WASHINGTON UNIVERSITY Department of Economics
Dissertation Examination Committee: Marcus Berliant, Chair Gaetano Antinolfi Steven Fazzari Barton Hamilton Gary Miller Chuck Moul
CHOICE IN HIGHER EDUCATION:
COLLEGE MAJORS FINANCIAL AID, AND TRANSITION TO THE LABOR MARKET
by
David Matthew Lang
A dissertation presented to the
Graduate School of Arts and Sciences
of Washington University in partial fulfillment of the requirements for the degree
of Doctor of Philosophy
May 2002 Saint Louis, Missouri
Trang 2UMI Number: 3065064
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Trang 3Copyright by David Matthew Lang
Trang 4Acknowledgments
I just want to thank everyone who made this day necessary - Yogi Berra
It is simply not possible to complete a doctoral program, and a dissertation in
particular, without some support and assistance [ want to take this opportunity to
acknowledge those individuals that helped me along the road to dissertation completion
I must begin by thanking my Dissertation Committee Chairperson, Marcus Berliant I am deeply indebted to Marcus for helping me take a good thought and turn it into a publishable paper I know that I have entered into an elite family of Marcus disciples and will do all I can to make my Uncle proud
I would like to thank Chuck Moul for all of his expertise and time Without him, I
would not yet be finished { look forward to our continued work together I thank
Bart Hamilton for his creativity and honest opinions regarding my work and maintaining an open door between the Economics Department and his office in the Business School [ also wish to thank Steve Fazzari for helping start graduate school off on the right foot and for his work as Department Chair
I am grateful for the financial support I received from Washington University as well as supplemental income from teaching positions at the University of Missouri,
St Louis and St Louis Community College Thank you all for letting me learn how
to be a teacher with your students and in your classrooms
For all of their technical and administrative assistance I thank Karen Rensing,
Trang 5Outside of Washington University Í thank the Department of Economics at Stanford University for providing an unparalleled undergraduate education I want to thank Ron Ehrenberg, Donna Ginther, Michael McPherson, and Morton Schapiro for all of their comments and criticism of my research [I thank the National Center for Education Statistics and the National Science Foundation for the use of their data and for their technical expertise
On a more personal note, I thank David Switzer for his friendship, athletic prowess, and ring-buying assistance during our years in St Louis [ wish to thank Stephanie Babinski and Beth Robertson for their frequent lunchtime companionship and keeping me entertained And [ also thank Kyra Haigh for Friday night dinners, clutch flag football receptions and keeping me on my toes [ am grateful to Dan Giedeman and Dino Falaschetti for their job market advice
These 6 years would have been a complete torture if it were not for the presence and friendship of Shawn Humphrey and James Marton This job market year, in particular, was made enjoyable because we were able to go through the process together I am very excited to make the transition with Shawn and James from fellow graduate students to colleagues
I thank my in-laws, Ralph and Hedy Grimaldi for their encouragement and for letting me take their daughter across the country to live in a tiny apartment with no
money I appreciate your faith in me [ thank my father, Lou Lang for his support,
financial and otherwise, throughout my academic endeavors I am indebted to my
grandparents and soothsayers Moodge and Pops, for calling me ‘Doctor David Lang’ 27 years, 10 Months, and 27 days before it was appropriate to do so I thank
my sisters, Shayna and Chelsea for reminding me that whether my students call me “Doctor” or “Professor,” I will always be “Davey” to them I thank Adam Lang and Mindy Tager for being my constant cheering section Through ups and downs, I can hear you both all the way across the country and love you for it
Trang 6I thank my mother and step-father, Linda and Gary Thompson for their support and understanding My mother taught me how to learn, how to argue, how to ask good
questions, how to find the right answers, and how to throw a baseball [t would take a
second dissertation to thank her adequately
Finally, my wife Brie, has had to put up with me during graduate classes, the creation of this dissertation, and the job market I thank her for continuing to love me in spite of it all, for coming to St Louis, and for talking me out of a tree whenever she needs to She is my one true love and my favorite economist
David Matthew Lang
St Louis, Missouri
Trang 7Dedication
O CAPTAIN! my Captain! our fearful trip is done, The ship has weather d every rack, the prize we sought is won
- Walt Whitman
This dissertation is dedicated in memory of Lee Palles who taught me
that time and tide wait for no man that a rolling stone gathers no moss
Trang 8Table of Contents Acknowledgements - -Q Tnhh he ii Dedication -.- On HH HH ni nh nàn V Abstract of the Dissertation -. - Sàn nseheeehe Vili P0 _.m:í, Ta eằeẮee Xx P.8) e2 xi
Chapter l: Introduction -.-. . Sàn nnenhneeeeee l
Trang 9khie 4 hon eee ee rece teense cessreceeeeensseeceeenenees
3.6 Appendix - - Sàn HH nh nh nh nh ni nà nh nhi ng 80
Chapter 4: Empirical Approaches to College Chọce - - - - 83
4.1 Introduction - . . - Ăn nh nh nh nh minh ni tim Hư 83
Trang 10ABSTRACT OF THE DISSERTATION Choice in Higher Education:
College Majors, Financial Aid, and Transition
to the Labor Market
by
David Matthew Lang
Doctor of Philosophy in Economics Washington University in St Louis 2002
Professor Marcus Berliant, Chairperson
This dissertation consists of 3 essays that investigate many of the decisions
that individuals make concerning their investment in higher education The first chapter considers the return to majors after controlling for occupation In addition, the effect of having ‘alignment’ between college major and job type on annual
earnings is examined By examining this alignment premium, we can address whether a college major is human capital or a signal by considering the relationship between work and acquired skills This chapter considers whether a college major, as
a heterogeneous input, is a Signal, General Human Cuapital or Specific Human
Capital The main implications of the theory are: 1 Job type and alignment do not affect the return to college majors that are General Human Capital: 2 Job type and alignment do affect the return to college majors that are Specific Human Capital; and 3 The return to college major would decline with additional experience if the college major serves as a signal The empirical evidence provides support for college majors
Trang 11as General, and in some cases Specific Human Capital but little support for the Signaling hypothesis
The second chapter explores the financial aid process A theoretical model is developed using a first-price sealed auction model This model is then evaluated using empirical evidence from the 1996 National Postsecondary Student Aid Study In particular, it is shown that the increase in total aid resulting from a student getting accepted at a second, third, fourth, and fifth school is approximately $548, $456, $363, and $270 respectively after controlling for ability, demographics, and
institutional characteristics
The third chapter examines the demand for higher education institutions This chapter contributes to the recent empirical literature on discrete choice models of
demand estimation in markets with heterogeneous consumers Some of the more
important studies concerning the demand for higher education are discussed and a direction for future research is suggested that allows for a more sophisticated and
complete analysis of this decision process The results of this estimation demonstrate
the trade-off students and their families make between the cost, location, and reputation of the colleges and universities
Trang 12tN 2.2 3.3 3.4 3.5 3.6 3A.1 3A.2 4.1 4.2 4.3 4.4 List of Tables
Means and Standard Deviations for Selected Vartables 25 Selected Regression Results: 1993 Annual Salary (Ln) of Bachelor's
Degree Reciplents - - cà nen nhe nen 28 Selected 1993 Annual Salary Regression Results for Men and Women, by
2 e e 3l
Selected 1993 Annual Salary Regression Results with [nteraction
¡-.: — 32
College-Occupational Flow 'Table -. Sàn shàneeeeeee 37
Standard Occupational Classification (SOC) and College Majors 40 Weighted Means and Standard Deviations for Selected Variables - NPSAS -dL:|AƠ .Ì.ỂỒƠƠƠ 64 Comparing Means between Private and Public Schools and their ki PP ences 66 Selected Regressions of 1995-1996 Financial Aid for Freshmen, 4-year Í[nstitutiOnS - cọ HH nh nh th nh mm ch 72
Regressions of 1995-1996 Financial Aid - Public vs Private Institutions
Private ÍnstitutÏOns -. - Ăn nàn nh nh hư, 74 Regressions of ¡995-996 Financial Aid with Tuition - - 75 Regressions of 1995-1996 Financial Aid - Competitiveness of 2n
Choice - - TQ HH HH màn nh nh tu mm ng 77
Most Important Reason for Selecting the College Attended — all
undergraduat€s - cà nh nh nh vn 8l
Selected Partial Correlation Coefficients - -. - - cà 82 Selected Descriptive Statistics by College ¡in the Sample 95
Selected Multinomial Logit (MNL) Estimates of College Choice 97 Summary of Selected Coefficients -. - sàn sàn 99
Trang 133.1
3.2 3.3
List of Figures
Type of Aid by Acceptances (All StudentS) - - se
Type of Aid by Acceptances (Public OnÌy) -. -Ÿàsằằằ eens
Type of Aid by Acceptances (Private ƠnÌy) . + sàehheeese
Trang 14Chapter 1: Introduction
Choice in higher education is essentially a series of decisions that an individual must make First an individual must choose whether to go to college or enter the labor force If the individual chooses to attend college, then she must determine the schools to which application should be made Next once accepted at
various schools, which one should be attended? Once in attendance the individual
must choose a major field of study Then, she must decide whether to go to graduate school or to enter the labor force These decisions taken together have a profound effect on future labor market outcomes This dissertation investigates three of these decisions in detail: which college major to select, how many applications to complete,
and which college to attend
Chapter 2: College Majors, Job Types and the Labor Market
This chapter analyzes why workers who complete one college major receive higher earnings than workers who complete another major do In order to address
this question, I consider three possible explanations The first is that college majors
provide the worker with General Human Capital (GHC) GHC would allow a worker to take the skills that they acquired in college to any job type and use those skills with
equal effectiveness The second explanation is that the college major is a form of Specific Human Capital (SHC) With SHC, a worker can only use the skills that she learns through the college major in certain occupations For example, an accounting major develops a set of skills that can only be used effectively if that individual
Trang 15potential employers of the individual worker’s potential productivity in various job types A theoretical model is developed which garners testable implications College majors are then analyzed using the 1993 National Survey of College Graduates
(NSCG) in order to categorize each major as predominantly GHC SHC or a signal Of course in actuality college majors are almost certainly a combination of these 3 effects The analysis also allows us to consider the salary effect of having alignment
between one’s college major and job type
Chapter 3: Financial Aid and Student Bargaining Power
This chapter considers whether students have the ability to act strategically in
order to increase their financial aid awards Further, it addresses whether students are currently engaging in this optimal strategy In order to explore this from a theoretical perspective, this chapter relies on the auction literature where students are
heterogeneous and colleges “bid” for the students that they wish to have matriculate The main implication of this model is that as a student gets accepted into more
institutions, her financial aid package should increase, holding student ability
constant This chapter uses the 1995-1995 National Postsecondary Student Aid Study
(NPSAS) that has detailed data concerning the financial aid that a student is awarded
as well as various demographic information, student test scores and the number of institutions to which a student is accepted for admission This information allows us to consider whether students are currently applying to the appropriate number of
Trang 16Chapter 4: Approaches for Modeling College Choice
This chapter reviews the various techniques that have been used in order to
model college choice in the literature and discusses the application of current
Industrial Organization (IO) approaches to the market for higher education While
extensive research has attempted to uncover the variables that determine a student's
choice of college, there has been surprisingly little unification of theory with data In
addition to this fault in the literature, no one has attempted to apply the [O literature
to this market In addition to reviewing this literature this chapter uses a simple Multinomial Logit (MNL) model to find some of the key variables in this decision
process I also suggest the implementation of a hedonic approach in order to more
Trang 17Chapter 2: College Majors, Job Types, and the Labor Market
2.1 Introduction
This chapter will consider the issue of choice of college major and the transition to the labor market We examine the relationship between college major
and occupation as well as the relevance of this relationship to earnings An underlying
question is whether college majors are General Human Capital accumulation that will transfer between occupations, job-Specific Human Capital or merely a signal of
worker productivity For example consider an individual who majored in accounting
and is deciding between a career as either an accountant or as an economist A
proponent of majors as job-specific training might expect that the accounting major would fair better as an accountant than an economist in terms of wages and job
tenure A proponent of majors as general human capital investment would give this individual equal likelihood of labor market success in both professions Furthermore,
a proponent of majors as a signal would claim that an individual completing an accounting major has signaled a level of productivity to potential employers
irrespective of any skills acquired during college In this study a unified framework
is presented and these theories are tested against each other
In order to analyze our data, college majors will be grouped into nineteen
categories Occupations will also be grouped into these same categories I will
utilize regression analysis to attempt to explain wage variations as a function of
college major, occupation, various demographic variables, and a variable indicating
Trang 18individuals whose college major category and occupation category ¡s the same and zero otherwise Ít is expected that this alignment variable will have a relatively small but significant impact on an individual’s wage rate In addition, these results will
help determine to what degree choosing a college major determines choice in
Trang 192.2 Literature Review
The previous literature in this area can be divided into two sections The first section consists of research involving college majors specifically Arcidiacono
(1998), Berger (1988), Daymont and Andrisani (1984), and Grogger and Eide (1995)
have completed recent work in this area Arcidiacono (1998) addresses this issue by forming a dynamic model of college and college major choice In his model, people sort into colleges and college majors by ability in order to maximize earnings As
individuals receive new information about their own ability, they can switch both colleges and majors to ensure that they continue to maximize earnings In
Arcidiacono’s empirical model he examines annual earnings as a function of
demographic information, a measure of college quality a measure of student ability
and four college major categories
Berger (1988) also examines college major choice but uses a static model Berger finds that individuals are more likely to choose majors that have a greater
stream of lifetime earnings However, he assumes that all majors are available to ail students He does not consider that some college majors may not be feasible to a student due to ability constraints Berger also estimates an annual earnings function controlling for five different college major categories
Trang 20helping others, being a leader, and/or working with people are very important, somewhat important, or not important when choosing an occupation They do not, however, control for the actual job choice of the individuals
Grogger and Eide (1995) use the change in the college major distribution over time to try to account for the rise in the college wage premium They use six college major categories as well as a few measures of ability both during and prior to
college They also add occupational controls to their analysis in order to make sure
that the college major is not merely being used as a proxy variable for future
occupation They conclude, “different college majors provide students with different skills, independent of the occupation that the student enters after graduation.”'
Neuman and Ziderman (1990) consider the labor market outcomes of people who had previously attended vocational schooling in Israel In their regressions on
earnings, they consider the sector of occupation eight dummy variables for subjects
of study, as well as a dummy variable for individuals who hold an occupation
“matched” to their subject of study They find that those workers who were directly matched to their subject of study had 9.6% higher monthly earnings than their
unmatched counterparts
The other literature critical to this discussion involves the Human Capital vs
Signaling Debate Michael Spence is the first to develop a comprehensive theory of
job market signaling Spence presents a model where there is an information
asymmetry since employers do not know the productive capabilities of potential employees at the time of hiring (Spence, 1973) This ditfers from the Human Capital
Trang 21
model where knowledge of the employee’s productive ability determines the hiring practices and wage rates utilized by firms.”
As early as 1974, economists were already attempting to expand and provide
empirical evidence for the signaling theory Layard and Psacharopoulos (1974)
develop a list of testable implications of this model including the prediction that
private returns to education should fall with experience Altonji and Pierret (1996) as well as Farber and Gibbons (1996) advance the signaling model by developing a dynamic model of learning in a competitive labor market Farber and Gibbons
predict, and empirically find a negative interaction between education and experience
in a log-wage regression Altonji and Pierret build on this learning model by considering how the speed of learning affects the value of an educational signal
They find that the slower an employer learns about the productivity of an employee, the more important the signaling value Belman and Heywood (1997) develop a
model of learning and signaling with the presence of job matching and still find that
the returns to educational signals will fall with additional work experience There have also been several papers that have attempted to empirically test the Signaling hypothesis, however there remains no consensus.” My study adds to this literature by
first developing a simple theoretical model of the labor market with General Human Capital, Specific Human Capital, and signaling, and then testing the implications of the theory with a very detailed data set
” For an excellent discussion of the differences and similarities between Human Capital Theory and
Signaling Theory as well as their predictions, see Weiss, 1995
Trang 222.3 Theoretical Models
Jacob Mincer developed the following ‘human capital earnings function’ (Mincer, 1974)
Iny= Øụ + ổ,s+ ổ,x+ x ` +£
In Mincer’s model, earnings (In y) are determined by experience (x) experience- squared, and years of schooling (s) This model has been used extensively over the years in many related forms to predict the return to schooling A contentious assumption in this model is that the schooling is completely homogeneous This implies, among other things, that all bachelors’ degrees requiring the same number of
years to complete should receive the same return to the individual Using this model an Engineering major is expected to get the same return as an English major as long as each degree has the same time requirement This model also omits variables concerning the application of the human capital obtained through schooling, suggesting that it does not matter what one does with her skills as long as she is
employed somewhere Furthermore, there is no interaction between experience and
the return to schooling in the human capital model [t is these assumptions that the following theory will address
Two models are presented The first model is a human capital model In this model the firms and the workers have complete information about each other There
Trang 23both general and speciftc human capital are considered The second model considers
college majors as signals In the signaling model, there is asymmetric information since the firms do not know the workers’ productivities Further, the college major merely serves as a signal of this productivity to the firm and has no productivity- enhancing quality
The Human Capital Model:
Consider an individual worker i who has a pre-collegiate productivity of ¢
units per year of production A worker type is therefore just the worker's pre-
collegiate productivity level
re (0,1)
The worker will choose a college major, m, and after completion of her schooling,
will join the labor force in a job type, j College majors and job types are arranged in order of increasing return to the worker Thus a worker with m=/ will be paid more than a worker of m=.5, ceteris paribus
me [0,1]
je [0,1]
Worker i’s utility function is increasing in salary s, and decreasing in major, m Higher paying majors require more effort on the part of the worker Let mm and ¡; be
Trang 24u,(S,m.t, J) =S,, my
f
The costs of higher ranked majors can be viewed as the time element and psychological costs of studying and learning to the worker as well as the opportunity
cost of studying Therefore in addition to majors being ranked in order of future return to the major, they are also being ranked in order of increasing difficulty
Further, note that with this functional form, the cost to obtain any particular college
major is lower for higher worker types and this is true for all majors This is not a
model of comparative advantage
Firms are risk-neutral and produce a numeraire good with pricel using
Constant Returns to Scale (CRS) technology Labor is supplied to the firms inelastically The profit function, /7, for a firm of type j is as follows:
IT, = XV, 2, — Sn,
V,, =f, + Bm, + D*(m,, j,)}m,
where , ¥ and A are constants, D(m,, j;) is a measure of the inverse distance between the major and the job type, n, is the number of workers of type i, j, is the job type of
worker i, and V;; is the post-collegiate productivity of the worker Profit is the sum of all post-collegiate productivities of the individual workers minus the sum of their
salaries Productivity is decomposed into three parts The first part is the pre-
collegiate productivity of the worker [#], the second part is the General Human Capital part [Am], and the third part is the Specific Human Capital part [D(mi, ji) ymi)
Trang 25related her education and occupation are), the larger the Specific Human Capital
component becomes
Firms will maximize profits by choosing n, for all i Equilibrium is reached when the salary of each worker equals the worker’s productivity Sy =V, s, =f, + Bm, + D*(m,, j, )n, The inverse distance function will be defined as follows”: Dựn,, j,) =\—|Lj, — m, | Inserting the equilibrium salary function into the worker`s utility function we obtain the following: ' "AM
It should be noted here that the distance function that is being used in this
model divides our worker optimization problem into 3 possible situations If j<m., then the worker is overeducated in the sense that she is obtaining a higher major than
is necessary to perform her job If j>m then she is undereducated If j=m, then we say that the worker is ‘aligned’ between college major and job type Another way of thinking about this is that the worker is just educated enough to successfully perform her job We will consider these three situations one at atime In all cases, workers
* This function is maximized where job type and college major are equal Ít also has the property that
Trang 26will choose a college major to maximize their utility Workers can perfectly predict
their salary sj for any choice of major and job Without loss of generality, I will
consider the cases where A = 1 For simplicity I will drop the subscripts Situation A: (Overeducated) Vi<m + m- u=t+ fm+yn— ym + jyn-— t du 2m Tm Oty 2mm t iy-—— = 0 Im t ft +Ƒy+jy) m (j<m')= 2+2 du 2 —~=-2y —<0 din” ữ f
This second order condition is always met since y is nonncgatIive and 7 is positive Therefore, m*(j < m*) is the major that will yield the highest utility for the worker
assuming the worker is overeducated The salary and indirect utility for Situation A
are located in the Appendix
Trang 27Situation B: (Undereducated) Vi>m + u =t+ Đn+ 1m + EmẺ — j#{m—T— t du 2m —— = B+y+2yn— jy-—— 0 dm t mj>m))=—~SE*t=jn 2—2 d*u 2 ——=2y-—<0 dm ự t
To insure that the second order condition holds, a restriction needs to be placed on 7
Specifically, 4 < / With this restriction in place m*(j > m*) is the optimal major for those undereducated The salary and indirect utility function are also in the Appendix Situation C: (Aligned) Vj =m u=t+ fmt yn— du 2m —=B+y-—=0 dm Bry t t + m'(j=m')= Bi y) dm- t
Since t>0, this second order condition always holds Again, the salary and indirect
Trang 28Of course, which of the 3 situations the worker is in is not exogenously
determined but rather is chosen by the worker The worker will choose the situation that results in the highest indirect utility function When > 0, 820 y20, and j > 0, and the additional restriction that emerged from the second order conditions (7 < /), it can be shown that
u(j = m*) > u(j > m*), and also that u(j = m*) > u(j < m*) Therefore the worker will choose to be aligned when these parameter restrictions are maintained As long as there is some General Human Capital component (8 > 0) and some Specific Human Capital component (7> 0) workers will be aligned The comparative statics are: dm _Btr.y dt 2 dm dm _' vo dB dy 2 ds (t7 dt 2 xọ ds’ ds — =— ="(Ppt apd (B+y)> 0
If a worker's pre-collegiate productivity increases, the worker will obtain a higher
major and will receive a higher salary once employed In addition, if the contribution of the major to general or specific productivity increases, then again the worker will obtain a higher major and receive a higher salary
There are 2 special cases to consider Note that so far we have assumed that
there is both a General and Specific Human Capital component of the major What happens when there is either only General Human Capital or only Specific Human Capital? In other words, we need to consider the cases where either B=O0or y=0 If
Trang 29a college major is General Human Capital only (y = 0) then the distance function no longer plays a role here since it is weighted by ¥ The utility function is now:
u =1+ fn-
f
The results here are identical to those in the general case presented before simply inserting zero for ¥ The difference is that job type does not matter in this case With no specific human capital the worker does not have to choose from among the three situations discussed previously The results here say nothing about whether or not a worker will become aligned because regardless, she will choose the major and salary suggested above On the other hand, if the college major is specific
human capital only (8 = 0), then the distance function remains in the salary function
+
tí =+(~|(J~m|)jym~“—
In summary common to all of the possible human capital models suggested
above is the prediction that if pre-collegiate productivity and/or contribution of the major to productivity increases, the optimal major and the equilibrium salary will also increase for the worker In addition, job type and, therefore alignment only matter when there is at least some portion of the college major that is Specific Human Capital If the major is solely General Human Capital then there is no reason to
expect workers to align their majors to their jobs
Trang 30The Signaling Model:
In the signaling model presented here, the firm does not know workers’ productivities and the college major serves merely as a signal of this productivity
The college major has no productivity-enhancing quality This is a departure from
the existing educational signaling literature Throughout much of the literature the
education attainment increases the worker's productivity in addition to providing information to the firms The problem with this approach is that it entangles the
human capital and signaling hypotheses such that it is no longer possible to discern
the partial effects from either individual hypothesis
Consider a 3-period signaling game with learning In the first period,
individuals choose college majors to maximize the utility function with expected
future salary In the second period, firms hire employees not knowing their actual
productivity but receive the college major as a signal and pay a salary based on expected productivity In the third period firms learn the true productivity of the employees and pay them accordingly The notation remains consistent here with the previously presented human capital models For simplicity and convenience, the worker types in the signaling model will be discrete rather than continuous Worker
type, f, is still the pre-collegiate level of productivity However, since the college
major is not productivity-enhancing, ¢ is also the post-collegiate level of productivity
me {0,1,2, N} Je {0,1,2, N}
Trang 31College majors, m, and job types, j, also remain ranked in order of increasing return
to the worker
Notice that there are N worker types but N+ /majors as well as job types S,2
and S,; are worker i’s salary in period 2 and period 3 respectively and 6 is the common time discount factor for all workers Worker i's utility function’ is:
+
tt, =#¿(0+8”$,L)~——
ổc [0.1]
Firms are risk-neutral and produce a numeraire good with price | with a Decreasing Returns to Scale (DRS) technology The firms make employment decisions and write new contracts in each period In the second period, firm / has the following profit function:
Il, = ¥ Fim), - YS
where F(m)® yields the productivity of a worker for a given major m and ny is the number of workers employed by the firm completing major m The profit for each firm is the total productivity of the workers minus the sum of their salaries The firms want to observe a separating equilibrium where workers of type ¢ = & choose a
college major m = k so that they can properly assign wages to maximize profits Each employee has a Reservation salary, R, that is the minimum they will
* Since this utility is quasi-linear, we need not be concerned about profit-sharing issues here
* F is a concave function
Trang 32accept to work Due to the information asymmetry, firms will set the salary of the workers with m=0 equal to R
S,.(0=R
—>u, = R-2 = RR
Without loss of generality the discount rate dis set equal to I
There are incentive constraints required to insure obtaining a separating equilibrium.’ Consider t = / We need to make sure that workers of type ¢ = / have no incentive to choose major m = 0 In other words in equilibrium workers should not choose a lower major Therefore, we must make sure that their utility from choosing m = / is at least as high as from choosing m = 0
I 5,,(1) TT 2R
Likewise, we want to make sure that type ¢ = 0 workers have no incentive to
choose major m = | However, this incentive constraint is not binding Therefore to obtain a separating equilibrium:
R+1s5S,()
From the firm’s optimization problem, it seems clear that the firm would choose the lowest possible salary in this range
S,()=R+1
—tt, =R+I~T=R
7A pooling (or partial pooling) equilibrium would be another possibility in signaling models but it is not realistic that all workers would choose the same major and would receive the same salary
Trang 33Similarly, there are incentive constraints regarding the salary of those with college major m = 2 To insure that no f = 2 workers choose m = /
and to insure that no type ¢ = / workers choose major m = 2 3 R >§2@)~T— Again, to obtain a separating equilibrium: ww 52 2 £5,,(2)SR+— 2 With the firm choosing the lowest salary in this range S,(2)=R+2 + —u,=R+2-——=R - Following this same logic for all majors and worker types a salary schedule is obtained M S,.(m)=R+—— f Since the equilibrium is separating, m = ¢ for all worker types Therefore, S, (m)ì= R+m, = R+t,
In the third period, firms have complete information about cạch worker”s
productivity Therefore, for firms to maximize the profit function below, the
Trang 341, = Din, -¥S,,n,
S, (0) = t,
To develop the testable implications of the signaling model we need to
examine the differences between the salary in the second and third periods Define A; as the difference between second period salary and third period salary
A, =S, -S,,
A,=(R+t,)—t,=R
A prediction of the signaling theory is that salary will fall as firms learn the
employee’s true productivity, provided that workers have some positive reservation
wage Furthermore, the decrease in salary will be equal to their reservation wage, which should also be equal to the starting salary of those with the lowest college majors Notice that there is no productivity gain between the second and third period here Therefore, testing the prediction empirically would require controlling for the
return to experience and looking for a decrease in the return to the major rather than a
decrease in the salary In this model, the labor market moves from the asymmetric
information of the second period to the perfect information of the third period
suddenly and completely In reality, this learning process certainly happens more gradually over significant time Altonji and Pierret (1996) examine this concept of
Trang 352.4 The Data
The data utilized in this study is selected from the 1993 National Survey of
College Graduates (NSCG), which is a National Science Foundation (NSF) survey of
215,000 individuals with a bachelor’s degree or higher at the time of the 1990 census
The survey includes demographic variables taken from the 1990 Decennial Census including occupation, age, race income and other variables The survey itself
contains detailed job-related questions as well as college-experience questions
This study includes all individuals from this survey satisfying the following
criteria: | No missing values for any of the variables being used: 2 Between the ages
of 25 and 60 in 1993; 3 Employed with a positive income: 4 Obtained a bachelor’s degree and no higher degree These 52,402 individuals were then analyzed in depth
There were 143 college major categories that the individuals had to choose from as
well as 125 job categories Both the college majors and the job categories were collapsed into 19 common categories.* An alignment variable was also created that
indicates whether or not there is a match between job type and college major This alignment variable is an extreme version of the distance function from the human
capital models previously presented This is the case where 2 is infinite (ie 2 > 0)
Here the distance function is either 0 or | rather than some value between 0 and 1
The reason for using this binary definition of alignment is to avoid the awkward
comparisons of semi-aligned major-occupation pairs For example consider comparing the relative alignments of two individuals who obtain engineering jobs It
Trang 36
seems clear that the worker who completed an engineering major should be
considered more aligned than the worker who completed a major in education
Likewise, a worker who completed an engineering major should be considered more aligned than a worker who completed a drama major However should a worker who
completed an education major be considered more aligned than a worker who completes a major in drama?
Table 2.1 shows the mean’ and standard deviation for the variables considered Note first that the individuals in this survey are predominantly white and
male In addition, there is a relatively large proportion of individuals in architecture
and engineering jobs (.166) and majors (.207) This is not meant to be representative
of the general population The original intent of the survey was to look at the college
and job experiences of individuals in the engineering and science fields In addition,
note that there are four job categories for which there are no college major category matches (Food Preparation and Serving Related, Personal Care and Service Office
and Administrative Support, and Trade) For these categories, there are no majors that fit the job descriptions of the Standard Occupational Classification system
Since the concept of alignment is being considered and analyzed it is of some interest
to look at the flow between college major and occupation A summary table of the
major-occupational flow is presented in the Appendix Table 2A.1 In this table, we find that while there is significant alignment between college majors and job types there is also a wide range of college major- job type flows For example, 66.5% of
” With the exception of Salary93, Lnearn93, Age93 and Experience the variables shown in the table
are all indicator variables where the variable is set equal to | when an individual meets the
requirements of the variable and is set equal to 0 otherwise Therefore, the mean for these variables
can be viewed as the proportion of the individuals that meet the requirement in question
Trang 37workers completing Architecture and Engineering majors find themselves in
Architecture and Engineering jobs But what do the remainder of these workers do?
It turns out that 11.3% have jobs in Management, 8.4% choose Computer and
Trang 38Means and Standard Deviations for Selected Variables Table 2.1 Variable Mean Standard Vanable Mean Standard Deviauon Deviation Salary93 43995 59 23I81.78 Female 358 479 Lasalary93 10.57 4842 Hispanic 046 210 Age93 40.143 8.508 Black 088 283 Experience 15.728 8.367 Nonwhite 219 414 East 208 406 Mamcd 720 +49 Midwest 213 409 Divorce 104 306 South 323 467 Never marned 176 381 West 257 437 Kids? 569 495
Management Job 125 331 Management Major 097 295 Business and Financial Job 16 320 Business and Financial Major 094 292 Computer and Math Job H2 315 Computer and Math Major 069 254 Architecture and Engineering Job 166 372 Architecture and Engineering 207 405
Mayor
Life and Physical Science Job 035 183 Life and Physical Scrence Mayor 086 280
Social Science Job 003 057 Social Science Major 126 332
Community and Social Service 033 180 Community and Social Service 021 142 Jub Mayor
Legal Job ool 038 Legal Major 002 047
Education and Library Job 083 274 Educauvion and Library Mayor 099 298 Arts Sports Media Etc Job 023 150 Arts, Sports, Media, Etc Mayor 097 396 Health Job O58 235 Health Mayor M8 214
Protective Service Job oll 106 Protective Services Mayor 010 100
Fuod and Related Job 004 060 Personal case and Service Job 014 117
Sales Job I03 303 Sales Major 029 167 Support Job O44 204
Trang 392.5 Results
Table 2.2 shows six regressions of annual earnings Spccifications [, II, and
V include demographic variables and majors only Specifications {I [V, and VI
include controls for job categories in addition to the demographic and college major
variables In specification I the Business and Financial Operations, Computer and Math, Architecture and Engineering, and Health major coefficients are all statistically significant and positive For example, the Architecture and Engineering Major has a
coefficient of 156 indicating a 15.6% premium for these majors compared to the
return of the omitted “Other Major” category In addition the Social Science Community and Social Service Education and Library Arts/Sports/Media/Etc Protective Services, and Farming/Fishing/Forestry major coefficients are all statistically significant and negative There is some variation in the value of various majors for men and women Women, for example receive a much higher premium from majoring in Computer and Math than their male counterparts (.199 compared
to 154) Also of interest to us is the coefficient of the Alignment Variable In
specification I, we find a coefficient of 051, indicating that there is about a 5% alignment premium If we look at how this differs for men and women, we find that
Women receive a much higher alignment premium (.103) then do Men (.013).'!
If we turn our attention to Specification I, we can see if this analysis changes
greatly when we add the controls for job types to the regressions By adding these
variables, we lose significance on some of the coetticients Architecture and Engineering remains the only significant positive coefficient All of the previously
!! In fact, the alignment premium in this regression is not significant tor men at the 5% significance
Trang 40significant negative coefficients remain significant but their magnitude varies significantly in some cases The coefficient on Alignment remains significantly
positive in this specification as well An additional trend to point out is that if we compare Specifications [ and II we see that for each of the significant coefficients in [ the new coefficient in II has become closer to zero and in some cases loses significance all together By adding the job type controls we are separating out two
separate effects on earnings: one from the skills obtained while in college, and the
other from where these skills are being utilized Including either majors or job types but not both assumes either that there are homogenous skills being developed across