Spatial analysis of the amenity value of green open space

ECOLOGICALECONOMICS66(2008)403–416

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ANALYSIS

Spatialanalysisoftheamenityvalueofgreenopenspace☆

Seong-HoonChoa,?,NeelamC.Poudyalb,RolandK.Robertsa

ab

DepartmentofAgriculturalEconomics,TheUniversityofTennessee,2621MorganCircle,Knoxville,TN37996-4518,UnitedStatesDepartmentofForestry,WildlifeandFisheries,274EllingtonPlantScienceBldg.,Knoxville,TN37996-4518,UnitedStates

ARTICLEINFO

Articlehistory:

Received24April2007Receivedinrevisedform27August2007

Accepted2October2007

Availableonline7November2007Keywords:Hedonicpricing

LocallyweightedregressionOpenspace

Spatialconfiguration

ABSTRACT

Theobjectiveofthisresearchistodeterminethespatialvariationinamenityvaluesforbothquantityandqualityofgreenopenspaceinthehousingmarket.Variablesrelatedtosize,proximity,spatialconfiguration,andspeciescompositionofopenspaceareendogenizedintheglobalandlocalmodelsinahedonicpriceframework.Empiricalevidenceshowsthatamenitiesofdifferentfeaturesofopenspacevaryaccordingtothedegreeofurbanization.Insummary,evergreentrees,adiverselandscapewithfragmentedforestpatches,andmorecomplexandnaturalforestedgesaremorehighlyvaluedinRural–Urbaninterfaces.Incontrast,deciduousandmixedforests,largerforestblocks,andsmoothlytrimmedandman-madeforestpatchboundariesaremorehighlyvaluedinurbancoreareas.Asspatialvariationinamenityvaluesdiffersacrossametropolitanarea,theneedforsite-specificlandusemanagementtofitthelocalcharacteristicsisrecognized.

©2007ElsevierB.V.Allrightsreserved.

1.Introduction

Sinceurbansprawlhaswidespreadramificationsforplantandanimalhabitatsandhumansociety,openspaceconser-vationbecomesamajorconcernoftheAmericancommunity.Between1998and2004,935outof1215conservationballotmeasureswerepassedintheUnitedStates,raisingcloseto$25billioninfundingforlandconservationin44states(TheTrustforPublicandLandTrustAlliance,2005).Votershavethusshownconsistentsupportforopenspaceprotection.Akeyquestion,however,istheextenttowhichpublicopenspaceiscapitalizedintonearbyresidentialpropertyvalues,andthuswouldincreasepropertytaxcollection.Estimatesoftheeffectofopenspaceonthevalueofnearbypropertywouldbeofuseinestimatingthecostofsuchinitiativesandprioritizingthelandparcelstobeconservedasopenspace.

McConnellandWalls(2005)reviewedmorethan60publishedarticlesthathaveattemptedtoestimatethevalue

ofopenspacesinthecategoriesofgeneralopenspace,parks,naturalareas,greenbelts,forestpreserves,wetlands,andagriculture.Hedonicmethodswithspatialanalysesusinggeographicalinformationsystems(GIS)havegainedpopular-ityinrecentyearsformeasuringthevalueofopenspace.Despitetheextensiveuseofthehedonicpropertymethodinvaluingopenspace,fewstudieshavevaluedthequalityofopenspace.Thequalityofopenspacecanbeclassifiedbycompositionandshapeofopenspace.Thevaluationofopen-spacecompositionfocusesonthecomparisonofamenityvaluesamongdifferenttypesofopenspace.AndersonandCordell(1988)foundthatahardwoodlandscapeisvaluedslightlymorethanapinewoodlandscape.

Thevaluationofopenspacewithregardtoitsspatialconfigurationhasbecomeamatterofinterest.Recentliteraturefocusedontheaestheticvalueofland-usediversityandlandscapequalityinthesurroundings(Geogheganetal.,1997;AcharyaandBennett,2001;Kestensetal.,http://wendang.chazidian.comingadvances

☆

SeniorauthorshipissharedbySeong-HoonChoandNeelamC.Poudyal.?Correspondingauthor.Tel.:+18659747411;fax:+18659749492.

E-mailaddresses:scho9@utk.edu(S.-H.Cho),npoudyal@utk.edu(N.C.Poudyal),rrobert3@utk.edu(R.K.

Roberts).

0921-8009/$–seefrontmatter©2007ElsevierB.V.Allrightsreserved.doi:

10.1016/j.ecolecon.2007.10.012

404

ECOLOGICALECONOMICS66(2008)403–416

inGIStechnology,thestudiesattemptedtomeasurehedonicvaluesofspatialconfigurationsofopenspace.Thesestudiesemployedvariousspatialindicescommonlyusedinlandscapeecologyresearch.Palmer(2004)andGeogheganetal.(1997)foundthatthecompositionandspatialpatternoflanduseinthesurroundingsaregoodpredictorsofscenicperceptionandhou-singvalue.AcharyaandBennett(2001)foundthathousingvalueisinfluencedbythelandscapestructureofaneighborhood.Morancho(2003)concludedthatretainingnumeroussmallgreenareasthroughoutacityispreferredtoasmallernumberoflargerparks.

Further,attemptshavebeenmadetovaluethequalityofwetlandsandagriculturalopenspaces.Mahanetal.(2000)evaluatedtheeffectsofwetlandquality,includingshape(e.g.,linearorareal)andcontent(e.g.,novegetation,withemergentvegetation,withscrub-shrub)onpropertyprices.DossandTaff(1996)usedmeasuresofwetlandcontenttoestimatemarginalvaluesofwetlandtypes.ReynoldsandRegalado(1998)alsoexaminedtheinfluencesonpropertypricesofdifferenttypesofwetlands,suchasforestedandemergentpalustrine,scrub-shrub,andshallowpondwetlands.Similarly,attemptshavebeenmadetodifferentiatethequalityofagriculturelands.Irwin(2002),Geoghegan(2002),andGeogheganetal.(2003)lookedattheeffectsofdifferenttypesofagriculturelandonhousingvalues.Theycategorizedagriculturelandintopotentiallydevelopableprivate,potentiallyundevelopableprivate,publiclyownedandaccessible,andconservationeasementtypes.Theyfoundthatvastdifferencescouldexistamongtheeffectsoflandqualityonpropertyvaluesasthequalityofagricultureopenspacechangeswiththeintensityoffarmingpractices.

Therearetwoproblematicimplicitassumptionstypicallymadeinprevioushedonicmodelsthathaveevaluatedopenspace.Thefirstcommonlyusedassumptionthatmaycausebiasedestimationisendogeneityoftheopenspacevariables.Assumingexogeneitydoesnotaddressthefundamentaliden-tificationproblemsofhousingvalues.Becausethelocationofopenspaceislargelydeterminedbymarketforces,mostopenspacevariables,exceptpublicorpreservedopenspace,willbeendogenoustothehousingprice.IrwinandBockstael(2001)addressedtheproblemofidentifyinglandusespillovers,whichariseinahedonicresidentialpricemodelwhentheopenspaceisprivatelyheldanddevelopable.TheyconductedaHausmanendogeneitytestandconcludedthattheirmeasuresforprivateopenspaceandprivatelyownedconservationlandswereendogenous,makingthecoefficientsforthesevariablesbiasedandinconsistent.Smithetal.(2002)consideredopenspacesthatare“fixed”,inthesensethatthelanduseisunlikelytochange(e.g.,publicparksandgolfcourses),differentfromopenspacesthatare“adjustable”,suchasagriculturalorvacantproperties.Theysuggestedthatbecausethelocationofadjustableopenspaceislargelydeterminedbymarketforces,itwillbesensitivetodiversityinbuyerexpectations,leadingtoendogeneityinthedispositionofsomelanduses.Walsh(2007)evaluatedopenspacepoliciesusinganempiricalapproachthatincorporatestheendogeneityofprivatelyheldopenspaceinalocationalequilibriumframework.

Thesecondproblematicassumptiontypicallyadoptedforevaluatingopenspaceusingthehedonicmodelisthatimplicitpricesareconstantacrossahousingmarket.Geogheganetal.(1997)appliedaspatialexpansionmethodthatdetectsa

spatiallyvaryingrelationshipatthelocallevel.Theirstudyrevealedthatthemarginalvaluesofland-usediversityemploy-ingmeasuresofpercentofopenspace,diversity,andfragmen-tationoflandusesvarybyproximitytothecentralbusinessdistrict(CBD).TheyfoundthatdiversityinlanduseinducesapositiveexternalityonthevalueofhousingintheimmediateareaandouteredgeoftheCBD,butitcreatesnegativeexternalitiesinareasbetweenthem.

AlthoughGeogheganetal.(1997)detectedvariationinmarginaleffectsusingaspatialexpansionmodel,themodelhassomelimitations.First,itisdependentonthecomplexityoftheexpansionequations.Asaresult,distributionsofspatiallyvaryingparameterestimatesmightconcealimportantlocalvariationswithinthebroadtrendsrepresentedbytheexpansionequations.Second,theformoftheexpansionequationsisdeterministicanddemandsaprioriknowledge(Fotheringhametal.,2002).Unlesstheexactpatternofnon-stationarityisknown,theselimitationslikelybiastheresultsfromthespatialexpansionmodel.Third,theirexpansionequationsdonotaddressthepotentialendogeneityofopenspacevariables.

Inaddressingsomeoftheselimitations,ChoandRoberts(2007)usedlocallyweightedregressiontoestimatespatialvariationinthevalueshouseholds’placeonopenspaceasmeasuredbyneighborhooddensity.Unlikethespatialexpan-sionmethod,noaprioriassumptionregardingaparticularformofspatialnon-stationarityisrequiredinthelocallyweightedregressionmodel(ClevelandandDevlin,1988).ChoandRoberts(2007)foundhigheramenityvaluesforlowerhousingdensityinsprawledareasrelativetourban-coreareas.Still,thehousingdensitymeasureusedforcapturingtheamenityvalueofopenspaceintheirstudywaslackinginthreeways.First,theydidnotaddresstheissueofopenspaceendogeneity.Second,theirmeasureofhousingdensitywasaroughproxyforopenspacebecauseitdidnotexcludenon-developableareas(e.g.,airportsandlandfills).Third,theirmeasureofhousingdensityonlyreflectedthequantityofopenspacewithoutdifferentiatingamongqualitiesofopenspace,e.g.,speciescompositionandlandscapeofforestedareas.

Thecurrentresearchwasdirectedtowardidentifyingthespatialvariationofamenityvaluesforbothquantityandqualityofopenspaceinthehousingmarket.Toachievetheobjective,openspacevariableswereendogenizedintheordinaryleastsquares(OLS)andlocallyweightedregressionswithinthehedonicpriceframework.Thequantityofopenspacewasmeasuredbyitssizeandproximitywhilethequalityofopenspacewasmeasuredbyitsspatialconfigurationandspeciescomposition.Marginalimplicitpricesfortheopenspacevariableswerecalculatedandtheirlocalmarginaleffectsweremappedtobetterunderstandthespatialvariationintheeffectsofopenspaceonhousingprices.Asspatialvariationinamenityvaluesdiffersacrossametropolitanarea,theneedforsite-specificlandusemanagementtofitthelocalcharacteristicsisrecognized.

2.

Methods

2.1.

Empiricalmodel

TheusualprocedurewastofirstestimatethehedonicmodelwithOLS.Endogeneityoftheopenspacevariableswasthen

ECOLOGICALECONOMICS66(2008)403–416

405

Table1–Definitionsofvariablesusedinthetwo-stagemodelVariable

Definition

StructuralvariablesHouseprice?Transactionpriceadjustedwithhouseprice

indexofKnoxvilleinyear2000dollarvalue($)

FinishedareaHousesquarefootage(m2)BuildingageAgeofthehousein2006(years)ParcelsizeSizeofparcel(m2)StoriesNumberofstoriesGarageDummyvariableforgarage(1ifgarage,

0otherwise)

BedroomNumberofbedroomsBrickDummyvariableforbricksiding(1ifbrick,

0otherwise)

PoolDummyvariableforswimmingpool(1ifpool,

0otherwise)

FireplaceNumberoffireplacesinhouseConditionDummyvariableforconditionofstructure

(1ifexcellent,verygoodandgood,0otherwise)

QualityDummyvariableforqualityofconstruction

(1ifexcellent,verygoodandgood,0otherwise)NeighborhoodvariablesPopulationNumberofpersonspersquarekm.incensus

densityblockgroupIncomeMedianhouseholdincomeforcensusblock

group($)

TraveltimetoAveragetraveltimetoworkforcensusblock

workgroup(min)VacancyrateHousingvacancyrateincensusblockgroupUnemploymentUnemploymentrateforcensusblockgroup

rate

ImpairmentNumberofwaterimpairmentsreportedin

thenearestwaterbody

DowntownDistancetothedowntown(m)WaterDistancetothenearestwaterbody(m)SizeofwaterSizeofthenearestwaterbody(m2)

bodySidewalkDistancetothenearestsidewalk(m)GolfcourseDistancetothenearestgolfcourse(m)RailroadDistancetothenearestrailroad(m)HighSchooldummyvariablesWest1ifWesthighschooldistrict,0otherwiseDoyle1ifDoylehighschooldistrict,0otherwisePowell1ifPowellhighschooldistrict,0otherwiseKarns1ifKarnshighschooldistrict,0otherwiseHalls1ifHallshighschooldistrict,0otherwiseGibbs1ifGibbshighschooldistrict,0otherwiseFulton1ifFultonhighschooldistrict,0otherwiseFarragut1ifFarraguthighschooldistrict,

0otherwise

Central1ifCentralhighschooldistrict,

0otherwise

Carter1ifCarterhighschooldistrict,

0otherwise

Bearden1ifBeardenhighschooldistrict,

0otherwise

Austin1ifAustinhighschooldistrict,

0otherwise(reference)OthervariablesSeasonDummyvariableforseasonofsale(1ifApril

throughSeptember,0otherwise)

Primerate

Averageprimeinterestratelessaverageinflationrate

(continuedonnextpage)

checkedwiththeSmith-BlundellTest(Wooldridge,2003,pp.484).Ifendogeneityoftheopenspacevariableswasdetected,theinstrumentalvariables(IV)approachwasusedtoaccountforopen-spaceendogeneity(IrwinandBockstael,2001),

Ri¼aXiþbP?iþeið1ÞPi¼dWiþgi

ð2Þ

whereRiisthevalueofthehouseinparceli;Xiisavectoroffactorsthatdeterminesthevalueforresidentialuseofparceli;Piisavectorofopenspacemeasuresaroundparceli;eiisa

randomdisturbanceterm;P

?iisthepredictedvaluefromEq.(2);Wiisavectorofopen-spaceinstrumentsforparceli;andηiisarandomdisturbanceterm.

Theoretically,sixopenspacemeasuresusedinthemodelwerethoughttobeendogenousbecausetheyarelargelydeterminedbymarketforces.Forexample,thenationalout-doorrecreationsurveydatasetshowsthat99%oftheforestlandinthestudyarea(cityofKnoxvilleandtownofFarragut)isprivatelyowned(Betz,1997)andpotentiallysubjecttochangeinresponsetomarketforces.Inthefirststage,Eq.(2)wasestimatedusingtheinstruments.Thechoiceoftheinstrumentalvariablefortheopenspaceequationisdifficultbecauseuniquenessoffunctionalformisratherarbitrary.Nonetheless,distancetodowntown,distancetonearestwaterbody,sizeofthenearestwaterbody,distancetosidewalk,distancetogolfcourseanddistancetorailroadwerechosenasuniqueinstrumentalvariablesforeachofthesixopenspaceequationsofdistancetonearestevergreenforestpatch,dis-tancetonearestdeciduousforestpatch,distancetonearestmixedforestpatch,forestpatchdensity,forestedgedensityandmeanpatchsizeofforest,respectively.Inthesecondstage,Eq.(1)wasestimatedwitheitherOLSorlocally-weightedleastsquaresregressionafterreplacingPtheirpredictedvaluesfromEq.(2)(P

?iwith

i).

406

ECOLOGICALECONOMICS66(2008)403–416

Fig.1–Thestudyareashowingthelocationofsamplehouses.

Henceforth,thelocallyweightedregressionmodeliscalledthe“localmodel”andtheOLSmodeliscalledthe“globalmodel”becausethelatermodelassumestherelationshiptobeconstanteverywhere.FollowingFotheringhametal.(2002),thesecondstagehedonicpriceequationforthelocalmodelisspecifiedas:??

?Ri¼b??X1þe

ð3Þ

Observationsforhousesincloserproximitytohouseihave

moreinfluenceintheestimationofthelocalparametersthanhouseslocatedfartheraway.Thatis,ÀÁ

?ðui;viÞ¼XTwðui;viÞXÀ1XTwðui;viÞYb

ð5Þ

?isavectorofvariablesincludingthepredictedopenwhereX

spacevariables,βisavectorofparameters,andεisavectorofrandomerrors.?isalogicalmultiplicationoperatorinwhicheachelementofβismultipliedbythecorrespondingelement

?and1isaconformablevectorof1's.WithnsetsoflocalofX

parameters,βtakestheform:b0ðu1;m1ÞBb0ðu2;m2Þb¼B@NNN

b0ðun;mnÞ

b1ðu1;m1Þb1ðu2;m2ÞNNNb1ðun;mnÞ

NNNNNNNNNNNN

1

bkðu1;m1Þbkðu2;m2ÞCCNNNAbkðun;mnÞ

?(ui,νi)representsanestimateofβ(ui,νi)andw(ui,νi)isanwhereβ

n×nspatialweightingmatrix.Anadaptivebi-weightfunctionisusedtogeographicallyweightedobservations.Thefunctionis“adaptive”inthesensethatthetraceofwexpandsorcontractsasthelocationchanges.Theadvantageofthisparticularweightingfunctionisthatithasthedesirablepropertiesofbeingcontinuouswhilegivingmoreweighttothenearestneighbors.Nearestneighborsarehypothesizedtoinfluenceeachotherbasedonacontinuousdecayfunction.Butobservationsoutsidetherangeofthenearestneighborsareassumedtohavenoinfluenceonhousei.Thebi-weightfunctionis

hÀÁ2i2

ifdijbdmaxðqÞ;otherwisewij¼0;wij¼1Àdij=dmaxðqÞ

ð6Þ

ð4Þ

where(ui,νi)denotesthecoordinates(longitude,latitude)of

housei.wherejrepresentsadatapointinspaceandirepresentsanypointinspacewherelocalparametersareestimated,dijis

the

ECOLOGICALECONOMICS66(2008)403–416

407

Table2–Descriptivestatisticsforvariablesusedinthetwo-stagemodelVariables

StructuralvariablesHouseprice($)Finishedarea(m2)Buildingage(years)Parcelsize(m2)StoriesGarageBedroomBrickPool

FireplaceConditionQuality

Neighborhoodvariables

Populationdensity(people/acre)Income($)

Traveltimetowork(min)Vacancyrate

UnemploymentrateImpairmentDowntown(m)Water(m)

Sizeofwater(m2)Sidewalk(m)Golfcourse(m)Railroad(m)

HighSchooldummyvariablesWestDoylePowellKarnsHallsGibbsFultonFarragutCentralCarterBeardenOthervariablesSeason

Primerate(%)

Openspaceamenities

Distancetonearestevergreenforestpatch(m)Distancetonearestdeciduousforestpatch(m)Distancetonearestmixedforestpatch(m)Forestpatchdensity(patches/100ha)Forestedgedensity(m/ha)Meanforestpatchsize(ha)Numberofobservations:9571.

Mean

117,786.70

168.6039.361791.39

1.260.533.000.250.050.670.590.39

Std.Dev.

94,609.26

89.1124.381873.79

0.430.490.710.430.210.600.490.48

Minimum

36,600

40.872164.1810000000

Maximum

1,803,683

1220.1410749,450.72

31811911

1.2824,092.91

21.590.060.040.4710,876.182078.652164.88394.102863.841622.720.8111,192.19

3.100.030.030.997601.971144.834247.33325.141375.171200.430.144482.00

0.000.000.000791.8313.462.447.08126.527.6030.0576,797.00

32.530.270.51330,168.616047.4111,987.402849.857071.836085.66

0.230.080.0020.040.00030.0050.130.180.170.020.070.420.280.040.210.010.070.330.380.370.140.260000000000011111111111

0.567.240.491.6304.6719.23

467.98325.51481.405.1734.553.75409.14283.07440.943.5232.397.280.300.300.300.000.000.002704.231558.073337.9815.32230.2687.72

Euclideandistancebetweenpointsiandj,anddmaxisthemaximumdistancebetweenobservationianditsqnearestneighbors(Fotheringhametal.,2002).Theweightattributedtoregressionpointiisone.Weightsattributedtothejobserva-tionsintheneighborhoodofiarelessthanoneandbecomezerowhenthedistancebetweeniandjisgreaterthandmax.Therefore,asdijincreases,theinfluenceofobservationjonlocalregressionpointidecreases.

2.2.Crossvalidation

Across-validationapproachselectstheoptimalnumberofneighbors(ClevelandandDevlin,1988).Thecross-validationfunctionis,

nÂXÃ2

?piðqÞyiÀyCrossvalidation¼min

q

i¼1

ð7Þ