Too Many PhD Graduates or Too Few Academic Job Openings: The Basic Reproductive Number R[subscript 0] in Academia

Abstract

The academic job market has become increasingly competitive for PhD graduates. In this note, we ask the basic question of 'Are we producing more PhDs than needed?' We take a systems approach and offer a 'birth rate' perspective: professors graduate PhDs who later become professors themselves, an analogue to how a population grows. We show that the reproduction rate in academia is very high. For example, in engineering, a professor in the US graduates 7.8 new PhDs during his/her whole career on average, and only one of these graduates can replace the professor's position. This implies that in a steady state, only 12.8% of PhD graduates can attain academic positions in the USA. The key insight is that the system in many places is saturated, far beyond capacity to absorb new PhDs in academia at the rates that they are being produced. Based on the analysis, we discuss policy implications.

Full text

■Research Note
Too Many PhD Graduates or Too Few
Academic Job Openings: The Basic
Reproductive Number R
0
in Academia
Richard C. Larson
1
, Navid Ghaffarzadegan
2
*and Yi Xue
1
1
Engineering Systems Division, Massachusetts Institute of Technology, Cambridge, MA, USA
2
Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA
The academic job market has become increasingly competitive for PhD graduates. In this
note, we ask the basic question of ‘Are we producing more PhDs than needed?’We take a
systems approach and offer a ‘birth rate’perspective: professors graduate PhDs who later
become professors themselves, an analogue to how a population grows. We show that the
reproduction rate in academia is very high. For example, in engineering, a professor in the
US graduates 7.8 new PhDs during his/her whole career on average, and only one of
these graduates can replace the professor’s position. This implies that in a steady state,
only 12.8% of PhD graduates can attain academic positions in the USA. The key insight
is that the system in many places is saturated, far beyond capacity to absorb new PhDs
in academia at the rates that they are being produced. Based on the analysis, we discuss
policy implications. Copyright © 2013 John Wiley & Sons, Ltd.
Keywords higher education policy; unemployment; R
0
; engineering workforce development;
research workforce development
INTRODUCTION
The academic job market has become more and
more competitive. PhD graduates are finding it
increasingly difficult to land tenure-track aca-
demic positions. Candidates are often expected
to have several publications in leading journals,
putting lots of pressure on them during their
training period. Many PhD graduates are unem-
ployed or underemployed (National Science Founda-
tion, 2012; Chapter 3). Reports even state that there
are PhD graduates on food stamps (Nichols, 2012).
Nowadays, less than 17% of new PhDs in science,
engineering and health-related fields find tenure-
track positions within 3 years after graduation
(National Science Foundation, 2012; Chapter 3).
ManyPhDswhodonotfind tenure-track positions
turn to positions outside academia. Others who
think that they will have better future opportunities
* Correspondence to: Navid Ghaffarzadegan, Grado Department of
Industrialand Systems Engineering, Virginia Tech, Blacksburg, VA, USA.
E-mail: navidg@vt.edu
Received 5 February 2013
Accepted 28 July 2013Copyright © 2013 John Wiley & Sons, Ltd.
Systems Research and Behavioral Science
Syst. Res. 31, 745–750 (2014)
Published online 9 September 2013 in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/sres.2210

accept relatively low-paying academic jobs such as
postdoctoral positions and stay in the market for a
prolongedperiod(Ghaffarzadeganet al., 2013).
Many engineering PhDs go the entrepreneurial
route and become involved in startups or work in
national research labs or commercial R&D centres.
Butourfocusisacademia.
On the demand side, the number of tenure-track
positions in a wide range of fields is steady or
changingveryslowly,ifatall(NationalScience
Foundation, 2012; Chapter 5). Except computer
science, which experienced rapid growth in the past
30 years, and life sciences with the average growth
of 1.5% per year, many fields have seen little
increase in their faculty slots (National Science
Foundation, 2012; Chapter 5). This means new hires
can only replace people who leave, as openings are
closely tracking retirement and exit rates. Addition-
ally, due to the abandonment of fixed retirement
age, the mean duration of a faculty career has
increased, resulting in a concomitant decrease in
new slots available (Larson and Gomez, 2012).
Considering the trends, a basic question to ask
is, ‘Are we producing more PhDs than needed?’
If yes, how far are we from a desired condition
in which every qualified applicant interested in
a tenure-track academic position can find such a
position? We focus on the endogenous nature of
the problem (Richardson, 2011) and borrow the
concept of R
0
in demography and epidemiology
(Sharpe and Lotka, 1911) to shed more light on
this problem. Our approach corroborates with
several arguments in favour of applying systems
approaches to the study of higher education (e.g.
Brown, 1999; Bianchi, 2010; Kennedy, 2011).
THE CONCEPT OF R
0
FOR ACADEMIA
R
0
denotes the basic reproductive number or rate.
In demography, R
0
is defined as the mean number
of baby girls that a typical newly born baby girl will
have in her lifetime. Neglecting infant deaths, if
R
0
>1.0, then the population will grow over time.
If R
0
<1.0, it will decline. And R
0
= 1.0 yields a
stable population. For example, R
0
for China and
the USA are currently estimated at 0.78 and 1.03,
respectively (CIA World Factbook, 2012). In epide-
miology, R
0
is the mean number of people that a
typical newly infected person will infect during
his or her infectious period, assuming that virtually
everyone in the population is susceptible to the
disease. If a disease has R
0
>1.0, there is initially
anexponentialgrowthinnumberofpeople
infected. For example, R
0
for seasonal flu is typically
about 1.2; for H1N1, it was reported to be in the
range of 1.4 to 1.6 (Barry, 2009; Brown, 2010);
and for the deadly 1918 ‘Great Influenza’,itwas
estimated to be as high as 4.0 (Astudillo, 2009).
Note that, in demography and epidemiology,
any R
0
value greater than 1.0 implies exponential
growth.
We can use the R
0
metaphor in academia and
offer the following definition:
R
0
is defined as the mean number of new PhD’s
that a typical tenure-track faculty member will
graduate during his or her academic career.
When R
0
= 1.0, each professor, on average,
graduates one new PhD that can replace him or
her. But, assuming a fixed number of faculty slots,
R
0
>1.0 means that there are more PhD graduates
than existing faculty positions. Depending on
magnitude, this may or may not be acceptable
because not all of PhD graduates desire
academic positions. For R
0
<1.0, the number of
PhDs in a field is declining and the field will
eventually die.
For academic fields with R
0
>1.0, an exponential
growth in university capacities would be required
so that every graduate has an opportunity to as-
sume a tenure-track position. If αis the ratio of the
number of PhD graduates interested in tenure-track
positions to the total number of PhD graduates, and
ris the average growth ratio of faculty slots, we
should have R0≤1þrT
αinordertohaveenoughaca-
demic openings for all PhD graduates, where Tis
the average period of career.
1
For example, given
1
If αratio of PhD graduates desire tenure-track positions, to have job
for everybody interested, we should have
αnew PhDs ¼exit rate þgrowth rate (1)
If the number of faculty members is F, the exit rate is approximately F
T
,
and growth rate is rF. Then, Equation (1) can be written as
αR0
T¼1
Tþr(2)
We can solve Equation (2) for
R0:Ro¼1þrT
α(3)
RESEARCH NOTE Syst. Res.
Copyright © 2013 John Wiley & Sons, Ltd. Syst. Res. 31, 745–750 (2014)
DOI: 10.1002/sres.2210
746 Richard C. Larson et al.

a yearly growth rate of 1%, and average career of
20 years in academia, assuming 50% of graduates
desire tenure-track positions, there will be at least
one opening per PhD graduate interested in aca-
demic jobs only if R
0
≤2.4. However, the actual
numbers for R
0
are often dramatically outside of
this range.
R
0
ESTIMATION
Let us start with a simple example from our home
university, the Massachusetts Institute of Technol-
ogy (MIT). The Institute’s total number of tenure-
track faculty members has remained essentially
around 1000 for over three decades. MIT under-
takes about 50 faculty searches each year, looking
almost exclusively for young assistant professors.
Applying Little’s Law (Little, 1961), the mean
MIT faculty career length is approximately 1000/
50 = 20 years (Larson and Gomez, 2012). Please
keep in mind that this is an average, and that some
assistant professors will leaveinlessthan7years,
and others obtaining tenure may remain on the fac-
ulty for up to 50 years. For the past 15 years, MIT
has been producing about 500 PhDs per year or
about 0.5 PhDs per faculty member per year. This
suggests that over a 20-year career of the average
MIT faculty member, she/he produces approxi-
mately 10 PhDs. To firstorderweseethatforthe
‘typical’MIT faculty member, R
0
= 10. Taking a ho-
listic view of academia, only one of these 10 could
‘replace’his/heradvisoraftertheadvisorleaves
the faculty. But that leaves nine newly minted
PhDs who cannot.
Now, we apply R
0
to the field of engineering
in academia in the USA. We use the 2011 data
from the American Society of Engineering
Education reporting the number of PhD gradu-
ates and faculty members for all engineering
departments in the United States.
2
The data are available at an aggregate level for
each field. By using the number of PhD graduates
in different engineering fields and the number of
tenure-track faculty members in those fields, we
can estimate the average number of PhD graduates
per faculty members in each field. In this dataset,
the number of faculty members includes all types
of engineering programmes at US institutions,
regardless of whether they grant PhD degrees or
not (such as 4-year undergraduate colleges). This
gives a more accurate estimation of the number of
faculty slots available in academia. Multiplying
the ratio of PhD graduates to faculty members with
the average duration of an academic career
provides an estimation of R
0
for different engineer-
ing fields in the USA. Based on Larson and Gomez
(2012), the average duration of a tenure-track career
was approximated to be 20 years. Results for differ-
ent engineering fields are depicted in Figure 1.
As Figure 1 shows, there is considerable variation
across fields with an average of R
0
=7.8 for the
whole field of engineering. Put simply, this indi-
cates that an average faculty member in a US higher
education institution’s engineering department
graduates 7.8 new PhDs during her or his career.
If the number of faculty positions remains constant,
a tenure-track position is only available for 1/7.8,
that is 12.8% of new PhD graduates. In order to
have faculty openings in the USA for 50% of the
graduates, the whole field would need to grow at
an improbable rate of 14% every year.
Interestingly, there is considerable variation
across the different engineering fields, with a
standard deviation of 4.6. Some fields have R
0
much higher than average, such as biomedical
(R
0
= 13.6) and environmental engineering
(R
0
= 19.0). Figure 1 also depicts fields with a
higher number of PhD graduates in 2011 with
darker bars. The field of Metallurgical and
Material Engineering, with more than 500 PhD
graduates per year, also has a high PhD pro-
duction rate, indicated by R
0
= 15.4.
At the other end of the spectrum, fields such as
Mining or Architectural Engineering do not
produce as many PhDs per faculty as the other
engineering fields with a R
0
close to one, and
the number of PhDs graduated in 2011 is low as
well, as depicted by the lighter bars. Unless
university capacities are shrinking in these two
fields, graduates should not have serious prob-
lems in finding academic positions.
2
Data from American Society for Engineering Education’s‘Engineer-
ing by the Numbers’2011 Report. http://www.asee.org/papers-
and-publications/publications/college-profiles/2011-profile-engineering-
statistics.pdf [24 September 2012]
Syst. Res. RESEARCH NOTE
Copyright © 2013 John Wiley & Sons, Ltd. Syst. Res. 31, 745–750 (2014)
DOI: 10.1002/sres.2210
The Basic Reproductive Number R
0
in Academia 747

CAVEATS
We recognize that in using a simple model, sev-
eral parameters that are not part of our analysis
may pose limitations (Ghaffarzadegan et al.,
2011). One consideration is that many engineer-
ing doctorates are not interested in academic
positions and may not even compete for
tenure-track positions in academia. Another
consideration is that some engineering gradu-
ates are foreign citizens who take academic
positions outside of the USA.
3
Another factor is
inter-field hiring. Engineering doctorates might
obtain positions in other fields such as science or
business, which would also diminish the gap.
Overall, these points do not affect our estima-
tion of R
0
, and the fact that in a steady state
condition, the physics of the system dictates that
1/R
0
of the population of engineering graduates
can find tenure-track faculty positions in engi-
neering departments at US higher education
institutions, regardless of their interest in such
positions. The rest of the population (11/R
0
)
should pursue other careers or find academic
positions in other fields or other countries.
Finally, we do not have a precise estimation of
the duration of an average academic career. In
our estimation of R
0
for the field of engineering,
we used the estimate of 20 years from our home
institute, MIT (Larson and Gomez, 2012). It is
likely that faculty members that leave MIT
pursue academic positions in other universities,
which implies that we might have underestimated
the duration of career in academia, and thus
underestimated R
0
. In other words, R
0
in engineer-
ing fields might be even higher than 7.8.
It is important to state that our intention in this
paper was not to introduce an optimal value for
R
0
, which might depend on several social and
behavioral factors such as people’s interest in
obtaining PhD level education and pursuing
academic careers. Our main intention was to
provide a simple concept and measurement tool
(Richardson, 2013), that can intuitively depict
supply side challenges in the academic job market
and provide first order, interesting policy insights.
3
About one third of Science, Technology, Engineering and Mathematics
PhDs are non-US citizens (Wasem 2012). Based on a report by National
Science Foundation (2012; Appendix 3–20), 77.2% of non-US citizen
doctorates of science and engineering who received their degree
between 2006 and 2009 intended to stay in the USA. This means 7.5%
of PhD graduates in Science, Technology, Engineering and Mathematics
fields will not pursue academic careers in the USA.
4
The report is available from http://www.asee.org/papers-and-
publications/publications/college-profiles/2011-profile-engineering-
statistics.pdf [24 September 2012].
1.0 1.0
2.5 3.2
5.5 5.6 5.8 6.7 7.1 7.2 7.4
8.7 9.1 9.1 9.5 10.310.8
13.613.7
15.4
19.0
0
2
4
6
8
10
12
14
16
18
20
R0
R0 for Entire Field of Engineering = 7.8
Figure 1 R
0
estimation for different engineering fields (based on authors’calculation from the American Society of
Engineering Education report
4
)
RESEARCH NOTE Syst. Res.
Copyright © 2013 John Wiley & Sons, Ltd. Syst. Res. 31, 745–750 (2014)
DOI: 10.1002/sres.2210
748 Richard C. Larson et al.

POLICY INSIGHTS
By applying the concept of R
0
to academia, we have
offered a ‘birth rate’perspective on challenges that
current PhD graduates face in the academic job
market. Our back-of-the-envelope calculations
suggest that R
0
for the entire engineering field is
7.8, which implies that in a steady state, only 1/7.8
(i.e. 12.8%) of PhD graduates in engineering can at-
tain academic positions in the USA. The key insight
is that the system in many places is saturated, far
beyond capacity to absorb new PhDs in academia
at the rates that they are being produced. In fields
where PhD graduates are relatively more interested
in finding academic positions, a high R
0
leads to
more competition amongst job market applicants.
OneresultofahighR
0
and many doctorates with
an interest in academic careers is significant growth
in postdoctoral appointments (e.g. see Federation of
American Societies for Experimental Biology, 2012;
Ghaffarzadegan et al., 2013).
High PhD reproduction in academia follows a
similar reinforcing feedback loop (Sterman, 2000;
Richardson, 2011) that creates population growth
in demography: more faculty members produce
more PhD graduates, some of whom become
new faculty members. The mechanism may
work stronger as an unintended consequence
of ramped up government funding on the
research enterprise (Teitelbaum, 2008; Gomez
et al., 2012; Larson et al., 2012). We see that it
can also affect the higher education enterprise,
exacerbate job market challenges and cause
more unemployment and underemployment of
PhD graduates.
In demography, any living population eventu-
ally meets a ceiling of limited resources. Similarly
in academia, the growing PhD population will
eventually hit the natural ceiling of limited
tenure-track positions. In some fields, it already
has hit that limit. The physics of the system
requires that the oversupply must move to non-
academic positions or be underemployed in
careers that require lesser degrees. Simply
increasing the number of faculty slots will not
solve the problem. More openings will increase
the numbers of professors, and given their high
‘birth rates,’the number of future PhD graduates.
It is a positive feedback loop.
Our results may appear to be at odds with the
national consensus of a current Science, Technol-
ogy, Engineering and Mathematics (STEM) crisis
in the USA. We admit that there is a great
demand for STEM graduates by American
employers and yet many new STEM PhDs
remain underemployed (Gomez et al., 2012). The
matching of graduates to STEM careers varies
markedly by degree level and specialization.
Our analysis has shown that there are more
STEM PhDs than the academic market can
absorb, while the number of young people with
lesser STEM credentials falls significantly short
of market demand. At the education enterprise
level, more focus on undergraduate and Masters’
level graduates can help ameliorate the STEM
workforce supply–demand imbalance.
Given the national need for continued strong
doctoral level research, an engineering design
puzzle persists: How to design the academic
research enterprise so as to perform the research
effectively while at the same time reducing the
‘PhD birth rate’of professors. It may mean that
we must accept continued growing use of post-
docs and other PhD-level researchers who will
never become tenure-track faculty members.
But, if this is true, we owe it to these young peo-
ple, before they embark on a doctoral path, to
manage appropriately their career expectations.
ACKNOWLEDGEMENTS
The National Institute of General Medical Sciences
of the National Institutes of Health supported this
work (Grant 5U01GM094141-02). The grant,
‘Developing a Scientific Workforce Analysis and
Modeling Framework,’was awarded to the Ohio
State University and the MIT. The discussion and
conclusions in this paper are those of the authors
and do not necessarily represent the views of the
National Institutes of Health, the Ohio State
University or MIT.
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0
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