Lifelong Employment Commitments in Academia
Kalyan Chatterjee
Robert C. Marshall
Department of Economics
Department of Economics
The Pennsylvania State University,
The Pennsylvania State University,
University Park, Pa. 16802, USA
University Park, Pa. 16802, USA.
kchatterjee@psu.edu
rmarshall@psu.edu
May 17, 2005
Abstract
Lifelong employment commitments are a relatively uncommon employment
contract. We …nd that three factors can explain their existence in academia –
(i) non-contractibility of output, (ii) discipline-speci…c investment by a faculty
member that enhances the chance of high output within the profession but that
also signi…cantly diminishes the faculty member’s outside-occupation alternatives and (iii) imperfect competition for a faculty member’s services within the
specialty. Severance contracts are permitted in the model but will never be
o¤ered in equilibrium by universities. Lifelong employment commitments arise
as the unique subgame perfect contract.
Acknowledgments. We thank Jordan Kurland of the AAUP as well as William Kovacic, General
Counsel of the Federal Trade Commision, for helpful discussions. Professor Chatterjee thanks the
American Philosophical Society for a sabbatical fellowship that provided …nancial support for this
work and Churchill College, Cambridge for hosting him as an Overseas Fellow during the sabbatical
period. We also thank the audiences at the various seminars where this paper has been presented
for useful comments.
1
1
Introduction
The employment contract in academia in the US is not typical of private sector employment in this country on at least two counts, namely the presence of “up or out"
reviews and the provision of lifetime tenure for those who pass the appropriate review. These two features need to be distinguished from each other. A newly hired
tenure-track assistant professor will be evaluated for tenure after a probationary period of …xed length. The review process has an "up or out" character to it. Of
course, dismissal is the "out" part of "up or out". However, di¤erent kinds of promotion are possible if the review process determined that "up" was appropriate, even
within the broad framework of such contracts. Tenure, which is a lifelong employment commitment, is one possibility. Other kinds are conceivable. For example, the
university could commit to lifelong future employment subject to a provision speci…ed
at the time of promotion whereby the university could dismiss the professor with a
pre-speci…ed severance payment. Or, the university could o¤er a commitment for a
pre-speci…ed time period and review the professor again at a later date to see if future
incremental employment commitments were warranted.
In this paper we do not seek to explain the …xed length of the probationary
period nor the "up or out" character of the review process. We take these as given.
Rather, our focus is on the lifelong employment commitment component of the tenure
contract. Our aim here is to explain why universities give up the right to dismiss
faculty after the probationary period.
Guaranteed lifetime employment is a comparatively rare form of employment relationship anywhere in the world.1 However, tenure is the rule rather than the ex1
Federal judges in the US and civil servants in several countries are appointed for life, presumably
so that they can pursue their duties without being afraid of popular opinion or the displeasure of
their elected superiors. In the private sector, one of the few examples of such a practice, though
not enshrined in a formal contract, is the famous Japanese system of lifetime employment, which
started in the mid-1950s. Only the larger Japanese companies follow this practice and it is coming
under severe pressure in a long recession. However, Hashimoto and Raisian (1985) show that the
system leads to signi…cantly longer associations with a given …rm than is the case, for example, in
the United States, where such lifetime employment is and was far from being guaranteed, though
sometimes expected.
It has been pointed out to us that public school teachers have tenure and it is very di¢ cult to
dismiss employees in many settings, even though they do not have formal tenure. We don’t wish to
claim that our model explains all labour practices and what individuals choose to negotiate away
in collective bargaining, but it does seem puzzling that of two individuals who did the identical
graduate degree, the one who works for, say Dupont, does not have tenure, while someone who
works at a university does. It is certainly puzzling to the person from Dupont.
2
ception for senior university professors in the United States- as of 1972, 94% of all
U.S. faculty served in institutions of higher learning that o¤ered tenure.2 . Of course,
a lifelong employment commitment does not imply that "anything goes" in terms of
the behavior and performance of the tenured professor. The American Association
of University Professors (AAUP) Policy Documents and Reports provides much of
the implicit de…nition of tenure.3 Though large salary cuts directed at individuals
are not mentioned in these documents, there is little doubt that such cuts constitute
e¤ective dismissal and, therefore, individual faculty are protected against these by
the institution of tenure.
Why is tenure such a common employment contract in universities? “Academic
freedom”is a common motivation o¤ered for lifelong employment commitments.4 One
interpretation of “academic freedom”is the "unencumbered right to pursue truth, no
matter how o¤ensive the question or potential answer may be to university administrators, students, alumni, trustees, state legislators, or signi…cant donors". Other
interpretations have to do with the right of academics to manage their own a¤airs.5
General freedom of speech is often considered part of academic freedom. But, how
convincing is the argument that academic freedom makes lifelong employment commitments necessary?
Suppose in the absence of lifelong employment commitments that any terminated
professor could quickly …nd comparable employment with comparable compensation,
that is, the market for the academic’s occupation6 was “thick”. Would the pursuit of
2
See Rosovsky, 1990, page 178, footnote 3.
Tenure is partly de…ned by the “1940 Statement on Academic Freedom and Tenure: with
1970 Interpretative Comments” as written and enforced by the American Association of University
Professors (AAUP). Tenure is also partly de…ned by the investigations of the AAUP when allegations
of violations arise as well as the consequent possible censures of academic administrations by the
AAUP (see Kurland 1980). The only legitimate grounds for termination of a tenured professor are
(i) gross neglect of duty, (ii) physical or mental incapacity, (iii) a serious moral lapse, or (iv) grave
institutional …nancial exigency (see Rosovsky (1990) page 178).
4
Whilst academic freedom is certainly a strong reason for tenure, it is not the whole story,
otherwise tenure should be granted to …xed-term instructors and assistant professors as well, since
their academic freedom is as worth protecting as that of more senior people.(Chait (2003) quotes a
book by Byrne (1997) on how such academic freedom can exist without tenure.)
Academic freedom is of course also important in public schools.
5
This interpretation goes back, according to Metzger (1955), to the University of Paris in the
13th century and its e¤orts to eliminate the right of its chancellor, a priest in Notre Dame, to issue
or to revoke licences for giving “ordinary lectures”.
6
We interpret “occupation” somewhat narrowly as …eld of specialization, since the thinness of
the market is a crucial component of our model. The quote below from Russell (1994-p.25) is a nice
description of the interaction between thinness of the market and specialization; the “occupation”
3
3
truth be substantially advanced by a commitment to lifelong employment? In other
words, if a donor to university A did not approve of Professor X’s work, but the
work was of high quality, surely there would exist another university in this thick
labor market that would be willing to employ Professor X in an e¤ort to enhance its
own scholarly reputation, if we agree for the moment that universities are concerned
primarily with such reputation.
Alternatively, suppose also that there was an infallible group of professional judges
for each and every discipline who could provide an accurate public measure of the
output of each professor within that discipline. Then contracts could be written that
conditioned upon output realizations. University administrators would be unable to
claim that high output was actually low since output would be veri…able.
Even if the outside opportunities of a professor deteriorated signi…cantly over
time, with veri…able output employment contracts could be written to condition on
the productivity of each and every faculty member. Similarly, in the absence of
veri…able output, if outside opportunities for any professor did not deteriorate with
time then a lifelong commitment of employment would provide no advantage to either
the employee or employer –the labor market outside of academia for the individual
would overcome the issue of non-veri…ability of output.
A book called "Academic Freedom" by the British historian Conrad Russell addresses the …rst point about the "thickness" of the market. As the Social Democratic
Party spokesman on education in the British House of Lords, Russell had to counter
arguments by supporters of the Conservative Prime Minister Margaret Thatcher (who
succeeded in weakening tenure in Britain in the 1980s) that market forces in the academic labour market would take care of egregious abuse by university administrators
and pressures that might lead to lower academic quality. Russell challenges the thickreferred to here is sixteenth-century German women’s history and not history in general.
(From Russell, p. 25).
Someone who has managed a steel works may, if dismissed, apply to manage a
telephone company. Whenever this absence of rigidity does not apply, the labour
market ceases to work e¤ectively.
These assumptions do not work in an academic context, because of the exceptionally
specialized nature of the knowledge involved. A historian who is dismissed cannot
simply apply for the next vacancy for a historian. He will not have the necessary
knowledge or the necessary skills..... A specialist in sixteenth-century German women’s
history will need to wait for the next job in sixteenth-century German women’s history,
and this may be an unconscionably long time coming.
4
ness of the market in the following quote (p. 26):
“A dismissed academic’s chances of re-employment in his own profession may often be so small as to be negligible. If he has invested 30
years of his life in acquiring skill in, for example, Egyptology, he has a
skill which is not marketable because no market in the subject exists. This
means that the likelihood that those dismissed from jobs in such subjects
will be deprived, not only of their jobs, but of their professions, must be
regarded as very high indeed. .... It is unwise to enter into so risky an
employment without being guaranteed some economic security in return.
Otherwise the bargain is too disadvantageous to the academic.” (Russell,
p. 26)
The passage above also mentions risk and the e¤ects of specialisation on the thickness of the market for an academic’s skills. Our paper will not need risk aversion to
obtain our result, but our model will have features corresponding to the other two
points mentioned by Russell. However, Russell does not mention contracts, presumably because he takes for granted the fact that a contingent, enforceable contract is
impossible to write.
Is output that di¢ cult to measure in academia?7 Perhaps it is not so di¢ cult
to accurately measure research productivity within one’s own sub…eld.8 But even
within a discipline it is not uncommon for professors in di¤erent sub…elds from that
of the professor under review to defer to colleagues in the sub…eld. In light of this
common occurrence it is clear that professors in completely di¤erent disciplines have
a great deal of di¢ culty in assessing the aggregate quality of another professor’s work.
This is true for university administrators as well, let alone third parties outside the
university. Teaching is even more di¢ cult to assess. Standard end-of-semester teaching evaluations will catch outliers on each side but provide little other information
7
“The performance of the activities of academic workers –teaching and scholarship –is certainly
hard to measure. These activities do not produce concrete, measurable products of easily discernible
quality; neither their output nor their inputs are easily observable or measurable.”(McPherson and
Winston, p. 111)
8
Research productivity depends on originality and the impact of the work concerned; impact
is typically not known until some time after the work is out and opinions often di¤er about the
originality of a contribution or the novelty of a paper. Of course, there often is a broad consensus
within a sub…eld about these things, but it would hardly stand up in court. We know of a case
(not a university either of us has been associated with), where administrators attempted to write
contracts on quality-weighted number of journal pages per author, but the scheme foundered on the
fact that journals do not have pages with the same number of words.
5
beyond the perceived popularity of the professor. Other aspects, such as the externalities provided by good colleagues, are even harder to measure. However, we need
only a weaker assumption in this paper, namely that output is not veri…able.9 Under
this assumption10 , we construct a model where universities compete for faculty but
the competition is imperfect, that is, markets are thin. Our primary result is the
emergence of lifelong employment commitments, over other alternatives, in equilibrium. Note that in our model, risk-neutrality is assumed throughout, so this is not
an insurance explanation.
In contrast to previous papers concerning features of tenure (discussed in the next
section), our model considers: (1) investment by faculty that is discipline speci…c (i.e.
not university speci…c); (2) explicit competition for “superstar” faculty; (3) tenure,
rather than promotion, in the sense that we do not concentrate on the “up-or-out”
aspect, which tenure shares, for example, with partnership arrangements in law …rms,
but focus instead on the commitment by the university not to terminate a faculty
member’s employment.
Before describing our model, it is perhaps best to clarify a few crucial features
of the model. Our paper is not about screening, though screening does occur in the
model. Only those faculty members who have produced high output in the probationary period are eligible for the award of tenure; others are screened out. However,
the initial probationary period is common to all up-or-out contracts and cannot be
the distinguishing feature of a model seeking to explain a commitment to lifelong
employment. We therefore concentrate on why tenure is necessary after the initial
probationary period, rather than a contract that promotes the high output faculty
member without giving him or her tenure (that is, leaving that person open to being
dismissed at the time of a future review). Our explanation for tenure has to do with
occupation (specialization)-speci…c (not university-speci…c) investments; we do not
focus on the …rst up-or-out decision, even though we certainly do not regard this as
irrelevant. It is often the case that such investment takes place during one’s graduate
school days and the faculty member realises the returns from this investment in the
9
Di¤erent aspects of academic output could be measurable to di¤erent levels; Baker, Gibbons and
Murphy (1994) show how writing contracts on the enforceable parts can lead to worse consequences
than no contract at all.
10
We assume that occupation-speci…c investment, which plays a major role in our story, is not
observable by the employer. In an earlier version, we had considered the case where it is observable
but not contractible, like output.
6
initial screening period before tenure. Additional human capital investment is often
necessary in the second phase of one’s career and we focus on this. This does not
mean that no one undertakes such investment in the screening period, just that we
do not focus on the screening period in this paper.
Two other points have been raised in comments about our basic assumptions.
First, even if one cannot verify output, one can write contracts on what one can verify (such as messages in the critiques of the Grossman-Hart-Moore model). Clearly,
writing contracts on quality-weighted journal pages published or teaching evaluations
can do more harm than good, as the previously cited paper by Baker, Gibbons and
Murphy points out. As to the general foundations of incomplete contracts, we have
nothing to add. We assume that the message games of implementation theory cannot
be used in academic employment contracts (an assumption that seems quite reasonable, based on casual empirical observation). Second, some colleagues have queried
the imperfectness of competition. Why doesn’t the supply of Egyptologists adjust
so that there are so few of them that one always gets snapped up when she is available? To some extent this has occurred in several academic …elds and sub…elds. But
people’s academic careers don’t start and end at exactly the same time and there
are frictions in the market-a job is not available exactly when one wants it. In our
model, there are two universities and two faculty members. Moreover, a university
can always “…ll in” by hiring from industry. So there is no overall excess supply of
academics. However, perceived quality di¤erences arise because of market outcomes
caused by heterogeneities in ability, and there might well be imbalances in supply
and demand given these realised output di¤erences. 11
This paper does not consider the aspects of academic freedom that have to do
with faculty governance and with freedom of speech. Once again, Russell’s book is
an excellent summary of the arguments for special provision for academics to guard
against attacks on these freedoms and the importance of these arguments is clear .12
In what has been described thus far, university administrators have been implicitly
assumed to be operating without their own incentive constraints. In fact, university
11
Surely it would be proving too much to argue that the market for the Kenneth Arrows and
Roger Penroses of our world adjusts dynamically to make supply equal to demand!
12
As a counter-example to the contention that academics do not need special protection in a
democratic society, Russell mentions his father, Bertrand Russell, one of the foremost intellectual
…gures of the twentieth century, who lost his college lecturership at Trinity College, Cambridge for
opposing British policy in the 1914-18 war, and whose appointment to teach logic in City College,
New York, was revoked in 1941 for his views on “Marriage and Morals”.
7
administrators, like any agents, are not social planners. Academic administrators
are concerned with the success of their university, and this can be inconsistent with
what is best from the perspective of advancing knowledge in each of the academic
disciplines. In this context, we show that tenure is not the preferred contract by
university administrators, as a consequence of this kind of agency problem, while if
this problem does not exist both employer and employee prefer tenure.
The paper proceeds as follows. We review the literature on tenure and up-or-out
contracts in Section 2. The model is presented in Section 3. Sections 4 through 7
contain the heart of the analysis and the results. We then provide a brief discussion
of the incentives of university administrators in Section 8. An early disclaimer: we
have tried to formulate the simplest model we can to demonstrate our point, without
striving for generality as far as technical assumptions are concerned. However, the
model still might not be considered simple, in that there are still many aspects that
require some care. We apologise if the working out of the intuition in a model does
not have the same degree of simplicity as the intuition itself.
2
Background and Previous Literature13
The Ross case at Stanford in 1900 is an important historical case often o¤ered to
illustrate the need for protecting academic freedom.14 Ross, an economist, expressed
some viewpoints that were contrary to the interests of the railroad industry. Stanford
was founded by a railroad baron and his surviving daughter took o¤ence at the
statements of Ross. Exerting great pressure on the President of Stanford University,
she eventually secured Ross’s dismissal. The Ross dismissal was critical because it
prompted a young philosophy professor at Stanford, Arthur Lovejoy, to resign. After
establishing a distinguished scholarly reputation over the ensuing 12 years, Lovejoy
was the prime instigator for the creation of the AAUP.
The AAUP founding members published the “General Declaration of Principles”
in the inaugural edition of the AAUP Bulletin (1915, pages 20-43). This is a remark13
The AAUP maintains two large …les of actual correspondence concerning the tenure debate
for the period 1915 to 1940. In addition, the AAUP maintains a historical library regarding the
evolution of tenure. We are grateful to Jordan Kurland of the AAUP for granting us access to these
…les and records.
14
In several articles, Metzger [1955, 1973, 1990] has provided a remarkably comprehensive history
of the evolution and development of tenure in American universities and readers who are interested
should consult these references.
8
able document in terms of its scope and clarity. The authors note that the impetus
for the creation of the AAUP, and the push for a uniform tenure contract, originated
with the unjust dismissal of several social scientists in the early part of the twentieth century (i.e. economists who were unjustly dismissed included Ross at Stanford,
Fisher at Wesleyan, and Nearing at Penn, see Pollitt and Kurland (1998)).
If a tenured professor is dismissed for cause other than moral turpitude15 , then the
1940 Statement provides for a severance payment of one year’s salary. This may give
the appearance that severance payments are part of the tenure contract. However,
this severance payment is not speci…ed as one which a university administrator can
activate, at their discretion, as part of the unilateral dismissal of an annoying member
of the faculty. In practice, the severance payment is only paid if a faculty member
cannot perform their duties, mentally and/or physically, or if the university closes the
tenure-home department of the faculty member for reasons of …nancial exigency. Note
that, per the “1940 Statement”, the conditions under which this severance payment
would be activated have nothing to do with deliberate actions of the tenured faculty
member. If a university administrator dismissed a tenured faculty member without
cause and o¤ered an unacceptable severance payment16 then both the university
and the administrator would almost surely be censured by the AAUP. Given the
importance of faculty committees in appointing university administrators, as well
as the public nature of an AAUP censure, it would be very costly in terms of an
administrator’s future career to engage in such behavior.
Tenure has little meaning if the administration can dramatically lower annual
salaries. Although some downward adjustments are legally possible with tenure it
is typically the case that a faculty members current nominal salary is viewed as the
minimum for all future years.17
Several papers have been written on tenure and/or up-or-out employment rules.
Kahn and Huberman (1988) …nd that up-or-out employment rules are a useful commitment device for employers. Employees can signi…cantly enhance productivity if
they make investments. A …rm can provide an incentive for the worker to make the
15
The “1970 Interpretative Comments” of the “1940 Statement” de…ne moral turpitude as “behavior that would evoke condemnation by the academic community generally”. An example would
be the explicit quid pro quo by a tenured faculty member of money or sex for grades.
16
Such cases typically result in civil litigation. Although there is substantial variance, the “typical”
out-of-court settlement is two years salary.
17
The “base” salary excludes summer months and administrative supplements. If these are included in compensation then salary will ‡uctuate much more.
9
investment by rewarding high output. However, without an up-or-out employment
contract a university would have an incentive to claim that a high output faculty
member is actually a low output one and then reduce, or not increase, the compensation of the professor. Correctly predicting this node, faculty would have diminished
incentives to invest, which is not in the long run interests of the university. An up-orout contract prevents the misrepresentation of output by the university since it would
have to terminate anyone who it claims to have realized low output. In other words,
an up-or-out contract is an important commitment device used by the university.
However, this motivation for tenure ignores the competition between universities for
professors, something that we explicitly model. Claiming that a high output professor
has produced low output is a formula for losing the professor to another institution,
unless of course the investment was institution-speci…c.
Waldman (1990) extends the work of Kahn and Huberman (1988) by allowing for
general human capital accumulation. Waldman’s analysis provides an explanation
for some of the commonly observed features of the wage path for academics.
Carmichael (1988) notes that tenure is an important commitment device for the
faculty of an academic department in terms of hiring decisions. Incumbent faculty,
who are the only ones quali…ed within the university to assess the quality of junior
or senior job applicants, will select the very best people from the pool provided that
there is no threat that the newly hired faculty will displace them. Tenure provides
the incumbent faculty with this insurance. It is not clear why this reasoning does not
apply in …elds outside academics as well. Also, we can …nd no discussions in the historical documents that either university administrators or professors were concerned
about this particular kind of inappropriate decision making by incumbent faculty.
A common thread exists in the papers of Demougin and Siow (1994) and O’Flaherty
and Siow (1992, 1995). Workers live for two periods. In every period there is a senior
experienced manager in each division of a company who manages an unskilled worker.
Because of the costs associated with hiring senior division managers from the outside
it is desirable to promote junior unskilled labor from within, provided they demonstrate themselves to be productive workers in the …rst period. An unskilled worker
who has not demonstrated su¢ cient productivity to become a division manager may
still be pro…table to retain as an employee in the second period, but then the …rm
forfeits the opportunity to review another junior person who might demonstrate suf…cient productivity to become a manager. In fact, the …rm wants to keep looking for
10
possible division managers, given the costs of hiring them from the outside. So, the
best contract is one that terminates junior people who demonstrate low productivity.
This is an up-or-out rule.
Finally, in the unpublished manuscript of Ito and Kahn (1986), risk-averse workers
are o¤ered a wage ‡oor and job security in order to curb disincentives for risky
speci…c human capital investments. This is similar in spirit to the Russell quote at
the beginning of our paper, but it does not address the basic question of why there
should be risk with su¢ cient market alternatives.
We turn now to the speci…cs of the model.
3
The Model
We consider the following model. There are two universities and two professors who
are each initially employed at separate universities, and a non-strategic entity called
"industry" from which replacement instructors can be hired and where professors can
seek alternate employment. In period zero each university …rst announces the type
of employment contract to be used, in this case either tenure after a probationary
period, severance or …xed-term (see the end of this section for details about these).
Each university has one slot (position), but can create an additional one at a small
cost. The universities each initially hires one professor; since professors are assumed
to be ex ante identical suppose this is done by random matching. Each professor
is either of high or low ability. The ability type of the professor is unknown to
each professor as well as the universities (no private information). At the end of
period zero an output realization occurs for each professor of success or failure. Only
successful professors are assumed to continue to period one. We focus attention on
the interesting case of each professor having successful output at the end of period
zero and surviving to period one. Outputs in all periods are observable, but not
contractible. This is a crucial feature of the model and follows the Grossman and
Hart (1986) and Hart and Moore (1990) framework for the …rm18
After the output realisations in period [0,1), the universities simultaneously o¤er
the terms of the contract, wage, pre-speci…ed severance if applicable and so on and
18
In fact, Hart (1995, p.38) mentions the university tenure decision as an example where performance could be observable but not veri…able in court.
11
the professor accepts or rejects.19 These are all publicly observable.At the beginning
of period one each professor, if he has accepted the o¤er made, makes a decision about
the magnitude of the discipline-speci…c investment he wishes to make. The magnitude
of each professor’s investment is observable only to the professor. Investment is costly
(with costs being strictly convex in amount of investment). Investment can only be
made at the beginning of period one – there is no investment allowed in period
zero or two. Investment positively in‡uences the chances of successful output for
high ability professors during both periods one and two. Investment has no impact
on the chance of success for low ability professors. Discipline-speci…c investment
is presumed to reduce the outside option that a professor has in industry.20 Each
faculty member is interested in maximizing his or her total expected wages less the
cost of any occupation-speci…c investment. All players are assumed risk-neutral and
interested in the sum of bene…ts minus costs over the periods of play.
At the beginning of period 2, after observing the output realizations the
following game takes place: university21 U1 moves …rst and makes a bid on professor
M2 or passes. U2 follows, makes a bid on M1 or passes. U1 then responds with a
counter-o¤er for its own employee or termination (if there is no tenure), followed by U2
for M2 . Each university can be silent at any stage. If both universities are silent in a
given stage, the last o¤ered salaries are binding and the employees accept or reject the
o¤er.22 If an employee does not accept either of the o¤ers or is terminated, he or she
goes into industry. If an employer is without an employee, she will hire an individual
from the outside market:If an employee is not bid for by the other university and
the one period contract has expired, he or she solicits an o¤er from industry. Then
industry conducts an interview of the professor using a technology that reveals to
industry the magnitude of the deterioration in the industry-speci…c productivity of
19
The terms are o¤ered after the contract; thus each university can react to the other’s choice of
contract
20
“The Report of Committee A on Academic Freedom and Academic Tenure”, AAUP Bulletin,
1918, notes the following. “It should be remembered, too, that the College or University professor
is a specialist. The market for his services is limited. In any one year, or series of years even, there
may be no positions available in which his special training and interests could be utilized.”
21
See below for notation.
22
If the wage o¤er to one’s own employee comes before the auction, we could potentially get a
continuum of subgame equilibria in certain cases (though they could be o¤ the equilibrium path in the
whole game). For example, if both employees have low realisations and have identical investments,
suppose U1 o¤ers its employee M1 a salary w strictly larger than M10 s industry outside option. In
simultaneous play U2 must also o¤er w to M2 ; otherwise U1 will bid for M2 . We thank Debraj Ray
for pointing out this possible di¢ culty in this alternative form of the game.
12
the professor (and thus the magnitude of the discipline-speci…c investment made in
period one). The employee shows the o¤er from industry to the current employer who
might choose to terminate or make a wage o¤er. The employee then either accepts
or rejects the wage o¤ered. If the wage o¤er is rejected, the employee gets his outside
option in industry and the employer obtains someone from industry. The more the
academic investment, the less the investment in the industry outside option and this
is re‡ected in a lower o¤er from industry. If the faculty member has tenure, then
she gets a predetermined guaranteed wage in the absence of a bid. If a severance
contract is in place, the university decides whether or not to activate the severance
clause and, if it is activated, the faculty member leaves and goes to industry and
the university hires someone from industry to …ll the slot. Any time the university
jettisons an incumbent professor it can hire someone from industry to "…ll in". If
output for one faculty member is a success while the output for another is a failure
then the university employing the latter professor will bid for the services of the
former professor23 –it is assumed that each university is interested in maximizing the
average net expected surplus per slot, where the net surplus is de…ned as the expected
output of the faculty member …lling the slot less the salary paid to this person.24
Some notation. There are two universities, labelled U1 and U2 ; and two members
of faculty, M1 and M2 : Mi could be a “high (H)”type, with initial probability o ; and
thereby produce a "success", i.e. valuable output (S) in each period with probability
pH and a failure (F) with complementary probability. A “low (L)” type produces a
success with probability pL and a failure with complementary probability. We assume
that pH > pL : If there is investment in one’s specialty of level i in period one (the
only period in which investment can occur), then the probability of success of the H
0
type in each of periods (1,2] and (2,3] becomes (permanently) pH = pH + i(1 pH ):
The value of pL is una¤ected. Investment i occurs at a cost c(i); where i 2 [0; 1]; c( ) is
strictly convex and at least twice continuously di¤erentiable with c0 (i) ! 1 as i ! 1
23
Each university has one slot (position), but can create an additional one at a small cost.
“By far the most dependable indicator of university status is the faculty’s degree of excellence
that determines everything else; a good faculty will attract good students, grants, alumni and
public support, and national and international recognition. The most e¤ective method to maintain
or increase reputation is to improve faculty quality. ... The move of a professorial superstar from one
institution to another can result in instant recognition.”[Rosovsky pages 229-231]. This well known
fact is the justi…cation for our objective of maximizing average payo¤. This objective, within our
model, implies that bidding will occur for only the highest achievers and those with most potential
for success.
24
13
and c0 (i) ! 0 as i ! 0: "Industry" o¤ers a per period bene…t of to an employee; this
is a faculty member’s outside option prior to investment. After investment the faculty
member’s outside option is (1 i):25 A success is assumed to have a value v = 1: A
failure has value v = 0: At t = 1; Ui o¤ers a contract to Mk :Three possible contracts26
can be o¤ered namely, (1) a one-period contract up for renewal or termination at
t = 2; with a wage speci…ed for the period (1,2] of w1 ; (2) a severance contract,
which will specify an amount sev that the university will pay the faculty member if
it chooses to terminate him or her at t = 2; and a wage w2sev to be paid if the faculty
member is retained up to t = 3 and (3) a tenure contract, where the university gives
up its right to terminate employment at t = 2 and speci…es a wage w2T that it will
guarantee the faculty member in the period (2,3]. If a subscript ’b’appears on any
wage it indicates that the wage is the result of bidding between the two universities for
the services of the professor.The quantity tk is the posterior probability of professor
k being a high ability type after a sequence of failures and successes in the previous
periods prior to t and after having made investment ik in period 1 if t 2.
3.1
Possible contracts
In general, the contract o¤ered at time 1 could be of the following general form:
(w1 ; d2 ; w2 (y1 ; y2 ; w1 ); s); where
w1 = wage paid in the …rst period i.e (1,2],
d2 = 0 or 1 if the employee is …red or retained as a function of output in the …rst
period,
25
This formulation is, of course, a simpli…cation. An alternative formulation is as follows. Let
represent investment in “industry”and let ( ) be a strictly concave, increasing, twice di¤erentiable
function of : Let the cost of investment be given by the strictly convex, twice di¤erentiable function
c(:) of investment. In industry, an employee will choose to maximize ( ) c( ): Let the maximizing
be
and the value of ( ) be (with some abuse of notation).
In academics, the payo¤ to investment in the spot market setting, which will be explicitly stated
later in the paper, is of the form
pY (i) + (1 p) ( ) c(i + ) where i is the investment in academics and Y (:); the expected
second-period payo¤ given the choices of the other player, is linear in i: (The linearity follows from
the assumptions made later in the paper.)
It is clear that if (1 p) 0 ( ) starts o¤ higher than pY 0 (i) but crosses it at some value A where
(1 p) ( A ) > c0 ( A ); then there will be some investment in industry and some in academics in the
spot market by the university employee. It is also clear that A < ; so that the value of ( A )
is less than : Therefore the possible investment in the academic option has decreased the outside
option in industry.
We work with the simpler formulation in the rest of the paper.
26
See the net subsection for a short discussion of possible contracts.
14
w2 (y1 ; y2 ; w1 ) = the wage paid in the second period conditional on the outputs y1
and y2 in the …rst period,
s = severance paid if dismissal, which could depend on the outputs as well.
The contract cannot condition on unobservable investment. The assumptions we
have made about non-veri…ability of output imply that none of the items listed above
can depend explicitly on the values of …rst period outputs either. Therefore, the
choice of dismissal or retention must be discretionary rather than contractual. The
contract can specify a wage in the second period, independent of outcome in the
…rst and specify that the university will match alternative o¤ers on a discretionary
basis. The …rst-period wage can be included in the contract, of course, and is chosen
optimally to satisfy the two-period individual rationality constraint of the professor.
We note that the university is committed to whatever contract is o¤ered and
accepted. So if the university gives up its discretion to dismiss a faculty member
and speci…es a minimal wage w2 ; this can be enforced because it is veri…able. No
issue of commitment arises with enforceable contracts because they are assumed to
be enforceable.
4
Analysis of the "Fixed Term" Contract
At many universities, there is a contract o¤ered to instructors who are neither tenured
nor tenure-track called a "Fixed Term" contract. The contract speci…es a period of
time for employment. It speci…es a wage. The contract can be renewed. This kind
of contract is increasingly common at U.S. universities. We begin our analysis with
the "Fixed Term" contract, where each university hires someone just for (1,2] and
discuss employer actions at the start of period 2. At that time, the investments, ik
are not observable by the universities. However, each employer has a belief about
the investments made by the individual faculty members. Let us assume that these
beliefs are symmetric, in the sense that the conjectures about ik ;which we denote by
ibk ; are point conjectures and are the same for k = 1; 2:27 In this case, the di¤erence
in expected output between the two faculty members is a function of the output
realisations in the preceding period (1,2]. If the conjectured investments had been
27
Chatterjee and Marshall (2003)have observable investment and an asymmetric pure strategy
equilibrium where faculty members choose di¤erent investment levels. It seems more natural to
have players who are perceived to be identical and without any private information about types to
take the same actions, as they do in this paper.
15
di¤erent, the di¤erence in expected outputs would have depended on 2k ; where this
represents the probability that Mk is a H type, given output in (1,2], and on ibk :
However, if the investments are believed to be the same, only the previous period’s
outputs matter.
Thus, if each faculty member has an S realization in period (1,2], an outcome we
denote by SS; or if the realisation is F F; the expected outputs are the same for the two
individuals and there is no bidding for the faculty members among the universities.28
In this case, the wages ultimately paid by the university will re‡ect the industry
outside option of (1 ik ), if a faculty member is retained. If a faculty employee is
not retained, the university employer hires someone from industry, whose probability
of being a H type is at most 0 : The expected output from this person (with zero
investment) is therefore Y0 = 0 (pH ) + (1
0 )pL :From the existing faculty member,
the expected output is Y1 (F ) = 2 (pH + i(1 pH )) + (1
2 )pL : Clearly, if Mk has
had two successes, the expected surplus from retaining the current employee is higher
than hiring outside, and the termination option will not be exercised. However, the
payo¤ to the employee Mk will be (1 i): If Mk has had a failure realisation in
period (1,2] then,
2k (S; F; ik )
=
0 pH (1
0 pH (1 ik )(1 pH )
:
ik )(1 pH )+(1 0 )pL (1 pL )
It could be worthwhile, if ik is very high, for the university Uk to terminate the
faculty member with a F realisation. This is because a high investment increases the
information content of a F realisation. However, Mk0 s payo¤ is una¤ected because
whether he is terminated or not, his payo¤ will remain (1 ik ), since the employer
makes the last o¤er and will therefore get all the surplus in the case of retention.
There is no bidding in these cases because the average payo¤ per slot for any university cannot increase by creating an additional slot and attempting to raid the other
university’s faculty member.
The auction therefore takes place when one of the faculty members has a F realisation and the other one has a S: Suppose Player M1 has a S: Let Yk be the expected
output of Player Mk in the last period, of course given the beliefs on investments.
Then Player M1 has a payo¤ from the bidding of Y1 Y2 + (1 bi2 ): Note that at the
28
This might seem odd — two successful faculty members are unable to obtain the bene…ts of
their success, because neither has a relative advantage. Introducing more universities and more
faculty members would increase the probability of at least one F realisation and hence some chance
of bidding for the successful ones.
16
time of bidding, the university uses the conjectured value of investment rather than
the actual value.
We also note that, in case U2 believes it will be optimal to dismiss M2 (because
a F realisation could be very informative if the investment were really bi2 ), the terms
Y2 + (1 bi2 ) above will be replaced by Y0 + : However, this will have no e¤ect
on Player Mk0 s investment decision in the period (1,2].
We summarise these observations in the following proposition.
Proposition 1 Consider the Fixed Term market in period 2 with employer beliefs
ib1 = ib2 : Then the wages o¤ered to the employees are as follows:
Realization in period (1,2] of S output by each of faculty members 1
and 2, denoted SS :
M1 obtains (1 i1 )
M2 obtains (1 i2 ):
Realization F F :
M1 obtains (1 i1 );
M2 obtains (1 i2 ):
Realization F S :
FT
FT
M1 gets (1 i1 ); M2 gets w2b
such that Y2 (S) w2b
= maxfY1 (F )
(1
ib1 ); Y0
g
(Realization SF can be analyzed in a similar way.).
4.1
Investment decisions by employees with Fixed Term market wages.
We now consider the occupation-speci…c investment undertaken by Mk in period (1,2].
This investment will not a¤ect the conjectures ibk ; however, it will a¤ect the output
in this period, and given the conjectured investments, the university’s belief that the
employee is of High type given the output realisation. The investment will a¤ect the
o¤er the employee is able to obtain from industry. Therefore, given i2 and ibk ; the
return that a given employee, say M1 ; is able to obtain from investment i1 is given
by R1F T below
R1F T (
11 ; i1 ; i2 )
FT
g+
= p1 (S)fp2 (S) (1 i1 ) + p2 (F )w2b
(1 p1 (S))( (1 i1 )) c(i1 )
17
(1)
Here pk (S) refers to the probability that Mk gets a success and pk (F ) the probability of a failure from Mk :
The next proposition characterizes this equilibrium.
Proposition 2 The Fixed Term market equilibrium investment level i satis…es:
(i) i1 = i2 = bik = i; k = 1; 2:
(ii)(First-order conditions)
(1
FT
p2 (S))(w2b
(1
p2 (S)(1
(1
i))
11 (1
pH )
(2)
p1 (S))
= c0 (iF T )
Proof. We rewrite (1) as follows;
FT
R1 = p1 (S)(p2 (S) 1) (1 i1 ) + p1 (S)(1 p2 (S))w2b
+ (1 i1 ) c(i1 ): (This
is just by using the fact that pk (S) + pk (F ) = 1:)
This is then the same as
FT
(1 i1 )) + (1 i1 ) c(i1 ):
p1 (S)(1 p2 (S))(w2b
We now di¤erentiate this with respect to i1 ; and set equal to 0. Note that the
FT
value of w2b
, the outcome of bidding, is set by the conjectured investments and is
not a¤ected by any di¤erence between the actual and conjectured investment.
The result is
FT
p1 (S) (1 p2 (S))
+ (1 p2 (S))(w2b
(1 i1 )) 11 (1 pH ) = c0 (i1 )
or, since p1 (S) = 11 [ph + i(1 ph )] + (1
11 )pL ;
FT
(1 p2 (S))(w2b
(1 i1 )) 11 (1 pH )
(1 p1 (S) (1 p2 (S))) = c0 (i1 );
as was to be shown. We denote the speci…c optimal value of i1 as iF T :
Part (i) of the proposition arises from the requirement that the conjectured investment must equal the real investment in equilibrium and that, given identical
conjectured investments, the expressions above are the same for di¤erent k and hence
the actual investments of the Mk must be the same.
The LHS of 2 is increasing in i; in fact the derivative with respect to i is (1
p2 (S)) 11 (1 pH ) + (1 p2 (S)) 11 (1 pH ):The RHS is also increasing because of
convexity. Since c0 (i) ! 1 as i ! 1; there must be an intersection below 1. Similarly,
as c0 (i) ! 0 as i ! 0; there must be an interior solution for i.
This is not yet a complete characterisation of equilibrium, because we have not
discussed the wage in (1,2]. This will turn out not to depend on the nature of the
18
contract and is therefore postponed until later.
5
Analysis of wage-severance contracts
We now consider the case where the universities both o¤er wage-severance contracts
at t = 1. There are two kinds of severance contract possible. We focus on one that
pre-speci…es a second-period wage of w2sev and a severance payment of sev with the
employer retaining the right to activate severance.29
A severance payment sev must satisfy the following feasibility condition for the
employer.
(Y0
)
(Yj
w2sev )
sev for some i
0
where Yj is the expected output of Mj in period two. In words, the surplus from
hiring from industry less the foregone surplus from dismissing the incumbent faculty
member must be at least as great as the severance payment.
We can write this as
0 (pH
pL ) + pL
2j (pH
or
(pH
pL )(
0
pL + bij (1
b
2j )- 2j ij (1
pH ))
pH )
(
pL
(
w2sev )
w2sev )
sev;
sev:
Clearly, the option of severance is only important if a player has a low output
realisation in (1,2]. In this case, given parameter values and given the conjectured
investment, it could be that the value of 2j is su¢ ciently low that activating severance
becomes optimal for the employer.30
For the employee to …nd severance acceptable ex post, it must be the case that
29
There is a second kind of severance contract where in the second period wage is not prespeci…ied.
Then the employer could always o¤er a wage of zero in period 2 and induce an employee to quit,
thus avoiding the payment s.
30
If severance is not activated, presumably the employee will not seek an industry outside option
and hence the true value of investment will not be available to the current employer, since the wage
is pre-speci…ed. If severance is activated, it has to be without this information.
19
w2sev
(1
i)
sev
Thus, we have
Yj ) + (w2sev
(Y0
)
sev
(w2sev
) + i:
Note that if Y0 < Yj then severance is infeasible.31 Namely, if the expected
output of an industry hire is strictly less than the expected output of an incumbent
faculty member who realizes a failure in the second period then there is no severance
payment that would be mutually agreeable to both the faculty member and the
university. In many disciplines it is di¢ cult to imagine how Y0 could be greater than
Yj . However, severance could be feasible. Ex ante acceptability to the employee
depends on the …rst-period wage and the probability of having the universities bid
for a high output realiser. The incentive e¤ects of a severance contract do not,
however, di¤er substantially from that of a Fixed Term market contract, if severance
is expected to be activated with a low realisation.
Given i2 and ibk ; the return that a given employee, say M1 ; is able to obtain from
investment i1 is given by R1 below
R1sev (
11 ; i1 ; i2 ; sev)
sev
= p1 (S)fp2 (S) w2sev + p2 (F )w2b
g+
(1 p1 (S))(sev + (1 i1 )) c(i1 )
(3)
The derivative of the objective function with respect to i1 yields
[(1
sev
p2 (S))(w2b
(1
i))
sev]
11 (1
pH )
(1
p2 (S))(1
p1 (S))
c0 (i) (4)
FT
Evaluation of this expression at the optimal i1 and the value of w2b
from the …rst
order condition in Proposition 2 yields a negative value for the derivative.32 Thus, the
optimal investment level with severance is lower than under the Fixed Term contract.
If the severance is never activated, so that w2 is always paid in the event of a low
realisation, the incentive e¤ects are similar to those for tenure, to be addresses in the
next section. However, the two di¤er if renegotiation were to occur. This will be
discussed in Section 7.
31
32
Of course, the condition is actually weaker. Namely, (Y0 Yj ) < i:
sev
FT
Since investment is lower with severance, it must be the case that w2b
< w2b
:
20
6
Lifelong Employment Commitments
We now consider lifelong employment commitments, consisting of a minimum secondperiod wage, w2T ; and a guaranteed job.33 We …rst consider the case when only one
of the universities o¤ers a tenured contract — suppose this is U1 while U2 o¤ers a
Fixed Term market contract as before.
The incentive to invest will now change; it will of course depend upon the level
at which w2T is set, as we will see. There will be additional e¤ects. In equilibrium,
the conjectured investments will equal the actual investments and the conjectured
T
investments will a¤ect the quantity w2b
: Also, an increase in investment by M1 will,
if foreseen correctly by M2 as must happen in equilibrium, increase p1 (S) and thus
reduce the amount that M2 invests. The return that a given employee, say M1 ; is
able to obtain from investment i1 is given by R1T below
R1T (
11 ; i1 ; i2 )
T
= p1 (S)fp2 (S)w2T + p2 (F )w2b
g+
T
(1 p1 (S))w2 c(i1 )
(5)
The new FOC is:
[(1
T
p2 (S))(w2b
w2T )]
11 (1
pH ) = c0 (iT )
(6)
Here iT is the amount invested in the tenure regime by M1 .(We adopt similar notation, iF T ;for the optimal investment under FT.) The assumption that the other
university still employs a Fixed Term contract does not a¤ect the form of the …rstT
and p2 (S):Comparing (6) to (2), we
order conditions. In equilibrium, it will a¤ect w2b
notice that a negative term involving has been eliminated from the left-hand side.
T
FT
Suppose w2b
w2T = w2b
(1 iF T ) this will increase the left-hand side and therefore
T
FT
(1 i),
increase the investment level, since c0 (:) is increasing. If w2b
w2T w2b
iT will be unambiguously greater than the investment level generated when U1 used
the Fixed Term contract. Given the contracts chosen by the di¤erent universities, the
equilibrium in the subgame must have correct conjectures. Therefore, biT1 > biF1 T :Then
0
M20 s investment, say i2 ; will be less than iF T ; since p1 (S) will now be higher.This will
33
In the analysis, it will appear that the guaranteed wage is the important feature and not the
guarantee of employment. However, this is not true, since in the spot market case, the wage is set
by the employee’s outside option, which is what he would get if he turned down the contract and
went into the market. Here the outside option is replaced by an “inside option” of w2T :
21
T
FT
also decrease p2 (S): Therefore w2b
> w2b
: Therefore, a su¢ cient condition for investment to increase under tenure is that w2T = (1 iT ): We emphasise that this is a
su¢ cient condition and the result could hold under weaker assumptions as well.(Note
T
FT
that since w2b
> w2b
; w2T > (1 iF T ) > (1 iT ) is certainly possible without
negating the result.)
Notice that the faculty member who is not on a tenured contract reduces his or
her level of investment, thus reducing expected output for the employer.
If we demonstrate that the university that o¤ers tenure gains from the additional
investment, we will have shown that o¤ering a Fixed Term market contract is not part
of a subgame perfect equilibrium strategy, since there is an incentive for a university
to deviate and o¤er a tenured contract. In order to do this, we need now to consider
the university’s payo¤.
6.1
The two-period individual rationality constraint and the
university’s payo¤.
In order to show that a university U1 would prefer o¤ering a tenure contract to a Fixed
Term market one, we consider the university’s decision problem. If U1 chooses a Fixed
Term market contract, then it has to choose just the …rst-period wage because the
second period (that is period (2,3]) wages will be determined by market conditions.
The …rst-period wage could include a signing bonus.
The wages o¤ered by the university have to satisfy two individual rationality
constraints. In the last period, the salary cannot be less than the outside option
available to a faculty member in that period-the outside option, as discussed can be
either a bid from the other university or the one available in industry. At the time the
initial contract is o¤ered (t = 1); all compensation in the …rst period (period(1,2]),
plus the expected last period wage less the cost of investment in period (1,2] must be
at least as great as the two periods of payment from industry, 2 . To minimise the
amount paid for a given investment level i, this ocnstriant will be satis…ed as a strict
equality.
Given this, we now show that the university bene…ts from the increased investment
by its faculty employee.
Proposition 3 If U2 follows a Fixed Term contract, U1 will deviate to a tenure
contract. Thus a Tenure contract is the best response to a Fixed-Term contract
22
Proof. Given that the wages paid in expected terms will be set equal to 2 ; no matter
what the optimal contract is, the university will compare the expected output less
the cost of equilibrium investment. Recalling that iT is the investment of a tenured
faculty member when the other faculty member is on a Fixed Term contract, whilst
i is the investment level of the Fixed Term faculty member and denoting by iF T the
(symmetric) optimal investment when both faculty members are on a Fixed Term
contract, U10 s expected surplus will increase by
11 (1
> f
11 (1
pH )(iT
iF T )
[c(iT )
pH )
c0 (iT )g(iT
c(iF T )]
iF T );
from strict convexity of c(:)
and, (since
iT > iF T from the comparison of (6) and (2)),
> 0; from 6.
The last inequality follows because in (6), 11 (1 pH ) is multiplied by two terms,
each less than 1, to give c0 (iT ) on the right-hand side. Therefore, 11 (1 pH ) must
itself be strictly greater than c0 (iT ):
We now need to show that tenure contracts do constitute the unique symmetric
subgame perfect equilibrium. The proof is similar to the one above but is reproduced
here for completeness.
Proposition 4 Tenure is the unique, symmetric perfect Bayes equilibrium contract.
Proof. To see this, we …rst consider (6), which is reproduced below in a modi…ed
form.
[(1
p2 (S))(Y1 (S)
Y2 (F ))]
11 (1
pH ) = c0 (iT )
(7)
Here iT is di¤erent from iT ; because we are now assuming that both universities
have chosen a tenure contract. In comparison with the case where U2 had chosen
the Fixed Term market, p2 (S) would be di¤erent and 22 (H j S) or 22 (H j F )
would be di¤erent, since the investment made by M2 would be di¤erent. (It is also
possible for wT2 to be di¤erent, though this washes out of the …rst order conditions,
23
provided it is the same for the two universities.) Suppose now that U1 deviates and
o¤ers a Fixed Term market contract. Everything else remaining the same, i1 will
decrease by (2). For M2 ; this will increase [(1 p1 (S))(Y2 (S) Y1 (F ) + (1 i1 )
(assuming correct conjectures on M10 s investment). This will increase M20 s investment
and further reduce M10 s: Therefore, in equilibrium, M10 s investment will decrease as a
result of the change and U1 will be worse o¤ by the same argument (strict convexity
of the cost function) used in the earlier proposition.34
We note that a tenure contract does not give the "…rst-best" investment level for
the university, because this would be given by maximising
2
11 [pH
+ i(1
pH )
pL ] + 2pL
c(i):
The …rst-order conditions for this are
2
11 (1
pH )
c0 (i ) = 0:
(8)
Comparing this with the …rst-order conditions for tenure, we notice that [(1
p2 (S))(Y1 (S) Y2 (F ))] < 2: (In fact the LHS is less than 1.)
This leads to the question whether tenure is a Prisoners’ Dilemma, as some
Thatcherites implicitly claimed, with universities being better o¤ under the FT contracts but stuck in a bad tenure equilibrium. However, we can show
Proposition 5 Investment and expected output are higher in the symmetric perfect
Bayes equilibrium where both universities o¤er tenure contracts than in the subgame
in which they both o¤er …xed-term contracts.
Proof. (Sketch) The proof involves a comparison of …rst-order conditions like the
earlier proofs here. These are:
(i) (1 pT2 (S))(Y1 (S; biT ) Y2 (F; biT )) 11 (1 pH ) = c0 (iT )
and
(ii) (1 pF2 T (S))(Y1 (S; biF T ) Y2 (F; biF T )) 11 (1 pH )
(1 pF1 T (S)(1 pF2 T (S)) =
c0 (iF T ); where the T and FT superscripts refer to the tenure and …xed-term contracts
respectively, now used by both universities.
34
U2 , the university o¤ering tenure, will be made better o¤ by the deviation by U1 :
24
+bi(1 pH ))
Here, for example, Y1 (S) = 11 (pHp(S)
(pH +bi(1 pH ) pL )+pL : A university’s
belief bi would a¤ect p(S) as well, but this dependence is suppressed for notational
convenience above.
Simplifying, we obtain (suppressing superscripts for convenience since this holds
for both T and FT expressions),
b
pH )
(1 p2 (S))(Y1 (S; bi) Y2 (F; bi)) = (1 p2 (S))[ 11 (pH + bi(1 pH ))f pH +pi(1
2 (S)
(1 pH )(1 bi)
g]
1 p2 (S)
b
b
(p
H +i(1 pH ) p2 (S)) 35
= 11 H +i(1 pH ))(p
:
p2 (S)
We can check that the derivative of this with respect to bi is positive.
Now evaluate the expression (i) above with i = iF T keeping bi = biF T : Clearly
the LHS of the expression (i) would now be greater than the RHS (since (ii) has an
additional negative term). In order to satisfy the …rst-order conditions, iT would have
to be greater than iF T so that the RHS of (i) increases. The LHS of (i) would also
increase as biT = iT in equilibrium. However, we have made assumptions on c(:) such
that an interior solution to (i) always exists. Hence the solution must in equilibrium
have a higher value of investment under T (the solution to (i) above) than under FT
(the solution to (ii) above).
Previous propositions have shown that the university is willing to pay (optimally)
for more investment than even the tenured professor will choose to undertake, hence
it would certainly be willing to pay for the additional investment and increment in
expected output between tenure and …xed-term.
We also note that the incentive properties of tenure are linked to the presence of
some competition, imperfect though it is. If there were no competition, the impossibility of contracting on performance would lead to the problem where the employer
would continue paying the low wage to successful employees as well as unsuccessful
ones, and this would completely erode the incentive to invest (if investment were
costly). Of course, in academics, there is an argument that people invest because it
is fun or because there is a sense of "mission" (see, for example, Besley and Ghatak
(2003) for an analysis of how mission makes high-powered incentives unnecessary for,
say, non-governmental organisations). In general, however, competition plays the role
here that up-or-out contracts do in the earlier literature, where investment is speci…c
to the current employer rather than to the profession. In the absence of competition
35
We are using p2 (S) in the calculations but p1 (S) would of course be identical given symmetry
of beliefs.
25
and "mission", tenure could be the worst possible contract.36
7
Severance contracts and renegotiation
In the context of the current model, we can make the following observations. Suppose
that for some reason, it becomes optimal at the time t = 2 for an employer to
replace the current employee with someone from “industry”. Although there are other
potential motivations, we assume this happens because a period one F realization is
an almost certain indication of a low type: pH is close to 1 for example. Then
> 0: It is now ex post optimal for the
2 (F ) ' 0 and an industry person has
employer to dismiss the employee if (1 i) is not too much less than :
7.1
Renegotiation with Risk Neutrality
We consider the case where the university renegotiates with its tenured employee
who has a F realization. Here the university might agree to pay sev if the employee
“retires”. Suppose the renegotiation takes place with the following extensive form.
Each is randomly chosen to make a proposal, which the other then accepts or rejects.
If the proposal is accepted, the agent leaves with severance sev and the university
hires an outside person from industry with surplus Y0
: If either rejects, the
T 37
T
university gets Y1 w2 and the employee w2 : The employee will accept as long as
sev + (1 i)
wT ; and the university as long as Y1 w2T
Y0
sev: The
employee’s expected payo¤ is the average of the smallest acceptable severance for
the employee and the largest acceptable severance for the employer, plus the outside
opportunity wage.
1
(Y0
2
(Y1
w2T ) + w2T
(1
i)) + (1
i)
The coe¢ cient of the (1 i) term in this expectation is =2: Consider the alternative where a pre-speci…ed wage wsev and severance sev are set down, to be activated
by the employer. Now so long as Y1 w2sev Y0
sev; the university will activate
36
This suggests a di¤erent model, where the university gives tenure only to those who exhibit the
sense of "mission". This does not appear to be the way that universities operate, with good reason,
because there is an obvious moral hazard problem here for the employees.
37
Here Y1 is a function of the conjectured investment, which is equal to the actual investment in
equilibrium.
26
severance. (If this inequality does not hold, severance is irrelevant.) The employee
will then get sev + (1 i) no matter who makes the proposal, and the coe¢ cient
of (1 i) is : Tenured contracts, even with renegotiation, therefore do better than
severance.38 This is because tenure determines the “outside option", if negotiation
breaks down, di¤erently from a pre-speci…ed severance contract.
8
Incentives in Academic Administration
From its outset, the AAUP articulated the position that administrators were concerned with the advance of their own universities and that this objective may di¤er
from disciplinary advance. For example, if a faculty member worked in an area of
regulatory economics that greatly advanced this sub…eld but the results were at odds
with the objectives of donors then the actions of university administrators may not
be consistent with those of the social planner. The Ross case at Stanford is a good
example. A further di¢ culty arises because the time frames in higher education for
realizations of output from investments can be much longer than the usual appointment periods of university administrators.
To model the incentives and objectives of academic administrators explicitly would
be quite a di¢ cult undertaking, since one would have to analyze the tradeo¤s between
immediately visible and veri…able results and longer-term, possibly more permanent
bene…ts. We adopt a simple, ad hoc approach to this by assuming that universities’
place a weight of = 1 on investment costs (the wage component is …xed at 2 ).
= 1 corresponds to the absence of an agency problem by administrators. In the
polar extreme assume that there is no investment under a …xed term contract. In this
case, for a su¢ ciently strong agency problem by the universities, there will be two
pure strategy Nash equilibria where the payo¤ to playing "Fixed Term, Fixed Term"
generates the highest payo¤. However, in the absence of the agency problem, as shown
in Proposition 5, the payo¤ is largest, and it is a dominant strategy equilibrium, for
each university to play "Tenure, Tenure". In this light, one could view the period
from 1915 to 1940 regarding the emergence of the AAUP and the uniform acceptance
38
If the university has all the bargaining power then tenure and severance will produce identical
investments. This is natural since the severance contract is set by the university at the beginning
of period 1 when it has all the bargaining power.The crucial e¤ect of tenure in this context is that
it changes the bargaining power.
27
of the tenure contract as one where the AAUP gradually educated universities of the
truly bene…cial nature of the tenure contract from the social planning perspective.
9
Conclusions
Our conclusions can be summarised as follows:
Contingent contracts for university faculty, based on output or investment, are
not possible since neither output nor investment are veri…able. Further, the accumulation of discipline-speci…c human capital by academics is often detrimental to their
opportunities outside their occupations. We have shown in this paper that the con‡uence of these e¤ects results in a lifetime employment contract. Employers prefer
it because it encourages increased levels of investment. Employees prefer it since it
prevents employers from taking advantage of the erosion of the outside opportunities
of employees as they strive for results in their discipline.
Of course, there might be other valid economic explanations for tenure, as well
as some of the academic freedom arguments mentioned in the introduction. We
have focussed on one set of arguments; our reading of the history of the emergence
of tenure suggested to us that informal analogues of our arguments appear in the
historical literature as well.
One obvious question at this point might be to query which of the various competing explanations for tenure is the “right" one. We feel that tenure has di¤erent
aspects and each of the existing explanations addresses some aspect, but that the
speci…c aspect of a voluntary commitment of lifetime employment after a probationary period requires some combination of factors like the ones in our model. The
explanations complement each other.
28
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31