Cahier 2001-18
LLUIS, Stéphanie
Département de sciences économiques
Université de Montréal
Faculté des arts et des sciences
C.P. 6128, succursale Centre-Ville
Montréal (Québec) H3C 3J7
Canada
http://www.sceco.umontreal.ca
SCECO-information@UMontreal.CA
Téléphone : (514) 343-6539
Télécopieur : (514) 343-7221
Ce cahier a également été publié par le Centre interuniversitaire de recherche en
économie quantitative (CIREQ) sous le numéro 18-2001.
This working paper was also published by the Center for Interuniversity Research in
Quantitative Economics (CIREQ), under number 18-2001.
CAHIER 2001-18
WAGE POLICY OF FIRMS : AN EMPIRICAL INVESTIGATION
Stéphanie LLUIS
1
1
Centre de recherche et développement en économique (C.R.D.E.) and Département
de sciences économiques, Université de Montréal
September 2001
___________________
The author wishes to thank Thomas Lemieux and Claude Montmarquette for their enduring support
through this project. The author is also grateful to Nicole Fortin, David Green, Craig Riddell,
Tom Crossley and Daniel Parent for valuable comments. Special thanks goes to Lars Vilhuber for
his help in accessing the GSOEP data. Financial and logistic support by the C.R.D.E. (Université de
Montréal) and CIRANO is gratefully acknowledged.
RÉSUMÉ
Cet article étudie la dynamique des salaires et la mobilité des travailleurs dans les
entreprises caractérisées par une structure hiérarchique des postes. L'objectif est d'établir
une spécification empirique et de tester le modèle théorique de Gibbons et Waldman (1999)
qui combine les notions de capital humain, d'avantage comparatif dans l'attribution des
postes aux travailleurs et d'apprentissage, afin de mesurer l'importance de ces éléments
dans la politique salariale des entreprises. Afin d'établir des conclusions générales sur les
caractéristiques communes de la politique de rémunération d'un ensemble représentatif
d'entreprises, l'estimation est appliquée aux données de l'enquête GSOEP (German
Socio-Economic Panel). Un autre avantage du GSOEP est de fournir le rang du travailleur dans
son entreprise, information qui n'est généralement pas disponible dans les données
d'enquête. Les résultats de l'estimation confirment la présence d'une répartition
non aléatoire des travailleurs dans les différents niveaux de l'échelle des postes dans
l'entreprise. Bien que l'habileté non observée constitue un facteur déterminant dans ce
mécanisme de répartition et dans la politique salariale résultante, les résultats ne montrent
pas d'évidence directe du rôle de l'apprentissage (de l'entreprise et du travailleur) de cette
habileté non observée. Finalement, les effets de rang restent importants même après
contrôle des caractéristiques mesurables et non mesurables du travailleur.
Mots clés : dynamique des salaires, mobilité dans l'entreprise, accumulation de capital
humain, hétérogénéité non observée, apprentissage
ABSTRACT
This paper analyzes the dynamics of wages and workers' mobility within firms with a
hierarchical structure of job levels. The theoretical model proposed by Gibbons and
Waldman (1999), that combines the notions of human capital accumulation, job rank
assignments based on comparative advantage and learning about workers' abilities, is
implemented empirically to measure the importance of these elements in explaining the
wage policy of firms. Survey data from the GSOEP (German Socio-Economic Panel) are
used to draw conclusions on the common features characterizing the wage policy of firms
from a large sample of firms. The GSOEP survey also provides information on the worker's
rank within his firm which is usually not available in other surveys. The results are
consistent with non-random selection of workers onto the rungs of a job ladder. There is no
direct evidence of learning about workers' unobserved abilities but the analysis reveals that
unmeasured ability is an important factor driving wage dynamics. Finally, job rank effects
remain significant even after controlling for measured and unmeasured characteristics.
Key words : wage dynamics, intra-firm mobility, human capital accumulation, unobserved
Thequestionofhowwagesaredeterminediscentraltothestudyoflaboureconomics. Thelarge
bodyoftheoreticalworkthatattemptstounderstandthefactorsgoverningwageoutcomeso ers
severalpossibleexplanations. Someofthemodelsarebasedontheconceptsof humancapital
(Becker (1975), Hashimoto (1981)), learning (Harris and Holmstrom (1982)), and matching
(Jovanovic (1979)). Other models look at the role of incentives in compensation. Examples
includetournamenttheory(LazearandRosen(1981))andeÆciencywagetheory(Shapiroand
Stiglitz (1984)).
Thelargevarietyoftheoreticalexplanationshasgeneratedanextensiveempiricalliterature
which has attempted to both utilize and distinguish between the competing theories. This
literaturehasfocusedonaspectsofthequestionsuchasthereturntointer rmmobilityonthe
partofworkers(BartelandBorjas(1981),Simonet(1998),TopelandWard(1992)),the
covari-ance structure of earnings acrossworkersand rms (Parent(1995), Topel and Ward (1992)),
andinter-industrywagedi erentials(KruegerandSummers(1988),GibbonsandKatz(1992)).
Thus far, littleempirical work hasbeen doneon questions relating to how jobs are assigned
to workersandtheresultinge ectsontheevolutionofintra rmwagestructuresandmobility
within the rm.
This paper presents an empirical study of the common features characterizing the wage
policy of rms. More precisely, it analyzes what is driving the dynamics of wages and the
workersmobilitywithinthe rm. Ononeextreme,onemightthinkaboutpaysettingsandjob
assignmentsbeingregulatedaccordingtosystematicbureaucraticrules. Ontheotherextreme,
payraisesandpromotionscouldbebasedonindividualability, withonlyhighabilityworkers
bene ttingfromit. Anotherpossibilityisthatwagegrowthandmobilityaredrivenbyrandom
productivity shocks. To study wage dynamics I use the theoretical framework proposed by
Gibbons and Waldman (1999) in which, given a hierarchical structure of job levels within
rms,thedeterminationofwagesdependsonhowworkers'abilitiesareevaluatedwithinajob
rank, given that each job rank has di erent skill requirements. The model speci es a wage
equation integrating the elements of human capital accumulation, job assignment based on
comparativeadvantage and learningabout the ability of workersto explain the dynamics of
wagesand promotions inside rms. This paperanalyzesthe importance of these elements in
explainingthewagepolicyof rms.
The idea that the structure of wages within rms mightbe empirically important is not
new to labour economists. Previousempirical studies on the subject, however, have mainly
been restricted to providing analysis of speci c questions on wage determination within the
rmwithoutreal attemptat relatingthem tothepredictionsofaformal theory. Other
stud-ies present stylized facts speci c to one or a few rms and although very informative, the
conclusions remainrestrictedtothetypeof rmanalyzed.
DoeringerandPiore(1971)areamongthe rsttopresentadetaileddescriptiveanalysisof
thecompensationschemeswithinasmallsampleofAmerican rms,but attemptstoformalise
their analysis are stillin the early stages. Onestrandof the literaturewhich examinesthese
issues,followsinthefootstepsofDoeringerandPiorebyusingdetailedobservationsononeora
few rms. Chiappori,SalanieandValentin(1999)takeaneconometricapproach,usingdataona
largeFrench rm,tostudyquestionsrelatedto\earlystarter-latebeginner"e ects(aprediction
ofthelearningtheory)onthewagesofindividualswhoremainwithintheinstitution. However
the data isspeci c to one rm, and theyrestrictthe analysis to oneparticular aspectof the
dynamics ofwagesand promotions. Namely, theytestthe factthat fortwoworkersin a rm
havingthesamewageinoneperiod,theworkerwiththelowestwagetheperiodbefore(de ned
asthe\latebeginner")hasahigherexpectedwagenextperiod. Baker,GibbsandHolmstrom
(1994a,b)studyseveralaspectsoftheinternalwagestructureofonemediumsizedU.S rmbut
theiranalysisisadescriptiveone. AnalternateapproachistakenbyMcCue(1996),whouses
attempt torelateher ndingstothetheoreticalliterature.
Anumberofstylizedfacts emergefromtheempiricalliteratureontheinternalwagepolicy
and mobilitywithin the rmsincethelast twentyyears. First, themain ndingonintra rm
mobility concerns serial correlation in promotion rates. 1
Rosenbaum (1984), Spilerman and
Petersen (1993), Baker, Gibbs and Holmstrom (1994 a,b), Podolny and Baron (1995) and
Chiapporiandal. (1996). Holdingtenureinthecurrentjobconstant,promotionratesdecrease
with tenure in the previous job. A related nding (although reported in only one rm) is
thatdemotionsarereallyrare. 2
Baker,GibbsandHolmstrom(1994a,b)Second,nominalwage
cuts areveryrare but realwagecutsare much morecommon. Partly becausenominal wage
increasesareratherinsensitivetoin ation, zeronominal increasesarenotrare. 3
Baker,Gibbs
and Holmstrom(1994 a,b) in the caseof one rmand Card and Hyslop(1995) nd identical
conclusions using the CPS and PSID. A related nding is found in Peltzman (2000). Using
datafromtheBLS,itisfoundthatoutputpricesincreasemorethantheydecreaseinresponse
to shocks in the cost of inputs. Increases in rm's labor costs would therefore induce real
wagedecreases. Third,thedynamicsofwageswithin the rmexhibitserial correlationinthe
sense thatarealwageincrease(decrease)todayisseriallycorrelatedwitharealwageincrease
(decrease)tomorow. 4
Hause(1980),LillardandWeiss(1979)andBaker,GibbsandHolmstrom
(1994a,b). Finally,studiesthatanalyzetherelationshipbetweenwagesandintra rmmobility
nd that wage increasesupon promotionare largerthanwithoutpromotion. 5
Murphy(1985)
Baker, Gibbs and Holmstrom (1994 a,b) and McCue (1996). However,wage increasesupon
promotion are small compared to the di erence in average wagesbetweentwojob levels. In
otherwords,signi cantvariationsinwagesremainwithineachlevelsothatwagesarenottied
to levels. In addition,wageincreasesforecastpromotionsin thesense that those whoreceive
larger wage increases get promoted morerapidly. 6
Baker, Gibbs and Holmstrom (1994 a,b).
McCue (1996) nds that a high wagetoday is positively correlated to promotiontomorrow,
and, in the samespirit, Topel and Ward (1992) nd that prior wage growth a ects mobility
evenafter controllingforthecurrentwage.
Collectively, these observations pose a challenge to the existing theoretical literature, as
noneoftheexistingtheoriescanexplainallofthesestylizedfacts. Inresponsetothischallenge,
GibbonsandWaldman(1999)proposeasynthesizedmodelwhichcombinesonthejob human
capitalaccumulation,jobassignmentbasedoncomparativeadvantageandlearningdynamics.
The predictions of their model are consistent with most of the stylized facts found in the
empiricalliterature. Theobjectiveof thispaperistoimplementempiricallytheGibbonsand
Waldmanmodelandperformtheestimationonalargesampleof rmsinordertotestitsability
toexplainthecommonfeaturescharacterizingthewagepolicyof rms. Inaddition,estimating
the model on the sample of workersremaining with their rm and comparing the results to
thoseobtainedfromthesamplethat includes rmchangersallowstodistinguishbetween rm
speci c e ects and individual speci c e ects transferable across rms in the analysis of the
wagedynamics.
TheestimationisperformedusingGMM techniques applied tothelongitudinaldata from
theGermanGSOEPovertheperiod1986-1996.Thissurveyprovidesinformationonthe
work-ers mobility between and within the rm and, more importantly for the analysis hereafter,
detailed information on the rank of the worker in his current occupation is available. The
Germancaseis aninterestingapplication ofthe modelbecausethe Germanlabourmarket is
thoughttodi ersigni cantlyfromtheU.Slabourmarket(which providesmanyofthe
obser-vations which motivateGibbonsandWaldman's research). Particularly,asshownbySimonet
(1998),inter rmjobmobilitydeclinesmuchearlierinaworkers'careerinGermanythaninthe
U.S.Thissuggeststhepossibilitythatintra- rmmobilitymaybemoreimportantinGermany
thanin theUnited States. Inaddition,becauseofthestrengthoftradeunionsand theirclose
relationship with employer'sassociations, German rmshaveto dealwith bureaucraticrules
ofcomparativeadvantageandlearning,whichseemtoexplaintheU.Sexperience,aremoreor
lessimportantinGermany.
Thepaperisorganizedasfollows. SectionIIprovidesadescriptionanda rstanalysisofthe
data. SectionIIIsketchesthetheoreticalmodelofGibbonsandWaldman andestablishesthe
frameworkoftheeconometricanalysisandhowthisrelatesto thetheory. SectionIVpresents
theresultsoftheestimations,andSectionVconcludes thepaper.
II. THE DATA
The data for the analysis come from the German Socio-Economic Panel. The GSOEP is
a representative longitudinal study of private households conducted every year in Germany
since 1984. This survey is unique for the analysis hereafter because it provides information
on movements between and within rms through a question about changes in the worker's
employment situation in the previous year. Most importantly, there is detailed information
on the rank occupied by the worker within his current occupation. To my knowledge, this
typeof informationisnotavailable inanyothersurveys. Thesetwopiecesof informationare
centraltothestudyofwageandmobilitydynamicswithinthe rm. Anotheradvantageisthat
information iscollectedoveralargesampleof individuals andtherefore, theanalysisof wage
dynamicsand intra rmmobilitycan bedoneforalargesample rms.
A. Data Selection
I considered information on the usual individual characteristics such as age, education, sex,
maritalstatus andnationality. Information onbonusesreceivedduringthepreviousyearand
on the duration of the employment contract (unlimited or limited length) are also available.
Wages are given on a monthly basis, corresponding to the month preceding the time of the
survey. For the rm's characteristics, the counterpart of using survey data is that precise
information on that partislimited. I used thetype ofindustry, whether the rmbelongs to
thepublicsectorand rmsize.
Thepanelspanstheyears1985to1996becauseinformationonmobilitywithin the rmis
not available in 1984. Since itcoverstheGerman reuni cation,I haveexcluded data onthe
former EastGerman populationto keepthe pre and post uni cation samples comparable. I
have selectedindividuals aged between20 and65 whoare workingat the time ofthe survey
on a full-time basis. I have excluded self-employed workersand put a restriction on wages
excluding anyobservationsbelow500DMpermonth. 7
Since inGermany, theminimumwage
variesbyindustry,thisboundshouldgiveareasonableminimuminordertoexcludeoutliersfor
wageswithoutloosingobservationsonlowwageworkerssuchastrainees. Finally,Iconsidered
the sampleofworkersremaining withtheir rmoveralltheperiod, reportingeither mobility
within the rm or no change in job situation. This leaves us with a sample consisting of
11159 observations (3487 workers). Appendix 1 describes the data selection in more details
andprovidesthesamplemeansofthemainvariablesused.
The objectiveof the next two subsections is to describethe data and to examine, in the
spirit oftheGibbonsandWaldman model, thelinksbetweenintra rmmobility, wagegrowth
and hierarchical levels of jobs for Germanworkers. Twoquestions will be addressed: What
are the main determinantsof intra rm mobility? By which channels doesintra rm mobility
in uence thedetermination ofwagesfromonehierarchicalleveltothenext? That is,howare
individual skills e ectsand hierarchicallevele ects re ectedin thewagepremium associated
to beingin ahigherrankon thejob ladder? Theanalysis of these pointsis basedon alogit
Inthissubsection,Iexaminethee ectofworkerand rmcharacteristicsonintra rmmobility.
The estimation method isbased onabinomiallogit model in which the bene t from moving
within the rm is a function of observable characteristics. The alternative to the choice of
intra rmmobilityisnochangesinemploymentsituationwithinthe rm. 8
Appendix2presents
thefrequenciesofthedi erenttypesofmobility.
Startingwithasetofbasecharacteristics,Ilookatthee ectofaddingparticularvariables
of interestontheprobability ofintra rmmobility. Amongthese variablesarelaggedbonuses
andlaggedrateofwagegrowth. 9
Thelagissuchthatbonusesandwagegrowthareconsidered
theyearbeforemobilitywithin the rm. Ifmobilitywithin the rmisdrivenbytheevolution
of the workersproductiveabilities, previouswagegrowth,where wagesre ect theevaluation
of abilities,shouldsigni cantlyincreasethechancesof futuremobilitywithin the rm. Inthe
same vein, obtaining abonus is a signalof improvementin the worker's productiveabilities
andshould haveapositiveimpactonfuturemobility.
Amongthebase characteristics,I includedummies fornationality,sexandmaritalstatus.
Years ofeducation are dividedinto three levels: primary (up to 10years),high school(11 to
13years)andcollege(14yearsandmore). Finally,Iconsideredaquadraticfunctionoftenure
de ned as the numberof years worked with the rm. Concerning thecharacteristicsrelated
to the rm,I include adummyfor large rms(2000employeesormore), theduration ofthe
employment contract (unlimited or not), eight industry dummies 10
I used the International
StandardIndustrialClassi cation(ISIC).andapublicsectordummy.
Results are shown in column 2 of Table I 11
Given that the dependent variable has few
responses (y =1) compared to non responses, using a probit model might produce di erent
results. I reestimatedthemodel with thenormaldistribution. Results(available onrequest)
are similar in which they leadto thesame conclusions in terms of marginale ect coeÆcient
andsigni canceofthecoeÆcients. forthebaselinemodel(column3showsthemarginale ect
ofeachvariablesontheprobabilityofintra rmmobility),andcolumn4and5forthee ectof
adding laggedbonusesandlaggedwagegrowth. Column 6showsthespeci cationcontaining
allthevariablesandcolumn7themarginale ectofthesevariables.
From column 2, one cansee that college degrees increase signi cantly the probability of
intra rmmoves(relativetoprimaryschool). Wecannoticethenegativee ectoftenurewithin
the rmonintra rmmobilitysuggestingthat workersmobilitywithin the rmoccursmostly
at thebeginning of the worker's career. In addition, we see that married individuals havea
signi cantlylowerprobabilityofintra rmmobility. Ontheotherhand,nationalityandgender
have nosigni cant impact. Forthe characteristicsrelated to the rm, weunsurprisingly see
that beingin alarge rm signi cantly increasesthe likelihood of intra rmmobility and but
that thefuture mobilityis independentofwhether the rmisin thepublicsectororwhether
thelabourcontractisofdeterminatelength.
Introducinglaggedbonus,asincolumn4,hasaparticularimpactonthevariables. Onecan
rst seethat the impactissigni cantlynegative: having receivedabonuslast yeardecreases
thechanceofintra rmmobilitytoday. Oneinterpretationisthatbonuswouldsubstituterather
thancomplementintra rmmobility. Ontheotherhand,bonusandpromotioncouldbeclosely
relatedandnotdistinguishable,thenegativeimpactoflaggedbonuscouldthenre ectthatlast
year'smobility(andbonusreceived)isnegativelycorrelatedtothechanceof mobilitytoday.
Introducing lagged wage growth in column 5 also has a noticeable impact on the other
variables. First, it increases signi cantly the probability of intra rm mobility next period.
The coeÆcientis particularly largecompared to the others. Inaddition, college education is
no longer signi cant. The results for all the other variables remain unchangedcompared to
column 2sothatthemaine ect ofcontrollingforlaggedwagegrowthisoncollegeeducation.
column 6where boththelaggedbonusandthewagegrowthareaddedaresimilarto thoseof
column5. Controllingforthelaggedbonusdoesnotaltertherelativelystrongimpactoflagged
wagegrowthonintra rmmobility.
Based onthe ideathat part ofwagegrowthre ects the worker'sproductiveabilities, the
signi cantimpactoflaggedwagegrowthonintra rmmobilityprovidesa rstpieceofevidence
supporting the role of ability as driving the worker's mobility within the rm. In order to
raÆne theanalysis of theinteractions betweenintra rm mobilityand the dynamicsof wages
within the rm,thenextsectioninvestigatestherelationbetweenthewagesandthedi erent
ranks that the workercan reach within his orher job. In particular, I am interested in the
wayindividualcharacteristicscomparedtojobrelatedcharacteristicsarere ectedinwages. To
analyzethispoint,Iusetheinformationonthedi erentranksofeachoccupationtoestablish
inter-rankwagedi erentials.
C. Inter-Rank Wage Di erentials
This section analyzes the contribution of job ranks relative to individual characteristics on
wages by estimating the impact of the worker'sskills on inter-rank wage di erentials. In a
second step, I present preliminary evidence on the importance of unobserved ability in the
determinationofwagesandanalyzewhethercomparativeadvantagebasedonmeasuredability
isimportant.
AninterestingfeatureoftheGSOEPsurveythatisrarelyfoundinothersurveysisthatit
providesinformationonthelevelorrankoccupiedbytheworkerinhiscurrentjob. Occupations
aregroupedin vecategories:Blue-collar,white-collar,civilservant,traineeandself-employed.
Iconsideredthe rstthreegiventhatself-employmentisnotrelevantfortheanalysisandthat
the trainee category is not in itself an occupation. 12
Individuals reporting trainees whowere
alsoreportedinoneoftheotheroccupationshavebeenretained. Eachoccupationisdividedin
severallevelsaccordingtothequali cationandresponsibilityrequirements. Sincethenumber
of ranks is not the same for all the jobs, I have de ned 4 ranks based on a more general
quali cation criterion:
1. unskilledorsemi-skilledwork
2. skilledwork
3. highlyskilledwork
4. executivework
Appendix 3 reports the raw wage di erentials(relativeto the rstrank) and average
in-dividual characteristics by rank. The di erentials increase along the ladder but in di erent
proportiondependingonthetypeofoccupationwithwhite-collaredworkersshowingthe
high-estdi erentialsineachrank. Althoughonemightexpectthattheserankwagepremiumre ect
theincreasingresponsibilitiesandtaskscomplexityrelatedtothehigherranks,onecanobserve
apositivecorrelationwithmeasuresofindividualabilitysuchaseducation. Thelinkwiththe
other characteristicsis howeverlessclear. A global measureof theworkers'sindividual
char-acteristics would be moreconvenient forthe analysis of theinteraction between theworker's
abilitiesandjob rankanditse ectonwageoutcomes.
Inordertosummarizeindividualcharacteristicsintoonevariablecharacterizingtheworker's
skills,IconsideredaOLSregressionofthewageleveloneducation,maritalstatus,sex,
nation-ality,experienceandsquaredexperience,industryandoccupationtypeovertheentireoriginal
sample of workers (before the sample selection has been done). I used the estimated
index. 13
This index, reported in the last column ofAppendix 3,correspondsto thepredicted
wageconditional onmeasuredindividualcharacteristics.
Column 1of TableII presents theresults of aregressionofwageson rankdummies with
controlsfor occupationsand industries. Onecan notice that those coeÆcientsare signi cant
andarelowerthantherawwagedi erentialsoftheAppendix 4Table(0.49,1.67and2.46in
theaggregatede nitionofranks)whennocontrolshavebeenconsidered. Column2ofTableII
considerstheimpactofaddingtheskillvariableonranke ects. Itshowsthattheskillvariable
ishighlysigni cantandcontrollingforskillsreducestheimpactoftherankdummies. However,
the wage di erentialsare still signi cant, increasing byrank from 0.12for rank2 to 0.68for
rank3and1.20forrank4(allwithrespectto rank1).
The next column of Table II presents the results of a xed-e ect estimation in order to
assess thepresence ofunmeasured (bythe econometrician)individual ability. Assuming that
it is time invariant and equally valued in the di erent ranks, it is possible to eliminate (or
controlfor)thistermby using rstdi erencemethod. If unmeasuredabilitydoesnotmatter
in thedeterminationofwages,the xed-e ectestimationresultsshouldbesimilartotheOLS
results. Onecan see from Column 3that the xed-e ectcoeÆcients on rankshavedropped
signi cantly, although still signi cant. This suggeststhat partof the rank wage premium is
explainedbyunmeasuredskillsandpartofitstillre ectsranke ects.
The notion that workers have a comparative advantage in some job ranks is equivalent
to say that along the successive rungs of the job ladder, skills are di erently rewarded and
that workerssortthemselvesintoagivenrank. Column4ofTableII considersthepossibility
that comparativeadvantageand self-selection operate on measured skills. Totake this into
account, I includedto the baselineregressionof column 1,interactions of theskill index and
the worker'sjobrank. Onecan seethat thecoeÆcientson theinteractionsare signi cant. A
test of equality of these coeÆcients leadsto the rejection ofthe null( 2
(3) of 103.43)which
con rmstheexistenceofdistinctvaluationsofmeasuredskillsin each rank.
The analysis of Section II has shown that past wage growth has a noticeable impact on
the likelihood of mobility within the rm. The wage premium associated with the di erent
ranks that the workercan attain in his career do notentirelyre ect the di erentials in task
and responsibilityrequirements(ranke ects)but alsothedi erentialsinmeasuredindividual
skills. Moreover,there isevidencethat eachjob levelisdi erentlysensitivetomeasuredskills
so thatworkersmayself-selectintothedi erentlevelshavingacomparativeadvantagein one
levelbasedontheirmeasuredskills. Finally, theresultsonthe rstdi erenceestimationlead
us to suspect that unmeasured ability may also matter in the explanation of the inter-rank
wagedi erentialsandthus,in thewagedynamics. All togetherthese resultssuggestthatthe
worker'sability seemto be agood candidate in the explanation of what is driving the wage
dynamicsandmobilitywithinthe rm. ThenextsectionpresentatheGibbonsandWaldman
modelinwhichabilitydrivesjoblevelassignmentsandwagedynamics.
III. MODELAND ECONOMETRIC FRAMEWORK
This section summarizes the Gibbons and Waldman model of intra rm mobility and wage
determination and highlightsthemodel'smain predictions. Theaim of themodel isto
char-acterize therelationshipbetweenaworker'scareerpathand theevolution ofhis wagewithin
the rm. It integrateswage determination and job assignmentsin a dynamic context, where
thewagepolicy ofthe rmisbasedoncomparativeadvantages andlearning. Inotherwords,
itendogenizesworkers'choicesofjobrankasworkersareassignedtothejob rankthat better
reward their productive abilities. In addition, it endogenizes mobilitybetween job ranks
rankofthejobladder.
More precisely, rms are modeled as consisting of various potentialjob assignments and,
becausejobs aredi erently sensitiveto ability,comparativeadvantagedeterminesthe
assign-ment ruleon thebasisof outputmaximization. Thedynamics is introduced in themodelby
considering thatoutputgrowswiththeworkers'accumulationofhumancapitalorproductive
abilitieseachperiod. Inaddition,output growsat adi erentspeeddependingonthe levelof
innateabilityoftheworker. All theworkersendupreachingtheupperlevelofthejobladder
but somegettherefaster thanothers. Wheninnateabilityisnotperfectly observed,learning
takes place and wages and mobility within the rm are driven by the evolutionof expected
ability.
A. Summary of the Model
The model consists of identical rms operating in a competitive environment and producing
output usinglabourastheonlyinput. All rmsconsistof athree-leveljobladderwhere jobs
are indexed byj =1;2or3. Jobsare de ned in advance,independent ofthe people who ll
them. Both rmsandworkersarerisk-neutralandhaveadiscountrateofzero.
Aworker'scareerlastsforTperiods. Workerihasinnateability,denotedby i ,whichcan beeitherhigh ( H )orlow( L
). Theworkerhasalsoe ectiveability, it
,de nedasthe
prod-uctofhisinnateabilityandsomefunctionf ofhislabor-marketexperiencex it priortoperiodt: it = i f(x it )withf 0 >0andf 00 0 (1)
Theproductiontechnologyissuchthat ifworkeriis assignedto jobj inperiodt thenhe
producesoutputy ijt where: y ijt =d j +c j ( it +" ijt ) (2) where d j
is thevalueof jobj independentof theworker'scharacteristicsandc j
measuresthe
sensitivityofjob j toe ectiveability. Theconstantsc j
andd j
areknownto alllabor-market
participants and it is assumed that c 3 > c 2 > c 1 and d 3 < d 2 < d 1 . " ijt is a noisy term
drawnindependentlyfrom anormaldistribution with meanzeroand variance 2
. Wagesare
determined by spot-market contracting. More precisely, at the beginning of each period, all
rmssimultaneouslyo ereachworkerawageforthatperiodandeachworkerchoosesthe rm
that o ersthehighestwage. Hence,competition among rmsyields wagesequalto expected
output. w ijt =Ey ijt =d j +c j it =d j +c j i f(x it ) (3)
EÆcienttaskassignmentisobtainedin thesensethat aworkerisassigned tothejob that
maximizeshis expectedoutput.
Inthecaseofperfectinformation, i
,iscommonknowledgeatthebeginningoftheworker's
careerandtherefore it
isalwaysknown. Inthiscase,jobassignmentsandwagesinequilibrium
aregivenaccordingtothefollowingrule:
1. If it
< 0
thenworkeriis assignedtojob1inperiod tandearns w it =d 1 +c 1 it . 2. If 0 < it < 00
thenworkeriisassignedtojob 2in periodtandearnsw it =d 2 +c 2 it . 3. If it > 00
thenworkeriisassignedtojob 3in periodtandearnsw it =d 3 +c 3 it .
where ( )denotesthee ectiveabilitylevelatwhichaworkerisequallyproductiveatjobs
1and2(2and 3). Inequilibrium,theworkersclimb thesuccessiverungsofthejob ladderas
theygainexperience.
Themodelunderperfectinformationcanexplainmostofthestylizedfactsoftheempirical
literature. Particularly,themodelexhibitstheabsenceofdemotions,serialcorrelationinwage
increases and in promotion rates, and the fact that wage increases predict promotions and
explainonlyafractionofthedi erencein averagewagesacrosslevels.
More precisely, there are no demotions in equilibrium because e ective ability increases
monotonically. Serial correlationin wage increasesoccurs becausee ective ability grows
dif-ferentlyforeachworkerdueto theirdi erentlevelsofinnateability. Thatis,foragivenlevel
ofexperience,highabilityworkerswillgethigherwageincreasesthan lowabilityworkersand
thesameorderingwillholdforwageincreasesat allexperience levels.
Themodel isableto explainserial correlationin promotionratesfor thesamereasons. If
0 and 00 0
arebothsuÆcientlylargethenhighabilityworkersarepromotedtojob2more
quicklyandspendlesstimeonjob2beforebeingpromotedtojob3. Moreover,sincethosewho
receivelargerwageincreasesarealsothose whoarepromoted tojob 2earlierin theircareers,
wageincreasespredictpromotions.
Finally,wageincreasesuponpromotionexplainafractionofthedi erencebetweenaverage
wagesacrosslevelsbecause,onaverage,partoftheworkersathigherlevelsaremoreexperienced
and thedi erencebetweenaveragewagesat di erentlevelsisgivenbytheaverageexperience
or e ective ability accumulated. This di erence is bigger than the average wage increase at
promotion whichcapturesthevalueofonlyone yearofexperience.
Inthecaseofperfectinformation,however,theexplanationforthelargewageincreasesupon
promotion isnot fully satisfactory. The model predicts average wageincreases at promotion
arehigherthaniftheworkerremainsinhiscurrentjobbecauseincreasesine ectiveabilityare
valuedinpartattherateofthecurrentjob(c j
)andinpartatthehigherrateofthenextjob
(c j
)ifpromotionoccurred.Forthesamereason,however,themodelpredictsthattheaverage
wageincreasesafter promotionwhich, accordingto theempirical ndings, should notbethe
case. Moreover,the monotonicity of thee ectiveabilityaccumulationfunction precludesthe
possibilityof realwagedecreases.
Wheninformationon innateabilityisimperfect(but symmetric),workersand rmsstart
with theinitialbeliefp 0
that agivenworkerisof innateability H andwith1 p 0 that heis L
. Learningtakesplace atthe end ofeachperiod whentherealization of aworker'soutput
for that period is revealed. Learning occursgradually becauseofthe productivityshock" ijt
,
whichintroducesnoiseintotheoutputproduced.
Tobeprecise,eachperiodaworker'soutputprovidesanoisysignal,z it
,abouthise ective
abilitywhere: z it =(y ijt d j )=c j = it +" ijt Notethat z it
isindependentof jobassignmentsothat learningtakesplaceidentically across
jobs. The agents' expectations of theinnate ability of workeri with x years of prior
labor-marketexperienceat periodt willthereforebeconditionedonthehistoryof signalsextracted
from theobservedoutputs. Formally,thisexpectationisde ned as:
e it =E( i jz it x ;:::;z it 1 )
Becauseoutputisalinearfunctionofe ectiveability,expectedoutputatthebeginningof
period t, and thereforewages, will be basedon expected e ectiveability (conditional onthe
informationsetoft 1). Taskassignmentineachperiodisthenbasedonthemaximizationof
toexplainthestylizedfactsdiscussedpreviouslyandallowsthemodeltoexplainthepossibility
of realwagedecreases. Themainargumentis basedonthefactthat thistime, wagesdepend
on expected innate ability whose evolutionis now driven by theevolution of agents' beliefs.
Becauseagentshaverationalexpectations,expectedinnateabilityfollowsamartingaleprocess:
e it = e it 1 +u it (4)
Thismeansthatthebestpredictionoffutureexpectedinnateabilityiscurrentexpectedability.
Inotherwords,anychangesincurrentbeliefsshouldbecausedbythearrivalofnewinformation
containedin the observed current output and could notbe predicted from previous realized
outputs.
The main di erence with the perfect information case is that now, a worker's expected
innate ability can fall from one period to the next if u it
is negative, and if the decrease is
suÆciently large, it will dominatethe increase due to humancapital accumulation and next
periodwagewillfall. Forthesamereason,therewill beapositivefrequencyofdemotions.
Serial correlation in wage increases continues to hold under the restriction of no
demo-tions. 14
However, serial correlation in promotion rates is nota clear prediction of the model
with learning. No matter how informative a worker'shistory of pastoutput is, an extreme
valueof thenextperiod outputcan radically changethe beliefs forthat period. SeeGibbons
andWaldmanforadiscussiononthispoint. Thereasoningisthesameasintheperfect
infor-mation case. Workerwhoexperience largewageincreasesbetweent and t+1are workerfor
whomexpectedinnateabilityatt+1hasincreased. Thismeansthatonaverage,theworker's
expectede ectiveabilitywillgrowfasterinthefuture. Largewageincreasesarethuspositively
correlatedtolargewageincreasesinthefuture.
Themodelgivespredictionsconsistentwiththefactthatwageincreasespredictpromotion.
A large wage increase indicates an increase in expected innate ability which means that on
averagee ective abilitywill growmorequicklyin thefuture so thattheworkerwillneed less
timeto reachthetargetlevelofexpectede ectiveabilityneededforpromotion.
Finally,thesizeoftheaveragewageincreaseonpromotionislargerthantheaveragewage
increasesbeforeand,thistime,afterpromotion. Theworkerpromotedattheendoftheperiod
had alarger increase in expected e ective ability than the worker notpromoted. The wage
increasewillthenbehigherforthisreasonandalsobecausetheincreaseinexpectedabilitywill
bevaluedat abiggerrate(c j+1
>c j
). Afterthepromotion,theexpectedchangein expected
innate ability is zero so the wage increase is smaller on average than the wage increase at
promotion. Wageincrease at promotionexplaina fraction ofthe di erencein averagewages
acrosslevelsbythesameargumentonageandlengthofhumancapitalaccumulationasinthe
perfectinformationcase.
Insummary, themodelunder perfect informationbasedon comparativeadvantagein the
assignmentofworkerstojoblevelscanexplaintheobservedserialcorrelationinwageincreases
andpromotionrates,thefactthatwageincreasespredictpromotionsbutthattheyexplainonly
afractionofthedi erenceinaveragewagesacrosslevels. Theintroductionoflearningallowsthe
possibilityof realwagedecreases and thataveragewageincreasesarehigher upon promotion
than before and after promotion. Under particular hypothesis on 0 and 00 0 , de ning
intervals of e ective ability in each job levels, the model leads to the prediction on absence
of demotions. Thus, themodelcan explainthe stylized facts highlightedin the literatureon
wagesandintra rmmobility.
The results of Section II, which suggest rst the presence of an unmeasured individual
ability term and second, that there is evidence of workers' self-selection due to comparative
advantageonmeasuredability, areconsistentwith the Gibbons andWaldman model. Given
thatunmeasured(orunobserved)abilityiscorrelatedwithmeasuredability,evidenceonthefact
method than the rst di erence method has to be used. In the next Section, I present the
econometricspeci cationofthemodelandtheestimationmethodwhichtakesintoaccountthe
comparativeadvantageandthelearningprinciplesbasedoninnateability.
B. Econometric Speci cation
Empiricalevidenceoninter-industrywagedi erentialshascreatedcontroversyonthe
estima-tion method used to explain them. Gibbons and Katz (1992) have presented a theoretical
model which emphasizesthe importance ofbothendogenous mobilitydriven bythe dynamic
evolutionofanunmeasuredabilitytermandendogenouschoiceofindustryorselfselectionof
workersintoindustries due to thedi erent sensitivityof industries'technologieswith respect
tothisabilityterm. ThemodelofGibbonsandWaldmanformalizestheseideasin thecontext
of the wage policy of the rm with endogenous choice of job levelsand endogenous mobility
betweenthesejoblevels. ThepurposeofthisSectionistopresentaneconometricspeci cation
ofthedynamicofwagesimpliedbythemodelofGibbonsandWaldmanwheretheendogeneity
problemsinducedbythecomparativeadvantageandthelearninghypothesescanbeaccounted
forandtherelativeimportance oftheire ects onthedynamicsofwagescanbeestimated.
Thespeci cationaccountsforthegeneralcaseofcomparativeadvantageandlearning(the
model under imperfect information). That is, the process for wages, equation (3) is written
usingtheexpectation ofworkers'ability, e it
.
In order to control for measurable individual characteristics, I included the skill variable
de ned previously. Employingdummies, D ijt
, indicatingtherankj of individual iat timet,
theequationtobeestimatedcanbewrittenas:
w ijt = J X j=1 D ijt d j + J X j=1 D ijt X it j + J X j=1 D ijt c j e it f(x it )+ it (5) where it
isameasurementerrorindependentofrankassignment,andX it
correspondstothe
skill variable. Comparativeadvantageis characterizedbythefactthat thecoeÆcients j
and
c j
varybyrankandlearningisrepresentedbytheconditionalexpectation e it
.
Estimatingequation(5)withOLSwouldgiveinconsistentestimates. Thecomparative
ad-vantagehypothesis implies that rank assignment is endogenous, so e it
is correlated with the
rank dummies. In addition, this term cannot be eliminated by rst-di erencing (5) because
it isinteractedwith theD ijt
terms. Holtz-Eakin,Neweyand Rosen(1988)analyzemodels in
which a xed e ect is interacted with year dummies and show that consistent estimates can
beobtainedbyquasi-di erencingtheequationofinterestandusing appropriate
instrumental-variable techniques. Lemieux (1998) applies this method to amodel in which the return to
a time-invariantunobservedcharacteristicis di erent in theunion and thenon-union sector.
Gibbons, Katz and Lemieux (1997)also use this method to analyze wagedi erentialsby
in-dustry and occupationin the presenceof unmeasured andunobservedabilityinteracted with
industryandoccupationdummies. Iapplythis methodtoestimatethewageequation(5).
C. Estimation Method
The rststepistoeliminate e it
e it = w ijt J j D ijt d j J j D ijt X it j it P J j D ijt c j f(x it ) (6)
The martingalepropertyof beliefs in innateabilitywhich links e it and e it 1 implies that we
cansubstitutesalaggedversionofthisequationinto(5). The nalequationisthereforegiven
by: w ijt = J X j=1 D ijt d j + J X j=1 D ijt X it j + P J j D ijt c j f(x it ) P J j D ijt 1 c j f(x it 1 ) w ijt 1 P J j D ijt c j f(x it ) P J j D ijt 1 c j f(x it 1 ) [ J X j=1 D ijt 1 d j + J X j=1 D ijt 1 X it 1 j ]+e it (7) where e it = it + J X j=1 D ijt u it P J j D ijt c j f(x it ) P J j D ijt 1 c j f(x it 1 ) it 1 (8)
This equation cannot beestimated using non-linear leastsquare becausew ijt 1
is correlated
with it 1
. Moreover, because of the presence of learning, the new information on innate
ability at time t, u it
, is correlated with D ijt
since beliefs on ability in uences the current
rankaÆliation. These problemscanbesolvedbychoosingappropriateinstrumentsforw ijt 1
and D ijt
, and consistent estimateswill beobtained. CallingZ i
the set of instruments, these
variableshavetosatisfythefollowingcondition:
E(e it
Z i
)=0 (9)
Theobjectiveisthentominimizethefollowingquadraticform:
min e( ) 0 Z(Z 0 Z) 1 Z 0 e( ) (10) where Z 0
Z is the covariance matrix of the vectorof moments Z 0
e( ), is the covariance
matrix of the errorterm e it
and is thevectorof parameters. Under homoscedasticity and
serial independence of theerror terms, = I (up to a constant 2
which disappears in the
minimization of (10)), so that the weighting matrix is equal to Z 0
Z and the method gives
a consistentNon-Linear Instrumental Variables estimator. An eÆcient estimator isobtained
by estimating . I will consider the two types of estimation using the SAS Non Linear IV
procedure.
Finally, the unmeasured abilityterm it
in the error term of equation (5) has to be
nor-malized tozero overtheobservationsin order toidentify all theparameters. 15
A proof ofthe
necessity of thisconstraint isgivenin Lemieux (1998). This isdone by addingthe following
equationto theoptimization of(10):
(1=TN) X i X t it =0 (11)
where N is thenumberof individuals,T isthenumberof periods foreachindividual and it
satis esequation (6).
Instruments are chosen using the identi cation assumption for estimation of panel data
equationsthat imposesstrictexogeneityofright-handsidevariablesormoreformally:
E( it =X i1 :::X iT ;D ij1 :::D ijT ; i )=0 (12)
abilityterm i
,focusingontheimpactofcomparativeadvantageandself-selectionofworkers
into thedi erentrankswithinnateabilityknownto allmarket participants. Inthiscase,the
innovationdrivingthemartingaleprocessforbeliefsdisappearsfromtheerrortermofequation
(7)andtheinstrumentsarechosentocorrectthecorrelationoflaggedwagewiththeerrorterm
it 1
,resultingfromthequasi-di erencingmethod.
Condition (12) provides aset of potentialinstruments sinceit states that conditional on
observed innate ability, individual characteristics and rank assignments each period are
in-dependent of the error term in the wage equation (5). In addition, since according to the
productiontechnology(equation(2)),newinformationcontainedintheobservationofcurrent
output hasthesameimpact acrossranks, conditionalon innateability andother measurable
characteristics,thecurrentchoice ofjoblevelisrandom. InthespiritofLemieux'sestimation
ofcomparativeadvantagementionedbefore,I considerasinstrumentsforthelaggedwagethe
historyofjob levelorrankdummyvariables. Inparticular, interactiontermsbetweenD ijt 1
and D ijt
whichgiveinformationonthecareerpathoftheworkerbetweent 1andt,should
help predict w ijt 1
. Indeed, accordingto the Gibbons and Waldman model, the choice of a
job level is in uenced by innate ability and should therefore be correlated to the wage but
uncorrelatedtotheerrorterm it
becauseofcondition(12).
Inthe imperfect information case,the presence oflearningintroduces anothercorrelation
problem. Now that innate ability evolves over time as beliefs change, the current choice of
job rank D ijt
is correlated to the changes in beliefs between t and t 1 (re ected in the
martingaleinnovationu it
whichappearsin theerrorterme it
). Therefore,D ijt
willhavetobe
instrumented. Thechoiceofinstrumentswillbefacilitatedthankstothemartingaleprocessfor
innateabilitywhichimpliesthatchangesinbeliefstodayareuncorrelatedtochangesinbeliefs
theperiodbefore. Therefore,itispossibletousethechoiceofjoblevelinthepreviousperiods,
D ijt 2
and D ijt 1
, because they are correlated to the changes in expected ability in period
t 2andt 1(helpingpredictD ijt
)but areuncorrelatedtothecurrentchangesu it
andthus,
uncorrelated to the error term e it
in the quasi-di erencing equation. As before, interaction
betweenD ijt 2
andD ijt 1
willalsobeconsidered.Thissetofvariableswillalsoprovidevalid
instrumentsforw ijt 1
forthesamereasonsasin thecaseofperfectinformation.
Theestimationresultswillbepresentedintwoparts. First,equation(7)isestimatedunder
the assumption of perfect information to emphasizethe impact ofcomparativeadvantageon
i
(observedbythemarketbut unmeasuredbytheeconometrician). Second,theestimationis
performedforthemodelwithcomparativeadvantageandlearningabout i
.
Notethat in bothcasestheelement f(xit) f(x
it 1 )
,representingtheratioof accumulated
expe-rience in t with regardto t 1, hasto be speci ed. Accordingto theMincer wageequation,
wageswhenstudied in log, are speci ed by apolynomialfunction of experience. Sincewages
hereareinlevel,itshouldbereasonabletoassumeanexponentialfunction ofthissame
poly-nomialinexperience. Thisleadstothefollowingfunctionalformfortheratiog(x it )= f(x it ) f(xit 1) 16 Assumingf(x it )=e 0 + 1 x it 2 x 2 it theng(x it )=e 1 + 2 2 2 x it . : g(x it )=b 0 e b 1 x it (13)
Going back to the Gibbons and Waldman model, the estimation of a ratio higher than
unity will con rm that the function f of human capital accumulation is non constant and
monotonicallyincreasingwithexperience. Inotherwords,itwillshowevidenceofunmeasured
(unobserved in the learning case) heterogeneity in the accumulation of human capital and
thereforeinwageincreasesandmobility. Accordingtothemodel,theevolutionoftheworker's
productive ability over time (de ned as the product of ability i
and the experience funtion
i
correlation in wage increases and in promotion rates as the rm observes (or expects) that
some individuals perform better than others, it assigns them to higher ranks. They receive
higherwageincreasesnotonlyasaresultofmobilitybetweenranksbutalsowithin arankas
they varyacrossworkersof di erenttype i
17
With anestimated b 1
signi cant,theratio will
vary with experiencewhich implies that accumulationof humancapital would notonly vary
acrossworkersbut alsoovertime..
IV. RESULTS AND INTERPRETATION
Theanalysisoftheresultsispresentedinfourparts. The rstpartfocusesontheestimationof
thewagedynamicsforworkersremaininginsidetheir rm(TableIII).Thesecondpartperforms
thesameestimationsbut thistimewiththesampleincludingworkerschanging rmstostudy
thepossibledi erencesintheimpactofmeasuredandunmeasured(unobserved)abilityonthe
wagedynamics(TableIV).Thethirdpartconcentratesontheestimationofthehumancapital
accumulationratio(TableV).The lastpartconsiders theestimationwithnon homoscedastic
errorsandtheproblemofclassi cationerrorsintherankvariables(TableVI).
A. Wage Dynamics Within Firms
Results, shown in the rstpartof TableIII,con rmthe importance ofnon randomselection
of workers based on unmeasured ability. The coeÆcients c j
which evaluate the impact of
unmeasured ability in each rank j are signi cant. Starting at 1 (normalization) for rank L,
theyrangefrom1.043forthemiddlerankM,to 1.475fortheupperrankUand1.600forthe
executiverankE. Theyaresigni cantlydi erentfromoneanotheraccordingto thejointtest
( 2
(3) of15.00)and, exceptfor rankM,arealsosigni cantlydi erentfrom thelowerrankL
( 2
(1) of10.10forU and4.69forE). Theseresultssuggestdistinctand increasingreturnsto
unmeasured abilitybyhierarchicallevel.
Theinter-rankwagedi erentialsd j
havedroppedbyabout80%comparedtotheOLSresults
in column (4) of TableII when onlycomparativeadvantageonmeasuredskills is considered.
ThecoeÆcientsrelatedtomeasuredskillsbyrank(the j
)arestillsigni cantlydi erentfrom
oneanother( 2
(3)of6.12forthejointtest)implyingthatcomparativeadvantageonmeasured
ability is still importantbut comparedto column (4) of Table II,its impactis smaller. One
can also notice that their impact is now decreasing with ranks, ranging from 0.735 in rank
L tobeingnot signi cantly di erentfrom 0 in thehighest rankE. Insummary, non random
selectionorcomparativeadvantageofworkersbasedonunmeasuredabilityseemstocapturean
importantpartofthevariationinthedynamicsofwageswithin the rmandthepartrelated
to measuredability becomes lessand less important as workersgo upthe ladder. Although
signi cantlyreduced,theranke ectsarestillsigni cant.
ThesecondpartofTableIIIreportstheresultsofthemodelwhenlearningaboutunobserved
abilityisconsidered. Onecanseethatonlytheranke ectforthemiddlerankMissigni cant.
Moreover, except for rank M and c M
, the slopes associated with unobserved ability are not
di erentfromoneanotherand notdi erentfrom thelowerrankslope. Theslopesassociated
with measured ability remain signi cant at all rank. Generally, the standard errors of the
coeÆcientsare largerthan inthecasewith nolearning. Resultsaremoreimpreciseandhard
to interpret. In fact, except for the middle rank M, the c j
which measure the impact of
unmeasured ability (unobserved in this case)in each rankare no longer increasing in ranks.
Fromtheseresults,itisratherdiÆculttodrawconclusionsaboutthee ectsoflearningonthe
wagedynamics. Theoverallimprecision oftheresultsmightcomefrom theuse ofsecondand
term b 0
, and onecan see that in the comparative advantage case it is signi cantly di erent
from one. Its estimated value of 1.024 gives,in log, a 2.37% growthrate for the function f
ofhumancapitalaccumulation. Inotherwords,controllingforallothermeasurableindividual
characteristics,one moreyearof experiencewithin the rmis associatedwith a2.37% wage
increasefortheaverageworker. Inthespeci cationwithlearning,theratioisnotsigni cantly
di erent from one, implying that the function f is constant or that there is no evidence of
unobservedheterogeneityintheworkers'humancapitalaccumulation.
Finally,notethatin bothestimationstheover-identi cationtest 18
Thestatisticofthetest
uses the optimized value of the objective function times the number of observations. The
distributionis 2
(l p)wherepisthenumberofparametersandlisthenumberofinstruments.
showsthat theinstrumentsusedare validsincethenullcannotberejected.
Summarizing the overall results, one can say that the dynamics of wages and workers'
mobilitywithinthe rmarecharacterizedbytheimportanceofnonrandomselectionofworkers
intojobranksandbythepresenceofunmeasuredheterogeneityinhumancapitalaccumulation
leading to theresult that wage increases are serially correlated. The inconclusive resultson
the presence of learning as the factor driving workers' mobility across job ranks, suggests
that Germanworkersare notmobile within the rm. Once theyenter the rm, they get to
the job rank that best suit their productive abilities and remain in that job thereafter. A
possibleexplanation for that is theimportance ofthe apprenticeship systemin Germany. In
this system, individuals receivetraining within a rmfor a certainperiod of time while still
completingschool. Duringthatperiod,boththe rmandtheworkerobtaininformationonthe
productivityof theemployer-employeematch andbothcan useitin theirfuture employment
decisions. Sincethesamplestudiedconsidersindividuals justafter enteringthelaborforceon
apermanentbasis,those workingwhilestillcompleting schoolhavenotbeenconsidered.
The results on serial correlation in wage increases (controlling for measurable individual
characteristics)is in contrast with theliterature mentioned earlierwhich nds anabsence of
serialcorrelationwhenestimatingthecovariancestructureofwagesandwageresiduals(Abowd
and Card(1989)and Topeland Ward(1992). However,it isin accordancewith studies that
analyzed the question with particular samples of workers (Hause (1980) who uses a sample
of white-collarSwedish malesand LillardandWeiss (1979)whostudy asample ofAmerican
scientists).
In theanalysis so far, I considered thesample of workersremaining with their rms and
the heterogeneity capturedin theresultscouldbeworker- rmspeci c ratherthan individual
speci c. Toexaminewhetherthee ectsofheterogeneityinhumancapitalaccumulation,
com-parativeadvantageandlearningdrivingthewagedynamicsaremoreindividualorworker- rm
speci c,Iestimate,inthenextSection,themodeloverasamplethatincludes rmchangers.
B. Wage Dynamics Within and Between Firms
The results from performing the estimations on the sample of workers moving within and
between rmsarepresentedinTableIV.Theyaresimilartothoseobtainedwiththesampleof
rmstayersconcerningthepresenceofnonrandomselectionandcomparativeadvantage.One
cannoticeanincreasinge ectofunmeasuredabilityandadecreasinge ectofmeasuredskills
with ranks. Ranke ects are also still signi cant. Also, the second part of the Table shows
that, asbefore, there isno clearevidence oflearning. 19
Because learningdoesnotseemto be
supported by the data, the analysis thereafter focuses on the speci cation with comparative
advantageonly.
In the comparative advantage case, the di erences between the estimations over the two
samplesliesin themagnitudeoftheslopecoeÆcientsrelatedtounmeasured abilityand
now higher. Moreprecisely, for theslopecoeÆcients on unmeasured ability, the e ect c E
is
twiceashighastheoneatthelowestrankLwhichishigherthaninthepreviousresults(c E
is
2.02comparedto 1.6inTableIII).On theotherhand,thecoeÆcientsassociatedwithmiddle
andupperranksc M
andc U
aresimilartothoseofTableIII.TheslopecoeÆcientonmeasured
skillsisnotsigni cantatthehighestrankE,asinthepreviouscase,butthecoeÆcients L
; M
and U
aremuch highernowthanin TableIII.
These resultssuggestthat theimpact ofunmeasured abilityon thewagedynamics seems
to be more individual speci c at the executive rank. At the lower ranks, the inclusion of
rmchangersdidnotchangethe impactofunmeasured abilityas much. On theotherhand,
theimpact ofmeasuredskillsishigherat theserankswhenobservationsonworkers'mobility
between rms are included in the sample. It can be concluded from these results that the
e ectofunmeasuredabilityatthelower,middleandupperranksdoesnotseemtoresultfrom
an individual speci c abilitye ect that would be transferableacross rmsbut results froma
worker- rmspeci c matchqualitye ect.
In summary, the wage policy of rms is characterized by the importance of non random
selectionof workersintojob ranksandtheexistenceofunmeasured heterogeneityin wage
in-creases. ThisresultissurprisinggiventhattheGermanlabormarketisregulatedbyunionsand
employers'associationswhichwouldsuggestthatpaysettingsaremorerelatedtobureaucratic
rules. Ontheotherhand,I ndevidencethattheranke ectsd j
arestillsigni cantevenafter
controllingformeasured and unmeasured characteristics. Note that these coeÆcientsalways
increase with rankswhich is notin accordance with the Gibbons and Waldman model's
as-sumptionthattheyshouldbedecreasingwithranks. Inthemodel, wagesareset accordingto
apiece-ratepaysystembasedonexpectedoutput. Boththeslopesand interceptsare
param-eters that aregiven tothe rmbut depend onthe equilibriumallocationof workers'skills to
jobranks. Workerswithlowlevelofskillsorperformanceareassignedto(andalsochoose)low
job ranks,wherethewageputstheleastweightonskills,i.e. withahighinterceptand a at
slope. Thehighlyskilledworkerendsupinahighjob rankwithawagemostlybasedonskills
(with alow interceptand ahigh slope). This negativecorrelation betweenthe interceptand
theslopeisnotasclearwhenwagesarenotonlyfunctionofskillsbutalsodependonthe rm's
bureaucraticrules. Theresultsheresuggestthattheinterceptsorranke ects re ectmore
ad-ministrativesettingsspeci ctothejobsuchastaskcomplexityandresponsibilityrequirements
whichincreasewithrankindependentlyoftheworker'sskilllevel.
C. Human Capital Accumulation
Theresultssofarcomefromtheestimationofthewageequationwithaconstantratioofhuman
capitalaccumulation. Workersaccumulateyearsofexperiencewithinthe rmatdi erentrates
butnomatterwhatperiodoftimeintheworker'scareer,oneadditionalyearofexperiencehas
thesameimpact. Onemightthinkhoweverthattheimpactisstrongeratthebeginningthanat
theendoftheworker'scareer. Ireestimatedthemodelconsideringthemoregeneralfunctional
formgivenin(13). ResultsareshowninTableVforthecasewithcomparativeadvantagebut
nolearning 20
Resultswithlearning,availableonrequest,didnotleadtoasigni cantestimation
ofthecoeÆcientsb 0
andb 1
.. Theratiohasbeenestimatedasafunctionofthenumberofyears
of tenure with the rm. The estimation using the number of years of potential experience
did not lead to the convergence of the objective function in the optimization process. Also,
convergencecouldnotbereachedfornootherfunctionalformfortheratiothantheoneshown
in tableV, wherethecoeÆcientb 0
isconstrainedtobeequaltoone. Finally,thetwopartsof
theTablerelatetotheestimationsonthetwodi erentsamplesusedpreviously.
Fortheresultsonthepresence ofnonrandomselectionofworkersinto jobranks,onecan
seethat theconclusionsarethesameasbefore. ThecoeÆcientsonmeasuredandunmeasured
ratio, the impact of tenure (coeÆent b 1
) is signi cant but very small and, contrary to what
was expected, it is positive. 21
According to the human capital theory, one additionalyear of
experienceshouldhaveadecreasingimpactwith increasingyearsof experiencewiththe rm.
Theratioisinfactveryclosetooneforthe rstyearoftenure(ratioof1.001)andstillremains
close toit after10 years(ratioof 1.01)leadingto estimatedwageincreasesof0.1% and 1%
respectively. Therefore,onecanreasonablyconcludethattheratiodoesnotseemtovarywith
theworker'stenureinthe rm.
D. Discussion of the Results
Despitetheprecedingevidenceonnonrandomselectionofworkersontothehierarchicallevels
of the rm's job ladder and on unmeasured ability driving thedynamics of wages, there are
several issues to keep in mind in anlysing the results. Among those is the assumption of
homoscedasticityoftheerrorterm. Sincethismightbeastronghypothesis,I reestimatedthe
equation,usinganestimateofin asecondstep,wherethe rststepestimatesbyNLIVwith
=I,usingtheresidualsfromtheestimationinthe rststeptoestimate(Hansen(1982)).
The resultsof this estimation arepresentedin the rstpartof TableVIfor thecomparative
advantagecase.
Generally,correctingforpossibleheteroscedasticityand/orautocorrelationoftheerrorterm
leadtomoreimpreciseestimates. Theresultsarequitedi erentfromthoseinTableIIIinterms
ofthemagnitudeandalsostandarderrorsofthecoeÆcients. Moreover,thevalueofthestatistic
of theoveridenti cationtest isnowquitehigh (58.99)leadingtorejectthehypothesisofvalid
instruments.
Thefactthatthestatisticofthetest(basedontheoptimizedvalueoftheobjectivefunction)
has a larger value when the covariance of the moments is estimated does not have a clear
explanation sincethereis noreasonto expectthat (Z 0
Z) 1
should belargerthan (Z 0
Z) 1
.
On the other hand,Altonji andSegal (1994) showthat although thechoice of the weighting
matrixasthevarianceofthemomentsgivesaneÆcientGMMestimatorasymptotically,itleads
to anestimatorwhichhaspoorsmallsampleproperties. UsingMonteCarloexperimentsthey
nd thatthe estimatoris biasedbecausesamplingerrorsin themomentsto beestimated are
correlatedwith samplingerrorsintheweightingmatrix(whichisafunction ofthecovariance
ofthesemoments). ThismayexplainwhythecoeÆcientsfoundandthevalueoftheobjective
function areverydi erent. Giventhatthesampleisnotparticularlylargetheresultswithout
theestimationoftheweightingmatrix,whichstillprovideconsistentestimates,maybefavored.
Anotherissuethathastobestressedisthepresenceofclassi cationerrorsinthereported
occupation ranks from year to year. Assuming that these errors are serially uncorrelated,
I reestimated the model with comparative advantage using the second lags of the variables.
Results, reportedin second partofTable VIare slightly di erentfrom thoseof TableIII. All
thecoeÆcientshavelargerstandarderrorsandtheb j
coeÆcientslosetheirexpectedincreasing
orderbyrank. This suggeststhatclassi cationerrorsmightbeimportant.
V. CONCLUSION
In this paper, I haveanalyzed the relativeimportance of di erent factorsexplaining the
dy-namicsofwagesand theworkersmobilitywithin rms. Todothis,I implementedempirically
the theoreticalmodel proposed by GibbonsandWaldman (1999)which combines thenotions
of human capital accumulation, job level assignments based on comparative advantage and
learningabouttheworker'sabilityto characterizethewagepolicyof rms.
dimension of the data allowsme to analyze thewage and mobility dynamics. Based on the
GermanGSOEP overtheyears1986 to 1996,theresultscanbesummarized in thefollowing
points.
Themaincommonfeaturescharacterizingthewagepolicy ofGerman rmsarethe
impor-tance of nonrandom selectionof workersinto job ranksand theevidence of heterogeneity in
humancapitalaccumulationleadingtoserialcorrelationinwageincreases. Whetherthesource
of heterogeneityisindividualspeci correlatedto thequalityoftheworker- rmmatch seems
to dependonthejobrankconsidered. Theunmeasuredabilitytermattheexecutiverankhas
alargere ect on thewagedynamics whenit isestimated overthe sampleof workersmoving
inside the rmaswell aschanging rms. Thee ects at thelower,middle andupperranksof
theworker'soccupationaresimilarwhetherornot rmchangersareincludedin thesample.
Theresultsofthispaperrevealtheimportanceofthequestionoftheassignmentofworkers
to job ranks on our understanding of wage dynamics within as well as between rms. The
evidence onthepresence ofnon-random selectionofworkersontothe rungsofthe jobladder
brings an helps explain the fact that the distribution of wages di ers from the distribution
of individual productivities at the level of the rm. These resultsshowthat wage dynamics
within the rmdependnotonlyontheworker'sability(innateabilityorqualityofthematch
worker- rm)butalsoonhowproductivethisability(ormatch)iswithinaspeci cjobrank. In
addition, thefact that therankpremiaremain signi canteven aftercontrollingformeasured
and unmeasured heterogeneity in the wage dynamics suggests that the rm's administrative
rulesconstituteanotherrelevantexplanatoryfactor.
TheestimationofthemodelofGibbonsandWaldmanleadtoarelativelygooddescription
of the German case and it would obviously be interesting to compare them with U.S. data.
To my knowledge, there is no American survey data with a questionon the job rank of the
worker. However,itwould bepossibleto constructvariablesonjob levelsbyusing the
three-digitcodesfromtheU.S.Censuswhichprovideadetailedclassi cationofoccupations. Future
researchshouldinvestigatethisissuebecauseifthemodelofGibbonsandWaldmanprovidesa
reasonableexplanationofwagedynamicsinGerman rmsitmaybeevenmorerelevantinU.S.
rms(wherethemobilityofworkers,onwhichthemodelisbased,ishigherthaninGermany).
ThemodelofGibbonsandWaldmanisbasedontheassumptionthatall rmsareidentical
andthereforehavethesamehierarchicalstructureandthesameproductiontechnology. Further
research could investigate the possibility that rms of di erent size di er in their internal
organizationassuggestedbytheempiricalevidenceontheimpactof rmsizeonwageoutcomes
(seeforexampleBrownandMedo (1989)). Thiscouldimplythattheproductivityofagiven
worker-job-levelmatch isdi erentinlargeandsmall rms.
Finally, one thing that is absent in the model of Gibbons and Waldman is the role of
incentivesinthedeterminationofthewagepolicyof rms. Lazear(2001)analyzesthequestion
of explaining the observeddecline in the worker'sproductivity after apromotion. Using the
GibbonsandWaldman theoreticalframework,heexplainsthe rm'sstrategicdecisionofwho
and when to promoteworkersin order to minimize the post promotion productivity decline.
GiventhattheGibbonsandWaldmanmodeliseasilyimplementableempirically,futureresearch
should investigate the possible empiricalapplications of the augmentedmodel that considers
a,b),PodolnyandBaron(1995)andChiapporiandal. (1996).
2. Baker,Gibbs andHolmstrom(1994a,b)
3. Baker, Gibbs and Holmstrom(1994a,b) in the case of one rm and Card and Hyslop
(1995) ndidenticalconclusionsusingtheCPSandPSID.Arelated ndingisfoundinPeltzman
(2000). UsingdatafromtheBLS,itisfoundthatoutputpricesincreasemorethantheydecrease
inresponsetoshocksinthecostofinputs. Increasesin rm'slaborcostswouldthereforeinduce
real wagedecreases.
4. Hause(1980),LillardandWeiss(1979)andBaker,GibbsandHolmstrom(1994a,b).
5. Murphy(1985)Baker,GibbsandHolmstrom(1994a,b)andMcCue(1996).
6. Baker,Gibbs andHolmstrom(1994a,b). McCue(1996) ndsthatahighwagetodayis
positivelycorrelatedto promotiontomorrow,and, in thesamespirit, TopelandWard(1992)
ndthat priorwagegrowtha ectsmobilityevenaftercontrollingforthecurrentwage.
7. Since in Germany, the minimum wage varies by industry, this bound should give a
reasonableminimuminordertoexcludeoutliersforwageswithoutloosingobservationsonlow
wageworkerssuch astrainees.
8. Appendix 2presentsthefrequenciesofthedi erenttypesofmobility.
9. Thelagcorrespondstotheyearbeforemobilitywithin the rm.
10. IusedtheInternationalStandardIndustrialClassi cation(ISIC).
11. Given that the dependent variable has few responses (y = 1) compared to non
re-sponses, using aprobit model might produce di erent results. I reestimated the model with
the normal distribution. Results(available onrequest) are similar in which they leadto the
sameconclusionsintermsofmarginale ect coeÆcientandsigni canceofthecoeÆcients.
12. Individuals reportingtrainees whowere also reportedin oneof theother occupations
havebeenretained.
13. This index, reported in the last column of Appendix 3,correspondsto thepredicted
wageconditional onmeasuredindividualcharacteristics.
14. However, serial correlation in promotion rates is not aclear prediction of the model
with learning. No matter how informative a worker'shistory of pastoutput is, an extreme
valueof thenextperiod outputcanradically changethe beliefs forthat period. SeeGibbons
andWaldman foradiscussiononthispoint.
15. Aproofofthenecessityofthisconstraintisgivenin Lemieux(1998).
16. Assumingf(x it )=e 0 + 1 x it 2 x 2 it theng(x it )=e 1 + 2 2 2 x it . 17. With anestimatedb 1
signi cant,theratiowillvarywithexperiencewhichimpliesthat
accumulationofhumancapitalwouldnotonlyvaryacrossworkersbut alsoovertime.
18. Thestatistic of the test uses the optimized valueof the objective function times the
numberofobservations. Thedistributionis 2
(l p)wherepisthenumberofparametersand
listhenumberofinstruments.
19. Because learningdoesnot seemto be supported by the data, the analysis thereafter
focusesonthespeci cationwithcomparativeadvantageonly.
20. Results withlearning, available onrequest, didnotlead to asigni cantestimation of
thecoeÆcientsb 0
andb 1
.
21. Accordingto thehumancapital theory, oneadditionalyear ofexperience shouldhave
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