Salary discrimination at the University of Colorado at Denver

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Salary discrimination at the University of Colorado at Denver
Ranney, Robert John
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Universities and colleges -- Faculty -- Salaries, etc ( fast )
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Includes bibliographical references.
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Arts, Department of Economics.
Statement of Responsibility:
by Robert John Ranney.

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University of Colorado Denver
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Full Text
Robert John Ranney
B.A., Metropolitan State College, 1983
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for. the degree of
Master of Arts
Department of Economics

This thesis for the Master of Arts degree by
Robert John Ranney
has been approved for the
Department of
John Morris

Ranney, Robert John (M.A., Economics)
Salary Discrimination at the University
of Colorado at Denver
Thesis directed by Associate Professor Naci Mocan
Utilizing data from professional vitae on
faculty publications and University personnel records on
salary information, two methodologies were used (forward
and reverse regression) to conduct an empirical test to
detect salary discrimination by race and gender. No
significant gender discrimination was observed, while a
mild indication of salary discrimination against non-
white faculty was noted. Promotion is the strongest
element in faculty salary determination at this
University while the marginal impact of publications
proves to have little effect on salaries.
The form and content of this abstract are approved,
recommend its publication.
Naci Mocan

I. INTRODUCTION................................1
Training and Experience...................5
Human Capital, Productivity
and Discrimination.....................10
III. ANALYTICAL FRAMEWORK.......................18
V. EMPIRICAL RESULTS..........................28
VI. TWO NOTIONS OF FAIRNESS....................37
Notes. . ..............................44
VII. CONCLUSIONS............................... 45

1. Ratio of Women's to Men's Hourly Earnings in
Manufacturing, 1950 1987......................... 2
2. Black/White Income Ratio........................... 11
3. Salaries of White and Minority Men................. 12
4. Means and Standard Deviations of the Variables.. 27
5. Estimated Salary Equations (SALARY)............... 29
6. Estimated Salary Equations (LOGSAL)............... 30
7. Estimated Salary Equations Reduced Form
(SALARY).......................................... 35
8. Estimated Salary Equations Reduced Form
(LOGSAL).......................................... 36
9. Reverse Regression Equations Structural Form
(SALARY).......................................... 42
10. Reverse Regression Equations Structural Form
(LOGSAL).......................................... 42
11. Reverse Regression Equations Reduced Form
(SALARY)........................................ 43
12. Reverse Regression Equations Reduced Form
(LOGSAL).......................................... 43

Many economic studies investigate salary
differences by race and gender, across various
industries, occupations and time periods. These studies
show the existence of striking income disparities
between minorities and whites and between men and women.
In the American economy, non-Hispanic white males earn
substantially higher wages than blacks. In 1955 the
wages of a typical male, year-round black worker were 61
percent of his white counterpart; in 1987, 71 percent.1
While this ratio has increased over time, a significant
disparity still exists. Salary differences also exist
between whites and other minorities. Hispanics earn
incomes averaging 74 percent of non-Hispanic white
males' in 1976.2 Similarly, the ratio of female to male
earnings was only 0.60.3 One study found women's
earnings were less than 60 percent of men's throughout
the 1960's and 1970's.4
Table 1 reports large discrepancies in earnings
between females and males exist internationally.
However, studies of salary differentials between any two
groups tell us very little if they do not control for

human capital. Human capital is a major determinant of
productivity. Productivity determines earnings.
Ratio of in TABLE Women's to Men Manufacturing, 1 's Hourly Earnings 1950 1987
Countrv 1950 1978 1987
Australia .66 .80 .80
Belgium .60 .70 .74
Denmark .64* .86 .84
Finland .65 .75 .77
France n.a. .77 .79
Germany (F.R.) .64 .73 .73
Greece .65** .69 .78
Ireland .58 .64 .67
Luxembourg .55+ .60 .61
Netherlands .61 .76 .79+++
New Zealand .63* .73 .72
Norway . 66 .80 .84
Sweden .70 .89 .90
Switzerland .65 .66 .67
UK .60 .69 .68
U.S.A. n.a. .61 .71++
Source: Francine Blau, Marianne Ferber, "Women's Work,
Women's Lives: A Comparative Economic Perspective", NBER
Working Paper. (Sept., 1990), no.3442, Page 16.
*1953, **1961, +1966, ++1983, +++1986
In this thesis I will overview human capital
theory and establish a theoretical framework for
determining if salary discrimination exists at the
College of Liberal Arts and Sciences at the University
of Colorado at Denver. Forward and reverse regression
techniques will be utilized in the empirical analysis.

1U.S. Bureau of Census, Money Income of
Households. Families, and Persons in the United States.
Consumer Income Series, P-60, no. 151, Table 28,(1984).
2U.S. Bureau of Census, Money Income in 1976 of
Families and Persons in the United States. Consumer
Income Series, P-60, no. 114, (July, 1978).
3Victor Fuchs, "Differences in Hourly Earnings
between Men and Women," Monthly Labor Review (May,
1971), Pages 9-15.
4U.S. Bureau of Census, Money Income of
Households. Families, and Persons in the United States.
Consumer Income Series, P-60, no. 151, Table 38,(1984).

The marginal productivity theory of factor
demand tells us that the greater the productivity of a
factor such as labor, the greater will be the demand for
it. Employers compete for workers by paying a wage equal
to a worker's marginal value to the firm. Workers, for
their part, compete against their peers in the labor
market and make choices of which employer to work for
and what occupation to pursue. Workers embody a set of
skills that may be "rented out" to employers.1 The
knowledge and skills of a worker constitutes a stock of
productive capital, which is termed human capital.
Labor's human capital, hence productivity, can be
enhanced by vocational training, formal education, on-
the-job experience, improved health care and any other
form of investment in human capital.2 This investment,
as in any other investment, involves both monetary and
non-monetary costs. Enhanced productivity increases
one's potential for higher earnings.
At the onset of one's career; human capital
increases through training (both formal and informal),
education, vocational training and experience. All of
these contribute to a rising earnings profile with

respect to age. At higher ages, however, the rate of
increase decreases because it becomes more difficult and
less feasible to increase the human capital at the same
rate. Earnings may even decline in later years of life
as the depreciation of human capital exceeds new
investment yielding a net decrease of human capital.
More highly educated and skilled individuals
generally earn more than others. An analysis of age-
earnings profiles reveals that the earnings profile of
college graduates lies above that of high-school
graduates which, in turn, is above that of elementary
school graduates. This pattern continues to hold for
post-college graduates and for any age level. In short,
the earnings profiles shift up as the level of education
rises, demonstrating the positive marginal return to
increases in human capital through additional years of
schooling. In 1985, the ratio of median incomes of
college graduates to high school graduates was 1.36 for
males and 1.40 for females.3
Training and Experience
On-the-job training and formal schooling are the
two most commonly sought after forms of investment in
human capital. On-the-job training consists of two
types: general and specific.
General training is that which is of value to a
number of firms. While on-the-job training should

increase the future marginal productivity of a worker
for the firms providing it, general training increases
it for other firms as well.4 Because general training
heightens the visibility of an individual from a human
capital perspective to a greater audience, the incentive
for the firm providing the training is decreased. A
firm which increases the attractiveness of an employee
to rival firms may well lose its investment if that
employee changes firms. Therefore, general training
requires the individual, rather than the firm, to bear
the cost associated to the training.
Persons receiving general training frequently
earn lower wages as a result of the firm trying to
reduce costs. Apprentice programs are an example. The
apprentice receives training at a reduced wage which
allows the employer to better absorb the costs of
training and non-productive time. The reduced wage a
commitment cost or opportunity cost associated with
training. As training proceeds, the employer raises the
wage to prevent the worker from being hired away by
another firm. The more attractive a worker's skills
become to employers, the greater mobility that worker
has in the job market. Therefore general training may
increase job instability by increasing employee
Specific training on the other hand, does not
increase mobility in the job market. Specific training

is of value to that firm alone. The classic example is
the military. Learning to operate a Patriot missile is
of great value to our country during war but of little
value in the private market. The skill set utilized by
the military in the operation of a Patriot missile does
not readily transfer to private firms. Moreover,
training costs associated with the specific training are
born by the firm, because the worker possesses little
incentive to bear the costs. Specific training increases
a worker's productivity which benefits the firm offering
training, and increases the worker's value to the firm.
However, other firms cannot use this increased
productivity because the skill sets developed are too
narrow in scope to be of use to all firms.6
Why would an employer invest in specific
training? The firm is paying a wage equal to the
worker's productivity and, in addition, paying for the
training of that employee. Once a worker's productivity
is enhanced, the firm will benefit from the increased
productivity over the life of the relationship.
Eventually, the worker may receive a wage below their
marginal value to the firm because the enhanced
productivity is of value only to the specific firm.6 The
options for an employee in that situation are few. Since
his or her increased productivity is only of value to
the present employer, the employee is unable to demand
the same or greater wage from a new employer.

As a worker gains experience at a job, he or she
learns new skills and perfects old ones. This experience
is, in part, the embodiment of general and specific
training learned on the job. Experience also consists of
less formal exposure to the workplace and the skill set
needed to complete productive work. A large portion of
the enhancement to a worker's job skills is the result
of training and exposure in the workplace. Experience
in a work environment increases a worker's store of
human capital thus raising his or her productivity and,
accordingly, earnings. Investments in training, both
general and specific, and experience are important
determinants of an individual's human capital.
Formal education also constitutes a major
component in formation of human capital. Schooling
offers a way to improve one's job and wage prospects.
Education is not without cost. One must pay for the
investment in schooling both in foregone wages which the
student would have earned had he or she not been in
school, as well as the costs associated with going to
school: books and tuition. In addition, there are
psychic costs to schooling because college can be
difficult and boring.7 One must make the outlay for
education and then recoup the investment in the future.

How is this investment decision made and what are the
long term benefits?
The costs of going to college are high. It is
estimated that in 1990, the monetary costs alone (direct
costs and foregone earnings) are in the range of
$12,000-$15,000 per year.8 If one is to recoup these
costs, then the benefits in the future must be at least
the same, if not greater, than the costs of education
after discounting for present value. There are three
variables which, formally or informally, must be taken
into account when deciding on whether or not to invest
in college. Several of these variables are functions of
an individual's personal characteristics (e.g. age)
while others are determined by market environment (e.g.
costs, expected earnings).
Age represents an important determinant of
educational choice. Age determines the period over which
one will receive the monetary rewards and benefits of
the education. The rewards of education for a 19 year
old contemplating entering college continue 20 years
longer than those awaiting a 39 year old, assuming the
average life expectancy. We would therefore expect
younger students would value an education more than
older students, ceteris paribus, because of the longer
payback period.9
The costs associated with education represent
another determinant in the educational decision. All

returns on investment decisions must take account of
outlay. Investments in schooling entail high costs in
tuition, books and fees, as well as foregone earnings.
As these costs rise, the expected return falls, ceteris
paribus, with the result that less educational
investment is taken.
Returns to schooling enter the educational
decision in an obvious manner. In 1985, the ratio of
median incomes of College graduates to High School
graduates (ages 25-34) was 1.36 for males. The ratio is
even more pronounced for females at 1.40.10 Without this
difference in potential salary, there would be little
incentive for prospective students to enter school and
incur the costs associated with schooling.
Human Capital. Productivity
and Discrimination
Discrimination in the labor market can be
defined as "the valuation in the labor market of the
personal characteristics of the worker unrelated to
productivity."11 Workers with high levels of education,
training and experience should possess higher
productivity, and consequently a higher wage. A worker
is presumably paid according to the value of this
marginal product and any wage differential unrelated to
productivity can be viewed as discrimination. Because
the level of human capital is the determinant of

productivity, if human capital characteristics are held
constant, salary differentials should not exist in the
absence of discrimination.
When dealing with discrimination it is
important to determine, therefore, whether salary
differences are caused by current labor market
discrimination or by factors such as experience,
opportunities for training, geographical mobility and
differences in education. If productivity is held
constant, any discrepancies in salary may then be
attributed to discrimination.12
Table 2 reports median income ratios between
Black and white males working full time.
Black/White Income Ratio
Year Ratio
1955 0.61
1960 0.66
1965 0.63
1970 0.70
1975 0.70
1980 0.70
1987 0.71
Source: U.S. Bureau of Census, Money Income of
Households. Families, and Persons in the United States.
Consumer Income Series, P-60(1984 no.151, Table 28).
As evident in the table black males' median
salaries varied from between 60 percent and 70 percent
of their white counterparts over the time period 1955 to
1987. The question is whether these differentials are

discriminatory. Differences between blacks and whites
may be due to differences in education, experience,
training and other forms of human capital. If this is
the case, the observed disparity in incomes are
attributable to variations in factors determining
productivity. Therefore, one must control for these
factors and then analyze the differences. Any variance
between black and white earnings may be attributed to
discrimination. In 1978, Gwartney and Long compared
salaries of white males with those of minority males
using data on earnings in 1969.13 The results, which are
recorded in Table 3, are of interest here.
Salaries of White/Minority Males
Percent of the
Differential Due to;
Earnings Percent of Personal Residual
1969 White Male Character as % of
Group (Dollars) Earnings istics Residual Earnings
(1) (2) (3) (4) (5) (6)
Japanese 8,938 .988 _
Chinese 7,669 .848 21.7 78.3 11.7
Filipino 6,167 .682 37.6 62.4 19.8
Mexican American 6,089 .673 75.9 24.1 7.9
Cuban 6,246 . 691 53.1 46.9 14.6
Puerto Rican 5,702 .631 68.6 31.4 11.5
Black 5,823 .644 47.5 52.5 13.3
Native American 6,153 . 680 58.3 41.7 13.4
Source: James B Gwartney, James E. Long, "The Relative
Earnings of Blacks and Other Minorities", Industrial and
Labor Relations Review. (April, 1978), Pages 336-346.

In their estimation of earnings, Gwartney and
Long control for productive characteristics to focus on
the residual attributable to discrimination. Column 3
reports with the exception of Japanese, and to a lesser
extent Chinese, minorities earn roughly 66 percent of a
white male's earnings. Columns 4 and 5 decompose this
observed differential into two parts: one attributable
to differences in human capital characteristics and the
other to discrimination. Column 6 reports the percent of
observed differential attributed to discrimination. For
example, in the case of Mexican-Americans the observed
wage differential is 32.7 percent, 24.1 percent of which
is due to discrimination (7.9 percent). Note that while
the Chinese males earn almost 85 percent as much as
white males, the differential attributed to
discrimination (11.7 percent) is almost as large as that
of black males (13.3 percent) who earn only 68 percent
what their white male counterparts earn.
Similar techniques are used to estimate
discrimination by gender. Women, in general, possess
different work histories than men. Those who marry and
raise children in their 20's suffer career interruption.
Women, traditionally, have borne heavy domestic
responsibilities which lessen their ability to undertake
occupations which require working long hours and
overtime.14 In addition, men have played a "breadwinner"

role in the past and wives would tend to "follow" their
husbands to new occupational locations thereby
interrupting their career life.15 All these factors
contribute to differences in career experience between
men and women. It is estimated that, in 1980, a 20 year
old female is expected to have a career life of 27.2
years, whereas a male of that age is expected to have a
career life of 36.8 years.16 This gap in career span
between men and women must be controlled for when
studying earnings differences. Studies have estimated
that when comparing wages of women to men holding human
capital characteristics constant, one half of a 30-40
percent wage differential is accounted for.17 A 15-20
percent differential is unexplained. This unexplained
earnings difference, some believe, may be attributed to
discrimination. However, there are two persuasive
explanations offered which attempt to resolve this
unexplained difference, occupational segregation and
dual labor market theory.
Occupational segregation exists when women
choose or are relegated to a low skill labor market. Due
to traditional interruptions in tenure, women may
exclude themselves from occupations which entail a
lengthy process of general training. In addition,
employers may not offer positions which require a
lengthy firm-specific training process due to actual or
perceived high turnover rates.18 Both of these serve to

restrict women to occupations which offer few
opportunities for increases in productivity attributable
to labor market experience.19
A second explanation for the wage differentials
by gender or race is the dual labor market. This
hypothesis proposes the existence of two labor markets,
primary and secondary.20 The primary labor market
contains well paid, stable jobs with good working
conditions. Entry to the primary market is restricted to
entry-level jobs. The selection process of candidates
for this market places a high value on future job
stability.21 The secondary labor market contains low
paying work in dead-end jobs with poor working
conditions. The secondary market is unstructured, with
little opportunity for advancement or incentive to
develop labor market experience. The ability to move
from the secondary market to the primary one is limited
though job candidates may possess requisite
characteristics which would indicate success in the
primary sector. Such an individual would receive a lower
wage in the secondary market, not because of differences
in productivity between that worker and an equal
counterpart in the primary market, but to the way the
secondary market is structured.

Donald G. Ehrenberg and Robert S. Smith, Modern
Labor Economics. 4th edition (New York, Harper Collins,
1991), Page 299.
2Roger N. Waud, Economics. 2nd edition, (New
York: Harper and Row, 1983), Pages 665-666.
3U.S. Department of Education, Digest of
Educational Statistics (Center for Educational
Statistics, 1986), Tables 4,6.
4Gary S. Becker, Human Capital A Theoretical
and Empirical Analysis, with Special Reference to
Education (National Bureau of Economic Research, 1964),
Chap. 2.
6Lloyd G. Reynolds, Labor Economics and Labor
Relations. (Prentiss Hall, Englewood Cliffs, N.J.,
1982), Page 120.
7Ehrenberg and Smith, Modern Labor Economics.
Page 301.
8Ibid, Page 303.
9Ibid, Page 305.
10Diaest of Educational Statistics. Tables 4,6.
13-Kenneth J. Arrow, "The Theory of
Discrimination," Discrimination in Labor Markets, ed.
Orley Ashenfelter and Albert Rees (Princeton,N.J.:
Princeton University Press, 1973), Chap. 3.
12Ehrenberg and Smith, Modern Labor Economics.
Page 531.
13James B. Gwartney and James E. Long, "The
Relative Earnings of Blacks and Other Minorities,"
Industrial and Labor Relations Review (April, 1978),
Pages 336-346.
14Ehrenberg and Smith, Modern Labor Economics.
Page 539.

16Jacob Mincer and Soloman Polachek, "Family
Investments in Human Capital: Earnings of Women,"
Journal of Political Economy. Vol. 82, No. 2
(March/April, 1974), Page 78.
17Morley Gunderson, "Male-Female Wage
Differentials and Policy Responses", Journal of Economic
Literature. Vol. 27 (March, 1989), Pages 46-72.
18prancine D. Blau and Carol L. Jusenius,
"Economists' Approaches to Sex Segregation in the Labor
Market," Women and the Workplace: The Implications of
Occupational Segregation, ed. Martha Blaxall and Barbara
Reagan ( Chicago, 111., University of Chicago Press,
1976) Pages 186-7.
20Michael J. Piore, "Jobs and Training: Manpower
Policy," The State and the Poor, ed. Steve Beer and
Robert Barringer (Cambridge, Mass., Winthrop Press,
1970). 21
21Blau and Jusenius, "Economists' Approaches to
Sex Segregation in the Labor Market", Page 197.

This study analyzes the existence of race
and/or gender discrimination in academia, within the
framework of the human capital model. College professors
comprise a homogeneous group of highly educated
individuals. They possess similar human capital
characteristics and are working in a well defined labor
market with measurable productivity. Salaries are viewed
as a function of human capital characteristics and
productivity. Rank, number of publications and tenure
status of professors are endogenous variables. These
variables are related with each other and with exogenous
variables, experience and specialization. These concepts
are embodied in the following model:
(1) S=fi(Exper,Rank,Ten,Dept,Pub,Eva1,D)
(2) Ten=f2(Exper,Rank,Dept,Pub,Eva1,D)
(3) Rank=f3(Exper,Dept,Pub,Eval,D)
(4) Pub=f4(Exper,Ten,Dept,S).
Equations (1) through (4) represent the structural
model. They yield information about the structure of the
system determined by human capital theory. Equation (1)
assumes the salary of a professor represented by (S) is
a function of job experience (Exper), rank as an

assistant, associate or full professor (Rank),
department of affiliation (Dept), number of publications
(Pub), student evaluations (Eval), and race and gender
(D) of that professor. Equation (2) relates tenure
status to experience, rank, department, publications,
evaluations of the professor and race and gender. The
rank of the professor is expressed as a function of
experience, department, publications, evaluations, and
race and gender in equation (3). Equation (4) indicates
the number of publications depends on experience,
department, salary and whether or not the professor has
tenure. Salary is included as an explanatory variable in
the publication equation because low salaries might
induce the professors to accept secondary or consulting
jobs. These jobs may reduce the number of publications.
Equations (l)-(3) include the department in
which a professor resides as an explanatory variable to
control for the influence of the labor market
conditions. Standard labor theory suggests that higher
demand for a certain occupation generates higher
salaries in that occupation. Therefore, in departments
where professors may be attracted away to jobs outside
of academia, salaries would be higher, ceteris paribus.
Equation (4) includes (Dept) to control for
inter-departmental differences in academic production.
For example, philosophy departments may put emphasis on
publishing books, economics departments place the

greatest weight on journal articles. Similarly, as a
typical economics department would consider two
publications a year as outstanding output, in a standard
physics department the average number of publications
may be six per year.
The primary focus is to determine whether race
and gender variables (D) are significant in equation
(1). Obtaining statistically significant coefficients
for race and gender variables in equation (1) would
imply that experience, rank, tenure, department,
publications, and student evaluations being the same,
differences exist in salaries attributable to race and
Equations (1)(4) constitute a framework of
simultaneous equations where salary, tenure, number of
publications and academic rank are endogenous variables.
The whole system could be estimated by full information
maximum likelihood, or equation by equation using two
stage least squares. However, the salary equation (1) is
unidentified, hence the system (1)(4) can not be
estimated in its present form. To address this problem,
we convert the system {1)(4) into the following
recursive form:
(1') S=f5(Exper,Rank,Ten,Dept,Pub,Eval,D)
(21) Ten=f5(Exper,Rank,Dept,Pub,Eval,D)
(3') Rank=f7(Exper,Dept,Pub,Eval,D)
(4*) Pub=fa(Exper,Dept,Eval,D),

the empirical counterpart of which is:
(1") S=ao+b2Exper+b2Rank+b3Ten+b4Dept+b5Pub+bgEval+b7D+us
(2") Ten=ai+c1Exper+c2Rank+C4Dept+C5Pub+C6Eval+c7D+ut
(3") Rank=a2+d1Exper+d2Rank+d4Dept+d5Pub+dgEval+d7D+ur
(4") Pub=a3+eiExper+e2Rank+d4Dept+e5Pub+egEval+e7D+Up
where a^, b^, c^, d^ and e^ are coefficients, and us,
u-t, ur and Up are i.i.d. error terms with zero mean and
constant variance. If
equations (l")-(4") can be estimated by ordinary least
squares (OLS).
To avoid problems associated with estimation of
the structural model, we substitute equations (2), (3)
and (4) into (1) one, obtaining:
(5) S=fg(Exper,Dept,Eva1,D),
which is the reduced form of the system because only the
exogenous variables appear on the right-hand side.
Student evaluations are considered exogenous. One
might argue, however, that it is an endogenous variable
which depends upon department, experience of the
instructor and tenure. This modification does not affect
the structural equation (1'). However, it would affect
the reduced form (5). We could estimate the alternative
reduced form where (Eval) is replaced by its
determinants. The reduced form would have the shape:
(5') S=fg(Exper,Dept,D).

The next two sections discuss the data set used
in this study and the estimation results of the
structural equation (1") and its variants, as well as
the reduced forms (5) and (5'), and their variants.

The data set used for this study contains
information about faculty of the College of Liberal Arts
and Sciences (CLAS) at the University of Colorado at
Denver with the exception of Fine Arts. Data for
Professors in Fine Arts do not correlate well with those
for other professors in CLAS due to differences in what
constituted a publication and how it should be counted.
The data set used for this study was derived from three
1. Curriculam Vitorum as supplied from the College
of Liberal Arts and Sciences by respective
2. Faculty data files supplied by the Office of
Planning and Institutional Research of the
3. Student Evaluations of Faculty performance as
published by the Student Government of the
University of Colorado at Denver.
The dependent and independent variables are listed below
with some theoretical justification for inclusion where

SALARY Salary for year ending December, 1989. (faculty
data file)
LOGSAL The natural logarithm of SALARY, (derived)
ASSOC A dichotomous variable indicating whether the
professor is an associate professor, (faculty data file)
ASST A dichotomous variable indicating whether the
professor is an assistant professor, (faculty data file)
TENURE A dichotomous variable indicating whether the
professor has achieved tenure, (faculty data file)
MALE A dichotomous variable indicating whether the
professor is male, (faculty data file)
WHITE A dichotomous variable indicating whether the
professor is white, (faculty data file)
EVAL A numerical value derived using student
evaluations published by the student government of the
University. (A+ =12, D- = 1). (student government)
EXPER The years since Ph.D. was attained. This is a
common indicator of years of experience as a professor.
Years at University of Colorado may not capture
experience gained at other schools or endeavors, (vitae)
EXPER2 The square of EXPER. Included to explain
possible non-linear impact of experience on salary,
CUEXPER Experience at UCD. (faculty data file)
CUEXPER2 The square of CUEXPER. Included to explain
possible non-linear impact of UCD experience on salary,

JOURNAL The number of refereed or non-refereed journal
articles written in a professor's career (vitae). Vitae
were submitted to the Dean of Arts and Sciences by
professors in 1989. It is assumed that they are "up to
date." Journal articles which were listed as "in press"
were counted as completed while those articles listed as
"in prep," "in review" or "submitted" were not. No
weighting was made for quality of the journal article.
Refereed and non-refereed articles often appeared
together and were sometimes marked as such, sometimes
not. Due to the inconsistency of the format of vitae, no
attempt was made to divide the publications into
refereed and non-refereed.
BOOK The number of books authored or co-authored in
the professor's career, (vitae)
CHAPTER The number of book chapters published in the
professor's career, (vitae)
OTHER The number of presentations, panels etc. in the
professor's career. (vitae)
TPUB The number of all books, journal articles,
chapters and other presentations or panels in the
professor's career. (vitae)
PSA A dichotomous variable, equal to 1 if the
professor's department is Anthropology, Psychology and
Sociology. (Faculty data file)

HDP A dichotomous variable, equal to 1 if the
professor's department is History, Philosophy, or
Political Science.
ENGC A dichotomous variable, equal to 1 if the
professor's department is English or Communications.
CPM A dichotomous variable, equal to 1 if the
professor's department is Chemistry, Physics or
BG A dichotomous variable, equal to 1 if the
professor's department is Biology, Geography or Geology.
ECON A dichotomous variable, equal to 1 if the
professor's department is Economics.
Table 4 presents means and standard deviations
of the aforementioned variables, broken out as totals
and as black/white and male/female. The SALARY statistic
shows on average, non-whites earn $7,308 less than
whites and women earn $4,352 less than males. Males have
slightly higher rates of publication than females and
whites in general have more total experience and CU
experience than non-whites. Non-whites represent 15
percent of faculty while women represent 22 percent of
faculty as a whole and 42 percent of non-white faculty.
Note that the means of ASST and ASSOC for non-white
faculty sum to 1.0, indicating there are no non-white
full professors, while 41 percent of white faculty are
full professors.

Means and Standard Deviations of the Variables*
Variables Totals Males Females Whites
19 .78
(17 .36)
13 .60
(13 .09)
21 .37
(17 .32)
(. 35)
. 14
( 35)
( 25)
# 16
( 37)
( 48)
(. 30)
* Numbers in parentheses are standard deviations.

Tables 5 and 6 report estimated coefficients of
the structural salary equation (1"). Table 5 is based on
regressions with SALARY as the dependent variable while
Table 6 uses the natural logarithm of salary (LOGSAL).
Model A on the left hand side, treats the number of
journal articles, books and book chapters included as
separate regressors. Model B, on the right hand side,
includes all publications aggregated as a single
regressor (TPUB). Overall the salary equations are
explained with an adjusted R2 of .74 or better for all
In Table 5, model A, the coefficients of EXPER and
EXPER2 are significant at the .07 and .05 level
respectively while in model B the level of significance
stands at .06 and .05 respectively. EXPER is positive,
and as one might expect, salary increases with
experience, EXPER2 is negative establishing that
experience increases at a decreasing rate. CUEXPER is
significant at the .03 level for both model A and B, with
a negative coefficient, demonstrating that salary falls,
all things being equal, as years at UCD increase.

Estimated Salary Equations
Explanatory Variables Dependent Variable Model A - SALARY Model
Constant 40676.50 40284.23
(5.34) (5.50)
EXPER 1001.12 1004.57
(1.84) (1.90)
EXPER2 -27.22 -27.24
(-1.95) (-2.01)
CUEXPER -1063.18 -1093.51
(-2.22) (-2.24)
CUEXPER2 16.59 17.55
(1.07) (1.23)
ASST -18086.30 -17869.09
(-4.54) (-4.69)
ASSOC -11032.77 -10967.86
(-5.01) (-5.16)
PSA 2370.23 2447.87
(0.81) (0.86)
HDP 4742.92 4639.28
(1.55) (1.56)
ECON 5936.33 5943.56
(1.67) (1.71)
ENGC 4352.52 4444.01
(1.39) (1.51)
CPM 4696.11 4768.14
(1.75) (1.81)
BG 264.36 351.45
(0.08) (0.11)
EVAL 431.91 439.65
(1.00) (1.04)
TENURE 2125.05 2403.92
(.59) (.70)
WHITE 2920.93 2916.38
(1.58) (1.60)
MALE -760.62 -669.74
(-.48) (-.44)
JOURNAL 139.26 -
(2.53) -
BOOK 141.10 -
(.38) -
CHAPTER 15.70 -
(.04) -
OTHER -144.60 -147.72
(-2.46) (-2.84)
TPUB - 138.56
Adjusted R2 VO .77
Observations 81 81
Numbers in parentheses are t-ratios

Estimated Salary Equations
Explanatory Variables Dependent Variable Model A - LOGSAL Model B
Constant 10.57 10.57
(58.41) (60.27)
EXPER .018 .018
(1.41) (1.40)
EXPER2 -.00054 -.00048
(-1.50) (-1.50)
CUEXPER -.020 -.020
(-1.78) (-1.89)
CUEXPER2 .0003 .0003
.89 .94
ASST -.45 -.45
(-4.71) (-4.91)
ASSOC -.23 -.23
(-4.33) (-4.51)
PSA .06 .07
(0.94) (1.03)
HDP .11 .11
(1.52) (1.58)
ECON .171 .174
(2.01) (2.09)
ENGC . 104 . 112
(1.39) (1.59)
CPM . 129 . 130
(2.01) (2.06)
BG .026 .029
(0.34) (0.39)
EVAL .0092 .0091
(.89) (.90)
TENURE .017 .022
(.19) (.26)
WHITE .077 .078
(1.73) (1.77)
MALE -.016 -.012
(-.42) (-.34)
JOURNAL .0029 -
(2.23) -
BOOK .0056 -
(.63) -
CHAPTER -.00001 -
(-.0013) -
OTHER -.0026 -.0027
(-1.97) (-2.18)
TPUB - .003
Adjusted R2 .74 .75
Observations 81 81
Numbers in parentheses are t-ratios

CUEXPER2 is positive showing that salary falls at a
decreasing rate. This provides clear empirical evidence
of salary compression. Professors are hired at market
salaries which lie above their department's averages.
However, once at UCD compression sets in. Salary advances
do not keep pace with offers to newer professors.
Rank, as one would expect, is significant. The
coefficients ASST and ASSOC are negative and significant
at the .01 level in both models A and B. An assistant
professor makes $18,086 less than full professor in model
A and an associate professor $11,032 less. In model B
these figures are $17,861 and $10,918 respectively. As
mentioned earlier, because there are no non-white full
professors, rank and promotions account for a great
proportion of the difference in average salaries between
white and non-white professors.
The coefficients of the Departmental dummies are
all positive. However, these differences are not
statistically significant except for CPM at the .08 level
for model A and .07 for model B, indicating that
departmental differences do not account for salary
differences except in the Chemistry, Physics and
Mathematics departments where being a member adds
approximately $4,700 to salary with respect to foreign
languages (LANG) which is the category left out.
Student evaluations (EVAL) and tenure appear to
have no significant impact on salary in either model.

Similarly, number of books and book chapters (CHAP)
written have no statistical impact in these models.
In model A, each journal article contributes $139
towards salary. The coefficient is positive at the .01
level. Model B yields similar results, with a one unit
increase in total publications (TPUB) also contributing
$139, significant at the .01 level.
Race (WHITE) proves to be a significant
determinant of salary differentials. Models A and B show
that whites make $2,921 and $2,916 more than non-whites.
The coefficients are mildly significant at the .12 and
.11 levels respectively.
Gender (MALE) proves insignificant as a salary
determinant in these models. While models A and B find
that males earn $760 and $670 less than females, these
coefficients are both statistically insignificant.
Note that a two-tailed test is used in
determining the significance of coefficients. This
implies that race and gender dichotomous variables may
have positive or negative values. The possibility of
finding discrimination against men or whites is not ruled
out. This discrimination could be observed, for example,
if the administration offers disproportionately higher
salaries to minorities or women to achieve affirmative
action or similar goals. As Tables 5 and 6 demonstrate,
the sign of the gender variable proved to be negative
(but insignificant).

Interestingly, the number of panel discussions
and conference presentations (OTHER) has a negative
impact on salary in both model A and B of -$144 and -$147
respectively. This may be explained by equating
conference travel and lodging with perquisites in lieu of
Estimated salary equations using the log of
salary (LOGSAL) yield roughly the same results as those
of salary demonstrated above (Table 6). EXPER is
significant at the .16 level for both models A and B.
EXPER2 is significant at the .14 level again for both
models. The variables ASST and ASSOC are significant at
the .01 level for both models as they were in the
equations above. Using the log of salary, department
variables, ECON and CPM, are both significant in models A
and B at the .05 and .04 level, respectively. Again, the
variables of publication are significant using LOGSAL,
however at a lower level than shown previously. JOURNAL
is significant at the .03 level and OTHER at the .05 and
.03 level for models A and B respectively. The variable
TPUB is significant at the .02 level. Table 6 indicates
that an increase in journal articles or total
publications results in an increase in salary by 0.3
percent. Along those lines, a one unit increase in OTHER
brings about a decrease by 0.26 percent in salary. Using
the mean salary of all professors, those percentages
translate into an increase of $122 and a decrease of

$106, respectively. The variable explaining race (WHITE)
is slightly greater in the LOGSAL equation at a
significance of .09 for both models A and B. Again, sex
(MALE) is insignificant.
When we use the reduced form equation explained
previously, the results are consistent with those seen
above. Tables 7 and 8 report results of the reduced form
equation, with model A representing the inclusion of
student evaluations (EVAL) and model B their exclusion.
In Table 7, using SALARY as the independent variable, all
variables relating to experience (EXPER, EXPER2, CUEXPER,
CUEXPER2) are significant at the .01 level in both models
A and B. Race (WHITE) is significant at the .12 level and
.06 level in models A and B, respectively. Regressing
LOGSAL against the same set of variables gives similar
results. All experience variables are significant at the
.01 level across both models and the race variable is
significant at the .07 and .04 level in models A and B,

Estimated Salary Equations*
Reduced Form
Explanatory Dependent Variable SALARY
Variables Model A Model B
Constant 13091.82 19091.11
(1.78) (3.66)
EXPER 3221.23 3062.08
(5.48) (5.34)
EXPER2 -60.15 -56.96
(-3.62) (-3.47)
CUEXPER -2351.51 -2185.14
(-3.95) (-3.78)
CUEXPER2 50.15 45.27
(2.59) (2.39)
PSA 3317.88 3022.90
(0.84) (0.76)
HDP 3089.55 3557.48
(0.76) (0.87)
ECON 6540.75 6739.87
(1.38) (1.42)
ENGC 2999.77 2952.55
(0.71) (0.70)
CPM 5679.03 5693.87
(1.49) (1.49)
BG 2454.13 2360.21
(0.56) (0.54)
EVAL 691.87
(1.15) -
WHITE 4127.15 4736.52
(1.62) (1.89)
MALE 713.63 477.38
(0.33) (0.22)
Adjusted R2 0.58 0.57
Observations 81 81
Numbers in parentheses are t-ratios

Estimated Salary Equations*
Reduced Form
Explanatory Independent Variable LOGSAL
Variables Model A Model B
Constant 9.90 10.03
(57.95) (83.01)
EXPER 0.072 0.068
(5.27) (5.16)
EXPER2 -0.0014 -0.0013
(-3.54) (-3.40)
CUEXPER -0.048 -0.048
(-3.50) (-3.40)
CUEXPER2 0.0010 0.0009
(2.34) (2.16)
PSA 0.094 0.088
(1.03) (0.96)
HDP 0.085 0.095
(0.89) (1.00)
ECON 0.20 0.21
(1.83) (1.87)
ENGC 0.093 0.092
(0.94) (0.93)
CPM 0.15 0.15
(1.71) (1.71)
BG 0.081 0.079
(0.80) (0.78)
EVAL 0.015 -
(1.06) -
WHITE 0.11 0.12
(1.83) (2.09)
MALE 0.018 0.013
(0.36) (0.26)
Adjusted R2 0.57 0.57
Observations 81 81
* Numbers in parentheses are t-ratios.

The theoretical framework, and its empirical
counterpart outlined and presented in preceding sections
are based on a particular concept of fairness. In this
view, the conditional distribution of rewards, given
qualifications should be the same for men and women, and
whites and non-whites. This notion of fairness, also
called 'Fairness 1," is tested by regressing a measure
of reward, typically salary, on proxies of
qualifications and dichotomous race and gender
variables, and observing if the coefficients of the race
and gender variables are statistically different from
To illustrate in a simplified example, let Y be
a reward measure, X be a measure of job qualifications
or performance, and D be a dichotomous variable to
indicate race (D=l if the person is white, and D=0
otherwise). To investigate Type 1 fairness one

where b is the coefficient of qualification, c is the
coefficient of the race variable and e is the white
noise disturbance term. The OLS estimation yields
(7) E(Y|X,D)=a'+b'X+c' D,
where b' and c' are the estimates of b and c. If c does
not equal 0, one can conclude that Type 1 unfairness
exists. Assume that the true model which determines the
reward is
(8) Y=a+b1X+b2 Z+cD+e
where Z is another relevant measure of qualifications,
but is not observed by the econometrician. In this case,
the estimating equation will have the form:
(9) Y=a+biX+cD+u, where u=b2Z+e.
If E(X D) is not equal to 0, that is, if the unobserved
performance indicator is correlated with the race
variable, X and u will be correlated in (9), one would
obtain a biased estimate of c.
Reverse regression is based on the concept of
"Type 2 Fairness." In this view, the conditional
distribution of relevant qualifications, given rewards,
should not differ across race/gender groups. Put
differently, it entails analyzing if whites possess
higher qualifications controlling for rewards by
estimating the following equation:
(10) X=a*+b*Y+c*D+e, the least square estimation of
which yields:
(11) E(X|Y,D)=a**+b**Y+c**D.

Note that if c>0 in equation (7), indicating Type 1
unfairness (salaries are higher when D=l, keeping
qualifications constant), c** in (11) should be
negative, implying that given the same reward, whites
have less qualifications.
When one has a vector of qualification measures,
equation (11) becomes
(11') E(Q|Y,D)=a**+b**Y+c**D, where Q=bX.
Q is an index of qualifications obtained from the
forward regression, weighted by the coefficients (b').
Goldberger2 formulates a framework in which salary
(Y), productivity (P), measured qualification (X), true
qualification (X*), and race (D) are interrelated as
(12) Y=P+aD+v, P=bX*, X*=gD+u, X=X*+e,
where v, u, and e are i.i.d., mutually independent
random error terms. According to (12), salary is a
stochastic function of productivity and race.
Productivity is a function of true qualifications; the
expected value of true qualification is a function of
race; and finally, measured qualifications are equal to
the true qualification plus an error term. Goldberger
demonstrates that, in this framework, forward regression
produces an estimate of (a) which is biased upward
(toward finding discrimination) and reverse regression
yields an estimate of (a) which is biased downward.
However, if the salary function is deterministic in

(12), then the reverse regression yields an unbiased
estimate of (a).
A slightly different framework can be depicted as
(13) Y=P+aD+v, P=bX+e, X=gD+u.
In this case, it is easy to show that the estimator of
(a) is unbiased in the forward regression.
In this study, because the forward regressions
did not produce significant race and gender
coefficients, whether the model is depicted by (13)
[where (a) is unbiased], or (12) [where (a) is
overestimated], is of little importance. Reverse
regression analysis is included for the sake of
completeness, not as an alternative to the forward
regression. Nevertheless, as one will see below, the
results of the reverse regressions are consistent with
the results of forward regressions.
Tables 9-12 below present the results of the
reverse regressions that correspond to structural and
reduced forms presented in Tables 5-8. For example, the
model A and B of Table 9 display the results of the
reverse regressions that pertain to model A and B of
Table 5. The results are consistent with those of
forward regressions. More precisely, one observes that
in structural forward regressions the coefficient of the
race dummy (WHITE) is positive and insignificant, and
the coefficient of the gender variable (MALE) is

negative and insignificant (Tables 5 and 6). Tables 9
and 10 display that in the reverse regressions
pertaining to those structural models the coefficients
of WHITE are negative and significant, and the
coefficients of MALE are positive and insignificant.
Similarly, Tables 7 and 8 reveal that in reduced form
models both race and gender dummies are positive and
insignificant. In Tables 11 and 12 the reverse
regression dichotomous race coefficients for the reduced
form equations are negative and insignificant; the
coefficient for the gender dummy is positive but
insignif icant.

Reverse Regression Equations*
Structural Form
Explanatory Variable Dependent Variable Model A - Qualification Index Model B
Constant 6360.60 6370.42
(3.19) (3.20)
SALARY 0.8057 0.8054
(17.87) (17.85)
MALE 1394.16 1304.26
(1.25) (1.17)
WHITE -1647.35 -1640.84
(-1.24) (-1.24)
Adjusted R2 .54 .53
Observations 81 81
* Numbers in parentheses are t-ratios. TABLE 10
Reverse Regression Equations* Structural Form
Explanatory Dependent Variable Qualification Index
Variable Model A Model B
Constant 2.218 2.224
(4.56) (4.57)
LOGSAL 0.7866 0.7860
(16.85) (16.82)
MALE 0.0306 0.027
(1.16) (1.02)
WHITE -0.4147 -0.0420
(-1.31) (-1.33)
Adjusted R2 .53 .53
Observations 81 81
* Numbers in parentheses are t-ratios.

Reverse Regression Equations*
Reduced Form
Reversed on Variable
Variable Model A Model B
Constant 14823.93 15116.87
(5.917) (6.024)
SALARY 0.5471 0.5381
(9.644) (9.472)
MALE 762.89 1028.32
(0.5437) (0.7318)
WHITE -1158.97 -1709.68
(-0.694) (-1.022)
Adjusted R2 .54 .54
Observations 81 81
* Numbers in parentheses are t-ratios. TABLE 12
Reverse Regression Equations* Reduced Form
Explanatory Reversed on Variable - Qualification Index
Variable Model A Model B
Constant 4.848 4.930
(8.19) (8.32)
LOGSAL 0.5335 0.5257
(9.38) (9.24)
MALE 0.0140 0.0195
(0.434) (0.608)
WHITE -0.030 -0.042
(-0.79) (-1.10)
Adjusted R2 .54 .53
Observations 81 81
* Numbers in parentheses are t-ratios.

1Delores A. Conway and Harry V. Roberts,
'Reverse Regression, Fairness and Employment
Discrimination," Journal of Business and Economic
Statistics (May, 1983) Pages 75-85. 2
2Arthur S. Goldberger, "Reverse Regression and
Salary Discrimination," The Journal of Human Resources.
Vol.19,No.3 (1984), Pages 293-318.

Human capital is a major determinant of
productivity, and productivity determines earnings.
Therefore, when measuring earnings differences between
two groups such as whites/non-whites and women/men, one
must control for human capital characteristics in order
to get an accurate picture of earnings differences.
After controlling for human capital characteristics, if
earnings differ, discrimination exists.
This study analyzes whether discrimination
exists, by race or gender, in the College of Liberal
Arts and Science at the University of Colorado at
Denver. Salary equations were estimated controlling for
productive and labor market characteristics of full-time
Also reviewed were a set of reverse regressions
where qualification measures were regressed on salaries
to investigate if non-whites or females have higher
qualifications controlling for salaries. Those results
were consistent with those from the forward regressions.
Those results demonstrate that women are paid on
a par with men in this College after controlling for
human capital characteristics. However, a mild

indication of discrimination against non-white faculty
was reported.
A positive correlation between salary and
experience was reported and is consistent with human
capital theory. The negative correlation between
experience at UCD and earnings is harder to explain.
When comparing earnings of two faculty members
possessing equal human capital characteristics, one
having five years experience at UCD; the other ten
years; the professor with ten years of UCD experience
would earn approximately 10 percent less than his
The strongest determinant of earnings is
promotion. A promotion from assistant to associate
professor adds a $7,000 increase to salary, whereas a
promotion from associate to full professor level brings
about an $11,000 increase, ceteris paribus.
Publications appear to have little effect on
earnings. The marginal addition to earnings of $140 for
each book and/or journal article would appear to offer
little incentive for publishing.
There are indications that non-white faculty may
have suffered from lack of promotional opportunities in
the past or by a shortage of non-whites in the market as
reflected by the lack of non-white full professors.
While this may explain the large difference in average
salaries between white and non-white faculty ($7,297),

when salaries are adjusted for differences in human
capital characteristics, this gap is greatly reduced.

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