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JournalofUrbanEconomics61(2007)319–344 www.elsevier.com/locate/jue Endogenous open space amenities in a locational equilibrium Randy Walsh UniversityofColoradoatBoulder,256UCB,Boulder,CO80309-0256,USA Received9December2004;revised25August2006 Availableonline25October2006 Abstract Little is known about the equilibrium impact of open space protection and growth control policies on theentiremetropolitanlandscape.Thispaperisaninitialattempttoevaluateopenspacepoliciesusingan empiricalapproachthatincorporatestheendogeneityofbothprivatelyheldopenspaceandlandconversion decisionsinalocationalequilibriumframework.Theanalysisyieldsfourstrikingresults.First,whenone allowsforendogenousadjustmentsinprivatelyheldopenspace,increasingthequantityoflandinpublic preservesmayactuallyleadtoadecreaseinthetotalquantityofopenspaceinametropolitanarea.Second, differentstrategiesforspendingthesameamountofmoneytopurchaseopenspacehavemarkedlydiffer- entlandscapeandwelfareimplications.Third,partialequilibriumwelfarecalculationsareextremelypoor predictorsoftheirgeneralequilibriumcounterparts.Andfinally,theanalysissuggeststhatwhileagrowth ringstrategyismosteffectiveinreducingtotaldevelopedacreageinthemetropolitanarea,thisreduction indevelopedacreageisassociatedwithalargenetwelfareloss. ©2006ElsevierInc.Allrightsreserved. 1. Introduction AcrosstheUnitedStateslocalandstategovernmentscontinuetoadoptprogramsforprotect- ing open space at a rapid pace. For example, according to the Trust for Public Lands, in 2005 there were 139 open space related ballot measures in the US. Of these, 111, or 80%, passed generating$2.7billionintotalfunds,$1.7billionofwhichisspecificallydedicatedforlandcon- servation purposes. The proponents of these measures are motivated by concerns that include recreationalaccess,habitatprotection,ecologicalservices,landscapeamenities,andthepreven- tion or reversal of perceived problems associated with urban sprawl. Opponents are concerned E-mailaddress:[email protected]. 0094-1190/$–seefrontmatter ©2006ElsevierInc.Allrightsreserved. doi:10.1016/j.jue.2006.09.002 320 R.Walsh/JournalofUrbanEconomics61(2007)319–344 about the efficiency of such policies and argue that, at least in some cases, they can be viewed asrent-seekingbylandownerswholooktousepublicdollarsand/orrestrictivezoningtoreduce thesupplyofdevelopablelandandthusdriveuppropertyvalues. Inspiteofthisongoingpolicydebate,thereisalackofempiricalevidenceastothelong-run generalequilibriumimpactsofopenspacepolicies.Theoristshavebeenactiveonthesubject,but empiricalwork hasbeenmainlyrestrictedtopartialequilibriumanalysisthatinformsus about thevaluethathousehold’splaceonopenspaceamenities—remaininglargelysilentonthelong- runlandmarketequilibriumandwelfareeffectsoftheseprograms.Giventhatthedistributionof landscapeamenitiesthatdriveopenspacepolicyareinherentlyafunctionofthepoliciesthem- selves,itisimportanttogobeyondanunderstandingofwhatindividual’svalueinthelandscape andtodevelopbetterempiricalmodelsofexactlywhatarethelongrunlandscapepatternsand welfare consequences associated with open space protection policies. This paper endeavors to fillthisvoid.WorkingwithdatafromWakeCounty,NorthCarolina,oneofthefastestgrowing metropolitan areas in the United States,1 a locational equilibrium model of household prefer- encesforlandscapeamenitiesisestimated.Theresultsfromthisestimationarecombinedwith anempiricalmodeloflandconversiondecisionstodevelopageneralequilibriummodelofthe landmarketinWakeCountythatincorporatestheendogenousformationoflandscapeamenities. Implementationoftheanalysisfocussesonaddressingfourkeyissuesassociatedwithmod- eling open space policies. First, open space amenities are inherently spatial. An acre of land protected at location A is not equal to an acre of land protected at location B. Second, non- marginal land protection policies will directly impact the land market equilibrium—leading households to make different location and lot size choices. Third, to evaluate how land pro- tectionpoliciesaffectthemarketequilibriumitisnecessarytotakeaccountofheterogeneityin propensityfordevelopmentacrossindividualparcels.Finally,householdadjustmentsinlocation andlotsizeinresponsetolandprotectionpoliciescreatenewpatternsofdevelopmentimplying thatsomeopenspaceamenitieswillbeendogenous. The key findings of the analysis are as follows. First, when one allows for endogenous ad- justmentsinprivatelyheldopenspace,increasingthequantityof landinpublicpreservesmay actuallyleadtoadecreaseinthetotalquantityofopenspaceinametropolitanarea.Second,spa- tiallydifferentstrategiesfor spendingthesameamountof moneytopurchaseopenspacehave markedlydifferentlandscapeandwelfareimplications.Third,partialequilibriumwelfarecalcu- lationsareextremelypoorpredictorsoftheirgeneralequilibriumcounterparts.Andfinally,the analysissuggeststhatwhileagrowthringstrategyismosteffectiveinreducingtotaldeveloped acreagein themetropolitanarea,this reductionindevelopedacreageis associatedwithalarge netwelfareloss. 2. Relatedliterature Whiletheauthorisawareofalmostnoempiricalworkonthegeneralequilibriumanalysisof amenitydrivenlandprotectionorzoningpolicies(seediscussionofCheshireandSheppard[1] fortheexceptionthatprovestherule),theredoesexistalargeempiricalliteratureonthecapital- izationofopenspaceamenitiesintohousingvalues.Forinstance,intheiroverviewoftheopen spacevaluationliterature,McConnellandWalls[2]surveyapproximately40hedonicopenspace studies.Amajorchallengeintheseeffortsistheneedtodevelopquantitativedescriptionsofopen 1 WakeCounty’spopulationexpandedfrom303,240in1980to513,901in1995.Constructionofnewsinglefamily homeshasexpandedfrom3500peryearto8000peryearoverthelast10years. R.Walsh/JournalofUrbanEconomics61(2007)319–344 321 space amenities. In their early work on open space amenities in Boulder Colorado, Correll et al.[3]suggestthatopenspaceisbothapublicgoodwhichbenefitseveryoneintheBoulderarea anda‘quasi-publicgood’duetodistancebasedexclusionofsomeprotectedparcels.Theopen spacemeasuresusedinmorerecentempiricalworkfollowasimilardichotomyandcantypically be classified as either ambient or area measures capturing the general landscape character2 or distance-basedmeasuresthatcapturedirectaccesstoopenspaceamenitiessuchasparks.3 Both types of amenity measures have been consistently found to be associated with higher property values. Several studies work within the mono-centric city framework to provide analysis of the im- pact of policies associated with “urban sprawl.”4 More recently, Bento et al. [14] evaluate the efficiencyanddistributionalimpactsofdifferentanti-sprawlpoliciesusinganumericalgeneral equilibriumframework.Whiletheseeffortsprovidevaluableinsightsintothelinkbetweenwel- fare,policyandcitysize,theyassumethatallopenspaceislocatedattheurbanboundary. AuniquedeparturetothisworkwithintheurbanframeworkistheanalysisofCheshireand Sheppard[1].CheshireandSheppardusehedonicmethodstoestimateimplicitpricesfor“ameni- tiesproducedbytheplanningsystem”5andthenimbedtheseestimatesinamodifiedmonocentric citymodel6 thatiscalibratedtodataforthecityofReadingintheUnitedKingdom.Thefitted modelisthenusedtocalculatethegrossmonetizedvalueofplanningbycalculatingthechange in household expenditure functions associated with the no planning outcome—assuming that without planning laws there would be no open space and that all industrial activity would be equallydistributedacrossthelandscape.Workingwithintheframeworkofthetraditionalurban modelallowsCheshireandSheppardtoimplicitlyincorporategeneralequilibriumadjustments intheiranalysis.Theirresultssuggestthatthereisanetlossfromplanningactivitiesthatmaybe ashighas3.9%ofannualincomes—withthelargestpositivebenefitsfromtheseactivitiesbeing associatedwiththeprovisionofaccessibleopenspace. The analysis presented here is similar to that of Cheshire and Sheppard in that it takes an empiricalgeneralequilibriumapproach.However,theunderlyingmodelismuchdifferent.The approach taken here extends the empirical locational equilibrium model initially developed by EppleandSieg[15].Methodologically,thepaperextendsthisapproachintwodimensions.First, theanalysisconsidersaNashequilibriumwithendogenouspublicgoodswherethesegoodsarise ‘naturally’asaresultoflandmarketoutcomes.ThisisincontrasttotheworkofEppleetal.[16] who consider endogenous public goods that are consistent with majority voting. Second, un- like previous work with empirical locational equilibrium models, the analysis incorporates an empiricallyestimatedsupplymodelintothelocationalequilibriumframework.7 2 Forexamplessee:GarrodandWillis[4],IrwinandBockstael[5],AcharyaandBennett[6],BatesandSanterre[7] andGeogheganetal.[8]. 3 Forexamplessee:BolitzereandNetusil[9],SchultzandKing[10],Smithetal.[11],andAndersonandWest[12]. 4 SeeforinstanceBrueckner[13]. 5 Theseamenitiesincludeaccessibleandnon-accessibleopenspaceandlimitationsonthedistributionofindustrial landuses. 6 Theseauthorsallowthebid–rentfunctiontovaryinaradiallysymmetricfashionalongdifferentdirectionsfromthe citycenter,incorporatepreferencesforbothaccessibleandnon-accessibleopenspacethatarisesoutoftheplanning process,andincorporateheterogeneityinpreferencesacrossdemographicgroups. 7 NotethatSiegetal.[17]adapttheEppleandSiegmodeltoaG.E.frameworkthatassumesconstantelasticityhousing supplyfunctions.Inthisworkhowever,theelasticityparameterisdeterminedad-hocandisassumedconstantacrossall locations. 322 R.Walsh/JournalofUrbanEconomics61(2007)319–344 3. Modelingopenspace The analysis begins by marrying a model of household preferences for residential lots and open space with a spatially delineated static representation of lot conversion decisions to yield anequilibriummodeloflandmarketsincorporatingtheendogenousdeterminationofprivately held open space. Household preferences over spatially delineated neighborhoods incorporate heterogeneityinincomeandtastesandincorporatestwodistincttypesofopenspaceamenities. Thedecisiontodevelopindividuallotsismodeledasafunctionofpricesandlotcharacteristics. Theseparcelspecificestimatesarethenaggregatedtoyieldneighborhoodlevelresidentialland supplyfunctions. 3.1. Householdpreferences Preferencesaredefinedovertwodistinctmeasuresofopenspace,Op,ameasureofthedis- tancefromagivenlotlocationtothenearestprotectedparcelofopenspace,andOn,ameasure ofthepercentageofagivenlot’sneighborhoodwhichisinopenspace(bothprotectedandun- protected).Foreachlotlocation,Op isassumedtobedeterminedastheresultofexogenousland protectionpolicies.8 On,ontheotherhand,isendogenoustothemodelandarisesfromtheag- gregationofdevelopmentdecisionsandtheexogenouslydeterminedlandprotectionpolicies—it isessentiallyaresidualequaltotheneighborhood’sarealessthesumofitsresidentialandcom- merciallydevelopedacreage.9 Householdi∈I maximizesitsutilitybychoosingneighborhoodj ∈J.Eachneighborhoodis characterizedbyitslandpriceP ,openspaceamenitiesOp andOn,andcontrolsforadditional j j j spatiallydelineatedamenitiesA .Householdsarecharacterizedbytheirincomey andtastefor j i neighborhoodamenitiesα .Implementationofthemodelisfacilitatedbyadoptingtheindirect i preferencespecificationgiveninEq.(1). (cid:4) (cid:6) (cid:2) (cid:3) (cid:2) (cid:3) V P ,Op,On,A |y ,α = 1 y1−ν− 1 BP(cid:5)η+1 G On,A αi j j j j i i 1−ν i 1+η j j j where: P(cid:5)(cid:2)P ,Op(cid:3)= Pj . (1) j j j 1+(Op)λ j The implications of this specification may not be immediately clear. First consider the role ofOp.Thisspecificationimplementsthepurere-packagingmodelsuggestedbyWillig[18]and treats the private services provided by differential access to protected open space as a quality adjustmenttoanindividualhousehold’slotsize.Underthisspecification,anindividualwillbe indifferentbetweenadoublingofherlotsizeoradoublingofthetransformedmeasureofopen spaceaccess:1+(Op)λ.Becausethepriceelasticityoflandislessthanoneandtheestimated j value of the augmentation parameter, λ, is positive, this pure re-packaging approach leads Op to have a substitutes relationship with residential lot size. This inverse relationship is readily apparentfrominspectionofEq.(2)below. 8 Asdiscussedbelow,inordertoimplementthemodel,thismeasureisaggregatedtotheneighborhoodlevel. 9 Fortractability,thelevelsofnon-residentialdevelopmentaretreatedasexogenousandarenotformallymodeled. R.Walsh/JournalofUrbanEconomics61(2007)319–344 323 TheoverallfunctionalfromisonesuggestedbyHanemann[19]10 thatresultsintheconstant price(η)andincome(ν)elasticitydemandspecificationgivenbyEq.(2). P(cid:5)ηyν Pηyν LD =B j i =B i . (2) i,j 1+(Op)λ [1+(Op)λ]1+η j j This functional form is a generalizationof Cobb–Douglass preferences which impose constant priceandincomeelasticitiesofmagnitudeone.11 Finally,theneighborhoodopenspacemeasureOn andcontrolsforadditionalneighborhood j specificamenitiesA enterthroughaseparableindexofneighborhoodpublicservices,G which j j isassumedtotaketheform: lnG =X(cid:3)γ +ε ,where X incorporatesboth On and A . ε is j j j j j j j assumedtobei.i.d.mean-zeroandcapturesunobservedneighborhoodattributes.12 Thepriceofland,P ,isassumedtoequaltheaverage1992landassessmentpersquarefoot13 j annualizedfollowingPoterba’s[20]approachforincorporatingtaxandappreciationeffects.In p the model, the privately capitalized open space component O is captured by including the j averagedistancefromahomeinneighborhoodj toaprotectedparcelofopenspace.Theneigh- borhood or endogenous component of open space, On equals the percentage of the land area j inzone j whichisundeveloped.Permanentincomeandheterogeneityinthetastefortheloca- tional attributes are introduced through y and α respectively. The distribution parameters for i i thesevariablesarenotdirectlyobservedandtheyareassumedtofollowabivariatelog-normal distribution. 3.2. Supply Price-inducedsupplyresponsesareincorporatedusinganempiricalmodeloftheconversion of land from undeveloped to residential use. The estimates from this model provide for each parcel a probability distribution of the reservation price at which the parcel will be converted (seeWalsh[21]).Basedontheseestimates,thelandsupplyfunctionmapsneighborhoodspecific t1a0tioHnafnaecmtoarnand’ospEteqd.(h3e.r2e1ias)gisivaednjubsyte1d+to(Ocopnt)rλo.lforanindexoflocationspecificamenities,g(Ojn,Aj).Theaugmen- j 11 ToshowthelinktoCobb–Douglasspreferences,takethelimitoftheindirectutilityasη→−1andν→1. 12 AsisrequiredwithintheEpple–Siegframework,thispreferencespecificationsatisfiestheconditionalsinglecross- ingpropertyinincomeandtastesforthelocationspecificamenityindex.Thusitimpliesstratificationintermsofthe augmentedpriceandthelevelofG.Intypicalapplicationssinglecrossingimpliessortingacrossproducts/zonesby qualityandprice.Herethesortingoccursinqualityandaugmentedprice,P(cid:5)= 1+(POjp)λ.Forafurtherdiscussionof j single-crossinginthiscontextseeEppleandSieg[15].Theslopeofindifferencecurvesinthe{G,P(cid:5)}planearegivenby: M(cid:2)α,y,B,G,P(cid:5)(cid:3)=ddGP(cid:5)(cid:7)(cid:7)(cid:7)(cid:7)V=V¯ =α(1−1νy1−GνB−P(cid:5)1ν+1ηBP(cid:5)η+1) (3) M(.)isstrictlyincreasinginαandyovertheplausiblerangeofparameterestimates. 13 Empirically,theneedtoidentifylandprices,asopposedtopricesforthelot-housebundleisproblematic.Asisdis- cussedinBatesandSanterre[7]theuseofassessedlandvaluestodeterminelandpriceshastheadvantageofaccounting forlocationaldifferencesinthevalueofland.Additionally,incontrasttotheuseofagriculturallandvaluesordataon thesalesofundevelopedlots,thisapproachprovidesacompletecoverageforlandvaluesinthecounty.However,this completecoveragecomesatthecostofusingthejudgmentofCountyassessorsinvaluingthelandandwillincorporate anybiasesassociatedwiththisprocess. 324 R.Walsh/JournalofUrbanEconomics61(2007)319–344 Fig.1.Impactoflandprotectiononresidentiallandsupplymodel. residential land prices P to the supply of residential land in each neighborhood S following j j Eq.(4). (cid:8) S (P )=L + F [P ]∗AREA (4) j j j kj j kj k∈j F [.]istheCDFforthereservationpriceofparcelk inzonej,AREA istheareaofparcelk kj kj andL istheareaoflandinresidentialuseinneighborhoodj asof1984.14 Figure1presentsa j graphicalrepresentationofEq.(4)undertheassumptionofalogisticdistributionofreservation prices. Figure1alsoillustrateshowgovernmentpurchasesoflandaffectsupplyinthemarket.New landprotectionhastwoeffectsonsupply.First,protectionreducestheaggregatesupplyofland (cid:3) availableforresidentialdevelopmentfromLutoLu.Inaddition,dependingonthedistribution ofreservationpricesfortheprotectedparcels,removalofparcelsfromthelandmarketwillcause adisplacementofthesupplycurve.Thedistributionofthereservationpricesofparcelsidentified for protection under each of the different policies will depend on the attributes of the parcels selectedfor protection.Figure1describes howtwopoliciesfor protectinganidenticalacreage oflandcanhavedifferenteffectsonsupply.Thefirstpolicyresultsinpurchasesofparcelswith relativelylowreservationpriceswhilethesecondpolicypurchasesparcelswithhighreservation prices. The second policy will have little effect on the land market until the demand reaches pointAwhilethefirstpolicyhasanimpactassoonasdemandincreasesaboveL .Thisexample l 14 Inthelandmarketequilibriummodel,landdevelopedpriorto1984istreatedasirreversiblydeveloped. R.Walsh/JournalofUrbanEconomics61(2007)319–344 325 demonstrates how heterogeneity in the characteristics of land parcels protected under differing policiescanaffectthesupplyresponse. 3.3. Equilibrium Thelandmarketoutcomedescribedbyindividualchoicesoflocationandlotsize{ji∗,di∗}i∈I arisesfromtheinteractionofsupplyanddemandintheresidentiallandmarket.Neithersideof themarketinternalizestheexternalitiesthatarisethroughtheneighborhoodcharactercomponent ofthemetropolitanlandscape,Ojn({ji∗,di∗}i∈I).Thisexternalitycomplicatescharacterizationof equilibrium. As consumers respond to exogenous changes in the market, not only will prices adjust,butchangesintheirlocationalchoicesandlanddemandswillleadtonewvaluesforthe endogenousopenspacemeasures.Theseopenspacechangestheninturnimplyrevisedconsumer landdemands. Givenafinitesetoflocationchoices,J andhouseholdsI,aNashequilibriumischaracterized byEqs.(5)–(8). (cid:9) (cid:10) (cid:11)(cid:12) ∀i j∗=argmax v P ,Op,On,A |y ,α , (5) i j∈J j j j j i i (cid:2) (cid:3) ∀i d∗ P ,Op|y ,α = 1 BP(cid:5)ηyν, (6) i j j i i 1+(Op)λ j i j (cid:13) (cid:8) (cid:2) (cid:3) ∀j L + F [P ]∗AREA = d∗ P ,Op|y ,α dF (y ,α ), (7) j kj j kj i j j i i yα i i k∈j(cid:2) (cid:3) {yi,αi}∈Cj ∀j Ojn=Ojn {ji∗,di∗}i∈I (8) C isthesetofy ,α realizationsforwhichcommunityj istheoptimalcommunity,andF is j i i yα thecumulativedensityfunctionfory ,α pairs. i i Equation(5)insuresthatallhouseholdschoosetheiroptimalneighborhoodand,conditional on choosing said neighborhood, Eq. (6) requires each household to consume their optimal lot size,asgivenbyRoy’sidentity.Equation(7)requiresthattheresidentiallandsupplyinzonej equalstheaggregatedemandinzonej.Finally,Eq.(8)statesthatthelevelofneighborhoodopen spaceinzonej,On,isdeterminedendogenouslyasthepercentageofallofthelandinzonej j thatisnotdevelopedinequilibrium. 3.4. Modellimitations Astrengthoftheproposedmodelisthatitsparsimoniousnaturefacilitatesdirectestimation ofthecomponentsofthesimulationmodelinaframeworkthatisconsistentwiththesimulation model’sunderlyingassumptions.Ofcourse,thistractabilitycomesatacost.Thekeylimitation ofthemodelistheverticalandhomogeneoustreatmentofcommunities.Forinstance,akeyde- terminantoflocationchoiceisjobaccessibility.Onewouldexpectindividualstoassigndiffering measuresofjobaccessibilitytothesamelocationdependingonworklocation.Inthemodel,be- causecommunitiesareverticallydifferentiated,allhouseholdsmustperceivethesamemeasure ofjobaccessibilityforeachlocation. Further, different locational amenities are likely associated with differing spatial scales. By definingdiscretezonesoverwhichtheseamenitylevelsareassumedconstantonerunstherisk of averaging out important differences. One possible solution would be to define very small 326 R.Walsh/JournalofUrbanEconomics61(2007)319–344 zones and thus average over much smaller areas. Unfortunately this approach runs into is- sues of tractability. In the end, the chosen approach represents a trade-off between richness of specificationandtractability.Asisdiscussedbelow,themodelfitstheobserveddataquitewell— suggestingthattherequiredparsimonydoesnotcomeattoohighacost. 4. Estimationofhouseholdpreferences The analysis extends the Epple–Sieg framework for estimating preferences based on the properties of locational equilibrium by allowing open space to have two effects on individual preferences.15Accesstoprotectedpublicland,Op,influencesdemandforlotsizedirectly,while theneighborhoodqualitymeasureOn actsattheextensivemargin,affectingcommunitychoice. The specification allows for heterogeneous tastes for the index of public goods G via the taste parameterα .Theestimationstrategyrecoversfoursetsofparameters:theparametersofthejoint i distribution of income and tastes for location specific amenities; the parameters of the indirect utilityfunction;theaugmentationparameterλ;and,theparametersofthepublicgoodindex. Following Epple and Sieg, a two-stage simulation-based procedure is used to estimate the model’s parameters. The first stage recovers the heterogeneity parameters, indirect utility pa- rameters, and the augmentation parameter by matching the models predictions to the observed 25th, 50th, and 75th parcel-size quantiles in each zone. This is done as follows. The price per unitlandineachzoneisfixedatitsobserved1992value.16 Foragivensetofparametervalues, the model is solved for the equilibrium allocation of households across zones, and the associ- atedoptimalequilibriumparcelpurchasesbyeachhousehold.Valuesofthepublicgoodindex, G ,...,G ,arechosensothatthenumberofhouseholdschoosingeachzoneinthecomputed 1 j equilibriumequalstheobservednumberofhouseholdsineachzone.Thepredictedquartilesof theequilibriumparcelsizeswithineachzonearethencalculated.Thedifferencebetweenthese predictedquartilesandtheobservedquartilesyieldsavectorofJX3distancesthatareweighted 15 Theapproachtakenhereisrelatedtotwoadditionalempiricalapproachestoestimatinghouseholdsortingmodels thathavebeendevelopedrecently.Bayer[22]extendsthedifferentiatedproductmodelofBerryetal.[23]toestimate anequilibriumsortingmodelofresidentialandschoolingdecisionsofhouseholdswithelementaryschool-agedchildren inCalifornia.Inamorerecentapplicationofthisapproach,Bayeretal.[24]userestrictedaccesscensusdatathatlinks householddemographicstocharacteristicsoftheactualresidenceandcensusblocktoestimateamodelofhousehold choiceinthegreaterSanFranciscoBayarea.Theiranalysisadoptsaprobabilisticnotionofhousingmarketequilibrium overafixedsetofhouseswithfixedcharacteristics.Inequilibrium,foreachhouse,thesumacrossindividualsofthe probabilityofoccupyingsaidhouseisequaltoone.Thesecondapproachisbasedonthecomputableequilibriummodel ofNechyba[25]andhasbeendevelopedbyFerreyra[26].Sheestimatesanempiricalmodelthatjointlydetermines schoolqualityandhouseholdresidentialandschoolchoiceswithinaneconomycomposedofmultiplepublicschool districtsandprivateschools.EquilibriumunderFerreyra’smodelinvolvesassignmentofhouseholdstoafixedstockof houseswithfixedcharacteristicssuchthateachhouseisoccupiedandnohouseholdcanbemadebetteroffrelocatingto adifferenthouse. Eachofthesetwoapproachesarevariantsofthebasicassignmentmodelwhichtreatsthequantityandcharacteristics ofthehousingstockineachregionasfixed.Thisassumptionisnotproblematicforthetypesofanalysisundertakenby Bayeretal.[24]andFerreyra[26].However,becauseofthecriticalconnectionbetweenchangingdevelopmentpatterns andopenspaceprovision,theassumptionsregardingthesupplysideoftheequilibriummodelmakestheseapproaches inappropriateforthecurrentanalysis. 16 Forestimation,zonepricesandpopulationsareassumedtoobservedwithouterror.Becausethepopulationsaretaken fromacompletecensusofthehousinglotsintheCounty,thepopulationassumptionisinnocuous.Thepriceassumption, whilemuchstronger,isnecessaryforthetractabilityofthemodel.Inparticular,thisallowsforthehouseholdpreference anddistributionparameterstobeestimatedwithoutregardtothelandsupplyfunctionwhichonlycomesintoplayin computingcounterfactuallandmarketequilibria. R.Walsh/JournalofUrbanEconomics61(2007)319–344 327 to form the econometric objective function. The weights in the objective function are chosen undertheassumptionthatdifferencesinfitbetweenthecomputedandempiricalquartilesarise fromsamplingerrorintheconstructionoftheobservedquartiles.Estimationentailsanon-linear searchforthesetofparametervaluesthatminimizestheobjectivefunction.17 Thesecondstage treatsthepublicgoodindexestimatedinthefirststageasthedependentvariableinanequation to estimate coefficients on observed zone level attributes (including privately held open space) thatinfluencethelevelofpublicgoodprovision. 5. Data The study area for this project is Wake County, North Carolina. The county includes the statecapitalandaportionoftheResearchTrianglePark.Ithasexperiencedrapiddevelopment and contains significant areas of protected and unprotected open space. The empirical model requires dividing the county into a set of spatially distinct choice alternatives. This task was implemented by aggregating up approximately 700 small spatial units labeled as nodes into 91 discrete zones,18 that are constructed to be as homogeneous as possible in location specific attributes. The 700+ nodes are defined by the Wake County Public School System to take ac- count of neighborhood and subdivision boundaries in establishing the primary and secondary schoolassignmentsfortheconsolidatedcounty-wideschoolsystem.Thenodeswereaggregated toproduceneighborhoodzoneswhoseboundariesreflecttheintersectionoflocaljurisdictional boundaries, major roadways and school attendance boundaries. Figure 2 shows the boundaries ofthe91zones. Informationonlotsize,1992taxassessments(distinguishedintoseparatelandandstructure assessments)andcurrentlandusewereassembledfromGISparceldataandtaxrecordssupplied by the Wake County Assessor’s Office. This data set contains information on approximately 230,000 parcels of land in Wake County. Collectively the parcels cover 510,677 acres of land andaccountfor95%oftheareaofWakeCounty,withtheremaining5%comprisedmainlyof roadsandroadrightofways.Eachparcelisidentifiedashavingoneof24landusecodes.Based onthesecodes,eachparcelisplacedintooneofthe5categoriespresentedinTable1.19 The endogenous or neighborhood component of open space, On is proxied for using the j percentageofeachzone’stotallandareawhichisinopenspace.Thismeasureiscomprisedofa mixtureofpubliclyprotectedlandandprivatelyheldlandinopenspaceusessuchasagriculture. p Thesecondmeasure,O ,capturestheaveragedistancetoprotectedopenspaceforeachhome j in a given zone. In order to construct this measure for each zone, a unified GIS description of morethan450individualparcelsofprotectedopenspaceinWakeCountywasassembledfrom dataprovidedbytheArmyCorpsofEngineers,NorthCarolinaDepartmentofEnvironmentand NaturalResourcesandlocalplanningagencies.TheshadedareasinFig.2depicttheseprotected parcels.ARCVIEWwasusedtocalculatethedistancefromeachlandparceltothenearestoneof these400+protectedareas.Finally,thesemeasuresarelinearlytransformedsothatOp∈{0,1} andthezonewiththelargestaveragedistancehasameasureof0andthezonewiththeshortest 17 Atechnicalappendixprovidingthedetailsoftheestimationisavailablefromtheauthor. 18 Throughoutthepaper,thetermszoneandneighborhoodareusedinterchangeably. 19 Privatelyheldopenspaceiscomprisedofthefollowinglanduses:agriculturaluses,vacant,cemetery,golfcourse, singlefamilyresidentialgreaterthan10acres,andallparcelsthatweredevelopedafter1992. 328 R.Walsh/JournalofUrbanEconomics61(2007)319–344 Shadedareasrepresentparcelsofprotectedopenspace. Fig.2.Mapof91zonesandprotectedopenspace. Table1 Landusesummaryfromparcelmaps Landuse Acres Percentageoftotal Business/Commercial 16,694 3.27% Residential 102,897 20.15% Protectedopenspace 81,084 15.88% Privatelyheldopenspace 295,566 57.88% Other 14,436 2.83% Total 510,677 100% averagedistancehasameasurecloseto1.20 Thisapproachcreatesameasurethatisincreasing inthelevelofamenityconveyed. 20 Specifically,Op=−averagedistancej−maxaveragedistance. maxaveragedistance

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allows for endogenous adjustments in privately held open space, increasing the quantity of land in public preserves R. Walsh / Journal of Urban Economics 61 (2007) 319–344 .. 3 report both the actual (circles) and predicted.
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