©CopyrightJASSS

AmitPatel,AndrewCrooksandNaoruKoizumi(2012)

Slumulation:AnAgent-BasedModelingApproachtoSlumFormations

JournalofArtificialSocietiesandSocialSimulation 15(4)2<http://jasss.soc.surrey.ac.uk/15/4/2.html>

Received:08-Aug-2011Accepted:21-Jun-2012Published:31-Oct-2012

Abstract

Slumsprovideshelterfornearlyonethirdoftheworld'surbanpopulation,mostoftheminthedevelopingworld.Slumulationrepresentsanagent-basedmodelwhichexploresquestionssuchasi)howslumscomeintoexistence,expandordisappearii)whereandwhentheyemergeinacityandiii)whichprocessesmayimprovehousingconditionsforurbanpoor.Themodelhasthreetypesofagentsthatinfluenceemergenceorsustenanceofslumsinacity:households,developersandpoliticians,eachofthemplayingdistinctroles.Wemodelamulti-scalespatialenvironmentinastylizedformthathashousingunitsatthemicro-scaleandelectoralwardsconsistingofmultiplehousingunitsatthemacro-scale.Slumsemergeasaresultofhuman-environmentinteractionprocessesandinter-scalefeedbackswithinourmodel.

Keywords:Slums,Housing,DevelopingCountries,UrbanPoor,InformalSettlements,Agent-BasedModeling

Introduction

1.1 Over900millionpeopleliveineitherslumsorsquattersettlements,anumberprojectedtoincreasetoapproximately2billionby2030(UN-Habitat2003).MostofthisgrowthisexpectedinthedevelopingworldespeciallyinAsiaandAfrica.Itispredictedthatmanylargecitiesindevelopingcountrieswillnearlydoubletheirpopulationby2020,butthedevelopmentofformalhousingwillnotbeabletokeeppacewiththisrapidurbanization(UN-Habitat2003).TheestimatesgivenaboveforslumpopulationarebasedonthedefinitionsuggestedbyUN-Habitat(2006),oneofthemostwidelyuseddefinitionsofslums.Accordingtothisdefinition,ahouseholdisaslumdwellerifitlacksanyofthefollowingfiveelements:i)accesstowater,ii)accesstosanitation,iii)securedtenure,iv)durablehousing,andv)sufficientlivingarea.Anadvantageofthisdefinitionisthatitdefinesaslumatthehouseholdlevel.Mostotherdefinitionsdefineaslumattheneighborhoodlevel(e.g.CensusofIndia2001;Neuwirth2005;RoyandAlsayyad2004),therebymakingitdifficulttodifferentiatebetweenlivingconditionsofthehouseholdswithinaslum.

1.2 Theproblemsofinadequatelyservicedandovercrowdedhousingusuallyoccupiedbyeconomicallyweakersectionsofsocietyarenotnew.HistoricalaccountsofslumsinEuropeandtheAmericasbetweenthe17thand19thcenturysuggestpossiblyworseslumconditionsthanthatseeninthedevelopingworldtoday.Fewcitiescangrowwithouttheexpansionofslumsandinformalemploymentintheirinitialgrowthperiod(Mumford1961).

1.3 Theinternationaldevelopmentcommunityhasrecognizedtheproliferationofslumsasanimportantsocietalissueforrapidlyurbanizingdevelopingcountries.Asaresponse,Target11oftheMillenniumDevelopmentGoals(MDG)aimstosignificantlyimprovelivesof100millionslumdwellersby2020(UnitedNations2000).NationalandLocalgovernmentsinmanydevelopingcountrieshavealsocalledforslumup-gradationandslumimprovementprograms.Forexample,thecurrentpresidentofIndiarecentlyannouncedapolicytargetedtomakeIndiaslum-freewithinthenextfiveyears(TimesofIndia2009),whichhasresultedinamassivehousingprogrammeinIndia(MHUPA2010).Theexpansionofurbanrenewalprogramsandagreaterfocusonmakingcitiesslum-freehastakenafrontseatamongpolicymakersinmostdevelopingcountriesaroundtheworld.

1.4 Whileavarietyofpolicyactions,rangingfromforcedevictionstoparticipatoryslumimprovements,havebeentakentoimprovethelivesofslumdwellers,slum-freecitiesstillremainadistantgoalformostdevelopingcountries.Forthepoliciestobemoreeffective,itisessentialtounderstandhowslumscomeintoexistence,howtheyexpand,andfinallywhichprocessesimprovehousingconditionsfortheurbanpoor.Thispaperattemptstoexplorethesekindsofquestionsusingasimulationapproach.Thepaperisorganizedasfollows:webrieflyreviewpasteffortsofslummodelingbeforedescribingouragent-basedmodelnamedSlumulation.WethenverifyourmodelandpresentsimulationresultsfromSlumulation.Finally,weconcludethepaperwithdiscussionandremarksonareasoffurtherwork.

PreviousEffortstoModelSlums

2.1 Slumformationhasbeenasubjectofinterestforseveraldisciplines:urbangeography,economics,sociology,politics,environmentalscienceanddemographytonamebutafew.Therehavebeenseveralattemptstoexplaintheforcesbehindslumformation.Hereweonlypresentabriefreviewoftheprominentresidentiallocationandslumformationmodels,whicharethemostcloselyrelatedtothemodelpresentedbelow.TheBurgess(1927)model(partofthe"ChicagoSchool")wasthefirstmodelinurbangeographytoidentifywhere"workingmen'shousing"and"zonesintransition"werelocatedintheformofghettosandslumsininnercitylocations.Overtimethe"ChicagoSchool"becamemorerigorouswiththeadvancesinneo-classicaleconomics.Inparticular,theworksofAlonso(1964),Muth(1969)andMills(1972)whichdemonstratedhowa"rent-gradient"ofdecliningpricesandrentsawayfromthecentercouldbecalculatedtopredictthelocationsofvariousgroupsofpeoplewithinacity.

2.2 Therehavebeenseveralattemptstoexplainslumformationusingurbancensusdatawithmodelslargelyknownasfactorialecology(seeJanson1980forareview).AmongstthemisShevkyandBell's(1955)modelofsocialareaanalysiswhichshowedthathouseholdswerespatiallyseparatedfromeachotherbasedonfivekeyfactors:i)socio-economicstatus,ii)familism,iii)ethnicity,iv)accessibility/spacetrade-offandv)socio-economicdisadvantage.Whilesuchworkallowsonetodefinedifferentareasofacity,theapproachhasoftenbeencriticizedforlackingalinkbetweentheoriesofsocialchangeandtherealitiesofarealdifferentiationwithincities(Johnston1971).Forexample,theseworkstelluslittleaboutthebehaviorandreasoningofwhypeopledecidetomovetoaspecific

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typeofarea.

2.3 Themajorityofpreviousmodelsthatexploredslumformationandcitygrowthapproachedtheproblemasastaticphenomenon(e.g.Alonso1964),whichhasbeenchallengedwiththegrowingrealizationthaturbanizationandslumformationarelargelydynamicprocesses.Dynamicmodelsthataccommodatethisfluxandcomplexityarethuscalledfor(Batty2005).Agent-basedmodeling(ABM)providesanidealframeworktostudysuchdynamicprocessesbecausetheyfocusonindividualagent'sbehaviorandtheirinteractionsgiverisetoaglobalphenomenaofinterest.Forexample,inSchelling's(1971)modelofsegregation,individualsaregiventhesimpleruleofchoosingalocationbasedononlyone-thirdofneighborsofsimilarrace.Butthisrule,whenappliedtomanyindividuals,givesrisetoahighlysegregatedspatialpatternglobally.Secondly,citiesarecomplexsystems,whicharemorethanasimplesumoftheirparts(Batty2005).Asimulationapproachprovidesusanopportunitytoexplorethepossibilityofsub-systems(e.g.slums)beingcomplexthemselvesbutalsobeingapartofanoverallcomplexsystem(e.g.thecity).

2.4 Whilethereisagrowingamountofworkfocusingonagent-basedmodelsandurbanization(see,forinstance,BenensonandTorrens2004;Batty2005;Heppenstalletal.2011),theuseofagent-basedmodelsforexploringslumformationisstillinitsinfancy.OnlyahandfulofattemptshavebeenmadetoexplainslumformationsusingABM,principalamongstthemareSietchiping(2004);Barros(2005);Vincent(2009)andAugustijn-Beckersetal.(2011).Sietchiping(2004)'scellular-automata(CA)modelisoneoftheearliestsimulation-basedattemptstopredictinformalsettlementsasatypeofland-usebyadaptingtheCA-basedurbangrowthmodelcalledSLEUTH(originallydevelopedbyClarkeetal.(1997)toincorporateinformalsettlements.However,suchamodeldoesnotcaptureindividualbehaviorandfocusesmoreonmathematicalcelltransitionsfrompreviousstatesofthesystem.Oneofthefirstattemptstodevelopanagent-basedmodelincorporatinghouseholdbehaviorparticularlyfocusingonslumsisthatofBarros(2005).Themodelexploredhowdecentralizeddecision-makingcanbeincorporatedintoslummodeling.Augustijn-Beckersetal.(2011)advancedABMintheslumliteraturebycreatinganagent-basedmodelbasedonempiricallyfoundedbehavioralrules.Furthermore,Vincent(2009)demonstratedthatsocio-economiccharacteristicsoftheinhabitantsofacityplaysasignificantroleinshapinggrowthpatternofinformalsettlements.

2.5 Whilealltheseeffortstookdifferentapproachestomodelinformalsettlements,fourmainpointsemerge.Thefirstisthatexplicitmodelingofthespatialenvironmentisimportantasslumsemergeindistinctareas.Secondly,slumsarearesultofhuman-environmentinteractions.Thirdly,individualhouseholdsmakelocationalchoicesandlastly,localgovernmentplaysanimportantroleasittakescity-wideactionssuchasslumevictionorslumup-gradationtoaltertheslumconditionsortoeradicatethem.Themodelsdiscussedaboveincorporateoneorsomeoftheseaspectsbutnoneofthemincorporatesallofthemintoasinglemodelingframework.

2.6 Ourstudyattemptstomodelacitysystemwhereseveralslumsform,growanddisappearasaresultofhuman-environmentinteractionsatmultiplespatialscales.Forexample,thehouseholdlevelbehaviorisconfrontedwiththecitylevelpoliticalforcesinamulti-scaleenvironment.Thispointofviewcallsforcreatingahuman-environmentinteractionmodelwherethehumanbehaviorismodeledinamulti-scalarspatialenvironment.Hence,ourmodelattemptstoincorporatethecomplexityofurbanmorphologycombinedwiththesocialcomplexityofhumanbehaviorinastylizedmanner.Although,multi-scalemodelingofurbansystemsisnotacompletelynewidea(O'Sullivan2009),thisisthefirstattempttobuildamulti-scalemodelofslumformationtothebestofourknowledge.

Slumulation:AnAgent-basedmodelofSlumFormation

3.1 ThekeyideabehindSlumulationistoconduct"thoughtexperiments"andask"what-if"typeofquestionsrelatedtoslumformation(EpsteinandAxtell1996).ItisastylizedmodelalaSchelling(1971).However,Schelling's(1971)modelfocusedonthegapbetweendesiredandavailablestructureoftheneighborhoods.Slumulationfocusesonagent-environmentinteractionwherethegapbetweenagents'economicabilityandthepriceandavailabilityofdwellingunitsintheenvironmentbecomesofgreaterimportance.

3.2 IntermsofAxtellandEpstein(1994)schemaofclassification,modelsthatportrayacaricatureoftheagentsbehaviorarecalled"Level0"modelswhereasthoseattainingqualitativeagreementwiththepatternsofemerging"macro-structures"are"Level1"models.Whilea"Level2"modelattainsquantitativeagreementsofemergingmacro-structures,a"Level3"modelattainsquantitativeagreementswithbothemergentmacro-structuresaswellasindividualagent'smicro-behavior.Asshownbelow,themodelpresentedhereisfarfromLevel2andLevel3atthisstageofdevelopment,howeveritisinqualitativeagreementwithempiricalmacro-structureofslumpatternsincities,andhencerepresentsa"Level1"typeofmodel.

3.3 Slumulationisconceptualizedasaspatialagent-basedmodelofacitythatconsistsofagents,theirattributes,behavioralandtransitionrulestiedtospatialentities(e.g.placestolive),whichallinteractthroughspaceandtime.Wedescribeeachoftheseelementsindetailbelow,firstdescribingthemainagentsbeforediscussingtheirbehavioralandtransitionrules.Theclassicaltheoriesandpriormodelingefforts(discussedintheprevioussection)provideabasisforourassumptionsregardingtheseelementsofSlumulation.

3.4 Themainagentsthatinfluencetheslumformationprocessasidentifiedfromtheliteraturearehouseholds,developersandlocalpoliticians(ParthasarthyandPothana1981;Singh1986;Chege1981;Bharucha2011).InSlumulation,thehouseholdagentsmakehousinglocationdecisions;thedeveloperagentscreatehousingunitsonvacatedhousingsitesthusaddingtotheexistinghousingstock;whilethepoliticianagentsprovideasubsidytoslum-dwellersinahopetogainvotesfromthem.Thissubsidydiscountsthe"economicrent"invaryingdegrees,whichinturnfacilitatestheretentionorevictionofexistingslumswithinanarea.InSlumulation,householdsareonthedemandsidewhiledevelopersandpoliticianscontrolthesupplyinthehousingmarket,however,bothdevelopers

andpoliticiansoperateatdifferentspatialscales.Consequently,theenvironmentisbuiltontwospatialscales.[1]Thefirstlayermodelshousingsitesinwhichhouseholdsmakelocationaldecisionsonwheretoliveanddevelopersmakedevelopmentdecisions.Thesecondlayerconsistsofelectoralwards,inwhichpoliticiansplaytheirrole.

HouseholdAgents

3.5 Householdsarethekeyagentsinthismodel.Oneofthemostimportantattributesforhouseholdsistheirincomelevel.Basedontheincomelevel,eachhouseholdfindsanaffordableplacetolive.Ifrentgoesbeyondwhatahouseholdcanafford,theyconsiderrelocatingtoanaffordableplaceinthenexttimeperiod.Aswithmanyexploratoryagent-basedmodels(e.g.Schelling1971),thetimeframeforthemodelispurelyhypotheticalbutisconsideredasyearlyintervals.Householdsalsobelongtooneofthethreeincome-groups,low,middleorhigh.Forsimplicityitisassumedthathouseholdscanonlyshareahousingsitewiththesameincome-groupwhentheychoosetoliveinamulti-familyhousingunitwithinasinglehousingsite.Nonetheless,thereisnorestrictiononlivingwithinaneighborhoodofahigherincomegroup.Weassumethatthereisanimplicitpreferenceforlivingclosetohigherincomegroupsaslongashouseholdscanaffordit.Poorhouseholdswhocannotaffordahousingunitcouldconsidersharingitwithotherhouseholds.Iftheydonotfindanotherhouseholdtosharewithinaspecifictime-frame,theyareforcedtomovetoanaffordableplaceelsewhere.Howlongahouseholdcansustainresidingatagivenlocationdespiteanunaffordablerentdependsonthehousehold'sfinancial"stayingpower"i.e.householdsinthelow-incomegroupcannotpayunaffordablerentsforalongperiodcomparedtothoseinthehigh-incomegroup.Financialstayingpowerisdiscussedfurtherbelow.

DeveloperAgents

3.6 Developersconstructhousingunitsinordertogainprofits.Theybuyvacantpropertiesthatwereonceoccupied.Theacquiredpropertiesarethendeveloped,usuallywithalargernumberofunits(e.g.anapartmentbuildingatasiteofaprevioussinglefamilyhouse).Developersholdapropertyuntilallthenewly

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developedunitsareoccupiedbyhouseholds.Adeveloperagentisactivatedonlyonahousingsitethatiscompletelyvacatedandremainsactiveonlyuntilallunitsareoccupied.Thedevelopersarenotexplicitlyshownasvisualobjectsinthemodelinterfacebuttheiractionsareincorporatedwithinthemodelprocesses.Thedevelopers'behaviorissimpleinthemodelpresentedhere,butweplantoelaborateitinfutureversionsofSlumulation.Forexample,thenumberofunitstobedevelopedvariesandischosenrandomlyinthecurrentimplementationbutinfutureversions,weplantoequipthemtosensethedemandforhousingataparticularlocationandbuildaccordingly.Whilewehavenotimplementedthisinthecurrentversionofthemodel,theymayalsoconsideroccupiedsitesfordevelopmentandbidapricetobuyit(andpotentiallycompetewithotherdevelopersinterestedinthesameproperty).Inthesamespirit,theymayofferkickbackstopoliticianagentstogetaslumevictedinordertodevelopabrownfieldsite.

PoliticianAgents

3.7 Inthemodelpoliticiansmonitorthedemographicsoftheirelectoralwards.Eachwardconsistsofmultiplehouseholds.Politiciansreducethe"effectiverent"forslum-dwellersinproportiontothepercentofslumpopulationineachwardinahopetowinvotesfromtheslum-dwellers.Thisrelatestothenotionofanimplicitsubsidyprovidedintheformoffavorablepoliciessuchasprotectionagainstevictionandthusexcludingaslumsitefromenteringaformalmarketprimarilytocreateanelectorate(GlaeserandShleifer2003;Murray2010).Slumdwellerslivinginwardswithahigherproportionofslumhouseholdspaylowerrentsthanthoselivinginthewardswithalowerproportionofslumhouseholds.Thisrelatestothenotionthatvotesofslum-dwellersaremoreimportantinthewardshavingahigherconcentrationofslums.Itiswellknowninliteraturethatpoliticsplayanimportantroleindeterminingevictionorpersistenceofaslum(e.g.Chege1981;Mahadevia&Narayanan1999).Politiciansareactiveagentsinalltimeperiodsandoperateattheelectoralwardscale.Politiciansarenotshownexplicitlyinthevisualization,buttheirbehaviorisreflectedinthecalculationofeffectiverents.Politician'sbehaviorrepresentedinthemodelissimple,butweplantomakeitmorerealisticinfutureversionsofSlumulation.Forexample,theymayevaluatethetradeoffbetweenkickbacksfromadeveloperandbenefitsofreceivingslumvotestomakeanevictionorretentiondecisionforanindividualslumpocket.However,eventhesimpleimplementationinthemodelpresentedherehasanimpactonmodeloutcomesasweshowinverificationsection.

Environment

3.8 Theenvironmentinourmodelisbothspatialandaspatial.Thespatialenvironmentconsistsoftwotypesofentitiesasmentionedearlier:i)housingsitesandii)electoralwards.Thehouseholdsoccupythesmallestspatialentity,ahousingsite,whichmayhousemultiplehouseholdsincaseofmulti-familyhousingsuchasapartmentsorslums.Thesecondspatialentity,electoralward,islargerinscaleanddividesthecityintoseveralpoliticalelectorates.Eachelectoralwardconsistsofmultiplehousingsitesinaspatiallycontiguousmanner.Thedemographicsofanelectoralwardisincorporatedintothedeterminationofasubsidybypoliticiansforslumdwellers.

3.9 Tocapturethedynamicsrelatingtocitygrowthandthechangesinincomeandpopulationcomposition,themodelalsohasanaspatialenvironment.Thecityeconomygrowsatauser-specifiedrate,whichinturndeterminesthechangeinincomelevelsofindividualhouseholds.Populationgrowthresultsfrombothnaturalgrowthandmigrationintothecity,whichisspecifiedaspopulationgrowthrateforsimplification.Newlyformedornewlyarrivedhouseholdssearchforahomethattheycanafford.Thecityeconomyisalsodividedintoformalandinformalsectors,whichiscommoninmanydevelopingcounties(Sethuraman1976;Field2011).Poorhouseholdsworkingininformalsectordonotseeasmuchupwardincomemobilitycomparedtothoseworkingintheformalsector(UrbanAge2007).

ModelingInterface

3.10 NetLogo5.0(Wilensky1999)waschosentobuildthemodelasitprovidestheabilitytoexplicitlymodelthespatialenvironmentandagentbehavior.ThemodelinterfaceofSlumulationisshowninFigure1.Toaidreplicationandexperimentation,Slumulationismadeavailableathttp://www.css.gmu.edu/Slums/.

3.11 AsiscommonwithmodelsdevelopedinNetLogo,experimentscanbeeasilycarriedoutbychanginginputparametervaluesusingtheslidersonthetop-leftofthegraphicaluserinterfaceasshowninFigure1.Onecanviewanupdatedvisualrepresentationofthecityovertime(centerofFigure1),togetherwiththetrendsofkeyoutputparameters(rightsectionofFigure1).Thegraphicaluserinterfacealsoallowsonetokeeptrackofeconomicanddemographicvariables(bottom-leftsectionofFigure1).Someindicatorsarealsodisplayedintheformofgraphsandmonitorsinordertosummarizethedynamicbehaviorofthesystemasthesimulationprogresses.Suchaninterfaceishelpfulinunderstandinganddebuggingofthemodel(Grimm2002).

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Figure1.GraphicalUserInterfaceforSlumulation

3.12 Thephysicalspaceinwhichhousingunitsandpoliticalwardsareplacedisasquaregridinatwo-dimensionalspace.Thelargersquaresarepoliticalwardsthatconsistofmanyhousingsitesrepresentedbythesmallersquares.Thehousingmarketconsistsofhousingsitesinthespatialenvironmentrepresentedbya51×51squaregridresultinginto2601housingsites.Eachsquareonthegridrepresentsonehousingsitebutitcanaccommodateasinglefamilyormultiplefamiliesdependingonthenumberofhousingunitsbuiltonit(e.g.atownhouse,anapartmentoraslum).Eachhousingunitatagivenlocationhasarentassociatedwithitthatahouseholdpaysinordertooccupyit.Forsimplicity,ownershipisnotdistinguishedhereandrentsareassumedtobeequivalenttothemortgagepaymentsforowner-occupiers.

3.13 Thecityisdividedintonineequalpoliticalwards,eachwardconsisting289housingsites.Thedemographicsofthewardskeepchangingasnewhouseholdsappearinthelandscapeandoldhouseholdsrelocateinthesimulationprocess.Theeffectiverentforagivensiteinawardissetbypoliticianagentsasafunctionofthedynamicallychangingproportionofslumdwellersintheward.

3.14 Thecolorintensityofthesmallersquaresshowsachoroplethofthepropertyrents;theprimepropertieshavethehighestrentsinthecityandareshowninbrightershadesofyellow,whereastheinappropriatepropertieshavethelowestrentsandareshownindarkershadesofyellowasshowninFigure2.Thetriangular-shapedobjectsinFigure2representhouseholdagents.Thecolorofeachtrianglerepresentstheincome-classthateachagentbelongsto;red,blueandgreenarerespectivelyassociatedwiththeagentsinlow,middleandhigh-incomegroups.

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Figure2.RentMapChoroplethoftheHousingUnitsOccupiedbytheDifferentIncome-Groups

TransitionandBehavioralRules

3.15 ThissectiondescribestransitionrulesforthevariousattributesofboththeagentsandthevariousspatialentitieswithinSlumulation.Thetransitionrulesdefinehoweachentitywillevolveovertimeasthesimulationprogresses.Italsodescribesthebehavioralrulesforthehouseholdagentsanditsmathematicalformulationinthemodel.Thebehavioralrulesdefinehowagentswillrespondtothechangesintheenvironment.Asinmanyagent-basedmodels,thetransitionandbehavioralrulesarefixedbutparameterizationoftheserulesareflexibleanduser-specified.Forexample,howtheeconomicgrowthaffectshousingpricesisspecifiedinthemodel,buttheuserscaneasilyalterthevalueoftheeconomicgrowthratetostudyitsimpactontheslumformationprocess.

HousingPrices

3.16 Althoughtheuserspecifiestheinitialcitysize,thepercentagesofprimeandinappropriatesiteswithinthecitylimits,theactuallocationandrentsfortherestofthehousingsitesaresetrandomlybythemodel.Withintheinitialcitylimits,rentsarerandomlydrawnfromanormaldistributionrangingfromthelowestrentsforaninappropriatesitetothehighestrentforaprimesite.Outsidetheinitialcitylimit,therentisinitiallysettozero.Thisassumptionissupportedbythenotionthatcitiesgrowandexpandintovirtuallyzeropricedrurallandintheperiphery(e.g.Alonso1964).However,asthesimulationprogresses,theimmediateperipherallandstartsgainingvalueasaresponsetotheanticipatedfuturedemand,aneffectalsoseenintherealworld.

3.17 Duringasimulationrun,rentmaychangeasaresultoftheneighborhoodeffect(capturedindiffusionratebelow)andeconomicgrowthofthecity.Rentforeachpropertyiscalculatedattheendofeachtimeperiod,withthenewrentRitofapropertyiattimetdefinedas:

(1)

wheredisthediffusionratedefinedbyuser.RjrepresentsrentatpropertyjintheMooreneighborhoodofthepropertyi.Gistheeconomicgrowthrateandβisthefractionofeconomicgrowthattributabletohousingmarket.Withthisspecificationinplace,rents(R)tendtomovetowardsneighborhoodaveragethroughpricediffusionovertime.Thisprocessalsoensuresthatperipheryisincreasinglyaddedintoinitialcityandthuspushestheboundariesofthecityoutwardintopreviouslyruralland.

3.18 However,theeffectiverentERthatahouseholdtakesintoconsideration,canbelowerthantheactualrentofaproperty.Theeffectiverenttakesintoaccountthedecisionsfrompoliticians,developersandslumdwellers.Politicianscanlowertheeffectiverentofaslumpropertyintheformofsubsidy.Developerscanaddmorehousingunitsonanexistingsitebyforexampleconvertingatownhouseintoapartments.Finally,slumdwellerscanincreasethenumberofhouseholdslivingonthesamesitethroughillegalsquatting.Thus,theeffectiverentperhousehold,ERitatsiteiattimetisgivenby:

(2)

whereNitiseitherthenumberofhouseholdsinaslumsite,orthenumberofunitsifthesiteisheldbyadeveloper.Inthelatercase,theunitsdonothavetobeoccupied.αjtindicatestheproportionofslumpopulationinthewardjattimet(rangingbetween0and1)whichdeterminesthelevelofsubsidyprovidedtoalltheslumsitesinthatward.Sitisabinaryslum-statusforthesiteiattimet(1ifthepropertyisaslum,0otherwise).

HouseholdIncomes

3.19 Theinitialpopulationofhouseholdsarecreatedwithinthecitylimitwhichisaninputspecifiedbytheuser.Atthestartofthesimulation,eachhousingsiteisoccupiedbyasinglehousehold,whoseincomelevelissettomatchtherentofthepropertythatitisoccupying.Thus,highincomehouseholdsarelocatedonprimepropertiesandviseversa.Eachhouseholdisalsoclassifiedasalow,mediumorhighincomehouseholdbasedonitsrelativeincomecomparedtotheaverageincomeinthecity.Households'incomelevelchangesasthesimulationprogressesandtheincome-groupmayalsochangeasaresult.Thenewlyformedormigranthouseholdsarerandomlyassignedanincomedrawnfromthedistributionoftheincomeinthecityatthattime.TheyarealsostochasticallyassignedtoeitherformalorinformallabormarketinsuchawaythatmaintainsthepredefinedproportionofworkersininformalsectorasreflectedbyInformalityIndex.

3.20 Atthestartofeachtimeperiodt,ahousehold'sincomeyitchangesbasedonvariousfactors,namely,itsincomeinprevioustimeperiod,yi(t-1),itslaborstatusfi,andtheeconomicgrowthrateG.Formallythiscanbewrittenas:

(3)

wherefiisabinaryvariableindicatingwhetherthehousehold'slaborstatusisformalorinformal.Ifhouseholdsareintheformalsector,theycanexperiencefull

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upwardincomemobilitycomparedtohouseholdsworkinginaninformalsectorwhocanonlyexperienceafraction(δ)intheirupwardincomemobility.

ResidentialMobility

3.21 Newlyformedorjustarrivedhouseholdssearchforanaffordablehousingunit.Theylocateatahousingunitthathastherent-payableRPktthatislessthantheircapacitytopayCit(thelatterisdefinedasapre-determinedfractionoftheirincomelevel).ThehouseholdsalreadyresidingonaparticularsitekeepcheckingthattheycancontinueresidingattheirpresentlocationsbycomparingtheirCitwiththeprevailingRPkt.Whentherent-payableexceedstheircapacitywithinacertainfractionoftheirincome,definedbytheprice-sensitivityRSit,thehouseholdsarewillingtosharetheunitwithanotherhouseholdofasimilarincome-groupandeffectivelydividethecostoftherent.RSitrangesbetween0and1.Thelowerpricesensitivityresultsintolowtoleranceforvolatilityinrent-payable.Thehouseholdscomparetheirabilitytopayrentwiththeprice-sensitivityadjustedrent-payablewhenconsideringthewillingnesstoshare.Theirtransitionruleis,remainopentosharetheunitif:

(4)

3.22 Furthermore,thereisalimittokeeplookingforanotherhouseholdtosharethehousingunit.Thefinancialstayingpower,FSit,determineshowlongtheycanstayatanunaffordablehousingunitinahopetogetahouseholdtosharewiththem.FSitrangesbetween0and1.Whentherentscrossthelimitbeyondtheirfinancialstayingpower,theyareforcedtoleavethecurrentplaceandstartsearchingforanaffordablehousingunitelsewhere.Theirtransitionruleis,startsearchingforahouseif:

(5)

PopulationGrowth

3.23 Themodelisinitiatedwithonehouseholdperhousingsitewithintheinitialcitylimitspecifiedbytheuser.ThepopulationPchangesattheuser-specifiedpopulationgrowthrateλduringthesimulation.Thepopulationgrowthrateisassumedtoincorporateboththenaturalgrowthandthemigration.Thus,thepopulationPtattimetincreasesto:

(6)

EconomicGrowth

3.24 TheinitialtotaloutputofthecityYisthesumofindividualincomesoftheinitialpopulation.TotaloutputchangesatuserspecifiedeconomicgrowthrateGasthesimulationprogresses.Thefractionofthisgrowth-rate(G)isalsousedfordeterminingappreciationrateofhousingpricesinthecityasspecifiedinEquation1earlier.ThetotaloutputYtattimetisthusdefinedas:

(7)

ATypicalSimulationTime-stepinSlumulation

3.25 Themodelisinitiatedwithaninitialpopulationofhouseholdagentsandhousingunitsoccupiedbythem.Auseralsospecifiesvariousparameterssuchasinitialcitysize,proportionofprimeandinappropriatelandinthecity,populationgrowthrate,economicgrowthrate,initialincomedistribution,pricediffusionrateforhousingandthelevelofinformalityoftheeconomy.Eachtime-stepisnotionallyconsideredtobeoneyearinthemodelandthesimulationisrunforuser-specifiednumberofyears.Outputsarerecordedforeachtimeperiod.Thefinalspatialrepresentationofthecityispreservedasamodeloutput.Figure3showshowdifferententitiesinteractineachtimeperiodduringthecourseofasimulation.

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Figure3.ModelLogicandInteractionsBetweenDifferentEntitiesDuringtheCourseofaSimulation

3.26 Whilemodel-widetemporalchangessuchasagents'incomeandhousingpricesareupdatedsynchronouslyattheendofeachtime-step,householdrelocationandtheresultingchangeinnewlyoccupiedhousingsites(i.e.occupancystatus,numberofoccupantsetc.)areupdatedasynchronously.Allactivehouseholdswhoaresearchingforanewlocationarerelocatedwithinthetime-stepbuttheyareinitiatedonebyoneinarandomizedorder.Duringthesimulation,eachvacatedhousingsiteisoccupiedbyanewlycreateddeveloperwhoseprincipalroleistocreatenewhousingunitsonthatsiteandholdthevacantunitsforfutureoccupancybyhouseholds.Developeragentsexitonceallnewlycreatedunitsareoccupied.

OutcomeMeasures

3.27 WeusedthefifthcriteriaoftheUN-Habitat(2006)definitionofaslumhouseholdi.e.insufficientlivingareatodeclareahousingsiteasaslum.Wechosethiscriteriaprimarilybecauseitistheonlycriteriathatreflectshousehold'schoice.Forexample,householdsmayinfluencethedecisionspertainingtothefirsttwocriteriaataparticularlocation(i.e.lackofwaterandsanitation),buttheseareprimarilytheoutcomesoflarge-scaleinfrastructureinvestmentdecisionsbypublicauthoritiesandareusuallytakenatneighborhoodorevenlargerareascale.Thethirdandfourthcriteriaoftheslumdefinition,namely,securedtenureanddurablestructure,canbeassumedtobedirectlyreflectedinprevailinghousingpricesandrents(e.g.ahousingunitwithadurablestructurewillbepricedhigherthanthatofonewithatemporarystructure).Housingdensityistheonlyparameterthatcollectively"emerges"fromindividualhousehold'slocationchoicesandinteractionwithotherhouseholdssuchassharingbehavior.Thehousingdensityparameterprovidesanoutcomemeasureresultingpurelyfromhouseholdbehaviorandhenceitisimportantfromtheperspectiveofbuildinganagent-basedmodel.WeintendtoincorporatetheotherfourcriteriaaspartofspatialenvironmentinfutureversionsofSlumulation.

3.28 Intherealworld,theinsufficientlivingspacecriteriaisoperationalizedasthreeormorepersonsperroomtodeclareahouseholdasaslumhousehold(UN-Habitat2006).Weimplementthiscriteriainourmodelbydeclaringahousingsiteasaslumifitisoccupiedbymorehouseholdsthanthenumberofunitsavailableonthatsite,aswedonotmodelhousingunitsattheroomlevelandhouseholdsattheindividuallevel.However,oursimplifiedmeasurecapturestheessenceoftheUN-Habitatcriteria.Onceahousingsiteisclassifiedasslumandnon-slum,aseriesofindicatorsarecalculatedtostudytheoveralloutcomeof

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themodel.Particularly,wereportaverageslumdensity,numberofslums,percentageslumpopulation,percentageareaunderslums,bothforthecenterandtheperipheryseparatelyaswellastheaveragefortheentirecity.Wealsocreategraphsshowingdensityforslumsaswellasforallthreeincomegroupsovertime.Similarly,wealsoreportslumsizedistributionfortheentirecityasshowninFigure1.

ModelVerification

4.1 EachinputparameterofSlumulationwasvariedtounderstanditseffectonthesimulationoutcome,inparticularthefinalpatternsofhousingdensity(forslumsaswellasforotherincome-groups)andthepercentageofslumpopulationinthecity.Werefertoverificationasameansofensuringthattheimplementedmodelmatchesitsdesign(NorthandMacal2007),aprocessthatinvolvescheckingthatthemodelbehavesasexpected.Suchverification,issometimesreferredtoastestingthe"innervalidity"ofthemodel(Brown2006).First,weranthemodelwiththeinputparametervaluesshowninTable1.Someofthevalueschosenasdefaultwerethosetypicallyfoundinthecitiesindevelopingworld.Forexample,thepopulationinIndiancitiesgrewat3%annuallyonanaveragebetween1991and2001(CensusofIndia2001).However,generalizableempiricaldataoncertainparametersareoftennotcollectedorpubliclyavailable.Insuchcases,wehavetakenourinformedjudgmentinchoosingthevalues.

Table1:InputParametersforaTypicalSimulationRun

InputParameters ValuesPopulationGrowthRate(λ) 3.0%EconomicGrowthRate(G) 2.0%HousingPriceGrowthRateFraction(β) 0.5InitialPrime-land 10.0%InitialInappropriate-land 10.0%NeighborhoodPriceDiffusionRate 3.0%Price-Sensitivity(RS) 0.1FinancialStayingPower(FS) 0.3InformalityIndex 0.7IncomeGrowthRateFractionforInformalSector(δ) 0.1FractionofIncomeavailableforHousingRent(C) 0.3InitialCityPopulation 361Politics OnDevelopment OnInitialInequality 10SimulationRunTime(T) 50

4.2 Thesimulationexperimentwasrunfor50timeperiods(years)andwasrepeated100times.Wehavechosen50time-stepsasitrepresentedalongenoughsimulationtimebutreadersinterestedinexploringthisfurthere.g.forlongertimeperiod,areencouragedtorunthemodelwhichisavailableathttp://css.gmu.edu/Slums.However,itneedstobenotedthatthesimulationstopsifphysicalspacerunsoutwhilehouseholdsaresearchingforanewlocationwhichlimitsthismodel'scapacitytotestpopulationgrowthscenariotoanextent.Choosingasmallercity-sizeastheinitialconditioncanhelptopartiallyovercomethislimitation.Weranthemodelwithsmallerinitialcity-sizefor150timeperiodsandfoundthatsomeoftheoutcomeparameterssuchasoverallslumpercentagestabilizesafterapproximately40timeperiodsandroughlyremainsatthatlevelfortheremainderoftherun.Itshouldalsobenotedthatourapproach,bydesign,istomakethismodeldynamicandhenceallpartsofthesystemneverreachesanequilibriumstateperse.Forexample,locationsofslumsspatiallyaltersovertime.Agentpopulationalsokeepsgrowingandhencethemodelcouldnotpossiblyreachanequilibriumstateinthestrictsense.

4.3 Figure4illustratesatypicalsimulationrun,wherethemapsshowthespatialdistributionoftherentsandthechartsshowtheevolutionofhousingdensityforeachincome-group,andthe%slumpopulation.AsisvisiblefromFigure4d,housingdensityincreasesforbothslumsandthelower-incomegroup(LIG)fromthebeginningofthesimulationsuggestinginabilityofthepoortokeepupwiththerisinghousingrents.Whereas,housingdensityforthehigher-incomegroup(HIG)virtuallyremainsthesamethroughoutthesimulationperiod,suggestingnoeconomichardshiponhousingfrontforthehigh-incomegroup.However,themiddle-incomegroup(MIG)alsoexperiencehardshipwhenfacedwiththerisinghousingrents,suggestingthatthemiddle-incomegroupoptsforhigh-densityhousingtypes(e.g.apartments)oversinglefamily-homes.

4.4 Themapsoftherentgradientsandlocationsofthevariousincome-grouphouseholdsinFigure4suggestanotherstory.Thelower-incomegrouptendstooccupytheperipheralhousingsitesbecauserentsarecomparativelylowintheperiphery.Thispatternissimilartothepatternsobservedinthedevelopingworldcities,wheresuchperipherizationofurbanslumsisdocumented,forexample,inseveralLatinAmericancities(seeBarros2005).However,lower-incomehouseholdsarealsooccupyingsomeofthemostexpensivehousingsitesinthelaterpartofthesimulation.Thesepropertiesaremadeaffordablebysharingextensivelywhichresultsinhighdensities.Thedensificationisdominantinthecentralwardbecausethealreadyhighproportionofslumhouseholdsbenefitfromthesubsidyprovidedbypoliticians.Thisresultisalsoinconfirmationwiththepoliticsofslums.Forexample,DharaviinthecityofMumbaioccupiesasitethatwouldbehighlypricedinformalmarketbutresidentshavenotbeenevicteddespiteseveralproposalsinthepast(MahadeviaandNarayan1999).

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Figure4.Typicalsimulationoutputs:initialconditions(a),housingrentgradientandoccupanciesattimet=25(b),andt=50(c).Housingdensityforslumsandotherincome-groups(d)slumsizedistributionatt=50(e),and%slumpopulationovertime(f)

4.5 Table2highlightsaverageslumpopulation,numberofslumsandslumdensityindifferentregionsofthecityfrommultiplesimulationrunsusingtheinputparametersfromTable1.Ourexploratorymodelproduceshousingconditionsthatareobservedinsomecitiesindevelopingcountries.Forinstance,inthecityofMumbai,thedensestslum,Dharavi,is11timesasdenseasthecity'saveragedensity(Mukhija2001;Rao2007).Thedensestsluminoursimulationis7.3timesdenserthanthecity'saveragedensity,whiletheproportionofslumpopulationinthesimulationis19.7%,whichareplausibleresults.However,individualcitiesvarydramaticallyinslumprevalence(UN-Habitat2008)andhencethegoalofthismodelisnottoproducetheactualpercentageofslumsforaparticularsimulatedcity.Ratheritsaimistoproduceoutcomesforawiderrangeofinstancesandthereforeitshouldbesensitivetoinputparametersasdiscussedinsubsequentmodelexperimentssection.Inthesimulationabove,slumshaveahigherdensityinthecentralelectoralward(2.69)comparedtoperipheralwards(2.30onaveragefor8peripheralwards)asshowninTable2.Thistrendisindicativeofhigherpricesprevailingincentralpartofthecitycombinedwithhouseholds'higherpreferencestoliveclosertothecenter.Furthermore,thehigh-densityhousingofmiddle-incomehouseholdsisalsovisibleinthecentralpartofthecitysuggestingtheconcentrationofhigh-rise/high-densityapartments.Developerswithinthemodelplayakeyroleinthisdensificationprocessbyfinancingandreplacingsingle-familyhousingwithmulti-familyapartments,therebyreducingeffectiverentperhousehold.

Table2:MeanofKeyOutputParametersatt=50for100simulationruns(Numbersinparenthesisindicatestandarddeviation)

OutputParameters City Center Periphery

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PercentSlumPopulation 19.0(0.3) 16.8(0.4) 19.7(0.4)PercentAreaunderSlums 10.1(0.2) 8.5(0.2) 10.6(0.2)SlumDensity 2.30(0.01) 2.69(0.04) 2.21(0.01)NumberofSlums 125(2) 24(1) 101(2)

4.6 Inthenextphaseofourmodelverification,weconfiguredvariousmodelcomponentsinmanydifferentwaystostudytheimpactofselectedmodelspecifications.Forexample,weranthemodelwithandwithoutpoliticiananddeveloperagents.Allotherparameterswerekeptthesameasourcontrolcase,reportedinTable1.Wealsoverifiedthatthepresenceorabsenceofeachcomponentimpactstheresultsinaplausiblemanner.AsseeninTable3,whenpoliticianagentsaredeactivated,slumpopulationinthecentralwarddecreasesfrom16.0%to13.9%(or24.8%to22.0%whendevelopmentisoff).Thistrendisindicativeofslum-dwellers'inabilitytoresisteconomicforces(reflectedinincreasinghousingrents)inabsenceofsubsidybythepoliticians.Similarly,whendevelopersareturnedinactive,slumsincreasealloverthecity.Thisoutcomeisindicativeofdevelopers'centralroleincreatingdensehousingtypesinhighlypricedsitesandthusmakinghousingaffordableatdesirablelocations.Inabsenceofsuchformaldensification,onewouldexpecttheriseinslumpopulationi.e.informaldivisionsofpropertiestomakethemmoreaffordable.

Table3:ImpactofPoliticsandDevelopmentComponentonModelOutcomes(Numbersinparenthesisindicatestandarddeviation)

OutputParametersPoliticsONDevelopmentON(Base)

PoliticsOFFDevelopmentON

PoliticsONDevelopmentOFF

PoliticsOFFDevelopmentOFF

PercentSlumPopulation

City 19.2(0.3) 18.7(0.2) 24.4(0.4) 25.3(0.2)Center 16.0(0.4) 13.9(0.3) 24.8(0.5) 22.0(0.4)Periphery 20.3(0.3) 20.2(0.3) 24.2(0.4) 26.1(0.3)

PercentAreaunderSlums

City 10.3(0.2) 10.1(0.1) 12.1(0.2) 12.5(0.1)Center 8.3(0.2) 7.3(0.1) 11.2(0.2) 9.6(0.2)Periphery 11.0(0.2) 11.0(0.2) 12.3(0.2) 13.3(0.1)

SlumDensity

City 2.26(0.01) 2.28(0.01) 2.35(0.01) 2.37(0.01)Center 2.54(0.04) 2.62(0.04) 2.62(0.03) 2.66(0.03)Periphery 2.20(0.01) 2.20(0.01) 2.28(0.01) 2.31(0.01)

NumberofSlums

City 128(2) 126(2) 158(2) 163(1)Center 24(1) 21(1) 32(1) 28(1)Periphery 105(1) 105(2) 125(2) 135(1)

4.7 Wehavealsoverifiedthemodelbychangingseveralothercomponentstostudytheirimpactsonmodeloutcomes.Forexample,wetestedthemodelfortwodifferenttypesofsearchprocesseswhenahouseholdconsidersrelocation:i)preferlocationsnearthecurrentlocation,orii)preferlocationsclosetothecenter.Whilethesearchprocessmighthaveanimpactonindividualhouseholds'residentialmobilitypatterns,wefoundthattheaggregateresultforvariousslummeasuressuchasthepercentageofslumpopulation,slumdensityandpercentslumarea,werenotverysensitivetothechoiceofsearchprocess.

4.8 Similarly,wealsotestedthemodelsensitivitiesofseveraldifferentspecificationsofthemodelwhoseoutputsarenotreportedinthispaperforbrevity.Forexample,wetestedhowtheruletodetermineavailabilityofhousingunitsinaslumchangedthemodeloutcomes.Inonescenariowemadeaslumsiteavailableforfurtheroccupancyeveniftheslumsiteiswithintheaffordabilityrangeofthecurrentresidents.Alternatively,asitisimplementedinthemodelpresentedhere,itcanberestrictedfrompotentialresidentswhenalltheoriginalresidentscanaffordit.Thischoiceofspecificationonavailabilityaffectssomeoftheoutcomemeasures.Forexample,thenumberofslumsarelesswhenwemakeslumsavailableforfurtheroccupancyirrespectiveofcurrentresidentsaffordabilitycriteria.However,thesearecommondilemmasfacedinagent-basedmodeling.Asaguidingprinciple,wehavechosentoincorporaterulesthatmakemoreintuitiveandlogicalsenseandonesthatareclosetotherealworld.

SimulationExperiments

5.1 Onceconfidencewasgainedpertainingtoinnerworkingsofthemodel,theparameterspacewasexploredbyvaryingvariousinputparameters,oneatatime.Theconfigurationshownintheprevioussection(Table1)actsasourbasescenariofortheseparametersweeps.Wetestedseveralmechanisms;thatofpopulationgrowthrate,economicgrowthrate,theinitialproportionofprimeandinappropriatelandandfinallythemixofformalandinformalemploymentinthecity.Eachsimulationexperimentwasrunwiththreedifferentvaluesfor50timeperiodsandwasrepeated100times.Thesimulationoutputspresentedbelowaremeansofthese100runsforeachscenario.Standarddeviationswerewithin2to4%rangeforalloftheseparametersandhencenotreportedforclarity.Wefirstsketchoutourrationaleforchoosingthesescenariosbeforepresentingtheresultsforeachscenariobelow.

PopulationGrowthRate

5.2 Moreandmorepeoplearelivingincitiesandthistrendisexpectedtocontinueinthenearfuture(UnitedNations2007)withunprecedentednumberslivinginslums(UN-Habitat2003).Inthisexperiment,wetesthowthepopulationgrowthinthecitycouldimpacttheslumconditions.Populationgrowthratewassetto2.0%,3.0%(basescenario)and4.0%.Weobservedthathigherpopulationgrowth(4%)leadstohigherpercentageslumpopulation(27.9%)whereasslowerpopulationgrowthleadstolowerpercentageslumpopulation(13.0%)asshowninTable4.Ofnoteisthenon-linearrelationshipwithpopulationgrowth.

Table4:ImpactofPopulationGrowthRateonModelOutcomes

OutputParameters PopulationGrowthRate2.0%

PopulationGrowthRate3.0%(Base)

PopulationGrowthRate4.0%

PercentSlumPopulation

City 13.0 19.0 27.9Center 14.2 16.3 12.1Periphery 12.1 20.0 30.5

PercentAreaunderSlums

City 7.4 10.1 14.3Center 8.1 8.2 4.9Periphery 7.0 10.7 15.9

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SlumDensity

City 2.24 2.30 2.44Center 2.43 2.68 3.12Periphery 2.09 2.21 2.41

NumberofSlums

City 54 126 283Center 23 24 14Periphery 31 102 269

5.3 Thehigherpopulationgrowthratealsoresultsinagreaternumberofslumsasopposedtodensificationofexistingslums.TheresultingslumformationpatternshowsahighernumberofperipheralslumsashighlightedinTable4.Thisisahypothesisworthtestingusingrealworlddata,whetherthehigherpaceofpopulationgrowthresultsintohigherperipherizationratherthanhigherdensities.Itseemsthatexploringnewlocationispreferredoverexploitingexistinglocationsduringtherapidpopulationgrowthperiod.Forexample,historically,citieshaveexpandedphysicallyduringperiodofincreasedmigration,andthedensificationprocesstookplacemuchlaterintheevolutionofacity(Sudhiraetal.2004).Rapidurbanizationisoftencitedasafactorintheslumformationprocessbutitisoftenlessunderstoodhowitplantsseedsforfutureslumformations.Itseemsfromthisexperimentthatfutureslumlocationsareidentifiedonthenewfrontierbynewmigrantsduringtherapidpopulationgrowthphaseofacity.

EconomicGrowthRate

5.4 Economicgrowthhasalargeimpactonwhypeoplemovetocities(UN-Habitat2010).Forexample,MumbaigrewexponentiallybyattractingmigrantsfromruralIndiaasitaddednewmanufacturingjobs(Yedla2003).Inordertostudyhoweconomicgrowthimpactsontheformationofslums,wetestedthreedifferentvaluesfortheeconomicgrowthrate:2.0%(basescenario),3.5%and5%whileallotherparameterswerekeptconstant.TheresultsaresummarizedinTable5.

Table5:ImpactofEconomicGrowthRateonModelOutcomes

OutputParameters EconomicGrowthRate2.0%(Base)

EconomicGrowthRate3.5%

EconomicGrowthRate5.0%

PercentSlumPopulation

City 19.2 16.8 15.9Center 16.3 13.5 10.9Periphery 20.2 18.0 17.5

PercentAreaunderSlums

City 10.2 9.0 8.3Center 8.2 6.6 4.7Periphery 10.9 9.7 9.4

SlumDensity

City 2.30 2.28 2.29Center 2.67 2.67 2.97Periphery 2.21 2.19 2.19

NumberofSlums

City 127 112 104Center 24 19 14Periphery 103 93 91

5.5 Theproportionofpopulationlivinginslumsdecreasesfrom19.2to15.9%.However,thereisnospatialimplicationasitisevidentfromthereductionexperiencedinbothcenterandperiphery.Thedensityofslumsremainsunaffected.Itisevidentfromthisexperimentthatthehighereconomicgrowthreducesthenumberofslumsfrom127to104.Oneagain,thenumberofslumsreducesbothincenterandperipherythusindicatingtheabsenceofanyspatialimplicationofeconomicgrowth.

InitialLandSupplyConditions

5.6 Citiesarehistoricallyendowedwithlandparcelsthatareconsideredprimeinthesensethattheyhaveeasyaccesstojobs,recreation,socialamenitiesandhaveadequateinfrastructureservices.Whereassomelandparcelsarenaturallyunsuitablefordevelopment,forexample,hazardoussitessuchasriverbeds,sitesnearpollutingindustriesorlandfills,siteswithpooraccessibilityfrommajortransportationnetworksorinadequatelyservicedintermsofwaterandsanitationetc.Wetesthowendowmentofhigherorlowerproportionofprimeorinappropriatelandparcelsinacityaffecttheslumformationprocess.Theinitialproportionofprime-landwassimulatedforthreetestvalues:10%(basevalue),20%and30%whileallotherparameterswerekeptconstant.TheresultsareshowninTable6.

Table6:ImpactofPrime-landonModelOutcomes

OutputParameters PrimeLand10%(Base)

PrimeLand20%

PrimeLand30%

PercentSlumPopulation

City 19.0 19.0 18.6Center 15.7 14.5 13.4Periphery 20.1 20.4 20.3

PercentAreaunderSlums

City 10.3 10.1 9.9Center 8.2 7.3 6.6Periphery 10.9 11.0 10.9

SlumDensity

City 2.27 2.28 2.26Center 2.59 2.67 2.64Periphery 2.20 2.20 2.20

NumberofSlums

City 127 126 125Center 24 21 19Periphery 104 105 106

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5.7 Anotableoutcomefromthisexperimentisareductioninthepercentageofslums,percentageareaunderslumsandanincreaseinslumdensityinthecentralpartofthecity.Thereisalsoahigherproportionofprime-landintheinitialcentralcitythatlower-incomehouseholdscannotafford.Lower-incomehouseholdsaccordinglyfacethesupplyconstraintwhichresultsintotheperipherizationofslumsorhigherdensitiesinrelativelylowernumberofexistingslumsinthecentralcity.Higherpricesarealsoobservedduetotheneighborhoodeffect(sitesnearprime-landobservespriceappreciationovertime).Itwouldbeworthinvestigatingthisresultwithrespecttorealworldcitiestoseeifthereisanypathdependenciesintheslumformationratebasedoninitiallandconditions.

5.8 Inthenextexperiment,weinvestigatedtheimpactofinappropriatelandsupply.Thesupplyofprimelandwaskeptconstantatthebasescenario(10%),butthepercentageofinappropriatelandwaschangedtothreedifferenttestvalues:10%(basescenario),20%and30%.TheresultsareshowninTable7.

Table7:ImpactofInappropriateLandSupplyonModelOutcomes

OutputParameters InappropriateLand10%(Base)

InappropriateLand20%

InappropriateLand30%

PercentSlumPopulation

City 18.9 18.9 18.9Center 16.3 16.4 17.6Periphery 19.8 19.8 19.2

PercentAreaunderSlums

City 10.2 10.1 10.0Center 8.6 8.3 8.8Periphery 10.7 10.7 10.4

SlumDensity

City 2.27 2.30 2.31Center 2.56 2.71 2.82Periphery 2.19 2.21 2.18

NumberofSlums

City 127 125 124Center 25 24 25Periphery 102 102 99

5.9 Ahigherinitialsupplyofinappropriatelandinthecenterresultsintoahigherslumpopulationinthecenteraswellashigherdensitiesinthoseslums.Itisinterestingthatwhiletheoverallnumberofslumsinthecentralcityactuallydeclines,theslumdensityincreasesindicatinggrowthofexistingslumsoriginallysitedoninappropriatelocations.Thisresulthasanalogieswithwhatwefindinrealworldcitiese.g.Dharavi,alargestsluminMumbai,whichwaspopulatedwithlargeinfluxofmigrantsin1920s(Clothey2006)onalandparcelthatwasinappropriatefordevelopment(forexample,therewerenoroadsinDharavianditwasanislandwithinmarshland).Theslumpersistseventodaydespitethatformaldevelopmenthastakenplaceinallsurroundingareas(MCGM2005).Similarpatternsarefoundelsewheree.g.landfillsites,suchasthoseinManila,Philippines(Abad1991).

Informal-formalSectorMix

5.10 Ithasbeennotedinliterature(e.g.Mitra2008;Tamaki2010)thatthepeopleemployedininformalsectorcannotexpectmuchupwardmobilityintheirincomescomparedtothoseemployedintheformalsector.Totestthis,weexplorehowthepercentageofslumpopulationchangeswithdifferentmixesofformalandinformalsectorsinthecityeconomy.Threetestvaluesoftheformalityindexweresimulated:0.1(basescenario,i.e.themajorityoftheworkforceisintheformalsector),0.4and0.7(i.e.thehigherproportionoftheworkforceisincreasinglyworkingtheinformalsector)whileallotherparameterswerekeptconstant.TheresultsareshowninTable8.Ofnoteisthatboththeoveralldensitiesandslumpopulationincreasesaseconomyhashigherinformality.Thisindicatesthatagreaternumberofpeopleworkingintheinformalsectorincreasestheincomeinequalitiesbutdoesnotresultintoaffordablehousingavailableforlowerincomegroupsandhenceresultsintohigherslumpopulation.

Table8:ImpactofInformalityonModelOutcomes

OutputParameters InformalityIndex0.1(Base)

InformalityIndex0.4

InformalityIndex0.7

PercentSlumPopulation

City 17.0 17.4 18.2Center 12.6 13.6 15.6Periphery 18.4 18.6 19.1

PercentAreaunderSlums

City 8.9 9.2 9.8Center 6.5 6.9 8.0Periphery 9.6 9.8 10.3

SlumDensity

City 2.22 2.24 2.27Center 2.42 2.49 2.62Periphery 2.19 2.19 2.19

NumberofSlums

City 116 118 121Center 19 20 23Periphery 98 98 99

5.11 TheresultspresentedherearebasedonexperimentsthatvaryoneparameteratatimebutmanyothertypeofexperimentscouldberunusingSlumulation.Forexample,varyingmultipleparameterssuchashigherformalizationcombinedwithhighereconomicgrowth.Similarly,allparameterscouldbechangedinordertofindasetofparametervaluesthatwouldreducethenumberofpeoplelivinginslums(orresultinnoslums).

DiscussionandFurtherWork

6.1 ThispaperhasattemptedtobuildanexploratoryABMcalledSlumulation,tomodelslumformationusingourexistingunderstandingofurbanizationprocesses,urbanmorphology,housingmarkets,andmigrants'behaviorwithinaspatialABMframework.Specifically,themodeladdstothesmallbutgrowingbodyofliteraturethatusesagent-basedmodelstoaidourunderstandingofslumformation.Slumsareresultsofacombinationofconditionspresentatvariousspatialscales,coupledwiththeinterplayofdifferentactors,rangingfromtheindividualhouseholdtolocalpoliticiansanddevelopers,allofwhichinfluencethe

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emergenceorpersistenceoftheslums.Webelievethatourapproachtomodelslumformationandexpansionisuniqueasitexplicitlyincorporatespoliticalbehaviorwithregardtopoliticalprotectionofslumcommunitiesbyexplicitlymodelingpoliticiansasagents.Similarly,aroleofdeveloperswhotransformlow-densityhousingintohigh-densityhousingismodeledtoanalyzetheimpactonbothformalhousingmarketgrowthandslumformation.Agent-basedmodelsofslumformationoftenignorethesetwoimportantactorsandtheirrolesinslumformationandexpansionprocess.Incorporatingtheseagentsalsorequiredourmodeltobemulti-scalarwhichisthenlackinginpriormodelingeffortswithregardtoslums.

6.2 Ourmodelsuggeststhathigherprotectionofslum-dwellersintheformofsubsidiesinlieuofslumvotesresultsintoslumswithhighdensities.Whileperipherizationofslumsslowsdownastheformationofnewslumsdecreases,severalslumspersistontheprime-landforalongeramountoftimeinthecenter.Virtually,noneoftheslumhouseholdsgetevicteddespitetherisingpricesinthecentralcitywhenpoliticianagentsareactive.Itshouldbenotedthatwedonotclaimthatslumsaremorelikelyindemocraticsocieties.Weonlyshowthatpoliticalrepresentationofslum-dwellersintheformofvotingrightsallowthemtoresisteconomicforcesbybuildinganelectorate.Insimulatingcitieswhereslum-dwellersarenotgivenvotingrights,ourmodelcouldeasilybeadaptedbyturningoffthepoliticsprovidedasaswitchinthemodelinterfaceaswedemonstratedabove.Thedevelopersprovideacentralroleinconvertinglow-densitymiddle-incomeneighborhoodsintohigh-densitymiddle-incomeneighborhoods.Thiscentralfunctionofdevelopersreleasestheupwardpressureonrealestate.Increaseddensityprovidedintheformalmannerresultsintobetterhousingconditionsdespitehigherdensities.

6.3 Moreoverourexperimentssuggestthateconomicgrowthandformal-infomalmixhasadirectimpactonslumformation.Itseemsthateconomicgrowthalonecannotalleviateslumissuesindevelopingworldcities.Itisnecessarytoincreaseformalitywhichhasatwo-prongedeffect:i)reducingincomeinequalityandii)housingpricesarewithinaffordabilitylimitsforallsectionsofsociety.Theseeffectsarewellcapturedinthemodelandsuggestthateconomicgrowthcombinedwithreducedinequalitymayreduceslumgrowthindevelopingworld.Similarly,thefastpaceofurbanizationisoftenconsideredadrivingforceforslumformation.However,ourexperimentssuggestthatcitiesexpandandincreasethesprawlbutdonotnecessarilyincreasehousingdensitiesbeyondacceptablelimitsduringarapidpopulationgrowthphase.

6.4 Thepurposeofthismodelisexplanatoryanditsimplyexplorestheoriesandgeneratesnewhypotheses.However,futureworkwillattempttomodelanactualmetropolitanareafromthedevelopingworld(suchasMumbai,India)andtakeittoa"Level2"modelintermsofAxtellandEpstein's(1994)classificationsystem.Inordertodoso,wewillneedtobuildontheempiricalworksofslumresearcherswhoexploreissuesrelatingto:managementofinformalsettlementswiththeaidofgeographicalinformationsystems(e.g.Sliuzasetal.2004);housingtransformation(e.g.Sheuya2004);aswellasissuespertainingtoinformallandmanagement(e.g.KombeandKreibich2000).

6.5 Also,forsimplicity,weassumedanormaldistributionwithrespecttoincomeforinitialpopulation.While,anormaldistributionisaconservativeapproach,infutureworkwewilltrymorerealisticincomedistributionssuchaslog-normalandexponential.Webelievethatsuchdistributionsareclosertorealityanditwillhelpustoadvancefutureversionsofourmodeltomorecloselymatchtherealworld.Nonetheless,themodeldidgenerate"real"worldpatternsofslumformationandsustenanceoverspaceandtime,offering"candidateexplanations"(Epstein1999)fortheemergenceofobservedpatterns.

6.6 Anotherdirectionofthemodelextensionistoincorporatemorecomplexbehaviorsandinteractions.Forexample,itmightbeinterestingtoexplorethecompetitionbetweenthedevelopersforthesites.However,thiswouldinvolvedevelopingamorecomplicatedlandmarketmechanismthanthatcurrentlyimplementedinthemodel.TheworkofFilatovaetal.(2009)couldbeagoodstartingpointforthis.Similarly,thecompetitionbetweentwopoliticalpartiescouldbeintroducedthatwouldworkinbothdirectionsratherthansimplyprotectingthepoor(Kim2011;Muis2010).Theroleofgovernmentisalsoimportantindevelopingnewgreen-fieldsitesbyprovidinginfrastructure,whichiscurrentlyabsentinthemodel.Theeconomicgrowthandformal-informalmixdeterminesthelevelofbudgetavailableforsuchadevelopmentandmaybecomemoreimportantparametersoncetheroleofgovernmentisintroducedinsupplyofservicedland.Dataonsomeoftheseinputparametersmightnotbeavailablereadilyforcitiesindevelopingcountries.However,onecanhopethatourmodelmayprecedeandguideempiricalworkinthisareaasisthecasewithmanyothertheoreticalandexploratoryworks(EpsteinandAxtell1996).

6.7 AsWilson(2000)writes,understandingcitiesrepresentoneofthegreatestchallengesofourtime.Asmorethanathirdoftheworld'spopulationcurrentlyliveinslums(UN-Habitat2003),webelievethatslumsrepresentagreatchallenge.Agent-basedmodelingisanusefultooltostudyquestionsrelatingtohowslumscomeintoexistence,howdotheyexpand,andwhichprocessesmaymakesomeslumsdisappear.Webelievethisisespeciallytruebecauseagent-basedmodelingisinherentlydynamicandfocusesonindividualbehaviorthatismanifestedintheformationofslums.

Acknowledgements

TheauthorswouldliketothanktheNationalScienceFoundationanditsGeographyandSpatialSciencesProgram(NSF-BCS-1225851).Inadditiontheauthorswouldalsoliketothankthethreeanonymousreviewersfortheirdetailedandhelpfulreviews.

Notes

1Slumulationcurrentlyonlytacklesthespatialscale.However,wenotethatdifferenttemporalscalesplayaroleandweareinvestigatinghowthiscanbeincorporatedintothemodel.Forexample,residentialmovementoccursatadifferenttemporalscalethanthatofpoliticalelectionsandthedevelopmentofland.

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