Methods of Pay and Earnings: A Longitudinal Analysis
Author(s): Daniel Parent
Source: ILR Review, Vol. 53, No. 1 (Oct., 1999), pp. 71-86
Published by: Sage Publications, Inc.
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METHODS OF PAY AND EARNINGS:
A LONGITUDINAL ANALYSIS
DANIEL PARENT*
Using data from the National Longitudinal Survey of Youth (1988-
90), the author investigates the relationship between methods of pay,
including piece rates and bonuses, and the level and variance of wages.
Among men, piece rate workers earned a premium compared to other
workers, but the evidence on bonuses is mixed. The author finds
evidence that female piece rate workers earned more than other female
workers once a control variable for the presence of dependents is
interacted with the piece rate variable. With controls for the wage
effects of schooling and experience, unobserved worker productivity is
found to have accounted for most of the wage variance among both male
and female piece rate workers; wage variance among workers not having
explicit pay for performance schemes, in contrast, was predominantly
due to other factors.
ver the past twenty years or so, a number
of theoretical models have been
developed to analyze the employment relationship,
with a particular focus on how
contracts can be structured to provide appropriate
incentives. Despite the rapid
pace at which information economics has
progressed, empirical investigations of the
implications of these models (let alone direct
testing of the models themselves) have
*The author is Assistant Professor at McGill University,
Researcher at the Centre de recherche et
developpement en economique (C.R.D.E.), and researcher
at the Centre interuniversitaire de recherche
en analyse des organisations (CIRANO). He
thanks Bentley MacLeod for many discussions on this
topic and seminar participants at the Princeton Labor
Lunch, Universite Laval, and Ecole des Hautes
Etudes Commerciales, Montreal, for useful comments.
He also thanks Princeton University for its hospitality
during a visit at which he did some of the work for this
study.
been rather rare. The obvious reason for
this neglect is the lack of data.
The objective in this paper is to examine
how piece rates and bonuses affect wages by
looking at three consecutive waves from
the National Longitudinal Survey of Youth
(NLSY) for the years 1988-90. Over that
three-year period, workers were asked if
part of their labor earnings was based on
job performance. They were also asked
what form of incentive schemes their employer
used. Thus, at the first level, we can
examine the extent to which incentive pay
was used in a relatively representative
sample of young workers.
Most previous studies have used crosssectional
data to analyze the same quesThe
data and computer programs used in this
paper can be obtained from the author at McGill
University, 855 Sherbrooke St. W., Montreal, Quebec
H3A 2T7, Canada.
Industrial and Labor Relations Review, Vol. 53, No. 1 (October 1999). ( by Cornell University.
0019-7939/99/5301 $01.00
71
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72 INDUSTRIAL AND LABOR RELATIONS REVIEW
tions. The longitudinal structure of the
NLSY data, however, opens up the possibility
of disentangling incentive effects from
pure selection effects by controlling for
unobserved worker and job-match heterogeneity.
Also, having three years of data
allows the estimation of a simple model of
the covariance structure of wages by type of
contract.
Modeling the covariance structure of
earnings has two benefits. First, it allows
one to determine what fraction of the unexplained
variance in earnings can be attributed
to unobserved worker heterogeneity,
since pay is closely tied to individual
performance when explicit incentives are
used. In addition, it allows an exploration
of the reasons for the frequent finding that
workers whose earnings are explicitly tied
to performance earn more, on average,
than salaried or hourly paid workers. To
investigate whether that pattern simply reflects
the payment of compensating differentials
for the increased risks faced by piece
rate workers (Seiler 1984), for example,
one needs to "purge" the total cross-sectional
wage variance of the part that comes
from unobserved worker heterogeneityan
exercise that requires the use of longitudinal
data.
Previous Research
The studies most comparable to the
present one are Ewing (1996), Brown
(1992), and Seiler (1984). In each of those
papers the authors used a large data set-a
wave of the NLSY (Ewing) or data from the
U.S. Bureau of Labor Statistics' Industry
Wage Surveys (Brown and Seiler) -to study
the use and wage impact of pay-for-performance
schemes.' The main finding from
these papers is that "incentive workers,"
piece rate workers in particular, earned
'The data sets employed in these three studies
were more representative of the labor force than were
the samples used in some of the recent work studying
the interaction between incentives, firm performance,
and top executive salaries. See, for example, Gibbons
and Murphy (1992) andJensen and Murphy (1990).
more, on average, than time-rated work-
ers.2
A recent paper by Lazear (1996) used
data from one company to study the effects
on productivity and wages of switching
hourly rated workers to piece rate contracts
(see also Pencavel 1977). Consistent with
previous results, Lazear found that moving
from an hourly wage to a piece rate caused
a 41% increase in productivity, as measured
by units of glass installed on automobiles.
The switch to piece rates also had the
effect of decreasing absenteeism, which is
another measure of worker productivity.
In addition, output variance increased with
the move to piece rates. Exploiting the fact
that he could follow the same workers before
and after the change, Lazear found
that sorting and incentives both played an
important role in this productivity gain,
with more than half the gain being due to
incentive effects.3 Finally, wages also increased
by an average of 9% following the
firm's decision to move to a piece rate
scheme.
Theoretical Considerations
Relationship between
Piece Rates and Earnings
Lazear's (1986) two-period model analyzes
the conditions under which piece rate
contracts are preferred to fixed salaries.
Lazear defines salaried workers as individuals
for whom
(1) W, = g(E),
where Et is some measure of
hours worked) in period t. For piece rate
workers,
(2) wt = f(qt),
2For a more structural approach to the study of
worker incentives, see also the work of Ferrall and
Shearer (1996) and Shearer (1996).
3Lazear distinguishes incentive effects from pure
selection effects by using fixed-effects regressions to
purge the data from unobserved fixed worker-firm
heterogeneity.
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METHODS OF PAY AND EARNINGS 73
where q, is output in period t. A crucial
assumption in Lazear's model is the existence
of a monitoring cost. Without such an
assumption, no fixed salary jobs would exist.
Let C be the monitoring cost, R the
piece rate, and q the (lifetime) output of
the worker. For piece rate jobs, we have
(3) w= Rq- C,
and for fixed salary jobs,
(4) w=E(q).
It is assumed that people can work in other
jobs at w*. If E(q) > w* and there are no
piece rate firms, then all workers work at
this firm. But this result is inefficient:
those for whom q < we should take the
alternative job. Separating them from the
others causes expected output to increase.
If both parties are equally uninformed as to
the productivity of the worker, then separation
can be achieved by putting everybody
in the piece rate job for a period of time in
order for both parties to learn q. After they
learn q, those with Rq > we stay in the piece
rate job. With asymmetric information,
less productive workers select themselves
into the salary jobs. The firms know that
they have attracted low-ability workers and
they pay accordingly. Thus, mean earnings
should be higher for piece rate workers
than for salaried workers. Pencavel (1977),
Seiler (1984), Brown (1992), and Lazear
(1996) each have found evidence that piece
rate workers are paid more than salaried
workers. Also, since pay and productivity
are more closely linked in the case of piece
rate contracts, the variance of wages for
piece rate workers should be greater than
for other workers. Seiler (1984) found
evidence from the Industry Wage Surveys
that wages are indeed more dispersed for
piece rate workers than for other workers.
He interpreted this finding as evidence
that piece rate workers are paid compensating
wage differentials for the increased risks
they face.
Intertemporal Strategic Behavior
Piece rates can be negatively related to
past output, because employers may use
past performance as an indicator of the
difficulty of a particular task. If workers
perform very well early on, employers will
come to believe that the task is relatively
easy and will, therefore, lower the pay rates
(or increase the performance standard).
This is the standard "ratchet effect." Realizing
this, workers may depress one period's
output in order to realize a better rate in
the next period. Lazear argued that this
strategic behavior can be undone by inflating
the piece rate in the first period. Workers
will respond with a higher effort level
even though they anticipate that the employer
will cut their rates in the second
period. Thus, if workers and employers
behave as Lazear suggests, we should see a
stronger effect of piece rates on earnings
early in the employment relationship than
later.
That prediction hinges completely on
the assumption that workers can fully commit
not to quit at the end of period one.
Employers must be in a position to exploit
some ex post monopsony power. Otherwise,
a competitive firm can attract workers
whose rates have been decreased.
This idea was formally developed by
Kanemoto and MacLeod (1991), who
showed that the existence of outside opportunities
can eliminate the ratchet effect,
even when workers incur mobility costs. In
the context of a two-period model, firms
compete for a fixed number of workers.
Competition among firms thus reduces ex
ante profits to zero. A cost C is borne by the
workers each time they take on a job (mobility
cost or cost of retraining). This cost
captures the fact that once a worker is in a
job, the firm has some monopsony power
over that person. The firm tries to exploit
this power by lowering rates (or increasing
sales targets) in the second period.
Kanemoto and MacLeod showed that for
sufficiently low mobility costs, competition
for what they call second-hand workers can
eliminate the ratchet effect. Unlike Lazear's
model, in their model efficient piece rate
contracts are possible without perfect com-
mitment.
Three predictions stem from these models.
First, more productive workers will
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74 INDUSTRIAL AND LABOR RELATIONS REVIEW
choose piece rate jobs (Lazear 1986). In
other words, any measured positive relationship
between piece rates and wages is
attributed to self-selection on the part of
workers. Thus, using fixed effect methods
should result in the elimination of all positive
effects. Second, since piece rate
schemes gear the worker's compensation
directly to output, the variance of wages
should be larger for piece ratejobs than for
salaried jobs. Finally, Lazear's model predicts
that the effect of piece rates should be
stronger early in the employment relationship,
while Kanemoto and MacLeod predict
no such time decreasing pattern.
Relationship between
Bonuses and Earnings
Piece rate or commission contracts are
explicit in nature: one gets paid a certain
contractually specified amount per unit
produced. Bonuses can be explicit as well,
such as when workers get rewarded for
achieving or surpassing a sales target. But
employers can also award bonuses on a
more discretionary basis. An implicit contract
between the worker and the firm might
specify that performances deemed satisfactory
by the employer will be rewarded by
the payment of a discretionary end-of-period
bonus. Such an implicit agreement
will be carried out only if both parties gain
by doing so. If they do not, nothing can
prevent them from reneging: workers will
not offer superior performance and firms
will not pay any bonus even if the worker
provides a high level of effort. For both
parties to keep their promises, the contract
has to be self-enforcing.4 (See Carmichael
1989 for a review of self-enforcing con-
tracts.)
One of the basic features of such an
employment relationship is the inherent
4Given the subjective nature of the performance
evaluation, such contracts are not legally binding,
that is, although observable by both parties, a "satisfactory"
performance level is not generally verifiable
in courts (or, at least, it is costly to verify).
conflict between short-term and long-term
interests. In the short term, the firm would
rather not pay a bonus and the worker
would rather not provide a superior effort
level. However, if either party reneges on
the implicit agreement, it will be punished:
shirking workers will not receive a bonus
and will get fired, while firms that do not
pay the bonus as promised will see their
workers quit.
These ideas were spelled out by MacLeod
and Malcomson (1989) in the context of a
repeated game model. They first showed
that for a self-enforcing contract to exist,
there has to be a surplus from continuing
the relationship: both parties are at least as
well off in the current contract as they
would be in market alternatives, and one of
them must be strictly better off. Second,
incentives can be provided either by paying
so-called "efficiency wages" (Shapiro and
Stiglitz 1984) or by paying end-of-period
bonuses. Since in that model bonuses occur
when workers receive no rent from the
relationship, it follows that total earnings
(base salary plus bonus) should be set equal
to the market alternative. Thus, there is no
reason to believe that in a cross-section of
workers, those paid bonuses should earn
more, on average, than other workers.5
Worker risk aversion could also imply the
payment of compensating differentials.
Since bonuses are tied to performance,
which in turns depends on ability, if workers
are uncertain about their ability, they
may ask for higher pay as insurance against
the possibility that they are low-productivity
individuals.
5Perhaps it would be more appropriate to say that
even if we find bonus workers are paid more on
average than time-rated workers, that result would
still be consistent with MacLeod and Malcomson
(1989). MacLeod and Malcomson's implicit contract
model predicts that when workers have no surplus
from the relationship, incentives are provided by
paying bonuses. Although total earnings (salary plus
bonus) do not have to be higher than for straight
salary workers, they may be higher for other reasons,
such as compensating differentials for higher effort
levels required from bonus workers.
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METHODS OF PAY AND EARNINGS 75
Data
The National Longitudinal Survey of
Youth data set covered 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
about their work environment. For
instance, we know if the respondents were
supervising other employees and whether
they had received a promotion since the
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
that is due to pay-for-performance. These
represent significant data limitations that
constrain the interpretation of the re-
sults.
The question pertaining to pay-for-performance
is the following:
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 any of these types of compensation.
Please do not include profit sharing
or employee stock purchase plans.
1. Piece rates.
2. Commissions.
3. Bonuses (based on job performance).
4. Stock options.
5. Tips.
6. Other.
Note that it is not possible to tell a priori
whether the bonuses refer to amounts paid
at the discretion of the employer when the
latter subjectively considers that the performance
of the employee is worthy of a
cash reward ("merit pay"), or whether they
merely represent another form of piece
rate, or even whether they are team bo-
nuses.
Some summary statistics are presented
in Table 1.6 I restrict the sample to indi-
6Note that the statistics are not weighted to reflect
the fact that the NLSY sample I am using includes the
viduals who were in the labor market on a
full-time basis, meaning (i) those whose
primary activity was either working fulltime,
on a temporary lay-off, or looking
actively for a job, and (ii) those who had
worked at least half the year since the last
interview and who were working at least 20
hours per week. Individuals excluded from
the sample are those who had been in the
military at any time, the self-employed, and
all public sector employees. Also, I exclude
observations for which real (1979-dollar)
hourly earnings are less than $1.00 or
greater than $100.00. These restrictions
leave an unbalanced sample of 8,137 observations
(3,844 workers). Of some importance
is the fact that the workers in this data
set are aged 23 to 33. Thus, the proportions
of managerial positions and true merit pay
jobs are smaller than in a representative
sample of the entire population.7
For comparison purposes, note that in
the Earnings Supplement to the January
1977 Current Population Survey (CPS), in
which workers are matched to their employers
through a Validation Survey, 4% of
the workers report being paid a piece rate
(out of 4,945 worker-observations), and
their employers also report that 4% of the
workers are paid a piece rate (out of 4,468
employer-observations), compared to the
9.4% reported in the NLSY. When I restrict
the CPS sample to workers who are less
then 34 years old, the percentage of piece
rate workers is even lower, at about 3.5%.
Part of the discrepancy in the percentage of
workers reporting they are paid a piece rate
stems, no doubt, from the different wording
of the questions themselves in the NLSY
and the CPS. In the NLSY, workers are
asked if any of their earnings are based on
minority and poverty subsamples. Doing so increases
the average hourly earnings and the average schooling,
but leaves the percentage of the sample paid
either a bonus or a piece rate essentially the same.
7Like Lazear (1986), I define piece rates as the
method of pay used by firms when they measure each
worker's output and tie wages to measured output.
Thus, in that sense, commissions are also piece rates
and are therefore labeled as such in the sample.
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76 INDUSTRIAL AND LABOR RELATIONS REVIEW
Table 1. Mean Sample Statistics.
Statistic Mean
Hourly Earnings (1979 dollars) 5.5
Age 28.0
Tenure 3.2
Schooling 12.4
Percentage Unionized 15.2
Percentage Female 43.4
Percentage Paid Piece Rates 9.4
Percentage Paid Bonuses 14.2
Sample Size 8,137
Number of Workers 3,844
piece rate pay. In the CPS, workers are
asked whether they are paid "on a piecework
basis" (as opposed to an hourly rate or
a salary), and the different pay methods are
mutually exclusive categories, which is not
the case for the NLSY. In other words,
someone reporting that she is paid on a
piecework basis in the CPS cannot report
being paid also on an hourly basis. Consequently,
it is likely that CPS workers report
the pay method from which they earn most
of their labor income.
Concerning bonuses in the CPS sample,
a little over 8% of the workers reported
receiving a bonus, and about 9.5% of the
corresponding employers declared having
paid one, compared to a figure of 14.2% for
my NLSY sample. Thus, while both bonuses
and piece rates apparently occurred
at a higher rate among workers in the CPS
than among those in the NLSY, the difference
is especially noticeable in the case of
piece rates. Note, however, that the CPS,
unlike the NLSY, contains no direct question
on bonuses based onjob performance.
To arrive at the above figures, I used a
question on the extra amounts that salaried
workers may have earned in tips, commissions,
or bonuses, deriving the percentage
of workers who earned bonuses by excluding
workers on commissions or who received
tips.
The Panel Study of Income Dynamics
(PSID) also contains a question on the
amounts earned in bonuses, commissions,
or overtime. Thus, one can also construct
a measure of bonus incidence using the
PSID by deleting commission and overtime
workers. As it turns out, the percentage of
workers in the PSID reporting a bonus in
1976 is very close to the percentage reported
in the CPS (8.6% and 8.0%, respectively)
and also, for the years 1988-90, very
close to the percentage reported in the
NLSY (12.4% in the PSID, compared to
14.2% in my NLSY sample).
Turning to the incidence of piece rates
and bonuses by occupation or industry,
over 38% of sales workers in my NLSY
sample report being paid a piece rate, followed
by operatives at less than 14%.8 Industries
where piece rates are frequently
observed are retail and wholesale trade
(11.8% of the observations in that industry),
finance, insurance, and real estate
(11.0%), and manufacturing (1 0.8%). The
frequency of bonuses is more evenly distributed
across occupations and industries
than is the frequency of piece rates. While
sales workers and managers stand out with
reported rates of 25.7% and 28.5%, respectively,
other 1-digit occupations report an
incidence ranging from 8% for service workers
to 14.9% for professional and technical
workers. The distribution across industry
shows that construction is the only 1-digit
industry with a bonus incidence of less than
10%, all other industries having a bonus
incidence ranging from 10.6% (agriculture,
forestry, and fisheries) to 18.2% (mining).
Although it seems reasonable to think
that many of the bonuses paid to managers
and especially to sales workers are in effect
another form of piece rate, in which pay is
based on the number of units sold or produced,
this conjecture is not so obvious for
professionals and clerical workers. The
fact that bonuses are more evenly distributed
than piece rates across occupations
and industries suggests that the bonuses
reported in these data are, to a degree, a
different form of incentive scheme.
8Remember that the label "piece rate" includes
commissions as well. Distinguishing between piece
rates and commissions as is done in the questionnaire
would reveal that commission contracts are most
common for sales workers while piece rate contracts
are most common for operatives.
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METHODS OF PAY AND EARNINGS 77
Table 2. Average Change in Log-Earnings by Gender and Type of Transition.
Pay Method in Year T+l
Men Women
Salary or Salary or
Pay Method in Year T Piece Rate Bonus Hourly Only Piece Rate Bonus Hourly Only
Panel A: Job Stayers Only
Piece Rate 0.061 0.143 -0.129 0.018 0.133 -0.101
(Obs.: Men, 177; Women, 117) [0.571] [0.339] [0.282] [0.658] [0.162] [0.282]
Bonus 0.129 0.057 -0.009 0.179 0.144 -0.007
(Obs.: Men, 303; Women, 186) [0.155] [0.505] [0.413] [0.167] [0.423] [0.475]
Salary or Hourly Only -0.063 0.113 0.020 -0.054 0.127 0.028
(Obs.: Men, 1,396; Women, 1,081) [0.031] [0.095] [0.881] [0.028] [0.079] [0.897]
Panel B: Job Changers Only
Piece Rate 0.227 0.228 -0.25 -0.021 0.116 0.035
(Obs.: Men, 79; Women, 32) [0.383] [0.213] [0.510] [0.313] [0.219] [0.594]
Bonus 0.221 0.083 -0.134 -0.245 0.021 -0.041
(Obs.: Men, 118; Women, 45) [0.125] [0.347] [0.583] [0.182] [0.228] [0.606]
Salary or Hourly Only 0.121 0.174 0.002 -0.102 -0.019 0.038
(Obs.: Men, 693; Women, 278) [0.102] [0.107] [0.820] [0.071] [0.091] [0.842]
Notes: Each cell entry represents the weighted average change in earnings for workers in year T+ 1 (T= 1988,
1989) who were paid either one of the pay methods in year T. The number of observations refers to Year T. The
numbers in brackets represent the transition rates between pay methods from Year T to Year T+ 1.
To further explore these data, Table 2
shows the average change in log earnings
between pay methods from one year to the
next as well as the associated rate of transition,
for men and women. As noted in the
theory section, self-selection of high-ability
people into piece rate contracts might help
explain the finding that workers paid piece
rates have higher earnings than salaried
workers. We can see that even within jobs,
there is movement from one pay method to
the next, although more for job changers
than for stayers.9
Among men, stayers and movers differ
considerably in the average change in log
earnings. Workers who change employers
while still being paid piece rates have a
much larger increase, on average, than
9The reason each row's percentages do not sum to
one is that some workers are paid both a bonus and a
piece rate. Also, the subsamples used to compute
these figures consist of workers who are observed in
two consecutive years. Workers who are present in
1988, absent in 1989, and back in the sample in 1990
are not included.
stayers do. The same is true for salaried
and hourly paid workers who move to a
piece rate contract with another firm. In
fact, stayers who experience the same type
of transition lose, on average. For both
movers and stayers, changing from a piece
rate scheme to a salary or hourly rate is
associated, on average, with a decrease in
earnings. These patterns are suggestive
that some selection is going on, with more
able workers who change firms and pay
method gaining when they move to a piece
rate contract.
Interestingly, the average changes in log
earnings for movers and stayers apparently
do not fit the same patterns for women as
for men, especially in the case ofjob changers.
In fact, as is shown below, some of
these gender differences are striking.
Estimation and Results
Methods of Pay and
the Effect on Earnings
Consider the following log-wage equa-
tion:
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78 INDUSTRIAL AND LABOR RELATIONS REVIEW
(5) lnw-t = X.tp + p,t8l + b +
nit R82 +f i
where w represents labor earnings per
hour of worker i at time t, X is a vector of
controls,10 Pit is equal to one if worker i is
paid a piece rate at time t and b i is a similar
indicator for the presence of a bonus, oci
represents unobserved worker productivity,
and Fit is an error term that is independently
and identically distributed.
Previous studies, such as Brown (1992),
Seiler (1984), and Ewing (1996), have all
found that piece rate workers earn more
than either salaried workers or hourly paid
workers. For comparison purposes, I first
estimate equation (5) using OLS to determine
whether the same empirical pattern is
present in these data. It is not clear a priori
what sign should be expected for 82' If most
of the bonuses paid have more in common
with piece rates than with merit pay, we
should expect an effect similar to that for
piece rates. If, instead, these bonuses are
more like merit pay cash rewards, then
according to models such as the one in
MacLeod and Malcomson (1989), there is
no reason to expect workers paid bonuses
to earn more, on average, than other work-
ers.
According to Lazear (1986), the empirical
regularities found in previous studies
can be attributed to workers selecting the
type of contract they prefer according to
their productivity. More able workers will
self-select into piece rate jobs, while other
workers choose time-rated jobs (or straight
salaries). Thus, any measured positive effect
of piece rates on earnings cannot be
attributed to an incentive effect. In other
words, switching all time-rated workers to
piece rate jobs would not cause an increase
in productivity (and wages). In terms of
I0This vector includes the number of years of
schooling, actual labor market experience and its
square, employer tenure and its square, and dummies
for gender, race, industry, occupation, region, and
health status. Also included is a dummy indicator for
increase in responsibilities.
equation (5), this means that p is positively
correlated with ox,. Consequently, if the
positive effect of piece rates on wages is due
solely to a selection bias, estimating (5)
with fixed-effects should result in the estimated
61 being close to zero. On the other
hand, if piece rates (and bonuses) provide
workers with better incentives than a salary
or an hourly rate, the measured effects
should not disappear once fixed-effects are
used.
However, even if piece rate workers are
found not to enjoy any wage premium once
fixed-effects are used, it would be premature
to conclude that incentives do not play
a role. Firms choose the pay method that
maximizes profits, given all the constraints,
be they technological or informational. If
incentives can be provided by paying salaries
or hourly rates, then one should not be
so surprised that in a cross-section of workers,
no pay methods seem to bring about
higher wages compared to the others. It
could just mean that all pay methods are
equally successful in getting workers to put
forth a satisfactory level of effort. Essentially,
finding a wage effect even after controlling
for selection indicates that incentive
effects are there, but finding no such
wage effect does not imply that incentives
are not provided.
A second prediction from Lazear's model
is that firms adjust rates upward in the first
period of the employment relationship to
provide sufficient incentives for workers to
give the first-best level of effort, even if the
workers know that employers cannot be
prevented from behaving opportunistically
in the second period by decreasing the
rates once they know the productivity of
their workers. If the bonus measure included
in the NLSY data is like a form of
piece rate for which workers get rewarded
if they surpass a quantitative target, then
this strategic interaction should also be at
work."I If, instead, bonuses reported in this
I "See Oyer (1998) for an analysis of the interaction
between incentives and sales seasonality. He showed
how salespersons may manipulate an incentive scheme
by varying their performance over their firms' fiscal
years.
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METHODS OF PAY AND EARNINGS 79
Table 3. Earnings Function Estimates.
(Dependent Variable: Log of Real Hourly Labor Income)
Men Women
1 2 3 1 2 3
Fixed-Eff. Fixed-Eff. Fixed-Eff. Fixed-Eff.
(Within- (Within- (Within- (WithinIndependent
Variable OLS Worker) Job) OLS Worker) Job)
Piece Rate 0.131 0.071 0.061 -0.015 -0.017 0.004
(0.027) (0.027) (0.033) (0.031) (0.035) (0.050)
Piece Rate x Tenure -0.014 -0.019 -0.017 -0.000 0.013 0.007
(0.007) (0.007) (0.007) (0.007) (0.008) (0.009)
Bonus 0.105 -0.016 -0.005 0.038 0.040 0.020
(0.023) (0.022) (0.024) (0.027) (0.026) (0.031)
Bonus x Tenure -0.011 0.008 0.006 0.012 -0.006 -0.004
(0.005) (0.005) (0.005) (0.006) (0.006) (0.007)
R-Squared 0.438 0.892 0.943 0.430 0.894 0.931
Sample Size 4,582 4,582 4,582 3,555 3,555 3,555
Notes: Other covariates include the number of years of schooling, experience and its square, and dummies
for race, industry, occupation, year, region, health status, and increase in responsibilities.
data set are more akin to merit pay, then no
such strategic interaction is at play. Although
I do not have the actual rates paid
to these workers and hence cannot directly
see whether these rates are high early in the
employment relationship only to be cut
later, one can get an idea of such strategic
behavior by interacting the incentive pay
dummies with employer tenure. According
to Lazear, if rates are set higher early in
the employment relationship than subsequently,
the measured effect of being paid
a piece rate (and, possibly, bonuses) should
be a negative function of tenure. We should
thus expect a negative sign for the interaction
term.
The results are reported in Table 3.
Looking at the results for men, we can see
in column 1 that OLS estimates indicate,
consistent with prior evidence, that piece
rate workers and bonus workers earn higher
average wages than workers paid on a hourly
basis or paid salaries. Interestingly, once
fixed-effects are used, the positive correlation
between the use of a piece rate and
wages does not disappear, and the effect of
being paid a bonus vanishes completely.
The same conclusion basically holds when
all variables are measured in deviation from
job-match means, thereby sweeping out any
fixed unobserved matching effect (column
3). The only difference between columns 2
and 3 is that the combined effect of a slightly
reduced coefficient with a larger standard
error makes the result borderline in statistical
significance (p-value of 0.0661).
These results suggest that piece rates,
but not bonuses, provide extra incentives
to increase productivity and wages. Note,
however, that while the total effect of piece
rates using OLS, taking into account the
negative interaction term with tenure, is
0.086 with an associated standard error of
0.026 when evaluated at the average tenure
level for men (3.2 years), the within-job
effect is virtually zero when evaluated at 3.2
years of tenure.
In the case of bonuses among male workers,
the positive impact measured with OLS
merely seems to reflect omitted ability variable
bias. Thus, controlling for unobserved
worker productivity, there is no evidence
that workers paid bonuses earn a premium
over those on an hourly or salary pay
scheme. This is consistent with MacLeod
and Malcomson's (1989) model of how
labor market conditions affect the form of
the contract (that is, base pay plus a bonus
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80 INDUSTRIAL AND LABOR RELATIONS REVIEW
versus straight salary) while the total amount
paid to workers remains the same.
However, this evidence should not be
construed as showing that bonuses have no
effect. Given the wording of the question
on bonuses, an affirmative answer to that
question does not necessarily imply that a
bonus was actually received by the worker,
only that the respondent's earnings are
based partly on bonuses. Hence, an attenuation
bias caused by measurement error
cannot be ruled out. Furthermore, this
problem is compounded when I use fixedeffects.
12
As for women, the results are quite striking
and strongly suggest that whether one
uses ordinary least-squares or fixed-effects
methods, "incentive contract" workers do
not earn more than other workers. It has
long been known that women's patterns of
labor force attachment differ from men's
due to (for example) fertility decisions.
Whether these forces also affect the role
incentives play for female workers is an
unexplored question to which I return be-
low.
I now turn my attention to the possibility
of strategic behavior between workers paid
piece rates and their employers (that is, the
ratchet effect). Looking first at the OLS
results for men, we can see that the effect
on wages seems to decline with tenure with
the employer. However, it would be rash to
interpret the negative interaction term as
reflecting the ratchet effect. As Table 2
shows, the self-selection of workers who
move from one pay method to another
could bias the results in various ways. The
descriptive statistics in the left portion of
Table 2 (the estimates for men) show that
workers who change employers and move
to a piece rate contract gain on average,
while those who stay with their employer
and move from a salary or hourly rate to a
piece rate lose on average. In fact, the
general pattern among men is forjob changers
to gain more than stayers from switch'2See
Card (1996) for an analysis of the effect of
union misclassification on the bias of OLS estimates.
ing to piece rates. The fact that those
gainers who move to a new employer are
then observed at lower tenure levels whereas
stayers who lose from switching to a piece
rate contract are observed at higher levels
of tenure would, by itself, tend to produce
a negative interaction term.
On the other hand, there are other transitions
in Table 2 that would tend to bias
the interaction coefficient in the other direction
for men. In Lazear's symmetric
information case (that is, neither the firm
nor the worker knows the worker's productivity
ex ante), only higher ability people
stay in piece rate jobs. The estimates for
men in the first row of Table 2 show that for
both job changers and job stayers, moving
from a piece rate to a salariedjob or hourly
rated job is associated with a substantial
decrease in earnings. Thus, looking at
stayers only, if the pool of piece rate workers
tends to be of higher quality as tenure
increases, that would tend to produce a
positive interaction term in an OLS regression.
Overall, it is not clear which form of
bias would dominate.
The results in columns 2 and 3 of Table
3 indicate that the coefficient is actually
slightly larger in absolute value with the use
of fixed-effects. 13 Thus, differencing out all
unobserved individual and job match heterogeneity
reinforces the OLS result and
tends to point toward positive selection of
workers into piece rate jobs as tenure increases.
14 I must emphasize again that these
data do not contain information on the
actual rates paid to workers (or the production
standards), which would make it easier
to analyze the ratchet effect and perhaps
make the results more convincing. Still,
the fact that in a cross-section of workers,
those paid piece rates tend to see their
wage premium (be it an ability premium or
an incentive premium) decrease with tenure
compared to time-rated workers seems
'3The difference, however, is not statistically sig-
nificant.
14By positive selection, I mean the process by which
higher-ability people select themselves into the piece
rate jobs.
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METHODS OF PAY AND EARNINGS 81
to be consistent with some ratcheting of the
rates/standards.
Another reason for the existence of such
a strong effect of piece rates on earnings at
low tenure levels could be career concerns
(Gibbons and Murphy 1992). Workers may
respond to incentives not only in order to
maximize current earnings but also to affect
other people's perceptions. Workers
who are successful in doing so may improve
their chances of getting promotions or future
wage increases. Thus, a prediction of
career concerns models is that since relatively
little is known about workers new to
their positions, effort will be higher at lower
tenure levels. Note that career concerns
considerations apply to all workers, not
only to those who are paid through explicit
incentive schemes. Consequently, if it were
true that career concerns affect everyone
irrespective of pay method, the interaction
term in Table 3 should be zero. The fact
that it is not may mean that it is relatively
easier for a young worker to affect the
perception of others when that worker is
paid a piece rate.
In the case of workers paid bonuses,
there is no evidence of a negative relationship
between tenure and the occurrence of
bonuses once fixed-effects are used.
Again, women have totally different patterns.
In terms of the selection explanation
given above, it is interesting to note that the
right-hand portion of Table 2 shows no
substantial difference in the average log
earnings change between femalejob changers
and job stayers: both lose, on average,
from moving to a piece rate contract, at
least when their previous pay method was a
salary or an hourly rate.
Why Are the Results
Different for Women?
Two potential explanations come to
mind. The first one relates to the fact that
women may work in occupations in which
ability does not matter quite as much as it
does for men, either because women choose
to work in those occupations or because of
occupational segregation. Controlling for
one-digit occupation is but a crude way of
trying to condition on such considerations.
To see whether refining the occupation
categories would make any change to the
results, I re-estimated the model with controls
for, respectively, two- and three-digit
occupation. In both cases, the results were
unchanged. In other words, even for workers
in the same closely defined occupation,
those who are paid a piece rate do not earn
more, on average, than others.
A second avenue worth exploring is the
role of fertility. Is having one or many
children at home influencing female workers'
responsiveness to incentive schemes
differently from men's? I examine that
possibility by interacting the piece rate
dummy with a dummy for the presence of
dependents at home. I construct two measures
for the dummy indicating the presence
of at least one dependent. From 1979
to 1988, respondents were directly asked
the following question:
Not counting (yourself/yourselves), but including
your children, how many persons are dependent
upon you [or your (husband/wife)]
for at least one-half their support?
Unfortunately, the following interviews only
asked for the number of children in the
household, which may not be as sharply
focused a question as the previous one,
given that there may be children in the
household for which the respondent is not
responsible. In 1989 respondents were also
asked whether they had had a child since
the previous interview. Thus, the first measure
uses the 1988 question on dependents
for those that are in the sample in 1988 and
then, for 1989 and 1990, I combine the
question on the number of children at
home with the 1989 question on having
had a child since the last interview to construct
a dummy variable equal to one if the
respondent has what I call at least one
dependent at home, and zero otherwise.
There are three potential problems with
using that measure: the presence of children
in the household does not necessarily
imply that those children are dependents;
many women who do give birth to a child
(and, possibly, men who declare having
had a child) are simply excluded from the
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82 INDUSTRIAL AND LABOR RELATIONS REVIEW
Table 4. Further Results: The Impact of Dependents.
(Dependent Variable: Log of Real Hourly Labor Income)
Men Women
1 2 3 4 1 2 3 4
Fixed-Eff. Fixed-Eff. Fixed-Eff. Fixed-Eff.
(Within- (Within- (Within- (WithinIndependent
Variable OLS Job) OLS Job) OLS Job) OLS Job)
Piece Rate 0.142 0.096 0.110 0.098 0.078 0.034 0.141 0.031
(0.030) (0.039) (0.034) (0.034) (0.038) (0.065) (0.044) (0.063)
Piece Rate x Dependent -0.047 -0.07 -0.048 -0.041 -0.163 -0.047 -0.213 -0.049
(0.035) (0.039) (0.039) (0.042) (0.040) (0.061) (0.045) (0.061)
R-Squared 0.430 0.944 0.437 0.936 0.429 0.931 0.425 0.926
Sample Size 4,582 4,582 3,667 3,667 3,555 3,555 2,730 2,730
Notes: Other covariates are the same as in Table 3. See text for details on the specifications.
sample because they are not in the labor
force at the time of the interview or they
have not worked a sufficient number of
weeks during the year; and the decision to
have children is endogenous, and simply
interacting the piece rate dummy and the
presence of dependents dummy establishes
no more than a statistical relationship.
For comparison purposes, I also construct
the following measure: only those
workers who are present (for the first time
in the sample) in 1988 are included in the
estimation, and the answer they give to the
1988 question on the number of dependents
is attributed to their record for interview
years 1989 and 1990. One reason for
using only that question is that it may largely
reflect past fertility decisions, which can be
taken to be exogenous. The other reason is
that the question itself is more focused.
Also, given that these workers are very
young, it is unlikely that one who has dependents
at home in 1988 does not have
any in the following years. 15
The results are presented in Table 4,
where specifications 1 and 2 refer to the
first measure while specifications 3 and 4
refer to the second measure discussed in
the preceding paragraph. The results using
OLS provide strong evidence that
women who have dependents may not be
150f course, had the same question been asked in
1989 and 1990, one could check that conjecture.
able to respond quite as much to an explicit
incentive scheme as can (a) women who
have no dependents or (b) men. When the
interaction term is included, the positive
relationship between piece rates and earnings
emerges quite clearly. This is especially
apparent in specification 3, where the
dummy for the presence of dependents is
constructed from the sharper 1988 question.
16
Note that adding the interaction term
for men does not markedly change the
results shown in Table 3, although it tends
to increase the effect of piece rates when
the withinjob estimator is used. To be
sure, the impact of the interaction term is
nowhere near what it is for women. Thus,
given the results in columns 2 and 4 of
Table 4, it appears that selection according
to ability matters also for women and that
this selection effect is largely hidden when
we ignore the presence of children. Concerning
the fixed-effects results (columns 2
and 4), part of the puzzle still remains,
although it must be noted that the coefficients
are not very precisely estimated: while
it is true that one cannot reject the null of
a zero effect, neither can one reject the null
of a 10% effect. Also, controlling for family
responsibilities does not change the result
'61n column 3, the piece rate effect for women is
0.029 when the interaction term is excluded and is
not statistically significant.
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METHODS OF PAY AND EARNINGS 83
Table 5. Minimum Distance Estimation of Covariance Structure, by Gender.
(Equally Weighted Minimum Distance Estimation; Standard Errors in Parentheses)
Men Women
Salaried Salaried
and Hourly Piece Rate Bonus and Hourly Piece Rate Bonus
Parameter Paid Workers Workers Workers Paid Workers Workers Workers
Variance of Unobserved 0.115 0.210 0.099 0.097 0.142 0.089
Worker Ability (0.004) (0.012) (0.010) (0.002) (0.026) (0.016)
Variance of i.i.d Component 0.050 0.028 0.052 0.044 0.061 0.060
(0.005) (0.017) (0.014) (0.002) (0.037) (0.022)
Chi-Square Statistic 8.7 2.5 5.1 0.5 6.1 3.2
Degrees of Freedom 4 4 4 4 4 4
Number of Workers 1,832 317 433 1,554 214 284
of an essentially zero effect for the tenurepiece
rate interaction term, even with OLS.
Methods of Pay and Wage Dispersion
The closer link between productivity and
pay that is a characteristic of piece rate
contracts should be reflected in the fact
that most of the unexplained variance resulting
from the estimation of equation (5)
is attributable to the variance of unobserved
worker productivity in the case of piece rate
workers. The first step to verifying this
prediction is to break the sample into three
subsamples according to method of pay
(piece rate, bonus, others)."7 Then, exploiting
again the longitudinal aspect of
the data set, I use the log wage observations
adjusted for schooling and labor market
experience to estimate a simple model of
the covariance structure of wages for each
'7More precisely, if a worker is paid according to a
piece rate contract in 1988 (say), then that worker is
part of the "piece rate subsample." If, in 1989, the
same worker is paid a bonus, then he or she belongs
to the "bonus subsample." If the worker is paid both
a piece rate and a bonus, whether during the same
interview year or in different years, I include that
person in both subsamples. If a worker reports a
piece rate one year and neither a piece rate nor a
bonus in another year, then that worker belongs to
the piece rate subsample for the year in which he or
she reports a piece rate, and belongs to the "others"
subsample for the year in which she or he reports only
a salary or an hourly rate.
type of pay method, using Chamberlain's
(1982, 1984) minimum distance estimator
adapted to unbalanced data.18 In other
words, the approach used is first to regress
(by year) the log wage on labor market
experience and schooling and then to use
the estimated residuals to compute estimates
of the unrestricted covariance matrix
of residuals. I then impose the restrictions
implied by the simple error component
structure given in equation (5) to
estimate the parameters of interest and to
test the fit of the model (see the appendix
for details).19
The results in Table 5 show that the
simple two-component model fits the data
quite well, as all goodness-of-fit statistics
are unsurprising values coming from a %2
(4) distribution. Looking first at men, note
that the relative contribution of unobserved
worker productivity is much larger for piece
rate workers than for other workers. This is
consistent with the view that pay is sensitive
to differences in productivity for piece rate
workers. Thus, although the simple explanation
of worker self-selection into piece
"8See Abowd and Card (1989) and Farber and
Gibbons (1996) for applications of these techniques.
'9Note that the results are not sensitive to different
specifications of the log wage equation estimated in
the first step. Various specifications including controls
for tenure, occupation, and industry were used
without altering the basic conclusions.
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84 INDUSTRIAL AND LABOR RELATIONS REVIEW
rate jobs does not seem to be the whole
story behind the wage premium that these
workers earn, the prediction of Lazear's
(1986) model concerning the dispersion of
wages for incentive workers is strongly supported.
Note also that since controlling for
unobserved ability accounts for a sizable
portion of the variance, Seiler's (1984) conjecture
that piece rate workers are rewarded
for facing higher income risks is not consistent
with the results reported here. The
results, at least for men, show that much of
the cross-sectional earnings variance for
piece rate workers is due to unobserved
worker heterogeneity, not to random
shocks.20
In Lazear's model, the reason earnings
are more dispersed for piece rate workers is
that output is more tightly linked to variation
in individual productivity. A related
explanation for the higher variance could
also be that for firms paying piece rates, the
underlying production technologies allow
heterogeneity in individual productivity.
However, if the work environment is characterized
by teamwork (Holmstrom 1982)
or multitasking (Holmstrom and Milgrom
1991, 1994), then it might not be possible
for firms to accommodate large differences
in productivity. The presence of teamwork
is, in some sense, equivalent to having
higher costs for monitoring individual output,
which, in Lazear's framework, makes
piece rates less desirable. However, the
provision of incentives in a multitasking
environment is a different problem. It
might be very cheap to monitor each
worker's output in such an environment,
but piece rates are likely not to be used if
firms care about other aspects of the job,
such as equipment maintenance or output
quality.21
20Seiler's explanation could still be true if workers
did not know their own productivity levels. Given the
possibility that they may turn out to be low-productivity
individuals, risk-averse workers would want to be
insured against that risk by asking for a premium.
2'For an analysis of the impact of these and other
factors on the form of the contract, see MacLeod and
Parent (1998).
Again, the results are not so clear-cut
for women, although it is still true that
the relative contribution of worker heterogeneity
to the total variance is larger
for piece rate workers than for other
workers.
Conclusion
I have found that the wage premium
enjoyed by male piece rate workers over
salaried or hourly paid workers does not
completely vanish once proper controls
are entered for unobserved worker and
job-match heterogeneity. For women,
there is no such evidence of a premium
when fixed-effects are used, although
controlling for family responsibilities
does make the OLS results similar to the
results for men.
The second most important result of
the study is that cross-sectional earnings
dispersion for piece rate workers is largely
accounted for by unobserved worker characteristics,
especially for men. As for the
part played by tenure, the finding that
for men the wage premium tends to decrease
with tenure seems to result at least
in part from different selection patterns
for job stayers compared to movers.
Some aspects of the data on methods
of pay contained in the NLSY restrict the
freedom with which the results presented
in this paper can be interpreted. Notably,
because the dollar amounts paid as
"incentive" pay are not known, it may be
that for many workers, much of their
labor income is in the form of hourly
rates or salaries, which are supplemented
by a certain amount of income earned
through pay-for-performance schemes.
Still, the results provide evidence that,
consistent with Lazear's (1996) findings
with company data, the wage effect of
piece rates is not all a product of selection:
there seems to be an influence of
incentives as well, at least for men. In
fact, an incentive effect accounts for close
to half of the total wage effect identified
using ordinary least squares analysis.
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METHODS OF PAY AND EARNINGS 85
APPENDIX
Let ett be the residual from a first-stage regression
of the log-wage on schooling and labor market experience.
Then we have
(6) e= lnw- Xt- ,
where X' is the vector of controls (experience and
schooling) and ? is the vector of the estimated parameters.
Then a natural estimator of the covariance
between the residuals at time t and at time s is given
by
(7) 6= N(7) 5t,s = N iYt, eiteis,
where N represents the number of workers.22 A
consistent estimator for the standard error of cf is
then given by
(8) Std(o )= k N2
Turning now to the restrictions imposed by the error
component structure suggested by equation (5), I
assume that the observed residual is given by
(9) eit = (Xi + c it
Therefore, the variance of the observed residuals at
period t is
(10) var(e,t) = E((Xi)2 + E(ei) 2= + Cy2
and the covariance between residuals at periods t and
S is
cov(e e,,) = E((i)2 + E(Citeis)2 = (2
since I am assuming that e is i.i.d. Thus, the model to
be estimated has the following linear structure:
(12) o'5= =1 + 02iDt,
where Dt = 1 if t = s and Dts = 0 otherwise, while e1 = aY2
and 02 = i 2. With 3 years of data, that means I have 6
distinct elements (per method of pay) to try to fit with
the two-component of variance representation given
by equations (10) and (11). The covariance model
given by these two equations militates that all diago-
22Note that because the data are unbalanced, the
number of workers used to compute the estimate is
not the same for each covariance element. To simplify
the exposition of the methodology, I assume that
the data are balanced.
nal elements should be equal and that all off-diagonal
elements should also be equal. This gives a total of
four restrictions to be imposed on the data.
To test these restrictions, I make use of the minimum
distance estimator proposed by Chamberlain
(1982, 1984). Succinctly, let m be the column vector
of the unique elements of the 3x3 cross-product
matrix of residuals for workers i. Then I calculate, for
each method of pay, the sample means of the elements
of mi, giving us the column vector m. The
model I want to estimate is a model for m. A consistent
estimator of the covariance matrix of the covariance
elements in m is given by
(13) I (mi m)(mi_ m)
The equally weighted minimum distance estimator
(EWMD) minimizes the following quadratic form
with respect to E):
(14) fl =[m - DE]'[m - DE],
where D is the design matrix made of ones and zeros
while E) = (cy2 cy 2) is the vector of parameters to be
estimated. On the other hand, the optimallyweighted
minimum distance estimator (OMD) minimizes with
respect to E) the quadratic form
(15) fl = [m - DE] Q-l [m - DE],
where Q is the covariance matrix of the vector of
covariance elements. Under the null hypothesis of a
correct specification in equation (12), the value of
the objective function (15) is distributed as a %2 with
degrees of freedom given by the number of restrictions
(the difference between the number of sample
moments to fit [6] and the number of parameters
[2] ) .23 Altonji and Segal (1994) discussed how small
sample size can lead to a substantial bias when the
OMD estimator is used in comparison to using the
identity matrix as the weighting matrix. Results are
thus presented for the more robust equally weighted
minimum distance estimator, which uses an identity
weighting matrix.24
23The computation of the %2 statistic for the EWMD
estimator differs somewhat different from that for the
omd. See the appendix in Abowd and Card (1989) for
the details.
24Results with the optimally weighted minimum
distance estimator are very similar.
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86 INDUSTRIAL AND LABOR RELATIONS REVIEW
REFERENCES
Abowd, John M., and David Card. 1989. "On the
Covariance Structure of Earnings and Hours
Changes." Econometrica, Vol. 57, No. 2, pp. 411-45.
Altonji,Joseph G., and Lewis M. Segal. 1994. "Small
Sample Bias in GMM Estimation of Covariance Structures."
NBER Technical Working Paper No. 156.
Brown, Charles. 1992. "Wage Levels and Methods of
Pay." Rand Journal of Economics, Vol. 23, No. 3, pp.
366-75.
Card, David. 1996. "The Effect of Unions on the
Structure of Wages: A Longitudinal Analysis."
Econometrica, Vol. 64, No. 5, pp. 957-79.
Carmichael, H. Lorne. 1989. "Self-Enforcing Contracts,
Shirking, and Life Cycle Incentives." Journal
of Economic Perspectives, Vol. 3, No. 4, pp. 65-83.
Chamberlain, Gary. 1982. "Multivariate Regression
Models for Panel Data." Journal ofEconometrics, Vol.
18, No. 1, pp. 5-46.
_ 1984. Panel Data, Vol. 2, Chap. 22, pp. 1247-
1318. Amsterdam: North-Holland.
Ewing, Bradley T. 1996. "Wages and PerformanceBased
Pay: Evidence from the NLSY." Economics
Letters, Vol. 51, No. 2, pp. 241-46.
Farber, Henry S., and Robert Gibbons. 1996. "Learning
and Wage Dynamics." Quarterly Journal of Economics,
Vol. 111, No. 4, pp. 1007-47.
Ferrall, Christopher, and Bruce Shearer. 1996. "Incentives
and Transaction Costs within the Firm:
Estimating an Agency Model Using Payroll Records."
Working Paper 908. Kingston, Ontario: Department
of Economics, Queen's University.
Gibbons, Robert, and KevinJ. Murphy. 1992. "Optimal
Incentive Contracts in the Presence of Career
Concerns: Theory and Evidence. " Journal of Political
Economy, Vol. 100 (june), pp. 468-505.
Holmstrom, Bengt. 1982. "Moral Hazard in Teams."
BellJournal of Economics, Vol. 13, No. 2, pp. 324-40.
Holmstrom, Bengt, and Paul Milgrom. 1991. "MultiTask
Principal Agent Analysis: Incentive Contracts,
Asset Ownership, and Job Design." Journal of Law,
Economics, and Organization, Vol. 7, No. 1, pp. 24-52.
. 1994. "The Firm as an Incentive System."
AmericanEconomic Review, Vol. 84, No. 4, pp. 972-91.
Jensen, Michael, and KevinJ. Murphy. 1990. "Performance
Pay and Top Management Incentives."
Journal of Political Economy, Vol. 98 (April), pp.
225-64.
Kanemoto, Yoshitsugu, and W. Bentley MacLeod.
1991. "The Ratchet Effect and the Market for Secondhand
Workers." Journal of Labor Economics, Vol.
9, No. 1, pp. 85-98.
Lazear, Edward P. 1986. "Salaries and Piece Rates."
Journal of Business, Vol. 59, No. 3, pp. 405-31.
. 1996. "Performance Pay and Productivity."
Technical Report 5672. Cambridge, Mass.: National
Bureau of Economic Research.
MacLeod, W. Bentley, and James M. Malcomson.
1989. "Implicit Contracts, Incentive Compatibility,
and Involuntary Unemployment. " Econometrica, Vol.
57, No. 2, pp. 447-80.
MacLeod, W. Bentley, and Daniel Parent. Forthcoming.
'Job Characteristics and the Form of Compensation."
Research in Labor Economics.
Oyer, Paul. 1998. "Fiscal Year Ends and Nonlinear
Incentive Contracts: The Effect on Business Seasonality.
" QuarterlyJournal of Economics, Vol. 1 1, No. 1,
pp. 149-85.
Pencavel, John. 1977. "Work Effort, on the Job
Screening, and Alternative Methods of Remuneration."
In Ronald G. Erhenberg, ed., Research in
Labor Economics, Vol. 1. Greenwich, Conn: JAI
Press.
Seiler, Eric. 1984. "Piece Rate vs. Time Rate: The
Effect of Incentives on Earnings." Review of Economics
and Statistics, Vol. 66, No. 3, pp. 363-76.
Shapiro, Carl, andJoseph E. Stiglitz. 1984. "Equilibrium
Unemployment as a Worker Discipline Device."
American Economic Review, Vol. 74, No. 3, pp.
433-44.
Shearer, Bruce. 1996. "Piece Rates, Principal-Agent
Models, and Productivity Profiles: Parametric and
Semi-Parametric Evidence from Payroll Records."
Journal of Human Resources, Vol. 31, No. 2, pp. 275-
303.
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