DynasticManagementFrancescoCaselliandNicolaGennaioliFirstDraft:April20 - PDF document

DynasticManagementFrancescoCaselliandNicolaGennaioliFirstDraft:April2002;ThisDraft:December2002HarvardUniversity,CEPR,andNBER(caselli@harvard.edu);HarvardUniversity(gen-naiol@fas.harvard.edu).WithusefulcommentsbyLuigiGuiso,CaseyMulligan,AndreiShleifer,andSilvanaTenreyro. AbstractDynasticmanagementistheinter-generationaltransmissionofcontroloverassetsthatistypicaloffamily-ownedrms.ItispervasivearoundtheWorld,butespeciallyindevelopingcountries.Wearguethatdynasticmanagementisapotentialsourceofciency:iftheheirtothefamilyrmhasnotalentformanagerialdecisionmaking,meritocracyfails.Wepresentasimplemodelthatstudiesthemacreconomiccausesandconsequencesofthisphenomenon.Inourmodel,theincidenceofdynasticmanagementdependsontheseverityofasset-marketimperfections,ontheeconomy’ssavingrate,andonthedegreeofinheritabilityoftalentacrossgenerations.Wethereforeintroducenovelchannelsthroughwhichnancial-marketfailuresandsavingratesaectaggregatetotalfactorproductivity.Numericalsimulationssuggestthatdynasticmanagementmaybeasubstantialcontributortoobservedcross-countrydierencesinproductivity. 1IntroductionThereisbroadagreementthatdierencesinaggregateTotalFactorProductivity(TFP)constitutealargefractionoftheexistingcross-countrydierencesinper-capitaincome.Thatis,notonlydopoorcountrieshavefewerproductiveresources,suchasphysicalandhumancapital,buttheyalsoemploythoseresourceslesseectivelythanrichcountries.Naturally,then,attentionisincreasinglyturningtopotentialexplanationsfortheseTFPdierences,andvariousauthorshaveemphasizedlagsintechnologyusion,inappropriatetechnology,ethnicconict,geography,vestedinterestsandotherinstitutionalfailures,andseveralothercauses.Webelieve,however,thatapotentiallycriticalsourceofineciencyhassofarbeenlargelyoverlooked:failuresofmeritocracy.Individualsaremanifestlyheterogeneousintheirdecision-makingskills.Dier-encesacrosscountriesintheaccuracywithwhichthebestdecisionmakersareselectedforimportantdecision-makingresponsibilities—i.e.dierencesinmeritocracy—canclearlyresultintodierencesinthereturnscountriesreapfromtheirproductivere-sources—i.e.dierencesinTFP.Meritocracycanfailspectacularlyinthepublicsector.Butmeritocracycanalsofailintheprivatesector.Thispaperstudiesthemacroeco-nomiccausesandconsequencesofaparticularprivate-sectornon-meritocraticprac-tice:theinter-generationaltransmissionofmanagerialresponsibilitiesinfamilyrms,awidelyobservedphenomenonthatwecalldynasticmanagement.Inafrictionlessworldthereislittleeconomicjusticationforthefactthatmanyrmsaremanagedbytheirowners.Whiletheallocationofcashowrightsshoulddependonthedistributionofwealth,andonincentivesforriskdiversication,theallocationofmanagerstormsshouldmainlydependonthedistributionofmanagerialtalent(presumably,withmoretalentedmanagersmanaginglargerassets—asinLucas,1978).Inreality,itveryoftenoccursthattheownershipofrmsisconcentratedinfew SeeIslam(1995),Caselli,Esquivel,andLefort(1996),KlenowandRodriguez(1997),HallandJones(1999),ParenteandPrescott(2000),Hendricks(2002),CaselliandColeman(2002),andCaselli(2003).Non-meritocracyinthepublicsectorisstudiedinCaselliandMorelli(2002).Ournotionoffailuresofmeritocracyisdistinctfromtheproblemofsociallyinecient“allocationoftalent”studiedbyMurphy,Shleifer,andVishny(1991).Theyareconcernedwithsituationswerethemosttalentedindividualssucceedatmaximizingtheprivatereturnontheirabilities,butthisdoesnotleadtosocial-returnmaximization.Failuresofmeritocracy,instead,aresituationswherethetalentedarepreventedfrommaximizingboththeprivateandthesocialreturnoftheirskills. hands—oftenmembersofafamily—andthatthesefamily-ownedrmsaremanagedbyfamilymembers.Thecombinationoffamilyownershipwithfamilymanagementgivesrisetodynasticmanagement:notonlythepropertyoftheasset,butalsoitsmanagement,passesonacrossgenerationsofthesamefamily.Thispracticeexistsvirtuallyeverywhereintheworld,butismuchmoreprevalentinpoorercountries.Itisclearthatatanypointintimetheidenticationofownershipandman-agementimpliesapotentialineciency,ifthedistributionsoftalentandwealthdonotcoincide.Whenonenoticesthedynasticaspectofsuchidentication,however,theciencygoesfrombeingpotentialtobeingavirtualcertainty:evenallowingforselfselectedinitiatorsoffamilybusinesses,unlessmanagerialtalentisperfectlycorrelatedacrossgenerations,itisinevitablethatassetswillsoonerorlaterendup“inthewronghands,”i.e.thoseofamanageriallyineptdescendant.Weproposeagrowthmodelwheredynasticmanagementarisesendogenously,andlookattheconsequencesofthisfailureofmeritocracyforthedynamicevolutionofTFPandcapitalaccumulation.Inourmodelthefrictionsthatgiverisetodynasticmanagementarefeaturesofacountry’snancialandcontractualinfrastructure.Untalentedheirsoffamilyrmswouldliketotransfercontroltonewtalentedowners,orhiretalentedmanagers.However,imperfectnancial-contractenforcementdiscouragesownershipchanges,andcostlymonitoringmakesitdiculttowritemanagerialcontracts.Sincetheseverityoftheseimpedimentstothetransferofcontroldependsontheseverityoftheasset-marketimperfections,cross-countryvariationinthelatterwillleadtocross-countryvariationintheincidenceofdynasticmanagement,andofTFPwithit.Hence,thepaperbringsoutanovelchannelthroughwhichnanceaectsdevelopment. Analternativewaytogeneratedynasticmanagementistoassumethatmembersofafamilythathashistoricallybeenassociatedwithaparticularrmderiveasenseofidentityfromcontinuingintheassociation(see,e.g.,Mann,1901).Thisisequivalenttoputtingthe“frictions”intheutilityfunction,andwouldgeneratedynasticmanagementevenineconomieswithperfectlyecientnancialmarkets,asfamilieswouldbemoretoleranttowardsuntalentedheirs.However,cross-countrydierencesintheincidenceofthephenomenonshouldstillvarywithnancial-marketimperfections,asthereshouldbethresholdsofineciencythatwouldbeintolerabletoeventhefamilieswithgreatestattachmenttorm.Furthermore,theimplicationsofdynasticmanagementforaggregateeciencyandgrowthwouldbesimilar.Another,morebenign,viewofdynasticmanagementisthatitiseasiertotransmitrm-specicmanagerialhumancapitaltoone’sospringthantooutsiders.Aswewilldiscuss,theempiricalevidenceisratherunfavorabletobenignviewsofdynasticmanagement.Moreover,eveniffamilymembersdohavegreaterrm-specichumancapital,itshouldonceagainbestillbetruethat—belowacertainleveloftalent—eciencystillrequiresatransferofcontrol.Hence,thesealternative Besidestheeciencyofnancialmarkets,twootherfactorsthatinuencethedynamicpropertiesofthemodelaretheintensityofthebequestmotiveacrossgener-ations—akintoaSoloviansavingrateinthecontextofourmodel—andthedegreeofintergenerationalheritabilityofmanagerialtalent.Ahighersavingrategenerallyimpliesgreaterbequestsreceivedbypotentialbuyersofrms.Sinceinourmodelthesebequestsareusedascollateral,inordertoovercomecontractualimperfections,thistendstofacilitatethetransferofcontrolrightsamongrms,andhencetendstoenhanceeciency.Therefore,themodelalsouncoversanovelsourceofcausationfromsavingtoproductivity.Ahigherdegreeofheritabilityofaparent’stalentbyherospringalsoincreasesTFP.Toseethis,considertwoextremecases:thecasewheretalentisperfectlycor-relatedacrossgenerations,andthecasewherethetalentofeachgenerationisdrawnfromindependentandidenticaldistributions.Withperfectcorrelationoftalentthein-cienciesassociatedwithdynasticmanagementbecomelessandlessimportantovertime,andeventuallydisappear.Thisisbecause,inourmodel,well-runrmsincreaseinsizerelativetotheaveragermsize,whilebadly-runrmsshrink.Sincetalentisperfectlypersistentthisimpliesthatasymptoticallywell-runrmsaccountfor100%ofthecapitalstock.Notsointhecasewheretalentisindependentlydistributedacrossgenerations:heretheinecienciespersistinthelongrun,asineveryperiodsomelargermsareinheritedbysomelow-talentindividuals,whowillinturnholdontocontrol.Intermediatecasesgenerateintermediateamountsofsteady-stateineciency.Besidesthekeyinsightsdescribedabove,themodelfeaturesawealthofaddi-tionaltestableimplications.First,wendthattheseverityoftheeectofnancialimperfectiononopportunitiesfortransfersofcontroldependsontherm’ssize.Ceterisparibus(i.e.foragivendegreeofcontractualimperfection)theineptownersofsmallrmsaremorewillingtopartwiththeirassetsthantheineptownersoflargerms.Intuitively,theoutsideoptionrepresentedbythelabormarketisamoreviablealter-nativewhenoneispartingwithasmall-scalebusinessthanwhenoneisrelinquishingcontroloveralargeempire.Furthermore,asmallercollateralisrequestedtopurchaseasmallrm,somoreagentsintheeconomycancollateralizethepurchaseofsmallrmsthanoflargerms.ThissizeeecthasinterestingandnovelimplicationsfortherelationbetweenthesizedistributionofrmsandTFP.Foragiveneconomy-widecap-italstock,afewlargermsimplyalargerconcentrationofassetsininepthandsthan storiesmaymitigate,butnoteliminate,theeciencycostsofdynasticmanagement. inthecaseofmanysmall-sizedrms:countrieswithmoreconcentratedownershipwillbelessecient.Inaddition,thereareinterestingfeedbackeectsbetweentheassetmarketandthelabormarket.Forexample,thelargertheoverallfractionofthecapitalstockthatismanagedcompetently,thehigherisaggregateTFP,andthusthehigheristheaveragewageintheeconomy.But,inturn,ahigheraveragewagemakesitlessprotableforalow-talentownertoholdontomanagerialresponsibilities,leadingtoevenmorermsbeingtransferredtotalentednewowners:thebenecialeectonTFPisthusmagnied.Thehigheraveragewagealsotranslatesintogreaterbequests,andhencemoreopportunitiesforcollateralizedcontroltransfers,furtherreinforcingthisvirtuouscycle.Weconcludethepaperwithnumericalsimulationsaimedatassessingthepo-tentialquantitativerelevanceoftheproblemofdynasticmanagement.Underareason-ablecalibrationoftheparameterthatregulatestheinter-generationalinheritabilityoftalent,wendseverepotentialconsequencesofdynasticmanagementonTFP.Inpar-ticular,thischannelalonecancauseacountrywithveryinecientnancialmarketstohaveTFPlevelsaslowas80%oftheTFPlevelsofacountrywithwellfunction-ingmarkets.Thesimulationsalsogeneratelargevariationsinsteadystatecapitalstocks.Finally,theshapeofthesteadystatesizedistributionofrmspredictedbythesimulationsisremarkablyconsistentwithempiricalevidence.2LiteratureReview2.1EmpiricalInthissub-sectionwereviewempiricalstudiesthatdocumentthefollowingfacts:(i)Familyownershipandfamilymanagementarepervasivearoundtheworld,particularlyindevelopingcountries,andincountrieswithinecientassetmarkets;(ii)Dynasticsuccessionisonaverageassociatedwithdeclinesinperformance,bothatthemicroandatthemacrolevel;(iii)Thereisastrongpositivecross-countryrelationbetweennancialdevelopmentandgrowth.Allthreesetsoffactsareimportantpredictionsofourmodel.Familyownershiparoundtheworld.Themostcomprehensivedataoncor-porateownershiparoundtheworldhasbeencollectedbyLaPorta,De-Silanesand Shleifer(1999),wholookatthecontrolstructureofthe20largestpubliclytradedcompaniesin27(mostlywealthy)economiesin1995.Onaverageacrossthesecoun-tries,familyownershipisthecontrolstructureof30%ofcompanies.Thenumbersforthemiddle-incomecountriesinthesampleareespeciallystriking:65%inArgentina,50%inGreece,100%inMexico,45%inPortugal;onlySouthKorea,witha20%inci-dence,isbelowthe“World”average.Furthermore,inalmost70%ofthefamily-ownedrmsthecontrollingfamilyisdirectlyinvolvedinmanagement(CEO,HonoraryChair-man,Chairman,orVice-Chairman).Becausethisisbasedoncomparisonsofthelastnamesofmanagersandowners,itprobablyconstitutesanunderestimate.Finally,countrieswithlowinvestorprotectionexhibita12%highershareoffamilyrmsthancountrieswithhighinvestorprotection.Byfocusingonlyonpubliclytradedcompanies,andonlyonmiddle-to-highincomecountries,LaPorta,De-Silanes,andShleiferalmostcertainlyunderestimatetheworld-wideimportanceoffamilyrms.The3,033respondentstotheArthurAndersen/Mass.MutualAmericanFamilyBusinessSurvey’97accountforcombinedrevenuesof$67.4billion,medianrevenuesof$9million,andmodalrevenuesof$10million,suggestingthatfamilybusinessesaccountforanimportantfractionofeventheUSeconomy.AccordingtoTheEconomist,twothirdsofGermany’ssmallandmediumbusinesses(Mittelstand)aremanagedbytheowners(October15th,1998),and40%ofmanagerialsuccessionsinvolvearelativeofthedepartingCEO(December13th,2001).Dreux(1990)andGersicketal.(1997),usingconservativeestimates,claimthattheproportionofrmsownedormanagedbyfamiliesintheworldisbetween65and80%.PerrowandLansberg(1990)emphasizetheimportanceofthesocalledLatinAmericangrupos,largeindustrialgroupsdiversiedonseveralsectorsthatremainunderthetightcontrolofthefounderandofhisheirs,andresorttoverylittleoutsideequitynanciers.TheEconomistreportsthatfamilyrmsgenerate70%oftotalsalesandnetproofthebiggest250Indianprivatecompanies(October5th,1996),andthatthetop15familiescontrolover60%oflistedcorporateassetsinIndonesia,between50and60% Itisfuntogothrougha(veryincomplete)listofmajorUScorporationswherethedescendantsofthefounderstillholdcriticaldecision-makingpositions:Hewlett-Packard,Wal-Mart,Motorola,Nordstrom,Coca-Cola(theglobalsymbolofAmericancapitalism),Ford,IBM,andTheNewYorkTimes(TheEconomist,November17th,2001).Inthisstudyafamilyrmisidentiedashavingauniqueprivateshareholderwhocontrolsmorethan20%ofthevotingrights.Thisisclearlyaveryrestrictivecriterion,asmuchsmallervotingsharesareusuallysucienttodeterminecontrol. inthePhilippinesandThailand,over30%inSouthKoreaandHongKong,andover20%inSingapore,Malaysia,andTaiwan(April7th,2001).Dynasticsuccessionandperformance.Clearlythispapertakesafairlyneg-ativeviewofdynasticmanagement,andsomeformalpiecesofempiricalevidencelendsupporttothisview.Volpin(2002)examinesthedeterminantsofexecutiveturnoverrmvaluationforallItaliantradedcompaniesfrom1986to1997,andndsthatpoorgovernance—asmeasuredbothasalowsensitivityofexecutivesturnovertoper-formance,andasalowQratio—ismorelikelywhenthecontrollingshareholdersarealsotopexecutives.AsimilarresultisfoundfortheUS.byDenisandDenis(1994).Alongsimilarlines,Perez-Gonzales(2001)examinesasampleofCEOtran-sitionsinfamilyrms.HedenesafamilyrmasonewheretheretiringCEOisrelatedtotherm’sfounder,andndsthatwhentheincomingCEOisrelatedtotheretiringCEOtherm’sperformancesuers,relativetothecasewhereincomingandretiringCEOsareunrelated.Forexample,returnsonassetsinthe“inheritedcontrol”casesfall20%withintwoyearsofthenewCEO’stenure,whileinunrelatedtransi-tionstheydon’tchangemuchonaverage.HealsondsthatcaseswhereinheritedcontrolisaccompaniedbydeclinesinperformancearelargelyexplainedbythepooracademicrecordoftheinheritingCEO.Thissuggests—consistentagainwiththeviewemphasizingproblemsofmanagerialquality—thattheeciencylossesarelinkedtothemanagerialabilities(orlackthereof)oftheheir.TheseresultsarealsoconsistentwiththoseobtainedbyMorck,StrangelandandYeung(2000),wholookatasampleofCanadianrmsmanagedbyheirsofthefounderandndthattheyunder-performsimilarUS.rmswithdispersedownership.TheMorck,StrangelandandYeungstudyalsocontainsamacroeconomicver-sionofthistest.TheyuseinformationfromForbes1000toshowthatcountriesinwhichbillionaires’heirswealthislargewithrespecttoGDPgrowlessthancountrieswhereitissmall.Ontheotherhand,countrieswherethewealthofself-madebusiness Consistentwithourmodel,thestoryonIndiaalsospeculatesthatnewregulationsaimedatenhancingtheprotectionofminorityshareholderswillleadtoarelaxationofthestrangleholdoffamiliesontheeconomy.However,healsondsthatrm’ssize(asmeasuredbyassets)doesnotpredictdynasticsuccession,whichisinconsistentwithourmodel(wheredynasticsuccessionshouldbemorelikelyinlargerrms).Thisresultisnotconclusive,however,ashissampleiscensored:itonlyincludesrmswithmorethan5milliondollarsinsales.Itcouldbethattheprobabilityofdynasticmanagementattensoutaboveacertainsizethreshold. entrepreneursbillionairesislargewithrespecttoGDP,growmorethancountrieswhereitissmall.Theseresultsseemtosuggestthathysteresisofcontrolalongdynasticlinesisanimportantdeterminantofmacroeconomicperformance.FinanceandGrowth.KingandLevine(1993)documentedapositiveasso-ciationbetweennancialdevelopmentandeconomicgrowth.Sincethentheirndingshavebeenreplicatedmanytimesover,mostnotablybyRajanandZingales(1998),whousedaninstrumental-variableapproachtomakeconsiderableprogresstowardses-tablishingacausallinkbetweenthetwo.Traditionally,theliteraturetendstoexplainthesendingsintermsofcoordinationofsavingandinvestmentdecisions:nancialmarketsmustallocatefundstothebestprojects.Inthecontextofourmodelthere-sultemergesinsteadthroughthereallocationofmanagerialcontrolofalreadyexistingassetstomoretalentedagents.2.2TheoreticalIneconomics,familyrmstendtobeviewedassecond-bestsolutionstoagencyproblems.Chami(2001)viewsthefamilyrmasaprincipal-agentrelationshipbetweenpar-ent/ownerandchild/employee.Trust,altruism,andtheprospectofsuccession(thatmakesthesonaclaimanttofutureprots)allmitigatetheagencyproblem,relativetothesituationwheretheparenthiresoutsideemployees.Heabstractsfromthepos-sibilitythatthechild(andheir)isuntalented.Thispossibility,instead,isconsideredbyBurkart,PanunziandShleifer(2002),whoviewfamilycontrolasaresponsetopoorshareholderprotection.Incountriescharacterizedbyrampantexpropriationofshareholdersbymanagers,theownersofproductiveassetsprefertoholdontocontrol,evenifanoutsidemanagerwouldbebettersuitedtoruntherm.Clearlyourpapertakesthesameviewofthesecond-bestproblemsolvedbyfamilyrmsasBurkart,PanunziandShleifer(2002).Ourcontributionistotakethestaticandpartial-equilibriummodeloffamilysuccessionwithpoorinvestorprotection,andembeditinageneralequilibriumgrowthmodel,whereweformalizetheinterac-tionsbetweenthelabormarketandtheassetmarket,thestochasticprocesslinkingthetalentsofparentsandchildren,andthemechanismsthatgiverisetocapitalaccumula-tionovertime.Thisallowsustostudytheimpactoffamilyrmsonlong-runaggregate Contributionsinbusinessandsociologyemphasizetheimportanceofsharedculturalvaluesandcommonbeliefsinfosteringcommitmentandlongrunplanning(Gersick1997,Lansberg1983,Davis1983). ciencyandcapitalaccumulation,athemethathasnotsofarbeenexploredineitherthecorporatenanceorthegrowthliterature.Asthereisanempiricalliteratureonnanceandgrowth,soisthereatheoreticalone.Bystressingnancialimperfectionsasoneofthesourcesofdynasticmanagement,clearlyourpaperisacontributioninthiseld.Particularlyrelatedtooursaremodelswherenancialimperfectionsaectoccupationalchoice,suchasBanerjeeandNew-man(1993),Ghatak,Morelli,andSj¨ostr¨om(2001),andespeciallyGhatak,Morelli,andSj¨ostr¨om(2002).Inthelatterpaper,asinours,collateralconstraintsimplythatrich-but-untalentedindividualsoccupymanagerialpositions,whilepoor-but-talentedonesare“workers.”Anothersimilarityisthatthewageratecreatesafeedbackeectbetweenthelabormarketandtheallocationoftalent,creatingthepotentialformul-tipleequilibriaanddevelopmenttraps.Indeed,thismultiplicityisthemainfocusoftheir(static)model.Wearemoreinterestedinintergenerationallinkages,andhenceintheeconomy’sdynamics.3TheModelWestudyaneconomyindiscretetime.Ineachperiodthereisacontinuum(ofmeasure1)ofone-period-livedindividuals.Anindividual’smanagerialtalentiscanbe ,orlow, isthefractionofagentsoftype .Eachagentengagesinasexualreproductionofoneospring,whowilllivenextperiod.Tothisospringtheagentbequeathsafractionofhisorhercurrentincome,whileconsumingtherest.Eachagentobjectiveistomaximizecurrentincome.Theeconomyisendowedwithameasurerms.Eachcombinesmanagerialinputwithcapitalandlabortoproduceoutputaccordingtotheproductionfunction:Thekeyassumptionisthattheeciencylevelectstheabilityofthemanager: Ontheotherhand,ourmicro-modeloffamilysuccessionismuchmorerudimentarythantheoneofBurkart,Panunzi,andShleifer(2002).Forexample,theirsisrichenoughthattheycandistinguishbetweentwotypesoffamilyrms:thosewherebothownershipandmanagementarekeptinthefamily,andthosewherethefamilymaintainsalargecontrollingstake,andexploitittokeepaparticularlywatchfuleyeontheoutsidemanagerithires.Theyndthattheformertypeoffamilyrmprevailsnacialmarketsareveryundeveloped,andthelatterwhentheyareatintermediatestagesofdevelopment(thewidelyownedcompanyprevailswhenmarketsarehighlydeveloped). ifthemanageristalentedthen ,ifheisnot,then .Eachrmmusthaveonemanagerandeachmanagercanonlymanageonerm.Investmentsincapitalareirreversibleandrm-specic:existingcapitalcannotbereallocatedamongrms,norconvertedbackintoconsumption.Hence,arm’scapitalchangesonlythroughnewinvestment(anddepreciation).Weassumethattimeisrequiredtobuild,soinvestmentdecisionschangethecapitalstockwithaoneperiodlag.Asaresultofthissetofassumptions,inagivenperiodisastatevariablefor.Finally,thenumberofrms,,isgivenandconstant.Wealsoassumesothatineciencydoesnotarisetriviallyforlackofasucientnumberofpotentialtalentedmanagers.Giventhissetup,fortheeconomyasawholethe“statevariables”atthebeginningofeachperiodarethesizedistributionofrms,andtheirallocationtoownerswithdierenttalent.Giventheseinitialconditions,ineachperiodthefollowingsequenceofeventsandactionstakeplace.First,amarketfortheownershipofmeets.Individualscanbuy(sharesin)rmsinexchangeforunitsofoutput,orinexchangeforpromisestodeliverunitsofoutputattheendoftheperiod.Thismeetingoftheassetmarketdeterminesanewdistributionofownership.Ownersthenturntothelabormarket,whereeachrmhiresworkersatacompetitivewage,.ThisdeterminesTheresourcesoftheeconomyhavingthusbeenallocated,productiontakesplace,givingriseforeachrmtooutputandpro.Itisherethatthecontractualfrictionsbite.Peoplewhohaveborrowedtobuysharesinrmsdecidewhetherornottorepaytheirdebts.Courtsinthiseconomyhavetheabilityofseizingafractionoftheresourcesofapartyinviolationofcontractualcommitments,suchasadebtorthatfailstorepaythecreditorinfull.Defaultdecisionstakethisfactintoaccount,anddeterminetheend-of-perioddistributionofincome.Giventheirincomes,agents Theone-manager,one-rmassumptionsimpliestheanalysisbutisnototherwisecrucial.Itcanbejustied,however,onthegroundthatamanager’stimeandenergyarelimited.Similarly,allowingforreversibilityofcapitalwouldcomplicatethings,butnotchangethemainconclusions.Atthesametime,irreversibilityofthekindweproposeisalsonotunrealistic.Theimportantassumptionisthatthenumberofrmsisxed,whichallowsustoabstractfromissuesofentry.Acaponthenumberofrmscouldbeendogenizedinthismodelbyintroducing(sucienclylarge)xedcostsofentry,whichdoesnotseemunrealistic,especiallyindevelopingcountries.Inthepresentcontextwithnoentryonecanthinkofasthenumberoflicenciesissuedbythegovernemnttooperateplants.Oronemaythinkofthemasaxednumberof“trees,”wherethegrowthandyieldofthetreedependsonthegardener’sability. proceedtoallocateittoconsumptionandbequestsasdetailedabove.InAppendixA.1wefurtherextendthismodeltoasituationwhere—asanalternativetosellingtherm—untalentedrmownerscantransfercontrolbyhiringatalentedmanager.Weshowthatthisextensiondoesnotchangeourqualitativeresults.Thereasonisthatmanager-ownerrelationshipsarealsogenerallymoreorlessviable,dependingonthequalityofaneconomy’scontract-enforcementinfrastructure.Countrieswherethecourtshaveadiculttimeenforcingdebtcontracts,willalsohaveadiculttimeprovidingmanagerswiththeincentivesnottostealarm’sprots—ifnotitsassets—fromtheowner-principal.Hence,whenonesolution(transferofownership)isunfeasible,somoreoftenthannotistheother(hiringamanager).4StaticEquilibriumInthissectionweabstractfrombequestsandosprings,wetakethestatevariables(initialdistributionofamongindividuals)asgiven,anddeterminethestaticequilibriumallocationofmanagerialtasksandoveralleciency.Inthenextsectionwelookatthedynamicimplications.4.1LaborMarketItisusefultobeginbycharacterizingrms’behavioronthelabormarket.Allrmown-ersseektomaximizeprots,whichinourcontextaregivenbytakingthewageasgiven.Theresultinglabordemandfunctioncanbeaggregatedamongrms,andtheaggregatelabordemandfunctionturnsouttobe w¶1 µs 1 + s 1 whereistheaggregatecapitalstock(or isthefractionoftheaggregatecapitalstockinrmsrunbyincompetentmanagers[ =Ri;Ai= (Ki isthefractionofrmsruncompetently[ =Ri;Ai= ].Notethat .Itshouldalsobeclearthattheterm 1 + s 1 isameasureoftheaverageeciencyintheeconomy.Thismakestheaggregatelabordemandfunctionveryintuitive.Becausetherearermsafractionofthepopulationworkasmanagers.Hence,theremaining1constitutestheaggregatelaborsupply.Settinglabor demandequaltolaborsupply,wecansolvefortheequilibriumwagerate:=(1 1f!µs 1 + s 1 Theequilibriumwagedependsontheaggregatecapital-laborratio,),andonthewaythecapitalstockisdistributedbetweentalentedandnon-talentedowners:thegreater ,thegreatertheoveralleciencyoftheeconomy,thehigherworkers’wages.Pluggingtherm’slabordemandandthewagefunctionsintheexpressionforrm’soutput,andaggregatingacrossrms,weobtainthefollowingexpressionforaggregateGDPperworker: 1f=ÃK 1f!µs 1 + s 1 where.Thisillustratestheniceaggregationpropertiesofthemodel:despitetheexistenceofarbitraryheterogeneityinthermdistributionofcapitalandeciency,aggregateoutputcanbedecomposedintothecontributionsofcapitalintensity,anda“TFP”term, 1 + s 1 .TFPinthismodelisentirelydeterminedbythefractionofthecapitalstockthatismanagedeciently, (andbythedierenceinrm-levelTFPbetweentalentedandnon-talentedowners, / ).Thismakes theendogenousvariableofgreatestinterestinthispaper.’sprotsaregivenby i (s 1 + s 1 )Ki whereisaggregateprots.Hence,theshareofaggregateproisabletocaptureisincreasingintherm’srelativesizeandinmanagerialtalent,Also,andmostnotably,isdecreasingin :throughtheaggregatewagethequalityofmanagementinotherrmsgeneratesanexternalityonsownprotability.4.2MarketforFirmsEquilibriumprotsandaggregateeciencydependonthemanagerialtalentoftheowner.Managerialresponsibilitiescanbere-allocatedfromlow-tohigh-talentindi-vidualsthroughtransferofownership.Inthissectionweassumethatindividuals(other ConsistentwiththeCobb-Douglasavorofaggregateoutput,itcanalsobeshownthatprotsareafractionofaggregateoutput,or.Itfollowsthattheaggregatewagebillis(1 rmowners)begintheperiodwithnoassets,andhencetheonlywayforthemtopurchaseownershiprightsonarmisthroughadebtcontract.Wewillrelaxthisrestrictionwhenweintroducebequestsinthenextsection.Thesalecontractforspeciesapricethatthebuyerwilltransfertothesellerattheendoftheperiod.Thebuyerwillnancethisrepaymentoutoftheproowfromtherm.Tominimizeincentivestodefaultthecontractspeciesthat,ifthebuyerfailstorepay,thesellerisentitledtoseizingtheproowfromtherm.However,theenforcementofcontractsisimperfect.Inparticular,everytimeapartytoacontractisindefaultofhiscontrac-tualobligations,courtsareonlyabletoseizeandtransfertotheplaintiafractionofthedebtor’sresources.ThereforewewillobservedefaultwheneverClearlyonlytransfersofpropertyfromlow-tohigh-abilityindividualswilltakeplace.Welookfortransactionsthattakeplaceatpricesthatdonottriggerdefault,i.e.thatsatisfythecondition.Suchtransactionsmustbeappealingtoboththesellerandthebuyer.Theseller’sparticipationconstraintis.Thelefthandsideishisincomeifhesells:theproceedsfromthesaleplusthewagesheearnsonthelabormarketonceheisfreefrommanagerialduties.Therighthandsideishisincomeifhedoesnotsell,i.e.theprotsfrom(ineptly)managingtherm.Forthebuyer,theanalogousconditionis:hecomparestheprotstreamfromowningtherm,netofpurchasingcost,tohisoutsideoptionrepresentedbythemarketwage.Rewritingthesethreeconditionsslightlyweseethatano-defaultsaleoccursifandonlyif:CombiningthersttwoconditionsgivesrisetotherestrictionIntuitively,isthe“pie”createdbythetalentedbuyer,andthelargeristhelargeristheslicethatthesellercancarveforherself.Inaddition,bysellingthermshegainsaccesstoawage,butlosesuntalentedpro.Thethirdconditiononly Introducingthepossibilityofborrowingfromthirdparties(e.g.foreignbanks)doesnotchangetheresults.ThereasonisthatitdoesnotchangetheIncentiveCompatibility,andBuyerandSellerParticipationconstraintsthatwestatebelow. imposestheadditionalrestrictionthat0,i.e.thatrmsareviable.Foreaseofexposition,weassumethatthisholdsforallrmsintherestoftheformalanalysis,butwillkeeptrackofthisconditioninthenumericalsimulations.Whileitisclearwhencontrolwillbetransferred,thepriceatwhichthistrans-fertakesplaceis(partially)indeterminate.Clearlythepricemustbeintherangeminanditmustdependonthebargainingpowerofthetwoparties.Inthecurrentcontextitseemslegitimatetoassumethatallofthebargainingpowerresidesintheseller.Thisisbecausewehaveassumedthattherearemoretalentedmanagersthantherearerms,sormsareinexcessdemand.Ifoneiswillingtoassumethatallofthebargainingpoweriswiththeseller,then=min4.3ImplicationsforMeritocracyEquation(4)isthekeynecessaryandsucientconditionforcontroloveranassettobetransferredfromalow-toahigh-talentindividual.Combiningthiswiththeprofunction(3)wendthatsalesofrmsarefeasibleforandonlyforrmsthatsatisfythecondition: 1 1 ¶ µs 1 + s 1 ¶Ki K+) 0(5)Itisimmediatethattherearetwomaincasestoconsider. 1/ .Inthiscase(5)isalwayssatised.Hence,allassetsareeciently Evenifapricethatavoidsdefaultdoesnotexist,thetwopartiesmaystillinpricipleagreetoatransferofpropertyiftheoutcomeofdefaultmakesbothbettero.TheconditionsthatmustbesatisedforthistooccurareNotethatwhenevertheconditionsforatransactionfeaturingdefaultaresatised,soaretheconditionsforatransactionwithnodefault.Hence,wecansimplyfocusontransactionswithnodefault,i.e.Wehaveimplicitlyassumedthatthereisonlyonebuyer,asopposedtoaconsortiumofbuyers.Aconsortiumofbuyerswouldhavetheexactsamecollectiveincentivetodefaultasasinglebuyer.Furthermore,theywouldfaceagencyproblemswithregardstothemanagementoftheasset. managedinequilibrium.Thistranspiresifislargeenough.Withgooden-forcementofcontractstheagencyproblemsthatgiverisetountalented-ownermanagementaresolvedthroughswiftandecientrecoursetothecourts.Untal-entedownerscansitbackandrelaxwhiletalentednewownersrunthebusiness.Thiscasealsoprevailswhen islargerelativeto ,orthedierencesinmanage-rialskillsarelarge.Thesearecaseswherethereisabigsurplusfromthetransferofmanagerialtasks,sothegainsfromtradeprovidestrongincentivestotransfercontrol. 1/ Inthiscasewhethercontrolistransferredornotdependsonabroadersetofparameters,bothaggregateandspecictotheindividualrm.Usingtheexpressionforequilibriumwages,equation(5)canberewrittenas K1 s 1 + s 1 f)·( )1 ³ ´1 Hence,thereisathresholdsize(relativetothesizeoftheeconomy)abovewhichmanagerialcontroldoesnotshifttotalentedindividuals,eveniftheownerisuntalented.Essentiallytheintuitionisthatitisalwaysbettertomanagealargermthantobeaworker:controlrightsoverlargeassetsgeneratelargereturnsevenifmanagerialskillsarelacking.Thethresholdsize,however,varieswiththemacroeconomicenvironment.Inparticular,thethresholdsizeincreasesifalargefractionofthecapitalstockiswellmanaged( large)andifthereismuchcompetition(large)betweenrms.Boththesevariablesimplyhigherwages,andhenceamoreattractiveoutsideoption.Theythereforehaveanimpactontheincentivestorelinquishcontrolbythe“marginal”untalentedowner.Finally,alarge“recoveryrate”,aswellasalargedierentialbetween ,bothincreasethemaximumsizebelowwhichcontrolistransferred.Theintuitionisthesameasinthepreviouscase:theseparametersincreasethegainsfromtrade.Finally,thethresholdsizefallswith,asalargercapitalshareincreasesproandthusthereturntoholdingontocontrol.Intheremainderoftheformalanalysis,wefocusontheinterestingcase, 1/ ,whereinecienciesarise. 4.4EquilibriumIntheprevioussubsectionwehavecharacterizedthesetofrmsthatchangemanagerialcontrolasafunctionof ,thefractionoftheoverallcapitalstockthatiswellmanaged.Clearly,though, isitselfanendogenousvariable,andindeeditisthevariableofinterestfromamacroeconomicstandpoint:itsummarizestheoveralllevelofeciencyoftheeconomy,andhencethelevelofwages,prots,andper-capitaincome.Inordertodeterminetheequilibriumlevelof ,weintroducethefollowingnotation.Wede,therelativesizeof.Wecall )thethresholdnedinequation(6),i.e.thelevelofsuchthatfor )thecontroloverdoesnotgettransferred.Wealsodenethe“statevariables” 0 as,respectively,theshareoftheaggregatecapitalstockinitiallyownedbylow-talentindividuals,andthesize-distributionfunctionofthecapitalinrmsinitiallyownedbylowtalentagents )isthemeasureofrmswithuntalentedownersandcapitalsharelessthan).Thenwehave: = s0+Z( s)0 rmsthatareinitiallyownedbyhigh-talentagentsendupunderbadmanagement,sotheequilibriumfractionofwell-managedcapitalincludesallthecapitalthatwasinitiallyallocatedtotalent, .Inaddition,allrmsinitiallyallocatedtolowtalentthatarebelowthethreshold )arealsotransferredtotalentedmanagement.Becausebothsidesof(7)areincreasing,itisclearthatthereisapotentialformultipleequilibriain .Forexample,therecouldbe“high”equilibriawheremuchoftheeconomy’sassetstockiswellmanaged,wagesarecorrespondinglyhigh,anduntal-entedrmownersarethereforewillingtopartwiththeirassets,therebysupportingthehigh-talentequilibrium.Viceversa,ifmostcapitalisbadlymanaged,wagesarelowanduntalentedownersholdontotheirassets,conrmingthelow-talentequilibrium.Whilethepossibilityofmultipleequilibriaisinterestinginitsownright,itcomplicatesconsiderablythetreatmentofdynamicsinthenextsection.Hence,intherestofthepaperwefocusonsituationswheretheequilibriumisunique.WeshowinAppendixA.2thatasimplerestrictiononthesetofpossibleinitialdensities, ensuresbothexistenceanduniquenessoftheequilibrium.Inparticular,theequilibrium isuniqueif(butnotonlyif) )issuchthat: 0()if) 1·( )1 ³ ´1 ¸ ( 1 1 Thisconditionimposesaboundonthemaximumamountofcapitalthatchangeshandsforanyrm-sizelevel.Itrulesoutmultipleequilibriabecauseitavoids“bigjumps”inthenumberoftransactions.Theconditionislikelytoholdwhenthedistribution )isverydispersedwithfatenoughtails.Whenthemodel’ssolution isunique,ithasthefollowingintuitivecomparative-staticproperties(alsoestablishedinAppendixA.2): Theeconomy’seciencyimproveswiththeeconomy’squalityofcontractenforcement.Thisisbecausemoreuntalentedownerscantransferman-agerialcontrolrightswithoutfearofbeingrippedo 0(holding constant).Largeeciencygainsfromtransferringcontrolincreasethegainsfromtradeandinducemorecontracting. Increasesinthenumberofrmsleadstogreateraggregateeciency.Morermsmeansmorecompetitiononthelabormarket,andhenceahigherrealwage.Thisinducesmoreownerstosell. 0.Alargercapitalshareboostsprotsanddepresseswages,reducingtheincentivetorelinquishownership. Initialconditionsmatter:becauseallrmsinitiallyinthehandoftalentedindividualsstayintheirhands,theequilibriumshareofwellmanagedcapitalisincreasingintheshareinitiallyallocatedtotalentedowners. G 0,bywhichwemeanthatifthesizedistributionofrmsinitiallyownedbylow-talentagentsbecomesmoreskewedtowardssmallsizes,overallciencyincreases.Thisisbecauseinthiscasealargerfractionoftheineptly-ownedcapitalstockfallsbelowthesalethreshold.Thisisanotherwayinwhichinitialconditionsmatter.Thestaticmodelthereforedeliversarichsetofpotentiallytestablepredictionsonthemacroeconomicaspectsoffamilyownership.Onecouldstophereandtryto bringtheseresultstothedata.However,thelasttwocomparativestaticresultsclearlycallforadynamicanalysis,asinadynamiccontext isnothingbutnextperiod’s 0, )issimilarlyaectedbythetransactionstakingplaceinthepreviousperiod.Hence,afulldescriptionofthepropertiesofthemodelrequiresadynamicanalysisofthepathsofthesestatevariables.5DynamicsWeintroducetwosourcesofintertemporallinkages.Therstisabequestmotive,andthesecondisamechanismfortheinter-generationaltransmissionofabilities.Onecouldsaythattherstregulatestheinter-temporaltransmissionofphysicalcapital,andthelatterofhumancapital.Weassumethatparentsarealtruistictowardstheirchildren,anddesiretobequeathpartoftheirincome.Inparticular,theyhave“warmglow”feelingstowardstheirospring,thatinducethemtobequeaththeirchildrenafractionoftheircurrentincomes:theirwageinthecaseofworkers,andtheirprots(netofanydebtservice)inthecaseofrmowners.Wefurtherassumethatownersofrmswillalwaysleavetheirbequestintheformofphysicalcapital,embodiedinthermtheypassontotheirspring,whileworkerswillbequeathintheformofunitsoftheconsumptiongood. Asdiscussedintheliteraturereview,ofcourse,thereisalreadysubstantialevidenceforthepropositionthataggregateeciencyincreaseswithnancialmarketeciency,i.e.for ThereisalsobroadagreementthatincreasesincompetitionleadtoTFPgains,or 0.However,asnotedbyNickell(1996),itissomewhathardtocomeupwithsimpletheoreticalexplanationsfornding.Ourresultisthereforeofinteresttotheliteratureontheeciency-enhancingeectsofcompetition.Wehavesimulatedthemodelforthemuchlessrestrictivecasewhereagentsbequeathafractionofalltheresourcestheyreceiveintheirlifetime,includingbequestsfromthepreviousgeneration,andthesalepriceofrmstheymayhavesold.Sincewefoundonlytrivialchangesinthequantitativeresults,westickheretotherestrictiveassumptions,whichaordmuchgreaterexpositionalsimplicity.Becauseofthetime-to-buildassumption,thetwoformsoftransmittingwealtharedierent.Inparticular,bequestsleftintheformofunitsoftheconsumptiongoodcannotbeusedtowardsincreasinganyrm’scapitalstockinthenextperiod.Thesechoicesofbequestvehiclescanberationalized(availableuponrequest)undertheassumptionthatparentscarenotonlyfortheamounttheybequeth,butalsoforthereturntotheirospringoftheamountbequethed.Undermostempiricallyrelevantcombinationsofparametervalues,rmownersbequethintheformofcapitalbecausecapitalhasahigherreturnforrmowners.Workersbequeththeconsumptiongoodbecausefortheirospring,whostartouttheperiodwithoutowningarm,thereturntocapitaliszero. Wealsoassumethatachild’sabilitydependsontheparent’s.Specically,withprobabilitychildrenwillinherittheirparents’talentlevel,andwithprobabilitytheywillbeofdierenttype.mayreectbothnaturalandnurturalsourcesofpersistenceinability.5.1ThePeriod-MarketforFirmsTheintroductionofdynamicsdoesnotchangetheanalysisofthelabormarket.How-ever,thepresenceofbequestschangesthesituationinthemarketforrms.Nowpotentialbuyerscanusetheamountstheyinheritedtopayupfrontforpartofthepurchasepriceofarm.Looselyspeaking,then,bequestscreateaformof“collateral”,thathelpsbuyerscircumvent,atleastpartially,theexistingcontractualimperfections.Asaresult,rmsthatwerenon-tradeableintheno-bequestscenariocannowchangehands.InAppendixA.3wederivetheperiod-thresholdforownershiptransfer.Un-talentedownerswillselltotalentedbuyersiftheirrm’srelativesizeislessthan st( sts t 1 + st 1 ¶wt1 µ 1 1 where )wasdenedaboveasthethresholdsizefortransferofownershipintheeconomywithnobequests.Thisformulaclarieshowmorermscanbesoldifpotentialbuyershavecollateral:the“sale”thresholdisincreasedbyaquantitythatdependson.Recallthatisthebequestleftbyworkerstotheirospring:thestrongerthebequestmotive,thelargerthebequestreceivedbythecurrentgeneration,themorermscanachieveeciencythroughownershipchange.Itisworthnotingthattheadditionofbequestsunderscoresthegeneralityofthethreshold-sizeresultuncoveredinthismodel.Withoutbequests,onlysmallaresoldbecauseonlyforsmallrmsistheoutsideoptionrepresentedbythemarketwageasubstantialfactorinanowner’sdecisiontotransfercontrol.Withbequests,however,orindeedwithanyothersourceofcollateral,thereisanentirelyindependentadditionalreasonforathresholdsize:salesofsmallrmsrequirelittlecollateral. Naturalextensionstothisassumptionincludemakingtheprobabilityofinheritancedierentacrossthetwotypes,aswellastomakealsodependonwhethertheparentisarmowneroraworker.Thislastassumptioncouldcapturetheexistenceofrm-specichumancapitalthatincreasestheprobabilitythatsomebodyraised“onthermpremises”bewellequippedtoruntherm. Alsofollowingthereasoningfromthestaticcase,thedebtincurredbybuyerisnowgivenby=min(Thenewelementisthe()inthesecondterm.Sinceiscash-on-handthatthebuyertransferstothesellerex-ante,whenthebuyer’sparticipationconstraintisbindingthedebtfallsbyacorrespondingamount.5.2CapitalAccumulationChangesinrmsizebetweenperiods+1dependonwhathappenedtotherminthepreviousperiod.Therearetwomaincases.Therstisthecaseofbequeathedbyparentswhoalreadyownedthermatthebeginningofthepreviousperiod(i.e.inheritedthermthemselves).Thesecondisthecaseinwhichtheparentacquiredownershipduringtheperiod.Intherstcase,theparent’sincomeissimply,andthebequestisAssuming,withoutlossofgenerality,thatcapitalfullydepreciatesinoneperiod,thisimpliesi,ti,t(10)Ifinsteadtheparentpurchasedtherm,hisincomeis.Usingequation(9)wethushave:i,tmaxi,t(11)Thisequationrevealsanunexpectednegativepotentialeectofmarketeciencyoncapitalaccumulation.Asincreases,thecontrolofrmsistransferredmoreoften,but—forrmsthatsellatprice—alsoatahigherprice.Sincethepurchasepricemustbenancedfromtherm’sprotstream,andsinceinvestmentinnewcapitalnancedfromprotsnetofdebtrepayments,ahighimpliesafallininvestmentfortheserms.Thisisaclassicformof“debtoverhang”familiartostudentsofcor-poratenance:leveragedacquisitionsarealmostalwaysfollowedbyaretrenchmentofinvestmentwhileallcashowisdevotedtodebtservice.Ofcourse,thisnegativeeectofmarketeciencyonaccumulationiscounter-balancedbythepositiveeectfrom Thisimpliesthatforsomemaybenegative.Thiscansimplybereinterpreted,withoutchangesisnotation,asasituationwherethebuyerwilluselessthanherentirecollateralizableresourcestobuytherm.Inpractice,shebuystheentirermforcash,andisstillleftwithsomeofthebequest. greatereciency,whichboostsprots.Hence,theneteectoncapitalaccumulationistheoreticallyambiguous.5.3EquilibriumThedynamicequilibriumofthemodelisrecursive,andcanbecomputedasfollows.Givenabeginning-of-perioddistributionofrmsizes,anallocationofinitialtalent,andtheprevious-periodwage,equation(8)determinesperiod’seciencylevel .Once isknown,alltheothermacrovariables,suchasaswellastheentiredistributionofrmprots,arereadilycomputed.Withrms’protsathand,thecapitalaccumulationequationsoftheprevioussub-sectiondeterminethenewdistributionofcapitalforperiod+1.Furthermore,giventhesizethreshold ),aswellastheinitialassignmentoftalent,itiseasytodeterminetheend-of-periodassignmentoftalent:allrmswhoseperiod-sizeisbelowthethresholdendtheperiodundertalentedownership,whilermsabovethethresholdendtheperiodunderthesametalentastheystarted.Atthebeginningofperiodthen,thequalityofeachrm’sownershipisdeterminedbyarandomdraw.Withprobability(theparameterregulatingtheintergenerationaltransmissionoftalent)thenewownerisofthesametypeasthelatestperiod-owner,whilewithprobability1sheisoftheoppositetype.TheformalequationsgoverningthisrecursiveequilibriumarereportedinAppendixA.4.5.4FullyPersistentTypesIngeneral,themodeldoesnotallowforclosedformsolutionsforthesteady-statevaluesoftheendogenousmacroeconomicvariables.Wethereforerelyonnumericalsimulationsinordertoassessthequalitativepropertiesofthedynamicmodel,aswell SeeGhatak,Morelli,andSj¨ostr¨om(2001)foradierentexampleofarelaxationofcredit-marketimperfectionsthatleadstoambiguouseectsonaggregateoutput.Thereisathirdcaserepresentedbyrmsthatdidnotoperateinperiodbecausetheyweretoosmalltomeettheviabilityconstraint0.Inthesecasestheownerletthecapitaldepreciateandjoinedthelabormarket.Hisincomeisthus.Sincehestillownsalicensetoproduce,hewillinvestinnewcapitalfortherm.Inthesecaseswehavei,t(12) asitsquantitativepotential.First,however,wedescribeonespecialcasethatdoeshaveaclosedformsolution.Thisisthecasewherechildrenalwaysinheritthetalentleveloftheirparents,or=1.Inthiscase,eachdynastyisidentiedwithagiventalent-level,deterministicallytransmittedfromparentstotheirosprings.Firmsinitiallyassignedtotalentedfamiliesneverchangehands.Firmsinitiallyassignedtountalentedfamiliespermanentlychangehandsifandwhentheyfallbelowthe“sell”threshold.Thebasicintuitionforwhatgoesoninthiscaseisthattherelativesizeofbadlymanagedrmsshrinks,whiletherelativesizeofwellmanagedrmsincreases.Thisisbecausethelatterhavegreaterprotsandthereforeineveryperiodtheyre-investalargeramount.Hence,inevitablyatsomepointbadly-runrmsfallbelowthesellthresholdandcurrentmembersoftalenteddynastiestakeovertheircontrol,andthermsstartgrowingagain.Clearly,thelong-runequilibriumoftheeconomyfeaturesfulleciency,irrespectiveofthedegreeofnancialimperfection.5.5SimulationsResultsInthegeneralcase,where1,ineveryperiodsomefractionoftalentedownersproduceuntalentedosprings.Inthesecases,theabilityoftheeconomytoachieveciencydependsonitsabilitytotransfercontroltonewtalentedbuyers.Herewepresentsimulationsaimedatassessinghowwelleconomiescharacterizedbydierentparameterstacklethistask.Inallourexperimentswesimulatethedynamicevolutionofaneconomypopu-latedby1000rms,and10000workers,whichistosaythatwesettheparameter1000/11000=0.09.Wealsorandomlygenerateaninitial(i.e.period-0)distributionofcapitalstocksacrossthe1000rms,usingauniformdistributiononthe[01]interval.Finally,werandomlyassignatalentindicator(loworhigh)totherstgenerationofowners.Initialtalentisdrawnfromabinomialdistributionwithparameter0which Indeed,inthiseconomyfulleciencywouldeventuallybeachievedeveniftherewasnomarketforrms.Withnomarketforrms,theshareofcapitalecientlyallocatedwouldfollowthedierenceequation: t 1 st 1 + st( 1 1 whichadmitsonlyonestableequilibriumwhereallthecapitalisecientlyemployed,i.e. =1.rmsneverchangehands,sincewell-managedrmsgrowfaster,eventuallytheywillaccountfora100%shareofthecapitalstock.Theresultgeneralizestothecasewherethemarketforrmsisopenexceptforthefactthatnowconvergencetofulleciencytakesplaceinnitetime. impliesthatacrossalleconomiesandacrossallperiods50percentofindividualsaretalented.Giventheseinitialconditions,weobservetheevolutionoftheeconomyforvariouscombinationsofthekeyparameters(“savingrate”),(marketimperfection), (ineciencyofuntalentedindividuals),and(inheritabilityoftalent).Sincealltheequationsofthemodelcouldberewrittenintermsof / ,wesimplyhold constantandequalto1.Thecapitalshareparameterisalsoheldconstant,at0.33,inallexperiments.Foreachofthesecombinationsofparameterswelettheeconomygrowover60periods(generations),thoughinpracticeconvergencetosteadystateseemstooccurinlessthan10.Wethencomputesteadystatevaluesfortheendogenousvariablesasaveragesoverperiods10to60,andcomparethesesteadystaterealizationsacrosscombinationsofthekeyparameters.Theremainderofthissectiondescribestheresultsoftheseexperiments.Wemostlyfocusonthetwobuildingblocksofper-workerincome:thecapitalstock,andthelevelofTotalFactorProductivity,whichinthismodelisgivenbytheexpression t 1 + st 1 Figure1plotsthemodel’spredictedsteadystatelevelofTFPforvariousvaluesand.Theformerismeasuredonthehorizontalaxis,whilethedierentcurvescorrespondtovaluesofthelattervaryingbetween10percent(lowestcurve)and50per-cent(highest). areheldconstantat0.8and0.7,respectively.Theformerchoiceismadearbitrarily,whilethelatterismotivatedbyevidenceontheinter-generationalcorrelationofIQscores,asdetailedinAppendixA.5.Wediscussvariationintheseparametersbelow.Thecurvesare(weakly)upwardsloping,indicatingthatimprovementsinnan-cialmarketsleadtoimprovementsingovernance:asincreasesmoreineptownersselltheirassetstotalentedmanagers.Therelationshiplevelso5,becauseatthisvalueandaboveitbecomespossibleforallineptownerstoselltheirrms.Thecurvealsorevealsthateciencyincreasesinthebequestrate.Thisisthecol-lateraleect:morebequeststurnintomorecollateral,andmoretalentedindividualscanacquirecontrolovertheeconomy’sassets.Quantitatively,theeectofisratherlarge:theeconomywiththemostinef-cientnancialmarketshasTFPlevelsaslowas85%oftheTFPlevelsofthemostcienteconomy.Ina93-countrydatasetfortheyear1996,the10thpercentileofthe Recallthatthethresholdfortheeconomytobefullyecientis 1/ .Abovethisthreshold,alltradestakeplace. Figure1:SteadyStateTFPTFPdistributioniscomputedtobeabout30%ofthe90thpercentile(Caselli,2003).Hence,thefractionoftheobservedTFPgapspotentiallyexplainedbythemodelisquitelarge.ThequantitativeeectofonTFPis,instead,mostlyfairlysmall.Figure2isanalogoustoFigure1,butplotsthesteadystatecapitalstock,(alwaysfor 8and7).Highercurvescorrespondtohighervalues:ahighersavingrateimpliesahighersteadystatecapitalstock.Thecapitalstock,however,turnsouttobealwaysdecreasinginthemarket-eciencyparameter,.Asdiscussedabove,inprincipleincreasesinhaveambiguouseectsoncapitalaccumulation:byincreasingeciencytheyincreaseprots,andthistendstoincreaseaccumulation.Butbyincreasingthenumberoftransactionstheyalsoincreasethenumberofrmswitha“debtoverhang”problem,whichhurtsaccumulation.Theseresultsshowthatthesecondeectalwaysdominatesinthesesimulations. Figure2:SteadyStateCapitalQuantitatively,variationingenerateslargevariationincapitalstocks:for10themostcapitalpoorcountry(10)hasroughly10%ofthecapitalstockofthemostcapitalrich(50),andthisratioisfairlystableacrossvaluesof.Inthedata,thecorresponding10th/90thpercentileratiois2percent,sothemodelcangeneratemostofthecross-countryvariationinthecapitalstock.Thequantitative Clearlyonecouldgenerateevenmorevariationbyletting5fortherichestcountries,butthiswouldbeimplausible.Note,incidentally,thatitwouldbeinappropriatetotrytocalibrateobservedsavingrates.Whilethevariationinsavingratesacrosscountriesismodest,ratesofrealinvestmentarehighlyvariablebecauseoflargediferencesintherelativepriceofinvestmentgoods(HsiehandKlenow,2002).Oursshouldbebroadlyconstruedtoalsoreectthisvariation.Amorerigorousapproachtocalibratrionwouldbetocalibratesonsavingrates,butthendividetheright-hand-sidesofequations(10)-(12)bythecountry-specicrelativepriceofinvestment.Thisisequivalenttohavingtwodierents:oneforworkers,andoneforrmowners.IntheCaselli(2003) ectsofgointhe“wrongway”:theymakeithardertoexplainthecross-countrydispersionof.Asitturnsout,however,theyaredominatedquantitativelybytheectsof:ifmovetogether(astheyclearlydo),thenhighcountrieswillstillberelativelycapitalrich. Figure3:SteadyStateTFPasfunctionof TheconclusionfromFigures1and2isthatnancialmarketeciencycanhavesizableeectsonTFPlevels(andsmallnegativeeectsoncapitalstocks),whilebequestmotiveshavesizableeectsoncapitalstocks(andsmallpositiveeectsonTFP).Combiningvariationalongboththeandthedimensionthemodel’squantitativeperformanceissatisfactory:acountrywith10and10wouldhave85%oftheTFP,and13%ofthecapitalstock,ofacountrywith=1and5.Outputwouldberoughly50%.Itseems,then,thatdynasticmanagementmaymatter. datasetvariationininvestmentpricesexceedsafactoroffour. Figure4:SizeDistributionofFirmsFigures1and2wereobtainedforparticularvaluesofthelow-eciencyparame-ter andskill-inheritability.Variationin hasambiguouseectsonTFP.Ontheonehand,increasesin reducesthe“damages”thatuntalentedmanagementprovokes.Ontheother,preciselyforthatreason,fewerrmsaretransferredfromuntalentedman-agerstotalentedones.ThersteecttendstoincreaseTFP,butthelattertendstoreduceit.Increasesinheritability,instead,unambiguouslyincreaseTFP,becauseitmeansthat“owningdynasties”willbemostlymade-upoftalentedagents.Toquan-tifytheseeects,Figure3presents—forvaryingvaluesof (horizontalaxis)anderentcurves)theofTFPofacountrywith1and1(recallthatthecorrespondingvalueforaneconomywith=1is1).Weseethattheambiguityintheectsof givesrisetoashapedpattern.Inparticular,when fallsbelow0.6thegainsfromtradingrmsaresolargeastooverwhelmevenextremeformsofnancial imperfection.Conversely,when =1dynasticmanagementisnotaproblem,asallagentsareequallytalented.Wecanalsoseethat,fortheintermediatevaluesof theTFPconsequencesofdynasticmanagementcanbefairlysevereevenforrelativelyhighintergenerationalinheritabilityoftalent.Theeectsofvariationinbothqualitativelyandquantitativelyfairlyinsensitivetoalternativevaluesof Itmayalsobeofinteresttoexaminethesizedistributionofrmsgeneratedbyerentcombinationsofparameters.Figure4plotsthesteady-statesizedistributionrms(denedasthesizedistributioninperiod60)forthefourcasesobtainedcombining1and=1,with1andvariesbycolumn,variesbyrow).Thestrikingfeatureoftheseplotsisthatinallcasesthesize-distributionrmsisskewedtotheright,andlooksapproximatelylog-normal.Thisisdespitethefactthattheseeconomiesallstartedoutinperiod0with(identically)uniformlydistributedrmsizes.Thisisanotableresultbecausereal-worldsizedistributionsrmsarealsoapproximatelylog-normal(SimonandBonini,1958,IjiriandSimon,1962,andcountlessothers).6ConclusionsThispaperhasarguedthatoneoftheadverseconsequencesofnancial-marketimper-fectionsisafailureofmeritocracy:untalentedheirsofproductiveassets—ratherthantalentedindividualsnotborntowealth—carrycriticaldecision-makingresponsibilities.Importantly,thisissoeventhoughtheuntalentedheirwishestotransfercontrol,andwoulddosoenthusiasticallywerenancialmarketsecient.Numericalsimulationsofagrowthmodelfeaturingdynasticmanagementshowthattheaggregateeciencycostsofthisfailureofmeritocracymaybesevere.Themodelalsoexploreshowtheincidenceofdynasticmanagement—andofitsadverseconsequences—varieswiththesavingrate,andwiththeinter-generationalpersistenceoftalent.Incross-countrydata,economicperformanceisclearlypositivelycorrelatedbothwithindicatorsofnancialmarketdevelopment,andwithsavingrates(appropriatelydened),andourmodelprovidesonecandidatesourceforthesecorrelations.Themodelalsohasanumberofinterestingnewpredictionsontherelationshipbetweeneciency,rmsize,andthesizedistributionofrms.Sincesmallrmsareeasiertosell,weexpectthedynastic-managementproblemtobemoresevereinlarge corporations,i.e.—onaverage—largecorporationsshouldbelessecient.Thereisanoldtraditionineconomicsoftryingtoestimatethesize-eciencyrelationship(e.g.Osborn,1950),butoursearchesforrecentcontributionshavedeliverednothinginthewayofsystematicstudieswithlargedatasetsandanadequatesetofcontrols.Itseemsthatthisquestionisnotofcurrentinteresttostudentsoftherm.Thereisalsothecloselyrelatedpredictionthatsmallerrmsaremorelikelytochangeownership.LichtenbergandSiegel(1987)didndthistobethecase,andasfarasweknowthisresulthasnotbeenchallenged.Afurtherconsequenceoftheseresultsisthatcountrieswithmoreconcentratedownershipofproductiveassetswillbelessecient,apredictionwehopetotestinfuturework.Aseeminglyimportantaspectofdynasticmanagementthatwehavenotfullyaddressedinthepresentmodelisthedeathofrmsatthetimeofsuccession.LottiandSantarelli(2002)showthatrmsurvival-hazardfunctionsdipdramaticallyaroundthetimeofretirementsoftheowner-founder.Theycitesuccessionproblem—unpreparedorunwillingheirs—andhighinheritancetaxesaskeycausesoffamily-rmdeath.Ourmodeldoesfeaturermshut-downsforperiodsinwhichthermistoosmalltooperate,buttheseshutdownsareunrelatedtothequalityoftheospringandtotaxes.Furthermore,suchshutdownsareonlytemporary.Anextensionofourmodelallowingforentryandexit,aswellasforcross-countryvariationininheritancetaxes,willbebothrealistic,andwillleadtoadditionalempiricalpredictions.Wehopetopursue LichtenbergandSiegel(1987)alsofoundthatinecientrmstendtochangeownership,andthatownershipchangeisfollowedbyabove-averageeciencygrowth.McGukinandNguyen(1995)conthesecondnding,butreversetheformer:moreecientrmstendtochangehands.Ourmodelhasnodeniteprdictionsonwhetheritismoreecientorlessecientrmsthataretansferredtonewowners.Ifthesaletakesplaceafewyearsintotheuntalentedheirincumbency,thentherewillbetimeforhisineptitudetoadverselyaecteciency,leadingtoaLichtenberg-Siegelresult.However,ifthesaletakesplaceearlyenough,orindeediftheselleristhetalentedretiringowner—smartenoughtoseethatherprogenywillmakeamessofthings—thenwewouldobservetheMcGukin—Nguyenresult.Ineithercase,above-averagegrowthineciencyafterthesalecouldbeeasilyaccomodatedbyasimpleextensionofthemodelwithmorethantwotalentlevels.Insuchamodel,newownerswouldalwaysbedrawnfromthehighesttalentcategory.SeealsoTheEconomistarticlescitesinSection2.Onewouldthinkthathighinheritancetaxeswouldalwaysbegoodinourmodel,astheybreakupthechainofdynasticsuccessions,andredistributeresourcestothetrulytalented.However,thisisnotnecessarilytrue.Ifskillsarehighlypersistent,dynasticsuccessioninsuresthatonaverageassetsaremanagedbyindividualswhoaremoretalentedthantheaverageindividualinsociety.Iftheinheritancetaxisredistributedrandomly,thenitseciencyconsequencesmaybeadverse.Hence, theseextensionsinfuturework. inheritancetaxesdonotnecessarilysubstitutefornancialdevelopment. AAppendicesA.1OpeningaMarketforManagersInthisappendixweopenupamarketwhereuntalentedownersofrmsmayhiretalentedworkerstorunoperationsasmanagers.Doesthiseliminatetheinecienciesassociatedwithdynasticmanagement?Acontractformanagerialservicesforspeciesthatthemanagerreceivesaxedremunerationandthatthemanagershouldturnallprots,netoflaborandmanagerialcosts,totheowner.Imperfectenforcementofcontracts,however,impliesthatthemanagerhastheabilitytoappro-priateafraction(1)oftheprots,inwhichcasetheownerswillonlyrecouptheamount.Ifthemanagersteals,heobviouslyforfeitsthemanagerialcompensation.Clearly,then,wewillobservestealingwhenever(1Giventhisagencyproblem,atalentedownerwillalwaysprefertodirectlyman-agehisownasset.Furthermore,untalentedownerswillonlyhiretalentedmanagers,iftheyhireatall.Welookformanagerialcontractsthatdonotinvitestealing,i.e.thatsatisfythecondition(1.Suchtransactionsmustbeappealingtoboththeownerandthemanager.Theowner’sparticipationconstraintisThelefthandsideishisincomeifhehiresamanger:the(well-managed)rmpronetofthemanager’scompensation,plusthewagesheearnsonthelabormarketonceheisfreefrommanagerialduties.Therighthandsideishisincomeifhedoesnothire,i.e.theprotsfrom(ineptly)managingthermhimself.Forthemanager,theanalogousconditionis:hecompareshispayasmanagertohisoutsideoptionrepresentedbythemarketwage.Rewritingthesethreeconditionsslightlyweseethatano-stealingmanagerialcontractcanbeconcludedifandonlyif:Combiningthersttwoconditionsgivesrisetotherestriction(13)Thethirdconditiondoesnotbite. Evenifathatdissuadesfromstealingdoesnotexist,thetwopartiesmaystillinpricipleagree Notethatequation(13)isexactlythesameasequation(4).Hence,amanagerialsolutiontotheuntalented-ownerproblemispossibleonlyisasalesolutionispossible,whichistosaythatintroducingmanagerialcontractsdoesnothingatalltoalleviatetheinecienciesgeneratedbydynasticmanagement.Therecouldhavebeenother—morestandard—waysofmodellingtheowner-manageragencyproblem.Wecouldhaveexplicitlyaddeduncertaintyonex-postprof-its,andmakeitcostlyfortheowners,butnotforthemanager,toobservetherealizationoftheprotshock.Themanagerwouldthenhaveanincentivetounder-reportproandstealtheunreportedamounts.Wehaveveriedthatthisversionproducesthesameresultsasthesimpleronewepresenthere.A.2Existence,UniquenessandPropertiesoftheEquilibriumintheStaticModelConsiderthefunction s 0+R( s)0g ).Theequilibriumshare isaxedpointofthisfunctionmapping[01]intoitself.If )isacontraction,thenanequilibriumexistsandisunique.Assume )iscontinuous.Let 1 beanytwopointsinn,1]with 2 .Thenwehavethat: s2)M( s1)¯¯¯=Z( s2)( s1)g 0()dh³ s2´³ max Usingequation(6),thelastexpressioncanrewrittenas s2 )max ),where toatransferofmanagerialdutiesiftheoutcomeofstealingmakesbothbettero.TheconditionsthatmustbesatisedforthistooccurareNotethatwhenevertheconditionsforacontractfeaturingstealingaresatised,soaretheconditionsforacontractwithnostealing.Hence,wecansimplyfocusoncontractswithnostealing.Whileitisclearwhencontrolwillbetransferred,themanagerialcompensationatwhichthistransfertakesplaceis(partially)indeterminate.Clearlythecompensationmustbeintherangemaxanditmustdependonthebargainingpowerofthetwoparties.Inthecurrentcontextitseemslegitimatetoassumethatallofthebargainingpowerresidesintheowner.Thereasonisthatwehaveassumedthattherearemoretalentedmanagersthantherearerms,somanagersareinexcesssupply.Ifoneiswillingtoassumethatallofthebargainingpoweriswiththeowner,then=max c=1 1 1 f)h( )1 ( )1 0.Hence,ifmax isacontraction.Thisistheconditionwestatedinthetext.Also,itisimmediatetoseethatfulleciency( =1)isnotanequilibrium(i.e.theequilibriumisinterior)aslongas(1) Nowconsiderthefunction s,x s0R( s)0g )whereisavectorofexogenousvariables,theequilibriumconditionis s,x)=0.Comparativestaticscanbecarriedoutaslongas =0.Itisimmediatetondoutthat: sc ( theassumptionthatallowedustoobtainuniquenessensures 0.Hence,thesign s istheoppositeofthesignof ,forany.Wehavethat: f=1 1f[( sg 0(( s0F 1 1 1 [( sg 0(( s0F s0=1F G 0=[( s 2F =1 1 1 s 1 + s 1 [( sg 0(( s 1 1 wheretoevaluate G wehaveconsideredlinearvariations where A.3Period-ThresholdAtalentedprospectivebuyer,endowedwithbequest,canapproachtheuntalentedownerofarmofsizeandoeradownpayment,aswellasapromisetocompletethepaymentofthepurchasepriceoutoftheprotstreamfromtherm.ReplicatingthereasoningofSection(4.2)wendthatthistransactionwillgothroughifandonlyif:Assumingthat 1/ thisinequalityimplicitlydenesthemaximumrmsizethatcanbepurchasedwithcollateral.Inparticular,substitutingfrom(3),the rmthatdownpaymentcouldpossiblygiveaccesstohassize 1 +s 1 w+µ 1 1 (14)Clearly,thelargerthedownpayment,thelargerthermthatcanbepurchased.NowconsidertheoptimalbiddingpolicyforaprospectivebuyerwithbequestSupposerstshedecidestoearmarkanamountfordownpaymentagainstthepurchaseofarm:whichrmsizewillshetrytotarget?Givenourassumptiononbargainingpower,thebuyer’send-of-periodpayoiftheparticipationconstraintisbinding,and(1iftheincentivecompatibilityconstraintisbinding.Since,thisis(weakly)increasingin,thebuyerwillalwaystargetthelargestavailablermamongthosethatcanbepurchasedagainstadownpaymentofNowconsidertheoptimalchoiceof.Ifthebuyerisindeedabletopurchasethelargestrmhecanaordwith,hisutilityiseitherindependentoforitis ))+.Usingequations(3)and(14)thiscanberewrittenas 1 1 1 +(1 1 1 1 which(using )canbeeasilyseentobemaximizedforHence,notonlywillthebuyertrytopurchasethelargestpossiblermgivenadownpayment,buthewillusehisentireresourcesasdownpayment.Inshort,hewillalwaysattempttobuythelargestrmhecanaord,i.e.armofsize ).Thisisintuitive,as istheconditionthatensurestheexistenceofgainsfromtrade.Nowrecallthatweassumedthatallworkersleavebequest.Sinceonlychildrenofworkerspurchaserms,wehaveforallbuyers.Substitutingthisin(14),aswellasequation(1)for,andrecallingthat,givesequation(8).Sincewehavealreadyshowedthatbuyersalwaysmaximizethesizeofthetheybuy,allrmswithsizelessthan )willalsochangehands.A.4Recursiveequilibriumnethethresholdimpliedbytheviabilityconstraint0as ).Itcanbeshownthat ).Deastheamountofcapitaltheeconomyinheritsfromthepreviousperiod.Whatfractionofthiscapitalwillendupbeingused intheproductionprocessdependsonthedistributionofrms’sizes,andinparticularonthecapitalshareemployedbyrmsthatwillshutdownfortheperiod.Alsode asthedistributionoftherms’sizes(withrespecttothebeginningofperiodcapitalstock)inheritedbyuntalentedagents,andasthedistributiontotalentedagents.Takethesedistributionsasgivenatthebeginningoftheperiod.Alsotakethetime1wageasgiven.Finally,letuscallthemeasureofrmsoperatinginperiod.Thentheperiod-equilibriumisdenedbythefollowingsetofequations: t()i#,¯st="Zvt)(K0t)d¯Gt((wt1, st)(K0t)vt)(K0t) ()#,ft=Zvt)(K0t)dh¯Gt( =(1 t 1 + st 1 =(1 st( sts t 1 + st 1 ¶wt1 µ 1 1 ¶Yt³K0t´,vt) (s t 1 + st 1 ) ft)¯1 Giventheequilibriumvaluesofthemacrovariables,theentiredistributionofproforthermsinthiseconomyisgivenbythesetofequations s t 1 + st 1 i,t(15)rmssuchthatand=0ifGiventhisproleofprots,equations(10),(11),and(12)describethenewsizedistributionofrmsinperiod+1,.Finally,theallocationoftalenttorms, t ,isgovernedbytheprobabilitythatchildreninherittheirparents’abilities.A.5CalibrationofBouchardandMcGue(1981)surveythegeneticresearchonIQ.Theirpaperisasum-maryof111studiesonfamilialresemblancesinmeasuredintelligence.Theyarguethat thepatternofaveragecorrelationsinIQscoresisconsistentwithapolygenictheoryofinheritance,whichsaysthatthehighertheproportionofgenestwopeoplehaveincommon,thehighertheaveragecorrelationbetweentheirIQ.Inparticular,theyestimatethattheaveragecorrelationofParent-OspringIQscoresis0.42.WecalibratebyassumingthattheIQscoreofapersonisdeterministicallyrelatedtohisability.Inparticular,weassumethat individualsscore“high”,orinIQtests,and score“low”,orcanthenbesetsoastoinsurethattheparent-ospringcorrelationoftalentis0.42.rstthatundertheassumedstochasticprocessfortalent,thesteadystatefractionoftalentedpeopleinthepopulationmustbe,regardlessofThisisbecauseparent-ospringlong-runinheritancepatternssatisfy:Theaveragescore,therefore,isEIQ+(1,andthevarianceisVIQEIQ+(1EIQFurthermore,theparents-childrencovariancecanbecomputedasfollows:CIQEIQQλ(1−η)+(1EIQEIQ)+(1)(1EIQ+(1Noticingthatthevarianceofscoresintheparentpopulationisthesameasinthechildrenpopulation,thecorrelationcoecientofparents’scores()withchildrenscores(P,C,isCIQ/VIQ.For2,thisboilsdowntoF,SHence,onecanestimateF,S+1)2.ForF,S42thisimplies 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