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.

2 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.

3 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).

4 Earlierreportsofthesameresultfor rmgrowthindevelopedcountriesincludeEvans (1987),Dunne,RobertsandSamuelson(1989),V ariamandKraybill(1992)andDunneandHughes( 1994).2 Otherformulationsofthepassivelearningmod elareLucas(1978)andLippmanandRumelt(1982 )therelationofwhichtotheJovanovicmodelan dothermodelsofcompetitiveselectionisdisc ussedinMengistae(1997).3 Theideathatentrepreneurialhumancapitalor `managementability'isamajordeterminantof inter- rmdi erencesintechnicale ciencyis,ofcourse,averyoldone( ,MarchakandAndrew,1944)andwasthethemeofc ontributionsofMundlak(1961)andHoch(1962) erencesto (1957)

5 Hasledtoawelldevelopedmethod-ologicaland empiricalliteratureonthemeasurementofe ,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).

6 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!

7 ,!it,registersapurelytemporary rmspeci 2!.Thecomponent, i,isa xedmeasureofthecostdisadvantageofthe ,itstruevalueisunknowntothe rm,whichonlyknowsthatthesamevalueisarand omdrawfromthedistributionN( ; 2 ) rmsandeach rmknowsthedistributionaswellastheexactfo rmof (:).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+!)

8 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.

9 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).

10 5wayoftestingforthepermanenceofinter- 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 .Togetherwiththeassumptionthatuiisuncorr elatedwithinputlevelstherestrictionui 0makesequation(5)arandom-e (1977)andMeeusenandvandenBroeck(1977).Wi thaddi-tionaldistributionalassumptionsab outuitherandom-e ectsproductionfrontiercanbeestimatedbyma ximumlikelihood,whichismoree cientthanFeasibleGLS, ,uiistruncatednormal, ,Ishallassumeintherestofthepaperthatuiis exponentialwithparameter.