Demographic Inertia and Women’s Representation
among Faculty in Higher Education*
Lowell L. Hargens
Ohio State University
J. Scott Long
Indiana University
December 2000
* We gratefully acknowledge the assistance and comments of Barbara Reskin and Jim Voytuk.
Demographic Inertia and Women’s Representation
among Faculty in Higher-Education
Abstract: Since 1970 women have substantially increased their representation at each
stage of the academic “pipeline,” but large gaps remain between men’s and women’s
presence and position in higher education. Assessing the magnitude of changes and
understanding progress toward parity in women’s participation in higher education
requires taking into account the demographic constraints on possible changes. We present
a simple model showing the degree to which demographic constraints limit the rate of
change in women’s representation in higher education. This model shows that, even in
the absence of discrimination, the span an entire career must pass before increases in the
entry of women into a profession are fully reflected at each step of the academic ladder.
Demographic models also show that rates of change in women’s representation depend
on such factors as the initial age and sex structure of the profession and its rate of growth.
Without considering demographic constraints, data on the percentage of women at each
stage of the career tell us little about women’s treatment in hiring and promotion
decisions. Our results also show that over one or two decades, policies that substantially
alter the likelihood of women obtaining faculty positions will have only small effects on
women’s representation.
During the past 30 years women have increased their representation in the professions of
law, medicine, science, and higher education. Still, women’s representation in the higher levels
of professions falls far short of their overall representation (e.g., Lomparis 1990, Valian 1998,
Glazer-Raymo 1999). For example, in 1975 women made up 25 percent of sociologists
employed full time by U.S. colleges and universities, but decade later they constituted only 27
percent, despite substantial increases in the proportion of Ph.D.s awarded to women (Roos 1997:
81). Noting that in 1994 women were 50 percent of assistant professors in sociology graduate
departments, 32 percent of associate professors, but only 17 percent of full professors, Roos
(1997: 80) concluded that “[women’s] representation in the recruitment pool has been
Demographic Inertia – 12/5/2000 – Page 1
sufficiently long standing that the percentage of females among full professors in graduate
departments in sociology should be greater than 17 percent.” Many assessments of women’s
changing representation use the imagery of a “pipeline” (e.g., Berryman 1983, U.S. Congress
1988, Widnall 1988) that at least implicitly uses women’s representation among those entering a
field as the standard for what women’s representation would be if there were no hiring
discrimination against women. In this paper we show that such conclusions are in error insofar as
they fail to take into account the demographic constraints that limit changes in group
composition. Although the 2-percent increase Roos reported may appear to be negligible, given
the effects of demographic inertia it may be the highest increase possible even in the absence of
discrimination against women.
In the case of women’s representation among college and university faculty, two
demographic characteristics in addition to women’s representation among new Ph.D.s are
consequential: (1) the initial age and sex composition of faculty members, and (2) changes in the
number of faculty positions. Using demographic projections, we show how these characteristics
constrain change in the sex composition of a discipline and the representation of women within
higher academic ranks, especially over a period of only one or two decades. Without detailed
information on these demographic constraints it is impossible to infer discrimination from data
on the proportional representation of women over time.
We begin by describing how demographic characteristics influence changes in the sex
composition of an academic discipline. Although we focus on higher-education faculty, our
discussion applies to other occupations or professions, such as engineering, medicine and the
law. In the second section of our paper we use projections to assess quantitatively the extent to
which several demographic characteristics can individually and jointly influence changes in (1)
Demographic Inertia – 12/5/2000 – Page 2
the sex composition of academic sociology and (2) women’s representation among full
professors of sociology.
How Demographic Inertia Constrains Population Composition
To show how demographic inertia influences the sex composition of the academic
labor force, we use a simple demographic model of the entry and aging of faculty through their
careers. Since our purpose is to show the effects of demographic constraints, we initially assume
that men and women are hired in proportion to their numbers among new Ph.D.s. This implies
that men and women are equally qualified when entering the job market and that hiring
departments do not discriminate on the basis of sex. Later we relax this simplifying assumption.
Effects of the Age-Sex Composition of Existing Faculty Members
We begin by considering simple models that illustrate how the existing age-sex
composition of a group constrains future compositional changes. Figure 1 presents three
population pyramids that show the changing sex composition of a hypothetical population of
academics from 1985 to 2015. A population pyramid is a pair of horizontal histograms, one for
each sex, with the length of each bar representing the percent of the total in an age-sex group.
We have divided the population into seven five-year age groups. To focus attention on certain of
these groups, we have shaded their bars and added labels to indicate when their members first
obtained faculty positions. In constructing these pyramids we have made four simplifying
assumptions: (1) all faculty enter their first positions at age 30, (2) there is no attrition before
retirement, (3) all faculty retire at age 65, and (4) the number of new faculty hired each year
equals the number who retire.
Demographic Inertia – 12/5/2000 – Page 3
1950-54
1980-84
12
9
6
3
Men: % of Total
0
65+
65+
65+
65+
65+
60-64
60-64
1980-84
60-64
60-64
55-59
55-59
1985-89
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35-39
1980-84
30-34
1985-89 30-34
0
3
6
9
12
Women: % of Total
A. 20 percent female in 1985.
12
9
6
3
Men: % of Total
0
30-34
30-34
0
3
6
9
12
Women: % of Total
B. 24 percent female in 1990.
12
9
6
3
Men: % of Total
0
0
3
6
9
12
Women: % of Total
C. 46 percent Female in 2015.
Figure 1: Changes in the age-sex structure of faculty after parity is reached in the sex composition of new
cohorts of Ph.D.s.
In Panel A, women are 20 percent of each of the seven cohorts. Given our assumption
that men and women are hired in proportion to their number among new Ph.D.s, this population
structure implies that women have made up 20 twenty percent of new Ph.D.s for at least 35
years. Panel B shows the effect of a sudden change in the proportion of new Ph.D.s who are
women--from 20 to 50 percent in 1985--on the overall sex composition of the population of
faculty members. During the five years from 1985 to 1990, for example, 14 percent of the faculty
retire, 20 percent of whom are women. These faculty are replaced by a newly hired cohort that is
50 percent female, which results in an net increase of only 4.2 percent in the percent of faculty
who are women. Thus, when the population size is constant, large changes in the sex
composition of new cohorts can only slightly affect the sex composition of the entire faculty
during a five-year period. In the longer run, the existing (disproportionately male) stock of
faculty members must retire before women’s representation among faculty can reach parity with
their representation among new Ph.D.s. Panel C shows the sex composition 25 years later, when
the last predominantly male cohort is about to retire. The faculty is now 46 percent female, and
in five years will finally reach parity with the percentage of new Ph.D.s who are female. As this
simple model illustrates, under conditions of equal ability, no discrimination, and a constant
Demographic Inertia – 12/5/2000 – Page 4
faculty size, it will take the length of an entire career (assumed to be 35 years in our example),
before changes in the sex composition of new Ph.D.s will be fully reflected in the overall sex
composition of the faculty.
The results shown in Figure 1 hold for the case in which the initial age-sex structure is
“rectangular” in shape, an unlikely case. What differences result when the initial age structure
not rectangular? Figure 2 presents three alternative age-sex structures produced by different past
growth patterns for higher education faculty. While in each case parity between the proportion of
faculty who are women and the proportion of new Ph.D.s who are women will take 35 years, the
differing initial age-sex structures affect the rate of convergence between the two proportions.
Panel A shows a population in which both sexes have a relatively young age structure, reflecting
long-term growth in the number of faculty positions. Maintaining the assumptions that the total
number of faculty subsequently remains constant and that the proportion of new Ph.D.s who are
women suddenly shifts to 50 percent, this structure will initially produce relatively slow
increases in the percent of faculty who are women because the number of faculty retiring is
initially small. Over time, the rate of growth will increase as larger numbers of retirements
produce increases in the numbers hired from the pool of new Ph.D.s.
25
20
15
10
5
Men: % of Total
0
65+
65+
65+
65+
65+
65+
60-64
60-64
60-64
60-64
60-64
60-64
55-59
55-59
55-59
55-59
55-59
55-59
50-54
50-54
50-54
50-54
50-54
50-54
45-49
45-49
45-49
45-49
45-49
45-49
40-44
40-44
40-44
40-44
40-44
40-44
35-39
35-39
35-39
35-39
35-39
35-39
30-34
30-34
30-34
30-34
0
5
10
15
20
25
Women: % of Total
A. Constant 30 percent growth.
25
20
15
10
5
Men: % of Total
0
30-34
30-34
0
5
10
15
20
25
Women: % of Total
B. Constant 30 percent contraction.
25
20
15
10
5
Men: % of Total
0
0
5
10
15
20
25
Women: % of Total
C. 5 percent contraction for men; 10
percent growth for women.
Figure 2: The effects of growth and contraction in the size of new cohorts on the initial age structure.
Demographic Inertia – 12/5/2000 – Page 5
Panel B shows a population where both sexes have a relatively old age structure because
of past contraction in the number of faculty. In this case, maintenance of a constant number of
faculty will at first produce faster growth in women’s representation among faculty and later
produce slower growth, with variation in the rate of growth again resulting from variation in the
size of retiring cohorts. Finally, Panel C shows an initial structure where men tend to be older
than women; which would result from past increases in the proportion of women among new
Ph.D.s relative to the number of men. This resembles the changes in the age structure in science
and engineering between 1973 and 1995 (Long 2001, Chapter 4) during which the proportion of
women entering increased while there was a steady decrease in the proportion of men. Under
these conditions, the maintenance of a constant number of faculty will initially lead to high
growth in the proportion of women due to the high proportions of retirements among male
faculty and the low proportions among women. Approaching the end of the 35-year period,
however, the rate of growth in women’s representation would taper off as the imbalance in the
proportions of each sex retiring declines.
The four possibilities shown in Figures 1 and 2 are only a few of the many possible initial
age-sex structures that might exist. Although differences among them produce many possible
patterns of growth in women’s representation among faculty, in all cases 35 years brings parity
with their representation among new Ph.D.s.
Effects of Growth or Decline in the Number of Faculty Positions
If the number of faculty positions changes over time, it will still take 35 years before
women’s representation among faculty will reach parity with their proportional representation
among new Ph.D.s. The greater the growth in the number of positions, however, the more rapid
the initial progress toward parity. This is because successively larger numbers of new faculty
Demographic Inertia – 12/5/2000 – Page 6
members are recruited from a pool of new Ph.D.s that is half female, causing the overall
proportion of female faculty to grow faster. Conversely, if the number of faculty positions
shrinks, fewer new Ph.D.s will be hired and the overall proportion of faculty hired from the pool
containing 50 percent women will be smaller. In the first case, early rapid growth in women’s
representation among faculty members will be balanced by slower growth later in the 35-year
period; in the second, slow growth early on will be balanced by faster growth later. Thus,
variation in the rate of growth of faculty positions produces variation in the rate of increase in
women’s representation among faculty members, but does not affect how long it will take before
there is parity in the representation of women.
Effects of Changes in the Sex Composition of the Pool of New Ph.D.s
Thus far we have assumed that at the beginning of any scenario half of new Ph.D.s are
women and that this proportion remains constant. If the proportion of new Ph.D.s who are
women continues to increase, however, the rate of growth in the proportion of faculty who are
women will also increase. Indeed, since the late 1960s women’s representation among new
doctorates has increased continuously in nearly all fields (Long 2001). Since the rate of increase
in the proportion of new Ph.D.s who are women will exceed the rate of increase in the proportion
of faculty who are women, the gap between these two proportions will widen. Another effect of
the steady increase in the proportion of women among new Ph.D.s is to postpone the date when
women’s representation among faculty can reach parity with their representation among new
Ph.D.s.
Effects of Patterns of Attrition
Our introductory remarks did not highlight the effects of various kinds of attrition in our
introductory remarks because results shown below suggest that their actual effects are
Demographic Inertia – 12/5/2000 – Page 7
empirically less important than those of the three demographic characteristics discussed above. It
is worth noting, however, that extreme patterns of attrition can produce many different outcomes
depending on whether they are the same for both sexeswhich is unlikely1and when attrition
tends to occur in the career. Such varying attrition patterns can both alter the rate of change in
the proportional representation of men and women among faculty members, and prevent
eventual parity between the sexes in their representation on the faculty and among new Ph.D.s.
To better appreciate the effects of these demographic constraints, we need quantitative
estimates of their magnitudes. In the remainder of this paper, we use demographic projections for
faculty in sociology to estimate the effects of demographic inertia. In most of our projections we
assume that male and female Ph.D.s are equally qualified for faculty positions and that
departments do not discriminate in hiring on the basis of sex. By examining the consequences of
demographic processes when discrimination is absent, one can assess the potential independent
effects that the various demographic characteristics have.
Women’s Representation in Sociology
To provide a quantitative picture of the effects of demographic inertia, we examine the
changing percentage of women among tenure track sociologists at U.S. colleges and universities
between 1970 and 2005. Sociology is an apt sector to illustrate the effects of demographic inertia
because new Ph.D.s in sociology generally begin their careers with academic teaching positions,
unlike many fields where postdoctoral fellowships and jobs in others sectors are common. In
addition, at least since 1960 the proportion of new sociology Ph.D.s earned by women has
1
We know, for example, that death rates among male academics exceed those for female academics
(Bowen and Sosa 1989:201), that females are less likely to obtain tenure than males (Long 2000, Chapter
6), and that females are more likely than males to leave academic positions early in their careers to care
for children or later in their careers to care for a parent (Long 2000, Chapter 6).
Demographic Inertia – 12/5/2000 – Page 8
closely followed the overall proportion of social science Ph.D.s going to women, so sociology
exemplifies changes in the social sciences (Long 2001, Chapter 3).
Our projections begin with the 1970 age-sex distribution of tenure track sociologists at
U.S. colleges and universities shown in Figure 3.2 The pyramid shows that women were a small
minority (10.7 percent). It also shows that the age distribution for women was substantially older
than that of male faculty, with 56 percent of the women but just 25 percent of the men being
between the ages of 46 and 55. By contrast, 42 percent of men but only 15 percent of the women
were younger than 40. Interestingly, this disparity in the sexes’ age structures held for higher
education faculty in general, according to the 1969 Carnegie Survey data.
61+
61+
56-60
51-55
46-50
41-45
36-40
-35
-35
20
15
10
5
Men: % of Total
0
0
5
10
15
20
Women: % of Total
Figure 3: 1970 population pyramid for tenure track sociologists. Source: Trow 1978.
The most complete analysis of the factors that produced this disparity among higher
education faculty was carried out by Bernard (1965: 41-74) who examined data on the supply
and demand for female Ph.D.s between 1930 and the mid-1960s. She concluded that supply-side
factors were chiefly responsible for the relative dearth of younger female faculty in the 1960s,
2
Lacking data for 1970, we use data from the 1969 Carnegie Commission National Survey of Higher
Education: Faculty Study (Trow 1978) collected in the spring of 1969.
Demographic Inertia – 12/5/2000 – Page 9
and stressed the importance of women’s increased participation during the late 1940s and 1950s
in nonacademic professional careers and in early marriage and childbearing. However, Bernard
also cited evidence of discrimination against women at the most prestigious colleges and
universities, a finding also reported by Caplow and McGee (1958) and Rossi (1970).
The demographic consequences of the disparate age distributions in Figure 3 are clear.
The lower representation of women in the younger cohorts prevented them from increasing their
representation among tenure track faculty during the 1980s as rapidly as they would have been
able to if their age distribution at the beginning of the period had mirrored that of men. Because
there were proportionally fewer young women than young men, proportionally fewer women had
the potential to achieve tenure and advance in rank. And because there were proportionally more
older women, proportionally more women retired in subsequent years than men.
To analyze the effects of demographic inertia on women’s representation among tenuretrack sociologists, we use cohort-component methods (Shryock et al. 1976: 443-453) to project
the age-sex distribution of tenure track sociologists in the years after 1970. We begin with the
age-sex structure for sociology at year T (1970 in our case) and project five-year cohorts at fiveyear intervals. The reduction in size of a cohort between T and T+5 is based on estimates of the
biological and occupational “survival rates”, for that cohort. The size of the youngest cohort at
T+5 is the difference between the total number of tenure track positions and the number of
surviving members of older cohorts. Finally, using data on the proportions of new sociology
Ph.D.s during the period from T to T+5 who are women, and assuming that women and men
have the same probabilities of being hired, we construct the age-sex structure of faculty at T+5.
From these projected age-sex structures we derive summary characteristics, such as the
proportion of faculty who are women, and show how those characteristics change over time.
Demographic Inertia – 12/5/2000 – Page 10
We begin by making projections using a set of realistic assumptions that are based on
published data about the demographics of sociology during this period. In order to gauge the
relative effects of the factors that affect the sex composition of tenure-track faculty, we then vary
each assumption. After investigating these effects, we model the impacts of various levels of sex
preference in the hiring process.
Data Sources for Projections
We used data from the Survey of Earned Doctorates (National Science Foundation, 19201995) to determine the sex composition of new sociology Ph.D.s. from 1970 to 1995. In 1970, 18
percent of the Ph.D.s went to women. This percentage steadily increased over the period,
although at a decreasing rate, and reached 50 percent during the early 1990s. Given the low rate
of increase in recent years, we projected this proportion to remain at 51 percent during 19962005.
Data on the number of tenure track sociology faculty from the 1969 Carnegie Survey and
the Survey of Doctorates Recipients (SDR) for the years 1973, 1979, 1989, and 1995 (National
Science Foundation, 1973-1995) were used to estimate a nonlinear regression for the number of
tenure track sociology positions. We then used this regression to project numbers of positions
through 2005.3 According to these analyses, the number of tenure track positions rose from 4,300
in 1970 to 6,800 in 1995. We estimated that the number will be approximately 7,300 by 2005.
Our projections of tenure-track survival rates are based on information on age-specific
quit rates from Fernandez (1978) and Bowen and Sosa (1989: 193-203), supplemented with data
from Tolbert et al. (1995: 577) on sex-specific faculty turnover rates for 50 sociology
departments over the period from 1977 to 1988. In general, women’s overall survival rates in our
Demographic Inertia – 12/5/2000 – Page 11
analyses are slightly lower than men’s at younger ages because of their higher quit rates, and
men’s are slightly lower beyond age 50 because of their higher mortality rates. Although we
report results only for models with sex-specific rates, omitting the sex differentials in quit rates
did not affect projections of the proportion of faculty who are women, indicating that such
differences are of minor significance in determining the sex composition. Our age and sexspecific survival rates, and the components we used to construct them, are presented in the
Appendix.
The Baseline Projections
Figure 4 shows the results of projecting the 1970 age-sex structure of tenure-track
sociologists for 1980, 1990, and 2000 using the methods and data described above. These
projections show how the population of faculty changes as women increase their representation
among new sociology Ph.D.s and, as a consequence, how the relatively old age structure of
female faculty in 1970 becomes a relatively young age structure by 1990. From these baseline
projections, we derive summary characteristics of the population as a whole, such as the
proportion of tenure track sociologists who are women. We then alter each variable underlying
the projections to show how it influences women’s representation among the faculty.
20
15
10
5
Men: % of Total
Panel A: 1980
0
61+
61+
61+
61+
61+
61+
56-60
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51-55
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-35
-35
-35
-35
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-35
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Women: % of Total
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Men: % of Total
Panel B: 1990
0
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Women: % of Total
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Women: % of Total
Panel C: 2000
The estimated regression was Y = -40028 + 1003.2 X – 5.269 X2 (R2=.91), where Y is the number of
tenure track positions and X is year (70, 73, 79, 89 and 95).
3
Demographic Inertia – 12/5/2000 – Page 12
Figure 4: Projected population pyramids for tenure-tack sociologists for 1980, 1990, and 2000.
Effects of the Sex-Composition of New Ph.D.s
Panel A of Figure 5 shows how the proportion of faculty who are women changes
between 1975 and 2005 in our baseline projections. Women’s projected representation among
faculty, shown by the solid line, increases almost linearly at about 0.9 percentage points per year
between 1970 and 2005.4 By contrast, the proportion of new Ph.D.s who are women, shown by
the dotted line, grew nonlinearly with the highest growth rates between 1970 and 1985.
Comparing the percent of new Ph.D.s who are women to the percent of faculty who are women
shows the effects of demographic inertia. For example, by tracing along the line perpendicular to
the y-axis at 20 percent, we see that 20 percent of the new Ph.D.s were women in 1971, but that
the projected percentage of faculty who are women does not reach 20 percent until 9 years later.
For 30 percent representation, the lag is approximately 13 years; for 40 percent, it is
approximately 17 years; and for 50 percent it will be even longer, although our projections do
not extend that far into the future. The varying lengths of the lag stem from changes in the rate of
increase in the percent of new Ph.D.s who are women. The lag is shorter in the earlier years of
because that is when the proportion of new Ph.D.s who are female--and therefore the proportion
of new faculty who are female--is increasing most rapidly. Because each new cohort of Ph.D.s
can comprise only a small fraction of the entire population of faculty, the percentage of women
4
Our projections are consistent with the empirical estimates that are available for four years. The 1979
SDR estimates 20 percent, with a 95 percent confidence interval from 18 to 22 percent, while our
projection for 1979 is 19 percent. The 1989 SDR estimates 25 percent, with a 95 percent confidence
interval from 21 to 30 percent, while our projection is 28 percent. The 1995 SDR estimates 33 percent,
with a 95 percent confidence interval from 27 to 39 percent, while our projection for is 35 percent.
Finally, a survey by the American Sociological Association for 1991-92 (Roos 1997), gives 29 percent
while our projection for 1991 is 30 percent. (The ASA survey does not permit us to construct a
confidence interval because it attempted to be a census.) As we note below in footnote 5, however, the
Demographic Inertia – 12/5/2000 – Page 13
in tenure track positions must grow more slowly than the percentage of women among new
Ph.D.s.
Faculty
New Ph.D.s
60
50
50
Percent Female
Percent Female
New Ph.D.s
60
40
30
20
10
0
1965
Faculty
40
30
20
10
1970 1975
1980
1985 1990
1995
2000 2005
2010
Year of Ph.D.
Panel A: Baseline projections based on the observed percent
of new Ph.D.s who are women.
0
1965
1970 1975
1980
1985 1990
1995
2000 2005
2010
Year of Ph.D.
Panel B: Projections based on an assumed constant 18
percent of new Ph.D.s being women.
Figure 5: Projected percent of tenure track sociology faculty who are women from 1970 to 2005 based on
alternative assumptions about changes in the sex-distribution of new Ph.D.s.
To demonstrate this point, Panel B of Figure 5 shows what would have happened if
women’s representation among new Ph.D.s had stayed constant at 18 percent (shown by the
horizontal, dashed line), its 1970 level. As expected given our assumption that all retire by age
65, it would take 35 years for women’s representation among faculty to reach the same level as
their proportion of new Ph.D.s. In this scenario the proportion of faculty who are women
increases nonlinearly, with the very low rate of increase in the 1980s resulting from retirements
among the proportionally large group of older female faculty during those years.
Figure 5 demonstrates the fallacy of assessing sex discrimination in hiring by comparing
women’s percentage among new Ph.D.s with their percentage of faculty members, as some
researchers have done (e.g., Rossi 1970, Menges and Exum 1983, Alpert 1989, Lomparis 1990,
Hensel 1991). This difference corresponds to the vertical distances between the solid and dashed
data on women’s representation in sociology so imprecise that they are also consistent with projections
from models that postulate hiring discrimination against women.
Demographic Inertia – 12/5/2000 – Page 14
lines in the two panels of Figure 5. Although both panels were constructed by assuming no sex
difference in the probability of being hired, until 2005 women’s representation among faculty
members is always below their representation among new Ph.D.s. In Panel A the size of the
difference varies over time, primarily due to women’s increased representation among new
Ph.D.s rather than to changes in departments’ propensity to fill tenure track jobs with women.
The difference between the percentage of women among new Ph.D.s and their percentage among
faculty implies discrimination only when the other variables influencing this difference have
been constant for many years or when their joint effects on the disparity can be factored out.
Effects of Other Demographic Forces
In this section we show how changes in other conditions besides the sex composition of
new Ph.D.s affect women’s representation among tenure track faculty. Our strategy is to vary
one variable at a time while holding others at the same levels used for the baseline projection in
Panel A of Figure 5. To help assess the effects of these changing conditions, the figures also
include data on women’s representation among new Ph.D.s and the baseline predictions.
Panel A of Figure 6 shows how the rate of growth in the number of faculty positions
affects women’s representation among faculty members. At one extreme we assume no growth
in the number positions since 1970 (represented by white circles) and at the other extreme
(represented by black circles) we assume that the number of positions grows linearly to 14,600 in
2005, which is double our estimate of what the actual number will be. The baseline projection
(shown by gray diamonds) falls between these extremes. The no-growth scenario shows lower
levels of female representation among faculty than the high-growth scenario, with the difference
between projections reaching 7 percentage points in 1985 and 1990. Both of the two extreme
projections show relatively steady rates of increase in the proportion of faculty who are women,
Demographic Inertia – 12/5/2000 – Page 15
however, with a widening gap until 1990 between that proportion and the proportion of new
Ph.D.s who are women.
No Growth
Baseline Projection
New Ph.D.s
Reversed Age Structure
60
60
50
50
Percent Female
Percent Female
New Ph.D.s
Rapid Growth
40
30
20
10
0
1965
Baseline Projection
No Exits
40
30
20
10
1970 1975
1980
1985 1990
Year of Ph.D.
Panel A: Different levels of growth
1995
2000 2005
2010
0
1965
1970 1975
1980
1985 1990
1995
2000 2005
2010
Year of Ph.D.
Panel B: Different age structures and rates of exit.
Figure 6: Projected percent of tenure track faculty who are women under alternative conditions affecting
the academic labor market.
What would have happened if women had the men’s relatively young age distribution and
men had the women’s relatively old one? This is shown in Panel B of Figure 6 by the line with
solid diamonds. At the beginning and end of the period under examination this projection differs
little from the baseline, shown by the gray diamonds. However, between 1985 and 1995 the
percent of women increases by about 6 points. As noted above, the older age structure for female
faculty in 1970 reduced the rate at which the percentage of women among faculty could increase,
and it is clear from the reversed age-structure projection that the sex differences in age structures
was responsible for the approximately linear increase in the percent women shown by the
baseline projection.
The projection marked with open circles in Panel B of Figure 6 shows the effect of the
counterfactual condition where no one leaves a tenure track position until retirement at age 65.
Even though this condition is extreme, the differences from the baseline projection are
surprisingly small, peaking at 3 percentage points. In another projection (not shown) we allowed
Demographic Inertia – 12/5/2000 – Page 16
sex differences in exit rates only in the case of death. This change raised women’s representation
among faculty over the baseline by no more than 1 percentage point between 1975 and 1990, and
between 1 and 2 points in later years. Thus, of the four demographic forces we have examined,
differences in exit rates have the smallest impact on women’s representation among tenure track
faculty.
Next we consider what would happen if all demographic conditions were “optimal” for
women. That is, the age structures is reversed, there is rapid growth in positions, and men and
women have identical exit rates, except for higher male mortality. Figure 7 shows that under
these propitious conditions, increases in the projected proportions of tenure track faculty who are
women are similar to the projections for a reversed age structure (Figure 6B). Starting in 1980,
however, the optimal-conditions projection is about 3 points higher than the reversed agestructure projection. Thus, even under these highly favorable conditions women’s representation
among faculty members converges slowly with their representation among recent Ph.D.s.
New Ph.D.s
Optimal Conditions
Baseline Projection
60
Percent Female
50
40
30
20
10
0
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
Year of Ph.D.
Figure 7: Projected percentage of tenure track sociology faculty who are women under the most favorable
conditions for increases in women’s representation.
In sum, the most consequential demographic force is the increase in women’s
representation among new sociology Ph.D.s. This factor not only produced a relatively rapid
Demographic Inertia – 12/5/2000 – Page 17
increase in the women’s representation among faculty members, but also increased the disparity
between women’s representation among new Ph.D.s and among faculty members between 1970
and 1990. The second most important force is the disparity in the age structures for men and
women. If the age structures for the two sexes had been the same in 1970, women’s increased
representation among faculty members would have paralleled their increased representation
among new Ph.D.s rather than being approximately linear. Third, if the number of faculty
positions had grown twice as rapidly, women’s representation among faculty members would
have been approximately 3 percentage points higher during most of the period covered by our
projections. Finally, disparities in exit rates between male and female faculty members have the
weakest effects on women’s representation.
Demographic Inertia – 12/5/2000 – Page 18
Modeling Sex Discrimination in Hiring
To this point our projections have assumed (1) that men and women have equal scholarly
competence and (2) that there is no discrimination in hiring. The potential effects of
discrimination can be modeled by introducing sex differences in the probabilities of being hired.
We do this in Figure 8, which shows projections under four conditions of discrimination, two
favoring men and two favoring women. We defined “moderate” discrimination as a condition
where one sex has a probability of being hired that is 30 percent higher and “strong”
discrimination as the condition where one sex’s probability of being hired is twice as high. Note
that in these projections all other demographic conditions are identical to those for the baseline
projections (shown as the solid line).
Male Preferemce
Strong Male
Baseline Projection
Female Preference
Strong Female
Estimated
70
Percent Female
60
50
40
30
20
10
0
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
Year of Ph.D.
Figure 8: Projected percentage of tenure track sociology faculty who are women under different levels of
sex discrimination. Note: Observed data for 1979, 1989, and 1995 (with 95% confidence intervals
indicated by error bars) are from the Survey of Doctorate Recipients; data for 1991 are from Roos (1997).
These projections yield three key findings. First, even with strong discrimination against
women, women’s representation among faculty still increases. This further testifies to the
powerful influence of women’s increased representation among new Ph.D.s. Second, standard
survey estimates of the women’s actual representation among faculty are not sufficiently precise
to allow one to detect anything but the most extreme levels of discrimination. Although
Demographic Inertia – 12/5/2000 – Page 19
differences among the four discrimination patterns become larger over time, only the projections
for conditions of strong sex discrimination are so discrepant with estimates from the Survey of
Doctoral Recipients that one can rule them out as being inconsistent with observed data (shown
with ‘s and error bars; see footnote 9 for details). It is very difficult to distinguish between the
two moderate discrimination patterns until after 1995 when they diverge by 10 percentage points,
which is the size of the 95 percent confidence intervals for current SDR estimates. Thus, both
precise estimates of women’s representation in tenure track positions and good information about
the demographic factors affecting that representation are necessary before aggregate-level data
can detect anything less than very strong patterns of sex discrimination in hiring.5 Third, the
results in Figure 8 show the extent to which demographic inertia limits increases in women’s
representation among faculty even if women were to have substantial advantages in obtaining
faculty positions. The distance between the line for moderate female preference and the line for
no preference is surprisingly small, and reaches only seven percentage points by 2005. Similarly,
even if women’s chance of obtaining positions had been double men’s, by the end of 35 years
they would have made up only 17 percent more of the faculty than if there were no sex
preference. These results are consistent with previous work by Feinberg (1984) showing that
during the span of only a few decades policies with substantial impacts on the flow of workers
into an occupation have surprisingly small effects on the composition of the occupation.
Women’s Representation among Full Professors
Although many have expressed concern about women’s slow rate of increase among
faculty members, there is even greater concern about women’s slow progress up the academic
5
This may partly explain why attempts to evaluate the assumption that the sexes have equal chances of
being hired for academic positions have been unable to discredit it (e.g., Cartter and Ruhter 1975, Becker
and Williams 1986).
Demographic Inertia – 12/5/2000 – Page 20
ladder. Researchers often cite the slowly growing proportion of full professors who are women,
and differences between the proportions of male and female faculty who are full professors, as
evidence of disparate treatment (e.g., Lomparis 1990, Dwyer et al. 1991, Roos 1997, Valian
1998, Glazer-Raymo 1999). However, these inferences may be unwarrented because, in addition
to women’s and men’s promotion chances, the proportion of full professors who are women is
sensitive to such demographic factors as the proportion of faculty who are women, the age
structure of female faculty, and women’s and men’s professional age structures. When a group is
substantially increasing its representation in a profession, it will necessarily have a young age
structure, and since age is related to promotion, this will lead to decrease in proportion of that
group who are full professors.
Furthermore, the relationship between professional age and the likelihood of being a full
professor varies when conditions in the academic labor market change. In times when the
demand for faculty exceeds the supply, promotion occurs earlier in the career than when the
supply exceeds the demand (Menard 1970, Hodgkinson 1971, Perrucci et al. 1983). A shift in the
relation between professional age and full professorship has undoubtedly affected the rates at
which women have become full professors. In the late 1960s, a favorable academic labor market
meant that new Ph.D.s--who were predominantly male--experienced relatively rapid promotion.
The less favorable labor market conditions since then have meant that subsequent Ph.D. cohorts-which have been increasingly female--have been promoted more slowly. To incorporate this
shift in the relationship between professional age and full professorship into our analyses, we
used data on all social sciences (since there were too few cases in sociology alone) from the 1969
Carnegie Survey and the 1979, 1989, and 1995 Surveys of Doctoral Recipients to estimate its
magnitude. We examined only men to avoid confounding the slowing of rates of promotion with
Demographic Inertia – 12/5/2000 – Page 21
the effects of discrimination against women. We then estimated curves relating professional
experience to the proportion who are full professors, as shown in Figure 9 for those who earned
their degrees in the late 1960s and those from the early 1980s.6 As suggested above, between
1970 and 1985 the data show substantial declines in the proportion who were full professors at a
given professional age, although these declines were concentrated in the first 20 years of
professional experience. We use these results in the following projections.
Late 1960s Ph.D.s
Early 1980s Ph.D.s
Percent Who Are Full Professors
100
90
80
70
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
Professional Age
Figure 9: Percent of male faculty who are full professors by professional age for two Ph.D. cohorts.
Figure 10 shows how three variables—the proportion of female faculty who are full
professors, the proportion of male faculty who are full professors, and the proportion of full
professors who are women—would change between 1970 and 2005 if the sexes had the same
chance of being promoted to full professor at any given professional age.7 This is obviously
counterfactual because previous studies have built a strong case that women’s chances of
attaining the rank of full professor at any given professional age are lower than those of
comparable men (Smart 1991, Long et al. 1993, Sonnert and Holton 1995, Toutkoushian 1999).
6
On the basis of previous findings (Long 2000, Chapter 6), we constrained these curves to have an
elongated S-shape with a plateau at 95 percent.
These projections are also based on estimates of women’s representation among faculty produced by the
baseline projections discussed above.
7
Demographic Inertia – 12/5/2000 – Page 22
As before, rather than to construct a model that accurately reflects all determinants of women’s
chances of becoming full professors, we want to illustrate the effects of demographic inertia.
Percent of Women who are Full Professors
Percent of Men who are Full Professors
Percent of Full Professors who are Women
60
50
Percent
40
30
20
10
0
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
Year
Figure 10: Projected percentage of: 1) women who are full professors; 2) men who are full
professors; and 3) full professors who are women, by year.
The proportion of full professors who are women, shown by the bottom curve, is fairly
stable between 1970 and 1990. This stability stems from two sources. First, the age structure of
women in 1970 was relatively old (see Figure 3). When the two largest cohorts of female faculty
reached the ages where the likelihood of being a full professor is highest, the two cohorts
succeeding them were not large enough to maintain women’s representation among full
professors (see Figure 4A). Women’s representation remained stable only because in the late
1980s the 1970 cohort of female Ph.D.s reached the age where a sizable fraction started
becoming full professors. The second factor is that the professional age structure for men was
younger at the beginning of the period. The increasing number of male full professors constrains
the increase in the percent of the full professors who are women. For example, in Figure 10
women’s representation among full professors declines slightly between 1970 and 1975 even
Demographic Inertia – 12/5/2000 – Page 23
though their age structure in Figure 3 suggests that it might increase.8 Although the proportion of
tenure track faculty who are women almost triples (from 11 percent to 29 percent, see Figure 5)
between 1970 and 1990, demographic inertia constrains the increase in the proportion of full
professors who are women to only three percent. Only in last 15 years of the projection do we
see an impact of women’s increased representation among faculty members on their
representation among full professors.9
Figure 10 also presents projections for the percent of women and of men who are full
professors. Given our assumption of no discrimination, these projections reflect changes in the
age structures of the two groups. The proportion of men who are full professors gradually
increases, reflecting the slowly increasing average age of male faculty members. In contrast, the
proportion of women who are full professors plummets between 1970 and 1985 due to the
combined effects of an initially old age structure and the rapid increase in the proportion of new
Ph.D.s who are women. After 1985 this proportion rises, but even in 2005 it is still 8 points
lower than the proportion of men at that rank. Furthermore, the vertical distance between these
two curves varies substantially, even though at any given professional age men and women have
the same likelihood (by the assumptions of our projections) of being a full professor.
As Alice learned from the Red Queen, sometimes “it takes all the running you can do to stay in the same
place.”
8
9
Once again, we have four estimates of the proportions of full professors in sociology who were female.
Data from the 1979 SDR give an estimate of 11 percent, while our projection for 1979 equals 13 percent.
Data from the 1989 SDR estimates 21 percent, while our projection for 1989 equals 15.6 percent. Data
from the 1995 SDR estimates 24 percent, while our projection for 1995 equals 23 percent. Finally, data
from the 1991 ASA survey estimates 19.5 percent, while our projection for 1991 equals 18 percent.
However, the SDR estimates are very imprecise. For example, a 95 percent confidence interval for the
1995 SDR extends from 16 to 32 percent. The SDR estimates are almost certainly also consistent with
what we know from other studies of sex differences in promotion to full professor; specifically, that
women are promoted more slowly than comparable men.
Demographic Inertia – 12/5/2000 – Page 24
All of the projections in Figure 10 are based on the shifting relationship between
professional age and full professorship given in Figure 9. How much did the trend toward later
promotion contribute to women’s low representation among full professors? To answer this
question we projected what would have happened if the relation between professional age and
full professorship had not changed. Using a curve midway between the two curves shown in
Figure 9 for the entire period between 1970 and 2005 we obtained results that never differed by
more than 2 percentage points from the results shown in Figure 10 (results not shown). Thus,
compared to the effects of the age-sex structure of sociology in 1970 and the increased
representation of women among new Ph.D.s, this source of lower female representation among
full professors was of minor importance.
Conclusion
We draw both methodological and substantive conclusions from our analyses. First,
data on women’s share of faculty members, tenured faculty, or full professors have been used
extensively in discussions of discrimination against women in hiring and promotion. Alone,
however, data on women’s representation in a field, changes in women’s representation,
women’s representation compared to men’s, or changes in women’s representation compared to
changes in men’s, are inadequate for drawing inferences about disparities in the sexes’ treatment
in hiring and promotion processes. Because these data are strongly influenced by such factors as
the age-sex distribution of a field’s members, the sex composition of new Ph.D.s, and the growth
of a discipline; one must take these demographic factors into account before drawing any
inferences about disparate treatment. One should therefore skeptically view conclusions about
sex-based disparities that are based on analyses that fail to take the effects of demographic inertia
into account.
Demographic Inertia – 12/5/2000 – Page 25
Our results also indicate that even when one has good information about the demographic
constraints limiting women’s representation, it may be impossible to detect moderate levels of
discrimination against women. This is because estimates of women’s representation that are
based on sample surveys, such as those derived from the SDR, are subject to sampling error.
Moderate discrimination against women can be expected to produce a 5- or 6-percent shortfall in
women’s representation compared to what we would observe if there were no discrimination (see
Figure 11). However, survey-based estimates of women’s actual representation that have
standard errors of 3 or 4 percent, such as the estimates yielded by current waves of the SDR, are
not sufficiently precise for researchers to detect these shortfalls. If one wishes to obtain a
defensible estimate of the extent of discrimination against women in academic hiring and
promotion processes, one needs to follow a cohort of new Ph.D.s through their careers.
Unfortunately, using this kind of study design typically gives results for points in the past rather
than for current conditions, and the experiences of new Ph.D.s five years ago may not be
generalizable to those who earned doctorates last year.
Even with the best aggregate data for a discipline, however, failing to find evidence of
women’s under representation does not mean that women in that discipline encounter no
discrimination. Women’s representation varies greatly across departments and institutions—
Tolbert and her colleagues, for example, report that women make up from 0 to 50 percent of
faculty in different units (Tolbert et al 1995, p. 566; Tolbert and Oberfield, 1991, p. 310)—and
favoritism toward men in one subset of units may be offset by favoritism toward women in
another subset. Probably a more realistic possibility is that favoritism toward men in a small
number of units might be offset by little or no favoritism among the majority. This possibility is
consistent with claims that discrimination against women has been strongest in high-prestige
Demographic Inertia – 12/5/2000 – Page 26
departments (Bernard 1965, Rossi 1970). To assess such possibilities one must examine the
representation of women in individual units (e.g., Tolbert and Oberfield 1991, Tolbert et al.
1995) rather than on overall disciplinary levels of representation.
Substantively, our results demonstrate the considerable power that demographic
conditions have on the composition of a profession (see also Feinberg 1984). It takes the length
of a career before changes in a group’s representation in the pool of new recruits will be fully
mirrored by the composition of the profession as a whole. Also, rates of compositional change
can vary greatly over time depending on initial conditions. In the case of college and university
faculty members, the relatively young age structure of men in the late 1960s and early 1970s and
the bulge of women in the middle and later stages of their careers produced slower growth in
women’s representation than would have occurred if both groups had the same age structure.
Such effects are especially notable for outcomes associated with the latter stages of a career. In
the case of women’s representation among full professors, for example, we have seen that initial
demographic conditions alone precluded much change for twenty years despite the substantial
increases in women’s representation among both new Ph.D.s and all faculty members. Thus, part
of the answer to Valian’s (1998) question “Why so slow?” is that even under gender-neutral
personnel practices, demographic inertia strongly limits possible change.
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