Agent-based models: understanding the economy from the ... · Topical articles Agent-based models:...

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Topical articles Agent-based models: understanding the economy 173

Agent-based models: understanding the economy from the bottom upBy Arthur Turrell of the Bank’s Advanced Analytics Division.(1)

• Agent-basedmodellinghaslongenjoyedsuccessinthenaturalsciences,providinginsightsintoeverythingfromcancertotheeventualfateoftheUniverse.

• Itissuitedtomodellingcomplexsystemssuchastheeconomy,particularlythoseinwhichdifferentagents’interactionscombinetoproduceunexpectedoutcomes.

• Ineconomics,agent-basedmodelshaveshownhowbusinesscyclesoccur,howthestatisticsobservedinfinancialmarkets(suchas‘fattails’)arise,andhowtheycanbeausefultoolinformulatingpolicy.

Overview

Agent-basedmodelsexplainthebehaviourofasystembysimulatingthebehaviourofeachindividual‘agent’withinit.Theseagentsandthesystemstheyinhabitcouldbetheconsumersinaneconomy,fishwithinashoal,particlesinagas,orevengalaxiesintheUniverse.

Thestrengthofthesemodelsisthattheyshowhowevenverysimplebehaviourscancombinefromthe‘bottomup’torecreatethemorecomplexbehavioursobservedintherealworld.Anexamplewouldbehowthedecisionsofeachindividualfishcreatetheseeminglyorganisedandunpredictablemovementsoftheshoal.

This‘bottom-up’approachisincontrasttomodelswhichare‘topdown’,andwhichpresumehowagents’behaviourswillcombinetogether,sometimesbyassumingthatallagentsareidentical.Thedifferentapproacheshavedifferentstrengths.

Theagent-basedapproachtoproblem-solvingbeganinthephysicalsciencesbuthasnowspreadtomanyotherdisciplinesincludingbiology,ecology,computerscienceandepidemiology.Inrecentyears,agent-basedmodelshavebecomemorecommonineconomics,includingattheBankofEngland.

Therearechallengestotheiruse,includingtheneedforadvancedprogrammingskills,theneedtocarefullyinterprettheirresults,andhowtobestselecttheappropriatebehavioursfortheagents.Inparticular,therearenotalwaysobviouscriteriaforchoosingwhichbehavioursarethemost

realistic.Theseissueshavebeenabarriertotheirmorewidespreadadoptionineconomics.

Despitebeinglesswidelyused,agent-basedmodelshaveproducedmanyimportantinsightsineconomics,includinghowthestatisticsobservedinfinancialmarketsarise,andhowbusinesscyclesoccur.

Recently,theBankofEnglandhasdevelopedagent-basedmodelsoftwomarkets:corporatebondsandhousing.Theincreasedavailabilityofdataandcomputationalpowermeanthatagent-basedmodellinglookssettogainimportanceasatoolforbothunderstandingtheeconomy,andforexploringtheconsequencesofpolicyactions.

(1) TheauthorwouldliketothankDavidBholatandChrisCaifortheirhelpinproducingthisarticle.

ENVIRONMENT

Agents Agent-agent interactions Agent-environment interactions

Summary figure Schematic of the typical elements of an agent-based model

174 Quarterly Bulletin 2016 Q4

Introduction

Thisarticleconsidersthestrengthsofagent-basedmodellingandthewaysthatitcanbeusedtohelpcentralbanksunderstandtheeconomy.ThesemodelsprovideacomplementtomoretraditionaleconomicmodellingwhichwascriticisedfollowingtheGreatRecession.(1)

Agent-basedmodelshavedifferentstrengthsandweaknessestootherapproachesineconomics.Theyhaveadvantagesindescribinghowthedifferentactionsandpropertiesofindividualagentscombinetodrivetheoverallbehaviourofsystems.

Thisarticleexplainsthemotivationbehinddevelopingmodelsandhowtheycanbeusedtobetterunderstandtheworld,beforediscussingmoredetailsofwhatmakesagent-basedmodelsdifferent.Itthendescribeshowthesemodelswerefirstdevelopedandusedindisciplinesoutsideofeconomics.

Thegeneralstrengthsandweaknessesofagent-basedmodelsarediscussed,withexamplesofhowtheiradvantageshavebeenusedtoimprovetheunderstandingofcertainmarkets.

Thepenultimatesectionisanoverviewofhowagent-basedmodelsarebeingappliedineconomicsingeneralandattheBankofEnglandspecifically.Finally,somethoughtisgiventohowthislineofmodellingmightbeusedinthefuture.

Agent-basedmodelsarecalledbydifferentnamesindifferentdisciplines,includingMonteCarlosimulations(inthephysicalsciences),individual-basedmodels(inbiologyandecology),agent-basedcomputationaleconomicsmodels(ineconomics)andmulti-agentsystems(incomputerscienceandlogistics).Thisarticleuses‘agent-basedmodel’torefertoanymodelinwhichtheinteractionsandbehavioursofalargenumberofheterogeneousagentsaresimulated,manuallyorbyacomputer.

ModellingModellingisubiquitousacrossacademicdisciplines,governmentsandtheprivatesector.Mostmodelsattempttoisolatetheunderlyingcausesofthebehaviourofsystems,removingextraneousdetailandfocusingonwhatmatterstothehypothesis,questionorpolicyunderconsideration.Modelsmaybeassimpleasthoughtexperimentsbut,inquantitativesubjects,ofteninvolvemathematicsandsimulation.

Usinganartificialandsimplifiedversionoftheworldallowsresearchersandpolicymakerstoexplorewhatmighthappenincertainscenarios.Inmacroeconomics,datamaybescarceandexperimentscanrarely,ifever,beperformedintherealworld,andthismakesmodelsespeciallyuseful.Differentmodelsare

goodforansweringdifferentquestionsandsoawiderangeofthemarerequired.

Allmodelsshouldbeabletoreproduce,asmuchaspossible,therealworldobservablestheyseektoexplain.Italsohelpsiftheyareeasytouseandinterpret,andiftheycanexplainthephenomenaassimplyaspossible.Overtime,modelswhichexplainrealitymoreadequatelyandmoreconciselyarefavoured,replacingthosewhichexplainitlesswell.

Agent-basedmodelsaresuitedtostudyingproblemsinwhichthecombinationoftheinteractionsofmanyagentsdrivestheoverallbehaviourofthesystem.Theysolveproblemsfromthe‘bottomup’ratherthanthroughrulesimposedfromthe‘topdown’.Typically,creatinganagent-basedmodelrequiresknowledgeofmathematics,statistics,andcomputerscience,aswellasthedisciplineinwhichitisbeingapplied.

Thesemodelsgettheirnamebecausetheyinvolvesimulatingalargenumberof‘agents’.Eachagentisaself-containedunitwhichfollowsitsownbehaviouralrules.Mostoften,thisisachievedwithinacomputersimulationbutitneednotbe.

Agentscouldrepresenttheconsumersinaneconomy,fishwithinashoal,particlesinagas,orevengalaxiesintheUniverse.Thebehavioursorrulesthatagentsfollowdependonthequestionofinterest.Somemodelshavemanydifferenttypesofagent,forinstancefirms,workersandgovernments.Thesemaythemselvesdiffer;forinstance,eachworkermighthaveadifferentproductivity,eachfirmadifferentsize.Agent-basedmodelshaveilluminatedasurprisinglywiderangeofsubjectsincludingmilitaryplanningandbattlefieldanalysis,operationalresearch,computerscience,biology,ecology,epidemiology,economics,socialsciencesandthephysicalsciences.

Withthem,suchvariedproblemsastheseparationofBrazilnutsfromothermixednuts,thebehaviouroftradersinthestockmarket,theflockingofbirds,thefallofancientcivilisations,thespreadofdisease,andtheeventualfateoftheUniversehavebeenexamined.

Inafewcases,resultswhichcouldonlyhavebeenobtainedthroughagent-basedmodellinghavesignificantlychangedthecourseofhistory:calculationsofthewaythatparticlesaretransportedthroughapileoffissilematerialinanuclearreactororweaponwouldbeprohibitivelydifficulttodoinanyotherway.

Theiruseineconomicscomeswithsomeparticularnuanceswhichareexploredinthisarticle.Inthenaturalsciences,agentbehavioursaretypicallymuchmoreconstrainedthanin

(1) SeeHaldane(2016).

economics.Becauseofthis,agent-basedmodelsineconomicstypicallyproduceinsightsratherthanquantitativeforecasts.Theyaretypicallyqualitativeratherthanquantitative,andtheyaregoodfordeterminingwhatscenariosmightoccurratherthanexactlywhatwilloccur.

Anagent-basedmodelineconomicswouldnotnormallybeappropriateforforecastingthepriceofaparticularasset,forexample.Butitcangiveanideaofwhatactionsbytradersmightmovethepricesofassets,orwhythesupplyofanassetismuchmorevolatilethanthedemandforit.Otherphenomenawhichtheyhaveexplainedindifferentcontextsincludecycles,bubbles,clusteredvolatility,firesalesofassets,andtheonsetof‘bear’and‘bull’markets.(1)Despitebeingmoresuitedtoinsightsthanquantitativeprediction,therehavebeensomesuccessfulexamplesofforecastingwithagent-basedmodelsineconomics;forexample,forthedemandforelectricityortherepaymentrateofmortgages.(2)

TheGreatRecessionprofoundlychallengedtheeconomicsprofession,particularlyeconomicmodelling.Itdemonstratedthattheeconomyiscomplex,andnotalwaysatastableequilibrium.Theafter-effectsofthecrisisarestillbeingfelt.Establishedtools,suchas‘dynamicstochasticgeneralequilibrium’models(3)havebeencriticised(4)fornothavingenoughtosayaboutthedynamicsofcrises.Agent-basedmodelsareoneresponsetothechallengeandthisarticleexplorestheirpotentialinaidingourunderstandingoftheeconomy.

Theremainderofthissectionillustrateshowthesemodelshavedevelopedandwhatusestheyhavepreviouslybeenputto.Then,thearticleturnstoaspecificexampleofagent-basedmodellingineconomicswhichdemonstratessomeoftheirgeneralfeatures.

Theoriginsofagent-basedmodellingTheinitialspurfordevelopingagent-basedmodelscameinthe1930swhenphysicistEnricoFermiwastryingtosolveproblemsinvolvingthetransportofneutrons,asub-atomicparticle,throughmatter.Neutrontransportwasdifficulttomodelaseachstepinaneutron’sjourneyisprobabilistic:thereisachancetheparticlewilldirectlyinteractwith,scatteroff,orpass-byotherparticles.Previousmethodshadtriedtocapturetheaggregatebehaviourofalltheneutronsatonce,buttheimmensenumberofdifferentpossibilitiesforneutronpathsthroughmattermadetheproblemverychallenging.

Fermidevelopedanewmethodtosolvetheseproblemsinwhichhetreatedtheneutronsindividually,usingamechanicaladdingmachinetoperformthecomputationsforeachindividualneutroninturn.Thetechniqueinvolvedgeneratingrandomnumbersandcomparingthemtotheprobabilitiesderivedfromtheory.Iftheprobabilityofaneutroncollidingwere0.8,andhegeneratedarandomnumbersmallerthan0.8,

healloweda‘simulated’neutrontocollide.Similartechniqueswereusedtofindtheoutgoingdirectionoftheneutronafterthecollision.Bydoingthisrepeatedly,andforalargenumberofsimulatedneutrons,Fermicouldbuildupapictureoftherealwaythatneutronswouldpassthroughmatter.Fermitookgreatdelightinastonishinghiscolleagueswiththeaccuracyofhispredictionswithout,initially,revealinghistrickoftreatingtheneutronslikeagents.(5)

Theagent-basedtechniquesFermiandcolleaguesdevelopedwentontoplayanimportantroleinthedevelopmentofnuclearweaponsandnuclearpower.AtaroundthesametimethatFermiwasdevelopinghistechnique,thefirstelectroniccomputerswerebecomingavailableattheworld’sleadingscientificinstitutions.Computingpowerremainskeytoagent-basedmodellingtoday,withsomeoftheworld’ssupercomputersbeingharnessedforevermoredetailedsimulations.(6)

By1947scientistshaddevelopedanameforthistechniquewhichreflecteditsprobabilisticnature:theMonteCarlomethod.ThestorygoesthatthenamewasinspiredbyStanislawUlam’suncle,whowouldoftenasktoborrowmoneybysayinghe‘justhadtogotoMonteCarlo’.In1949,MetropolisandUlampublishedapapertogetherentitledThe Monte Carlo Method(7)whichexplainedthemanyusesofthenewtechniqueofusingrandomnumberstotackleproblems.Notallofthesewereagent-basedmodelsbutallreliedonusingartificiallygeneratedrandomnumberstosolveproblems.ThismoregeneralMonteCarlotechniquehasbeenappliedverywidely,forinstancetocalculatingsolutionstoequationswithmanyparameters,tothemanagementofriskandcatastrophes,andtoinvestmentsinfinance.

ThemoregeneralMonteCarlomethodhasthestrengththatitcanveryefficientlyexplorealargenumberofpossibilities.Forinstance,theusualwayforFermi’sneutronproblemtohavebeentreatedwouldhavebeentocreateagridofeverysinglepossibilityandthenfillinwhathappensforeachofthem.Thismeansthatevenimplausiblyunlikelyscenariosarecomputed.MonteCarloinsteadfocusesonthemostlikelyoutcomes.Thispropertycanmakethedifferencetowhetheraparticularproblemissolvableornot.TheMonteCarlomethodcanalsodealwithdistributions,forinstanceacrossincome,whicharenotdescribedbyanormaldistribution.(8)

(1) SeeZeeman(1974).(2) SeeGeanakoploset al(2012).(3) Aclassofmodelsinwhichmarketsareassumedtosimultaneouslyclear;see

Burgesset al(2013).(4) SeeMankiw(2006);Haldane(2016);Ascari,FagioloandRoventini(2015).(5) SeeMetropolis(1987).(6) LawrenceLivermoreNationalLaboratory(2013),‘Recordsimulationsconductedon

LawrenceLivermoresupercomputer’,availableathttps://www.llnl.gov/news/record-simulations-conducted-lawrence-livermore-supercomputer.

(7) SeeMetropolisandUlam(1949).(8)Normaldistributionsarewhatphysicalproperties,suchasheight,tendtofollowand

theyhaveawell-knownmathematicaldescription.TheyarealsoknownasGaussiandistributionsor‘bell-curves’.Manypropertiessuchaswealth,income,orfirmsizedonotfollowanormaldistribution.

Thesearestrengthswhichagent-basedmodelsinheritfromthemoregeneraltechnique.However,thisarticlefocusessolelyonMonteCarlosimulation,alsoknownasagent-basedmodelling.Thisseekstodescribeasystemofinteractingagentsandtheevolutionofthatsystem,ratherthancalculatethesolutiontoasingleequation.Inthisarticle,MonteCarlosimulationandagent-basedmodellingareusedsynonymously.

Agent-basedmodellinghasbeenusedacrossawiderangeofdisciplines,asdiscussedintheboxonpage177.Beforeembarkingonthestrengthsandweaknessesofagent-basedmodels,asimpleexampleispresentedwhichillustratessomeoftheirgeneralfeatures.ThisexampleisanearlyandinfluentialmodelbyeconomicsNobelMemorialprizelaureateThomasSchelling.

An early agent-based model in economicsInthelate1960sandearly70s,ThomasSchelling(1)developedamodelthatseekstounderstandtheeffectsofagents’preferencesaboutwheretheylive.ThedescriptionbelowdoesnotexactlyfollowSchelling’soriginalexample,butretainsitsmostsalientfeatures.

ImaginetherearetwospeciesnamedEconsandHumanswhoco-exist.Econsarealwaysrational.Humansareemotionalandsometimesmakemistakes.AlthoughEconsandHumanspeacefullyco-existandliveinthesamecity,theyeachhaveaslightpreferenceforlivingclosertothesamespecies.

Thispropensitytowanttobenearothersoftheirtypecanbecharacterisedbyanumberf,whichcanbethoughtofastheirstrengthofpreference.Itrepresentsthefractionofneighboursthattheyideallywishtobeofthesamespecies,withanfof1meaningthattheywillonlybehappyifalloftheirneighboursareofthesamespecies.

Ifagentsofeithertypeareunhappy,theycanchoosetomovehouseand,atrandom,aregivenanewproperty.Overtime,moreandmoreagentswillbehappywithwheretheyliveandstopmoving.Usingsimulations,Figure 1showsaninitialneighbourhoodofHumansandEconswhichismixed.

WhathappensiftheHumansandEconsarenowallowedtomovearounduntilalmostallofthemare‘happy’accordingtothevalueoff?Figure 2showsoneexamplesimulationwithf=25%;theagentsremaingenerallyinter-mixed.WhatissurprisingishowquicklythemixofHumansandEconsbecomessegregatedasfincreases.Figure 3showsanexampleofafinaldistributionwithf=26%.

Theagentsarenowclearlysegregated,eventhoughthechangeintheirpreferenceswasverysmallfromFigure 2.Thisisanexampleofa‘tippingpoint’,alsoknowninthephysicalsciencesasa‘phasetransition’.Itisasudden,emergentchangeintheoverallsystem.Tippingpointslikethiscanoccur

insystemswhicharecoupledtogetherbytheiragents;here,asmallchangeinfcanmeanthatalmosteveryonehastomoveinordertosatisfytheirnewpreferences.Asaresult,theneighbourhoodcanlookverydifferentafterthechangeinf.

Humans Econs

Figure 1 The initial distribution of Humans and Econs

Humans Econs

Figure 2 The final distribution of Humans and Econs with f=25%

Humans Econs

(1) SeeSchelling(1969,1971);foranexampleseewww.jeromecukier.net/projects/models/segregate.html.

Agent-based modelling across disciplines

Agent-basedmodellingsoonbecameaverypopulartechniqueinthephysicalsciences;(1)anearlypaperhasreceivedover30,000citationsbyotherresearchers.(2)Deepinsightshaveemerged,forinstancethatthestructureoftheUniversemaybeflatratherthancurved,(3)meaningthattheUniverseisunlikelytoendina‘BigCrunch’withallmatterconcentratedatasinglepointinspace.

Therangeofapplicationsinthephysicalsciencestodayisbroadindeedandincludesplasmaphysics,(4)particle-basedcancertherapies,materialsscience,crystallisation,magnetismandnuclearfusion.(5)Oneunexpectedapplication,publishedwiththetitleWhy the Brazil Nuts Are on Top,(6)simulatedhowmixednutssegregateovertimeinabag,researchwhichhashadimportantimplicationsforindustriesdealingwithparticulatemattersuchaspharmaceuticalsandmanufacturing.

Computersciencehasalsoseenheavyuseofthetechnique.ThepolymathJohnvonNeumannisbestknownineconomicsforhisworkongametheorybuthewasalsoaformidablecomputerscientist.Ina1948lecturehedescribeshisideafor‘cellularautomata’.Theseareartificialmodelsof‘cells’,whichlooklikefilledsquaresonaboard(similartotheSchellingmodeldiscussedinthisarticle).(7)VonNeumannfoundthat,contrarytointuition,verysimplerulesforthecellagentsgaverisetopuzzlinglycomplexbehaviourwhichlookslife-like.Thisisaso-calledemergentbehaviourbecauseitisalmostimpossibletopredictbasedontheruleswhichtheindividualagentsfollow.

Themilitarywereearlyadoptersofagent-basedmodelling.Wargameshadbeenplayedwithboardanddiceformanyyears,buttherewasaswitchtocomputationalagentsinthe1960s.Aswellasbeingusedtounderstandthedynamicsofpastbattles,suchashowoptimalthesearchingoperationsoftheBritishArmywereindetectingGermanU-boatsintheBayofBiscay,(8)theyaretodayusedbytheworld’slargestarmiestoformulatemilitarystrategy.Inrecenttimes,theautomatedbehaviourofagentsinwarmodelshasspilledoverintorealitywiththedevelopmentofautonomousweaponsandvehicles.

Thistrendisalsoreflectedincivilapplicationsofautonomousrobots.Mostrecently,therehasbeenmuchworkonmultipleautonomousroboticssystemsinwhichtheagentsarerobotsthatneedtodecidehowtomoveaboutintherealworld,forinstanceindriverlesscars.Itisextremelyusefultobeablemodelthebehaviourofautonomousrobotsbeforetryingthemoutinthefield.Forsometasks,centralisedcontrolofallrobotsisnotfeasiblesodesigningindividualbehaviourswhichproducetheoveralldesiredoutcomeisimportant.

Biologistsandecologistbegansimulatingthebehaviouroforganismswithinanenvironmentusingagent-basedmodelsinthe1980s.Thesemodelswereextendedtoincludemorecomplexphenomena,suchasagent-environmentinteractions.Anexampleistheresearchonmarineorganismswhichincludesbehaviourssuchasswimming,feeding,beingpreyedupon,andorganisms’interactionswithoceancurrents.Oneofthemanyapplicationsofthissortofmodelcouldbeexamininghoworganismsfairwithhigheroceantemperatures,orhigherconcentrationsofCO2.

Successesofthesemodelsincludepredictingthespawninglocationsoffish,explaininghowthetroutinLakeMichigan,USA,becamecontaminated,anddescribinghowsociallylearnedbehavioursleadtodistinctculturalgroupsamongmammals.Inthesecasestheadvantageofanagent-basedmodelwastobeabletoincludemanydifferentagentsandagentbehavioursinasinglemodelwhichcouldberunmillionsoftimestodeterminethemostprobableoutcomes.

Recentapplicationshavefocusedonconservationandmigration,includingthemanagementofforests,thetimingofanimalmigrations,andthepopulationpressuresonendangeredspecies.Forinstance,onemodelisoftheendangeredtigerpopulationinNepal;itusestheobservedbehaviourofindividualtigerstoexplorefutureconservationscenarios.(10)

Animportanthealth-relatedapplicationofagent-basedmodelsisinepidemiology—thestudyofthespreadofdiseases.Agoodunderstandingofthecomplexdynamicsofepidemicscouldsavemillionsoflives.Agent-basedmodelshaveallowedcountry-specificinformationsuchasgeographicaldata,commutingpatterns,agedistributionsandothercensusinformationtobetakenintoaccount.(11)

Inbiology,agent-basedmodelsarenowbeingusedtosimulateentireanimalcells,cancers,bacteriaandeventheeffectsofnewdrugsonpatients.Otherapplicationsincludeairtrafficcontrol(inwhichagentsrepresentaircraftandco-ordinatetominimisefueluse),transportationsystems(matchingagentstodestinations),crowdcontrolinemergencysituations,shoppingpatterns,predictinglandusepatterns(12)andnon-playeragentsincomputergames.

(1) SeeHaldane(2016)formore.(2) SeeMetropoliset al(1953).(3) SeeDaviset al (1985).(4) SeeTurrell,SherlockandRose(2015).(5) SeeTurrell(2013).(6) SeeRosatoet al(1987).(7) SeevonNeumann(1951);anexamplemaybefoundat

www.jeromecukier.net/projects/models/ca.html.(8) SeeCarl(2015);ChampagneandHill(2009).(9) SeeWerneret al(2001).(10)SeeCarteret al(2015).(11) SeeDegliAttiet al (2008).(12)SeeHeppenstallet al(2011).

Figure 4showswhatcanhappenwhenallagentshaveverystrongpreferences.

Schelling’smodelisverysimplebutitshowshowevenmildchangesinpreferencescanleadtosignificantchangesatthemacro-level.

Figure 5 showsthatstrikinglysimilarpatternsmaybeseenintheUSCensusdataforChicago.However,therearemanydifferencesbetweenthesimplemodelpresentedandtherealworld;preferencesmaynotbesymmetricacrossgroupsasisassumedinthebasicSchellingmodel,therearemanypracticalbarrierstomoving(suchasbudgetconstraints)andwhatwaslabelledas‘preference’islikelytobemuchricherinreality,reflectingthecomplicatedsocio-economichistoricalrelationshipsbetweengroups.

What is agent-based modelling good (and bad) for?

Theprevioussectiongaveaspecificexampleofthekindsofinsightswhichcomeoutofagent-basedmodels.Acrossmanyoftheirapplications,thereareasetofrecurringstrengthsandweaknesseswhichareexploredinthissection.Particularreferenceismadetotheapplicationsofthesemodelstoproblemsineconomicsandthesocialsciences.

StrengthsEmergentbehaviourThesinglemostpowerfulfeatureofagent-basedmodellingisthattheindividualactionsoftheagentscombinetoproducemacroscopic(1)behaviour.

Agoodexampleofthisistheherdingofsheeportheflockingofbirds.(2)Individualbehaviourscombinetoproduceaneffectwhichlooksorganisedevenwhentherulesforeachagentareincrediblysimple.(3)Trafficjamsareanotherfamiliarandunwelcomeexample;modelsandexperimentshaveshownthatjamscanresultevenwhenthereisnoimpedimenttotraffic.(4)Peoplecanherdintheireconomicactionsandexpectationstoo,forinstanceintheirexpectationsaboutinflation.Thishasdirectconsequencesfortheeconomy.

ThemostimportantexampleofemergentbehaviourineconomicsisAdamSmith’smetaphoroftheinvisiblehand:howtheself-interestedactionsofrealagentsintheeconomycombinetoproducesociallyoptimaloutcomes.Oneofthestrengthsofagent-basedmodellingisthatthisinvisiblehandismadevisibleanditsworkingsmaybeexamined.Thisisincontrasttosomeothermodelapproachesinwhichtheactionsofmanyindividualsareassumedtoleadtoaparticularoutcome,oftenusingasinglerepresentativeagent.Thissimplificationisvalidinsomecasesbutnotallcombinationsofbehaviourscanberepresentedbytheactionsofasingleagent.(5)

HeterogeneityAsindividualagentsaremodelled,itispossibletoexploretheconsequencesofagentsbeingheterogeneous;thatisagentsbeingdifferentinsomeway,perhapsbyincome,preferences,educationorproductivity.

Incorporatingheterogeneityallowsforthemodellingofmuchricherbehaviour.Inequalityisagoodexample—aggregatewealthcanincreasebutifitisonlyasmallfractionofthepopulationdrivingthisphenomenonitwouldsuggestvery

Humans Econs

Figure 5 US Census data for Chicago showing segregation(a)

Source:http://demographics.coopercenter.org/DotMap/.

(a) NateSilver,538.com;seehttp://fivethirtyeight.com/features/the-most-diverse-cities-are-often-the-most-segregated/.

(1) Atthelargescale,inthiscasethesizeofthesystemwhichtheagentsinhabit.(2) SeeMacyandWiller(2002).(3) Anexamplemaybefoundatwww.tjansson.dk/2012/11/yabi-yet-another-boids-

implementation-simulation-of-flocking-animals/.(4)Anexampleofanagent-basedmodeloftrafficjamscanberuninyourinternet

browseratwww.traffic-simulation.de/.(5) Thisisanexampleofthe‘fallacyofcomposition’.

differentunderlyingeconomicreasonsthaniftheentirepopulationwerebecomingwealthier.

StylisedfactsPerhapsthegreatestsuccessofagent-basedmodelsineconomicshasbeenexplainingthestylisedfactsobservedinassetmarkets.(1)(2)Thereareanumberofphenomenaobservedempiricallyinthemarketsforassetssuchasbondsorequitieswhicharenotexplainedbytraditionaleconomictheory.Someofthetwomostwidelyseenacrossmarketsare:

• Clusteredvolatility,inwhichthestandarddeviationofreturnsonanassetexhibitstrendswhichare‘clustered’intime.(3)

• ‘Fattails’,inwhichextremeeventssuchaslargepricechangesoccurmorefrequentlythanwouldbeexpectedifanormal(orGaussian)distributionwasassumedandfarbeyondwhatwouldbeexpectediftraderswerebehavingrationally.AnexampleisshowninChart 1.

TheSanta Fe Artificial Stock Market(4)isagoodexampleofhowtradingactivitiescanaffectaggregatemarketstatistics.Thismodelissimilarinmanyrespectstoatraditionaleconomicmodelbutwiththeimportantdistinctionthatagentshaveheterogeneousexpectationsofreturns.Thismakesitimpossibleforoneagenttoknowwhatotheragents’expectationsare,andthusimpossibletoformanunambiguousandrationalexpectationofprice.Instead,agentsadaptivelylearnusingarangeofexpectationmodels.Anevolutionaryprocessoccursonagents’strategies;theyareconstantlyupdatedinlightoftheactualpathofthemarket.Interestingly,themodelproducestworegimes—onewhichlookslikestherationalexpectationsworldwithamarketpriceatthefundamentalpriceofthefinancialproduct,andoneinwhichclusteredvolatilityand‘fattails’occur.Rapidevolution

ofstrategiescausesthenon-rationalmarketswhicharemorelikethoseobservedinreality.

Manyagent-basedmodelshaveshownthatchartistortrend-basedtrading(inwhichtradersfollowthetrenddirectionofprices),andalsoleverage,(5)cancontributetopriceovershoots,andthatthiscandriveclusteredvolatility,hightradingvolumesandfattails.(6)

RealisticbehavioursThegenerationofrealisticbehaviour,basedonobservedbehaviour,canbeastrengthofagent-basedmodels.Researchinbehaviouraleconomicshasshownthatpeopleoftenuseheuristics(7)whenmakingdecisionsandthattheyarenotfullyrational.Thesebehaviourscanbecollectivelydescribedas‘boundedrationality’.Anexampleisthatpeoplereactmorenegativelytolossthantheydopositivelytogain,aphenomenonknownaslossaversion.Thereareseveralmodelswhichexplorewhathappenswhenpurelyrationaloptionsarenotavailableoraretoocostly,orwhenagents’environmentschangeovertime.(8)

ExploringthepossibilitiesOneoftheadvantagesofagent-basedmodellingisthatitcanveryefficientlyexplorealargenumberofpossibilities.Probabilisticrulesappliedtoeachindividualagentinturncanbeasimplerwayofexploringscenariosthanworkingouthowtheentirepopulationofagentsshouldbehavetogether.Anexampleisinthetransportofparticles,andwasthepromptforFermitooriginallydeveloptheMonteCarlomethod.Anotherisinepidemiology,whichcansimilarlybemodelledeitherwithsetsofequationswhichtrytosummariseallbehaviouratonce,oranagent-basedmodel.Theequationapproachquicklybecomescomplicatedasmoreandmoreagentpropertiesthatarerelevanttodisease(suchashealth,age,andevencommutingpattern)areintroduced.Oragent-basedmodelscanbeappliedtoconflictinwhicharelativelyinflexiblesetofequationsmodellingtherateofchangeofsizeofarmiescanbereplacedwithagent-basedmodelswhichcancapturethefullheterogeneityofcombatantsinmodernwarfare.

(1) SeeHongandStein(1999).(2) SeeCutler,PoterbaandSummers(1989);LuxandMarchesi(1999,2000).(3) SeeCont(2007).(4) SeeLeBaron,ArthurandPalmer(1999).(5) SeeThurner,FarmerandGeanakoplos(2012).(6) SeeTesfatsion(2002).(7) Heuristicsare‘rulesofthumb’formakingdecisionswhichsimplifytheprocessbut

maynotalwaysgivetheoptimaldecisioninallcircumstances.(8) SeeGodeandSunder(1993);Farmer,PatelliandZovko(2005);Challetand

Zhang(1997);Hommes(2006);Axelrod(2006).

Equity prices

Best Gaussian fit

40 20 0 20 40– +

Probability density

Month-on-month change, per cent

Chart 1 Not normal: changes in the price of equities have a fat-tailed distribution (1709–2016)

Sources:Hills,ThomasandDimsdale(2016)andBankcalculations.

Complexity,non-linearityandmultipleequilibriaAnotherstrengthofagent-basedmodelsisthattheycandescribecomplexsystems.Complexsystemsarecharacterisedbyhavingmanyinterconnectedparts,havingvariableswhichcanchangedramaticallyandwhichcandemonstrateself-organisation.Additionally,complexsystemsundergosudden,dramatictransitions,sometimescalledphasetransitions.Recentworkonagent-basedmodelsofthemacroeconomyhasdescribedphasetransitionsbetweenlowandhighunemployment.(1)Theeconomydisplaysmanyofthecharacteristicsassociatedwithcomplexsystems.

WeaknessesToomuchfreedom?Whileitistruethatagent-basedmodellinghasmanystrengths,italsopresentschallenges.

Inmanyways,thegreateststrength—theflexibilitytomodelsuchavastrangeofscenarios—isalsothegreatestweakness.Thesheerextentofchoiceinconstructingagent-basedmodelsascomparedtomoretraditionaleconomicmodelsmeansthatmodellersfacetheproblemofselectingtherightcomponentsfortheproblemathand.Simulationresultscanvarydramaticallydependingonwhichassumptionsareused,somodellersmusttakegreatcareinchoosingthem.Furtherworkisneededtodevelopobjectivemeansforchoosingthemostappropriateassumptions.

TheLucascritiqueThehugerangeofbehavioursavailableforagentsmeansthatagent-basedmodelscanbevulnerabletotheLucascritique.Thiscritiquecentresaroundthefactthatagents’choicesmaynotfollowhistoricallyobservedrelationshipswhenpolicyinterventionsaremadewhicharepremisedonthoserelationships.Inprinciple,agentbehaviourscanbedesignedtorespondtochangingcircumstancesbutthereisatrade-offbetweencreatingagentsthatwillalwaysfollowtheiroptimalcourseofactionandbuildingsimple,understandablemodels.Thisiswhyfullyrationalbehaviourisusefulasanapproximation:itgivesanunambiguousandrelativelysimplesetofrulesforhowagentscanalwaysactintheirownbestinterests.

Eachagent-basedmodelshouldbeasLucas-critiqueproofaspossiblebutoftenthemostinterestingbehaviours—suchasboundedrationality—aretheoneswhicharethemostdifficulttomakerobusttothecritique.

DifficulttogeneraliseTheproliferationofchoicesinconstructingagent-basedmodelsleadstoanotherweakness,whichisthattheytendtobebespoke.Forinstance,theagent-basedmodelwhichtellsushowbondsaretradedisunlikelytobeveryhelpfulforansweringquestionsaboutthehousingmarket.

CalibrationandinterpretationCalibrationinvolvesadjustingthemodeltofitwiththeknownfacts,forinstanceinitialisingitwithempiricaldata.Validationischeckingthattheoutputofthemodelisreasonablegivenwhatisknown,andperhapscross-checkingitwithothermodelsorvariationsintheassumptions.Ifamodelcontainsmanydifferentoptionsinhowitisconstructed,itcanspuriouslyreproducedatathatlooksimilartoempiricaldata.Thisisknownasoverfitting,anditisaproblemforallmodels.Calibrationisevenmoredifficultinagent-basedmodels,however,becausetheytypicallyproducestylisedfactsratherthanquantitativeforecastsandtherearevariouswaystheagreementwithempiricallyobservedstylisedfactscouldbeassessed.

Theresultsofagent-basedmodelscanalsobedifficulttocommunicatebecausetheymustbepresentedalongsidetheassumptionsusedtocreatethem.Althoughtrueofallmodelstosomeextent,thisproblemislessacutewithmodelsbasedonhistoricaldataaloneastheyusecommonstatisticaltechniques.Norisitthecasewithmodelsbasedonrationalexpectations;ifagentscanonlyactperfectlyrationallythenthereisastrongconstraintwhichiseasilyunderstoodacrossallsimilarmodels.Whenusingagent-basedmodellingtoinformthechoicesofpolicymakers,thisweaknesscanbeabarrier.

Finally,itcanbedifficulttounderstandhowchangingmodelinputsaffectthemodeloutput.Thisisanunavoidablefeatureofcomplexsystems,andoftherealworlditself.Itisincontrasttomoreanalyticallytractablemodelsinwhichtheeffectsofchangingaparametermayhaveamuchclearereconomicinterpretation.Althougheveryagent-basedmodeldoeshaveauniquemathematicalrepresentation,theequationswouldbedifficulttotranscribefromacomputerprogramme.

Despitethesechallenges,agent-basedmodelsprovideanimportanttoolforunderstandingtheworld,andonewhichhasdeliveredinanastonishingrangeofscenarios.

Wenowturntohowthesemodelscanimproveourunderstandingoftheeconomyasawhole,atopicwhichisespeciallyrelevanttocentralbanks.

Macroeconomic agent-based modelling

Themacroeconomyischaracterisedbyhavingbusinesscycles:fluctuationsinthegrowthofGDParounditslong-termtrend.Instandardmacroeconomicmodelling,thesefluctuationsaretheresultofunexplained(‘exogenous’)shocks.(2)Forinstance,inflationwouldbeforcedtosuddenlychangebutnotasa

(1) SeeGualdiet al(2015).(2) Ashockcouldbedescribedasanunexpectedanddiscontinuouschangeinavariable.

consequenceofanyemergentphenomenawithinthemodel.Thesearecalledexogenousshocks.

Intherealworld,thefluctuationsinGDParelikelytobeendogenous—thatis,generatedbytheeconomyitself.Agent-basedmodelsprovideawayofmakingthesefluctuationsendogenous,andthereforealsoprovidearoutetounderstandingtheircausesandwhatpoliciesmightaffectthem.TheGreatRecessionisacompellingexampleofareasonwhypolicymakersneedtounderstandwhatdrivesthesefluctuations.

Severalagent-basedmodelshavebeenputtingtogetherthedifferentelementsandagentswhicharerequiredtorealisticallyreproducethestylisedfactsoftheeconomyofanentirecountry,orevenseveralcountriesinterlinkedbytrade.Theseelementsincludetheentryandexitoffirms,(1)endogenousinnovation,monetarypolicyandfiscalpolicy.

Oneofthesemacroeconomicmodelsespeciallyaddressesmonetarypolicy.(2)Init,therearefirms,consumers,andpriceswhicharechangedaccordingtosimpleexpectations.Businesscyclessimilartothoseobservedinrealityaregenerated.Asimulatedexperimentshowsthatanactivemonetarypolicy,formulatedaccordingtoasimplerule,(3)reducesthesizeofthefluctuationsinGDPrelativetohavingastaticpolicyrule.Thisoccursbecausefirms’demandforcreditfallswhenthecentralbankraisesinterestratesaccordingtotherule.

Anothermodel(4)featuresaneconomycomposedofheterogeneouscapitalandconsumption-goodfirms,alabourforce,banks,agovernmentandacentralbank.Capital-goodfirmsperformresearchandproduceheterogeneousmachinetools.Consumption-goodfirmsinvestinnewmachinesandproduceahomogeneousconsumptiongood.Consumption-goodfirmsfinancetheirproductionandinvestmentsprimarilywiththeirliquidassetsand,ifrequired,bankcredit.Capital-goodfirmsproduceusingcashadvancedbytheirconsumers,ratherthanusingbanks.

Byincorporatingthefinancialsector,thismodelisabletoreproducemanyfeaturesseeninempiricalmacroeconomics,includingthecyclesinGDP,investmentandconsumption,aswellasthevolatilityofthesethreevariablesrelativetoeachother.Bankingcrisesarealsoanemergentphenomenaofthemodel;ashighproductionandinvestmentlevelsraisefirms’debt,thefirms’networthdecreases,increasingtheircreditrisk.Banksthenrationcreditandforcefirmstocurbproductionandinvestment,withthepotentialtotriggerarecession.Bankfailuresemergefromtheaccumulationofloanlossesonbanks’balancesheets.Themodelallowsforabetterunderstandingofthechainofeventswhichleadtobankingcrises.Confidencethattheseeventsdoreflecttherealworldsituationcanbegainedfromthereproductionof

stylisedfactssuchasthedistributionofbankingcrisisdurationsbeingveryclosetotheempiricalone.

ExperimentsonmonetarypolicywiththismodelsuggestthatadualmandatetotargetbothinflationandunemploymentresultinahigheraveragegrowthinGDPwithlowervolatilitythantargetinginflationaloneachieves.

Othermacroeconomicagent-basedmodels(5)havelookedathowinterestratesareset,(6)(7)athowliquiditytrapscanbeendogenously(8)generated(9)andattheeffectsofunconventionalmonetarypolicy.(10)

Thecostincomplexityofthesemacromodelsisbalancedbytheinsightswhicharegenerated.Theycanreproduceanimpressivelistofmacroeconomicstylisedfacts:businesscycles;theprocyclicalityofproductivity,nominalwages,firms’debt,bankprofitsandinflation;thecountercyclicalityofunemployment,(11)prices,mark-ups,andloanlosses;andtheappearanceoffattailsinthedistributionofoutputgrowth.Alternativeandcomplementarymodels,suchasdynamicstochasticgeneralequilibriummodels,havenotbeenabletogenerateallofthesephenomenaendogenously.(12)Thesemodelstherebyaidtheunderstandingofhowcomplexmacro-levelphenomenaemergefromunderlyingmicro-levelphenomena.

Thesestrongempiricalcredentialslendconfidencetotheconclusionsofpolicyexperimentsundertakenwithagent-basedmodels.Theflexibilityofthemodelsmeansthatextremelyfine-tunedregulationcanbe‘tested’usingthem.Examplesmightincludetheeffectofregulationonliquidityandprofitability,theinteractionofmicroandmacroprudentialpolicies,orhowcreditnetworkscangiverisetobusinesscyclesandfinancialcrises.(13)Asanexample,theNASDAQstockexchangehasusedanagent-basedmodeltodesignregulationwhicheliminatesloopholesthatcouldbeabusedbyitsusers.(14)

Thenextsectiondiscussestwoagent-basedmodelswhichhavebeendevelopedintheBankandwhichattempttoreplicatethestylisedfactsobservedintwodifferentmarkets:corporatebondsandhousing.

(1) SeeEliasson(1991).(2) SeeGattiandDesiderio(2015).(3) TheTaylorrule;seeTaylor(1993).(4) SeeDosiet al (2015);thismodelincorporatesaspectsofKeynesian,Schumpeterian

andMinskianeconomics.(5) SeeDilaver,JumpandLevine(2016).(6) SeeDelliGattiet al(2005).(7) SeeRaberto,TeglioandCincotti(2008).(8) Havinganinternalcauseratherthanbeingtheresultofanexternalshock.(9) SeeOeffner(2008).(10)SeeCincotti,RabertoandTeglio(2010).(11) SeeGualdiet al(2015).(12)SeeAscari,FagioloandRoventini(2015).(13)SeeGatti,GaffeoandGallegati(2010).(14)SeeBonabeau(2002).

Agent-based modelling in the Bank of England

Trading in corporate bonds by open-ended mutual funds(1)

Anagent-basedmodeldesignedtocapturesomeofthedynamicsoftradingincorporatebondsbyopen-endedmutualfundswasdevelopedwithintheBank.Themodelaimedtobeasparsimoniousaspossiblewhilereproducingrealisticbehaviourforthemarket.

Theassetsunderthemanagementofcorporatebondfundshavemorethandoubledsincethe2008financialcrisis.Atthesametime,concernsaboutthefragilityoffixed-incomemarketshavegrown.Despitethemarketbeinglarger,thereareworriesthattherehasbeenareductioninmarketliquidity,sothatlargeordershavemoreofaneffectonprices.

Thedynamicsofthismarkethaveimportantimplicationsforfinancialstability.Overshootingduringadjustmentsinthepriceofcorporatebondsmayunnecessarilyreducetheabilityofsomecompaniestoservicerefinanceddebt,threateningtheirsolvency.Somefirmsmayalsobedeterredfromraisingnewfinancing.Inextremis,thiscouldcauseanimpairmentofthesupplyofcredittotherealeconomy.

AstylisedpictureofthemodelcanbeseeninFigure 6.Therearearepresentativepoolofinvestors,asinglemarketmakerthroughwhichalltradesaremade,andthreedistincttypesoffund.Themodelendogenouslyreproducesoneoftheimportantstylisedfactsobservedinthecorporatebondmarket:thedistributionofdailylog-pricereturns.ThisisshowninChart 2,wheretheempiricalobservationsarefromaUSinvestment-gradecorporatebondindex.Theverytailendsofthedistributiondonotmatchtheempiricaldata;asituationwhichcouldpotentiallybeimprovedbysacrificingsomeoftheparsimonyofthemodel.However,theoverallfitofthedistributionisagoodmatchtodata.

Themodellooksathowinvestorsredeemingthecorporatebondsheldforthembyopen-endedmutualfundscancausefeedbackloopsinwhichbondpricesfallfurther.

Forexample,ifinterestratesweretorise,existingcorporatebondsmightbecomelessattractiveandredemptionscouldtakeplaceassomeinvestorspulltheirwealthout.Investorswhoredeemtheirbondsfirstgetagoodpricewhenfundssellthem,butpoorliquiditymaycausebondpricestofall.Thesepricefallscouldpromptremaininginvestorstoredeemtheirbondstoo,sothatfundshavetoselloffmorebondsandpricesfallevenfurther.Afeedbackloopofredemptionstakesplaceinwhichwealthisdestroyedandthosewhomaketheinitialredemptionsenjoyafirst-moveradvantage.Thisissimilartothechainofeventswhichcausedbankrunsbeforetheadventofdepositinsurance.

Simulatedexperimentswereundertakenwiththismodel.Theaimwastounderstandhowchangesinthebehavioursoftradersinbondsmightaffecttheextentofdislocationinpriceandyieldfollowingashock.

Theshockusedwastofunds’expectationsaboutthefractionofcompaniesthatwillfailinagivenyear,alsoknownastheexpectedlossrate.Thiscreatesanegativefeedbackloopinthepriceforbonds.Iffundsexpectmorecompaniestofail,theyarelikelytodemandhigheryieldsfrombondstocompensatethemforthis—soasuddenchangeintheexpectedlossratepushesdownonprices.Theaftermathofthisisseeninovershootsinbothpriceandyieldbeforetheysettledowntheirvalues.ThestepsinthefeedbackloopareshowninFigure 7.

(1) SeeBraun-Munzinger,LiuandTurrell(2016).

Corporate bond market

Value traders

Momentumtraders Passive funds

Investor

Market makerNoise

Figure 6 Schematic of an agent-based model of the corporate bond market

Daily log-price return

8 6 4 2 0 2 4 6 8

10-0Probability densitySimulation

Pre-crisis

CrisisPost-crisis

Chart 2 Reproducing stylised facts: the distribution of daily log-price returns

Giventheshock,anditsknowneffectsin‘normal’times,scenariosinwhichthetradingbehaviourwasdifferentcouldbeexplored.

Inoneofthesescenarios,theeffectofanincreaseinthefractionoffundswithpassivetradingstrategieswasexplored.Thisledtoasurprisingresult;thereisatailriskofsevereovershootswhenthepresenceofpassiveinvestmentfundsincreases.Anotherfindingisthatifallfundsweretoincreasethetimewindowoverwhichredemptionsweremadebyinvestors,theextentofpricedislocationwouldbesignificantlyreducedintimesofcrisis.ThisisbecausethefeedbackloopshowninFigure 7isstrongerwheninvestorswithdrawanamountofwealthonasingledayasopposedtowithdrawingitoveralongertimeperiod.

An agent-based model of the UK housing market(1)

Thehousingmarkethasoftenbeenasourceoffinancialstressandcrisis,lookingacrossawiderangeofcountriesandawidespanoftime.Themarketexhibitsclearandsignificantcyclicality.Capturingthesecyclicaldynamicsisnotstraightforwardandonepotentialreasonisthatthehousingmarketcomprisesmanytypesofparticipant—forinstancerenters,first-timebuyers,andbuy-to-letlandlords.Theseagentsareheterogeneousbyincome,gearingandlocation,sotheyhavedifferentincentives.Thecombinationoftheiractionsgivesrisetothecyclicaldynamics.

Inadditiontoabankingsector(mortgagelender)andacentralbank,themodelcompriseshouseholdsofthreetypes:

• renterswhodecidewhethertoattempttobuyahousewhentheirrentalcontractendsand,ifso,howmuchtobid;

• owner-occupierswhodecidewhethertoselltheirhouseandbuyanewoneand,ifso,howmuchtobid/askfortheproperty;and

• buy-to-letinvestorswhodecidewhethertoselltheirrentalpropertyand/orbuyanewoneand,ifso,howmuchtobid/askfortheproperty.Theyalsodecidewhethertorentoutapropertyand,ifso,howmuchrenttocharge.

Thebehaviouralrulesofthumbthathouseholdsfollowwhenmakingthesedecisionsarebasedonfactorssuchastheirexpectedrentalpayments,housepriceappreciationandmortgagecost.Thesehouseholdsdiffernotonlybytype,butalsobyage,income,bankbalances,rentalpaymentandotherproperties.

Animportantfeatureofthemodelisthatitincludesanexplicitbankingsector,whichprovidesmortgagecredittohouseholdsandwhichsetsthetermsandconditionsavailabletoborrowersinthemortgagemarket.Thebankingsector’slendingdecisionsarethemselvessubjecttoregulationbyacentralbank,whichsetsloantoincome(LTI),loantovalue(LTV),andinterestcoverratiopolicies(ICR).Thevariousdifferentagents,andtheirinterlinkages,areshowninFigure 8.

ThismodelwascalibratedusinghousingmarketdatasourcesandhouseholdsurveyssothattheagentsinthemodelhavecharacteristicswhichmatchthoseintheUKpopulationoveraparticularperiodoftime.Itincludesbehaviouralcharacteristicssuchashowoftenandbyhowmuchthepriceofahouseisreducedifitremainsunsold.

Funds’ demand forbonds is reduced

Price falls as market makersees reduced demand

Returns to investors fall as aconsequence of price drop

Investors reduce allocationof cash to funds

Shock toexpectedloss rate

Funds’ wealth is reduced

Figure 7 Capturing non-linear relationships: the feedback loop following a shock to funds’ expected loss rate

(1) SeeBaptistaet al(2016).

Central bank

sets caps on LTV, LTIand ICR ratios, andaffordability tests

Ownershipmarket

Rental market

Buy-to-letinvestors

Renters

Households

SocialhousingOwner-occupiers

givesmortgages

Figure 8 Agents and interactions in the housing market model

Oneofthekeyfeaturesofthemodelisthatitisabletoendogenouslygeneratereal-worldhousepricecyclesgeneratedbythemodelinChart 3.ItalsoreproduceskeyaspectsoftheUKhousingmarket,suchastheempiricaldistributionoftheshareofloansbyloantoincomebandbasedontheProductSalesDatabase(PSD)ofUKmortgages.ThisisshowninChart 4.

Themodelwasusedtolookatseveralscenariosforthehousingmarket.Inone,alargerbuy-to-letmarketwasfoundtocausemuchlargerswingsinhousepricesduringcycles.Inanother,theeffectofamacroprudentialpolicythatlimitslenderstomakingamaximumof15%ofitsmortgagesatloantoincomeratiosgreaterthan3.5wasexplored(thepre-existingBankpolicyisaratioof4.5).Withthislimitinplace,theendogenouscyclesinhousepricegeneratedbythemodelaredampened.

The future for agent-based modelling in economics

Agent-basedmodelsineconomicsthriveondata.Moredatameansfewerassumptionsneedtobemade,andmoreofthestructureofthemodelcanbebasedonwhatisobserved.Fortunatelyformodellers,theamountofmicroeconomicdatawhichisavailableisincreasingconsiderablyandopportunitiestorefinemodelsarelikelytobeinreadysupply.

Therelentlessimprovementsincomputerprocessingpoweralsoprovidenewopportunitiestomodeltheeconomyonevermoregranularscales,andwithmorecomplexbehaviours.

Inthefuture,theabilitytoincorporaterealisticbehaviourscouldbeexploitedfurtherasartificialintelligencematures.Thetechniqueknownasmachinelearningiswidelyusedbytechcompaniesto,forinstance,suggestthefilmsthataconsumermightliketowatch.(1)Inthefuture,thesetechniquescouldbeusedto‘train’anartificialagenttobehavelikearealconsumerorfirm.Advancedartificialintelligencecouldmakeagent-basedmodelsmoreLucas-critiqueproofbyhavingagentsrespondrealisticallytonewcircumstances.Aglimpseintowhatispossibleinthisrespectwasgivenrecentlywhenanartificialintelligencerepeatedlybeatatrainedfighterpilotinanair-to-aircombatsimulation(2)—anextremelydemandingscenarioforacomputer.Recentprogressbycomputersatvariousgames,includingGoandJeopardy!addweighttothisargument.

Therearelessexoticwaysinwhichprogressmightbeachieved,forinstancewiththedevelopmentofastandardsetoftoolsforcalibratingandvalidatingagent-basedmodels.Anotherwaytomeetsomeofthecriticismlevelledatthesemodelsisforresearcherstoinvestigatethemostparsimoniousmodelspossiblewhichstillreproduceobservedstylisedfacts.

Withrespecttocentralbanks,therearethreeparticularlypromisingareasofdevelopmentforagent-basedmodelling.Thefirstistheongoingapplicationofmacroeconomicagent-basedmodelstomonetarypolicy.Severalmodelswhichexplicitlyincludecentralbankshavenowbeenestablishedandareonhandtoexaminepolicyquestions.Thesecondisinmodellingthebankingandfinancialsector,todeterminehowfinancialstressistransmittedthroughthesystemasawhole.Third,researchingthepotentialimpactoftheintroductionofacentralbankdigitalcurrencycouldbeexploredusinganagent-basedmodel.Asrecentlydescribed,(3)somespecificationsforacentralbankissueddigitalcurrencycouldhaveconsequencesforfinancialstability.Anagent-basedmodelmaybesuitedforanalysingtheeffectsof

Simulation time (years)0 5 10 15 20 25 30 35 40

House price index

Chart 3 A benchmark run of the model showing boom and bust cycles in the house price index

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 More

Share of total loans, per cent

Loan to income band

Model simulation

PSD data

Chart 4 The model can reproduce the loan to income distribution for the United Kingdom

(1) SeeFriedman,HastieandTibshirani(2001).(2) SeeErnestet al(2016).(3) SeetheBankofEngland’sresearchquestionsoncentralbankdigitalcurrencies,

availableatwww.bankofengland.co.uk/research/Documents/onebank/cbdc.pdf.

thedifferentpossiblespecificationsofacentralbankdigitalcurrency.

Conclusion

Sincetheirinception,agent-basedmodelshavebroughtawealthofinsightstothoseproblemstowhichtheyaresuited.Theyhavefounduseinanastonishinglydiverserangeofsubjects;fromtigerstotraders,fromparticlestopeople.

Thisincludescomplexsystemsgenerally,butparticularlythoseinwhichoutcomesemergefromindividuals’choicesoragentsareheterogeneous.Thishasobvious,usefulapplicationstomodellingtheeconomyandmanyexampleshavedemonstratedhowagent-basedmodelsineconomicscanaidtheunderstandingofempiricallyobservedphenomena.

A‘bottom-up’perspectiveontheeconomyisacompellingcomplement(1)tothe‘top-down’approacheswhicharealreadywidelyused.

Theagent-basedapproachcomeswithdifficultiesofitsown,especiallyaroundtheassumptionsandvalidity,butthefutureholdspromiseintheserespects,partlyduetoeverimprovingtechniquesbutalsobecauseoftheavailabilityofrichdatasetstocalibratethemodelsagainst.

Agent-basedmodelshaveanimportantplaceinunderstanding,andevendesigning,markets,andprovideauniqueplatformforaugmentingpolicymakers’judgementsabouttheeconomy.

(1) SeeFagioloandRoventini(2012).

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