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ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
Rat Race Redux
Adverse Selection
in
the Determination of Work
Hours
Working Paper No. 3638-93
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
Rat Race Redux
Adverse Selection
in
the Determination of Work
Hours
Working Paper No. 3638-93
December, 1993
M
Landers
Renee
Boston College Law School
James B. Rebitzer
Sloan School,
MIT
Lowell J. Taylor
Heinz School of Public Policy and Management
Carnegie Mellon University
JAN
RF
2 5 1994
Rat Race Redux:
Adverse Selection in the Determination of Work Hours
by
Renee M. Landers
James B. Rebitzer
Lowell
Assistant Professor,
Associate Professor
Assistant Professor
Boston College Law School
885 Centre Street
02159-1 163
Newton Centre,
(ph) 617-552-4396
Sloan School,
MA
MIT
E52-567
50 Memorial Drive
Cambridge MA 02139
(ph) 617-253-7782
DRAFT
Comments Welcome
Printing: 12/14/93
J.
Taylor
Heinz School of Public Policy
and Management
Carnegie Mellon University.
Pittsburgh,
PA
15213
(ph) 412-268-3278
ABSTRACT
This paper makes the case for the importance of adverse selection
hours
in
managerial and professional jobs.
in
the determination of work
The focus of our investigation
is
large law firms.
We
argue that the income sharing that characterizes legal partnerships creates incentives to promote
associates with propensities to work very hard. Since the propensity to work hard is
unobservable, law firms rely upon indicators of this propensity, especially an associate's record of
billable
hours
Using a simple adverse selection model, we demonstrate that the use of work hours as an
indicator may lead firms to impose work norms entailing inefficiently long hours. In addition,
find that firms
hours
The
may not
We find
logic of our
adjust these
norms
in
response to an influx of employees desiring short
empirical support for our model with data
model
is
we
we
collect
from two large law
firms.
Adverse selection in hours may
where there are strong complementarities among groups of
not limited to professional partnerships
also be important in settings
professional employees (e.g. software production teams) or in competition for promotion to high
level
managerial positions
1.
The United
three decades,
States'
women
work
force
is in
Introduction
the midst of a demographic revolution.
entered the labor force at an unprecedented rate and they remained
jobs even after they married and had children (Goldin, 1990).
and working outside the
home
will, all else
counterparts from previous generations
true of the current cohort of
ways
in
in
typically
to these
which firms respond to increases
in
in
past
at their
are raising children
work hours than
their
male
had stay-at-home wives. The same may be
working women. The labor market
workforce demographics
Recently discovered trends
Women who
equal, desire shorter
who
men married
consequences of the sea change
the
Over the
the
will
be determined,
number of employees
in large part,
by
desiring shorter hours.
the historical evolution of work hours suggest
some
drift
towards shorter hours, but the pace and direction of change varies across different education
groups.
Coleman and Pencavel (1993a, Table
14, p.
280) find a downwards cohort trend
in
weekly and annual hours for white men with 15 or fewer years of schooling over the period 19401988.
In contrast,
white
men
with 16 or more years of schooling exhibit apositive cohort trend
for both these hours measures.
trended
downwards
for white
more years of schooling,
1
A
parallel study
women
like their
with 15 or fewer years of schooling.
Women with
male counterparts, display an upward trend
worked (Coleman and Pencavel, 1993b, Table
In this study,
by the same authors finds that annual hours
13, p. 667).
hours are the number of hours worked at
with positive earnings, and weeks worked
in the
in
16 or
annual hours
2
all
wage and salary employees
census. The hours trend
jobs for male
year prior to the
described above appeared in a regression that controlled for changes in real
GNP,
cohort size, and
average hourly earnings.
These figures were calculated for female wage and salary employees who worked in the week and
the year prior to the survey. Weeks worked included weeks of paid vacations and of paid sick
educated women, a downward trend in weekly hours was partially offset by
weeks worked per year, with the net trend in annual hours still being negative. For
women with more than 16 years of schooling, there was no cohort trend in weekly hours, but there
was a dramatic increase in the number of weeks worked per year (see Coleman and Pencavel,
leave.
For
less
increases in
Table 13,
p.
667).
According to textbook economic theory, market competition forces firms to
link
work
hours tightly to the preferences of individual employees. Firms that more closely match the hours
preferences of their employees will find that they can attract desirable employees
Conventional theory therefore predicts that most individuals
maximizing number of hours (conditional on
educated workers must then
must
reflect their
The
heavily
in
the
The reduction
in
work hours
for less
3
interpretation of the hours trends suggested by the conventional
In this paper,
utility
number of employees wanting reduced
continued and increasing preference for long hours.
on the assumption
employees
an increase
wage)
be working the
lower wage.
and increasing number of work hours for college educated employees
Similarly, the high
hours
reflect
their
will
at a
that
model depends
employers can directly observe the relevant characteristics of
we show
that
when
this
assumption
is
violated,
work hours may be
determined through a process quite different from that described by the textbook model
particular, firms
may
use long
work hours
In
(or other performance measures that entail long
work
hours) as an indicator of some valuable, yet hard to observe, characteristics of employees.
indicator plays a role in determining hiring or promotions, then issues of adverse selection
appear
to
in the
determination of work hours.
Employees desiring short hours
will
If this
may
have an incentive
camouflage themselves as long-hour workers- perhaps by agreeing to more work hours than
they would otherwise desire
at their
norms with hours long enough
hour employee. The
result
current wage.
Firms
to discourage a short-hour
of this process
is
will
respond by establishing work
employee from pretending to be a long-
that employers
may
require too
from employees. The employers also may not be able to quickly or
many work
hours
easily adjust these hours as
For both men and women, annual hours worked were longer for college than for high school
in 1988. Annual hours worked for college educated white men was 2,243
educated employees
in
women the comparable figures are 1,797
and 1,531 respectively. For men, much of the difference between education groups was found at
the upper tail of the weekly hours distribution. For women, much of the difference was found in
the lower tail of the weekly hours and weeks worked per vear distributions (Coleman and Pencavel,
1993a and 1993b Tables 3).
1988 and 1,909 for high school educated employees. For
more short-hour employees
From
enter the labor market.
this perspective,
one of the causes of
the divergence in hours between college educated and non-college educated workers described by
Coleman and Pencavel, may be a greater incidence of adverse
work hours
in
high
skill
selection in the determination of
labor markets.
George Akerlof first proposed the idea
can lead to overwork
that adverse selection
in his
paper "The Economics of Caste and of the Rat Race and Other Woeful Tales" (Akerlof, 1976). 4
Akerlof s demonstration that overwork equilibria are possible was presented
in
a self-consciously
unrealistic numerical example. This created the unfortunate impression that the rat race
equilibrium
was an
interesting theoretical
example of market
but one having
failure,
little
connection to the operation of actual labor markets. In this paper
we
the empirical relevance of rat race equilibria to a potentially large
number of professional and
managerial jobs.
for
a.
We
do
this
seek to
make
the case for
by developing and testing a model of adverse selection
work hours
in
particular type of business organization, large law firms.
It
may seem incongruous
to
examine models with claims to broad
applicability in such a
narrowly defined setting. Large law firms, however, share two characteristics that make them a
convenient vehicle for the study of adverse selection
simple internal structure. In general there are only
associates,
who
are employees, and partners.
in
work
hours. First, law firms have a very
two broad
classes
The key promotion
in
of professionals
in
the firm,
the firm involves the decision
to allow associates to purchase an equity stake in the enterprise.
The second important
revenue sharing
partners
among
makes each
the firm to
work
feature of law firms
partners (Gilson and
individual partner's
hard.
Since the
that there
is
nearly always
some degree of
Mnookin, 1985). The sharing of revenues among
income dependent on the willingness of other partners
money making
Holmstrom (1982) developed a
is
activities
in
of other partners are hard to observe
similar idea in the context of a signaling model.
studied a model with both signaling and adverse selection processes.
describe equilibrium overwork in the context of an efficiency
Gale (1992)
Rebitzer and Taylor (1993)
wage model.
directly,
there are strong incentives to allow into the partnership only those associates with a
propensity to work very hard. 5
The propensity
to
work hard
upon an indicator of work
offered at
The use of hours
problems discussed above. Indeed,
all in
legal partnerships
we
and associates
firms therefore
of hours worked
as an indicator creates
who
to rely
or, nearly
the adverse
all
may
not be
prefer long hours will typically find
work an
long number of
inefficiently
of short-hour attorneys
In these cases an increase in the proportion
come
demonstrate that short hour jobs
will
themselves subjected to a work norm requiring them to
hours
Law
not directly observable.
propensities, an associate's record
equivalently, hours billed to clients.
selection
is
have no effect on the number of short-hour jobs a law firm offers and
in
the labor force will
may even cause
firms to
implement more stringent work norms. 6
This
last
prediction
is
of particular importance for the study of lawyers because the
profession has experienced a demographic revolution of its own.
about 3 percent of the attorneys
percent until 1975.
By
in
the United States. 7
1987, 16.2 percent of lawyers
5
discuss later in the paper, similar issues
production technologies described
in
1,
Figure
would appear when
in
constituted
5
were female. Currently about 40 percent of
from law schools are female (Rosen, 1992, Table
complementarities across co-equal employees
women
1967
This figure fluctuated between 2 and
the graduates
As we
In
legal
an organization,
1
and
p.
222).
Adapting
there are strong
e.g. in the
case of o-nng type
Kremer (1993).
The argument in this paper is similar in some respects to that developed in Schor's recent
bestseller, The Overworked American We, like Schor, contend that competitive forces can lead to
persistent overwork. We differ from Schor however in two important and interrelated ways. First,
we attribute overwork to a specific rrucroeconomic mechanism that is quite different than those
implicit in Schor's writings. Secondly, our model suggests that overwork is most likely to appear
in professional and managerial settings. Schor, in contrast, makes the claim that overwork is
.
ubiquitous.
The
first
woman
generally found
admitted to the bar
it
United States was Belle Mansfield
difficult to obtain apprenticeships or
entrance at law schools
male policy
in the
until 1927.
was most pronounced
in
1869.
Women
admittance to law schools. Resistance to
the elite East Coast schools.
Harvard began accepting
in
women
in
1949.
The
Columbia had an
all
early cohorts of women in
law schools frequently suffered blatant discrimination and harassment (Berger Morello, 1986).
to this shift in the labor force
a central issue for
is
ways, the story of the legal profession...
increase in
women
in
law
firms.
As Sherwin Rosen put
the 1970's and 1980's
is
"...in
many
the entry of women; the huge
represents one of the largest demographic changes ever observed in
...
American professions" (Rosen,
The paper proceeds
determinants of work hours
promotion decisions. In
p.
222). 8
as follows: In the next section (section 2)
in a
we
present a model of the
law firm where partners use hours as an indicator when making
this setting
it
is
easy to find cases where (1) associates
are inefficiently long, and (2) firms will not offer short-hour jobs even as the
desiring short hours in the workforce increases.
our model using data
it
we
collected from
two
In section 3
large law firms.
we
work hours
that
number of attorneys
offer an empirical investigation of
In the conclusion
we
consider the
relevance of rat race models to the determination of work hours in other professional and
managerial settings.
2.
2.
1
Adverse Selection and The Determination of Work Hours
Attorneys and Firms
In this section
model
and
we examine
We suppose there are two
differ only
the determination of work hours in the context of a simple
types of attorneys. These attorneys are equally productive,
with regard to preferences over leisure. 9
have depressed work hours. A
in private practice worked 200
or more hours per month. A follow-up survey in 1990 found that 50 percent worked 200 or more
hours per month (American Bar Association, 1991, p. 22 Table 19). This same survey found that
part-tune or reduced hour work was most common for attorneys in a solo practice. Roughly 23
percent of lawyers in solo practice work part-tune and reduced hours compared to 7 percent for
junior assistant attorneys and 3 percent for partners (American Bar Association, 1991, Table 28,
The rapid
influx of women throughout the 1980's does not
seem
to
1984 survey of the legal profession found that 35 percent of lawyers
p.26).
Throughout
this
paper
activities as leisure.
It
we
follow the conventional practice of referring to non-market
work
should be clear, however, that our usage of the term leisure includes such
important and non-leisurely activities as child and elder care.
All attorneys participate in the labor
function of consumption,
and hours worked,
c,
The discount
that period's earnings.
market for two periods. In each period
rate
Consumption
h.
For simplicity
is r
we
period
in the
utility is
a
always equal to
is
specify utility in a period to be
:
u,(c,h)=c-b h
(1)
t
where t=l or 2 indexes the
lower weight on the
disutility
There are two
always work
in a
individual's type.
distinct
We
let b,
> b 2 so
,
that type-2 individuals place a
of work than do type-1 individuals.
ways
in
which
legal services
spot market (e.g., self employment)
in
can be produced. Attorneys can
which an hour of work
wage
production of m, units of output In a competitive spot market the
the specified utility function, optimal
h; =
(2)
1
2b
t
will
w^m,.
Given
be
t
working
(3)
for each type
be
^,
as illustrated in Figure
individuals
work hours
will
results in the
in
At the optimal hours,
1.
h*,
and consumption,
c*
= w,h*,
utility for
the spot market can be written
u,(c\h;) =
^.
4b
t
The second way
in
which
legal services
can be produced
somewhat more
is
involved.
We
imagine that there are some aspects to the production of legal services that are best accomplished
by attorneys working
in
small teams, and
partnerships in the market
One might
we suppose
think of them as an oligopolistic fringe to the otherwise
competitive market for legal services. Partnerships will exist only
partners
is
individual
higher in this setting.
working
in
We assume this to
the team be
m
2
number of such
that there are a limited
> m,. As we
if output
be the case and
let
per hour for the
output per hour for an
will discuss shortly, partners hire additional
attorneys as employees of their firm and these "associates" have productivity m,.
To keep
notation manageable
we
will
suppose that the optimal size of each partnership
two. For the moment, think of the two partners as having jointly purchased the partnership
beginning of the period, with each paying
X for his
share.
The partners agree
output for the period and the revenue from the sale of the partnership
at the
is
at the
to evenly divide
beginning of the next
period.
Once
in a
partnership, the optimal
work
decision for one partner, say individual A,
is
the
solution to
max -^(h A +h B )-b A h A
(4)
where
h B represents the hours chosen by the other partner.
Obviously, the return to being a partner
type, but
in this
context depends not only on an individual's
on the type of the other partner. This suggests that a partner
paired with a type-2 individual over a type-1 individual.
partnerships
is
The
clear.
by the partners.
The
workers
will
always prefer being
intuition for this feature
financial return to the partnership is half
All else equal, type-2
will
of
of the output produced jointly
be inclined to work longer hours, and
produce more output, than type-1 workers.
Let Vj, be the
of the
individual net
utility
utility
a type
of a job
s
individual gets
in the
from being
in a partnership
spot market. Then, using (3) and (4)
it
with a type
is
t
easy to show
that
(5)
V
st
=m^[l/16b s + l/8b ]-w?/4b s
.
t
Notice that given
b,
>
b2
,
we have V 22 > V 21 and V 12 > V u
.
Any
attorney will always prefer to
be paired with a type-2 partner.
Given
type,
this set up, the
value a partnership position depends crucially on the individual's
and also on what type he thinks the other partner might be.
From
prospective partner, the higher the probability that the other partner
the
amount he
will
be willing to pay for a position
current partners to put in place a
mechanism
is
in the partnership.
that ensures
it
is
the viewpoint of a
type-2, the higher will be
This, in turn, will lead the
common knowledge
that
all
prospective buyers of the partnership are type-2 individuals.
2.2 Equilibrium with Observable
In this section
find a "baseline"
to
we assume
Type
that firms
know whether
a
worker
complete information equilibrium. The set-up
have two partners
who
is
is
type-1 or type-2 in order to
simple.
are attorneys in their second period. Firms
Each
firm
is
presumed
employ L associates who
1
8
are first-period attorneys.
bidders
among
At the end of each period the partners
the junior associates
a competitive auction. 10
in
nearly ubiquitous practice of promoting the next cohort
sell
two
highest
This auction corresponds to the
of partners from the firms current cohort
1J
of associates.
both types of attorneys accept positions
In equilibrium
in
the spot market, earning
w, = m,. Only type-2 workers are offered positions as associates
The reason
the firm to the
in the partnerships,
wage
however.
suggested by our analysis above. As associates, the two types of individuals are
is
perfect substitutes.
Partners, however, are concerned not only about current production, but also
about the future value of their firm
allowed to bid for the firm, and
if
it
This value
is
is
maximized
common knowledge
Given the assurance that both partners
will
if
type-2 workers exclusively are
that this will
be the firm's policy
be type-2, the steady state market price of a
partnership, X, will solve
(6)
X = V„+
—
1
where, using
V„ =
r
(5),
3m
:
16b 2
We assume V 22
10
+
is
w,
4b 2
positive; the existence
of partnerships
is efficient.
12
what follows we assume that the two highest bidders are certain to purchase the firm.
model can be expressed as a lottery in which the bidders purchase the firm with
less
than 1 Introducing a lottery into our setup does not change our central
probability
some
conclusions about the nature of the labor market equilibrium or the determination of work hours.
In
Alternatively, the
.
1
In this
model the auctioning of the law firm
is
a convenient device for ensuring that the current
generation of partners has an interest in maximizing the discounted present value of future net
income produced by die firm. The purchase of the firm by new partners is most easily imagined as
an outright exchange of cash for equity and some firms do literally require partners to 'buy into the
partnership'. The actual transaction, however, need not take this form and in most cases it does
not.
In
our two period model, the new partners could 'purchase' the firm by accepting reduced
salaries.
If we complicated the
model by allowing partners
to stay for a
number of periods,
the
purchase of the firm could take the form of a steep salary-tenure profile for partners.
12
This will be the case
jobs by enough,
if
i.e, if
the level of productivity in a partnership exceeds that of the spot market
m
2
> v4/3m.
.
Notice that
Type-1 workers
available.
work
attorneys
type-
in this equilibrium,
type-2 workers are indifferent between the various jobs
find positions in the spot market.
their preferred
all
number of hours, with type-2 attorneys working longer hours than
1
Does Incomplete Information Change
2.3
Importantly, for our analysis,
In this section
We
unobservable.
equilibrium
start
ask
The
the
full
when
information equilibrium pertains
by supposing that the equilibrium does
full
all
associates
work optimal
in the equilibrium,
consider associates
first.
A
We
hours.
information equilibrium exits
from the behavior specified
We
if
exist; that
is,
types are
we
think about an
which type-2 workers exclusively accept positions as associates and bid for
in
partnerships, and
concept:
we
the Equilibrium?
when no
when
adopt the Rothschild-Stiglitz equilibrium
actor can increase
this actor takes others'
utility
by deviating
behavior as given.
type-2 worker clearly cannot benefit from accepting the
jobs normally held by type-1 workers, which pay Wj at hours h"
.
Suppose, though, that a
"maverick" type-1 attorney were to accept a job as a junior associate by pretending to be a type-2
individual.
For
this
maverick, there would be a loss
be working longer hours than would be optimal.
On
in utility in
the
first
period, because she
would
the other hand, she could purchase a
partnership for the second period of her career, at the going price of X, and be assured of getting
paired with a type-2 individual.
The
cost to the maverick in the second period
is
just the
opportunity cost of owning the partnership period for one period, rX/(l+r), which from
V 22 On the
.
V, a
(6), is
other hand, the benefit of being matched with a type-2 individual in a partnership
is
.
If
V 12
<
V 22 we
,
do indeed have an incomplete information equilibrium
to the complete information equilibrium.
would not be
This describes a "no envy" case.
that corresponds
A type-1
individual
interested in accepting a position held by a type-2 individual even if by doing so she
could fool the employer into thinking she was a type-2 individual.
A far more interesting case is
10
where
V 12
>
V 22
13
In this instance
.
Vp-V,.,
-&
^+
.'
/
L 'x
u,(w,h : ,h ; ) +
The
too
much
There
right
increase the utility of a type-1 individual to adopt the
u,(\v,h*,h*)
1+r
or equivalently, using
-^—rb
may
This "envy" case will occur when:
maverick strategy
(?)
it
(2), (3)
~>~
(l
:
1
and
+
r)
'
"
'
,
1+r
r
L
:
/2)
.
J
hand side of expression (7) must be negative (see footnote
larger than b :
exist conditions
Expression (7) gives us our
inequality (7) holds.
,
under which
it
will
information equilibrium cannot pertain
Although the
full
equilibrium not very
much
when short-hour
in
in
Thus,
if b, is
important
first
not
result:
The
the perfect information equilibrium
full
in this case.
information equilibrium cannot apply
might suspect that a market
13).
be profitable for a type-1 worker to seek associate
positions that are occupied by type-2 workers
that
u,(w,h!,h|)
(5), if
-w,-(m
+
,. ...
>u,(w,h,,h,) +
when
inequality (7) holds,
we
which there were only a very few type-1 workers would achieve an
different
from the perfect information case.
In particular,
attorneys are rare, the long hour attorneys might be
still
work
may be
it
the utility
maximizing number of hours.
We can
easily
examine
this
proposed "equilibrium"
they hope will be type-2 workers. These individuals
wage
w,.
Then
that there are so
at the
end of the period the firm
few type-1 workers
in the
This will occur
if
2m,>m 2 A
.
h*
hours
period
in
is
0,
hires associates
1,
at the
which
is
close to zero.
at
who
competitive
auctioned off to the highest bidders.
market that any one firm expects
worker, and the probability of this happening
13
is
work
Each partnership
Suppose
most one type-1
So long
as hours remain
tempting, but incorrect, interpretation of this inequality might be
nch firms where m 2 is large. To clarify this point, we note
where there were P partners, V 12 >V 22 when Pm,>m 2 We have not modeled the
determinants of P in this paper. If, as seems reasonable, P were a concave function of m,, then the
envy case would be more likely as m 2 increases.
that the
envy case
that in die case
is
less likely in very
.
11
=
rV:2 /(l +
toX =
r)
+eV
r[(l-9)V::
:
,]/(l
+
r).
14
Again using the Rothschild-Stiglitz definition of equilibrium,
can be an equilibrium only
firm that increases by
The new
change
X
value of the firm to each partner will suffer a small discrete decline, from
at h*, the
some
of hours
level
if
in the firm's net
is
no actor has the incentive to
h*
note that this outcome
Consider though, a
alter their behavior.
amount the number of hours
small
we
it
requires of junior associates.
+ Ah. Given that the product per hour of an associate
income from the L associates
will
is
m
t
,
the
be
L[m,h; - vv,h;] - L[m, (h'2 + Ah) - (w, + Aw)(h 2 + Ah)] = -LAw(h; + Ah).
(8)
Of course
if
associates are being asked to
work
How
+ Aw.
w,, they must also be paid a higher wage, w,
induce associates to
work more hours
large
then they consider optimal
must the change
wage be
in
these extra hours? Using the utility function specified in (1),
at
to
we must
have
+Aw)(ht +Ah)-b : (h': +Ah) =
(w,
(9)
where, from (2) and (3) respectively,
we
u-,(w,h2,hj)
note that h*
= Wj/(2b 2 ) and
u 2 (w,h;, h'2
)
= w*/(4b 2 ).
Substituting these expressions into (9) and rearranging terms gives
(10)
This
in
A\v(h;+Ah) =
b : (Ah)
:
.
turn can be substituted into (8) to demonstrate that the change in the net
firm's associates
decrease
income as a
in net
If this
due to the policy of increasing hours
were the
result
of their
workers
will therefore
14
.
at the
who
in
in
firm value
is
in
.
This implies that firms suffer a
policy, but this decrease
hours, no single firm
that extends
is
would have an
its
required hours also
hours
who
will
continue to offer positions with
ensure that the firm will have only
r9[V 22 -V 21 ]/(l+r). Substituting from expression
terms of model parameters as
m^bj)
second order.
wishes to work for the firm. Type-1
other firms
This means that a small increase
The change
V 22 -V 21
seek employment
-Lb 2 (Ah) 2
However, a firm
order cost on any type-1 worker
first
hours set to h'2
work
sole effect of increasing
incentive to require hours greater than h*.
imposes a
new hours
is
income from the
-1
-(b,)"'l/8 >
0.
(5),
we can
express
12
type-2 workers
that
is
in its
described
exceed the loss
in
associate pool.
work
2.4
in
hours, the increase in firm value must
h'2
In situations
where
partners in firms, any individual firm will benefit by
Put differently,
.
result:
in
the "envy" case described by
all
associates
number of hours (conditional on the wage).
Separating Equilibrium
Having ruled out
hours,
a discrete increase in the value of the firm
equilibrium cannot be characterized by partnerships in which
the utility maximizing
A
become
some amount above
(7), the
is
income. This leads us to our second major
short-hour attorneys might wish to
expression
net result
footnote 14. For a small changes
in net
increasing hours
The
we
a pooling equilibrium in
turn to a description of an alternative separating equilibrium that can exist in a labor
market with unobservable types
to
work optimal hours given
h'2
and
enough
h*.
We
Figure 2 sketches the basic idea.
productivity m,
= w,, hours
for the
If
each type of attorney were
two types of attorney would be
have already shown, however, that partnerships can benefit by setting hours high
to discourage type-1 individuals
offer the
which firms allow associates to work optimal
wage— hours package
(w2,h2)
from applying
in
Figure
2,
for associate positions.
If partnerships
type-2 individuals will accept such positions,
but type-1 workers will not. Type-1 workers will not take such jobs because the loss of utility of
accepting an associate position will equal any possible gain from access to a partnership
More
formally,
we
note that (w2,h2) must be set so as to meet (1) the "participation
constraint," that type-2 workers are willing to take the jobs, and (2) the "separating condition,'"
that type-1
workers
will not accept the positions.
These two conditions are respectively
expressed by the following expressions:
(11)
u.(w2h2,h2)>u 2 (w,hj,hj)
(12)
-^-/v
and
i:
-rx/(l + r)\<u,(w,h;.h;)-u,(w2h2)
—
13
X
where
the price of a partnership in the proposed separating equilibrium. 15
is
Can
be an equilibrium'7 The crucial issue
this
wage— hours packages
offering the
(
is if
firms in the separating equilibrium prefer
w:,h2), as defined by (1 1) and (12), to simply abandoning
the separating strategy and accepting the possibility of selling the partnership in the next period to
type-1 workers.
Our
let
step
first
the firm choose
from
to find the value
is
w
rX
....
=
(13)
1
+
The next
step
is
)-(l +
+
"
r
where the expression
The
final
step
that the implication
The
as
right
shown
in
We
15
for
is
Vn
when
separating equilibrium.
We
\4b,
4b ;
it is
~2
~2
2
!
terms that
-b, h 2 -b, h 2 \
"
'
common knowledge
.
/
that future partners will be
must solve
4b,
comes from
to establish that
of (13) and (14)
(5).
X
exceeds
X'.
To demonstrate
see this
last step,
we
note
is
hand side of (15) must be positive.
A
partnership operating in a separating equilibrium
Figure 2 will never wish to abandon the separation strategy in favor of letting type-1
workers into
become
16b,
wL
r)(
8b :
to observe that
—
./wf
\
type-1, the value of the firm, say X',
1
find after rearranging
2
-—
\ 16b,
r
we
wL
—m; + —m;-+ 4b,/
/
in the
and h 2 so that inequalities (11) and (12) are binding. Then substituting
2
and (5) into (11) and (12)
(2), (3)
of the partnership, X,
its
pool of associates.
have thus demonstrated that
in situations
where short-hour attorneys might wish
partners in the elite oligopolistic fringe of law firms, there can exist a separating
Note that rX/
(1
+
r) is just the
opportunity cost of holding the partnership for one period.
to
14
equilibrium
In this
otherwise wish to
equilibrium associates are required to
work
at the
work more hours than they would
going wage.
2.5 Discussion
We
have argued that the income sharing characteristic of partnerships creates strong
incentives to screen potential partners for their propensity to
record of hours
situations
worked
utility
hard.
are used as an indicator in promotion decisions,
where associates are required
maximizing
work
conditional
Our model of adverse
to
it
is
an associate's
easy to identify
work more hours than they would
if
they were simply
on the current wage.
selection in the determination of work hours need not be limited to
professional partnerships
Rat race equilibria can be expected
three criteria hold: (1) the
members of a group
members;
(2) the output
of the group can be
individual
members; and
(3)
benefit
any group where the following
from the productive
members of the group have
In these
in
significantly influenced
Criteria 2 suggests that adverse selection in hours
type production technology.
When
activity
by the work
the ability to establish
may be
particularly likely in
of other group
effort
of
work norms.
groups using o-ring
groups compiementarites among employees are such
that
small differences in an individual's level of performance can generate large differences in the value
of output produced by the group.
product
life
16
Teams of professionals developing new products with
cycles (e.g., software engineers)
may
short
therefore be especially likely to be characterized
by excessive work norms.
Rat race effects might also appear
hierarchical settings
effect
'
6
their influence
Kremer (1993) argues
list
the competition for managerial positions in
where the actions of managers high up
on output through
very long
in
in
the hierarchy have a multiplicative
on employees lower down
in
the hierarchy (Rosen, 1982).
"o-nng" production functions are ubiquitous and can account
of otherwise anomalous features of labor markets.
that
for a
15
The
we
separating equilibrium
Of more
information case.
identify
the
h]
of a
maximum
economy
makes
made
(6)
is
clearly inefficient relative to the full
interest is the finding that the equilibrium
even given information constraints. This point
effect
is
hours law
when
close to zero.
is
most
can be inefficient
easily established if
we
consider the
the proportion of type- 1 ("short-hour") workers in
A maximum hours law that prohibits hours in
excess of
impossible for firms to maintain a separating equilibrium. Type-1 attorneys are
it
better off by this law because they gain access to previously unobtainable
partnerships that offer
workers are
reservation
them higher
utility
indifferent to the passage
maximum
in the
spot market. Long-hour
of the law because they continue to receive
Since type-1 associates are
utility.
indifferent to a
than jobs
made
better off and type-2 associates are
hours law, the separating equilibrium will be inefficient
where the law improves the position of the partners who currently own the
The
benefit
of the
maximum
in labor costs is
hours law to current partners results from the firm's
whose presence reduces the value of the
If a single firm
we have
always exceed the benefits.
The
inability to
work
hours.
cost of the
maximum
screen out short hour
it
will
be certain to
attract only
already demonstrated that the costs of such a
Things are
The
firm.
abandons stringent work norms,
short-hour attorneys and
firms.
independent of the actions taken by other
firms or the proportion of type-2 attorneys in the labor force.
associates
cases
hours law to current partners derives from the fact
they will no longer have to compensate type-2 associates for excessive
magnitude of this reduction
in
different,
move
will
however, under a law compelling all
firms to simultaneously abandon the separating equilibrium. In this case, the failure to
screen out short-hour workers will reduce the value of the firm to each partner by r6[V 22 -
V 21 ]/(l+r) (see footnote
situation
where no
where
it
is
14).
Thus
as 6 falls towards zero,
we
are certain to encounter a
profitable for all firms to simultaneously reduce their
individual firm will have the incentive to undertake such a
move.
work norms,
but
A maximum
16
hours law would,
in this situation,
make
current partners better off without making any of
the associates worse off.
Our
separating equilibrium also has the property that increases in the
number of
short-hour attorneys will not lead to a shortening of associate hours in law firms. In the
model
specified above, the
number of hours required of associates
in
law firms
We can get even
with respect to the proportion of the workforce desiring short hours.
stronger results
if
we
allow the
wage
in the self
invariant
is
employment sector to
fall
number of
as the
short-hour attorneys increase. In this situation, the gain from pretending to be a long-hour
attorney increases and firms will have to
make
discourage short hour applicants. Thus firms
short hour attorneys by increasing the
the
work norm more
may respond
stringent to
to an increase in the
number of
minimum number of acceptable work hours
for
associates.
A final
In comparison to the hypothetical
partnerships.
limited
feature of the separating equilibrium concerns the distribution of access to
by custom, the
attorneys
who
3.
rat race equilibria offers
work hours
Empirical Investigation of Work Hours
The preceding
section described
how
early in their careers.
in
adverse selection
Large
in
In this
Law
Firms
the competition for
positions in legal partnerships could lead firms to require excessive
associates.
are
reduced access to partnerships for
are unwilling to endure excessive
An
economy where excessive hours
work hours from
17
we
section
hours
report the results of an empirical investigation of the determination of associate
in large
law
work
firms.
The Data
3.1
We collected
law firms
in
the data for this study in a survey of associates and partners at
a large Northeastern
city.
19
The surveys asked
about their work hours, billable hours, and attitudes towards
were distributed and 133 were returned
for a response rate
all
two major
associates on a partnership track
work
hours.
of 62 percent.
A total
of 216 surveys
A simultaneous
survey
questioned the partners at these firms about the decision to promote associates to partners.
distributed 188 surveys and received responses
Columns
Rows
57.
1
1,
1
and 2 of Table
1
present descriptive statistics for our sample of associates. 20
The average respondent graduated from law school
The average age of respondents
in
for non-respondents.
None of the
1988.
1-3 are statistically significant. 21
differences
This
believe that our sample of respondents
in
We find that
fact,
is
in
1989 while the average non-
31.8 years compared to 32.8
between respondents and non-respondents
combined with the high response
is fairly
rate, leads
in
rows
us to
representative of the population of associates at
these firms.
The survey was conducted during
distributed at
The
20
our sample.
percent of the survey respondents are male compared to 58.5 percent for the non-
respondent graduated
19
in
2 and 3 compare the characteristics of respondents and non-respondents.
respondents.
work
from 64.4 percent of the partners
We
Firm
1
the
Summer of
1993. Three waves of questionnaires were
and. on the advice of management, two waves were distributed at Firm
2.
ultimate response rate at both firms were nearly identical.
In order to conceal the identity
of participating firms and survey respondents,
we
present averages
pooled across both firms.
2
'
Data on the age and year of law school graduation was collected from the Martindale-Hubbel legal
This directory does not list all the associates in a firm. Even when an associate was
listed in the director}.', information about age was sometimes not included. In the end we learned
the age of 44 out of the 83 non-respondents. Year of law school graduation was available for 47
directory.
non-respondents.
18
Rows
4-6 describe other characteristics of associates and their jobs. The average job
tenure of associates in our sample
3.6 years.
is
On
average 70.7 percent of the respondents are
married or living with a significant other, and 32.6 percent had children
salary of associates
Rows
is
$79, 1 54.
8-13 present different measures of work hours.
Rows
of billable and non-billable hours worked per month. Associates
hours.
work 220 hours per month. Rows 9a-9c present
The 25th
percentile,
mean and 75th
Associates
In
part-timers
were
women
in the
75th
the distribution of monthly billable
in
rows 8a-9c include both part-time and
our sample of 133 associates only 9 worked part-time (see row
attorneys.
work 180
percentile are respectively 150, 160 and 180 hours
month. The monthly hours figures
billed per
8a-8c present the distribution
the 25th percentile
in
hours per month. The median associate works 200 hours per month.
percentile
The average annual
10).
All
with children. The average monthly hours of these part-time
full-time
of these
women
is
140.
Rows
1 1
and 12 present data on weekend work patterns. In an average week, 30.3
percent of the associates do not
20.5 percent
work
a
associates surveyed
things are different.
work
3.2
whole day and
worked two
work both weekend
full
.52 percent
47.7 percent
work one and
weekend days during
work
half a
weekend
a half weekend days.
a typical week.
day,
None of the
During a busy week
work
a
whole day, 26 percent work one and a half days and 23.7
days.
Hours Preferences, Hours Worked and Promotion
One of the
implications of the adverse selection equilibria that distinguish them from
information equilibria
be
1
at all,
Only 0.76 percent do not work weekends during a busy week, 10.7 percent
half a day, 38.9 percent
percent
work weekends
utility
is
the possibility that associates in law firms
work more hours
full
than would
maximizing given the wage.
Figure 2 suggests a simple strategy for investigating this "overwork" hypothesis.
individual
would
like to
work
h' hours at the
going wage, but
will
A type
2
be required to work h; hours.
19
In principle,
like to
overworked employees could be
identified
by asking individuals whether they would
reduce their current work hours given their current wage. If hours constraint are
would require respondents
prevalent, however, this question
that they
may
who
employees
when making
not have anticipated
their
to consider a hypothetical option
consumption plans. This means that
might otherwise desire shorter hours may previously have
commitments expecting an income
hours. These financial
level
achieved only
at the
commitments (which include things
school tuition payments for children) would preclude a
made
financial
current (and excessive) level of work
like
mortgage payments, car
downwards adjustment
in
and
loans,
work hours
at
the current wage.
we adopted
For these reasons
than asking
how
would
associates
an alternative approach to identifying overwork. Rather
wage
increase.
The
We know from the first-order conditions that the term in
is
[ ]
would
adjust hours in response to a small
increase
/i
is
(from equation
r\
.
changes
in the
work hours or
.
how
they
derived from such a
wage
1)
—
,
wage, the new
leaves
level
of utility
maximizing
level
in
in this case,
With these
5
It
follows that for small
virtually identical if the individual optimally adjusts
If the costs
of adjusting work hours are greater
income, a population of individuals
in
at the utility
income. This sort of "near rational" behavior should be observed
dh/dw
is
non-zero. Things are different at h 2
brackets will be negative and individuals can
hours by
zero at h'2
of hours should generally want to keep hours the same and take a wage increase
form of an increase
even when, as
is
work hours unchanged.
than the costs of adapting to an increase
the
utility
asked
dU
... ..dh-,--.
= h,+[w-2b,h,]
dw
dw
(16)
in the
we
adjust hours given their current wage,
relationships in mind,
we
make themselves
.
Here the expression
better off by reducing
in
work hours
asked associates to pick from 3 choices: (1) decrease
percent with no change in income over the coming year, (2) keep hours the same over
coming year with
a 5 percent increase in income, or (3) increase hours
by
5 percent
over the
20
coming year with
Table
2.
If
22
a 10 percent increase in income.
The
most associates were working optimal hours,
"near rational" behavior and choose alternative number
2.
column
results are reported in
we would
Indeed
of
1
expect them to engage
we found
in
that 25.56 percent of
respondents indicated that they would like to keep their hours unchanged and enjoy a 5 percent
However, 65.4 1 percent of the associates indicated
increase in income
that they
would
reducing work hours and keeping income unchanged over the coming year. This
we would
expect
The "near
in
our adverse selection model where associates are
rational" behavior described
adjusting hours are high
we
Our case
above
for excessive
will
is
prefer
the pattern
at hi rather than hj.
be most apparent where the costs of
work norms would
therefore be strengthened
found that even among associates with high costs of hours adjustment, the majority would
to reduce
to care for
young
children creates obvious costs to adjusting
additional hour of work requires finding an additional hour of child care.
also create additional child-care costs
if,
as
is
work
often the case, child care providers are not
An
to another provider.
It
who
attorney
changes from 50 to 45 work hours per week may not be able to reduce child care hours by
week without changing
Every
hours.
Reducing hours may
completely flexible with regard to the number of hours of child care per week.
seems reasonable, therefore,
5
that
associates with children should have higher costs of hours adjustment than other associates.
if
associates are working the utility maximizing
Column 2 of Table 2
given the low average age
child less than 6 years old.
The surveys
number of hours.
presents the responses of associates with children.
As expected
our sample, 34 of the 43 respondents with children had
We
find,
at least
one
however, that 60 percent of the associates want to reduce
what a 5 percent change in work hours would mean
working different hours. For example, an associate working 200 hours per month
also included a table describing
for associates
would
in
Thus
number of hours, we would expect the majority of
associates with children to want to continue working the current
22
like
work hours
The need
hours per
if
learn from the table that a 5 percent
change
in
hours would imply an increase or decrease of
one eight hour day per month or 12 eight hour days per year.
21
hours.
This figure
quite close to that found for the entire survey.
is
the distribution of hours preferences
was
the
same
for associates with and without children could
23
not be rejected at conventional significance levels.
associates
who
Column
time and
presents the comparable results for associates
who have
children.
increase by reducing
wage
We find
24
work hours
that 76. 19 percent
It
who
is that,
work hours
anomalous to observe
that
some
in
is
when
associates receive their next year's
put this argument in
this interpretation
some
23
hours.
are married to partners working
work
full
all,
hours.
of associate lawyers have
economic theory does not require
wage
increase.
wage
It
increase by cutting back hours.
seems implausible. Should
wage
that
therefore need not be
we
really believe that
increase they will begin cutting back their hours?
perspective, consider that associates in their fourth year at these
firms have salaries roughly 30 percent above starting level associates with
in
work
More
consistent with the conventional labor
individuals respond to a
reflection,
however,
After
response to a
Upon
To
increase to reduce
for unexplained reasons, a large proportion
backwards bending labor supply curves
individuals increase
not have children.
thus appears that associates with high costs of hours
alternative interpretation of Table 2 that
supply model
who do
results for
of associates would respond to a wage
adjustment are as likely as other associates to want to reduce
An
of Table 2 presents the
3
are married to spouses holding full-time jobs but
than 78 percent of these associates would use a 5 percent
Column 4
Indeed, the hypothesis that
no appreciable decline
average hours. 25
A Wilcoxon rank sum test of the null hypothesis that associates with and without children were
drawn from populations having the same medians produces a z statistic of 0.554. Thus the null
hypothesis cannot be rejected at conventional significance levels.
24
Using a Wilcoxon rank sum test one cannot reject the hypothesis that the sample of associates in
columns 3 and 4 of Table 2 were drawn from populations having the same medians. The z score
produced by
25
The
effect
this test is 0.60.
of tenure on mean
and years of
was estimated by regressing the log of earnings on job tenure
The coefficient on tenure was roughly 0.077 with a t-statistic
regressing various hours measures against the same two variables
salaries
prior legal experience.
greater than 11.
yielded a small
In contrast,
and
statistically insignificant coefficient
on job tenure. These
results
were not
22
Table 3 presents descriptive
and
in
Particularly
same (row
no case are the differences
noteworthy
7).
wanting to reduce, keep the same, or
The "reduce hours" and the "keep the same hours"
increase hours of work
similar
statistics for associates
is
in the
means across these groups
the finding that the annual salaries across these
associates look very
statistically significant.
two groups
are the
This casts further doubt on the backwards bending labor supply curve explanation,
because the "income effect" implicit
in the
work hours question
same across
are likely to be the
groups.
The
to
have
"increase hours" group
less legal
salaries.
is
a
little bit
different
experience prior to joining the current firm and therefore slightly lower average
possible that associates in this group are trying to "catch up" to other associates in
It is
the firm by accumulating
hours" group (9)
is
more
experience.
In any case, the
of overwork recorded
described by our adverse selection model,
we
promotions
indicate the importance
partnership.
Secondly,
qualities that the firm
partners
were asked
in
in
Table 2
To
in
the "increase
indeed the result of the processes
work hours
address this issue,
three different ways. First,
we
of billable hours and other factors
we
is
should also find that
indicator in the promotion to partnership decision.
in
number of associates
small.
If the high incidence
work hours
from the other two. In general they tend
in
in partners.
Third,
we examine
asked each attorney
we conducted
billed as
in the firm to
an indicator of
an experiment
to evaluate different hypothetical associates for promotion.
each of these investigations
the role of
determining promotion to
asked each attorney the importance of hours
might look for
are an important
in
which
We describe
in turn.
Factors Important in Promotion Respondents were asked to evaluate the importance of
:
12 different factors that were likely to play a role in the promotion process in these law firms.
Importance was measured using a
altered
five point scale
where
by the inclusion of other variables controlling
children, or gender.
1
was not important, 2 was
for marital status,
slightly
number and age of
23
was moderately
important, 3
importance. Table 4
of 4 or
5.
Column
1
lists
important, 4
was very
important, and 5
the fraction of respondents
who
was of the utmost
claimed that a factor had an importance
presents the results for associates and column 2 presents the results for
partners.
It is
clear
from inspection
that associates
factors are important in the promotion process.
columns
in
Table 4
is
0.992.
The
and partners have similar views about which
The
correlation coefficient
between the two
vast majority of associates (90 percent) and partners (99
percent) clearly view the quality of work product as important in promotion decisions.
Willingness to
work hard
is
also considered important by large
percent) and partners (89 percent).
important by a
much
number of hours
billed to clients
is
seen to be
smaller proportion of associates (68 percent) and partners (52 percent).
Indeed, billable hours ranked 7th
Hours
In contrast the
numbers of associates (96
in
importance for both associates and partners.
as an Indicator Quite a different picture
emerges when attorneys are asked about
the importance of billable hours as an indicator of other traits and achievements relevant to the
partnership decision. Respondents
were asked to evaluate the importance of billable hours as an
indicator for 5 of the 12 factors listed in Table 4.
important indicator and
assigned a value of
1
for partners
who
believe that billable hours are an
also believe that the factor itself was important in
and zero otherwise. 26
quality of work product
much importance
who
Attorneys
was very important
Thus 46 percent of associates reported
in
percent.
It is
clear
that the
promotion decisions and that partners assigned
to billable hours as an indicator of work product quality.
was 39
promotion were
from inspection of the two columns
The comparable
in
figure
Table 5 that similar
proportions of associates and partners view hours as an important indicator of underlying
associate abilities and accomplishments.
26
The
correlation coefficient
between rows
1-5
of columns
The importance of hours as an indicator was measured by the same 5 point scale described in the
previous paragraph. Hours were classified as an important indicator whenever the respondent
indicated that they were very important (4) or of the utmost importance (5).
24
1
and 2
is
associates (92 percent) and partners (78 percent)
willingness to
limited to
for
which
work long hours when
work
propensities.
billable
In our
in
view
signaling value of work hours
hours was also an important indicator was
Our
:
third
3.
The median
for partners
not
was
2.
approach to assessing the importance of
promotion involved asking partners to evaluate hypothetical promotion
first
is
sample of associates, the median number of important factors
Each partner was randomly assigned to one of four
The
partners, a large majority of
hours as an important indicator of a
billable
However, the
required.
Hypothetical Promotion Decisions
work hours
among
Consistent with our model of income sharing
0.94.
cases.
different cases.
case asked the partner to evaluate George Davidson, an associate described as
follows:
George Davidson has distinguished himself as a very capable lawyer. He has handled
difficuJt cases, often
attorney.
He
with good
In addition,
results.
George
is
a very hard working
volunteers for more work and can regularly be found at the office nights
and weekends.
Although George
engaging
is
and
style
not the pre-eminent authority in his field, he has a bright and
is
To date George has had little
new clients to the firm and it is therefore
well liked by other lawyers.
opportunity to demonstrate his ability to attract
difficult to assess his potential in this area.
The second case was
The
and
identical to the first
third scenario
-
but
George Davidson became Sandra Davidson.
added the following paragraph
in
between the two presented
in
cases
1
2.
George took a month of leave after the birth of his son. Upon returning to work, he
stopped his practice of working nights and weekends and the result has been a marked
reduction in his billable hours over the past three years.
be interested in shifting to a reduced hour schedule
if
He
has indicated that he would
he should have a second child
in
the near future.
The
fourth scenario
was
the
same
as the third, but
George was changed
to Sandra.
After reading their assigned case, partners were asked the likely degree of support they
would give George (or Sandra)
in
an actual promotion decision
what degree of support they would give
new
clients.
if the
A
follow up question asked
candidate had demonstrated
some
ability to attract
25
The
6.
Columns
partners' assessments
1
of the short and long hour job candidates are presented
Table
and 2 compare the degree of support George and Sandra received when they had
not yet demonstrated that they have an ability to bring in
partners indicate very heavy support and 3
new
When working
an important effect on promotion decisions.
.03 percent
1
clients.
It is
clear
long hours 1.72 percent of the
heavy support for promotion. The
and 4 report the reactions of partners when the associate demonstrates some
Looking across columns,
clients to the firm.
candidates with
some
indicated that they
it
ability to attract clients.
who have some
work hours have
percent and 17.54 percent respectively. Columns 3
figures for the short-hour equivalents are
for candidates
in
is
new
clear that partner's increased their support for
It is
also clear that hours continue to matter even
ability to bring in clients.
would give heavy support
ability to bring
For example, 20.34 percent of partners
working long hours compared
to associates
to 1.75
percent for short-hour associates.
A convenient way
probit
to
summarize the
where the dependent variable
of this exercise are presented
to attract
new
clients
demonstrated some
is
in
is
Table
of the four scenarios
results
7.
Column
1
ability to attract clients.
The
right
insignificant coefficients
on
partner's evaluation
when
when
hand side variables
were allowed
work hours
MALE CANDIDATE,
fall.
means
The
results
the candidate's ability
the candidate has
to vary.
SHORT-HOUR CANDIDATE,
indicates that support for promotion/a//s as
on the
reports estimates
unclear and column 2 reports estimates
and positive coefficients on
to estimate an ordered
the partner's degree of support for promotion.
represent the dimensions along which the scenarios
significant
is
in
in
the equations
The
statistically
columns
1
and 2
Similarly the small and statistically
that
gender per se had no direct
effect
of associates. 27
The importance of work hours documented
in
representative survey of attorneys conducted
Table 7
is
also reflected in a nationally
by the American Bar Association.
In this survey
59.3 percent of respondents believed that reduced hour or part-time employment limited
opportunities for advancement including partnership (American
Bar Association, 1991,
p. 27).
26
3.3
How
are
Work Norms Communicated and Enforced 7
Our model of adverse
to establish
model,
we
work norms
makes
selection
the case that large law firms have strong incentives
entailing an inefficiently high
number of hours. Consistent with
report evidence that a substantial fraction of associates are
hours are used as an indicator
An
in the
important issue that
enforce work norms.
One
work
that
promotion process.
we have
possibility
so far ignored
to simply
is
A
minimum number of hours each month.
enforce and some firms do impose
overworked and
this
rule
minimum
is
which firms communicate and
in
an associate that they must
tell
of this kind
billable
way
the
is
attractive
hours requirements
because
bill
it is
Minimum
some
easy to
billable
hours
requirements are problematic, however, because they do not take account of things that are
beyond the control of the associates,
business services
policy, but
above
this
An
it
is
One of the two
understood
e.g.,
a recession that reduces
demand
minimum
firms in our sample has an explicit
at this firm that
for legal (and other)
billable
hours
acceptable performance requires hours substantially
minimum. 28
alternative
and more
number of hours with respect
firm can then
tell
flexible
way
to the average
to establish
work norms
number of hours
associates that they are doing badly
if
they
billed
fall
is
to scale the acceptable
by associates
in
very far below the
median) number of hours worked by associates. Indeed the firms
in
the firm.
mean
A
(or
our study regularly distribute
reports to partners on the billable hours of all associates in the firm.
To
decisions,
establish the role that the distribution
we
followed the question on
questions about shifts
what
28
their
in
of work hours plays
work hours
A
if
they
knew
work hour
preferences presented Table 2 above with
the distribution of hours in the firm.
hours preferences would be
in individual
Half of the associates were asked
that the majority
of other associates
in the
1990 survey by the American Bar Association finds that written or unwritten billable hours
The proportion of respondents working with
requirements are widespread in larger private firms.
no billable hours requirement increases as the size of the law firm falls (American Bar Association,
1991, Table 20
p.
22)
27
firm had increased their
what
their
hours preferences would be
firm had decreased
work hours by
The answers
first
work hours by
The other
5 percent.
if
they
knew
were asked
half of the associates
of other associates
that the majority
in the
5 percent.
to these follow
up questions are presented
in
Table
8.
The columns of the
panel of Table 8 presents an associate's preferred response to a 5 percent increase in wages.
The rows of the
table presents the
same
associate's preferred response
once she
is
informed that
the majority of other associates in the firm have increased their billable and nonbillable hours by 5
percent.
work hours
In a conventional labor supply model, individual
independently of the distribution of work hours of other associates
therefore expect
that significant
observations to
all
hours preferences
well.
thing.
B
of Table
also find that
8
is
the
same
as Panel
of other associates
some
A we instead find
of work hours
if
they
of preferences when other associates increase
is
is
in
associates
were asked to consider the
the firm reduce their
work hours when they
work hours by
in hours.
of the row and column variables are the same cannot be
small in our sample.
A Wilcoxon sign rank test yields
a
The number of attorneys reporting underwork or
We cannot,
z-statistic
therefore,
tell if
the asymmetric response to
of -5.28.
A Wilcoxon signed-rank test of the hypothesis that the two distributions are identical
statistic
of 1.28.
5 percent.
considerably smaller than that observed for an increase
that the distribution
near optimal hours
A except
do so as
rejected at conventional significance levels. 30
30
should
believe others will
associates reduce
The response, however,
The hypothesis
29
their desired level
We
Indeed the hypothesis that the distribution of original
identical with the distribution
possibility that the majority
Here we
the firm.
strongly rejected. 29
is
Panel
is
do the same
in
along the diagonal of the table. In panel
numbers of respondents would increase
learned that others will
work hours
lie
decisions are determined
yields
az
28
changes
in
in the firm's
hours distribution
the hours distribution or
An
is
due to
different responses to
due to our small sample
alternative interpretation
of the
among
shifts
size.
results in
Table 8 might revolve around the problem of
coordinating the activities of groups of attorneys. If attorneys
contact
upward or downward
attorneys, then a 5 percent increase in
work
in
teams requiring face to face
one attorney's hours would require other
group members to also increase hours 5 percent. Our survey evidence does not allow us to
directly assess the
importance of these types of coordination
that associates in large firms are
commonly spend
It is
worth noting, however,
a substantial proportion of work time on legal
This type of activity consists
research and writing.
issues.
unlikely to require substantial face-to-face contact
in large
among
measure of solitary
library
work and
is
attorneys. 31
3.4 Discussion
The prediction
effort
employees overwork early
Agency models
selection models.
work
that
in
in their
career
is
not unique to adverse
which firms back load compensation
to elicit high levels of
from employees can also produce a similar pattern (see Lazear, 1981, and Kahn and
Lang, 1992). 32
The agency explanation may be
particularly relevant in the context
of law
firms.
Economists and legal scholars frequently interpret the up-or-out promotion practices of these
3
1
To
get
some
idea of the disposition of associate
described in the American Bar Associate report,
work time, we analyzed the survey of lawyers
The State of the Legal Profession 1990 This
.
survey contains information on the use of work tune for 68 associates in large private firms
those with
more than 90
attorneys).
The
(i.e.
associates were asked what percent of work time they
spent on various activities. Responses were grouped into five categories: 0-5 percent, 6-20
21-49 percent, 50-74 percent and more than 75 percent. Assigning each respondent to the
mid-point of their category, we find that the mean associate in large firms spent 28 percent of
work tune on research/memo writing and 20 percent of work time drafting instruments.
percent,
Holmstrom
(
1982) shows that signaling models can also generate rat race equilibia
professional and managerial employees overwork early in their career. His model
spirit to
our adverse selection model.
information
(e.g.,
indicator (here
It
is
in
which
similar in
differs in that, like all signaling models, the hidden
work hard) is held by the same party that determines the use of the
Holmstrom's goal was to demonstrate that introducing reputation into
propensity to
work
hours).
a dynamic labor market model will not eliminate the labor market distortions resulting from
imperfect information.
To make
this point
more
Holmstrom assumes that markets will,
employee and set wages accordingly.
strongly,
over time, learn the true characteristics of the individual
29
firms as an incentive compatible
means of inducing associates
to post
performance bonds
in the
form of deferred compensation (Gilson and Mnookin, 1989). As an empirical matter, the amount
of deferred compensation
in large
law firms
is
substantial (Rebitzer
and Taylor, 1992).
Adverse selection and agency problems are not mutually exclusive. Firms trying
short-hour attorneys out of partnerships through long hour norms
may
also
to keep
back load
compensation with an eye towards increasing the incentives of long-hour associates to work hard
or to invest
in specific
of overwork
context, the
in
human
the agency
overwork
capital.
model
that results
is
It
should be noted, however, that the economic significance
different than in the adverse selection model.
from back loading compensation
is
In the agency
efficient with respect to
information constraints. Moreover, firms will be indifferent between hiring equally productive
short and long-hour workers, even though both types of workers will
careers
Evidence of widespread overwork
is
overwork
early in their
therefore necessary but not sufficient to establish
the claim that law firms are inefficient and sluggish in providing jobs suited to short-hour
employees. The simplest version of the agency model does not require that employers prefer long
or short hour workers.
Our
short-hour associates offers
Our
in
findings that partners are
some
finding of widespread
more
willing to
promote long hour than
additional support for adverse selection.
overwork among associates
is
contrary to the results reported
other studies using data from large scale surveys of workers in the United States and Canada
(Kahn and Lang, 1991 and 1992). 33
One
explanation for this discrepancy
is
that large scale
surveys do not offer a sufficiently detailed look into the structure of professional and managerial
33
Kahn and Lang (1992
)
analyze the hours preferences of non salaried, working heads of households
ages 25-54 in the Panel Study of Income Dynamics. They find that 41 percent of their sample
would prefer to work more hours
work less. Better information on
more work were available. Only 4 percent would prefer to
work hours is available from the Survey of Work
Reduction supplement to the Canadian Labor Force Survey. Using this data Kahn and Lang
(1991) find that for nonunion men, 40.6 percent want to work more hours, 45.5 percent want their
current hours; and 13.8 percent want fewer hours. The figures for women were 32 percent wanting
more hours, 51.1 percent wanting the same hours and 16.9 percent wanting reduced hours (Kahn
and Lang, 1988, Table 2). Interestingly Kahn and Lang find some evidence that the ratio of actual
to desired work hours increases in higher wage and education groups.
if
desired
30
In law, for example,
employment relationships
among lawyers
An
in
one would not expect to see overwork reported
solo practice or in government jobs.
low incidence of overwork reported
alternative explanation for the
surveys concerns the
way
that the critical questions
on desired work hours are posed.
U.S. and Canadian surveys, employees were essentially asked
level, like to
work more or
less
prevalent, this question puts
if
In both the
they would, at their current
the position of responding to a hypothetical choice that
in
when making
they
may
who
might otherwise desire shorter hours
consumption
plans.
previously have
made
their
may
This means that employees
financial
commitments
expecting an income level achieved only at the current (and excessive) level of work hours
financial
commitments
preclude a
posed
in
(e.g.,
wage
hours than they are currently working. If hours constraints are
employees
not have anticipated
in large scale
mortgage payments, car
downwards adjustment
in
work hours
loans,
These
and school tuition payments) would
at the current
wage. In contrast, the question
our survey allows associates to adjust work hours conditional on a wage 5 percent
higher than their current wage. This
by employees
in
wage
increase
is
presumably closer to the wage anticipated
previous periods and therefore gives more scope for a
downwards adjustment
in
work hours
4.
This paper
makes
Conclusion
the case for the importance of adverse selection models to the
determination of work hours
of our empirical investigation
in
is
managerial and professional employment relationships.
been law
firms.
We argue that the income
characteristic of legal partnerships creates incentives to,
all
else equal,
with the greatest propensity to work hard. Since this propensity
is
sharing that
In particular,
law firms
rely
upon an
associate's record
is
promote those associates
unobservable, law firms
use indicators of this propensity for the purpose of selecting associates for promotion to
partnership.
The focus
of billable hours.
will
31
Using a simple model,
is
it
easy to find instances where these practices lead to the
imposition of work norms entailing inefficiently long
not adjust
work norms
in
and partners view
hours as an important indicator
We
large law firms.
in
promotion decisions. The response
this
conclusion as well.
firms differ from other professional service providers in that the indicator used in
is
denominated
in
terms of hours.
in
our model that requires indicators have
in
order to generate overwork
among
It is
this characteristic.
that the indicator
is
race equilibria should occur
billed
two
numbers of associates work too many hours. In addition, both associates
billable
promotion decisions
rat
In such cases, firms will also
using survey data from
of partners to hypothetical promotion scenarios supports
Law
hours.
response to an influx of employees desiring short hours.
We test the implications of our model
find evidence that large
work
important to note that there
All that is
is
nothing
needed from an indicator
be an increasing function of work hours. Thus
associates in major consultancies, even though clients are
by the project rather than the hour.
Our model of adverse
groups of co-equal employees
(1) the
members of a group
selection
is
not be limited to professional partnerships.
Among
other organizations, rat race equilibria can be expected wherever
in
benefit
from the productive
activity
of other group members;
(2) the
output of the group can be significantly influenced by the work effort of individual members; and
(3)
members of the group have
the ability to establish
work norms. Thus, we might expect
race equilibria to be observed in academic departments of research universities
faculty benefit
where tenured
from the research reputation of other members of their department.
expect adverse selection
in
hours to occur
in
rat
work groups where complementaries
We would
also
are such that
small differences in an individual's level of performance can generate large differences in the value
of output produced by the group (Kremer 1993). Teams of professionals developing new
products with short product
life
by excessive work norms.
Rat race effects might also appear
positions in hierarchical settings
may
cycles (e.g., software engineers)
where the
effects
in
of managerial
therefore be characterized
the competition for managerial
effort high
up
in the hierarchy
32
have a multiplicative effect on output through their influence on employees lower
down
in the
hierarchy (Rosen, 1982)
The discussion
the determination of
in section
We
work hours
Partnership
two.
profession
so far has emphasized the efficiency consequences of adverse selection in
in
close by returning to a distributional issue
the large law firms
Not only do partners
in large
we
firms earn
study are the
elite
likely to
is
be true
in
that, relative to situations
more money than other attorneys (Rebitzer
other settings where adverse selection
where hours are
limited by
is
This selection process
disproportionate
may have
custom or law,
rat
emerge victorious from
It is
the profession.
It
The
follows then
race equilibria reduce
work hours
early in their
the effect, although not the intent, of keeping a
number of qualified women out of leadership
professional organizations. 34
in
important
access to powerful positions for those unwilling to tolerate excessive
careers.
briefly raised
positions in the legal
and Taylor, 1992), they also constitute the source of much of the leadership
same
we
also possible that the
a rat race are those
who
positions in business and
male and female professionals
who
are personally least well equipped to address the
consequences that shifting demographics have for professional and managerial employment
relationships
The consequences of this
an important question not yet addressed
selection pressure for the adaptability
in
of organizations
the economics of professional and managerial labor
markets.
34
This gender effect results from the current fact that
activities continues.
women
For comparisons of the time men and
bear the
women
lion's
spend
share of non-market
in
non-market work
activities see Fuchs (1986), Leete-Guy and Schor (1990), and Justin and Stafford (1991).
is
33
References
"The Economics of Caste and of the Rat Race and Other Woeful Tales,"
Quarterly Journal of Economics November 1976, vol. 90, p. 599-617.
Akerlof, George.
,
Amercian Bar Association, Young Lawyers Division, The State of the Legal Profession
American Bar Association, 1990.
Coleman Mary
and Pencavel John. "Trends
T.
1940," Industrial and Labor Relations
Coleman Mary
in the Market Work Behavior of Women Since
Review July 1993a, vol. 46 no. 4, p. 653-676.
,
and Pencavel John. "Changes
T.
1940," Industrial and Labor Relations
"His and Hers: Gender Differences
Labor Economics July 1986, vol. 4 no. 3 pt.
,
Studies
in
January 1993b, vol 46 no.
,
Since
p.653-676.
2,
Work
and Income, 1969-1979," Journal of
S245-S272.
2, p.
Walrasian Theory of Markets with Adverse Selection," Review of Economic
"A
1992,
.
Work Hours of Male Employees
in the
Review
Fuchs, Victor.
Gale, Douglas.
.
p.
229-255.
Ronald and Mnookin, Robert. "Coming of Age in a Corporate Law Firm: The Economics
of Associate Career Paths," Stanford Law Review 1989, vol. 41, p. 567-95.
Gilson,
.
Ronald and Mnookin, Robert. "Sharing
Inquiry into the Corporate Law Firm and
Review 1985, vol. 37, p. 313-92.
Gilson,
Among
the
Human
How Partners
Capitalists:
An Economic
Split Profits," Stanford
Law
.
Goldin, Claudia.
New
York,
Understanding the Gender Gap:
NY: Oxford
An Economic
History of American
Women
.
University Press, 1990.
HolmstrOm, Bengt. "Managerial Incentive Schemes- a Dynamic Perspective." in Essays
Economics and Management in Honour of Lars Wahlbeck Helsinki: Swenska
in
.
Handelshogkolan, 1982.
Juster,
Thomas
P. "The Allocation of Time: Empirical Findings, Behavioral
Problems
of
Measurement,"
Journal of Economic Literature June 1991,
Models, and the
vol. 29 no. 2, p. 471-522.
F.
and Stafford, Frank
.
Kahn, Shulamit and Lang, Kevin. "Constraints on the Choice of Work Hours: Agency versus
Specific-Capital," Journal of Human Resources Fall 1992, vol. 27 no. 4.
.
Kahn, Shulamit and Lang, Kevin. "The Effects of Hours Constraints on Labor Supply Estimates,"
Review of Economics and Statistics. November 1991, vol. 73 no. 4, p. 605-61 1.
Kremer, Michael. "The O-ring Theory of Economic Development," Quarterly Journal of
Economics August 1993,
.
vol. 108, no. 3, p.
55 1-576.
34
Lazear,
Edward P. "Agency, Earnings Profiles, Productivity, and Hours
Economic Review September 1981, vol. 71, no. 4, p. 606-20.
Restrictions," American
,
"Assessing the Time Squeeze Hypothesis: Estimates of
Market and Non-Market Hours in the United States, 1969-1987," forthcoming in Winter
Leete-Guy, Laura and Schoi.
1994, vol. 33 no
Martindale-Hubbell
Law
Morello, Karen Berger
Juliet.
1
Directory'.
The
Summit,
Invisible Bar:
N
The
J.:
MartindaJe-Hubbell.
Woman Lawyer in
America 1638 to the Present
.
Boston, Mass: Beacon Press, 1986.
Rebitzer, James
B
and Taylor, Lowell
Employer Size Wage Effect
in
J.
"Efficiency
the Job
Wages and Employment
for Lawyers," Working
Market
Rents:
The
Paper, (October
1992).
"Do Labor Markets Provide Enough Short Hour Jobs 9
of Work Hours and Work Incentives," Working Paper (November 1993)
Rebitzer, James B. and Taylor, Lowell
An
Analysis
J.
Rosen, Sherwin "The Market For Lawyers," Journal of Law and Economics
35,
p.
.
October 1992,
vol.
215-246.
Rosen, Sherwin, "Authority, Control, and the Distribution of Earnings," Bell Journal of
Economics Autumn 1982,
,
vol. 13, p. 31 1-323.
M. and Stiglitz, J. "Equilibrium in Competitive Insurance Markets: An Essay on
Economics of Imperfect Information." Quarterly Journal of Economics 1976, vol.
Rothchild,
.
the
80,
p.629-49.
Schor, Juliet
B The Overworked American: The Unexpected
Basic Books, 1991.
Decline of Leisure
.
New
York:
Table
1
Descriptive Statistics of Associates Included in the Survey
Table 2
How Associates Would Choose to Use a Hypothetical 5% Wage Increase
Associates
Associates
Married Associates
Whose Spouses Work
Full time
Table 3
Characteristics of Associates by Hours Preferences
Associate
Would Choose
Use
5% Wage by:
(1)
(2)
(3)
Reducing
Keeping
Current Hours
Increasing
Hours
(1) Percent Male
to
5%
Hours
5%
Table 4
Fraction of Associates and Partners Who Consider
The Following Factors Very Important for Promotion to Partnership
Factor
in
the
Promotion Decision:
1
Table 5
Fraction of Associates and Partners Who
Considered Billable Hours an Important Indicator of
A Factor Viewed As Important For Promotion.
'
Factor
in the
Promotion Decision
Table 6
Degree of Support for a Hypothetical Candidate for Promotion to Partner
Ability to Attract Clients
Is
Degree of Support
Unclear
Some Demonstrated
Ability
to Attract Clients
Table 7
Ordered Probit Estimates of the Determinants of
Support for a Hypothetical Candidate for Promotion to Partner
(t-statistics)
of Candidate to
Attract Clients is Unclear
Ability
Candidate Demonstrated
Some
Ability to Attract
Clients
Support for Promotion
Dependent Variable:
Short-Hour Candidate
Male Candidate
N
1
Support was recorded
moderate support; 4=
in
1
Support for Promotion
0.45
0.65
(2.16)
(3.16)
0.02
-0.01
(OH)
(-0,06)
115
116
4.70
10.25
a 5 point scale where: l=very heavy support;
little
support and 5= very
little
support.
2= heavy
support;
1
3=
Table 8
Changes in Hours Preferences of Associates
As The Distribution of Hours in the Firm Shifts
Original
Preferences
When
Increase Hours
2
Others
Hours Preferences:
1
Figure
1
and Type 2 Attorneys
The Full Information Equilibrium
Hours for Type
c
1
in
= wh
hours
Figure 2
Hours for Associates
in
The Separating Equilibrium
'2
c.
hours
h
V 12
-
V22
C
1
+r
2
-
C
2
2
h
2
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ill
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1
Date Due
NOV
1
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