MIT LIBRARIES
3
1060 DQTDlSat.
7
mmm
9B
i
KBHll HftRHl
iHltemn
9.. 1-
;
;
..:
-:
'
Sii
jwnfuai.unif'
hm
:
lm
i
r
1HH
3 fuBSASIEs] g
^W
<?
ao.SG3
working paper
department
of economics
OPTIMAL INCENTIVE CONTRACTS IN THE
PRESENCE OF CAREER CONCERNS:
THEORY AND EVIDENCE
Robert Gibbons
Kevin J. Murphy
Number 563
August 1990
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
OPTIMAL INCENTIVE CONTRACTS IN THE
PRESENCE OF CAREER CONCERNS:
THEORY AND EVIDENCE
Robert Gibbons
Kevin J. Murphy-
Number 563
August 1990
MEXICO: REAL PER CAPITA INCOME
(INDEX 1980-100)
1978
1982
1983
19B4-
MEXICO: THE REAL WAGE
1985
IN
1986
1987
1988
1989
1990
MANUFACTURING
(INDEX 1980=100)
110
105 -
100 -
1970
1980
1982
1984
1986
1988
1990
OPTIMAL INCENTIVE CONTRACTS IN THE PRESENCE OF
CAREER CONCERNS: THEORY AND EVIDENCE*
Robert Gibbons
MIT and NBER
Kevin
J.
Murphy
University of Rochester
First Draft: July, 1989
This Revision: August, 1990
Abstract
—
This paper studies career concerns concerns about the effects of current
performance on future compensation and describes how optimal incentive
—
contracts are affected when career concerns are taken into account. Career concerns
arise frequently: they occur whenever the market uses a worker's current output to
update its belief about the worker's ability and competition then forces future wages
(or wage contracts) to reflect these updated beliefs. Career concerns are stronger
when a worker is further from retirement, because a longer prospective career
increases the return to changing the market's belief.
In the presence of career concerns, the optimal compensation contract
optimizes total incentives the combination of the implicit incentives from career
concerns and the explicit incentives from the compensation contract. Thus, the
explicit incentives from the optimal compensation contract should be strongest
when a worker is close to retirement We find empirical support for this prediction
in the relation between chief-executive compensation and stock-market
performance.
—
*
We are very grateful to Bengt Holmstrom, David Kreps, Meg Meyer, and Jean Tirole for substantial advice and
this paper's long gestation. We are also grateful for helpful comments from David Card,
encouragement during
Henry Farber, Seonghoon Joon, Eugene Kandel, Alan Krueger, Bruce Meyer, Sherwin Rosen, Michael
Wiesbach, and Jerold Zimmerman, and from seminar audiences at BU, Harvard (Kennedy School), Kentucky,
Northwestern, NYU, Oxford, Princeton, Queen's, Rochester, Yale (S.O.M.), and the 1989 summer meetings of
the Econometric Society and of the NBER Labor Studies Group. Richard Sloan and Kathleen Jones provided
able research assistance. Financial support from the following sources is also gratefully acknowledged: the NSF
(grants 1ST 86-09691 and SES 88-09200), and the Industrial Relations Section at Princeton University
(Gibbons); and the John M. Olin Foundation and the Managerial Economics Research Center, University of
Rochester (Murphy).
Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium
Member
Libraries
http://www.archive.org/details/optimalincentiveOOgibb
OPTIMAL INCENTIVE CONTRACTS IN THE PRESENCE OF
CAREER CONCERNS: THEORY AND EVIDENCE
Robert Gibbons and Kevin
J.
Murphy
Introduction
1.
—concerns about
This paper studies career concerns
on future compensation
— and describes how optimal
career concerns must be taken into account.
whenever the
(internal or external) labor
belief about the worker's ability
the effects of current
performance
incentive contracts are affected
when
Career concerns arise frequently: they occur
market uses a worker's current output
and then bases future wages on these updated
to update its
beliefs. In
such
a setting, the worker will want to take actions the market cannot observe, in an attempt to
increase output and thus influence the market's belief; in equilibrium, however, the market will
anticipate these actions
and so draw the correct inference about
Career concerns are stronger
output.
when
a
worker
is
further
ability
from the observed
from retirement, because a
longer prospective career increases the return to changing the market's belief.
further
from retirement thus
is
willing to take
more
A worker who is
costly unobservable actions in an attempt to
influence the market's belief.
Career concerns were
first
discussed by
Fama
(1980),
who argued
that incentive
contracts are not necessary because managers are disciplined through the managerial labor
market: superior performances will generate high
Holmstrom (1982) showed
effects,
it is
typically
that although
wage
offers;
poor performances, low
offers.
such labor-market discipline can have substantial
not a perfect substitute for contracts: in the absence of contracts, managers
work
too hard in early years (while the market
is still
assessing the manager's ability)
Robert Gibbons and Kevin
J.
Murphy
and not hard enough in
concerns can
We
later years.
contracts are necessary to provide
In this paper,
we add
August, 1990
2
conclude from Fama's and Holmstrom's work that
managers with optimal incentives.
contracts to the
Fama-Holmstrom model.
We
show
that career
create important incentives, even in the presence of incentive contracts.
still
Accordingly, in the presence of career concerns, the optimal compensation contract optimizes
total incentives
—
explicit incentives
the combination of the implicit incentives
from
the
from career concerns and the
compensation contract. Because the implicit incentives from career
concerns are weakest for workers close to retirement, explicit incentives from the optimal
compensation contract should be strongest for such workers, while for young workers
it
could
be optimal for current pay to be completely independent of current performance.
Our formal model examines
the career concerns that arise
from competition among
current and prospective employers in an external labor market, but career concerns also arise in
internal labor markets, in
among
two ways.
supervisors within the
external labor market.
First,
same
Second, even
competition
division) can
if there is
distinguish between effort and ability. Although
we
mimic
within a firm (or even
the competition
we
study in the
only one supervisor, career concerns arise
promotions are based on a worker's assessed
labor markets,
among divisions
ability but the supervisor
we do
expect analogous results to hold:
not
cannot perfectly
model career concerns
Implicit incentives
if
in internal
from promotion
opportunities should be weakest for workers close to retirement and stronger where promotion
opportunities are plentiful rather than scarce (as in expanding organizations).
Current pay
should be most sensitive to current performance for workers close to retirement and for
workers with no promotion opportunities (such as workers
at the
top of the corporate hierarchy
or other job ladder, and workers in declining organizations). 1
In addition to analyzing the characteristics of optimal incentive contracts in the presence
of career concerns, this paper also examines the empirical support for the career-concerns
1
Rosen (1986) makes a similar observation in the context of elimination tournaments or promotion ladders:
win an early round can be big even if the prize for winning that round is small, because winning
the incentive to
also buys entry to subsequent rounds with larger prizes.
Robert Gibbons and Kevin J. Murphy
model
in a particular setting: the relation
We
market performance.
example, that each
compensation for
CEOs more than
10% change
CEOs
between chief-executive compensation and stock-
study longitudinal pay and performance data on a large sample of
(CEOs) and
chief executive officers
August, 1990
3
find empirical support for the model.
in shareholder wealth corresponds to
less than three years
1.5% changes
in cash
three years from retirement.
from compensation
issues associated with
wage
contracts, our
from career concerns and the
model incorporates several of
Of
concerns are to
arise, the fourth is
these five elements of the model, the
something like
explicit
the fundamental
determination: incentives, learning, market forces, contracts, and
risk aversion.
fifth (or
estimate, for
from retirement, but only .9% pay changes for
In order to analyze both the implicit incentives
incentives
We
it) is
necessary
if explicit
first
three are necessary if career
incentives are to be considered, and the
necessary so that optimal contracts do not completely eliminate
career concerns. Other models of career concerns
and MacLeod and Malcomson (1988)
not risk aversion or contracts. 2
—such
as
Fama
(1980),
Holmstrom
(1982),
—
incorporate incentives, learning, and market forces, but
Other dynamic agency models
— such
as
Lambert (1983),
Rogerson (1985), Murphy (1986), Holmstrom and Milgrom (1987), and Fudenberg,
—
Holmstrom, and Milgrom (1987)
learning or market forces.
Holmstrom (1982)
—
incorporate incentives, contracts, and risk-aversion, but not
Finally, other
dynamic insurance models
— such
as Harris and
incorporate risk-aversion, contracts, learning, and market forces, but not
incentives. 3
2
Career concerns are related to the "ratchet effect" that arises in dynamic models of regulated firms, such as
and Tirole (1985), Baron and Bcsanko (1987), and Laffont and Tirole (1988). These models
ignore the market forces analyzed in this paper because there does not exist a market of prospective regulators,
but the assumption that the regulator cannot commit to ignore information once it has been revealed has a
similar effect. Lazear (1986) and Gibbons (1987) study the ratchet effect in models of the employment
relationship, but also ignore market forces because the worker's private information concerns a firm-specific
Freixas, Guesnerie,
such as job difficulty. Aron (1987) and Kanemoto and MacLeod (1987) study the ratchet effect in
models of the employment relationship that include market forces because the worker's private information
attribute,
concerns a worker-specific attribute, such as
3
Holmstrom and Ricart
ability.
Costa (1986) extend the Harris-HolmstrOm model by adding an observable action
based on private information, as opposed to the unobservable action based on symmetric information considered
here. MacDonald (1982) and Murphy (1986) analyze the effects of learning and market forces on job
assignment, rather than on insurance contracts.
i
Robert Gibbons and Kevin J. Murphy
Theoretical Analysis
2.
Consider a worker
who works
stochastic production process in
y =
l
+
Ti
+
al
et
worker and
mean mo and
In period
periods.
which output
(y t )
is
the
sum of
The
variance o^.
is
exponential
assume
U(wi,
We
w
t
the
error terms are
r\
Normally distributed with
is
Normally distributed with mean zero and
employers are risk-neutral but
tj.
that the
worker has the following
utility function:
(2.2)
where
that
(n.),
symmetric (but imperfect) information about the worker's
variance c^, and are independent of each other and of ability,
We
the worker's ability
(t{):
prospective employers believe that
all
worker controls a
the
t,
.
Before production begins, there
ability: the
T
for
worker's non-negative effort (aO, and noise
(2.1)
August, 1990
4
is
the
...,
wT
wage paid
assume further
assumption that
g'"
a 1;
;
period
in
that g(a t )
>
is
...,
is
aT )
t
=
-
exp (
and g(aO
convex and
is
-r{£[=1
5
lA [w
a (monetary)
satisfies g'(0)
=
t
g(a t )]})
-
measure of
0, g'(°°)
=
°°,
,
disutility
and
g'"
>
of
effort.
0.
(The
a sufficient condition for certain maximization problems to be
concave and for several intuitwe comparative-static results
to hold.)
Note
that (2.2) is not the
additively separable exponential utility function often encountered in the literature: (2.2) implies
that the
worker
is
(computed using
market.
Our
indifferent
among
all
deterministic
wage streams with
5 as the discount factor), just as if the
results are similar in spirit but
and
that the
worker has no access
worker had access
more complicated
conventional assumptions that the worker's exponential
to credit; see the
constant present value
utility
to a perfect capital
to express
function
is
under the more
additively separable
Appendix. Given our empirical focus on
Robert Gibbons and Kevin J. Murphy
CEO pay,
however,
no access
to credit.
To keep our
(i.e.,
are linear
to
theoretical analysis simple,
(Al) short-term
possibilities:
term
seems more reasonable
it
August, 1990
5
CEO needs
no rather than has
we make two assumptions
about contracting
assume
one-period) contracts are linear in output; and (A2) long-
(i.e.,
Our assumption
multi-period) contracts are not feasible.
is
that the
obviously convenient:
we wish
that short-term contracts
to formalize the idea that contractual incentives
should be strong when career-concern incentives are weak, and the strength of the contractual
incentives
is
easily
summarized by
and Milgrom (1987) demonstrate
model much
that a
(but lacking the uncertainty about the agent's ability,
the optimal contract is linear.
(In the
Holmstrom-Milgrom argument extends
Our assumption
(again, in the
exist but
r\)
can be reinterpreted so as
Appendix, we discuss the extent
The idea
at
to
our model
ensure that
which
to
the
our model.)
assumption
that this
must be Pareto-efficient
renegotiation-proof.
to
like the single-period version of
that long-term contracts are not feasible
Appendix)
Holmstrom
the slope of the linear contract. Furthermore,
is
We show
equivalent to assuming that long-term contracts
each date; that
that contracts
can be reinterpreted.
is,
long-term contracts must be
should be renegotiation-proof has been widely
accepted in recent work; see, for example, Dewatripont (1989) on contracting under adverse
selection,
Fudenberg and Tirole (1989) on contracting under moral hazard, and Hart and
Moore (1988) on incomplete
implementation).
mimics
In our model, renegotiation
the effect of competition
We now derive the
state the results for the
4
contracting under symmetric information
among
(i.e.,
Nash
between the worker and a single employer
the current
and prospective employers. 4
optimal compensation contracts for the two-period case and then
T-period case.
Another potential role for long-term contracts is consumption-smoothing; see Lambert (1983), Rogerson
Murphy (1986). Fudenberg, Holmstrom, and Milgrom (1987) show, however, that if the agent has
perfect access to credit then the optimal long-term contract is equivalent to a sequence of optimal short-term
contracts. In our model, the fact that the worker needs no access to credit, as described in connection with (2.2),
eliminates this consumption-smoothing role for long-term contracts.
(1985), and
Robert Gibbons and Kevin J. Murphy
August, 1990
6
The Two -Period Model
The timing of the two-period model
is
as follows.
At
the beginning of the first period,
prospective employers simultaneously offer a worker single-period linear
form wi(yi) =
is
ci
+
biyi.
no need for employers
The worker chooses
period, the firm
the
{i.e.,
wage
contracts of the
(Recall that information is symmetric, although imperfect, so there
to offer
most
menus of contracts
attractive contract
in
order to induce workers to self-select.)
and begins production. At the end of the
the first-period employer) and the market
(i.e.,
first
prospective employers)
observe yi and then simultaneously offer the worker single -period linear wage contracts of the
form W2(y2) = C2 + b2y2- These second-period contract offers
on
yi,
depend implicitly
because first-period output will convey information about the worker's
described below.
The
force of our assumption (A2), however,
can depend on first-period output only in
commitment
most
will of course
at the
beginning of the
first
this implicit
period.
is
ability, as
that second-period contracts
manner, rather than explicitly through
Once
again, the
worker
is free to
choose the
attractive contract.
Given these compensation contracts (where,
for
now, the parameters
ci, bi, C2,
are arbitrary), the worker's expected utility (from the perspective of the first period)
following function of
(2.3)
From
-
first-
E { exp
and second-period
(-r[ci
+ bifa+ai+ei)
-g(ai)]
-
and
rS[c 2
is
the
a2:
+ b 2 (r|+a2+£2) -gte)])
}
the perspective of the second period, however, after ai has been chosen and yi has been
observed, the worker's expected
(2.4)
effort, ai
and b2
-
utility is
exp (-rS-^C! + biyi
-g(ai)] )•
E { exp
( -r[c 2
so the worker's second-period effort choice problem reduces to
+ b 2 (ii+a2+e2) -gte)])
|
yi }
,
Robert Gibbons and Kevin J. Murphy
"£*
(2.5)
-
E { exp
August,
7
+ b 2 (r,+a 2 +e 2 ) -g(a 2 )])
( -r[c 2
|
yi }
1
990
•
3|C
The worker's optimal second-period
g'(a 2 )
(2.6)
= b2
effort, a 2 (b 2 ), therefore satisfies the first-order
condition
.
Competition among prospective second-period employers implies that the contract the
worker accepts for the second period must earn zero expected
profits, so (after
normalizing the
price of output to unity), c 2 (b 2 ) satisfies
c 2 (b 2 )
(2.7)
Using
=
(l-b 2 )E{y 2
yi }.
|
worker's first-period output equals the
ability
of the worker's second-period output given the
(2.1), the conditional expectation
and the optimal second-period
sum of
effort
the conditional expectation of the worker's
induced by the contract:
E{y 2 |y 1 }=E{T1 |y 1 }+a2 (b 2 ).
(2.8)
To compute
the conditional expectation of the worker's ability, the market
must extract the
relevant information about the worker's ability from the observed first-period output, and this
requires a conjecture about the worker's first-period effort.
Suppose the market conjectures
become
that the worker's first-period effort
to pure-strategy equilibria.)
(1970), the conditional distribution of
(As will
r\
Using well known formulas from DeGroot
given the observed first-period output yi
Normal with mean
na\
ai.
clear below, in equilibrium the market's conjecture about the worker's effort is correct.
We restrict attention
(2.9)
was
-
i
\
mi(yi,ai)=
J m°
+
CT
—
-j-°
<rz
(yi
-
+ a
2
Sl)
I
is
then
Robert Gibbons and Kevin J. Murphy
August, 1990
8
and variance
(2.10)
°i
=
+ a e2
c£
We
include &\ in the notation
—a +
convenient to define Z\
i
m^yi,
ai) for expositional clarity in
tne conditional variance of
°"c>
T|
+
e2
what follows.
It is
given the observed
also
first-
period output yi.
Substituting the appropriate expressions into (2.4) yields the worker's expected utility
(from the perspective of the second period) for an arbitrary b2, given first-period output
The market thus believes
(2.11)
-
E{exp
that the optimal second-period slope, bj,
( -r[c 2 (b 2 )
=
where the righthand
distributed with
-
side of (2.11)
mean
u.
is
Optimizing
(2.1 1)
-
I
yi }
g(a*(b 2 ))
-|rb^ ])
derived using the observation that
if
x
is
,
Normally
and variance a2 then
E{exp(-kx)} =exp(-ku + ^k2a 2 )
(2.12)
maximizes
+ b 2 (r,+a2(b 2 )+ e2 ) -g(a*(b 2 ))])
exp ( -rim^y^aO + a*(b 2 )
y^
and implicitly differentiating
.
(2.6) yields the first-order condition for b2, the
optimal second-period slope: 5
(2.13)
b2
=
1
5
Note
+rl
2
2
g"[ai(b 2)]
Lazear and Rosen (1981), who derive it
more general (static) utility function U(w-g(a)). Thus, (2.13)
and approximately optimal more generally.
that (2.13) is identical to the result given in footnote 8 in
using a second-order Taylor approximation to the
is
precisely optimal given (2.2)
Robert Gibbons and Kevin J. Murphy
Using the assumption
concave, so (2.13)
uncertainty (L^
).
that g'"
>
0,
straightforward to
it is
that D2 is
independent of
yi,
of implicit incentives from career concerns, because
output on the second-period contract
given in
show both
(i.e.,
it
and
implies that the effect of first-period
the career-concern effect)
is
limited to the intercept
(2.7).
yi, the worker's first-period incentive
(2.14)
(r)
which greatly simplifies the analysis
Given the optimal second-period contract derived above, with
on
that (2.11) is strictly
as well as that b2 decreases with both risk-aversion
is sufficient,
Note also
August, 1990
9
-E{exp
(-r[ci
problem
is to
choose
ai to
its
implicit
dependence
maximize
+bi(Ti+ai+e 1 )-g(ai)] -r6[C2(b|) + bJ(Ti+aJ(bJ)+e2) -g(a*(b*))])}.
Substituting (2.8) and (2.9) into (2.7) yields
c 2 (b2)= (l-bl)
(2.15)
(<£
m
2
+ a (yi-ii)
*„*A
+a2(b2)
„* + „?
: + °s
'
V
The
worker's optimal first-period effort, ai (bi), therefore satisfies the first-order condition
(2.16)
The
g'( ai )
=
bi
+
5
g2
=
bl
+
5 (1-bJ)
total incentive for first-period effort,
— —
JL
denoted by Bi,
=
Bi
is
thus the
.
sum of
the explicit
incentive from the first-period compensation contract, bi, and the implicit incentive from career
concerns, 8(l-b2)a^/(c^+c^).
(2.13),
The career-concerns
incentive
and increases (decreases) with the uncertainty about
Note
that the expressions
period effort, ai, as given.
is
positive, since
ability (production),
0<b2<l from
c^
(c^).
above take the market's second-period conjecture about
Thus, (2.16) characterizes the worker's best response to
conjecture. In equilibrium, the market's conjecture
must be
first-
this
correct, but the necessary fixed-
Robert Gibbons and Kevin J. Murphy
point computation
conjecture
is trivial
August, 1990
10
because (2.16) does not depend on
Therefore, the equilibrium
aj.
is
ai=a?(bi)
(2.17)
.
Competition ensures
(A2), expected profits
that firms earn zero
must be zero
in
expected
Because of assumption
profits.
each period. Hence,
d(bi) = (l-bi)E(yi) = (l-bi)[mo+af (bi)]
(2.18)
Substituting ai(bi) and Ci(bi) into (2.14) and applying (2.12) yields the worker's expected
utility
(from the perspective of the
(2.19)
-
period) for an arbitrary bj:
first
exp( -r[m + af (bi)
-
g(a?(bi))]
-
r5[m + a*(b*)
.exp(ir2[(B 1+ 5b2) 2 S?
where Bi
sum of explicit and
reflects the
first-period slope, bi
„, m
.
(2.20)
bi
,
where
z] =
*
is
+
r
-
the variance of
r\
+
this
generalized in the T-period model, so
comparing the three terms
The
first
g
,
1u *,
5 (l-b2)
Z\ g"[af(bi)]
The main conclusion from
to the result.
2B 5b*al])
1
,
implicit incentives, as defined in (2.16).
1
2
a Q + a|
g(aj(b?))])
The optimal
thus satisfies the first-order condition
=
1
-
-
o£
r 5
2
b* a g"[at(bi)]
+ cl
*
:
:
1
+
z] g"[a?(bi)]
r
e\.
two-period model
we
is
that bi
<
give only the intuition here.
in (2.20) to the single
term
— og
b2
As
.
is
This result
is
apparent from
expression in (2.13), three effects contribute
in (2.20) reflects a
noise-reduction effect: learning about the
Robert Gibbons and Kevin J. Murphy
August, 1990
11
2
worker's ability causes the conditional variance of output to decline over time (Z 2
optimal tradeoff between insurance and incentives shifts towards the
tl] g"[a2(b2)]} < b2
(2.16);
it
•
The second term
so the
I.]),
—
over time
/
1
{ 1
+
from
in (2.20) is the career-concerns effect, familiar
implies that optimal explicit incentives are adjusted to account for career-concerns
incentives by imposing a lower pay-performance relation
third
latter
<
term
when
human-capital-insurance effect: risk-averase workers with
in (2.20) reflects a
uncertain ability want insurance against low realizations of ability; in our
must take the form of a reduction
The worker's demand
optimal for
The career-concerns
difficulties for
this
for human-capital insurance can be quite strong.
worker against low realizations of
negative slopes (bi < 0) even
model
insurance
in the slope of the first-period contract.
total first-period incentives to
incentives. 6
The
career concerns are high.
when
be negative (B\ < 0)
ability
if
the benefits
In fact,
from insuring
exceed the benefits of providing positive
effect in (2.20) suggests that optimal contracts
total
our analysis. Negative
it is
the
effort
can have
incentives are positive, but this possibility creates no
total incentives, in contrast, require a reinterpretation
of
the first-order condition (2.16). In order to handle the possibility of negative total incentives in
a simple way,
we
we now assume
that effort
continue to assume that g(a)
is
can be either positive or negative and that
convex and
satisfies g'(0)
=
0, g'(°°)
interpret negative effort as hiding or stealing output; our assumptions
activities are increasingly difficult
The
the margin, as
may be
on
°°,
and
g(a)
g'"
imply
>
= -°°;
0.
We
that such
realistic.
T-Period Model
The
now
on
=
g(-°°)
three equations that
be written as follows:
summarize the workings of the competitive labor market can
First, the zero-expected-profit constraint in
period
t is
6
Suppose, for example, that there is no noise in production (i.e., g\ = 0). Then first-period output perfectly
2
reveals the worker's ability, so a\ - 0. Since there is no uncertainty in the second period (i.e., 1\ = af + a =
0), the optimal slope is b 2 = 1, which imposes substantial human-capital risk on the worker: second-period pay
moves one-for-one with the worker's actual ability, and not at all with the market's assessment of the worker's
2
ability based on first-period output (because C2(b2) in (2.15) is zero). If 5 = 1 and g(a) = [a ]/2 then the total
first-period incentive is
B = bj = (1
x
-
r
al
)/(!
+ ro 2 ), which
clearly can be negative.
Robert Gibbons and Kevin J. Murphy
cl
(2.21)
=
(l-b
l
)E{y
l
August. 1990
12
lyi,... I y,.i}.
Second, the conditional expectation E{y t lyi,..., y t _i)
E{y t lyi,..., y t.i) =
(2.22)
where
and
m^
is
mn
+
at
is
,
the market's expectation of the worker's ability as of the beginning of period
a t is the market's conjecture
about the effort the worker will supply in period
t.
t,
Finally,
the market's conditional expectation of the worker's ability, given the observed history of prior
outputs (yi,
...,y t -i)
and
its
conjectures about prior effort levels
(a.\, ...,a t _i), is
t-i
a2
m .i(yi,
(2.23)
t
...,y t .i; ai, ...,a t .i)=
m
+
cx
2
cr
+
2
£(y T
aT )
-
*
(t-l)g 2
Substituting these three equations into the worker's utility function (2.2) and applying
from a sequence of contracts with
(2.12) yields the worker's expected utility
(bi,
...,
arbitrary slopes
by) and associated intercepts given by (2.21), given the market's effort conjectures
(&i, ...,ar)
and the worker's effort choices
(ai,
...,
a t ).
(See the Appendix for this
computation, as well as the others omitted below.) The worker's optimal effort level in period
t,
at
,
then solves a first-order condition analogous to (2.16):
(2.24)
g'(af)
= b +
t
IS^It
dat
= b +
T=t+i
Naturally, a t depends on b t and (b l+ i,
...,
t
2
y-t(l-bt)
by), but not
:
o^
x=t+l
on
(bi,
...,
f~—
(ai
worker's expected utility from the sequence of contracts with slopes (bi,
...,
written as
B
t
b t -i).
=
In equilibrium, the market's conjectures are correct: (ai,
-
+ (T-l)a 2
...,ar)
,
...,
ay
).
The
br) can then be
Robert Gibbons and Kevin J. Murphy
(2.25)
-
exp(
-r [
August, 1990
1
1 5^
(mo + a?
+ \ r2
z
g(af ))]
-
t=i
For now, take
Bi from
(b2,
(2.24),
<
...,
B =
2 26 >
-
:
i
which solves the
—^x
1
+rz'
1
bl=
(2 27)
-
T-T7X
i
1
' 1
B,) 2
o 2]).
t>i
affect only a*.
Since
g'(ai
)
=
to the first-period total
first-order condition
ra 2
g"(a?)
l
fiH B t
-
J:l*.
+rztg"(ai)
;
g"(ai)
Applying (2.24) then yields the optimal
£ (5
+
t=i
convenient to optimize (2.25) with respect
bx),
2
t=i
bx) as given. Recall that changes in
...,
it is
incentive, Bi(b2,
£ 5*-* BO 2 o
[(
.
1
,
*/
first-period contract slope bi (b2,
st-i(l-bt)
2
"
l+rZig"(ai)
bj),
2
;'
ot+(t-l)a„
t=2
ra 2
,
•..,
I 8»-l B
g"(af)
t
t=2
1
+
r
I
2
g"(a*)
Finally, using (2.27) recursively yields the optimal slopes (bi
working backwards
to bi(b2,
...,
,
...,
b-r),
bx).
We now provide a partial characterization of the optimal slopes
bx for
all
t
Appendix
<
T; that
sensitivity
those
t
b* < bx for
(in fact,
all
t
<T
We
:
t
=
1, ...,
T) b t <
:
suspect that the optimal slopes typically increase
we have been unable
is sufficient
of pay to performance
more than
{b t
contractual incentives are strongest for those about to retire. (See the
for the derivation.)
monotonically with
result that
is,
beginning with br and
is
for our empirical work, in which
greater for
x years from retirement,
to construct a counter-example), but the
CEOs
where
less than x years
we show
that the
from retirement than for
x equals two, three, or four years.
Robert Gibbons and Kevin J. Murpiiy
August, 1990
14
Evidence on Career Concerns for Chief Executive Officers
3.
Testing our model involves estimating the pay-performance relation between the agent's
compensation
(i.e.,
the wage, w, in our model's notation)
and the principal's objective
(i.e.,
output net of the wage, y-w) and detecting changes in the estimated pay-performance relation
(i.e.,
the slope of the compensation contract, b) as the
data necessary to analyze the model
is difficult
and-file workers that contain data
(measured
or firm level).
consider the agency relationship between the shareholders and the
shareholder-CEO relationship
is
data on the
(i.e.,
CEO's compensation
measured with available
by the market value of the
Third, under the assumption that
data: shareholders desire to
firm's
common
stock. 7
Although the managerial labor market
is
model require uncertainty about
firm
The assumption
is strictly
We
-
common
maximize
objective that
their wealth, as
measured
compensation
policies,
The career-concerns
the worker's ability, but
in
which
to investigate
may
not be ideally
it
effects analyzed in our
most CEOs are long-time employees
that well diversified shareholders are risk neutral with respect to the returns of
correct only
when
is
8
an attractive laboratory
characteristics and effects of incentive
suited for an investigation of career concerns.
7
to
are publicly available in corporate proxy statements issued in
shareholders are approximately risk neutral, the principals have a
many of the
managers
take actions that increase shareholder wealth). Second, detailed longitudinal
conjunction with annual shareholders' meetings.
easily
of a
an archetypal principal-agent relationship: widely
diffuse shareholders, through delegation of authority to the board of directors, hire
supply effort
CEO
We focus on this particular agency relationship for several reasons.
publicly held corporation.
First, the
because existing longitudinal datasets for rank-
on wages seldom also contain data on performance
at the individual, divisional,
We
worker nears retirement. Obtaining the
any given
the firm's returns are uncorrelated with market returns.
ignore debt by focussing on shareholder wealth instead of the combined wealth of shareholders and
bondholders; Smith and Warner (1979) argue that explicit bond covenants are designed to mitigate the agency
problems between managers and bondholders.
Robert Gibbons and Kevin J. Murphy
CEO,
before being appointed
so shareholders (as well as potential alternative employers)
have precise information about the
CEO
compensation
employers
who
ability of a
our model
in
August, 1990
15
is
new CEO. 9
determined by a competitive market of prospective
CEO's managerial
The
ability.
fact that
join another, coupled with the likely existence of large
capital, suggests that a
We
competitive market of the kind
of a newly appointed
different
new
information
is
CEOs rarely leave oneFigure 2to
amounts of organization-specific human
we assume may
not exist. 10
believe that these issues do not pose substantial problems for our empirical
analysis, for the following reasons.
ability
In addition, the expected level of
continuously revise their bids for the CEO's service as
revealed regarding the
may
from the
skills
CEO
First,
because the
skills
is
unlikely to yield precise information about the
performance as CEO. Furthermore,
quickly, both because
it is
difficult to isolate the
determine firm performance and because (as
environment
ability in the
required to pilot a corporation are quite
required at lower levels in the organization; the performance of an
individual as vice president, for example,
individual's potential
shareholders are likely to be uncertain about the
may renew
this uncertainty
not be resolved
CEO's contribution from other
we
factors that
discuss below) a change in the firm's
the shareholders' uncertainty about the
previous environment had
may
CEO's
ability,
even
if his
become known.
Second, our assumption of a competitive market of prospective employers implies that
a
CEO
receives the full benefit from an increase in the market's estimate of his managerial
ability (and bears the full cost
unchanged, however,
if
from
Our
a decrease in the estimate).
we assume instead
that the
CEO receives
qualitative results are
(bears) some, rather than
of the increased (decreased) rent associated with changes in the market's estimate of his
One model
relationship
9
that
would predict such rent sharing
between the
CEO
and
his shareholders,
is
a bilateral-monopoly
where the rent
to
ability.
model of
be divided
is
all,
the
the return
The median CEO in our sample of nearly 3,000 CEOs described below worked in his firm 16 years before
ascending to the top position.
10
Note, however, that Fama's (1980) and Holmstrom's (1982) early work on career concerns for top
managers relies exclusively on just such a managerial labor market to provide managerial incentives.
•
Robert Gibbons and Kevin J. Murphy
on the CEO's organization-specific
compensation contract under
same kinds of
(implicit
and
August, 1990
1
this
capital: in
each period, the slope of the CEO's linear
new formulation of our model would be determined by
explicit) incentive considerations that arise in
but the intercept would be determined by bargaining
constraint implied
power rather than
the
our original model,
the zero-expected-profit
by a competitive market of potential employers. 11
A Longitudinal Sample of Chief Executive Officers
We
following
in
test the
implications of our career-concerns model using data constructed by
chief executive officers listed in the Executive Compensation Surveys published
all
Forbes from 1971
These surveys, derived from corporate proxy statements,
to 1989.
include 2,972 executives serving in 1,493 of the nation's largest corporations during the fiscal
years 1970-1988, or a total of 15,148 CEO-years of data. In order to distinguish
to retirement
left their
from
CEOs
with longer horizons,
we
initially restrict
CEOs
our analysis to
close
CEOs who
firms during the 1970-1988 sample period, using data from the 1990 Forbes survey
to identify
CEOs whose
last fiscal
year was 1988.
This subsample includes 1,631 CEOs,
representing 916 firms and 8,786 CEO-years.
Our model assumes
executive
is
appointed
CEO position
that a
CEO,
is
CEO experiences something like the following career path: an
paid based on the performance of his firm, and remains in the
until retirement, at
which point his career ends.
by presenting results that suggest
We begin our empirical analysis
that such a career path is typical.
Figure
histograms describing the frequency distributions of tenure in the firm, tenure as
age,
all
measured
at the
date the
CEO
leaves office, for the 1,631
during the 1970-1988 sample period. Panels
A
and
B
of Figure
CEOs
1
show
1
presents
CEO, and
leaving their office
that,
upon leaving
If the sole objective of this paper were to deepen our understanding of CEO compensation then we would
have developed this rent-sharing model rather than the competitive-market model developed above. We think it
likely, however, that career concerns arise for many workers other than CEOs and that the competitive-market
model applies more naturally than does the rent-sharing model for many of these other workers. Thus, in
choosing to develop the competitive-market model we were in part attempting to convey this larger potential
scope of the career-concerns model.
Robert Gibbons and Kevin J. Murphy
average
office, the
CEO has
been
position for over ten years.
in his firm for
Panel
60% were
normal retirement age:
August, 1990
1
C shows
almost thirty years and has been in the
most executives leave
that
between 60 and 66 when they
their position near
31% were
and
left,
CEO
ages 64 or
65.
There
either steps
also evidence
is
down
from other sources
that
when
the typical
into retirement or continues to serve the firm in a reduced, semi-retirement
capacity. Vancil (1987) estimates that
75%
CEOs remain
of departing
This evidence seems inconsistent with the hypothesis that
directors.
firm, since
CEOs
ill
on
their firms' boards
of
CEOs move from firm
to
joining rival firms are unlikely to maintain close relationships with their
former employers. Vancil finds that an additional 6.4% die while in
because of
CEO leaves office he
health.
In our
own
sample,
we
their firm during the
sample period became
period.
we
In addition,
office;
CEO
We found that fewer than 6%
Who
post-departure Who's
appeared in Who's
Who
absence of these data
Figure
remaining as
their firms
are
from
Panel
1
is
of these
1.4% joined law firms or
information on
40%
prior to their departure);
who
left
of another sample firm by the end of the
searched (the 1985 edition of) Who's
after leaving their firm; another
others resign
find that only 36 of the 1,631 (2.2%)
Who
in
departure information on the subset (of about half) of our 1,631 departing
firms before 1985.
many
we
CEOs joined
universities.
of the departed
America
for post-
CEOs who left their
another corporation
We were unable to find
CEOs
(most of
whom
believe that the most likely cause for the
retirement or death.
also presents a histogram describing the frequency distribution of years
CEO for the 8,786 CEO-year observations from the subsample of CEOs leaving
during the sample period: Panel
CEOs
in
one of their
D shows that about half the CEO-year observations
last three full fiscal
years in office. Note that the distribution in
D is not representative of the full population,
the sample period can have at
longitudinal dataset.
most 18 years
since
CEOs who
—
left in office
the
leave their firms during
number of years covered by our
Robert Gibbons and Kevin J. Murphy
Figure
is
1
based on
all
CEOs
1,631
In our empirical work,
period.
August, 1990
18
leaving office during the 1970-1988 sample
however, we analyze first-differences and eliminate
observations with missing pay and performance data; this leaves 1,292
CEO-year observations.
corporations, or 6,737
In
what follows we refer
subsample as the completed-spells subsample. Table
completed-spells subsample.
been
in his position for
three to four years.
Column
(1)
shows
presents
1
that the average
He receives
90% comes
consumer price index
1
in the
subsample has
form of a base salary and
in the
and subsequent analyses are adjusted for
for the closing
month of the
1988-constant dollars. Adjusted for inflation, the average
We
CEO
statistics for the
annual compensation (excluding both grants of and gains from
annual bonus. All monetary variables in Table
by 6.6% per
summary
to the latter
almost nine years, and will continue in his position for an additional
exercising stock options) of $616,300, of which
inflation (using the
CEOs representing 785
CEO's
fiscal year) to represent
salary
and bonus has grown
year.
matched the Forbes compensation data
performance data obtained from the Compustat data
in 1988-constant dollars (although the
median
is
files.
Average firm
only $2.2
(in
We define the change in shareholder wealth, AV
market value of common stock
(in millions) at the
inflation-adjusted rate of return
The sample average change
on
common
beginning of the
sales
exceed $4
t,
firms in the completedas the inflation-adjusted
fiscal
year multiplied by the
stock (including splits and dividends):
in shareholder wealth is a
billion
Shareholders have realized
billion).
average inflation-adjusted returns of 1.8% over the sample period
spells subsample).
and stock-price
to fiscal-year sales
$56 million loss with
AV =V .ir
t
t
t.
a standard
deviation of $1.9 billion.
Columns
(2)
and
(3)
of Table
1
report the
same summary
statistics for
two subsamples
of the completed-spells subsample: column (2) consists of CEO-year observations in which the
CEO is in his
Panel
and
A
last three full fiscal years;
shows
that
CEOs
their position than
column
(3) consists of the
complementary subsample.
near retirement are older and have served longer in both their firm
CEOs
with
many
years remaining.
Panel
B shows
that
CEOs
near
Robert Gibbons and Kevin J. Murphy
August, 1990
19
CEOs
retirement are better paid than
with
many
years remaining.
deviations of pay changes and percentage pay changes are higher for
performance (and hence more variable) as
CEOs
CEOs
near retirement;
we
pay becomes more sensitive
interpret these results as indirectly supporting the hypothesis that
to
The means and standard
C
approach retirement. Panel
shows
that
average firm size (as measured by either sales or market value) and average firm performance
(as
measured by
similar in the
The
change
either the
in shareholder
wealth or the shareholders' rate of return) are
two subsamples.
last
row of Table
shows
1
that
CEOs
with
many
years until retirement are over-
represented in the early years of the sample. This over-representation
CEOs
methodology: the completed-spells subsample includes only
is
a direct result of our
actually leaving office
between 1970 and 1988, so there cannot be any CEO-year observations with more than three
years remaining in the last three sample years, 1986-88.
An Empirical Specification for CEO
describes the optimal linear relation between compensation and output in
Our model
period
w
t,
t
Contracts in the Presence of Career Concerns
and y t
.
We
assume
that shareholders seek to
maximize
their wealth,
and we
consider two alternative empirical representations of output, yt in terms of shareholder wealth,
,
V
t.
First,
one could interpret y as the change
t
compensation contract
linear
w (yt) = c
t
t
+
in shareholder wealth in period
bty t simply
t;
w = c + b AV
becomes
t
one could interpret output y t as end-of-period firm value, y =
t
t
V
t.
t
t.
in this case, the
Alternatively,
In an efficient capital
market, beginning-of-period firm value equals the conditional expectation of end-of-period firm
value:
=
yt
-
(3.1)
V _i
t
E{y
= E{y
t lyi,...,
w
t lyi,...,
yt-i),
t
=
ct
y
t
_i).
Therefore, the change in shareholder wealth in period
and the linear compensation contract
+ b t [AV t +E{y t lyi,..., y t-i}].
w
t
=
ct
+
biy t
becomes
t is
AV
t
Both approaches share the feature
that the coefficient
approaches yield qualitatively similar
largely because
it is
more
August, 1990
20
Robert Gibbons and Kevin J. Murphy
tractable (as will
AV
is
t
b t consequently, the two
;
what follows, we take the second approach,
In
results.
on
become
clear below).
Substituting (2.21) and (2.22) into (3.1) yields
w
(3.2)
but (3.2)
is
m
=
t
+
t _i
+ b AVt
at
t
not convenient to estimate because
variable that depends on
all
m
t
_!
is
an individual-specific time-varying
prior realizations of output, as described in (2.23).
Because we
interpret y t as end-of-period firm value, however, the first-difference of (3.2) is a
Substituting (2.22) into the definition of change in
tractable empirical specification:
shareholder wealth,
lagged version of
m
(3.3)
AV = y
t
E{y
-
t
t -i
=
m
t _2
L
= yn
t _i
<$
+
y t -i}, yields
lyi,...,
AV
this expression,
oi+(t-l)a
2
-
a t-i
-
AV
t
=y
t
at
CEO
t
effort
t
t
and
this year's
a2
,
o^+(t-l)a
2
which suggests the empirical specification
Aw
(3.5)
where
ot t
= Aa
t,
(3 t
t
=
oc
t
+
pt
AV
= b and y
t
,
t
t
+
f
Yt
t -i.
Substituting the
AVu
Aw = Aa + b AV +
t
m
t
and
AV _i
t
,
<&
i
o^+(t-l)a 2
bt-
>t-l
CEO compensation are a
last year's
wealth:
(3.4)
-
m -2, into (2.23) then yields
Thus, the first-difference of (3.2) implies that year-to-year changes in
function of the change in
more
AVM
,
change
in
shareholder
Robert Gibbons and Kevin J. Murphy
we
In our model,
August, 1990
21
take the worker's total career to be fixed.
A
worker with fewer
periods remaining therefore has worked for more periods, so the market has a more precise
belief about his ability.
career lengths
(i.e.,
As Panel
completed durations
on the empirical specification
remaining
in a
of exposition,
state these
monotonically with
HI
.
(3.5),
CEO's career and
we
A of Figure
t;
the
1
illustrates,
in office).
we
however,
CEOs
have heterogeneous
In formulating testable hypotheses based
therefore distinguish between the
number of years already spent
hypotheses for the case
in
number of
For ease
in office (tenure).
which the optimal slope b
t
years
increases
analogous hypotheses can be derived from the result that b t < bj
CEO constant, the
increases as tfie CEO nears retirement.
Holding tenure as
slope of the compensation contract, pt
,
Career concerns provide fewer incentives as the CEO nears retirement, so
by current compensation increase.
the incentives provided
H2. Holding years remaining as
contract,
CEO
constant, the slope of the compensation
p increases with tenure as CEO.
t,
The optimal
relation between pay and current performance in part reflects
with incentives to
the trade-off between the goal of providing the
increase shareholder wealth and the goal of providing efficient risk-sharing
for the risk-averse CEO. The optimal pay-performance relation increases
when the variance of output decreases, since at the same pay-performance
CEO
CEO bears less risk as variance decreases. The CEO's true
managerial ability becomes estimated more precisely as tenure increases;
consequendy, the variance of y t decreases and the pay-performance relation
relation the
increases as the
H3
.
Holding tenure as
CEO's
CEO
tenure increases.
constant, the coefficient
period t-1, yt decreases as the
,
CEO
on shareholder-wealth change
in
nears retirement.
on the change in shareholder wealth in period t-1 has two
and -b t_i. The first term reflects the effect of
AV _i on the updated estimate of ability in period t; this effect depends only
on tenure as CEO and is independent of years to go. The second term
The
coefficient
components,
a£/(a^+(t-l)cr£)
t
decreases as the CEO nears retirement
concerns provide smaller incentives.
H4. Holding years remaining as
shareholder wealth in period
CEO
t-1,
{i.e.,
b
t _i
increases) since career
constant, the coefficient on the change in
y decreases with tenure as
t
,
CEO.
Robert Gibbons and Kevin J. Murphy
Both
22
a^/(of+(t- 1 )al)
and -b
August, 1990
decrease as tenure increases because the
t _i
estimate of managerial ability becomes
Performance Pay and Years Left as
Hypothesis HI predicts
performance
hypothesis
will
more
precise.
CEO
that the relation
be higher for executives close
between
CEO
A
to retirement.
pay changes and current
way
simple
to evaluate this
estimate a regression that allows the pay-performance relation to vary with
is to
years remaining as
CEO:
18
Aw = a + pAV +
(3.6)
it
it
^p
I T (CEO has x years
left) it
*AV
,
it
T=0
where (CEO has x years
remaining in his career
left)i t is
a
dummy
in fiscal year
performance relation increases as the
least four potential
CEOs
measure
analysis, since
CEO
salaries,
(3.6) directly,
AVj
t,
is
net of
>
the
-
however.
payments
th
CEO
has x years
the slope of the pay-
>
Pi
\
-
•> PisFirst,
to the
There are
at
our empirical
CEO, while our
before these payments. This difference has a negligible effect on our
compensation
Second, while Aw; t should include
on
nears retirement, Po
problems with estimating
is
if
Under Hypothesis HI,
t.
definition of shareholder-wealth change,
theoretical
variable equal to one
is trivial
all
compared
to
changes
in the
value of the firm.
forms of compensation, the Forbes surveys include data
bonuses, and some minor additional forms of compensation but do not include data
on grants of stock and stock options. To the extent
that a
CEO's holdings of stock
in the firm
increase with tenure, stockholdings will act to increase incentives as career-concern incentives
decrease, so our estimates of the change in the pay-performance relation as the
retirement
may
concerns.
To
underestimate the shareholders'
the extent that
however, our estimates
compensation
CEOs
may
total
CEO
nears
response to the issue of decreasing career
decrease their stock holdings as they near retirement,
simply reflect the effort to provide incentives through
to replace those formerly
induced through stock ownership.
Robert Gibbons and Kevin J. Murphy
August, 1990
23
A third problem with direct estimation of (3.6), as noted in connection with Table
that
CEOs
1, is
near retirement are over-represented in the later years of the completed-spells
subsample, so the estimates of the p x's from (3.6) for the
CEO
subsamples will reflect secular
trends in incentive compensation in addition to the effects of career concerns.
Appendix Figure Al, the
relation
As shown
in
between pay and performance has increased over the past
decade, so the estimate of p T 's for
CEOs
near retirement are likely to he biased upward.
Fourth, and perhaps most important, (3.6) assumes that the relation between pay and
CEOs
performance differs across
remaining as
performance
—
CEO
One
in shareholder
firm value
Awt/AVO
may
decline with firm size both because the variance of
wealth increases with firm size and because the CEO's direct effect on
may decrease
We
years
potentially important source of heterogeneity is firm size: the
optimal pay-performance relation
changes
number of
does not allow for other sources of heterogeneity in the pay-
(3.6)
relation.
(and within a CEO's career) only by the
show below
with firm
size.
connection with Table 3) that the pay-performance relation
(i.e.,
varies significantly with firm size but that the pay-performance elasticity
(i.e.,
Aln(w t)/Aln(V t))
is
(in
almost invariant to firm
related heterogeneity
size.
We
therefore attempt to control for size-
by converting the regression variables
to logarithmic
changes and then
estimating an elasticity form of (3.6) that allows the pay-performance elasticity to vary across
years:
1988
Aln(w
(3.7)
it)
=
Van (n
a+
th
year
dummy)i t
n=1972
1988
18
+
[Po
+^Pt(CEO
has x years
left) it
year
th
year dummy)i t ]*Aln(V iL),
Aln(Vjt)=ln(l-i-ri t ) is the continuously accrued rate of return
dummy)i
t
is
a
dummy
logarithmic change in the
12
p n (n
n=1972
T=0
where
+ ]T
variable equal to one if n=t.
CEO's
salary and
bonus
(in
We
on
common
stock and (n*
define Aln(w; t ) as the annual
thousands). 12
We also used a more comprehensive measure of compensation that includes fringe benefits, and contingent
(but non-stock) remuneration.
The
qualitative results from these regressions are similar to those presented in the
Robert Gibbons and Kevin
J.
Murphy
24
August, 1990
Figure 2 depicts the estimated pay-performance elasticities from (3.7) for
grouped based on
or
their years
CEO. (To
remaining as
more years remaining have been pooled.) The
.06,
which
is
CEOs
simplify the figure, observations with 15
figure
drawn assuming
is
CEOs
the average of the 17 estimated year coefficients.
a year effect of
in their final year,
second-to-last year, or third-to-last year have estimated pay-performance elasticities of .179,
.199,
and .184, respectively. Each of these estimated
estimated elasticity for
CEOs
elasticities is significantly
higher than the
year (.120) or sixth-to-last year (.115); no
in their fifth to last
other pairs of coefficients in Figure 2 (including pairs involving the highest estimated elasticity
for
CEOs in
5%
their eleventh-to-last year) are significantly different at the
Figure 2 suggests
that, in general,
pay-performance
level.
elasticities are
higher for
CEOs
nearing retirement, but also suggests that separate coefficients based on years remaining as
CEO are estimated with large standard errors.
correspond to
we
CEOs
Since the only significant differences in Figure 2
in their last three years vs.
CEOs
with more than three years remaining,
divided the completed-spell subsample into two groups and estimated the following
regression:
1988
Aln(wi t) = ao + ai (Few Years
(3.8)
Left)it
+
^^(n
111
year
dummy)i
t
1988
+
[Po
+
P!(Few Years
Left)i t
+ ]£Pn(n th
year
dummy) ]*Aln(V;
it
t ),
n=1972
where (Few Years
Left)it is a
dummy variable
years of his career in fiscal year
Column
(1)
if
the
i
CEO
lh
is in
the last three
t.
of Table 2 reports estimates of regression (3.8) for the completed-spells
subsample.
CEOs
category.
The (unreported) estimated
interactions range
equal to one
serving in their last three years as
from .02
CEO are assigned
coefficients
to .20, indicating that
to the
"Few Years
on the (Shareholder Return)* (Year)
CEOs
with
many
years remaining receive
between .2% and 2.0% raises for every 10% return realized by shareholders.
tables, but the significance levels are generally
additional measures of compensation.
much
Left"
The
lower, reflecting the noisiness of the data on these
Robert Gibbons and Kevin J. Murphy
25
Return*(Few Years Left) coefficient
is
August, 1990
also positive, suggesting that
remaining receive an additional .44% raise for every
Return*(Few Years Left) coefficient
is
10%
CEOs
with few years
return realized by shareholders.
highly significant (t=3.0), which
we
The
interpret as
empirical support for the Hypothesis HI.
Our
arbitrary,
Few Years
definition of
Left
— CEOs
and we re-estimated the regression
definitions of
Few Years
in their last three years
column
is
admittedly
(1) of
Table 2 for three alternative
Left: executives in their last one, two,
and four years as CEO. The
in
estimated Return*(Few Years Left) interaction coefficient
significant except
—
when Few Years
Left
is
defined as
CEOs
is
positive in all cases and
in their final year;
we
believe this
insignificance reflects both small sample size and non-performance-related payments
CEOs in
is
made
to
their last year.
The
hypothesis:
results in
CEOs whose
performance
remaining
Table 2 support hypothesis HI, but also support an alternative
total stay in office is
elasticities than
until retirement.
do
CEOs who
only a few years
may have
higher pay-
stay in office longer, independent of years
We tested this alternative hypothesis by repeating the regressions in
Table 2 for the subsample of
CEOs who had
None of the qualitative results
spent at least five years in office upon retirement.
in Table 2 are changed, suggesting that our results are not driven
by cross-sectional (negative) correlation between
total
time in office and the pay-performance
elasticity.
Performance Pay and
Hypothesis
performance
CEO Tenure
H2
predicts that, holding years remaining as
elasticity increases
less uncertainty.
which includes controls
for
CEO
variable that equals one
the
CEO is in
with shareholder return.
constant, the pay-
with tenure because managerial ability becomes estimated with
We test this hypothesis in
if
CEO
the regression reported in
tenure: the
new
regressors are
his first four years as
Our model
column
"Low
(2)
of Table
Tenure," a
CEO, and Low Tenure
2,
dummy
interacted
predicts a negative coefficient on the
(Low
Robert Gibbons and Kevin J. Murphy
Tenure)*(Return) interaction.
26
The
positive (but insignificant) coefficient in
Under
inconsistent with this hypothesis.
however, the pay-performance relation
Holmstrom, 1982)
as
T| t+ i
=
Ti
t
+
v t>
that
August, 1990
is
managerial ability
(2) is
a plausible alternative formulation of the theory,
not predicted to increase with tenure: suppose (as in
is
not a fixed parameter
r\
but rather varies over time
where the innovations v are independent and Normally
distributed.
t
steady state, the market's uncertainty about the CEO's ability
independent of the CEO's tenure.
column
Thus, hypothesis
H2 would
is
In the
time-invariant and so
not be a prediction of this
alternative model.
Estimates Based on the Full Sample
The completed-spells subsample of 1,292 CEOs
their firm during the
who
actually leave
1970-1988 sample period represents only about half of the 1,900
(11,359 CEO-years) in the
full
sample
observations with missing data).
subsample include
(6,737 CEO-years)
CEOs
still
(after constructing first differences
CEOs
in the full
sample but not
in the
serving at the end of the 1988 fiscal year and
CEOs
and eliminating
completed-spells
CEOs
of firms that
were deleted from the Forbes survey. 13 Data from these additional observations are useful for
two reasons.
First,
although
corresponds to one of his
tell
we cannot
last three
tell
whether the CEO's
years in office, for
many CEO-year
whether he has more than three years remaining as CEO.
additional observations can be used to estimate
more
(3) of
observations
CEOs who do
can
2.
(2) for the full
not leave their firms during the sample period.
regression contains two additional explanatory variables: "Can't Tell If
A
we
Second, data from these
Table 2 reports results from the re-estimation of column
sample of CEOs, including
13
observed year
precisely the year effects and shareholder
return*year interactions in columns (1) and (2) of Table
Column
final
Few Years
The
Left," a
of 623 firms were deleted from the Forbes surveys during the 1970-1988 sample period. Of
"going concerns" as of 1989, 290 were acquired by or merged with another firm (127 of these
were acquired or merged within two years of the Forbes delisting), and 56 liquidated, went bankrupt, or went
these,
total
277 are
private.
still
Robert Gibbons and Kevin J. Murphy
27
August, 1990
dummy variable that equals one if the CEO-year observation
on a
CEO who does not belong
dummy variable with
(2)
to the completed-spells
is in
the last three years of the data
subsample, and an interaction of
Shareholder Return. The results are similar to those reported
in
this
column
and are consistent with the primary implication of the career-concerns theory: the pay-
performance
elasticity increases as the
CEO approaches retirement.
Years Remaining and Pay for Lagged Performance
Hypotheses
H3
H4
and
predict that the relation between current
CEO pay changes and
the previous year's performance should decline with both years remaining as
We re-estimated
tenure.
CEO and CEO
the regressions in Table 2 after including lagged shareholder return
and interactions of lagged return with Few Years Left,
dummy variables. The magnitude
Low
Tenure, and the seventeen year
and significance of the coefficients reported
in
Table 2 were
not affected by including lagged performance, reflecting the low correlation between current
and past stock
returns.
The
coefficients
on the new interaction terms
Years Left) and (Lagged Return)*(Low Tenure)
hypotheses
H3 and H4 are not
—were
—(Lagged Return)* (Few
insignificant in all regressions. Thus,
supported by our data.
Performance Pay and Expected Years Left as
CEO
In formalizing the theory of optimal contracts in the presence of career concerns, we^
assume
that the
CEO's
final year is
known with
certainty, but
executives retire earlier or later than they were expected to
on optimal
CEO
explicit incentives
than on the
CEO's
may
therefore
retire.
depend more on
actual years remaining (as
it
The
seems
likely that
many
effect of career concerns
the expected years remaining as
measured
after retirement has
been
observed).
As shown
in Panel
C of Figure
1
,
many
executives leave their position
age 64 or 65. One estimate of the expected years remaining
until the
CEO reaches
65.
We re-estimated
is
the regression in
the
when
they reach
number of years remaining
column
(1) of
Table 2 after
re-
Robert Gibbons and Kevin J. Murphy
defining
the
"Few Years
CEO is
The
coefficient
is
(i.e.,
dummy
variable that equals one
if
within three years of reaching age 65, or older than age 65).
Thus, hypothesis
HI
is
not supported
when
"years remaining until
used as a proxy for expected years remaining.
We
also conducted a three-stage investigation in
spells
subsample
board
at the
to estimate the
CEO's
beginning of each period, including age, firm and
We
sample, and set the
for all
was
used the completed-
CEO
tenure,
and prior
CEO-year observations
dummy variable (Few Expected Years Left)
the estimated horizon
first
sales,
then used these estimated parameters from
compute estimated years remaining
the first stage to
less than three years.
Finally,
we
in the full
equal to one for an observation
used
this
new dummy
variable
of regression 3.8) with and without year and tenure effects.
to re-estimate versions
coefficient
which we
years remaining using information available to the
stock-price performance, and compensation.
if
Left," a
on the interaction term (Return)*(Few Expected Years Left) was positive but
statistically insignificant.
age 65"
"Few Expected Years
Left" as
age 62 or older
August, 1990
28
The
on the interaction term (Return)*(Few Expected Years Left) was positive but
insignificant (using the uncorrected standard errors) in all regressions.
not supported
when expected
years remaining
is
Thus hypothesis HI
is
substituted for actual years remaining in this
way.
The board of
directors' assessment of a
information not available to us, including the
or explicit mandatory retirement policies.
experiments reported above
—
years remaining
is that
— using
CEO's
One
CEO's horizon
is
obviously based on
health, potential replacements,
and implicit
interpretation of the insignificance
from both
either age-based or regression-based proxies for expected
actual years remaining
proxy for expected years remaining than
is
(i.e.,
"Few Years
Left" in Table 2)
is
a better
either the age-based or the regression-based proxy.
Both the age- and regression-based proxies tend
to classify older executives into the
Few
CEOs
tend to be excluded from this group.
But
Expected Years Left group, while younger
many
older
CEOs have
long remaining careers (and therefore have small explicit incentives,
according to our model); including these
CEOs
in
our "Few Expected Years Left" category
Robert Gibbons and Kevin J. Murphy
biases
downward
29
the coefficient
August, 1990
on the (Retum)*(Few Expected Years Left)
the market expects a lengthy subsequent career.
"Few Expected Years
when they
Left" category
Similarly, excluding
interaction term if
young CEOs from
the
are in fact near retirement (and therefore have
large explicit incentives, according to our model) also biases the interaction coefficient
downward.
Other Sources of Heterogeneity
As
in the
Pay -Performance Relation
noted previously, regression (3.6) allows the pay-performance relation to vary with
years remaining as
CEO,
but ignores other potential sources of pay-performance heterogeneity,
such as the effects of firm
we
In this section,
size.
justify
specification to control for size-related heterogeneity, and
control for other potential (but
Column
(1) of
(3.8) for the 1,292
also describe our attempts to
unknown) forms of heterogeneity.
Table 3 reports estimates of the non-logarithmic version of regression
CEOs
is
subsample. The coefficient on the interaction
in the completed-spells
A(Shareholder Wealth)*(Few Years Left)
performance relation
we
our use of the logarithmic
is
positive but insignificant, suggesting that the pay-
independent of years remaining as
includes two interaction terms,
AV *Sales
t
and
relation to vary quadratically with firm size as
CEO. The regression
AV *Sales 2
t
,
to
measured by net
in
column
(2)
allow the pay-performance
sales (in millions of 1988-
constant dollars). Based on average values for the (AShareholder Wealth)* (Year) effects, the
coefficients suggest that
CEOs in median
size firms (sales of $2.0 billion) receive average
changes of .930 for every $1,000 change in shareholder wealth.
(sales of
$400 million) and 90 th percentile
column
Years Left) coefficient, although
The
(1) to
(2) increases the
it
at the
10 th percentile
(sales of $8.2 billion) receive average
of .990 and .700, respectively, for every $1,000 change
size interaction terms in
CEOs
in shareholder wealth.
pay
pay changes
Including the
magnitude and significance of the
AV *(Few
t
remains insignificant.
increase in the interaction A(Shareholder Wealth)*(Few Years Left) from column
column
(2) of
Table 3 suggests that
it
is
important to control for size-related
Robert Gibbons and Kevin J. Murphy
30
heterogeneity in the pay-performance relation
compensation contracts. One
on the observation
that the
August, 1990
when
testing for career concerns in
common way of controlling
pay-performance
CEO
for size-related heterogeneity, based
elasticity is relatively invariant to firm size, is to
convert the regression variables to percentage changes or logarithmic changes; see, for
example, Coughlan and Schmidt (1985) and Gibbons and Murphy (1990).
Column
column
(1)
(3)
of Table
performance
of Table 3 simply repeats the elasticity specification (3.8) reported in
Column
2.
elasticity to
(4)
of Table 3 includes interaction variables to allow the pay-
vary quadratically with size as measured by net
sales.
Although the
size-interaction variables are individually insignificant, they are jointly significant (at the
level), indicating that
pay-performance
elasticities are slightly
2%
higher for larger firms. The
estimated coefficient on the (Shareholder Return)*(Few Years Left) interaction in column
(4),
column
(3).
however,
is
extremely close
These results suggest
in
magnitude and significance
that the logarithmic specification
to its counterpart in
removes the
from the estimated
size bias
career-concerns coefficient.
Although the logarithmic specification controls for
performance
relation, other sources
size-related heterogeneity in the pay-
of potentially important heterogeneity remain.
Some
of the
heterogeneity reflects secular trends, which can be controlled for by including year interaction
variables, but other possible sources of heterogeneity include reflect firm or industry factors
not yet incorporated into our theory or specification.
by allowing the pay-performance
elasticity to
We attempted to control for these factors
vary across firms:
1988
Aln(wi t )
(3.9)
=
a;
+ ai(Few
Years
Left)it
+
^an
(n
th
year
dummy)i
t
n=1972
1988
[Pi
+
Pi(Few Years
Left)i t
I
+ ]T PnCn*
year dummy); t ]*Aln(Vi t ),
n=1972
where
oq
and
P;
are firm-specific intercepts and pay-performance elasticities, respectively.
Robert Gibbons and Kevin J. Murphy
We
subsample
August. 1990
31
estimated (3.9) for the subsample of 625
that
had
at least
four years of data. 14
The estimated
Left)it is positive (Pi=.0297) but insignificant (t=1.4).
in
magnitude
performance
to the coefficient in
elasticities to
somewhat diminished
performance
column
(1) of
The point
the completed-spells
(Few Years
coefficient on
estimate, however,
is
similar
Table 2 (Pi=.0436), which constrained the pay-
Thus, our support of hypothesis
be equal across firms.
after controlling for firm-specific heterogeneity
elasticity to
HI
is
by allowing the pay-
vary across firms.
Conclusion
4.
The driving
CEOs from
force behind our theoretical analysis is that an individual's actions are
influenced by career concerns.
We extend previous research by showing that career concerns
can have important effects on incentives even in the presence of contracts.
We also show that
optimal compensation contracts neutralize career-concern incentives by optimizing the total
incentives
when
—
from the contract and from career concerns
explicit contractual incentives are high
implicit career-concern incentives are low, and vice versa. In developing our model,
we
have kept the analysis tractable by making strong assumptions. Weaker assumptions would
—
undoubtedly allow additional effects to emerge, but our primary qualitative results
that career
concerns affect incentives and that optimal contracts account for these implicit incentives
seem
likely to be
robust
Perhaps the most natural application of the idea that optimal incentive contracts optimize
total incentives is to promotions. 15
It
would be useful
contracts in the presence of career concerns with a
14
We estimated (3.9) in two stages.
to integrate our
model of optimal
dynamic model of learning and job
we regressed the dependent and each of the independent
by CEO. In the second stage, we regressed the residual from
regression involving the dependent variable in (3.9) on the residuals from the first-stage
In the first stage,
variables in (3.9) on shareholder return, AlnCVjt),
the first-stage
regressions involving the independent variables in (3.9). After adjusting standard errors for the correct degrees of
freedom, the results from the second-stage regression are equivalent to estimating (3.9) with CEO-specific
intercepts and slopes (on shareholder return).
15
Rosen's (1986) model can be interpreted in terms of promotions but does not allow new jobs to have new
technologies or for workers to be matched to jobs.
Robert Gibbons and Kevin J. Murphy
assignment. The
latter
August. 1990
32
could involve symmetric learning, as in
MacDonald (1982) and Murphy
(1986), or asymmetric learning (where the current employer learns a worker's ability faster
than a prospective employer does), as in
model would endogenize
career
we
transitions
take as exogenous.
We
Waldman
(1984) and Ricart
i
Costa (1988). Such a
between jobs, which would improve upon the T-period
expect the development of such models, together with the
development of new data sources on internal organization,
research on incentives and organizations.
to
be an important part of future
Robert Gibbons and Kevin J. Murphy
33
August, 1990
Appendix
This Appendix discusses four issues: (1) the difference between the multiplicative
exponential utility function (2.2) and the additive exponential
assumption that short-term contracts are
(4) the solution to the
1)
The
Utility
utility function; (2) the
linear; (3) renegotiation-proof
long-term contracts; and
T-period model.
Function
We now adopt the more conventional assumptions that the worker's exponential utility
function
is
additively separable and that the worker has
case, these assumptions
(Al.l)
U(wi,
to credit. In the
ai, a 2 )
;
=
-
exp (-r[wi
role of career concerns,
-
g(ai)])
-
5 exp (-r[w 2
we continue to impose
-
g(a 2 )])
is
particular, (2.13)
then the
same whether we use
and (2.15) continue
.
assumptions (Al) and
(A2): short-term contracts are linear and long-term contracts are not feasible.
period problem
two-period
imply that
w2
on the
In order to focus
no access
The second-
(2.2) or (Al.l) for the utility function; in
Given the market's conjecture
to hold.
equilibrium play in the second period, however, the worker's first-period problem
is
ai
and
now
to
choose ai to maximize
(A1.2)
-
E{exp
=
(-r[ci
+
-
bi(r,+ai+ei)
g(ai)]) }
b^+a^b*)-^)
-
5E{exp
-
exp (-r[mo + (l-bi)ai + biai
-
6 exp (-r[mo + a2 (b 2 )
(-r[c 2 (b|)
+
-
-
g(ai)
g(a2 (b 2 ))
+
-
-
g(a*(b*))]) }
-rb^])
(l-b 2 )p(ai-ai)- \
r2>j2(l-p2) + p 2)])
,
Robert Gibbons and Kevin J. Murphy
where p = o^/
(o^
+
first-order condition
(A1.3)
34
The worker's optimal
o£).
=
g'(ai)
EXP2 =
bi
+
5 (1-b*)
—JL-
(-r[(l-bi)ai
exp(-r[a2(b*)
-
Thus, the worker's equilibrium expected
-
exp (-r[mo +
-
where
(A1.5)
ai is given
-
g( ai )
||p
•
-
-
biai
g(aj(bj))
utility
- Bi
where
,
g(ai) -^rb]Z]])
+
and
(l-bj)p(ai-ai)
given an arbitrary
-
2
2
\ rZ?[b2 (l-p )
first- period
+
slope bi
p2]])
.
is
-|rb£?j)
-
g(a*(b*))
by (A1.3). The optimal bi therefore
-
^(baftl-p 2) +
satisfies the first-order
p2)])
,
condition
[l-g'CaiHa^rbiL
bi
=
1
It
ai
+
5 exp (-r[mo + aj(b|)
Implicitly differentiating
(A 1.6)
first-period effort, aj (bi), therefore satisfies a
analogous to (2.16):
EXP1 = exp
(A1.4)
August, 1990
(A 1.3) and solving for
1
-
+
r
a'i
implies that
(Bi -bi)
*,
z\ g"[ar(bi)]
remains only to show that bi as given by (A 1.6)
Intuitively, this inequality holds for the
is less
same reasons given
than b2 as given by (2.13).
in the text: noise reduction, career
concerns, and human-capital insurance. Formally, suppose bi
>
b2-
Since g'(ai)
= Bi >
bi
>
Robert Gibbons and Kevin J. Murphy
b2 =
and g" >
g'(a2)
0,
35
>
then follows that ai
it
August, 1990
&2-
Since
g"'
£
0,
we have
>
g"(ai)
g"(a2),
so Zj g"(ai) > Zj g"(a2), but this implies bi< b2, a contradiction.
2) Linear Short-Term Contracts
To keep our
theoretical analysis simple,
contracts are linear in output.
in the
n.)
that short-term
Holmstrom and Milgrom (1987) demonstrate
like the single-period version of
ability,
we assumed
(i.e.,
that a
one-period)
model much
our model (but lacking the uncertainty about the agent's
can be reinterpreted so as to ensure that the optimal contract
Holmstrom-Milgrom model
is to
The key
is linear.
reinterpret output in the single-period
step
model as the
aggregate of outputs over time in an underlying dynamic model, as follows:
Suppose a worker
on a day-to-day
basis.
either high or low,
is to
Each
be employed for a year, but can control the production process
day's production is an independent Bernoulli
and increased
effort
trial (i.e.,
output
is
on a given day increases the probability of output being
high that day). The worker observes output each day, and so can choose future effort levels in
response to past output realizations. After rewriting the worker's
accommodate
this
utility
function in (2.2) to
underlying dynamic model, Holmstrom and Milgrom show that the optimal
compensation contract for the year
is
equivalent to repeating the static contract that
is
optimal
for each one-day incentive problem. Therefore, the optimal contract for the year depends on
only the aggregate output produced during the year and
is
linear in this aggregate. 16
limit (as the output that a Bernoulli trial represents shrinks
instant, in a suitably
from
that
of a day to that of an
normalized fashion), the worker continuously controls the
dimensional Brownian motion. Again, the optimal compensation contract
output, and
now
In the
aggregate output
is
Normally
Holmstrom-Milgrom model, a
In the
is
drift
of a one-
linear in aggregate
distributed, just as is £[ in (2.1).
contract that
is
linear in year-end aggregate output
provides the agent with a constant incentive for effort on each day of the year (while a step-
1
to
The optimal one-day
be paid
if
output
is
low
incentive contract specifies a
(x~).
If there are
Hw + + (N-H)w" = H(w + -w") + Nw", which
is
H
wage
w+
to
be paid
if
output
is
high (x + ), and a wage
high-output days during an N-day year, then the year's
indeed linear
in the year's output,
Hx + +
(N-H)x".
wage
w
is
Robert Gibbons and Kevin J. Murphy
August. 1990
36
function contract of the kind analyzed by Mirrlees (1974) would provide very different
We
incentives).
believe that there
constant incentive for effort, even
for insurance.
assuming
Given
the
a
is
when
good deal
to
be said for providing the agent with a
uncertainty about the agent's ability creates a
Holmstrom-Milgrom
linearity result,
new need
our assumption (Al) amounts to
provided by reducing the slope of the linear contract that would
that this insurance is
be optimal in the absence of such uncertainty.
3) Renegotiation-proof Long-Term Contracts
We now relax
assume
our assumption that long-term contracts are not feasible. Instead,
that (linear) long-term contracts are feasible but
To keep
renegotiation-proof) at each date.
Suppose
period case.
the
must be Pareto-efficient
that at the beginning of the first period, prospective
that the contract the
employers
worker accepts binds both the firm and the worker, but
parties will renegotiate the contract if
period
(i.e.,
it is
We
that the
Pareto-inefficient at the beginning of the second
after first-period output is observed).
We continue to assume that one-period contracts must be linear: wj(yi) = ci
W2(yi,y2)
(i.e.,
argument simple, we consider only the two-
simultaneously offer a worker fwo-period contracts of the form (wi(yi), W2(yi,y2)).
assume
we
=
+ b2iyi + b22y2- Renegotiation-proofness then implies
C2
that b22
+
biyi and
= b2 from
(2.13) and hence that the worker's second-period effort choice is a2(b2) satisfying (2.6).
Furthermore, given the
first-
function (2.2),
utility
and second-period wages on
we
can set b2i = 0: any desired dependence of
first-period output
can be replicated through the appropriate
choice of bi. Thus, the worker's optimal first-period effort choice
order condition g'(ai)
=
The
bi.
first-period competition
therefore amounts to choosing ci, bi, and C2 to
(A3.1)
-E{exp
(-r[ci
rS[c 2
among
given by the
-
g(a0]
+ b2(r,+a2(b2)+e 2 )
-
g(a*(b2))])
first-
prospective employers
maximize the worker's expected
+bi(Ti+at(bi)+ £l )
-
ai (bi) is
}
utility,
Robert Gibbons and Kevin J. Murphy
37
August, 1990
subject to a zero-expected-profit constraint for the firm,
(A3.2)
ci
Arguments
+
5c 2
= (l-bi)[mo +
parallel to those in the text then
(A3.3)
bi
1
+rE 2
1
which
is
show
r
1
=
+ 5(l-b*)[mo+
a?(bi)]
g"[a 1 (b 1 )]
precisely the optimized value of
that the optimal first-period slope satisfies
2
b* a g"[af (bi)]
5
+rL 2
1
a*(b*)]
g"[a 1 (b 1 )]
I
Bj given
—the optimal
in the text
career-concerns model. Thus, the sequence of one-period contracts
the text provide exactly the
same
would
incentives as
total incentive in the
we identify
as optimal in
the optimal renegotiation-proof long-term
contract derived here.
4)
The
T-Period Model
We
first
derive the first-order conditions (2.24) and the optimal total incentives and
contract slopes (2.26) and (2.27).
We then prove that for any
t
<
T, bf
< bp.
Substituting (2.21), (2.22), and (2.23) into the worker's utility function (2.2) yields
the worker's utility
intercepts given
choices (ai,
(A4.1)
...,
U
by
a^),
from a sequence of contracts with slopes
-
...,
bj) and associated
(2.21), given the market's conjectures (ai, ...,ar), the worker's effort
and the output realizations
= -exp(-r{Xli5
=
(bi,
exp ( -r{
Xli
5
t- 1
1- 1
[c t
(yi,
...,
yx):
+ b y -g(a )]})
l
t
t
"
[(1-bOfit
+
% +ff
°2
q
+b tyt
"
g(*)
Robert Gibbons and Kevin J. Murphy
August, 1990
38
0-btK
;?^2S.'.<*-w]})
=
-
exp ( -r{
Xl
1' 1
t
5
(l-b t )crf
+
yr
S
exp (
5
-r {
Xli
1" 1
[fit
+
(1 - b
y-t
= l+1
^P ( -r(£Ii
m
+
[d-bOSt + ^"+
(t-l)4
btyi
g(a °
"
^«
(yt
-a t))]})
<£+(T-l)a.
^"^"
°
"
g(aO +
B
t
(y t
-
fi
-
g(aO +
B
t
(a t
-
a,)] } )
t )]
ff
M
[St
+
^w^°2
}
exp(-r{£T iSM Bt (Ti+EO })
where B t
is
To
,
defined in (2.24).
apply (2.12) to the
distributed with
mean
M = (EIi
V
)
=
Maximizing
8t "
(XLs
t
last
term in (A4.1), note that
^J=1 5
worker's expected
"1
B
t
(T|
+ e t)
is
Normally
M and variance V, where
lB t) mo
-1
md
B )2a ^ + XI
t
5l 1
(
lB t) 2 ^
the worker's expected utility with respect to (ai,
conditions (2.24).
1
...,
After imposing the equilibrium condition
utility
aj) then yields the first-order
(ai, ...,ar)
from a sequence of contracts with slopes
(bi,
...,
=
(ai
,
—, aj), the
by) becomes
Robert Gibbons and Kevin J. Murphy
EU -
(A4.2)
—
August, 1990
XL, *-'[? + ££^j§
p ( -r{
( 1 r2 {
«P
which simplifies
39
(££,
5-1 B,)2 of +
and then yields the optimal
to (2.25)
Jftft
££,
+ B,mo]
)
B,)2 of } )
(a'"'
total incentives
,
given in (2.26) and the
optimal contract slopes given in (2.27).
We now show that b
t
< br
for any
t
<
The proof involves
T.
the following
Lemma.
T
Lemma. For each
€
t
{1,
T-l},
....
£6W B*^0.
T=t+1
By
Proof.
induction. For
=
T-l, (2.26) implies
(l-Bf)-rg"(at)^Bf =
(A4.3)
where
t
(for
any
t)
L^
=
cf^
Bt >
because
,
+ a2 and a2= a 2 a2 I
,
(ta
2
+ a 2)
is
the conditional variance of
T
the previous
t
output observations. For
t
<
T-l, suppose
£ S1
^
" 1" 1
BT >
We must
0.
T)
show
T=t+2
(A4.4)
X 5™ B*
=5B
t
*i
first-order condition for
1
(A4.5)
B,!i
1
>
,
or
B
t
*i
>
-
-
r
B l+ i, which
o2
g»(a,!o
£ 5™-
1
B*
.
T=t+2
T=t+2
T=t+1
But the
I S™" B*
+5
is
adapted from (2.26),
l
5^-t-l
is
B*T
—^%
=
1
+
r
which implies the second inequality
We first show that Bf < Bj.
2
Z H g"(a l+ i)
,
in (A4.4).
Q.E.D.
Restate the first-order condition for
B
t
,
given
(A4.5), as
Robert Gibbons and
(A4.6)
Kiivin
-
(1
J.
B?)
Murphy
40
rg"(a t ) [B?Z? +
-
August, 1990
I 8™ B*
<5&
]
=
T=t + 1
Since the objective function (analogous to (2.26) but restated for period
sid of (A4.6)
lefthand side
and only
negative (positive)
is
when evaluated
at
B >
t
(<)
t) is
B
t
concave
Thus,
.
B
in
B
<
t
t,
the
B-f if
if
(A4.7)
(1 -
Bft
-
[B^
rg"(a T )
£ 8™ B*
+ a?
]
<
,
i=t+i
where g"(a
(A4.6) becomes g"(ax) in (A4.7) because g'(a l (B l )) =
in
t)
Substituting (A4.3) into (A4.7) and applying
A
sic
To show
that
b t < br,
it
now
suffices to
show
the
Lemma shows
t
that
(2.24).
B* < Bj.
that
2
T
(T
I
(A4.8)
Zp < 1% and
B from
>
S^Cl-b*)
+ Cc-l)a£
o£
x=t+i
in (2.24); that is
rr
5(i_b* 1 )- r
(A4.9)
+
tCT
for
all
°e
which follows
negative,
bj <
1.
if
B* <
For
t
<
implies that b t+i
1
b^ <
for all
1
t.
2
T
JL_
+ 8
o
Given
S
rp-
5^-t-l
T= t+ 2
t.
1,
oi
-
>
,
+ (x-l)a 2
Since the lefthand side of (A4.6) evaluated
this,
(A4.9) follows by induction: For
T-l, suppose the second term in (A4.9)
<
°
(1-b*)
which completes the proof.
is
positive.
Then
t
at
Bt =
= T-l we have
the fact that
B
t
+i
1
is
that
<
1
Robert Gibbons and Kevin J. Murphy
41
August, 1990
References
Aron, D. (1987), "Worker Reputation and Productivity Incentives," Journal of Labor
Economics, 5: S87-S106.
Baron, D., and D. Besanko (1987), "Commitment and Fairness
Relationship," Review of Economic Studies, 54: 413-436.
in a
Dynamic Regulatory
Coughlan, A. and R. Schmidt (1985), "Executive Compensation, Management Turnover, and
Firm Performance: An Empirical Investigation," Journal of Accounting and
Economics, 7: 43-66.
DeGroot, M. (1970), Optimal Statistical Decisions,
New York:
McGraw-Hill.
Dewatripont, M. (1989), "Renegotiation and Information Revelation Over Time:
Optimal Labor Contracts," Quarterly Journal of Economics, 104: 589-619.
Fama, E. (1980), "Agency Problems and
Economy, 88: 288-307.
the
The Case
of
Theory of the Firm," Journal of Political
Freixas, X., R. Guesnerie, and J. Tirole (1985), "Planning under Incomplete Information and
the Ratchet Effect," Review of Economic Studies, 52: 173-191.
Fudenberg, D., B. Holmstrom, and P. Milgrom (1989), "Short-term Contracts and LongTerm Agency Relationships," forthcoming in Journal of Economic Theory.
and J. Tirole (1989), "Moral Hazard and Renegotiation in Agency Contracts,"
forthcoming in Econometrica.
Gibbons, R. (1987), "Piece-Rate Incentive Schemes," Journal of Labor Economics,
429.
and K.J. Murphy (1990), "Relative Performance Evaluation
and Labor Relations Review, 43: 30S-51S.
5:
413-
for Chief Executive
Officers," Industrial
Harris,
M. and
B. Holmstrom (1982), "A Theory of
Wage Dynamics," Review
of Economic
Studies, 49: 315-33.
Hart, O. and
J.
Moore
(1988), "Incomplete Contracts and Renegotiation," Econometrica, 56:
755-85.
—
Holmstrom, B. (1982), "Managerial Incentive Schemes A Dynamic Perspective," in Essays
in Economics and Management in Honour of Lars Wahlbeck, Helsinki, Finland.
and P. Milgrom (1987), "Aggregation and Linearity in the Provision of
Intertemporal Incentives," Econometrica, 55: 303-328.
and J. Ricart i Costa (1986), "Managerial Incentives and Capital Management,"
Quarterly Journal of Economics, 101: 835-860.
Kanemoto, Y. and B. MacLeod (1987), "The Ratchet Effect, the Market for Senior Workers,
and Intertemporal Commitment," Working Paper, Department of Economics, Queen's
University.
Robert Gibbons and Kevin J. Murphy
42
August. 1990
J. -J., and J. Tirole (1988), "The Dynamics of Incentive Contracts," Econometrica,
56:1153-1175.
Laffont,
Lambert, R. (1983), "Long Term Contracts and Moral Hazard," Bell Journal of Economics,
14: 441-52.
Lazear, E. (1986), "Salaries and Piece Rates," Journal of Business, 59: 405-431.
and S. Rosen (1981), "Rank-Order Tournaments as Optimum Labor Contracts,"
Journal of Political Economy, 89: 841-864.
MacDonald, G. (1982), "A Market Equilibrium Theory of Job Assignment and Sequential
Accumulation of Information," American Economic Review, 72: 1038-55.
J. Malcomson (1988), "Reputation and Hierarchy
Employment," Journal of Political Economy, 96: 832-854.
MacLeod, B. and
Mirrlees,
J.
in
Dynamic Models of
(1974), "Notes on Welfare Economics, Information, and Uncertainty," in Essays
on Economic Behavior Under Uncertainty, M. Balch, D. McFadden, and
(eds.), Amsterdam: North-Holland Publishing Co.
S.
Wu
A
Murphy,
K.J. (1986), "Incentives, Learning, and Compensation:
Theoretical and Empirical
Investigation of Managerial Labor Contracts," Rand Journal of Economics, 17: 59-76.
Ricart
i
Costa (1988), "Managerial Task Assignment and Promotions," Econometrica, 56: 44966.
Rogerson,
W.
(1985), "Repeated Moral Hazard," Econometrica, 53: 69-76.
Rosen,
and Incentives in Elimination Tournaments," American Economic
701-15.
Review, 76:
Smith,
C, and J. Warner (1979), "On Financial Contracting:
Covenants," Journal of Financial Economics, 7: 1 17-161.
S. (1986), "Prizes
Vancil, R. (1987), Passing the Baton:
Managing
the Process of
An
CEO
Analysis of Bond
Succession, Boston:
Harvard Business School Press.
Waldman, M.
(1984), "Job Assignment, Signaling, and Efficiency,"
15: 255-287.
Economics,
Rand Journal of
Robert Gibbons and Kevin J. Murpiiy
43
August, 1990
Figure
Frequency Distributions for
for
1
CEO Tenure, Firm Tenure, Age, and Years Remaining in Office
CEOs Leaving Office
During the 1970-1988 Sample Period 8
A
Panel
Panel B
70
_
Mean:
28.1
Median:
30.9
50
S
LiA
30
gL
20
10
_
10
5
Years as
Note:
25
i
30
Leaving Office
23 CEOs who left after more than 34
10
5
Years
CEO When
Histogram docs not include
years as
20
15
Note:
CEO.
lA.
20
15
in
30
25
40
35
45
50
Firm When Leaving Office
Histogram does not include 18
CEOs who
left after
more than 50
years in their firm.
C
Panel
Panel
D
oo
c^
300-
Mean.-
615
Median:
45
50
Age
Note:
63.4
of
55
60
CEO When
Histogram does not include 8
65
70
Leaving Office
CEOs who
left after
age 80.
es
^t
c*i
ti
H H
75
-^
©
H ^
c*>
Years Left
Note:
so
w>
*f
m
ts
—
'
H
in Office
Histogram does not include 107 CEO-years for CEOs with more
than 14 years remaining. (Histogram is based only on CEOs who
actually leave office during the sample period; these CEOs have at
most 18 years remaining).
based on 1,631 CEOs, representing 916 firms and 8,786 CEO-Years, leaving their
The empirical results in the paper are based on the subsample that
remains after constructing first-differences and eliminating observations with missing performance data. This
subsample includes 1,292 CEOs serving in 785 firms, or a total of 6,737 CEO-years.
Histograms and
statistics are
firms during the 1970-1988 sample period.
Robert Gibbons and Kevin J. Murpiiy
44
Tabic
Tenure, Compensation, and Corporate
Summary
August, 1990
1
Statistics for
"Complctcd-Spcll Sample" of CEOs Leaving
Office During the 1970-1988 Sample Period, Grouped by Years Remaining as
All
CEOs
leaving
Variable
Number of CEO-Years
CEOs
CEOs
in their
Sample Period
Last Three
Years in Office
(1)
(2)
office during
not in
their Last
Years
CEO a
in
Test Statistic
Three
Office
for
Differcnceb
(3)
(4)
6,737
3,117
3,620
59.1
61.2
57.3
/=29.4*
Firm
26.8
28.4
25.4
r=10.8*
Mean Tenure as CEO
8.9
9.6
8.2
1=8.6*
3.8
1.0
6.2
1=93.7*
$562,500
$592,800
$536,400
1=8.0*
$616,300
$649,000
$588,200
1=6.8*
$25,500
$123,300
$28,400
$140,400
$22,900
$106,500
F=1.7*
6.6%
23.3%
7.0%
26.7%
6.2%
20.0%
F=1.8*
$4,239
$4,417
$4,087
$2,352
$2,510
$2,215
1=2.1*
$53
$1,892
$19
$2,077
$83
$1,717
F=l.5*
1.8%
31.5%
1.8%
31.2%
1.8%
t=0.l*
31.8%
F=1.0*
1979.5
1979.1
1976.5
1=24.4
Panel A.
CEO Characteristics
Mean Age
Mean Tenure
in
Mean Years remaining
until
end of final
fiscal
as
CEO
year
Panel B.
Compensation
Statistics
Mean
Salary +
Mean
Total Compensation d
A(Salary
Bonus
+ Bonus)
Mean:
Std Dev:
A%(Salary + Bonus)
Mean:
Std Dev:
1=1.8
1=1.3
Panel C.
Firm Characteristics
Mean
($millions)
Total Sales
Mean Market Value of Stock
A(Shareholder Wealth)
Mean:
Std Dev:
Shareholder Return e
Mean:
Std Dev:
Mean
*
Fiscal
Year
The sample
is
constructed from longitudinal data reported in Forbes on 1,292
their firms during the
b
1970-1988 sample period.
* indicates that the difference
equality of subsample variances
Monetary variables
CEOs
1=-1.5
1=1.4
serving in 785 firms
who
leave
are in 1988-constant dollars.
between columns (2) and (3) is significant
with 3,116 and 3,619 degrees of freedom.
at the
5%
level.
F-statistics test the
c
(Tenure as CEO) and (Years Remaining as CEO) are evaluated in the middle of the fiscal year. Thus, a CEO retiring at
fiscal year-end would have .5 years remaining. This measure understates actual years remaining since it ignores
time served after the end of the CEO's final full fiscal year.
d
Total Compensation includes salary, bonus, value of restricted stock, savings and thrift plans, and other benefits
but does not include the value of stock options granted or the gains from exercising stock options.
e
Cumulative
rate of return
on
common
stock, defined as log(l
+ annual
return).
Robert Gibbons and Kevin J. Murphy
45
August, 1990
Figure 2
Estimated Pay-Performance Elasticities, by Years Remaining as
CEO
0.25
0.20
5
w
cs
£ 0.15-
au
ft-
0.10-
I
cs
ft-
a
0»
*!
0.05
53
E
V)
0.00
Years Left
in Office
The
figure depicts estimated coefficients from equation (3.7) in the text, given below, and is drawn
assuming a year effect of .06, which is the average of the 17 estimated year coefficients. The group
T-15 includes a small number of CEOs with more than 15 years remaining.
1988
Aln(w it ) =
a+ > a n (n tn year
dummy)j t
n=1972
1988
18
[p\)+^P T (CEO has
T years
left)i t +
Y
Pn(
nth y ear
dummy )j t ]*Aln(V
it )
n=1972
v=o
Each of the estimated elasticities for CEOs in their final year, second-to-last year, or third-to-last
year (.179, .199, and .184, respectively) is significantly higher than the estimated elasticity for
CEOs in their fifth to last year (.120) or sixth-to-last year (.115); no other pairs of coefficients in
the figure (including pairs involving the highest estimated elasticity, for
to-last year) are significantly different at the
5%
level.
CEOs
in their eleventh-
Robert Gibbons and Kevin J. Murphy
46
August. 1990
TABLE 2
Coefficients of Ordinary Least Squares Regressions of
Aln(CEO
Salary
+ Bonus) on Shareholder Return,
including interactions to allow the Pay-Performance Relation to vary with
Year, Years as
CEO, and Years Remaining
(t-statistics in
as
CEO a
parentheses)
Dependent Variable: Aln(CEO Salary + Bonus)
Independent
Variable
Predicted
Subsample of CEOs who
Sign
Retire Between 1975-1988
Full
Sample
(1)
(2)
(3)
Few Years Leftb
(Dummy Variable)
-.0090
-.0056
-.0085
(-2.0)
(-1.2)
(-2.0)
Low Tenurec
(Dummy Variable)
—
.0396
.0434
(8.4)
(11.2)
—
-.0095
Can't
tell if
(Dummy
—
Few Years Leftd
Variable)
(Few Years
(-1.4)
.0436
.0429
.0383
(3.0)
(3.0)
(2.9)
—
.0032
.0199
(0.2)
(1.6)
—
—
.0335
r2
.0833
.0929
.0927
Sample Size
6,730
6,730
11,359
Left)
(+)
*(Shareholder Return)
(Low Tenure)
(-)
*(Sharcholdcr Return)
(Can't
tell if
Few Years
Left)
"(Shareholder Return)
The sample
is
(1.8)
constructed from longitudinal data reported in Forbes on 2,236 CEOs serving in 1,204 firms
The subsample in column (1) includes 1,292 CEOs serving in 785 firms leaving their
from 1970-1988.
firms during the sample period.
Compensation
is
measured
in
thousands of 1988-constant dollars.
All
regressions also include intercepts, year dummies, Shareholder Return and Shareholder Return interacted
with the year dummies, allowing the pay-performance elasticity to vary by year.
a dummy variable that equals one if the CEO is in his last three years as CEO.
dummy variable that equals one if the CEO is in his first four years as CEO.
(Can't tell if Few Years Left) is a dummy variable that equals one if the CEO-year observation
three years of the data on a CEO who does not belong to the completed-spells subsample.
'Few Years Left)
(Low Tenure)
is
is
a
is
in the last
Robert Gibbons and Kevin J. Murphy
47
August. 1990
TABLE 3
A(CEO Salary + Bonus) on A(Sharcholder
Wealth) and Aln(CEO Salary + Bonus) on Shareholder Return, including interactions to allow
the Pay-Performance Relation to vary with Years Remaining as CEO and with
Firm Size as measured by Sales
Coefficients of Ordinary Least Squares Regressions of
(t-statistics in
parentheses)
Dependent Variable:
Dependent Variable:
A(CEO
Independent Variable
Salary
•
+ Bonus)
+ Bonus)
(3)
(4)
-3.06
-2.63
-.0090
-.0091
(-1.0)
(-0.9)
(-2.0)
(-2.0)
7
—
—
12
—
—
—
—
—
(AShareholder Wealth)*(Sales)
Salary
(2)
(1)
Few Years Leftb
(Dummy Variable)
Aln(CEO
-4.1X10"
(-4.2)
—
(AShareholdcr Wcalth)*(Salcs) 2
3.1xl0
(3.7)
(AShareholder Wealth)*(Few Years Left)
.0008
.0025
(0.4)
(1.2)
2.7x1 O 6
(Shareholder Retum)*(Sales)
(1.5)
(Shareholder Retum)*(Sales) 2
-3.2xl0
12
(-0.1)
(Shareholder Return)*(Few Years Left)
.0436
.0432
(3.0)
(3.0)
R2
.0426
.0452
.0833
.0845
Sample Size
6,727
6,727
6,730
6,730
CEOs serving in 785 firms
Compensation is measured in thousands of
1988-constant dollars; A(Shareholder Wealth) and Sales are measured in millions of 1988-constant
dollars. All regressions include intercepts and year dummies. Columns (1) and (2) include AShareholder
Wealth and AShareholder Wealth interacted with the year dummies, allowing the pay-performance
sensitivity to vary by year; columns (3) and (4) include Shareholder Return and Shareholder Return
interacted with the year dummies, allowing the pay-performance elasticity to vary by year.
The sample
who
is
constructed from longitudinal data reported in Forbes on 1,292
leave their firms during the 1970-1988 sample period.
^Few Years Left)
is
a
dummy variable
that equals
one
if
the
CEO
is
in his last three years as
CEO.
Robert Gibbons and Kevin J. Murphy
48
August, 1990
Appendix Figure Al
Time Trends
in the
Estimated Relation Between Pay and Performance, 1971-1988
>> $0.12.
•5
A
$0.10,
e
I
Pay-Performance
Estimated change in
\^
$0.08 -
to
Sensitivity:
CEO Salary + Bonus
each $1,000 Change
in
corresponding
Shareholder Wealth.
I
u
C
ca
E
$0.06'
f
Pay-Performance
I
1
Sensitivity:
8-Year Linear Trend
$0.04re
cu,
$0.02
$0.00.
W
$-0.02.
— —
t
i
— —
t
-\
— —
i
t
Figure A
Estimated pay-performance scnsiliviiies, by year. Figure is based on annual regressions
+ Bonus-Sihousands) on A(Sharcholder Wealth-Smillions) using Forbes data
on 2,236 CEOs serving in 1,204 firms. Each year's regression is based on approximately
650 observations.
of A(Salary
0.45-
f
"I 0.40-1
I
Pay-Performance Elasticity:
% change in CEO Salary + Bonus corresponding
to each % Change in Shareholder Wealth.
Estimated
V^
1
0.35-
c
re
Pay-Performance Elasticity:
1 8-Year Linear Trend
0.30-
E
-r 0.2501
0.20cs
Figure A2
Estimated pay-performance elasticities, by year. Figure is based on annual regressions
+ Bonus-Slhousands) on Aln(Shareholder Wealth-Smillions) using Forbes
data on 2,236 CEOs serving in 1,204 firms.
Each year's regression is based on
of Aln(Salary
approximately 650 observations.
38, 3
055
Date Due
08
ftyj
U Ml
«<3*
Lib-26-67
Hit
3
c,
oa o
0070156b
7
H
mi
HnHHI
IMlSP
pa
dill
£8Bgm
KHBSKaP
KmHn
sHSraHBRB
Ji HraHnHHI
m if£SMl
nm
HHHBHi
IS
:
-.;,•.
:.'';;.:.
Bill
111
SrasssSSlfflp