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M AY / J U N E 1 9 9 9
W. Bentley MacLeod is professor of economics and law at the University of Southern California. Daniel Parent is researcher at the Center
for Inter-university Research on the Analysis of Organizations (CIRANO), Montreal, Quebec, and an assistant professor at McGill University,
Montreal, Quebec. The authors thank Joseph Ritter and Jim Rebitzer for helpful comments. They gratefully acknowledge the financial support
of National Science Foundation, Grant SBR-9709333, the Federal Reserve Bank of St. Louis, and CIRANO. Daniel Parent's research is supported
in part by Quebec's FCAR.
Job Characteristics, Wages, and
the Employment
Contract
W. Bentley MacLeod
and Daniel Parent
T
his paper explores some of the determinants of compensation in the United
States. We suggest that compensation
systems should be viewed as an integral
part of the production process. We also
wish to highlight the diversity in observed
systems of pay that is often overlooked
when examining wage trends from a
macroeconomic perspective.1 A goal of
the work reviewed here is to introduce
compensation models that make predictions based upon observed job characteristics, and illustrate how compensation form
may respond to changes in both the nature
of work and labor-market conditions.
The extent to which we are able to relate
compensation to job characteristics is very
much limited by the data. Fortunately, available data sets do have some information that
we can use. In this essay we use both the
National Longitudinal Survey of Youth (NLSY)
and the Panel Study on Income Dynamics
(PSID) to explore these issues. These data
are not perfect, but they do provide information on some quite distinctive compensation practices. Table 1 reports the
incidence of pay method by occupation for
the NLSY. Workers were asked if during
the current year they received any of the
following types of compensation:
1. Hourly: Pay that depends upon the
number of hours worked.
2. Salary: Pay by fixed period, such as
weekly, monthly or yearly. Hours of
work may vary from pay period to
pay period, with no corresponding
change in salary.
3. Piece Rate: Payment based upon the
number of pieces produced by the
worker, typically a supplement to
hourly pay. For the PSID, workers are
also asked if they are paid a combination consisting of an hourly rate
and a piece rate.
4. Commission: Pay based upon some
dollar measure of output, such as
sales in the last period, typically
commissions supplement salary pay.
For the PSID, workers are also asked
if they are paid a combination consisting of a salary and commission.
5. Bonus: Pay above one’s salary or
hourly pay that is not contractually
linked to a measure of performance,
and hence its level is at the discretion
of the employer.
6. Promotion: Movement to a higher
rank, usually, though not always,
associated with greater pay.2
This list does not exhaust the types of
pay that we observe in practice, though it
does move beyond the types of pay that
would be considered in most macroeconomic
models. In the next section, we briefly review
the standard agency model. This model,
the starting point for the economic theory
of contracts, helps us understand the
conditions under which a firm should
link measures of performance to pay. As
Table 1 illustrates, however, explicit payfor-performance contracts are by no means
ubiquitous. In a later section entitled
“Opportunism and Contract Complexity,”
we will explore the limitations of the agency
model in the context of Williamson’s (1975)
concept of opportunism.
When the employment relation is complex, then pay-for-performance contracts
are incomplete, and hence workers may
engage in inefficient opportunistic behavior.
A solution to this problem, discussed in a
section entitled “Relational Contracts,” is
to use a relational contract that delays
specifying rewards and exact performance
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
13
1
However, there are a large
number of possible models of
compensation, as nicely outlined in the review of Ritter and
Taylor (1997).
2
See the Data Appendix for the
exact question pertaining to
pay-for-performance in the
NLSY.
M AY / J U N E 1 9 9 9
Table 1
Pay Method by Occupation
National Longitudinal Survey of Youth (NLSY) 1988-90
Occupation
Managers and admin.except farm
Writers, artists, etc.
Sales workers
Prof., tech, except eng. techn.
Personal service workers
Secretaries
Engineering and science techn.
Clerical and unskilled 1*
Office machine operators
Clerical and unskilled 2**
Transport equip. operatives
Food service workers
Mechanics and repairmen
Cleaning service workers
Craftsmen and kindred 1***
Precision machine operatives
Laborers, except farm
Health service workers
Textile operators
Operatives exc. precis. machines
and textile
Hourly
Salary
Piece Rate
Commission
Bonus
Promotion
19.98%
21.84%
25.07%
27.94%
36.81%
37.20%
42.37%
43.18%
43.88%
48.76%
50.48%
52.46%
53.16%
54.46%
60.32%
60.44%
60.71%
65.99%
66.67%
80.02%
78.16%
74.94%
72.06%
63.19%
62.80%
57.63%
56.83%
56.12%
51.24%
49.52%
47.55%
46.84%
45.55%
39.68%
39.56%
39.29%
34.01%
33.33%
0.68%
2.30%
0.78%
0.43%
1.84%
1.02%
0.00%
1.34%
0.84%
1.99%
3.38%
0.52%
4.54%
1.49%
2.67%
36.81%
6.02%
2.03%
9.76%
9.84%
9.20%
37.98%
1.99%
20.25%
1.37%
5.09%
3.12%
1.27%
1.74%
8.21%
1.29%
9.56%
0.50%
1.60%
1.10%
1.88%
0.51%
0.71%
28.46%
17.24%
25.58%
15.46%
9.20%
11.60%
9.32%
13.21%
13.50%
10.20%
13.53%
7.49%
9.89%
7.43%
10.68%
9.34%
10.34%
8.63%
11.43%
18.91%
14.94%
11.37%
13.76%
9.82%
13.99%
18.64%
16.32%
14.77%
14.93%
10.14%
11.37%
12.16%
9.90%
17.97%
10.44%
13.16%
9.65%
10.00%
68.93%
31.07%
8.75%
1.79%
10.54%
7.32%
* From bank tellers to meter readers for utilities (Census 301 to 334)
**From shipping clerks to ticket agents and other miscellaneous clerks (Census 374 to 395)
***From auto accessory installers to machinist apprentices (Census 401 to 462)
owned by the principal.3 There are three
basic ingredients in such a model:
1. The agent is risk averse.
2. The output of the agent is a
stochastic function of effort.
3. The agent’s effort is imperfectly
observable.
For simplicity, assume that the principal
is risk neutral, given that the agent is risk
averse, this implies that the individual
would prefer to receive a fixed income
stream that is independent of the project’s
fortunes. Given that effort is not easily
observable, however, this may give rise to
moral hazard: The agent may choose less
than the efficient level of effort. The prin-
expectations until after the worker has
selected effort. Under the appropriate conditions, this provides a solution to the
problem of opportunistic behavior. Moreover, it has the empirical prediction that
firms are more likely to use bonus pay
rather than efficiency wages when labor
markets are tight. We test and find some
support for this hypothesis. The final section
of the paper contains concluding remarks.
3
See Hart and Holmstrom
(1987) for a good overview of
the agency model. See also
Gibbons (1995) for a more upto-date review of this literature.
AGENCY THEORY
The agency model begins with a principal who wishes to hire an agent to carry
out a task, usually involving the assets
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
14
M AY / J U N E 1 9 9 9
cipal can provide incentives for performance
by making the agent’s pay conditional
upon the available performance measures.
More formally, suppose that the agent’s
preferences are given by:
Notice that even though the principal
cannot directly observe the actions of the
agent, the contract is designed so that in
equilibrium the agent chooses to work
hard. Assuming that the solution can be
characterized by the first order conditions
for the optimum, then the optimal
contract solves the following equation:
U (ω , e ) = u (ω ) − υ e ,
(1)
where ωis income and e [{L,H} is low or
high effort. The utility for income is assumed
to be twice differentiable, and satisfy
u ′( ω ) > 0, u ′′( ω ) < 0 for every ω> 0. The
disutility for effort satisfies υH > υL > 0. The
effort of the agent results in a stochastic
output denominated in dollars, y e Y # R,
as well as a vector of performance measures,
m = {m1,...,mn} e M. Let fe (y,m) denote the
joint distribution of y and m as a function
of effort, where it is assumed that fe (y,m) >
0 for all (y,m) [Y ×M.4 Let us further suppose that it is efficient for the agent to
produce a high level of effort (otherwise
the problem is trivial), and that the
principal offers a wage contract that is a
function of the observable signals (y,m),
given by w + c(y,m).
In this case the principal agent
problem is given by:
(
(5)
)
subject to:
(4)
{(
)}
E U c( y, m), H ≥ U , and
{(
)} { (
E U c( y, m), H ≥ E U c( y, m), L
)}
where
{(
E U c( y, m), e
(
)
where µ, λ≥ 0 are the LaGrange multipliers
associated with constraints 3 and 4,
respectively. If there were no moral hazard
problem, then constraint 4 would not be
binding, and λ= 0 with the optimal
contract given by a constant wage ω∗ satisfying υ′(ω∗)= 1/υ′(ω∗)= 1/µ.
The interesting case is when moral
hazard is a problem, and λ> 0. In that case,
the sensitivity of the contract to y and m
depends upon the behavior of the
f L ( y ,m)
likelihood ratio r ( y, m) = def
. When
f H ( y ,m)
the likelihood ratio is a decreasing function
of y, called the monotone likelihood ratio
condition, then the optimal contract will be
increasing in y. This condition implies that
FH first-order stochastically dominates FL
(though the converse is not true). As
discussed in detail by Hart and Holmstrom
(1987), the intuition is that a high y signals
high effort, and the agent should receive a
greater reward. In equilibrium the principal
has correct expectations concerning worker
effort, and the signaling effect is to provide
ex ante incentives, and does not provide
information to the principal per se. The signaling perspective does provide guidance
about when additional measures of performance should be incorporated into the
optimal contract, as shown in the following
proposition.5
Proposition 1. Suppose that the solution
to the principal agent problem satisfies the
first-order condition 5, then the optimal contract c* (y,m) depends upon the signal mi
if and only ∂r ( y, m) / ∂mi ≠ 0 for some value
(y,m).
∫ y − c( y,m ) fH ( y, m) dyd m,
(2) max
c(.,.)
(3)
f L ( y, m)
= µ + λ 1 −
,
f H ( y, m)
u ′ c * ( y, m)
1
)} =
∫ υ (c (y, m)) fH ( y, m) dyd m − υ e .
Constraint 3 is the individual rationality
constraint that ensures the agent receives
as much as his or her next best alternative,
–denoted U . The next constraint, 4, is the
incentive constraint that ensures that the
agent prefers to work hard rather than to shirk.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
15
4
This is the so-called full-support assumption that is a necessary (though not sufficient)
condition to use the first-order
approach to characterize the
optimum. Harris and Raviv
(1979) show that if the support moves with effort then one
can implement the first best.
We also assume that the density is a differentiable function of
y and m.
5
See Holmstrom (1982) for
more details.
M AY / J U N E 1 9 9 9
6
7
We use a linear probability
model rather than a logit or
probit because we can better
control for selection effects and
misclassification error. The
main drawback of a linear probability model is that it is less
efficient, but in general it is
more robust to specification
errors than a nonlinear model
would be. Note also that the
standard errors are adjusted
for group effects (see e.g.,
Moulton, 1986) and that we
take into account possible
selection (into occupation)
effects. See MacLeod and
Parent (1997) for complete
details.
To correct for misclassification
error, we borrow from Krueger
and Summers (1988).
For example, if mi represents the clothes
of the agent or their hairstyle, and these
provide no information concerning their
effort, then they should not enter into the
optimal contract. Any other measures,
however, such as customer complaints,
supervisor reports, etc., that provide
additional information concerning performance above and beyond y should be
included in the optimal contract, even if
the contract already depends upon y.
Consider for example a sales person
who is paid on commission. Sales is a discrete variable that depends upon a number
of factors, including price, buyer preferences,
store location, etc. Hence a sale may be
made even if a salesperson is rude (for
example, the buyers had to purchase the
good immediately and could not search
further). Rudeness, however, is likely to
affect the probability of a sale in many
cases. Even if the sale is consummated,
the optimal contract would entail a penalty
if the customers report to the manager that
the salesperson is rude. The model
predicts that even a single report of rudeness should generate a negative financial
consequence, and more generally, as Gibbons (1995) observes, agency theory
generically predicts a sensitivity to
available performance measures that we
rarely observe in practice.
were asked in 1979 and 1982, which we
can use to carry out a preliminary investigation of the relationship between
performance pay and job characteristics.
The relevant question in those years was:
“We would like to know what kind of
opportunities this job offers you. How
much opportunity does this job give you?
A minimum amount, not too much, a
moderate amount, quite a lot, or a
maximum amount?
1. To do a number of things (variety).
2. Deal with people.
3. For independent thought or action
(autonomy).
4. Friendships.
5. To do a job from beginning to end
(probe if necessary: that is, the
chance to do the whole job)
(complete TASK).”
Answers are re-coded to zero if respondents answer either “a minimum amount,
not too much, or a moderate amount,” while
they are re-coded to one if respondents
answered either one of the last two possibilities. For each one of 20 occupation cells,
we compute the average of the answers in
both the 1979 and the 1982 surveys.
We then merge these averages to each corresponding occupation category for the
1988-90 period. This, of course, is a crude
way to proxy the different dimensions of the
jobs, but we think that it is not too unreasonable to assume that jobs that are in the
same occupation cell may share some
common characteristics.
In Table 2 we report the results from a
linear probability model of different types
of performance pay.6 Given that piece rate
workers also are categorized as wage earners
(notice that all workers are categorized as
either wage or salary workers), then we can
ask what job characteristics are associated
with the use of piece rates. These results
are reported in the first two columns, with
the second column correcting for biases
that may be introduced due to misclassification of worker occupation.7
Notice that requiring workers to perform
complete tasks is negatively related to the
use of piece rates. This may suggest that
individuals on straight wages are more
Some Evidence
To understand why performance-pay
contracts are not ubiquitous, we begin by
looking at some of the determinants of
performance pay. Even if agency theory
is not a complete model, it still provides
important insights into the necessary
conditions for the use of a performance
measure. In particular, jobs for which
the cost of obtaining good measures are
low should have a higher incidence of performance pay. As we can see from Table 1,
we have data from the NLSY that describes
certain types of performance pay during
the 1988-90 period. Unfortunately, no
questions pertaining to the characteristics
of the jobs were asked in the NLSY during
the 1988-90 period. But such questions
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 1 9 9 9
Table 2
The Effect of Job Attribute on the Likelihood of a Compensation
Characteristic Based upon the National Longitudinal Survey of
Youth (NLSY) (1988-90)
Is the following
attribute important
in your job?
Piece Rate(1)
vs.
Hourly Wage (0)
Commission (1)
vs.
Salary and/or
Bonus Pay (0)
Bonus + Salary (1)
vs.
Salary + Termin.
Contract (0)
Autonomy
-0.1331
(0.5382)
-0.1835
(0.3536)
1.5634
(0.4433)
2.2259
(0.5464)
0.982
-0.9165
1.1825
-0.5275
Complete Task
-1.4971
(0.6352)
-1.4102
(0.4173)
-0.7975
(0.5231)
-1.2647
(0.5960)
0.3077
(0.9044)
-0.4598
(0.6226)
Variety
0.9406
(0.4795)
0.6816
(0.3451)
-1.1221
(0.3949)
-1.156
(0.4429)
-1.1146
(0.7175)
-0.5263
(0.4700)
Friendships
-0.5213
(0.6105)
-0.0419
(0.4029)
-0.3344
(0.5052)
-0.5861
(0.6794)
-0.3302
(1.2908)
-0.6134
(0.6012)
Deal with People
-0.0435
(0.1921)
0.0611
(0.1262)
0.2367
(0.1582)
0.1735
(0.3429)
0.1426
(0.2593)
0.4136
(0.1883)
Correction for
Misclassification?
No
Yes
No
Yes
No
Yes
F-Test of No Selection
(P-Value)
Sample Size
0.0878
3927
0.2599
3927
4238
0.7084
4238
3832
3832
Notes: Standard errors are in parentheses, with 5 percent significance given in white, and 1 percent significance in grey. These are
adjusted for structural group effects where applicable. Other covariates include tenure, labor market experience, and dummies for
region, industry, year, residence in Standard Metropolitan Statistical Area (SMSA), unemployment rate, schooling, union status, and
increase in responsibility.
likely to be assigned specific tasks, with
target completion dates, this is consistent
with our view that a worker is paid a fixed
hourly wage but does not imply a lack of
incentive pay. Rather, the worker is paid
for the time spent on the job, where he or
she is required to achieve a satisfactory
level of performance. Relative to piecerate contracts, tasks with less variety
would be easier to monitor on a day-to-day
basis, hence performance can be measured
in terms of acceptable/unacceptable, with
termination being the consequence if there
is unacceptable performance.
The Autonomy variable has positive
sign in the Commission vs. Fixed-Salary
regression, while the complete task
variable is negative. Given that commission
workers are rewarded based upon a measure
of output, direct monitoring is less necessary and hence they have more autonomy.
This also implies that those workers who
are not paid commissions would be more
closely monitored, an observation that is
consistent with the negative coefficient for
the Complete Task variable.
Consistent with earlier results by
Brown (1990), we find that Variety has a
negative effect on the likelihood that commission contracts are used. This result
does not follow directly from the agency
theory that would predict the use of more,
not less, performance pay. In the next section we outline a model based upon
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 1 9 9 9
Williamson’s (1975) notion of opportunism,
which may help explain this effect. It is
also interesting to observe that job characteristics have little impact upon the choice
of whether to use bonus pay.
If bonus pay is not directly related to job
characteristics, then what is its role? The
use of bonus pay is not a prediction of the
agency model because it is not an explicit
function of a performance measure, rather
it is the consequence of some subjective
performance-evaluation system. More
generally, the data also suggests that for
many workers, contracted-performance pay
(piece rate or commission) is not always
an important ingredient of compensation,
especially when Variety is important—
even though agency theory predicts that
even imperfect measures of performance
should be incorporated into pay. In the
next section we discuss how a model of
contract incompleteness based upon a
simple complexity argument can explain
both the use of noncontingent pay and
why the incidence of bonus pay may not
depend upon job characteristics.
view. Recall that in an agency model
the optimal contract incorporates the
incentives for shirking via the IncentiveCompatibility constraint, and thus, firms
would never be surprised by worker
behavior ex ante. Kerr’s observation of
unexpected, dysfunctional behavior ex post
is consistent with Williamson’s (1975)
notion of opportunism: self-interest
seeking with guile.
In the context of an agency
relationship, we define guile as behavior
that takes advantage of the incentive system
by increasing the agent’s payoff at the
expense of the principals that is not anticipated via the Incentive Constraint. For
example, consider a firm that rewards typists based upon the measured number of
keystrokes per day. This is a clear pay-forperformance contract committing the firm
to a pay method that is a simple function of
“output.” The difficulty with this system,
as was discovered when the system was
implemented at one firm, is that one typist
discovered that she could increase her
income by pressing the same key repeatedly.
Had the firm anticipated this behavior,
it would have implemented additional
monitoring to ensure the quality of output.
The agency model explicitly assumes that
all possible types of dysfunctional behavior
are anticipated and controlled with the
appropriate contract terms and conditions.
Hence, the introduction of a negative
behavior such as guile necessarily requires
the relaxation of the complete-contracts
assumption, which in turn requires a fundamental modification of the standard
economic model of decision-making.8
The conceptual starting point is to view
contract incompleteness as arising from the
problem of exchanging complex goods, such
as labor services. A distinguishing feature of
a complex good, relative to an exchange of
a simple good or commodity, is that quality
is difficult to define, and therefore difficult to
enforce using a contingent contract enforced
by the threat of a court action. Secondly, both
the creation of complex goods and the formation of contracts to govern their exchange
are innovative activities that do not fit easily
into the standard agency model.
OPPORTUNISM AND
CONTRACT COMPLEXITY
8
See MacLeod (1997) for a
complete discussion of this
point.
What we learn from the agency model
is that generically optimal contracts should
incorporate all available performance measures. This implies that pay-for-performance should be the norm rather than the
exception. There is a large body of evidence in the management literature that
emphasizes the dysfunctional attributes of
performance pay. For example, if we were
to reward computer programmers based
upon the number of lines of code that they
produce, then the likely consequence is
not necessarily high output, but many
lines of inefficient and error-ridden code.
An immediate response is that lines of
code is not an appropriate measure of
output. As the famous study by Kerr
(1975) eloquently illustrates, many organizations and firms have implemented
pay-for-performance systems, only later to
discover that they result in dysfunctional
behavior from the organization’s point of
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
18
M AY / J U N E 1 9 9 9
The problem can be illustrated formally
with a simple model of employment based
upon the multitasking model of Holmstrom
and Milgrom (1991):
1. The principal and agent agree on
compensation and expectations for
performance (which may include
the continuation of a previous
agreement).
2. The state of the world ω t ∈ Ω
is revealed.
3. The agent divides a time endowment
of Y among k different tasks: y t ∈ℜ K .
4. The principle pays the agent Wt.
5. Both principle and agent decide
whether to continue the relationship
or not.
The date is denoted by the subscript t,
and K is the number of possible tasks. The
twist upon the previous literature concerns
the interpretation of the state of nature.
Suppose that both the costs and benefits of
different actions are unknown ex ante; for
example, a fireman may not know which
house will catch fire; how difficult it will be
to put out the fire; nor is he able to anticipate the set of actions that will need to be
carried out upon entering the burning
house. A state space that incorporates
uncertain costs and benefits for each of the
possible tasks can be defined as follows:
(6)
Ω=
The quadratic term implies that the marginal
cost of effort in a single task is increasing
with effort, ensuring an interior optimum.
The function δ(yit ) is 1 if yit is positive and
zero otherwise, which implies that there is
a fixed cost f of supplying a positive level
of effort to a particular task. When there
are a large number of tasks this implies
that the individual will supply effort to
only a subset of possible tasks.
The benefits and costs have been modeled
as functions, however it is explicitly assumed
that a measurement system does not exist.
Consider a secretary who carries out a variety
of tasks including typing, answering the
phone, filing, making travel reservations, etc.
The costs and benefits for these different
activities vary with the day-to-day demands
of the office. For example, several people
in the office may need to go to the same
conference, raising the productivity of allocating time to travel plans, and resulting in
a cutback in typing throughput. On the
cost side, if the conference occurs during a
busy period (for example college convocation),
then one may have to call several hotels to
find accommodations. Not only do these
costs and benefits vary in an independent
way from day-to-day, it is not clear (at least
to me) how one would construct a measurement system to directly compare the costs
and benefits of the different actions.
Notice that in the principal agent model
it assumed that all signals, m, are verifiable
and can be used to construct an explicit
contract; however the yit are assumed to not
be measurable. Here, we suppose that the
yit can be observed, but there exists no
contractible m. For example, if one had a
measure of individual contribution,
m t = α T y t , this could be used to construct
an efficient, explicit contract. For many, if
not most jobs, it is very difficult to construct
such a measure.
The lack of a measurement system
aggregating performance implies that the
contract must explicitly describe each state
and specify the appropriate associated
action.9 This is common in many contracts.
For example, the contract for a singer at a
concert may explicitly list acceptable reasons, such as laryngitis, that excuse the
{{α ,...,α } × {β ,..., β }} ,
1
n
{
where α k ∈ α 1 ,..., α n
1
k
m
}
denotes one of n levels of productivity for
task k, while
{
β k ∈ β 1 ,..., β m
}
represents one of the m cost levels for task
k. The total benefit from an effort choice
yt is defined by αTyt (boldface represents a
vector), while the total cost to the worker
of producing this effort is
(7)
C( yt , β) ≡ ∑
K
i=1
(
2
i yit
)
− δ ( yit ) f .
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
19
9
This assumption can be contrasted with the agency
approach to compensation as
outlined in Baker (1992) and
Holmstrom and Milgrom
(1991). This work examines
the optimal way to incorporate
imperfect signals of worker performance into the pay package.
M AY / J U N E 1 9 9 9
Table 3
Cost of a Complete-State Contingent Contract
Number of Tasks
Number of Cost and
Performance Levels
2
5
10
15
2
$0.16
$10
$10,000
$10 million
3
$0.81
$600
$35 million
$2 trillion
4
$2.56
$10,000
$11 billion
$11,000 trillion
5
$6.25
$100,000
$1,000 billion
$10 million trillion
Cost of a contract clause:
1 cent
–where U is the one-period alternative utility
for the worker. Following Townsend (1979)
and Dye (1985), let us suppose that there
is a cost for including additional contract
contingencies, given by γ per contingency.
For this multitasking model one has the
following result.
Proposition 2. The cost of implementing
the complete contract procedure when
all states occur with positive probability
is nkmkγ.
What is important to observe is that the
cost of the contract is an exponential function of the number of tasks. The literature
on computational complexity emphasizes
the impossibility of implementing algorithms
whose costs are exponential in the size of
the problem (see Garey and Johnson, 1979).
To see why this is the case, suppose that
γ = 1 cent, and that the number of cost and
performance levels are the same (n = m).
Table 3 presents the costs of the complete
contract as a function of the number of
tasks and effort levels.
As one can see, the use of a complete
contract when there are more than say 10
tasks is impossible. Furthermore, given
that these costs reflect the number of
underlying states, dynamic programming
is impossible because one could not compute the expected value of the relationship.
Observe that the piece rate contracts
correspond to basing compensation on
one dimension of output. In this simple
individual from providing the contracted
upon services. Formally the contract is a
function
c : Ω → X = ℜ × ℜk ,
where for each state w e Ω, the
(
)
c(ω ) = ω (ω ), y(ω ) ∈ X
defines the wage payment and the output
expected from the agent. This assumption
differs from the incomplete contracts literature where it is assumed that such a
contract is impossible, while maintaining
the hypothesis that individuals understand
all the possible outcomes and can recontract
based on the ex post realization of the state.
For this model an efficient complete
contract,
(
)
c * (ω ) = ω (ω ), y(ω ) ,
is the solution to the following program:
(8) y (ω ) ∈ arg max a y′ − C( y′, β),
y′
subject to:
k
(9)
y ≡ ∑ yi′ = Y ,
i=1
and
(10)
(
)
w(ω ) = U + C y(ω ), β ,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
20
M AY / J U N E 1 9 9 9
setup complete contracts are very inexpensive; therefore, they should be observed
when there is a small number of tasks to
be measured.
A solution to the problem of
complexity is to use an ex post evaluation
of the employee using supervisor reports.
The subjective nature of these reports
make third-party enforcement impossible.
Hence, performance depends upon what
MacNeil (1974) calls a relational contract,
which is discussed in more detail in the
next section. Given that direct supervision
of the employee is an essential ingredient
of the relational contract, then not only
should workers in such contracts have
less autonomy, but they also should have
well-defined goals that are determined
by their supervisors.
contingent contract with no ex post evaluation).10 The theory developed in MacLeod
and Malcomson (1989) makes some
predictions concerning the effect of market
alternatives for workers upon the
incidence of bonus pay that we briefly outline here.
Suppose the employment contract is
given by c={w,b}, where w is a fixed wage
that is paid at the end of the period regardless of performance, and b ≥ 0 is a
discretionary bonus payment that depends
on the firm’s subjective ex post evaluation
of performance. Given this contract, individual utility and firm profits are given by:
RELATIONAL CONTRACTS
(11)
U (c) = ω + b − υ e + δ U c ,
(12)
Π (c) = θ e − w − b + δ Π c ,
where e [ {0,1} is a noncontractible effort
choice taken by the worker, Uc and Πc are
the utility and profit, respectively, from
continuing the relationship, assumed to be
discounted at the rate δ. The parameters υ
and θare respectively the cost and benefit
of one unit of effort.
The implicit agreement between the
firm and worker requires the firm to pay
the bonus if and only if the worker selects
the high level of effort.11 Should either
party shirk, then the relationship is termi––nated immediately. Letting U and Π
denote the market alternatives for the
worker and the firm, then a contract is
self-enforcing if and only if the following
incentive conditions are satisfied:
When an explicit contract is not possible, the firm must rely upon some form
of ex post incentive to ensure performance.
There are essentially three types of
noncontracted ex post rewards that we
observe in the NLSY:
1. Termination contracts—pay the
worker a fixed salary, and fire the
worker at the end of the period if
performance is not satisfactory.
2. Bonus contract—pay the worker a
discretionary bonus at the end of
the period that depends on
performance.
3. Deferred compensation—reward the
worker with a promotion or permanent wage increase.
Bonus pay and deferred compensation
are not perfect substitutes since a promotion entails a permanent increase in
income. Given that we are using only
indicators rather than levels, however, we
have coded bonuses and deferred compensation into the same category. This
reduces the error associated with imputing
the true value of the promotion. Between
10 percent to 14 percent of the individuals
in our data set receive some form of bonus
pay (as opposed to piece rates or commissions, which are forms of complete
(
)
(13)
δ U c − U ≥ υ − b,
(14)
δ Π c − Π ≥ b.
(
)
Notice that it is necessary to pay a bonus
–
only if d(Uc-U ) < v. For example. if unemployment rates for the worker were to
–increase, this would lower U and increase
–
the likelihood that d(Uc-U) ≥ v. In this case,
the threat of termination alone provides
sufficient incentives for the worker not to
shirk. Conversely, with a tight local labor
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
21
10Some individuals in the NLSY
data receive both piece rates
and bonuses. They are a small
fraction of our sample, however, and so we do not explicitly
consider this case.
11MacLeod and Malcomson
(1989) prove that there is no
loss of generality when contracts are restricted to take this
form.
M AY / J U N E 1 9 9 9
Table 4
Tobit Analysis of Determinants of Bonus Pay
Panel Study of Income Dynamics (1984-91) $1979
(Standard Errors in Parenthesis)
Variable
All Observations
SMSA Workers Only
Local Unemployment Rate
-360.47
(76.97)
-357.2
(76.83)
Industry Unemployment Rate
(one-digit)
-91.36
(328.33)
-125.58
(77.96)
Schooling
186.98
(66.65)
200.69
(66.63)
Union
-1920.59 -2059.63 -1869.24
(554.94) (548.56) (559.72)
-2165.24 -2408.64 -2258.56
(982.56) (970.28) (995.49)
Potential Experience
-10.73
(20.80)
-11.6
(20.52)
-52.79
(20.21)
38.8
(35.39)
39.57
(35.46)
-9.38
(34.29)
Tenure
14.63
(26.12)
15.63
(25.69)
30.94
(26.20)
26.38
(44.00)
30.67
(43.00)
40.91
(44.16)
Live in a SMSA
571.09
657.22
347.53
(345.38) (344.84) (103.79)
Yes
No
Yes*
-7724
-7733.5
-7721.6
5119
5119
5119
Industry Dummies
Yes
Log Likelihood
-14116
N
10217
No
-525.37
(75.41)
-893.73
(152.61)
-396.76 -36.86
(598.02) (133.36)
-47.69
(56.34)
Yes*
-14124.2 -14113.6
10217
-570.49 -542.78
(158.22) (157.94)
10217
242.25 277.29
(107.46) (107.66)
-6.64
(92.18)
Note: Workers paid commissions are excluded from the analysis. Additional regressors include time and occupation dummies, as well as
a dummy for being married.
*A full set of Year X Industry (one-digit) dummies.
market, when the worker can always
find alternative work easily, the incentive
constraints imply that some form of
end-of-the-period bonus must be paid.
Therefore, we expect the incidence of
bonus pay to be a decreasing function of
the local unemployment rate.
In Table 4 we present some evidence
of this effect using the Panel Study on
Income Dynamics. We also explore the
effect of both the local and industry unemployment rates upon the amount of bonus
pay. Table 5 shows the same relationship
regarding the incidence of bonuses/promotions in the NLSY. One explanation for
the incidence/amount-of-bonus pay is as a
form of profit sharing between the firm
and the worker. Most firm’s profits are
correlated with industry rather than local
unemployment rates. When this is the
case, it implies that bonus pay incidence
will increase with a decrease in the
industry unemployment rate, while the
local rate would be unimportant. The selfenforcing contract model makes the
opposite prediction.
As we can see from the regression
results, the industry rate is not significant,
while the local unemployment rate has a
negative impact upon the amount and the
incidence of bonus pay. Also, as we would
expect, this effect is stronger when we
restrict analysis to urban areas where
workers would have better market alterna-
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
22
M AY / J U N E 1 9 9 9
Table 5
tives. More surprising for us, is the fact
that the local labor market effect increases
in the PSID data set when we add controls
for time-varying industry effects. If bonus
pay were the result of profit sharing, then
the addition of such controls would make
the effect of local unemployment either
small or less precise, whereas we observe
exactly the opposite.
In this model we have assumed that the
supervisor can perfectly observe performance
ex post. We could add imperfect observability,
as in Shapiro and Stiglitz (1984), and obtain
the same result. It is sometimes believed
that it is imperfect observability that generates an efficiency wage. As the results of
Holmstrom (1982) demonstrate, however,
an imperfect but contractible measure of
output would completely eliminate the equilibrium unemployment result for a standard
efficiency wage model. Hence, the use of
bonus pay and/or efficiency wages are a consequence of increases in job complexity that
make it impossible to fully specify ex ante an
employer’s performance expectations.
Therefore, our results provide more
support for efficiency-wage type models. In
the absence of bonus pay, an efficiencywage model implies that the wage must be
above market clearing, and if unemployment
falls this may lead to an increase in inflation.
Recently, the economy has appeared to have
both low inflation and low unemployment.
This could occur if firms move towards a
system of bonus pay, rather than raise
wages. In Figure 1 we illustrate the trend in
the incidence of bonus pay, inflation, and
unemployment from 1976 until 1991.
While this is not a test, it does show a definite upward trend in the use of bonus pay
during this period.
Fixed-Effect Results—NLSY 1988-90
Bonus/Promotion
vs.
Termination
Contract
(Bonus=1)
(Salaried Workers
Only)
Bonus/Promotion
vs.
Termination
Contract
(Bonus=1)
(All Noncommission
Workers)
Autonomy
0.982
(0.9165)
0.5743
(0.8136)
Complete Task
0.3077
(0.9044)
0.0397
(0.8621)
Variety
-1.1146
(0.7175)
-0.793
(0.6839)
Friendships
-0.3302
(1.2908)
0.4767
(1.2377)
Deal with People
0.1426
(0.2593)
0.4306
(0.2472)
Unemployment Rate
in Local Labor Market
-0.0774
(0.0161)
-0.0321
(0.0159)
Unemployment Rate
in Industry
-0.0299
(0.0225)
0.0123
(0.0213)
Schooling
-0.0104
(0.0316)
0.0134
(0.0206)
Union
-0.0807
(0.0336)
0.0092
(0.0264)
3832
7682
Variable
Sample Size
Note: Standard errors are in parentheses, with 5 percent significance given in white, and 1
percent significance in grey. These are adjusted for structural group effects where applicable.
Other covariates include tenure, labor market experience, and dummies for region, industry,
year, residence in Standard Metropolitan Statistical Area, and increase in responsibility.
explain the data. Rather, the data suggests that
compensation systems depend on explicit
performance measures when these accurately
measure the contribution of work. In
complex environments, firms must depend
upon subjective measures of performance
associated with ex post rewards to the worker.
We have also presented evidence showing
that the amount of bonus pay is dependent
upon the state of the local labor market.
One benefit of bonus pay is that its level can
be adjusted easily from year-to-year in
response to business cycle fluctuations,
CONCLUSIONS
In this essay we have reviewed some
preliminary evidence relating job characteristics to the form of compensation. Our
main message is that we observe a variety
of compensation systems used in practice,
the form of which depends upon job characteristics. There is no single economic
model of contract formation that can
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
23
M AY / J U N E 1 9 9 9
which as Weitzman (1985) has argued, can
result in both low unemployment and low
inflation. The recent trend increase in the
use of bonus pay may be one reason why
inflation has not increased, even though the
United States also is experiencing low
unemployment.
Currently, we do not know if this trend
is the consequence of secular changes in
the nature of work, or the result of innovative activity on the part of the firm. Given
that the form of compensation is likely to
affect the responsiveness of incomes to
inflation and business cycle fluctuations, it
is important to better understand the reasons for these changes. We can conclude
that it is an oversimplification to view wage
formation as the simple consequence of
supply and demand forces, and that better
understanding the source of variation in
pay systems may have important implications for the nature of monetary policy, a
question we hope to explore in future work.
Kerr, Steven. “On the Folly of Rewarding A, While Hoping for B,”
Academy of Management Journal (December 1975), pp. 769-83.
Krueger, Alan B., and Lawrence H. Summers. “Efficiency Wages and the
Inter-Industry Wage Structure,” Econometrica (March 1988),
pp. 259-94.
MacLeod, W. Bentley. “Complexity, Bounded Rationality and Heuristic
Search,” mimeo, University of Southern California, (August 1997).
_______, and James M. Malcomson. “Implicit Contracts, Incentive
Compatibility, and Involuntary Unemployment,” Econometrica (March
1989), pp. 447-80.
_______, and Daniel Parent. “Jobs Characteristics and the Form of
Compensation,” mimeo, University of Southern California (1997).
MacNeil, Ian R. “The Many Futures of Contracts,” Southern California
Law Review (1974), pp. 691-816.
Moulton, Brent R. “Random Group Effects and the Precision of
Regression Estimates,” Journal of Econometrics (August 1986),
pp. 385-97.
Ritter, Joseph A. and Lowell J. Taylor. “Economic Models of Employee
Motivation,” this Review 79 (September/October, 1997), pp. 3-21.
REFERENCES
Baker, George. “Incentive Contracts and Performance Measurement,”
Journal of Political Economy (June 1992), pp. 598-614.
Shapiro, Carl, and Joseph E. Stiglitz. “Equilibrium Unemployment as a
Worker Discipline Device,” American Economic Review (June 1984),
pp. 433-44.
Brown, Charles. “Firm’s Choice of Method of Pay,” Industrial and
Labour Relations Review (Special Issue 1990), pp. 165S-82S.
Dye, Ronald A. “Costly Contract Contingencies,” International Economic
Review (February 1985), pp. 233-50.
Townsend, Robert. “Optimal Contracts and Competitive Markets with
Costly State Verification,” Journal of Economic Theory (October 1979),
pp. 265-2.
Garey, Michael R. and David S. Johnson. Computers and Intractability,
W. H. Freeman and Co., 1979.
Weitzman, Martin L. “Profit Sharing as Macroeconomic Policy,”
American Economic Review (May 1985), pp. 41-45.
Gibbons, Robert. “The Employment Relationship,” mimeo, survey paper
prepared for the Seventh World Congress of the Econometric Society,
Tokyo, August 1995.
Williamson, Oliver. Markets and Hierarchies: Analysis and Antitrust
Implications, The Free Press (1975).
Hart, Oliver D., and Bengt Holmström. “The Theory of Contracts,”
Advances in Economic Theory, Fifth World Congress., Truman Bewley,
ed., Cambridge University Press, 1987, pp. 71-155.
Holmstrom, Bengt. “Moral Hazard in Teams,” Bell Journal of
Economics (Autumn 1982), pp. 324-40.
_______, and Paul Milgrom. “Multi-Task Principal-Agent Analyses:
Incentive Contracts, Asset Ownership, and Job Design,” Journal of
Law, Economics, and Organization (1991), pp. 24-52.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
24
M AY / J U N E 1 9 9 9
DATA APPENDIX
any of these types of compensation. Please
do not include profit sharing or employee
stock purchase plans.
National Longitudinal Survey of
Youth (1988-90)
The National Longitudinal Survey of
Youth (NLSY) data set surveyed 12,686
young males and females who were
between the ages of 14 and 21 in 1979. In
1988, 1989, and 1990, respondents were
asked whether all or part of their earnings
were based on job performance. They
were also asked a few questions on their
work environment. For instance, we
know if the respondents were supervising
other employees and whether they had
received a promotion since their last interview. Unfortunately, we do not know the
precise dollar amounts of incentive pay
received by workers nor do we know the
proportion of their earnings which is due
to pay-for-performance.
We asked the following question
pertaining to pay-for-performance: “The
earnings on some jobs are based all or in
part on how a person performs the job
(hand card D). On this card are some
examples of earnings that are based on job
performance. Please tell me if any of the
earnings on your job (are/were) based on
1. Piece rates.
2. Commissions.
3. Bonuses (based on job
performance).
4. Stock options.
5. Tips.
6. Other.”
They also were asked whether they
had received a promotion on their current/
most recent job since the last interview.
We restricted the sample to individuals
who were in the labor market on a fulltime basis. The people who were
considered as meeting that criterion
were those:
1. Whose primary activity was either
working full-time, on a temporary
lay-off or looking actively for a job,
2. Who had worked at least half the
year since the last interview and
who were working at least 20
hours per week.
Table 6
Average Real Wage Change, NLSY 1988-90
No Promotion
No Bonus
Bonus
Only
Promotion
Only
Bonus and
Promotion
All Jobs
6.7%
7.6%
12.0%
11.6%
Within Existing Employment
Relationships Only
6.2%
7.2%
11.7%
3.8%
Incidence of Different Combinations, NLSY 1988-90
No Promotion
No Bonus
Bonus
Only
Promotion
Only
Bonus and
Promotion
All Jobs
72.3%
10.5%
13.5%
3.7%
First Time Observed
With Employer
72.7%
9.8%
13.7%
3.8%
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
25
M AY / J U N E 1 9 9 9
Figure 1
Computation of Bonuses from
PSID Data
Evolution of Bonus Incidence
in the United States.
Variables V5285, V5784, V6393,
V6983, V7575, V8267, V8875, V10258,
V11399, V12798, V13900, V14915,
V16415, V17831, V19131, and V20431:
“Head’s income from bonuses, overtime,
and/or commissions.”
Note that starting with interview year
1986, the codebook specifies that the
values for this variable represented any
extra bonus, overtime and commissions
income not included in heads of
household's income from wages and
salaries during the preceding calendar year.
Therefore, it is possible that some workers
who actually received a bonus from their
employer did not report it separately from
their usual. income.
Variables V5419, V5906, V6517, V7120,
V7743, V8405, V9036, and V10563: “Did
you work any overtime which isn’t reported in
[average hours per week worked last year]?”
Variables V11142, V12541, V13741,
V14831, V16331, V17740, V19044, and
V20340: “The values for this variable [...]
represent the annual overtime hours
worked on all main jobs, if reported separately from regular work hours.”
Variables V4515, V5426, V5913,
V6524, V7127, V7720, V8388, V9019,
V10468, V11659, V13062, V14162,
V15170, V16671, V18109, V19409:
“How is that? Neither salaried nor paid
hourly.”
This question refers to the method of
pay where the respondent was paid neither
a straight salary nor an hourly rate. From
this question, we were able to identify
those workers paid commissions or a base
salary plus commissions.
Variables V10465, V11656, V13059,
V14159, V15167, V16668, V18106,
V19406: This is the overtime hourly rate
for salaried workers.
Variables V10467, V11658, V13061,
V14161, V15169, V16670, V18108,
V19408: This is the overtime hourly rate
for hourly paid workers.
Variables V10469, V11660, V13063,
V14163, V15171, V16672, V18110,
PSID 1976-91
16
14
% Paid Bonuses
12
10
8
Unemployment Rate
6
Inflation Rate
4
2
0
1976 77 78 79 80 81 82 83 84 85 86 87 88 89 90 1991
Individuals excluded from the sample
were those who have been in the military
at any time, the self-employed, and all
public-sector employees. These restrictions
left us with an unbalanced sample of 8,165
observations (3,847 workers), of which
3,832 were paid either a salary or a salary
and a bonus.
The Panel Study of Income
Dynamics (PSID), (1976-91)
12In the PSID, data on hours
worked during year t, as well
as on total labor earnings,
bonuses/commissions/overtime income, and overtime
hours, are asked at the year
t+1 interview. Thus, we actually use data covering interview
years 1976-92.
13Since we cannot separately
identify the amount of income
derived exclusively par from
commissions, we have to
remove these workers from the
calculations. Note that removing all negative estimates of
the bonuses probably biases the
par mean bonus paid upward.
The sample consisted of white male
heads of households aged 18 to 64 with
positive earnings for the period spanning
the years 1976-91.12 Individuals in the
public sector and those who worked less
than 500 hours were excluded from the
analysis. We know whether each worker
was paid a piece rate, a commission, an
hourly rate, or a salary. One interesting
feature of the PSID for the 1976-91 period
is the fact that we were able to determine
whether a worker received a bonus during
the last year. In the PSID questionnaire,
workers were asked the amount of money
they received from either working overtime,
or from commissions, or from bonuses
paid by the employer. Given that workers
reported either their number of overtime
hours worked (or simply that they worked
overtime) as well as the hourly rate for
overtime, we were able to compute an estimate of the amounts paid in bonuses.13
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
26
M AY / J U N E 1 9 9 9
V19410: This is the overtime hourly rate
for workers not paid either a salary or an
hourly rate.
Since no information on overtime
hours is available before 1984, we could not
compute an estimate of overtime income
for the years 1976-83. Thus, we simply
deleted from the sample all workers who
report working overtime between 1976 and
1983 and those who report positive hours
of overtime work between 1984 and 1991.14
We also deleted commission workers.
It is worth repeating that we may have
a noisy measure of bonuses paid. The reason
is that the questions on overtime are not
clear cut because workers were NOT asked
to report any overtime activity during the
previous calendar year. Instead, they were
asked to report all overtime work not already
included in the usual hours per-week worked.
Measures of Local Labor Market Conditions. From the beginning of the PSID
to interview year 1989, questionnaires were
sent to state employment offices asking
about current labor market conditions in
these counties. Specifically, the unemployment rate measure refers to a specific period
during the corresponding interview year.
For interview year 1976, the reference
month is August; for interview years 197779, it is November; for interview years
1981 and 1983, it is December, while for
interview years, 1982, 1984-88, it is
September.
Starting with interview year 1990, they
replaced the variables about the availability
of unskilled jobs and unemployment rates
with the average annual unemployment
rates for the respondents’ counties for the
calendar year prior to the interview. These
figures come from the U.S. Bureau of Labor
Statistics (BLS) Local Area Unemployment
Statistics Program. The industry (1 digit)
level unemployment rate series also comes
from the BLS.
14Restricting the sample to 1984-
91 and using the amount earned
in overtime to compute bonuses does not change the results,
apart from the standard errors.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
27
M AY / J U N E 1 9 9 9
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
28
M AY / J U N E 1 9 9 9
James B. Rebitzer is the Frank Tracy Carleton Professor of Economics at Case Western Reserve University.
Commentary
incentive contract should pay attention to
all informative indirect measures of output
(e.g. rudeness by a sales person) as well as
output (sales). M & P correctly observe
that compensation is not nearly as responsive to these direct and indirect performance
measures as our model would suggest. The
question then becomes what’s wrong with
the principal agent model? What follows
are some answers.
James B. Rebitzer
A
new consensus is emerging among
labor economists: Wage formation
is the result of something more than
the interaction of supply and demand.
Organizations structure compensation as
part of the larger task of structuring incentives and other features of employment
relationships. Competitive labor market
forces play a role in this design process,
but so do many other things.
The core empirical problem posed by
this new view of wage determination is
understanding the enormous diversity we
observe in the structure of compensation.
In my view, understanding this diversity
is as important to organizational economics
as understanding the diversity of species
was to natural history in the 19th century.
Unlike the natural historians, however, our
theoretical prowess far outstrips our empirical knowledge. As a result, our theories
are at grave risk of diverting our attention
towards the wrong phenomena.
The paper by Bentley Macleod and
Daniel Parent is important because it
builds a bridge between theory and
empirics. I think that it goes about as far
as you can with the conventional labor
economics data sets. As a result of Macleod
and Parent’s (henceforth referred to as M
& P) efforts, I found myself having to confront directly the issue of how organizationally minded economists should undertake
the empirical study of compensation.
Complex Tasks
The most novel feature of M & P’s analysis of principal agent models is their
analysis of how difficult it is to write a
complete contract when tasks are even a
little bit complex. In their framework, the
cost of implementing a complete contract
is nkmkg where k is the number of tasks, g
is the cost of writing a contract provision,
and n and m are the number of productivity
and cost levels associated with each task.
Because costs increase exponentially with
the number of tasks, an optimal contract
can’t be written when there is even a small
amount of complexity. The clear implication
is that “constrained optimal” incentive
schemes (i.e. those designed while taking
into account the costs of writing complex
contracts) will typically focus on a subset
of informative actions and outcomes.
If complexity causes firms to operate
with incentives that do not include all
informative measures of input and output,
then multi-task issues must be very
commonplace. Multi-task models apply
to settings where only a subset of value
creating activities can be metered and
incented. In a multi-task world, high powered incentives are costly because they
divert effort and attention away from valuable, but hard to meter, activities.1 M & P
go on to suggest that the problem of contract complexity can be resolved by relational
contracts (i.e. incentive arrangements that
rely on noncontracted, ex post rewards
based on the subjective evaluations of the
THEORY
The authors begin with a very nice
exposition of a principal agent model of
incentive design. The key points of the
model are: (i) incentives are costly because
agents are risk averse; (ii) the optimal
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
29
1 Holmstrom and Milgrom
(1991) argue that some multitask problems can be reduced
by the design of jobs.
M AY / J U N E 1 9 9 9
supervisor). This is an interesting claim.
I don’t think, however, that M & P adequately address the question of how
subjective, ex post evaluations solve the
complexity problem.
I see two classes of answers to this
question. The first answer focuses on subjective evaluations of complex behaviors.
Human beings are very good at parsing
information that is very complex and
messy. We can form accurate judgements
about things that we couldn’t begin to
write down in an explicit contract or algorithm. Think how easily young children
solve the problem of recognizing faces or
understanding a sentence, both problems
that are notoriously difficult to write down
explicitly. Subjective impressions about
the contributions of individual employees
may, therefore, be a “good enough” foundation on which to anchor incentive pay.
The second approach focuses on timing.
By relying on ex post assessments, managers
can reduce the complexity of the assessment
task because they do not need to consider
states of nature that didn’t actually occur.
Accepting for the moment that incentive schemes based on subjective, ex post
assessments and rewards solve the complexity problem, it seems clear that relational contracts raise other problems. In
particular, subjective incentive schemes
require that supervised employees trust
supervisors to fairly assess and evaluate
performance.2 Arranging things so that
employees can trust the subjective assessments of managers is no doubt difficult
and costly. I would have liked to see M & P
analyze the benefits and costs of relational
contracts relative to feasible principal
agent contracts (i.e., a contract that relies
on a small number of indicators) and to
then identify conditions under which one
incentive scheme outperforms the other.
2 See Baker, Gibbons and
Murphy’s (1994) analysis of
incentive compatible implicit
contracts.
3 See Levy and Murnane (1996)
and Ichniowski, Shaw, and
Prennushi (1997).
incentives that ignores job design is probably going to get important things wrong.
Casual examination of the literature
on high-performance work organizations
suggests what organizations want from
their employees is problem solving.
Specifically, employers increasingly want
to combine the tacit information available
to front-line employees with their
problem-solving skills to achieve higher
levels of quality and service. Car manufacturers and steel companies want production
workers to use local, tacit information to
sustain a process of continuous quality
improvement. Insurance companies want
their front-line employees (those having
direct contact with customers) to have the
information, knowledge and communication skills to offer full-service, one-stop
shopping to all customers.3
Problem-solving responsibilities (and
the associated “soft tasks” like communication and team work) are extremely complex
and, following M & P’s logic, are probably
impossible to fully specify ex ante. My
impression is that high performance organizations spend at least as much time and
effort on job design as incentives. Experts,
for example, are divided on the importance
of incentives for modern manufacturing,
but they are unanimous on the importance
of such job-design issues as problem-solving
teams and giving employees responsibility
for their own quality control. Economics
offers only the most rudimentary theory
of job design and this lacunae poses a real
problem for developing economic theories
of incentive design.
The Sociology of Groups
Another limitation of principal agent
models (one that M & P are aware of but
didn’t write about in this paper) has to do
with the individualistic nature of the production process in the principal agent
model. A large amount of human productive activity takes place in small groups
and the sociology of groups must matter
for the design of incentives.
In standard principal agent models,
incentive pay is costly because employees
Job Design and Problem Solving
The principal agent model takes jobs,
or tasks, as given. This view is certainly
too narrow. Organizations design both
jobs and incentives to elicit desirable
behaviors from employees. A theory of
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30
M AY / J U N E 1 9 9 9
are risk averse. Thus, risk aversion causes
employers to operate with lower-powered
incentives than would otherwise be the
case. Small groups, however, create additional incentive costs. If, for example,
individuals care about their income relative
to others in the work group, firms may
eschew high-powered incentives to avoid
morale-lowering invidious comparisons.
Concerns about morale may cause supervisors with responsibility for performance
evaluation to alter their evaluations so that
all individuals perform “above the average.”
In this way, group sociology will alter the
functioning of the relational contracts
described by M & P. Group sociology also
can make problematic incentives based on
objective performance measures. If individuals in groups can engage in mutual
help activities, high-powered incentives
based on individual output can discourage
valuable mutual help activities in groups.4
The sociology of small groups does
more than create incentive costs. Informal
interactions among members of the group
can also create additional incentive instruments—notably peer pressure. If individuals
in a work group have superior information
about local conditions than managers,
mobilizing peer pressure can significantly
improve performance.
they are normally conceived nor
expectations of future consequences
enter directly into the calculus…Rule
following is grounded in a logic of
appropriateness… The process is not
random, arbitrary or trivial. It is systematic reasoning, and often quite
complicated. In those respects, the
logic of appropriateness is quite comparable to the logic of consequences.
But rule-based decision-making proceeds in a way different from rational
decision-making. The reasoning
process is one of establishing identities and matching rules to recognized
situations. (March 1994, p. 57-58)
In a similar vein, some sociologists
and a few economists have written about
the detrimental effect that high-powered
incentives can have on intrinsic motivation.
Consider, for example, Akerlof’s (1982)
gift-exchange models. In Akerlof’s models
individuals are powerfully motivated by a
desire to take actions that are appropriate
to the relationship they have with their
employer. By offering high and stable
wages, employers can reduce opportunism
by inducing individuals to adopt actions
appropriate to a gift exchange. Close monitoring and/or high-powered incentives, in
contrast, cause individuals to adopt actions
appropriate with a low-trust situation.
Why might high-powered incentives
undermine intrinsic motivation? I haven’t
found a convincing answer to this question.5
One plausible possibility is that incentives
work differently depending on the beliefs
employees attribute to management’s use of
incentives. Close monitoring may send the
message that the employer doesn’t believe
employees are reliable people. Perhaps highpowered incentives send a similar signal.
Two provocative implications flow
from the social psychological view of
incentive problems:
The Social Psychology of Incentives
The principal agent model requires
that individuals be rational opportunists.
This means that individuals take actions
now with expectations about how these
actions will influence their future economic
welfare. This view of decision-making is
ubiquitous in economics but not elsewhere.
Consider, for example, the following quote
from James March’s How Decisions Happen.
March argues that rule-following can be
more important than rationality in the
operation of incentives.
4 These issues are analyzed in
• Individuals may be less opportunistic
than conventional models suppose; and
• Treating people as if they were opportunistic can create more opportunism.
When individuals and organizations
fulfill identities, they follow rules or
procedures that they see as appropriate to the situation in which they find
themselves. Neither preferences as
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
31
Encinosa, Gaynor, and Rebitzer
(1998).
5 See Kreps (1997) for an
intriguing statement of the
problem.
M AY / J U N E 1 9 9 9
These claims are inherently difficult to
investigate empirically because the smartest
opportunists will shirk only where it is
hardest to catch them. If, however, they
are correct, the principal agent model
profoundly misunderstands the ways in
which incentives motivate behavior.
offers me a great deal of autonomy, variety
and task completion. It is not hard to
imagine, however, that a manufacturer’s
representative might report that she also
enjoys lots of autonomy, variety and task
completion. Does this mean that autonomy,
variety and task completion mean the
same thing in these two occupations? I
don’t think so.
Using cross-occupational variation
in a small number of job characteristics to
explain individual compensation strikes
me as especially tricky because of the
plethora of omitted variables that may be
correlated with occupation-level job characteristics. Piece rates make good sense
for manufacturers’ representatives but not
for university professors, because the
product of the former occupation is easy
to measure and the output of the latter
is complex, multi-dimensional and hard
to measure. As this example (and our previous discussion) indicates, some of the
most interesting omitted variables are likely
to relate to job-design issues because job
design and incentives are likely to be
jointly determined.
The third set of empirical results in the
paper concern the relationship between
unemployment rates and the likelihood of
bonus pay. M & P ask us to imagine relational contracts in which there are essentially two types of ex post sanctions/rewards,
dismissal or the payment of a bonus. They
argue that as local unemployment rates fall,
dismissal threats become less effective, so
firms come to rely increasingly on bonuses
as an alternative incentive mechanism. This
logic implies that the incidence of bonus
pay will be a decreasing function of the
worker’s unemployment rate. If local unemployment rates are a good measure of the
worker’s alternative job opportunities,
we would then expect the incidence of
bonus pay to decline as local unemployment increases.
An alternative explanation is that
bonuses are a form of profit sharing, and
their incidence should, therefore, be positively correlated to firm profits. If industry
unemployment rates are a good proxy for
profits, we would then expect the incidence
EMPIRICS
M & P’s empirical excursions use data
from conventional microeconomic surveys
(NLSY 88-90 and the PSID) to examine the
incidence of different types of compensation.
In the first set of results (Table 1), M
& P present cross-occupational variation
in the form of compensation. From these
results, it is clear that the form of compensation varies in intriguing ways with broad
occupational categories. Piece rates, for
example, are used widely for precision
machine operatives (36.81%) and not for
textile operators (9.76%). Not surprisingly,
sales workers are frequently paid by commission (37.98%), but so are personal
service workers (20.25%). These results
are intriguing, but relying on such broad
occupational averages may conceal as
much as they reveal. My own research on
incentives in medical groups has convinced
me that there is enormous heterogeneity of
compensation arrangements even within
narrowly defined physician specialties
(Encinosa, Gaynor and Rebitzer, 1998).
I would be interested, therefore, in seeing
a breakdown of the variation within and
between the broad occupation group listed
in Table 1.
The second set of empirical results
(M & P’s Table 2) indicate that occupational
characteristics do matter for the incidence
of piece rates and commissions. The
authors regress the type of compensation
an individual receives against occupationlevel averages of perceived job autonomy,
task completion and variety. The finding
that autonomy, task completion and variety
matter for the form of compensation is
intriguing, but difficult to interpret because
it relies upon the interpretations that
respondents give to these concepts. My
job as an economics professor, for instance,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
32
M AY / J U N E 1 9 9 9
of bonus pay to rise as industry unemployment rates fall.
The results in M & P’s Table 3 indicate
that the industry unemployment rate has
little effect on the incidence of bonuses
while the local unemployment rate has a
negative impact. I am not convinced by
this interpretation of the results. It seems
to me that local and industry unemployment
rates are poor proxies for the underlying
variables of interest. Profits for firms
offering geographically restricted services
(e.g., hotels, restaurants, hospitals, cabs,
etc.) are more likely to be affected by local
rather than industry unemployment rates.
Profits at manufacturing enterprises also
may respond more to local than industrylevel unemployment if firms are heavily
dependent on a local customer.
M & P’s model hypothesis is that relational contracts are not incentive-compatible
where the worker faces high unemployment.
They investigate this idea using annual
unemployment rate variation. Relational
contracts, however, depend critically on
trust and firms should therefore be loathe to
alter them in response to short-term spikes
in the unemployment rate. Thus, investigation of M and P’s hypothesis should rely on
relatively long-term shifts in unemployment.
Indeed, an interesting extension of M & P’s
empirical work would be to examine the
effect of short- and long-term movements
in the unemployment rate. If short-term
movements have more influence on
compensation than long-term movements,
this would argue against the incentivecompatible, relational contracts.
If I am right that conventional data are
not up to task of understanding the determinants of compensation, then what would
the right data look like? I think the ideal
data set would have the following features:
• Data on a large number of firms in a
specific industry and employees in
specific jobs;
• Data on the form of compensation
contract as well as compensation
outcomes;
• Qualitative interviews about what
managers and employees see as
critical tasks of the job;
• Information on how employee
behaviors varied with variation in
the form of compensation, intensity
of supervision, job design and
work setting.
It is clear to me that the demanding
data-collection efforts entailed by this list
would only be manageable for narrowly
focused case studies. For the same reason,
it is unlikely that any single study would
succeed in collecting data along all four
dimensions at the same time. If large
numbers of empirical organizational economists joined their colleagues in sociology
and went about the business of collecting
and analyzing this sort of data, we would
be left with a rich assortment of case
studies. Each of these studies would be
limited and inadequate for developing a
general theory of compensation. Taken
together, however, these studies could
(like the natural histories of 19th century
biology) form patterns that we could then
use to construct a suitable and general
theory of compensation.
WHAT WOULD THE RIGHT
DATA SET LOOK LIKE?
M & P’s paper is important because it
takes good and reasonable economic models
of compensation and compares their predictions to the patterns visible in the data.
The problems they encounter in their
empirics stem from the fact that the information collected in conventional microeconomic data sets are simply too distant
from the phenomena of interest (i.e., jobs
and incentives in organizations).
REFERENCES
Akerlof, George A. “Labor Contracts as Partial Gift Exchanges.” Quarterly
Journal of Economics, (November 1982, 97:4), pp. 543-69.
Baker, George, Robert Gibbons, and Kevin J. Murphy. “Subjective
Performance Measures in Optimal Incentive Contracts.” Quarterly
Journal of Economics, (November 1994), pp. 1125-56.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
33
M AY / J U N E 1 9 9 9
Encinosa, William E., Martin Gaynor, and James B. Rebitzer. “The
Sociology of Groups and the Economics of Incentives: Theory
and Evidence On Incentives in Medical Groups,” (unpublished,
May 1998).
Holmstrom, Bengt and Paul Milgrom. “Multi-task Principal-Agent
Analyses: Incentive Contracts, Asset Ownership, and Job Design.”
Journal of Law, Economics and Organization, (Spring 1991),
pp. 24-52.
Ichniowski, Casey, Katheryn Shaw, and Giovanna Prennushi. “The Effects
of Human Resource Management Practices on Productivity: A Study of
Steel Finishing Lines.” American Economic Review, (June 1997),
pp. 291-313.
Kreps, David M. “Intrinsic Motivation and Extrinsic Incentives.”
American Economic Review, (May 1997), pp. 359-64.
March, James G., A Primer on Decision Making: How Decisions Happen,
New York: The Free Press, (1994).
Murnane, Richard J. and Frank Levy, Teaching The New Basic Skills,
New York: The Free Press, (1996).
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 19 9 9
Truman Bewley is an Alfred Cowles Professor of Economics at Yale University. He is deeply grateful to Joseph Ritter for insightful comments on
various drafts of this paper.
Work Motivation
I strove to avoid sample bias by holding
interviews in a large and diverse set of companies as well as by using many distinct
avenues of approach to gain access to them.
Using these methods, I avoided talking to
people from only a few circles of friends.
The companies represented a broad spectrum
of industries and a full range of sizes and
financial conditions. Some were bankrupt,
many were shrinking and experiencing heavy
layoffs, and some were growing rapidly.
Some had been founded only recently,
while most were well-established. Some were
unionized, whereas many had no union
presence. Some were public corporations
and others were closely held or family-owned.
I made a point of finding businesses that
had cut or frozen pay during the recession.
There were few such; most firms continued
to grant regular raises. My method did not
yield a valid opinion survey nor reliable
statistics on the incidence of various business practices. I believe, however, that I
gathered valuable information about what
happens in the labor market during a recession and what business people and labor
leaders think about layoffs and pay cuts.
The explanation of wage rigidity given by
more than 275 business people and labor leaders
I interviewed was based on views of worker
motivation that deviate from the standard
model. In this paper, I formulate a somewhat
speculative model of work motivation
stimulated by what I heard. The model
incorporates ideas from psychology into the
utility-maximizing framework of economics.
Truman Bewley
D
uring 1992 and 1993, I undertook a
field study in the Northeast of the
United States to learn why wages and
salaries seldom fall during recessions.1
I interviewed more than 330 business people,
labor leaders, counselors of unemployed
workers, labor market intermediaries
(headhunters), labor lawyers, and management consultants. The purpose of the study
was exploratory; much of my effort went
into the search for hypotheses rather than
tests of specific ones. For this reason, I did
not require informants to answer a fixed
list of questions, but informed them of the
purpose of the study and invited them to
tell me what they thought was relevant.
I intervened only occasionally to seek
clarification, show interest, or nudge
the discussion in new directions.
Only after informants had spoken at
length did I ask specific questions to cover
points that interested me. I usually avoided
asking about economic theories until the end
of interviews. Such questions sometimes
stopped conversation, because the theories
seemed naive and the questions led respondents to try to think like an economist,
rather than to explain their world concretely
in their own terms. Some business people
refused such open-ended interviews, probably because they feared that while talking
loosely they might say something that would
embarrass them or hurt their company. I
concluded that low response rates might
make a random sample unrepresentative.
(I had much less difficulty gaining the cooperation of the other types of respondents.)
Most interviews with business people were
obtained through personal contacts or by
telephoning people and persuading them
to cooperate. Often, people I interviewed
arranged further interviews.
WAGE RIGIDITY AND MORALE
In this section, I will summarize what
I heard in interviews, giving the reasons for
wage rigidity explained to me by business
people and labor leaders. In the first instance,
the resistance to pay reduction came from
managers, not from workers, though it
was anticipated employee discontent that
motivated management to oppose pay cuts.
The discontent, usually described as poor
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
35
1
The results of the study are
reported in a book, entitled
Why Wages Don’t Fall During a
Recession, to be published by
Harvard University Press in
1999.
M AY / J U N E 19 9 9
morale, would not necessarily be expressed
openly. Nonetheless, business people believed
it could be harmful enough to cause monetary losses that would exceed the savings
from a pay cut.
The downward rigidity of the pay of
existing and of newly hired employees
have separate explanations. The reason
almost all managers gave for not cutting
the pay of existing employees was concern
about morale. New employees would
probably object little if, before they applied
for their jobs, pay rates for new hires had
fallen by no more than the pay of existing
employees in the same jobs. New employees,
in contrast, feel it is inequitable to be paid
according to a scale lower than the one that
applied to colleagues that were hired earlier.
For this reason, downward pay rigidity for
new hires exists only because the pay of
existing employees is rigid. The pay of new
hires is usually downwardly flexible when
co-workers do not have enough contact
with each other to know each other’s pay.
This circumstance arises typically when
labor turnover is high and when a large
fraction of the employees work part-time
on schedules that seldom overlap. Typical
examples are floor crews in fast-food
restaurants and in supermarkets.
Good morale means many things in
industry: a willingness to cooperate with
company objectives, a sense of common
purpose consistent with the firm’s goals,
enthusiasm for the job, happiness, toleration
of unpleasantness, moral behavior, and
mutual trust. Business people value good
morale because it reduces labor turnover,
makes it easier to recruit good workers, and
increases the productivity of the existing
work force. The increase in productivity
arises not so much because employees
work harder at assigned tasks that are
monitored, but because workers do the
right thing even when no one is watching.
They do extra things without instruction,
make suggestions for improvements, help
each other, and share information with
each other and with superiors. Good
morale is thought to be especially important
for productivity in jobs where it is difficult
to monitor performance, where good
performance requires imagination and creativity, and where workers must deal with
customers. Morale is important in the latter
case, because employees handle customers
better when cheerful.
The morale of existing employees is
hurt by pay cuts because of what may be
called the insult effect and the standard of
living effect. The latter occurs because
lower living standards distract and aggravate
workers and cause them to blame the company for the difficult adaptation to lower
incomes. The insult effect occurs because
workers associate pay with self-worth and
recognition of their value to the company.
Many workers receive regular increases,
grow used to them, and interpret them as
recognition of loyalty and good performance.
Hence, a pay cut is interpreted as a signal
of dissatisfaction with employees, even if
everyone’s pay is reduced. These effects
apply to both real and nominal pay reduction, though the effects of an abrupt nominal
cut are stronger than those of a slow decline
in the purchasing power of pay.
Another reason a pay cut is interpreted
as an affront is that it is viewed as unfair,
because the company takes something away
while giving nothing in return. A pay cut is
not felt to be insulting if management can
convince workers that the reduction is justified; that is, if it prevents a large number of
layoffs. Pay cuts typically occur when a
business is in danger of closing or has trouble
competing in product markets. In these
circumstances, workers usually accept cuts.
Such circumstances are rare, however. A
central fact of life for most businesses is that
pay rates have little impact on total employment. That is, in most firms the elasticity of
demand for labor is small. Pay cuts are more
common among firms where this elasticity
is high.
Business people and labor leaders were
confident they usually could convince
employees, with some effort, that pay cuts
were justified, if indeed they were. I was
told that workers refuse to believe what
they are told about company difficulties
only when management has a reputation
for duplicity, when relations between management and union representatives are bad,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
36
M AY / J U N E 19 9 9
or when workers recoil from facing reality.
I found little support for the many theories
of wage rigidity based on information asymmetries, and, in particular, theories based
on the assumption that management cannot
persuade workers that low profits or competitive conditions require pay reduction. The
general thrust of what was said was that
normally information flows freely enough
within businesses so that most employees
know when their company is in trouble.
In some small- and medium-sized companies,
the workers may know this before management does, because it is low-level employees
who take orders and keep accounts, and
gossip spreads quickly.
Nevertheless, asymmetries of information
underlie the explanation of wage rigidity.
Morale is important for productivity because
management finds it prohibitively expensive
to monitor employees closely. For this reason,
companies rely on workers to do what they
are supposed to do without being told, even
when supervisors are unlikely to check up on
them or never do so. Workers are likely to be
so cooperative only if they have good morale.
Though employees expect to share
in company success through pay increases,
they do not expect to share in its losses
by having their pay reduced. Adjusting
to lower income is too painful for workers
to endure relative to the sacrifices made
by company owners, and pay cuts raise
the awkward issue of the disparity
between the incomes of workers
and owners.
Morale is fragile and can be destroyed
quickly by matters more minor than pay
cuts. It can be hurt by any form of unfair
or inequitable treatment by management,
where the standards of fairness, especially
regarding pay differentials, are often determined by company or industry traditions
rather than by absolute standards of justice.
Good morale normally takes a long
time to build. It is fostered by:
• Recognition and reward of contributions to the company;
• Good explanations of the social contribution of the company’s products; and
• Good explanations of a worker’s role in
the production process.
Collective activities within the
company, such as charity drives and company picnics, also improve morale, as does
almost anything that encourages workers
to think of people other than themselves.
Morale is hurt by threats, such as threats
of being fired if performance is substandard.
Though companies fire some workers, it is
thought to be a bad business practice to have
people work in a negative, menacing atmosphere. Just this style of management is
sometimes used, however, with low-level
and low-paid labor doing short-term jobs
that are easily monitored. Firing is most
useful for ridding an organization of
scoundrels and ne’er-do-wells rather than
as a way of motivating ordinary workers to
perform. Positive incentives and an optimistic
atmosphere encourage performance more
effectively than do threats. Most workers
want to do well and will do so, if given the
opportunity, and if they understand what
they are supposed to do. Furthermore, many
people enjoy their work.2 A sense of pride,
duty, and accomplishment can make even
disagreeable jobs bearable. Nevertheless,
strict discipline is necessary for good morale,
for if some workers are allowed to get away
with slacking, those who work hard feel they
are being treated inequitably.
What has been said is a fair summary,
I believe, of the dominant views of business
people and labor leaders. I now turn to
the problem of formulating these ideas
in ways that may be useful for economic
theory.
INTERPRETATION OF MORALE
• Frank, but good, relations between
subordinates and superiors;
Good morale has three components:
• Identification with the organization or
internalization of its objectives,
• Prospects for economic security and
progress within the company;
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
37
2
Juster (1985) found in a survey that ordinary people preferred work to activities
associated with leisure.
M AY / J U N E 19 9 9
• Good moods, and
unconsciously or semi-consciously. Conscious mental operations are slow, though
adaptable. Unconscious ones are rapid, though
restricted to learned routines. Thus, it is
hard to learn to play the piano or to speak
a foreign language, but, once those skills are
learned, they occur smoothly and with only
general conscious direction. Identity includes
many such mental subroutines. For instance,
it would be nearly impossible to function
socially if we constantly weighed self-interest
against collective advantage. These calculations are replaced, in most cases, by rules
about how we should behave, who are our
friends or foes, and what we should expect
of them. Those rules are all part of identity.
In summary, the function of identity is to
make mental activity more efficient, and
identity’s mental mechanism is a set of
unconscious goals and mental subroutines.
An additional advantage to an individual
of group identification is that it contributes
to his or her sense of being powerful, valuable, important, and wanted. A sense of
self-worth is needed by people because it
gives them a reason to survive and promote
their own interests. Without a sense of
worth and the power to shape their own
lives, people can be incapacitated by what
psychologists call learned helplessness
(Gleitman, 1995, pp. 133-35).
An obvious benefit of group identity
is that it makes it easier to work with other
people, which is important because most
productive human activities require cooperation. This benefit does not explain
morale’s fragility, however. Its function
may be to protect individual self-interest.
Though commitment to a group helps
overcome prisoner’s dilemma or free-rider
problems arising in cooperative activity, the
same sense of responsibility exposes individuals to exploitation. It is useful to have a
system that balances private and group
advantage, and conventional standards of
fairness offer an orderly way of accomplishing
this. These establish rules of reciprocation
among group members and between them
and the organization, and the duties specified
by these rules are accepted by members
when they agree emotionally to join. Perhaps the brittleness of morale is a
• Trust and mutual affinity among
members of the organization.
A person may be judged to have internalized the objectives of their organization
if they act to advance its interests without
specific instructions and without any possibility of being monitored and rewarded.
Identification is manifested by internalizing
the organization’s objectives as well as by
actions that demonstrate membership and
by expressing feelings of belonging. Moods
are states of mind that affect work habits and
the pleasure or displeasure derived from
work. Cooperation within an organization is
fostered by a network of trusting relationships among employees. Cooperation may
not be directed toward helping the organization, however, unless members accept its
objectives. Though the social network is an
important component of morale, it is not hurt
by pay cutting, so I give it little attention.3
Identity and Internalization
3
Some industrial psychologists
measure morale as the existence of effective groups
(Blum, 1956, pp. 163-69).
It is clear that human beings have the
capacity to identify with organizations and
to internalize codes of behavior and the
interests of others. Experimentally, it is easy
to induce people to identify with a group
and to act in its interests (Tajfel, 1970, and
Turner, 1987). Children show empathy for
others at a young age and learn to internalize
social and moral rules (Gleitman, 1995, pp.
550-58). It is impossible to know whether
the capacities for empathy, morality, and
group identity are accidental or if long ago
they evolved in humanity because they
increased chances of survival, nor do we
need to know the answer to this question.
What is important is that the capacities exist.
A psychological theory of organizational
identity should describe its function or
purpose and the mental mechanism of which
it is a part. Identity, in general, is a person’s
image of who they are. One advantage of
identity is that it simplifies mental processes
by summarizing a person’s goals and providing
a set of rules for how to behave. A great
deal of what we do mentally is done
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
38
M AY / J U N E 19 9 9
self-protective reflex provoked by violation
of fairness standards. Reading a psychology
textbook, such as Gleitman (1995), makes
it clear that many parts of the nervous
system operate through offsetting pairs of
activating and inhibiting signals. The teetering between group commitment and
indignant rebellion may reflect just such a
pairing that is built into the psyche.
It remains to be explained why unjustified
pay cuts impair identification with the
employer. A superficial answer, given earlier,
is that they are regarded as unfair. Fairness
specifies rules of reciprocation and workers
receive nothing in exchange for a pay cut that
saves few jobs. It might be that in a different
world, workers would view wages and salaries
coolly as fluctuating market prices and would
accept price declines as a normal part of
business life, just as salespeople accept large
income fluctuations. Most people do not think
this way. I was told many times that workers
do not view themselves as commodities
and inevitably interpret pay cuts as statements
about how satisfied the company is with them,
because, in their experience, pay increases
signal appreciation of workers’ contribution.
with a lion hunting an antelope. In chasing
an antelope, the lion expends energy, loses
time, and risks injury. These costs must be
weighed against the probability of catching
the prey and the pleasure of eating it. Imagine
that the lion unconsciously, or half consciously,
weighs the costs against the benefits before
deciding whether to chase his prey and
before choosing the level of physical effort
to expend on the pursuit. Once he makes
his decision, the lion’s mind automatically
adjusts his mood and level of nervous and
physical arousal to handle the effort required.
If the lion decides not to go after the antelope,
he will not be aroused. He will feel lazy and
may find running uncomfortable. In contrast,
if he decides to try for a kill, he will be mobilized, excited, and will probably be exhilarated
by the effort. Given this decision, he will
consciously decide how much effort to put
into the hunt and how to go about it. We
may imagine that the lion’s unconscious
mind chooses the mood and level of arousal
so that his conscious mind chooses an effort
level that optimizes a utility that is unconscious. This unconscious utility depends on
the probability of success, energy expenditure,
and risk of injury. The lion’s unconscious
choice of mood may be constrained by his
preexisting state of mind. If he just lost his
wives to a rival, he may be discouraged and
not feel like hunting, whereas if he is a
hopeful young bachelor, he may feel vigorous.
Another illuminating analogy may be that
of a virtuoso pianist. For an appreciative
and sensitive audience, she will probably play
at her best and love doing so. If she hears
snores and catcalls, she will no doubt feel
her fingers stiffen, stumble, and hate playing.
It is important, in my opinion, to
recognize that mood automatically adjusts
to fit the perceived net benefits of tasks. I
believe it is general human experience that
capacities to act and perceptions of pain or
pleasure depend on circumstances. Danger
stimulates us to fight or flee. Anger makes
us ignore pain and danger. Though deprivation of life’s necessities causes us discomfort
and unhappiness, we get used to prolonged
hardship, probably so that we can cope
with the unavoidable misery. Soldiers and
prisoners living in frightful conditions
Mood, Work Effort, and Its Disutility
Managers and labor leaders did not usually speak of jobs as disagreeable, but assumed
that employees liked to work. They said that
one of the bad effects of layoff was loss of
the pleasure of working and of social contacts
on the job. If, in the standard model of work,
however, we assume that effort brings positive rather than negative utility, then people
should work hard, even if they have no
financial incentive to do so. This implication
conflicts with common sense. Though volunteer labor makes important contributions
to society, it is hard to imagine that it would
succeed in producing ordinary economic
output. Other phenomena that are inconsistent with the usual model of work effort are
the importance of mood to job performance
and satisfaction from work. I was told that
bad moods are distracting and that they
increase fatigue, discomfort, and accidents.
In order to make sense of these observations, it may be helpful to consider an analogy
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
39
M AY / J U N E 19 9 9
eventually cheer up and joke about their
state, though, of course, they are not happy.
It is a mistake to separate the disutility of
labor from the utility of its reward, or to
imagine that labor is normally perceived as
disagreeable. The utilities of labor and its
reward interact.
level there. These conclusions seem consistent with reality. The model does not
distinguish reward from punishment, despite
the fact that this distinction is crucial in
reality. There is no way of determining what
level of utility marks the boundary between
punishment and reward.
I now modify the above model to obtain
one that retains its plausible conclusions
and yet does not represent labor as a burden.
It gives a role to emotion in mobilizing and
directing the powers of mind and body and
includes a distinction between reward and
punishment. I try to model mood, because
it has an important role in the explanations
of wage rigidity given by managers and labor
leaders. The model is suggested by the
analogies described in the previous section.
Focus on an action (or program of
actions), e, to be taken by a person over a
fixed period of time. Though e may be
thought of as effort, it is better to interpret
it as productive activity. The action has an
unconsciously felt mental and physical cost,
measured as the number, C(e), and earns
income w(e), which might be a wage paid by
an employer.4 The unconsciously felt benefit
to the worker of the wage is the number
B(w(e)), and the net unconscious gain is
A FORMAL MODEL
In the usual incentive model, a worker
expends effort, e, which is a non-negative
number, and receives in exchange a wage,
w(e), which is a non-decreasing function of
e. The worker chooses e so as to maximize
u(w(e)) – c(e),
where both u and c are increasing functions
and u is concave and c is convex. The first
term is the utility of consumption purchased
with the wage and the second term is the
disutility of effort. In this model, the
consumer prefers to expend as little effort
as possible to earn a given income, so that if
the wage does not increase with effort, the
consumer expends none of it whatsoever.
Because effort creates disutility, people acting
according to the model would experience
work as unpleasant, which is contrary to
what most people say (Juster, 1985). If we
try to escape this difficulty by assuming that
c(e) is zero, then the worker offers the maximum effort possible if w(e) increases with
e, an implication that contradicts common
sense. This difficulty can be evaded by
assuming that c(e) decreases with e until it
reaches a certain level, beyond which it
increases. If the functions u and c are
differentiable, then the optimum level of
effort satisfies the equation
4
5
The earnings, w(e), could be a
vector including pay, praise,
promotion, and other rewards.
Here, and elsewhere, I choose
the additively separable functional form for convenience of
exposition, not out of conviction.
B(w(e)) – C(e).5
Unconscious goals could include the basic
psychological drives as well as fidelity to
family, firm, or country. Assume that the
function B is increasing and strictly concave.
I propose that people unconsciously adjust
their mood and general state of mobilization
so that conscious choices maximize B(w(e))
– C(e). The conscious person does not
choose e but makes a decision (or program
of decisions), d. The actual action taken
is e = E(d,m), where m is the person’s mood
and state of mental and physical arousal.
The decision d might correspond to the pace
of work desired by the person, whereas
E(d,m) is the realized pace of work; the
person might actually work faster or
slower than he or she intended. The person’s consciously experienced utility is
U(w(E(d,m)), m) + V(E(d,m), m), where the
first term is the utility of the earnings and
du(w( e )) dc( e )
=
,
de
de
from which it is easy to see that increasing
the level of the function w(e) by adding a
positive constant decreases effort (or, more
accurately, does not increase it), whereas
optimal effort increases (or does not decrease)
when the slope of w(e) at the optimum is
increased without increasing the function’s
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
40
M AY / J U N E 19 9 9
Figure 1
the second is the utility from the action
itself. The person chooses the decision, d
= D(m, w), so as to solve the problem
[
B
]
max U( w( E( d , m )), m ) + V( E( d , m ), m ) ,
d ∈D
Northeast
Frontier
where D is the set of possible decisions.
The unconscious side of the person chooses
the mood, m, so as to maximize the unconscious utility, that is, to solve the problem
[
Optimum
B – C = constant
The Set of Possible Pairs,
(–C(E(D(m, w), m))),
B(w(E(D(m, w), m)))
max B( w( E( D( m, w ), m )))
m ∈M
− C( E( D( m, w ), m )) ,
]
where M is the set of possible moods.
If the person has a preexisting state of
mind or mood, then his or her unconscious
self may not be able to choose m freely, but
must chose from a subset, SM, of M. The
subset SM may be thought of as representing
the restrictions imposed by solution of a
larger unconscious utility maximization
problem that determines the context of the
one under consideration. For instance, the
person may be frightened by some danger,
which may be escaped through the actions
under consideration.
When interpreted properly, the standard
results mentioned earlier (regarding incentives) apply to the new model. Imagine a
two-dimensional plot with –C(E(D(m, w),
m)) on the abscissa and B(w(E(D(m, w),
m))) on the ordinate, as in Figure 1. The
unconscious self chooses m to maximize
the sum of the two components, so that
the northeast frontier of the plot is the relevant set of points. I compare two earnings
functions, w and w′, and assume that
–C
If w9 is w plus a positive constant, then, because
of the strict concavity of the function B,
the northeast frontier of {(–C(e), B(w′(e))):
e ∈ E} is no steeper than that of {(–C(e),
B(w(e))): e ∈ E}. It follows that at the optimum
the disutility of effort, C(e), is no higher
with the earnings function w′ than with
the function w.
The second standard result regarding
incentives is that making w steeper at the
optimum does not decrease effort. In the
new model, it is not possible to speak of
the slope of w because the action variable,
e, may not be a number. By an analogous
definition, however, w′ is “at least as steep”
as w at e if w′(e) = w(e), where e is the
optimum for w, and if w′(e) ≥ w(e), whenever w(e) ≥ w(e), and w′(e) ≤ w(e), whenever
w(e) ≤ w(e). Given this definition, it is
obvious that if w′ is at least as steep as w at
e, then –C(e′) ≤ – C(e ) and w′(e′) ≥ w(e),
where e′ is the optimum with earnings function w′. That is, steepening the earnings
function does not decrease the unconscious
disutility of effort at the optimum.
The utility V(E(d, m), m) may increase
with effort if mood favors exertion, though
V may decrease with effort when it is increased
beyond a point appropriate for the mood.
What I have in mind may be explained by
returning to the usual model in which the
effort variable is a number corresponding
{E(D(m,w),m): m ∈ SM}
= {E(D(m,w′),m):m ∈ SM} ≡ E,
so that the set of possible actions achievable
by manipulation of mood does not depend
on the earnings function. Then, the twodimensional plots are of the sets
{( −C(e), B(w( e ))): e ∈ E}
and {( −C(e), B(w′(e))): e ∈ E}.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
41
M AY / J U N E 19 9 9
to the pace of work. In this spirit, assume
for the moment that d and m are non-negative numbers, where larger values of m
correspond to a better mood. Assume also
that E(d, m) = d, and that w(e) = e, so that e
and w can be suppressed. Finally, assume
that U and V are twice differentiable functions satisfying the following conditions:
rationality take account of limits on the ability
of the conscious mind to reason and use
information. No doubt, sentiment influences
imperfect logic, so that a more realistic version of the above model should take account
of the effect of mood on reasoning.
The model accomplishes the objectives
of giving mood a role in motivation and
allows workers to enjoy positive utility from
work, while preserving the obvious common
sense results about the impact of financial
incentives. The model fails to permit a
distinction between reward and punishment,
however, nor does it include morale or
explain why pay reductions have such a
severe impact on mood.
∂U( d,m )
∂2U( d,m )
∂2U( d,m )
> 0,
<
0
,
> 0,
∂d
∂m ∂d
∂d 2
∂V( 0, m )
∂2 V( d,m )
> 0,
< 0,
∂d
∂d 2
∂2 V( d,m )
and
> 0,
∂m ∂d
Reward and Punishment
for all d and m. Let d = D(m) be the solution to the problem
I now assume that the unconscious
mind forms a notion of what is normal in
terms of unconscious living standards.
This idea of normality may be useful to an
individual for two reasons: It tells the
mind what to store as habits or mental
subroutines, and it serves as a trigger level
for alarm. The mind adapts habits to the
way of life that it expects to be normal.
Decline of living standards below a normal
level signals the unconscious that something
is wrong. This provokes anger, unhappiness,
or distress. These moods, in turn, stimulate the conscious mind to find solutions
for the problems that have arisen. It is not
efficient for the conscious mind constantly
to be stimulated and on the look-out for
new solutions. Bad moods and the efforts
they incite are exhausting. Therefore, bad
moods should be called upon only when
needed. The normal or expected path of
welfare may grow, shrink, or fluctuate over
time. For instance, salespeople expect their
income to fluctuate sharply and probably
react badly only to prolonged patterns of
low income. A fall in welfare below the
expected level may not trigger alarm if the
conscious mind can persuade the unconscious
that there is no reason to worry, the bad
situation will soon be rectified, or there is
nothing that can be done. The unconscious
probably adapts gradually to lower welfare,
as do the soldiers I mentioned earlier.
max[U(d,m) + V(d, m)].
d $0
Under the given conditions, it is easy to see
that D is a nondecreasing function of m and
is increasing at values of m for which D(m)
> 0. That is, improved mood increases
effort. Notice also that at the optimum,
∂V(d, m)
< 0,
∂d
so that the worker finds increased effort
unpleasant. From now on, I drop the
assumption that d and m are numbers.
Rationality
It is natural to ask whether people
behaving as in the above model are rational.
Economists define people to be rational if
they reason correctly and use all available
information in order to maximize their
utility. The model is consistent with rationality, if we allow utility maximization to
occur at two levels, the conscious and the
unconscious. The effect of mood on realized
actions and on conscious objectives does not
contradict rationality. In a loose sense,
however, the model is inconsistent with
rationality. Realistic models of conventional
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
42
M AY / J U N E 19 9 9
Rewards may be defined as payments
that provide welfare in excess of the normal
level, whereas punishments may be defined
as payments that bring welfare below the
normal level. Punishments have a greater
impact than rewards because they provoke
a powerful negative emotional reaction while
rewards trigger no corresponding positive
reaction. Rewards or punishments that are
too frequent become normal and so lose
their impact, a matter of concern to managers.
A pay cut causes anxiety and discontent
because the fall in the worker’s welfare below
the normal level both triggers bad moods
and requires the worker to adopt new habits
that are appropriate to the new standard of
living. Cuts that are perceived as justified
are thought of as inevitable, so that they
do not provoke a strongly negative mood.
It is easy to incorporate a normal welfare level in an intertemporal version of
the formal model. The external conditions
of the person’s decision problem at one time,
t, are defined by the earnings function,
wt(e), and by the set of possible decisions,
Dt. Let the function Dt(m, wt ) be the solution to the problem
coercion precisely. Presumably, it implies a
lack of freedom, but a person who is
coerced into doing something, strictly
speaking, also chooses to do it, for he or
she could refuse to comply and suffer the
consequences. Also, everyone works under
some degree of compulsion. For instance,
stealing from the company or punching
the boss will usually lead to automatic dismissal. In a sense, people are forced not to
do these things. Similarly, blatant insubordination can cause firing, so that, in this
sense, workers are compelled to take orders.
When managers spoke of coercion,
they did not refer to cases such as these. A
rough definition of what they had in mind
might be to say that a worker is compelled
to do something if not doing it results in
punishment and if the worker would do
something else if there were no threat of
punishment and he or she had good morale.
The key aspects of coercion that managers
and labor leaders found demotivating were
that they frightened people and diminished
self-confidence. Though fear is understood
by everyone to be a powerful and useful
motivator, managers typically use threats
only to discourage extreme behavior. They
do not want workers to be preoccupied
with fear, because it distracts and undermines
self-confidence. The latter is important,
because it frees the mind and body to act
smoothly and efficiently. An apprehensive
person consciously thinks through every
step of what they do lest they make a mistake. Conscious thought overrides the
mental subroutines that guide much of what
people do. In relation to the formal model,
lack of self-confidence limits the set of moods
to a disadvantageous subset. Extreme
forms of coercion may lead to the learned
helplessness that I mentioned earlier.
max [U ( wt ( E( d , m)), m) + V ( E( d , m), m)] .
d ∈ Dt
The unconscious welfare in period t is
[
Wt = max B(wt ( E( Dt ( m, wt ), m )))
m ∈ SM
− C( E( Dt ( m, wt ), m )) .
]
The expected or normal welfare level
may be assumed to be a constant, W , so
that the person reacts with anger and discontent when Wt falls below W.
Coercion and Freedom
EXTENSION TO MORALE
Managers and labor leaders stressed
that workers are energized by the feeling
that they control their lives. They are
antagonized and made passive by compulsion and excessive control. These matters
are beyond the scope of the model presented
here and are not easy to think about carefully. For instance, it is difficult to define
Recall that morale has two key aspects,
mood and internalization of organizational
objectives. Internalization may be expressed
by including the firm’s objectives with those
of the worker. This procedure is
appropriate, since utility functions are
inferred from behavior and workers who
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
43
M AY / J U N E 19 9 9
internalize their firm’s objectives act as if
these were their own. Formally, let R(e) be
the revenue the firm earns from a worker’s
output, so that the firm’s profit is R(e) – w(e).
Internalization may be expressed formally
by adding multiples of the firm’s profit to
the worker’s conscious and unconscious
utility functions, so that these become
w, is constant and that improvements in
morale enlarge SM in such a way as to make
available actions or effort levels, e, that increase
R(e) for each level of C(e) and increase R(e)
more, the greater is C(e). Imagine a twodimensional diagram, such as Figure 2, with
–C(e) on the abscissa and B(w) + µ1[R(e) –
w] on the ordinate. Then, improvement in
morale causes the northeast frontier of the set
of possible points (–C(e), B(w) + µ1[R(e)w]) to rise vertically in such a way that the
vertical increase is greater, the larger is C(e)
(i.e., the smaller is –C(e)). Because w is
constant, it follows that the new optimum
yields a higher value of R(e) and a lower
value of –C(e). In other words, improved
morale affects mood in such a way as to
increase profits.
Let us assume that the utility functions
B and U are differentiable with respect to
income, w, so that the unconscious and
conscious marginal utilities of income, dB/dw
and ∂U/ ∂w, respectively, are well-defined.
It must be that
B(w(e)) + µ1[R(e) – w(e)] – C(e)
and
U(w(e), m) + µ2[R(e) – w(e)] + V(e, m),
respectively, where µ1 and µ2 are constants
that are positive if morale is good. The
impact of morale on mood may be expressed
by varying the subset SM of possible moods
available to the unconscious side of the person.
Improvements in morale increase the size
of the set SM, thereby giving the unconscious
a larger selection of possible states of mind.
Improvements in mood, resulting from
improved morale, do not decrease and may
indeed increase the maximized value of
the unconscious objective function
B(w(e)) + µ1[R(e) – w(e)] – C(e), because
it is maximized over a larger set of moods.
That is, if d = D(m, w) solves the problem
[
[
(1)
]
(2)
]
then the value of
max {B( w( E( D( m, w ), m)))
+ µ1[ R( E( D( m, w ), m))
− w( E ( D( m, w ), m )) ]
− C( E ( D( m, w ), m))}
6
Akerlof and Kranton (1998)
model the moral aspects of
identity as internalized rules
that restrict the utility function.
µ2 <
∂U ( w( e ), m )
,
∂w
for levels of e and m that are actually realized. If these inequalities did not hold, the
worker would be indifferent to having his
or her wage increased, or would prefer to
have it reduced, consequences that are
contrary to common sense.
The inclusion of profit in the worker’s
utility function does not portray the sort
of good morale that inhibits theft. According to inequalities 1 and 2, workers could
improve their welfare by stealing from the
employer. In order to give a utilitarian
interpretation to moral values, it is necessary
either to include punishment, introduce a
sense of guilt, or have people take into
account the consequences of having other
people break the moral codes they break
themselves.6
Though the model cannot explain the
impact of morale on morality, it does cap-
− w( E( d , m )) + V( E( d , m ), m )
m ∈ SM
dB(w(e))
dw
and
max U( w( E( d , m )), m ) + µ2 R( E( d , m ))
d ∈D
µ1 <
increases as the size of the set SM increases.
Without more assumptions, it is not
possible to say whether the effect of improved
morale on mood increases profits. A plausible
set of assumptions is that the wage function,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
44
M AY / J U N E 19 9 9
Figure 2
ture important consequences of good
morale. Using the argument made in the
previous section, it is easy to show that the
inclusion of the terms µ1[R(e) – w(e)] and
µ2[R(e) – w(e)] does not decrease profits.
More precisely, profits do not decrease,
provided µ1 is positive and provided the
inclusion of these terms does not change
the set of actions, e, which is achievable by
varying mood, m. In order to see why, let e
be the choice of e that maximizes B(w(e))
– C(e) and let e′ be the choice of e that
maximizes B(w(e)) + µ1[R(e) – w(e)] –
C(e). Then,
B+µ1(R–w)
Optimum with good moods
from good morale
Optimum with
poorer moods
from bad morale
B(w(e′)) + µ1[R(e′) – w(e′)] – C(e′)
≥ B(w(e)) + µ1[R(e) – w(e)] – C(e)
–C
≥ B(w(e′)) + µ1[R(e)
– w(e)] – C(e′),
incentives by assuming that w(e) = w0 +
w1R(e), where w1 > 0. Let us assume that
the firm varies w0 and w1 so that w0 +
w1R(e) remains constant, where e is the
worker’s choice of action. Now, hold w0,
w0′, and w1′ fixed, where w1′ > w1. Let us
also assume that B is linear, that is, B(w) =
bw, where b is a positive number. By
inequality 1, we must assume that b > µ1.
I show that increasing w1 to w1′ increases
profits. Let e and e′ be the worker’s
optimal choices of e when the wage is
w0+ w1R(e) and w0′+ w1′ R(e), respectively.
By the optimality of e and e′ it follows that
which implies that R(e′) – w(e′) ≥ R(e) –
w(e), as is to be shown.
Financial Incentives and Morale
Next, I show that financial incentives
and morale complement each other. An
argument similar to the one that was just
made shows that increasing µ1 does not
decrease (and may increase) profits, for
any wage function w, including ones
offering financial incentives. In order to
see how to make the argument, assume
that µ1′ > µ1, notice that
(3) b[w0 + w1R(e)]+ µ1[R(e)
B(w(e)) + µ1′[R(e) – w(e)] – C(e)
–w0 – w1R(e)] – C(e)
= B(w(e)) + µ1[R(e) – w(e)] – C(e)
≥ b[w0 + w1R(e′)]+ µ1[R(e′)
+ (µ1′ – µ1)[R(e) – w(e)],
–w0 –w1R(e′)] –C(e′)
and assume that increasing µ1 to µ1′ does
not change the set of actions achievable by
varying mood.
I show that if µ1 is positive, then
increasing financial incentives increases
profits, provided the function B is not too
concave and provided the change in µ1
does not change the set of actions attainable
by choice of mood. I introduce explicit
and
(4) b[w0′ +w1′R(e′)]+µ1[R(e′) –w0′
– w1′R(e′)]– C(e′)
≥ b[w0′ +w1′R(e)]+µ1[R(e) –w0′
– w1′R(e)]– C(e).
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 19 9 9
Bn(wn(yn(en ))) +µ n1 [R(y(e1, ..... , eN ))
These inequalities imply that
– w1(y1(e1 )) – ..... – wN (yN (eN ))] – C(en ),
(b – µ1)w1[R(e) – R(e′)]
≥ C(e) – C(e′) + µ1[R(e′) – R(e)]
≥ (b – µ1)w1′[R(e) – R(e′)].
and his or her conscious utility is
Un(wn(yn(En(dn, mn))), mn)
Because b – µ1 > 0 and w1′ > w1, the last
inequalities imply that
+ µ n2[R(y(E1(d1, m1 ), ..... , EN (dN , mN )))
– w1(y1(E1(d1, m1 ))) – .....
R(e′) ≥ R(e).
– wN(yN(EN(dN , mN )))]+V(En(dn, mn), mn).
Since by assumption w0 + w1R(e) = w0′ +
w1′R(e′), it follows that profits are not
decreased by increasing incentives. Profits
would be increased strictly if there were
strict inequality in either of inequalities 3
and 4. In this case, profits still would
increase if the function B(w) were a
slightly concave approximation to the
linear function bw. It is easy to make an
example in which B is very concave and
increased incentives decrease profits.
completes the argument that increased
incentives may increase profits, even
when morale is good, just as improved
morale increases profits even when
workers receive financial incentives.
In this sense, incentives and morale
are complements.
Interaction among the N workers suggests
a coordination game, for they all derive
utility from profits. In order to see the
connection more clearly, let us assume that
workers’ moods adjust so that the utility of
labor, V(En(dn, mn), mn), is the same for all
decisions dn actually adopted by the workers,
so that this term may be ignored. In addition, suppress mood and the distinction
between the conscious choice, dn, and the
realized action, en, and focus on conscious
utility, since cooperation is arranged deliberately. Suppose that the choice of action
has two components, selection of a method
of production and the selection of effort,
which is thought of as the pace of work.
Since effort is influenced by mood, which
is governed unconsciously and almost
automatically, it makes sense to ignore the
effort part of actions and to think of the
actions solely as production methods.
Under these assumptions, the relevant
utility functions are
Cooperation
The model can be used to demonstrate
one reason good morale fosters cooperation
among workers; it gives them a common
objective. Let there be N workers and let
the subscript n indicate variables and functions applying to the nth worker. The
employer observes worker n’s output to be
(5) Un(wn(yn(en ))) + µ n2[R(y(e1, ..... , eN))
– w1(y1(e1)) – ..... – wN(yN(eN ))],
yn(en) = yn(En(dn, mn))
for n = 1, ..... , N. If the parameters µ n2 are
positive and the functions wn are constant,
as would be the case for truly fixed wages,
then, in effect, the workers play a coordination game with payoff R(y(e1, ..... , eN)) for
all players, and the obvious solution is to
maximize this payoff jointly. Management
normally gives workers at least some
financial incentives linked to individual
and pays him or her
wn (yn(en)) = wn(yn(En(dn, mn))).
The actual output of all N workers is
y(e1, ..... , eN ) = y(E1(d1, m1 ), ..... , EN(dN, m N )).
Worker n’s unconscious utility is
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 19 9 9
performance, however, such as production
targets, performance evaluations, promotion
criteria, and piece rates. I was told that it
is difficult to design incentives so that the
workers’ financial interests are entirely
consistent with those of the firm. An
important function of good morale is to
motivate workers to act in the firm’s
interest, even when it conflicts with their
own financial advantage. I show that the
above model includes this function. More
precisely, I argue that cooperation induced
by internalization of the firm’s goals
increases profits.
Suppose that morale is neutral. That
is, suppose that µ n 2 = 0, for all n. In addition, suppose that the wage functions, wn,
include financial incentives. For each n,
let en be that value of en that maximizes
Un (wn (yn (en ))). With these choices of
effort, the firm’s profit is
> R( y(e 1 , ....., e N ))
− w1( y1( e )) − ..... − wN ( yN ( e N )).
1
That is, internalization of the firm’s objectives increases profits.
Information Sharing
One of the reasons it is difficult to give
workers incentives consistent with the firm’s
objectives is that the conditions workers
face change frequently, so that the actions
that are correct, from the employer’s point
of view, also change. If management knew
conditions precisely, it could order workers
to do exactly what was needed or it could
include the conditions in the specification
of incentives. Often, however, only the
workers observe the relevant changes in
circumstances. Managers said that one of
the benefits of good morale is that it induces
workers to share information with each other
and with their superiors. This advantage
can be introduced into the above model by
having company revenues depend on
random variables observed by the workers
alone. For instance, assume that worker n
observes the random variable θn and that
company revenue depends on all the θn, so
that utility function 5 becomes
R(y(e1, ..... , eN))
– w1(y1(e1)) – ..... – wN(yN(eN)).
In contrast, suppose now that morale
is good, so that the µ n 2 are all positive.
Though it is hard to say how the workers
would behave, it would be to_their mutual
_
advantage to choose actions (e 1, ..... , e N)
that:
• Were a Nash equilibrium for the game
with payoffs as in function 5,
Un(wn(yn(en)))
+ µ n2[R(y(e1, ..... , eN, θ1, ....., θN))
– w1(y1(e1)) – ..... – wN(yN(eN))].
• And gave each worker, n, a payoff
exceeding
If all workers reveal the values they observe
of the θn , then workers can cooperate more
effectively. Expected profits, and hence, the
expected individual utilities that are earned
from cooperation will not decrease (and may
increase), provided the parameters µ n2 are
all positive. Hence, workers have a positive
incentive to share their observations with
each other and with management.
Un(wn(yn(en))) + µ 2[R(y(e1, ..... , eN))
– w1(y1(e1)) – ..... – wN(yN(eN))].
Suppose that such an equilibrium exists.
Because of the form of utility function 5
and because µ n 2 is positive and e n
maximizes Un(wn(yn(en))), for all n, it
follows that
Morale vs. Coercion
R( e 1 ,....., e N ) − w1( e1 ) − ..... − wN ( e N )
Managers explained that the chief
disadvantage of using threats to obtain
cooperation is the loss of worker initiative.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
47
M AY / J U N E 19 9 9
max[pÎãI – w]
Though force may succeed in making
people work with great intensity, people
working under such pressure may only
make a show of cooperation and may not
use their heads to help the firm. I was told
that coercion works well for tasks that are
easily monitored and when management
knows what employees should do. Managers
said that compulsion is inefficient when
workers know best what they ought to do
because of information they alone receive.
I express these ideas formally using an
example in which I suppress mood, the
unconscious, and the distinction between
decisions and realized effort, since these
variables are irrelevant here. Suppose a
worker may do one of two types of tasks, A
and B, and that these are performed with
intensities, IA and IB, respectively, where IA
and IB are non-negative numbers. The
action e = (i, I) is task i done with intensity
I, where i = A or B. Let the disutility of
doing either task, i, with intensity I be –V(i,
I) = I2 and let the utility of wage w be simply
U(w) = w. Suppose that one, and only one,
of the tasks is profitable; management does
not know which task is profitable, and the
worker can learn which is profitable at a
small cost in utility. Suppose further that
management observes the intensity level;
task A is profitable with probability p,
where 1/2 < p < 1; and a task done with
intensity I earns revenues R(i, I) = ÎãI,
when it is profitable, and earns no revenue
otherwise. Finally, suppose that to retain
the worker, management has to offer a
reservation utility level of at least 1/16. If
the firm obtains cooperation through threats,
morale is zero and the worker cannot be
counted on to do the task that is profitable.
In this case, optimal management strategy
is to set the wage, w, equal to [1 + (2p)4/3]/16,
to fix the task to be A, and to require work
intensity, I, to be (2p) 2/3/4, for these values
solve the profit maximization problem
w,I
s.t. w – I2 ≥ 1/16.
The firm fires the worker if work intensity
is less than (2p)2/3/4, in which case the
worker earns his or her reservation utility
level of 1/16. The firm’s expected profits
are the positive number [3p(2p)2/3/8] – 1/16,
and expected revenues are [p(2p)1/3]/2.
Suppose management does not threaten,
but depends on positive morale. Assume
that in this case the morale parameter, µ2,
equals 1/2. Then the worker’s total utility
function is
U(w) + V(I) + µ2[R(i, I) – w] =
w – I2 + 0.5[R(i, I) – w],
minus a small quantity if the worker verifies which task is profitable. Assuming the
worker knows which task is profitable, he
or she solves the problem
max [– I2 + 0.5 ÎãI ],
I
so that work intensity is I = 1/4, which is
less than the intensity in the previous case
with compulsion and no morale. Because
the worker chooses the profitable task,
however, the firm’s expected revenues are
ÎãI = 1/2, which exceeds the level with no
morale. If the firm continues to pay wage
w = [1 + (2p)4/3]/16, then total expected
worker utility, U(w) + V(I) + µ2 [R(i, I) – w],
is at least 1/16, and expected profits are
higher with positive morale than with no
morale, unless [p(2p)1/3]/2 > 1/2, that is,
unless p > 0.51/4 ≅ 0.84. That is, coercion is
more profitable than dependence on morale
alone only if management knows with
high probability which task is profitable.
This result corresponds to the intuition I
wish to express.
max[pR(A, I) – w]
Testing the Model
w,I
s.t. U(w) + V(I) ≥ 1/16.
The proposed model of work motivation might be tested by psychological
experiments. One implication of the
model is that the utility or disutility of
or
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
48
M AY / J U N E 19 9 9
work effort depends on expected reward.
In testing this implication, it would not be
correct to measure the disutility of effort
by offering people a choice between effort
and something else, such as having to pay
a certain amount of money, for that choice
would affect the context of the work, and
hence, might affect mood. Something might
be learned, however, by asking people how
they feel about their efforts. By looking for
consistency in people’s reactions to various
work and reward situations, it might be possible to test for the existence of an unconscious
utility function and even to estimate it.
CONCLUSION
The usual model describes a worker’s
trade-off between financial reward and the
disutility of labor and has no place for morale.
Neither managers nor labor leaders, however, dwelled on the unpleasantness of
work, but rather stressed its benefits.
Managers spoke as if one of their primary
tasks was to maintain good morale, and
labor leaders also emphasized its importance.
In view of these observations, it seems
appropriate to replace the usual model with
one more consistent with the observations
of people running workplaces. I do not
know whether my own suggestions are
correct. Perhaps further empirical inquiry
will give a firmer basis for theory.
REFERENCES
Akerlof, George A., and Rachel E. Kranton. “Economics and Identity,”
Russell Sage Foundation Working Paper No.136, August 1998.
Blum, Milton L. Industrial Psychology and Its Social Foundations,
New York: Harper and Row, 1956.
Gleitman, Henry. Psychology, New York: W. W. Norton, 1995.
Juster, F. Thomas. “Preferences for Work and Leisure,” in Time, Goods,
and Well-Being, F. Thomas Juster, and Frank P. Stafford, eds., Institute
for Social Research, University of Michigan, 1985, pp. 333-51.
Tajfel, Henri. “Experiments in Intergroup Discrimination,” Scientific
American (November 1970), pp. 96-102.
Turner, John C. Rediscovering the Social Group: Self-Categorization
Theory, Oxford, UK: Basil Blackwell, 1987.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
49
M AY / J U N E 19 9 9
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
50
M AY / J U N E 1 9 9 9
Lowell J. Taylor is a professor of economics at the H. John Heinz III School of Public Policy and Management at Carnegie Mellon University.
Commentary
Professor Bewley describes the central
conclusion of his work as follows:
From the interviews, I conclude that
wage rigidity stems from a desire to
encourage loyalty, a motive that superficially seems incompatible with layoffs. My findings support none of the
existing economic theories of wage
rigidity, except those emphasizing the
impact of pay cuts on morale. Other
theories fail in part because they are
based on the unrealistic psychological
assumptions that people’s abilities do
not depend on their state of mind and
that they are rational in the simplistic
sense that they maximize a utility that
depends only on their own consumption and working conditions, not on
the welfare of others.
Lowell J. Taylor
I
n preparing my comment on Truman
Bewley’s work, I had the privilege of
reading a draft of Professor Bewley’s
forthcoming book, Why Wages Don’t Fall
During a Recession. This book describes
an extensive field study, in which Professor
Bewley interviewed hundreds of business
managers and labor leaders, seeking to
understand the puzzling phenomenon of
wage rigidity. The paper presented here is
an outgrowth of this project. Before turning to the paper itself, I would like to make
a few comments about the research enterprise more generally.
I am quite enthusiastic about the manuscript I read. There are three reasons why
you should read this book. First, you will
learn a lot of economics. In the course of
discussing ideas raised in his interviews,
Professor Bewley cites and discusses a vast
literature (his book cites more than 1,000
papers!). The book provides an engaging
way of becoming acquainted with the issues
currently under debate in the study of motivation, compensation, labor markets, and
macroeconomics. Second, the research
makes important headway in understanding
the nature of rigidities in labor markets.
Bewley makes a number of striking and
controversial claims about labor markets,
but always in a clear, well-reasoned, and convincing manner. Finally, the book will challenge you to think hard about how to “do
economics.” Economic theorists generally
implicitly follow the path laid out by Milton
Friedman (1953): We hope that even though
our assumptions are often self-consciously
unrealistic, useful predictions about behavior
can nonetheless be derived. Bewley’s book
reminds us that when assumptions drift
too far from reality, theory is a futile exercise
with no hope of shedding light on behavior.
The paper presented at this conference
provides theoretical musings designed to
encourage readers to think about a world
in which morale and mood are part of
human behavior.
The idea here is to lay out a formal
representation in which workers’ decisions
depend not merely on balancing utility
of earnings against disutility of effort, but
depend as well on morale—an internalization of organizational objectives—and
mood—the worker’s psychological state
of mind. I do not know if the formalizations provided here or in the books are the
most fruitful ways of incorporating morale
and mood into models of worker-firm
interactions.1 Nonetheless, the exercise is
useful as a way of clarifying how explicit
consideration of mood and morale can
change the usual predictions of agency
theory. Indeed, it is clear that people do
pay attention to the well-being of others,
and that the way in which they do this
depends critically on their own “mood.”
Bewley’s work persuades me that this general idea can be important in understanding many features of workplace behavior.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
51
1
The model and discussion
presented here are somewhat
different than those in the book
(and those presented at the
conference itself). Readers
are again encouraged to look
at the book as well.
M AY / J U N E 1 9 9 9
A simple story of a “rude driver”
might provide a useful way of thinking
about these kinds of motivation. Suppose
you are traveling by automobile to an
important engagement for which you
definitely do not want to be late. Construction has closed the left lane of the
highway, and you are stuck waiting, not
too patiently, in the right lane as traffic
inches its way toward the construction
site. You notice in your rearview mirror
a lone car whizzing past the “merge
right” signs, bypassing drivers—yourself
included—who have dutifully pulled into
the right lane. The driver proceeds to the
very last spot at which the car can physically remain in the left lane and signals
right, hoping to pull in front of you! What
do you do? Do you let him in or not?
The self-interest model normally
employed by economists provides an
easy answer. Letting the driver pull into
your lane imposes a cost—it increases the
probability that you will be late for your
engagement—and gives you no benefit, so
you do not let him in. Economists understand, though, that this simple way of
viewing the problem is not exactly right.
People are routinely altruistic; they pay
attention to others’ well-being. There are
many examples in which ideas are incorporated into formal economic models,
including, for instance, Gary Becker’s
(1991) work on the family and Matthew
Rabin’s (1993) theory of fairness. In the
current context, you would surely be
willing to let the driver pull in front of
you if you noticed a pregnant woman in
the car who appeared to be in labor.
The idea here is simple: People
care about others and are often willing
to sacrifice their own material well-being
to benefit others. Moreover, in models
like Rabin’s and in empirical work like
Andreoni and Miller (1996), people incorporate others’ welfare into their own decision-making in generally predictable ways.
For example, Andreoni and Miller conduct
experiments which demonstrate that individuals’ willingness to sacrifice money
varies with the extent to which other
individuals benefit from the sacrifice.
Returning to the scenario of the rude
driver, though, it is clear that something
besides even the altruism of Rabin is at
work in most people’s decision-making.
Your decision of whether to let the driver
pull in front may well depend not only on
your assessment of the potential benefits
to the driver (e.g., does he have a pregnant
passenger?), but also on your gut-level
belief about the driver’s motives. If you
believe the driver is indeed being rude or
obnoxious, you may be anxious not to let
him; you might even be willing to suffer
some cost to avoid letting him in. On the
other hand, if there is some indication that
the driver was merely confused (perhaps
he has an out-of-state license plate and a
befuddled, contrite look on his face), you
will be more inclined to let him in. The
point is that your utility function evidently
depends, at a minimum, on three factors:
first, your own narrow, self-interested goal—
to move through traffic as quickly as possible; second, your internalization of the
other driver’s goals; and, third, your own
mental state, which in this case follows
from your assessment of the other driver’s
motives. This last part of the decisionmaking process may be transparent at the
time or may work at a largely subconscious level. It is self-evidently important
in the rude driver scenario, and it may be
important in other contexts as well.
By section 4 of his paper, Bewley works
up to a representation of worker preferences that perhaps parallels the observations we glean from the rude driver scenario.
Bewley’s characterization of utility, both
“conscious” and “unconscious,” depends, as
usual, on compensation and effort. It incorporates also an internalization of the goal of
the firm’s owners. This altruistic component
is not generally included in theorists’ representations of preferences, but as just noted,
it is sometimes incorporated; it appears, for
instance, as a central component in George
Akerlof’s (1982) gift exchange model of
worker-firm interaction. Bewley pushes
further, though, by positing a model that
includes “morale,” which he suggests has
two key aspects: an internalization of the
firm’s goal (firm profit) and his mental state
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
52
M AY / J U N E 1 9 9 9
or mood. As in the rude driver story, an
individual’s behavior is affected by his own
personal objectives and by an inclination
to at least consider the well-being of others
(in this case the employer), but all of this
is tempered by a more elusive construct—
mood or mental state.
Building from this basic representation
of worker preferences, Bewley derives a
number of implications that seem in accord
with the observations he gathered in his
field research. In so doing, he clearly
demonstrates the viability and value of constructing a model that pays serious attention to motivations that (realistically) move
beyond the usual assumption in principal–
agent models. Bewley’s work covers lots
of ground, making suggestions about how
to incorporate mood and morale, and also
exploring cooperation, information sharing,
and the relative merits of managers’ use of
morale and coercion.
This is a valuable contribution to
behavioral economics as applied to the
workplace; it provides seed ideas that
other economists will find useful in doing
their own theoretical work. Economists
may find alternative ways of constructing
realistic models of work motivation, models that include a serious effort to incorporate features like morale and mood. In
this enterprise, they will do well to follow
Professor Bewley’s exemplary effort to see
that their formal representations are firmly
rooted in careful systematic observation of
the real world.
REFERENCES
Akerlof, George A. “Labor Contracts as Partial Gift Exchange,”
Quarterly Journal of Economics 96 (November 1982), pp. 543-69.
Andreoni, James, and John H. Miller. “Giving According to GARP,”
Working Paper, Carnegie Mellon University, (1996).
Becker, Gary. A Treatise on the Family, Harvard University Press,
(1991).
Friedman, Milton. “The Methodology of Positive Economics,” Part 1 in
Essays in Positive Economics, University of Chicago Press, (1953).
Rabin , Matthew. “Incorporating Fairness into Game Theory and
Economics,” American Economic Review 83 (December 1993),
pp. 1281-302.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
53
M AY / J U N E 1 9 9 9
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
54
M AY / J U N E 1 9 9 9
Wouter J. den Haan, Garey Ramey, and Joel Watson are associate professors of economics at the University of California, San Diego.
Den Haan is also a member of the NBER. The authors thank Marty Eichenbaum and Bob Hall for helpful conversations. Ramey and Watson
thank the NSF for financial support under grant SBR-965868.
ContractTheoretic
Approaches to
Wages and
Displacement
influencing the form of worker compensation. Moreover, the responses of aggregate
wages and employment to business-cycle
shocks are sensitive to the structure of
worker/firm contracting. Overall, our
study establishes that the particular form
of contracting imperfections can have
major implications for economic outcomes.
This highlights the importance of going
beyond the reduced-form analysis of contracting that typifies much of the
macroeconomics literature.
Our key assumption throughout is
that firms and workers maintain long-term
contractual relationships, whereby a particular
firm and worker transact repeatedly until
their relationship is severed. Within a unified theoretical framework, we consider two
types of contracting imperfections in labor
relationships. First, relationships may be
subject to limited verifiability, whereby
external enforcement authorities are unable
to compel payments conditioned on the full
set of actions chosen by the contracting
partners. For example, the authorities may
be unable to ascertain whether severance of
the relationship was due to the worker’s
action or the firm’s action. Second, desirable
contracts may be infeasible due to the worker’s limited liquidity, which prevents the
worker from making payments to the firm.1
We demonstrate that privately
inefficient breakup of relationships may
occur in the presence of limited verifiability;
that is, limited verifiability leads contracts
to be fragile. The fundamental idea is that
when a negative shock hits, the joint
returns to cooperation between the firm
and worker may be insufficient to offset
the collective inducements to behave dishonestly, so there is no way to specify
transfers between the firm and worker that
can preserve the relationship. Increased
verifiability leads to more robust relationships, more direct punishments for
misbehavior, and a wider set of optimal
compensation schemes. The worker’s
relative bargaining position always
Wouter J. den Haan,
Garey Ramey, and
Joel Watson
M
odels of moral hazard in labor relationships have proven to be useful
in explaining a variety of important
macroeconomic phenomena. The existence of involuntary unemployment has
been linked to the need to provide incentives for workers to choose high effort
(Shapiro and Stiglitz, 1984). Further,
since wage levels are important for workers’ incentives, adjustment of wages in
response to cyclical shocks may be subject
to contractual constraints. This may help
to explain the low observed variability
of average wages relative to employment
levels (Danthine and Donaldson, 1990,
1995; Strand, 1992; MacLeod, Malcomson
and Gomme, 1994). More recently, contracting problems have been tied to
inefficient severance of employment relationships, giving a mechanism whereby
business cycle shocks may be magnified
and made more persistent (Ramey and
Watson, 1997a).
This paper focuses on the contracttheoretic underpinnings of wage
adjustment and worker displacement in
moral-hazard models of the labor market.
We show that contracting imperfections
play a key role in determining the fragility
of employment relationships in the face of
shocks to productivity, as well as
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
55
1 Our analysis omits some other
aspects of labor contracts that
have been considered in the
literature. First, we assume
risk-neutral workers, so wage
payments do not play any
insurance role, in contrast to
implicit contract models.
Second, renegotiation of wage
contracts is allowed, meaning
that inefficient severance cannot occur as a consequence of
failure to renegotiate. Implicit
contract models are surveyed
in Romer (1996, ch.10); see
Boldrin and Horvath (1995)
for a recent empirical implementation. Suppression of
renegotation as a cause of displacement is considered in
Hashimoto and Yu (1980) and
Hall and Lazear (1984).
M AY / J U N E 1 9 9 9
2 Our recent analysis of lending
relationships and liquidity flows
(den Haan, Ramey, and Watson,
1999a) incorporates a contracting framework that is a
special case of the one considered here. More tangentially
related is den Haan, Ramey,
and Watson (1999b), which
explores the theoretical foundation of stylized facts about compensation over a worker’s
career and the experiences of
displaced workers.
3 For example, one component
of our theory is the view that
discretionary transfers are subject to renegotiation.
determines his total compensation, while
the particular forms of payment may be
influenced by the requirements of contracting.
Performance bonding, for example, arises
naturally in settings of unrestricted
liquidity, but may be circumscribed when
the worker is liquidity constrained. Moreover, since the form of compensation is
identified by the timing and conditioning of
payments, informal notions such as salary
may be ambiguous.
Our framework also allows for a more
precise analysis of the role of wage premia
in solving labor contracting problems. We
say that a worker obtains an efficiency wage
when, in contract negotiation, the firm and
worker must directly weigh reducing the
worker’s compensation against motivating
effort. We demonstrate that, in the absence
of liquidity constraints, effort incentives
are driven by verifiability, bargaining power,
and the state of the matching market, but
not by the worker’s current period compensation. Thus, in a precise sense, efficiency
wages play no role in helping to preserve
relationships. When the worker is liquidity constrained, however, the incentive
constraint may bind at the time of contract
negotiation, as a consequence of the worker’s inability to make payments to the firm
that would implement the unconstrained
bargaining outcome. Thus, efficiency wages
may emerge as added restrictions on wage
determination when workers are liquidity
constrained.
To analyze how contracting imperfections affect market outcomes, we posit
that relationships are formed on a
matching market, as in Pissarides (1985)
and Mortensen and Pissarides (1994).
We consider an example in which a limited
liquidity specification with efficiency
wages but no fragility is contrasted with
a limited verifiability specification that
is subject to fragility. In response to a
permanent shock to the distribution
of productivity, the presence of limited
liquidity does serve to dampen wage
adjustment, relative to a completecontracting benchmark. However, the
dampening is much more pronounced
in the limited verifiability case, as the
severance of low-productivity relationships
greatly reduces the sensitivity of average
wages to the shock. Moreover, the effect
of the shock on total employment is greatly
magnified as a consequence of fragility.
Our example illustrates how models that
emphasize displacement may be much
more potent for explaining wage adjustment
and propagation of shocks than models
stressing wage effects within a given
employment contract.
The framework presented in this paper
builds on the contracting model of Ramey
and Watson (1997a), who first developed
the theoretical foundation of fragility and
the related magnification of shocks. The
present paper is also related to our earlier
work on endogenous destruction margins
and propagation of shocks, as reported
in den Haan, Ramey, and Watson (1997).
Here we address a wider range of contractual
imperfections (including liquidity constraints
and a range of verifiability conditions), we
incorporate wage determination, and we
consider adjustment of average wages in
market equilibrium.2 Our framework is
also related to the work of MacLeod and
Malcomson (1989, 1993, 1998). MacLeod
and Malcomson focus on the timing and
enforcement of compensation, using a
model in which parties can make both
externally enforced and discretionary
transfers. Two contractual forms are
emphasized: efficiency wages (which they
define as the use of high wages with the
threat of severance) and performance pay
(defined by the use of discretionary
bonuses). They demonstrate how the
form of compensation depends on labor
market conditions and equilibrium beliefs,
interpreting the latter as a “social norm
for a fair wage.” Our work, in contrast,
addresses (a) a broader range of
contracting settings, including different
restrictions pertaining to verifiability and
liquidity; (b) inefficient severance of relationships following shocks; and (c) issues
of propagation in the macroeconomy. We
also take a different approach to modeling
contract determination, whereby negotiation (and renegotiation) between workers
and firms is directly incorporated.3
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
56
M AY / J U N E 1 9 9 9
Figure 1
On the issue of contractual form, we
obtain results different from those of
MacLeod and Malcomson.
The main body of this paper is divided
into four sections. The first introduces the
basic model of an employment relationship.
The second considers enforcement under
various contracting environments, which
differ in terms of what can be verified to a
third party. The third section discusses
efficiency wages and limited liquidity, while
the fourth derives market outcomes from a
matching setup.
Timing of Actions in
Employment Relationships
In each period:
THE MODEL
Employment Relationships
Employment relationships consist of
one worker and one firm who interact in
periods t = 1, 2, ... until their relationship
is severed. The firm is represented by a
manager. Both the worker and manager
make a private effort choice (high or low)
that contributes to production. In addition,
the parties negotiate a contract specifying
transfers as a function of verifiable information. If both agents exert high effort during
production, then the cooperative output
level z t is realized. We assume that zt
varies randomly across periods, taking the
value z G in the good production state and
z B in the bad state, with z G > z B > 0. For
simplicity, z t is assumed to be realized
independently in each period, with r
denoting the probability that z t = z B.
The realization of z t , contracting,
and effort choices within a period occur
in three phases, as illustrated in Figure 1.
In phase 1, the worker and manager
observe the realized value of z t for that
period, then negotiate a contract that
governs current-period interaction. If they
reach an agreement, the contract specifies
which decisions the agents will make in
subsequent phases, as well as a profile of
contingent payments. Disagreement leads
to severance of the relationship, with the
worker and manager obtaining outside
option values of bw + ww and b m + w m,
respectively. The parameters b j reflect
current-period benefits received when
Phase 1:
Contract Negotiation
D
Phase 2:
Manager Effort Choice
A
Phase 3:
Worker Effort Choice
B
C
the relationship is severed in phase 1
(e.g., the worker may obtain unemployment
benefits), while the parameters w j indicate
the discounted values of future benefits,
which may include returns from new relationships formed in the future. Severance
as a result of disagreement will be referred
to as outcome D. Further details of the
contract negotiation are discussed below.
The manager makes his effort choice
in phase 2. Low effort leads to outcome A,
where the manager obtains a current-period
private benefit of x m, while the worker
receives no benefit. Worker effort is selected
in phase 3; there, low effort leads to
outcome B, in which the worker receives
a current-period private benefit of x w and
the manager obtains zero. Under either
low-effort outcome, output is zero and
the relationship is severed at the end of
the period. On the other hand, high effort
by both agents induces the cooperative
outcome C, in which case output is z t and
the relationship continues into the next
period. The manager is assumed to appropriate the output.4
We assume x j > b j for both j, meaning
that agents gain more in the current period
from staying in the relationship and putting
out low effor
t, than from leaving the
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
57
4 The model is easily extended
to introduce imperfect monitoring of effort choices, as follows.
In phase 2, outcome A is
reached with a positive probability under either effort choice
of the manager, with low effort
implying a greater probability
of reaching A. Similarly, in
phase 3 the probability of
outcome B is higher when the
worker chooses low effort.
Thus, the contract cannot be
conditioned directly on the
effort choices, but only on the
observable outcomes.
M AY / J U N E 1 9 9 9
where x = x w+x m. The first inequality in
assumption 1 implies that the agents prefer
the robust outcome under either production
state, so that the robust outcome is efficient.
The remaining two inequalities will determine the conditions under which the
agents can find a contract that supports
the robust and fragile solutions, as
discussed below.
relationship in phase 1. Observe, however,
that when an agent chooses low effort,
his partner forgoes the opportunity to
obtain b j. We also assume that x j < b w + bm,
meaning the agents will never agree in
phase 1 to induce outcomes A or B.
Interpretations for our assumptions
are discussed below.
We now compute the value of the
relationship under various outcomes.
First, the agents may choose high effort
under both z G and z B in every period, in
which case the relationship never breaks
up. In this robust solution, the value of the
relationship is given by
Contracting
At the start of each period, the worker
and manager negotiate a short-term contract
that specifies payments from the manager
to the worker conditional on the
productivity level z k, k = G, B, and on the
outcome of productive interaction (A, B, or
C). The set of feasible contracts is generally constrained by the limits of the external
enforcement institution. Payments might
also be subject to liquidity constraints.
Let sCk denote the payment made to the
worker in the event that outcome C is realized, under productivity level zk, k = G, B.
Since the manager directly appropriates zk
when outcome C is reached, his currentperiod payoff in this case is zk – sCk , while
the worker obtains sCk . Transfers conditioned
on outcomes A and B will be written sA
and sB, respectively; these transfers will
not need to depend on k. In addition, the
agents may agree on up-front transfers s0k,
made at the time of contracting in phase 1.
We adopt the convention that negative
values of sCk , sA, sB and s0k denote transfers
from the worker to the manager.
The worker and manager also formulate a joint plan for how they will behave
in the future, which yields an expected
continuation value g. For example, if
the agents intend to implement a robust
solution, then g=g R. We look for a specification of behavior, consisting of explicit
contracts and individual actions over time,
that satisfies four conditions. First, agents’
expectations about g accurately reflect
the value of continuing the relationship.
Second, in each period, agents make their
effort choices in a utility-maximizing manner,
given g and the values of transfers agreed
to under the contract. Third, short-term
(1 − ρ ) zG + ρ z B ,
1− β
where b is the agents’ common discount
factor. We let g R denote the discounted
continuation value of the relationship in
this case:
g =
R
[
β (1 − ρ )z G + ρ z B
1− β
].
Second, the agents may agree to select
high effort when z G is realized, but to
sever the relationship under z B. In this
fragile solution, in each period the
relationship breaks up with probability r.
The discounted future value of the
relationship in this case satisfies
[
(
]
)
g F = β (1 − ρ ) z G + g F + ρ ( b + w) ,
where b = bw + bm and w= ww + wm. Solving
for gF yields
gF =
β (1 − ρ )z G + ρβ (b + w)
1 − (1 − ρ )β
.
Finally, the agents may agree to sever the
relationship under both z G and z B and the
relationship breaks up in period 1, having
value b + w.
We impose a final assumption:
(1) b + w < z B + g R < x + w < z G + g F ,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
58
M AY / J U N E 1 9 9 9
contract negotiation is resolved according
to the Nash bargaining solution. Here, the
agents recognize that they are implicitly
bargaining over the total value of the
relationship, which is the sum of currentperiod returns and the continuation value g
(assuming the agents are able to maintain
the relationship into the next period).
The worker’s and manager’s bargaining
weights are p w and p m, respectively, and
the disagreement point is outcome D.
The parameters p w and p m are nonnegative
and satisfy p w + p m = 1. Fourth, the best
equilibrium satisfying the first three
conditions is selected by the firm and
worker.5 In light of assumption 1, the
firm and worker will chose the robust
solution if it can be supported. Next
in line is the fragile solution, followed
by immediate severance.
a larger private benefit than does unemployment (this is the assumption x j > b j,
j = w, m). The most direct way to interpret
this assumption is that employment
relationships convey perks that are themselves attractive, apart from personal costs
associated with high effort. Further,
unemployment may involve private costs,
such as psychic harm and search costs,
that are not incurred within active relationships. Note that private benefits are zero
for agents who exert high effort in a relationship, which serves to normalize utility.6
Low effort and severance. We have
assumed that low effort by either the
worker or manager leads the employment
relationship to be severed. There are two
basic motivations for this assumption.
First, low effort may induce rapid decay
in the productivity of the relationship, to
the point where returns to continuation
fall short of operating costs. For the manager, low effort might also be directly tied
to liquidation; for example, the manager
may sell off essential assets. Second, contractual enforcement mechanisms used by
the partners to sustain cooperation may
entail a costly and time-consuming dispute
resolution process in the event that either
agent chooses low effort; see Ramey and
Watson (1997b) for a detailed discussion
of such mechanisms. When dispute resolution costs are sufficiently high, the
worker and manager will opt to sever
their relationship.
As another possibility for contractual
agreement, the agents might seek to
temporarily suspend their relationship
when high effort is unsustainable, for
example, through a layoff, in order to
preserve match capital. Such suspensions
will be infeasible, however, if returns from
the relationship would experience rapid
deterioration without active inputs of
effort. For example, production equipment
or organization may depreciate during the
suspension, or market dominance may be
permanently lost. Further, as will become
clearer below, contracts that support
temporary suspension will be infeasible
if a third-party enforcement authority
Interpretation
Effort choices and unemployment benefits.
Our model of employment relationships
allows for effort choices by both workers
and managerial personnel. These choices
can be interpreted in a number of ways.
The most familiar interpretation involves
personal exertion, and here we augment
the usual shirking model by specifying
that, in addition to worker effort, managerial effort is also important for production.
Further, low effort may entail activities
that are directly harmful to production,
such as theft. Managers may also abuse
their power to direct workers’ activities,
by unexpectedly assigning them to
undesirable tasks.
An agent obtains a current-period
private benefit when he chooses low effort.
Alternatively, the agents can agree to dissolve
their relationship at the start of the period
and obtain current-period benefits outside
the relationship. A key assumption of our
model is that these unemployment benefits
become unavailable once agents have agreed
to a contract and have proceeded to phase
2; that is, the agents must make a commitment to production activities that rule out
outside benefits in the current period. We
have also assumed that low effort conveys
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
59
5 The first three properties
define a negotiation equilibrium,
which is simply a specification
of behavior consistent with private incentives and the Nash
bargaining solution. Specifically,
the Nash solution implies that,
given g, the surplus of the relationship at the time of negotiation (which is z k + g – b – w )
is shared in proportions defined
by the bargaining weights. The
fourth property implies that, at
the meta-level of negotiating
over negotiation equilibria, the
firm and worker select the equilibrium that maximizes their
joint returns. For example, if
they could sustain both the values g R and g F, then they are
assumed to select the preferred
plan yielding g R. In our framework, there will always be an
equilibrium that is maximal in
every period.
6 Our setup admits the standard
shirking model, in which firms
behave more passively. The
standard model is obtained by
m
m
setting b = x = 0, so that the
manager obtains neither unemployment benefits nor benefits
from low effort. In this case,
the manager’s incentive to agree
to the contract at phase 1 are
identical to his incentive to
choose high effort at phase 2,
so in effect the manager does
not make an effort choice.
M AY / J U N E 1 9 9 9
7 MacLeod and Malcomson’s
(1989, 1993, 1998) bonus
payment is like sCk , although
they assume it is discretionary;
for example, the firm is not
contractually committed to
make the payment. In our
framework, firms would never
make discretionary transfers
following production, and only
what is enforceable matters.
8 In our setting, short- and long-
term contracts differ only to the
extent that agents can enforce
a transfer conditional on outcome D occurring in the next
period. To see this, consider
two contracting environments:
(a) short-term, as described in
the text; and (b) long-term,
with a recontracting option in
each period. Fix the scope of
what can be verified and
enforced within a given period,
and assume that the agents
have symmetric information
whenever they negotiate. Then
(a) and (b) support exactly the
same behavior over time, if in
setting (b) the agents cannot
condition transfers on outcome
D occurring in the next period.
Further, the latter restriction on
setting (b) may be implied by
limited liability, in that the legal
institution might not enforce
transfers conditional on severance unless there is cause for
awarding damages. In most of
the work presented here,
options for long-term contracting do not affect our results.
9 This is without loss of generali-
ty, given that in each period the
agents maximize their joint
value over feasible equilibria.
EXTERNAL ENFORCEMENT
AND VERIFIABILITY
is unable to tell whether suspension
resulted from a breach of contract by
one of the parties.
While severance following low effort
is our benchmark case, the model can
also cover situations in which temporary
suspension is feasible. This is done by
setting w j = g j – a j, j = w, m, where gw
and g m give the discounted values to the
worker and manager, respectively, of
continuing the relationship into the next
period, and a m and a w are the costs
of maintaining the relationship while
not producing.
Full Verifiability
The agents’ ability to find a contract that
supports the robust solution will depend on
whether they are able to enforce the needed
contingent transfer payments. This, in turn,
depends on what external enforcement
authorities can observe about the currentperiod effort choices. We begin by considering
the case of full verifiability, in which the
external authority can perfectly observe
which of the outcomes A, B, or C is realized.
In this case, the robust solution is supported
and, therefore, it is selected by the agents.
This is confirmed by checking the four
conditions of our contracting solution.
Since the outcome must be C in every
period under the robust solution, the
worker’s total compensation is given by
the stream of payments s G0 + s GC and s B0 + s CB
for periods having the good state and
bad state, respectively. Note that we are
assuming the agents select the same contract
in each period.9 Bargaining in each period
determines the discounted value of this
payment stream. This is characterized by
Contracted transfer payments. The model
allows for contracts specifying an up-front
transfer to the worker, s0k, as well as a
transfer that is made conditional on
choices of high effort by both agents, sCk .
The former can be interpreted as a “salary,”
in that it is paid in return for the worker’s
commitment to forgo his unemployment
benefit and commit to production
activities for some interval of time, while
the latter represents a “performance
payment,” received only after the
successful completion of production.7
The transfers sA and sB are used to impose
direct punishments for low effort and
can be interpreted as damages stipulated
by the contract for nonper- formance, or
penalties imposed by an external legal or
regulatory authority.
(2) sk0 + sCk + g wR
= π w zk + g R − b − w
(
)
+ b + w , k = G , B,
w
w
where gwR indicates the discounted
future value to the worker of continuing
the relationship:
Contract duration. We have assumed that
agents can write only short-term contracts,
specifying transfers that are enforceable
within the current period. In this
contracting environment, the transfers sA
and sB can be thought of as severance payments (in addition to punishments), since
the relationship is dissolved following low
effort. Note that agents are free to sever
their relationship following outcome C,
but such a decision is made in phase 1 of
the next period, after the current contract
expires. Thus, by short-term contract we
mean that the agents cannot stipulate to
transfers conditional on whether they
reach agreement in the negotiation phase
of the next period.8
g
wR
=
[
(
) (
β (1 − ρ ) s0G + sCG + ρ s0B + sCB
1− β
)] .
To interpret equation 2, note that the left
side is the worker’s value of continuing the
relationship under the cooperative plan.
The Nash solution dictates that s0k and sCk
be set so that this value is equal to the
worker’s outside option plus his share of
the surplus of the relationship. The above
two equalities capture the first and third
conditions of equilibrium. To verify the
second condition, note that outcome C
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
60
M AY / J U N E 1 9 9 9
is consistent with the agents’ private incentives at phases 2 and 3 if and only if
solution can be supported. Adding the
incentive conditions 3 and 4 gives
k
k
R
wR
m
m
(3) z − sC + g − g ≥ x − s A + w
(5)
and
(4)
z k + g R ≥ x + w,
which fails when k = B, given assumption 1.
Thus, in the bad productivity state, either
the manager or the worker will have an
incentive to choose low effort, no matter
what value of s is proposed. Limitations
on verifiability, in the form of inability to
condition severance transfers on the reason
for severance, imply that the robust solution
becomes infeasible. The key problem is that
the joint surplus from cooperative behavior,
given by z B + g R, falls short of the sum of
the agents’ returns from low effort, which
are x m + wm and xw + ww.
Despite their inability to achieve the
robust solution, the agents can find a contract that supports the fragile solution.
We can specify s G0 + s GC to satisfy
sCk + g wR ≥ x w + s B + ww .
Inequalities 3 and 4 can be satisfied for
each k by making sA sufficiently positive
and sB sufficiently negative, that is, by
imposing sufficiently large punishments
for choosing low effort. Since the robust
solution maximizes the joint value of the
relationship in each period (from phase 1,
where negotiation occurs), the fourth
contracting condition also holds.
Beyond the requirements on sA and sB,
there is wide latitude for selecting salary
and performance payments that satisfy
equation 2, and there is essentially no
distinction between the two kinds of
payment. For example, contracts might
involve performance payments only, or
salaries only; in the latter case, the worker’s
incentive to choose high effort is supported
by the loss of future-period salary payments,
rather than current- and future-period
performance payments.
(6) sG0 + sCG + g wF
= π w zG + g F − b − w + b w + w w ,
(
)
where gwF gives the worker’s discounted
future value of continuation in the fragile
solution:
g
Limited Verifiability
Now suppose the enforcement
authority can enforce payments conditional
on severance of the relationship due to low
effort, but the authority cannot ascertain
which agent’s low effort choice caused the
separation. That is, the authority cannot
distinguish between outcomes A and B.
Remember that the agents cannot contract
on severance following outcome C, since
this would occur in the next period. However, the agents can still specify the transfer
sCk contingent on C occurring. Further
recall that, at the time of negotiation, there
is no outstanding contract specifying transfers in the event of outcome D.
Given the limitation on what can
be observed, the contract can specify only
a single severance transfer s, where sA = sB
= s. Let us check whether the robust
wF
=
[
(
) (
β (1 − ρ ) s0G + sCG + ρ b w + w w
1 − β (1 − ρ )
)] .
Thus, the first and third equilibrium conditions are satisfied. Since zG + gF > x + w,
we can find a value sGC – s satisfying
(
)
G
G
F
wF
m
m
(7) z − sC − s + g − g ≥ x + w
and
(8)
(s
G
C
)
− s + g wF ≥ x w + ww ,
and clearly each agent has an incentive to
choose high effort in the good state. Thus,
the relationship continues as long as the
good state is realized, while in the bad
state the relationship is severed. Finally,
the fourth equilibrium condition follows
from the fact that z G + g F > b + w; that is,
the fragile solution is superior to immediate
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
61
M AY / J U N E 1 9 9 9
up-front transfer, s0G, and receives recompense
sGC only in the event that high effort is realized. To the extent that sGC, is fixed by
inequalities 7 and 8, higher values of p m
correspond to larger bonding measures.
severance, while the robust solution is
infeasible. Importantly, severance is inefficient for the agents, since z B + g R > b + w
implies that the agents would prefer the
robust solution if it could be implemented.
Observe further that there is a large range
of payment profiles that can support the
fragile solution; for example, if higher sGC is
specified, then the severance transfers will
be correspondingly increased to preserve
inequalities 7 and 8, and sG0 will be reduced
to maintain equation 6. As in the case of
full verifiability, here the worker’s total
compensation, driven by relative bargaining
powers, does not determine the exact form
of compensation.
The analysis is similar for the case in
which disagreement or low effort imply
temporary layoff as opposed to severance.
For example, suppose aw = a m = 0. In this
instance, assumption 1 is replaced by b <
zB < x < zG. Under the robust solution with
temporary layoffs, we have w = gR ; since
equation 6 continues to be necessary for
satisfaction of the incentive constraints, it
follows that the robust solution cannot be
implemented as a consequence of zB < x.
Further, it is easy to verify that the fragile
solution, which involves layoffs in the
bad state, can be implemented, and the
assumption b < zB implies that the layoffs
are inefficient.
Noncontractible Worker Effort. The
actions of some agents may be unobservable
to the enforcement authority, even as transfers can be conditioned on the behavior of
other agents. Consider the case in which
the worker’s effort is noncontractible in
this sense. Thus, the authority cannot disinguish between outcomes B and C, although
A is still separately observable.10 In contrast
to the case of limited verifiability, it is possible to implement the robust solution in
this environment. First, the manager’s
incentive constraint (inequality 3) can be
satisfied by choosing sufficiently large sA.
Since sB = s kC , however, the worker’s
constraint (inequality 4) now becomes
(9)
Observe that current-period choices of
s0k and sCk cannot affect whether inequality
9 is satisfied. It follows that the robust
outcome is sustainable if and only if
inequality 9 holds at values of the transfer
payments that solve equation 2, which will
tend to occur when p w is large or when xw
is small. Thus, through their effect on the
worker’s expected future compensation,
bargaining weights have an impact on
incentives, although they have no implications for the form of compensation (salary
versus performance pay).
Other Cases
10 It is implicit in this assumption
that the authority cannot tell
whether severance is the result
of worker low effort in the
current period or failure to reach
agreement in the following
period; for example, the
current-period contract does
not extend to cover separations
that occur as a result of the
worker’s low effort.
g wR ≥ x w + ww .
Limited Liability. Agents may be protected
from liability for payments in the event
that the relationship is severed. This
serves as a further restriction on the case
of limited verifiability, where sA = sB = 0 is
now imposed. It is easy to see that there is
a solution to expressions 6-8 satisfying this
restriction: sGC is pinned down by inequalities 7 and 8, and sG0 is then chosen to
satisfy equation 6. Interestingly, a contract
of this form may involve bond-posting by
the worker. For example, a high positive
value of sGC may be specified in order to
sustain the worker’s incentives to choose
high effort, combined with a negative
value of sG0 that implements the bargaining
solution. Here the worker makes an
Nonverifiability. Finally, consider the
case in which the enforcement authority
cannot distinguish between any of the
outcomes A, B, and C. Thus, there is a
single transfer payment sk that is enforced
under all three outcomes. Note first that
the robust solution cannot be forced in
this case, as adding inequalities 3 and 4 for
k = B implies violation of the assumption
zB + gR < x + w. Next, the fragile solution
can be enforced if the following conditions
hold for the value of gwF determined
by equation 6:
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
62
M AY / J U N E 1 9 9 9
(10)
z G + g F − g wF ≥ x m + wm ,
(11)
g wF ≥ x w + ww .
mental to the idea of an efficiency wage is
that motivating the worker to choose high
effort places a binding constraint on wage
setting, so that wages cannot be cut without
inducing low effort. In other words, when
the firm and worker negotiate over wages in
a period, they confront a trade-off between
the worker’s compensation and effort incentives. In this section we show, however,
that such a trade-off never arises in the contracting setting considered thus far. Thus,
there is no scope for efficiency-wage effects
in contracting models of this form.11
Consider the incentive constraints for
the manager and worker, which we can
write generally as
As in the previous case, the agents’ relative
bargaining weights influence whether
cooperation can be sustained. Note that
these conditions are unaltered if it is
instead assumed that the enforcement
authority cannot enforce any transfers at
all, since all needed transfers can be made
using the up-front payment s0G.
Summary
Observability of actions within the
relationship by external authorities plays a
key role in determining how successful
agents can be in solving their contracting
problems. Full verifiability implies that
the complete range of necessary transfer
payments can be enforced, allowing the
most efficient solution to be implemented.
In contrast, nonverifiability rules out
efficiency, and even the fragile solution
becomes unenforceable for a range of parameter values. Between these two extremes,
various possibilities arise. When verifiability
is limited in the sense that severance
payments cannot be conditioned on the
reason for severance, only the fragile solution is implementable; when worker effort
is noncontractible, the bargaining outcome
determines the solution, and there will be
no production in any state when the worker’s bargaining power is sufficiently small.
Finally, except in the case of limited
liability, the split of the worker’s compensation between salary and performance
payments plays no role in implementing
the various solutions.
z k − sCk + g j − g wj ≥ x m − s A + wm
and
sCk + g wj ≥ x w + s B + ww .
Observe that, in addition to the parameters
zk, xm, xw, wm, and ww that are fixed from
the perspective of the manager and worker,
these constraints depend on three sets of
parameters. First, there is the joint continuation value g j, which is maximized when
the agents select the best equilibrium
(either robust, fragile, or immediate severance). Since higher values of g j relax the
incentive constraints, there is no trade-off
between compensation and incentives at
the level of equilibrium selection. Second,
the constraints involve the manager and
worker’s shares of the continuation value,
described by g j – gwj and gwj. Given g j,
these values are tied down by negotiation
in future periods, which in turn is fully
determined by bargaining weights and the
fixed disagreement point D. In other words,
from the agents’ perspective at the negotiation phase in any given period, they have
no control over continuation values in a
way that forces them to address a trade-off
between compensation and incentives.
The third set of parameters comprise
the contracted transfers sA, sB, and sCk .
These are directly controlled by the worker
and firm in the current period. Note,
however, that the up-front transfer s0k does
EFFICIENCY WAGES
Efficiency Wages and Contract
Negotiation
The literature on moral hazard in labor
relationships has placed great emphasis on
solving worker incentive problems through
the payment of efficiency wages. Funda-
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
63
11 The term “efficiency wages” is
also used in connection with
the idea that incentive problems lead to involuntary unemployment. Regardless of
incentive problems, however,
employed workers fare better
than unemployed workers
whenever employment relationships entail quasi-rents (as
when matching is costly/frictional) and workers have some
bargaining power. Further, as
argued by Carmichael (1985),
involuntary unemployment is
not a necessary consequence of
incentive problems.
M AY / J U N E 1 9 9 9
not appear in the incentive constraints. As
a free parameter, s0k can be set to affect any
division of the relationship’s value between
the firm and worker, with no implications
for the provision of incentives in the current
period.12 As a result, during contract negotiation, there is absolutely no trade-off between
compensating the worker and inducing high
effort, and so there is no payment of
efficiency wages.13
This is not to say that incentive
constraints are unimportant. Our point is
that consideration of incentives in employment relationships should center on the
satisfaction of incentive constraints given
the contracting and matching environment,
which may or may not generate phenomena
such as efficiency wages. Importantly, the
contracting environment is described by
bargaining powers, whether negotiation is
recurrent, and the extent of verifiability.
sCB + g wR < x w + ww ≤ sCG + g wR .
Here the agents must agree to a higher
value of s CB when the bad state is realized,
in order to induce the worker to choose
high effort. Correspondingly, sCG will be
chosen at a lower value in order to maintain
equation 2 in the good state. It may be
that sCG must be lowered so much that
inequality 12 becomes binding even in
the good state. In any event, we have
(
and it follows that the worker receives an
efficiency wage in the bad state. Observe
that the worker obtains a value strictly in
excess of his outside option even when
p w = 0; in this case, compensation is equal
in both states, and efficiency wages are
paid in both states. We conclude that
efficiency wages may emerge when worker
liquidity constraints rule out the use of direct
penalties or worker bonding to enforce high
effort. It should be noted that the manager
must give up some of his bargaining surplus
when efficiency wages are needed, which
may lead to disagreement and inefficient
severance despite the existence of full
verifiability. Whenever inequality 12 is
binding, the manager obtains a payoff of
zk + gR – xw – ww, which can lie below his
outside option value bm + wm even when
agreement is reachable in the absence of
liquidity constraints. A similar analysis
may be carried out for the other contracting
environments, where prospects for
obtaining productive solutions are also
reduced by the addition of a worker
liquidity constraint.14
Worker Liquidity Constraints
12 Note that only in the case of
nonverifiability is the value s0k
constrained to equal one of the
other contracted transfers. In
this case, however, the externally enforced transfers disappear from the incentive
constraints altogether.
13 This conclusion remains valid
when effort choices are imperfectly monitored; see note 4.
Imperfect monitoring affects
the values of g j and g wj that
can be achieved and alters the
form of the incentive constraints, but it remains the case
that sOk can be freely varied to
effect any desired division of
surplus.
14See Dickens, et al. (1989) for
an informal discussion of legal
and social constraints to bonding that can motivate payment
of efficiency wages. These
authors also consider the tradeoff between costly monitoring
and performance payments as
mechanisms for eliciting effort.
Efficiency-wage effects emerge if the
worker is unable to make payments to the
manager, because of insufficient worker liquidity. A worker liquidity constraint can be
introduced into the model by requiring
that all transfer payments be nonnegative.
Consider the implications of this constraint
in the case of full verifiability. Since sB >_ 0,
supporting the robust solution requires
that inequality 4 be replaced by
(12)
)
sCB + g wR > π w z B + g R − b − w + b w + ww ,
sCk + g wR ≥ x w + ww ,
where gwR is determined by equation 2.
Inequality 12 is made as slack as possible
by setting the salaries s0k equal to zero
and compensating the worker completely
through performance payments. If
inequality 12 still does not hold, then sCk
must be raised above the value determined
by equation 2 in order to induce high effort,
so that inequality 12 becomes binding
in sCk . In this case, a trade-off between
compensation and incentives is clearly
present, and we can say that an efficiency
wage is paid in state k.
As one possibility, suppose that equation 2 with s0k = 0 implies the following:
Relation to Other Models
In this section, we consider how the
efficiency wage issue is treated in a few of
the standard models of dynamic labor contracting found in the literature. The model
of Shapiro and Stiglitz (1984) can be viewed
as producing a trade-off between worker
compensation and incentives by constraining
the kinds of contracts that firms may offer
to workers. In essence, firms are required
to offer a single, stationary wage. Over
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
64
M AY / J U N E 1 9 9 9
multiple periods of time, firms are
committed to the same transfer in each
period, conditional on no discovery of
shirking. In fact, firms would prefer to offer
a low wage in the current period, with
only the promise of higher wages later.15
MacLeod and Malcomson’s (1989,
1993, 1998) theory is designed to rectify
such inconsistencies by explicitly modeling
the contracting process. They provide a
more rigorous foundation for the kinds of
market phenomena of interest to the early
efficiency-wage literature, such as involuntary unemployment. By tying prevailing
labor contracts to a social norm, however,
their model does not incorporate trade-offs
between compensation and incentives
at the level of individual employment relationships. Rather, compensation and
incentives are together traded off against
social sanctions.16
In Ramey and Watson (1997a),
firm/worker pairs determine long-term
contracts through direct bilateral negotiation,
and they are not influenced by social
norms. Like the model presented here,
however, there is no tension between compensation and incentives, so efficiency
wages are not at issue. Through the use of
an up-front transfer, a firm and worker can
manage any split of the relationship’s value,
while implementing the best outcome that
verifiability will allow. The present model
takes the contracting framework a step further by incorporating the negotiation phase
in each period of interaction, which implies
that ongoing surplus division is moderated
by bargaining weights.17
managers can elect to post vacancies at a
cost of c > 0. For simplicity, we assume that
unmatched workers bear no search costs.
The flow of new matches in a period is
given by a standard matching function,
m(U,V), where U indicates the mass of
unmatched workers and V gives the mass
of managers who post vacancies.18
The matching process is assumed to
take place in phase C at the same time as
production occurs in active relationships.
Thus, workers whose relationships are
severed in phases D, A, or B can enter the
current-period matching pool. Further,
to ensure that the pool of unemployed
workers does not become empty, we assume
that, with probability r x, relationships are
severed for exogenous reasons. Exogenous
separations occur in phase 1, and workers
who experience these separations can also
enter the current-period matching pool.
We consider two types of steady-state
equilibria of the model, distinguished
by whether contracting solutions within
relationships are robust or fragile. For
robust and fragile equilibria, respectively,
the discounted future values of relationships
are determined by
MARKET OUTCOMES
where wR and wF give the values of outside
options in robust and fragile equilibria.
The value of the worker’s outside option in
either case satisfies
{(
)[(1 − ρ) z
+ ρ (b + w )}
gR = β 1 − ρ x
x
and
G
+ ρ zB + β g R
]
R
)
{( ) (
+ [1 − (1 − ρ ) (1 − ρ )](b + w )},
g F = β 1 − ρ x (1 − ρ ) z G + β g F
x
We now describe how employment
relationships are formed in steady-state
matching equilibria. Assume that the labor
market contains a unit mass of workers,
each of whom either begins a period
matched with a manager in an employment
relationship or begins the period in a pool
of unmatched workers seeking to locate a
manager. In addition, there is a large
number of potential managers. At the
beginning of each period, unmatched
w wj =
m(U , V )
U
F
g wj
m(U , V ) wj
+ 1 −
βw , j = R, F ,
U
where g wR and g wF are determined by
equations 2 and 6, respectively. Because of
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
65
15 Resolving this issue requires a
more complete model of contract determination, as
Carmichael’s (1985) critique of
the Shapiro-Stiglitz (1984)
model indicates.
16 In MacLeod and Malcomson
(1998), if a firm offers any
contract not in accord with the
norm, it is branded as a
deviant, and workers at this
firm shirk forever after. In
MacLeod and Malcomson
(1989), the social coordination
role is modeled more abstractly
in terms of prevailing equilibrium beliefs. Incidentally, since
a matched firm and worker do
not have direct control over
their joint plan of behavior in
the theory of MacLeod and
Malcomson, total inaction can
be supported as an equilibrium.
17 Ramey and Watson (1997a)
also incorporate what one
might call an efficiency investment: Since the firm makes a
noncontractible investment that
affects incentives and value, it
faces a direct trade-off between
compensating the worker (by
raising or lowering the value of
the relationship) and satisfying
incentive constraints.
18 Added assumptions are ordinari-
ly imposed to guarantee existence of equilibrium and to
facilitate theoretical analysis of
steady-states and dynamics.
We do not lay out these
assumptions here, since we
restrict our attention to a single
numerical example.
M AY / J U N E 1 9 9 9
particular parameterization of the model.
Equilibrium employment and average
wages under the four cases are traced out
as r rises from zero, at the upper righthand corner of all four curves, to 0.04.
For comparison, the values at r = 0.02 are
indicated by dots.19
Consider first the case of full verifiability,
in which workers and managers are able to
write robust contracts. The right-most
curve in Figure 2 depicts employment and
average wages for this case. A productivity
shock taking the form of an increase in r
shifts the outcome down the curve, so that
employment and wages both fall. Since
relationships are robust, the rise in r has
no effect on the breakup probability.
Employment is lower only because managers
are less willing to post vacancies, given
that average productivity is lower. The
reduction in wages also reflects lower
average productivity, as well as a reduced
value of the worker’s matching probability.
Next, the case of full verifiability with
worker liquidity constraints, as discussed
in the previous section, is considered
for two values of the worker matching
probability. For p w = 1/2, equilibria are
robust, and the worker liquidity constraint
binds in the bad productivity state; thus,
efficiency wages are paid only in the bad
state. In this case, wages adjust a little less
relative to employment, when compared to
the full verifiability case, but the effect is
slight. Setting p w = 0 yields robust equilibria
with efficiency wages paid in both states,
and relative wage adjustment declines a bit
more.20 In these cases, worker liquidity
constraints restrict the decline in wages as
r rises, and the dampening effect on wage
adjustment is more pronounced as the liquidity constraint binds in a larger number
of states.
Finally, the case of limited verifiability,
described in the external enforcement and
verifiability section, is shown as the left-most
curve. Equilibria are fragile in this case; in
particular, inequality 1 holds at the value
w = wF. As r rises, employment reductions
become much sharper due to the increase
in the probability of severance. Average
productivity is also reduced relative to the
Figure 2
Average Wages and Employment
in Steady-State Equilibria
Wages
0.865
Efficiency Wages
(Worker’s Bargaining Weight = 0)
0.860
0.855
Limited Verifiability
0.850
Efficiency Wages
(Worker’s Bargaining Weight = 0.5)
0.845
Full Verifiability
0.840
0.9125
0.9175
0.9225
0.9275
Employment
0.9325
0.9375
NOTE: This figure plots the combinations of employment and average wages that are obtained
in the specified contracting environment for different values of r (the probability of the “bad”
state occuring). The dots correspond to values of r = 0.02.
free entry of managers into the vacancy
pool, the value of managers’ outside option
is zero, and we have the following freeentry condition:
m (U , V )
(
)
g j − g wj = c , j = R, F.
V
Finally, the number of employed workers
and the size of the unemployment pool are
given by
(
)
N = 1 − ρ x (1 − ρ ) N + m (U , V )
and
[ (
)
]
U = 1 − 1 − ρ x (1 − ρ ) N.
19Parameter values are z G = 1,
z B = 0.5, x w = 1.25, x m = 1.45,
b w = b m = 0.2, b = 0.96,
m(U, V) = 0.25U 0.5V 0.5,
c = 0.157, and r x= 0.07 .
We also have p w = 0.5 except
for one case where we set p w = 0.
20We have renormalized the
p w = 0 economy to equate
employment and wages at
r = 0 under the various cases.
Observe that the latter two equations
conform to the assumption that workers
whose relationships are severed enter the
unemployment pool in the current period.
We model cyclical shocks as changes
in r holding other parameters fixed. To
keep the analysis simple, we look at comparative statics of steady states as a function of
r. Thus, we approximate the business
cycle by studying the economy’s long-run
response to a highly persistent productivity
shock. This is a good approximation when
the cycle has a low frequency and/or
response is rapid. Figure 2 shows results
for four contracting environments under a
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
66
M AY / J U N E 1 9 9 9
earlier cases, since output in bad states is
zero, rather than z B. The latter effect also
tends to reduce employment, by depressing
vacancies, and it causes wage reductions to
be much greater. Thus, the higher breakup
probabilities lead shocks to be significantly
magnified when contracts are restricted by
limited verifiability. Observe further that
relative wage adjustment is substantially
less when compared to the other cases, as
the higher probability of breakups serves
to shift the cross-sectional distribution of
wages toward relatively high productivity
relationships.
Overall, this example demonstrates
that efficiency-wage effects can dampen
wage adjustments, as past authors have
suggested, but that the scope for efficiency
wages as a mechanism for propagating
shocks is limited. Fragility effects deriving
from limited verifiability, on the other
hand, can produce large magnification of
shocks; further, changes in the composition
of jobs generates more dampening in the
adjustment of wages.21
employment and the relatively dampened
character of wage adjustments. Broad
cyclical swings in job destruction rates
have been documented by Davis,
Haltiwanger, and Schuh (1996), who
also highlight the large number of macroeconomic questions that may be linked to
job creation and destruction. From the
quantitative standpoint, den Haan, Ramey,
and Watson (1997) show how fluctuations
in job destruction rates can serve as an
important mechanism for propagation
of business cycle shocks. The heavy focus
of much past work on wage-setting within
a given set of employment contracts may
be misplaced.
Third, interactions between credit
market imperfections and imperfections
in labor contracting can yield interesting
new implications. In this paper, we have
linked the occurrence of efficiency wages
with worker liquidity constraints. More
broadly, the ability to solve contracting
problems is closely tied to credit-market
trading, and these ties may prove to be of
central importance in accounting for
macroeconomic phenomena.
CONCLUSION
On the basis of the preceding results,
we offer three broad conclusions. First,
the particular form of imperfections that
are present in the contracting environment
can have major implications for economic
outcomes. In moving from limited liquidity
to limited verifiability, for example, the
implications for important variables such
as employment, wages and job displacement
probabilities can be radically altered.
“Reduced-form” analysis of contracting
imperfections that have been prevalent in
much past macroeconomic literature may
hide too much of the key underlying structure. Contractual outcomes depend on the
way firms and workers meet and negotiate,
and this demands a new theoretical perspective and reformulation of conventional
notions, such as the idea of efficiency wages.
Second, economic effects deriving
from severance of employment relationships
warrant very close attention as explanations
for observed phenomena, including the
occurrence of large cyclical fluctuations in
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21As mentioned earlier, inefficient
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68
M AY / J U N E 1 9 9 9
Christopher Foote is an assistant professor of economics at Harvard University.
Commentary
The authors contend that long-term
employment relationships can survive
even in bad aggregate states if the agents
can successfully commit themselves not
to shirk, but this requires low effort to be
detectable by a court so that it can bring
about the required intermediate exchanges.
The setup reminded me of an unemployed
worker in the Shapiro-Stiglitz model; such
a worker would like to be hired at the prevailing wage, but his offer is not accepted
because he cannot make a credible promise
not to shirk. Here, in the case of perfect
verifiability, the offer is accepted even
when the production value is low because
shirking is detected with probability one
and can be proven in court. This brings
about the required intermediate transfer
from the worker to the firm. (Another
difference between this model and the
Shapiro-Stiglitz framework is that in this
model the workers can post bonds for jobs
via negative values of the initial payment
s k0 , a point to which I will return below).
When verification of effort is not possible
in the DRW model, the intermediate-payment strategy for the robust employment
contract fails. The constant benefit of
shirking is too large and tempting for either
the worker or the firm, relative to the low
outcome from production.
The model has several interesting
microeconomic implications. But even
though the possibility of initial, intermediate,
and final payments makes the model very
versatile, I am not sure that it is general
enough to speak definitively on the issue
of salary versus performance pay in an
optimal compensation policy. The applicability of the model for this issue hinges on
whether a negative payment to a worker in
the initial period (s k0 < 0) can be thought of
as a salary, or rather, as some sort of negative bond reflecting the ex ante terms of
trade in the labor market. Because such
bonds can eliminate involuntary unemployment when effort elicitation is a problem,
such bonds have featured prominently in
Christopher Foote
T
his stimulating paper by den Haan,
Ramey, and Watson (DRW) seeks to
contribute to two literatures. First, it
helps answer the microeconomic question
of when firms will use performance pay
rather than salaries to motivate workers.
Second, it examines the microeconomic
issue of why employment relationships
appear so fragile with respect to aggregate
shocks. The overarching goal is to show
that these two literatures are related, or, as
the authors put it, “the particular form of
imperfections that are present in the contracting environment can have major
implications for economic outcomes.”
The central result of the paper is that
employment contracts often are robust
with respect to aggregate shocks only if the
effort choices of both the worker and the
firm are verifiable and contractable. The
paper is exceptionally clear and insightful;
even though the model is simple, the authors
can analyze a surprisingly large number
of special cases. As a result, it is a great
paper for a volume that seeks an integrated
study of the macroeconomics of the labor
market. I will comment first on the structure of the model and then discuss its
micro and macro implications.
The nicely parsimonious model is
based around three possible exchanges
between the worker and the firm. The
two parties begin the period by negotiating
the contract and making an initial exchange
(s k0 ), which depends on the aggregate state
k. In the negotiation process, they promise
to make intermediate exchanges ( s A and
s B ) if one of the parties shirks. Finally,
if both parties provide the required levels
of high effort, production completes satisfactorily and the firm receives the output,
making a final exchange (s kC ) to the worker.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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work of this kind. Yet the authors claim
that in their model, a positive value s k0 is
like a salary, while the final payment, sCk ,
resembles performance-based pay. Therefore, they suggest that their model can
speak to the performance-pay versus salary
issue. Yet the DRW model does not allow
the worker both to post a bond (which
would require s k0 < 0) and receive a salary
(which would require s k0 > 0). As a result,
I am not sure that the model can be
considered a general case of the previous
models in the effort-elicitation literature.
An alternative interpretation of the salaryvs.-performance-pay distinction in the
DRW model would be that some average
value of the end-of-production payment
(which could be denoted s C ) would be
more like a salary, while the time-varying
payments (sCk ) are similar performancebased pay. The point is that a salary is
generally a constant payment received by
the worker regardless of how much output
is produced, yet if production does not
take place, no salary is received.
A larger microeconomic goal of
the paper is to investigate the effects of
nonverifiability of effort in employment
relationships. To make the model tractable,
the authors make some simplifying
assumptions expressed in inequality 1.
One implication of the assumptions is
that the promise of continuing the job
is generally not enough to preserve a
current match in the bad state today,
unless there is some verifiability of effort.
Basically, firms and workers will not
stick it out through the bad times in
order to enjoy the good times again later
on. As the paper shows, however, the
continuation value of the job in the
different states (the g’s) are themselves
functions of the common discount factor
(b), the probability of the bad state (r),
and the relative levels of the productive
outcomes (zG and zB). Therefore, underlying
the assumptions in inequality 1 are implicit
assumptions about preferences and the
stochastic properties of aggregate shocks.
Indeed, firms and workers may want to
endure the bad times even without verifiability—if the discount rate is small enough
or bad aggregate shocks are rare enough—
but particular values of the underlying
parameters, which imply that verifiability
is required for a robust contract, are
not obvious.
A third comment on the micro-structure
of the model involves the relationship of
this model to work involving specific
investments in the employment relationship.
Papers by Caballero and Hammour stress
the “fundamental transformation” that
employment relationships undergo when
searching workers and firms find one
another, or when either side of the employment relationship invests in capital that
is specific to the match. Both of these
phenomena transform the employment
relationship into a bilateral monopoly
where the ex ante terms of trade may not
carry over to the ex post Nash bargain over
the surplus in the match. In reading this
paper, I was curious to know whether
there was a simple mapping between its
shirking interpretation and the specific
capital basis of other work. It may be that
the shirking model is a particularly strong
form of the specific capital model. For
example, consider the type of specific capital that is created simply when a searching
worker finds a specific job. Match capital
is created because the firm no longer has
to pay the costs of posting the vacancy and
the worker can start earning wages rather
than spend time looking for a job. The
outside alternatives of the worker, the firm,
and the exogenously determined bargaining
weights (the p ’s) determine how the surplus
is divided in both models; though in the
DRW setup, the worker or the firm receives
an additional reward (the benefit to shirking)
if the match breaks up. In the specific capital model, a party who leaves the match
does not receive this type of benefit. It
would be interesting to know if there is a
simple way to link both the shirking and
specific-capital interpretations of the
employment relationship.
One way that ex ante terms of trade
can be reflected ex post in the employment
match is when the workers post a bond.
One of the cases discussed by the authors
is that of “limited liquidity,” which argues
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that low liquidity may prevent workers
from paying a bond. The inability to pay a
bond opens up the possibility that efficiency
wages may be paid in order to elicit effort.
Several economists, however, have pointed
out that the utility cost of a bond payment
may vary inversely to the worker’s liquid
assets. Workers with low liquidity may
find it hard to post a bond, but it is
precisely these workers who will be
quite averse to shirking and losing their
bond if they get caught shirking. Of
course, the power of very small bonds to
motivate liquidity-constrained workers
depends on marginal utility going to negative infinity as assets go to zero, so the
outside benefits, b, may prevent this from
occurring in the DRW setup.
I now turn to the macroeconomic
implications of the model. One of the key
questions in cyclical macroeconomics is
why so many employment relationships
break up during recessions. Pioneering
work by Davis, Haltiwanger and Schuh
showed that (at least in manufacturing)
the drop in employment that occurs when
recessions begin comes not from a decline
in the creation of new jobs, but rather, a
large spike in the destruction of existing
jobs. Several authors have suggested that
the spike in job destruction at the onset of
recessions may be linked to the economy’s
amplification mechanism, by which moderate innovations to productivity or
aggregate demand may bring about large
movements in employment and output.
Not surprisingly, a number of theories to
explain the burst in job destruction have
been advanced. One branch of the literature stresses “cleansing” effects of
recessions. Large numbers of jobs are
destroyed in recessions because a large
number of jobs are typically close to the
margin of unprofitability at any point in
time. Convex job-creation costs for the
aggregate economy mean that it is more
efficient for these older jobs to be destroyed
than for the rate of new job creation to drop.
A second branch of the job destruction literature stresses the “pit stop” role of
recessions. Just as the real business cycle
literature contends that recessions are a
good time to enjoy leisure, that pit-stop
view suggests that recessions are good
times to reorganize production.
This paper can be placed in a branch
of the economic literature that contends
that the increase in job destruction is a
primary result of some imperfection or
friction in the labor market; here, the friction is nonverifiability. Other papers of
this kind suggest that job destruction is
high during recessions because wages
cannot fall. Two potential causes of wage
rigidity are the suppression of wage renegotiation (since bargaining is costly and
may encourage opportunistic behavior)
and efficiency wages (the need to motivate
workers provides a floor through which
wages cannot fall). The DRW model suggests that nonverifiability, rather than the
suppression of negotiations or efficiency
wages, can better explain the cyclical
dynamics of the labor market. The authors
implicitly argue against the suppression
of the renegotiation model by having the
worker and firm bargain at the start of
every production period. The suppressed
renegotiation models imply that the firm
and the worker would like to renegotiate
and stay together, but doing so would result
in redoing the employment contract and
thereby violate some social norm. The
DRW paper suggests, in contrast, that
firms and workers are not averse to
renegotating, but they prefer to separate in
bad times because they cannot make a
credible promise not to shirk without
external verifiability.
The paper argues against the efficiencywage-model-with-verifiability more explicitly
with the experiments displayed in DRW’s
Figure 2. Recall that efficiency wages arise
in the DRW framework if workers are unable
to post a bond and the value of the final
payment they can receive at the end of
production is not large enough to prevent
them from shirking. In this case, the firm
must raise the worker’s total compensation
(here, just the final payment) above the
level implied by the worker’s bargaining
weight, p w. In this way, the worker is
encouraged not to shirk and an efficiencywage trade-off arises. This is due to the
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M AY / J U N E 1 9 9 9
inverse relationship between the total
compensation of the worker and his incentive to shirk. The firm is prevented from
shirking because of the verifiability
assumption. Should it fail to provide high
effort, the court will assess a payment to
the worker of sA. The efficiency-wage
cases analyzed in Figure 2 are, therefore,
ones of robust contracts, because the efficiency wage and the monitoring of the
firm by the court combine to keep the parties honest. Figure 2 shows that the three
verifiable contracts result in little amplification of shocks, which are modeled as an
increase in the breakup parameter r. Even
the two contracts that imply efficiency
wages are robust, in part because firm
behavior can be verified. On the other
hand, the nonverifiable (“severance
payment only”) contract results in substantial amplification of the increase in r.
Employment relationships break up
because no mechanism exists to ensure
high effort.
My main concern with this result
is that I am not sure it portrays efficiency
wages in the most familiar way. The
efficiency-wage model in this paper is
essentially backloaded compensation,
which is paid only when the worker does
not shirk, an event that is detected with
probability one. (Of course, there may
be an incentive for the firm to shirk when
compensation is backloaded, but the courts
are assumed to regulate the firm’s behavior
since verification is assumed in these cases.)
Another interpretation of efficiency wages,
however, might affirm that they arise
when worker misbehavior is detected only
imperfectly and, therefore, the workers may
consider the shirking decision differently.
The differences in the two interpretations
for macro behavior of the two views of efficiency wages are not obvious immediately.
Another question I have is how general
equilibrium effects work in the macro simulations of DRW’s Figure 2. The general
equilibrium is important because the previous work by Caballero and Hammour
has shown that high unemployment
during a recession can result from wage
rigidity engendered by specific-capital
investments. The high unemployment
is an equilibrium response of the economy
to wage rigidity, as it disciplines the wage
demands of insiders. I am curious to know
whether a similar effect is operating here.
All in all, I found this paper well
worth the time and effort it took to study
the subject carefully. And I hope the
graduate students enrolled in my next
“Macroeconomics of the Labor Market”
course do so as well.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
72
M AY / J U N E 1 9 9 9
Gilles Saint-Paul is a professor at Universitat Pompeu Fabra and a fellow of the CEPR. He is grateful to the Bank of Spain and the Centre
de Recerca en Economia Internacional, Universitat Pompeu Fabra, as well as Chris Waller and participants at the Federal Reserve Bank of
Saint Louis annual conference, and seminar participants at the Bank of Italy, Rome and CEMFI, Madrid for helpful comments and suggestions.
Assessing
the Political
Viability of
Labor Market
Reform:
The Case of
Employment
Protection
wage. In 1994, the Swedish government
lost the elections because it had lowered
the unemployment benefit replacement
ratio from 90 percent to 80 percent. After
reunification, the German government
gave in to western unions’ pressure and
allowed eastern wages to converge rapidly
to western levels, despite large productivity differentials and the need to restructure
the eastern economy, which led to substantially higher unemployment rates in the
East than in the West.
In my view, an understanding of the
political determinants of labor market
institutions is a crucial prerequisite for
being able to implement structural reforms
that are acceptable to those social groups
that potentially may block these reforms.
While we believe that the set of institutions that prevail in many European
countries form a coherent whole, given
the complexity of the issue it is often
more convenient to analyze these institutions separately from each other. In this
paper we focus on employment protection
legislation (also called “firing costs”). We
want to know who gains and who loses
from such regulation, and what will be
the equilibrium level of employment
protection. We abstract from other rigidities—we do not ignore them, but take
them as given, ignoring that they, too,
are the outcome of the political process.
Why firing costs rather than other institutions? This is partly a matter of taste and I
have discussed other institutions elsewhere.1
But there are several reasons why employment protection is more relevant than other
rigidities when one deals with the political
economy of reform. First, it is regularly
pointed out by employers as one of the
most severe constraints on their incentives
to create jobs. Second, it is somewhat more
renegotiable than minimum wages or unemployment benefits. Some reductions in firing
costs have been observed in various countries
in the eighties and nineties. We have not
seen similar reductions in unemployment
Gilles Saint-Paul
T
here is somewhat of a consensus
among economists that labor market
rigidities are responsible for high
unemployment in Europe, and in particular for its most alarming aspects such as
its long duration and high incidence on
youth. Unemployment benefits lower
the incentive for job search and increase
wage pressure by insiders. Minimum
wages price the least skilled out of the
market. Firing costs deter hiring, thus
reducing labor demand, and hamper the
economy’s ability to deal with uncertainty and structural change. This is
why experts frequently recommend
making the labor market more flexible,
as is exemplified by the conclusions of
the recent OECD Jobs Study (1995).
But, in practice, few of the remedies
economists advocate pass the test of political viability. In 1994, an attempt by the
French government to lower the minimum
wage for young workers was followed by
violent demonstrations, and the government eventually withdrew its reform proposal. In 1995, in order to be elected, a
French presidential candidate put on its
platform an increase in the minimum
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
73
1
For example, Saint-Paul
(1996a, b).
M AY / J U N E 1 9 9 9
2 See Saint-Paul (1996b).
3 See, for example, Bentolila
and Bertola (1990).
4 See Cohen, Lefranc, and
Saint-Paul (1997), Blanchard
and Portugal (1998).
compensation or minimum wage laws.
Unemployment benefits are seen as part of
the “welfare state” and attempts to reduce
them often are interpreted as a first blow to
the whole welfare state, while the minimum
wage is often an untouchable symbol.2 Third,
while firing costs’ impact on employment is
actually unclear,3 they clearly increase unemployment duration. If anything, the key
difference between Europe and the United
States is not so much the former’s higher
unemployment rate—which partly reflects
composition effects and a greater incentive
to register as unemployed—as Europe’s much
larger unemployment duration.4
Behind the political support for
employment protection lies the existence
of rents in favor of the employed, which
arise due to imperfections in the labor
market. We understand firing costs as a
device to protect the rents of incumbent
employees. The greater these rents, the
greater their incentive to support protective measures.
We define the “rent” as the welfare
differential between an employed and
an unemployed worker. In a perfectly
competitive labor market, this differential
should be equal to zero, because any worker
looking for a job would find one instantaneously at the going equilibrium wage.
Thus, there would be no welfare difference
between the employed and the unemployed. In practice, the employed have
rents, that is, they are strictly better off
than the unemployed. The size of these
rents depends on their bargaining power
(their ability to prevent the unemployed
from underbidding them, which itself is
affected by labor market institutions), and
also how closely their work effort can be
monitored by employers. The rent is a
measure of how far wage setting is from
competitive behavior; the higher the rent,
the less competitive wage formation and
the higher the natural rate of unemployment. Most of the essence of labor market
reform is about eliminating the rent. This
is certainly true of any reform of the minimum wage and the bargaining process, or
of any change that makes it easier for outsiders to compete with insiders: hiring
rules, work rules, and many aspects of
employment protection. Here, however,
we take the workers’ bargaining power as
given, and consider what happens when
people vote on a firing cost that does not
directly affect their bargaining power.
Rents have important consequences
for the political preferences of incumbent
employees. This is because the rent tells
us how much they lose if they lose their
jobs, or how much they are willing to pay
for keeping them. The greater the rent, the
greater the aversion of insiders to unemployment and the greater the political support for employment protection legislation.
Employment protection legislation is complex; it associates to each cause of firing a
set of constraints imposed on the employer.
These constraints include severance payments, administrative supervision, obligation to provide the displaced workers with
job counseling and to give them priority
over hiring by the same conglomerate,
unions’ right of scrutiny and appeal, etc.
To some extent, these constraints increase
the employee’s bargaining power by making it more difficult for the employer to
resist wage demands by refusing to employ
the worker any longer. The direct effect
of firing costs, however, is to make it more
costly for the firm to adjust its labor force
when facing a fall in demand. Because
we want to isolate the pure employment
protection effect of firing costs, we shall
assume that it does not affect the workers’
bargaining power.
Unlike my previous work on the same
topic (Saint-Paul, 1993, 1997), this paper
pays a lot of attention to the role of firing
costs in the growth process when obsolescence—or “creative destruction”—is an
important aspect of growth. In our vintage
capital model, each match gradually
becomes obsolete (because its productivity
fails to catch up with the latest technology)
until it is destroyed, at which time the worker
becomes unemployed. We assume people
vote between two levels of the firing cost
(a “flexible” and a “rigid” one). In our
model, firing costs increase the life span of
any match by inducing firms to postpone
the date of economic obsolescence.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 1 9 9 9
In voting in favor of employment protection, incumbent employees trade off
lower living standards (because employment protection maintains workers in less
productive activities) against longer job
duration. The support for employment
protection will then depend on the value
of the latter relative to the cost of the former. We highlight two key determinants
of this trade-off: first, the workers’ bargaining power; second, the economy’s growth
rate—more precisely its rate of creative
destruction. Let us explain briefly the
mechanisms that underlie the effect of
these two parameters.
The rent. The value of longer job
duration to incumbent workers is proportional to the rent, or equivalently, their
bargaining power; long job duration would
not be valued if the employed were not
earning rents above the unemployed. The
cost of job loss would then be zero, and so
would the support for employment protection. This result tells us that there exists
a “complementarity” between firing costs
and other labor market rigidities to the
extent that the latter increases workers’
bargaining power.
One important consequence is the
existence of complementarities across
policy reforms. A comprehensive labor
market reform attacks those rigidities—
one that increases workers’ bargaining
power at the same time that it reduces firing costs—is more likely to be successful
than one that only tackles the latter aspect.
Creative destruction. Firing costs reduce
the economy’s average productivity by maintaining a fraction of the workforce in vintages
that are older than the most up-to-date technology. In equilibrium, this ends up reducing
wages and living standards. Now, this effect
will be stronger, the greater the productivity
gap between old vintages and new vintages,
that is, the greater the growth rate. A higher
growth rate consequently reduces the political
support for employment protection legislation, because it increases its cost in terms of
lower wages.
We show that the political support for
firing costs typically comes from a fraction
of the employed workers: those who work in
matches that are not too old, nor too young.
In the first case, workers are going to lose
their jobs quickly; they are better off unemployed in a flexible society than employed
in a rigid society. In the second case (which
may be degenerate and reduced to an empty
set), workers consider that the end of their
job is pretty remote and are not willing to
pay the cost of employment regulation.
We supplement our analytical reasoning
with some evidence suggesting that increases in firing costs tend to occur at times when
workers’ weight in bargaining is high, and,
conversely, reductions in firing costs take
place when bargaining power is low. This
is in accordance with our model.
EMPLOYMENT
PROTECTION IN A
RENOVATING ECONOMY
Let us consider a world with different
vintages of capital.5 At any point in time
t there is a state-of-the-art technology that
allows production of at units of output
with one unit of labor, where at is assumed
to grow at a constant exogenous rate g, so
that at = a0 e gt. There is free entry of firms
(considered as hiring a single worker) in
the state-of-the-art technology; but once
a firm has entered, it cannot upgrade. It is
stuck with the level prevailing at the time
of entry.
If exit were costless, firms would enter
the market for a very small amount of time
and then disappear, because competition
by new entrants would constantly drive
wages up to the state-of-the art technology
level, thus making any old plant unprofitable. We assume, however, that exit is
costly so that in order to close at time T
the firm pays a firing cost in terms of output, equal to FaT .6 We assume that this
firing cost is wasted. Firing costs imply
that unprofitable plants, instead of closing,
will continue until losses become so large
that it is actually preferable to pay the firing cost and close the position. By the
same token, for new jobs to be created,
it must be the case that they run positive
profits in the beginning of their lifetime,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
75
5 This is in a fashion somewhat
similar to Caballero and
Hammour (1994). Another
option would be to rule out
growth and assume that once
in the market, firms suffer
shocks to their productivity
level, and that they can freely
enter the market at the maximum possible level, as in
Mortensen and Pissarides
(1994) or Saint-Paul (1997).
6 Dependence on the productivity
trend implies that the firing cost
grows at the same rate as the rest
of the economy, and, therefore,
does not become negligible relative to the surplus of a match.
M AY / J U N E 1 9 9 9
to compensate for the future losses associated with the firing cost. Therefore, wages
cannot be as high as the state-of-the art
technology level, contrary to what would
happen absent exit costs.
Firms and workers can freely borrow
and lend at the real interest rate r. We
assume r > g, which guarantees that the
present discounted value of income
streams will be well defined.
Workers are homogenous and negotiate
wages in an imperfectly competitive fashion,
thus being able to raise their welfare strictly
above their outside opportunity—that is,
the welfare of an unemployed worker.
Consequently, in equilibrium, there is a
positive stock of involuntarily unemployed
workers who wait to find a job created
by a new entrant.
At any time t the net value of a firm
that entered the market at date s is equal
to the present discounted value of its profits minus the (discounted) firing cost it
has to pay upon termination:
(1)
We now turn to wage determination.
Our key assumption is that workers can
appropriate a share of the surplus generated by the match gross of the firing cost.
Formally, this is equivalent to
(5)
where ϕ is the share of the gross surplus
that the worker is able to appropriate, bat
is the income flow of an unemployed
worker (for example, the unemployment
benefits he is paid), θ t is the probability
per unit of time that an unemployed
worker finds a job, while
(6)
− r u− t
J ( s, t ) = ∫tT ( s )( a s − w( s, u ))e ( )du
where w(s, u) is the bargained wage
between firms and workers at date u,
which will be determined below.
The firm sets its exit time optimally
by maximizing expression 1 with respect
to T(s). The first order condition is:
7 If the firing cost is large enough,
it may be optimal for the firm to
never fire the worker. In that
case the condition is:
(3) w(s, t ) − as < (r − g) Fat
∀t ≥ s
8 For a formal derivation of that
wage formation schedule, see
Saint-Paul (1998).
w( s, T ( s)) − as = (r − g) FaT ( s ) .
The left-hand side is the loss per period
made by the firm while the right-hand side
is the annuity value of the firing cost. Note
that faster growth reduces the annuity value
of the firing cost: As they are indexed on the
economy’s growth trend, postponing dismissal increases the value of the firing cost.
This effect reduces the opportunity cost of
firing today.7 Finally, the free-entry condition implies that the net value of the firm
is zero at the time it enters the market:
(4)
S(t ) = ∫ tT ( t ) at e − r ( u − t ) du
is simply the present discounted value of
the firm’s gross output.
The meaning of equation 5 is as
follows. The last term is the fraction
of the match’s output appropriated by
the worker. The first two terms are the
worker’s “alternative wage,” or outside
option, that is, the wage that would make
him just indifferent between being unemployed and working for that firm. The
first term represents the unemployed’s
flow of income, while the second term
represents the contribution to his welfare
of the future rents he will appropriate
from his next jobs. It is larger, the greater
the probability of finding a job and the
larger the share of the surplus appropriated by the worker.8
The probability of finding a job,
θ t , is the key endogenous variable
that determines the adjustment of the
labor market. Its equilibrium value is
determined by the free-entry condition,
equation 4, that requires that the net
value of a newborn firm be equal to
zero. If the labor market were too tight,
relative to that equilibrium value of θ ,
wages would be too high and new firms’
net value would be negative. Consequently, firms would not enter the
market, which would reduce the jobfinding probability and push wages
downwards to the point where the
free-entry condition is met again.
−Fa T ( s )e − r( T ( s )− t ) ,
(2)
w( s, t ) = bat + θtϕ S(t ) + ϕ as ,
J (t, t ) = 0.
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76
M AY / J U N E 1 9 9 9
EQUILIBRIUM
Figure 1
Equilibrium
Determination
We are now in a position to compute
the equilibrium of our economy. To do so,
we limit ourselves to a “steady state,” that
is, a balanced growth path where wages
and output grow at rate g, while unemployment, labor market tightness θ, and
the duration of a job are constant. Let us
call that constant duration x.
To do so, we proceed as follows. First,
note that the firm’s present discounted output, in steady state, is simply equal to
u
W
P
W
P
x
(7)
S(t ) = at
1− e
r
− rx
.
The term (1– e –rx) /r is simply the present discounted equivalent of a constant,
unit flow of income over a time interval of
length x. Substituting equation 7 into the
wage equation 5 we get that
(8)
The left-hand side is the present discounted value of profits, gross of the firing
cost,9 and the right-hand side is equal to
the firing cost. The equation tells us that
under free entry the cumulated profits
must exactly cover the firing cost. As long
as F < (1 − ϕ ) / r, equation 10 defines a
unique equilibrium value of x. If F is
greater than (1 − ϕ ) / r , then it is optimal
for firms never to close, a case we rule out
by assumption.
The equilibrium is determined in
Figure 1 by the intersection of two schedules, a downward sloping schedule WW
defined by equation 9, and a vertical one
PP defined by equation 10.
The equilibrium has the following
properties:
• An increase in ϕ , the workers’ bargaining power, shifts PP to the right
and WW downward (Figure 2a).
Consequently, the duration of
matches increases and labor market
tightness declines. An increase in ϕ
directly increases labor costs, which
reduces incentives for job creation
but makes it affordable to close later.
At the same time, profits fall, so the
job must last longer in equilibrium
in order for cumulated profits to
cover the firing cost.
• An increase in F, the firing cost,
shifts PP to the right and WW
1 − e − rx
r
− g(t − s )
),
+ϕe
w (s, t ) = at (b + θϕ
where, as previously, the first two terms
represent the alternative wage and the last
term the rent earned on one’s current job.
Using that condition, we can rewrite the
optimal closing condition, equation 2, as
(9)
1 − e − rx
r
= ( r − g ) F.
(ϕ − 1)e − gx + b + θϕ
This is a first equation that gives us a relationship between x and θ . This is a decreasing equilibrium relationship that tells us that
a tighter labor market pushes wages up, thus
forcing firms to close at an earlier time.
Next, using the free-entry condition 4
along with the wage equation 5 and with
equation 7, then making use of equation 9,
we get a second equation that determines x:
− rx
− gx
1 ge − re
(10) (1 − ϕ ) +
r (r − g)
r
= F.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
77
9 They are discounted at the
closing date of the firm and
expressed in productivity units
at that time.
M AY / J U N E 1 9 9 9
upward, (Figure 2b). A higher
firing cost makes it optimal to
postpone the closing time, and
jobs must last longer for cumulated
profits to cover the firing cost.
Despite the upward shift in WW,
θ unambiguously falls: Labor
market tightness is reduced as
increased firing costs discourage
hirings. The upward shift in WW
simply means that at any given job
duration, one would require higher
wages and therefore tighter labor
markets for closing to be optimal.
• An increase in g, the growth rate,
unambiguously shifts PP to
the left while WW shifts down
(Figure 2c). Faster growth
increases the pace of obsolescence via more rapid wage growth
within existing matches, and also
because the growth of firing costs
is faster, as they are indexed on
the economy’s average productivity level. The incentives to fire
are therefore increased: Matches
are shorter (PP shifts to the left),
while the degree of labor market
tightness that makes it optimal to
fire falls (WW shifts down). The
net effect on θ is ambiguous as
WW is downward sloping.
Next, it is possible to characterize the
equilibrium unemployment rate and the
steady-state distribution of employment
across vintages. In steady state, the density
of employment in firms aged z is constant
and equal to 1/x. If l is total employment,
then the number of jobs destroyed per unit
of time is l/x. In steady state, this must be
equal to the outflow from unemployment,
which is equal to θ (1 – l). This allows us
to compute the unemployment rate as a
function of θ and x:
Figure 2a
Impact of an increase
in worker's weight
in bargaining
u
W
P
W
P
x
Figure 2b
Impact of an increase
in firing costs
u
P
W
P
W
x
Figure 2c
Impact of an increase
in the growth rate
u
W
P
(11)
W
u=
1/ x
1
=
.
θ + 1 / x 1 + xθ
P
x
It should be noted that unemployment
is not necessarily higher when firing costs
are lower. A lower firing cost increases θ ,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
78
M AY / J U N E 1 9 9 9
which tends to reduce u, but reduces x,
which tends to increase u. Job creation
is higher but so is job destruction, so
unemployment may either rise or decline.
This is well known from the analysis of
firing costs.10
One can further compute aggregate
output in steady state. It is simply equal
to the product of employment and average
productivity. Given that employment is
uniformly distributed over all vintages,
the latter is simply equal to
assume that there are only two alternatives, reflecting the fact that there is some
indivisibility in the design of legislation
and that political agendas are often formulated in a binary fashion. We will typically
consider that the status quo is the “rigid
society,” so that initially workers are distributed over plants aged between 0 and x R .
We also assume, for simplicity, that when
we do comparative statics the underlying
values of the firing costs FR and FF are
altered so as to maintain the two options
invariant in terms of plant duration.
at ∫0x e − gu du
1 − e − gx
= at
.
x
gx
The Shape of Preferences for
Employment Protection
The first step is to compute the utility
of the employed and unemployed voters as
a function of the collectively decided firing
cost. The utility of the unemployed is
given simply by the present discounted
value of the alternative wage, that is, of the
first two terms in 8. Its value is
At any point in time t output is therefore equal to
yt = at
θ 1 − e − gx
.
1 + xθ
g
Note that in the extreme case, where
the firing cost goes to zero, so does x, while θ
goes to infinity. The labor market converges
to a situation where both the job creation
rate and the job destruction rate are infinite.
As technology changes continuously and is
embodied into new vintages, it is optimal to
close firms an instant after they have been
created. As a result, people move constantly
between employment and unemployment:
It is as if unemployment were equally
shared among the workforce. Furthermore,
because of free entry, the wage is always
equal to at, the state-of-the art productivity,
and is higher than it would be for any positive level of the firing cost.
With that discussion, we conclude the
characterization of equilibrium. We now
proceed and discuss voting on firing costs.
Vu ( t ; x ) =
a 0e gt
r−g
1 − e −rx
× b + θϕ
r .
As future alternative wages grow at
rate− g , this stream of income is discounted
at rate r − g . Substituting in the equilibrium conditions, equations 9 and 10, we see
that this is equivalent to
(12)
Vu ( t ; x ) =
a 0e gt
(1 − ϕ )
r−g
1 − e −rx
.
× 1 − g
r
VOTING ON FIRING COSTS
This formula allows us to express the
utility of the employed as a function solely
of the equilibrium value of plant’s lifetime, x.
As for the utility of employed workers,
it depends on which plant they are working at. The older the plant, the lower the
time left for reaping their rent, and the
In the sequel, we will assume that
society votes once and for all between
two alternatives: a “rigid” society associated with a firing cost FR and a plant life x R ,
and a “flexible” society associated
with FF < FR and x F < x R . Therefore, we
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
79
10Bentolila and Bertola (1990).
M AY / J U N E 1 9 9 9
lower their utility. More precisely, an
employed’s utility is the sum of an unemployed’s utility and the present discounted
value of the employed’s share of the gross
surplus between now and the closing time.
The corresponding value is
highest probability of finding a job and
the highest wage, it is the one preferred
by the unemployed.
Turning now to the employed, equation 13 implies that their utility is always
decreasing with z and increasing with x
if and only if
1 − e − rx 1 − ϕ
(13) Ve (z , t; x ) = a 0e gt 1 − g
r r − g
−r x −z
1−e ( )
; z ≤ x.
+ϕ e − gz
r
(14)
e( r − g) z >
g(1 − ϕ )
.
ϕ (r − g)
For any given x, workers in older
firms have a lower utility than workers
in younger firms, as they expect their rent
from employment to be exhausted earlier.
The marginal gain from increasing
firing costs is larger, the older the vintage
where the worker is working. This is
because the remaining duration of their
job increases more, in proportional terms,
than those of workers at younger plants.
Consequently, a marginal increase in firing
costs would be supported by those workers whose vintage is greater than a critical
z*, defined by
The last term in the brackets represents the present discounted value of the
rent to be earned until the current job
elapses. It is larger, the larger the voted
value of x, and smaller, the larger the
current age of the job z.
It is important to note that equation 13
is only valid if x ≥ z . Once people have
voted on x, all firms with age z > x, if any,
instantaneously disappear and fire their
workers. Therefore, the utility of any
worker in a plant older than x is by definition equal to the utility of an unemployed:
g(1 − ϕ )
ln
ϕ (r − g)
z* =
.
r−g
Ve ( z, t; x ) = Vu (t, x ), z ≤ x .
This property tells us that in some
sense workers at older plants like firing
costs better, but it should be remembered
that we actually rule out voting on a marginal increase in firing costs as we only
consider two alternatives.
Note that if
In equations 12 and 13, F is treated as a
function of x as defined by equation 10; that
is, voting on F or voting on x are equivalent
given the relationship between the two that
must hold in equilibrium. In the sequel, we
find it easier to consider that workers actually vote between two values of x.
How do, now, the preferences of the
people for firing costs depend on their labor
market status? Beginning with the unemployed, equation 12 clearly implies that
their utility is strictly decreasing with x. The
unemployed prefer the lowest possible value
of x (or, alternatively, F). In the F = 0 equilibrium, people move constantly between
employment and unemployment so that it
is as if the total amount of work were shared
perfectly among people. The incumbent
employee’s advantage for tomorrow’s jobs
is eliminated; as this equilibrium yields the
(15)
ϕ > g / r,
then the numerator is negative (or equivalently, the right-hand side of 14 is lower
than 1), which implies that all employed
workers benefit from a marginal increase
in firing costs.
In the sequel, we shall assume that
condition 15 holds, and discuss the
case ϕ > g / r later.
Figure 3 illustrates how preferences
depend on x for various types of workers
in the case where ϕ > g / r . The down-
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
80
M AY / J U N E 1 9 9 9
ward sloping curve Cu represents the
preferences of an unemployed worker.
C0 represents the preferences of a worker
at a newly created plant. Cz represents
the utility of a worker at a plant of age
z for x > z. It is important to note that
for x < z, his utility is given by Cu . Cz ′
represents the utility of a worker with
z ′ > z . As z increases, Cz shifts down
and its slope shifts up. While people
employed at old plants enjoy firing costs
more at the margin than people working
at new plants, they also are increasingly
unhappy as the age of their plant increases.
Figure 3
Preferences according to plant age and
employment status
C0
Cz
C z’
Cu
Voting Between Two Values of the
Firing Cost
z
We now turn to the question of who
will favor flexibility and who will oppose
it when people choose between x R and x F.
Figure 3 is a useful starting point. As the
unemployed’s utility is monotonically
decreasing in x, they clearly support the
lowest value of the firing cost. What about
the employed? They typically split into
two groups, as illustrated in Figure 4. There
exists a critical plant age z̃ such that workers in plants older than z̃ favor flexibility
while workers below z̃ favor rigidity. In
the rigid society, workers at plants of age
z̃ get exactly the same utility as an unemployed worker of the flexible society.
Workers of the first group are in a
match that is about to expire. They have
consumed most of their rent and expect
to be soon unemployed and to suffer from
the low job creation rate and the low productivity of the economy. They would be
better off either with an increase in firing
cost beyond x R, but such an increase is not
on the political agenda, or with a decrease
in firing costs. Thus, if the status quo is
the rigid society, they end up voting for
the flexible one. The reason why this
“lost generation” prefers flexibility is that
they will soon be constrained to a “new
start” anyway, and the flexible society is
the one that gives them the best chances.
If the status quo is the flexible society, this
group would not exist since z̃ is always
greater than x R.
z’
x
Figure 4
Interest groups among the employed,
>g/r
ϕ
C0
C ~z
Group 1
Cu
Group 2
xF
~
z xR
Workers such that x F < x < z˜ prefer
to maintain the rigid society: They will lose
their jobs if the economy were to shift to
flexibility, and their jobs will last long
enough to make rigidity worthwhile for
them. Workers such that x < x F will not
lose their jobs if the economy becomes flexible. They prefer the rigid society because it
increases the length of time over which they
reap their rent, while the prospects of job
loss is too remote for them to worry about
the low rate of job creation.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
81
x
M AY / J U N E 1 9 9 9
Effects of Growth and Workers’
Bargaining Power
Their net loss from rigidity is decreasing
with ϕ . As ϕ increases, other labor market
rigidities are more important relative to firing costs in reducing the unemployed’s job
prospects so that their welfare loss between
the high and low firing cost societies is
actually reduced.
Finally, those workers who would
lose their jobs if the economy were to shift
from rigidity to flexibility have a gain from
flexibility equal to
How do the parameters of the model
affect the outcome? The two parameters in
which we are most interested are ϕ , the
workers’ bargaining power, and g, the
growth rate.
To analyze the effect of these parameters, it is useful to distinguish between
three groups: those who work at a vintage
young enough (z < xF) so that they would
be employed in both the rigid and the flexible world; the unemployed; and those
who are employed in the rigid world but
would lose their job if society decided to
become flexible (z > xF). Let us start with
an increase in the workers’ bargaining
power ϕ. In general, for a given F, a change
in ϕ affects x. Now, for simplicity, we
assume that the two alternatives are specified in terms of x rather than F. That is, we
assume that the two job lengths x R and x F
do not change. As equation 13 shows, an
increase in ϕ reduces the first term in brackets—the value of being unemployed—but
increases the second term—the rent. As
rents are higher, incumbent employees are
more in favor of employment protection.
Consider workers that would be
employed in both worlds, that is, such
that z < x F . Their net gain from being in
the rigid world instead of the flexible one is
Ge′ ( z, t; x ) = Ve ( z, t; x R ) − Vu ( z, t; x F )
e − rx F − e − rx R 1 − ϕ g
= a 0e gt −
r−g r
r
− r( x R − z )
1−e
+ ϕ e − gx
r
(
)
= Vu (z , t; x R ) − Vu (z , t; x F )
(
+ Ve (z , t; x R ) − Vu (z , t; x R ).
This is the sum of the (negative)
welfare gain of the unemployed, which,
as we have seen, increases with ϕ and
the employee’s rents in the rigid economy,
which also clearly increase with ϕ . Thus,
these people gain more, or lose less, from
rigidity when ϕ increases.
Therefore, in an economy with a high
value of ϕ —powerful employees—a given
individual, whether working in a plant of
any age z or unemployed, will always be
more in favor of rigidity than in a world
were ϕ is low. Is it obvious, then, that the
political support for the rigid society is
greater? The answer is no. For it is also
true that unemployment is higher when ϕ
is large, which tends to push up the number of people who oppose rigidity, even
though these people lose less from rigidity than if ϕ were small. What is clear,
however, is that within the employed, the
support for rigidity increases, meaning
that the critical plant age increases.
( z̃ must satisfy Ge′ ( z˜ , t; x ) = 0 , and that
function is decreasing with z and shifts
up when ϕ increases.) If labor market
institutions were mostly determined
by the employed, say because they are
Ge ( z, t; x ) = Ve ( z, t; x R ) − Ve ( z, t; x F )
e − rx F − e − rx R
=
r
1−ϕ g
gt
× ϕ e ( r − g )z −
a 0e .
r −g r
This is clearly increasing with ϕ . As for
the unemployed, their welfare difference
between the two economies is
Gu (t; x ) = Vu ( z, t; x R ) − Vu ( z, t; x F )
e − rx F − e − rx R 1 − ϕ g
gt
= −
r − g r a0 e .
r
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82
M AY / J U N E 1 9 9 9
better organized collectively or because
the unemployed have a low rate of participation in elections, then the political
support for rigidity would unambiguously
increase when ϕ rises. Another way to
put it is to say that controlling for the
unemployment rate, the high firing cost is
more likely to be chosen when ϕ is higher.
What happens, now, when the growth
rate is larger? If we compare the high
growth economy and its low growth counterpart at two points in time when they
have the same technological level, which
amounts to holding a0egt constant in our
comparisons, the above formulae imply
that an increase in g reduces Ge, Gu, and
Ge′ . Consequently, faster growth unambiguously reduces the political support
for employment protection if we hold the
stock of unemployment constant.
The growth rate acts in two ways.
First, it increases the obsolescence rate
and, therefore, the deadweight cost of
maintaining relatively unproductive
matches idle. This in itself reduces the
support for employment protection.
Second, faster growth tends to reduce
the effective discount rate applied to the
future: Incumbent workers put more
weight on the lower job finding rate they
will experience once their current match
is dissolved, because future jobs pay more.
This also tends to reduce the support for
employment protection.
Figure 5
Three groups in the
ϕ <g/r case
C
0
C z*
C~
z
Group 1
Group 2
z*
x
F
Group 3
~z
x
R
plants older than z̃ are about to lose their
jobs and oppose rigidity for the reasons
already explained. Those who work in
plants between z* and z̃ gain more from
rigidity than what they lose. Thus, among
the employed, labor market reform (in the
sense of a deregulation) would be supported by an “extreme coalition” of people
working in either the most dynamic plants
or plants that soon will become obsolete.
Another property of this case is that
the maximum welfare point is actually
attained at x = 0. Since workers at young
plants are always happier, given x, than
workers at old plants, and since those at
plants just created (z = 0) have a utility
which is decreasing with x, there would
be unanimity in favor of a zero firing cost,
if this is a feasible outcome.
Conversely, if the status quo is x = 0
then all employed workers work in plants
of age z = 0. A necessary condition for
zero firing costs to remain a political equilibrium is therefore that workers at plants
with z = 0 would be worse off if firing costs
were higher, which given equation 14, is
precisely equivalent to ϕ < g / r .
Therefore, for a “flexible” society to
be stable (in the sense that people will
not want to change its institutions), it
must be the case that the worker’s share
The ϕ < g/r Case
What happens now if ϕ < g / r ?
Equation 14 implies that workers with
sufficiently small z will have a utility
strictly decreasing with x. As illustrated
on Figure 5, the flexible society is preferred by a group of workers who work
in the most recent plants. These workers
lose more, in terms of lower wages, than
they gain in terms of a postponed dismissal. There are now three interest
groups among the employed. Those
who work at plants younger than z* have
a utility that is decreasing with the firing
cost, so that they will always prefer the
flexible economy. Those who work at
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
83
x
M AY / J U N E 1 9 9 9
of the surplus does not exceed the ratio
between the growth rate and the interest
rate. This simple formula (which we are
tempted to label the “golden rule of flexibility”) is a useful shortcut for thinking
about the determinants of the political
support for flexibility.
approach would be to take the share of
labor in national income. This share,
however, typically reflects other phenomena as well, such as variations in factor
inputs as a reaction to changes in factor
prices. Bentolila and Saint-Paul (1998)
show that such movements are associated
with a relationship between the labor share
and the capital/output ratio. To proxy for
workers’ bargaining power, we just take
the residual of a first-difference regression
of the labor share on the capital/output
ratio.11 Our results are conditional on
the validity of that proxy, which clearly
may be questioned. The capital/output
ratio filters out many sources of movements of the labor share unrelated to bargaining power, but other sources remain.12
One should also keep in mind that our
measure is positively related to the economic cycle, so that correlation between
that measure and the timing of reforms
may also capture other mechanisms. The
results we present, therefore, should be
interpreted with caution.
Figures 6 through 10 represent the
evolution of our measure of the workers’
bargaining power for the five largest
European countries. These figures are not
comparable across countries and the initial
value cannot be interpreted. Only the evolution within each country is meaningful.
The evolution of our measure is somewhat related to the reforms that actually
took place.13 For example, in Spain, our
measure dropped sharply between 1978
and 1984, suggesting the opening of a
“window of opportunity” for reducing firing costs in 1984. It is precisely that year
that a major reform was introduced with
the liberalization of the use of temporary
contracts. Prior to that reform temporary
contracts mostly were restricted to work
of temporary nature, as in many other
European countries, and temporary contracts only accounted for 10 percent of the
workforce. In 1984, however, the government made it possible to use those contracts over a wide range of circumstances.
This amounted to a substantial reduction
of firing costs as employers could simply
hire a worker on a temporary contract
ASSESSING THE VIABILITY
OF LABOR MARKET
REFORMS: DO GOVERNMENTS REDUCE FIRING
COSTS WHEN BARGAINING
POWER IS LOW?
11See Bentolila and Saint-Paul
(1998) for more details.
12Again, we refer the reader to
Bentolila and Saint-Paul
(1998) for a detailed analysis.
13See Saint-Paul (1996b) for
a discussion of these reforms
and their determinants. In
that paper, I actually ignore the
role of workers’ rent, focusing
on the employed’s exposure to
unemployment and on the number of unemployed workers as
factors important for the viability
of reform.
The above analysis suggests that
there are three important determinants
of reform, namely the workers’ bargaining
power, the growth rate, and the interest
rate. It is, therefore, tempting to take
these predictions to the data and see how
they square with reality. Now the question
arises of how literally one can interpret
our results. For example, the importance
of the growth rate, in our analysis, captures the role of the rate of renovation of
old plants in the long run. By contrast,
macroeconomic data on growth mostly
capture cyclical fluctuations and changes
in the underlying trend of productivity
that may not be associated with changes
in creative destruction. The real interest
rate may not play a big role if incumbent
employees have only an imperfect access
to capital markets.
Furthermore, what is relevant for
people’s voting behavior is not the current
level of the growth rate and the interest
rate, but the whole path that they are
expected to follow in the future.
For that reason, we prefer to focus
on perhaps the most robust prediction of
the model, that is, the positive relationship
between the workers’ bargaining power
and the support for employment protection.
Our strategy is to construct a time series
for that bargaining power for a selection
of European countries and see if it bears a
relationship with the timing of reforms.
How can one construct a proxy for
workers’ share in bargaining? One simple
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
84
M AY / J U N E 1 9 9 9
Figure 6
and fail to renew that contract when it
expired if they wanted to get rid of the
worker. The graph for Spain tells us that
this reform came into effect at a time when
the rent of the employed had substantially
declined from the peak it had reached in
the mid-seventies, so that the resistance
of the insiders to such a reduction in
firing costs was considerably lower than
if one had attempted to implement it in,
say, 1980.
In the United Kingdom, the fall in
workers’ bargaining power apparently
occurred earlier than in Spain, so that
the window of opportunity began in the
late seventies/early eighties. Again, this
squares with our theory, because this interval coincides with the rise to power of a
conservative government, who subsequently engaged in comprehensive labor
market reform, including a reduction
of firing costs. Note that despite these
reforms, workers’ bargaining power seems
to go up again thereafter; this captures the
high wage inflation of the second half of
the eighties, but there was no reversal of
the reforms.
In France, the decline of workers’ bargaining power occurs somewhat later than
in Spain and the U.K.; but again, the opening of the window of opportunity, 1986,
coincides with the rise to power of a conservative government and a reduction in firing
costs—namely, the suppression of the compulsory administrative approval for layoffs,
which was established in 1974 (at a time
of rising bargaining power but before it
reached its peak). Our proxy, on the other
hand, fails to account for an increase in firing costs that was implemented in 1989
when the Left returned to power.
Reforms that reduce firing costs
have been much milder in Germany
than in Spain, perhaps reflecting a society that needs greater consensus to move
ahead and is, therefore, more likely to
stay where it is. Nevertheless, the timing
of the reform matches our analysis well.
As in Spain, temporary contracts were
liberalized in 1984 (although this was
much more timid than in Spain), after
a sharp drop of our estimated workers’
Worker's Bargaining Power, Spain
0.08
0.06
0.04
0.02
0.00
-0.02
72
74
76
78
80
82
84
86
88
90
92
94
92
94
Figure 7
Worker's Bargaining Power, U.K.
0.04
0.02
0.00
-0.02
-0.04
-0.06
-0.08
-0.10
72
74
76
78
80
82
84
86
88
bargaining power.
Of all the countries we deal with,
Italy is the one most characterized by
“stop-and-go” policies. Reductions in
firing costs alternate frequently with
increases in firing costs. For that reason,
one should not expect our proxy to work
too well. But, in fact, it does a reasonable
job at explaining the twists of policy.
Firing costs were reduced in 1977, 1984,
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
85
90
M AY / J U N E 1 9 9 9
1986, and 1987, following drops in our
measure of the bargaining power. They
were increased in 1989 and 1990, at times
when the employed’s rent appears to be
high. Finally, there was a further reduction
in firing costs in 1991, a move that our
proxy clearly fails to predict.
Obviously, this evidence is only indicative and leaves a lot of room for qualifications, alternative interpretations, and further
research. However, it is suggestive that one
can actually identify some regularities in the
timing of labor market reforms.
Figure 8
Worker's Bargaining Power, France
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
72
74
76
78
80
82
84
86
88
90
92
CONCLUSION
94
In this paper, we have studied the
circumstances under which there will
be sufficient support for a high level of
employment protection. We have argued
that two key determinants of such support
are the employed’s share in bargaining
and the rate of growth of the economy.
The political viability of a reduction in
firing costs is highest for low levels of
the employee’s share and or high growth
rates. The prediction of our model bears
some resemblance to the real world’s
experience, although one cannot hope
for sharp empirical tests when dealing
with political-economy models.
Figure 9
Worker's Bargaining Power, Germany
0.06
0.04
0.02
0.00
-0.02
-0.04
72
74
76
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80
82
84
86
88
90
92
94
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Figure 10
__________, and Gilles Saint-Paul. “Explaining Movements in the
Labor Share,” Centre for Economic Policy Research, Discussion Paper
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Worker's Bargaining Power, Italy
0.08
Blanchard, Olivier, and Pedro Portugal “What Hides Behind an
Unemployment Rate: Comparing of Portuguese and U.S.
Unemployment,” mimeo, MIT, June 1998.
0.04
Caballero, Ricardo and Mohamad Hammour. “The Cleansing Effect
of Recessions,” American Economic Review (December 1994),
pp. 1350-68.
0.00
Cohen, Daniel, Arnaud Lefranc, and Gilles Saint-Paul. “French
Unemployment: A Transatlantic Perspective,” Economic Policy:
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90
92
Mortensen, Dale and Christopher Pissarides. “Job Creation and Job
Destruction in the Theory of Unemployment,” Review of Economic
Studies (July 1994), pp. 397-415.
94
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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OECD. The OECD Jobs Study, Paris: OECD, January 1995.
Saint-Paul, Gilles. “On the Political Economy of Labor Market Flexibility,”
NBER Macroeconomics Annual 1993, Cambridge: MIT Press, 1993,
pp. 151-87.
__________. “Labour Market Institutions and the Cohesion of
the Middle Class,” International Tax and Public Finance (July 1996a),
pp. 385-95.
__________. “Exploring the Political Economy of Labour Market
Institutions,” Economic Policy: A European Forum (October 1996b),
pp. 263-300.
__________. “The Rise and Persistence of Rigidities,” American
Economic Review (May 1997), pp. 290-94.
__________. “The Political Economy of Firing Costs,” mimeo,
Universitat Pompeu Fabra, Barcelona, October 1998.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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MARCH/APRIL 1999
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Christopher J. Waller holds the Carol Martin Gatton Chair of Macroeconomics and Monetary Economics at the University of Kentucky.
Commentary
since this is cheaper than firing the workers
and incurring the firing cost. Thus, not
surprisingly, Saint-Paul finds that firing
costs lengthen job matches and reduce the
probability that the unemployed workers
find jobs.
The firing cost has three key effects on
workers’ lifetime utility:
Christopher J. Waller
W
ith the advent of the European Monetary Union (EMU), members will
lose one policy tool (the exchange
rate) for dealing with asymmetric shocks to
their economies. Consequently, some other
macroeconomic variable or market must
become more flexible to eliminate excess
demand or supply of output and employment. It is generally argued that labor markets must become more flexible in Europe
to compensate for the loss of independent
monetary policies as a stabilization tool.
It is generally believed that firing costs
in Europe are much higher than in the
United States, hence, to make labor markets
more flexible, firing costs need to be lowered. Firing costs are affected by labor legislation, and therefore, politics enter the
picture when discussing whether or not to
lower firing costs. While lowering firing
costs will benefit unemployed workers,
firing costs generate rents for employed
workers and it is unlikely that workers
would give up those rents willingly. Therefore, to study the political viability of policies aimed at lowering firing costs, we need
an economic model that reflects the benefits and costs of firing costs in a dynamic
model of employment. This is the task
undertaken by Gilles Saint-Paul in his paper.
Saint-Paul uses a pseudo-search/
matching model with exogenous productivity growth to study how firing costs
affect the length of job matches. A worker’s
productivity is constant during a match,
although average productivity is rising in
the economy. Upon being fired, a worker
instantly acquires the average level of productivity in the economy.
Firing costs generate “rents” for workers
that must be paid out of firm profits: After
some critical date, firms subsidize workers
whose wage exceeds their productivity,
•
It lengthens the period they collect the
rent (improves utility).
•
It lowers the average productivity, and
thus, lifetime income (reduces utility).
•
It worsens the probability of finding a
job when unemployed (reduces utility).
Having ascertained the benefits and
costs to workers from the existence of
firing costs, Saint-Paul then asks, “Who
would favor an increase in the magnitude
of firing costs?”
He considers a majority-rule voting
equilibrium to see how individual workers
would vote between two possible firing
cost policies to see if a majority of workers
would support changing the firing cost
from its current level. The author then
examines who would prefer moving
towards a higher firing cost from the low
firing cost regime and vice versa. It is clear
that unemployed workers always favor lowering firing costs, since this would shorten
job matches and increase their probability
of finding a job.
What about employed workers? They
typically divide into three groups based on
the relative age of their job. Because the
rent is acquired towards the end of a match,
the present discounted value of the rent in
the future is of less value to workers in
“young” matches. In general, the last two
effects dominate for these workers so they
oppose a policy that increases firing costs.
Workers in old matches are collecting
the largest rent so they benefit the most
from the first effect. Because they are near
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the end of their current match, however,
they worry the most about finding a job
since they soon will be unemployed. This
latter effect is dominant for them.
Since the workers in relatively young
and relatively old matches support lowering firing costs, who is left to support the
policy? Well, the only workers left are
those in middle-age matches. The middleage workers are the ones just entering the
rent-collecting phase so reducing firing
costs significantly reduces the rents they
are about to collect. Furthermore, their
match is still sufficiently young to make
the future cost of lower job-finding probability of little importance. Consequently,
this is the group that would actually
support increasing firing costs.
Saint-Paul shows that if high firing
costs are the status quo, most of the cases
correspond to a majority of workers
favoring a move to lower firing costs. On
the other hand, if a low-firing cost economy
is the status quo, then the outcome is not so
clear. Under some parameterizations of the
model, workers would be in favor of moving
to a more rigid economy, while under other
parameterizations they will be opposed to it.
Finally, they may be divided over whether or
not to move to a more rigid economy.
As a friend of mine is fond of saying,
the value of discussing a paper is that you
have to dig into the assumptions of the
model and that is where all of the bodies
are buried. Although all models have
bodies buried in them, with Saint-Paul’s
paper I often felt I was on the trail of a
serial killer. So where are the bodies
buried in this model?
My first question is—What are “firms”
in this model? Who owns them and does it
matter? In perfect competition with no
fixed costs or capital, the wage bill is equal
to output, so workers extract the entire surplus from production. This is a common
view of firms in all constant-returns-to-scale
models of production—input payments
exhaust the output. Hence, firms are
merely a veil.
With firing costs, however, the firms
receive some surplus early in the match
and then subsidize workers later in the
match. What do firms do with the surplus
and how do they pay for the subsidy that
occurs later in the match? If they save it
to finance the subsidy later, then there
should be an intertemporal financing constraint on the firms, much like a firm faces
with pension fund obligations. An intertemporal financing condition is missing in
the model. If firms save the surplus early
in the match and use it to pay the rent to
workers later in the match, then workers
(in effect) are paying for the firing costs
via smaller shares of the output earlier in
the match—something Saint-Paul was
trying to avoid.
If firms do not save their share of
the surplus, what do they do with it? Do
the owners of the firm consume it? Is it
transferred to workers via lump-sum equiproportionate transfers? If matches were
perfectly deterministic in length, then
an intertemporal compensation scheme
would require firms have zero surpluses on
net. In this model, however, some matches
end early for random reasons. These firms
clearly end up with net surpluses from the
match. What do they do with them? The
model is completely silent on this entire
issue. If firm owners receive some of the
surplus from trade, then they too will have
a stake, and presumably a vote, in any referendum on firing cost. But alas, in this
model, only workers vote—owners of firms
do not.
Why do workers prefer this type of compensation scheme to some other? The
author assumes that financial markets are
perfect. This implies that workers can
borrow and lend to achieve their desired
consumption path over time regardless of
the timing of income receipts. In this case,
workers simply want the highest lifetime
present discounted value of income, which
occurs in a perfectly competitive labor market. Thus, why would workers want to
distort markets by voting for firing costs?
Another problem I have is with the
voting analysis in the model. Since voting
is over a single issue (firing costs), then
the median voter model should work well.
Simply determine the magnitude of the
firing costs that maximizes the utility of
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each worker by match age and take the
median value of those maximums. The
only remaining question is whether the
median voter’s preferred firing cost is zero.
Unfortunately, in this model, preferences
over firing costs are not single-peaked. The
reason for this is that a vote by the majority
to lower firing costs would cause workers
in old matches to be fired immediately.
Being fired lowers utility due to job loss
but also causes an immediate increase in
productivity that raises the probability of
finding a job and, therefore, increases lifetime utility. Hence, there is a certain age
of a match in which these two forces offset
each other and workers are indifferent to
lowering firing costs and leaving them
unchanged. Consequently, preferences over
firing-cost policies are not single-peaked,
which creates multiplicity of voting equilibria and possibly Condorcet voting cycles.1
This greatly complicates the analysis of the
voting equilibrium and requires numerical
analysis to study the problem.
There is an easy way around this
voting complexity—grandfathering.
The source of the voting complexity arises
from the threat that older workers will be
fired if firing costs are lowered. To eliminate this, simply grandfather all current
matches against the change in firing costs
and only apply the lower firing costs to
new matches. Grandfathering current
voters from the undesirable consequences
of changed policies is an age-old method
of pushing through socially desirable policies. As an example, a university I was
once associated with wanted to lower its
faculty contributions to TIAA-CREF to
reduce generous labor benefits. Not surprisingly, this proposal was a nonstarter
with the faculty until the administration
grandfathered the current faculty from the
benefit cuts and imposed the cuts on new
hires from a certain date onward. This
policy was supported by the faculty and
implemented. The moral of the story is
that grandfathering dramatically alters
people’s voting behavior and can greatly
simplify the voting outcome.
Another problem I have with the model
is that firms supposedly have free entry
and do not face search frictions in finding
workers, whereas workers do face some
search frictions in finding firms. So, I am
puzzled why anyone is unemployed in
equilibrium since you need both sides to
face frictions. Unemployment implies
workers can’t find firms and vice versa.
But if firms face no search frictions, then
as soon as a match ends, a competitive
firm should swoop in and instantly hire the
worker. In fact, the current firm should
simply rehire the worker instantly, since
productivity increases occur instantly and
costlessly upon separation.2 If firms do
face search frictions, then it would seem
that the free-entry condition does not produce a zero-valued unmatched firm and the
solutions to the model are thus incorrect.
In summary, I conclude that the author
is working on an interesting and important
labor problem, particularly as it applies to
Europe. He also has adopted an interesting model for studying the issue and has
obtained some interesting and plausible
results for thinking about how voters will
line up either in favor of or in opposition
to changing labor laws. Unfortunately, for
my tastes, there are some additional bodies
buried in the model’s intellectual basement
that need to be exhumed before I believe the
author has accurately captured the essence
of the problem.
1 Condorcet cycles arise when
preferences over outcomes are
intransitive, i.e., A is preferred
to B, B is preferred to C, but C
is preferred to A.
2
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
91
A similar problem occurs in
monetary search models with
barter trade; pairs of traders
who have a double-coincidence
of wants meet and trade but
then separate. It seems irrational to separate once traders
pair up in successful matches
but this is the typical assumption of money search models
and, after reading this paper,
apparently also is typical of
labor search models.
M AY / J U N E 1 9 9 9
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 1 9 9 9
Erica L. Groshen heads the domestic research function at the Federal Reserve Bank of New York and Mark E. Schweitzer is an economist in the
research department of the Federal Reserve Bank of Cleveland. The authors appreciate the helpful comments of John Haltiwanger, Kenneth
Troske, Joseph Ritter and conference participants at the St. Louis Fed and the Society for Labor Economists. They also thank Amanda Moses
and Jennifer Ransom for excellent research assistance.
Firms’ Wage
Adjustments: A
Break from the
Past?
(a period noted for both low inflation and
unemployment rates) differed from historical
patterns. Another interesting question is
whether some subset of jobs tends to react
first to inflationary or deflationary stimuli.
For our investigation of these
questions, we examine a long (39-year)
time series of wages for a panel of mobile
occupations for a set of employers in three
Midwestern cities. We study wage changes
during years with rising, falling, and
steady inflation to identify regularities that
could broaden our understanding of the
inflationary process at the micro level.
Inflation (as measured by changes in
the Consumer Price Index) and nominal
wage growth (as measured in the means of
the data set we study, as well as in national
series) are largely co-timed. In this paper,
we treat wage changes as caused by inflation.
This approach does not reflect a stand on
whether inflation is primarily a price-pull
or cost-push phenomenon. Rather, this
perspective reflects the experience of inflation from the individual worker or firm’s
point of view.
That is, our approach is consistent
with how human resource managers (the
agents who propose and justify pay increases
in most large U.S. firms) describe their
salary-adjustment policies. Personnel
managers typically report that they use local
cost-of-living increases and the wages paid
by other employers to guide their wage
adjustments. Though potentially compatible with many economic theories of wage
adjustment (including firms’ price-taking
in labor markets), these policies suggest
that wage changes react to inflation instead
of driving it. At a macroeconomic level, the
managers’ policies should tend to tie pay
increases to inflation and productivity growth
on a lagging or contemporaneous basis.
The paper proceeds as follows. First
we describe the wage-setting process in
large firms and discuss the reasons why
wage change distributions may not be neutral with respect to inflation. Then we
Erica L. Groshen and
Mark E. Schweitzer
D
espite advances in understanding the
policies that cause inflation, economists know little about inflation’s
manifestations and transmission in the
marketplace. For example, how does
inflation affect wages in an economy composed of heterogeneous agents making
individual optimizing decisions? We
know that there is a wide dispersion of
wage changes in any year (Groshen and
Schweitzer 1999). In this paper we ask
whether inflation and its changes alter the
distribution of wage shocks—rather than
being neutral for the distribution as conventional theories of wage adjustment
would suggest.
Distributional effects on wage changes
have been the subject of conjecture by academic, policy, and business economists,
but rarely the subject of systematic inquiry.
Altered distributions in the presence of
inflation would indicate that simple wage
models—i.e., ones based on representative
or aggregate agents—are inadequate to
describe the complexity of wage determination. Initially, characterizing the nature
of this complexity allows us to identify the
variety of labor-market responses to shocks.
From there, we can develop and evaluate
richer models of the wage-setting process.
Insights into the distribution of wage
changes should also be helpful for monitoring
the economy. For example, one question
of particular current interest is whether
the wage-setting process during the 1990s
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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describe the data. The fourth section
describes our main results on the distributional effects of inflation. To test for robustness,
we also consider the impact of unemployment and changes in returns to education
on wage-change distributions. The fifth
section investigates two policy-relevant
questions: whether some jobs tend to be
the first to respond to changes in inflation,
and whether wage changes in the 1990s
have deviated from historical patterns.
The sixth section summarizes and concludes.
and product prices.2 Management aims
to maintain the company’s profitability by
not over- or underpaying employees to
prevent both excessively high labor costs
and unwanted turnover. Many employers
pursue this goal by maintaining some ongoing
desired parity with other employers.
During the second stage, each corporate division allocates its share of the salary
budget among its workers to match market
wages and reward performance. Employers
often need to reconfigure wage differences
among occupations in their divisions to
respond to external influences. In a competitive labor market, an occupation’s
wages reflect the amount and kind of
training necessary, working conditions,
and whether such workers are in short
supply compared to the firms’ need for
them. These circumstances can change as
technology, products, demographics, or
input prices shift.
INFLATION IN THE LABOR
MARKET—THE AGENTS’
PERSPECTIVES
In this section, we describe the wagesetting practices of large U.S. employers,
such as those observed in the CSS. Large
employers are of particular interest for this
study because they provide a majority of
jobs (over half and not shrinking) in the
U.S. labor market. In addition, their behavior
is more likely to deviate from the competitive price-taking model than are small
firms’ actions.
Why Inflation Affects the
Distribution of Wage Shocks
The process described above can be
incorporated into a formal wage-setting
model that allows for period-by-period
heterogeneity in wages and their changes.3
Crucially, though, as long as individuals
optimize over leisure and consumption, a
general, observed increase in the price
level will shift the wage-change distribution
equivalently for all firms. This uniform
response to inflation is characteristic of
any wage determination model with representative or aggregate agents.
Hence, we must move beyond simple
representative or aggregate agents to find
factors that make the distribution of wage
changes sensitive (non-neutral) with respect
to inflation. We posit three main sources.
First, if the firms’ inflation outlooks differ,
their wage changes will differ (if contracting
is nominal and fixed for a period of time).
Any employer’s mistakes in projecting product
price growth shows up uniformly in the
wages of all its workers.
Second, nominal wages may be rigid.
That is, workers may experience a discrete
rise in the disutility of their effort after
Wage-Setting Practices in Large Firms
1
Compensation includes wages,
benefits, and working conditions. For simplicity, we focus
on wages in this analysis.
Wages are the largest and most
flexible part of compensation
and are most subject to the
effects of inflation.
2
In a unionized company, wage
determination also involves
negotiation with union leaders
and a long (usually three-year)
time horizon.
3
One example would be the
Sparks (1986) model, which is
itself a generalization of efficiency wage models of Shapiro
and Stiglitz (1984).
Inflation affects the labor market by
influencing workers’ expectations and firms’
wage-setting practices and compensation
schemes. In economies with competitive
labor, capital, and product markets, comparable workers at equivalent jobs should be
compensated similarly.1 If an employer
sets wages too low, employee morale and
productivity may suffer, and turnover may
rise—all resulting in lower profits. If an
employer pays too much, however, it will
also experience lower profits or have to lay
off workers because it will be unable to
price products competitively and still be
profitable. Thus, inflation is a key factor
in workers’ and firms’ wage setting.
The annual wage-setting process in a
large firm typically has two stages. In the
first stage, an employer’s senior management
sets the average wage change for its work
force—to reflect inflation forecasts, labor
market surveys, and projections of sales
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 1 9 9 9
nominal wage cuts. This story is consistent
with prevalence of nominally priced contracts
in the U.S. economy. If firms do avoid nominal wage cuts, the workers most affected
are those whose occupation gets a negative
shock, no matter what type of firm they
are in. So, in an economy with downward
rigidity, the variance of occupational wage
changes rises with the level of inflation—
until the rigidity no longer binds.
Finally, business-cycle phenomenon
may alter the supply of workers in other
ways that are correlated with inflation—
yielding further non-neutralities in the
distribution of wage changes.
fall—resulting in smaller nominal wage
increases than typical. Thus, lower wage
increases may occur more often or be associated with different conditions than in the past.
Alternatively, others have argued that
wage setting has been altered by the persistence of very low inflation (below 3 percent).
In a low-inflation environment, competition
could pressure participants to accept more
flexible practices—particularly practices
that permit nominal pay cuts. Examples of
such innovations already exist and would
proliferate, such as bonus and incentive
pay, and contingent contracts.
Widespread use of such pay schemes
would overcome the constraints of downward nominal wage rigidity, allowing lower
overall wage changes. In addition, the lowest
wage changes for particular occupations
within firms might be less restricted—that
is, lower than expected, based on previous
patterns.
Have Things Changed in the 1990s?
Two schools of thought argue that wage
setting during the 1990s has been different
than in previous years. One set of analysts
suggests that workers have become more
insecure since the 1980s, because of employer
downsizing and the elimination of lifetime
jobs in the U.S. The other points to changes
due to the persistence of the low-inflation
environment.
According to a recent series of articles
in the New York Times, the leading explanation of why inflation has been so limited
these last three years—despite low unemployment rates—is that wage demands
have been held down by an unusually high
degree of “worker uncertainty.”4 Substantial research effort has gone into identifying
and disputing the sources of this presumed
insecurity in the face of a buoyant labor
market. The most commonly mentioned
reasons include the threat of middle-management layoffs, competition with foreign
workers, and less unionization. These factors could reduce wage inflation by making
workers think twice before requesting
higher wages, even if their firms’ balance
sheets have improved.
If this is the case, then some employers
that in the past would have maintained or
elevated their market wage position, no
longer feel the need to do so. In an efficiency
wage model, alternative employers are
exogenously less attractive to workers, so
the efficiency wage firms’ offers should
THE COMMUNITY
SALARY SURVEY
This study uses annual private salary
data from a survey that the Federal Reserve
Bank of Cleveland has conducted in Cleveland, Cincinnati, and Pittsburgh since 1927
to assist its annual salary budget process.
The analysis data set reports wages for
detailed occupations, by employer from
1957 through 1996.
The data set has three major selling
points for this study. First, the wages
recorded here are less prone to random
reporting error than household data because
they are derived from administrative records.
Second, the data are longer-lived than any
source previously investigated. Third,
because employer data records wages in
the way most meaningful to firms, it is
preferable to household or aggregate data for
studying impacts on the firms’ wage setting.
This perspective appropriately reflects the
strategies used by firms to adjust wage
bills (e.g., promotions, reassignments or
reorganization), but not the potentially
confounding means used by individual
workers to adjust their earnings (e.g.,
taking second jobs or changing hours).
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
95
4
Peter Passell, “A Pulse that
Lingers,” The New York Times,
July 22, 1997, p. A1.
M AY / J U N E 1 9 9 9
Table 1
well-developed markets.9 Many occupations
are divided into grade levels, reflecting
responsibility and experience. In the
analysis, to avoid unnecessary restrictions,
we consider each occupational grade in
each city to be a separate occupation.
Thus, the total number of occupations in
Table 2 exceeds the number surveyed
during any given year. For example, 83
occupational grades were surveyed in
1996, yielding 240 occupations across the
three cities. On average, each employer
reports wages for about 27 occupations.
Although the CSS is conducted annually,
the month surveyed has changed several
times. Throughout the paper, results for
any year refer to the time between the preceding survey and the one conducted in
that year—usually a 12-month span, but
occasionally not. When we examine data
means for periods longer or shorter than a
year, we annualize the changes so they can
be compared directly across years. All data
merged have been adjusted to the extent
possible to reflect time spans consistent with
those in the CSS. We have repeated most
of the exercises reported in this paper on the
subset of years that covered exactly a year
and find no qualitative difference in results.
We also incorporate standard measures
of inflation and national output-per-hour
in our analysis (see Table 3). As a measure
of general inflation experienced in the
country, we use percentage changes in the
monthly averages of the Consumer Price
Index (CPI) for all Urban Workers. Our
labor productivity measure is the Nonfarm
Business Sector Output per Hour Worked
(pre-chain-weights).
In order to investigate the distribution
of wage adjustments under different inflationary environments, we use two schemes
to differentiate among years. First, we label
all years as years of increasing, stable or
decreasing inflation, using a 60.5% cutoff
for the CPI. For example, years when the
inflation rate rose by more than 0.5 percentage
points are considered years of increasing
inflation. Second, we identify multi-year
episodes of inflationary changes as periods
where the economy experienced two or
more consecutive years of increasing, stable o r
Description of the Annual Wage
Adjustment Data Set
Drawn from the CSS, 1957-1996
Total Number of Job-Cell Wage Adjustments Observed
73,094
Number of Years of Changes
39
Average Number of Observations Per Year
1,874
Mean Log Wage Adjustment
0.048
Standard Deviation of Log Wage Adjustment
0.086
NOTE: All numbers reported are for the first-differenced data set.
SOURCE: Authors‘ calculations from the Federal Reserve Bank of Cleveland
Community Salary Survey.
5
6
Job-cell-year observations
where the calculated change in
log wages exceeds 0.50 in
absolute value are deleted from
the sample on the assumption
that most of these arise from
reporting or recording errors.
Over 1,000 observations are
imputed from cases where jobcells are observed two years
apart. The imputed one-year
changes are simply half of the
two-year differences. Many of
the results reported here were
also run without the imputed
observations. Their inclusion
does not affect the results.
Comparison of the coefficients
estimated separately for means
and medians for some years
where both were available (1974
and 1981-1990) suggests that
they are highly correlated (correlation coefficients of .97 to
.99). Coefficients estimated
with medians show more variation than those estimated on
means and are more highly correlated over time, however this
is consistent with medians
being a more robust measurement of central tendency.
Table 1 describes the dimensions of
the CSS wage-change data set. From wage
levels, we compute 73,094 annual wage
changes for occupation-employer (job)
cells observed in adjacent years.5 Each
observation gives the change in the log of
the mean or median salary for all individuals employed in an occupation-employer
cell. Since medians should be more robust
to outliers yet only means were recorded
before 1974, our results use means through
1974 and medians for the years thereafter.6
Cash bonuses are included as part of the
salary, although fringe benefits are not.
Participants in each city are chosen to
be representative of large employers in the
area. Until 1995, the number of companies
participating trended up from 66 to over
80 per year (see Table 2). On average,
they stay in the sample for almost 13 years
each. Since each participant judges which
establishments to include in the survey,
depending on its internal organization, we
use “employer,” a purposely vague term, to
mean the employing firm, establishment,
division, or collection of local establishments
for which the participating entity chooses
to report wages.7 The industries included
vary widely, although the emphasis is on
obtaining employers with many employees
in the occupations surveyed.8
The occupations surveyed (43 to 100
each year) are exclusively nonproduction
jobs that are found in most industries,
with relatively high inter-firm mobility, and
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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Table 2
Description of CSS Data by Year
End
Number of:
Year
Job cells
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
Total
1,336
1,557
1,714
1,669
1,701
1,881
1,910
2,032
2,123
1,965
1,967
2,128
1,972
853
854
1,262
1,477
1,335
1,379
1,391
789
1,674
2,418
2,689
2,196
2,185
2,013
2,274
2,272
2,396
2,437
2,401
2,407
2,505
2,536
2,398
2,355
2,128
1,841
1,345
75,765
Occupations*
94
94
103
103
103
109
112
113
124
125
125
124
114
49
49
66
90
96
101
104
60
197
267
295
186
193
190
213
212
220
226
222
225
222
223
223
223
223
241
240
6,187
Mean Log Wage Adjustment in:
Employers
73
83
88
86
88
93
90
96
95
89
89
94
97
36
36
38
57
73
73
72
72
68
75
79
83
82
75
80
79
82
80
82
81
84
89
84
89
84
69
51
3,002
Cleveland
Cincinnati
Pittsburgh
0.051
0.049
0.040
0.036
0.039
0.024
0.019
0.026
0.021
0.040
0.037
0.046
0.066
0.068
0.061
0.061
0.056
0.126
0.074
0.065
0.030
0.052
0.064
0.095
0.086
0.072
0.050
0.047
0.040
0.042
0.031
0.036
0.045
0.052
0.038
0.039
0.032
0.027
0.027
0.040
0.049
0.046
0.054
0.048
0.032
0.035
0.022
0.026
0.022
0.026
0.045
0.042
0.044
0.050
**
**
**
0.095
0.084
0.063
0.057
0.021
0.063
0.071
0.074
0.089
0.092
0.055
0.058
0.044
0.044
0.037
0.037
0.041
0.046
0.045
0.042
0.026
0.029
0.031
0.032
0.048
0.045
0.050
0.070
0.034
0.036
0.024
0.024
0.023
0.010
0.038
0.035
0.042
0.049
**
**
**
**
0.139
0.090
0.078
0.052
0.066
0.069
0.087
0.059
0.078
0.073
0.063
0.042
0.037
0.038
0.023
0.036
0.024
0.035
0.043
0.040
0.025
0.019
0.030
0.048
* Occupations are counted separately for each city.
** In 1970-72, the CSS is missing Cincinnati; in 1970-73, the CSS is missing Pittsburgh.
SOURCE: Authors’ calculations from the Federal Reserve Bank of Cleveland Community Salary Survey, 1956-1996.
decreasing rates of inflation. Table 4,
which appears on page 100, shows how the
years under investigation (1957-1996) are
categorized by these criteria.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
97
7
Some include workers in all
branches in the metropolitan
area; others report wages for
only the office surveyed. Since
a participant's choice of the
entities to include presumably
reflects those for which wage
policies are actually administered jointly, the ambiguity
here is not particularly troublesome.
8
The employers surveyed include
government agencies, banks,
manufacturers, wholesalers,
retailers, utilities, universities,
hospitals, and insurance firms.
9
They include office (e.g., secretaries and clerks), maintenance
(e.g., mechanics and painters),
technical (e.g., computer operators and analysts), supervisory
(e.g., payroll and guard supervisors), and professional (e.g.,
accountants, attorneys, and
economists) occupations. Job
descriptions for each are at
least two paragraphs long.
M AY / J U N E 1 9 9 9
Table 3
Means and Standard Deviations of CSS Wage Adjustment
Components and Other Economic Indicators
Mean
Standard
Deviation
∆ Occupation-Employer Log Wage
Current U.S. CPI-Ua
0.048
0.046
0.084
0.034
∆ Output/Hourb
0.016
0.062
0.016
0.014
College to High School (H.S.) Wage Premium
0.000
0.545
0.009
0.156
High School to Less than High School Premium
0.337
0.134
Percentage Change in College to H.S. Wage
2.18
7.38
Percentage Change in H.S. to Less than H.S. Wage
2.78
9.01
Variable
Unemployment Ratec
∆ Unemployment Ratec
a Change during salary survey year in the BLS Consumer Price Index for all Urban Workers (CPI-U) for the United States.
b Change during salary survey year in the BLS Nonfarm Business Sector Output per Hour Worked.
c U.S. civilian unemployment rate.
SOURCES: Authors’ calculations from the Federal Reserve Bank of Cleveland Community Salary Survey, 1957-1996.
U.S. Bureau of Labor Statistics (BLS).
As a check for our results focusing on
business cycle variables, we also control
for the long-run rise in earnings inequality.
Limited earnings inequality measures are
available for the full period of this paper,
1957 to 1996. The best measures available
are median earnings by education level. Even
this series is missing a few years during the
1950s. We interpolate to fill in these gaps
on the justification that these controls are
offered to account for long run trends.
inflation and productivity growth, versus
1.3 percentage points lower over the full
sample. This suggests that the early 1990s
had somewhat weaker than usual wage
growth, given inflation and the measured
gains in productivity.
As for timing, at the annual frequency of CSS data, wages and prices can
be described reasonably as changing
contemporaneously. Compared to the
contemporaneous correlation between
inflation and mean wage growth of 0.82,
the correlations are substantially lower for
wage growth leading inflation by one year
(0.59) or two years (0.35). The alternative—
that wage growth follows inflation—is
better supported. The correlation with
wage growth lagging inflation by one year
is 0.83. It falls to 0.69 with a two-year
lag. It also is clear that during particular
periods, wage growth exceeded inflation or
CPI growth, with or without subsequent
increases in the inflation rate. Overall,
this source of detailed wage data supports
a relationship between wage growth, inflation and productivity growth, at least at an
aggregate level.
Wage Adjustments and Inflation
Figure 1 confirms that CSS wage changes
are generally synchronized with inflation.
The correlation between the mean CSS
wage adjustment and inflation (CPI) is
high (0.82). Overall, though, CSS wage
growth has a higher mean (by 0.37) than
the CPI, because it includes the benefits of
productivity growth. Recent wage growth
has averaged much closer to the inflation
rate (wage growth led by only 0.08
percentage points in the 1990s). From
1990 to 1996 mean wage growth was 1.7
percentage points lower than the sum of
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
98
M AY / J U N E 1 9 9 9
Figure 1
Inflation and the Dispersion of
Wage Changes
Mean Log Wage Changes, Productivity,
and Inflation
Figure 2 relates the distribution of log
wage changes in the CSS to the CPI during
the period. The line with circles shows the
percentage change in the CPI. The other
lines show the 10th, 25th, median, 75th,
and 90th percentile log wage changes for
cells in the CSS. If inflation were neutral
with respect to the distribution of wage
changes, there would be no relationship
between the level of inflation and the
widening of the gap between the top and
bottom lines on the figure. We would
expect the lines to roughly parallel the
level of inflation. Instead, the quantile
lines show a marked tendency to widen as
the level of inflation rises.
For example, in 1996, the inflation rate
was 3.0%. In the CSS that year, the median
cell had a wage change of 3.4%, while the
10th and 90th percentiles had wage changes
of –4.7% and 12.5%, respectively. Thus,
factors that affect the size of percentile
wage changes increase the value of a good
shock or a bad one in a particular year.
One aspect of interest for interpreting
our findings is whether wage changes are
correlated with wage levels. If the dispersion of wages remained constant over time,
we would expect no correlation between
wage levels and changes. Wages in the CSS,
however, like those in other U.S. data sources,
show a recent widening inequality (Groshen
1991). Thus, the overall correlation coefficient between log wage levels and changes
in the CSS is 0.13. Annually, the correlations
range from 0.33 in 1977 down to 0.06 in
1982. Thus, in all years, higher-wage workers
tended to receive bigger proportional raises
than did low-wage workers. Yet the correlation is fairly low, so our findings say
more about what drives the size of good
and bad wage shocks than about what happens to good versus bad jobs.
20%
Inflation + Productivity Growth
CPI-U Inflation
CSS Mean wage Change
16%
12%
8%
4%
0%
57
61
65
69
73
77
81
Salary Survey Year
85
89
93
This figure shows annualized percentage change by salary survey year,
which is not always equal to 12 months. Notably in 1974.
Figure 2
Distribution of Log Wage Changes,
from 1957 to 1996
Percentiles of Cell Wage Changes vs. Inflation
Percentiles: 10, 25, 50, 75, & 90. Dots indicate inflation rate.
Percent change
20
10
0
-10
60
65
70
75
80
Year
85
utions, we use quantile regressions of wage
changes on various measures of inflation
and other controls. Quantile regressions
(developed by Koenker and Basset, 1978)
estimate the correlates of wage changes in
various parts of the distribution.
Formally, the estimator minimizes a
weighted sum of absolute deviations of
the residuals:
How Inflation Affects Wage Gains
in the Tails
To formally test for and explore the
impact of inflation on wage change distrib-
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
99
90
95
M AY / J U N E 1 9 9 9
Table 4
Classi cation of Sample Years by In ation Direction and Episode
Year
Inflation
(CPI)
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
0.036
0.004
0.015
0.015
0.011
0.011
0.014
0.012
0.028
0.026
0.039
0.053
0.061
0.044
0.035
0.048
0.108
0.079
0.055
0.064
0.085
0.118
0.153
0.106
0.072
0.025
0.047
0.036
0.016
0.038
0.039
0.050
0.048
0.044
0.032
0.028
0.028
0.028
0.030
Inflation
Change
(∆CPI)
0.000
– 0.033
0.012
– 0.001
– 0.004
0.000
0.003
– 0.002
0.016
– 0.002
0.014
0.013
0.008
– 0.017
– 0.010
0.013
0.059
– 0.029
– 0.024
0.009
0.021
0.034
0.035
– 0.047
– 0.034
– 0.047
0.023
– 0.011
– 0.020
0.022
0.001
0.011
– 0.002
– 0.005
– 0.012
– 0.003
– 0.001
– 0.000
0.002
Direction of Inflation*
Stable
Increase
Decrease
Episodes of Inflation**
Stable
Increase
Decrease
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
* An increase in inflation is defined as an increase in ∆CPI equal to or larger than 0.5%. Likewise, a decrease in inflation is defined as
a decrease in ∆CPI equal to or less than 0.5%.
** An episode of inflation stability is defined as a period of two or more consecutive years when inflation was stable. Similarly, an
episode of increasing (decreasing) inflation is defined as two or more consecutive years of increasing (decreasing) inflation.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
100
M AY / J U N E 1 9 9 9
Table 5
Simple Quantile Regressions for Total Cell
Mean Wage Changes in the CSS
∑ hi yi − ∑ β j x ij ,
i
j
2q
if yi − ∑ β j x ij > 0
j
i
where hi =
,
(
)
−
−
≤
2
1
0
q
if
y
β
x
∑ j ij
i
j
(Standard Errors in Parentheses)
Independent
Variable
yi and xij are the ith observation of the
dependent and independent variables. βj
is a vector of regression parameters. The
estimates are for quantile of interest, q.
The predictions of the estimator are the
expected change in wages at the qth quantile conditional on the values of the
independent variables xij.
Thus, we can distinguish between
conditions which raise (or lower) the upperend wage changes, and those that primarily
affect lower-end wage changes. If the
estimated model were parameterized identically over the distribution of wage changes,
then an OLS regression would yield very
similar coefficients. Indeed, this is the
reason that the median regression often is
recommended as a robust (less susceptible
to outliers) alternative to OLS regression.
Koenker and Basset (1982) show that
differences in parameter estimates at alternative quantiles convert into a very general
test for heteroscedasticity. The test offers
advantages over more common tests because
it is robust to nonGaussian errors. We prefer
it because the quantile estimators help elucidate the nature of the heterogeneity. The
test statistic (interested readers are referred
to Koenker and Bassett, 1982, for the
formula), focuses on whether coefficient
differences are significant given the quantile estimator measure of distribution
of residuals.
We report three sets of results, with
increasing complexity. The first set shows
the simplest estimates—for the effect of
CPI inflation alone. Under the null
hypothesis of inflation’s neutrality on the
distribution of wage changes, we expect a
coefficient of one on the level of inflation
for every quantile. In the next set of
regressions, we also include inflation’s
square, to allow for nonlinearity. Under
the null, the coefficient on this should be
90th
75th
Quantile
50th
25th
10th
Inflation
CPI
0.949
(0.020)
0.707
(0.008)
0.555
(0.005)
0.432
(0.009)
0.067
(0.023)
Constant
0.084
(0.001)
0.049
(0.000)
0.025
(0.000)
-0.001
(0.001)
-0.034
(0.001)
Pseudo R2
0.060
0.065
0.046
0.015
0.000
KoenkerBasset χ2
T = 713.0
degrees of freedom = 2
Number of observations = 73,094
zero for all quantiles. Two additional variables capture any incremental influence of
the level of inflation when inflation is falling
(by more than 0.5 percentage points) or
rising. Under the null, these coefficients
should also be zero. In addition, we include
the unemployment rate, the change in the
unemployment rate, output per hour and
its square in the regressions to control for
the business cycle and real wage gains.
Table 5 shows the simplest results.
The first row shows how the level of inflation affects wage gains by quantile in the
distribution of wage changes. As expected,
and as we saw in Figure 2, wage changes
in the 90th percentile rise almost one-forone with inflation. That is, the coefficient
on CPI is 0.949. Wage gains in the lower
tails amount to only a fraction of the inflation rate, however. The corresponding
coefficient for the 10th percentile is 0.067;
showing surprisingly low sensitivity to
changes in prices. Thus, the disparity
between wage changes in the upper and
lower tails rises with inflation.
Does this mean that the model predictions imply a growing disconnect between
wages levels and prices? No, for two reasons.
1) The estimates for the intercept term are
positive and statistically significant (except
at the 25th and 10th percentiles), allowing most
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
101
Prob. < 0.005
M AY / J U N E 1 9 9 9
wage changes to keep up with the average
level of inflation. This combination results
in wage change predictions that are less
variable than inflation, but similar in their
mean levels—as implied by Figure 2. Estimated constants do decline from the 90th
to 10th percentile, preserving a distinct
pattern of divergent outcomes. 2) The regression results are for wage changes. If
the set of affected jobs vary substantially
from period-to-period, then being behind
in one period may be made up in another.
This issue will be explored in Section 5 of
this paper.
While the apparent explanatory power
of the regressions is fairly low—particularly
for the lower quantiles—we detect some
very robust statistical relationships. In
evaluating the results, it is crucial to
realize that the psuedo-R2 we report is not
directly comparable to the traditional R2.
This measure,
just decreased, the wage distribution will
be narrower than it would have been otherwise. Raises of most workers are essentially
insensitive to inflation drops in the first
year after inflation declines. That is, the
sum of the two coefficients on CPI and its
negative change is close to zero for the
25th, median and higher quantiles. The
workers in the 10th percentile, however,
actually gain higher raises than they would
have under last year’s inflation rate, all else
being equal. Thus, inflation decreases tend
to narrow the distribution of wage changes.
Inflation increases are associated with
additional wage gains in all quantiles. These
bonuses are smallest for the median (0.377),
but higher for workers at both extremes.
Since the bonus coefficient for the 90th
percentile (0.507) is smaller than the gain
for the 10th percentile (0.792), inflation
increases moderately narrow the distribution of wage changes, all else being equal.
That is, while higher inflation rates
widen the distribution, either increases or
decreases modestly narrow the distribution
in the year they are sustained.
By contrast to the higher sensitivity of
upper quantile wage gains to inflation
levels, unemployment exerts most of its
influence on the lower quantiles of wage
growth. High unemployment depresses
wage gains sharply in the bottom quantiles,
with little effect on upper quantile raises.
The coefficient of 0.701 on unemployment
for the 10th percentile predicts that wage
gains in the bottom decile will be 0.7 percentage points lower if unemployment is
one percentage point lower, all else being
equal. The opposite-signed coefficients on
change in unemployment suggest that the
effect of unemployment on wage growth is
subject to a lag.
Finally, the results for our proxy for
productivity growth show a nonlinear relationship with wage changes at all quantiles.
The coefficients for output-per-hour are
positive with little variation among quantiles.
This suggests that when productivity
growth is slow, workers receive 30 to 50
percent of productivity gains in their paychecks. The coefficients on the quadratic
term, however, suggest that this effect is
sum of weighted deviations
about the estimated quantile
,
pseudo R = 1 −
sum of weighted deviations
about the raw quantile
2
only approaches 1 when each observation
is predicted as a conditional quantile.
Thus, the estimator can yield accurate
predictions of the quantile with a low
psuedo-R2, as long as the weighted deviations are symmetric around the prediction.
Table 6 adds considerable flexibility
to the ways in which inflation can affect
wage changes, as well as controls for
unemployment and productivity. The
bottom row shows that the addition of
these terms does improve the fit of the
equations, but by less than half in all cases.
Thus, the level of inflation alone is a key
element in predicting the size wage
changes among quantiles. Crucially, the
first row of the table shows that the basic
decline in sensitivity to inflation as wage
shocks get worse is maintained in the
more complex model.
Accelerating and decelerating
inflation, per se, also have modest effects
on the distribution of wage changes. For
any given inflation level, if inflation has
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
102
M AY / J U N E 1 9 9 9
Table 6
Quantile Regressions for Total Cell Mean Wage Changes
in the CSS With Controls for Productivity and Unemployment
(Standard Errors in Parentheses)
Independent
Variable
90th
75th
Quantile
50th
25th
10th
Inflation
CPI
0.962
(0.069)
0.766
(0.030)
0.634
(0.017)
0.547
(0.011)
0.216
(0.086)
Inflation Squared
100*(CPI)2
-0.011
(0.004)
-0.010
(0.002)
-0.008
(0.001)
-0.015
(0.001)
-0.016
(0.005)
Decreasing Inflation
(∆CPI≤-0.05)*∆CPI
-0.896
(0.078)
-0.913
(0.033)
-0.684
(0.019)
-0.558
(0.013)
-0.662
(0.097)
Increasing Inflation
(∆CPI≥0.05)*∆CPI
0.507
(0.102)
0.628
(0.044)
0.377
(0.026)
0.448
(0.018)
0.792
(0.131)
Unemployment Rate
0.182
(0.057)
-0.105
(0.025)
-0.049
(0.015)
-0.250
(0.010)
-0.701
(0.070)
Change in
Unemployment Rate
-0.051
(0.098)
0.075
(0.042)
0.142
(0.025)
0.380
(0.016)
0.736
(0.121)
Productivity Growth
∆Output/Hour
0.371
(0.123)
0.479
(0.052)
0.478
(0.030)
0.381
(0.020)
0.410
(0.154)
Prod. Growth Sqd.
100*(∆Output/Hour)2
-0.087
(0.030)
-0.096
(0.013)
-0.108
(0.007)
-0.090
(0.005)
-0.051
(0.037)
Constant
0.062
(0.004)
0.041
(0.002)
0.019
(0.001)
0.007
(0.001)
-0.007
(0.005)
Pseudo R2
0.071
0.081
0.060
0.022
0.007
Koenker-Basset χ2
T = 953.8
degrees of freedom = 2
Prob. < 0.005
Number of observations = 73,094
attenuated when productivity growth is
fastest. Nevertheless, workers in the
lowest quantile (with its coefficient of
–5.060) may benefit more from higher productivity than do the upper quantiles,
narrowing wage adjustment distributions
when productivity growth is faster.
Are these differences statistically
significant? Testing for heteroscedasticity
in wage changes according to the level of
inflation yields a strong rejection of the
null hypothesis. Despite the inclusion of
controls for the direction of inflation
changes and other business cycle
factors, the Koenker-Basset test for
heteroscedasticity yields values well
beyond conventional levels of statistical
significance.
Summarizing broadly, the highest
wage changes in a year increase with inflation. Wage changes at the lower tails,
however, are more influenced by the
unemployment rate. Given statistical significance of these differences, we now turn
to the question of whether the effects are
economically relevant.
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
103
M AY / J U N E 1 9 9 9
Figure 3
and constant unemployment and productivity growth for the sample period. We
also overlay the actual values for the
percentile (the line without circles). For
the median and 90th quantile, the fit is
very close—information on inflation alone
is sufficient to produce a reasonably close
fit. The fit is markedly worse for 10th percentile wages, however. Until the mid-1970s,
wage growth at the bottom is underpredicted.
Then the model overpredicts wage changes
until the late 1980s. This figure illustrates
the points that median and upper tail wage
changes are highly responsive to the inflationary environment—much more so than
are wage changes at the lower tails.
Most strikingly, however, this figure
shows that the response of the various
quantiles to inflation captures most of the
path of the dispersion of wage shock over
time. Thus, inflation can be seen as the
main driving factor in the variation of
wage shocks over time.
Figure 4 illustrates the point further by
showing how the full set of quantiles in Table 6
would respond to a hypothetical inflation
path. Suppose that over a forty-year span,
inflation started at zero, then rose by one
percentage point per year until it reached
fifteen percent at year sixteen. After being
stable at fifteen percent for four more
years, then it fell by one percent per year,
until it reached zero at year 36 and was
stable until year 40. Figure 4 shows the
five predicted paths of quantile wage
changes for this scenario. The contrast
among the paths is quite stark. The higher
the quantile, the more responsive wages
are to inflation. Indeed, wages in the 10th
percentile show very little response at all.
We now repeat these exercises to illustrate the impact of unemployment. The
exercise shown in Figure 5 is analogous to
that in Figure 3, but with inflation held
constant and the unemployment rate
allowed to follow its historical path from
1957 to 1996. Again, the line with the circles shows the model predictions under
these circumstances, while the unmarked
line represents actual values. Overall, the
relationship with unemployment is a less
accurate predictor of quantile wage changes
Model Predictions When Only
Inflation Rate Varies
Percentiles: 10, 50, & 90. Circles indicate model.
Percent change
20
10
0
-10
60
65
70
75
80
85
90
95
Year
Figure 4
Model Predictions for Rising
and Falling Inflation Rate
Percentiles: 10, 25, 50, 75, & 90.
Percent change
20
10
0
-10
0
10
20
Year
30
40
Isolating Factors’ Effects on the
Distribution of Wage Changes
Since the model estimated in Table 6 is
complex, we construct some illustrative
scenarios to gauge the total impact of inflation and unemployment on wage changes.
Figure 3 compares the impact of inflation
on wage gains in the 10th, 50th, and 90th
percentiles. For each percentile, we plot
predicted values of wage changes (shown
as circles), given realized inflation rates
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Figure 5
than is inflation. In contrast however, variations in unemployment predicting wage
changes do much better for the 10th decile
than they do for the median or 90th percentile.
Figure 6 constructs a hypothetical
scenario to illustrate the differing responsiveness of wage change deciles to unemployment
paths. In this exercise, we begin with an
unemployment rate of four percent, raise it
by 0.5 percentage points per year until it
reaches ten percent. Then we hold it steady
for five years, followed by a 0.5 percentage
point per-year drop until it reaches four
percent and stays constant for ten years.
Again, the contrast in responsiveness among
the quantiles is stark. But unemployment
(in contrast to inflation) has its most potent
impact on the lowest quantiles of wage changes.
The median shows very little response,
and the 90th percentile even has a counterintuitive pattern—albeit a muted one.
These figures highlight the differing
responses of the quantiles to inflation and
unemployment shock. They illustrate the
generalization that wage gains of those in
the higher quantiles rise steadily with
inflation, while wage gains of those in the
lower tails (that is, those suffering the
largest negative shocks) are determined
mostly by the unemployment rate. They
also show that during the period from
1957 to 1996, inflation was the main determinant of the dispersion of wage shocks.
The finding that the impact of these
factors on wage changes varies substantially
by quantile suggests that even our relatively
detailed model of how wages react to inflation and other business-cycle variables
doesn’t capture all of the important issues.
Indeed, a complete econometric model
would need to predict widely varying
levels of matching nominal wage growth to
inflation and employer responsiveness to
general slackness in the labor market.
Nonetheless, this statistical representation
of wage change provides a useful description of typical patterns.
Model Predictions When Only
Unemployment Rate Varies
Percentiles: 10, 50, & 90. Circles indicate model.
Percent change
20
10
0
-10
60
65
70
75
80
85
90
95
Year
Figure 6
Model Predictions for Rising and
Falling Unemployment Rate
Percentiles: 10, 25, 50, 75, & 90.
Percent change
10
0
-10
0
10
20
Year
30
sation. Many researchers have documented
a substantial increase in earnings inequality
in the United States during the period
studied. This rise in inequality also occurs
in the CSS (Groshen 1991). While this
increasing inequality must be reflected in
wage changes, the exact nature of the relationship is unclear. Perhaps rising inequality
raises the variance of wage changes because
the distribution of desired wages is more
dispersed, allowing for larger possible
changes. Or, wage adjustments might be
larger during periods when some shock to
the labor market is increasing inequality.
Rising Earnings Inequality?
The path of inflation is not the only
systematic trend that might affect compen-
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10 Schweitzer
(1997) shows that
educational differentials are the
most substantial measured factor in the rise in earnings
inequality.
In addition, it is possible that inequality
rose in ways that did not affect the distribution of wage changes. For example, the
correlation of individual wage changes
over time might rise, leaving the size
distribution of wage changes unaffected.
Given our focus on inflation, the rise
in earnings inequality argues for conducting
probes with suitable control variables. To
this end we reestimate our quantile regressions with controls for the ratios of median
earnings of workers of different education
levels. This measure of inequality is available back further than other inequality
series. In addition, these ratios are highly
correlated with the variance of log wages
over the period when microdata is available
(starting in 1972).10
The two included wage ratios are college graduates versus high school graduates
and high school graduates versus high
school dropouts. The CSS includes occupations that employ workers at each of
these three levels, although it is slanted
toward more skilled occupations. Since
we are uncertain about how rising earnings
inequality alters the distribution of wage
changes, we introduce controls for both
the level and the percentage change in the
education wage differentials.
Adding these earnings inequality variables to the previous estimates is intended
to show what relationships are robust to
the inclusion of these variables. Table 7
shows the results.
First, we note that differences in the
estimated wage changes by quantile remain.
Indeed, the heteroscedasticity test based on
the difference between the inflation coefficient at the 25th, 50th, and 75th percentiles
continues to be significant, because the
difference in the coefficient estimates at
the 75th and 50th percentiles are still large.
Thus, control for inequality adds support
to the conclusion that the wage change
distribution reacts nonuniformly to labor
market shocks.
Nevertheless, wage inequality does
appear to influence the distribution of
wage changes. Coefficient estimates on
the inequality measures are significantly
different from zero in almost all quantiles.
Inclusion of the level of wage inequality
and its trend improve the fit of the quantile
regressions (the psuedo-R2s rise) in Table
6. The fit of the upper half of the distribution is improved more substantially by the
inclusion of inequality controls than is the
fit in the lower half.
In addition, although most signs on the
coefficients estimated in Table 6 are preserved,
some point estimates change markedly. Two
general patterns stand out. First, including
inequality controls does not substantially
alter the role of inflation on wage changes.
While the coefficients on the level of inflation for the lower quantiles are now larger,
they remain smaller than those of the high
quantiles. Furthermore, the size of the negative coefficients on their quadratic terms
also are substantially larger. Similarly, the
impact of sharp changes in the inflation rate
on wage changes is changed little for decreases
and slightly muted for increases. Replicated
Figures 2, 3 and 4 using the inflation coefficients from Table 7 are parallel those shown
above, although muted differences in the
response to inflation between upper and lower
quantiles are evident in the analog to Figure 3.
Second, both the productivity and unemployment variables appear to be more heavily
related to the inclusion of inequality in their
impacts on the distribution than does inflation. Coefficient changes were larger and
their patterns were more strongly altered.
Overall, inequality controls do not remedy
the inability of a single equation model (of
the type estimated here) to describe the factors
that determine wage adjustments consistently
across the distribution of wage adjustments.
These controls do point out a relationship
between unemployment and productivity
variables and the rise of inequality in the
United States. This interesting, but possibly
spurious, relationship suggests an area for
further study.
TWO POLICY-RELEVANT
QUESTIONS
Are there Bellwether Jobs?
One possible explanation for the
finding that wage changes are highly vari-
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Table 7
Quantile Regressions for Total Cell Mean Wage Changes in the CSS,
Including Inequality Variables
(Standard Errors in Parentheses)
Independent
Variable
90th
75th
Quantile
50th
25th
10th
Inflation
CPI
0.819
(0.078)
0.830
(0.036)
0.737
(0.019)
0.767
(0.051)
0.553
(0.086)
Inflation Squared
100*(CPI)2
0.006
(0.005)
-0.010
(0.002)
-0.011
(0.001)
-0.022
(0.003)
-0.031
(0.005)
Decreasing Inflation
(∆CPI≥-0.05)*∆CPI
-1.297
(0.100)
-0.986
(0.044)
-0.743
(0.023)
-0.680
(0.064)
-0.522
(0.110)
Increasing Inflation
(∆CPI≥0.05)*∆CPI
0.405
(0.103)
0.393
(0.048)
0.217
(0.026)
0.317
(0.061)
0.591
(0.118)
Unemployment Rate
0.335
(0.089)
0.217
(0.041)
-0.202
(0.022)
-0.029
(0.051)
-0.226
(0.098)
Change in
Unemployment Rate
-0.700
(0.151)
-0.285
(0.069)
0.151
(0.037)
-0.027
(0.108)
0.506
(0.167)
Productivity Growth
∆Output/Hour
-0.116
(0.137)
0.080
(0.062)
0.225
(0.033)
0.170
(0.080)
0.173
(0.152)
Prod. Growth Sqd.
100*(∆Output/Hour)2
0.026
(0.035)
-0.037
(0.015)
-0.066
(0.008)
-0.042
(0.021)
-0.027
(0.037)
Col. to H.S.
Ratio of median wage
0.053
(0.017)
0.008
(0.008)
0.016
(0.004)
0.036
(0.011)
0.022
(0.019)
∆ Col. to H.S.
∆ Ratio of median wage
-0.070
(0.020)
-0.038
(0.005)
-0.026
(0.003)
-0.007
(0.003)
0.021
(0.012)
H.S. to Dropout
Ratio of median wage
-0.063
(0.023)
-0.052
(0.010)
-0.052
(0.006)
-0.071
(0.016)
-0.093
(0.026)
∆ H.S. to Dropout
∆ Ratio of median wage
0.042
(0.008)
0.018
(0.004)
-0.010
(0.002)
-0.007
(0.004)
0.010
(0.009)
Constant
0.046
(0.008)
0.036
(0.004)
0.011
(0.002)
-0.010
(0.005)
-0.023
(0.009)
Pseudo R2
0.075
0.086
0.063
0.023
0.008
Koenker-Basset χ2
T = 281.7
degrees of freedom = 2
Prob. < 0.005
Number of observations = 71,537
able is that the wage adjustments of certain
occupations, employers, or occupationemployer cells are continually more
responsive to inflation than are others.
The CSS measures wages in nonproduction
occupations with the thickest, best-
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Table 8
Spearman Rank Order Correlations of Wage Changes Across
Years, by Type of In ationary Episode
A. EPISODES OF STABLE INFLATION
Years
Within-Episode, One-Year Correlations
Between-Episode First-Year Correlations
1st, 2nd
2nd, 3rd
3rd, 4th
4th, 5th
1961
1961-65
-0.125
(0.000)
-0.191
(0.000)
-0.086
(0.001)
-0.118
(0.000)
1991-92
0.071
(0.002)
-
-
-
1991
-0.055
(0.497)
1993-96
-0.057
(0.017)
-0.019
(0.460)
0.085
(0.004)
-
1993
-0.040
(0.644)
1991
-0.044
(0.053)
B. EPISODES OF INCREASING INFLATION
Years
Within-Episode, One-Year Correlations
Between-Episode First-Year Correlations
1st, 2nd
2nd, 3rd
3rd, 4th
1968
1968-70
-0.100
(0.000)
-0.325
(0.000)
-
1974-75
0.129
(0.000)
-
-
1974
-0.005
(0.890)
1977-80
-0.008
(0.839)
-0.123
(0.000)
-0.158
(0.000)
1977
-0.163
(0.002)
1974
-0.027
(0.502)
C. EPISODES OF DECREASING INFLATION
Years
Within-Episode, One-Year Correlations
1st, 2nd
2nd, 3rd
3rd, 4th
1971-72
-0.012
(0.745)
-
-
1975-76
0.141
(0.000)
-
-
1981-84
-0.089
(0.000)
1985-86
-0.025
(0.311)
-0.060
(0.017)
-
Between-Episode First-Year Correlations
1971
0.012
(0.619)
-
defined, inter-industry markets. Thus, it
should capture mobile workers—those likely
to be most sensitive to market conditions.
1975
1975
0.043
(0.403)
1981
-0.021
(0.784)
-0.013
(0.800)
1985
-0.061
(0.457)
-0.103
(0.065)
1981
-0.052
(0.058)
In addition, the large employers in the CSS
are arguably more able to track relevant
market changes than smaller employers.
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For monitoring and policy purposes,
tracking bellwether jobs could provide
useful signals of inflationary pressures.
To investigate whether such bellwether
jobs are likely to exist, we look for evidence
of serial correlation in wage changes within
and between types of inflationary episodes.
Table 8 presents the results. The top panel
focuses on the three periods of stable inflation during our sample time frame. The
stability during these times provides a
basis for comparison for the periods of
rising and falling inflation. The first four
columns present correlation coefficients
between consecutive years during these
three episodes. Were the majority of
divergences in wage changes during these
periods reflective of long-term divergent
trends in occupation or employer differentials,
these correlations would be positive—an
above-average change during one year is
likely to be followed by a similar one
during the next year. On the other hand,
if they reflected errors and corrections, or
normal compositional changes in the
workforce (promotions, hires, etc.) the
correlations would be negative: An unusually big average increase in one year is
likely to be followed by a below-average
adjustment next year.
During the stable periods, most (five
out of eight) of the one-year correlations
are statistically significant and negative,
suggesting the importance of error, corrections and compositional shifts in the wage
changes we observe. Across episodes, the
correlations are essentially zero, suggesting
that no particular type of job tends to benefit (or lose out) more than others during
periods of stable inflation.
The middle panel repeats the exercise
for periods of increasing inflation during
the sample years. Again, most of the correlations are statistically significant and
negative—providing no evidence in
support of bellwether jobs. Indeed, it
looks as though deviations from the
median during rising inflation are even
more likely to be compensated for later on
than if they occur during periods of
stability. And across episodes, jobs that
were early, fast movers in one period of
Figure 7
Model Predictions vs Actual Quantities:
1990-1996
Percentiles: 10, 25, 50, 75, & 90. Circles indicate model.
15
Percent change
10
5
0
-5
90
92
94
Year
inflation are, if anything, less likely to lead
the way during subsequent episodes.
The bottom panel looks at periods of
declining inflation. When inflation is
declining, the evidence of mean reversion
seen in the upper two panels is attenuated.
Most of the correlation coefficients are
small and poorly identified, suggesting an
even more random process. And again,
across episodes, there is no evidence to
suggest the existence of bellwether jobs.
Thus, the evidence thus far argues
strongly against the existence of bellwether
jobs whose wage changes could signal
inflationary changes. If bellwether jobs
exist, they are a very small proportion of
jobs in occupations or firms typical of the
CSS. That is, they may be in smaller firms,
or in production occupations, for example.
In the CSS, being out on a tail is often preceded or followed by an opposite-tail wage
change during the previous or following
year. Which jobs land in one of the tails
appears to be idiosyncratic, however,
rather than a permanent feature of the job.
Are the 90s Different?
Our last empirical exercise examines
whether the wage changes during the 1990s
deviated from historical patterns, as some
analysts suggest. We compare the actual
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path of wage-change quantiles during the
1990s to predictions based on the historical
model estimated in Table 6. We want to
see if the lower quantiles had much less
wage growth during the 1990s than
expected, given the underlying rates of
inflation, productivity and unemployment.
Figure 7 shows the results of the exercise. Each quantile is represented with two
lines: its actual wage change (the unmarked
line) and the model prediction (the line
with circles). For most of the period, the
model fits quite well. Only for 1994, 1995
and 1996 does the model miss much.
During those years, the actual wage
change was lower than the model
predicted for the 10th percentile wage
change by one to two percentage points.
For the other parts of the distribution, the
model performs quite well. Thus, the evidence of a sea change in wage-setting
behaviors finds little support in the CSS so far.
(highest) wage shocks in any
year rises almost one-for-one
with the level of inflation.
• The lowest wage changes in any
year do not rise much with
inflation.
2. Other factors (including unemployment, inequality, and productivity
growth) also affect the dispersion of
wage changes. In particular:
• Bad wage shocks are mitigated
when unemployment is low.
In addition, from a monetary policy or
monitoring perspective, we add two
intriguing findings:
1. Wage changes are slightly negatively
autocorrelated over time.
• Negative autocorrelations refute
the notion of bellwether jobs (i.e.,
occupations or firms that regularly lead the way when prices
rise) and suggests that inflation
causes errors and corrections.
CONCLUSION
We have examined the Federal Reserve
Bank of Cleveland Community Salary Survey
from 1957 to 1996 for the impact of inflation on the size of good or bad wage shocks.
Most importantly, our exploratory exercise
uncovers strong evidence that the pattern
of wage changes is not neutral with respect
to inflation and other economic conditions.
This finding suggests that the influence
of errors and corrections, nominal rigidities,
or business-cycle influences on wage-setting
varies substantially within the labor market.
These regularities provide a new window for
comparing the behavior of wages with model
predictions in our competitive economy.
In particular, we find that representative or
aggregate agent models abstract from
important determinants of wage changes.
We summarize our main findings as
follows:
1. The dominant factor in predicting
the distribution of wage changes is
the inflationary environment. In
particular, wage change dispersion is
higher if inflation is higher because:
• Small autocorrelations refute
the existence of a permanent
competitive fringe of firms or
occupations and suggests that
many jobs sustain occasional
wage shocks.
2. There are no apparent changes in the
early 1990s. The pattern of wage
growth was predictable for the low
levels of inflation and unemployment
during the period.
Under standard models of wage determination, many of these findings are puzzling.
As such, they open the door to new areas
for exploration. The next steps are to examine
other wage data to confirm the patterns
visible here, to refine our understanding of
the patterns, and to test the predictions of
particular variants of wage-setting models
against observed patterns.
• The magnitude of the best
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REFERENCES
Groshen, Erica L. “Rising Inequality in a Salary Survey: Another Piece
of the Puzzle,” Federal Reserve Bank of Cleveland Working Paper
9121, December 1991.
_______, and Mark E. Schweitzer. “Identifying Inflation’s Grease
and Sand Effects in the Labor Market,“ in The Costs and Benefits of
Price Stability, Martin Feldstein, ed., University of Chicago Press,
1999, pp. 273-308.
Koenker, Roger, and Gilbert Basset, Jr. “Regression Quantiles,”
Econometrica (January 1978), pp. 33-50.
_______, and _______. “Robust Tests for Heteroscedasticity
Based on Regression Quantiles,” Econometrica (January 1982),
pp. 43-61.
Schweitzer, Mark E. “Workforce Composition and Earnings Inequality,”
Federal Reserve Bank of Cleveland Economic Review (2nd Quarter
1997), pp. 13-24.
Shapiro, Carl, and Joseph E. Stiglitz. “Equilibrium Unemployment as a
Worker Discipline Device,” American Economic Review (June 1984),
pp. 433-44.
Sparks, Roger. “A Model of Involuntary Unemployment and Wage
Rigidity: Worker Incentives and the Threat of Dismissal,” Journal of
Labor Economics (October 1986), pp. 560-81.
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F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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John C. Haltiwanger is a professor of economics at the University of Maryland.
Commentary
tigates the relationship between the distribution of wage adjustments at the micro
level and inflation.
The paper is primarily an empirical
exercise. The question at hand is whether
changes in the rate of inflation have a neutral effect on the distribution of wage adjustments at the micro level. A simple view is
that inflation should affect all participants
similarly (i.e., all relevant parties simply
care about real wages) and thus inflation
should have little or no impact on the distribution of wage adjustments. The striking finding that emerges is that inflation
is dramatically non-neutral in terms of its
impact on the distribution of wage adjustments. Moreover, the pattern of nonneutrality is quite interesting. Wage changes
at the upper tail of the wage change distribution respond to a much greater extent
than wage changes in the lower tail of the
wage distribution. The authors also investigate two related interesting questions
about the nature of this non-neutrality.
First, they ask the question as to whether
there are bellweather jobs—in the sense
that perhaps the non-neutrality is such
that wages respond to inflation for some
types of jobs more quickly than for others.
They find little or no evidence for bellweather jobs. Second, they ask the question
about whether this non-neutrality has
changed over time, with a particular emphasis
on the 1990s. The motivation for the
focus on the latter is the popular perception that wage responses to inflation have
been mitigated during the 1990s due to
increased job insecurity and that this
would, in turn, impact the nature of the
non-neutrality. They find little or no evidence of changes in the non-neutrality.
While I find the basic facts and related
empirical exercises quite interesting, this
work is somewhat difficult to interpret,
given the lack of much of an overall conceptual framework to help us understand
the possible sources of connections between
changes in inflation and changes in the
John C. Haltiwanger
T
his fine paper fits into a growing literature in macroeconomics that emphasizes the idea that it is difficult, if not
impossible, to understand aggregate fluctuations without understanding the underlying
behavior of heterogeneous microeconomic
agents. It is self-evident that individual
households, workers and businesses have
heterogeneous characteristics and are subject
to idiosyncratic events that yield dramatically different outcomes at the microeconomic
level. This heterogeneity in microeconomic outcomes typically dwarfs aggregate
fluctuations so that for most households
and businesses, the macro economy is a relatively unimportant factor in determining
their fortunes. In spite of this overwhelming micro heterogeneity, macroeconomists
have traditionally abstracted from this heterogeneity because the common view is
that the micro heterogeneity washes out
in the aggregate. Thus, macroeconomists
have traditionally developed models
describing the behavior of the typical firm
or the typical worker and worried relatively
little about the differences in outcomes
across economic agents.
The growing availability of micro panel
data on households and businesses (and in
some cases linked employer-employee
micro data) has made it increasingly clear
that this traditional approach misses important aspects of aggregate fluctuations. That
is, there is often a strong connection (albeit
with questions about the direction of
causality) between the aggregate fluctuations
and the nature and extent of heterogeneity of
outcomes across agents. Technically, the
issue is often whether there is a connection between the fluctuations in the first
and higher moments of the distributions
of outcomes. In the current paper, this is
precisely the question, as the paper inves-
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distribution of wage adjustments. This is
not really a criticism of the current paper,
but rather illustrates the need for a conceptual framework to help interpret these
interesting findings. Put differently, we
need to consider the sources of heterogeneity in wage adjustments at the most
basic level and how this heterogeneity is
likely to interact with changes in the rate
of inflation.
Many factors may be at work in the
underlying distribution of wage adjustments. Changes in relative labor supply
and labor demand for workers of different
characteristics (both those that are easily
observable to the researcher and those that
are not) are obviously important in this
context. The institutional structure (e.g.,
unionization) and differences in the manner
that wages are determined by sector or firm
also are likely to be important.
In considering these alternative possible factors, in light of the findings in this
paper, it is useful to consider what we know
about changes in the structure of labor markets during the sample period for this
analysis. One of the primary recent empirical findings from applied labor economics
research is the observation that there have
been systematic increases in the dispersion
of wages across workers during the last
few decades. While the sources of this
rising wage inequality are still somewhat
in dispute, there is a growing consensus
that this rising wage inequality is due to a
rising relative demand for skilled workers.
The sources of the latter might be changing
technology (broadly defined) or changing
world markets but, nevertheless, the return
to being skilled has risen during this period
of time. These fundamental changes in the
dispersion of wages are closely linked to
the changes in the distribution of wage
adjustments. Moreover, the rising wage
inequality was especially dramatic during
the 1970s and 1980s—a period in which
the rate of inflation is high and there are
large associated changes in the distribution
of wage adjustments. Thus, one question
that arises is whether any aspects of their
findings are spurious. Perhaps what is driving the results are the underlying factors
that cause rising wage inequality and that
the timing of these factors corresponds to
a period with many dramatic changes in
the U.S. economy.
Another related and relevant hypothesis is that it is no coincidence that the
observed long-run structural adjustments
in the labor market were bunched during
this period of volatile business-cycle fluctuations. That is, either the business-cycle
fluctuations caused a change in the timing
of the structural adjustment, or the businesscycle fluctuations were partly due to the
intense period of structural adjustment.
Moreover, since this period of turbulence
in labor markets is also associated with high
and volatile rates of inflation, this may
underlie the connection between inflation
and the distribution of wage adjustments.
All of this discussion is speculative, however. The main point is that it will be difficult to sort out the factors that generate
this paper’s interesting results without a
conceptual structure (and associated
empirical analysis) to help us understand
the factors driving the distribution of wage
adjustments and the potential link to inflation. More generally, the question is whether the results are driven mostly by the
turbulent events of the 1970s and 1980s—
a period in which there were substantial
fluctuations in macro variables like inflation and unemployment, and a period of
substantial structural change in the economy and labor market.
I have some other relatively minor concerns about specific aspects of the analysis.
While the CSS appears to be a very rich and
unique dataset, there are concerns about
the representativeness of the sample. It is
intended to be representative of large
employers in the area. Since the sample
period here is so long, these concerns may
be especially important. That is, not only
is one concerned about how representative
the sample is at a given moment, but also
whether its representativeness has changed
over time. A somewhat related concern
is that their analysis is in terms of the
unweighted wage adjustment distribution
—an interesting alternative would be to
consider the hours-weighted wage-adjust-
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ment distribution. If their results are driven
by occupation/employers with small hours
weights, then the results are of less interest.
Finally, the authors make a relatively
big deal about the finding of weak or negative autocorrelations in wage adjustments.
They want to interpret this as evidence
against bellweather occupation and jobs.
This interpretation may be correct, but
there may be a number of factors underlying the weak or negative autocorrelations
in changes observed in the data. For
example, it may be that wage adjustments
are lumpy at the micro level (due perhaps
to some rigidities or fixed adjustment
costs) which can lead to weak and negative autocorrelation. This would yield a
very different interpretation of the findings. To sort out these alternatives, we
need more structure and further analysis.
To sum up, this paper represents an
installment on a very nice research agenda
with a rich and unique dataset. This particular installment offers some interesting
new “facts.” While there may be some
concerns about the robustness of these
facts to measurement concerns and about
whether the results are idiosyncratic to the
turbulence of the 1970s and 1980s, they
are interesting and deserve further consideration. We need more structure to interpret and understand these new facts, but
that awaits another installment from these
authors or in studies stimulated by these
new facts.
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F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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Kenneth J. McLaughlin is an associate professor in the Department of Economics at Hunter College and the Graduate School of the City University of
New York. The author wishes to thank David Lebow, Gil Maduro, Joseph Ritter, Richard Startz, and participants at the Federal Reserve Bank of
St. Louis’ Twenty-Third Annual Economic Policy Conference, and participants in seminars at Hunter College and the Federal Reserve Banks of Atlanta
and New York.
Are Nominal
Wage Changes
Skewed Away
From Wage
Cuts?
Correlations of these properties with inflation also help to identify skewness away
from nominal wage cuts.
Although these papers have much
in common, the specific techniques, data
sets, and even conclusions vary. With a
series of simple calculations on a single data
set, I intend to integrate the main results
from this new and exciting area of research
to shed light on an important question for
macroeconomic policy and economic theory: Are nominal wage changes skewed away
from wage cuts? In particular, does downward nominal rigidity censor some wouldbe wage cuts, transforming some wage
changes that would be negative into zerowage changes? To answer this question, I
document key properties of the distribution
of wage changes in panel data. I show that
tests based on the familiar skewness coefficient are particularly weak in the presence
of fat-tailed distributions, such as the distribution of wage changes, so I introduce
symmetrically differenced histograms, a
convenient way to detect asymmetries
visually. I also apply mean-median differences and sign tests of symmetry to the
wage change data.
Evidence of skewness of wage changes
is decisive; however, establishing that wage
changes are skewed away from wage cuts
requires more than evidence of skewness
of wage changes. Is downward nominal
rigidity the source of the skewness of wage
changes, or is the distribution of wage
changes more generally skewed? To sort
this out, I calculate measures of thinning, a
reduction in the frequency of wage change
observations below zero (Lebow, Stockton,
and Wascher 1995; Card and Hyslop 1997;
and Kahn 1997); the calculations do point
to the thinning of wage cuts.
A complete explanation also must
account for two other features of wage
change distributions. First, by focusing
on wage changes close to the median, I
show that wage changes are skewed right
over a range that has nothing to do with
Kenneth J. McLaughlin
R
eal-wage cuts are much more common
than nominal wage cuts. Why? By
definition, real cuts must be more common if inflation is positive. Yet there might
be more to it. Perhaps workers suffer from
money illusion. Maybe managers cannot
cut pay in nominal terms, but they can cut
real wages. As a result, a low-inflation
economy might be a high unemployment
economy. And moderate inflation might
“grease the wheels” of the labor market.
These issues are being addressed in
a burgeoning body of literature on wage
changes in panel data (McLaughlin 1994;
Lebow, Stockton, and Wascher 1995; Craig
1995; Akerlof, Dickens, and Perry 1996;
Card and Hyslop 1997; Kahn 1997; Altonji
and Devereux 1997; Crawford and Harrison
1997; and Christofides and Stengos 1998).
To detect the existence of downward rigidity
of nominal wages, this literature identifies
properties of the distribution of wage changes:
• The frequency of wage cuts
• A spike or mass-point of observations with no change in pay
• Skewness
• Thinning of the distribution
below zero
• Holes in the distribution
around zero
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downward nominal rigidity at zero. This
violates the mirror-image assumption of one
thinning estimator; consequently, Lebow,
Stockton, and Wascher; and Card and Hyslop
overestimate the thinning of nominal wage
cuts. Second, I show that skewness of wage
changes is basically unrelated to inflation;
that is, higher inflation does not reduce
the impact of any nominal wage rigidity.
I begin by introducing the issues and
methods in the context of the literature.
intrayear data from the Survey of Income
and Program Participation (SIPP); Card
and Hyslop (1997) using the PSID and
matched samples from the Current Population
Survey (CPS); and Kahn (1997) using
the PSID confirms my findings of surprisingly frequent reported wage cuts even
for stayers.
Regarding the complementary question
of downward rigidity, my analysis was limited to computing (a) the size of the spike
at no change in pay and (b) skewness coefficients. I found that an additional 7 percent
of the stayers report no change in pay from
year to year, and that the distribution of
wage changes was skewed to the right, away
from wage cuts (McLaughlin 1994).1
Lebow, Stockton, and Wascher; Card and
Hyslop; and Kahn also document the spike,
although Card and Hyslop (1997, note 13)
find a substantially larger spike by analyzing hourly workers. Some of the spike at
zero could be due to variation in interview
dates in the PSID. Lebow, Stockton, and
Wascher estimate that 1 percentage point
of an 8-percentage-point spike is attributable to interviews occurring within a year.
They also estimate that an additional 3
percentage points are due to rounding of
wage reports. Card and Hyslop (1997,
p. 83), on their CPS sample of hourly
workers, also estimate that about half of
the spike is attributable to rounding errors.
This literature takes a variety of
approaches to estimating skewness of wage
changes. Using the skewness coefficient, I
found that the overall distribution of wage
changes is skewed to the right; however, I
also reported that the distributions of wage
changes of nonunion workers, nonminimum-wage workers, and salaried workers
are dead-on symmetric (McLaughlin 1994,
Table 2). Similarly, Lebow, Stockton, and
Wascher report small positive skewness
coefficients for all stayers, and sizable positive skewness coefficients for hourly workers. (See also Crawford and Harrison (1997)
and Christofides and Stengos (1998) for
skewness estimates of wage changes in
Canadian union contract data.)
The subsequent literature focuses on
the complementary question by estimating
ONE LITERATURE,
TWO QUESTIONS
1
Card and Hyslop (1997, pp. 7576) conjecture that I failed
to detect nominally induced
asymmetries because I pooled
annual distributions of real-wage
changes. But pooling the distributions had no bearing on my
conclusions. I reported the spike
at zero and positive skewness;
I also found that wage changes
vary closely with inflation, skewness does not vary with inflation,
and wage changes of nonunion
and nonminimum-wage workers
are symmetric (McLaughlin
1994). These findings led me
to conclude that there was little
evidence of downward nominal
wage rigidity.
One can go a long way toward reconciling disparate conclusions in the literature
by drawing a single distinction. That is,
one must distinguish between the level or
frequency of nominal wage cuts and the
sensitivity of nominal cuts to downward
rigidities. There is a distinct possibility
that nominal wage cuts are common and
wage changes are skewed away from wage
cuts. The first property of nominal wage
changes answers the question, “How common are wage cuts in nominal terms?”
The second property answers a complementary but distinct question: Is there
evidence of downward rigidity reducing
the frequency of nominal wage cuts? One
could conclude that nominal wage cuts
are common and that they would be more
common if nominal wages were not
downwardly rigid.
Wage Cuts Are Common,
But Are They Common Enough?
In McLaughlin (1994), I documented
that real-wage cuts are frequent and nominal
wage cuts are not rare. Using survey-week
data from the Panel Study of Income
Dynamics (PSID), I found that 43 percent
of workers who do not change employers
(i.e., stayers) suffer real cuts in straight-time
pay (hourly wage or salary) on the main
job. For about 17 percent of the sample,
the wage cuts are nominal. The subsequent
literature focuses on nominal wage changes.
Research by Lebow, Stockton, and Wascher
(1995) using the PSID; Craig (1995) using
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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whether nominal wage cuts are too rare;
that is, whether the left side of the distribution is too thin below zero (Lebow, Stockton,
and Wascher 1995; Card and Hyslop 1997;
Kahn 1997). Lebow, Stockton, and
Wascher’s measure of skewness subtracts
the proportion of observations below zero
from the proportion above twice the median.
Since zero and twice the median are the
same distance from the median, this thinness measure would be zero for symmetric
distributions and positive for right-skewed
distributions. Their skewness measure is
6.8, so the left tail below zero is about 7
percentage points thinner than its mirror
image on the right side of the distribution.
Card and Hyslop also assume that the right
tail would be the mirror image of the left
in the absence of nominal rigidity. For
each year, they provide kernel estimates
(basically smoothing) of the actual and
counterfactual histograms and find a range
of thinning from 6 to 14 percentage points,
depending on the year. These are in line
with Lebow, Stockton, and Wascher’s estimate of 10-percentage-point thinning for
hourly workers.
By using year-to-year variation in the
position of the wage change distribution,
Kahn (1997) estimates the extent of nominal
rigidities without imposing the mirrorimage assumption. One checks whether
bars of the wage-change histogram tend
to be shorter in years when those bars lie
below zero. For instance, is the third bar
below the median shorter in those years
when it lies below zero? Kahn’s regression
estimates, which weight the effects across
bars, imply that 9 percent of hourly workers’
would-be wage cuts are censored at zero.
The only evidence of downward rigidity
for salaried workers is early in her sample
period (before 1982), but this evidence
appears to be dominated by more frequent
than expected nominal cuts after 1982.
With the two questions distinguished,
the papers in this literature share much in
common. Nominal wage cuts are not rare,
but there is evidence of a spike at zero,
positive or right skew of distribution, and
thinning of the distribution below zero.
The evidence is much weaker, however, for
salaried workers and nonunion workers.
Another common feature is that about
three-quarters of would-be wage cuts actually occur. Removing downward nominal
rigidity would increase the frequency of
reported wage cuts of stayers from the
observed 17 percent to 22 percent (using
Kahn’s estimates of thinning) or from 18
percent up to 24 percent (using Lebow,
Stockton, and Wascher’s estimates of thinning). Even in the CPS sample of hourly
wage workers, about three-quarters of the
predicted wage cuts appear in the data
(Card and Hyslop 1997).
If nominal wages are downwardly rigid,
then there should be less skewness and thinning in high inflation periods. The evidence
on this important point is mixed. I found that
the skewness coefficient is positively correlated with anticipated and unanticipated
inflation, which is not consistent with inflation relaxing the impact of nominal wage
rigidity (McLaughlin 1994, note 12). Lebow,
Stockton, and Wascher’s (1995) thinness
measure is not significantly correlated with
inflation on their sample of all stayers, although
the correlation is negative for hourly workers. On the CPS sample of hourly workers,
Card and Hyslop (1997) find less thinning in
high inflation periods. Hence any evidence
of inflation reducing the impact of nominal
wage rigidity is limited to hourly workers.
But Are Wage Cuts Common?
Perhaps survey reports of wages are
riddled with error and the appearance of
nominal wage cuts is illusory. The wage
variables in these surveys refer to straighttime pay on the main job during the survey
week or the most recent pay period; wages
are not generated by dividing annual earnings last year by annual hours worked.
Indeed, for the SIPP data on hourly workers,
a respondent is asked what the hourly wage
rate was on his last pay stub (Craig 1995).
But the role of measurement error in inflating reported wage cuts deserves scrutiny.
To identify the frequency of true wage
cuts, I estimated the variance of the measurement error component and applied a
mean-preserving compression to correct
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the distribution of wage changes (McLaughlin
1994). I took three very different tacks to
estimate the error variance:
industry, occupation, location, and year.
Since very few of the reported wage cuts
align with union wage concessions, Shea
concludes that most nominal wage cuts in
the PSID are attributable to measurement
error. A problem with Shea’s method is that
wages of union workers change without
corresponding changes in union pay scales.
Union wages are typically assigned to jobs,
and workers regularly move from job to job
in some union firms. This was the case in
the large manufacturing firm used in the
PSID’s Validation Study; indeed, workers
in the validation study had great difficulty
reporting hourly wages because they
changed job assignments week-to-week and
even day-to-day (Bound, Brown, Duncan,
and Rodgers 1994).3
Altonji and Devereux (1997) provide
maximum-likelihood estimates of an
empirical model of wage rigidity and measurement error. They exploit cross-sectional variation in the position of the wage
change distribution to estimate thinning.
That is, Altonji and Devereux replace
Kahn’s (1997) time-series variation with
cross-sectional variation in the distribution’s
position, and they add a distributional
assumption in the process. In addition,
Altonji and Devereux simultaneously
estimate the variance of the measurement
component. For their model to account
for the spike at zero nominal wage growth,
small wage cuts must be censored. Hence,
the presence of small wage cuts in the data
must (in their model) be attributed to
measurement error. Altonji and Devereux
conclude that about 80 percent of observed
wage cuts are an artifact of measurement
error; however, this would overstate the
extent of measurement error if some small
wage cuts were genuine.
The extent of measurement error
is important for assessing the frequency
of nominal wage cuts but not for the
complementary question posed in this
paper: Is there evidence of downward
rigidity reducing the frequency of nominal
wage cuts? Adding a symmetric measurement-error component would not bias
any of the skewness tests or thinning
measures.
• First, I drew reliability measures
of wage change variables from
validation studies (Bound and
Krueger 1991; Bound, Brown,
Duncan, and Rodgers 1994).
• Second, I used the frequency of
reported nominal wage cuts of
minimum-wage workers, which
were assumed to be due to measurement error.
• Third, I associated measurement
error with the stationary component
of wage change residuals, and the
random walk component of wages
was classified as true variation.
2 Akerlof, Dickens, and Perry
(1996, note 10) criticize my
use of a mean-preserving compression to correct the distribution of wage changes. Their
criticism builds from the
assumption that the true distribution of wage changes is asymmetric. Wage changes are not
severely skewed, however, and
Akerlof, Dickens, and Perry do
not assess how sensitive my
corrections are to mild asymmetries. In addition, one can redo
my calculations on symmetric
subsamples without affecting
any of my conclusions
(McLaughlin 1999).
3 This point was driven home
recently when a colleague of
mine reported that his salary
for the new academic year had
dropped 25 percent. The union
pay scale governing his employment has not changed in years,
but he had completed his term
as acting dean.
The three methods pointed to a single
conclusion. Although significant measurement error is present in wage changes,
wage cuts remain fairly common in the
corrected distributions.2 In particular, my
most conservative measurement error correction reduced the frequency of nominal
wage cuts from 17 percent to 12 percent.
Suspicious that measurement error is
the source of reported nominal wage cuts,
Akerlof, Dickens, and Perry (1996) asked
respondents in a Washington, D.C., telephone
survey whether they had experienced wage
cuts during the previous year. That is, rather
than differencing wage responses across
years, Akerlof, Dickens, and Perry asked a
single qualitative question directly. About
3 percent of the stayers reported cuts in base
pay. Akerlof, Dickens, and Perry conclude
that the frequency of wage cuts in panel data
is an artifact of measurement error. It is well
known, however, that survey respondents
under report embarrassing personal information, so this survey instrument probably
undercounts wage cuts.
In a comment on Card and Hyslop
(1997), Shea (1997) assesses the reliability
of wage reports of union workers in the
PSID. Shea matches union workers in
the PSID to union wage settlements by
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WAGE CHANGES IN THE PSID
Table 1
To determine whether wage changes
are skewed away from wage cuts, I use
data from the PSID, which has followed
thousands of households since 1968. The
PSID includes annual observations covering
survey week pay with the main employer.
My measure of wages is the respondent’s
report of his survey week pay on his main
job. For hourly workers, I use the straighttime hourly wage rate. For salaried workers;
I do not convert salaries into hourly wage
rates; hours-induced wage variability
might mask salary rigidity. This is particularly important in light of the errors in
reported hours of work (Bound, Brown,
Duncan, and Rodgers 1994). Wage
changes are the annual differences of
log wages times 100.
My data set combines the PSID’s 1992
cross-year individual file with 22 annual
family files. Because downward wage
rigidities are not expected to be important
for workers who change employers, the
sample is limited to household heads
(since 1971) and spouses (since 1979)
who stayed with their employers since the
previous year (i.e., stayers). To be included
in the sample, a worker must also report
his wage in adjacent years.4 In the resulting
sample, 5,887 persons contribute 34,633
person-year observations on wage changes
—an average of nearly six wage-change
observations per person.
Nominal Wage Changes and Inflation
Panel Study of Income Dynamics, 1971-92
Inflation Process
ARIMA (0,1,1) AR(3) ARIMA (0,1,1)
Variable
Intercept
Inflation
3.309
(.602)
.840
(.103)
Anticipated Inflation
Unanticipated Inflation
R2
No. of Observations
Unit of Observations
.777
21
Annual Avg.
3.063
(.589)
.880
0(.101)
.584
0(.176)
.810
21
Annual Avg.
2.847
(.645)
.928
0(.113)
.592
0(.183)
.805
21
Annual Avg.
a
Least-squares regressions with standard errors in parentheses. Nominal wage changes are for
stayers in the PSID; inflation is based on the GDP Deflator. All variables are computed as annual
differences of logs.
b
Additional regressors include years of age and education, as well as indicators of sex, race, marriage, disability, occupation, industry, and union status, and change in union status; an intercept
is also included.
of stayers, I compute the average rate-ofchange of nominal wage over the previous
year. Table 1 contains the results of
regressing this annual wage change variable
(in percentage terms) on the rate of inflation, based on the GDP Deflator. Consistent
with my earlier findings (McLaughlin
1994, p. 403), nominal wages move closely
with the price level. The estimated effect
is .84, which is 1.6 standard deviations
from one, so the hypothesis that nominal
wages and prices move one for one is
not rejected. The test is not decisive,
so a suspicion of incomplete indexing
of wages to prices might remain.
However, suspicion of incomplete
indexing or money illusion vanishes if the
inflation rate is partitioned into anticipated
and unanticipated components. To reach
this conclusion, I use time-series methods
to generate one-step-ahead forecasts of
inflation (i.e., anticipated inflation) and
forecast errors (i.e., unanticipated inflation). Like Pearce (1979), and Fama and
Gibbons (1984), I find that the inflation
rate is the sum of a random-walk component and a stationary component; in par-
Do Wage Changes Reflect
Money Illusion?
The bigger issue is money illusion.
Downward wage rigidities associated with
infrequent wage cuts would constitute
money illusion, but placing the issue in a
wider context is essential. The broader
question is: How do nominal wages move
with the price level? Or equivalently: How
does the rate-of-change of nominal wages
vary with the inflation rate? Perhaps some
nominal wage cuts are censored at zero, but
the overall distribution of wage changes
could be tightly linked to inflation.
This is the case in longitudinal data
from the PSID. For each annual sample
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
121
.918
0(.049)
.717
0(.100)
.018
34,633
Individual b
4 Also excluded are top-coded
observations, which were common during the mid-1970s. See
McLaughlin (1999) for details of
the sample exclusions.
M AY / J U N E 1 9 9 9
5
The result also is confirmed in
aggregate data (e.g., Startz,
this issue). The principal
advantage of using panel data
is in controlling for sample
composition; in addition,
using panel data at the
individual level allows for
additional regressors.
6 Ahmad and Li (1997) have
proposed a formal test of
symmetry that is closely related
to symmetrically differenced histograms, and their test has been
applied to Canadian wage-change
data by Christofides and Stengos
(1998). The test amounts to
summing the squares of the values of the symmetrically differenced histogram. Ahmad and Li
prove that the kernel-based test
statistic is asymptotically normal.
Subtracting the Left Side
from the Right Side
ticular, the first difference of the inflation
rate follows a first-order moving-average
process (i.e., MA(1)), so the inflation rate
is an integrated first-order moving-average
(i.e., ARIMA(0,1,1)) process. (Details are
available on request.)
Table 1 displays the results of regressing
nominal wage changes on anticipated and
unanticipated inflation rates. Nominal wage
changes move one-for-one with anticipated
inflation, and there is a strong (but weaker) positive relationship between nominal
wage changes and unanticipated inflation.
The results are robust to alternative specifications of the time-series process. For instance,
in Table 1, the relationship between nominal wage changes and inflation components
is essentially unchanged if a third-order
autoregressive model is used to compute
anticipated and unanticipated inflation
rates. So incomplete indexing of nominal
wages to prices appears to reflect that
inflation is not fully anticipated.
This result is confirmed on individuallevel data from the PSID.5 Here I regress
an individuals’ nominal wage change on
anticipated and unanticipated inflation
rates, as well as on the labor economist’s
standard set of regressors (including years
of age and education and indicators of sex,
race, occupation, industry, and union status). The estimated effects of the inflation
components, which are reported in Table 1,
confirm the pattern. From the relationship
between nominal wage changes and components of inflation, there is no evidence
of money illusion.
In terms of monetary policy, this
suggests no role for moderate inflation in
greasing the wheels of the labor market.
Suppose, however, that one detects evidence of nominal rigidity by focusing on
the nominal wage change distribution
around zero. Such evidence of money
illusion might be treated as a problem
to be solved by monetary policy, but
downward rigidity around zero should
be treated as a higher-order problem.
The wider context—that the overall
distribution of nominal wage changes
moves one-for-one with anticipated
inflation—must not be dropped.
Visual inspection of a distribution can
sometimes reliably detect departures from
symmetry. But visually inspecting the histogram, matching bars on each side of the
distribution, can be misleading if departures from symmetry are not severe. This
is particularly important in the current
context, where stayers’ wage change histograms in the PSID appear to be fairly
symmetric (McLaughlin 1994).
To aid the eye, I present symmetrically
differenced histograms. I compute the
histogram based on equal-sized intervals
around the median, flip the left side of
the distribution over onto the right, and
difference the two.6 Here I subtract the
left from the right, so a positive (negative)
value indicates that the right (left) side
of the distributions is thicker than the
left (right) side over that particular
interval. Since the histogram sums to
100 percent (with 50 percent on each
side of the median), the symmetrically
differenced histogram sums to zero.
For a sample drawn from a symmetric
distribution, the symmetrically differenced
histogram would be a scatter of points
along the zero line. Alternatively, suppose
the left side of the nominal wage change
distribution was thinned below zero, with
these would-be wage cuts piling up at zero.
Such a density function is illustrated in the
upper-left panel of Figure 1, and its symmetrically differenced histogram in the
lower-left panel. Since the spike at zero
lies below the median, the symmetrically
differenced histogram has a negative spike
at twice the median. (A reference line is
drawn at the median.) Values are zero up
to twice the median, and positive values
beyond this point reflect that the left tail
is thinner than the right.
In addition, perhaps some small wage
increases or decreases are censored at zero.
The right two panels of Figure 1 illustrate
such a density function and its symmetrically differenced histogram. By censoring
half of the small wage changes, two positive
spikes surround the negative spike in the
lower-right panel. So if nominal rigidities
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
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M AY / J U N E 1 9 9 9
Figure 1
Censoring Wage Cuts and Small Wage Changes
-45
-30
-15
0
15
30
45
-45
60
-30
Some Wage Cuts Censored
15
30
45
60
20
30
40
50
-4
0
0
10
20
30
40
50
-2
-4
-6
median
10
Fraction X 100
0
-2
-6
0
2
median
Fraction X 100
2
0
-15
Some Wage Cuts and Small Wage Changes Censored
-8
-8
Symmetrically Differenced Histogram
censor some wage cuts and some small
wage changes, the symmetrically differenced
histogram should resemble the lower-right
panel of Figure 1.
For the sample of stayers in the PSID,
the symmetrically differenced histogram
in Figure 2 does resemble the lower-right
panel in Figure 1. (The stayers’ histogram
of wage changes is also depicted in Figure
2.) Small positive spikes surround a large
negative spike at twice the median, which
indicates some censoring of small wage
changes. Values tend to be positive for
wage changes beyond twice the median,
which indicates that, below zero, the left
side of the distribution is thinner than the
right. But this symmetrically differenced
histogram reveals more than partial censoring of small wage changes and wage
cuts. Two negative values appear just
to the right of the median reference line.
Thus, wage changes just to the left of
the median are more common than those
just to the right of the median. This prop-
Symmetrically Differenced Histogram
erty is common for right-skewed distributions, such as the log-normal. But the
presence of this property in the context
of wage changes is important. There is
more to the skewness of the wage change
distribution than is implied by the censoring of some wage cuts and some small
wage changes.
Test Statistics
Visual evidence from the symmetrically
differenced histograms can be put to formal
tests by computing the skewness coefficient,
the mean-median difference, and the sign
test statistic. On a sample of size N from
distribution function F, I test the null
hypothesis H0 that the distribution of
wage changes x is symmetric; that is,
F(x)=1–F(–x) for all values of the random
variable x.
The skewness coefficient, perhaps the
most familiar measure of symmetry, is the
ratio of the third central moment of x to
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
123
M AY / J U N E 1 9 9 9
Figure 2
tions severely inflate the variance of
the test statistic; that is, fat tails produce
high-variance skewness coefficients.
This explains why skewness coefficients
applied to wage change distributions,
which have fat tails (McLaughlin 1994),
tend to jump around from sample to sample (Crawford and Harrison 1997) and
are sensitive to tail observations (Lebow,
Stockton, and Wascher 1995). Properly
computed standard errors reflect this,
but long-tails render the test weak in
detecting even strongly skewed alternative
distributions. Indeed, the skewness coefficient has trouble detecting the asymmetry
of the log-normal distribution
(McLaughlin 1999).
Table 2 provides a good illustration
of this problem with the skewness coefficient. Despite the apparent skewness of
the wage change distribution in the PSID,
a test based on the skewness coefficient
fails to reject the null hypothesis of symmetry. The estimated skewness coefficient
is .36, but its standard error is .30; however, since the distribution of wage changes
has fat tails, this test’s failure to detect
skewness is not surprising.
Most tables of critical values for
the skewness coefficient are based on a
normal distribution of x. If the distribution of x has fat tails, such critical values
are biased toward zero, which generates
a problem with false positives. For comparison, Table 2 also includes the standard
error of the skewness coefficient under
normality. This standard error is as small
as .01. Symmetry is clearly rejected,
but at this point, whether the rejection
is valid or spurious remains unknown.
A simple by-product of positive
(negative) skewness is that the mean
lies to the right (left) of the median,
which motivates the mean-median difference
(Hotelling and Solomons 1932) as a test.
Under the null hypothesis of symmetry, the
difference between the mean and the median is expected to be zero; furthermore, if
the median m is treated as known, then by
the Central Limit Theorem, the meanmedian difference is asymptotically
normal with variance s2/N. The mean-
Distribution of Nominal Wage Changes
for Stayers
0.12
Fraction
0.09
0.06
0.03
0
-40
-30
-20
-10
0
10
20
Histogram
30
30
40
40
50
0
0
10
20
50
-2
-4
median
Fraction X 100
2
-6
-8
Symmetrically Differenced Histogram
the cubed standard deviation of x. Under
the null hypothesis H0 , the asymptotic distribution of the skewness coefficient is
normal with mean zero and variance:
9 µ6 − 6 µ 4 s 2
+
N
Ns 2
where s is the standard deviation of x, and
µk denotes the kth central moment of x
(Gupta 1967). If F were the normal distribution, then the variance of the skewness
coefficient would simplify to 6/N.
As a test of symmetry, the skewness
coefficient has problems with false negatives. First, some skewed distributions
have zero third moments (Mood, Graybill,
and Boes 1974, p. 76). Second, because
the skewness coefficient is sensitive to
tail observations, the fourth and sixth
moments associated with fat-tail distribu-
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
124
M AY / J U N E 1 9 9 9
Table 2
median difference reported in Table 2 is .81
percentage points, which clearly rejects
symmetry in favor of a wage change distribution skewed away from wage cuts.
Indeed, the mean is estimated to be 8.4
standard errors to the right of the median.
What lies between the mean and the
median also contributes to a test of symmetry. The sign test statistic (e.g., Gastwirth
1971) counts (and signs) the observations
between the mean and median. Under H0,
the number of observations below the mean
is distributed binomial with parameters N
and 1/2. By invoking the normal approximation to the binomial, the number of
observations between the mean and the
median is approximately normal with mean
zero and variance N/4. In Table 2, results
of the sign test applied to wage changes in
the PSID also reject the null hypothesis of
symmetry. In a sample of this size, it
would not be surprising to find 100 or so
observations between the mean and the
median. More than 1,200 observations lie
between the mean and median, however.
Table 2 also contains a check of the
sensitivity of the symmetry tests to the
presence of the spike at zero. If all the
zero-wage-change observations were
would-be wage cuts or small wage changes
censored at zero, these observations would
belong in the calculations. Alternatively,
these observations could reflect the rounding of wage responses or the timing of the
survey (with some wages changing soon
after the survey date). Neither factor constitutes an asymmetry of wage changes. By
removing the spike at nominal zero, the
skewness tests can isolate the contribution
of “thinning” the distribution below zero.
In the lower half of Table 2, I report the
skewness test statistics on the sample that
excludes observations with no change in
nominal wages. All three skewness test
statistics fall, providing weaker rejections
of symmetry. But wage changes remain
skewed right.
Skewness Test Statisticsa
Panel Study of Income Dynamics, 1971-92
Sample
Including the Spike
at Zero
±48 Point Band Around
the Median
±5 Point Band Around
the Median
Excluding the Spike
at Zero
±48 Point Band Around
the Median
±5 Point Band Around
the Median
a
Skewness
Coefficient
0.335
(0.298)
[0.013]
0.077
(0.024)
[0.013]
0.058
(0.012)
[0.020]
0.248
(0.291)
[0.014]
–0.023
(0.024)
[0.014]
0.151
(0.012)
[0.020]
Mean –
Median
0.811
(0.096)
Sign
Test
1,242.5
(93.1)
Thinness
Measure
7.89
0.687
(0.070)
1,068.5
(91.8)
7.85
0.065
(0.022)
200.5
(59.8)
0.586
(0.104)
837.5
(89.2)
4.11
0.470
(0.075)
725.5
(87.9)
4.04
0.206
(0.023)
302.0
(60.1)
The sample contains 34,633 observations on the wage changes of firm stayers. Standard errors
of the test statistics are reported in parentheses; displayed in brackets are the standard errors of
the skewness coefficient under the assumption of normality.
ness away from wage cuts. To address
this question, Table 2 includes Lebow,
Stockton, and Wascher’s (1995) measure
of thinning, the proportion above twice
the median minus the proportion below
zero. The wage change distribution below
zero is nearly 8 percentage points thinner
than its mirror image on the right side of
the distribution. If zero wage change
observations are excluded, the thinness
measure falls to about 4 percentage points.
Intertemporal variation in the wage
change distribution provides another way
to identify thinning of the distribution
below zero (Kahn 1997). This idea is
simple and powerful. Take an interval a
few percentage points below the median.
When nominal wage growth is high
(i.e., when inflation tends to be high),
that interval lies above zero. In low nominal wage growth years, that interval might
lie below zero. (In some years, the interval
might span zero.) Kahn’s idea is to compare
the histogram’s values for that interval
when it lies to the right and left of zero.
Thinning of the Distribution
Below Zero
While these tests reveal skewness,
they do not address the question of skew-
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
125
M AY / J U N E 1 9 9 9
7 Composition of my sample from
the PSID does vary: The universe of wage respondents
widened beginning in 1976,
and household spouses are
included beginning in 1979.
8 Unfortunately, properties of
symmetry test statistics can
reverse as the band around the
median narrows. For instance,
with a log-normal distribution,
as the band around the median
becomes very narrow, the
skewness test statistics change
sign. The ±5 percentage point
band appears to be wide
enough to avoid this problem,
but I prefer to rely on the clear
evidence in Figure 2.
If the value of the histogram on the interval
is smaller when it lies below zero, there is
evidence of wage changes being skewed
away from wage cuts.
Kahn estimates econometric specifications that essentially weight all the intervals
that move above and below zero. But her
idea can be implemented most directly by
picking a few intervals that pass zero. My
symmetrically differenced histograms use
intervals two percentage points wide. The
third and fourth intervals below the median (i.e., 4-6 and 6-8 percentage points
below the median) lie above zero in high
inflation years and below zero in low inflation years. For each interval, Table 3 reports
values of the histogram in years when the
interval was above and below zero. Wage
change observations on interval 3 are 2.1
percent more common when that interval
lies above zero. For interval 4, the difference
of the histogram values is only .4 percent.
As with any difference estimator, there is
the question of a control group. If the sample
in low wage-growth years has lower variance
of wage changes, the tails of the distribution
would be thinner even if would-be wage cuts
were not censored at zero. Perhaps the composition of the sample differs when nominal
wage changes are higher, or as Card and
Hyslop (1997, p. 86) argue, perhaps the dispersion of wage changes is affected by inflation.7 This issue can be addressed with a
difference-in-difference estimator. I use the
change in the corresponding interval above
the median as the control. Difference-in-difference estimates in Table 3 are a bit larger:
2.5 on interval 3 and 1.9 on interval 4.
Overall, these histogram difference estimates
do point to a thinning of tails below nominal
zero, with a thinning of one-third to one-half
of would-be cuts near zero.
these observations would not be affected
by any downward nominal rigidity at zero.
That is, the distribution’s right side is predicted to be heavier than its left side over
the range of wage cuts, but not over the
entire range of wage changes. These implications can be checked directly.
First, to check whether skewness is
limited to tail observations, I exclude wagechange observations that contribute to the
bottom and top histogram bars in Figure 2.
This eliminates 1.19 percent from the left
side and 1.44 percent from the right, so
these tail observations contribute to the
right skew. Skewness test statistics are
computed on the remaining wage-change
observations, which lie within 48 percentage
points of the median. The results in Table 2
reveal that positive skewness survives trimming the tails. Extreme wage change
observations do not account for all of
the skewness, a result consistent with
downward nominal rigidities.
Second, based on the symmetrically
differenced histogram in the lower panel of
Figure 2, wage changes just to the left of
the median are more common than those
just to the right of the median. This property is typical of right-skewed distributions
such as the log-normal. In Table 2, on the
sample of wage changes within 5 percentage points of the median, the test statistics
reject symmetry.8 Since this band does not
include wage cuts, the spike at zero, or
small wage increases, the source of skewness of wage changes is not limited to the
censoring of would-be wage cuts and small
wage changes. Skewness seems to be a
more general property of wage changes.
Skewness close to the median presents a
problem for the thinning estimates of Lebow,
Stockton, and Wascher (1995) and Card and
Hyslop (1997); these estimates rely on the
mirror-image assumption that the distribution of wage changes would be symmetric if
not for downward nominal rigidity. If the
overall distribution were skewed right,
which is consistent with the evidence close
to the median, then the mirror-image
assumption would be violated, and their estimates of thinning would overstate the extent
of downward nominal rigidity.
Are Censored Wage Cuts
the Only Source of Skewness?
If thinning of the wage-change distribution below zero were the only source of
skewness, then (a) extreme tail observations would not be the main source of
skewness, and (b) wage changes close to
the median would be symmetric, since
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
126
M AY / J U N E 1 9 9 9
Table 3
How severe is the bias? This depends on
how skewed the overall distribution would
have to be to generate the observed skewness
near the median. One could generalize from
the estimates of skewness near the median
to generate an overall distribution that is
skewed for reasons unrelated to downward
nominal rigidities. In particular, the BoxCox transformation that renders the observations close to the median symmetric
could be applied to the overall distribution
to generate a counterfactual distribution.9
A corrected estimate of thinning differences the proportions of wage cuts in the
actual and counterfactual distributions.10
Although skewness near the median
might not appear strong in Table 2, observations near the median are strongly skewed,
more skewed than can be explained by even
a log-normal distribution. In particular,
sending the Box-Cox parameter to zero is
not sufficient to produce symmetry near
the median. The implied counterfactual
distribution would be so strongly skewed
that “corrected” estimates of thinning
would identify upward nominal rigidity.
Although these unreported results do not
qualify as serious corrections, they are
instructive. Skewness near the median is
too severe to ignore; and estimates of thinning by Lebow, Stockton, and Wascher and
Card and Hyslop probably overstate the
extent of downward nominal rigidity substantially.
Histogram Difference Estimates of Downward
Nominal Rigiditiesa
Panel Study of Income Dynamics, 1971-92
Sample
Left of Median
Years When Interval Is Above Zero
Years When Interval Is Below Zero
Difference
Right of Median
Years When Intervalb Is Above Zero
Years When Intervalb Is Below Zero
Difference
Difference-in-Difference
Interval 3
Interval 4
-6.29
-4.23
-2.06
-3.36
-2.96
-0.40
-4.43
-5.82
–0.39
-2.45
-4.57
-6.04
–1.47
-1.87
a
Table entries are histogram values and differences in histogram values. The length of each interval is two percentage points. Intervals 3 and 4 lie 4-6 and 6-8 percentage points away from
year-specific medians.
b
Histogram values to the right of the median are computed separately for years when the indicated interval to the left of the median lies above and below zero.
tion periods. To test this, I compute each
test statistic (i.e., skewness coefficient,
mean-median difference, sign test, and
thinness measure) annually. (The four
test statistics are highly correlated across
years.) The results of correlating the
annual test statistics with inflation are
reported in Table 4. The correlations are
small and statistically insignificant, and
only the thinness measure’s correlation is
negative. So wage changes in the PSID
contain no evidence of less skewed distributions of wage changes in years when
inflation was higher.
This result is robust to partitioning
inflation into anticipated and unanticipated components. For inflation to grease
the wheels, it must shift the distribution
of wage changes away from zero, and this
is more likely for anticipated inflation.
Table 4 contains correlations of the skewness statistics separately with anticipated
and unanticipated inflation. Based on the
three main skewness measures, neither
anticipated nor unanticipated inflation
reduces the skewness of nominal wage
changes. Only the thinness measure correlates significantly negatively with anticipated inflation.
The negative correlations of inflation
and anticipated inflation with the thinness
Does Inflation Reduce Skewness
Away From Wage Cuts?
The evidence that wage changes are
skewed is definitive, but inflation’s role
remains to be determined. Does inflation
render less restrictive a constraint against
nominal wage cuts? Or, if the nominal
rigidity at zero is the source of skewness
away from wage cuts, does inflation
reduce the skewness of the wage change
distribution? By identifying how the test
statistics vary with inflation, this can be
checked directly.
If inflation relaxes the constraint,
then skewness of the distribution of wage
changes would be less severe in high-infla-
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
127
9 The Box-Cox transformation is
(y –1)λ / λ, where y is 1+∆w.
For 0 ≤ λ < 1, this transformation is strictly concave, which
reduces skewness to the right.
10 This is a difference-in-difference
estimator. Wage-change observations close to the median
constitute the control group,
which are unaffected by the
treatment of downward nominal rigidity. These observations
are used to estimate how much
thicker the right side would be
than the left in the absence of
downward nominal rigidity.
This adjustment factor is then
differenced from Lebow,
Stockton, and Wascher’s or
Card and Hyslop’s difference
estimates.
M AY / J U N E 1 9 9 9
not sensitive to skewness unrelated to
downward nominal rigidity.
The evidence of strong skewness near
the median leaves little role for downward
nominal wage rigidity, and this is confirmed
by little evidence of negative correlations
between the skewness test statistics and
inflation. Alternatively, if I had found
strong negative correlations with inflation,
then the detected skewness near the median
would not be sufficiently strong to account
for overall skewness and thinning. The
complementarity of these tests—near the
median and correlations with inflation—
is particularly useful in explaining differences across groups. With only downward
nominal rigidity, groups with strong skewness should have strong negative correlations with inflation. This link would be
broken if there were evidence—in the form
of skewness near the median—of an intervening factor, another source of skewness.
Table 4
Correlations of Skewness Statistics
With Inflation
Panel Study of Income Dynamics, 1971-92
Sample and Test Statistic
All Workers
Skewness Coefficient
Mean-Median Difference
Sign Test Statistic
Thinness MeasureUnion Workers
Skewness Coefficient
Mean-Median Difference
Sign Test Statistic
Thinness MeasureNonunion Workers
Skewness Coefficient
Mean-Median Difference
Sign Test Statistic
Thinness MeasureHourly Workers
Skewness Coefficient
Mean-Median Difference
Sign Test Statistic
Thinness MeasureSalaried Workers
Skewness Coefficient
Mean-Median Difference
Sign Test Statistic
Thinness Measurea
Inflation
Anticipated
Inflation
Unanticipated
Inflation
-0.30
-0.07
-0.08
–0.33
-0.23
–0.14
–0.08
–0.50
0.10
0.36
0.27
0.31
-0.03
–0.55
–0.53
–0.60
–0.14
–0.69
–0.66
–0.68
0.34
0.36
0.34
0.27
-0.29
-0.21
-0.16
–0.10
-0.24
-0.11
-0.07
–0.12
0.06
0.18
0.16
0.05
-0.02
–0.04
–0.10
–0.65
-0.05
–0.37
–0.38
–0.79
0.06
0.72
0.60
0.31
-0.44
-0.14
-0.24
-0.27
-0.37
-0.08
-0.17
-0.06
0.13
0.12
0.14
0.42
Do Unions and Method of
Pay Matter?
My results cover the sample of stayers.
Yet the literature has drawn a sharp distinction between hourly and salaried workers
(i.e., by method of pay), and perhaps a distinction should be drawn between union
and nonunion workers. Do unions and
method of pay matter?
Table 5 contains the skewness test
statistics, including difference-in-difference estimates based on histogram shifts,
by union status and method of pay. Wage
changes of both union and nonunion
workers are skewed right, although the
wage changes of nonunion workers seem
to be more highly skewed. This contradicts my evidence, based on the skewness
coefficient, that wage changes of nonunion
workers are symmetric (McLaughlin 1994).
The high variance of the skewness coefficient in the presence of a fat-tailed wagechange distribution resolves the paradox.
A sharper distinction emerges between
hourly and salaried workers. The evidence
of right-skewed wage changes for hourly
workers is overwhelming; wage changes of
salaried workers are also skewed, but the
Correlations are computed on 21 annual observations. The sign test statistic is normalized by its
standard deviation.
11 Since Card and Hyslop (1997)
use the same thinness measure, their evidence of less thinning in high inflation periods
suffers from the same bias.
measure are probably biased down. The
median wage change varies with inflation,
hence thinning is measured farther out in
the distribution’s tails in high inflation
years. Maintain the mirror-image assumption, and the correlation of thinness with
inflation detects inflation’s role in relaxing
any constraint of nominal wage cuts. Drop
the mirror-image assumption, and the correlation is almost surely biased down.
Suppose the distribution of wage changes
is skewed right for reasons unrelated to
downward rigidity. Then moving farther
out in the tails surely reduces the measure
of thinness even in the absence of downward nominal rigidity. Consequently, the
correlation of Lebow, Stockton, and
Wascher’s thinness measure with inflation
is biased down.11 Correlations of the other
symmetry test statistics with inflation are
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
128
M AY / J U N E 1 9 9 9
Table 5
Skewness Test Statistics by Union Status and Method of Paya
Panel Study of Income Dynamics, 1971-92
Sample
b
Entire Histogram
Union Workers
Sample
Size
Skewness
Coefficient
Mean –
Median
Sign
Test
Thinness
Measure
28,013
0.087
(0.232)
0.226
(0.362)
1.674
(1.341)
0.049
(0.288)
0.615
(0.151)
0.773
(0.126)
1.106
(0.108)
0.326
(0.175)
286.5
(44.7)
721.5
(75.4)
839.5
(59.7)
161.0
(60.7)
26.23
0.90
1.09
28.24
2.55
0.60
10.85
NA
1.79
24.74
1.21
0.03
0.028
(0.023)
0.062
(0.015)
0.047
(0.017)
0.022
(0.020)
0.011
(0.043)
0.057
(0.028)
0.055
(0.031)
0.083
(0.038)
16.5
(31.0)
140.0
(46.9)
120.0
(42.0)
265.0
(35.3)
Nonunion Workers
22,749
Hourly Workers
14,271
Salaried Workers
14,758
5 Point Band Around the Median
Union Workers
Difference-in-Difference
Interval 3 Interval 4
23,845
Nonunion Workers
28,796
Hourly Workers
27,056
Salaried Workers
24,996
a 34,633 observations are the wage changes of firm stayers. Standard errors of the test statistics are reported in parentheses.
b Observations that change union status are excluded from the analysis by union, and those that change method of pay are excluded from the analysis by
method of pay.
departure from symmetry is much weaker.
For instance, thinning is less than half as
severe for salaried workers.
Table 5 also contains “near the median”
skewness tests by union status and method
of pay. Again, skewness near the median
does not reflect downward nominal rigidity.
Near the median, wage changes of union
workers are symmetric, while those of nonunion workers are clearly skewed. This
contrasts with the results by method of
pay. Both hourly and salaried workers’
wage changes are weakly skewed right
near the median. So, except in the case of
union workers, there is evidence that the
estimates of Lebow, Stockton, and Wascher
as well as Card and Hyslop overstate the
role of nominal rigidity in thinning the
wage change distribution below zero.
If the source of skewness were downward rigidity, then the skewness coefficients
would be negatively correlated with inflation, and this is confirmed in Table 4 for
union and hourly workers. On the union
and hourly samples, correlations of three of
the four test statistics with anticipated inflation (in the second column) are negative
and fairly strong. There is no evidence of
inflation relaxing downward nominal rigidity for nonunion and salaried workers.
Integrating these results, I find that the
skewness of union workers’ wage changes
is all attributable to nominal rigidity. There
is no evidence of skewness near the median, and the skewness statistics are negatively correlated with anticipated inflation.
The source of the strongly skewed wage
changes of nonunion workers, however, is
not nominal rigidity. The skewness statistics are not correlated with anticipated
inflation, and strong skewness of nonunion workers’ wage changes near the
median confirms the result. The wage
changes of hourly workers are strongly
skewed right, and some of this is unrelated
to nominal rigidity (based on skewness near
the median); since anticipated inflation
reduces the skewness of hourly workers’
wage changes, some of the skewness is a
consequence of nominal rigidity. There is
F E D E R A L R E S E R V E B A N K O F S T. L O U I S
129
M AY / J U N E 1 9 9 9
no evidence of downward nominal rigidity
for salaried workers. Indeed, salaried workers’ wage changes exhibit only mild skewness; that mild skewness is present near the
median, and none of the skewness statistics
is negatively correlated with inflation.
The union/nonunion comparison highlights the complementarity between the
“near the median” and “inflation correlation” tests. Although the wage changes of
nonunion workers are more skewed than
those of union workers, correlations with
inflation offer no evidence of downward
nominal rigidity for nonunion workers.
This would be anomalous if not for the evidence of strong skewness of nonunion
workers’ wage changes near the median.
And this constitutes evidence of an intervening factor, another source of skewness.
more likely to be truncated by turnover.
By analyzing the sample of stayers, we
introduce a bias toward right skew in the
distribution of wage changes. And the size
of the bias is unknown.
Third, pooling of samples with different distributions can generate spurious
skewness. For instance, pooling samples
of workers from different industries, as I
have done herein, mixes the industry
wage-change distributions. Mixing does
not preserve symmetry (McLaughlin
1999), so pooling industry samples might
skew the distribution of wage changes
even if each industry’s distribution were
symmetric. Although this bias is potentially serious, I find that it is not the source
of skewness in the overall distribution
(McLaughlin 1999).
IF NOT NOMINAL RIGIDITY,
THEN WHAT?
WHAT DOES THIS MEAN
FOR MONETARY POLICY?
A theme emerges: There is more to
skewness of the wage-change distribution
than downward nominal rigidity. If the
source of skewness is not nominal rigidity,
then what is it? Consider three possibilities. First, perhaps there is an aversion to
wage cuts in real terms, and this thins the
left side of the distribution of real wage
changes. Since inflationary expectations
vary across employment matches, a focal
point at zero real-wage change is not
implied. Downward real-wage rigidity
simply implies that wage changes would
be skewed to the right.
Second, self-selection skews wage
changes to the right (Weiss and Landau
1984). The economic intuition is simple.
We observe the distribution of accepted
wage offers. Some wage offers are not
accepted, and these are more likely to
come from the left side of the wage-change
distribution. Offer a worker a 20 percent
wage increase, and he would be likely to
accept it; offer that worker a 20 percent
cut in pay and he would be likely to quit.
Indeed, rather than offer a worker a 20
percent cut, the employer would probably
just lay him off. Hence, wage changes
from the left side of the distribution are
My purpose has been to identify common patterns and themes in the burgeoning literature on wage changes in panel
data. Using data from the PSID, I confirm
that wage changes are skewed to the right,
there is a spike at no change in nominal
pay, and below zero, the left side of the distribution is thinner than the right side.
These patterns have been identified in the
literature, but I cast new light on the subject.
I use several test statistics to detect
asymmetry, and I show that, with the
exception of the skewness coefficient,
skewness tests are not sensitive to the
choice of a test statistic. I identify the
source of the problem others have found
with the skewness coefficient: The fat tails
of the wage change distribution tend to
produce high-variance skewness coefficients. In response to Card and Hyslop’s
(1997) criticism of Kahn’s (1997) histogram difference estimator of thinning, I
estimate a difference-in-difference version
of Kahn’s estimator, which strengthens her
results. Since as much as half of the spike
at zero change in nominal wages might be
attributable to rounding errors and the
timing of survey interviews, I retest for
skewness excluding these observations.
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The evidence of skewness is weaker, but the
null hypothesis of symmetric wage changes
is still rejected.
There is more to the skewness of wage
changes than can be attributed to downward rigidity at zero. Here I break with
the literature. First, I place the issue of
downward rigidity in a wider context by
documenting that nominal wage changes
move one-for-one with anticipated inflation. Second, checking the mirror-image
assumption of Lebow, Stockton, and
Wascher (1995), and Card and Hyslop
(1997), I find that wage changes near the
median are skewed. This implies that the
estimates of thinning of nominal wage cuts
by Lebow, Stockton, and Wascher, as well
as Card and Hyslop, overstate the extent of
downward nominal rigidity. It also means
that wage changes are skewed for reasons
unrelated to nominal rigidity, perhaps as a
result of self-selection associated with efficient turnover. Third, confirming my suspicion that skewness is not attributable to
nominal rigidity, I find that the skewness
of wage changes is unrelated to inflation,
anticipated inflation, or unanticipated
inflation. Fourth, although nonunion
workers’ wage changes are skewed to the
right, the source of the skewness is not
downward rigidity. Yet the weakly skewed
wage changes of union workers do reflect
downward rigidity, because union workers’
wage changes near the median are not
skewed, and the test statistics on the union
sample are negatively correlated with
anticipated inflation.
Few areas of economic research have
more direct implications for economic
policy than this one. The thorn in the side
of the policy recommendation of stable
prices (i.e., zero inflation) has been the
labor market. Workers are subject to
money illusion in the form of downward
rigidity of nominal wages, or so the story
goes. I do detect some nominal rigidity
for union and hourly workers, but the
magnitudes are smaller than others have
found. And one must always remember
the wider context: Nominal wages of
workers who do not change employers
do move one-for-one with anticipated
inflation. Consequently, the labor market
is not much of a thorn in the side of
zero-inflation monetary policy.
REFERENCES
Akerlof, George, William Dickens, and George Perry. “The
Macroeconomics of Low Inflation,” Brookings Papers on Economic
Activity (1996), pp. 1-59.
Altonji, Joseph, and Paul Devereux. “The Extent and Consequences of
Downward Nominal Wage Rigidity.” Manuscript, (October 1997).
Ahmad, Ibrahim, and Qi Li. “Testing Symmetry of an Unknown Density
Function by the Kernel Method,” Journal of Nonparametric Statistics 7
(1997), pp. 279-93.
Bound, John, Charles Brown, Greg Duncan, and Willard Rodgers. “Evidence
on the Validity of Cross-Sectional and Longitudinal Labor Market Data,”
Journal of Labor Economics 12, (July 1994), pp. 345-68.
________, and Alan Krueger. “The Extent of Measurement Error in
Longitudinal Earnings Data: Do Two Wrongs Make a Right?” Journal
of Labor Economics 9, (January 1991), pp. 1-24.
Card, David, and Dean Hyslop. “Does Inflation ‘Grease the Wheels of
the Labor Market’?” In Reducing Inflation: Motivation and Strategy,
Christina Romer and David Romer, eds., National Bureau of Economic
Research Studies in Business Cycles, v. 30, University of Chicago
Press, 1997, pp. 114-121.
Christofides, Louis, and Thanasis Stengos. “The Symmetry of the WageChange Distribution: Non-Parametric Tests Using Contract and Survey
Data.” Manuscript, (July 1998).
Craig, Ben. “Are Wages Inflexible?” Economic Commentary, Federal
Reserve Bank of Cleveland (April 1, 1995).
Crawford, Allan, and Alan Harrison. “Testing for Downward Rigidity in
Nominal Wage Rates,” Price Stability, Inflation Targets and Monetary
Policy, Bank of Canada (1997), pp. 179-218.
Fama, Eugene, and Michael Gibbons. “A Comparison of Inflation Forecasts,”
Journal of Monetary Economics 13 (May 1984), pp. 327-48.
Gastwirth, Joseph. “On the Sign Test for Symmetry.” Journal of the
American Statistical Association 66 (December 1971), pp. 821-23.
Gupta, Milan K. “An Asymptotically Nonparametric Test of Symmetry.”
Annals of Mathematical Statistics 38 (1967), pp. 849-66.
Hotelling, Harold, and Leonard Solomons. “The Limits of a Measure of
Skewness,” Annals of Mathematical Statistics 3 (1932), pp. 141-42.
Kahn, Shulamit. “Evidence of Nominal Wage Stickiness from Microdata,”
American Economic Review 87 (December 1997), pp. 993-1008.
Lebow, David, David Stockton, and William Wascher. “Inflation,
Nominal Wage Rigidity, and the Efficiency of Labor Markets,” Board of
Governors of the Federal Reserve System, Finance and Economics
Discussion Series: 94-45, (October 1995).
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McLaughlin, Kenneth. “Rigid Wages?” Journal of Monetary Economics
34 (December 1994), pp. 383-414.
__________. “Testing for Asymmetry in the Distribution of Wage
Changes.” Manuscript, (1999).
Mood, Alexander, Franklin Graybill, and Duane Boes. Introduction to the
Theory of Statistics, 3rd ed., McGraw-Hill, New York, 1974.
Pearce, Douglas. “Comparing Survey and Rational Measures of Expected
Inflation: Forecast Performance and Interest Rate Effects,” Journal of
Money, Credit, and Banking 11 (November 1979), pp. 447-56.
Shea, John. “Comment,” In Reducing Inflation: Motivation and
Strategy, Christina Romer and David Romer eds. National Bureau of
Economic Research Studies in Business Cycles, v. 30, University of
Chicago Press, 1997, pp. 114-121.
Startz, Richard. “Discussion of ‘Are Nominal Wage Changes Skewed
Away From Wage Cuts?’” This Review, this issue.
Weiss, Andrew, and Henry Landau. “Mobility and Wages,” Economics
Letters 1,5 (1984), pp. 97-102.
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Richard Startz is a professor of economics at the University of Washington.
Commentary
inflation rate. The argument for a zero
inflation rate is that zero is a magic number for political reasons and reasons of
transparency. The argument for 2 percent
is that nominal wages are downward rigid,
and that 2 percent allows for more flexible
real wages. So McLaughlin’s paper bears
precisely on the central question of mediumterm monetary policy.
Second, using micro data is exactly
the right way to answer this sort of question. It also is a lot of work. You have to
worry about measurement error. You have
to worry about exact definitions of survey
data. And so forth. McLaughlin’s paper is
very well done and deserves a great deal of
appreciation for both the quantity and the
quality of the work.
By way of final preface, where does
wage rigidity fit into macro? Specifically,
in a recession, why don’t wages drop to clear
the market? Let me give the old-fashioned
answer. There are at least four places where
wage rigidity fits:
First, from an old-fashioned Keynesian
viewpoint, the labor market is driven by the
demand side as in:
Richard Startz
W
hen I was an undergraduate, I was
told that maybe a little inflation was
a good thing because nominal
wages are downward rigid. What’s more,
back then this accounted in part for the
Phillips curve being curved—being relatively flat at low inflation rates and steeper at
high inflation rates. At low inflation rates,
you had to have a lot of unemployment to
get rid of a little inflation because nominal
wage cuts are so painful. Downward wage
rigidity is regarded as one of those truths
that are so self-evident that there is no need
to look at the data. Professor McLaughlin
has actually looked at the facts and said, “If
it’s so self-evident, why doesn’t it show up
in the data?” Or, at the very least, said, “It’s
not nearly so simple.”
Let me outline six points for consideration.
• Where does wage rigidity fit into macro?
• Do nominal wage changes move onefor-one with inflation?
• Are wage changes skewed?
• Does the skewness change with
inflation?
• Is the spike at zero big? Does its size
change with inflation?
• What about the spread of the distribution? Does it change with inflation?
w
L = LD .
p
If the real wage doesn’t drop, too much
unemployment results. In this situation, if
nominal wages are downward rigid, then
real wages surely will be.
Second, consider a model in which the
real money supply matters: perhaps quantity theory, perhaps Keynesian with a Pigou
effect, or perhaps ISLM.
(1)
Let me begin by saying that Professor
McLaughlin’s topic is really important, that
it is really important to the Federal Reserve,
and that it is really important at exactly this
point in history. If you take a policy window of the last two or three years and the
next two or three years (assuming a similar
economy) a critical question for monetary
policy is whether we should aim for a steady
zero inflation rate or for a steady 2 percent
(2) Y = v M or Y = C Y , M + I + G
p
p
or ISLM
(3)
P = µW
Suppose firms set prices as a markup
over wages—maybe a competitive markup,
maybe something different. Here, nominal
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M AY / J U N E 1 9 9 9
data. This is neither better nor worse than
using the usual macro data except that it is
limited to 21 annual data points. We all agree
that, in the long run, the real wage is neutral
with respect to inflation. But the short to
medium run matters, and 21 data points are
not enough to answer the question. I’m not
saying that the answer is wrong, just that you
cannot get a definitive answer this way.
I decided to do a very small amount of
sensitivity analysis. The numbers in Table 1,
0.84 and 0.88, are the two numbers I think
the author wanted to emphasize. Regressing
wage on price inflation results in a coefficient
that is marginally statistically different from
one. The coefficient also says that 7 percent
inflation lowers the real wage about 1 percent.
I guess that’s a small effect—but I’d like to
know if a sustained 7 percent inflation
would lower the real wage 1 percent every
year. We then split the effect into anticipated
and unanticipated and see that the anticipated
effect is somewhat smaller.
Eschewing the daunting task of trying
to replicate the micro data, I chose the first
likely looking variable from the DRI (Data
Resources, Inc.) database. The left-most
panel of Table 1 shows McLaughlin’s
numbers. The middle panel replicates his
regressions using my data to demonstrate
that the data differences are not important.
In the right-hand panel, I augmented the
author’s specification with very simple
dynamics in the form of a Koyck lag. With
the augmented specification, 7 percent
inflation lowers the real wage by 2.3 percent,
which is a lot. Even using anticipated inflation, the coefficient is statistically below
one and economically is really far from
one. This does not mean the right panel
is better than the left; it just means that
21 annual data points are not the right
way to answer this question.
Are wage changes skewed? Absolutely!
Some people have taken this as evidence
that the lower tail is truncated. Of course,
while truncation may imply skewness,
skewness need not imply truncation. The
author did something clever; he looked for
skewness far from zero and found it. So
while there is some truncation, there are
other factors producing skewness. So we
Figure 1
Illustration of Phillips Curves
with Nominal vs. Real Wage Rigidity
w
w
High π e
Nominal wage
rigidity
Low π e
High π e
Real wage
rigidity
u
u*
wage rigidity causes nominal price rigidity
and prevents the consumer price index
from dropping to pull the economy out
of recession.
The third place where wage rigidity
shows up is in the slope of the Phillips
curve at low inflation rates. (See Figure 1.)
If it is hard to force down wages, then
the sacrifice ratio is really bad at low or
negative inflation rates. One way to think
about real vs. nominal rigidity is to ask
whether the sacrifice ratio worsens specifically near zero or just at inflation rates
close to expected inflation.
Fourth, and last, rigidity just messes
up allocational efficiency.
The paper is excellent. Nonetheless,
nobody gives a discussant credit for saying
nice things; so I want to discuss the one part
with which I disagree and then make a few
suggestions for other ways of working with
the data.
The only part of the paper with which
I take issue is the conclusion that “nominal
wage changes move one-for-one with anticipated inflation, and are even closely linked to
unanticipated inflation.” This is a question
about averages, that is, macro data. The
author has averaged his micro wage change
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Table 1
Regression of Wage Inflation on Price Inflation
Variable
Inflation
Author Inflation Process
Macro Data Inflation Process
Macro Data Inflation Process
ARIMA(0,1,1)
ARIMA(0,1,1)
ARIMA(0,1,1)
AR(3)
AR(3)
.840
(.103)
AR(3)
.865
(.083)
.666
(.123)
Anticipated
Inflation
.880
(.101)
.928
(.113)
.876
(.082)
.930
(.098)
.722
(.139)
.719
(.186)
Unanticipated
Inflation
.584
(.176)
.592
(.805)
.678
(.161)
.710
(.152)
.554
(.191)
.625
(.172)
Lagged-Wage
Inflation
.284
(.139)
.183
(.174)
.238
(.186)
AR(1)
-.060
(.260)
.169
(.331)
.026
(.333)
Notes on macro data:
price = GDP price deflator (DRI GDNFPC)
wage = Hourly compensation nonfinancial corp. (DRI LCPB)
should be careful about interpreting skewness per se as evidence of wage rigidity.
Is this skewness correlated with inflation? The author’s Table 4 says no. If
skewness results from wage rigidity and
inflation reduces wage rigidity, then inflation should reduce skewness. Strikingly,
there is no evidence for inflation reducing
skewness. I wonder if there is a way to
estimate the power of these tests, in the
economic rather than statistical sense.
One suggestion is to write a simple model
of nominal wage setting calibrated twice—
once for parameters where all would agree
that nominal rigidity is important and one
with the opposite assumption. Then one
would generate simulated data from each,
compute the statistics in Table 4, and
determine the extent to which the two
simulation results differ.
Is there a big spike at zero? There is a
spike, but what metric tells us whether the
spike is large? In addition to the size of the
spike, the author discussed the amount of
censoring. It would be useful to have a
table or some guided comparison of the
zero spike and estimated censoring against
inflation to see if it tells the same story.
Let me turn to the question of the variance
of wage changes rather than the skewness.
Take an example from life. I wear two hats.
I spend 80 percent of my time as an economist and another 80 percent as department
chair. I assign wage changes in my department, so for the University of Washington I
know what the process is. The University of
Washington faculty is about a third the size
of the PSID sample. Straight-time wages are
downward rigid. By this I mean there is no
place on the form I complete to lower wages.
It literally cannot happen. And I hazard the
same thing is true for half the attendees of the
October meeting.
When I give raises I have a dollar-budget constraint as well as a non-negativity
constraint. So downward rigidity cannot
have any effect on the average wage change.
The histogram in Figure 2 gives a fictional,
but I think accurate, picture of what happens at different inflation rates. At a 10
percent average increase, there are maybe
two raises at 6 percent to one raise at 18
percent. At a 4 percent average increase,
there might be two raises at 2 percent to
one raise at 8 percent. At high inflation,
there’s a 12 percent change in relative real
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scientific work that is enormously informative on a fundamental policy question; in this
case, “How much inflation should we have?”
Figure 2
Illustrative (but Fictitious) Histogram
of Wage Increases in High vs. Low
Inflation Regimes
Number of raises
High inflation regime
Low inflation regime
0
2
4
6
10
12
8
Rate of wage increase
14
16
18
20
wages. At 4 percent inflation there is only
a 6 percent change in relative real wages.
The former correctly reflects productivity.
Thus, inflation does give us more efficient
wage setting, but lower inflation in our
case squeezes both tails. I’m not sure the
squeezing of both tails would show up
in any of the measures used in this paper.
Further research might include comparing
data from institutions with known nominal
wage rigidity with data from institutions
known to have flexible wages.
During the discussion at the October
meeting, Bill Poole offered a telling objection to my illustrative histogram. Some
people are denied tenure; effectively, their
wage change is –100 percent! Much of the
wage rigidity literature carefully looks only
at “nonmovers.” If we think carefully about
the role of wages in labor markets, we know
that labor force adjustments occur on both
the intensive (hours) and extensive (hire/
fire) margins. McLaughlin’s paper focuses
on nonmovers, as it should; but perhaps
there is more work to be done on the linkage between wage rigidity and the intensive
versus extensive margin of labor force
adjustment.
In summary, this is a stimulating paper
that leaves the reader begging for more. It
also is a great example of narrowly focused
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