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A. a.(1)(a) i) a)S ($0 ($0 0 (($0 0 0  A_ekqwDocumentDocument StyleI.1.A.a.(1)(a)i)a)jo4Tech InitInitialize Technical StyleS #   1 .1 .1 .1 .1 .1 .1 .1 S  CuyTechnicalTechnical Document Style11.11.1.11.1.1.11.1.1.1.11.1.1.1.1.11.1.1.1.1.1.11.1.1.1.1.1.1.1x?t2PleadingHeader for numbered pleading paper %  &U(   XXX  XXXXXXX  XXXXXXXX  XXXXXXXX  XXXXXXXX  XX'  ''''  ''''XX?e('*dE*??e('*dE*?ll1ll2ll3ll4ll5ll6ll7ll8ll910111213141516171819202122232425262728  .+(G3$ d!XXXX  W %\  `*Times New RomanTTB21, 2, 3,Numbers.0..($      d!XXXX   [PXX+XX    2  .  ݀Excludingthefourfirmswhoparticipatedinthisstudy,thedistributionofremaining { propertymanagementfirmsbyapproximatesize(i.e.,numberofrentalunits)isasfollows:   `  NumberofRentalUnits   p NumberofFirms 6    `    100< h      p   3     `    100200     p   8     `    200300     p   5 v    `    300400     p   2 _    `    >400 h      p   3 H ThissummaryisbasedonTheOuterBanksVacationGuide1994,asourceformostofthe   Realtorshandlingpropertiesintheareaandatelephonepollofthefirmsconductedtoestimatethenumberofpropertieseachfirmmanagedasof1994.  d!XXXX   [PXX+XX    3  .  ݀Therentalpricesvaryaccordingtoseason,andincludetheoffseasonprice(generally  January1toearlyMay),thepreseasonprice(earlyMaytomidJune),thepeakseasonprice(midJunetolateAugust),andthepostseasonprice(lateAugusttoearlySeptember).OffseasonpricesalsoapplybetweenlateAugustandtheendofthecalendaryear.Becausetheoffseasonhasverylittleweeklyrentalactivity,thisseasonisnotincludedinouranalysis. ' d!9XXXX   [PXX+X9X    17  .  ݀Theweightedaverageindexisanaverageoftheestimatedpermanentemployeeswages w  andtemporaryemployeeswagesweightedbythenumberofemployeesofeachtype.TheStoneindexistheaverageofthelogoftheestimatedpermanentemployeeswagesandtemporaryemployeeswages,weightedbythecontributionoftheemployeetypetototalpayroll.  d!XXXX   5.Withthiscontractualrelationship,weareabletofocusourmodelontheinteractionsbetween ( therentalfirmsandconsumers.Osborne[1995]considerstheinteractionsbetweenrentalfirmsandownersofthepropertiesandexaminestheunderlyingpropertiesoftheindustrystandardcommissionrate.  d!XXXX   [PXX+XX    7  .  ݀TheformatforthemodelinTirole's[1988]structureusesasimplequasilinearutility   functionwithoneindexofproduct'sdistinguishingcharacteristicsorquality,andanumerairegood(withapriceofunity).Inthissettingthefirm'sprofitmaximizingdecisionsonapriceschedulecanbedescribedasprofitmaximizationsubjecttotheparticipationandincentivecompatibilityconditionsthatspecifyhowconsumers"areknown"toreacttotheseprices.Givenadistributionofdifferenttypesofconsumers,marginalpriceswillbemarkedupovermarginalcostsbasedontheinversehazardratethatdescribesthedistributionofconsumertypesandwiththatdescriptionislinkedtothefirm'smarginalrevenueschedule.ThelinkisanalogoustotheonedescribedbyBulowandRoberts[1989]inthecontextofoptimalauctionstrategies. ; d!XXXX   [PXX+XX    11  .  ݀ThesameissuesariseforthemodelsusedbyBerryetal.[1995],Goldberg[1995,1996]. & Whereveritisassumedthateachfirmcanproducemultipledifferentiatedproducts,withinfirmcostconditionsaswellasmarketdemandconsiderationsinfluencehowpricesareselectedtomaximizeprofitsandwhethertheequilibriumpricesareintheinteriorofthefirmspricingstrategyset.  d!XXXX   [PXX+XX    12  .  ݀Feenstra'sresultsarederivedformodelswheretherearenointeractionsbetweenobservable + individualconsumers'characteristicsandunobservableproductcharacteristics,whiletheBerryetal.[1995]andGoldberg[1995]empiricalapplicationsallowforthem.Thekeyresultsfor - ouranalysisistheweakseparabilityofaggregateutilityfunctionsinthepriceandattributesofeachvariety.Thesamefunctionofpriceandqualityappliestoallconsumers.Thisiswhatallowstheisolationofmarginalvalueofcharacteristicsfromthehedonicpricefunction.Feenstra[1995]seemstoimplythatalltheseresultshavenotbeenrecognized,suggestingattheoutsetofhispaperthefollowingcharacterizationoftheliterature:8  Whilehedonicregressionsandassociatedhedonicpriceindexesareusedinmanyapplications,thetheoryunderlyingthesemethodsisnotwelldeveloped.ThemodelofRosen[1974]isoftenusedtotheoreticallyjustifytherelationbetweenmarketspricesandthecharacteristicsofgoods,thoughitisnotobviouswhatthismarketrelationimpliesaboutthewelfarefrompurchasinggoodsembodyingthecharacteristics.(p.634)    Hisclosingsentenceinthisquoteseemstoosweepingacritiqueofpastliterature.Itisfairtosuggestthelinkbetweenhedonicpricefunctionsandpriceindexeshasnotbeenasclearlydevelopedashenowoffers.However,thewelfarepropertieshavebeenwellunderstoodandhisresultsforthecaseofidenticalindividualsrecognizedsinceFreeman[1974].SeeFreeman[1993],Palmquist[1991],andMcConnell[1993]fordiscussionsoftheinterpretationofthemodelinthecontextofnonmarketvaluation.  d!XXXX   [PXX+XX    13  .  ݀Thenortherntownshipsaremuchlessdevelopedthanthesoutherntownshipsandso  whetherornotpropertiesarelocatedintheseareasaretreatedasapotentialcharacteristicforwhichfirmsmaydevelopapricestrategyover.  d!9XXXX   [PXX+X9X    14  .  ݀TheTiaoGoldberger[1962]testallowsanullhypothesisspecifictoindividualcoefficients F inaregressionmodeltobetestedacrossmodelsestimatedwithdifferentindependentvariablesandsamples.Theonlyinformationrequiredtoimplementthetestistheestimatesoftheindividualmodels(notapooledestimateacrosssamples,asinaChowtest).Theteststatisticisdefinedasfollows:8AWGCz Xx p @Xdddddddd@x %#l # v ThisisdistributedasacentralFdistribution(forordinarylastsquaresestimates)withM1and}=QG73z X  p@@@((# %#l #}}=]G73z X  p @@@$)#((#l}degreesoffreedom.Misthenumberofsamples,Tsisthenumberofobservations x&2                             ineachsample,Ksisthenumberofregressorsineachsample,Spisthesumofsquared \(  residualsforeachsample,andpsisthediagonalelementofthemomentmatrix,(x)ls|kT{Lxs)1forthe E)  sthsamplecorrespondingtotheestimatedparameterbs,and}=SG73z X F p @@@G ,#$)#l+G}߀isaweightedaverageofthe .*   estimatedparametersacrosssamples,definedas: j+$  8WGCz Xx p @Xdddddddd@uxL #Lll 'dxd Level 1 Level 2 Level 3 Level 4 Level 5(F29$ d!XXXX  W ($ (    ) 5674M << deUU)2V  Z 2CG Times (W1) Regular g -  [P%XXXX    6  .  ݀9XX{XXTheanalysesofBerry,Levinsohn,andPakes[1995]andFeenstraandLevinsohn[1995]are  distinguishedbytheirmethodsusedtoindexproductsinrelationshiptocharacteristicsandconsumerpreferences.Forexample,Berry,Levinsohn,andPakesderivethispricingrulefromautilityspecificationthatislinearinthelogsofproductcharacteristicsandhasrandomcoefficientstoallowforunobservedproductcharacteristics.Ontheotherhand,FeenstraandLevinsohndevelopananalogousexpressionthatincorporatesthe marketspacecharacteristicsarelinkedusingweightedharmonicmeansofpriceadjusted distancesincharacteristicsspace.#XX+X9Xt#Ԅ Level 1 Level 2 Level 3 Level 4 Level 5($     ;6<4A<< c  [P%XXXX    20  .  ݀Thisfollows9XX{XXԀbecause}=G 73z X C p @@@xl},whereMCismarginalcostandPistheoverall  rent.Also,the biasinourestimatedmarginalpricesaregivenbypi=(P/MC) MWTPi,  whereMWTPiisthemarginalwillingnesstopayforcharacteristicI,andpi=themarginalprice z (rent).Thus,theestimatesofthemarginalvaluearecomputedwiththeadjustment(1+R)pi c ,whereRislessthanzero.#XX+X9Xm#9XX+XX kL #XX+X9X,#3F?``I^Iofm{g? {n$IIzs?bhsV?b?ps_`MysK`Sss`Tus7 `K s?(?)2`(t`1`)`( `)ykmpzzv2impDmbzz2immm/vxSxxw}S~ h j Sj j i o q Sq q p hAjTioAqTp{F,.`,.T,`*`>,T `  ` citz itRztikt iqitzitztikt p it c it z it{ xp Eittiktq(r)D([,n)?T1Z ([ )1WT,!%~6G4&OLE 2.0 Box <=8C HKKKK( $ Figure  1    [P%XXXX    21  .  9XX{XXԀForinstance,anoceansidehomemaybethehomejustnexttoanoceanfronthouseorthe  lasthomeinarowalongastreetleadinguptotheocean.Thus,theexactproximityofthe oceansidehousestotheshorelinevaries,whileourcategoricalmeasureofproximitydoesnot.#XX+X9X^#U Xt=XN5tz!tXt N7i gg i zP i t X i t Hh!zt[X3thNzNtXNt(0,{...o,[)D0i 71 ( )[}1(o1)1m,../.v()N], 7R IDsGPDsGP bBAR  69#XXXX   7 (  1  )   U`(X_{0`t}`,``...``X_{N`t}`,``z_t`)~=~X_{0`t}~+~sumfrom{i``=``1}toN``g_i``(z_{i`t})``X_{i`t}~+~H`[`h_1`(z_{1`t})``X_{1`t}`,``...``h_N`(z_{N`t})``X_{N`t}`]``,  69#XXXX   7 (  2  )   69#XXXX    7 (  4  )  xP7itxFo7ixQ7itdxY7txWH7txW7it4x7x(x,x,lx,0x)x, {partial`c_{it}`(z_{it}^*)}over{partial`z_{ikt}}~=~{partial`pi_i`(q_{it}^*,``z_{it}^*)}over{partial`z_{ikt}}``left[`1~~left({p_{it}^*````c_{it}`(z_{it}^*)}overp_{it}^*right)`left(`1over{sigma_{ikt}}right)`right]``,-I7s>()T sKZsR % d!XXXX   [PXX+XX    18  .  ݀Resultsforthepreferredspecificationofeachfirm'sresidualdemandfunctionindicatedan $ autoregressivepatternintheerrortermsforfirm1(atalagoftwoperiods),andforfirm4(atalagofoneandnineteenperiods).Noautocorrelationwasdetectedforfirm3,andfirm2hadinsufficientdatatotestforautocorrelation.Theseriesofpriceandquantityobservationsforfirm2wasdiscontinuous.Theyearsinwhichthepriceandquantityindexescouldbecreatedwere1989,1991,and1992.Thissplitinthesampleimpliedthereweretoofewobservationsfortheempiricalanalysisofautocorrelation.  d!XXXX   [PXX+XX    19  .  ݀Theinstrumentsusedinthefirststageregressionincludedthedummyvariablesforthe  , nationalholidays,thewageindexforeatinganddrinkingestablishments,andtheutilizationrateofpropertiesbytheirowners.Theautocorrelationadjustmentalsorequiredthefirststage - regressiontoincludethelaggedvaluesofeachofthevariablescorrespondingtothelagperiodidentifiedintheanalysisofsecondstageresidualsforeachfirmsmodel.ThesensitivityoftheresidualdemandfunctionstovariationsinthespecificationoftheTSLSmodelswasconsidered.Eightvariationsofeachmodelwereestimatedforeachfirm.Thesemodelsvariedtheinstrumentalvariablesincludedinthefirststageregression,andwhetherornotStoneorweightedaveragewageindexeswereincludedinthesecondstageregression,andwhetherornotthewageindexforeatinganddrinkingestablishmentswasincludedinthesecondstageregression.Theestimatesoftheresidualdemandelasticityforfirms1and4wereextremelystableacrossthisspecificationsearch,varyingfrom0.271to0.343forfirm1,andbetweenτ0.098to0.117forfirm4.Theresultsforfirms2and3arelessrobust(thedataforthesefirmsarelimited).Thereweretwosignificantestimatesoftheresidualdemandelasticityforfirm2,andtheywere0.137(reported)and0.215.Therewerefoursignificantestimatesoftheresidualdemandelasticityforfirm3,andtheyrangedfrom0.239(reported)to0.385. CRight ParRight-Aligned Paragraph NumbersI.A.1.a.(1)(a)i)a)%\  `$Times NewRomanXXj\  P6G;XP%\  `*Times New RomanTTX\  P6G;P(+$XXXX   d pBAR ~__EEEHP LaserJet 5M (PCL)24 :do ́ HP5MPCL.PRS,\,\H !L- 0 d&0 d dK Kdkk' dxd Level 1 Level 2 Level 3 Level 4 Level 5(!$ Table    m6nlA<< b%\  `$Times NewRoman&&a\  P6G;&PTable_ATable_BTable_CTable_DTable_E 69#XXXX    7 (  3  )  ݁Level 1Level 2Level 3Level 4Level 5'\  `TimesRomanMtLevel 1Level 2Level 3Level 4Level 5 Kln``P_t~=~SUMfromk``{P_{tk}``R_{tk}}over{TR_{t}}~ln``{Phat}_{tk}:sGb6lC<< C%\  `$Times NewRomanXXj\  P6G;XP+AApGebddidd2  d!XXXX   [PXX+XX    4  .  ݀Onceacontracthasbeenmade,itishighlyunusualforapropertyownertochangerental o! firmsduringarentalyear.Asidefromthelegalcostsofalteringacontract,therearealsoothersignificantcoststoswitchingfirmsduringtherentalseason.Forinstance,oncetherentalbookletshavebeendistributed(typicallybyFebruary),disseminatinginformationaboutanyadditionallistingsisquitecostly.Also,mostofthereservationsfortheupcomingrentalseasonaremadebylatewinter.Thus,oncetheseasonisunderway,switchingrentalfirmsbecomesinfeasiblefromapracticalperspective.  [P%XXXX    8  .  ݀Bycontrast,9XX{XXԀBerry,etal.[1995]andFeenstraandLevinsohn[1995]developmicroconsistent  structuresofconsumerbehaviorthatallowsforconsumerheterogeneityandderivesfromtheaggregateofthesedemandsanoligopolypricingrule.#XX+X9Xk#Theirframeworksdonotrequireaclosedformexpressionforaggregatedemand.Thepricingrulescanbeused,withassumptionsaboutthepreferencestructureandthenatureoftheequilibrium,todescribethenatureofthecompetitionandthedemandfordifferentiatedgoods.($$   1  lnilnPjtRkP{wtk RwtkkxTRm7t8PtkIFeC `boldSUMfroms(T_s`-`K_s) Phat@bsbspis67spCsII(/)(>1/s)). Phat ,P_it~=~F_i`(Q_it,~Y_t,~W_t,~W_{it})``,(}1)9 egR6pgi7MCx7PJpgi" V 69#XXXX    3  sigma_{ikt}~=~left({partialpi_i}oversm{partialq_{it}}right)`left({partialpi_i}oversm{partialz_{ikt}}right)`vert80vert80``p_{it}^*  `left({partial^2`pi_i}oversm{partialq_{it}`partialz_{ikt}}right) V [PXXXX    15  .  ݀Thecoefficientsforthemoreeasilyreproduciblecharacteristicsofaunit,suchasthe Q  presenceofamicrowave,dishwasher,colortelevision,etc.,werealmostuniformlynotsignificantlydifferentacrossfirmsinanyyear.(G3[P$ d!XXXX  W   0  .  d!XXXX   [PXX+XX    16  .  ݀Thelogicusedtoderivetheinverseresidualdemandfunctionbeginswithaninverse   demandfunction:8WGCz Xx p @Xdddddddd@x#l"0x    whereQitisavectorofquantityindexesofallotherfirmsandallothervariablesareasdefined  forequation(4).Thebasicstructureimpliedbyallthepricingmodelswediscussedreliesonsometypeofpricemarkupequation,giveningeneraltermsas:8WGCz Xx p @Xdddddddd@x##lQx   Am withthemarginalcostfunction,MCi,afunctionofownquantity,thecostvariablesspecificto Y  firmi(Wit),thecostvariablescommontotheindustry(Wt).Allothervariablesareasdefined Bn  above.Ananaloguetotheabovetwoequationscanbedefinedforeachoftheothern1firmsinthemarket.SolvingtheresultingsystemofequationsforQit,thevectorofquantitiesofthese @  n1firms,impliesthefollowingsetofequations:8WGCz Xx p @Xdddddddd@xA##ls 0x ]!`     Substitutingtheseequationsintotheinversedemandyieldstheinverseresidualdemandfunction.xP7itxf17ixQ?7itxQ7itxY=7t4x7Tx(x,3x,ax)x,xP7itxMCgixQu7itFxW7itxW7t i xQ 7it xQf 7it7 xY 7t4xax# 7x(x,Cx,x) x( x, x, x)Sx, xxQ7itOxQ`xQ7itxYP7txW7tbxWU7it7x7x(Fx,tx,x,x)* x. `boldF~=~{SUMfromsleft(`(b_s``-``bBAR`)^2``vert30vert30``p_s`right)}  over{left({(M-1)}SUMfroms`S_s`vert50vert50`  SUMfroms(T_s`-`K_s)right)} Cbbar~=~{Sumfroms(b_s`/p_s)}OVER{sumfroms(1/p_s)}``. !P_it~=~f_i(Q_it,~Q_{it},~Y_t)``, V 69#XXXX    3  BP_it~~MC^i(Q_it,~W_it,~W_t`)~=~LAMBDA^i(Q_it,~Q_{it},~Y_t)``, V 69#XXXX    3   [P%XXXX    9  .  ݚ9XX{XXԀThisgeneralformalsoparallelsthepricingrulesdevelopedinMussaandRosen[1978]and  МTirole[1988]formonopolydecisionswithmultipleproductswhenaconsumerstypeofpreferencesareonlyknownafterherchoicehasbeenmade.#XX+X9X^#9XX+XX#XX]XX9XX]# ,Q_{it}~=~Q`(`Q_it,~Y_t,~W_t,~W_{it}`)``.  [P%XXXX    10  .  9XX{XXԀ#XX+X9X^#Ԛ9XX+XXԀFormally,f82"`x < `$ "l\ kf,evaluatedat{q)li|k*{<t,z)li|k*{<t}.Theassumptionsused  tocharacterizehowthispricesubstitutioneffectismeasuredparalleltheconditionsdescribedbyWillig[1978]torecovertheHicksiandemandforqualityfromthedemandsforlinkedprivategoods.SeealsoBockstaelandMcConnell[1993].#XX+X9X٣# 0(`1~+~eta_R`)`p_i~ ~{MC}oversmP``p_i p_i~=~pBAR``b_ik%!S!!!*iktddiqdditddi?zddsiktkps8itddziqdditOzddiktdk,},,,,L,,!h!iIoIphhiopKhi o p)7dd%2 eSUPbSUBiSUP2(hH  Z 2CG Times (W1) Regular > [P%XXXX    1  .  ݀9XX{XXFeenstra[1995]developmentofthewelfarepropertiesofhedonicpriceindexesprovidesthe   basicframeworkforourempiricalanalysis.#XX+X9X`#(G3$ d!XXXX  W S=3|1"u,^:DPddDDDdp4D48dddddddddd88pppX|pDL|pp||D8D\dDXdXdXDdd88d8ddddDL8ddddX`(`lDl\DDD4DDDDDDdDdXXXXXX|X|X|X|XD8D8D8D8ddddddddddXdbdddpdXXXXXXX~|X|X|X|XddddddddD8D8D8D8pLd|8|P|8|D|8dvddddDDDpLpLpLpL|T|8|8ddddddd|X|X|Xd|8dDpL|8dd~dd|XD88d44dd$/NHxxH\dDXddddd8@d<@d<DDXXdDDxddHxxHppDX<dxtldpxx1plll 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TO-%-,,?J-Tj)<1<,,?< T ?$$,,? $T.<"",,?" T$,,?T1<"",," T#$,,T32K=K,,&K T+P-%-,,J-T,DbPb,,?b<7WCW,,XWsj4t,F5F,,Fs d!XXXX  W ݛ ` {XX9^(#Revised"(US //US , ( ?8/30/96!  9XX9Ԉ  * @t + ENVIRONMENTALAMENITIESASSOURCESFOR X   PRODUCTDIFFERENTIATIONANDMARKETPOWER  A byLauraL.OsborneandV.KerrySmith*    ~  ENVIRONMENTALAMENITIESASSOURCESFOR  PRODUCTDIFFERENTIATIONANDMARKETPOWER   byLauraL.OsborneandV.KerrySmith T Abstract  X     Thispaperevaluatestheimportanceofsitespecificenvironmentalamenitiesasasourceofproductdifferentiatingmarketpower.Usingestimatesfromhedonicpriceequationsandresidualdemandmodels,theanalysisrecoversfirmspecificestimatesofpricemarkupandestimatesofthemarginalwillingnesstopayforaccesstocoastalbeaches.TheapplicationusedintheanalysisinvolvesrentalpriceandoccupancydataforseveralthousandbeachpropertiesalongaportionoftheNorthCarolinacoastlineduringthe1987to1992rentalseasons.KeyWords:JELClassificationNos:L10,Q26,L83  $$ 7XXdX{Xd7x   I.  INTRODUCTION     Thispaperevaluatestheroleofenvironmentalamenitiesasdeterminantsofpricemarkupsfordifferentiatedgoods.Ourresultsfromhedonicpriceandresidualdemandmodelssuggestthatamenitiescanprovideasourceofmarketpower.Threecomponentsoftheanalysissupportthisconclusion:(1)significantdifferencesinhedonicpricefunctionsestimatedforindividualfirmsthatpostyearlypriceschedulesforanarrayofproducts,andtheseproductsarepartlydistinguishedbythesitespecificamenitiestheyprovide;(2)significantdifferencesinestimatesoftheinverseresidualdemandelasticitiesbyfirm;and(3)significantdifferencesacrossfirmsinthemarginalpricesbutnotintheestimatesofthemarginalvaluefortheenvironmentalamenitygivingrisetosomeoftheproductdifferentiation.  Toourknowledgethispaperreportsthefirstempiricalevidencethatsitespecificamenitiescancontributetoafirmsabilitytoexercisemarketpower.Understandingtheroleofnoncompetitivemarketsforenvironmentalamenitiesisimportantforanumberofreasons.Themostapparentofthesemotivationsistheinterpretationofresultsfromnonmarketvaluationmethods.Toestimatetheeconomicvalueforanonmarketenvironmentalresource,thesevaluationmethodsoftenrelyontheassumptionsofcompetitivemarketsandspecificconnectionsbetweenaprivategoodandthenonmarketgood.Applyingindirectmethodswhenmarketsarenotcompetitiverequiresunderstandingtheimplicationsofnoncompetitiveinfluencesforwhatcanbelearnedaboutenvironmentalresourcesmarginalvalues.Anotherimportantconsiderationinvolvesthepolicyquestionsthatariseonceitisacknowledgedthatenvironmentalamenitiesprovideasourceofproductdifferentiatingmarketpowerforlocationspecificgoods.Controlovertheconditionsofaccesstofederalpubliclandsandthecomplementaryresources *$&* ontheselandsthroughconcessions,permitsforactivities,andotheruserelatedcontractsϜprovidesanopportunitytoconveymarketpowertoprivateoperatorswhowinthesecontracts.Underthesecircumstances,contractdesignorregulationoftheprivatefirmspricingdecisionsrequiresunderstandingoftheeffectsoftheinteractionbetweenproductdifferentiationandpricingindetermininghowmarketpowercanleadtoinefficiencieswithdifferentiatedgoods.  OurapplicationinvolvesseveralthousandbeachpropertyrentalsalongaportionoftheNorthCarolinacoastlineduringthe1987to1992rentalseasons.Thepropertiesarerentedonaweeklybasisandaremanagedbyprivatefirms.Becausecontractsbetweenpropertyownersandthemanagementfirmsfollowthecalendaryearandarerarelybroken,firmsfacesignificantcapacitylimitationswhentheyposttheirpriceschedule(typicallypostedinJanuaryorFebruaryfortheupcomingcalenderyear).Thepostedrentalpricesarecombinedwithoccupancyrecordsforeachproperty(byfirm)tocomposepaneldataforthesixyearperiod,whichisusedtoevaluatetheroleofenvironmentalamenitiesasasourceofproductdifferentiationandmarketpower.  Inthenextsection,wedescribehowourmodelingstrategyrelatestotherapidlygrowingliteratureontheempiricalmodelingoffirmbehaviorwithdifferentiatedproducts(e.g.Berry,Levinsohn,andPakes[1995],Goldberg[1995,1996],andFeenstraandLevinsohn[1995]).SectionIIIdescribesourdataandestimatedhedonicpriceandresidualdemandfunctions.Inthelastsection,weusethehedonicpricefunctionsandtheestimatedresidualdemandelasticitiestocomputetheimplied competitivemarginalvalueforbeachaccessanddiscusstheimplicationsofourfindings. *:&* Ї II.  MODELINGFRAMEWORK     Overthepastdecade,therehasbeengrowinginterestindevelopingtheoreticallyconsistentempiricalmodelsoffirmbehaviorinmarketsinvolvingdifferentiatedproducts.BeginningwithBresnahans[1987]studyoftheautomobileindustry,thesemodelshavegenerallyadoptedaframeworkthatusesadiscretechoicemodeltodescribeconsumerdemand,assumingafairlysimplespecificationtorepresentallconsumersutilityfunctionsintermsofexogenousandobservedcharacteristics.Recentwork(Berry,LevinsohnandPakes[1995])hasincorporatedunobservablecharacteristicsintothistypeofmodel.Ourmethodologyisconsistentwiththislogicbutapproachesestimationfromadifferentperspectivethatconnectsthepropertiesofthehedonicpricefunctionasestimatedunderconditionsofmarketpowerandpricemarkupstotheunderlyingmarginalvaluesforamenitiesofdifferentiatedproducts *.  *  1      ׀Weaccomplishthis  byconstructingqualityadjusted,aggregatequantityindexestoestimateresidualdemandfunctionsatthefirmlevel.Theseestimatedfunctionsarethenusedtoprovidecompositeestimatesofthepricemarkupsthatcanbelinkedtothecharacteristicsofthedifferentiatedproduct. A.  Background  #"   NorthCarolinahasnumerousbarrierislandsalongitscoastline.Thethreenorthernbarrierislandsarereferredtoasthe OuterBanks.BecauseaccesstotheseislandsislimitedtoferriesandonebridgeatManteo,N.C.,theareahasfewgeographicsubstitutes.Ourstudyareaisthenorthernmostisland,BodieIsland,withfourtownsNagsHead,KillDevilHills, *$&* KittyHawk,andDuckcontainingabout8,000permanentresidentsinapproximately45squaremiles.ThisareaisgeographicallyseparatedfromotherNCoceanvacationareasbynationalparksonboththenorthernandsouthernboundaries.Figure1providesamapofthearea.Propertymanagementfirmsvaryinsizebasedonthenumberofpropertiestheyhandle,rangingfromthosewithlessthan100propertiestothelargesthavingover400properties.Ouranalysisrequiredaccesstotheweeklyoccupancyrecordsforeachpropertyovertime.Fourfirmscooperatedinprovidingthesedata.Thesefourfirmsprovideexamplesofthethefullrangeoffirmsizesandaccountforabout40%ofthemarket. + *  2       n    TheprimarymarketperiodisbetweenMayandSeptember.Therentalsaregenerallyavailableinweeklytimeunits.Managementfirmsposttheirweeklyrentalpricesforeachrentalseasoninbrochurespublishedatthebeginningofthecalendaryear.Thesebrochuresalsocontainphotographsanddetaileddescriptionsoftheproperties.Table1summarizesthenumberofproperties,the1992averageweeklyrent,andtherangeofrentsacrossthefirmsinoursample.ThesesummariesaredistinguishedbylocationinrelationtotheAtlanticOceanandtheAlbermarleSoundforthethreeprimaryrentalperiods:thepreseason,peakseason,andpostseason. , *  3      ׀PostedrentsinthesethreeseasonsaredesignatedasPrerent,Peakrent,andPostrent, N respectively.  Threetypesofeconomicagentscombinetocreatethebeachcottagerentalmarket:(1)ownersofthecottages,(2)therentalfirmsthatmanagethepropertiesforthoseowners,and(3)theconsumerswhorentthepropertiesforvacationpurposes.Themarketmaybethoughtofastwobilateralinteractionsbetweenthesethreetypesofparticipants.Inoneinteraction,consumersenterintocontractsforweeklycottagerentalswiththepropertymanagementfirm *:&* offeringrentals.Intheotherinteraction,therentalfirmscontractwiththeindividualownerstomanagethepropertiesoverthecourseofacalendaryear.Propertyownersbeginnewcontracts,orrenewpreviouscontractsforthenextyear'srentalseasoninthefallofeachyear,beforerentalbrochuresareprintedanddistributed. ـThisaspectofthemarketimpliesthepricingdecisiontakesplaceafterthemanagementfirmhasfullknowledgeofalltheunitsitwillberepresentingfortheyear.  *  4      ׀Anindustrystandardcontractualrelationshipbetweenownersand    rentalfirmsalsoexistedoverthefulltimeperiodofourstudy.Thesecontractsspecifiedthatfirmsreceiveafixedpercentageoftherentalpriceeachtimethepropertyisrented.Thispercentagewasfixedacrossfirms,andacrossproperties.Withafixedcommissionrate,wemaymodeltherentalfirm'sgoalasmaximizingthedifferencebetweentotalrevenueandtotalcostsineachweek.Thisisaccomplishedthroughtherentalfirmschoiceofapricescheduleforitsproductline. . *  5      ׀Ourmodelinthenextsectiondescribeseachfirmsdecisionsaboutthese  postedpriceschedules(orrentalbrochures). B.  PricingwithProductDifferentiation  ,|   Thereisconsiderablesimilarityinthepricingruleimpliedbyawidearrayofthecurrentliteraturesmodelsfordescribingfirmsbehaviorinthepresenceofproductdifferentiation.Thesemodelsrecognizethatpeoplehavedifferenttastesforthedifferentiatedcommoditiesandthenuseoneofavarietyofspecificationstodescribehowthemarketshareofaparticularproducttypeisaffectedbypricingdecisions,consumercharacteristics,andunobservables. : *  6      ׀In F'"& noncompetitivemarketstructures,pricesaremarkedupovermarginalcostsbasedonsomevariationinaninversehazardratefunctionthatgenerallydescribeshoweachfirmsmarginal *:&* revenuerelatestoconsumerspreferencesovercharacteristics. / *  7      ׀Eachfirmsmarginalrevenue  isderived(dependingontheobjectivesoftheanalysis)byconsideringeitherpriceorqualityvariations,andsolvingtheequilibriumconditionforthepricingrule.  OneexampleofamodeldescribingnoncompetitivepricingofdifferentiatedproductsisFeenstras[1995]analysiswherefirmspriceschedulesaredependentonaggregate(acrossconsumers)responsestopricingdecisions.  *  8      כHismodelisparticularlyusefulwhenanalysismust    takeplacewithoutfullydisaggregatedinformationonconsumerpreferences.ItusesthelogicofAnderson,dePalma,andThisse[1992],alongwithMcFaddens[1978]resultsforthecaseofthegeneralizedextremevaluedistribution,torepresentanaggregateofdifferentindividualspreferenceswithasinglerepresentativeindividualsutilityfunction.Thisispossibleinspecialcaseswherethedemandfunctionsderivedfromtherepresentativeindividualspreferencesarethesameastheaggregateacrossindividualsforeachcommodity.Equation(1)correspondstotheaggregatedirectutilityfunction(anditsassociatedaggregateindirectutilityfunction)thatyieldthesamedemandsasthetotalexpecteddemandsfromallMindividualsinthecaseofqualityadjustedpricesandconstantmarginalutilityofincome.o8WKT9)%p 0  ` %UU##lmo (#(#         (#(#where  zt󀀀= ` vectorofcharacteristicsoverallproducttypes t% $ 0  zit=vectorofthecharacteristicsofproducttypeIconsumedinperiodt(I=1,2,...,]&!%(#(#    ` N),whichiscomprisedofkobservablecharacteristics,thuszitR)l+|kk{k, F'"&   Xit= ` Mxit,aggregateamountofgoodxiconsumedbyallindividuals, 1(#'   M= numberofindividuals, )j$(   xit󀀀= individualconsumptionofithproducttype(I=1,2,...,N), *S%)   X0t= Mx0t=amountofthenumeraireconsumedinaggregateinperiodt, *<&*   gi(zit)=scalarmeasureofproductquality,,gi/,zi0. +%'+ AssumingaNashequilibriaexistsinpricesandthecharacteristicsofeachproducttype{p)li|k*{<t,  z)li|k*{<t},theexpressiondescribingafirmschoiceofanequilibriumproductlineanditsprice  scheduleis:l8\EX6&"p 0  `UU#& l Tl (#(#         (#(#where  cit(zit)=themarginalcostofaunitofxiinperiodt,     pit󀀀= thepriceofxiinperiodt,     qit󀀀= thequalityadjustedpricethatholdsutilityconstantandisdefinedby-i(pit n  ,zit), W  Ѐ  !i()-i1(pit,zit), @   %ikt= theelasticityofsubstitutionbetweenqitandziktinthefunctionpit=!i(qit )y ,zit). K Equation(2)describestherelationshipbetweenthemarginalcostofeachcharacteristic(perunitoftherelevantproducttype)anditsmarginalvalue.  *  9      כThedivergencebetweenthetwodepends  onthepricecostmarkupfortheproducttypeandtheroleoftheproductdifferentiatingcharacteristicsininfluencingtheconversionratebetweenunadjustedandqualityadjustedunitsofeachcommodity(i.e.,xi).Thispuresubstitutionmeasure,representedby%ikt,describeshow e theamountofagoodanditsdistinguishingcharacteristicsrelatetoeachother,holdingutilityconstant.Itismeasuredusingthepriceadjustmentfunction!i(qit,zit).  *  10      כ " !   Ofcourse,thenatureoftheequilibriumwilldependonthespecificsofthepricinggameassumedtocharacterizeeachapplication.CaplinandNalebuff[1991]establishexistenceconditionsforthesingleproductfirmoperatingwheretherearedifferentiatedproducts.Theydemonstratethatthereexistpricessatisfyingthesetypesofpricingrulesthataregloballyprofitmaximizingforallthefirmsinthemarket.Toourknowledge,theiranalysishasnotbeen +#'+ generalizedtothecaseofmultiproductfirms. 0 *  11      ׀Whilethisdoesnotaffectempiricalapplications  (becausetheyrelyprimarilyonthefirstorderconditions),itdoesultimatelyaffecttheirusefulnessininterpretingtheconsequencesofpolicychanges.  TouseFeenstrasresultsinourcase,weassumeloglinearmarginalcosts,pricesgreaterthanmarginalcosts,andqualityadjustedpricesgivenby1i[(pi󀄀gi(zi))/hi(zi)](where,1i>0,  H 1i>0,hi>0,,g򀛀i/,z򀛀i0,and,hi/,zi0).Inthiscase,asemilog(inprice)hedonic    regressionwilloverstatethemarginalvalueofcharacteristicsbytheamountofthepricecostratio.Thisresultimpliestheeffectsofmarketstructureareconveyedthroughtheestimatedhedonicrentequations(Feenstra[1995],p.648).  Ouranalysisrecognizesthatahedonicpricefunctioncanbeusedtodescribethefirmsresponsetoitsperceptionofconsumerdemandsfordifferentiatedproducts.Asaresult,thehedonicfunctioncapturesboththemarginalvalueandthepricecostmargin.Thecoefficientofeachcharacteristicexceedsthemarginalvaluerelativetotheproductpricebyexactlytheamountoftheprice/costratio. 1 *  12      ׀Inourmodel,theseassumptionsimplythatanaggregate b demandmodelintermsofqualityadjustedpricesoffersaconsistentwaytomeasuremarketpower.Moreover,theseestimatescanbeusedtorecoverestimatesofthemarginalvalueofcharacteristicsbecauseweknowhowtheprice/costmarkupaffectsthehedonicpricefunction.Thus,ourestimationprocessusesafirmspricingstrategiesasembodiedinthepostedpricefunctions,alongwiththeoutcomesofthosestrategies(theoccupancyrates)toestimatefirmspecificmeasuresofmarketpowerandexaminetheeffectsofmarketpoweronthemarginalvaluesrevealedfromthehedonicpricefunctions.Ourmodelisimplementedinthreesteps:(a)estimationoffirmspecifichedonicpricefunctionsbyyearandseason;(b)constructionof *B&* weeklyqualityadjustedpriceindexesforthepropertiesmanagedbyeachfirmandtheaggregatequantityindeximpliedbythispriceindex;and(c)estimationoffirmspecificresidualdemandmodelstocharacterizethemarketpowerexercisedbyeachfirm.Combiningtheresultsfromeachofthesestepspermitsmeasuresofthemarginalvalueofsitespecificamenitiestoberecoveredfrom(a). III.  ESTIMATION      Thefourpropertymanagementfirmsthatcompriseourdatasetwillbereferredtonumerically,withfirm1beingthelargestfirmandfirm4beingthesmallest.Thedataforthefourfirmsrelatetotheirrentalexperiencebetween1987to1992.Thepropertiesthefirmshandledchangedoverthestudyperiod.Firm1hada60%increaseinthenumberofpropertiesitmanagedoverthesixyearperiodcomprisingoursample,firm2hada41%increaseinsize,firm3stayedapproximatelyconstantinsize,andthesmallest,firm4,decreasedslightlyinsize.Therentalbookletsforeachfirmincludefourrentalpricesforthedifferentseasons(seefootnote#3)andinformationthatallowedthirtyninepropertycharacteristicstobedefined. A.  FirmSpecificHedonicPriceIndexes  !     Overtheperiod1987through1992,itwouldbepossibletoestimatetwentyfourhedonicpricefunctions(sixyearstimesfourseasons)forapropertymanagementfirmwithcompleteinformationfromtherentalbrochures.Asemilogfunctionalformwasselectedforthehedonicpriceindex,andspecificationanalyseswereconductedoverthethirtyninecharacteristicsthatcouldpotentiallycontributetothepricingstrategyforeachfirm.Characteristicsfallintoone *:&* ofthreecategories:thosedescribingsize(suchasthenumberofbedrooms,bathrooms,andstories),thosedescribingquality(suchasthepresenceofanairconditioneroradishwasher),andthosedescribinglocationoftheproperty(proximitytotheshoreline,orwhetherthepropertyislocatedinoneofthenorthernorsoutherntownships). 2 *  13      ׀Table2summarizesthe & v characteristicsincludedinthepreferredspecificationsforeachfirm.Overall,theestimatedcoefficientsofthehedonicrentfunctionswereconsistentwithpriorexpectations.Theestimatesindicatedthattheproximityofapropertytotheoceancontributeslargepercentageincreasesinaproperty'srent.Forinstance,aunitlocatedoceanfrontmayreceiveamarkupofover60%ascomparedtobeinglocatedbetweenthehighways,ceterisparibus.Thenumberofbedrooms @ andbathrooms,andthepresenceofairconditioningprovidethenextlargestadditionstorent(eachgenerallyrangingfrom7%to15%).Testsforstabilityofthecoefficientestimatesovertime,withineachseason,indicateeachfirmspricingstrategyasdisplayedinthesehedonicpricefunctionswasgenerallyquitestableoverthetimeperiod.  Totestfordifferencesinthepricingstrategiesforeachcharacteristicacrossfirms,TiaoGoldberger[1962]Ftestswereappliedtothehedonicrentfunctionsestimatedforeachyear. 3 *  14      ׀ 0 Thisstatisticteststhenullhypothesisthatanindividualcoefficientisequalacrossfirms.Ourresultssuggestthatthefourfirmsdisplaydifferentpricingstrategiesasembodiedintheirpostedrentschedulesineachoftheyearsthatwehavedata.Thevariablesthatwereconsistentlydifferentacrossfirmsinvolvedthesize(asindicatedbythenumberofbedrooms),theunittype(whetheracottageorcondominium),andthelocationoftheproperties(whetherthepropertyisoceanfront,oceanside,orfurtherinland,andwhethertheunitislocatedinanorthernorsoutherntown).  *  15      ׀Thesetestresultswerenotaffectedbythespecificationselected *>&* forthehedonicrentfunctionswithineachfirm.Thatis,ourconclusionsdidnotchangewhenthetestsusedcoefficientsfromacommonspecificationfittoeachfirm'sdata,orwhentheyusedfirmspecificspecificationsselectedto bestfiteachfirm'sprice/characteristicofferings.Thesetestsimplythattherearedifferencesintherentalpoliciesofthefirmsformostoftheseasonsofeachyear,andthesedifferencesseemtobefocusedonnonreproduciblecharacteristicsofarentalunit.Theseestimatesoffirmspecificpricingstrategiesofferthefirstevidencethatfirmsmayhavetheabilitytomarkuppricesovermarginalcosts. B.  FirmSpecificAggregatePriceandQuantityIndexes  @   Inourapplication,whereeachfirmmanagesalargenumberofproperties,thesetofitspostedrentstogetherwithitsoccupancyrecordwilldeterminetheextentof realizedmarkupovercost.Toapproximatethismeasureweutilizearentindexthatcombinesthe biasedmarginalpricesestimatedfromourhedonicrentequationsforeachfirmandthepropertyspecificoccupancyrates(Rtk).Thehedonicrentequationsforeachfirmdescribestheirprice Z schedules,basedontheirexpectationsofconsumerpreferences.Theoccupancyratesreflecttheconsumersreactionstoeachfirm'srentschedule.Thus,combiningthesemeasuresintofirmspecificaggregaterentindexescreatesindexesofafirmsrealizedpriceinfluenceinthemarket.  Eachhedonicpricefunctionthatisusedtoestimatethefirmspecificaggregaterentfunctionsisdistinguishedbyfirmyearseasonunits.Equation(3)definestheStoneaggregaterentindexformedfromthesehedonicregressions.8|XHDzx p %UU@Xdddddddd@L,#)l'p (#(#   *:&* wheretdenotestheweek,kdenotesthehouse,Rtkisa(0,1)variableequalto1ifhousekwas  occupied(rented)inweektandequalto0otherwise,Ptkisthepostedrentalpriceofhousek  inweekt,}=MG73z X F p @@@GnF l+G}tkisthepredictedrentalpriceofhousekinweekt,andTRtisthetotalrevenuefor T thefirminweekt.Thepredictedrentalprices,}=OG73z X F p @@@Gn nF l+G}tk,arecomputedbyevaluatingthefirm   specifichedonicpricefunctionfortherelevantseasonofeachyearateachunitsbundleofcharacteristics.Theoccupancyindicator,Rtk,includesintheaggregaterentindexonlythose f  propertiesthatarerentedinaspecificweek.Consequently,thereisadifferentmixofpropertiesthatareincludedinthecalculationofthefirm'saggregaterentindexforeachweek.Thus,whileanindividualpropertysrentsdonotvarywithinaseason,thefirmsrentindexwillvaryasthecompositionofpropertiesoccupiedchanges.Aconsistentquantityindexisderivedfromtheaggregaterentindexbydividingtotalrevenueineachweekbytherentindex. C.  FirmSpecificResidualDemandsforBeachProperties  $   Giventhattherentalfirmshavesomedegreeofmarketpower,ouraggregaterentindexwillreflectprice/costmarkups(astheyhavebeenrealizedinthemixofoccupiedunitsamongeachfirmsproperties).Weusetheseindexestoestimatearesidualdemandmodel(BakerandBresnahan[1988])foreachfirmtoderivefromitthe averagerealizedmarkupimpliedbythemarketresponsetoeachfirmsrentschedule.Equation(4)definestheinverseresidualdemandforrentalpropertiesforfirmi:  *  16       &"$ 8ZYUEAzx p UU@Xdddddddd@L*#n l0x (#(#      (#(#whereQitistheconsistentquantityindexforfirmi,Ytisasetofdemandvariablesrelevantto 6,'* weekt,Wtisasetofvariablesdescribingindustrywideinfluencesoncostsinweekt,andWit  isavectoroffirmspecificinfluencestootherfirmscostsinweekt(i.e.,costsforallfirmbutfirmi,andthereforedesignatedwithi).WtandWitidentifyfirmisaveragerealizeddemand T bycontrollingfortheinfluenceofotherfirmsindeterminingthemarketprice,andsotheeffectoffirmithroughPiisassessedseparately.Thus,weexpectFi()toreflecttheoverallprice  H costmargin.Equation(4)isspecifiedasadoublelogfunctionsotheestimatedparameterforquantitycanbeinterpretedastheinverseresidualdemandelasticityforeachfirm.  Demandproxyvariables(i.e.theYts)usedinouranalysiswerewagesineatingand n  drinkingestablishments(SICtwodigitcode58)anddummyvariablesidentifyingnationalholidays.Dummyvariablesidentifyingtheseasons(pre,peak,andpostseason)werealsoincludedintheresidualdemandmodelstoreflectdifferencesinoveralldemandbyseason.Toisolatethecostsofallfirmsbutfirmifromindustrylevelcosts,Witwasmeasuredbyfirm    specificwageindexesandWtwasmeasuredbyawageindexfortherealestatesector(SICtwo   p digitcode65)ofDareCounty,thecountythatincludestheOuterBanks.ThefirmspecificwageindexeswereconstructedusingconfidentialemploymentandwagedataprovidedbytheEmploymentSecurityCommissionofNorthCarolina.Thenumberofemployeesateachfirmineachmonthandthetotalwagepaymentsforeachfirminaquarterwereusedtocreateweeklywageindexes.MonthlyrealestateemploymentlevelsandquarterlypayrollfigureswerecompiledfromvariousissuesofEmploymentandWagesinNorthCarolina.Thedatafortherealestatesectorareinthesameformatasthedatafortheindividualfirms,andsothesamemethodswereusedtocreatethefirmspecificorindustrywidewageindexes.Boththefirmspecificandindustrywidewageindexesarecomputedaseitheraweightedaverageindexora *:&* Stoneindex. - *  17          Toillustratetheseasonalnatureofthemarketaswellasthehighoccupancylevels,theoccupancyratesforarepresentativelargeandsmallfirmaregraphedfor1991and1992infigure2.Thegraphbeginswiththestartofthepreseason(earlyMay)andendswithfinishofthepostseason(thelastweekofSeptember).Toattempttoaccountfortheseasonalnatureofthemarket,aninteractiontermbetweeneachoftheseasondummyvariables,andthequantitysoldbyaparticularfirminthepreviousyearisincludedineachfirm'sfinalresidualdemandspecification.Thelaggedinteractiontermsuggeststhatdemandinthecurrentperiodisrelatedtodemandinthesameperiodofthepreviousyear.Therelevantlagstructureisthesameweekinthepreviousyear.  Theresidualdemandmodelsrelyonthepriceandquantityindexescreatedwithweeklyoccupancyrecordsforeachproperty.Unfortunately,noneofthefourfirmshadalloftherequiredinformationforallpossibleyears.Asaresult,threetofiveyearsofweeklypriceindexeswerecreatedforeachfirm.Becauseeachfirmisestimatedseparately,thesedifferencesonlyinfluencecomparisonsmadeoftheoverallresults.Fortunately,thetimespaninvolvedisrelativelyshort,andtherewerenoappreciabledisruptionstotourisminNorthCarolinaduringthisperiod.Thus,thedifferencesinsampleperiodforeachfirmareunlikelytoaffectcrossfirmcomparisons.Givena19weekrecreationseasoneachyear(betweenMayandSeptember),andwiththreetofiveyearsofrecordsforeachfirm,between57and95weeklypriceandquantityobservationswereavailableforestimation.  Toaccountforsimultaneity,aninstrumentalvariableestimatorallowingforautocorrelationwiththelaggedendogenousvariablesisestimatedbasedonFairs[1970] *:&* modificationtotwostageleastsquares(TSLS). _ *  18      ׀Theestimatedresidualdemandfunctions,  adjustedforautocorrelation(asrelevant)arereportedinTable3.Theestimatesfortheresidualdemandelasticitiesareallsignificantatleastatthe.05levelwithinverseelasticitiesof0.314forfirm1,0.137forfirm2,0.239forfirm3,and0.115forfirm4. ` *  19      ׀Firm1,thelargest & v firm,displaysthestrongestevidenceofmarketpowerwithanestimatedmarkupof31%.Firm4,thesmallestfirm,displaysthesmallestevidenceofmarketpowerwithanaveragemarkupestimatedtobe11%.TiaoGoldbergerFtestswerealsoappliedtoeachfirm'sestimatesoftheinverseresidualdemandelasticitytotestwhethertheyaresignificantlydifferentacrossfirms.Thesetestsdistinguishfirm1fromfirms2and4.Firms2and4arenotsignificantlydifferentfromeachotheratthe95%levelofconfidence.Firm3,withestimatedmarkupof24%liesbetweenthatoffirm1andfirms2and4,butitisalsonotsignificantlydifferentfromanyoneofthesethreeestimates. IV.  AMENITIESANDMARKETPOWER Z    Recallthatwithasemilogspecificationforthehedonicpricefunctionsandthe ,| assumptionofloglinearmarginalcosts,Feenstras[1995]analysisdemonstratesthatthecoefficientofeachcharacteristicinthehedonicpricefunctionisnotequaltothecharacteristicsmarginalvalue,buttothemarginalvaluescaledbytheprice/costmargin.Thisresultimpliesthatmultiplyingtheestimatedcoefficientinthehedonicpricefunctionby(1+R),whereR t% $ istheinverseresidualdemandelasticity(R<0,andisalsotheestimatedprice/costmarkup), F'"& yieldsthemarginalvaluewewouldtypicallyexpecttorecoverastheestimatedcoefficientfromasemiloghedonicrentmodel. > *  20      ׀Inotherwords,foragivenpostedmarginalprice(rent),itis *:&* stillpossibletoestimatethemarginalvalueofeachcharacteristicinthenoncompetitiveequilibrium.  Ourmodelforconsumerbehavioralsoimpliesthatthemeasuresofthemarginalvalueforanycharacteristicwouldbeequalacrossfirms(whenevaluatedatthesamevectorofotherattributes),butthisisdifficulttoapply.Wehaveassumedconsumershaveidenticalpreferences(exceptforrandomerrorsindependentofproductcharacteristics).Inthiscase,theequilibriumundercompetitiveconditionswouldbedescribedbyasinglehedonicpricefunctionandthatfunctionshouldrevealthemarginalwillingnesstopayschedule(Freeman[1993]).Thisresultisnotespeciallyusefulinourcasebecausewewouldexpectadifferentmarketequilibriumtoprevailunderimperfectlycompetitiveconditions.Thus,theassumptionthatindividualsmarginalwillingnesstopayfunctionswillbethesamedoesnotallowustorecoverthemfromthehedonicpricefunctions.Wemustmeasureeachfirmsmarkupfactor.Indeed,evenifwefullyaccepttheFeenstraresultandassumeeachfirmssemilogrentequationcanrevealthesamemarginalwillingnesstopayfunction,atestofthehypothesiswouldrequireisolatingcomparableproperties.  Tofurtherdefinewhatwecanexpecttorecoverfromourhedonicpricefunctions,afewfeaturesofthedataneedtobeconsidered.ThecoastlinealongtheportionoftheOuterBankscomprisingourstudyisfairlyhomogenousintermsofwidthandquality.Theoceanfrontpropertiesinthisareaalsoconveyafairlyhomogenousmeasureofbeachaccessandbeachview.Thus,givenanapproximatelycompetitivemarketforland,wewouldexpectlocationspecificprices(rents)forourmeasureofthischaracteristic(theoceanfrontcategoricalvariable)tobeequalizedacrossfirmssinceitcapturesonlythishomogenouscharacteristic.However,theother *:&* locationmeasures(e.g.,oceanside,roadside,andbetweenthehighways)imperfectlyreflectproximitytotheshorelineandmayalsoreflectotherpositive(ornegative)landuses(e.g.,Ϝproximitytostoresand/orbusyintersections). H *  21      כSincethevariablesavailabletorepresent T locationsotherthantheoceanfrontcannotcontrolfortheseadditionaleffects,ourestimatesofthemarginalvaluesfromthehedonicmodelmayreflectmorethanpurelocationeffects.Withsuchimperfectmeasuresoflocationcharacteristics,itisnotclearthatthemarginalvaluesforanyofthelocationvariablesotherthantheoceanfrontlocationshouldbeequalizedacrossfirms(orevenacrossproperties)duetotransactionsonthelandmarket.  Thus,itwouldseemweonlyhaveaclearhypothesisforestimatesofthemarginalvalueinthecaseoftheeffectofanoceanfrontlocationitshouldbeequalacrossfirmssincethemarketforthesesiteswillexertanequalizinginfluence.However,thereisnoreasontoexpectthemarginalvaluesforanycharacteristicotherthantheoceanfrontlocationtobeequalacrossfirmswheneachisevaluatedfortheaveragepropertymanagedbyafirm.ThisisthecasebecauseeventhoughFeenstrasanalysisimpliesthepricemarkupeffectscanbeseparatedfromtheeffectsofpreferencesinthehedonicpriceequation,itdoesnotassurewewouldbeevaluatingthemarginalwillingnesstopayatthesamepointacrossfirms.Thus,touseourargumentforoceanfrontpropertiestotesttheFeenstramodel,weneedtoconsidertwohypotheses.Thefirstconcernsthemarginalpricesforoceanfrontlocationsandthesecondthemarginalvaluesfortheselocations.Marketpower(andtheassociatedpricemarkupsbyfirm)shouldimplydifferentmarginalpricesforoceanfrontlocationsacrossfirms.Totheextentthislocationcanbetreatedasseparatefromothercharacteristics,andmoresubjecttotheinfluencearbitragethroughlandmarkets,thenwewouldexpectthemarginalvaluetobeequalizedacross *:&* firms.  Toevaluatethesehypothesesweconsiderthemarginalpricesandestimatedmarginalvaluesfortheoceanfrontandoceansidelocations,aswellastwomoreeasilyreproducedhousingcharacteristicswhetherornotthepropertyhadcentralairconditioningandthenumberofbedrooms.EachofthesecharacteristicswasasignificantdeterminantofthefourfirmsrentschedulesandtheTiaoGoldbergertestsindicatedtheyhadsignificantlydifferenteffectsacrossfirms.Table4summarizestheestimatedmarginalprice,marginalvalue,meanprice,andoccupancyratebyfirmandcharacteristicforthepeakseasonof1992.  Testingthehypothesisofequalmarginalvaluesforattributesrequiresadjustmentsforthenatureofsomeofourmeasuresofsitecharacteristicsasdummyvariables.UsingtheϜHalvorsenPalmquist[1980]Kennedy[1981]adjustmentandpairwiseapplicationofttests,weconcludethattherearenosignificantdifferencesintheestimatedmarginalvaluesforthepremier  categoryofbeachaccesstheoceanfrontlocationforanypairoffirms.Therearesignificantdifferencesintheestimatedmarginalprices.Thepairwisetstatisticsforbothtestsarepresented ^ intable5.Forthemostpart,pairwisetestsforboththemarginalpricesandthemarginalvaluesoftheothertypesofbeachaccessconditionsaswellasthereproduciblecharacteristicsaresignificantlydifferentacrossfirms.Thus,totheextentourargumentthatthemarginalvaluefortheoceanfrontlocation(whichreflectstheeffectsofpurelandrentsforahomogeneouscharacteristic)shouldbeequalizedacrossfirms,thenourtestofequalityofthemarginalvaluesalsosupportsFeenstrasproposedstrategyfordecomposingmarketpowerandvaluationmeasures.Thisfindinginturnwouldimplythedecompositionoffersplausibleestimatesofmarginalvaluesforothercharacteristicswherethereisnotabasisforassuminganothermarket *B&* wouldinducemarginalvaluestobeequalizedacrossfirms.Italsooffersindirectsupportofourmethodofrecoveringmeasuresofmarketpowerinthepresenceofdifferentiatedproducts.  Whileresultsforpre,postandoffseasonhedonicrentmodelsarenotincludedinTable4,thesefindingsarenotasclearcutasforthepeakseason.Inthosecases,mostpairwisecomparisonsofadjustedprices(i.e.estimatesofmarginalvalues)aresignificantlydifferentbetweenthefirmsinvolved.ThisistobeexpectedbecausetheimplicitlogicoftheBertrandmodelforpricingstrategiesrequirescapacityconstraintsforpersistentpricecostmargins.Theoccupancyratesduringthesenonpeakseasonsmaynotbesufficienttoallowfornoncompetitivepricingstrategies.  Inourapplicationfirmsappearedtousesitespecificenvironmentalattributesasimportantsourcesofproductdifferentiation.Ifthisresultisconfirmedinothersituationswherelocationcanconveydifferentialaccesstoenvironmentresources,thenitoffersanotherreasonforspecialattentiontopolicydesignwhentraditionalsourcesofregulation(e.g.,monopolypower)interactwithsocialregulation.MuchoftheattentionintheearlyenvironmentalliteraturefocusedonextendingBuchanans[1969]demonstrationthatenvironmentalpolicycould,inthepresenceofϜmonopoly,exaggeratewelfarelosses.Here,theissueisthatenvironmentalpoliciesofferopportunitiestoconveytheabilitytodifferentiatecommoditiesbyprovidingsuperioraccesstovaluableenvironmentalamenitiesandthereforecouldconveymarketpower.Whilethisissuehasbeenappreciatedataconceptuallevel,toourknowledge,therehasbeennoempiricalevidenceofthepotentialimportanceofenvironmentalamenitiesassourcesofmarketpower.  Ourfindingsmaywellbeofinterestforotherreasonsaswell.Theysuggestthatthelinksbetweenhedonicpricefunctionsandstructuraldescriptionsofconsumerpreferences *:&* (Feenstra[1995])offersalternative,lesscomputationallyburdensomemodelingstrategiestodescribepricingbehaviorfornoncompetitivemarketswithdifferentiatedgoods.      Endnotes     *AssistantProfessorofEconomicsandSeniorAssociateofthePolicyResearchCenter,Georgia  StateUniversity,andArtsandSciencesProfessorofEnvironmentalEconomics,DukeUniversity,andUniversityFellow,ResourcesfortheFuture,respectively.ThanksareduetoRayPalmquist,DavidFlath,MattKahn,andDixieReavesforcommentsonearlierdraftsofthisϜresearchandtoPaulaRubioforpreparingandeditingseveralearlierdrafts.PartialsupportforthisresearchwasprovidedbytheUNCSeaGrantProgramunderSeaGrant#R/MRD25.  /        й   TR'3 Letter Landscape3''3Letter (Landscape)3'TTable1.Crosstabulationofrentalratesbyproximitytotheoceanin1992.a M *hqr dh,d ,td ,td ,%td ,td ,%td ,td ,t +  1jj"  _ 1 .j! jj . 4je% j 4@fDPrerent 7je( je 7@Peakrent ;jej( je ;@&;(Postrent Mjj<$   jej hMЀRow GN 5eej$8 x jj 5MeanPrice 9eej(! a "eej 9MinimumPrice/MaximumPrice 9eej( J "eej 9MeanPrice 9eej(! a "eej 9MinimumPrice/MaximumPrice 9eej( J "eej 9MeanPrice ;eejj(! a "eej ;MinimumPrice/MaximumPrice RjC(! a " 0 h eejj `ROceanfront :e+ "j :487 :e+ "e :888 :e+ "e :265/2075 :e+ "e :1265 :e+ "e :330/2995 :e+ "e :919 >ej+ "e >275/2150 Oej@( " ` ej `OOceanside 7ee(\ "ej 7623 7ee(\ "ee 7636 7ee(\ "ee 7250/1500 7ee(\ "ee 7893 7ee(\ "ee 7320/2300 7ee(\ "ee 7659 ;eej(\ "ee ;260/1500 Oej@(\ " ` eej `ORoadSide 7ee("ej 7130 7ee("ee 7549 7ee("ee 7230/1495 7ee("ee 7756 7ee("ee 7300/2050 7ee("ee 7568 ;eej("ee ;235/1495 Oej@(" ` eej `OBetweentheHighways 7ee('"ej 7335 7ee(>"ee 7450 7ee(>"ee 7220/995 7ee(>"ee 7610 7ee(>"ee 7300/1225 7ee(>"ee 7464 ;eej(>"ee ;220/995 Mejj<(>" ` eej MSoundside 9eej(X"ejj 9124 9eej(X"eej 9519 9eej(X"eej 9275/1200 9eej(X"eej 9706 9eej(X"eej 9375/1500 9eej(X"eej 9539 ;eejj(X"eej ;295/12008.,X" 0   eejj 8aThePropertyManagementCommitteeoftheDareCountyBoardofRealtorsdevelopedacategoricalsystemdescribingrelativeposition Z ofpropertytotheshoreline.ThissystemisusedbyallRealtors.Therearefivecategoriesthatdescribeproximityofapropertytotheshoreline:oceanfront(OF),oceanside(OS),roadside(RS),betweenthehighways(BH),andsoundside(SS).Therearetwomajorthoroughfareswhichrunperpendiculartothecoastlineandmustbecrossedbyfoottogettotheshore.Theseroadsareusedastheboundariesforthecategories.TheoceansideunitsaretotheeastofHighway158Business,abusytwolanehighway.Theunitsbetweenthehighways(includingroadsideunits)arelocatedinbetweenHighway158BusinessandHighway158Bypass.TheBypassisafivelanemajorthoroughfare.SoundsidehomesarelocatedtothewestofHighway158Bypass.    TRMt3''3 Letter Landscape3'Letter (Portrait)'3Letter (Landscape)TTable2.Summaryofthepreferredhedonicpricefunctionforeachfirm.'  9&&{X9X*st ddd td td %td td %td td t qr,b d ,td ,td ,td ,t +  1jj"  x1 8jej%9jj 8Frequencythecoefficientissignificantatthe90%level̀ofconfidence(atotalof24seasonspossible).75%=18to24seasons;50%=12to17seasons;̀25%=6to11seasons. Pjj?+" x  jej `XPVariable 2eej! jj 2Firm1 9eej( "eej 9Firm2 9eej( "eej 9Firm3 ;eejj( "eej ;Firm4( Fj7( " X0 ` eejj 0XFIntercept 0e! Q j 075% 7e( Q "e 775% 7e( Q "e 775% ;ej( Q "e ;75% Oej@( Q " X 0 ej 0XONumberofBedrooms 0ee!A  ej 075% 7ee(A  "ee 775% 7ee(A  "ee 775% ;eej(A  "ee ;50% Oej@(A  " X 0 eej 0XONumberofBaths 0ee!q ej 075% 7ee(q "ee 775% 7ee(q "ee 775% ;eej(q "ee ;75% Oej@(q " X 0 eej 0XOCentralairconditioningpresent(=1) 0ee! ej 075% 7ee( "ee 775% 7ee( "ee 775% ;eej( "ee ;75% Oej@( " X 0 eej 0XODishwasherpresent(=1) 0ee! ej 075% 7ee( "ee 775% 7ee( "ee 725% ;eej( "ee ;50% Oej@( " X 0 eej 0XOWasherpresent(=1) 0ee!A ej 075% 7ee(A "ee 725% 7ee(A "ee 775% ;eej(A "ee ;50% Oej@(A " X 0 eej 0XOMicrowavepresent(=1) 0ee!1qej 0Є* 7ee(1q"ee 7Є 7ee(1q"ee 750% ;eej(1q"ee ;Є Oej@(1q" X 0 eej 0XOColortelevisionpresent(=1) 0ee!aej 025% 7ee(a"ee 750% 7ee(a"ee 775% ;eej(a"ee ;Є Oej@(a" X 0 eej 0XOPhonepresent(=1) 0ee!ej 0Є 7ee("ee 750% 7ee("ee 7Є ;eej("ee ;Є Oej@(" X 0 eej 0XOCarpetingpresent(=1) 0ee!ej 050% 7ee("ee 7Є 7ee("ee 7Є ;eej("ee ;Є Oej@(" X 0 eej 0XOObservationdeckpresent(=1) 0ee!1ej 075% 7ee(1"ee 7Є 7ee(1"ee 7Є ;eej(1"ee ;25% Oej@(1" X 0 eej 0XOAdeckispresent(=1) 0ee!!a ej 0Є 7ee(!a "ee 7Є 7ee(!a "ee 7Є ;eej(!a "ee ;25% Oej@(!a " X 0 eej 0XOOutdoorshowerispresent(=1) 0ee!Q"ej 0Є 7ee(Q""ee 7Є 7ee(Q""ee 7Є ;eej(Q""ee ;25% Oej@(Q"" X 0 eej 0XOFireplacepresent(=1) 0ee!$ej 075% 7ee($"ee 775% 7ee($"ee 750% ;eej($"ee ;50% Oej@($" X 0 eej 0XOJacuzzipresent(=1) 0ee!&ej 075% 7ee(&"ee 7Є 7ee(&"ee 7Є ;eej(&"ee ;Є Oej@(&" X 0 eej 0XOScreenedporchpresent(=1) 0ee!!(ej 0Є 7ee(!("ee 7Є 7ee(!("ee 7Є ;eej(!("ee ;75% Oej@(!(" X 0 eej 0XORentalUnitisasinglehouse,(=1) 0ee!Q*ej 075% 7ee(Q*"ee 7Є 7ee(Q*"ee 775% ;eej(Q*"ee ;75% Oej@(Q*" X 0 eej 0XONumberofstories 0ee!A,ej 0Є 7ee(A,"ee 725% 7ee(A,"ee 750% ;eej(A,"ee ;50% Oej@(A," X 0 eej 0XOHasanoceanview(=1) 0ee!q .ej 0Є 7ee(q ."ee 725% 7ee(q ."ee 775% ;eej(q ."ee ;25% Oej@(q ." X 0 eej 0XOPropertyislocatedoceanfront(=1) 0ee!!0ej 075% 7ee(!0"ee 775% 7ee(!0"ee 775% ;eej(!0"ee ;75% Oej@(!0" X 0 eej 0XOPropertyislocatedoceanside(=1) 0ee!"2ej 075% 7ee("2"ee 725% 7ee("2"ee 775% ;eej("2"ee ;75% Oej@("2" X 0 eej 0XOPropertyislocatedroadside(=1) 0ee!$A 4ej 075% 7ee($A 4"ee 7Є 7ee($A 4"ee 750% ;eej($A 4"ee ;75% Mejj<($A 4" X 0 eej 8XMPropertyislocatedinthenortherntownsofthestudyarea(=1) 2eej! &I"7ejj 275% 9eej(1%q!6"eej 975% 9eej(1%q!6"eej 950% ;eejj(1%q!6"eej ;50%8.,1%q!6" X0 8  eejj 89XX&9&'Dependentvariableislog(Price). ':$: (Firm4haddataavailablefortheyears1988to1992only.Thus,75%equals13to18seasons, (#%; 50%equals9to12seasons,and22%equals4to8seasons.*Factorsnotincludedinthefinalspecificationofthehedonicregressionsandarenotedwith"".  *&= XXTR'3Mt3''3Letter (Landscape)3'Letter (Portrait)TTable3.Summaryofresidualdemandequationestimatedforeachfirm.ThedependentvariableisLog(Price).H9&&+X9X*uv9ddb d td td td t st,x d ,gtd ,Wtd ,td ,td ,td ,td ,td ,t +  1jj"  1VariableName 4je%qjj 4@kFirm1CoefficientEstimatevElasticity q (pvalue)wEstimate' 7je(Ije 7@Firm2CoefficientEstimateG Elasticity q (pvalue)G Estimate 7je(Ije 7@#$Firm3CoefficientEstimateq%((Elasticity q (pvalue)%((Estimate ;jej(Ije ;@s+y,Firm4CoefficientEstimate<-/Elasticity q (pvalue)o-/Estimate Kej<$I  jej KIntercept 0ee!Qej 05.167 Q (0.0001) 7ee(]  "ee 7 7ee(Q"ee 78.377 Q (0.0001) 7ee(]  "ee 7 7ee(Q"ee 76.439 Q (0.0001) 7ee(]  "ee 7 7ee(Q"ee 71.694 Q (0.0001) ;eej(]  "ee ; Oej@(Q"  eej OLog(Quantity) 0ee! A ej 0Є0.314  A  (0.0001) 7ee(M  "ee 7 7ee( A "ee 7Є0.137  A  (0.0210) 7ee(M  "ee 7 7ee( A "ee 7Є0.239  A  (0.0012) 7ee(M  "ee 7 7ee( A "ee 7Є0.115  A  (0.0054) ;eej(M  "ee ; Oej@( A "  eej 8OCostIndexforOtherFirms(FirmSpecificWageIndexes) 0ee!a ej 00.000520  1  (0.0203) 7ee(= "ee 70.211 7ee( 1 "ee 70.233489*  1  (0.0001) 7ee(= "ee 71.343 7ee( 1 "ee 7Є0.007442  1  (0.0041) 7ee(= "ee 7Є2.798 7ee( 1 "ee 7Ѐ0.362478*  1  (0.0004) ;eej(= "ee ;2.152 Oej@( 1 " 8 eej 8OCostIndexfortheIndustry(WageIndexfortheRealEstateSector) 0ee!A ej 0Є0.002039 i  (0.0001) 7ee(u "ee 7Є0.536 7ee(i "ee 7Є0.500632* i  (0.0002) 7ee(u "ee 7Є2.810 7ee(i "ee 70.014460 i  (0.0004) 7ee(u "ee 73.631 7ee(i "ee 7Ѐ0.278302* i  (0.0005) ;eej(u "ee ;Є1.561 Oej@(i " 8 eej 8OPreSeasonIndicatortimesLaggedQuantity 0ee!yej 00.000588  (0.0001) 7ee(U"ee 70.233 7ee("ee 70.002142**  (0.0002) 7ee(U"ee 70.271 7ee("ee 70.001354  (0.0001) 7ee(U"ee 70.356 7ee("ee 70.002873  (0.0001) ;eej(U"ee ;0.214 Oej@(" 8 eej 8OPeakSeasonIndicatortimesLaggedQuantity 0ee! ej 00.001093 1 (0.0001) 7ee("ee 70.667 7ee(1"ee 70.003573** 1 (0.0001) 7ee("ee 70.631 7ee(1"ee 70.001396 1 (0.0001) 7ee("ee 70.470 7ee(1"ee 70.004458 1 (0.0001) ;eej("ee ;0.486 Oej@(1" 8 eej 8OPostSeasonIndicatortimesLaggedQuantity \ 0ee!Aej 00.000715 i (0.0001) 7ee("ee 70.306 7ee(i"ee 70.001790** i (0.0001) 7ee("ee 70.358 7ee(i"ee 70.000563 i (0.0001) 7ee("ee 70.205 7ee(i"ee 70.002610 i (0.0001) ;eej("ee ;0.238 Oej@(i" 8 eej 8OIndexofOverallDemand(WageIndexforRestaurantsandBars) 0ee!y!ej 0 7ee(I"ee 7 7ee(I"ee 7 7ee(I"ee 7 7ee(I"ee 7Є0.003115 I (0.0692) 7ee(U"ee 7Є0.504 7ee(I"ee 7 ;eej(I"ee ; Mejj<(I" 8 eej M 6eej% ejj 6N=73,R2=0.8217   Fstatistic=57.057 @eej/ 5!"eej @N=56,R2=0.9362   Fstatistic=122.323 @eej/ 5!"eej @N=37,R2=0.8146   Fstatistic=18.83 Beejj/ 5!"eej BN=37,R2=0.9267   Fstatistic=65.32;1/5!" 0  eejj ;9XX&9&'Allelasticityestimatesarecomputedatthesamplemeans. Z$ *TheStoneindexversionofthesevariablesareusedinthisfirm'sresidualdemandfunction.Otherwise,theweightedaverageindexwas C% used.**Becausefirm2hasdiscontinuousdata,avariablewithlagquantitycouldnotbecreated.Thus,thewageindexforeatinganddrinking ' establishments(inthecurrentyear)isinteractedwiththeseasonaldummyvariableforthisfirm.  ( TRMt3''33'Letter (Portrait)'3Letter (Landscape)THXHXTable4.EstimatesoftheValueofBeachAccessConditionalonCompositepriceMarkupsforthePeakSeasonin1992.a 1 *wx d 9dx d gtd Wtd td td td td td t uv, d ,4d ,td ,td ,Ftd ,t +  7jjj&  Px7Firm(ElasticityEstimate) Njjj=.Mjjj NEstimatedVariable/Parameter Pjej=.Mjjj PProductCharacteristic TjjC+{3" x P jej PXT 9jj(Ujj 9 5eej$Ujj 5OceanFront 9eej("eej 9OceanSide 9eej("eej 9CentralAirConditioning ;eejj("eej ;NumberofBedrooms Jj;(" X0 P eejj XJ  Firm1(R=.31) ?j0.  99,j ?MeanPriceb 0e!O  j 0$1347(516) 7e(8  "e 7$893(233) ?ej,8  "e ?$956(415) H>+8  " X  ej 0XH &ej !   &OccupancyRate(%)b,c PeeAb  ej  @S@77@S@P77 weeh=y 1 "  @S@77 @S@ee  T@83T@w83 eejl=y 1 "  T@83 T@ee  @S@77@S@  77 h^Ky 1 #  @S@77 X 0 @S@eej Xh &ej K  &MarginalPrice(Rent)d 0ee!D ej 0483(12.3) 7ee(D "ee 7139(2.30) 7ee(D "ee 7  144(3.78) ;eej(D  ee ;129(1.18) E;(D " X  eej XE  &ej u-  &MarginalValuee 0ee! ej 0331(22.83) 7ee(n"ee 796(6.31) 7ee(n"ee 7  99(6.83) ;eej(n ee ;89(5.73) UejD(n" X  eej XU  Firm2(R=.14) Hej9.< tt 0ej HMeanPriceb 0ee!ej 0$1430(505) 7ee("ee 7$915(278) ?eej,"ee ?  $966(393) H>+# X  eej 0XH &ej  &OccupancyRate(%)b,c PeeA ej  T@80T@P80 weeh=!"  T@80 T@ee  @T@81@T@w81 eejl=!"  @T@81 @T@ee  S@79S@  79 h^K!#  S@79 X 0 S@eej Xh &ej  &MarginalPrice(Rent)d 0ee!4ej 0408(12.90) 7ee(4"ee 750(1.10) 7ee(4"ee 7  73(2.64) ;eej(4 ee ;133(1.96) E;(4" X  eej XE &ej  &MarginalValuee 0ee!u-ej 0353(25.95) 7ee(^"ee 743(3.02) 7ee(^"ee 7  63(4.75) ;eej(^ ee ;115(7.83) UejD(^" X  eej XU  Firm3(R=.24) Hej9., & tt4ej HMeanPriceb 0ee!W!ej 0$1088(470) 7ee(@""ee 7$884(230) ?eej,@""ee ?  $858(382) H>+@"# X  eej 0XH &ej q)# &OccupancyRate(%)b,c PeeAj%ej  T@82T@P82 weeh=$"  T@82 T@ee  @V@89@V@w89 eejl=$"  @V@89 @V@ee  Q@70Q@  70 h^K$#  Q@70 X 0 Q@eej Xh &ej S& &MarginalPrice(Rent)d 0ee! (ej 0395(17.23) 7ee( ("ee 7161(4.79) 7ee( ("ee 7  88(3.64) ;eej( ( ee ;122(2.05) E;( (" X  eej XE &ej !}) &MarginalValuee 0ee!"*ej 0300(29.41) 7ee(#+"ee 7122(11.32) 7ee(#+"ee 7  67(6.53) ;eej(#+ ee ;93(8.26) Lejj;(#+" X  eej XL  Firm4(R=.11) Hej9.(%2 tt58ejj HMeanPriceb 0ee!G$ -ej 0$784(240) 7ee(0%!."ee 7$656(201) ?eej,0%!."ee ?  $674(205) H>+0%!.# X  eej 0XH &ej &"/ &OccupancyRate(%)b,c PeeAZ'$1ej  @U@85@U@P85 weeh=q&)#0"  @U@85 @U@ee  U@87U@w87 eejl=q&)#0"  U@87 U@ee  S@78S@  78 h^Kq&)#0#  S@78 X 0 S@eej Xh &ej C($2 &MarginalPrice(Rent)d 0ee!)<&4ej 0396(20.82) 7ee()<&4"ee 7293(21.00) 7ee()<&4"ee 7  40(1.38) ;eej()<&4 ee ;31(0.68) E;()<&4" X  eej XE (ejj m*%'5 (MarginalValuee 9eej(*}'6ejj 9350(23.89) 9eej(+f(7"eej 9259(21.73) 9eej(+f(7"eej 9  35(2.00) 2eejj+f(7 eej 2  16(0.18)8.,+f(7  X   eejj 8(Notesonnextpage)  -8*: aStandardDeviationsareinparenthesis. 1 bForthelocationattributes,themeansoftheactualrentalpricesandoccupancyratesarecomputed  overpropertiesattherelevantlocation.Forthecharacteristics,themeansoftheactualrentalpricesandoccupancyratesarecomputedoverallpropertiesmanagedbythefirm.cTheoccupancyratesforfirm2arefortheyear1989,themostrecentyearforwhichthereisdata.  dThemarginalprices,pi,arecomputedas}=CG73z X l] p& @@@m jnm},with}=fG73z X @ p& @@@A  jnA}߀themeanofthepostedrentandbithe v relevantcoefficientestimate.Whentheattributeisaqualitativevariable,biisreplacedbyeb9+X9X 9i#XX 1#&&XX#9&&~ &&1#󀄀1.   #9XX&9&1#Becausetheestimatedcoefficientshadsmallvariances,theconventionalcorrectionforbiashadno  t appreciateeffect.TheasymptoticvarianceestimateusesafirstorderTaylorserieswithVar(pi)=p2  ]   Var(bi)andVar(bi)=bi=J:6z \ @P p @@@4  lIvGVar(bi)forthequalitativevariables.  F  eThemarginalvaluesarecomputedwiththeadjustment(1+R)pi,whereRislessthanzero.TheR   arespecifictoeachfirm,thepiaredrawnfromfirmspecificestimatesfor1992.TheVar(MWTPi)    pi2 Var(R)+(1+R)2 Var(pi).9&&+X9X   #9XX&9&5#  u  Table5.TestsforEqualityofEstimatedMarginalPricesandMarginalWillingnesstoPayAcrossFirms.*yz9dd d 4d td td Ftd t wx, d ,td ,td ,Ftd ,Ft +  7jjj&  Px7FirmsBeingCompared Pjej=.{3K<jjj PProductCharacteristic TjjC+{3" x P jej PXT 5eej$djj 5OceanFront 9eej(]"eej 9OceanSide 9eej(]"eej 9CentralAirConditioning ;eejj(]"eej ;NumberofBedrooms Fj7(]" X0 P eejj XF /j  j /@)tWttests@@.WComparingMarginalPriceEstimatesa Bjj3$   X  j 0XBFirm1/Firm2 RjeC 7 jj (\@4.19(\@R4.19 |jem? 7 " (\@4.19 (\@je \(|A@34.97\(|A@|34.97 }jen@ 7 " \(|A@34.97 \(|A@je {G.@15.49{G.@}15.49 jejn@ 7 " {G.@15.49 {G.@je Q-1.57QЄ1.57 rejcK 7 " Q-1.57 X 0 Qjej 0XrFirm1/Firm3 ReeC x ej (\@4.19(\@R4.19 |eem? x " (\@4.19 (\@ee Gz-4.02Gz|Є4.02 }een@ x " Gz-4.02 Gzee p= #%@10.57p= #%@}10.57 eejm@ x " p= #%@10.57 p= #%@ee q= ףp @3.18q= ףp @3.18 qejbJ x " q= ףp @3.18 X 0 q= ףp @eej 0XqFirm1/Firm4 ReeC ej  ףp= @3.63 ףp= @R3.63 |eem? "  ףp= @3.63  ףp= @ee Gz-7.27Gz|Є7.27 }een@ " Gz-7.27 Gzee fffff9@25.90fffff9@}25.90 eejn@ " fffff9@25.90 fffff9@ee (\P@66.74(\P@66.74 rejcK " (\P@66.74 X 0 (\P@eej 0XrFirm2/Firm3 ReeCB ej ?0.65?R0.65 }een?B " ?0.65 ?ee = ףp}6-22.49= ףp}6}Є22.49 ~eeoAB " = ףp}6-22.49 = ףp}6ee RQ -3.54RQ ~Є3.54 eejm@B " RQ -3.54 RQ ee HzG@3.91HzG@3.91 qejbJB " HzG@3.91 X 0 HzG@eej 0XqFirm2/Firm4 ReeC; ej (\?0.53(\?R0.53 }een?; " (\?0.53 (\?ee '-11.55'}Є11.55 ~eeoA; " '-11.55 'ee Q&@11.01Q&@~11.01 eejn@; " Q&@11.01 Q&@ee ףp= F@45.43ףp= F@45.43 pejj_K; " ףp= F@45.43 X 0 ףp= F@eej `XpFirm3/Firm4 UeejD|ejj {Gz-0.04{GzUЄ0.04 eejn@|" {Gz-0.04 {Gzeej (\-6.14(\Є6.14 eejn@|" (\-6.14 (\eej  ףp= )@12.52 ףp= )@12.52 eejjn@|"  ףp= )@12.52  ףp= )@eej \(