Age-SizeE®ectsinFirmGrowthandProductive …

1 Age-SizeE ectsinFirmGrowthandProductiveE ciency :TheCaseofManufacturingEstablishme ntsinEthiopiaTayeMengistaeAugust1998 AbstractSeveralstudiesindevelopedeconomi eshavereportedthattherateofgrowthofsmall rmsdecreaseswith 's(1982)versionofthepassivelearningmodel ofcompetitiveselectionandiscon rmedbydataonarandomsampleofmanufacturing ectsin rmgrowthtoanunderlyingdistributionofof rmsbytechnicale ciency , nd, rst,thatthesamee ectsasdetectedintheEthiopiandataarematch edbytime-invariantinter- rmdi erencesintechnicale ,thedataexhibitage-sizee ectsintechnicale ciencyaswell,wherebybigger rmsaremoree cientgivenageandolder rmsaremoree , rmageand rmsizemainlyproxyforownerhumancapitalvar iablesinasfarastheyexplaine ,itisnotthecasethatsome rmsaremoree cientthanothersbecausetheyarebiggerorold erbuttheotherwayround:some rmsarebiggerorlongerlivedthanothersbecau setheyhaveprovedtobemoree ciencybutissigni ,thelevelformalschoolingcompletedhasbyfa rthestrongestin uenceone 'saccesstobusinessnetworksandhisorhereth nicityalsohavesigni cante ,thereisnoevidencethate ciencydependsonanyoneofpre-ownershipempl oymentexperienceinthecurrentindustry, :ProductiveE ciency ,FirmGrowth,SizeDistributionofFirm s,Entrepreneurship,MarketSelection, cation:D24,D92,L11, rmsinEthiopiacon rm ndingsofearlierstudiesindevelopedeconomi esthattherateofgrowthofsmall rmsdecreaseswithinitial rmsizeandinitial 's(1982)versionofthepassivelearningmodel ofthedynamicsofowner-managed rms, ,thepossibilityremainsthatthesameage-siz ee ectsdetectedinthegrowthofgroupof rmsareindeedoutcomesofpassivelearningine xitorexpansiondecisions,thentheunderlyin gproductiondatamustexhibitpermanentandsy stematicinter- rmdi erencesintechnicale ciency .

2 Thecurrente ciencyofa rmmustbepredictedbye ciencyinthepastwhilein-creasinginthecurr entsizeandageofthe ,weshouldbeabletotraceage-sizee ectsine ciencytothelatter'sdependenceonentrepren eur-ialhumancapital(Lucas,1978)3orlocati onaladvantage(Jovanovic,1982)asarguablyt hemostenduringofa rm' ,Ibelieve,isthe ,aretheretime-invariantinter- rme ciencydi erencesinthesampletomatchtheobservedage- sizee ectingrowth?Secondly,isthereamatchingage -sizee ectin rmleveltechnicale ciency ?Thirdly,dohumancapitalandlocation variablessu -cientlyexplainage-sizee ectsine ciency ?Thecaseforpassivelearningasanimpo rtantfeatureofthelifecycleofownermanaged rmsisstrongerifeachofthesequestionsisans weredinthea (Mengis-tae,1997).Earlierreportsofthesam eresultfor rmgrowthindevelopedcountriesincludeEvans (1987),Dunne,RobertsandSamuelson(1989),V ariamandKraybill(1992)andDunneandHughes( 1994).2 Otherformulationsofthepassivelearningmod elareLucas(1978)andLippmanandRumelt(1982 )therelationofwhichtotheJovanovicmodelan dothermodelsofcompetitiveselectionisdisc ussedinMengistae(1997).

3 3 Theideathatentrepreneurialhumancapitalor `managementability'isamajordeterminantof inter- rmdi erencesintechnicale ciencyis,ofcourse,averyoldone( ,MarchakandAndrew,1944)andwasthethemeofc ontributionsofMundlak(1961)andHoch(1962) erencesto (1957)hasledtoawelldevelopedmethod-ologi calandempiricalliteratureonthemeasuremen tofe ,nopreviousstudyhasexaminedtherelationsh ipbetweenmeasurede ciencydif-ferencesandgrowthperformancein thesampleof ,noneofthestudiesthathavereportedage-siz ee ectsin rmgrowthwhiletestingselectionmodelshasat temptedtolinkthee ectstotheunderly-ingdistributionofe ,itisafeatureoftheexistingliteratureon rmlevele ciencythatvariablesareoftenchosenonanad- hocbasisaspossibledeterminantsofe ciencyamonga rm' ,thepassivelearningmodelestablishesahier archybetween rmsizeand rmageontheonehandandentrepreneurialhuman capitalandlocationontheotherinthedetermi nationof rmlevele ciencyscores:totheextentthatage-sizee ectsine rmdi erencesintechnicale (1968),Aigner,LovellandSchmidt(1977),Mee usenandvandenBroeck(1977),PittandLee(198 1)andBatteseandCoeli(1988).

4 Bauer(1991)andGreen(1993) (1980)andSchmidt(1986) (1993)isthe rstempiricalstudysofarthatIknowoftohavea nalysedinter- rmdi erencesine ndingofthestudyisthatthetimepathofthemea nleveloftechnicale ciencyishigherforincumbentsthanforfreshe ntrantswhich,inturn,isgreaterthantheaver agee ciencyoffailing ,thestudydoesnotdirectlyexaminethelinkbe tweene ciencyandgrowthperformanceamongsurviving rms, 'sformulationofthepassivelearningmodelag e-sizee ectsin rmgrowthandsurvivalarisefrompermanentbut competitiveinter- ,i,ofanindustryfacesacostfunctionthatisi denticaltotheindustryaverageorfrontierup tomultiplicationbyastrictlypositivetrans formation, (:),ofarandomerrorcomposedoftwoadditivec omponents iand! ,!it,registersapurelytemporary rmspeci 2!.Thecomponent, i,isa xedmeasureofthecostdisadvantageofthe ,itstruevalueisunknowntothe rm,whichonlyknowsthatthesamevalueisarand omdrawfromthedistributionN( ; 2 ) rmsandeach rmknowsthedistributionaswellastheexactfo rmof (:).

5 Because iisunknown,productiondecisionsarebasedon whatthe rmestimatesittobegivenpastrealisationsof ( i+!it).Productionthuscoincideswithaproce ssofBayesianupdatingofestimatesinthecour seofwhichthe ,theprecisionofestimatesincreaseswiththe durationofthe rm' iistoohighexperienceaseriesofbadcostshoc ks,updatetheircostestimatesupwardsaccord ingly, iisrelativelylowexperienceabetterserieso fshocks, rmsthatdosurvivetheselectionprocess,ther ateofgrowthdecreasesin rmsizeand (:) rmlevelcostfunctionassumedintheJovanovic modeliscit=c(q) ( i+!it)(1)Bytheprincipleofduality iisamonotonicandstrictlydecreasingtransf ormationofa rmspeci cproductivityparameteruiwhile!itisasimil artransformationofapurelytemporaryand rmspeci crandomproductivityshock (1)canbewrittenas4qit=h(z; )exp(ui+ it)(2)whereqitistheoutputof rmiduringperiodtforagivenvectorofinputsz , isavectorofparametersand ( i+!it)= [exp(ui+ it)];(3) 0<0 Forcomparabilityofresultswiththoseofprev iousempiricalwork,Iwillfurtherassumethat theproductionfunctionisCobb-Douglasandes timateyit= 0+mXj=1 jxjit+ui+ it(4)wheremisthenumberoffactorinputs, iisassumedtobearandomdrawfromaknowncommo ndistribu-tion, itiswhitenoisewithvariance 2.

6 Intheabsenceofanyrestrictiononthevalueof ui,thesumofthe rsttwotermsontherighthandsideofequation( 4)de nestheaverageproductionfunctionoftheindu stryfromwhichthedeviationoftheproduction techniqueof rmsizeand,therefore, (4)togetherwiththeassumptionthatthereisi ndeedsuchcorrelationasthe xede ectsav-erageproductionfunctionmodelofint er- rme ciencydi 's(1986)distinctionbetweenthe xed-e ectsandrandom-e ectsspeci ca-tionsofvariancecomponentmodelsontheba sisofwhetherornotindividuale (Mund-lak,1978).OntheotherhandtheGLSesti matorisconsistentandattainstheCramer-Rao lowerboundsunderthealternativerandome ,aHausman(1978)testofthe xede ectsaverageproductionfunctionmodelisaway oftestingwhethere ciencydependson rme ciencydi erence,namely,Mundlak(1961),Hoch(1962)an dTimmer(1971).5wayoftestingforthepermane nceofinter- rme ciencydi erenceistocon-ducttheBreuch-Pagan(1980)L agrangeMultipliertestoftheOLSformulation ofequation(4)againsttherandome ,wemaycarryoutalikelihoodratiotestoftheO LSmodelagainstthe xede (4)areBLUE onlyiftherestrictionofno rme ectsisvalidinboththe xede ectsandrandome xede ectsmodelandtothat 2u=0intherandome ("it"is)=0forallt6=s,where"it=ui+ ("2it)= 2.

7 Togetherwiththeassumptionthatuiisuncorre latedwithinputlevelstherestrictionui 0makesequation(5)arandom-e (1977)andMeeusenandvandenBroeck(1977).Wi thaddi-tionaldistributionalassumptionsab outuitherandom-e ectsproductionfrontiercanbeestimatedbyma ximumlikelihood,whichismoree cientthanFeasibleGLS, ,uiistruncatednormal, ,Ishallassumeintherestofthepaperthatuiis exponentialwithparameter .Giventherandome ectsfrontiermodel,thetechnicaline ciencyof (1988)haveproposedanunbiasedandconsisten tpredictorofjuijwhichisgivenfortheunbala ncedpanelcasebyeui=E(ui="i1;:::;"iTi)=bE i+b i[ (bEi=b i)= (bEi=b i)](5)where,bEi=b i +(1 b i)ei;b i=1+(b u=b );ei=T 1iTiXt=1eit;b i=b 2"qb i; (:)isthestandardnormalpdf, (:)isthestandardnormalcdf;eitistheresidu alcorrespondingtotheobservationon rmiattimet,Tiisthenumberofobserva-7 ThisamountstosayingthatGLScannotdiscrimi natebetweentheaverageproductionfunc-tion andproduction-frontierformulationsofinte r- rme ciencydi rmi.

8 Andthehatsymbolover , u, ,and " ciencyinthe xede ectsaverageproductionfunctionmodelisb i=max(bui) bui(6)wherebuiareestimated rm xede ectsfrontiermodelagainstthealternativeth at"it=ui+ itisdistributediidnormalwithmeanzeroandv ariance 2 isatestfortheexistenceofpermanentinter- rmdi erencesintechnicale ectsfrontiermodelagainstthe xede ectsmodelteststhenullthatuiisindependent of (4)undertheGauss-Markovassumptionsas`Mod elI',totherandom-e ectsfrontierproductionmodelas`ModelIIA', totherandom-e ectsaverageproductionfunctionmodelas`Mod elIIB'andtothe xede ectsmodelas`ModelIII'. rme ciencydi rstusedbyTimmer(1971),whoregressedestima tedFarrelmeasuresoftechnicale ciencyon (1991) ectsmodeltothecaseofunbalancedpanelsisdi scussedinHsiao(1986)andBaltagi(1995).Pit tandLee(1981)derivethelikelihoodfunction ofModelIIAforthebalancedpanelcasewithnor mal-half-normalerrortermswhileSeale(1990 ) (1991) ,forexample,inMartinandPage(1983),Kalira jan(1990)andReif-schneiderandStevenson(1 991).

9 Alternatively,wecanreplacetheFarellmeasu reasthedependentvariablebyascoreofe ciencythatisapositive,monotonictransform ationoftheformerbutisunrestrictedinrange (Lovell,1993).Theproblemwiththisapproach isthat,ifinputlevelsarecorrelatedwithtec hnicale ciencycontrarytowhatModelsIIAassumes,the ywillalsobecorrelatedwiththevery rmcharacteristicsthatareexpectedtoexplai nthevariationine ciency ,thetechniqueshouldbeusedonlyifthe Hausemantestdecisivelyrejectsthe xede ciencywas rstusedinPittandLee(1981).Itavoidsthebia sinherentinthe rstapproachbyincluding ,theappropriatespeci cationofthefrontierofModelIIAisyit=H(x;c : ;a)+ it+ui(7)wherecisavectorof rmcharacteristicsandaisthevectorofthecor respond-ingcoe ciencyisthenassessedbymeansoftheusualspe ci cationtestsandbylookingatwhathappenstoth eestimateof 2uasweincludethecharacteristicsinthespec i ,afterall,thatinputlevelsaresu cientlycorrelatedwiththe rmcharacteristicsnowaddedtothespeci rm xede ectsofModelIIIon rstusedbyPittandLee(1981).

10 Themethodisnotsubjecttotheomittedvariabl eproblemofthe ectsformulationiscomfortablyrejectedinfa vourof xede ,though,wheninputlevelsareuncorrelatedwi thindividual rme rmlevele ciencybasedontheapproachwillbelesse cientthantheirrandom-e rmcharacteristicsinthespeci ,achoicecouldnotbemadebetweenthe ciencyhadtoberegressedon8 rmcharacteristicsoverthefullsampleof ,therandom-e ectsmodelwasrejectedinfavourofthe xede ciencyscorespooledacrossindustriescouldn otthereforehavebeenjusti ciencyusedinapplyingthe rstapproachisdenotedbyDPANU andisde nedasthedeviationoftheBattese-Coelipredi c-tor,eui, ,asimilartransformationofestimated rm xede ects,denotedbySCOREF,isusedasadependentv ariableinsteadofindividual rme nedasthedeviationof rm xede ectsfromtheindustrysamplemeanofthee ,eui, xede rstoftheseisthatthereareage-sizee ectsine rmageand rmsizeproxyforentrepreneurialhumancapita landlocationaladvantageinasfarastheyexpl aine ciencyleadstohigher rstpropositioniscorrectthenownerhumancap italandlocationvariablesshouldentirelyex plainobservedinter- rme ciencydi ,theregressionofe ciencyscoreson rmageand rmsizeonlyshouldhaveatleastasmuchexplana torypowerasthealternativeregressionofthe samescoresonhumancapitalandlocationvaria bles, cientsofage-sizevariableswouldnotalsobea shighlysigni ectsine ectthatsurvivesthefullcontrolforvariatio ninentrepreneurialhumancapitalandlocatio nadvantagewouldsuggestalternativesources suchaseconomiesofscaleandcompetitive9 Theadditionofindustrydummiesinthee , ,agee ectsthatwouldfailtodisappearwhenwefullyc ontrolforhumancapitalandlocationmaysigna lothersourcessuchasthein uenceof rmageonreplacementcostsofcapitaland,henc e,one rme ciencydi.