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Cahier 2001-18

LLUIS, Stéphanie

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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.

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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.

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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

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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

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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

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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

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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.

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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

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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

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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 .

(12)

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

(13)

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

(14)

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

(15)

 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)

(16)

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

(17)

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

(18)

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

(19)

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

(20)

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.

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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

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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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[1] Abowd, J. and D. Card (1989)\On the CovarianceStructure of Earnings and Hours

Changes,"Econometrica57, 411{445.

[2] Altonji, J. G. and L. M. Segal (1996) \Small-Sample Bias in GMM Estimation of

CovarianceStructures,"JournalofBusinessandEconomic Statistics14, 353{366.

[3] Baker, G., M. Gibbs, and B. Holmstrom (1994a) \The Internal Economics of the

Firm: EvidencefrompersonnelData,"QuarterlyJournalof Economics109,881{919.

[4] (1994b)\TheWagePolicyofaFirm,"QuarterlyJournalofEconomics109,921{955.

[5] Baker,M.(1997)\Growth-RateHeterogeneityandtheCovarianceStructureofLife-Cycle

Earnings,"Journalof Labor Economics15, 338{375.

[6] Bartel, A. and G. Borjas (1981) \Wage Growth and Job Turnover: An Empirical

Analysis,"inStudiesinLaborMarkets.UniversityofChicagoPress.

[7] Beaudry,P. andJ. DiNardo(1991)\TheE ectofImplicitContractsonmovementof

Wages overthe Business Cycle: Evidence from Microdata," Journal of Political Economy

99, 665{688.

[8] Becker, G. (1975)Human Capital: A Theoretical and Empirical Analysis With Special

ReferencetoEducation.UniversityofChicagoPress.

[9] Chiappori, P-A, B.

Salani

e, and J. Valentin(1999)\Early StarterversusLate

Be-ginners,"Journalof Political Economy107,731{760.

[10] Depecker, J.P etS. Milano(1995)Economie etsociete allemande.

[11] Doeringer, P. andM. Piore (1971)InternalLaborMarkets andManpowerAnalysis.

HealthLexingtonBooks.

[12] Farber, HandR.Gibbons(1996)\LearningandWageDynamics,"QuarterlyJournal

of Economics111,1007{1047.

[13] Gibbons,R.(1997)\IncentivesandCareersinOrganizations,"inKreps,D.andK.Wallis,

eds., Advancesin Economics andEconometrics: Theory and Applications, chapter1,pages

1{37.CambridgeUniversityPress.

[14] Gibbons, R. and L. Katz (1992) \Does Unmeasured Ability Explain Inter-Industry

WageDi erentials?,"Reviewof Economics Studies59,515{535.

[15] Gibbons,R.,L.Katz,andT.Lemieux(1997)\UnmeasuredAbility,Unobserved

Abil-ity,and Inter-IndustryWageDi erentials,".

[16] Gibbons,R.andM.Waldman(1999)\ATheoryofWageandPromotionDynamicsin

InternalLabor Markets,"QuarterlyJournalof Economics114,1321{1358.

[17] Harris, M. and B. Holmstrom (1982) \A Theory of Wage Dynamics," Review of

Economic Studies49,315{333.

[18] Hashimoto,M.(1981)\Firm-Speci cHumanCapitalasaSharedInvestment,"American

Economic Review71, 475{481.

[19] Hause, J.(1980)\TheFineStructureofEarningsandtheOn-the-JobTraining

Hypoth-esis,"Econometrica48,1013{1030.

[20] Holtz-Eakin, D., W. Newey, and H. Rosen (1988)\EstimatingVector

Figure

TABLE IV: Wage Dynamics Within and Between Firms
TABLE V: W age Dynamics and Human Capital Accumulation Ratio

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