WorkingPaperNo.1099

AStock-FlowConsistentModelofEmulation,Debt,andPersonalIncomeInequality

by

FrancescoRuggeri

UniversityofSalerno

RiccardoPariboni

UniversityofSiena

and

GiulianoToshiroYajima

LevyEconomicsInstitute

October2025

TheauthorswouldliketothankStevenFazzari,RicardoSumma,LucasTexeira,ArielDvoskinandtheparticipantstothe22ndSTOREPConferenceand6thDemandLedWorkshopfortheircommentstoearlierdraftsofthispaper.

Theusualdisclaimersapply.Correspondingauthor:gyajima@

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ABSTRACT

Divergenttrendsinincomeandconsumptioninequality—withthefirstincreasingsubstantiallymorethanthelatter—areanestablished,stylizedfactfortheUSeconomyinthelastdecades.

Thesametimeperiodalsoexperiencedasteadyincreaseinhouseholddebt,plausiblynot

independentfromthepatternsinincomedistributionandconsumptionasmentioned.Inthis

article,wedevelopastock-flowmodelthattriestoreplicatesomeofthesedynamics.We

emphasizetheroleplayedbychangingbehavioralattitudestowardconsumptionanddemandforhouseholdloansbyintroducinganemulationmechanismthatlinksthedesiredconsumptionforhouseholdsofagivenquintilewiththerealizedconsumptionoftheimmediatelysuperior

quintile.Furthermore,weleveragetheavailabledataonincomedistributionquintile

consumption,income,andwealthtoestimatethoseattitudesempirically.Themodel,albeit

simpleandessentialinnature,showstheJanus-likefacesofhouseholddebtandemphasizesthepredator-prey–likedynamicsimpliedbyadebt-ledprocess,inwhichfreshborrowingincreasesaggregatedemandandoutput,whichfeedstheabilitytoborrowandconsumemore;atthesametime,thestockofaccumulateddebt“preys”onincomeduetothecontractionaryforcesofthe

repaymentmechanism.Throughasimpleandstylizedrepresentationofthemultipleinteractionsbetweenincomedistribution,consumption,anddebt,wealsoformalizeandhighlighthowthebenefitsofaprocessofdebt-ledgrowthareasymmetricallydistributedandreinforcethesamedetrimentaltendenciesinincomedistributionthatledtotheemergenceofdebtasanecessary

engineofgrowth.

JELCODES:E12;E21;D31

KEYWORDS:Stock-FlowConsistentModel;PersonalIncomeInequality;Emulation;Debt

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1.INTRODUCTION

Thelastdecadeswitnessedasharpincreaseinhouseholddebt,especiallyin,butnotlimitedto,Anglo-Saxoncountries,bothinabsoluteandindebt-to-incomeratioterms.ParticularlyfromtheonsetoftheGreatRecession,theissuehascometotheforefrontofeconomicdebates(PikettyandSaez2014;Franketal.2014;RanaldiandMilanovi?2022;Bottaetal.2021)andhasbeenwidelydiscussedintheliterature.Partofthisliteraturemulledoveroriginsandcausesof

growingprivateindebtedness,whileseveralothercontributionsexploredtheconsequencesandimplicationsofthisphenomenon.

Amongthemostpopularexplanationsofgrowingindebtedness,thereliesanargumentwhichlinksitwithtrendsinincomedistributionandincomeinequalityobservableinmostadvancedeconomies:inthefaceofstagnatingincomesformiddle-andlow-incomehouseholds,the

attemptto“keepupwiththeJoneses”andmaintainingrainedconsumptionhabits—butalsotosatisfybasicneedsnolongerguaranteedbyashrinkingstate—ledthosesamehouseholdsto

borrowatanincreasingrate.

Ontheotherhand,whenlookingattheoutcomesofthisprocess,atradeoffhasbeenmade

explicitinsomeliterature(ChristenandMorgan2005;Franketal.2014;BertrandandMorse2016):short-rungains—consistinginapartialandtemporaryrelieftotheaggregatedemand-generationproblemsimpliedbyshiftsinincomedistributioninfavorofhigh-incomeandlow-propensitytoconsumesegmentsofthepopulation—wenthandinhandwithlong-runstructuralfinancialinstability,whicheventuallyprovedunsustainable.

Startingfromsomeempiricalfacts,wedevelopastock-flowconsistentmodelthattriesto

replicatesomeofthedynamicsinplace(mostly)inAnglo-Saxoneconomiesduringthe20yearsleadingtotheGreatRecession.Inthemodel,weemphasizetheroleplayedbychanging

behavioralattitudestowardconsumptionanddemandforloansbyhouseholdsbyintroducinganemulationmechanismthatlinksdesiredconsumptionofagivenquintile’shouseholdswiththerealizedconsumptionoftheimmediatelysuperiorquintile.Furthermore,weleveragethedataavailabilityforconsumption,incomeandwealthforquintilesofincomedistributiontoestimate

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thoseattitudesempirically.Themodel,albeitsimpleandessentialinnature,showstheJanus-likefacesofhouseholddebt:borrowingtofinanceconsumptionincreasesthelevelofaggregate

demandandoutput,but,atthesametime,freshborrowingincreasesthelevelofthestockof

debt.Thestockofdebtexertsacontractionarypressureonaggregatedemand,because

repaymentaffectsmoneybalancesandtransfersresourcesfromhighpropensitytospendagentstolowpropensitytospendones.Theinteractionofthesephenomena,hence,createsasortof

“predator-prey”typedynamic,inwhichfreshborrowingincreasesincome,whichfeedsthe

abilitytoborrowandconsumemore;atthesametime,thestockofaccumulateddebt“preys”onincome,duetothecontractionaryforcesoftherepaymentmechanism.Interestingly,our

model—andthesimulationsbasedonit—iscapableofmimickingafeaturethathas

characterizedtheUSeconomyinthelastdecades—namely,adivergenceinthepatternsof

incomeandconsumptioninequality.AshasbeenrecentlyemphasizedandrestatedbyMeyerandSullivan(2023),thesubstantialincreaseintheformerhasbeenmatchedbyamuchmilderriseinthelatter.Throughoutthisarticle,weproposeananalyticalexplanationforthis,basedonlowerquintilehouseholds’emulativebehaviorcumindebtedness,whichwebelievecantellatleastapartofthefullstory.

Ourmodelhasobviouslimitations:forexample,thebehaviorofthefinancialsectorishighly

simplified.Nevertheless,thestylizedtheoreticalconstructionwedevelopprovidesanovel

perspectiveontheinteractionsbetweenincomedistribution,consumption,anddebt,moving

beyondexistingcontributions.Inparticular,weformalizeandhighlighthowthebenefitsofdebt-ledgrowthareasymmetricallydistributed,reinforcingthesameregressivetendenciesinincomedistributionthatmadedebtanecessaryengineofgrowthinthefirstplace.Crucially,unlike

muchofthepreviousliterature,ouranalysisisempiricallycalibratedtoUSdata,whichallowsustobridgetheoreticalinsightswithobservedmacroeconomicdynamics.Inthisway,weadd

explanatorypowertoongoingdebatesonthelinkbetweeninequality,householdborrowing,andmacroeconomicinstability.

Thepaperisstructuredasfollows:Section2showsstylizedfactsaboutthedynamicsofdebt,

consumption,income,andwealthinequalityintheUStoprovideasnapshotofthereal-world

trendsthatmotivatedthiswork.Section3offersaconcisereviewoftheliterature,whileSection

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4introducesourmodel.InSection5wediscussthecalibrationofourmodelandperformsomesimulations.Section6presentssomescenarioanalysisandSection7concludes.

2.STYLIZEDFACTS

Aheavilyskeweddistributionofincomeandwealthisastructuralandwell-knownfeatureoftheUSeconomy,extensivelyscrutinizedanddiscussedintheliterature.Afewstylizedfactshelp

capturetheessenceofthephenomenon.Forexample,bylookingatdisposableincomeandnetwealthsharesbyquintiles,itcanbenotedthatthebottom20percentofthedistribution

consistentlyreceived,overthelastthreedecades,onlyaround5percentofthetotal,whilethetopquintilehasbeenabletoappropriateabouthalfoftotaldisposableincomeandagrowingshareoftotalnetwealth,sittingat70percentaccordingtothelatestavailabledata.

Figure1.DisposableIncomeSharesbyQuintile

Source:BLS,BEA,FRB

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Figure2.NetWealthSharesbyQuintile

Source:BLS,BEA,FRB

Analternativeandcomplementarywayofvisuallyinspectingthesamedynamicsinvolves

lookingattheratiobetweenthedisposableincomeofthetopquintiledividedbythedisposableincomeoftheotherquintiles,asitisshowninfig.3.Itresultsfromthelatter,forexample,thattheaggregatedisposableincomeofthetop20percenthasbeensteadilyincreasingwithrespecttothatofthebottom20percent,settlinginthelastyearsataproportionofmorethan16to1.

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Figure3.DisposableIncomeTop20%—Bottom20%RatiobyQuintile

Source:BLS,BEA,FRB.Note:Indexis100forBottom20percent

Adifferentpictureemerges,however,whenrepeatingthesameexercisewithconsumption

insteadofdisposableincome.AscanbeseeninFigure4,consumptionofthetopquintile

comparedtothatofthebottomdisplaysamorestablepattern—albeitwithoscillations—atmuchlowerlevels.

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Figure4.ConsumptionTop20%-Bottom20%RatiobyQuintile

Source:BLS,BEA,FRB.Note:Indexis100forthebottom20percent

Unsurprisingly,amirrorimageofwhathasjustbeendescribedisofferedbytheratioof

consumptionoverdisposableincome(seeFigure5):thelowerquintileconsumesmorethan

twiceitsdisposableincome,andtheratioislowerthehigherwemoveupthedistributionladder.

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Figure5.ConsumptiontoDisposableIncomeRatiobyQuintile

Source:BLS,BEA,FRB

Thereisnoprizeforguessinghowhouseholdsinthelowestquintilecanaffordsimilarpatternsofconsumption.Figure6—outstandingliabilitiesoverdisposableincome—showsapeakfor

indebtednessofthebottom20percentattheonsetoftheGreatRecessionandasubsequent

slowlydecreasingtrend,butthemagnitudeisstilljustslightlybelow120percentofdisposableincome.

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Figure6.DebttoDisposableIncomeRatiobyQuintile

Source:BLS,BEA,FRB

Additionally,outstandingliabilitiesofthebottom20percenthavegrownoverthelast35yearsatamuchfasterpacethanthoseofthetop20percent(seeFigure7),ascanbeinferredfromthe

behavioroftheratiobetweenthelatterandtheformer.

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Figure7.DebtTop20%-Bottom20%byQuintile

Source:BLS,BEA,FRB.Note:Indexis100forthebottom20percent

3.LITERATUREREVIEW

AftertheGreatRecession,differentstudieshavediscussedtheimportanceofhousehold

spendingdecisionsingeneratingthedynamicthatshapedthefinancialcrisis(MianandSufi

2017;2018).Consistentwithwhathasbeenarguedextensivelyintheliterature(seevanTreeck[2014]foranexhaustivesurveyoftheliterature),webelievethatatleastaportionofthisprocesscanbeexplainedbylookingattheunderlyingtrendsinincomeinequalitybrieflyhintedatintheprevioussection.Thatisnot,however,theendofthestory,giventhatshiftsinincome

distributioncouldnotexplain—bythemselves—whathappenedtoconsumptionintheUSinpast

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decades.Thisimpliestheneedtomoveonfromatreatmentofaggregateconsumptionasa“passive”variable,whichissimplyafunctionofincome,wealthandtheirdistribution.

Severalworksanalyzehowhouseholdspendingcanbelargely“independent”fromincome.Theconceptofa“passiveconsumptionfunction”makessensewhenhouseholdsfacea“hardbudgetconstraint,”asituationinwhichhouseholdscanrelyjustontheirincomeandontheirpast

savingstospend.However,ifhouseholdshavetheoptiontoborrowtofinancetheiroutlays,thepictureisradicallydifferent.Inthiscase,theconsumptionfunctionbecomes,toacertainextent,independentofincomeandcanbeinfluencedbyothervariableslikehouseholds'willingnesstoborrow,thewillingnesstolendbythefinancialsector,householdwealth,and“peereffects.”

Startingfromthis,weproposeanexplanationofthepathsofconsumption,savingandborrowingofthehouseholdsectorintheUSbasedonasomewhattraditionalbutalsorelativelyneglectedviewofhoweconomicagentsmakedecisions.

FollowingtheinsightofDuesenberry(1949),wetreathouseholddecisionsaboutconsumptionandsavingasinfluencednotonlybytheirownincomeandwealth(andtheattempttomaximizetheirownutility),butasshapedbyotherfactors,suchastheconsumptionpatternsof“others.”Hence,consumerspurchaseproductsnotonlyfortheirfunctionalutilitybutalsofortheirsocialmeaning.Thisalsoresonateswiththeconceptofconspicuousconsumption,ascanbefoundintheclassicworkofVeblen(1975)[1899],whichunderlinedoveracenturyagotheindividuals'concernsaboutthesocialvisibilityofconsumptionandthepresenceofastrongpropensityforstatusconsiderations.Consumption,accordingtothisview,nolongerhasthesimpletaskof

satisfyinganindividual'smaterialnecessities,butalsobecomesasignaloftheadherencetobothacertainsocialstructureandacommongroundofvaluesandhabits.Furthermore,inacontextofextremelyfragmentaryinformationandheavyuncertainty,households’behaviorwouldbe

drivenbysocialnormswhicharemostlydeterminedbythehabitsandthebehaviorofthereferencegroups,ingeneralconstitutedbywealthierandmoresuccessfulhouseholds.

Thisinterpretationofconsumers’decisionshasbeendiscussedbyseveralauthorssuchasFrank,Levine,andDijk(2010),BertrandandMorse(2016),andChristenandMorgan(2005),justto

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mentionafew.Frank,Levine,andDijk(2014)usetheterm“expenditurecascades”todescribethebehaviorofagentswhorespondtochangesinconsumptionpatternsofthoseabovethembychangingtheirownconsumptionpattern:“Increasedexpenditurebysomepeopleleadsothers

justbelowthemontheincomescaletospendmoreaswell,inturnleadingothersjustbelowthesecondgrouptospendmore,andsoon”(Franketal.2014,57).

Fortheauthors,people'sevaluationsofwhattheyconsumeareheavilydependentoncontext.

Modificationsinonegroup'sspendingshifttheframeofreferencethatdefinesconsumption

standardsforothersjustbelowthemontheincomescale,leadingtoarippleeffectofincreasedexpendituredowntheincomeladder.Theveryconceptofexpenditurecascadesisrootedin

Duesenberry’s(1949)relativeincomehypothesis,whichexplicitlyacknowledgesthat

individualscomparetheirconsumptiontothatofothers.WhileforDuesenberrythecomparisoneffectisgeneral,fortheauthorsdiscussedabove,peopletendtolooktothoseabovethemontheincomescaleratherthanthosebelowwhenformingtheirconsumptionstandards.Therefore,

whenahigher-incomegroupincreasesitsspendingoncertaingoods(e.g.,largerhouses,moreexpensivecars,etc.),thisraisestheperceivedstandardofwhatisconsideredadequateornormalforthegroupjustbelowtheminincome.Tokeepup,ortoavoidfeelingdeprivedrelativetothisnewstandard,thesecondgroupalsotendstoincreasetheirspending.Thisprocesscontinues,

witheachincreaseinspendingbyoneincomegroupinfluencingthespendingofthegroupjustbelowit,creatingacascadeofexpenditurethroughouttheeconomy.

Movingalongsimilarlogicallines,BertrandandMorse(2016)introducetheconceptof“trickle-downconsumption”andshowhow,sincetheearly1980s,growthinlocalinequalityhasbeen

associatedwithachangeinconsumptionofthelowerpartoftheincomedistribution,asnon-richhouseholdsrampuptheirconsumptiontokeepupwithwealthierneighbors.

ChristenandMorgan(2005)arguethatincomeinequalitycreatestheneedforlow-income

householdstousedebtinordertokeeptheirconsumptionlevelsuprelativetowealthier

households.Accordingtotheauthors,insteadofrelyingonaprocessofutilitymaximization,householdstendtobedrivenandinfluencedbytheconsumptionhabitsofthoseabovethemintheincomedistributionrankingorofthosewhorepresentaparticularsocialreference.Inthis

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context,whatisdefinedasacceptableinschool,housing,clothing,transportation,andother

categoriesdependsonhowmuchothersspend,withconspicuousconsumptiondynamicsthat

createa“positionalarmsrace,”sinceitestablishescontinuouslyevolvingnew,andmore

expensive,referencepoints.Sinceindividualsstrivetoimproveormaintaintheirsocialstanding,consumptionbecomesatooltosignaltheeconomicstatustokeepupwiththesocialcompetition.Inthiscontext,adynamicofpersistentlyunequalincomedistributioncanexacerbatethis

positionalconsumptionrace,withanimpactonthedynamicofdemandintheshortandlongruns.

Inordertoprovideananalyticalinfrastructuretotheintuitionswehavebrieflymentionedsofar,werelyonstock-flowconsistentmodeling.Themainreasonisthatthisclassofmodelsis

particularlyapttostudytheimpactoffinancialvariables—thinkof,forexample,thestockofdebt—ontherealsideoftheeconomy(BarwellandBurrows2014,45).Stock-flowconsistent(SFC)modelsconstructanaccountingframeworkthatsystematicallyrecordsallrelationshipsbetweensectors,flows,andstocks.Buildingonthisstructure,behavioralequationsand

accountingidentitiesareintroducedinsuchawaythatconsistencyisensuredbetweenthe

behaviorofflows(suchasincome,consumption,andinvestment)andthedynamicsofstocks(suchaswealthanddebt),ensuringeveryflowhasacounterpartandthatnothingdisappearsfromthesystem

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(NikiforosandZezza2018).

DifferentSFCmodelshavebeendevelopedtodescribetheinteractionofrisingincome

inequality,financialdevelopmentandchangingattitudestowardexpenditure.Kapellerand

Schutz(2014)presentanSFCmodelwherebytheinteractionbetweenhouseholds’“conspicuousconsumptionnorms”andbanks’looseningcreditstandardscangenerateinstability—thatis,a“Minsky–Veblencycle.”Detzer(2018)usesanopeneconomySFCmodeltodescribehow

1Wecansummarizethemaintenetsofstock-flowconsistentmodellingbyrelying,onceagain,onNikiforosandZezza(2018):1.Flowconsistency:Everymonetaryflowcomesfromsomewhereandgoessomewhere.Asaresult,thereareno“blackholes”inthesystem;2.Stockconsistency:Thefinancialliabilitiesofanagentorsectorarethefinancialassetsofsomeotheragentorsector;3.Stock-flowconsistency:Everyflowimpliesthechangeinoneormorestocks.Asaresult,theend-of-periodstocksareobtainedbycumulatingtherelevantflowsandtakingintoaccountpossiblecapitalgains;4.Quadrupleentry:Thesethreeprinciples,then,implyafourthone:thateverytransactioninvolvesaquadrupleentryinaccounting.Forexample,whenahouseholdpurchasesaproductfromafirm,theaccountingregistersanincreaseintherevenuesofthefirmandtheexpenditureofthehousehold,andatthesametimeadecreaseinatleastoneasset(orincreaseinaliability)ofthehouseholdandcorrespondinglyan

increaseinataleastoneassetofthefirm.

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unequalincomedistributionandfinancialderegulationhaveshapeddifferentgrowthregimes,whoseinteractionsledtotheglobalimbalancesthatprecededtheGreatRecession:thedebt-ledgrowthregimes,whereprivatedebt,thusthefinancialsector,isthemaindriveroftheeconomicactivity,andanexport-ledgrowthregimes,wherecurrentaccountsurplusesspurgrowth.

Carnevalietal.(2024)followDetzerindescribinghowtheinteractionbetweenthesetwotypesofeconomycancreatefinancialinstability.Belabedetal.(2018)useathree-country(US,China,andGermany)SFCmodel.

Boththeexport-ledgrowthoftheeconomiesofChinaandGermanyandthecredit-ledgrowthoftheUSeconomy(beforetheGlobalFinancialCrisis)aregeneratedbyabottom-upredistributionofdomesticincomes.Ruggeri(2023)usestheSFCframeworkinaclosedeconomytostudyhowtheinteractionbetweentwoclassesofhouseholds,banksandthehousingmarketcangenerate

fluctuationsthatresembletheonedescribedbythefinancialaccelerator.Lu(2025)developsanempiricalSFCmacroeconomicmodelfortheUKtomonitorhouseholddebtdynamicsunder

differentscenarios,includingthehousing-creditreinforcingcycle.Inasimilarvein,ByrialzenandRaza(2020)buildalarge-scaleSFCmodeltodiscusstheroleofhouseholddebtwithintheDanisheconomy.Szymborska(2022)showshowthecompositionofUShouseholdbalance

sheetshaschangedovertime,withwealthierhouseholdsgainingmorefromfinancialasset

growthwhilelower-incomegroupsremainheavilyindebted.Gobbietal.(2024)highlighthowunconventionalmonetarypolicies,suchasquantitativeeasing,tendtobenefittherichby

inflatingassetprices,thusreinforcingexistingwealthinequalities.Furthermore,ABM-SFC

modelsincorporatinghouseholdheterogeneityandsocialnormsexplorehowindividual

behavior,shapedbypeereffectsandincomedistribution,influencesmacroeconomicdynamics.Cardaci(2018)andCardaciandSaraceno(2019)showhowstatus-drivenconsumptioncan

amplifyinequalityandfinancialfragility.

Fierroetal.(2023)andBottaetal.(2021)furtherintegrateadaptiveagentbehaviorintoSFC

frameworks,highlightinghowsocialcomparisonsandheterogeneousexpectationsaffect

consumption,indebtedness,andeconomicstability.Therelationshipbetweenautonomous

demandanddebtaccumulationhasbeenalsoexploredintheliterature.Pariboni(2016)buildsasupermultipliermodeltostudythesustainabilityofdebt-drivenautonomousconsumption,while

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Pedrosaetal(2023)useanSFCsupermultipliermodeltostudyhowdifferentdebt-driven

autonomousdemandscomingfromthegovernmentandthehouseholdsectorimpactgrowthandfinancialstability.DiBucchianicoetal.(2024)buildasupermultipliermodelinwhichgrowthisdrivenbyworkers’debtaccumulationaswellasrentiers’consumptionoutofinterest.AvritzerandBrochier(2025)buildamodelwheredebt-financedhouseholdautonomousconsumption

drivesgrowthtostudythestabilityconditionofthesegrowthdynamics.

4.MODELDESCRIPTION

StartingfromthestylizedfactspresentedinSection2,wewanttodiscusshowthedemand

generationprocesscomingfromthehouseholdsectorintheUScanbeexplainedbychanging

attitudestowardconsumption,savingandthedemandforcredit,andhowthesedynamicscan

haveaneffectonpersonalincomeinequalityandgrowth.Inthissection,wepresentastylizedmodelofaneconomythatisdemand-ledbothintheshortandinthelongrun.Ourfocusis,in

particular,ontheroleplayedbythedebt-financedconsumptionofaportionofthehousehold

sectorinshapingtheevolutionoverthelongrunofoursimpleeconomy.Thelatter,asdescribedinthemodel,iscomposedofthreesectors:households,firms,andbanks.Thehouseholdsectorissplitintoincomequintiles.Eachquintilereceivesfourkindsofincomes,namelywages,

distributedprofitsfrombothfinancialandnon-financialcorporationsandinterestincomefromtheiraccumulatedstockofassets.

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Table1:TransactionFlowMatrix

Households

Firms

Banks

Su

m

Q1Q2Q3Q4Q5

Current

Capital

Consumption

Investment

-cq1-cq2-cq3-cq4-cq5

-ct

+I-I

0

0

Wages

Firms,

profits

Banks

profits

Intereston

Assets

Liabilities

+INTaq1+INTaq2+INTaq3+INTaq4+INTaq5-INTlq1+INTlq2-INTlq3-INTlq4-INTlq5

-INTlf

-INTa

+INTl

0

0

Changeinthe

stockof

Assets

Liabilities

-Δaq1-Δaq2

+Δlq1+Δlq2

-Δaq3

+Δlq3

-Δaq4

+Δlq4

-Δaq5

+Δlq5

+Δlf

+Δa

-Δl

0

0

Sum

000000000

Source:ownelaboration

Wedramaticallysimplifiedtheflowofthefunds-sideoftheeconomy.Thus,theonlyfinancialassetsandliabilitiesoftheeconomyaremadeupofbanks’depositsandloans.Moreover,

householdsownbothfirmsandbanksandreceivedividendsfromthem.Thepricelevelisassumedconstantacrossallperiods.

Aggregateoutputismade,fromtheincomeside,bythesumofincomesreceivedbyallquintiles,

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grossofundistributedprofitsandconsumptionoffixedcapital(depreciationallowances).

1.Y=ΣYDqx+Πuf+DA

Fromtheexpenditureside,aggregateoutputismadeofaggregateconsumptionandfirms,productiveinvestment.

2.Y=Σcqx+I

4.1Households

Eachquintile,s(qx)consumptiondemandisdrivenbydisposableincomeandtheaccumulatedstockofwealth,andhasanautonomouscomponent(c0qx),asshowninequation(3).

Consumptioninexcessofdisposableincomeisfinancedbyloansfromfinancialintermediaries(equation4).

3.cqx=c0qx+αqxYDqx+βqxwqxt-1

4.Lqx=Lqx-1+cqx一YDq

Thefoursourcesofincomeinoureconomyaredescribedbyequation(6).Conversely,

householdsbuildupsavingsifdisposableincomeisinexcessofconsumptiondemandasseeninequation(5).

5.wqx=wqx-1+YDqx一cqx

6.YDqx=wBqx+INTAqx+Πfqx+ΠBqx一INTLqx

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Thosesavingsareinvestedintheonlyinterest-bearingassetavailableintheeconomy,namelytimedeposits(equation7).Networthismadeupofthoseassetsnetoftheoutstandingstockofliabilities(loans,equation8).

7.Wqx=Dqx

8.NWqx=Dqx-Lqx

4.2Firms

Grossbusinessinvestmentiscompletelyinducedbyincome(asinSerrano1995;Cesarattoetal.2003;FreitasandSerrano2015),asshowninequation(9).Firms’profitsareequaltothesumoftheinflowsfromconsumptionbyhouseholds(cqx)andInvestment(I),minustheoutflows

representedbythewagespaidtoemployees(WBqx)andtheinterestonloans(INTLfqx).

9.I=hy+DA

10.ΠF=Σcqx+I-WBqx-INTLfqx

Theinvestmentshareofoutput(netofdepreciation)isgivenbyequation(11)andreactsto