©CopyrightJASSS

BirnurÖzbaş,OnurÖzgünandYamanBarlas(2014)

ModelingandSimulationoftheEndogenousDynamicsofHousingMarketCycles

JournalofArtificialSocietiesandSocialSimulation 17(1)19<http://jasss.soc.surrey.ac.uk/17/1/19.html>

Received:07-Apr-2013Accepted:08-Sep-2013Published:31-Jan-2014

Abstract

Thepurposeofthisstudyistomodelandanalyzebysimulationthedynamicsofendogenouslycreatedoscillationsinrealestate(housing)prices.Asystemdynamicssimulationmodelisbuilttounderstandsomeofthestructuralsourcesofcyclesinthekeyhousingmarketvariables,fromtheperspectiveofconstructioncompanies.Themodelfocusesontheeconomicbalancedynamicsbetweensupplyanddemand.Becauseoftheunavoidabledelaysintheperceptionoftherealestatemarketconditionsandconstructionofnewbuildings,pricesandrelatedmarketvariablesexhibitstrongoscillations.Twopoliciesaretestedtoreducetheoscillations:decreasingtheconstructiontime,andtakingintoaccountthehousesunderconstructioninstartingnewprojects.Bothpoliciesyieldsignificantlyreducedoscillations,morestablebehaviors.

Keywords:RealEstateModeling,HousingCycles,PriceOscillations,SystemDynamics,Socio-EconomicSimulation

Introduction

1.1 Realestatemarketingeneral,housinginparticularisoneofthemostdynamicandunpredictableeconomicsectors(Hiang&Webb2007;Muetal.2009).Moreover,therealestatesectorinvolveslargeandinfluentialinvestments,thusaffectingthewholeeconomyandthelabormarketprofoundly.Typically,housingmarketsexhibitoscillatorybehaviors,withcycleperiodsrangingfromafewyearstoafewdecades(Wheaton1999).Aswillbeseenintheliteraturereviewbelow,endogenousstructureofthehousingsectoritselfcanplayasignificantroleinthecreationofsuchcycles:Apositivehousingdemandmovementcausesthepricestorise(Aokietal.2004).Evenafternewconstructions,thepricesmaycontinuetorise,sinceexpectationsareformedbypastmovementsintheprices.Thepricespeakwhenconstructionsovershootthedemand,atwhichpointthepricesstarttodecline.Thisprocesssetsoffarepeatingcycleintheprices,construction,andthestockofhouses.Withinthisdynamicenvironment,constructioncompaniesfaceagreatriskofloss(orachanceofprofit)duetotheoscillatorybehavioroftheprices.Iftheyjustreacttothepricesandstartorphaseouttheirprojectsaccordingly,theymayhaveunsoldhousesinthebusttimesornotenoughhousesintheboomtimes.Becauseoftheunavoidabledelaysinthesystem,companiesmustforeseethedemandmovementsandstarttheirprojectswellbeforethedemandstartsrising.Theincreaseinthepopulationgrowthmakesthemarketevenmorecomplexandhardertopredict(Genta1989;DiPasquale&Wheaton1994;Aokietal.2004;Sæther2008).

1.2 Additionaltoitseconomicdynamics,housingdevelopmentisaprocessthatoperatesasaconnectedsequenceofevents.Theseseriesofevents(i.e.siteidentification,feasibilityanalysis,design,productionandoccupation)transformavacantsiteoraredundantorobsoletepropertyintoanewuse.Throughthisdevelopmentprocessmanydifferentactorsandinstitutionssuchasdevelopers,owners,occupiers,lenders,contractorsandsub-contractors,architects,technologists,localgovernment,consultants,engineersplaydifferentroles(Wyatt2007).Inevitably,theseoperationsandplayersareaffectedbymanydifferentfactorssuchaslong-termsocialtrends,nationalandglobaleconomicconditions,environmentalamenities,andgovernmentpolicies(Wyatt2007;Selim2009).SimilarlyeconomiccrisisandglobaleconomicrecessionshavedifferenteffectsonrealestatemarketsinUSandEurope(Deloitte2010).TheparametersandassumptionsofourstudyarederivedfromTurkeywhererealestatemarketisgrowingwithspeed(Binay&Salman2008).AccordingtoKeskin(2008)housingpricesareaffectedbyhousesize,levelandageofthebuildingandsafety(especiallyearthquakerisk)andsecurityofthesite,averageincome,timespentinthecityandneighborsatisfaction.Inadditiontothesedeterminantsotherhousingmarketvariables,rapidurbanizationandurbanpopulationgrowthstrengthenthehousingmarketinTurkey(Coskun2011).

1.3 Duetothedynamicstock-flownatureofthehousingvariables,stock-flowmodelsofhousingsectorhavebeenwidelyusedsince1960s(DiPasquale&Wheaton1994;Fair1972;Maisel1963).Thecommonfeatureofthesemodelsisthattheyrepresenttherelationshipsbetweenthehousingstocksandtheirflowsbydifference/differentialequations.Mostofthesemodelsareusedtoreflectthephysicalconversionprocessofconstructionstohousesupply.However,thisphysicalprocessisonlyapartofthesystem.Instudiesthatmodelonlyapartofthesystem,thedynamicsandforecastshavetobebasedonvariablesexogenoustothemodel.Themajorityofthestudiesinthehousingliteraturebuildeconometricmodelsbasedonthisstock-flowstructurethatseektoexplainorforecastexogenouslythedynamicsofthesystemvariables.Overtheyears,manyimprovementshavebeenmadeinstock-flowmodeling,byusingevidencefromliteratureandrepresentingmorevariablesendogenouslyinthemodel.Aswillbeseenbelow,thereisathreadofliteraturethatseekstoexplainthemarketbehavioralmostendogenouslybasedonmoreelaboratestock-flowmodels.Ourstudybelongsinthisbranchofliterature,byadoptinga"systems"perspectivetotheproblemofhousingpricecycles.Itmeansthatwefocusonhowsystemcomponents,inthiscase,thesupply,demandandprice,relateddecisionsanddelays,allinteractwitheachother.Insteadofseeingtheproblemasanopensystemthatisdeterminedbyexternalforces,weidentifyfeedbackloopsbetweenthesystemvariables,toexplaintheoscillations.Thesefeedbackloopsincludenotonlythephysicalprocesseslikeconstructionorpriceadjustment,butalsothementalprocessesofdecisionmakers,likeeffectofpriceonnewconstructiondecisionsorperceptionformations.Toformallyrepresenttheseprocesses,weusesystemdynamicsmethodology,amodelingandsimulationdisciplinethatusesmultiplestock-flowstructuresandfeedbackloopstoanalyzecomplexsocio-economicdynamicsystems

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(Forrester1961;Sterman2000).

1.4 Systemdynamicsusesstockandflowvariablestodenotetheprocessesthatcanbeexpressedbyadifferential(ordifference)equation:therateofchangeofastockisthenetsumofitsflows.Thestockschangethroughtheirflows,andtheflowscanbefunctionsofanyvariablesinthemodel.Stocksareusedtorepresentnotonlyphysicalaccumulations(likestockofhouses),butalsointangibleaccumulations(likeexpectationsthatdevelopovertime).Oneoftheuniquefeaturesofsystemdynamicsapproachisthatitholdsasystemic(holistic)worldview.Thissystemicperspectivemeansstrivingtobuildmodelsthatincorporateendogenouslyallvariablesthatarerelevanttotheproblem.Thus,theoutputsofthemodelaredrivennotbytheexternalfactors,butbytheinternalstructureofthemodel.Theinternalstructurecomprisesthefeedbackloopsformedbyinterdependenciesbetweenvariables.

1.5 Ourmodelbuildsuponpreviousstock-flowmodelsofhousingmarkets,aswellasgenericstructuresusedinsystemdynamicsliteraturetorepresentcommonphysicalandmentalprocesses.Itisadynamicmodelofthedemandandsupplysidesoftherealestatemarketinamajorandstillgrowingcity.Themodelisagenericoneandlikelytobereasonablyvalidforanydevelopingurbanarea.However,theparametersandassumptionsarebasedonthecityofIstanbul,Turkey.

1.6 InSection2ofthepaper,aliteraturereviewoftherelatedstudiesispresented.Then,themethodologyisdescribedinSection3.InSection4,themodelisexplainedandthevalidationprocessissummarized.Finally,scenarioandpolicyanalysisresultsarepresented.

LiteratureReview

2.1 Ourmodelisacontinuoustime,nonlinear,non-equilibrium,dynamicstock-flowmodelthatconsistsoffeedbacksinbothsupplyanddemandsidesofthesystem.Themodelparticularlyfocusesonendogenouslycreatedcyclesofhousingmarketinthelongtermfromtheconstructorcompanyperspective.Althoughcurrentliteratureincludesmanymodelsthatpossessoneormanyoftheseproperties,ourmodelisuniqueinthesensethatitcombinesalltheseaspects.

2.2 Priceisoneofthekeyvariablesofthehousingsector,aswellasourmodel.Causalmechanismsthatdrivethehousingpricedynamics,whichconstitutethecoreofourmodel,havebeensubjectofmanymodel-basedstudiesinthepast50years.Anas(1978)developsarecursivedynamicmodelofurbanresidentialgrowth.Themodelfocusesonhowconsumption,housingprices,andlandrentsadjustovertime.Inastudythatisnothousing-specific,FershtmanandFishman(1992)usesadynamicsearchmodeltodemonstratethatthepriceofacommoditycanshowcyclicalbehaviorduetoendogenousdynamicinteractionsbetweenbuyersandfirms,withoutanyexternalinterventiontothesystem.ChicagoPrototypeHousingMarketModelpresentedinAnasandArnott(1993)isamulti-dimensional,discrete-time,dynamicequilibriummodelthatreflectsassetbid-price,housingstockadjustmentandmarketclearingprocesses.Itisapolicy-orientedmodelwithamediumtermtimehorizon(10years)focusingmainlyonthedynamicsofthesubcomponentsofthesystem.Meen(2000)developsamathematicalmodelincludinghouseprices,constructions,costandinterestratesandtheirinteractionstoanalyzehousingcyclesoftheUKmarket.Filatovaetal.(2009)developsanagent-basedmodelthatincludesbehavioraldriversofland-markettransactionsonboththebuyerandsellersides.Murphy(2010)presentsadynamicmicro-econometricmodelofhousingsupplytoexplainthevolatilityinpricesintheSanFranciscoBayArea.

2.3 Amongthedynamicmodelsofhousingmarket,thestock-flowmodelsareofparticularinteresttous(asexplainedinSection3).Astudycanbeclassifiedasstock-flowmodelifithasaconceptualizationofthesystembasedonstockandflowsinadynamicperspective.Inoneoftheearlystudies,Maisel(1963)presentsamodelwithtwobasicstocks:stockofdwellingsandinventoryunderconstruction,whichareconnectedthroughcompletionsflow.Theinflow,calledstarts,isdeterminedbybuilders,bytakingintoaccountthestockandsomeexternalfactors.Thisisarathersimpleframeworkfocusingmainlyonthesupplysideofthesystem.Smith(1969)usesasimilarstructureforthehousingmarket,butpresentsamoreelaboratemodelofthemortgagemarketandrelatestothedemandsideofthehousingmarket.However,themodeldoesnotincludeseparatesupplyanddemandequations,meaningthatequilibriumisassumed.Fair(1972)summarizesafewothermodelsthatassumeequilibriumbetweendemandandsupply.

2.4 Weibull(1983)presentsathree-stockstructuretorepresentdemand,supplyandpriceinacontinuous-timedynamicmodel.Themodelaccountsfornonlinearitiespresentinthesystem,butlackstheconstructionandinvestmentsideoftheproblem.Poterba(1984)usesamodelcomposedoftwodifferentialequationsforhousingstockandprice.Althoughthismodelrepresentspriceendogenously,itlackssomerelateddelaysandfeedbackloops.ThepaperbyDiPasqualeandWheaton(1994)providesasummaryofhistoricaldevelopmentofstock-flowbasedhousingmodelsanddevelopsadynamicstock-flowmodelofhousingmarkettounderstanditsaggregatebehavior.Authorsalsoimprovetheearlierstock-flowmodelsbyincludinggradualpriceadjustment,expectationformationandafeedbackloopcontrollingnewconstructions.Althoughthismodelreflectstheessentialbackboneofadynamichousingmodel,thereisonlyonemajorfeedbackloop,whichisfromhousingstocktotheconstructionstartsthroughprice.ThemodeldevelopedbyDiPasqualeandWheaton(1994)hasbeenmodifiedbyTu(2004)andappliedtoSingaporeprivatehousingmarket.Jiangetal.(2010)alsomodifiesthestock-flowmodelofDiPasqualeandWheaton(1994)toanalyzethefactorsdrivinghousingmarketcyclesinChina.Yetthesemodificationsdonotenrichthemodelstructurebutmerelyadaptthemodeltodifferentlocations.

2.5 Althoughtheaforementionedstudiesuseastock-flowstructuretheyareessentiallydata-driven,exogenousmodelsthatseektoexplainandpredictpricefluctuations.Somestudies,ontheotherhand,useendogenousstock-flowstructurestogeneratethedynamicbehaviorofthehousingmarket.Forinstance,Barras(2005)buildsasetofdifferenceequationstoexplainendogenouslythecyclicalbehaviorhousingmarket.Themodelaccountsfortwotypesofdemandcreation:duetogrowthandduetoturnover.Therearedelaystructuresinrent(orprice)adjustment,occupierresponsetorentchanges,constructionstarts,andconstructioncompletions.However,thismodelignorestheeffectofpriceondemandandthematchingprocessbetweensupplyanddemand.Likewise,Eskinazietal.(2011)createsasystemdynamicsmodelfortheNetherlandshousingmarketbasedonDiPasqualeandWheatonmodel.

2.6 Thereareotherexamplesofhousing-relatedstudiesinthesystemdynamicsliterature.J.Forrester'sUrbanDynamicsmodel(1970)isoneofthefirstsystemdynamicsmodelsdealingwiththehousingdynamicsinanurbanarea.Itfocusesontheconnectionsbetweenthelabor,businessandhousingsectors,butdoesnotincludevariablesaboutprice.Recently,Kummerow(1999)presentsasystemdynamicsmodelforcyclicalofficeoversupplyproblem.Hismodelconsistsofasinglebalancingfeedbackloopbetweenvacancyrateandsupply,assumingallotherfactorsexternal.Thepaperassertsthatthesupplylag,theadjustmenttimeandthetendencyofoversupplyareresponsibleforthecyclesandtheycanserveasleveragevariablesforreducingthecycles.Hong-MinhandStrohhecker(2002)presentsasystemdynamicsmodelfortheprivatehousingsupplychainstoassesstheimpactofre-engineeringscenariosonconstructionperformanceandtostudytheimpactofre-engineeringpoliciesondemandamplifications.Hoetal.(2010)presentsamodelofhousingmarketofTaichungCityinTaiwantodeterminetheeffectivenessofvariousgovernmentpolicies.Genta(1989)andSæther(2008)developsystemdynamicsmodelstoexplainthehousingcyclesinBostonandNorway,respectively.

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2.7 Onedistinctivepropertyofourmodelisitsendogenousfocus.Inourstudy,likeothersystemdynamics-basedstudies,wemainlyfocusonthedynamicsgeneratedbytheinteractionsbetweenthesystemvariables.Asasystemdynamicsmodel,itsdynamicbehaviorsareendogenouslygenerated,ratherthanbeingexternallydata-driven.Theaimisnottoforecastthehousepricesatspecifictimepoints,buttounderstandhowandwhythepricecyclesoccur.Themodelisnotonlyvalidfortheequilibriumstatebuthasthecapabilitytoreflectthetransientdynamicsinthehousingmarket.

2.8 Unlikethesystemdynamicsmodelscitedabove,ourmodelisbuiltfromtheperspectiveofconstructioncompanies.Theproblemownerisimportantbecauseitdeterminesthemodelboundary.Sinceourmodelisconstructer-oriented,itinvolveseconomicdecision-makingprocessesofthecompanies.Duetothefactthatconstructioncompaniesdonothavedirectinfluenceonhouseholds'buyingdecisions,thedemandsideandthepurchasingpowerofthecustomersaremodeledinlessdetail.Theproblemperspectiveisalsorelevantinidentifyingfeasiblepolicyinterventionsandevaluatingtheiroutcomes.Ourrecommendedpoliciesmodifydecisionparametersthatareundercontrolofconstructionsector,andtheevaluationofthesepoliciesconsiderstheireffectsonprofits.

2.9 Structure-wise,ourmodelalsobringsseveralimprovementstotheexistingmodelsintheliterature.Thetraditionalassumptioninthestock-flowmodelisthatthemarketclearsquickly(DiPasqualeandWheaton1994).However,thepriceadjustmentmechanismandthesearchprocesscancausesignificanttimelagsthatcanaffectthedynamicbehavior.Althoughgradualpriceadjustmentisafeatureofsomeearliermodels(forexample,DiPasquale&Wheaton1994;Barras2005;Eskinazietal.2011),noothermodelthatwereviewedexplicitlymodelsthesearchprocessanditseffectonsalesduration.Moreover,manymodelseitherassumedemandtobeexternal(Maisel1963;Kummerow1999;Sæther2008),orsolelydependentonsupply(Barras2005;Jiangetal.2010),ignoringtheeffectofpriceondemand.Byincludingallthesefeedbackloops,arichstructureiscreatedwhichiscapableofproducingdifferentbehaviorsendogenously.

Methodology

3.1 Systemdynamicsisamodel-basedmethodologytoanalyzecomplexdynamicsystemsinvolvingfeedbackinteractions.Thebasicelementsofasystemdynamicsmodelarestocksandflows.Astockvariablerepresentsanentitythatgraduallyaccumulatesordiminishesovertime.Aflowistherateofchangeofastock.Mathematically,therelationshipbetweenstocksandflowscorrespondstodifferential(ordifference)equations.Apartfromstocksandflows,thereareauxiliaryvariablesthatrepresentthestock-to-flowlinksexplicitly.FeedbackcorrespondstoasituationwhereXinfluencesY,andYinturninfluencesXthroughachainofcausalrelationships.Therearetwotypesoffeedbackloops;apositivefeedbackloopmeansthataninitialchange(increaseordecrease)inavariablewilleventuallycausethesamevariabletochangeinthesamedirection.Onthecontrary,anegativefeedbackloophasabalancingeffect:aninitialchangeinavariablewilleventuallycausethesamevariabletochangeintheoppositedirection(SeeFigure2foranillustrationoffeedbackloops).Sincevariablesinasystemareinterconnectedthroughfeedbackloops,thebehaviorofanyvariableisdependentonthewholesystem.Formoreinformationonsystemdynamicsmethodologysee,forinstance,Barlas(2002)andSterman(2000).

3.2 Themotivationofthisstudyistoinvestigatethestructuralreasonsbehindthecyclicbehaviorofthemainhousingvariables.Themodelboundaryisselectedlargeenoughtomakesurethecausalmechanismsthatdrivethesystembehaviorlieinsidetheboundary,assuggestedinsystemdynamicsliterature(Forrester1987).Thedynamichypothesisispresentedusingacausal-loopdiagram(Figure2),whichexplainshowvariablesarelinkedtoeachother.Thisconceptualmodelisthentranslatedtoaformalmathematicalmodelintheformofastock-flowdiagramandequations(Figure3).Afterverificationandvalidationsteps,thecausesoftheoscillatorybehaviorcanbeidentifiedbyaseriesofsimulationexperiments.Withtheaidofsuchamodel,itispossibletodesignimprovementpoliciestodampentheoscillationsandanalyzetheireffectsonthewholesystem.

3.3 ThemodelisdevelopedandimplementedusingSTELLA9.1.4(iseesystems2009).InSTELLAandmostcomputersimulationapplicationsofsystemdynamicsmodels,thedynamicrelationshipsbetweentheelements,includingvariables,parameters,andexternalinputs,arecapturedintheinterfaceinformsofequations,graphsandfunctions(asgiveninAppendix)usinguser-friendlyvisualtools.Itisaflexiblewayforbuildingsimulationmodelsfromcausalloopsorstocksandflows.Whensimulationrunsarecarriedout,varioustypesofgraphsandtablesaretheoutputsfromSTELLA.Themodelcanbedownloadedfrom:http://www.openabm.org/model/3936/.

TheModel

4.1 Themodelisbuiltfromtheperspectiveoftheconstructioncompanies.Specifically,thedecisionmakercouldbeatradechamber,anassociationoraconsortiumofconstructioncompanies.So,themodelfocusesontheconstructionchainsandthedecision-makingprocessesofthecompanies.Thisdynamicmodelseekstoexplainthestructuralcausesofhousingmarketoscillationsandtestalternativepoliciesthatmayimprovethedecisionmakingprocessoftheconstructioncompanies.

4.2 Therealestatepricesareknowntoexhibitoscillatorybehaviorsinreallife(Wheaton1999).InFigure1,thede-trendedratioofrealestaterentindextotheoverallpriceindexinIstanbulisusedasareferencebehaviorforthemodel.Therentpricesareusedasareferencebecauselong-termhousepricedataseriesforIstanbulisnotavailable.RentandhousepricesinIstanbulareingeneralassumedtobestronglycorrelated,whichlogicallymakessense.Moreoverthestronglinkagebetweenrentsandpricesinhousingisalsoshownintheliterature(Hargreaves2008;Gallin2008).WebelievethatthebehavioroftherentpriceisagoodproxyfortherealestatepricebehaviorforIstanbul.

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Figure1.Areferencebehaviorforthemodel:Thelinerepresentsthede-trendedratioofrealestaterentindextotheoverallpriceindexinIstanbul

4.3 Thetimeunitofthemodelisinyearssincethemajortimedelaysandtheratesofchangesaremeasuredintermsofyears.Thetimehorizonis60yearsbetween1970and2030.Themotivationforselectingalongrangeistobeabletoobserveatleastafewcycles.

4.4 Themodelincludesthefollowingelements;thehousesunderconstruction,forsale,andsold;thedemandforhouses;theprice,andtheprofit.Thecitypopulationcontinuouslyincreaseswithimmigrationandbirths,whichistakenasanexternalinputtothemodel.Thecostofbuildinghousesisalsomodeledasaninputthatchangesovertime.Theeffectofnationaleconomyontheconstructioncompaniesisnotconsidered.Wealsoassumedthatthereispracticallynolandlimitationforbuildingnewhouses.Thereisanupperboundfortheconstructionrate,whichreflectstheconstraintsonthelabor,capitalandotherresourcelimitationsfortheconstructors.Theparametervaluesinthemodelaremostlybasedonroughestimatesduetolackofstatisticaldataregardingtheseparameters.Sincethismodeldoesnotaimtoforecastthespecificvaluesofvariablesinthemarket,ourfocushasbeenstructuralvalidityratherthannumericprecisionoftheparameters.

Figure2.Thecausalloopdiagramofthemodel

ModelStructure

4.5 ThecausalloopdiagramshowninFigure2presentstheinteractionsbetweenvariablesthatconstitutetheenginebehindtheoscillatorydynamics.Sincethecausalloopdiagramisaqualitativedescriptionofthesystem'sfeedbackstructure,itshowsonlythemajorvariables.Arrowsshowhowthevariablesaffecteachotherceterisparibus.AnarrowwithapositivesignmeansthatachangeinXcausesYtochangeinthesamedirection,otherthingsbeingequal.AnegativeinfluencemeansachangeinXcausesYtochangeintheoppositedirection.The||signimpliesadelaybeforean

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effectreachesavariable.Figure3showsthestock-flowdiagramofthemodel.Stock-flowdiagramcorrespondstotheformalquantitativemodelusedinsimulations.EachvariablehasacorrespondingequationintheAppendix.

4.6 Intheremainingpartofthissection,weexplainmajorfeedbackloopsandcriticalformulations.Wereferreaderstothecausal-loopdiagram(Figure2)whenfeedbackloopsarediscussed,andtothestock-flowdiagram(Figure3)whenspecificformulationsarediscussed.

4.7 Threemajorbalancing(negative)feedbackloopsgovernthebehaviorofthesystem,aswillbedescribedbelow:demand-price,supply-priceandsupply-demandloops.Abalancingloopcounteractsanydisturbanceinvariablesintheloop,forcingthesystemtoseekanequilibrium.

Figure3.Thestock-flowdiagramofthemodel.Rectanglesstandforthestocksandpipeswithvalvesstandfortheflows.Othervariablesareauxiliariesorparameters.

Thelifecycleofhouses

4.8 Likemoststock-flowmodels,ourmodelrepresentsthelifecycleofhousesbyaseriesofstocksvariables:housesunderconstruction,newhouses,andsoldhouses(Maisel1963).Twoflowvariablesconnectthestocks:constructionrateandsalesrate.Constructionrateislimitedbyconstructioncapacity,whichisaresultofphysicalresourcelimitations.Thenewprojectsfirstturnintoconstructionsandthentonewhousesafteraconstructiondelay.

4.9 Salesrateisdependentonbothsupplyanddemand.Soldhousesaredemolishedafteranaveragelifetimeof40years.

Demandcreationprocess

4.10 Inthemodel,potentialbuyersisastockvariablethatrepresentsthehouseholdswhoneedahousefordwelling(seeFigure3).Newpotentialbuyersarecreatedbytwoways:demandcreatedduetodemolition(naturalturnover)andincreaseinnumberofhouseholds(demandcreationduetopopulationgrowth)(Barras2005).Potentialbuyersstockdecreasesbydemandsatisfactionrate(whichisequaltothesalesrate).Thisstockanditsflowsarethusdefinedinthefollowingdifferentialequation:

d(PotentialBuyers)/dt=Netincreaseinnumberofhouseholds+Demandcreationrateduetodemolition−Demandsatisfactionrate

(1)

Thedifferentialequationsshowthecontinuousrateofchangeofthestocks.Inordertoevaluatethemincomputersimulation,asmalltimestep(dt)isusedtocomputethevalueofthestock.Itsvalueattimet+dtiscomputediterativelyasfollows:

PotentialBuyerst+dt=PotentialBuyerst+(Netincreaseinnumberofhouseholds+Demandcreationrateduetodemolition−Demandsatisfactionrate)×dt

(2)

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Theaboveformofsimulationequationholdsingeneralforallstockequations.

4.11 Netincreaseinnumberofhouseholdsshowsthenumberofnewhousesdemandedbythepopulation(households)annually.ItisanexternalinputasgiveninFigure4,basedonhistorichouseholdincreaseratesofIstanbulundertheassumptionthatonehouseholdcreatesonehousedemandundernormalpriceconditions.Thefuturevaluesareextrapolatedbasedoncurrenttrend.

Figure4.NetIncreaseinNumberofHouseholdsovertime(modelinput).

4.12 Whilevariablepotentialbuyersrepresentsthepopulationneedingahousefordwelling,itisnotnecessarilyequaltotheactualdemandonthemarket.Theprevailingmarketpricehasaneffectonthedemand.Specifically,demandisdependentoneffectofpriceondemandandpotentialbuyersasshownEquation3.

Demand=Potentialbuyers×Effectofpriceondemand (3)

4.13 EffectofpriceondemandisadecreasingfunctionofpriceandhistoricalpriceasillustratedinFigure5.Whentheaveragehousepriceishigherthanhistoricalprice,peopletendtodecreasethedemandorviceversa.Whenpriceisequaltohistoricalprice,theeffectfunctiontakesthevalueof1.Thismakesdemandequaltopotentialbuyers,thenormaldemandlevel.

Figure5.EffectofPriceonDemand

4.14 Suchnonlineareffectformulationsareusedthroughoutthemodeltoexpresscausalrelationsbetweenvariables.Theadvantageofusingeffectfunctionsisthefreedomtoexpressanykindofnonlinearrelationwithoutbeinglimitedbycertainhard-to-present/understandmathematicalexpressions.

Demand-Priceloop

4.15 Thisloopreflectstheclassicalbalancingprocessofdemandthroughprice(SeeFigure2).Supposethatatsomegiventimethesystemisinequilibriumanddemandsuddenlyincreases(maybeduetoasuddenimmigration).Thisriseindemanddecreasessupply/demandratio.Sinceittakessometimeformarketactorstoperceiveandrespondtothischange,priceincreases,afteradelay.Weusedafirst-orderinformationdelaystructuretorepresentthisprocess,whichiswidelyusedinsystem-dynamicsliterature(Sterman2000)tomodeldelayedperceptions(seeAppendix).Increasedpricecausesdemandtofallback.Asimilarlogicalsequenceofsuccessiveeffectsalsoholdsforaninitialdecreaseofdemand,aswellasanyothervariableintheloop.

Constructionstartprocess

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4.16 Costistakentobeanexternalinputthatchangeswitheconomicconditions,whicharenotexplicitlyincludedinthemodel,asgivenbyFigure6.

Figure6.Averagecostofdwellingunits(modelinput)

4.17 Thecostdataarebasedon1970–2008statisticsofaveragecostofdwellingunitsinTurkey,providedbyTurkishStatisticalInstitute.Thedataaredeflatedtoyear2009pricesandsmoothedbynonparametricregressiontoavoidsuddenchangesinthemodel.

4.18 Thedifferencebetweenpriceandcostdeterminesprofit.AsdemonstratedbyKenny(1999),constructioncompaniespassanyincreaseinthecoststothebuyers,inordertomaintainprofitmargins.Thisfactisreflectedinourmodelasnormalprofitthatdependsoncostandprofitmargin.Normalprofitisthebenchmarkvalueforprofit,usedtocomparetheattractivenessoftheprofitobtainablebystartingnewprojects(seeFigure3).Theratioofexpectedprofittonormalprofitdetermineseffectofprofitonconstructionstartrate,whichisaconcaveincreasingfunction,similartoFigure7.Thedifferencebetweennewhousesandpotentialbuyersisexcessdemand,asshownbelow.

ExcessDemand=PotentialBuyers−NewHouses (4)

Thisexcessdemandcannotbeknownaccuratelyandtheconstructionfirmsestimateitbyanexponentialsmoothingprocess.

4.19 WhileBarras(2005)modelstheconstructionprocessasastock-adjustmentstructurewithadesiredlevelofbuildingstock(occupiedornot)thatchangewitheconomicgrowth,ourapproachreflectstheconstructorpointofview.Inourmodel,insteadoftryingtoreachadesiredhousingstock,thefirmsaimtomeetestimatedexcessdemandbystartingnewconstructions.Iftheyexpectahigherprofitthantheirnormalprofits,theirwillingnesstomeetexcessdemandincreases.Thenewprojectsturnintoconstructionsandafteraconstructiondelay,tonewhousesandthendemolishes.Constructionrateislimitedbyconstructioncapacity,whichrepresentstheconstraintsofavailableresources.

Supply-Priceloop

4.20 Anothermajorloopisthesupply-pricefeedbackloop(seeFigure2).Whenpricerises,profitincreases.Increasedprofitgraduallyincreasesexpectedprofit.Companiescomparetheirexpectedprofitwithnormalprofit(sincecompaniescannotknowtheexactprofitthatcanbeobtained,aninformationdelaystructureisusedtorepresenttheprofitexpectationprocessofthefirms).Ifexpectedprofitishigherthannormalprofit,constructionstartraterises.Throughthephysicalprocessofconstruction,housesunderconstructionyieldnewhouses.Theincreasedstockofnewhouses(thesupply)increasesthesupply/demandratio.Theriseofsupply/demandratiocreatesareductioninprice.Thisisanegativefeedbackloopinvolvingseveraldelays.Althougheventuallyanypricechangeiscompensatedbytheeffectofnewconstructions,thedelaysslowdowntheprocessandcausethepricetooscillate.

Supplystockcontrolloop

4.21 Thereisanegativeloopbetweentheexcessdemandandthesupply(seeFigure2).Asexplainedabove,estimatedexcessdemandstimulatesnewconstructionsandthenewhousesforsale.Thisconstructiondecreasestheexcessdemand,whichclosesthebalancingfeedbackloop.Thisloopisanalogoustoaninventorycontrolstructurethattriestokeeptheinventoryconstantatatarget.Inourmodel,inventorycorrespondstonewhousesandtargetisthenumberofpotentialbuyers.

Price

4.22 Priceisanchoredonindicatedcostandadjustedbyeffectofsupply/demandratioonprice(SeeFigure3).Indicatedpriceistheexpectedaveragepriceofahouseundernormalsupply/demandconditions.Itisassumedthat,indicatedpriceis10%higherthantheperceivedcostofbuildingahouse.Perceivedcostisthesmoothedversionoftheaveragebuildingcostinthemarket.Kenny(1999)demonstratedthathousepricesadjustpositivelyinresponsetoanyexcessdemandforhousing.Inlinewiththatobservation,Effectofsupply/demandratioonpriceismodeledasadecreasingS-shapedfunction(seeAppendix)similartotheformulationsavailableintheliterature(Genta1989).

SalesProcess

4.23 Salesoccurwhennewhousesanddemandarebothavailable.Searchtheoryregardsresidentialhousingmarketasasamplingprocessofavailablehouseswithconstantrate,whichcontinueuntilbuyerfindsanacceptablehouse(Haurin1988).Thus,theavailabilityofhousesrelativetothedemanddeterminesthespeedofsales,whichisquantifiedinourmodelasfollows:

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Salestime=NormalSalestime×Effectofsupply/demandratioonsalestime

(5)

4.24 Normalsalestime(1year)istheaveragetimespentinmatchingthedemandandthesupplyundernormalmarketconditions.Effectofsupply/demandratioonsalestimeisanincreasingconcavefunctionof1/perceivedsupplydemandratioasgiveninFigure7.Itisassumedthatifperceivedsupply/demandratiodecreases,salestimeincreasessinceittakeslongertimeforpeopletofindanewhousemeetingtheirneeds(astheprobabilityoffindingamatchdecreases).

Figure7.EffectofSupply/DemandRatioonSalesTime

4.25 Possiblesalesistheaveragerateatwhichnewhousescanbesoldincurrentsalestime,withouttakingthedemandintoconsideration.Desiredsales,ontheotherhand,istheaveragerateatwhichdemandcanbemet,ignoringthesupply.Salesrateistherealizedrateofsales,whichistheminimumofdesiredandpossiblesalesrates.

Supply-DemandLoop

4.26 Thislooprepresentsthebalancingprocessbetweensupplyanddemand,throughsalesandprice(SeeFigure2).Asdemandincreasessalesraterises.Thisreducesthesupplyandraisesprice,afteradelay.Therisenpricehasanegativeeffectondemand.

SupplyandDemandSelf-CorrectionLoops

4.27 Theseareminornaturalfeedbackloopsthatareresultsofstockscontrollingtheiroutflows.Increasedsupplyofhousesgivesrisetofastersales,whichinturndecreasesthesupplyitself.Asimilarprocessworksforthedemand.

SupplyAdjustmentthroughSalesTime

4.28 Thisloopconstitutesanextrabalancingprocessforthenewhousesstock(seeFigures2and3).Whenthelevelofnewhousesbecomeslargerthanthedemand,theincreasedavailabilityofnewhousesshortenstheprocessofsupply-demandmatching,thusshortensthesalestime.Decreasedsalestimeleadstoincreaseddesiredsalesandpossiblesales,whichmeanshighersalesrate,whichinturnbalancesofftheriseinthenewhousesstock.Thusanyincreaseinnewhousesstock,otherthingsbeingequal,inducesanincreaseinsalesrate(outflow),whichinturnresultsinanegativemovementinnewhouses(stock).Thisnegativefeedbackloopshowsthebalancingnatureoftheprocess.

ModelBehavior

4.29 Figure8showsthedynamicbehaviorsgeneratedbythebasemodel.Pricefollowsthegeneraltrendofcost(seeFigure8(a)).Duetotheeffectofprofitmargin,theaveragepriceis26%higherthantheaveragecost.Therangeoftherealizedprofitmarginisbetween0%and46%.Moreimportantly,priceexhibitsoscillationswithanaverageperiodof7years.Themainreasonbehindthisoscillationisthenegativeloopandthedelaysbetweendemandcreationandnewhouseconstruction.Thisdelayincludesthetimespentinstartingnewprojectsaswellastheconstructionduration.Duringthisperiod,duetoshortageofsupply,whichcanbeseenasadecreaseinsupply/demandratioinFigure8(b),priceincreases.Theconstructionfirmsdonottakeintoaccounttheconstructionsinprogressandcontinuetostartnewprojectsinordertobenefitfromthehighprofitsinthemarket.Astheconstructionsarecompleted,thedemandhasalreadybeenmet,andanexcesssupplyemerges,whichcausesadecreaseinprice.Thelagbetweenthedemandandthesupply(newhouses)isclearlyseeninFigure8(c).

4.30 AsseeninFigure8(d),effectofprofitontheconstructionstartrateisusuallycloseto1,whichmeansthatthecompaniestrytoconstructnewhousesasmuchasexcessdemand.Sometimes,expectedprofitfallsbelownormalprofitasshowninFigure8(e).Thiscausesadecreaseineffectofprofitonconstructionstartrateandtheconstructioncompaniesdecidetomeetasmallerportionofestimatedexcessdemand.

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(a)Behaviourofcost(input)andprice(output)

(b)Behaviourofsupply/demandratioanditseffectonprice

(c)Behaviourofdemandandnewhouses

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(d)Behaviourofconstructionstartrateandtheeffectofprofitonit.(Impliedconstructionstartrateisdefinedasestimatedexcessdemanddividedbyconstructionrealizationtime)

(e)Behaviourofprofit-relatedvariablesFigure8.Behaviorsofthebasemodel

Validation

4.31 Sincesystemdynamicsmodelsarelong-termbehavior-orienteddescriptivemodels,theirvaliditycannotbemeasuredbytheircapabilitiesofmakingpointforecasts.Rather,theyareevaluatedintermsoftheirstructuraladequacyandtheirpowerofgeneratingvalidbehaviorpatterns.Validityofthebehaviorscanbecheckedagainstavailablerealbehaviorpatterns,oragainstlogicallypredictedbehaviorsunderextremeconditions.Thus,therearetwomainaspectsofvalidationofsystemdynamicsmodels:structurevalidityandbehaviorvalidity(Barlas1989,1996;Saysel&Barlas2006).Structurevalidityisassuringthatmodelstructureisinagreementwiththerelationsexistinginthereallife.Behaviorvaliditytests,ontheotherhand,assessifthemodelandtherealsystemproducesimilaroutputbehaviorpatterns.ValidationtestsappliedinthisstudyarebasedonthemethodologygiveninBarlas(1996).Oneshouldkeepinmindthatincausal-descriptivemodeling,theessenceofvalidityisstructurevalidity:withoutavalidstructure,outputbehaviorvaliditycanbemeaningless,entirelycoincidental.Behaviorvalidityisusefulandmeaningful,onlyafterstructurevalidityhasbeenestablished.

4.32 Forthestructurevalidity,wemadeuseofrelationsfromliteraturethatareproventobeconsistentwiththerealsystem.Ourmodelmakesuseofmanykeyconceptsandstructuresthatareusedinthehousingeconomicsliterature:achainofstocksrepresentinghousesunderconstructionandnewhouses(Maisel1963);thedependenceofconstructionstartrateonthedifferencebetweensupplyanddemand(DiPasquale&Wheaton1994);gradualpriceadjustment(DiPasquale&Wheaton1994);twotypesofdemandcreation:duetogrowthandduetoturnover(Barras2005);demandamplificationwhenpriceishigh(Kenny1999);anddelaysinpriceformation,demandandprofitestimation,constructionstartsandcompletions(Barras2005).Wealsoincorporatestructurescommonlyusedinsystemdynamicsliteraturetomodelsimilarphenomena:usinginformationdelaystructurestomodeladaptiveexpectations(Sterman2000);'effect'formulationstoexpressnonlinearcausalrelations(Barlas2002);agingchainstorepresentconsecutivematerialdelayswhereflowsareconserved(Forrester1970).

4.33 Additionally,theunitsoftheleftandrighthandsidesofallequationsarecheckedandverifiedthattheyareconsistent.Fortestingthelogicalvalidityofmodelbehavior,wecomparedthemodelbehaviorunderextremeconditionswiththelogicallyexpectedbehaviorinthesameconditions.Forexample,inoneofsuchextremeconditiontest,wesettheinitialvalueofthepotentialbuyersstockandnetincreaseinnumberofhouseholdstozeroandshowedthatthehousesunderconstructionarecompletedbutnonewhousesareconstructed(Figure9(a))andthepriceisonlyaffectedfromchangesinthecostasgiveninFigure9(b).Inanothertest,wesetcosttoaconstantvalue,asgiveninFigure10.Underthiscondition,theoscillatorybehaviorofpricestillexistswhichshowsthattheoscillatorybehaviorofpriceisaresultofthemodel'sinternalstructureitself,notaresultoftheexternalinputs.Thisresultisparticularlyimportant,asitshowsthatthebehaviorvalidityofthemodelisobtainednotbyfine-tunedexternalinputs,butbytheinternalstructureofthemodel('rightbehaviorfortherightreasons'principle).

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(a)Behaviourofhousingvariableswhenthereisnodemand

(b)BehaviourofcostandpricewhenthereisnodemandFigure9.Resultsoftheextremeconditionvalidationruns.

Figure10.Behaviorofpricewhencostisconstant.

4.34 Toensurethebehaviorvalidityofthemodel,themodeloutputsshouldbeconsistentwiththerealdata.Itisknownthattherealestatepricestypicallyshowoscillatorybehaviorsinreallife(Figure1andFershtman&Fishman1992;Meen2000;Jiangetal.2010;Genta1989;Sæther2008).AsFigure8(a)shows,thebehaviorofthepricevariablegeneratedbythemodelalsooscillatessimilarly.AnInternationalMonetaryFundstudy(Helbling&Terrones2003)analyzedhousingpricecyclesin14developedeconomiesoverthe1970to2001period.Over75cyclesidentified,thecycleperiodisintherangeof0.5–10.5yearswithanaverageofaround4years.SuchrichdataforIstanbulrealestatemarketisnotavailable.ButasgiveninFigure1,theratioofrealestaterentindextotheoverallpriceindexinIstanbulisavailable,whichcanbeusedforvalidationpurposes.Thisdataseriesshowsoscillationsof6–8years.ThemodeloutputforpricegiveninFigure8(a)shows7-yearpricecycles,whichiswithintherangeofIMFdataandconsistentwithcycleperiodsofIstanbulrealestateindex.

ScenarioandPolicyAnalysis

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5.1 Inordertopreventtheundesiredoscillatorybehaviors,weneedtoidentifytheleveragepointsthatcanbeusedtocreatechangesinthesystem.Thismodelprovidesausefulplatformfordeterminationofsuchparameters.Özbaşetal.(2008)performsasensitivityanalysisofanearlierversionofthemodelpresentedinthispaper.Thestudyshowsthattheamplitudeofthepricecyclesissignificantlyaffectedbyconstructiontime.Asconstructiontimefalls,theamplitudeofthepricecyclesalsofalls.Inviewofthisfact,weconductascenarioanalysisthatevaluatesthechangesinthemodelwhentheconstructiontimeisdecreased.

5.2 Finallywealsoanalyzetheeffectsofapolicythatcanbeappliedbytheproblemowner,whichmaybeatradechamber,anassociationoraconsortiumofrealestateconstructioncompanies.Thepoliciesareevaluatedintermsoftheireffectsonthepriceoscillations.

DecreasingConstructionTime

5.3 Ourbasemodelassumesthattheaverageconstructioncompletiontimeisabout550days.Variousfactorsincludinglaborandmaterialshortages,financialdifficulties,poorprojectmanagement,inadequatedesignandtechnologicallimitationscauselongdelaysinconstructionprojects.Withthepressureofincreasingcompetitionandwiththehelpoftechnologicalandmanagerialstrategies,thedelaysinconstructionprojectscanbesignificantlyreduced.Thetechnologicalstrategiesmayincludestandardizationandrepetitionofbuildingelements,increasingphysicalcapabilitiesofmachinery,adoptingmoreefficientconstructionscheduling,orincreaseduseofprecastcomponents.Themanagerialstrategiesmayinvolveeffectivesitemanagement,providingdecisionaids,bettercommunicationandcoordination(Chan&Kumaraswamy2002).

5.4 Thisscenariotestswhathappensiftheaverageconstructiontimeisgraduallydecreasedto150dayslinearlyina10-yearperiodstartingfromtheyear2010.AsseeninFigure11(a),thepricecyclesdampoutandeventuallyalmostdisappear.However,completedampingtakesaboutsixdecades(whichcannotbefullyobservedwithinthetimehorizonofthemodeloutputs).

(a)Behaviourofcost(input)andprice(output)

(b)BehaviourofdemandandnewhousesFigure11.Behaviorofkeyvariableswhenconstructiontimeisdecreasedby73%fromtheyear2010to

2020.

5.5 Thestabilizedbehaviorofpriceaffectsthewholesystemandothervariablessuchasdemand,newhouses(See11(b))andprofitgraduallyapproachasteadystateafterthepolicyisimplemented.Thisprovidesapredictableandsafeenvironmentforthecompanies.Inamorestablerealestatesector,therewillbelessdistortion,lowerriskofunemploymentandincreasedoutputduetoreducedmismatchbetweensupplyanddemand.Less

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volatilesectorcreatesamuchpredictablefinancialenvironment,whichresultsinlowercreditriskassessment.

CompaniesTakeintoAccountHousesunderConstruction

5.6 Normallycompaniesdonothaveenoughinformationaboutothercompanies'housesunderconstruction.Inthispolicy,weassumethatacentralassociationofcompaniesgathersdataonthenumberofhousesunderconstruction,providesthecompanieswiththisinformationandpromotestheapplicationofthepolicyatleastbythemajorityofthecompanies.Previously,excessdemandwascomputedwithouttakinghousesunderconstructionintoaccountasgiveninEquation4.Inthenewpolicy,thecompaniesusetheinformationabouthousesunderconstructioninestimatingexcessdemandasshowninEquation6.

ExcessDemand=Potentialbuyers−NewHouses−Housesunderconstruction (6)

Thisway,theunnecessaryhouseconstructionisavoided,whichwasthemaincauseofthepriceoscillations.Figure12(a)showsbehaviorofpricewhenthispolicyisappliedaftertheyear2010.Thispolicymakesthepricecyclesdisappearalmostimmediately,buttheequilibriumpricelevelofthispolicyishigherthanthatofthepreviousscenario.

(a)Behaviourofcost(input)andprice(output)

(b)BehaviourofprofitFigure12.Behaviorofkeyvariableswhencompaniesstartconsideringhousesunderconstructionintheirdecisionsaftertheyear

2010.

5.7 Likeprice,profitoscillatesuntilnewpolicyisadoptedintheyear2010.Afterthenewpolicy,profitcomestoasteadybehavior(seeFigure12(b)).Whenwecomparetheaverageyearlyprofitsofpre-policyandpost-policyperiods,a13%increaseisobserved.Thatis,consideringhousesunderconstructioninconstructiondecisionsmakesthemarketstableandalsoincreasestheprofits.Inastabilizedmarketthecompanieswillalsoenjoythepreviouslymentionedbenefits.Finallynotethatinrealityperfectinformationabouthousesunderconstructionwouldnotbeavailabletothedecisionmakers.Amorerealisticversionofthisidealscenariocanbeeasilyimplementedinourmodel,byincorporatingandestimationdelayandestimationerrorinhousesunderconstructioninthedecisionequation.Inthiscase,theoscillatorybehaviorswouldagainbestabilized,butnottotheextremeextentobtainedintheidealizedpolicy(SeeFigure13).

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Figure13.Behaviorofcostandpricewhencompaniesstartconsideringhousesunderconstructionwithaone-yeardelayand10%erroraftertheyear2010.

5.8 Realisticcombinationoftheabovetwopolicies;Amildreductionoftheconstructiondelaysandanimperfect/delayedaccesstothe"numberofhousesunderconstruction"informationwouldhavemorereal-liferelevance.Inthiscase,theoscillatorybehaviorofthebasemodelisagainstabilized(SeeFigure14).

Figure14.Behaviorofcostandpricewhenconstructiontimeisdecreasedby42%fromtheyear2010to2020,andcompaniesstartconsideringhousesunderconstructionwithaone-yeardelayand10%erroraftertheyear2010.

Conclusion

6.1 Thepurposeofthisstudyistomodelandanalyzebysimulationthedynamicsofendogenouslycreatedoscillationsinrealestate(housing)prices.Asystemdynamicssimulationmodelisbuilttounderstandsomeofthestructuralsourcesofcyclesinthekeyhousingmarketvariables,fromtheperspectiveofconstructioncompanies.Themodelfocusesontheeconomicbalancedynamicsbetweensupplyanddemand.Becauseoftheunavoidabledelaysintheperceptionoftherealestatemarketconditionsandconstructionofnewbuildings,pricesandrelatedmarketvariablesexhibitstrongoscillations.Twopoliciesaretestedtoreducetheoscillations:decreasingtheconstructiontime,andtakingintoaccountthehousesunderconstructioninstartingnewprojects.Bothpoliciescreatesignificantlyreducedoscillations,morestablebehaviors.

6.2 Realestatemarketsexhibitcyclicbehaviorsworldwide.Themainreasonbehindthesecyclesistheimbalancebetweenthedemandandthesupply,whichiscausedbythedelaysinvolvedinconstructiondecisionsandincompletingtheconstructions.Eventhoughconstructioncompaniesknowabouttheoscillatorybehaviorsofthemarket,theytrytotakeautonomousactionstoincreasetheirprofitsintheboomtimes.Additionallydecisionstakenduringboomandboosttimesalterthepricecycles.Inotherwords,priceoscillationsaretoalargeextentproducedbytheveryactionsthatthesecompaniestake.Themainparadoxisthatcompaniesdoknowaboutthecycles,buttheydonotchangetheirmainstrategiestoeliminatethem,becausetheybelievethatthesecyclesareexogenouslycreated,notasaresultoftheirveryownpolicies.Thisparadoxisdemonstratedbythemodelandisoneofthemainmotivationsbehindthestudy.Theresultingcomplexatmospherecreatesavolatileandunstableenvironmentforthecompanies.Inordertocreateamorestableenvironment,thecompaniesshouldactincoordination,sincenosinglecompanyhasenoughpowertocontrolthemarket.

6.3 Wedevelopasystemdynamicssimulationmodelofhousingmarkettounderstandthecausalmechanismsthatresultincyclicbehaviorofthemarket.Themodelisbuiltfromtheperspectiveofanassociationofconstructionofcompaniesinacity,whichhasenoughpowertoguidethehousingmarket.ThestructureofthemodelisgenericfordevelopingcitiesandtheparametersarechosenfromthecityofIstanbul.Threemajorbalancingfeedbackloopsdeterminethebehaviorofthemodel:demand-price,supply-priceandsupply-demandloops.Thesebalancingfeedbackloopsimplythatthereisanaturaltendencytowardsstabilizationofthesystem.However,significantdelaysintheseloopsresultinanoscillatorybehavioroftheprice.Thus,

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weseethatdelaysarethecriticalcomponentsofthissystemthatcanbeusedasaleveragetoreduceundesiredoscillations.Basedonthisobservation,weproposealternativepoliciestoreducetheoscillationsbydecreasingdelaydurations.

6.4 Inonesimulationscenario,theconstructiondelaysarereducedbytechnologicalandmanagerialstrategies.Agradualdecreaseofconstructiontimesby73%in10yearseventuallycausespricecyclestodampenovertime.However,thecompleteeliminationofcyclestakesplaceina60-yearperiod,beyondthetimehorizonofthebasesimulations.Sincethefulltransitiontakesalongtime,theadaptationoftheconstructioncompaniestothechangingenvironmentshouldnotbedifficult.Ontheotherhand,thesystemmustbepatientenoughtoenjoythefullbenefitsofthispolicy,and60yearsmaybetoolongtoberealisticinthissense.

6.5 Inanalternativepolicy,weassumethattheconstructioncompanieshaveaccesstothe"numberofhousesunderconstruction"informationwhentheystartnewprojects.Thisinformationcanpreventcompaniesbuildingmorehousesthannecessary,whichwasyieldingexcesssupplyandoscillationsinthebasescenario.Withthenewpolicy,thepriceoscillationsareeliminatedinamuchshorterperiodoftimecomparedtothefirstpolicy.Suchaquickchangeinthemarketbehaviormaybehardtoadopt,butitresultsina13%increaseintheyearlyprofitswhenthepolicyshowsitsfulleffect.Realisticcombinationoftheabovetwopolicies;Amildreductionoftheconstructiondelaysandanimperfect/delayedaccesstothe"numberofhousesunderconstruction"informationwouldhavemorereal-liferelevance.Inthiscase,theoscillatorybehaviorofthebasemodelismoderatelystabilized.

6.6 Sincethemodelrepresentsthemaincausalrelationshipsthatarerelevanttothehousingmarketcycles,itcanalsoserveasabasisforforeseeingthereactionofthemarkettootherchangesinthesystem.Withthehelpofthismodel,itwillbepossibletoanalyzehowsensitivetheoscillationsaretochangesinsomeparameterssuchassalestime,constructiontimeandprofitmargin.Variousotherpolicyalternativescanbetestedbyminormodificationsinthemodel.Itisalsopossibletomodifyandadaptthemodeltodifferentspecificcitiesandregionsaroundtheworld.

Appendix:ModelEquations

ConstructionRealizationTime=0.4yearsConstructionStartRate[houses/yr]=EstimatedExcessDemand×EffectofProfitonConstructionStartRate/ConstructionRealizationTimeHousesunderConstruction(t)[houses]=HousesunderConstruction(t−dt)+(ConstructionStartRate−ConstructionRate)×dtHousesunderConstruction(1970)=40000housesConstructionTime=1.5yearsPotentialConstructionRate[houses/yr]=(HousesunderConstruction/ConstructionTime)ConstructionCapacity[houses/yr]=GRAPH(t)

Figure15.ConstructionCapacity

EffectofCapacityonConstructionRate[Unitless]=GRAPH(ConstructionCapacity/PotentialConstructionRate)

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Figure16.EffectofCapacityonConstructionRate

ConstructionRate[houses/yr]=PotentialConstructionRate×EffectofCapacityonConstructionRateNewHouses(t)[houses]=NewHouses(t−dt)+(ConstructionRate−SalesRate)×dtNewHouses(1970)=60000housesSalesRate[houses/yr]=MIN(Possiblesales,DesiredSales)SoldHouses(t)[houses]=SoldHouses(t−dt)+(SalesRate−DemolitionRate)×dtSoldHouses(1970)=600000housesHouseLife=40yearsDemolitionRate[houses/yr]=SoldHouses/HouseLifeNetIncreaseinNumberofHouseholds[households/yr]=GRAPH(t)

Figure17.NetIncreaseinNumberofHouseholds

PotentialBuyers(t)[households]=PotentialBuyers(t−dt)+(NetIncreaseinNumberofHouseholds+DemandCreationDuetoDemolition−DemandSatisfactionRate)×dtPotentialBuyers(1970)=60000householdsDwellers(t)[households]=Dwellers(t−dt)+(DemandSatisfactionRate−DemandCreationDuetoDemolition)×dtDwellers(1970)=600000householdsDemandSatisfactionRate[households/yr]=SalesRate/DemandperHouseholdDemandCreationDuetoDemolition[households/yr]=DemolitionRateRate/DemandperHouseholdDemand[houses]=Potentialbuyers×DemandperHousehold×EffectofPriceonDemandDemandperHousehold=1house/householdCost[TL]=GRAPH(t)

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Figure18.Cost

PerceivedCost(t)[TL]=PerceivedCost(t−dt)+(PerceivedCostAdjustmentRate)×dtPerceivedCost(1970)=19100TLPerceivedCostAdjustmentTime=0.5yearsPerceivedCostAdjustmentRate[TL/yr]=(Cost−PerceivedCost)/PerceivedCostAdjustmentTimeAcceptedProfitMargin=0.1Indicatedprice[TL]=PerceivedCost×(1+AcceptedProfitMargin)Price[TL]=IndicatedPrice×EffectofSupply/DemandonPriceHistoricalPrice(t)[TL]=HistoricalPrice(t−dt)+(HistoricalPriceAdjustmentRate)×dtHistoricalPrice(1970)=25000TLHistoricalPriceAdjustmentRate[TL/year]=(Price−HistoricalPrice)/HistoricalPriceAdjustmentTimeHistoricalPriceAdjustmentTime=5yearsSupply/DemandRatio[Unitless]=Newhouses/DemandPerceivedSupply/DemandRatio(t)[unitless]=PerceivedSupply/DemandRatio(t−dt)+(PerceivedSupply/DemandRatioAdjustmentRate)×dtPerceivedSupply/DemandRatioAdjustmentRate[Unitless]=(Supply/DemandRatio−PerceivedSupply/DemandRatio)/PerceivedSupply/DemandRatioAdjustmentTimePerceivedSupply/DemandRatioAdjustmentTime=0.2yearsEffectofSupply/DemandonPrice[Unitless]=GRAPH(PerceivedSupply/DemandRatio)

Figure19.EffectofSupply/DemandonPrice

EffectofPriceonDemand[Unitless]=GRAPH(Price/HistoricalPrice)

Figure20.EffectofPriceonDemand

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EffectofSupply/DemandonSalesTime[Unitless]=GRAPH(1/PerceivedSupplyDemandRatio )

Figure21.EffectofSupply/DemandonSalesTime

NormalSalesTime=1yearSalesTime[years]=NormalSalesTime×EffectofSupply/DemandonSalesTimePossiblesales[houses/yr]=Newhouses/SalesTimeDesiredSales[houses/yr]=Demand/SalesTimeProfit[TL]=Price−CostExpectedProfit(t)[TL]=ExpectedProfit(t−dt)+(ExpectedProfitAdjustmentRate)×dtExpectedProfit(1970)=4000TLExpectedProfitAdjustmentTime=5yearsExpectedProfitAdjustmentRate[TL/yr]=(Profit−ExpectedProfit)/ExpectedProfitAdjustmentTimeProfitMargin=0.25NormalProfit[TL]=Cost×ProfitMarginEffectofProfitonConstructionStartRate[Unitless]=GRAPH(ExpectedProfit/NormalProfit)

Figure22.EffectofProfitonConstructionStartRate

ExcessDemand[houses]=PotentialBuyers−NewhousesEstimatedExcessDemand(t)[houses]=EstimatedExcessDemand(t−dt)+(ExcessDemandAdjustmentFlow)×dtEstimatedExcessDemand(1970)=10000housesExcessDemandEstimationTime=1yearExcessDemandAdjustmentFlow[houses/yr]=(ExcessDemand−EstimatedExcessDemand)/ExcessDemandEstimationTime

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