Optimal Monetary and Macroprudential Policies under Fire-Sale Externalities

OptimalMonetaryandMacroprudentialPoliciesunderFire-SaleExternalities FloraLutzWP/23/51 IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate. TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement. 2023 MAR ©2023InternationalMonetaryFundWP/23/51 IMFWorkingPaper FinanceDepartment OptimalMonetaryandMacroprudentialPoliciesunderFire-SaleExternalitiesFloraLutz AuthorizedfordistributionbyCarloA.E.SdralevichMarch2023 IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement. ABSTRACT:Iprovideanintegratedanalysisofmonetaryandmacroprudentialpoliciesinamodeleconomyfeaturingafinancialfrictionandanominalwagerigidity.Inthisset-up,themonetaryauthorityfacesatrade-offbetweenmacroeconomicandfinancialstability:Whileexpansionarycounter-cyclicalmonetarypolicypreventsinvoluntaryunemployment,italsoamplifiesaninefficientreallocationofcapitalacrosssectors.Themaincontributionoftheanalysisisthreefold:Firstithighlightsanovelchannelthroughwhichmonetarypolicycanimpactfinancialstability.Second,itshowsthat,byitself,monetarypolicycansignificantlymitigatethewedgebetweentheconstrainedefficientandthecompetitiveallocation.Third,regardlessoftheavailabilityofmacroprudentialtools,stabilizingdemandisusuallynotoptimalformonetarypolicy. RECOMMENDEDCITATION:F.Lutz.2023.“OptimalMonetaryandMacroprudentialPoliciesunderFire-SaleExternalities.”IMFWorkingPaperWP/23/51,InternationalMonetaryFund,WashingtonD.C. JELClassificationNumbers: D62,E24,E44,E52,E61, Keywords: MonetaryPolicy;MacroprudentialPolicy;Fire-sales;PecuniaryExternalities;Unemployment, Author’sE-MailAddress: FLutz@imf.org *ThisstudyhasgreatlybenefittedfromthecommentsofPaulPichler,GerhardSorger,AlejandroCunat,AntonKorinek,HaraldFadinger,NicolasErnestoMagudandseminarparticipantsattheViennaGraduateSchoolofEconomics. ContentsPage I.Introduction4 II.TheModel9 A.Households9 B.TheTraditionalSector10 C.TheBankingSector12 D.TheCentralBank14 III.TheUnregulatedCompetitiveEquilibrium14 IV.TheConstrained-EfficientAllocation19 V.SocialInefficienciesandOptimalPolicy24 A.ImplementingtheConstrainedEfficientAllocation25 B.SocialInefficienciesandMonetaryPolicy26 VI.OptimalMonetaryPolicywithLimitedMacroprudentialInstruments27 A.NoAccesstoMacroprudentialPolicyTools27 B.Limitedmacroprudentialpolicy29 VII.NumericalIllustration30 VIII.Conclusion34 References35 Appendices A.First-bestAllocation40 B.ModelExtensions40 B.1.EndogenousTraditionalSectorEndowmente40 B.2.StochasticTotalFactorProductivity41 C.ProofsOmittedintheMainText42 C.1.ProofofLemma142 C.2.ProofofLemma243 C.3.ProofofProposition144 C.4.ProofofLemma344 C.5.ProofofLemma445 C.6.ProofofProposition246 C.7.ProofofLemma547 C.8.ProofofLemma648 C.9.ProofofProposition348 C.10.ProofofProposition450 C.11.ProofofProposition551 Tables Figures 1.FullEmploymentvs.FixedPriceRegime31 2.Competitivevs.ConstrainedEfficientAllocation32 3.Welfare33 4.OptimalMacroprudentialRegulation34 I.INTRODUCTION The2008financialcrisishasledtothewideagreementthatnewtoolsareneededtomitigateexcessiverisktakinginthefinancialsector.Thisperceptionhasfosteredthedesignandim-plementationofmacroprudentialtoolsaroundtheworld.1Whilemacroprudentialpoliciesfocusonthemitigationofsystemicrisksinthefinancialsector,ongoingdebatesinacademiaandpoliticshavehighlightedcriticalspilloversbetweenfinancialstabilityandmonetarypol-icyobjectiveswhichhavetraditionallyfocusedonmacroeconomicstability.Empiricalevi-dencesuggeststhatmonetarypolicycanaffectrisktakinginthefinancialsectorwhiletightmacroprudentialregulationsmaycurbeconomicactivity.2Thisraisesimportantquestionsabouttheinteractionofmacroprudentialandmonetarypolicy,including:(1)Howdoesop-timalmacroprudentialpolicydependonthemonetarypolicyregime?(2)Whichobjectivesshouldmonetarypolicypursue?(3)Andhowdoesoptimalmonetarypolicydependontheavailabilityofmacroprudentialtools? Inthispaper,Iaddressthesequestionsinamodeleconomywitharationaleformacropruden-tialpolicyduetoapecuniaryexternality(basedonKaraandOzsoy(2019))andwithanon-neutralroleformonetarypolicyduetoadownwardnominalwagerigidity(asinSchmitt-GrohéandUribe(2016)).Thecombinationofafinancialfrictionandanominalrigidityin-ducesatrade-offformonetaryauthoritiesbetweenmacroeconomicandfinancialstability:Whileexpansionarymonetarypolicycanpreventinvoluntaryunemploymentincrisesstates,italsoreducesassetpricesandtherebyamplifiesaninefficientcapitalreallocationacrosssec-tors.Thetheoreticalanalysisyieldsthreemainfindings.First,thearticlehighlightsanovelchannelthroughwhichmonetarypolicyimpactsfinancialstability.Second,Ishowthat,byitself,monetarypolicycansignificantlymitigatethewedgebetweentheconstrainedeffi-cientandthedecentralizedallocation.Optimalmacroprudentialinterventionsarethuscriti-callyshapedbythemonetaryp