Montréal
Série Scientifique
Scientific Series
2001s-05
The Effect of
Pay-for-Performance
Contracts on Wages
Daniel Parent
CIRANO
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research teams.
Les organisations-partenaires / The Partner Organizations
•École des Hautes Études Commerciales
•École Polytechnique
•Université Concordia
•Université de Montréal
•Université du Québec à Montréal
•Université Laval
•Université McGill
•MEQ
•MRST
•Alcan Aluminium Ltée
•AXA Canada
•Banque du Canada
•Banque Laurentienne
•Banque Nationale du Canada
•Banque Royale du Canada
•Bell Québec
•Bombardier
•Bourse de Montréal
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•Fédération des caisses populaires Desjardins de Montréal et de l’Ouest-du-Québec
•Hydro-Québec
•Imasco
•Industrie Canada
•Pratt & Whitney Canada Inc.
•Raymond Chabot Grant Thornton
•Ville de Montréal
© 2001 Daniel Parent. Tous droits réservés. All rights reserved.
Reproduction partielle permise avec citation du document source, incluant la notice ©.
Short sections may be quoted without explicit permission, if full credit, including © notice, is given to the source.
Ce document est publié dans l’intention de rendre accessibles les résultats préliminaires
de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions.
Les idées et les opinions émises sont sous l’unique responsabilité des auteurs, et ne
représentent pas nécessairement les positions du CIRANO ou de ses partenaires.
This paper presents preliminary research carried out at CIRANO and aims at
encouraging discussion and comment. The observations and viewpoints expressed are the
sole responsibility of the authors. They do not necessarily represent positions of CIRANO
or its partners.
The Effect of Pay-for-Performance Contracts on Wages
*
Daniel Parent
†
Résumé / Abstract
Cet article cherche à évaluer le rôle joué par les avantages comparés eu
égard au résultat fréquemment rencontré qui veut que les travailleurs payés à la
pièce ou par commission soient mieux rémunérés que les travailleurs salariés
(incluant ceux qui sont payés à l'heure). Selon le modèle de Lazear (1986), la
sensibilité de la rémunération à la pièce par rapport à la productivité est plus
grande que dans les boulots salariés. Les avantages comparés impliquent donc que
les travailleurs intrinsèquement plus productifs choisiront des contrats dans
lesquels la rémunération est à la pièce. Ce processus d'auto-sélection selon les
avantages comparés a comme conséquence que l'utilisation des méthodes dites
d'effets fixes donnera des estimés biasés du véritable effet incitatif de ce type de
contrat. Avec des données du National Longitudinal Survey of Youth et du Panel
Study of Income Dynamics, je trouve que l'auto-sélection selon lesavantages
comparé de même que l'apprentissage des caractéristiques individuelles semblent
jouer un rôle important dans les cas des travailleurs qui sont soit en début de
carrière ou qui débutent une nouvelle relation d'emploi. En ce qui concerne les
travailleurs plus âgés, le rendement à la productivité est essentiellement le même
peu importe la méthode de rémunération employée par la firme. Enfin, j'estime un
effet incitatif d'environ 11 % en exploitant les variations dans la méthode de
rémunération pour un même individu à l'intérieur d'une relation d'emploi.
In this paper, I investigate the role played by learning and self-selection
according to comparative advantage in the often reported result that piece rate
workers (including commissions) earn more on average compared to other
workers. With comparative advantage, the returns to skills are different according
to whether one works under a piece rate contract or not. If that is the case, as
Lazear (1986)’s model suggests, then using standard fixed effects methods will not
provide consistent estimates of the true causal (or incentive) effect of explicit
contracts. Using non-linear instrumental variable techniques with data from the
National Longitudinal Survey of Youth and the Panel Study of Income Dynamics,
I find that comparative advantage along with learning about worker skills seem to
play a significant role for workers who are either at an early stage in their career
or who are observed for the first time in a given job-match, when the learning
process matters. In other words, for those younger/early tenure workers, the
*
Corresponding Author: Daniel Parent, CIRANO, 2020 University Street, 25
th
floor, Montréal, Qc, Canada
H3A 2A5
Tel.: (514) 398-4846
Fax: (514) 985-4039
email: [email protected]
I wish to thank seminar participants at the University of Illinois at Urbana-Champaign and at Carleton for useful
comments and suggestions. I also wish to thank Hank Farber and Bentley MacLeod for useful comments on a
previous version.
return to skills is lower in non-incentive jobs. For older workers, the return to
skills is basically the same across pay methods, which is consistent with the notion
that workers are eventually paid according to their fully revealed skill level,
irrespective of how they are paid. Finally, by exploiting the within-job variation in
pay methods, I am able to identify an incentive effect of about 11%.
Mots Clés :
Rémunération à la pièce, auto-sélection, effets incitatifs
There is a growing body of evidence which shows that performance pay
workers (piece rate orcommission workers) earn more on average compared
to salariedor hourly rated workers (see, e.g., Pencavel (1977), Seiler (1984),
Brown (1992), Ewing (1996), Lazear (1996)). One can think of two main
explanations for this relationship between explicit pay-for-performance
con-tractsand thewage structure. On theone hand,itispossiblethatpiecerate
workers havestronger incentivestoworkhard. However, even absentany
in-centive eects, the self-selection of inherently more productive workers into
those jobs will produce a positive correlation between average earnings and
the occurrence of pay-for-performance contracts (see Lazear (1986)). More
productiveworkers willself-selectintothosejobs because onlyforthem isit
worth ittoindirectlypay the(higher)monitoringcostsassociatedwithpiece
rates through reduced wages. Recent papers by Lazear (1996) and Parent
(1999) have attempted to control for this selection eect by exploiting the
longitudinal dimension of the data sets employed to control for unobserved
worker productivity and job-match quality. In Lazear's case study, he was
abletoexploitthefactthattheworkers'paymethodchangedfromanhourly
rate to a piece rate to do a simple before-after comparison in productivity,
wages, turnover, and absenteeism. Hisresults showed a substantial increase
in productivity that was partly the result of selectioneects and partly the
result of a pure incentive eect. With a very dierent data set (the
Na-tional Longitudinal Survey of Youth (NLSY)), Parent (1999) qualitatively
found the same result in terms of the impact onwages. In both papers, the
underlying assumptions are that the return to skills is the same across pay
methods and that conditional on the time-invariant unobserved
productiv-ity component (as well as on all observables), the choice of pay methods is
strictly exogenous. While this rationalizes the use of xed-eect methods
to control forunobserved factors, it may not provideconsistent estimates of
of compensation.
The objective in this paper is to determine the extent to which workers
do select themselves into jobs oering dierent methods of compensation
based on comparative advantage and on learning about one's skills. This
later aspect is important because it in uences both the initial choice of a
compensation scheme and the decision to eventually switch pay methods.
To empirically study these issues, I make use of the method of moments
estimation methodology developed by Lemieux (1998) and applied in the
context of the eect of unions onthe structure of wages. 1
The Lazear (1986) model (see also Brown (1990)) predicts that wages
should be moresensitiveto skillsinpiece rate jobs. Therefore, assessing the
empirical validity of this prediction is of obvious interest. For example, if
the return toskills isnot very dierent across pay methods, thus suggesting
that comparative advantage considerations may not be all that important,
then this may call into question some of the assumptions underlying the
theoreticalmodel. Notealsothatthiswouldvalidatethe useof simple
xed-eect methods. In fact, if selection was completely random, one would not
even need to use rst-dierences: ordinary least squares would su ce to
produce an unbiased estimate of the incentive eect. However, researchers
routinelyuse rst-dierencestocontrolfornonrandomselectioneven though
it is not clear that it necessarily follows from an economic model of
self-selection.
In a related vein, Prendergast (2000) notes that explicit incentive
con-tracts tend to be found in environments with often large random
uctua-tions, such as sales. This observation seems at odds with the notion that 1
SeealsoGibbons,Katz,andLemieux(1997)foracloselyrelatedapplicationto inter-industry wage dierentials in which workers sort themselves acrossindustries based on comparative advantage and on learning about their initially unobserved skills. I come back belowonwhylearningisanecessaryingredientin thepresentcontextto makethe modelempiricallymeaningful.
model would suggest, yet is consistent with the fact that the empirical
evi-denceonthetrade-obetweenrisksandincentivesissomewhatcontroversial,
some authors nding support for the predicted tradeo (e.g. Aggarwal and
Samwick(1999))whileothersdonot(Garen(1994)). Prendergastthennotes
that in relatively stable or less risky environments, rms may intensify the
monitoring of inputs simply because the link between eort and output is
quite direct. Consequently itis not clear that monitoringconsiderations are
completely absent from non-incentive jobs. If that is the case, one may
ex-pect to nd that perhapsthe sensitivity of output and wages to skillsis not
that dierent inpiece rate jobs compared totime rated/salariedjobs.
Many other models of optimal sorting rely onthe notionof comparative
advantage. Forexample, Rosen (1982) develops a modelin which itis
opti-mal for high ability people to be sorted in jobs where their impact is the
greatest, such as inexecutive jobs. As a consequence, the earnings
distribu-tionwillbeskewedbecausethoseatthetopwilltendtoseetheirwagesgrow
more than proportionately with respect to their skills. Hence, the return to
skills willbehigherinhigh impact jobs. Arelatedmodelcombining
learn-ingandhumancapitalaccumulationcanbefoundinGibbonsand Waldman
(1999). Also, MacLeod and Malcomson (1988) explore the endogenous
cre-ation of a hierarchy in an environment characterized by moral hazard and
adverseselection. Workers areinitiallypooledandthroughtheaccumulation
of output observations, the rm optimally assigns the best/hardest working
among them to the higher ranks. This implies that pay should not be very
sensitivetoskilldierentialsfornewlabormarketentrant. Incontrast,older
workers, about whom all available information has been accumulated will
be sorted to the ranks that correspond to their skill level. Consequently,
we would expect to observe that the return to skills is lower for younger
compared to older workers, allelse being equal.
focusontherelatedquestionofwhether wagesre ectthefactthatpiecerate
contracts essentially reveal worker productivity immediately while salaries
or hourly rates may not do so initially. If this is true, then we should see
evidenceofdierentialreturnstoskillsacrosspaymethods. Also,takinginto
account this selectionprocess, I want toestimatewhether switching workers
to piece rate contracts can beexpected tohave atrue incentive eect.
Withdata fromthe National LongitudinalSurvey of Youth(NLSY) and
the Panel Study of Income Dynamics (PSID), the results show that
unob-served skills are rewarded dierently in incentive jobs compared to jobs
which pay either hourly rates or salaries. Interestingly, this is true only in
the case of workers who areeither earlyintheir careers, such asthe workers
surveyed inthe NLSY, orwho are observed for the rst time ina given
em-ployment relationship. IfI focus onlyon jobstayers only, there issomewhat
less evidence that self-selection into piece rate contracts according to
com-parative advantage matters a great deal, although I still nd evidence of it
in the case of youngerworkers in both the PSID and the NLSY.
Thus, ontheone hand,the results provide supporttothe ideathat
com-parative advantage does play a role. Secondly, the fact that the return to
skills does not seem to vary across pay methods in the case of either older
workers or workers repeatedly observed in the same job is suggestive that
whateverinformationlabormarketparticipantsneedtolearnaboutthe
pro-ductivityoftheworkers isfullyrevealed eventually. Inaddition,even though
selectionaccording tocomparativeadvantage isshown tobe empirically
rel-evant, I provide evidence that the selection mechanism does not appear to
beone-sided inthe sensethatworkersatbothendsof theskilldistribution
seem tochoose piecerate contracts. Althoughthis isnotconsistentwith the
basicLazearmodelinwhichselectionisone-sided,itcaneasilybereconciled
with Brown (1990)'sreformulationofthe Lazearmodelinwhichworkers are
The results on the extent of the true incentive eect are somewhat
mixed. On the one hand, results obtained by exploiting the within-worker
variationinpaymethodssuggestthatselectioneectsaretheprimaryreason
for the often reported result that incentive workers are paid more than
others. This is particularly true in the case of the NLSY, but also for the
subset of workers in the PSID who are in the same age range as those in
the NLSY.On the otherhand, ifI use insteadthewithin-jobvariation(thus
controlling for any unobserved matching eect), the results using the PSID
point toward a true wage eect of about 11 percent. Interestingly, it turns
out that while the measured eect of explicit pay-for-performance contracts
on wages is within range of the wage impact estimated previously in the
literature, itissubstantiallylarger than theimpactestimatedwith standard
xed-eects, atleastinthecase ofthePSID.This latter,perhapssurprising,
result stems mainly fromtaking intoaccount the endogeneity of the change
inpaymethod. Thisendogeneityproblemiscausedbyeitherlearningeects
or, more likely, by misclassi cation of pay methods. As is well known (e.g.
see Card(1996)),this aspectisapotentiallyimportantsourceofattenuation
bias in a wage equation,especially ina longitudinalsetting.
Thepaperisstructuredasfollows. Thenextsectionsummarizesprevious
resultsintheliterature. Section3thenbrie youtlinesthe Lazearmodeland
itsoptimal assignment rule inwhich workers with more skillsend up injobs
wheresuchskillshaveahigherreturn. IalsooutlineBrowns'reformulationin
termsof workers beinghomogeneousinproductiveabilitybut heterogeneous
as to the cost of eort. The estimation methodology is discussed next in
Section 4. The data are presented in Section5 and the results in Section6.
centive Eects
Although researchers have in the past found that incentive workers earn
more on average than other similar workers, much of the evidence came
fromcross-sectionaldata andone can neverrule out thatthe wage premium
earned by performance-pay workers in these data was simply the result of
confoundingeects,suchasunobservedworkerproductivityorsystematically
dierentunobserved working conditions.
Onewaytoatleastpartlygetaroundthoseproblemsistouse paneldata.
Threerecentpapers,twoofwhichbeingcase-studies, haveexploitedthat
di-mension. Lazear (1996) measures the changes in productivity and wages
followingthe decisionby alarge autoglass company toswitch paymethods,
going from time rates to piece rates. He nds large eects on productivity
(24% when one controls for selection eects through rst-dierences). Also,
controllingforworkerquality,he ndsthattheswitchinvolvedanincreaseof
about 9% inwages. Using threestraightwavesof the NationalLongitudinal
Survey of Youth, Parent (1999) nds thatcontrolling forunobserved worker
and job-match eects, piece rate workers still earn a 6-7% wage premium.
Unfortunately, it is impossible with the NLSY to determine the
productiv-ity eect, althoughone could arguethat unless rms have some monopsony
power, workers shouldbepaid accordingtothevalue oftheirmarginal
prod-uct. Shearer (1999), on the other hand, solved the self-selection issue by
having a tree planting company in British Columbiarandomly assign some
of its workers to either xed wages or piece rates. The productivity of the
workers was recorded on a daily basis and controls were included for land
quality. 2
Hisexperimentalresultsindicatethatthe incentiveeect ofpaying
workers a piece rate is about 20%, and it should be emphasized that given 2
Some plots were at and thus workerscould plant a lot of trees in a day, whereas othersweresteeplyslopedwithalotofdebrisontheground,whichmadeitverydi cult fortheworkers.
biases that selection according tocomparative advantage might create.
Thegoalofthispaperisto ndout,usingnon-experimentaldata,whether
suchaselectionmechanismisimportant,whichhas implicationsonhow
con- dentwecanbeininterpretingstandard xed-eectestimatesasrepresenting
the true incentiveeects ofpiece ratecontracts. Put dierently,this paper's
objectiveistoseewhetheronecanreadilygeneralizetheexistingresultsfrom
case studies to the overall populationof workers.
3 Theoretical Considerations
3.1 Relationship between Piece Rates and Wages
As shown in Lazear (1986), dierent methods of pay allow workers to sort
themselvesamong rms. Zero expected pro tsare assumed throughout and
we alsoassumethat workers know theirproductive abilitybut not the rms
unless they incur a monitoring cost M. Thus workers can be in a rm that
pays asalarySwhichisindependentofproductivity orinapiece rate rm
that pays a wage W = M. Thus the worker chooses the piece rate rm
if and onlyif:
M >S
and the others choose to work in the salary rm. Provided that M > 0,
there willbe rms oeringS >0. Firmspayingsalarieswillknowthey have
attracted workers of lower average quality and they will pay a salary equal
to the expected productivity ofthat subsample of workers:
S =E( j < )
moves one-for-onewith skills inpiece rates. More generally, we may simply
allowskillsto be rewarded dierently inthe twotypes of jobs: 3 lnw m =a m +b m
with m=(salary,piecerate) and
a s >a p ;b s <b p ;
This optimal sorting of workers is illustrated in Figure 1 in the case where
b s
=0.
3.2 Brown's Reformulation
Notethat theforegoingmodelsays nothingaboutthe incentivesprovided to
a given worker, which are commonly thought to be the reason rms might
want to oer explicit pay-for-performance contracts in the rst place. To
examine the eort dimension, Brown (1990) reformulates the problem by
assuming that homogeneous workers in terms of productivity are
heteroge-neous in terms of their eort cost function. In addition, he assumes that
rms oering salaries can costlessly enforce aminimum level of eortE.
Letthe worker's utility function be expressed as:
U(w;e)=w C(e)
wherewisthewage,eiseortandwehaveC 0
>0andC 00
>0. Forexample,
one couldassume the followingfunctional form:
U(w;e)=w e
2
N 3
work harder. The worker's problemisthen tochoose thejob which provides
the greatest utility. With the rm not monitoring eort in the salary job,
the workerchooses e
=E and getsutilityU =S E
2 N
where,again,Sisthe
constant salary paid by the rm. Assuming, as in the previous paragraph,
that the wage inthe piecerate jobisw=e M,where isMthe monitoring
cost,thepiecerateworkerchoosesaneortlevelthatmaximizesthefollowing
expression:
U(e)=e M e
2
N
The rst order condition for this problem issuch that
e
= N
2
with utility given by
U(e )= N 4 M
From gure 2,we can see that, given the chosen parameterization, not only
will high energy workers self-select into piece rate jobs but so will low
en-ergy ones as well. 4
Consequently, even though the problem is reformulated
intermsofthechoiceofeort, westillbasicallyhaveaself-selectionmodel,
the major dierencewith the basic Lazearmodelbeingthat we donot have
a single threshold selection mechanism. Instead, both low and high cost
of eortworkers may prefer piece rates. I willpresent below some evidence
onthe natureof theselectionprocess. This ispotentiallyimportantbecause
standard selectivity correction procedures, such asHeckman's two-step
esti-mator, provide consistent estimates of the parameters of interest only when
selection isone-sided. 4
Brownfullyrecognized thispossibility, butdismissedits empiricalimportancebased ontheresultsine.g. Pencavel(1977)andSeiler(1984). Consequently,hefocusedonthe one-sidednessoftheselectioneect.
The reasonthat pay is not as sensitive to skills insalaried/hourly paid jobs
comparedtoincentivejobsisthat rmsdonottakethetroubleofmonitoring
performance to revealthe exact skilllevel of itsworkers. In other words, as
pointed out in the previous section, if skills were all perfectly observables
there would be no salary jobs and everyone would bepaid a piece rate. 5
In
the present context, I assume that the standard controls such as years of
completed education, age, and health conditions are in fact observed by all
labormarketparticipants. Consequently,thereisnoreasonthat rmsshould
pay for them dierentlyaccording to the pay method. 6
Themoreinterestingcaseinvolvesskillswhichareunobserved toboththe
econometricianand alllabormarketparticipants. Twotypesofcontractsare
oeredinthelabormarket,pieceratecontractsandstraightsalaries. Salaries
are assumedtobeset atthe startofeachperiodbasedonalltheinformation
available. Firms and workers alike form beliefs about the workers'
produc-tivity based on some prior distribution and they update those beliefs in a
standard Bayesian manner after observing the output at the end of each
period. 7
More speci cally, let i
be the unobserved ability of worker i. The
standard normal learning model assumes that i
comes from a prior
distri-bution andeachperiodallparticipantsobserve anoutput signaland update
their beliefs about i
. Let m it
be the best predictor of i
given the full 5
Leaving aside, of course, important issues such as multitasking which may render counter-productivethetheuseofpiece ratesevenwhenskills areperfectly observable.
6
Inothercontexts,itmakessense toassumethatthereturnsto allobservable dimen-sionsarerewardeddierentlydependingontheinstitutionalenvironment. Forexample,in Lemieux(1998)'sunioncase,paycompressionislikelytobeaunionpolicy. Consequently, highlyeducatedindividualsmayberewardeddierentlyintheunionvs. nonunionsector. Another way of justifying theassumption that observableskills are equallyrewarded in all rms,irrespectiveofthepaymethod,istoobservethatmostcommissionorpiecerate workersearn abasesalaryorabasehourly rate. This base paywouldre ectdierences in skillsacrossworkers.
7
SeeFarberand Gibbons(1996)forafull expositionofthis bayesianlearning mecha-nismandanapplicationtowagedynamics. Thelearningapparatusisalsoessentiallythe sameastheonedevelopedinJovanovic(1979)'smatchingmodel.
it martingale: m it =m it 1 +v it (1) where v it
is the innovation term orthogonal to m it 1
. As we will see
be-low,this martingaleproperty,eveninthe absenceofcomparativeadvantage,
renders xed-eectinconsistentbecause, infact,theunobservedproductivity
componentisnot xed. Iturnnext totheempiricalimplementationofa
self-selection model according to comparative advantage and in which learning
about unobserved skills is allowed.
4 Empirical Framework
4.1 The Model
InthissectionIoutlinethemethod-ofmomentsestimatorproposedbyLemieux
(1998)inthecontextoftheeectofunionsonthewagestructure. The
appli-cation here is a straightforward adaptation of Lemieux's methodology with
the exception thatI willalso takeintoaccountlearning onthe part of labor
market participants, asis done,in e.g. Gibbons, Katz, and Lemieux (1997).
Assuming for the moment that the unobserved productivity component
is xed, let the logwage of worker iat time tbewritten as:
lnw p it =Æ p +X it + i + p i
in piece rate jobs,and
lnw s it =Æ s +X it + i + s i
in salaried jobs, where X it
is a vector of controls including age, education,
region, etc., i
is a time-invariant unobserved (to the econometrician)
pro-ductivity parameter, Æ p
and Æ s
rate jobs), and the 0
s represent residual terms. IfI re-writethis expression
in concentrated formwe have:
lnw it =Æ s +X it +P it Æ+ i [P it + (1 P it )]+" it (2) where P it
is a performance pay dummy indicator, Æ = Æ p
Æ s
represents
the true average eect of performance pay contracts on wages (excluding
selection eects), and " it
is the residualerror term. According tothe model
presented in the previous section, we would therefore expect to have <1
for salaried workers. In fact, in the extreme case, = 0 i.e. compensation
does not depend at allonskills.
In standard xed-eect models, = 1 regardless of the method of pay
and therefore can be dierenced out. In general though, as is clear from
equation.(2), rst-dierencesmethods willnot produce consistent estimates
of (Æ, ) unless we have good reasons to believe that unobserved skills are
independentof thechoiceof paymethod. Butthen, wewould noteven need
touse rst-dierencestogetconsistentestimatesoftheparameters: ordinary
least-squares would beappropriate. However, itisclearly notappropriatein
this case if self-selection into pay methods according tocomparative
advan-tage is relevant.
Nowiftheunobserved productivitycomponentisunobservedtoboth the
econometrician and all labormarket participants, then equation (2) can be
rewritten as lnw it =Æ s +X it +P it Æ+m it 1 [P it + (1 P it )]+" it (3)
Notethat Iamimplicitlyassumingthatthe worker's pay inthesalaryjobis
based on all the information available at the end of period t-1, m it 1
. It is
immediatelyapparentfromequation(3)thateven inthe absenceof
rst-dierenced wage equation is lnw it =X it +m it 1 +P it Æ+" it (4)
As it is, the innovation term v it 1
= m it 1
m it 2
is correlated with the
changeinpaymethodthroughthesameprocessthatledunobservedabilityto
becorrelated withthe originalchoiceof pay method. Consequently, the pay
methodchangedummyisanendogenousvariableandhastobeinstrumented.
Suitable instruments can be found by exploiting the panel dimension of the
data set. More onthat below. 8
Notethat I amsidesteppingthe issue of the dierentialinformation
con-tentof anoutputsignalinapiecerate jobcomparedtoasalaryjob. Infact,
I am implicitlyassuming that itis the same. This issimply forexpositional
purposes. Infact, the timingof wage paymentstothe workers isvery
dier-entinpieceratejobsthaninsalariedjobs. Whileitissensibletoassumethat
salaries at time t are set prior to observing outputat time t (hence salaries
depend onm it 1
, not m it
), inpiece rate jobs payment is made after output
is realizedand information has been revealed. The basic mechanism I have
in mind is that there is a pooling of skills in salaried jobs, which results in
pay not being quite as sensitive to skill dierentials, while piece rates entail
no such pooling, inwhichcase pay varies directly with skills.
Now if weincorporatecomparative advantage inthe model and we solve
equation (2) for m it 1 we get: m it 1 = [lnw it (Æ s +P it Æ+X it )]+" it 1 ] [P it + (1 P it )] (5)
Takingthe rstlagofthis expression andsubstitutingitform it 2
inthelaw 8
Another reasonfor instrumenting thepaymethod dummyis measurementerror. If paymethodsaremisclassi edthentheobservedpiecerateindicatorwillbecorrelatedwith theerrorterm,irrespectiveofwhetherthere islearningornot. Theresultingattenuation biascanbesubstantialwithpaneldatamodels(Card(1996)).
it 1 it 2 it 1 lnw it =Æ s +P it Æ+X it + [P it + (1 P it )] [P it 1 + (1 P it 1 )] (lnw it 1 Æ s P it 1 Æ X it 1 )+! it where ! it = [P it + (1 P it )] [P it 1 + (1 P it 1 )] " it 1 +v it 1 [P it + (1 P it )]+" it (6)
Theresultingequationcanbeestimatedbynonlineartwo-stageleastsquares,
provided we can nd suitable instruments for ln w it 1
. A non linear
regres-sion will produce inconsistent estimates because ln w it 1
is an endogenous
variabledue toitscorrelationwith" it 1
:Alsothepay methoddummyneeds
tobeinstrumented because ofitscorrelation withv it 1
through the learning
process.
4.2 Instruments
GiventhatIhaveatleastthreeyearsofdatainbothpanels,Icanuselnw it 2 as an instrument for ln w
it 1
. In addition, the lagged pay method dummy
P it 1
can be used to instrument P it
along with a full set of interactions
betweenP it 1
and theotherexplanatoryvariables(theX 0
s). Similarly,P it 2
can be used as an instrument as well as its interaction with the lagged X 0
s
and with P it 1
.
I willalso exploit another source of arguably exogenous variationin pay
methods. Prior workby e.g. Brown (1990) and MacLeod and Parent(1999)
has shown that job characteristics are alsoan important determinant of the
use of incentive pay. For example, jobs in which workers are expected to
do a variety of tasks have been found to be strongly negatively correlated
mance exists. Conversely, more complex jobs in which multitasking is the
norm avoid paying workers based on explicit incentives. One reason is the
absence of a mutually agreed upon simple measure of performance.
Conse-quently,Ihavemergeddataonjobcharacteristicsfromthe1991Dictionnary
of Occupational Titles (DOT) tothe NLSY and PSID data sets. More
pre-cisely, I convert (and aggregate) the DOT job characteristics data to their
corresponding Census 3-digit occupation averages and merge the resulting
aggregated DOTcharacteristics tothe PSID and the NLSYby 3-digit
occu-pations. The jobcharacteristics measures I use are the degree of complexity
withwhichworkersinagivenoccupationcellhavetofacealongthefollowing
dimensions: dealing with either data, people or things; mathematical,
lan-guage,numeric,verbal,spatialskills;therequiredlevelofvocationaltraining,
and howmuch learningis needed toperform the tasks. Ofcourse, it can be
argued thatworkers forman occupation matchbased inpart ontheir tastes
for either one of these job characteristics, which calls into question whether
they can really be used as instruments if, for instance, workers are willing
to trade wages for more orless of the job attributes. It turns out that
rely-ingonly onthe lagged values of the regressors as instruments producesvery
similar results, except forthe precisionof the estimates.
Letting Z be the matrix of valid instruments, it is then straightforward
to exploit the standard orthogonality condition between the variables in Z
and the residual term ! it
in equation (6) to obtain consistent Generalized
Method of Moments estimates by minimizingthe followingquadratic form
S(;W)= 1 N (! 0 Z)W(Z 0 !) (7)
where W is a positive de nite weighting matrix and = ( ; ;Æ). 9
Note 9
The optimalchoiceof the weighting matrixis W =Z 0
Z where isthe covariance matrixoftheerrorterm!. Letting=I would alsoprovideconsistentalbeitine cient estimates. I computed an estimate of by rst obtaining consistent estimates of the
provides a overidenti cation 2
test statistic with degrees of freedom given
by the number of overidenti cationrestrictions.
4.3 Unobserved Job-Match Skills
The treatmentof unobserved job-matchproductivityis straightforward
pro-vided that the return to unobserved job-speci c skills within a job is the
same asthe returnstounobserved workerskills. 10
Letthe expectedlogwage
of individual iin job j attime t be given by:
lnw ijt =Æ s +X ijt +P ijt Æ+m ijt 1 [P ijt + (1 P ijt )]+" ijt (8) where m ijt 1 =m ijt 2 +v ijt 1
and the total match productivity m ijt 1 can bedecomposed as m ijt 1 = it 1 + ijt 1
i.e. the worker's total productivity inagiven match depends onboth apart
thatistransferableacrossemployers( it 1
)andapartthatismatch-speci c
( ijt 1
). Exploiting the within-jobvariationin the data results innot being
able to separatelyidentify each component.
parametersusing theidentitymatrix. ThenI calculatedtheempiricalcovariancematrix of theresultingresidualsand re-estimatedthemodels using
b
. Forthisapplication, the pointestimateswerenotverysensitivetothechoiceoftheweightingmatrix.
10
This,ofcourse,neednotbethecase. Byde nition,job-speci cskillshavenomarket valueandhencethe rmneednotgivethoserentstotheworker.
Giventhatexplicit incentivecontractsare potentiallymoresensitivetoskills
we would expect that the average wage dierencebetween performance pay
and otherworkers would re ectboth the dierencein the average skill level
in the two types of jobs as well as the dierent returns given a certain skill
level, in addition to the true aect (Æ). 11
More precisely, let the average
wage ineach pay method be given by
lnw p =Æ p +X p + p lnw s =Æ s +X s + s
then the average wage gap is given by
lnw p lnw s =Æ+(X p X s ) + p s
Rearranging this equation, we can express it in terms of the dierences in
the returnsand the dierences inskills:
lnw p lnw s =[Æ+(1 ) p ]+[(X p X s ) + ( p s )] (9)
The rst term on the right-hand side of equation (9) represents the eect
of performance pay contracts onperformance pay workers (the eect of the
treatment on the treated) while the second term indicates the magnitude
of the selection bias. Æ represents the average eect of performance pay
contracts on any given worker drawn from the whole populationof workers.
Depending on the dierence in skills between performance pay workers and 11
Whatfollowsis, ofcourse, notquiteconsistentwithourhypothesizedmodel in that it assumesthat theunobservedproductivity componentis time-invariant. However,this decomposition helps in highlighting thesources of any discrepancy between the average payofincentiveworkersandthatofsalaried/hourlyratedworkers.
may be larger or smaller. More particularly,if negativeselection dominates
in the sense that p
< s
, then it is possible that the incentive eect Æ is
positivewhile the average (raw) wage gap is negative.
5 The Data
5.1 National Longitudinal Survey of Youth (1988-1990)
The National Longitudinal Survey of Youth data set surveyed 12,686young
males and females who were between the age of 14and 21 in1979. In 1988,
1989, and 1990,respondentswere asked whether allorpartof their earnings
werebasedonjobperformance. Theywerealsoaskedafewquestionsontheir
workenvironment. Forinstance,weknowiftherespondentsweresupervising
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 which isdue topay-for-performance.
The question pertainingtopay-for-performance isthe following:
THE EARNINGS ON SOME JOBS ARE BASED ALL OR IN PART
ONHOWAPERSONPERFORMSTHEJOB(HANDCARDD).ONTHIS
CARD ARESOME EXAMPLESOFEARNINGS THATAREBASED ON
JOBPERFORMANCE.PLEASE TELLMEIFANYOFTHEEARNINGS
ON YOURJOB (ARE/WERE) BASED ON ANY OF THESE TYPES OF
COMPENSATION.PLEASE DONOT INCLUDEPROFITSHARING OR
EMPLOYEE STOCK PURCHASE PLANS.
1. PIECE RATES.
2. COMMISSIONS.
3. BONUSES (BASED ON JOB PERFORMANCE).
4. STOCK OPTIONS.
I restrict the sample to males who were in the labor market on a
full-time basis and who are members of the originalrepresentativecross-section.
The people who were considered as meeting that criterion were (i) those
whose primary activity was either working full-time, on a temporary lay-o
or looking actively for a job, (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 have been in
the militaryat any time, the self-employed and allpublic sector employees.
Also, I exclude observations for which real ($79) hourly earnings are less
than $1.00or greaterthan$100.00. Inaddition,I willonlybeusing workers
who are observed in all three years. The reason is that I need to account
for the endogeneity of pay method change by using variables lagged twice
as instruments forthe current period's pay method. These restrictions leave
mewithasampleof 1,220workers. Somesummarystatisticsarereportedin
Panel A of Table 1.
5.2 Panel Study of Income Dynamics (1981-1992)
The sample consists of 8,407 male heads of households aged 18 to 64 with
positiveearnings forthe periodspanning the years 1981-1992. 12
Individuals
inthepublicsectorandwhoworkedlessthan500hoursareexcludedfromthe
analysis. We know whether each worker is paid a piece rate, a commission,
an hourly rate or a salary. As we can see, the fraction of workers reporting
beingpaidapiecerateissubstantiallylowerinthePSID. Thisistrue even if
werestrictthePSIDsampletopeopleofroughlythesameageasthoseinthe
NLSY. One likely reason for that is the way the questions on pay methods
are formulatedinthePSID.Workersare rstasked whethertheyare paidan 12
InthePSID, dataonhours workedduring yeart, aswellasontotallaborearnings, bonuses/commissions/overtime income, and overtime hours, are asked at the year t+1 interview. Thus I actually usedata coveringinterviewyears1981-1993. Notethat I use membersoftheoriginalcross-section(thefull PSIDincludesaPovertySubsample).
paid either a salary or an hourly rate specify their pay method (piece rate
or piece rate + hourly/salary, commissions or commissions + salary, etc.)
Thus, contrary to the NLSY where respondents are not forced to choose
among mutually exclusive categories, the PSID likely makes people report
the pay method fromwhichthey earn most of their laborincome.
5.3 Evidence on Selection Eects
Ifnon randomselectionintopaymethodsisof anyimportance,we shouldat
leastbeableto ndsomedescriptiveevidenceofitinthedierentialpatterns
of earnings changes across methods of pay. The basic Lazear model would
suggest that workers who move out of explicit incentive contracts and
self-select into salaried jobs should suer a wage loss because employers expect
this self-selectedgroupofworkers tobelessproductivethanthe overallwork
force. Conversely, only the more productive ones should move into a piece
rate job or acommission job.
Overall, the evidence presented inTable 3 providessome support to the
notion that movement in and out of explicit contracts follows the predicted
patterns. For example, if we look at job changers (Panel B), moving from
a salary/hourly rate to a piece rate or commission contract is associated
with a 12.1% wage gain on average, while the reverse move involves large
losses (-25.7%). Also, if we look at the average earningschange for workers
who move fromapiece rate/commissionjobtoasalary/hourlyrate jobwith
the same employer, we can see that workers suer a average loss of about
13%. Interestingly, job stayers who move from a salary/hourly rate to a
piece rate suer a wage decline of 6.3%, which, on the surface, is not quite
consistent with the basic model in which only the more productive workers
select themselvesinto incentivecontracts. 13
13
Itisconsistentthoughwiththenotionthattheseworkersmightbeabletopoolwith more productiveworkersearly on in the employment relationship. As they accumulate
changesfrom one pay method toanotheras wellas kernel density estimates
of the distribution of log hourly earnings by pay method, net of the eect
of all observables. 14
As can beseen from Figure3, the typicalpattern of pay
method change is one in which at most two such changes occurs. This is
particularly true for job changers. Still, there are workers who seem to go
back and forthbetween pay methods, althoughone has tobe worried about
possiblemisclassi cationof the pay methods.
The distribution of log hourly earnings by pay methods reveals that not
allpiece rateworkers come fromthe upperpart of theearningsdistribution.
In fact, if I use only the subsetof workers who are observed inonly one pay
method orthe other in all years and estimatethe worker-speci c intercepts
ina log-wage equation,the resultingplots shown inFigure5A suggests that
the selectionof workers into piece rate jobs does not appear to be trivialin
the senseof being one-sided. Althoughit shouldbestressed that thisisonly
indicative, it seems that the ability to adjust the pace of work upward or
downward attractsworkers of all ability. This isperhapsclearer when one
doesthesameexerciseusingonlythe subsampleofworkerswhoare observed
at least twice ineach pay method (Figure5B) and for whom I can compute
a pair of individual intercepts: one for piece work and the other for salary
work. This separation of types allowed by piece rates appears to be more
consistent with Brown (1990)'s reformulation of the basic Lazear model, at
least with the PSID data. 15
Of course, some important considerations are left out in the foregoing
analysis. One is task assignment. Workers may be reassigned by their
em-ployertootherjobswhichmaycarry dierentpay. Also,reassigningworkers
tenureandlearningaboutworkerproductivitytakesplace, thisshould becomemore dif- cult.
14
Thelistofobservablesincludesaquadraticinage,region,year,industry,occupation, andunioncoveragedummies.
15
in an environment in which it may be suitableto use, say, piece rates when
in the previous job it was not. In other words, job characteristics, and not
only worker characteristics, are also an important determinant of contract
form, asis suggested by e.g. Brown (1990) orGaren (1998).
5.4 Other Data Related Problems
One important di culty I face is the fact that I only have low-frequency
wage observations i.e. I basically have to rely on annual observations to
identify the parameters of the model, particularly the return to unobserved
skills parameter. It isconceivable thatit maybe di cultto ndsupportfor
the model simplybecauseworkers are not observed onamore frequent basis
as would be the case if I had monthly or even weekly data. Simply put, it
seemsreasonabletosupposethatwagesdore ectskillseventually,nomatter
howpeopleare paid. Thus, havingtorelyonyearlyobservations mayfail to
revealthe greater short-term sensitivity of wages to skills in piece rate jobs
or, atleast, may underestimate it.
Inaddition,misclassi cationofpaymethodsislikelytoplayarole. More
particularly, one would expect reporting errors to attenuate the measured
wage eect toward zero, especially whenusing rst-dierences.
6 Results
Ifwelookat rstattheresultsfortheNLSYpresentedinTable3,wecansee
that simplyignoring selection issues by using OLS would lead us to believe
that explicit incentive contracts are associated with higher average hourly
earnings. This holds true even with rst-dierences, althoughthe estimates
are not very precise. Given that misclassi cation of pay methods would
tend to impart an attenuation bias, the higher coe cient estimated with
individuals choose to work inthose jobs.
However, using rst-dierencesalongwithinstrumentalvariablestoallow
for learningeects reduces the estimatesubstantially. Turning tothe GMM
estimatesincolumn4ofTable3,wecanseethatcomparativeadvantagedoes
appear to be an important determinant of the choice of pay methods. The
returntoskillsissigni cantlydierentfromoneinsalariedjobsandthewage
eectisessentiallyreducedtozero. Note,however, thattheoveridenti cation
teststatisticsuggeststhattheoveridenti cationrestrictionsmaynotbevalid.
Muchthesameconclusionconcerningtheeectofcomparativeadvantage
emerges when we look at the results obtained by exploiting repeated
obser-vationsinagiven job-match. However, the resultsalsostronglysuggestthat
classi cationerrorswithinjobsmaybeamuchmoresevere problem. Simply
using instrumentalvariablesestimationalongwith rst-dierencesresultsin
a wage impactmore than twice as large as the one measured with standard
dierencing.
Turning now the PSID sample, I am able to exploit the larger sample
(and longertimedimension)toestimatethemodels forthe subsampleofjob
changers only. Focusing rst on the within-worker estimation results, one
can see thatselection according tocomparativeadvantage clearly seems not
to be as important. With the full sample, the return to skills is not
signi -cantlydierentacrosspaymethods. Inaddition,itappears thatattenuation
bias plays a major role in relation to learning eects as the results using
instrumental variables point toward a much larger wage eect. The same
overall conclusions hold when we look at job stayers only. Indeed, perhaps
not surprisingly,the attenuationbias ismoresevere than forthefullsample.
Inaddition,theGMMestimateoftheincentiveeectisvirtuallythesameas
whenIignorecomparativeadvantage. Thisisalsotruefortheoverallsample
but it appears that the distinction between job stayers and job changers is
compar-bias inthe estimated wage eect.
For comparability purposes, I also estimated the same models using the
subsample ofworkers ofthe sameage asthoseintheNLSY.Toreconcile the
dierences in the age distribution between the two samples for the workers
aged between 23and 32,I rst computedthe samplefrequencies of each age
cells with the NLSY and then I use thosefrequencies toweight the
observa-tions in the PSID. As can be seen fromthe lastcolumns inpanels A and B,
the results are remarkably similar to those obtained with the NLSY:
com-parativeadvantage reallyseemtomatterearlyinone'scareerorinone'sjob.
In both panels,the returnto skillsis below one and is preciselyestimated.
Again,a troublesomefeatureof the resultsisthe magnitudeof the
overi-denti cation test statistics. Results obtained when I exclude the DOT job
characteristics from the list of instruments were very similar, albeit
some-what lessprecise. The 2
statisticswerealsoclosertotheacceptanceregion,
especiallyin the case of the NLSY.
6.1 Summary of Results
Overall, the results suggestthat:
Comparative advantage matters mainly for younger workers or
work-ers who are observed for the rst time in a given employment
rela-tionship (the job changers). When I turn to exploiting the within-job
variation in the data, I nd weaker evidence that the return to skills
varies across pay methods, althoughit stillholds for younger workers.
In other words, there is strong evidence that some partial pooling of
workerswithdierentskillsoccursearlyonasthemarketisinthe
pro-cess of assessing worker productivity. Eventually, though, pay re ects
individualskills.
sub-endogeneity bias may be caused by either learningeects or
measure-menterrorinthepaymethoddummy. Thislattereect seemstocause
astrongattenuationbiasinmodelsthatexploitthewithin-jobvariation
in the data.
Assuming that the return toskills is the same across pay methodsfor
workersrepeatedlyobserved inthesamejob,one canget consistent
es-timatesofthetrue incentiveeectby usingwithin-job rst-dierence
models combined with instrumental variable estimation.
Basedontheresultsusing thefullPSID, theincentiveeect ofexplicit
pay-for-performance contracts is inthe neighborhood of 11%.
Asforthe resultsusingthewithin-jobvariationinthe NLSY,itshould
bepointed out that while the estimated coe cient obtained by GMM
is actually negative (column 3of Panel B), the standard error is quite
large. The test of a zero wage impact thus has ratherlowpower.
7 Conclusion
This paper has investigated the role played by comparative advantage in
directing workers' choice of a pay method. I have found relatively strong
support for the notion that pay is more sensitive to skillsin jobs where pay
is output-based in the case of younger workers or workers who are new to
their job.
My overall assessment of the results would be that as long as one has a
sample of workers who are fairly representative of the overall workforce, as
is more likely to be the case with the PSID, then rst-dierence estimates
obtainedbyexploitingthewithin-jobvariationinthedataareprobablyclose
tothetrue wage impact,providedone controlsforthepresence of
set, such as the one used by Lazear (1996). This may explain why the
esti-mates presented here are fairly close to those obtained by Lazear. However,
it really seems that the combination of learningand self-selection according
to comparative advantage that appears to be very important early in one's
career should makeus abit more cautiousabout results obtained with data
on younger workers. It may very well be that there isa true incentive eect
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