CAHIER 18-2001
WAGE POLICY OF FIRMS :
AN EMPIRICAL INVESTIGATION
CAHIER 18-2001
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
heterogeneity, learning
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 one particular 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 the PanelStudyofIncomeDynamics to examinetheimportance ofpromotions andintra rm
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 promotion tomorrow, 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 governingthesettingofwagesandjobassignments,whichcoulda ectthereturnstointra rm
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 modeloftheprobabilityofintra rmmobilityandoninter-rankwagedi erentialsestimations.
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 asthe 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. Lagged wage growth may be a more accurate measure of individual skills than the level of
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 coeÆ-cientsassociatedwitheducation,experience,maritalstatus,genderandnationalitytocompute
index. 13
This index, reported in the last column ofAppendix 3,correspondsto thepredicted wageconditional onmeasuredindividualcharacteristics.
Column 1of TableII presents theresults of aregressionof wageson 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. Onecanseethat 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 sothatworkersmayself-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 be-cause, ifthe productiveabilitiesof theworkersare notperfectly observed, boththe rmand
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;2or 3. 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 nedas the 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-ferentlyforeachworkerdue totheirdi erentlevelsofinnateability. Thatis,foragivenlevel of experience,highabilityworkerswillgethigherwageincreasesthan lowabilityworkersand thesameorderingwillholdforwageincreasesat allexperiencelevels.
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 promotionwhichcapturesthevalueofonlyone yearofexperience.
Inthecaseofperfectinformation,however,theexplanationforthelargewageincreasesupon promotion is notfully 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 possibilityofrealwagedecreases.
Wheninformationon innateabilityis imperfect(but symmetric),workersand rmsstart with theinitialbeliefp
0
that agivenworkerisof innateability H andwith1 p 0 that heis L
. Learningtakesplace at theend 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 currentexpectedoutput.
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 sothattheworkerwillneed 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 thatworkersalsohaveacomparativeadvantageonunmeasuredabilityisexpectedtobefound.
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 the errorterms, = 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
Aproof 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.Thisset ofvariableswillalsoprovidevalid 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(x
it ) f(xit 1)
,representingtheratioof accumulated expe-rience in t with regardto t 1, hasto be speci ed. Accordingto theMincer wageequation, wageswhenstudied in log, are speci edby apolynomialfunction of experience. Sincewages hereareinlevel,itshouldbereasonableto assumeanexponentialfunction 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 f) is drivenby anunmeasured abilityterm and sinceit enterslinearly in the wagefunction,
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 erentfromone anotheraccordingto 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 thirdlagsofthevariablesfortheinstrumentswhichleadstoasubstantiallossofobservations.
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 andbothcanuseitin 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 mea-suredskillsforthedi erentranks. Theslopeassociatedwithunmeasuredabilityatthehighest
now higher. Moreprecisely, for theslopecoeÆcients on unmeasured ability, the e ect c E
is twiceashighastheoneatthelowestrankLwhichishigherthaninthepreviousresults(c
E is 2.02comparedto 1.6inTableIII). Ontheother hand,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 form givenin(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.
Fortheresultsonthepresenceofnonrandomselectionofworkersinto jobranks,one can seethat theconclusionsarethesameasbefore. ThecoeÆcientsonmeasuredandunmeasured ability andthe ranke ects are similar to those from the rst partofTablesIII and IVwith
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 rmas well 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 theroleofincentives.
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 a clearprediction 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 adecreasingimpactwithincreasingyearsofexperiencewiththe rm.
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LogitEstimationof IntrafirmMobility a
Model b
Baseline Marg. Lagged Lagged All Marg.
Speci cation E ect Bonus WageGr. Variables E ect
HighSc. 0.293 0.011 0.249 0.048 0.052 0.001 (0.181) (0.189) (0.337) (0.336) College 0.566*** 0.022 0.557** 0.508 0.505 0.010 (0.216) (0.225) (0.387) (0.236) Tenure -0.086*** -0.002 -.0008 -0.098** -0.100** -0.001 (0.022) (0.027) (0.041) (0.041) German 0.138 0.005 0.262 0.112 0.106 0.002 (0.227) (0.229) (0.431) (0.432) Female -0.181 -0.007 -0.275*** -0.088 -0.088 -0.002 (0.119) (0.126) (0.203) (0.203) Married -0.334*** -0.013 -0.299*** -0.316* -0.315* -0.006 (0.112) (0.116) (0.192) (0.192) Size 0.634*** 0.025 0.733*** 0.531*** 0.526*** 0.010 (0.112) (0.121) (0.180) (0.180) Contract -0.149 -0.006 0.214 -0.322 -0.335 -0.006 (0.221) (0.241) (0.389) (0.388) Public 0.188 0.007 0.225 0.268 0.257 0.005 (0.174) (.180) (0.267) (0.270) Lbonus - - -1.888*** - 0.329 0.006 (0.144) (0.441) LwageGr - - - 2.280*** 2.293*** 0.041 (0.744) (0.744)
a-Thenumberofobservationsfory=1is638overatotalof14493.
b-Allspeci cationsincludedummiesforindustry,occupationsandaquadraticfunction oftenureandacubicfunctionofthewagegrowthrate.
Wage Differentialsby JobRank Models a (1) (2) (3) (4) Variables b
OLS OLS FE OLSwithCA
Skill - 1.589*** 1.653*** -(0.034) (0.092) RankL - - -RankM 0.357*** 0.121*** 0.021* 0.20*** (0.019) (0.016) (0.015) (0.020) RankU 1.373*** 0.684*** 0.157*** 0.70*** (0.039) (0.035) (0.019) (0.039) RankX 2.195*** 1.204*** 0.219*** 0.92*** (0.077) (0.068) (0.032) (0.119) Skill*RankL - - - 1.21*** (0.041) Skill*RankM - - - 1.53*** (0.065) Skill*RankU - - - 1.99*** (0.082) Skill*RankX - - - 2.37*** (0.180) Adj. R2 0.48 0.62 0.11 0.63 Observations 11159 11159 11159 11159
Test ofEqualityofslopes 103.43
p-valueofthe 2
-test .000
a-Dependentvariableiswageinlevelinthousandofmarks. Standarderrorshavebeen computedusingtheWhitecorrection.
b-Arealsoincludedaredummiesforthetypeofcontract,large rmsize,publicsector, occupations,industriesandyears.
