speeches · January 25, 2018

Regional President Speech

James Bullard · President

DOES A LOW-INTEREST-RATE REGIME HARM SAVERS? JamesBullard PresidentandCEO NonlinearModelsinMacroeconomicsandFinanceforan UnstableWorld NorgesBank Jan. 26,2018 Oslo,Norway Anyopinionsexpressedherearetheauthor’sanddonotnecessarilyreflectthoseoftheFOMC. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Overview INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END THIS TALK ThisacademictalkwaspreviouslypresentedinLondon,UK,in July2017,inSanJose,CostaRica,inAugust2017,andatthe AdvancedWorkshopforCentralBankers—Northwestern University,inSeptember2017. Theresultsherearepreliminaryandtheoreticalinnature. Feedbackiswelcome. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Low Interest Rates and Saving INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END LOW INTEREST RATES AND SAVING Sincethe2007-2009financialcrisisandrecession,realand nominalinterestratesinadvancedeconomieshavebeen exceptionallylowcomparedwithpostwarnorms. Icallthisa“low-interest-rateregime.” Acriticismofmonetarypolicyinadvancedeconomiesfollowing thecrisishasbeenthatthelow-interest-rateregimehasbeen detrimentalforsavers. Thispresentationsuggeststhatthelow-interest-rateregimemay notbe“harmfultosavers.” INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END LOW INTEREST RATES EMPIRICALLY FIGURE: Source:FederalReserveBoard,U.S.DepartmentoftheTreasury, BankofEngland,EuropeanCentralBankandJapan’sMinistryofFinance. Lastobservation:Jan.22,2018. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END THE LINE OF ARGUMENT Inthemodelpresentedhere,householdcreditmarketswillplay anessentialrole. Thereareno“stickyprices.”Instead,thekeyfrictioninthe economyisnon-statecontingentnominalcontracting(NSCNC)in householdcreditmarkets. Monetarypolicywillbeabletorepairthisfrictionentirelyby usingaversionofnominalGDPtargeting. Therewillbeanaggregateproductivityshockfollowinga regime-switchingstochasticprocess,yieldinga high-real-interest-rateandalow-real-interest-rateregime. Mainresult: Undertheoptimalmonetarypolicy,theallocationof resourceswillbefirst-bestintratemporallyineitherthehighorthelow regime. Inthissense,alow-interest-rateregimewillnotbedetrimentalto savers(oranyotherhouseholds). INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Credit Market Friction INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END HOUSEHOLD CREDIT IN A DSGE MODEL Istudyaneconomywithalargeprivatecreditmarketthatis essentialtogoodmacroeconomicperformance. Ifthehouseholdcreditmarketisnotworkingproperly,some householdswillconsumemuchlessthanothers. TheNSCNCfrictionmeansthismarketwillnotworkwellonits own. Theroleofmonetarypolicywillbetorepairthisfrictionby restoringcompletemarkets. IignoreZLBissuesinthistalk. Seethecompanionpaperby Azariadis,Bullard,SinghandSuda(2015),availableonmyweb page. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END INCOME AND WEALTH INEQUALITY Thereisalotofincomeandwealthinequalityinthisstylized model. Theroleofcreditmarkets,iftheyworkcorrectly,willbeto reallocateunevenincomeacrossthelifecycleintoperfectlyequal percapitaconsumption. Themodelequilibriumwillnaturallyrank: thewealthGinicoefficient>theincomeGinicoefficient>the consumptionGinicoefficient. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END HOW LARGE ARE THESE MARKETS? AccordingtoMianandSufi(AER,2011),theratioofhousehold debttoGDPintheU.S.wasabout1.15beforeitballoonedto 1.65duringthe2000s. Intoday’sdollars,thatwouldbeequivalenttogoingfromabout $19.5trilliontoabout$28trillioninhouseholddebt,comprised mostlyofmortgagedebt. Disruptingthesemarketsmightbequitecostlyfortheeconomy, sotheNSCNCfrictioncouldbequiteimportant. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Environment INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END SYMMETRY ASSUMPTIONS Imakeasetofimportant“symmetryassumptions”sothatwe canbetterunderstandtheequilibriumofthemodelevenwith substantialheterogeneity. Theseassumptionsinvolvethesymmetryofthelifecycle productivityendowmentpatternofthehouseholds,alongwith logpreferences,nodiscounting,andnopopulationgrowth. Theseassumptionshelpdelivertheresultthatintheequilibrium Istudy: Therealinterestrateisexactlyequaltotheoutputgrowthrateatevery date,eveninthestochasticeconomy. Thisinturncreatesasetofeasytounderstandbaselineresults forthiseconomy. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END LIFE CYCLE MODELS Generalequilibriumlifecycleeconomy=many-period overlappinggenerations. Keyvariablesareprivately-issueddebt,realinterestratesand inflation. Thinkofprivately-issueddebt=“mortgage-backedsecurities.” Thistalkhasinelasticlaborsupply. Elasticlaborsupplycanbe added—formoreonthis,seethecompanionpaperbyBullard andSingh(2017),availableonmywebpage. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END ENVIRONMENT DETAILS ThemodelisastandardT+1-periodsDSGElife-cycle endowmenteconomy. Anewgenerationofidenticalhouseholdsisbornateachdate. HouseholdsliveforT+1periods. AnyT 2willwork;Iprefer (cid:21) T+1=241(quarterly);oddvaluesareconvenient. ThemonetarypolicymakerascontrollingthepricelevelP(t) directly. Foramoreelaborateversionwithexplicitmoney demand,seeAzariadis,Bullard,Singh,andSuda(2015). INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END PREFERENCES Allparticipanthouseholdsenteringtheeconomyatdatethave logpreferenceswithnodiscounting T ∑ V =E lnc (t+j), t t t j=0 wherec (t+j) >0isthedatet+jconsumptionofthe t householdbornatdatet. Householdsthatenteredtheeconomyatpreviousdateshave similarpreferencesandcarryanet-asset-holdingpositioninto datet.Householdsentertheeconomyandleavetheeconomy withzeronetassets. Otherassumptions: Within-cohortagentsareidentical,no populationgrowth,nocapital,nodefault,flexibleprices,no borrowingconstraints. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END LIFE-CYCLE PRODUCTIVITY Allparticipanthouseholdsareendowedwithanidentical productivityprofileovertheirlifetime. Theprofilebeginsatalowvalue,risestoapeakinthemiddle periodoflife,andthendeclinestothelowvalue. Iassumethe“lowvalue”isboundedawayfromzeroforthis talk. Theproductivityprofileissymmetric. Agentscanselltheirproductivityunitsavailableatdatetinthe labormarketatthecompetitiverealwage. Thecross-sectionalincomedistributionintheeconomyisthis profilemultipliedbytherealwageatthatdate. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END LIFE-CYCLE PRODUCTIVITY = CROSS SECTION 1.0 0.8 0.6 0.4 0.2 50 100 150 200 FIGURE: Aschematicproductivityendowmentprofileforcreditmarket participantsalsorepresentsthecrosssectionofhouseholdsatdatet.The profileissymmetricandpeaksinthemiddleperiodofthelifecycle.About 50percentofthehouseholdsearn75percentofthelaborincomeinthecredit sectorforη=1. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END KEY FRICTION: NSCNC Loansaredispersedandrepaidintheunitofaccount—thatis,in nominalterms—andarenotcontingentonincomerealizations. Therearetwoaspectstothisfriction: Thenon-statecontingentaspectmeansthatrealallocationswillbe perturbedbythisfriction,and Thenominalaspectmeansthatthemonetaryauthoritymaybeable torepairthedistortion. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END STOCHASTIC STRUCTURE AggregaterealoutputisproducedasY(t) =Q(t)L(t),where L(t)isthelaborinputandQ(t)istheleveloftechnology. ThetechnologyQ(t)improvesatastochasticrateλ(t,t+1). Thecompetitiverealwageperproductivityunit,w(t),isthen givenby w(t+1) = λ(t,t+1)w(t), (1) wherew(0) >0. Iwillmakeassumptionsconcerningλ(t,t+1)suchthatthe economygrowsonaverage. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END REGIME SWITCHING IfollowBullardandSingh(IER,2012,Section2.4)todefinea two-stateregime-switchingprocessforλ. Thereisahigh-growthstatewithmeanλH andalow-growth statewithmeanλL,suchthat1< λL < λH. Withineachregime,thereisadditivenoisedescribedbyσ(cid:101)(t), whereσisascalefactorand(cid:101)(t) i.i.d.N(0,1). (cid:24) Alatentvariables(t)determinestheregimeandfollowsa first-orderMarkovprocess. Theresultingprocessforλ(t,t+1)canbewrittenasanAR(1) processwithanonstandarderrorterm. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END TIMING PROTOCOL Atthebeginningofdatet,naturemovesfirstandchooses λ(t 1,t),whichimpliesavalueforw(t). (cid:0) Thepolicymakermovesnextandchoosesavaluefortheprice level,P(t). Householdsthendecidehowmuchtoconsumeandsave. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END NOMINAL INTEREST RATE Participanthouseholdscontractbyfixingthenominalinterest rateoneperiodinadvance. Thenon-statecontingentgrossnominalinterestrate,thecontract rate,isgivenby c (t) P(t) Rn(t,t+1) (cid:0) 1 =E t c ( t t+1)P(t+1) . (2) (cid:20) t (cid:21) Thisratedependsontheexpectedgrossrateofconsumption growthandtheexpectedgrossrateofinflation. IntheequilibriumIstudy,consumptiongrowthratesarethe sameforallhouseholds,sothisconditionisalsothesameforall thehouseholdsbornatpreviousdates. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END COMPLETE MARKETS WITH NSCNC Thecountercyclicalpricelevelpolicyruledeliverscomplete marketsallocations: Rn(t 1,t) P(t) = (cid:0) P(t 1), (3) λr(t 1,t) (cid:0) (cid:0) whereλrindicatesarealizationoftheshockandRnisthe expectationgiveninthepreviousslide. ThisissimilartoSheedy(BPEA,2014)andKoenig(IJCB,2013). Giventhispolicyrule,householdswillconsumeequalamounts ofavailableproductioninthecreditsector. Thisis“equityshare contracting,”whichisoptimalunderhomotheticpreferences. Thispricelevelrulerendersthehouseholds’date-tdecision problemdeterministicbecauseitperfectlyinsuresthehousehold againstfutureshockstoincome. Consumptionandassetholdingsfluctuatefromperiodto period,butinproportiontothevalueofw(t). INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END STATIONARY EQUILIBRIA Welett ( ∞,+∞). 2 (cid:0) Weonlyconsiderstationaryequilibriaundertheperfectly crediblepolicyrulegoverningP(t). WeletR(t)bethegrossrealrateofreturninthecreditmarket. Stationaryequilibriumisasequence f R(t),P(t) gt + = ∞ ∞ suchthat marketsclear,householdssolvetheiroptimizationp(cid:0)roblems, andthepolicymakercrediblyadherestothestatedpolicyrule. Thekeyconditionisthatnetaggregateassetholding,A(t),nets outamongparticipanthouseholds. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Graphs INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END LABOR INCOME CHANGES IN CROSS SECTION 1.0 0.8 0.6 0.4 0.2 50 100 150 200 FIGURE: Howlaborincomechangesacrosscohortswhentherealwage increases10percentforη=1. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END NET ASSET HOLDING IN CROSS SECTION 15 10 5 50 100 150 200 5 10 15 FIGURE: Netassetholdingbycohortalongthecompletemarketsbalanced growthpathwithη=1.Borrowing,thenegativevaluestotheleft,peaksat stage60ofthelifecycle(age~35),whilepositiveassetspeakatstage180of thelifecycle(age~65).About25percentofthepopulationholdsabout75 percentoftheassets. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END CHANGE IN NET ASSET HOLDING IN CROSS SECTION 20 10 50 100 150 200 10 20 FIGURE: Hownetassetholdingchangesbycohortwhentherealwage increasesby10percentwhenη=1. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END CONSUMPTION IN CROSS SECTION 1.0 0.8 0.6 0.4 0.2 50 100 150 200 FIGURE: Schematicrepresentationofconsumption,theflatline,versuslabor income,thebell-shapedcurve,bycohortalongthecompletemarkets balancedgrowthpathwithw(t)=1andη=1.Theprivatecreditmarket completelysolvesthepoint-in-timeincomeinequalityproblem. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END CHANGE IN CONSUMPTION IN CROSS SECTION 1.0 0.8 0.6 0.4 0.2 0 50 100 150 200 FIGURE: Howlaborincomeandconsumptionchangebycohortwhenthe realwageincreasesby10percentwithη=1. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Complete Markets INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END COMPLETE MARKETS VIA NGDP TARGETING Thiseconomycouldbemiredinthelow-interest-rateregimefor alongtime,dependingonassumptionsconcerningthe persistenceoftheproductivityregimes. Nevertheless,monetarypolicycandeliverfirst-best intratemporalallocationsviathepricelevelruledescribedearlier whichinduces“equitysharecontracting.”Thisoccursbothwith regimesandacrossregimes. ThepolicymakeriscompletelymitigatingtheNSCNCfrictionand restoringtheWickselliannaturalrateofinterest. Thereisnosenseinwhichsaversare“hurt”inthe low-interest-rateregime(norareborrowers“helped”). INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END CAVEATS Thepolicymakerhereisallowedtoobservetheshockandthen offsetitwiththeappropriatesettingforP(t). Thisisunrealistic, butsimilartobaselineNewKeynesianmodelsinwhich policymakerscanappropriatelyoffsetincomingshocks. Thelow-real-interest-rateregimeisassociatedwithaslowerrate ofgrowthinrealwagesandrealoutput. Householdswould ratherbeinthehighergrowthregimeinthissense. Butthe productivitygrowthregimeistakenasanexogenousprocess chosenbynaturehere. Monetarypolicycannotswitchtheeconomytothehigh-growth regime,butitcanconductanoptimalpolicygiventheregime. Monetarypolicycanbeuseful,butnotsousefulastocreatehigh realgrowth. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END MORE CAVEATS Ifocusonanequilibriumwheretherealinterestrateequalsthe outputgrowthrateeveryperiodinthestochasticeconomy. Theremaybeotherequilibria. Resultswouldstillholdifthereweretwoormorelifetime productivityprofiles,allowingforintracohortincomeinequality. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Perceptions INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END INACCURATE PERCEPTIONS OF REGIMES Inthispresentation,thepolicymakerandtheprivatesector agentshaverationalexpectations,meaningtheyunderstandthe natureoftheregime-switchingprocessdrivingtheeconomy. Whatiftheyhadamisspecifiedmodelinwhichtheyexpected theeconomytoreturntoafixedmean? Itremainsforfuturereseachtounderstandhowtheseresults maybealteredinthisscenario. Nevertheless,thismaybeoccurringinactualU.S.monetary policy. ThefollowingchartsillustratethispossibilityusingrecentU.S. data. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END POLICYMAKER PERCEPTIONS FIGURE: Source:FederalReserveBoardandauthor’scalculations.Last observation:December2017. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END PRIVATE SECTOR PERCEPTIONS FIGURE: Source:FRBofPhiladelphiaandauthor’scalculations.Last observation:2017-Q3. INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END Conclusions INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END CONCLUSIONS Thedesirebehindmanyactualpolicychoicesoverthelast severalyearshasbeentohelphouseholdcreditmarkets, especiallymortgagemarkets,performbetter. Thecreditmarketherecanbeinterpretedasaresidential mortgagemarket—“mortgage-backedsecurities.” MonetarypolicycanalleviatetheNSCNCfrictionandrestore thesmoothfunctioningofthecreditmarket. Thispolicyresultremainseveniftheeconomyswitches infrequentlybetweenhigh-andlow-real-interest-rateregimes. Onesentencesummary: “Onecannotreadwelfareimplications offoftheobservationoftherealinterestratealone.” INTRO LOWINTERESTRATES&SAVING FRICTION ENVIRONMENT GRAPHS POLICY PERCEPTIONS END NATURAL VS. UNNATURAL REAL INTEREST RATES Herethemonetarypolicymakercanrestorethefirst-best intratemporalallocationofresourcesbymovingthepricelevelto achievetheWickselliannaturalrealrateofinterestforthe economy,withthenaturalrateitselffluctuatingaccordingtoa regime-switchingprocess. Thisanalysiscanprovideagoodbaselineforthinkingaboutthe currentsituationinadvancedeconomiesiflowrealinterestrates canbemostlyattributedtofactorsexogenoustomonetarypolicy. However,whatiflowrealinterestratesareattributedtomonetary policyitself (asmanycriticsnodoubtwouldargue)? Thenitmaybethecasethatthoseratesaredistortionaryandcould hurtsomesegmentsofsociety.Thatcouldbeanalyzedhere,sayby havingthepolicymakersetthe“wrongvalueforP(t)”each period.Thatwouldrequireacomputationalsolutionasopposedto thepencil-and-papersolutionusedinthistalk.

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APA

James Bullard (2018, January 25). Regional President Speech. Speeches, Federal Reserve. https://whenthefedspeaks.com/doc/regional_speeche_20180126_james_bullard

BibTeX

@misc{wtfs_regional_speeche_20180126_james_bullard,
  author = {James Bullard},
  title = {Regional President Speech},
  year = {2018},
  month = {Jan},
  howpublished = {Speeches, Federal Reserve},
  url = {https://whenthefedspeaks.com/doc/regional_speeche_20180126_james_bullard},
  note = {Retrieved via When the Fed Speaks corpus}
}