016114



95

2.6 Appendix 2

Summary statistics from this data would suggest that loan debt plays some role in

higher educational choices, or at least is an underlying determinant in education and

career decisions for students from this university. In the graduating class of 2003, the

only graduating class to answer the relevant survey questions, only 9 % of students would

have chosen a different major considering the loans they accumulated. The fact that such

a low number wish to change their major demonstrates one of two behaviors : Either most

students are forward looking enough to choose their major based in part based upon the

loan debt they were to accumulate; or students—and relatively few students at that—finally consider loan debt only closer to graduating. In constructing the system of

simultaneous equations estimated in this study, we show how the former is most likely

the case—that loan debt does influence final major choice. This is one reason underlying

the argument that major choice is endogenous in the equation below. However, it still

might be the case that the latter—loan debt does not influence major choice for most

students until they are about to graduate—might be a more accurate description of the

effect loan debt has on major. If this is the case major choice would not be endogenous

through the system of equations presented in this paper.

Loans i = X i + Major choice i + u i

An even higher 12% of students with $25,000 or more worth of debt said that they

would have chosen a different major given the total loan debt they accumulated by their

senior year. Other statistics from the 2003 graduating class would suggest that loan debt

also plays a part in student’s post-graduation choices. When asked whether loan debt

will play a part in delaying post baccalaureate plans, 40% of students responded that their



96

post-bac plans would be delayed due to their accumulated loan debt. When asked

whether loan debt played a part in their career choices, 46% of students responded that

their debt played a part in the career path they will take.



GENDER AND ETHNICITY OF GRADUATES FROM SELECTIVE UNIVERSITY

1997, 1999, 2001 and 2003 graduating cohorts

MALE FEMALE TOTAL

WHITE 3375 2821 6196

Percent of Row 54.47% 45.53% 100.00%Percent of Column 83.75% 82.53% 83.19%

BLACK 107 97 204


ASIAN 158 141 299


LATINO 244 223 467


MULTIRACIAL 64 68 132


OTHER RACE 50 47 97


UNKNOWN RACE 32 21 53

Percent of Row 60.38% 39.62% 100.00%

Percent of Column 0.79% 0.61% 0.71%

TOTAL 4030 3418 7448


97



98

DESCIPTIVE STATISTICS & M E A N S

Males and Females from Selective University1997, 1999, 2001 and 2003 graduating cohorts

MEN: N =4030

Percent of allmajors

Percentgoing to

gradschool

Salary(2003 $)

Total Loans(2003 $)

Engineers 14.76% 16.97% 47,213 21,969

Business 34.19% 9.65% 44,297 20,670

NaturalSciences

9.23% 35.75% 41,577 21,527

Social Sciences 15.24% 27.03% 41,389 20,199

Humanities 15.88% 19.84% 36,921 18,625

Architecture 2.16% 3.44% 32,702 28,830(5yr progr)

Pre Professional 7.62% 55.70% 30,232 20,699

WOMEN: N = 3418Engineers 5.38% 11.96% 47,530 22,074

Business 24.20% 8.95% 42,980 19,709

NaturalSciences

12.00% 32.19% 38,400 20,590

Social Sciences 24.02% 27.28% 38,572 19,750

Humanities 22.91% 21.58% 35,901 19,420

Architecture 2.19% 1.33% 33,793 29,420(5yr progr)

Pre Professional 8.66% 51.01% 35,213 18,358



99

TABLE 1A: MONKS REPLICATION:

Probit results of the impact of loan debt on graduate school attendanceSelective University Sample

DEP VAR:GRAD SCHPLANS

ESTIMATE STD.ERR

DEP VAR:GRAD SCH.PLANS

ESTIMATE STD.ERR

Intercept -3.3095 0.3877 Intercept -3.2951 0.3870Female -0.0807 0.0516 Female -0.0800 0.0515College GPA 0.6440** 0.0779 College GPA 0.6385** 0.0774Father’sEducation:Grad School

-0.0744 0.1058 Father’sEducation:Grad School

-0.0778 0.1057

Father’sEducation:College

-0.0991 0.0999 Father’sEducation:College

-0.0997 0.0997

Mother’sEducation: GradSchool

-0.1313 0.0918 Mother’sEducation: GradSchool

-0.1342 0.0916

Mother’sEducation:College

-0.0613 0.0819 Mother’sEducation:College

-0.0648 0.0818

SAT / 100 0.0547* 0.0257 SAT / 100 0.0556* 0.0257Black 0.3726* 0.1782 Black 0.3626* 0.1783

Asian -0.0050 0.1305 Asian -0.0025 0.1304Latino 0.1012 0.0993 Latino 0.1036 0.0992Multiracial 0.0703 0.1732 Multiracial 0.0611 0.1729Unknown Race -0.0032 0.3572 Unknown Race 0.0043 0.3571Drive to Achieve:Medium

0.1835 0.1426 Drive to Achieve:Medium

0.1839 0.1422

Drive to Achieve:High

0.3321* 0.1456 Drive to Achieve:High

0.3321* 0.1453

Parental Income:30K -50K

-0.2152 0.1222 Parental Income:30K -50K

-0.2075 0.1219

Parental Income:50K -100K

-0.1953 0.1092 Parental Income:50K -100K

-0.1980 0.1087

Parental Income:over 100K

-0.1902 0.1159 Parental Income:over 100K

-0.2038 0.1151

Engineer -0.1748 0.0922 Engineer -0.1730 0.0919Business -0.4771** 0.0757 Business -0.4727* 0.0755Social Sciences 0.1684* 0.0759 Social Sciences 0.1701 0.0757Natural Sciences 0.5092** 0.0884 Natural Sciences 0.5128** 0.0882



100

PreprofessionalStudies

1.0929** 0.0994 PreprofessionalStudies

1.0988** 0.0993

Architecture -1.0115** 0.2300 Architecture -1.0120** 0.2302Loans (2,000-4,999)

-0.2717* 0.1365 Log Loans -0.0107 0.0064

Loans (5,000-9.999)

-0.1429 0.1053 Graduated in 1999 0.0864 0.0890

Loans(10,000-14.999)

-0.1566 0.0865 Graduated in 2001 0.0882 0.0841

Loans(15,00019.999)

-0.0768 0.0831 Graduated in 2003 0.1986* 0.0798

Loans(20,000-24.999)

-0.0656 0.0890

Loans(25,000-29.999)

-0.0622 0.0934

Loans(30,000-49.999)

-0.0614 0.1491

Loans (50,000and above)

-0.2135 0.1604

Graduated in1999

0.0860 0.0891

Graduated in2001

0.0918 0.0843

Graduated in2003

0.1991 0.0803



101

TABLE 1 B:MONKS REPLICATION

Probit model for estimating the impact of loans on attending professional schoolSelective University Sample

DEPENDENT VAR: PLANS TOENROLL IN PROFESSIONALSCHOOL

ESTIMATE STANDARD ERROR

Intercept -3.7954 0.7934Female -0.0758 0.1477College GPA 0.2659 0.0922Father’s Education: Grad School 0.0875 0.1922Father’s Education: College -0.0254 0.1827Mother’s Education: Grad

School-0.1354 0.1639

Mother’s Education: College -0.1120 0.1454SAT / 100 0.2107** 0.0490Black 0.3272 0.3467Asian 0.4856* 0.2425Latino 0.4948** 0.1852Multiracial -0.0444 0.3159Unknown Race 0.4912 0.6450Drive to Achieve: Medium 0.0271 0.3084Drive to Achieve: High 0.3508 0.3119Parental Income: 30K -50K 0.0177** 0.2130Parental Income: 50K -100K 0.0594 0.1510

Parental Income: over 100K 0.1205 0.2099Engineer -1.3110** 0.2155Business -0.2147 0.1519Social Sciences 0.2170 0.1340Natural Sciences 0.1908 0.1425PreProfessional Studies 1.2943* 0.1566Architecture -6.3765 4679.194Loans (2,000 -4,999) -0.0567 0.2798Loans (5,000-9.999) -0.1438 0.1906Loans (10,000-14.999) -0.1871 0.1615Loans (15,000-19.999) -0.1299 0.1500Loans (20,000-24.999) -0.0882 0.1634Loans (25,000-29.999) 0.0663 0.1712Loans (30,000-49.999) 0.2154 0.2609Loans (50,000 and above) -0.5419 0.2925Graduated in 1999 -0.0328 0.1713Graduated in 2001 -0.2836 0.1603Graduated in 2003 -0.2776 0.1546



102

TABLE 1C:

MONKS REPLICATION:

Probit estimating the impact of loan debt upon the decision to change major

Selective University Sample Obs: (4713)DEPENDENT VAR:CHANGE IN COLLEGEMAJOR

ESTIMATE STANDARD ERROR

Intercept 1.0081 0.2799College GPA -0.4620** 0.0592Female 0.0747 0.0396Father’s Education:

Grad School-0.0684 0.0890

Father’s Education:

College

-0.0877 0.0855

Mother’s Education:Grad School

0.0498 0.0743

Mother’s Education:College

0.0803 0.0677

SAT / 100 0.0516 ** 0.0197Black 0.2682 0.1568Asian 0.0593 0.1005Latino 0.0100 0.0843Nonwhite 0.1070 0.1466Unknown Race -0.0491 0.2597Engineer -0.9984** 0.0759Business -0.1693** 0.0564Natural Sciences -0.0913 0.0723Social Sciences 0.1901** 0.0619PreProfessional Studies -0.8079** 0.0781Architecture 6.3018 2787.357Loans (2,000 -4,999) -0.0173 0.1185Loans (5,000-9.999) 0.0579 0.0894Loans (10,000-14.999) 0.0078 0.0703Loans (15,000-19.999) 0.0266 0.0636Loans (20,000-24.999) 0.0340 0.0720

Loans (25,000-29.999) -0.0167 0.0791Loans (30,000-49.999) 0.2196 0.1357

Loans (50,000 and above) 0.1878 0.1386Parental Income: 30K -

50K0.1948 0.1107



103

Parental Income: 50K -100K

0.1201 0.0995

Parental Income: over100K

0.1629 0.1032

Graduated in 1999 0.0242 0.0618

Graduated in 2001 -0.0295 0.0613Graduated in 2003 -0.0395 0.0614



105

ParentalIncome: 50K-100K

0.0037 0.1197 ParentalIncome: 50K -100K

-0.0790 0.1692

ParentalIncome:

over 100K

0.1656 0.1271 ParentalIncome: over

100K

0.0511 0.1778

Loans (2,000-4,999)

0.0610 0.1495 Loans (2,000 -4,999)

0.1218 0.2100

Loans(5,000-9.999)

0.2262* 0.1107 Loans (5,000-9.999)

0.2182 0.1530

Loans(10,000-14.999)

0.1143 0.0943 Loans (10,000-14.999)

0.1164 0.1312

Loans(15,000-19.999)

-0.0020 0.0937 Loans (15,000-19.999)

-0.0825 0.1278

Loans(20,000-24.999)

0.1337 0.0982 Loans (20,000-24.999)

0.1494 0.1381

Loans(25,000-29.999)

0.1594 0.1037 Loans (25,000-29.999)

0.3300* 0.1481

Loans(30,000-49.999)

0.1814 0.1654 Loans (30,000-49.999)

0.0658 0.2226

Loans(50,000 andabove)

0.1997 0.1651 Loans (50,000and above)

0.1178 0.2221

Graduatedin 1999

0.3042** 0.0959 Graduated in1999

0.4956** 0.1341

Graduatedin 2001

0.2009* 0.0922 Graduated in2001

0.2485* 0.1259

Graduatedin 2003

0.1112 0.0895 Graduated in2003

0.1297 0.1227

Log Loans 0.0128 0.0072



106

TABLE 2.AREPLICATION OF ST. JOHN:

OLS regression: Estimating the impact of loan debt on choosing a higher earnings major

Obs. (3270)R-Square 0.2240Adj R-Sq 0.2137

DEPENDANT VAR: RANKINGOF MAJORS (1-7)

ESTIMATE STD. ERROR

Intercept 3.80096 0.43628College Gpa -0.23531** 0.08577Female -0.33315** 0.05809Sat / 100 0.09322** 0.02864Father’s Education: Grad

School-0.20042 0.11774

Father’s Education: College -0.08247 0.11155Grad -0.79031** 0.06042Double Major -0.57105** 0.06091Mother’s Education: Grad

School-0.19998 0.10253

Mother’s Education: College -0.10498 0.09175Black 0.22168 0.20011Asian -0.06031 0.14318Latino 0.21820 0.11084Unknown Race 0.75926 0.43557Multiracial 0.12169 0.18684Varsity athlete 0.03740 0.06415Drive To Achieve: Medium 0.39257* 0.15784Drive To Achieve: High 0.34293* 0.16285Parental Income: 30k -50k 0.07291 0.13622Parental Income: 50k -100k 0.12517 0.12265Parental Income: Over 100K 0.10627 0.13058Loans (2,000-4,999) 0.21109 0.18523Loans (5,000-9,999) -0.15620 0.14592Loans (10,000-14,999) 0.43253* 0.11503Loans (15,000-19,999) 0.17969 0.09441

Loans (20,000-24,999) -0.01685 0.10178Loans (25,000-29,999) 0.20338 0.12264Loans (30,000-34,999) 0.04632 0.17754Loans (35,000-39,999) 0.04632 0.17754Loans (40,000-49,999) 0.05113 0.13059Loans (2,000-4,999)0 0.15237 0.11462Graduated In 1999 0.13628 0.09752



107

Graduated In 2001 0.12745 0.09266Graduated In 2003 0.24937** 0.08863Party 11 hours/ week 0.26247** 0.08301Party 3-10 hours/ week 0.13719* 0.06570Clubs 11 hours/ week 0.16040 0.11465Clubs 3-10 hours/ week 0.04352 0.06905Being Well off highly important 0.87480** 0.11246Being Well off somewhat

important0.48847** 0.08271

Math ability High 0.56260** 0.05854Writing ability High -0.36250** 0.06042Artistic ability High -1.14412** 0.11760Artistic ability Medium -0.42113** 0.05907

Log Loans

R-Square 0.2189Adj R-Sq 0.2107

0.01313 0.00728



108

TABLE 2BREPLICATION OF ST. JOHN:

OLS regression: Estimating the impact of loan debt on choosing a higher earnings major

R-Square 0.2697Adj R-Sq 0.2600DEPENDENT VAR: RANKINGOF MAJORS 1-14

ESTIMATE STD. ERROR

Intercept 4.31554 1.07179College GPA -0.54447** 0.21072Female -1.15595** 0.14271Sat / 100 0.28681** 0.07035Father’s Education: Grad School -0.56545 0.28926Father’s Education: College -0.26918 0.27405Graduate School Plans -1.96552** 0.14843Double Major -1.53073** 0.14963Mother’s Education: Grad

School-0.41327 0.25189

Mother’s Education: College -0.12938 0.22541Black 0.56814 0.49161Asian 0.00006158 0.35175Latino 0.70342** 0.27230Unknown Race 1.52908 1.07006Multiracial 0.55126 0.45900

Varsity athlete 0.18906 0.15761Drive To Achieve: Medium 1.20286** 0.38776Drive To Achieve: High 1.24173** 0.40007Parental Income: 30k -50k 0.13114 0.33464Parental Income: 50k -100k 0.30486 0.30131Parental Income: Over 100K 0.27595 0.32080Loans (2,000-4,999) 0.51879 0.45506Loans (5,000-9,999) -0.42003 0.35848Loans (10,000-14,999) 0.98056** 0.28259Loans (15,000-19,999) 0.49903* 0.23194Loans (20,000-24,999) 0.04273 0.25004Loans (25,000-29,999) 0.46669 0.30129Loans (30,000-34,999) 0.62190* 0.30902Loans (35,000-39,999) 0.03813 0.43616Loans (40,000-49,999) 0.14188 0.32082Loans (50,000 and up) 0.40052 0.28159Graduated in 1999 0.29572 0.23958Graduated in 2001 0.36659 0.22763



109

Graduated in 2003 0.50417* 0.21774Party 11 Hours/ Week 0.69944** 0.20394Party 3-10 Hours/ Week 0.41455* 0.16141Clubs 11 Hours/ Week 0.22114 0.28167Clubs 3-10 Hours/ Week 0.06292 0.16963Being Well off highly important 2.45204** 0.27629Being Well off somewhat

important1.42909** 0.20320

Math ability High 1.72403** 0.14381Writing ability High -1.14722** 0.14844Artistic ability High -2.94318** 0.28892Artistic ability Medium -1.08188** 0.14511

Substitution Log Loans For LoanDummies

Log Loans

R-Square 0.2653Adj R-Sq 0.2576

0.03469* 0.01789



110

Table 3A: Weiler Replication

Estimating the impact of log loan debt on graduate school attendance

Durbin-Wu-Hausman test: Testing the exogeneity of loan debt

1st stageNo. Obs = 2640R-squared = .2948

DEP VAR:LOG OF LOANS

ESTIMATE STD.ERROR

female -0.06881 0.138829SAT / 100 0.182128** 0.06456Black 0.700674 0.475069Asian 0.355823 0.367557Latino 0.993278** 0.27387Unknown Race -0.21952 1.024618Multiracial 1.071572* 0.465564Father’s Education: GradSchool

-0.04589 0.287243

Father’s Education: College 0.542643* 0.268598Mother’s Education: GradSchool

-0.15802 0.252851

Mother’s Education: College -0.33765 0.224476

Parental Income: 30K -50K -0.19812 0.323518Parental Income: 50K -100K -0.24438 0.293014Parental Income: over 100K -2.19328** 0.318177Graduated in 1999 1.675134** 0.242151Graduated in 2001 -0.11083 0.233296Graduated in 2003 -1.43723** 0.219318Has HAS FGSL 1.987134** 0.155551

_cons 4.526947 0.888368



111

TABLE 3B.WEILER REPLICATION

Estimating the impact of log loan debt on graduate school attendance

Durbin-Wu-Hausman test: Testing the exogeneity of loan debt

2nd stage

No. Obs = 2638Pseudo R2 = .1445

DEP VAR:GRAD SCHOOL PLANS

ESTIMATE STD. ERROR

COLLEGE GPA 0.735347 0.083836female -0.10467 0.056036

SAT / 100 0.022059 0.02886Black 0.240639 0.192009Asian -0.00342 0.146686Latino 0.142365 0.111231Unknown Race -0.06754 0.373759Multiracial 0.224625 0.18765Father’s Education: GradSchool

-0.15818 0.112275

Father’s Education: College -0.11834 0.104781Mother’s Education: GradSchool

-0.11683 0.098898

Mother’s Education:College

-0.08124 0.087862

Parental Income: 50K -100K

-0.06709 0.076903

Parental Income: over 100K -0.22016 0.116687Graduated in 1999 0.00854 0.106167Graduated in 2001 0.029335 0.091752Graduated in 2003 0.112003 0.091521Engineer -0.15998 0.099105Business -0.5060** 0.082904

Social Sciences 0.197393* 0.083547Natural Sciences 0.429425** 0.097166Architecture -0.92574** 0.22651Preprofessional Studies 1.259394** 0.112618Log of Loans -0.06233* 0.02607Loan Residuals 0.055757* 0.027322

_cons -2.41021 0.410821



112

TABLE 3C:WEILER REPLICATION:

Two Stage Probit IV: Estimating the impact of log loan debt on graduate schoolattendance

2 ND StageObs 3545 Wald chi2(24) = 414.88Prob > chi2 = 0.0000

Wald testof exogeneity Chi2 (1) = 4.18 Prob > chi2 = .0410

The null hypothesis that loan debt is exogenous can be rejected

DEP VAR: GRAD SCHOOLPLANS

ESTIMATE STD.ERROR

Log Loans* -0.0613* 0.025809College GPA 0.701218** 0.085383Female -0.09829 0.056496Sat / 100 0.026581 0.029771Black 1/5 0.234507 0.193515Asian -0.00642 0.148075Latino 0.137621 0.111714Unknown Race -0.06672 0.3771Multiracial 0.221568 0.189314Father’s Education: GradSchool

-0.15238 0.113253

Father’s Education: College -0.11511 0.105978Mother’s Education: Grad

School

-0.11996 0.100026

Mother’s Education: College -0.08179 0.088758Parental Income: 50k -100k -0.06476 0.077562Parental Income: Over 100K -0.2149 0.116055Graduated In 1999 0.008992 0.107243Graduated In 2001 0.030011 0.092643Graduated In 2003 0.113012 0.092214Engineer -0.13391 0.100266Business -0.49227** 0.083864Social Sciences 0.221775** 0.084774Natural Sciences 0.428035** 0.098259Architecture -0.85046** 0.228837PreProfessional Studies 1.251413** 0.113812

_Cons -2.38503 0.418382



113

TABLE 4A:CHOICE OF MAJOR AND LOAN DEBT: FIRST APPROXIMATION

OLS Results: Estimating the impact of a student’s choice of major on log loan debt

Baseline major: Humanities Number of obs = 3545R-squared = 0.3061Adj. R-square=0.2977


ESTIMATE STD.ERROR

Female -0.23951 0.13348Grad school plans -0.26621 0.141814Black 1.167971* 0.462729Asian 0.240029 0.331428Latino 1.049024** 0.254314Multiracial 0.733922 0.438544Unknown Race -0.59166 0.95848Engineer 0.533094* 0.267187High earning business majors 0.195567 0.216624Low earning business majors 0.354227 0.302296Social Sciences 0.102273 0.207714Natural Sciences 0.198805 0.25415PreProfessional Studies -0.02774 0.276134Architecture 1.04142* 0.436006

SAT / 100 0.186429** 0.062854Varsity athlete -0.19128 0.168537Father’s Education: Grad School -0.51415 0.269396Father’s Education: College 0.071526 0.254501Mother’s Education: Grad School -0.68133** 0.234436Mother’s Education: College -0.47977* 0.210795Drive to Achieve: High 0.1621 0.375761Drive to Achieve: Medium 0.047486 0.366065Parental Income: 50K -100K 0.765719** 0.164182Parental Income: over 100K -1.35257** 0.178858Graduated in 1999 1.634034** 0.221744Graduated in 2001 -0.05698 0.210804Graduated in 2003 -0.08189 0.344086Being Well off highly important -0.90338** 0.258933Being Well off somewhatimportant

-0.4428* 0.190023

Worked for pay 11hrs/week 1.641308** 0.163802Worked for pay: 3-10 hours / 1.2305** 0.147626



114

weekFather has professionaloccupation

-0.74681** 0.230174

HAS FGSL 1.767108** 0.130366Has several credit cards 1.605265** 0.312073

Catholic 0.316313* 0.157179Writing ability high 0.103568 0.320701Writing ability medium 0.466451 0.284604Math ability High -0.25572 0.264143Math ability High -0.02838 0.202533Artistic ability High 0.206299 0.280877Artistic ability Medium 0.065315 0.136393

_cons 2.365577 1.023251



115

TABLE 4B:CHOICE OF MAJOR AND LOAN DEBT: FIRST APPROXIMATION

OLS Results: Estimating the impact of a student’s choice of major on log loan debt

Baseline majors: All majors other than Engineering


ESTIMATE STD.ERROR

Female -0.25679 0.132144Graduate School Plans -0.33584* 0.132473Black 1.164073* 0.462134Asian 0.244038 0.33112Latino 1.042904** 0.254131

Multiracial 0.729212 0.43845Unknown Race -0.59754 0.958083High Earnings Major (Engineer) 0.362775 0.212842Sat / 100 0.17811** 0.062241Varsity Athlete -0.19707 0.168455Father’s Education: Grad School -0.53709* 0.268856Father’s Education: College 0.063284 0.254373Mother’s Education: Grad School -0.67269** 0.23406Mother’s Education: College -0.48646* 0.210568Drive To Achieve: High 0.208687 0.374626

Drive To Achieve: Medium 0.085111 0.365439Parental Income: 50k -100k 0.754038** 0.164071Parental Income: Over 100K -1.36737** 0.178572Graduated In 1999 1.621105** 0.221443Graduated In 2001 -0.04892 0.210508Graduated In 2003 -0.08998 0.343303Being Well Off Highly Important -0.8608** 0.252046Being Well Off SomewhatImportant

-0.41501** 0.187321

Worked For Pay 11hrs/Week 1.629238** 0.163181

Worked For Pay: 3-10 Hours PerWeek

1.224886** 0.147253

Father Has ProfessionalOccupation

-0.76157** 0.229982

Has FGSL 1.765193** 0.130248Has Several Credit Cards 1.578678** 0.311767Catholic 0.319159* 0.156936



116

Writing Ability High -0.00882 0.313811Writing Ability Medium 0.408444 0.283408Math Ability High -0.21307 0.253976Math Ability High 0.011776 0.197303Artistic Ability High 0.292008 0.268939Artistic Ability Medium 0.072422 0.1342585 th Year Graduate 0.471838 0.532068

_Cons 2.668051 1.009106



117

TABLE 5:Choice of Major and Loan Debt

Two Stage Least Squares: Estimating the impact of a student’s choice of major on logloans

with Durbin-Wu-Hausman exogeneity test: (Null: Choice of Major is Exogenous)


ESTIMATE STD.ERROR

High Earnings Major Choice* 0.712715* 0.429467Female -0.29707* 0.143904Grad -0.4263** 0.142172Black 0.964777* 0.519058Asian 0.18007 0.354188Latino 0.902722** 0.272586Multiracial 0.597105 0.466551Unknown Race -0.75685 1.000013Sat / 100 0.155001* 0.06909Varsity Athlete -0.18644 0.180032Father’s Education: Grad School -0.63473* 0.284629Father’s Education: College 0.10437 0.268246Mother’s Education: Grad School -0.58597* 0.248691Mother’s Education: College -0.41611 0.222641Drive To Achieve: High 0.392079 0.417978

Drive To Achieve: Medium 0.314514 0.405459Parental Income: 50k -100k 0.768499** 0.172594Parental Income: Over 100K -1.26166** 0.188861Graduated In 1999 1.503542** 0.236784Graduated In 2001 -0.17546 0.224982Graduated In 2003 -0.20538 0.373843Being Well Off Highly Important -0.69844** 0.271452Being Well Off SomewhatImportant

-0.3408 0.200734

Worked For Pay 11hrs/Week 1.539012** 0.17319Worked For Pay: 3-10 Hours /

Week

1.120036** 0.156681

Father Has ProfessionalOccupation

-0.76384** 0.24644

Has FGSL 1.74362** 0.1381Has Several Credit Cards 1.640512** 0.340022Catholic 0.313729 0.166894Writing Ability High 0.238026 0.345335



118

Writing Ability Medium 0.475658 0.306071Math Ability High -0.34481 0.2993Math Ability High -0.04158 0.212055Academic Ability Medium -1.09014 0.660583Academic Ability High -1.13421 0.67441Helping Others Highly Important 0.949686* 0.4610015 th Year Graduates 0.058143 0.164145Helping Others SomewhatImportant

0.914796 0.472624

Party 11 Hours/ Week -0.58078* 0.201726Party 3-10 Hours/ Week -0.31346* 0.157728

_cons 3.002653* 1.366015

Tests of endogeneity of: high earnings major choiceHo: Regressor is exogenousDurbin-Wu-Hausman chi-sq test: 0.45006 Chi-sq(1) P-value = 0.50231

Cannot reject the Null of exogeneity



120

Worked For Pay: 3-10 Hours PerWeek

0.034307 0.091717

Father Has Professional Occupation -0.09534 0.15848Has FGSL -0.08937 0.083935Has Several Credit Cards -0.23133 0.227076Catholic -0.0127 0.102556Writing Ability High -1.22105** 0.191921Writing Ability Medium -0.38574** 0.140427Math Ability High 1.921804** 0.320525Math Ability High 1.086049** 0.30994Artistic Ability High -0.42087* 0.2083Artistic Ability Medium -0.00215 0.085232Academic Ability Medium -0.42818 0.38177Helping Others Highly Important -0.13816 0.231282

Helping Others in SomewhatImportant

0.075818 0.235056

Party 11 Hours/ Week -0.4421* 0.129861Party 3-10 Hours/ Week -0.00456 0.093031Academic Ability High -0.45475 0.389575Freshman Major is Engineer 1.66056** 0.082009Double Major -1.56548** 0.204351

_Cons -4.4132 0.792879



121

TABLE 6 B:CHOICE OF MAJOR AND LOAN DEBT: TWO STAGE PROBIT LEAST SQUARES

Estimating the impact of the choice of a high earnings major (engineering) on loans

Second Stage OLS results:

with instrument (*) and corrected standard errors


ESTIMATE STD.ERROR

Instrument for the choice of a highearnings major*

0.140969* 0.065436

Female -0.2359 0.138335

Grad -0.32827* 0.13511Black 1.024991* 0.465086Asian 0.208722 0.331177Latino 0.944675** 0.25574Multiracial 0.674296 0.438452Unknown Race -0.59181 0.960057Sat / 100 0.142821* 0.066028Varsity Athlete -0.18261 0.168617Father’s Education: Grad School -0.48984* 0.269132Father’s Education: College 0.128819 0.255157Mother’s Education: Grad School -0.65774** 0.23412Mother’s Education: College -0.48883* 0.210658Drive To Achieve: High 0.090343 0.377771Drive To Achieve: Medium -0.01665 0.367538Parental Income: 50k -100k 0.75545** 0.164256Parental Income: Over 100K -1.29866** 0.179548Graduated In 1999 1.597018** 0.221667Graduated In 2001 -0.01553 0.211803Graduated In 2003 -0.05449 0.345022Being Well Off Highly Important -0.73522** 0.255849Being Well Off Somewhat Important -0.39075** 0.190523

Worked For Pay 11hrs/Week 1.679261** 0.165387Worked For Pay: 3-10 Hours / Week 1.229246** 0.147374Father Has Professional Occupation -0.74424** 0.230427Has FGSL 1.771085** 0.130344Has Several Credit Cards 1.608836** 0.312651Catholic 0.319107* 0.157586Writing Ability High 0.152333 0.336062



122

Writing Ability Medium 0.442156 0.286945Math Ability High -0.50452 0.306972Math Ability High -0.17213 0.218889Artistic Ability High 0.274973 0.270998Artistic Ability Medium 0.035867 0.134679Academic Ability Medium -0.07111 0.147404Helping Others very Important 0.960914* 0.442739Helping Others somewhat Important 0.952965* 0.453213Party 11 Hours/ Week -0.49046* 0.192654Party 3-10 Hours/ Week -0.29951* 0.1491165 th Year Graduate 0.294502 0.310483

_Cons 2.915122 1.14624



3.7 Appendix 3:

TABLE 1:

SECOND MAJORS AND EARNINGS: SELECTIVE UNIVERSITY

OLS earnings regression: Estimating the impact second majors on log earnings

Observations: 1013 553 460R-Squared: 0.3045 0.3163 0.355Sample: Full Sample Men WomenDEP. VAR:

Log earningsESTIMATE STD.

ERRESTIMATE STD.

ERR ESTIMATE STD.

ERR

Sat / 100 0.010526 0.0089 0.0269826* 0.0130 -0.00799 0.0128

Female -0.00979 0.0175Black 0.065761 0.0703 0.0632492 0.1059 0.121849 0.0957Asian 0.11814** 0.0424 0.0813796 0.0667 0.1618311** 0.0565Latino 0.05899 0.0398 0.0865975 0.0592 0.011741 0.0548Unknown Race -0.27282** 0.1123 -.379051** 0.1322 0.165702 0.2580Multiracial 0.102919 0.0851 .094268 .08576 0.127187 0.0874Engineer 0.315165** 0.0401 0.2816976** 0.0611 0.388684** 0.0574High EarningsBusiness Major

0.213208** 0.0341 .2016237 ** 0.0562 0.2407143** 0.0465

Low EarningsBusiness Major

0.073548 0.0409 0.1185221 0.0718 0.04521 0.0507

NaturalSciences

0.112698** 0.0452 0.1485652* 0.0748 0.111698* 0.0586

Social Sciences 0.08782* 0.0380 0.1691139 * 0.0658 0.020044 0.0480Architecture -0.0429 0.0524 -0.100735 0.0879 0.003301 0.0674PreProfessionalStudies

-0.18701* 0.0807 -0.2126754* 0.1046 -0.08675 0.1418

Father’sEducation:Grad School

0.07561 0.0398 0.0418978 0.0525 0.107985 0.0647

Father’s

Education:College

0.068386 0.0382 0.0378438 0.0506 0.095612 0.0622

Mother’sEducation:Grad School

-0.02331 0.0316 -0.0051143 0.0435 -0.05208 0.0470


-0.03647 0.0290 -0.0354316 0.0396 -0.03804 0.0431

123



Drive ToAchieve: High

0.132769 0.0967 0.1466106 0.1138 -0.00302 0.2373

Drive ToAchieve:Medium

0.071376 0.0962 0.0468647 0.1132 -0.03349 0.2358

ParentalIncome: 50k -100k

0.025867 0.0235 0.0544013 0.0342 0.009613 0.0324

ParentalIncome: Over100K

0.025835 0.0234 0.0453248 0.0353 0.001712 0.0317

Graduated In1999

0.083121** 0.0232 0.0727867* 0.0334 0.1210564** 0.0327

Graduated In2001

0.154184** 0.0243 0.1643106** 0.0354 0.1604022** 0.0343

Graduated In2003

0.078271** 0.0233 0.0602118 0.0334 0.1496579** 0.0333

Father Is AProfessional

0.00657 0.0265 0.0295735 0.0372 -0.01396 0.0381

AcademicAbility High

-0.11996 0.1080 -0.133958 0.1245 0.074655 0.3003

AcademicAbility Medium

-0.16031 0.1067 -0.1668744 0.1224 0.015383 0.2999

Math AbilityHigh

-0.01352 0.0369 -0.0168518 0.0555 -0.00797 0.0518

Math AbilityMedium

0.006434 0.0310 0.0113146 0.0496 0.032414 0.0402

Writing AbilityHigh

-0.02859 0.0379 -0.0103427 0.0520 -0.02379 0.0603

Writing AbilityMedium

-0.00984 0.0321 -0.0152354 0.0451 0.029908 0.0501

Party 11Hours/Week

0.035263 0.0249 -0.0009769 0.0367 .0859686** 0.0278

Artistic AbilityHigh

-0.01717 0.0395 -0.0066764 0.0511 -0.02193 0.0651

Party 3-10Hours/ Week

0.021079 0.0213 0.0089901 0.0320 0.036121 0.0296

Double Major 0.0360090.0200 0.0022149 0.0290

.0859686 **0.0279

Female*DoubleMajor

.0638185* 0.0276

College GPA 0.039197 0.0277 0.0379307 0.0385 0.040499 0.0417Catholic 0.056493** 0.0215 0.0284122 0.0311 .0940555** 0.0303High SchoolGPA(A)

0.022119 0.0193 0.0243718 0.0275 .0082743 0.0278

124



Study 11Hours/Week

-0.12084** 0.0509 -0.138075* 0.0620 0.029631 0.1119

Study 3-10Hours/Week

-0.12869** 0.0511 -0.1392717* 0.0625 .0142317 .03037

Being Well Off

HighlyImportant

0.140282** 0.0377 0.1834507** 0.0528 0.04185 0.0576

Being Well OffSomewhatImportant

0.105765** 0.0321 0.139653** 0.0465 0.02404 0.0462

Work CloselyRelated ToMajor

0.060047** 0.0200 0.0933143** 0.0284 .0141093 0.0294

_Cons 9.997501 0.157512 9.824364 0.2134 9.999237 .28743

125



Graduated In1999

0.118421 0.0242 0.1294301** 0.0351 0.091266** 0.0330

Graduated In2001

0.261104 0.0250 0.2752559** 0.0359 0.216032** 0.0347

Graduated In

2003

0.134633 0.0242 0.1457118** 0.0346 0.106649** 0.0362

Father Is AProfessional

-0.00994 0.0274 0.012788 0.0389 -0.05096 0.0342

Academic AbilityHigh

0.113995 0.1269 0.192299 0.1583 -0.12325 0.0388

Academic AbilityMedium

0.071676 0.1258 0.164275 0.1568 -0.19338 0.2616

Math AbilityHigh

-0.05849 0.0418 -0.10107 0.0607 -0.04789 0.2607

Math AbilityMedium

-0.02461 0.0360 -0.08328 0.0544 0.00099 0.0613

Writing AbilityHigh

-0.0271 0.0393 -0.05764 0.0521 0.044418 0.0483

Writing AbilityMedium

0.005936 0.0334 -0.02911 0.0467 0.071061 0.0662

Party 11Hours/Week

0.037448 0.0279 0.068341 0.0432 0.008681 0.0487

Artistic AbilityHigh

0.13816 0.0468 0.102191 0.0568 0.2179585* 0.0386

Party 3-10Hours/ Week

0.018815 0.0256 0.06261 0.0412 -0.02682 0.0964

Double Major 0.052653 0.0188 0.030943 0.0264 0.061694 0.0332College GPA 0.040281 0.0292 0.050315 0.0392 0.013018 0.0278Catholic -0.00221 0.0238 -0.02317 0.0334 0.035183 0.0457High School GPA(A)

-0.01232 0.0206 0.010502 0.0287 -0.03546 0.0346

Study 11Hours/Week

-0.05528 0.0535 -0.02003 0.0605 0.078437 0.0299

Study 3-10Hours/Week

-0.06381 0.0531 -0.047 0.0592 0.08746 0.1958

Being Well OffHighly Important

0.015326 0.0595 0.056352 0.0884 -0.01931 0.1966

Being Well OffSomewhatImportant

0.012481 0.0568 0.053283 0.0858 -0.01128 0.0898

Work CloselyRelated To Major

0.08653 0.0553 0.058612 0.0324 -0.01331 0.0850

_Cons 9.935025 0.1784 9.842021 .228314 10.27238 0.3379

127



128

TABLE 3A:SECOND MAJORS AND EARNINGS: SELECTIVE UNIVERSITY

Heckman Procedure for sample selection into labor marketEstimating the impact of second majors on log earnings

Censored Obs 41622nd Stage Uncensored Obs 1013Obs 5175

DEP VAR:LOG

EARNINGS

ESTIMATE STD.ERROR

ESTIMATE STD.ERROR

Sat / 100 0.009749 0.0088 Graduated

In 19990.0849467** 0.0228

Female -0.010593 0.0172 GraduatedIn 2001

0.1581227** 0.0240

Black 0.0639923 0.0689 GraduatedIn 2003

0.0782258** 0.0228

Asian 0.1164025** 0.0416 Father Is AProfessional

0.0076877 0.0260

Latino 0.0610624 0.0390 AcademicAbility High

-0.109246 0.1059

Unknown Race -0.26143* 0.1102 AcademicAbilityMedium

-0.150163 0.1046

Multiracial 0.1030749 0.0833 MathAbility High

-0.013088 0.0361

Engineer 0.3096871** 0.0395 MathAbilityMedium

0.0079662 0.0304

High EarningsBusiness Major

0.2093238** 0.0336 WritingAbility High

-0.025639 0.0372

Low EarningsBusiness Major

0.069689 0.0401 WritingAbilityMedium

-0.006816 0.0316

NaturalSciences

0.1099744** 0.0442 Party 11Hours/Week

0.0337308 0.0244

Social Sciences 0.0864755* 0.0372 ArtisticAbility High

-0.011773 0.0389

Architecture -0.047383 0.0514 Party 3-10Hours/Week

0.0195053 0.0209

PreProfessionalStudies

-0.177535** 0.0791 DoubleMajor

0.0355955 0.0196



129


0.0758558* 0.0390 CollegeGPA

0.0358322 0.0273

Father’s

Education:College

0.0695532 0.0374

Female*

DoubleMajor

.0692613 .03659


-0.023386 0.0310 Catholic 0.0564466** 0.0211


-0.036333 0.0284 High SchoolGPA (A)

0.0208387 0.0190

Drive ToAchieve: High

0.1200668 0.0951 Study 11Hours/Week

-0.119831** 0.0499

Drive To

Achieve:Medium

0.0616468 0.0944 Study 3-10

Hours/Week

-0.127645** 0.0500

ParentalIncome: 50k -100k

0.0241581 0.0231 Being WellOff HighlyImportant

0.1368227** 0.0370

ParentalIncome: Over100K

0.0232303 0.0230 Being WellOffSomewhatImportant

0.1015959** 0.0315

_Cons 10.07679 0.1649 WorkCloselyRelated ToMajor

0.0137518 0.0395

SEPARATEMALE &

MALES: DoubleMajor

-.0069323 .0280998

FEMALEREGRESSIONS

FEMALES: DoubleMajor

.0843825** .0266341



130

TABLE 3B:SECOND MAJORS AND EARNINGS: SELECTIVE UNIVERSITY

Heckman Procedure for sample selection into labor market

Estimating the impact of second majors on log earnings

Business College Only

DEP VAR:LOG EARNINGS

ESTIMATE STD. ERROR

FULL SAMPLE: Double Major .0459689* .0180954MALES: Double Major .0317302 0.025004FEMALES: Double Major .0711934* .0277767



131

TABLE 4:SECOND MAJORS AND EARNINGS: COLLEGE AND BEYOND 1976 COHORT

OLS Regression: Estimating the impact of second major on log earnings

(No ability controls)

Number of Obs 12195R-Square 0.2975

DEP VAR:LOG

EARNINGS

ESTIMATE STD.ERROR

ESTIMATE STD.ERROR

Intercept 10.19352** 0.11405 Private High

School0.03208* 0.01644

SAT average ofuniversity

0.05742 * 0.01100 Catholic HighSchool

0.04987** 0.01696

SAT /100 -0.02553** 0.0072 Women’sCollege

0.05934* 0.02925

Female -0.28144** 0.01202 PrivateUniversity

0.08837** 0.01708

Black -0.04228 0.02646 Liberal ArtsCollege

-0.00657 0.02328

Hispanic 0.04495 0.04696 ObtainedAdvancedDegree

0.06008** 0.01220

Asian 0.11269** 0.03765 ClergyOccupation

-0.51408** 0.05020

Other 0.15044 0.0880 ClericalOccupation

-0.42410** 0.04519

Unknown Race -0.03736* 0.01585 ComputerOccupation

0.02057 0.02785

Top 10% ofH.S. class

0.01057 0.01478 EngineerOccupation

-0.04419 0.02675

Varsity Athlete 0.09279** 0.01895 ExecutiveOccupation

0.26122** 0.01607

Engineer 0.20068** 0.02047 FinanceOccupation

0.40369** 0.02576

NaturalSciences

0.15886** 0.02192 DoctorOccupation

0.60300** 0.02306

Social Sciences 0.14287** 0.01595 HealthOccupation

-0.04993 0.03339

Business 0.20279** 0.02001 InsuranceOccupation

0.15611** 0.05156



132

Other Majors 0.06694** 0.01684 Law Occupation 0.33587** 0.02093Double Major 0.04473* 0.02105 Consulting

Occupation0.32055** 0.04874

Mother’sEducation:

Grad School

0.02606 0.01502 MarketingOccupation

0.13317** 0.02500


0.07295** 0.01607 MilitaryOccupationOccupation

-0.10924 0.10146


0.05076** 0.019 Math & ScienceOccupation

-0.17412** 0.03470


0.02081 0.01557 Social ScienceOccupation

-0.22711** 0.04141

Job SatisfactionHigh

0.15509** 0.01047 Writer ArtistAthleteOccupation

-0.12271** 0.03039

College GPA 0.33930** 0.02168 OtherOccupation

-0.23936** 0.03224

Results for separate wage regressions for males and females are not shown here butresults from these regressions include the finding that similar to what was observed forthe single selective university, female engineering and business majors have a muchhigher earnings advantage over female humanities majors than male engineering and

business majors have over male humanities majors. The same result was found forfemale natural science majors. Unlike results found for the single university, doublemajoring for men was correlated with having 5% higher earnings over non-doublemajors. Female double majors in the College and Beyond sample received no earnings

premium.



133

TABLE 4:SECOND MAJORS AND EARNINGS: COLLEGE AND BEYOND 1976 COHORT

OLS Regression: Estimating the impact of second major on log earnings

(With ability controls: Selection on observable and unobservable characteristics)

Number of Observations 6224Missing Values 2304R-Square 0.3469

Dependant:Log Earnings

ESTIMATE STD.ERROR

ESTIMATE STD.ERROR

Intercept 10.33672** 0.12646 InsuranceOccupation

0.13884** 0.05163

Sat Average Of

University

0.04375** 0.01184 Law Occupation 0.30689** 0.02117

Sat /100 -0.02416** 0.00503 ConsultingOccupation

0.28517** 0.04872

Female -0.25840** 0.01256 MarketingOccupation

0.12108** 0.02502

Black -0.05244** 0.02701 MilitaryOccupation

-0.22638 0.14447

Hispanic -0.06603 0.04747 Math & ScienceOccupation

-0.16923** 0.03475

Asian 0.11405** 0.03821 Social ScienceOccupation

-0.21679* 0.04146

Other Race 0.13881 0.08813 Writer ArtistAthleteOccupation

-0.11083** 0.03042

Unknown Race -0.03570 0.01631 OtherOccupation

-0.24112** 0.03221

Top 10% OfH.S. Class

0.15044 0.02199 Job SatisfactionHigh

0.14569** 0.01448

Varsity Athlete 0.08164** 0.01930 ObtainedAdvanced Degree

0.05989** 0.01223

Engineer 0.19427** 0.02147 College GPA 0.35164** 0.02209NaturalSciences

0.15349** 0.02246 Writing AbilityHigh

-0.02834 0.01490

Social Sciences 0.11729** 0.01617 Math AbilityHigh

-0.00157 0.02328

Business 0.20113** 0.02908 Academic AbilityHigh

-0.03668* 0.02063

Other Majors 0.06506** 0.02042 Athletic AbilityHigh

0.03669* 0.01448



134

Double Major 0.03859* 0.02104 Artistic AbilityHigh

-0.02634 0.01572


0.01717 0.01505 Highly cheerful -0.04498* 0.02207


0.05963** 0.01614 Highly Driven 0.02818 0.01761


0.04660** 0.01901 High LeadershipAbility

0.02762 0.01614


0.01684 0.01558 HighlyMechanical

-0.01106 0.02286

Private HighSchool

0.03627* 0.01669 Highly Attractive 0.07267** 0.02449

Catholic HighSchool

0.04414** 0.02462 Highly Popular 0.02428 0.02751

Women’sCollege

0.06899* 0.03136 Speaking AbilityHigh

-0.01394 0.0226

PrivateUniversity

0.08521** 0.02789 Highly Confidentin Intellect

-0.04081 0.0252

Liberal ArtsCollege

-0.0227 0.0367 Highly Sensitive -0.00949 0.0215

ClergyOccupation

-0.52298** 0.05022 Highly Stubborn 0.02301 0.01376

ClericalOccupation

-0.42776** 0.04522 Highly SociallyConfident

0.03615* 0.01676

ComputerOccupation

0.00574 0.03829 HighlyUnderstanding

-0.03903 0.01536

EngineerOccupation

-0.04854 0.03822 Highly Popularwith OppositeSex

0.05633 0.01942

ExecutiveOccupation

0.25682** 0.01613

FinanceOccupation

0.39230** 0.02581 DummyGroups(196)

DoctorOccupation

0.59279** 0.02313

HealthOccupation

-0.07048 0.04768



136

At the individual level, the goal of the economic agent is to maximize one’s self-

interest, and therefore individuals will make choices that will maximize their own self

interest, pushing them to consume more subject to constraints. Holding preferences

constant, economic theory assumes that if an individual is able to consume more, they are

better off. Income then becomes a determinant of an individual’s well being or

happiness.

For better or worse, at the national aggregate level, national income is often used

as an indicator of happiness or well being. However, as national income increases, many

economists would argue that a nation’s well being will not necessarily increase, as thereare many costs associated with economic activity and progress. Only if the “winners”,

those who benefit from these economic activities can compensate the “losers”, those who

bear the costs of economic progress, could national income be used to proxy for well

being. This compensation test, can the “losers” be compensated by “winners”?—and

this does not necessarily mean that they will be—is often used to allow national income

proxy for national well being. 1

Both at the individual and at the national level, income or earnings changes are

assumed to change our levels of happiness and satisfaction. There are many that might

say that income is a relatively unimportant factor in determining our happiness or

satisfaction. In a search for a combined science that attempts to discern what actually

does makes people happy, so that more can be done to make our society better off,

economist Richard Layard relays this observation; “economics equates changes in the

happiness of society with changes in its purchasing power—or roughly so. I have never

accepted that view, and the history of the last fifty years has disproved it, on average

1 Layard, 134



137

people are no happier today than people were 50 years ago. Yet at the same time average

incomes have more than doubled.” 2

So why might changes in absolute income or earnings be ineffectual in

determining happiness? According to Layard, increases in an individual’s absolute

income may only raise that individual’s reference group of comparison. In other words

when an individual gets more income, the “Joneses” they want to keep up with also

become wealthier. Also, decreases in absolute income can at times be associated with

increases in happiness if at the same time our relative income status improves. For

Layard, an individual’s relative income, or their perceived relative income instead ofabsolute income is a more relevant determinant of happiness. So, if our absolute

income—or purchasing power—does not add to the overall happiness of individuals or

society, then what things actually do increase our overall satisfaction with life? Other

variables which Layard says might influence happiness more than income include family,

work, community and friendships, health, personal freedoms and values.

This paper does not attempt to answer the question of how much changes in

income effects overall happiness, but instead will use data from the College and Beyond

to determine if there is empirical evidence of a relationship between increased earnings

and overall satisfaction with life among a group of college graduates who we assume are

strongly influenced in their college choices by expected earnings. An ordered probit is

estimated that attempts to explain the effect that higher earnings has on an ordered scale

that measures “overall satisfaction with life” for the sample of students in the College and

Beyond 1976 cohort. The results are shown in Table 6 of this Appendix.

2 Layard, 3



139

affect people’s happiness more than absolute earnings. He sites a study which analyzes

the income-happiness issue more deeply and finds that an individual’s perceived relative

income has a stronger effect on individual happiness than absolute income. 3 In other

words, people are happier when their incomes are higher relative to people in their

comparison group—“the Joneses”. The results provided here cannot untangle whether an

individuals increased satisfaction is driven strictly by increases in absolute income or

perceived relative income, but they do seem to support some basic economic

assumptions, that increases in earnings are correlated with an increased measure of

happiness. The significant correlation between happiness and family, friends, work,health and even obtaining an advanced degree also demonstrate the complexity of

variables beyond just earnings that determine individual happiness.

What is important, however, and what motivated this postlude was the pursuit to

find evidence that might indicate that increased levels of earnings are correlated with

increases in levels of individual happiness. This correlation which did appear in this data

seems to corroborate the conclusion that students are acting rationally when they make

decisions based upon expected returns because their later realized earnings will in fact be

influential to their happiness after college.

3 Layard , 46



REFERENCES : ESSAY 1

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142



Rivkin, Steven G. 1995 “Black White Differences in Schooling and Employment” The

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143



REFERENCES: ESSAY 2

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King, Tracey and Ellynne Bannon 2002 “The Burden of Borrowing: A Report on theRising Rates of Student Debt” The State PIRG’s Higher Education Project ,Washington D.C.

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Maddala, G.S., 1983 Limited Dependant and Qualitative Variables in EconometricsCambridge, Cambridge University Press

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144



St. John, Edward P. 1994 “The Influence of Debt on Choice of Major” Journal of Student Financial Aid Vol.24 No. 1

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145



REFERENCES: ESSAY 3

Arciadiano, Peter 2003 “Ability Sorting and The Return to College Major” Duke Economics Working papers.

Betts, Julian 1996 “What do Students Know About Wages? Evidence from a Survey ofUndergraduates” Journal of Human Resources Vol. 31 No: 1 27-56

Brewer, Dominic; Eide, Eric; and Ehrenberg, Donald 1999, “Does it Pay to Attend andElite Private University: Cross-Cohort Evidence on the Effect of College Type onEarnings” Journal of Human Resources Vol. 34, Issue 1, pp104-123

Card, David, 2001 “Estimating the Return to Schooling: Progress on Some PersistentEconometric Problems” Econometrica 69 pp 1127-1160

Dale, Stacy Berg. and Krueger, Alan B. 1999 “Estimating the Payoff to Attending a more

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Slater, Robert B. 1996, “The College-Course Majors Offerings Blacks the BestFinancial Rewards” Journal of Blacks in Higher Education No. 12, 84-87

146



Strayer, Wayne, 2002, “The Returns to School Quality: College Choice andEarnings” Journal of Labor Economics , Vol 20: No. 3

Weinberger, Caherine, 1998, “Race and Gender Gaps in the Market for Recent CollegeGraduates” Industrial Relations , Vol. 37 No. 1

essay on the determinants and implications of the choice of undergraduate major

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