Regional President Speech

SOCIAL LEARNING FOR THE MASSES JamesBullard FederalReserveBankofSt. Louis Computational&ExperimentalEconomicsWorkshop SimonFraserUniversity Feb. 4,2023 Vancouver,BritishColumbia AnyopinionsexpressedhereareourownanddonotnecessarilyreflectthoseoftheFOMC. 1 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS Introduction 2 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS THE INTELLECTUAL LEGACY OF JASMINA ARIFOVIC JasminaArifovic(JA)wasapioneerintheapplicationofartificialintelligenceto macroeconomics,helpingustogaininsightintothequestion,“Howisequilibrium achieved?” JAideaswillbeevenmoreimportantinthedecadesaheadasmacroeconomistswork withmoreandmoregranularmodels: moreagents,moredetails,moreshocks,more frictions. Thispaper: Howisequilibriumachievedinthesemorecomplexenvironments? Anearlierandmorepreliminaryversionofthistalkwasgivenunderthetitle “ConjecturesonLearninginKrusell-Smith-typeEconomies”atthe2021BankofCanada AnnualEconomicConferenceonNov.10,2021. 3 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS A MORE COMPLEX ECONOMY IstudyastylizedDSGEheterogeneousagentlifecyclemodelwithaknown competitiveequilibriumfeaturingGinicoefficientsclosetothoseintheU.S.data. Themodelfeaturesthreeaggregateshocksaswellasidiosyncraticrisk,butalso featurespoliciesthatcanmitigateboththeaggregateriskandtheidiosyncraticrisk. Awelfaretheoremstatesthesenseinwhichthesepoliciescanachieveanoptimal allocationofresources. Thesubtextinthistalkisthatmodelsinthisclassrepresent,broadly,thecurrentand futuredirectionofmacroeconomics,andthatthelearningliteraturewillhavetocontinue torefinemethodstoprovideinsightfortheseenvironments. 4 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS LEARNING Ithenturntodiscusshowagentsmightlearninthisrelativelycomplex macroeconomicsettingifagentbehaviorisatsomepointdisturbed. IwillconcludethatsociallearningaspromotedbyJasminaArifovicislikelyto providethebestpathforward. Unmodifiedconceptsofeconometriclearningpromotedandstudiedextensivelyinthe existingliteraturearelesslikelytobeappropriateinthisenvironment. 5 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS Core argument 6 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS AN OLDER TRANSITION TIME RESULT Supposetheeconomyisinitiallyonabalancedgrowthpathbutissuddenly disruptedbya“one-time,large,unanticipatedshock.” Thisshockisaboveandbeyondtheshocksenvisionedwithintheambientstochastic environmentofthemodel. Tofixideas,thinkofanunanticipated“financialcrisis”oranunanticipated“pandemic.” Inarelatedclassofhetergeneousagentmodels,anearliergenerationofquantitative studyemphasizedperfectforesighttransitiontimesfollowingadisturbanceofthis type. Thatliteraturefoundthattransitiontimesarelong—measuredinyearsor decades—inthisrelatedclassofmodels. 7 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS WHY SLOW CONVERGENCE? Theslowconvergencewasbecausethedisruptedagentsexperiencingtheshock wouldhavetocompletetheirlifecycleandexitthemodelbeforethelong-run balancedgrowthpathcanbeachieved. Takenliterally,onemightconcludethatactualmacroeconomiessubjecttooccasional “large,unanticipatedshocks”wouldnearlyalwaysbeintransition,evenif householdshadrationalexpectationsfollowingthelargeshock. Examples:AuerbachandKotlikoff(DynamicFiscalPolicy,1987);seealsoCogleyand Sargent(JME,2008)inwhichthelargeshocktwiststhepriorsofaBayesianlearnerand leadstoslowlearningoversubsequentdecades. 8 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS RELATIVELY FAST CONVERGENCE IN THE U.S. DATA IwillcalibratetheDSGEmodelusedinthispapertoU.S.dataassumingU.S. macroeconomicpoliciesareinfacttheoptimalonesthemodelrequires. IwillthenprovideprimafacieevidencethatactualconvergencetimesinU.S. economicdatafollowinga“large,unanticipatedshock”areanorderofmagnitude shorterthanintheearlierliterature. Inparticular,thesetransitiontimesaremeasuredinquartersratherthanyearsor decades. 9 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS SOCIAL LEARNING FOR THE MASSES Thissuggeststhatinreality,theU.S.economy—despiteitscomplexity—doesnot seemtofollowthetypesofslowadjustmentpathsemphasizedinsomeoftheearlier literature. IwillsuggestthattherapidconvergenceobservedintheU.S.datacouldoccurif thereissubstantialcommunciationacrossthesociety—sociallearningas implementedbyJA. IntheeconomyIdescribe,thiscanoccurbecausetherearemanymillionsofagents thathavealreadylearnedandretainedthe“DNA”ofoptimaldecisionrulesfor consumption,assetsandhoursworkedbeforetheshockoccurred. Otheragentsthatmaynotknowthesedecisionrulescanlearnrelativelyquicklyfrom thosethatdo. Icallthisphenomenon“sociallearningforthemasses.” 10 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS Environment 11 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS ENVIRONMENT BASICS Ateachdatet,anewcontinuumofhouseholdsenterstheeconomy,makeseconomic decisionsoverT+1=241dates,thenexitstheeconomy. (Tofixideas,thinkof≈1m agentsperquarterlycohort.) Thiscorrespondstoanagententeringtheeconomyasadecision-makeratage20and exitingasadecision-makeratage80,inclusiveofendpoints,andmakingeconomic decisionsataquarterlyfrequency. ResultsareperfectlygeneralforthechoiceofT,withhighervaluescorrespondingto decision-makingatmorefrequentintervals. Thisclassofmodelshasa“paper-and-pencil”equilibriumsolution,andsoit providesasimplebenchmarkmodelforheterogeneous-agentmacroeconomieswith aggregateshocks. 12 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS RISKS FACED BY HOUSEHOLDS Therearebothaggregateriskandidiosyncraticrisk. Idiosyncraticriskisborneasaproductivity-profilescalingshockastheagententers theeconomy,andalsointheformofsimplei.i.d.unemploymentriskateachdate. Monetaryandfiscalpolicymakersprovideaformofinsuranceagainsttheaggregate risk,andalabormarketauthorityprovidesunemploymentinsurance. Theidiosyncraticriskborneastheagententerstheeconomyviathe productivity-profilescalingshockisuninsurable. Awelfaretheoremdescribesthesenseinwhichtheequilibriumstudiedhere representsafirst-bestallocationofresources. 13 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS ASSETS Therearethreenominallydenominatedassets: privatelyissueddebt,publiclyissued debtandcapital. WethinkoftheseasrepresentingU.S.datacounterparts: (1)mortgage-backed securities(MBS),(2)federallyissueddebtand(3)physicalcapital,respectively. IntheU.S.data,MBSnetout,butfederallyissueddebtandphysicalcapitalarein positivenetsupplyandwetargetavalueoftheassets-to-GDPratioequalto 1.23+3.32=4.55. 14 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS NOMINAL CONTRACTING Thecreditmarketfrictionisnon-statecontingentnominalcontracting(NSCNC):All debtcontractsarestatedinnominalterms,withastatednominalinterestrate,and repaymentisnotstate-contingent. Theroleofmonetarypolicyistoadjustthepriceleveleachperiodinordertoconvert thesenominal,non-statecontingentcontractsintoreal,state-contingentcontracts. 15 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS HOUSEHOLD TYPES Householdtypes: “lifecycle”(LC)and“hand-to-mouth” (HTM). Thelife-cyclehouseholdsareassignedahump-shapedproductivityprofileatthe beginningoftheirlifecycle. Accordingly,theyneedtousecreditmarkets(hold assets)tosmoothlife-cycleconsumption. Thehand-to-mouthhouseholdsareassignedaperfectlyflatproductivityprofileas theyentertheeconomy. Accordingly,theyneverneedtousecreditmarketsand insteadconsumetheirlaborincomeeachperiod. 16 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS ATTAINING THE CORRECT ASSET LEVEL TheeconomywithonlyLChouseholdswantstoholdassetsequaltoA/4Y=5.71,a valuewhichisconsiderablyhigherthanthevalueobservedintheU.S.data,whichis 4.55. TheeconomywithonlyHTMhouseholdswouldbe“Spartan,”andwouldholdno assetsatall. WewilladjustthefractionofHTMhouseholdsinordertomatchtheassets-to-GDP ratiointheU.S.data. 17 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS PREFERENCES Eachhouseholdi∈ (0,1)enteringtheeconomyatdatethaspreferences(thesamefor bothLCandHTMtypes) T ∑ U = [ηlnc˜ (t+s)+(1−η)lnℓ (t+s)]. t,i t,i t,i s=0 Wedefinec˜ (t+s) =D(t+s)c (t+s),whereD(t+s)isthestateofaggregate t,i t,i demandatdatet+s.Thestateofdemandevolvesas D t = δ(t−1,t)D t−1 , whereδ(t−1,t)isthegrossgrowthrateofdemand,whichfollowsanappropriate stochasticprocessthatkeepsD(t) >0∀t. 18 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS PRODUCTIVITY PROFILES Agentsenteringtheeconomydrawascalingfactorxfromalognormaldistribution andreceiveaproductivityprofilethatisascaledversionofabaselineprofile,e : s e =x·e , s,i s whereforLCagentseLC =1+p exp (cid:20) − (cid:16) s−p2 (cid:17)4 (cid:21) ,andwherep ,p andp are s 1 p3 1 2 3 chosentomatchcalibrationtargetsgivenbelow,andforHTMagents eHTM =h(1/T)∑T eLCwhereh∈ (0,1). s s=0 s Huggett,VenturaandYaron(AER,2011)arguethatdifferencesininitialconditionsare moreimportantthandifferencesinshocksforlifetimeearnings. Wethinkofallendowmentsateachdateascontaininglinearlabortaxfactor(1−τu), withτusetforallhouseholdsineachcohortbythelaborauthoritytofundunemployment insurance.Thistypeoftaxwillnotdistortlaborsupplyinthismodel. 19 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS TECHNOLOGY AggregaterealoutputY(t)isgivenby Y(t) = [D(t)Q(t)N(t)]1−αK(t)α[L(t)]1−α , (1) whereK(t)istherealvalueofthephysicalcapitalstock,L(t)istheaggregate effectivehumancapitalsupply(hours×productivityofvarioushouseholds),Q(t)is aproductivityindex,N(t)indexesthesizeofthelaborforce,andD(t)isthestateof aggregatedemand. Q,NandDgrowatstochasticgrossratesλ,νandδrespectively. Theseassumptionsmeanthatrealoutputgrowsatthestochasticrateλνδeachperiod. TheaggregatedemandassumptionisasimpleversionofBai,R´ıos-RullandStoresletten (unpublished,2019). Thelaborforcegrowthassumptionaffectsallcohortsproportionatelyandcanbe interpretedas“immigration.” 20 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS NOMINAL CONTRACTING AND TIMING PROTOCOL Undertheassumptionsoutlined,thecontractnominalinterestrateisgivenby Rn(t,t+1)−1 =E (cid:20) c˜ t,i (t) P(t) (cid:21) . (2) t c˜ (t+1)P(t+1) t,i Thetimingprotocolis: (1)Natureassignsnewentrantproductivityprofilesandalso drawsaggregateshocks;(2)Thefiscalauthorityissuesnominaldebt;(3)The monetaryauthoritysetsthepricelevel;(4)Householdschoosedatetconsumption, hoursworkedandnetassetholding. Householdswillbeabletomakedatetdecisionswithoutreferencetofuture uncertainty,asthemonetarypolicymakerisprovidingatypeofperfectinsurance. 21 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS THE FISCAL AUTHORITY Thefullycrediblenominaldebtissuanceprocessisgivenby B(t) =Rn(t−1,t)B(t−1), (3) whereB(t)isthetotallevelofnominaldebtandB(0) >0. Thefiscalauthorityisissuingenoughnewdebttomaintainthelevelofassetsinthe economyattheappropriatelevel. 22 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS THE MONETARY AUTHORITY Themonetaryauthoritycontrolsthepriceleveldirectlyandimplementsaprice-level pathcriterion Rn(t−1,t) P(t) = P(t−1). (4) δ(t−1,t)λ(t−1,t)ν(t−1,t) Thiscriterionimplementscountercyclicalprice-levelmovementsrelativetothe expectationembodiedinthecontractrateRn(t−1,t). SeeKoenig(IJCB,2013)andSheedy(BPEA,2014)onNGDPtargeting. SeeAndolfatto,etal.(unpublished,2021,p.14)foradiscussionofhowthiscriterion relatestoasimilarNewKeynesian“targetingcriterion”developedbyGiannoniand Woodford(2004,pp.101-2). 23 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS COMPETITIVE EQUILIBRIUM AND SOCIAL WELFARE Solution: Guessandverifythatthereisacompetitiveequilibriuminwhichthereal rateofinterestisalwaysequaltothestochasticrateofrealoutputgrowth. The“Wickselliannaturalrealrateofinterest”forthiseconomy. Asocialplannerwouldconcludethattheallocationofresourcesisasocialoptimum provided(i)theplannerplacesequalweightonallhouseholdsforalltime,(ii)the plannerdiscountsbackwardandforwardintimeatthestochasticrealrateofinterest, (iii)theplannercannotalterthedistributionofproductivityprofileswithinthe cohort,whicharedecidedbynatureatthebeginningofthelifecycle,(iv)theplanner cannotalterthetaxrateτu. 24 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS Calibration 25 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS MAPPING TO THE DATA AdjustcohortsizebasedondatafromtheU.S.CensusBureau. Setthebaselinehump-shapedlife-cycleproductivityprofilesuchthathouseholds endogenouslychoosetoworkthehoursworkedbyageintheU.S.data. Chooseηtomatchaveragetimedevotedtomarketworkacrosstheeconomy. SetthefractionofHTMhouseholds(whodonotholdassets)suchthattheaggregate levelofassetstooutput,A/(4Y),matchestheU.S.data(4.55),withnetassets definedascapital,K/(4Y) =3.32,plusgovernmentissueddebt,B/(4Y) =1.23. Choosethewithin-cohortstandarddeviationsofproductivityforlife-cycleand hand-to-mouthhouseholds,σ andσ ,respectively,toapproachthe lc htm pre-taxes-and-transfersGinicoefficientsforincomeandfinancialwealthintheU.S. data. 26 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS BASELINE LIFE-CYCLE PRODUCTIVITY 1.5 1 0.5 0 60 120 180 240 quarters FIGURE:Baselineendowmentprofileoflife-cycleagents. 27 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS THE MASS OF LIFE-CYCLE PRODUCTIVITY 3 2 1 0 0 60 120 180 240 quarters FIGURE:Themassofendowmentprofiles:life-cycleagents(blue)andhand-to-mouthagentsfor h=0.5(red).Thedashedlinesdenotethe25thandthe75thpercentileoftheendowment distributions. 28 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS HOURS WORKED BY AGE 0.3 0.2 0.1 Data Model 0 0 60 120 180 240 quarters FIGURE:Hoursworkedbyageforlife-cyclehouseholds:U.S.data(blue)andcalibratedmodel(red). 29 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS POPULATION WEIGHTS -3 10 5 4 3 2 Data Smoothed data 1 0 60 120 180 240 quarters FIGURE:Populationweights:U.S.data(blue)and4thdegreepolynomialsmoothed(red). 30 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS ASSETS AND GINI COEFFICIENTS Model U.S.data h 0.50 − σ 1.24 − lc σ 1.03 − htm A/(4Y) 4.55 4.55 G 0.74 0.78 W G 0.66 0.63 Y G 0.62† 0.32‡ C TABLE:Parametervaluesandassociatedassets-to-outputratioandGinicoefficientsinthemodel equilibriumvs.theU.S.data. † TheconsumptionGiniinthemodelisbasedonapre-taxes-and-transfersincomeconcept. ‡ TheconsumptionGiniinthedataisbasedonapost-taxes-and-transfersincomeconcept. 31 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS THE CONSUMPTION GINI Theconsumption(outofpre-taxes-and-transfersincome)Giniinthemodel equilibriumisG =0.62. c IntheU.S.data,theconsumption(outofpost-taxes-and-transfersincome)Giniis0.32, abouthalfaslarge. ThemodelissayingthattheneteffectoftaxesandtransfersintheU.S.dataisenough toreduceconsumptioninequalitybyhalf. Someevidence:UsingGermandata,Haan,Kemptner,andProwse(workingpaper,2018) usealife-cyclemodeltoestimatethatthetax-and-transfersystemissufficienttooffset 54%oftheinequalityinlifetimeearnings. 32 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS MARGINAL PROPENSITIES TO CONSUME SCHEMATIC Life-cycle agents 8 Hand-to-mouth agents 6 4 2 1 0 0 60 120 180 240 quarters FIGURE:Crosssection:Schematicofthemarginalpropensitytoconsumeoutoflaborincomeby cohortforlife-cycleagents.TheMPCdoesnotdependontheendowmentscalingfactor. Hand-to-mouthagentshaveaMPCofone. 33 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS MORE ASPECTS OF EQUILIBRIUM FIT TO U.S. DATA Themodeliscalibratedtomatchhoursworkedbycohortforlife-cyclehouseholds. Heckman: Appropriatelyspecified“wageregressions”willsuggesthourschanges areindependentofrealwagechanges. ThemodelcanbecalibratedtofitU.S.realoutputgrowthexactly,attributingthe growthinparttotechnologicalimprovement,laborforcegrowthuniformacross cohorts,andthestateofaggregatedemand. Themodelpredictsthatconsumptiongrowthwillbeequalizedacrosshouseholdsat differentagesanddifferentincomelevels: economicgrowthgets“sharedout” appropriately. Theincome,wealthandconsumptiondistributionsaremaintainedbyasmoothly operatingcreditmarketwiththecorrectinterestrate. 34 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS Learning 35 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS NOMINAL RETURNS Themodelequilibriumpredictsequalizednominalandrealreturnsforthreeassets underoptimalmonetarypolicy: capital,MBSandTreasuries. Theseassetsarenotfurtherdifferentiatedinsidethemodel. Tocomparewiththedata,weneedanassetrepresentingareturntocapitalina formatwithriskcharacteristicssimilartoMBSandTreasuries. Onecandidateisahigh-qualitycorporatebond. Iwilluseaseven-yearnominalinvestment-gradecorporatebondmetric. Inthe modelandthedata,thistypeofbondhasaseven-yearhorizonbutcanberefinanced eachperiod. 36 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS NOMINAL RETURNS VERSUS NOMINAL OUTPUT GROWTH Themodelequilibriumpredictsthatthenominalreturnontheassetsshouldbeequal tothenominalconsumptiongrowthrate,or,equivalentlyinthemodel,thenominal outputgrowthrate. Thispredictionholdsinperiodsofrelativestabilitywithoptimalmonetary,fiscal, andlabormarketpolicy. Inthesecircumstancestheprivatesectorisabletosetnominaldebtcontractsrelying onthemonetaryauthoritytosetthepricelevelthatratifiesthosedebtcontracts ex-post. 37 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS LARGE UNANTICIPATED SHOCKS IwillarguethattheU.S.economyhasbeendisturbedbytwolargeunanticipated shockssince2005: (1)theglobalfinancialcrisis(GFC),and(2)theglobalpandemic. Formypurposes,theseeventsaresimply“largedisturbances”outsidethescopeof thismodel. Theinterimperiod,2011-2019,fitsthemodelassumptionsbetterandwemayexpect themodeltoprovideabetterfittothedataduringthistimeframe. ItdoesnottakelongfortheequilibriumconditionstobemetaftertheGFC. 38 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS MODEL VERSUS U.S. DATA Percent 30 Nominal consumption growth Lewis-Mertens-Stock index + core PCE inflation 20 7-yearhigh-qualitybondyield The economy has returned to equilibrium 10 0 -10 Disturbances -20 Jan-05 Jan-08 Jan-11 Jan-14 Jan-17 Jan-20 FIGURE:In”normaltimes,”nominalconsumptiongrowthandnominalyieldsareclose,aspredicted bythemodel. 39 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS WHAT THE CHART SHOWS MeasuresofU.S.nominalconsumptiongrowthandnominalGDPgrowthona 12-monthbasisareapproximatelyequaltothenominalreturnona7-yearhigh qualitycorporatebondbetween2011and2019,aspredictedbythemodel equilibrium. However,nominalgrowthratesandinterestratesareconsiderablydifferentduring large,unanticipatedshocksliketheGFCandthepandemic. Thechartsuggeststhattheconditionsofmacroeconomicequilibriumwere re-establishedrelativelyquicklyaftertheGFC,andalsoappeartobeclosetobeing re-establishedfollowingthepandemic. 40 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS ECONOMETRIC LEARNING Thestandardapproachtolearning—replaceagentsinthemodelwith econometriciansasinCogleyandSargent(JME,2008)—mightinterpretthelarge shocksasmomentswhererationalexpectationswerebadlydisturbedacrossall agentsintheeconomy: youngandold,richandpoor. Forecaststhatplacedconsiderableweightonthechaoticobservationsfromthecrisis couldleadtoimportantchangesineconomicbehavior,whichcouldthenfeedback andcontinuetokeeptheeconomyawayfromitslong-runequilibriumforsometime. Thisvisionoflearningseemstobeatoddswiththedatainthefigure. 41 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS SOCIAL LEARNING ThismodelhasdecisionrulesforLChouseholdsi∈ (0,1): c˜ t−s,i (t) = x lc ηe¯w(t), (5) e¯ ℓ t−s,i (t) = (1−η) e , (6) s a t−s,i (t) =x w(t) (cid:40)(cid:34) ∑ s e (cid:35) − (cid:18) s+1 (cid:19) ∑ T e (cid:41) , (7) P(t) lc j T+1 j j=0 j=0 fors=0,...,T,wheree¯istheaveragebaselineendowmentforLCagentsandx isthe lc scalefactorforagentiwithinthecohort,andforHTMagentss=0,...,T : c˜htm (t) = x ηhe¯w(t), (8) t−s,i htm ℓhtm (t) = 1−η, (9) t−s,i ahtm (t) = 0. (10) t−s,i 42 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS SEEDED WITH DNA Householdsintheequilibriumofthismodelhaveverydifferentincomes,levelsof consumption,andassets. Nevertheless,theycanlearnfromeachotherduetothefactthattheseoptimal decisionrulesaretransferableacrossagentsbecausetheyadjustforageand productivityintheappropriateway. Furthermore,mostagentswouldhavehadtolearnthesedecisionrulesbeforethe large,unanticipatedshockoccurred. Theeconomyisineffectseededwithasortof“DNA”—known,previouslylearned decisionrules—evenafterthelargeshockoccursandbeginstodissipate. 43 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS SOCIAL LEARNING AftertheGFC,forinstance,therewouldbesomecohortswhoseonlyexperienceas decision-makersintheeconomywasduringthecrisis. However,therewouldbemanymoreagentsinthesociety,95%ormore,thatwould haveknowledgeofoptimaldecision-makinginnormaltimes. Theseknowndecisionrulesarerelativelysimpleandcanpropagateexponentially quicklythroughthepopulationfollowingthelargeshock,returningtheeconomyto equilibriuminshortorder. This“sociallearningforthemasses”ismorelikelytobethesuccessfullearning conceptinlargeheterogeneousagenteconomies. 44 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS Conclusions 45 INTRODUCTION COREARGUMENT ENVIRONMENT CALIBRATION LEARNING CONCLUSIONS JASMINA ARIFOVIC’S CONTRIBUTIONS JAwasapioneerintheapplicationofmethodsfromartificialintelligenceto macroeconomicstotrytohelpanswerthequestion,“Howisequilibriumachieved?” Ihavearguedherethatthecombinationofherinsightsandthelikelyfuturedirection ofmacroeconomicresearchsuggeststhatthisworkwillbeevenmoreimportantin thedecadesahead. 46

James Bullard (2023, February 3). Regional President Speech. Speeches, Federal Reserve. https://whenthefedspeaks.com/doc/regional_speeche_20230204_james_bullard

@misc{wtfs_regional_speeche_20230204_james_bullard,
  author = {James Bullard},
  title = {Regional President Speech},
  year = {2023},
  month = {Feb},
  howpublished = {Speeches, Federal Reserve},
  url = {https://whenthefedspeaks.com/doc/regional_speeche_20230204_james_bullard},
  note = {Retrieved via When the Fed Speaks corpus}
}