Endogenous open space amenities in a locational equilibrium

26 Pages·2007·0.59 MB·English

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