Community Composition and the Provision of Local P

JournalofPublicEconomics44(1991)217-237.North-HollandCommunitycompositionandtheprovisionoflocalpublicgoodsAnonnativeanalysisRobertM.SchwabandWallaceE.Oates*UniversityofMaryland,CollegePark,MD20742,USAReceivedMarch1990,revisedversionreceivedJuly1990Thereisconsiderableevidencesuggestingthatthecompositionofthecommunity-thatis,thecharacteristicsoftheresidentsthemselves-playsacentralroleindetermininglevelsofimportantpublicoutputssuchaseducationandpublicsafety.Thispaperexploresthenormativeimplicationsofthisevidence.Weshowthatoptimalcommunitycompositioninvolvesatrade-ofTbetweenthegainsfromhomogeneityindemandsamongresidentsandthegainsfromheterogeneityintheproductionofthosegoods.Theanalysisestablishesaroleforequalizingintergovernmentalgrantsonefficiencygrounds:suchgrantscanprovidetheneededincentivesforsustainingheterogeneouscommunities.1.IntroductionThecornerstoneofthetheoryoflocalfinanceistheTieboutmodelunderwhichmobileconsumersseekoutacommunityofresidencethatbestsatisfiestheirpreferencesforlocalpublicgoods.InthelimitingcasedescribedbyTiebout,thissortingprocessleadstoanefficientoutcome,oneinwhichtheresidentsineachcommunityhaveidenticaldemandsforthepublicgood.TheTieboutoutcomedependscriticallyuponanumberofquitestrongassumptions:costlessmobilityandthe'exogeneity'ofincome,tonameonlytwo.Theseassumptionshavebeenanalyzedextensivelyintheliterature.Aseeminglymoreinnocuousassumptioninthemodelisthepresumptionofidenticalproductionfunctionsandinputprices-withtheimplicationthatallcommunitieshavethesamecostfunctionfortheprovisionoflocalpublicservices.Theassumptionofidenticalcostfunctionsiscommonlymadeintheanalysisofcompetitivefirmsintheprivatesector-indeed,itisonetowhichwehardlygiveasecondthought..OatesisalsoaUniversityFellowatResourcesfortheFuture.WearegratefultotheNationalScienceFoundationforsupportofthisresearch.WealsothankJanBrueckner,RichardArnott,DavidWildasin,andtwoanonymousrefereesfortheirhelpfulcommentsandsuggestionsonearlierdrafts.0047-2727/91/$03.50@1991-ElsevierSciencePublishersB.V.(North-Holland)-----------------------218R.M.SchwabandW.E.Oates,CommunitycompositionThisassumption,however,ismuchmoresuspectinthecontextoflocalpublicgoods.Itisourcontentionthatcostfunctionsforthemostimportantlocalservicesareunlikelytobeidentical;ourclaim,inshort,isthatinitsapplicationtocertainkeylocalpublicgoods,the'productionfunction'envisionedinthebasicTieboutmodelisincompleteandmisleading[Oates(1977,1981)].Thereisconsiderableevidencesuggestingthatthecompositionofthecommunity-thatis,thecharacteristicsoftheresidentsthemselves-playsacentralroleindetermininglevelsofpublicoutputs.Manystudiesindicate,forexample,thatthelevelofattainmentinaschoolsystemorthelevelofsafetyinaneighborhooddependsnotsomuchontheinstructionalstafforfrequencyofpolicepatrolsasonthecharacteristicsoftheresidentsofthejurisdiction.Ourobjectiveinthispaperistoexplorethenormativeimplicationsofthiscontention.1Wesetforthamodelinwhichtheproductionfunctionforlocalpublicgoodscontainsasanexplicitargumentthecompositionofthecommunity.Byfocusingtheanalysisonthe'price'offinaloutputs,weareabletoderiveasetofintelligiblefirst-orderconditionsthatcharacterizeanoptimalallocationofindividualsamongcommunities.Wefindthat,ingeneral,efficientcommunitycompositionnolongerinvolveshomogeneouscommunities.Thegainsfrominteractionsintheproductionoflocalpublicgoodsmustbeplayedoffagainstthegainsfromhavingpopulationsthatarehomogeneousindemand.Inthisgeneralframework,theTieboutoutcomeemergesasaspecial,limitingcaseinwhichcommunitycompositionhasnoeffectonthelevelofpublicoutput.2Furtherconsiderationoftheseconditionsforoptimalcommunitycompo-sitionsuggeststhat,unliketheTieboutworld,decentralizedchoicewillnotnecessarilyleadtoanefficientoutcome.Inthemodel,individuallocationdecisionsencompassaformofexternality,sinceanindividual'spresenceinacommunitywillaffectthecostperheadofprovidinglocalservices.Efficiencyrequiresthatcommunitiesbeallowedtodiscriminateamongresidentsinthelevyingoflocaltaxes;typically,thisimpliesthatlocalcommunitieswouldlTherehas,incidentally,beensomeworkdevelopingthepositiveimplicationsofthismatter.Hamilton(1983)hasarguedconvincinglythatthefailuretoaccountforcommunitycharacteris-ticsintheproductionoflocalserviceshasledtosignificantbiasesintheestimationoftheincomeelasticityofdemandandexcessivelylargeestimatesofthemagnitudeoftheflypapereffect.SchwabandZampelli(1987),inanempiricalstudyofpublicsafety,providesomeevidenceinsupportofHamilton'scontention.2Thereisanotherclassofmobilitymodelsthatgivesrisetoheterogeneousjurisdictions.These'regional'modelsrequirethatindividualsworkandresideinthesamejurisduction.Thesourceofheterogeneityinthesemodelsistheneedforboth'skilled'and'unskilled'workersintheproductionofprivategoods.Therethusemergesatrade-offbetweentheneededmixofresidentsforprivateproductionandthegainsfromhomogeneityintheconsumptionoflocalpublicgoods[Berglas(1976),McGuire(1988)].Ourmodeldoesnotrequireindividualstoliveandworkinthesamecommunity.Thegainfromheterogeneityinourmodelstemsfrominteractionsintheproduct