Redistribution and the Monetary-Fiscal Policy Mix

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Redistribution and the Monetary–Fiscal Policy Mix Saroj Bhattarai, Jae Won Lee, Choongryul Yang 2021-013 Please cite this paper as: Bhattarai, Saroj, Jae Won Lee, and Choongryul Yang (2022). “Redistribution and the Monetary–Fiscal Policy Mix,” Finance and Economics Discussion Series 2021-013r1. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2021.013r1. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Redistribution and the Monetary–Fiscal Policy Mix∗ Saroj Bhattarai† Jae Won Lee‡ Choongryul Yang§ Univ. ofTexas-Austin SeoulNationalUniv. FederalReserveBoard andCAMA Abstract We show that the effectiveness of redistribution policy is tied to how much inflation itgenerates,andthereby,tomonetary-fiscaladjustmentsthatultimatelyfinancethetransfers. Inthemonetaryregime,taxesincreasetofinancetransferswhileinthefiscalregime, inflationrises,imposinginflationtaxesonpublicdebtholders. Weshowanalyticallythat thefiscalregimegenerateslargerandmorepersistentinflationthanthemonetaryregime. Inatwo-sectormodel,wequantifytheeffectsoftheCARESActinaCOVIDrecession. Wefindthattransfermultipliersarelarger,andthatmoreover,redistributionisParetoimproving,underthefiscalregime. JELclassification: E53;E62;E63 Keywords: Household heterogeneity, Redistribution, Monetary-fiscal policy mix, Transfermultiplier,Welfareevaluation,COVID-19,CARESAct ∗We thank David Andolfatto, Guido Ascari, Oli Coibion, Marco Del Negro, Miguel Faria-e-Castro, Refet Gurkaynak,YoonsooLee,EricMengus,GernotMuller,TaisukeNakata,WoongYongPark,Christiaanvander Kwaak,seminarparticipantsatMonashUniversity,NorthCarolinaStateUniversity,NewYorkUniversity–Abu Dhabi, CAFRAL–Reserve Bank of India, Hanyang University, Sogang University, Seoul National University and University of Tokyo, and conference participants at the Bank of Denmark/Deutsche Bundesbank/Bank of NorwayJointConferenceonStabilizationPolicies,CEPR/BankofItaly8thConferenceonMoney,Bankingand Finance,CEPR/KeioUniversity6thInternationalMacroeconomicsandFinanceConference,27thInternational Conference on Computing in Economics and Finance, 3rd Warsaw Money-Macro-Finance Conference, KIF- KAEA-KAFA Conference, North American Winter and Summer Meetings of the Econometric Society, and Federal Reserve Board Research Webinar for helpful comments. The views expressed here are those of the authorsanddonotnecessarilyreflectthoseoftheFederalReserveBoardortheFederalReserveSystem. First version: December2020. Thisversion: September2022. †DepartmentofEconomics,UniversityofTexasatAustinandCAMA,2225Speedway,StopC3100,Austin, TX78712,U.S.A.Email: saroj.bhattarai@austin.utexas.edu. ‡DepartmentofEconomics,SeoulNationalUniversity,1Gwanak-ro,Gwanak-gu,Seoul08826,SouthKorea. Email: jwlee7@snu.ac.kr. §Federal Reserve Board of Governors, 20th Street and Constitution Avenue NW, Washington, DC 20551, U.S.A.Email: choongryul.yang@frb.gov. 1

1 Introduction Recently, the U.S. experienced the two largest contractions after World War II—the Great Recession and the COVID-19 recession. The government responded to them with unprecedented fiscal measures—namely the American Recovery and Reinvestment Act of 2009 and the Coronavirus Aid, Relief, and Economic Security (CARES) Act of 2020. These fiscal responses included significant transfer components, and they have renewed interest in the effectiveness of transfer policies in rebooting the economy and improving household welfare. They have raised several research questions. What are the macroeconomic effects of redistributionpoliciesthattransferresourcesfromonesetofagentsintheeconomytoanother? What are the determinants of the transfer multiplier? When is the transfer multiplier large? What arethewelfareimplicationsofsuchpolicies? In a dynamic general equilibrium model, one would have to take numerous factors into account to answer the above questions. In this paper, we focus on the source of financing and show how the government finances transfers has a first-order importance for their effectiveness. Our focus is motivated by the ongoing rapid increase in public debt caused by the large-scale transfer programs. This eventually requires fiscal and/or monetary adjustments, whichwouldultimatelyfinancecurrenttransfers. Wecomparetwodistinctwaystofinancetransfersinatwo-agentNewKeynesian(TANK) model. Inthemodel,asetofhouseholdsareunabletoborrowandlendtosmoothconsumption over time. A transfer policy redistributes resources toward such “hand-to-mouth” (HTM) households and away from “Ricardian” households that own government bonds.1 In the first policyregime,thegovernmentraisestaxes. Inflationisthenstabilizedintheusualwaybythe central bank. We call this case the “monetary regime.” In the second regime, the government commits itself to no adjustments in taxes, and the central bank allows inflation to rise to stabilize the real value of debt, thereby imposing “inflation taxes” on households that hold nominalgovernmentdebt. Inthis“fiscalregime,”thefiscaltheoryofthepriceleveloperates. We find that the effectiveness of transfer policy is directly tied to how much inflation it generates. A transfer policy is inflationary irrespective of the policy regimes in the model. It is, however, more inflationary in the fiscal regime than in the monetary regime. Therefore,inflation-financedtransferscanbeusedtofightdeflationarypressuresduringrecessions, therebypreventingoutputandconsumptionofbothtypesofhouseholdsfromdroppingsignificantly. Asaresult,thewelfareofbothhouseholdtypesishigherwhentransfersareinflation- 1Aswedescribeinfurtherdetaillater,inourapplication,wethinkoftheseHTMhouseholdsasworkingin theservicesectorthatisaffectedbyalargenegativesectoralshock. 2

financedthanwhentheyaretax-financed. Furthermore,somewhatsurprisingly,inflation-financedtransferscanproduceaParetoimprovement relative to the no-transfer case. Notice that, since the model features staggered Calvo-type price setting, inflation is not a free lunch: it generates, ceteris paribus, significant resource misallocation, which leads to a decrease in labor productivity and in welfare. These negativeeffectsofinflationare,however,outweighedbythepositiveeffectsofinflationinthe low-inflation environment considered in this paper. In fact, without an inflationary intervention,theeconomywouldexperiencedeflation,sothereislittlecostofinflation. Our paper starts with a simple flexible-price model that permits analytical results, which allowsustoilluminatethefiscaltheorymechanisminaheterogeneous-householdframework. This model also serves as a useful reference point, as the two policy regimes produce exactly the same multipliers for output and consumption and an identical level of household welfare, even if inflation dynamics are different. This is due to two features. First, both conventional taxes, which are assumed to be lump sum, and inflation taxes are non-distortionary. Second, priceflexibilityshutsdownanyfeedbackeffectsfrominflationonrealvariables.2 For inflation, the fiscal regime gives rise to higher and more persistent inflation than the monetary regime. In particular, transfers affect inflation through two channels in this regime. First, an increase in transfers leads directly to an increase in public debt, which accumulates overtime. Consequently,inflationrisestostabilizetherealvalueofdebt. Second,anincrease in transfers may indirectly raise future public debt through an interest rate channel. Redistribution changes Ricardian household consumption, which in turn affects real interest rates and thus outstanding public debt in the following periods. That is, redistribution generates a new valuation effect through real interest rate changes, an effect that is absent in the standard one-agent model often used to analyze the fiscal regime. This interest rate channel may lead toafurtherincreaseininflation. Showingthesetwoeffectsexplicitlyinanonlineartwo-agent modelisacontributionofourpaper. We then build on the analytical results and proceed to a quantitative analysis employing a two-sector TANK model. Relative to the simplified version, the quantitative model includes severalrealisticfeaturesthatbreaktheuniformityofthetworegimesintermsofthemultipliers. The two most important are nominal rigidities and the “COVID shocks.” Sticky prices areimportant,astransfersnowcanincreaseoutputthroughtheusualNewKeynesianchannel by generating inflation—on top of the classical labor supply channel. Introducing shocks is also consequential as the multipliers are generally state-dependent. In particular, the COVID 2Thetransfermultiplierforoutputissmallyetstillpositiveduetotheclassicallaborsupplychannel. RedistributioncausesRicardianhouseholdconsumptiontofall,creatinganegative“wealtheffect”onlaborsupply. 3

shocks cause the economy to fall into what we refer to as a “COVID recession” as well as a liquiditytrap,inwhichtheeffectsofredistributioncanbedifferentquantitatively.3 Specifically, we suppose that the COVID shocks consist of adverse aggregate and sectorspecific demand shocks and sector-specific labor supply shocks. The sector-specific shocks intend to capture the observation that “locked out of work” and “fear of unsafe consumption” featuresaremorepronouncedincertainsectorsoftheeconomy.4 Situatingthemodeleconomy inaCOVID-recession-likeenvironment,wecalibratethesizeoftransferstomatchthetransfer amountintheCARESActandstudyhowtheeconomyrespondstoredistributionpolicy. We find that the transfer multipliers are significantly larger under the fiscal regime than under the monetary regime, primarily because of the difference in inflation dynamics. For instance, the four-year cumulative multiplier for aggregate output is 1.732 in the monetary regimewhileitis5.552inthefiscalregime. Thismultiplierisgreaterthanunityevenunderthe monetary regime, thanks to nominal rigidities and the binding zero lower bound (ZLB). Just asstrikinglydifferentarethefour-yearcumulativeconsumptionmultipliers. FortheRicardian households, it is negative -0.002 in the monetary regime and 3.078 in the fiscal regime, while fortheHTMhouseholds,itis7.409inthemonetaryregimeand13.652inthefiscalregime.5 Weisolatetheroleplayedbyvariousmodelelementsindrivingourquantitativeresultsusingcounterfactualexercises. Theunusuallylargemultipliersreportedabove,especiallyunder the fiscal regime, result from the economy being situated in the historically severe COVIDrecession with large deflationary pressures. For example, shutting down the COVID shocks, the four-year cumulative multiplier for aggregate output is 1.490 in the monetary regime, while it is 2.696 in the fiscal regime. This result underscores the state-dependency of policy effects. Importantly, the difference in the multipliers for output and consumption between the two regimes gets larger in the presence of COVID shocks, which implies that while both labor-tax-financed transfers and inflation-financed transfers are more effective in the COVID recession than in a normal environment, the latter is even more so. In addition, we also find thatrelyingonlabortaxesratherthanlump-sumtaxesinthemonetaryregimeplaysarole. Overall,asaconsequence,thecontractioninoutputandconsumptionismuchmoremuted whentransfersarefinancedbyinflationtaxes. Specifically,transfers,wheninflation-financed, would reduce the output loss caused by the COVID shocks by roughly 4.1 percentage points 3Anotherdifferencefromtheanalyticalmodelisthatthegovernmentraises(gradually)labortaxes,ratherthan lump-sumtaxes,inthemonetaryregime,which,throughdistortionaryeffects,influencesthetransfermultipliers. 4We decompose the U.S. economy into two sectors—(1) transportation, recreation, and food service sector and (2) the rest of the economy—and let the HTM households work in the former sector and the Ricardian householdsworkintheothersectorsthatarelessaffectedbytheCOVIDpandemic. 5ThepositiveRicardianhouseholdconsumptionmultiplierisunique,evenqualitatively,inthefiscalregime. 4

at the trough compared to no-intervention case. We also find that the expansionary effects of inflation-financed transfers are so large that such redistribution policy generates a Pareto improvement: It increases the welfare of both the recipients and sources of transfers, even taking into account the resources taken away from the Ricardian household and the fact that the Ricardian household’s leisure decreases as a result of output increases and distortions generatedbyhighandpersistentinflation. Ourpaperbuildsonseveralstrandsoftheliterature. Itisrelatedtothefiscal-monetaryinteractionsliteratureasoriginallydevelopedinLeeper(1991),Sims(1994),Woodford(1994), Cochrane (2001), Schmitt-Grohé and Uribe (2000), and Bassetto (2002).6 Sims (2011) introduced long-term debt under this regime in a sticky price model, which Cochrane (2018) usedtoanalyzeinflationdynamicsfollowingtheGreatRecession. Analyticalcharacterization of the fiscal regime in a linearized sticky price model is in Bhattarai, Lee, and Park (2014). Our additional analytical contribution here is to derive the fully nonlinear results of this fiscal regime in a tractable two-agent model. Motivated by the COVID crisis and the CARES Act, we then assess the quantitative effects of redistribution policy as well as its welfare implicationsinatwo-sector,two-agentnonlinearmodel. We build on two-agent models as originally developed in Campbell and Mankiw (1989), Galí, López-Salido, and Vallés (2007), and Bilbiie (2018). Moreover, Bilbiie, Monacelli, and Perotti (2013), closely related to this paper, show that different financing schemes affect the size of the output transfer multiplier in a TANK model. However, they only consider the monetary regime. Our main contribution is to assess the effects of redistribution policy in suchanenvironmentandshowhowitdependsonthemonetary-fiscalpolicymix.7 Recently there have been several contributions to an analysis of macroeconomic effects of the COVID crisis. Our quantitative two-sector, two-agent model is closest to the important workofGuerrieri,Lorenzoni,Straub,andWerning(2020). Inassessingthequantitativeeffects of fiscal policy during the pandemic using a model with household heterogeneity, we are also related to Faria-e-Castro (2021) and Bayer, Born, Luetticke, and Müller (2020). Our relative contribution is in showing how the effects of redistribution depend on the monetaryfiscal policy regime and then assessing both quantitative effects and welfare implications by matchingsomeimportantaggregateandsectoralaspectsoftheU.S.data. Our paper is also related to recent papers that analyze monetary-fiscal policy interactions in TANK models—in particular, Bhattarai, Lee, Park, and Yang (2022), Bianchi, Faccini, 6Canzoneri,Cumby,andDiba(2010)andLeeperandLeith(2016)arerecentsurveysofthisliterature. 7MotivatedbytheARRAAct,OhandReis(2012)assesstheeffectsoftransfersinamodelwithincomplete consumptioninsurance,alsoconsideringonlythemonetaryregime. 5

and Melosi (2021), and Motyovszki (2020). Bhattarai et al. (2022) study the effects of a one-time permanent capital tax rate change in a model that features capital-skill complementarity. Bianchietal.(2021)andMotyovszki(2020)aremotivatedbytheCOVIDcrisisandare closelyrelatedtoouranalysis.8 Ourrelativecontributionanalyticallyisanonlinearsolutionof a TANK model under the two regimes. On the quantitative side, while these studies focus on thepositiveimplicationsoftransfersunderthedifferentregimes,weadditionallyprovidewelfare implications for different types of households. We also emphasize that the positive and normative implications of redistribution are state-dependent and that inflation-financed transfers are disproportionately more effective than tax-financed transfers in a COVID-recessionlikeenvironmentinwhichbothsector-specificandaggregateshockshittheeconomy. Finally, our paper is also related to the government spending multiplier literature, as the effects of transfer policy in two-agent models share some common elements with the effects ofgovernmentspendingpolicyinrepresentativeagentmodels. Thus,inconnectingtheeffects to the nature of monetary policy, the binding ZLB, and the monetary-fiscal policy regime, our work builds on important contributions in the government spending multiplier literature byWoodford(2011),Christiano,Eichenbaum,andRebelo(2011),Eggertsson(2011),Leeper, Traum,andWalker(2017),andJacobson,Leeper,andPreston(2019). Beck-FriisandWillems (2017), in particular, show analytically that the government spending multiplier is greater underthefiscalregimethanunderthemonetaryregimeinthelinearizedstickypricemodel. 2 Simple Model and Redistribution Policy Wepresentasimplemodelthatyieldsanalyticalresultsoneffectsofredistributionpolicy. 2.1 Model There are two types of households: Ricardian and HTM. The Ricardian household makes optimal labor supply and consumption/savings decisions, while the HTM household simply consumes government transfers every period. In this setup, we analytically show the effects on inflation of transferring resources away from the Ricardian households and towards the 8Bianchietal.(2021)showthatinflatingawayatargetedfractionofdebtwillincreasetheeffectivenessofthe fiscalstimulusinamedium-scalemodelwhileMotyovszki(2020)considersasmall-openeconomyenvironment. BianchiandMelosi(2019)showsthatthefiscalregimeimprovesrepresentativehousehold’swelfare. Weshow that the fiscal regime leads to a Pareto improvement in a two-agent model where the redistribution policy is aimedatcombatingasymmetriceffectsofapandemic, andwherethepolicytrade-offisonusingdistortionary labor taxes vs. inflation taxes to finance such redistribution. We find that a key driver of our welfare results is state-dependenteffectsoftheredistributionpolicy,includingthosethatcomefromnon-linearity. 6

HTM households and point out that these effects depend critically on how the transfer policy isfinanced. 2.1.1 Households Ricardian Households. The Ricardian households, of measure 1−λ, take prices as given andchoose{CR,LR,BR}tomaximize t t t (cid:88) ∞ βt (cid:34) logCR−χ (cid:0) LR t (cid:1)1+ϕ(cid:35) t 1+ϕ t=0 subjecttoastandardNo-ponzi-gameconstraintandasequenceofflowbudgetconstraints BR BR CR+ t = (1+i ) t−1 +w LR+ΨR−τR, t P t−1 P t t t t t t where CR is consumption, LR is hours, BR is nominal government debt, ΨR is real profits, t t t t τR is lump-sum taxes, P is the price level, w is the real wage, and i is the nominal interest t t t t rate. The discountfactorand theinverse ofthe Frischelasticityare denotedbyβ ∈ (0,1)and ϕ ≥ 0 respectively. The superscript, R, represents “Ricardian.” The flow budget constraints canbewrittenas 1 CR+bR = (1+i ) bR +w LR+ΨR−τR, t t t−1 Π t−1 t t t t t wherebR = B t R istherealvalueofdebtandΠ = Pt isthegrossrateofinflation. t Pt t Pt−1 Optimality conditions are given by the Euler equation, the intra-termporal labor supply condition,andthetransversalitycondition(TVC): CR (1+i ) t+1 = β t , (2.1) CR Π t t+1 χ (cid:0) LR(cid:1)ϕ CR = w , (2.2) t t t (cid:20) 1 (cid:18) BR(cid:19)(cid:21) lim βt t = 0. (2.3) t→∞ C t R P t Hand-to-Mouth Households. The HTM households, of measure λ, simply consume governmenttransfers,sH,everyperiod(CH = sH). Thesuperscript,H,represents“HTM.” t t t 2.1.2 Firm A representative firm in the competitive product market chooses hours, L , in each period to t maximizeprofits: Ψ = Y −w L , t t t t 7

subjecttotheproductionfunction Y = L . (2.4) t t Zeroprofitconditionimplies w = 1. (2.5) t 2.1.3 Government Thegovernmentissuesone-periodnominaldebt,B . Itsbudgetconstraint(GBC)is t B B t t−1 = (1+i ) −τ +s , t−1 t t P P t t wheres istransfersandτ istaxes. Itcanbere-writtenas t t (1+i ) t−1 b = b −τ +s , (2.6) t t−1 t t Π t whereb = Bt istherealvalueofdebt. Transfer,s ,isexogenousanddeterministic. t Pt t Monetaryandtaxpolicyrulesare 1+i (cid:18) Π (cid:19)φ t t = , (2.7) 1+¯i Π¯ (τ −τ¯) = ψ(b −¯b), (2.8) t t−1 where φ and ψ determine the responsiveness of the policy instruments to inflation and government indebtedness respectively. The steady-state values of inflation, debt, and transfers, (cid:8) Π ¯ , ¯ b,s¯ (cid:9) ,aresetbypolicymakersandgivenexogenously.9 2.1.4 AggregationandtheResourceConstraint Aggregating the variables over the households yields s = λsH, τ = (1−λ)τR, b = t t t t t (1−λ)bR, L = (1−λ)LR, and Ψ = (1−λ)ΨR. Combining household and governt t t t t ment budget constraints gives the resource constraint, (1−λ)CR +λCH = Y . The resource t t t constraint, together with the HTM household budget constraint, implies that output is simply dividedbetweenthetwotypesofhouseholdsas: 1 1 1 CH = s , CR = Y − s . (2.9) t λ t t 1−λ t 1−λ t 9Weabstractfromgovernmentspendinghere,butpresentanextensionwithitinAppendixB.2. 8

2.2 Effects of Redistribution Policy We now show the effects of transferring resources away from the Ricardian households and towards the HTM households. The government can finance such a transfer program in two distinct ways. In the first policy regime, the government raises taxes sufficiently. Inflation is then stabilized in the usual way by the central bank. In the second regime, the government does not raise taxes, and the central bank allows inflation to rise to stabilize the real value of debt, thereby imposing “inflation taxes” on the Ricardian households that hold nominal governmentdebt. Thefiscaltheoryofthepriceleveloperatesinthiscase. (cid:8) (cid:9) We solve for the equilibrium time path of Y ,CR,CH,Π ,i ,b ,τ given exogenous t t t t t t t {s }. Output and consumption of the two households, and thus their welfare, are indepent dent of whether the government relies on conventional or inflation taxes. We first consider those policy-invariant variables in Section 2.2.1. The alternative financing schemes, however, generatequitedifferentinflationdynamics,whichisthemainfocusofthissimplemodel. The determinationoftherateofinflationisdetailedinSection2.2.2. 2.2.1 OutputandConsumption Westartwithoutput. Equation(2.2)canbewrittenas Y = χ−1(1−λ)1+ϕY−ϕ+s (2.10) t t t using Equations (2.4), (2.5), (2.9), and L = (1−λ)LR. Equation (2.10) implicitly defines t t outputasafunctionoftransfers: Y = Y (s ). Onecanobtainthe“transfermultiplier”as t t dY (s ) 1 t = . ds t 1+(1−λ)1+ϕ ϕY −(1+ϕ) χ t Noticethat0 ≤ dYt ≤ 1. dst An increase in transfers raises output, but not from the Keynesian demand-side reason. The channel here instead is purely classical and supply-side: An increase in s causes Rit cardian household consumption to fall, creating a negative “wealth effect” on labor supply. The households supply more hours for a given wage rate, which in turn raises output.10 The multiplier is maximized (dY /ds = 1) when labor supply is perfectly elastic (ϕ = 0) while t t it is minimized (dY /ds = 0) when the Ricardian household does not value leisure (χ = 0), t t 10Thechannelisthesameastheeffectofgovernmentspendinginaone-agentmodel. Infact,anincreasein governmentspendinghasexactlythesameeffectonoutputandinflationasanincreaseintransfersofthesame amountinthissimplemodel. ThisresultisshowninAppendixB.2. 9

whichshutsdownthewealtheffect. TheRicardianhouseholdconsumptionisobtainedfromEquation(2.9)as 1 CR = CR(s ) ≡ [Y (s )−s ]. (2.11) t t 1−λ t t Thederivativeis dCR(s ) 1 (cid:20) dY (s ) (cid:21) t t = −1 ≤ 0. ds 1−λ ds t t As will be clear below, how Ricardian household consumption depends on transfers matter for inflation dynamics as it affects the real interest rate. That is, there is a valuation effect on governmentdebtduetochangesintherealinterestrate. Thisinterestratechanneloftransfers is absent in the model with a representative household, where transfers have no redistributive role,orwithaperfectlyelasticlaborsupply. Notice that both tax types are non-distorting in this model. Consequently, for given {s }, t thealternativewaystofinancetransfers(i.e.,thepolicyregimes)havenoeffectonoutputand consumption,asseenabove. 2.2.2 Inflation Wenowturntotherestofthevariables,{Π ,i ,b ,τ }∞ ,withafocusoninflationdeterminat t t t t=0 tion, given a path of {s }∞ . The equilibrium time path of {Π ,i ,b ,τ } satisfies the system t t=0 t t t t ofdifferenceequations(2.1),(2.6),(2.7)and(2.8),theterminalconditiongivenbyTVC(2.3), andtheinitialconditions,b andi . −1 −1 Thesystemcanbesimplifiedas: (cid:18) Π (cid:19) CR (cid:18) Π (cid:19)φ t+1 = t t , (2.12) Π¯ CR Π¯ t+1 (cid:34) (cid:35) (cid:34) (cid:35) (cid:0) b −¯b (cid:1) = β−1 C t R −ψ (b −¯b)+(s −s¯)+¯b β−1 C t R −β−1 ∀t ≥ 1 (2.13) t CR t−1 t CR t−1 t−1 (cid:0) b −¯b (cid:1) = β−1 (cid:18) Π¯ −1 (cid:19) ¯b+(s −s¯) att = 0, (2.14) 0 0 Π 0 (cid:8) (cid:9) which determines {Π ,b } given {s } and CR , where note that from Equation (2.11), the t t t t ¯ latterisasimplefunctionoftransfers;s¯andbarethesteady-statevaluesof(exogenous)transfers and debt.11 Equation (2.12), obtained by combining the Euler equation and the monetary policy rule, shows how future inflation (Π ) depends on current inflation (Π ) and the real t+1 t rate captured by CR /CR. Equation (2.13) is the GBC for t ≥ 1 after we substitute out the t+1 t 11OnlineAppendixAprovidesdetail. 10

nominal interest rate (1 + i ) and taxes (τ ) using the Euler equation and the fiscal policy t−1 t rule. Equation (2.14) is the GBC at t = 0. This looks different from Equation (2.13) because i isexogenous,andthuscannotbereplacedbytheEulerequation. −1 Equation(2.13)describeshowthedeviationoftherealvalueofdebtfromthesteadystate, (cid:0) ¯(cid:1) b −b ,evolves overtime. Anincreaseintransfers overitssteadystate value(s > s¯)affects t debt dynamics directly and indirectly. First, ceteris paribus, such an increase causes b , debt t ¯ carried over to the next period, to rise above b. This direct effect is captured by the second term,(s −s¯),ontherighthandsideofEquation(2.13). Second,achangeintransfersaffects t RicardianhouseholdconsumptionasshowninEquation(2.11)andhencetherealinterestrate, which in turn influences debt dynamics. This indirect effect is reflected by r ≡= β−1 C t R t−1 CR t−1 in Equation (2.13), and operates even when the current period debt stays at the steady state ¯ (i.e. b = b). The reason is a change in interest payments for a given amount of debt—as t−1 (cid:104) (cid:105) showninthelastterm, ¯ b β−1 C t R −β−1 . CR t−1 In solving the system, we consider a redistribution program in which {s }∞ can have t t=0 arbitrary values greater than s¯until a time period T, and then s = s¯for t ≥ T + 1. In this t case,regardlessofthehistoryuntiltimeT +1,startingT +2,Equation(2.13)becomes (cid:0) b − ¯ b (cid:1) = (cid:0) β−1 −ψ (cid:1) (b − ¯ b). t t−1 How the TVC is satisfied depends on the fiscal policy parameter ψ. When ψ > 0, debt dynamicssatisfiestheTVCregardlessofthevalueofb .12 Whenψ ≤ 0,however,theTVC T+1 ¯ requires b = b, which can be achieved when monetary policy allows inflation to adjust by T+1 therequiredamount. Below,wediscusseachcaseinturn. Inflation under the Monetary Regime. When ψ > 0, inflation is solely determined by Equation(2.12)whichbecomes (cid:18) Π (cid:19) (cid:18) Π (cid:19)φ t+1 t = fort ≥ T +1, ¯ ¯ Π Π as CR, Ricardian household consumption, is constant. In this case, if we were to consider t φ < 1, the system of Equations (2.12)–(2.14) does not pin down initial inflation Π , and the 0 modelpermitsmultiplenon-explosivesolutions. We therefore, instead consider the standard case, φ > 1, which we call the monetary regime. Thisregimeproducesmultipleequilibriainwhichinflationisunboundedandaunique boundedequilibrium.13 Herewefocusontheboundedequilibrium. Inthiscase,itisnecessary 12Inaddition,ψshouldnotbetoobig. Wedonotexplicitlyconsidersuchempiricallyirrelevantcases. 13WeruleoutthecaseinwhichthepricelevelapproacheszerobytheTVC. 11

that ΠT+1 = 1. Given this “stability” condition on inflation, one can pin down Π from t = 0 Π¯ t toT alongthesaddlepath. Inparticular,inflationbeforeT +1canbesolvedbackwardusing Equation(2.12). Theinitialinflationisgivenby Π 0 = CR(s¯)φT 1 +1 (cid:20) 1 (cid:21) φ 1 = (cid:89) T (cid:20) CR(s¯) (cid:21) φ 1 . (2.15) Π¯ CR(s )CR(s )···CR(s ) CR(s ) T T−1 0 t t=0 InflationinthefollowingperiodsisthendeterminedbyEquation(2.12). Equation (2.15) shows that an increase in transfers is inflationary as the Ricardian household consumption declines below the pre-transfer level. The magnitude of the effect depends on the response of monetary policy (measured by φ), the size of transfer increases, and the duration of the redistribution program. Most importantly, the effect is transitory: When the redistributionprogramends,inflationreturnsimmediatelytothesteady-statevalue. Inflation under the Fiscal Regime. We now consider the fiscal regime where ψ ≤ 0 and φ < 1. Solving for inflation involves a similar procedure as in the monetary regime. We first identifyaterminalconditionandthenfollowthesaddlepathtopindowninitialinflation. ¯ As mentioned above, when ψ ≤ 0, the TVC requires b = b. Given this terminal T+1 condition, debt in preceding periods can be solved backward using Equation (2.13). Finally, given the solved b , the time-0 GBC Equation (2.14) determines initial inflation Π , after 0 0 whichEquation(2.12)producesanon-explosivetimepathofinflation. Todevelopintuition,letusfirstconsiderasimplecaseinwhichtransfersincreaseonlyfor ¯ one period: s > s¯and s = s¯afterwards. In this case, it is necessary that b = b; otherwise, 0 t 1 theTVCwouldbeviolated. TheGBCatt = 1isthengivenas     (cid:124) (cid:0) b 1 (cid:123) − (cid:122) ¯b (cid:1) (cid:125) =    β−1 C C R R ( ( s s¯ 0 ) ) −ψ    (b 0 −¯b)+( (cid:124) s 1 (cid:123) − (cid:122) s¯ (cid:125) )+¯b    β−1 C C R R ( ( s s¯ 0 ) ) −β−1   , (2.16) =0 (cid:124) (cid:123)(cid:122) (cid:125) =0 (cid:124) (cid:123)(cid:122) (cid:125) >1 >1 ¯ fromwhichwecanobtaintheinitialdebtlevelb ensuringthatb equalsb: 0 1 (cid:20) CR(s¯) (cid:21)−1(cid:20) CR(s¯) (cid:21) b =¯b−¯b β−1 −ψ β−1 −β−1 . 0 CR(s ) CR(s ) 0 0 ¯ ¯ Theterminalcondition(b = b)requiresb todeclinebelowb. Forthistohappen,Π adjusts 1 0 0 accordingtoEquation(2.14): Π 1 0 = . (2.17) Π¯ 1− β (s −s¯)−β (cid:104) β−1 CR(s¯) −ψ (cid:105)−1(cid:104) β−1 CR(s¯) −β−1 (cid:105) ¯b 0 CR(s0) CR(s0) 12

The redistribution policy is more inflationary under the fiscal regime than under the monetary regime. Inflation rises by more on impact: Π in Equation (2.17) is greater than Π in 0 0 Equation (2.15) even under the most dovish monetary regime (i.e. whenφ → 1.).14 More importantly, the one-time transitory increase in transfers has persistent effects on inflation here, whiletheeffectlastsonlyforoneperiodunderthemonetaryregime.15 Theresultaboveholdswithouttheinterestratechannel. Thepresenceofthethirdtermin the denominator, −β[r −ψ]−1[r −r¯], however, does cause Π to increase by more than it 0 0 0 wouldinananalogousmodelwitharepresentativehouseholdwheretransferchangeshaveno effect on the real interest rate.16 This term results from increased interest payments that exert an upward pressure on b (see Equation (2.16)). The upward pressure is offset by a further 1 decreaseinb ,whichisgeneratedbyagreaterincreaseinΠ . 0 0 The solution under a multi-period redistribution program can be similarly obtained. Suppose s = s > s¯for 0 ≤ t ≤ T.17 To obtain initial inflation, we use the property that the real t 0 interest rate is constant throughout except for the last period of a program; that is, r = r¯for t 0 ≤ t ≤ T −1andr > r¯. Equation(2.17)thengeneralizesto t Π 1 0 = , Π¯ 1− β (s −s¯) (cid:80)T (β−1−ψ)−k −β(r −ψ)−1(r −r¯)(β−1−ψ)−T ¯b 0 k=0 T T which,likeEquation(2.17),revealsbothdirectandindirect(valuation)channels. 2.3 Summary and an Extension to Nominal Rigidities To summarize, transferring resources from Ricardian to HTM households is inflationary regardless of the financing schemes considered. The fiscal regime, however, generates greater andmorepersistentinflationthanthemonetaryregime. Thenextsectionexploresquantitative implicationsinamoregeneralenvironmentwithstickypriceswheresuchdifferentialinflation 14An analytical proof under a mild sufficient condition is provided in Online Appendix A.5. In addition, we numerically verify this result in the simple and the quantitative model for a broad set of parameter values. Moreover,inAppendixB.1,weshowthatourresultsbroadlyholdeveninthepresenceofatemporaryshockthat drivestherealratenegative. Forextensiveanalysesofthefiscaltheoryinalowinterestenvironment, werefer thereadertoBassettoandCui(2018),Brunnermeier,Merkel,andSannikov(2020),andMiaoandSu(2021). 15Underthefiscalregime,φgovernsthesizeandpersistenceofinflationresponseintheensuingperiodsvia theFisherrelationship. Whenφ=0,inflationrespondsfortwoperiodsinthissimplesetup. 16Inthatmodel,thetermwoulddropbecause C 1 R =1. CR 0 17Online Appendix A.5 provides the discussion of a general multi-period redistribution program in which {s }T isanarbitrarysequence. t t=0 13

dynamicsresultindistinctallocationsandwelfarelevels–unlikeinthesimplemodel.18 3 Quantitative Model and COVID Application We now present a quantitative version of the model with an application focused on the economic crisis induced by COVID, modeled by introducing demand and supply shocks, and subsequent transfer policy, as embedded in the CARES Act. Compared to the simple model, themainextensionisadevelopmentofatwo-sectorproductionstructurewithstickyprices,as wellastheintroductionofdistortionarytaxessuchthatthetrade-offbetweendifferentsources of financing government debt is meaningful. We describe the model succinctly below, with detailsinOnlineAppendixB. 3.1 Model There are two distinct—Ricardian and HTM—sectors. Ricardian households work in the former,andtheHTMhouseholdswork inthelatter. Eachsectorproducesadistinctgood, which isinturnproducedindifferentiatedvarieties. Pricesofdifferentiatedvarietiesaresticky. Firms in both sectors are owned by the Ricardian households. The government finances transfers to theHTMhouseholdsbylevyingdistortionarylabortaxesontheRicardianhouseholds. Inthe fiscalregime,partialfinancingalsohappensbyinflatingawaynominaldebt. 3.1.1 RicardianSector Households. Ricardian(R)households,ofmeasure1−λ,solvetheproblem (cid:88) ∞ (cid:34)(cid:0) CR (cid:1)1−σ (cid:0) LR (cid:1)1+ϕ(cid:35) max βtexp(ηξ) t −χ t {CR,LR, Bt R } t=0 t 1−σ 1+ϕ t t Pt R subjecttoastandardNo-ponzi-gameconstraintandasequenceofflowbudgetconstraints 1 (cid:0) (cid:1) CR +bR = (1+i ) bR + 1−τR wRLR +ΨR, t t t−1 ΠR t−1 L,t t t t t 18OnlineappendixAalsocontainsasimplemodelwithstickyprices. Quantitatively,apriori,itisunclearif higher and more persistent inflation under the fiscal regime improves Ricardian household welfare in a sticky price model because while their consumption would not decrease as much, they would have to work more not onlytoproducemoreoutputbutinaddition,highandpersistentinflationinthefiscalregimeproducesresource misallocations,whichincreaselaborhoursrequiredtoproducethesameamountoffinaloutput. 14

where ηξ is a preference shock.19 Labor tax, τR wRLR, constitutes one way in which the t L,t t t governmentfinancestransferstotheHTMhousehold. ConsumptiongoodCR isaCESaggregator(ε > 0)ofthetwosectoralconsumptiongoods t C t R = (cid:104) (α) 1 ε (cid:0) C R R ,t (cid:1)ε− ε 1 +(1−α) 1 ε (cid:0) exp(ζ H,t )C H R ,t (cid:1)ε− ε 1(cid:105) ε− ε 1 where CR and CR are R-household’s demand for R-sector and for HTM-sector goods, re- R,t H,t spectively. α is Ricardian households’ consumption weight on R-sector goods and ζ is a H,t demand shock that is specific for HTM goods. Let us define for future use, one of the relative (cid:16) PR (cid:17) prices, X ≡ R,t , where PR is the R-sector’s good price while PR is the CPI price R,t PR R,t t t indexoftheR-household. Withineachsector,differentiatedvarietiesareproducedundermonopolistic competition. Thus, CR and CR are Dixit-Stiglitz aggregates of a continuum of R,t H,t varietieswithanelasticityofsubstitution,θ > 1. Firms. Firmsproducedifferentiatedvarietiesusingthelinearproductionfunction,Y (i) = R,t L (i), and set prices according to the Calvo friction, where ωR is the probability of not R,t getting a chance to adjust prices. There is no price discrimination across sectors for varieties andweimposethelawofoneprice. 3.1.2 Hand-to-MouthSector Households. HTMhouseholds,ofmeasureλ,solvetheproblem (cid:16) (cid:17)1+ϕ (cid:0) CH (cid:1)1−σ (1+η t ξ)LH t max t −χH {CH,LH} 1−σ 1+ϕ t t subjecttotheflowbudgetconstraint CH = wHLH +Q sH, t t t t t whereηξ isashocktodisutilityfromlabor,wH istherealwage,andLH islaborsupply. Note t t t that relativeprice, Q ≡ P t R , appears intransfers as forfiscal variables weuse the CPIfor the t PH t Ricardianhouseholdasdeflator. CH isaCESaggregatoroftheconsumptiongoodsproducedinthetwosectors t C t H = (cid:104) (1−α) 1 ε (cid:0) exp(ζ H,t )C H H ,t (cid:1)ε− ε 1 +(α) 1 ε (cid:0) C R H ,t (cid:1)ε− ε 1(cid:105) ε− ε 1 , where1−α isHTMhouseholds’consumptionweightontheHTM-sectorgoodsandζ isa H,t demandshockspecificforHTM-sectorgoods.20 Letusdefineforfutureuseoneoftherelative 19Theothernotationsarethesameasbefore. 20Weimposethesameconsumptionbasketacrosshouseholdsmotivatedbythedata,implyingthatQ =1. t 15

PH prices, X ≡ H,t, where PH is the HTM sector’s good price while PH is the CPI price H,t PH H,t t t index of the HTM household. C and C are Dixit-Stiglitz aggregates of a continuum HH,t HR,t ofvarietieswithanelasticityofsubstitution,θ > 1. Firms. Firmsproducedifferentiatedvarietiesusingthelinearproductionfunction,Y (i) = H,t L (i), and set prices according to the Calvo friction, where ωH is the probability of not get- H,t tingachancetoadjustprices. 3.1.3 Government ThegovernmentflowbudgetconstraintisgivenbyB +TL = (1+i )B +PRs ,wheretax t t t−1 t−1 t t revenues TL = (1−λ)τR PRwRLR. Transfer (deflated by CPI of the Ricardian household), t L,t t t t s ,isexogenousanddeterministic. Notethat,s = λsH andb = (1−λ)bR. t t t t t Monetaryandtaxpolicyrulesareofthefeedbacktypeswith“smoothing”,givenby 1+i (cid:40) 1 (cid:18) 1+i (cid:19)ρ1 (cid:18) 1+i (cid:19)ρ2 (cid:34) (cid:18) Π (cid:19)φ(cid:18) Y (cid:19)φx (cid:18) Y (cid:19)φ∆y (cid:35)(1−ρ1−ρ2)(cid:41) t t−1 t−2 t t t = max , , 1+¯i 1+¯i 1+¯i 1+¯i Π¯ Y¯ Y t−1 (cid:18) b −¯b (cid:19) τR −τ¯R = ρ (τR −τ¯R)+(1−ρ )ψ t−1 , L,t L L L,t−1 L L L ¯b whereΠ = (1−λ)ΠR+λΠH istheaverageinflation,Y isaggregateoutputwhichisdefined t t t t later, and the zero lower bound on the nominal rate applies.21 As in the simple model, the monetaryregimewillfeaturelargeenoughmonetaryandtaxruleresponsecoefficients,φand ψ , such that government debt sustainability does not need to be ensured via inflation. In L contrast, in the fiscal regime, a low enough tax rule coefficient, ψ , implies that monetary L policyhastobeaccommodativeviaalowenoughφ,suchthatdebtis(atleastpartly)financed viainflation. Thepolicyrulesfeaturesmoothing,asgivenbyρ ,ρ ,andρ ,andthemonetary 1 2 L policyrulefeaturesfeedbacktooutput(givenbyφ )andoutputgrowth(givenbyφ ).22 x ∆y 3.1.4 MarketClearing,Aggregation,ResourceConstraints Given wages and prices, labor and good markets clear in equilibrium. Define economy-wide consumption as C = (1−λ)CR +λQ CH. Then, an aggregate resource constraint is given t t t t by Y = C = X Y +X Q Y . Lastly, by aggregating firms’ production functions, we t t R,t R,t H,t t H,t 21Whether we define the price index in the monetary policy rule as population weighted as above, or as consumptionbasketshareweighted(usingαastheweightforΠR),doesnotmatterquantitatively. t 22The monetary policy rule specification follows Coibion and Gorodnichenko (2011). As we do not have productivityshocksinthemodel,wedonotincludeanoutput“gap”termintherule. 16

canderiveaggregatesectoraloutputs,(1−λ)LR = Y Ξ andλLH = Y Ξ ,whereΞ t R,t R,t t H,t H,t j,t forj ∈ {R,H}isthepricedispersiontermarisingfromstickyprices.23 3.2 Data and Calibration We pick parameter values based on long-run averages or from the literature while calibrating the shocks to match employment and inflation dynamics during the COVID crisis. Table 1 presentsourcalibration. ThedataaredescribedindetailinAppendixA. The model is calibrated at a two-month frequency with a time discount factor of β = 0.9932. WesettheinverseoftheFrischelasticity(ϕ)tobe0.3andtheinverseoftheelasticity of intertemporal substitution (σ) to be 1.0, following Gertler and Karadi (2011). We set the elasticityofsubstitutionacrossfirmstobefour(θ = 4),whichcorrespondstoarecentestimate ofaveragemarkupof33percent(Hall,2018). WeassumethattheRicardianandHTMgoods aresubstitutesbysettingtheelasticity((cid:15))as2.0,toensurethatourresultsarenotbeingdriven by the assumption of complementarity in consumption of sectoral goods. We pick the Calvo parameters for the Ricardian sector as ωR = 0.75 and for the HTM sector as ωH = 0.80, which are consistent with estimates in Carvalho, Lee, and Park (2021).24 Finally, the steadystategrossinflationis1. WesetthefractionofHTMhouseholds(λ)tobe0.23,basedonemploymentshareofretail trade, transportation and warehousing, and leisure and hospitality sectors in the U.S. Bureau of Labor Statistics (BLS).25 We use the 2019 Consumer Expenditure Surveys (CEX) data to calibrate α, the share parameters in the consumption baskets. We assume households in the top 80 percentile of the income distribution as Ricardian households and set 1−α as 0.28 to matchtheirconsumptionsharefortransportationandfoodawayfromhome.26 For the steady-state of fiscal variables, we use federal debt, federal receipts, and current government transfer payments data from 1990:Q1 through 2020:Q1. We use post-Volcker estimates in Coibion and Gorodnichenko (2011) to set the Taylor rule parameters under the monetaryregime. WealsousethetaxruleestimatesinBhattarai,Lee,andPark(2016)forthe taxruleparametersunderthemonetaryregime. 23AllmodeldetailsandequilibriumconditionderivationsareinOnlineAppendixB. 24HTM-sectorincludesTransportation,Recreational,andFoodservices,andRicardiansectoristherestofthe economy.WetakesectoralaveragesforthepriceinfrequencyestimatesbasedonCarvalho,Lee,andPark(2021), whichimplya8-monthand10-monthdurationofpricechangesfortheRicardianandHTMsectorrespectively. 25Using the Panel Study of Income Dynamics data, Aguiar, Bils, and Boar (2020) estimate 23% of HTM householdswhosenetworthislessthantwomonthstheirlaborearnings. 26Thisvalueofαisthesameifweassumehouseholdsinthebottom20percentileoftheincomedistributionas HTMhouseholdsandtargettheirconsumptionshares,whichiswhywemodeledthesameconsumptionbasket forthetwohouseholds. 17

Table1: Calibration Value Description Sources Households β 0.9932 Timepreference 2-monthfrequency σ 1.0 InverseofEIS GertlerandKaradi(2011) ϕ 0.3 InverseofFrischelasticity GertlerandKaradi(2011) χ 3.08 RicardianLaborsupplydisutility L¯R=0.3(BLSData) χH 3.53 HTMLaborsupplydisutilityparameter L¯H =0.25(BLSData) Employmentshareofretail, λ 0.23 FractionofHTMhouseholds transportation,leisure/hospitality Consumptionweight α 0.72 ConsumerExpenditureSurveysdata onRicardiangoods Firms θ 4.0 Elasticityofsubstitutionacrossfirms Steady-statemarkup:33%(Hall,2018) Elasticityofsubstitutionbetween ε 2.0 Assigned RicardianandHTMgoods ωR 0.75 CalvoparameterforRicardiansector Carvalhoetal.(2021) ωH 0.80 CalvoparameterforHTMsector Carvalhoetal.(2021) Government ¯b 0.509 Steady-statedebttoGDP Data(1990Q1–2020Q1) 6Y¯ T¯L 0.122 Steady-statelabortaxrevenuetoGDP Data(1990Q1–2020Q1) Y¯ s¯ 0.127 Steady-statetransferstoGDP Data(1990Q1–2020Q1) Y¯ MonetaryandFiscalPolicyRules ρ (1.12,0.0) Interestratesmoothinglag1 CoibionandGorodnichenko(2011) 1 ρ (-0.18,0.0) Interestratesmoothinglag2 CoibionandGorodnichenko(2011) 2 φ (1.58,0.0) Interestrateresponsetoinflation CoibionandGorodnichenko(2011) π φ (0.11,0.0) Interestrateresponsetooutput CoibionandGorodnichenko(2011) x φ (2.21,0.0) Interestrateresponsetooutputgrowth CoibionandGorodnichenko(2011) ∆y ρ (0.84,0.0) Labortaxsmoothing Bhattaraietal.(2016) L ψ (0.1,0.0) Labortaxrateresponsetodebt Bhattaraietal.(2016) L Shocks Totalhoursforretail, ηH (-9%,17%,17%) SizeofHTMlabordisutilityshock t transportation,leisure/hospitality Totalhoursexcludingretail, ηξ (-7%,-22%,-21%) SizeofRicardianpreferenceshock t transportation,leisure/hospitality PCEInflationforrecreation, ζ (-4%,-0.9%,3%) SizeofHTMsectordemandshock H,t transportation,foodservices s 26.8% Sizeoftransferdistribution 2020CARESAct t Notes:Thistableshowsmodelparametervaluesusedforourbaselinesimulation.SeeSection3.2fordetails. To examine the dynamic effects of transfer policy, we calibrate the size of transfer distribution using the transfer amounts specified in the CARES Act, which came into operation in mid-April. Inparticular,wetargetthesumofthreekeycomponentsoftheAct: $293billionto provide one-time tax rebates to individuals; (ii) $268 billion to expand unemployment benefits;and(iii)$150billionintransferstostateandlocalgovernments. Thesethreecomponents 18

oftheCARESActconsistofaround3.4percentofGDP.Givenourcalibrationofsteady-state government transfers, this in turn amounts to an increase in transfers of 26.8 percent.27 In our baseline exercise of transfer policy, we assume that the total amount of transfer is equally distributedoversixmonths—thatis,threeperiods. A key component of our calibration is how we choose the shock sizes. The size of the three shocks (ηH,ηξ,ξ ) are estimated to match the dynamics, under the monetary regime t t H,t with transfer policy, of total hours for both the HTM and Ricardian sectors and inflation for theHTMsector,asgiveninAppendixFigureA.1. Inourbaselinecalibration,weassumethat thethreeshocksinthemodelareoverafterthreeperiods. In particular, we set the size of HTM sector labor disutility shocks to match BLS total hours changes from April through August in HTM sectors (retail trade, transportation and warehousing, and leisure and hospitality sectors). We then calibrate the size of the Ricardian preference shocks to match BLS total hours changes for sectors excluding HTM sectors, also fromAprilthroughAugust. Finally,wesetthesizeofHTMsector-specificdemandshocksto matchthePCEinflationforrecreation,transportation,andfoodservicessectorsfromtheU.S. Bureau of Economic Analysis.28 The three shocks series can perfectly match the dynamics of total hours and inflation from April through August, as reported in detail in Panel A of AppendixTableC.1. Moreover,PanelBofAppendixTableC.1showsthatourcalibrationisnotcompletelyoff regardingthematchwithseveralnon-targetedmoments. Forexample,aggregateconsumption and output dynamics in the model are close to that in the data. In terms of sectoral consumption,themodeldynamicsisclosetotherealPCEsectoraldatainitially.29 3.3 Quantitative Results Wenowpresentquantitativeresultsonimplicationsofredistributionpolicyduringacrisis. 3.3.1 DynamicEffectsofTransferPolicy We show how key variables evolve over time in response to the COVID shocks—a combination of aggregate and sector-specific demand and supply shocks as discussed above. We then 27InasensitivityanalysisinSection3.4.2, wedropthetaxrebatecomponentoftheCARESActwhilecalibratingthetransferincrease. 28Whilethisintuitivelydescribesourestimationprocedure,wematchjointlythedatawithallshocks. 29Intermsofanon-targetedmomentthatwedonotmatchaswell,ourcalibrationimpliesabiggerdropininflationintheRicardiansectorthanthedata. Achangeinmodelparametersand/orcalibrationstrategytomatchthis momentwillhowever,adverselyaffectthecurrentlygoodnon-targetedfitwithrespecttoaggregateconsumption, aswellaspotentiallymaketheZLBnotbindinginthemonetaryregime,whichwouldbecounterfactual. 19

0 0 10 -5 0 -5 -10 -10 -10 -20 -15 -30 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 1 1 0 0 -5 -1 -1 -2 -10 -3 -2 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 2 4 6 8 10 12 1.5 0.3 6 1 0.2 4 0.1 2 0.5 0 0 0 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Figure1: RedistributionPolicywithDifferentPolicyRegimes Notes:ThisfigureshowsdynamicsofkeyvariablesinresponsetotheCOVIDshocksunderdifferentregimes. Blue solid lines represent the monetary regime without transfers. Red dashed lines, green dotted lines, and orangedashedlinesrepresentrespectivelythefiscalregimewithouttransfers,themonetaryregimewithtransfers, and the fiscal regime with transfers. The unit is percent deviation from the steady-state level of each variable,exceptforthebottomleftpanel,whereweshowthelevelofthenetinterestrate. illustratetheeffectsofanincreaseintransfersforthetworegimes. TheseresultsareinFigure 1, which presents four different scenarios: the monetary regime with and without transfers to the HTM households and the fiscal regime with and without transfers. Throughout, the duration of the redistribution policy is three periods (six months), which coincides with the durationoftheshocks.30 Let us first look at the benchmark case, where the policymakers just stick to the usual macro policy (i.e. monetary regime) without redistribution. In this benchmark, the COVID shocks generate significant short-run contractions in aggregate output and household con- 30Wesolvethemodelnon-linearlyunderperfectforesight,andnon-linearityisimportantforthequantitative results. All the model variables converge back to the steady state in the long run. Initial debt is also at steady state,sothatwecanfocusondebtdynamicsduetoCOVIDshocks. InSection3.4.4,weconsideracasewhere initialdebtisabovesteadystate. 20

sumptionofbothtypes,asshownbythesolidbluelinesinthefirstrowofthefigure. Thecontraction leads to a decline in inflation (as shown in the second row) and in labor tax revenues, bothofwhichinturnincreasetherealvalueofgovernmentdebt. Thegovernmentrespondsby increasing the tax rate to stabilize debt under this standard monetary regime. Meanwhile, the central bank decreases the nominal interest rate in response to the decline in inflation. These policyresponsesareshowninthebottomrowofthefigure. NoticethattheZLBendogenously bindsinourmodelduringthepandemic,withoutuscalibratingitasatarget. Now, let us introduce the redistribution program to the monetary regime, the results of which are shown by the dotted green lines in Figure 1.31 Overall, the effects of the redistribution program are largely in line with what we have shown using the simple model in Section 2. One major difference from the simple model is that the redistribution program is more expansionaryherebecauseboththeclassicallaborsupplychannelandtheKeynesianchannel operatethankstonominalrigidities,aswediscussedinSection2.3. Transfers(directly)increaseHTMhouseholdconsumptionanddecreaseRicardianhousehold consumption (due to both the resulting increase in the tax rate and the mechanism outlined in the simple model) relative to the benchmark. These are the direct effects of the redistribution. As discussed in Section 2, however, the redistribution program is inflationary, as shown by the difference between the solid blue lines and the dotted green lines in the second row. This indirectly has a positive effect on household consumption of both types through general equilibrium. In particular, Ricardian household consumption does not appear to drop compared to the benchmark case as the indirect positive effect of the redistribution on Ricardianhouseholdconsumptioncountervailsthedirectnegativeeffect. Letusnowturntothefiscalregimewhereneitherthetaxratenorthenominalinterestrate changes. The effect of the redistribution program under this regime is shown by the dashed orange lines in Figure 1. Redistribution is more expansionary under this regime than under the monetary regime. Consequently, aggregate and Ricardian sector output and consumption of both types do not drop as much as in the monetary regime—as shown by the orange lines thatarelocatedabovethegreenlinesinthefirstfourpanelsofFigure1. As in the simple model, the fifth and sixth panels of Figure 1 reveal that the fiscal regime generatesgreaterandmorepersistentinflationthanthemonetaryregime,asthatstabilizesthe real value of government debt without relying on labor taxes. Due to nominal rigidities, this inturnhaslargerandlonger-lastingpositiveeffectsonoutputandconsumption. Furthermore, theZLBbindsinthemonetaryregimeaswediscussedabove,whichpreventsthecentralbank from decreasing the policy rate according to the monetary policy rule, and leads to a bigger 31Aswediscussedbefore,transfersincreaseby26.8percentintotalandareevenlydistributedover3periods. 21

Table2: TransferMultipliers MonetaryRegime FiscalRegime MM(Y) MM(Y ) MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t ImpactMultipliers 1.923 1.863 0.119 7.828 2.949 2.726 1.166 8.788 4-YearCumulativeMultiplier 1.732 2.023 -0.002 7.409 5.552 5.429 3.078 13.652 Notes:Thistableshowsthetransfermultipliersunderthemonetaryandfiscalregimes.Mi(X)representthecumulativetransfer t multiplierofvariableXatt-horizonunderiregime.Wereportimpactmultipliers(t=0)aswellas4–year(t=24)cumulative multiplierswhenthegovernmentdistributestransfersevenlyover6months. dropinthemonetaryregime. Thismechanismisnotrelevantforthefiscalregime. 3.3.2 TransferMultipliers As a way to summarize these dynamic responses with and without redistribution policy, we now present results in terms of transfer multipliers for output and consumption. The transfer multiplierforoutput,forinstance,underregimei ∈ {M,F}isdefinedas (cid:32)(cid:80)t βh(Y˜i−YM) (cid:33) Mi(Y) = h=0 h h , t (cid:80)t βhs h=0 h whereY ˜i isoutputathorizonhunderi-regimewithtransfers,YM isoutputathorizonhunder h h the monetary regime without transfers (i.e. the benchmark), and s is transfers at horizon h h. The multipliers for Ricardian sector output and the two consumption under i-regime— denoted respectively by Mi(YR), Mi(CR) and Mi(CH)—are similarly defined. Following t t t thegovernmentspendingmultiplierliterature,weconsiderimpactmultiplier(t = 0)aswellas 4–year(t = 24)cumulativemultipliers,whichallowsforaconsiderationofdynamiceffectsin themodel. Thesedynamiceffectsareimportantforouranalysisasthemodelfeaturesseveral sourcesofendogenouspersistence,includingpolicyrules. Note that in calculating these multipliers, our benchmark case, as in Section 3.3.1, is always the monetary regime without transfers.32 This is the most relevant case to study, as we want to answer the question: Given a transfer policy we want to implement, what are the differencesbetweenusinglabortaxesorinflationtaxestofinancetheincreaseindebt? Table2showsthataggregateoutputandRicardiansectoroutputmultipliersarebothabove 1 in the monetary regime. Similarly, the CH multiplier is above the simple model benchmark of (1/λ), which would be 4.35 according to our calibration. The binding ZLB, sticky prices, and the COVID shocks contribute to the greater multipliers in this quantitative model—as detailedbelowinSection3.4.1. 32Althoughincalibratingthemodel,weusethemonetaryregimewithtransferpolicytomatchthedata. 22

Table3: WelfareGains MonetaryRegime FiscalRegime Long-run Short-run Long-run Short-run (t = 4) (t = 4) RicardianHousehold -0.014 -1.465 0.011 -1.214 HTMHousehold 0.076 6.277 0.118 7.774 Notes: This table shows long- and short-run welfare gains resulting from the redistribution, compared to the monetary regime without transfer distribution. The values are the difference in the welfare measure (µi ) t,k betweenthetransfercases(underthetworegimes)andthethemonetaryregimewithouttransfers. Table 2 also shows that those multipliers are even higher in the fiscal regime. In fact, uniquely, even the CR multiplier is now positive in the fiscal regime for all horizons. The fact that the 4-year cumulative multiplier for CR is positive in the fiscal regime distinguishes it from the monetary regime where it is negative.33 The persistent inflation dynamics in this regime lead to persistent real effects due to sticky prices, which contributes to these higher multipliers. Later, in Section 3.4.1, we delve more deeply into the mechanisms that produce suchlargedifferencesinthemultipliersbetweenthetworegimes. 3.3.3 WelfareEffectsofTransferPolicy We finally show the effects on household welfare of the redistribution program. We consider both short- and long-run welfare effects. To this end, we implicitly define our measure of welfaregainforhouseholdoftypei ∈ {R,H},µi ,as t,k t t (cid:88) βjU (cid:0) Ci,Li(cid:1) = (cid:88) βjU (cid:0)(cid:0) 1+µi (cid:1) C¯i,L¯i(cid:1) , j j t,k j=0 j=0 where (cid:8) C ¯i,L ¯i (cid:9) is the steady-state level of type-i household’s consumption and hours, and (cid:8) (cid:9) Ci,Li are the time path of type-i household’s consumption and hours under the different j j transferdurationpolicies(indexedbyk). Inthisway,µi measureswelfaregainsfromperiod t,k 0 till (arbitrary) period t in units of a percentage of the steady-state (or pre-COVID) level of consumption—when the redistribution program lasts for k periods.34 The lifetime (total) welfare gain is then measured by µi ≡ lim µi , often the focus of the business cycle ∞,k t→∞ t,k literature. Recall that, unless otherwise noted, we report the case in which k = 3; that is, the durationoftheredistributioncoincideswiththedurationoftheshocks. 33Inthesimplemodelwhereinflationisneutral,weshowedanalyticallythatthismultiplierisnegative. 34Itmeasureswelfaregainsatthepointwhentheagentsare2×tmonthsoldsincetheinitialCOVIDshocks. 23

1.4 12 0 1.2 10 1 -0.5 8 0.8 -1 6 0.6 -1.5 4 0.4 -2 2 0.2 0 0 0 3 6 9 12 15 0 3 6 9 12 15 0 3 6 9 12 15 Figure2: Short-RunWelfareGainsComparison Notes:Thisfigurepresentstheshort-runwelfaregainsresultingfromtheredistribution,comparedtotheeconomywithouttransferredistribution. Thevaluesarethedifferenceinthewelfaremeasures(µi )betweenthe t,k transfercases(undermonetaryandfiscalregimes)andthewithout-transfercaseunderthemonetaryregime asafunctionoftime. We find that whether the government introduces the redistribution program and how it is financed make a very small difference for the lifetime welfare for both types of households. This result is presented in Table 3. For example, the redistribution program financed by inflation taxes, that is the fiscal regime, increases the HTM households’ lifetime welfare by 0.118 percentage point and increases the Ricardian households’ lifetime welfare by 0.011 percentage point, compared to the benchmark. This result is expected because the COVID shocks under consideration are short-lived, which implies the recession is only a small bump in the lifetime.35 Despite this caveat on the quantitative magnitudes, our key qualitative finding is that of a Pareto improvement (only) under the fiscal regime, compared to the benchmark case ofnotransferpolicyinthemonetaryregime. Transfers and how they are financed matter much more in the short run. Figure 2 presents the aggregate and both households’ welfare gains over time. The redistribution program, regardless of the policy regimes, increases the welfare of the HTM households significantly in the short run. The gains, however, are even bigger when the program is inflation-financed. For example, the HTM households’ welfare gains over the first 8 months (at t=4) from such redistribution amount to 7.774 percentage points of the steady-state consumption under the fiscal regime and 6.277 percentage points under the monetary regime, as reported in Table 3. TheRicardianhouseholdswouldsufferwelfarelosseswithredistributionintheshortrun,but 35Weshutdownallshocksotherthanthethree-periodCOVIDshocksoverthelifetime.Therefore,thisexercise isdifferentfromtheusualonesinthebusinesscycleliterature. 24

Table4: TransferMultipliersDecomposition MonetaryRegime FiscalRegime MM t (Y) MM t (YR) MM t (CR) MM t (CH) MF t (Y) MF t (YR) MF t (CR) MF t (CH) PanelA:ImpactMultipliers TotalEffect 1.923 1.863 0.119 7.828 2.949 2.726 1.166 8.788 CovidEffectwithTransfer -11.628 -7.422 -2.567 -41.289 -12.571 -8.178 -2.403 -45.856 TransferEffectwithoutCovid 2.670 2.464 -0.911 14.394 4.640 4.083 -0.028 19.920 CovidEffectwithoutTransfer -10.881 -6.821 -3.597 -34.723 -10.881 -6.821 -3.597 -34.723 PanelB:4-YearCumulativeMultipliers TotalEffect 1.732 2.023 -0.002 7.409 5.552 5.429 3.078 13.652 CovidEffectwithTransfer -10.954 -7.083 -7.786 -21.321 -8.340 -4.779 -5.558 -17.447 TransferEffectwithoutCovid 1.490 1.703 -1.107 9.991 2.696 2.805 -0.256 12.359 CovidEffectwithoutTransfer -11.196 -7.403 -8.891 -18.739 -11.196 -7.403 -8.891 -18.739 Notes: Thistableshowsthedecompositionofthetransfermultipliersforaggregateoutput,Ricardiansectoroutput,Ricardianconsumption andHTMconsumption,asgiveninEquation(3.1). Mi(X)representthecumulativetransfermultiplierofvariableXatt-horizonunderi t regime.Wereportimpactmultipliers(t=0)aswellas4–year(t=24)cumulativemultipliers. thelossesarerelativelymilderunderthefiscalregime: att=4,thelossesare1.214percentage pointsunderthefiscalregimeand1.465percentagepointsunderthemonetaryregime. 3.4 Extensions and Sensitivity Analysis Wenowconsidersomeimportantextensionsandsensitivityanalysis. 3.4.1 InspectingtheMechanismsofTransferMultipliers As our main extension, we do several exercises to inspect the mechanisms that drive transfer multipliers across the two regimes. First, we decompose the transfer multiplier into three differentcomponentsinTable4,whereinthisdecomposition,theoutputmultiplier,forinstance, underregimei ∈ {M,F}is (cid:32)(cid:80)t βh(Y˜i−Y˜i ) (cid:33) (cid:32)(cid:80)t βh(Y˜i −Y¯) (cid:33) (cid:32)(cid:80)t βh(YM −Y¯) (cid:33) Mi(Y)= h=0 h noshock,h + h=0 noshock,h − h=0 h t (cid:80)t βhs (cid:80)t βhs (cid:80)t βhs h=0 h h=0 h h=0 h (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) COVIDEffectwithTransfer TransferEffectwithoutCOVIDShocks COVIDEffectwithoutTransfer (3.1) where Y ˜i is output at horizon h under i-regime with both transfers and COVID shocks, h Y ˜i is output at horizon h under i-regime with transfers, but without COVID shocks, noshock,h YM isoutputunderthemonetaryregimewithCOVIDshocks,butwithout transfers,Y ¯ isouth putatsteady-state,ands istransfersathorizonh. Notethatthethirdeffectisthesameacross h regimes,whilethefirsttwoaredifferentastheycomputetheeffectforagivenregime. 25

As Table 4 shows, even without the COVID shocks, the transfer multipliers are higher in the fiscal regime. This result is captured by the second component in Equation (3.1). For example, this component of the 4-year cumulative multiplier for output is 2.696 under the fiscal regime, while it is only 1.49 under the monetary regime. The main reason for these resultsisthehighandpersistenteffectsoninflationinthefiscalregime. We now consider the state-dependence of the transfer multipliers, first within and then across the regimes. First, in each of the two regimes, the 4-year cumulative transfer multipliers for output and Ricardian consumption conditional on no COVID shocks (i.e. the second component) are less than the total multipliers. In the absence of the COVID shocks—that is, if the economy were in the steady state—transfer-induced inflation, while boosting the economy, would also generate inefficient price dispersion, which in turn would lead to resource misallocations and decrease labor productivity. However, if the economy were already in a COVID-recession,inflationarypressuresresultingfromredistributionwouldactuallycounteractdeflation,therebydecreasing,ratherthanincreasing,theextentofsuchpricedispersion. In addition,inthecaseofmonetaryregime,theZLBisirrelevantwithnoCOVIDshocks,which meansthattransfer-inducedinflationarypressuresdonotleadtoasstrongaboostinRicardian consumptionastherealinterestratedoesnotdecreasestrongly. Second, comparing the two regimes, the transfer multipliers are more state-dependent in thefiscalregimethaninthemonetaryregime. Thatis,transfersaredisproportionatelymoreeffectiveinthefiscalregimethaninthemonetaryregimewhentheeconomyfallsintoaCOVIDrecession. Thereasonisthattheaforementioned“counteracting”forceismuchstrongerinthe fiscalregimethatproduceshigherandmorepersistentinflation.36 Table4showsthatthelarge difference in the 4-year cumulative multipliers between the two regimes is driven quantitatively by the first component, which captures how the effectiveness of transfers depends on thepresenceofCOVIDshocks. Thisisameasureofstatedependence. Besidesthestatedependence,ourquantitativemodelincludestwoadditionalfeaturesthat break the uniformity—obtained in the simple, analytical model—of the two regimes in terms of the multipliers. They are nominal rigidities and distortionary labor taxes. In order to isolate the role of these two features, we delve more into the second component of the transfer multipliersinEquation(3.1)throughcounterfactualexercises. For reference, Panel A of Table 5 first re-reports the second component in the presence of the two features.37 We then remove nominal rigidities (in Panel B) and further remove distor- 36WecanseethisinthefifthpanelofFigure1. Withouttransfer,asshownbytheblueline,theCOVIDshocks generateasignificantdeflation,whichcanbeundonebyinflation-financedtransfers(shownbytheorangeline). 37ThevaluesinthepanelarethusthesameasthoseinthethirdrowofeachpanelofTable4. 26

Table5: TransferMultiplierswithoutCOVIDShocks MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:WithoutCOVIDshocksunderstickyprice ImpactMultipliers 2.670 2.464 -0.911 14.394 4.640 4.083 -0.028 19.920 4-YearCumulativeMultiplier 1.490 1.703 -1.107 9.991 2.696 2.805 -0.256 12.359 PanelB:WithoutCOVIDshocksunderflexibleprice ImpactMultipliers 0.184 0.931 -0.747 3.230 0.184 0.931 -0.747 3.230 4-YearCumulativeMultiplier -0.115 0.63 -1.095 3.094 0.184 0.931 -0.747 3.230 PanelC:WithoutCOVIDshocksunderflexiblepriceandlump-sumtaxadjustment ImpactMultipliers 0.184 0.931 -0.747 3.230 0.184 0.931 -0.747 3.230 4-YearCumulativeMultiplier 0.184 0.931 -0.747 3.230 0.184 0.931 -0.747 3.230 Notes:ThistableshowsthetransfermultiplierswithoutCOVIDshocks.PanelAreportsmultipliersunderstickypricesanddistortionarylabortaxes.PanelsBreportsmultipliersunderflexiblepricesanddistortionarylabortaxes.PanelsCreportsmultipliers underflexiblepricesandnon-distortionarylump-sumtaxes. tionary labor taxes (in Panel C). The last version is quite close to our analytical model. This exercise thus progressively allows an analysis of which elements are responsible for differencesbetweenthesimpleandthequantitativemodelresults—besidestheCOVIDshocks. PanelBofTable5showsthatthemultipliersdecreasesubstantiallywithflexibleprices,as is often also found in the government spending multiplier literature. In fact, now the impact multipliers are the same across the regimes, as was the case in our simple, analytical model, as different inflation dynamics do not affect real allocations. Moreover, output multipliers are now below 1, the Ricardian consumption multiplier is negative, and the HTM consumption multiplier is closer to 4.35, the analytical model solution.38 The cumulative multipliers are different from the impact multiplier in the monetary regime—unlike the simple, analytical model—due to dynamics of distortionary labor taxes. To make this clear, Panel C of Table 5 showsthecasewheretheincreaseintransfersarefinancedbylump-sumtaxesontheRicardian household. Then, all the multipliers are the same across the regimes and over horizons, as in thesimple,analyticalmodel. Finally, to further explore the mechanisms that underlie the multipliers, and in particular to emphasize the role of heterogeneity, we now analyze an alternative model economy with a representative Ricardian household. For this exercise, for a clear comparison, we start the economyfromsteady-stateandwithouttheCOVIDshocks. 38Thesimplemodelwould predictaRicardiansectoroutputmultiplierof0.644and Ricardianconsumption multiplierof-0.464. Notethatthesimplemodelimposeslogutilityandisalsoaone-sectorenvironment. 27

Table6: TransferMultipliersandInflationVolatilitywithoutCOVIDShocks MonetaryRegime FiscalRegime MM(Y) MM(CR) VarM(Π) MF(Y) MF(CR) VarF(Π) t t t t t t PanelA:BaselineModel ImpactMultipliers 2.670 -0.911 4.640 -0.028 1 1.975 4-YearCumulativeMultiplier 1.490 -1.107 2.696 -0.256 PanelB:RepresentativeAgentModel ImpactMultipliers 0.043 0.043 0.575 0.575 0.042 0.598 4-YearCumulativeMultiplier -0.303 -0.303 0.683 0.683 PanelC:RepresentativeAgentModelwithLump-sumTax ImpactMultipliers 0 0 0.575 0.575 0 0.598 4-YearCumulativeMultiplier 0 0 0.683 0.683 Notes: Thistableshowsthetransfermultipliersandinflationvolatilityduetothetransferdistributionunderthemonetary andfiscalregimeswithoutCOVIDshocks. Vari(Π)represent(normalized)volatilityofinflationduetotransferdistrit butionunderiregime,whichisnormalizedto1forthevolatilityunderthemonetaryregimeofthebaselinemodel. Panel A,B,andCshowtheresultsunderthebaselinemodel,undertherepresentativemodelwithdistortionarylabortaxes,and undertherepresentativemodelwithlump-sumtaxadjustment,respectively. First, our simple model suggests that under the fiscal regime, inflation should be less volatileintherepresentativeagenteconomythaninthebaselineeconomyduetolackofinterest rate channel. That is indeed what we find in Table 6, comparing Panel A with Panel B. In addition,inflationvolatilityislowerintherepresentativeagenteconomyalsointhemonetary regime. What is the mechanism? Under the monetary regime in a representative agent economy, the only reason inflation even responds at all to a transfer shock is due to distortionary labor taxes that lead to a failure of Ricardian equivalence. This generates a positive, but very small, response of inflation. As Panel C shows, once we remove distortionary labor taxes, thereisnoeffectoninflationinthemonetaryregime.39 Next, given lower inflation responses, with sticky prices, we expect lower output multipliers, which is also what we find for both the monetary and fiscal regimes, comparing Panel A with Panel B.40 The upshot is that the TANK economy has higher inflation volatility and outputmultipliersthantherepresentativeagenteconomyforbothpolicyregimes. 39Forthefiscalregime,thischangemakesnodifferenceaslabortaxesareconstant. Alsoanalternateintuition for why the transfer increase is more inflationary in the TANK economy under the monetary regime is that a transfer increase in the TANK economy is similar to a government spending increase in a representative agent economy. Then, we are essentially comparing effectsof governmentspending vs. transfersin a representative agenteconomy,andwhereitiswell-understoodthatgovernmentspendingisinflationary. 40NoticethatRicardianconsumptionandoutputmultipliersareidenticalintherepresentativeagenteconomy. 28

3.4.2 AlternativeCalibrationswithDifferentTransferPolicies We consider three alternative calibration strategies for transfer policy.41 Appendix Tables C.2 andC.3presenttheresultsfromthesealternativecalibrationexercises. Alternative calibration with transfer excluding one-time tax rebate First, we calibrate the size of the transfer increase in the model by excluding the one-time $600 individual tax rebates in the CARES Act. The main motivation is the survey finding in Coibion, Gorodnichenko, and Weber (2020) that on average, only about 40% of tax rebates appears to have been spent by households. The size of transfer change decreases from 26.8% to 15.7% when we exclude the individual tax rebates. Panel A of Appendix Table C.2 shows that the multipliers are essentially the same as before under the monetary regime. For the fiscal regime however, the multipliers are even bigger. Panel A of Appendix Table C.3 shows that welfare results are robust to this alternative calibration of transfer policy, with a Pareto improvement onlyinthefiscalregime. Alternative calibration with transfer excluding unemployment benefit Second, we calibrate the size of the transfer increase in the model by excluding the unemployment insurance benefits extended in the CARES Act. The main motivation is the fact that our model does not feature classical unemployment due to search and matching frictions. The size of transfer change decreases from 26.8% to 16.7% when we exclude unemployment benefits. Panel B of Appendix Table C.2 shows that the multipliers are essentially the same as before under the monetary regime while for the fiscal regime, the multipliers are even bigger. Panel B of AppendixTableC.3showsthatwelfareresultsarerobusttothisalternativecalibrationoftransfer policy,withaParetoimprovementonlyinthefiscalregime. Alternativecalibrationwithone-timetaxrebatetobothRicardianandHTM Third,we consider the case where the one-time tax rebate components are distributed equally to both theHTMandRicardianhouseholds. Themainmotivationisthefactthatinthedata,thesetax rebatesmightnothavebeenastargetedtotheHTMhouseholdsasassumedinourmodel. For thisanalysis,wecontinuetoassumethattheunemploymentinsurancebenefitsandtransfersto state and local governments continue to be only distributed to HTM. As expected, Panel C of AppendixTableC.2showsthatthemultipliersareoveralllowerthanbeforeforbothregimes. Importantly,thefiscalregimecontinuestofeaturehighermultipliersthanthemonetaryregime. Moreover,PanelCofAppendixTableC.3showsthateventhiscase,welfareresultsarerobust, 41Whenwemakechangeshere,were-calibratethemodeltomatchthesametargetsasbefore. 29

withaParetoimprovementonlyinthefiscalregime.42 3.4.3 ModelExtensions We now present results based on some model extensions. The details of the extended models areinOnlineAppendixB.3. AddingGovernmentSpending Asonemodelextension,weconsidergovernmentspending on goods in the model, which does not enter utility. First, we simply introduce steady-state government spending, where we set the steady-state government spending to output ratio (G¯ ) Y¯ tobe0.15,inlinewiththeUSdataaveragefrom1990Q1through2020Q1. Wethenreportthe transfer multiplier results in Panel A of Appendix Table C.4 and the welfare results in Panel A of Appendix Table C.5. Overall, the results are overall very similar to the case without steady-stategovernmentspending. Ourkeyresultsthattransfermultipliersarelarger,andthat thereisaParetoimprovement,inthefiscalregimecontinuetoholdinthisextension. Next, we allow government spending to increase from steady-state following the COVID shocks, exactly analogous to our main experiment of a transfer increase. This allows us to compute government spending multipliers and welfare effects of increases in government spending, which we report in Panels B of Appendix Tables C.4 and C.5 respectively. The results are overall very similar to transfer multipliers, and in particular, government spending multipliers are larger and there is a Pareto improvement in the fiscal regime. This reinforces the point we made earlier in the analytical model that transfer shocks and government spendingshockshavesimilarpropagationandimplicationsinourmodel. Finally, for the monetary regime, we re-do the transfer increase with COVID shocks experiment allowing government spending to decrease, as opposed to labor taxes increasing.43 Thus,governmentspendingfollows G −G¯ (cid:18) G −G¯(cid:19) (cid:18) b −¯b (cid:19) t t−1 t−1 = ρ +(1−ρ )ψ +ε , G¯ G G¯ G G ¯b G,t where we calibrated the parameters of this rule to the same values as for our baseline labor tax rate rule. Appendix Table C.6 presents the transfer multipliers and welfare results, which 42Finally,givenpossiblemismatchbetweenmodelfrequencyandtimingoftransferreceiptsintherealworld, inPanelDofAppendixTableC.2weconsiderthecasewherethetransferinthefirstperiodisonlyhalfofthe transferincreaseinthenexttwoperiods,whileimposingthatthetotalamountoftransferincreaseisstill26.8% ofthesteadystateleveloftransfer. Ourresultsarerobusttothisalternatepathoftransferincrease. 43Thisgovernmentspendingadjustmentisrelevantonlyforthemonetaryregimeasunderthefiscalregime, thethoughtexperimentisthatofnostandardfiscaladjustmentatall. 30

areverysimilartothoseinAppendixTablesC.4andC.5forthelabortaxrateadjustment.44 Money-in-the-Utility Function Our quantitative model is cash-less. As an extension, we now introduce (non-interest bearing) cash into the economy, where we follow Chari, Kehoe, and McGrattan (2002) by introducing a money-in-the-utility function for Ricardian households. The motivation is that this allows us to consider a classical channel through which inflationcanaffectmodeldynamicsandwelfareviarealbalances. Inthismodelextension,Ricardianhouseholdssolvetheproblem   max (cid:88) ∞ βt(1−σ)−1 (cid:32) ν (cid:0) CR(cid:1)η− η 1 +(1−ν) (cid:18) M t (cid:19)η− η 1(cid:33)η( η 1 − − 1 σ) −χ(1+ϕ)−1(cid:0) LR(cid:1)1+ϕ {C t R,LR t ,bR t , P M t R t}t=0  t P t t  subjecttoastandardNo-Ponzi-gameconstraintandasequenceofflowbudgetconstraints CR+bR+ M t = (1+i ) 1 bR + M t−1 + (cid:0) 1−τR (cid:1) wRLR+ΨR. t t P t−1 ΠR t−1 P L,t t t t t t t The optimality condition over real balances, mR = M t R , gives rise to a money-demand equat Pt tion shown in Online Appendix B.3.2. Due to non-separability in the utility function, real balances now will affect model dynamics in the monetary regime. In the fiscal regime however, as our baseline parameterization is that of a constant nominal rate, this extension does notaffectmodeldynamics. Consistent with Chari et al. (2002), we set ν = 0.94 and η = 0.40 and for concreteness, solve the model without COVID shocks. Appendix Table C.8 reports that the multipliers continue to be higher in the fiscal regime. As we explained above, for the fiscal regime, the results here are identical to those in Table 4 for the case of no COVID shocks, while they are similarbutslightlysmallerthanthoseinTable4forthemonetaryregime. InflationaryCost-PushShocks Animportantcaveattoourquantitativeresultssofaristhe assumption that other than COVID shocks, there are no other shocks in the economy. To address this shortcoming partially, and to make our analysis more relevant for current events, we now introduce an inflationary shock (ξπ) directly into the firm’s optimal prices. Further t details of this extension are in Online Appendix B.3.3. This is akin to cost-push shocks in standardstickypricemodelsintheliterature. Weassumeξπ = ρ ξ +ε andsetρ = 0.5, t π t−1 π,t π such that these shocks persistently impinge on the model even after the COVID shocks are 44Forcompleteness,inAppendixTableC.7,wealsopresentresultsongovernmentspendingmultiplierswith sucharuleandshowthattheyarequalitativelysimilartothosehere. 31

over, and consider two cases for the shock size, a 10%-shock and a 20%-shock. We then re-calibratethemodeltomatchthesamedataasinourbaselineanalysis. Appendix Table C.9 reports the transfer multiplier results. Compared to our baseline results in Table 2, the multipliers are slightly higher in the monetary regime and slightly lower inthefiscalregime. Themainreasonisthatasweexplainedbefore,inadeflationaryenvironment,higherinflationisbeneficialinthemonetaryregimewheretheinterestrateisstuckatthe ZLB. This allows the real rate to decline and as a result we see that qualitatively a new result appears with the 4-year Ricardian consumption multiplier turning slightly positive. Our main result that transfer multipliers are higher in the fiscal regime continue to hold with this extension that incorporates inflationary shocks.45 For this extension, Appendix Table C.10 reports the welfare results. As in our baseline results in Table 3, transfer policy is Pareto improving onlyinthefiscalregime. 3.4.4 SensitivityAnalysis Alternative Calibration with Above Steady State Initial Debt Our baseline calibration wasbasedoninitialgovernmentdebtatthesteady-state. Thisisourpreferredspecificationas it allows us to focus on debt dynamics following the COVID crisis induced by shocks. Moreover,thefiscalregimeisinflationarywithanypositiveoutstandingdebt,evenwithoutshocks, which further introduces a new component to model dynamics and can make interpretation harder.46 Nevertheless, to assess the robustness of our results, we now recalibrate the model with initial government debt above its steady-state level. In particular, we set debt at time 0—one period before the first wave of COVID shocks hit the model economy—to be 10% higher than the steady-state. Panel A of Appendix Table C.11 shows the transfer multipliers under this new calibration while Panel A of Appendix Table C.12 shows the corresponding welfare results. Theresultsarethesameasthosefromourbaselinecalibration. Notice that, in our baseline calibration, we use the average US debt-to-GDP ratio from 1990Q1 through 2020Q1 to calibrate steady-state debt-to-GDP ratio (50.9%). As an alternative sensitivity analysis, we set this variable to match the average US debt-to-GDP ratio from 2010Q1 through 2020Q1 (71.8%) and calibrate the COVID shocks allowing time-0 debt to be 10% higher than its steady-state value. In this case, the debt-to-GDP ratio at time 0 in the modelexactlymatchesthe2019Q4debt-to-GDPratiointhedata. AsshowninPanelBofAppendix Tables C.11 and C.12, the results for multipliers and welfare gains from this alternate 45TheimpulseresponsesforthismodelextensionareinAppendixFigureC.1. 46ThisisshownanalyticallyinthelinearizedstickypricemodelinBhattaraietal.(2014). 32

calibrationarethesameasthosefromourbaselinecalibration.47 DifferentDurationofBindingZLB Inourmainanalysis,thedurationofbindingZLBunderthemonetaryregimeisfourperiodsandessentiallycoincideswiththedurationofshocks, which is three periods. We now do a sensitivity check on how our multiplier results get affected if we increase the persistence of the Ricardian household’s discount factor shock by modelling it as an AR(1) process, which in turn increases the duration of binding ZLB. The results are reported in Appendix Table C.14, where we progressively increase the duration of bindingZLBfromfourtoeightperiods. Theresultsshowthatmultipliersdonotchangemuch in the monetary regime with increased duration of binding ZLB, but they do increase further inthefiscalregime. Thisisanotherexampleofhigherdegreeofstatedependenceinthefiscal regime: AsalongerZLBismoredeflationaryandrecessionary,theeffectivenessofincreasing transfersinthefiscalregimeishigher. Size and Sign Dependence of Transfer Multipliers We now explore further the state dependence of transfer multipliers in our model in terms of the size and sign of transfer change. That is, we compute transfer multipliers for transfer increases and decreases and of varying magnitudes. To clarify the new nature of this state-dependence, we do so by computing the model for the case without COVID shocks, as our focus so far has been on state-dependence generated by COVID shocks.48 Appendix Figure C.2 presents the impact and 4-year cumulative multipliers for different sign/sizes of transfer shocks. As we can see, within a regime, transferincreasesanddecreasesdonothaveexactlysymmetriceffect. Moreover,forthesame regime and sign, the multipliers also depend on the size. For transfer increases, output multipliers increase with size of the transfers. Thus, there is size and sign related state dependence intransfermultipliers,whichisonlypossibletoseeduetoournon-linearsolutionmethod. Only Discount Factor Shocks We calibrated our model with three types of shocks, Ricardian household discount factor shocks, HTM labor disutility shock, and HTM sector specific demand shock, and jointly matched dynamics of three variables in the data. As a sensitivity check, we now compute multipliers in our model while feeding-in only the Ricardian household discount factor shock, which is a canonical demand shock in sticky price models.49 Appendix Table C.15 shows these results. Focusing on 4-year multipliers, they are quite similar toourbaselineresults,withsomehighereffectsinthefiscalregime. 47Thatoursimulationfeaturesshocksmakesadifferencetosomeaspectofourresults,asshowninAppendix TableC.13. Ifwestarttheeconomywithahighinitialdebt,anddonotconsidershockstoreplicatetheCOVID recession,thenmultipliersarelowerthanthebaselinecalibration(withoutshocks). 48Inaddition,ananalysisofadecreaseintransfersduringaCOVID-recessionmightnotbeverycompelling. 49Inthisexercise,wedonotrecalibratethemodelwithonlythisshock. 33

4 Conclusion Ourpapermakesclearthathowtransfersareultimatelyfinancedisafirst-orderissuefortheir effectiveness. It arguably matters more than other factors identified in the literature, which typicallyreportsmoderatetransfermultipliers. Wefindthatinflation-financedtransfers(fiscal regime)aresignificantlymoreeffectivethantax-financedtransfers(monetaryregime)inboth boostingtheeconomyandimprovingwelfare. We first consider a simple two-agent model that permits analytical results and illuminates the mechanisms through which redistribution generates inflation in both policy regimes. We then proceed to a quantitative analysis and show that inflation-financed transfers fight deflationary pressures in a COVID-recession-like environment, thereby preventing output and consumption from dropping significantly. Such inflation-induced expansionary effects are so largethatredistributioncaninfactproduceaParetoimprovement. Theresultthatinflatingawaypublicdebtcanbeawin-winsolutionforboththerecipients andthesourcesofthetransfersinadeeprecessionisencouraging,yetitisnotwithoutcaveats. Most importantly, we have assumed that there will be no further shocks in the post-COVID crisis period. High inflation is however, generally costly for social welfare and the fiscal regime might not necessarily be desired in normal situations. Therefore, our results should not be taken literally as a suggestion of a permanent interest rate peg by the Fed and no fiscal adjustment ever by the Treasury as such a policy recommendation might not hold in a richer stochastic model with various recurring shocks. Generally, our perfect foresight non-linear solutionmethodmissestherolefutureuncertaintycanhaveoncurrentprivatesectorbehavior, whichisshowntobeimportantfortheeffectsofCARESActinBayeretal.(2020). Infuturework,wecanempiricallyexplorewhetherfiscalpolicysignificantlyaffectsinflationary expectations, along the lines found recently in a randomized control trial by Coibion, Gorodnichenko, and Weber (2021). In addition, a comparative analysis in future of the Covid recession and the Great Recession is potentially interesting as inflation dynamics were quite different between the two: inflation remained relatively subdued post Great Recession, compared to the present time. Our results suggest that state dependency must have played a role as the size of fiscal expansions as well as the persistence and the size of the contractionary shocks differed significantly in these two episodes. Finally, fiscal regime based policy implementationwouldnotbeasstraightforwardinanenvironmentwhereeconomicagentstakeinto account the possibility of regime switching by policymakers when the recession is over. We leaveamorecomprehensiveanalysisofsuchinterestingissuesforfutureresearch. 34

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Appendix A Data Description Employment and Total Hours. We use total employment and total hours data from U.S. Bureau of Labor Statistics. We define HTM sector as the sum of the following three sectors: Retail Trade (NAICS 44–45), Transportation and Warehousing (NAICS 48–49), and Leisure andHospitality(NAICS71–72). Consumption and Inflation. We use real Personal Consumption Expenditure (PCE) data andPCEinflationfromU.S.BureauofEconomicAnalysis. WedefineHTMsectorasthesum ofthefollowingthreesectors: Transportationservices,Recreationservices,andFoodservices andaccommodations. We also use 2019 Consumer Expenditure Surveys (CEX) data to calibrate both Ricardian and HTM households’ share parameters in the consumption baskets. We assume households inthetop80percentileincomedistributionasRicardianhouseholdsandmatchtheirconsumption share for transportation, entertainment, and food away from home. Similarly, we assume households in bottom 20 percentile income distribution as HTM households and match their consumptionshareforthesethreesectors. Fiscal Variables. We use government current transfer payments (A084RC1Q027SBEA in FRED) to calibrate steady-state transfers to GDP ratio. We also use federal debt held by the public data (FYGFDPUN in FRED) to calibrate debt to GDP ratio. Finally, we use compensation of employees, paid: wages and salaries (A4102C1Q027SBEA in FRED), proprietors’ income(PROPINCinFRED),andfederalgovernmentcurrentreceipts: contributionsforgovernment social insurance (W780RC1Q027SBEA in FRED) data to calibrate steady-state labor tax revenue to GDP ratio. The sample period for these variables is from 1990Q1 through 2020Q1. Transfer Distribution from CARES Act. We calibrate the size of transfer distribution using the transfer amounts specified in Coronavirus Aid, Relief and Economy Security Act (CARES Act), which came into operation in mid–April. In particular, we target the sum of three key components of the Act: $293 billion to provide one-time tax rebates to individuals; (ii) $268 billion to expand unemployment benefits; (iii) $150 billion in transfers to state and local governments. These three components of the CARES Act consist of around 3.4 percent ofGDP.Inasensitivityanalysis,wecountonlycomponents(ii)and(iii)above. Employment,Inflation,andConsumptionDynamicsin2020 AppendixFigureA.1presents dynamics of employment, hours, inflation, and consumption based on such a two-sector de- 38

0 −−> CARES Act (Apr. 15) −10 −20 −30 −40 0202 .naJ morf noitaiveD tnecreP Panel A: Employment 0 −10 −20 Total −30 Retail, Transportation, Leisure and Hospitality Others −40 1 2 3 4 5 6 7 8 2020 0202 .naJ morf noitaiveD tnecreP Panel B: Total Hours Total Retail, Transportation, Leisure and Hospitality Others 1 2 3 4 5 6 7 8 2020 10 0 −10 −20 −30 −40 −50 −60 −70 0202 .naJ morf noitaiveD tnecreP Panel C: Real PCE 1 .5 0 −.5 −1 Total Transportation, Recreation, −1.5 and Food Services Others −2 1 2 3 4 5 6 7 8 2020 0202 .naJ morf noitaiveD tnecreP Panel D: PCE Inflation Total Transportation, Recreation, and Food Services Others 1 2 3 4 5 6 7 8 2020 AppendixFigureA.1: AggregateandSectoralEffectsofCOVIDCrisis Notes:ThisfigureshowsthedynamicsofkeyvariablesfromJanuary2020.PanelsAandBshowemploymentandtotalhoursdynamics inU.S.BureauofLaborStatistics,respectively.Blacklinesaredynamicsoftotalvariableandredlinesrepresentretail,transportation, leisure,andhospitalitysector,andbluelinesrepresentallothersectors.PanelsCandDpresentrealpersonalconsumptionexpenditure andPCEinflationinU.S.BureauofEconomicAnalysis,respectively.Blacklinesaredynamicsoftotalvariableandredlinesrepresent transportation,recreationandfoodservicessector,andbluelinesrepresentallothersectors. Sources:U.S.BureauofEconomicAnalysis,U.S.BureauofLaborStatistics composition of the U.S. economy. We show with the vertical dashed line when transfer paymentsfromtheCARESActstartedtogetmailed. Asisclear,therewasasharpadverseeffect on employment/hours in the HTM sector following the COVID crisis. Moreover, inflation in this sector also fell. Finally, while the HTM sector was disproportionately affected, there was also an aggregate, economy-wide contraction and fall in inflation as well. We calibrate the COVID shocks to perfectly re-produce the dynamics of hours in the two sectors and that of inflation in the HTM sector, thereby situating the model economy in a COVID-recessionlike environment. We then calibrate the size of transfers to match the transfer amount in the CARES Act and study how the economy responds to the redistribution policy under several alternativescenarios. 39

Appendix B Simple Model Extension In this appendix, we extend our simple model presented in Section 2 with government spendingandpreferenceshocks. B.1 Simple Model with Preference Shocks Consider the simple model with preference shocks, ξ . The system of equilibrium equations t canbesummarizedas: CR exp(ξ )1+i t+1 = β t+1 t CR exp(ξ ) Π t t t+1 (cid:18) s (cid:19)ϕ χ CR + t CR = 1 t 1−λ t 1+i t−1 b = b −τ +s t t−1 t t Π t 1+i (cid:18) Π (cid:19)φ t t = 1+¯i Π ¯ (cid:0) ¯(cid:1) τ −τ¯ = ψ b −b t t−1 WefirstconsiderthecaseofinfiniteFrischelasticity. AppendixFigureB.1showstheIRFs to transfer shocks and Appedix Figure B.2 shows the variable responses to transfer shocks under different size of preference shocks. Next, we consider the case of ϕ = 2. Appendix Figure B.3 shows the IRFs and Appedix Figure B.4 shows the variable responses to transfer shocksunderdifferentsizeofpreferenceshockswithϕ = 2. They show that the fiscal regime leads to higher inflation (in total, even if not for both periods in all cases) than the monetary regime under transfer increases, when such shocks hit that drive interest rate to negative temporarily. In fact, for infinite Frisch elasticity, the following proposition shows that total inflation is higher in the fiscal regime compared to the monetaryregime. Proposition1. log ΠM 0 +log ΠM 1 < log ΠF 0 +log ΠF 1 withinfiniteFrischelasticity. Π¯ Π¯ Π¯ Π¯ Proof. Considerthesystemofequilibriumconditions: Π CR 1+ξβ (cid:18) Π (cid:19)φ t+1 = t t+1 t Π ¯ CR 1+ξβ Π ¯ t+1 t 40

(cid:34) (cid:35) (cid:34) (cid:35) 1 CR 1+ξβ 1 CR 1+ξβ b − ¯ b = t t−1 −ψ (cid:0) b − ¯ b (cid:1) +(s −s¯)+ ¯ b t t−1 −1 t β CR 1+ξβ t−1 t β CR 1+ξβ t−1 t t−1 t (cid:18) ¯ (cid:19) 1 Π ¯ ¯ b −b = −1 b+(s −s¯). 0 0 β Π 0 NotethatwithinfiniteFrisch(ϕ = 0),CR = C ¯R forallt. UnderM-regimewithone-time t shock(s = (1+ξs)s¯,ξβ = 0,s = s¯): 0 0 t>0 t>0 ΠM (cid:16) (cid:17)1 ΠM 0 = 1+ξβ φ and 1 = 1 Π ¯ 0 Π ¯ ΠM ΠM 1 (cid:16) (cid:17) 1 log 0 +log 1 = log 1+ξβ (cid:104) ξβ < 0 Π ¯ Π ¯ φ 0 φ 0 Under F-regime with one-time shock (s = (1+ξs)s¯, ξβ = 0, s = s¯) and φ = 0, 0 0 t>0 t>0 ¯ ψ = 0: then,b = band t>0 ΠF 1 1 = Π ¯ 1+ξ 0 ΠF 1 1+ξβ 0 = = 0 ¯ (cid:16) (cid:17) (cid:16) (cid:17) Π 1−β 1 −1+ξss¯ 1+(1+β)ξβ −βs¯ξs 1+ξβ 1+ξβ 0¯b 0 ¯b 0 0 0 b − ¯ b = ξss¯+(s −s¯) 0 0 0 Then,   ΠF ΠF (cid:16) (cid:17) 1+ξβ log Π ¯ 0 +log Π ¯ 1 = −log 1+ξ 0 β +log 1+(1+β)ξβ −β 0 s¯ξs (cid:16) 1+ξβ (cid:17) 0 ¯b 0 0 (cid:16) s¯ (cid:16) (cid:17)(cid:17) = −log 1+(1+β)ξβ −β ξs 1+ξβ 0 ¯ b 0 0 s¯ (cid:16) (cid:17) (cid:104) −(1+β)ξβ +β ξs 1+ξβ . 0 ¯ b 0 0 Then,−1 < ξβ < 0andξs > 0,log ΠF 0 +log ΠF 1 > 0. 0 0 Π¯ Π¯ Thus, ΠF ΠF ΠM ΠM log 0 +log 1 > 0 > log 0 +log 1 ¯ ¯ ¯ ¯ Π Π Π Π 41

1 1 1 0.15 0.15 0.5 0.1 0.1 0 0.5 0.5 0.05 0.05 -0.5 -1 0 0 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0.3 0 0 0.3 0.15 0.2 0.2 0.1 0.1 -0.05 -0.05 0.1 0.05 0 -0.1 -0.1 -0.1 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 AppendixFigureB.1: IRFswithϕ = 0(InfiniteFrischelasticity) 0.5 2.5 0.5 0 2 0 -0.5 1.5 -0.5 -1 1 -1 -1.5 0.5 -2 0 -1.5 -2 -1.6 -1.2 -0.8 -0.4 0 -2 -1.6 -1.2 -0.8 -0.4 0 -2 -1.6 -1.2 -0.8 -0.4 0 2.5 0.015 0.015 2 0.01 0.01 1.5 0.005 0.005 1 0 0 0.5 -0.005 -0.005 0 -0.01 -0.01 -2 -1.6 -1.2 -0.8 -0.4 0 -2 -1.6 -1.2 -0.8 -0.4 0 -2 -1.6 -1.2 -0.8 -0.4 0 Appendix Figure B.2: Variable Responses by Different Size of Beta Shocks with ϕ = 0 (InfiniteFrischelasticity) 42

0 1 1 0.04 0.04 0.03 0.03 -0.05 0.5 0.5 0.02 0.02 0.01 0.01 -0.1 0 0 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 1 1 0.4 0 0 0.5 0.3 0.5 0.2 0 -0.5 -0.5 0.1 -0.5 0 0 -1 -1 -1 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 AppendixFigureB.3: IRFswithϕ = 2(Frischelasticity): T = 1,T = 1 transfer betashock 1 4 0.5 0 0 3 -0.5 -1 2 -1 -1.5 -2 1 -2 -3 0 -2.5 -4 -1 -3 -4 -3.2 -2.4 -1.6 -0.8 0 -4 -3.2 -2.4 -1.6 -0.8 0 -4 -3.2 -2.4 -1.6 -0.8 0 4 0.02 0.02 3 0.01 0.01 2 0 0 1 -0.01 -0.01 0 -0.02 -0.02 -1 -0.03 -0.03 -4 -3.2 -2.4 -1.6 -0.8 0 -4 -3.2 -2.4 -1.6 -0.8 0 -4 -3.2 -2.4 -1.6 -0.8 0 Appendix Figure B.4: Variable Responses by Different Size of Beta Shocks with ϕ = 2 (Frischelasticity): T = 1,T = 1 transfer betashock 43

B.2 Government Spending Shocks in the Simple Model Fortheeffectsofgovernmentspendingshocksinthesimplemodel,wepointouthowtransfer andgovernmentspendingchangesareisomorphic. Thesystemofequilibriumequationsis: CR 1+i t+1 = β t CR Π t t+1 (cid:18) s +G (cid:19)ϕ χ CR + t t CR = 1 t 1−λ t 1+i t−1 b = b −τ +s +G t t−1 t t t Π t 1+i (cid:18) Π (cid:19)φ t t = 1+¯i Π ¯ (cid:0) ¯(cid:1) τ −τ¯ = ψ b −b . t t−1 Weseethatexogenouschangesins andG havetheidenticaleffectsonthemodeldynamics. t t B.3 Government Spending Feedback Rule in the Simple Model We consider endogenous feedback rules for government spending and present numerical resultsbelowforafewparameterizations. Thegovernmentspendingrulethenis ¯ (cid:0) ¯(cid:1) G −G = ψ b −b t G t−1 Under the fiscal regime, ψ = 0 by definition (i.e. no primary surplus adjustment in this G regime), so whether government spending or taxes adjust (or more precisely, do not adjust at all)inthemodeldoesnotmatter. Under the monetary regime, ψ < 0. That is, although an increase in transfer is not met G by a decrease in government spending of the equal size in all periods (like in the previous bullet point), government spending does decrease gradually. So we should expect to see a qualitatively similar result as before. Figure B.5 illustrates the result in the simple model. We can see that inflation and output increase by less in the government spending adjustment case thanintaxadjustmentcase,broadlyconfirmingourstatementaboveandyourconjecture. For acomparison,AppendixFigureB.6showstheIRFswithInfiniteFrischelasticity. 44

0.06 1 0.1 0.05 0.06 0.04 0.8 0 0.04 0.04 0.02 0.02 0.6 -0.1 0.03 0 0 0.4 -0.2 0.02 -0.02 -0.02 0.2 -0.3 0.01 -0.04 -0.04 0 -0.4 0 0 2 4 0 2 4 0 2 4 0 2 4 0 2 4 Appendix Figure B.5: IRFs under the Monetary Regime with Government Spending Adjustment: FrischElasticity=1/2 1 0.15 1 0 0.05 0.1 0.8 -0.1 0.04 0.5 0.05 0.6 -0.2 0.03 0 0 0.4 -0.3 0.02 -0.5 -0.05 0.2 -0.4 0.01 -1 -0.1 0 -0.5 0 0 2 4 0 2 4 0 2 4 0 2 4 0 2 4 Appendix Figure B.6: IRFs under the Monetary Regime with Government Spending Adjustment: InfiniteFrischElasticity 45

Appendix C Additional Tables and Figures AppendixTableC.1: DataandModelMoments Time Data Model PanelA:Targetedmoments(percentdeviationfromJanuary) TotalHoursforretail,transportation,leisure/hospitality April -16.4% -16.4% June -18.7% -18.7% August -12.9% -12.9% TotalHoursexcludingretail,transportation,leisure/hospitality April -6.62% -6.62% June -8.64% -8.64% August -6.26% -6.26% PCEInflationforrecreation,transportation,foodservices April -0.95% -0.95% June -0.20% -0.20% August 0.08% 0.08% PanelB:Non-targetedmoments(percentdeviationfromJanuary) PCEInflationexcludingrecreation,transportation,foodservices April -0.15% -2.81% June -0.10% -4.96% August 0.56% -5.37% RealPCEforrecreation,transportation,foodservices April -40.7% -23.4% June -38.1% -0.46% August -27.7% 12.1% RealPCEexcludingrecreation,transportation,foodservices April -7.79% -4.37% June -3.75% -16.6% August -0.44% -16.4% RealPCE April -12.3% -10.2% June -8.50% -11.7% August -4.21% -7.64% RealGDP(percentdeviationfromQ1) Q2 -8.93% -8.06% Q3 -2.06% -2.12% Notes: Thistableshowsmomentsofthedataandsimulatedseriesfromthebaselinemodel. PanelAshowstargeted moments and Panel B shows non-targeted moments. Data moments are expressed as the percent deviation from the averagevaluesofoutcomevariablesinJanuaryandFebruary2020. 46

AppendixTableC.2: TransferMultipliersUnderAlternativeCalibrations MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:Alternativecalibrationexcludingone-timetaxrebates(15.8%transferincreases) ImpactMultipliers 1.957 1.901 0.120 7.967 3.371 3.101 1.579 9.238 4-YearCumulativeMultiplier 1.785 2.107 -0.015 7.678 7.459 7.167 4.565 16.932 PanelB:Alternativecalibrationexcludingunemploymentbenefitcomponents(16.7%transferincreases) ImpactMultipliers 1.953 1.898 0.120 7.954 3.312 3.049 1.519 9.180 4-YearCumulativeMultiplier 1.780 2.099 -0.014 7.652 7.186 6.920 4.350 16.470 PanelC:AlternativecalibrationwithtaxrebatestobothRicardianandHTMhouseholds ImpactMultipliers 1.332 1.294 0.078 5.435 2.167 2.001 0.938 6.190 4-YearCumulativeMultiplier 1.236 1.453 0.020 5.217 4.582 4.436 2.722 10.672 PanelD:AlternativecalibrationwithtransferdistributionstartingfromApril2020 ImpactMultipliers 1.774 1.959 0.255 6.748 3.5 3.41 2.011 8.374 4-YearCumulativeMultiplier 1.723 2.105 0.029 7.267 5.538 5.503 3.109 13.491 Notes: This table shows the transfer multipliers for the models under monetary and fiscal regimes when we re-calibrate the baselinemodel.Mi(X)representthecumulativetransfermultiplierofvariableXatt-horizonunderiregime.Wereportimpact t multipliersand4-yearcumulativemultiplierswhengovernmentdistributestransfersequallyover6months. AppendixTableC.3: WelfareGainsUnderAlternativeCalibrations MonetaryRegime FiscalRegime Long-run Short-run Long-run Short-run (t=4) (t=4) PanelA:Excludingone-timetaxrebates(15.8%transferincreases) RicardianHousehold -0.009 -0.897 0.013 -0.693 HTMHousehold 0.046 3.752 0.083 5.010 PanelB:Excludingunemploymentbenefitcomponents(16.7%transferincreases) RicardianHousehold -0.009 -0.950 0.012 -0.742 HTMHousehold 0.048 3.983 0.086 5.263 PanelC:TaxrebatestobothRicardianandHTMhouseholds RicardianHousehold -0.016 -1.039 0.004 -0.831 HTMHousehold 0.084 4.365 0.124 5.630 PanelD:AlternativecalibrationwithtransferdistributionstartingfromApril2020 RicardianHousehold -0.014 -1.493 0.012 -1.236 HTMHousehold 0.073 6.183 0.115 7.657 Notes: Thistableshowslong-andshort-runwelfaregainsresultingfromtheredistribution, comparedtothe modelswithoutredistribution. Thevaluesarethedifferenceinthewelfaremeasure(µi )betweenthetransfer t,k cases(underthetworegimes)andthebenchmarkcase(themonetaryregimewithouttransfers). 47

AppendixTableC.4: TransferandGovernmentSpendingMultiplierswithTaxAdjustment MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:TransferMultiplierswithsteady-stategovtspending ImpactMultipliers 1.875 1.836 0.079 7.757 2.915 2.689 1.108 8.829 4-YearCumulativeMultiplier 1.669 2.039 -0.010 7.165 5.655 5.575 3.032 14.243 PanelB:GovernmentSpendingMultipliers ImpactMultipliers 1.218 1.068 0.026 0.847 2.386 2.027 1.251 1.826 4-YearCumulativeMultiplier 1.138 1.068 -0.182 1.186 5.414 4.814 3.261 8.185 Notes: This table shows the transfer multipliers for the models under monetary and fiscal regimes when we re-calibrate the baselinemodel.Mi(X)representthecumulativetransfermultiplierofvariableXatt-horizonunderiregime.Wereportimpact t multipliersand4-yearcumulativemultiplierswhengovernmentdistributestransfersequallyover6months. AppendixTableC.5: WelfareGainswithTaxAdjustment MonetaryRegime FiscalRegime Long-run Short-run Long-run Short-run (t = 4) (t = 4) PanelA:Welfaregainswithtransfershocksandsteady-stategovtspending RicardianHousehold -0.017 -1.954 0.015 -1.618 HTMHousehold 0.073 6.111 0.119 7.939 PanelB:Welfaregainswithgovernmentspendingshocks RicardianHousehold -0.015 -1.138 0.01 -0.504 HTMHousehold 0.006 0.779 0.069 2.456 Notes: This table shows long- and short-run welfare gains resulting from the redistribution, compared to the modelswithoutredistribution. Thevaluesarethedifferenceinthewelfaremeasure(µi )betweenthetransfer t,k cases(underthetworegimes)andthebenchmarkcase(themonetaryregimewithouttransfers). 48

AppendixTableC.6: TransferMultipliersandWelfareGainswithGovernmentSpendingAdjustmentintheMonetaryRegime PanelA:TransferMultipliers MM(Y) MM(Y ) MM(CR) MM(CH) t t R t t ImpactMultipliers 1.866 1.833 0.066 7.759 4-YearCumulativeMultiplier 1.65 2.054 -0.022 7.143 PanelB:Welfaregains Long-run Short-run(t = 4) RicardianHousehold -0.015 -1.973 HTMHousehold 0.072 6.05 Notes: Thistableshowsthetransfermultipliersandwelfaregainsforthemodelwithgovernmentspending adjustment under monetary regime. Panel A reports impact multipliers and 4-year cumulative multipliers when government distributes transfers equally over 6 months. Panel B shows long- and short-run welfare gains resulting from the redistribution, compared to the model without redistribution. The values are the differenceinthewelfaremeasures(µi )betweenthewith-transfercaseandthewithout-transfercaseunder t,k monetaryregime. Appendix Table C.7: Government Spending Multipliers with Government Spending Adjustment MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:GovernmentSpendingMultipliers ImpactMultipliers 1.194 1.051 0.001 0.828 2.464 2.100 1.338 1.878 4-YearCumulativeMultiplier 1.275 1.226 -0.013 1.221 5.299 4.62 1.904 9.497 Notes: This table shows the transfer multipliers for the models under monetary and fiscal regimes when we re-calibrate the baselinemodel.Mi(X)representthecumulativetransfermultiplierofvariableXatt-horizonunderiregime.Wereportimpact t multipliersand4-yearcumulativemultiplierswhengovernmentdistributestransfersequallyover6months. AppendixTableC.8: TransferMultiplierswithMoney-In-the-Utility MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:MIU ImpactMultipliers 2.211 2.067 -1.203 13.388 4.640 4.083 -0.028 19.920 4-YearCumulativeMultiplier 1.043 1.284 -1.463 9.246 2.696 2.805 -0.256 12.359 Notes: This table shows the transfer multipliers for the models under monetary and fiscal regimes when we re-calibrate the baselinemodel.Mi(X)representthecumulativetransfermultiplierofvariableXatt-horizonunderiregime.Wereportimpact t multipliersand4-yearcumulativemultiplierswhengovernmentdistributestransfersequallyover6months. 49

AppendixTableC.9: TransferMultiplierswithInflationaryCost-PushShocks MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:10%Shock ImpactMultipliers 1.947 1.874 0.158 7.803 2.915 2.691 1.16 8.662 4-YearCumulativeMultiplier 1.795 2.033 0.102 7.337 5.364 5.197 2.824 13.678 PanelB:20%Shock ImpactMultipliers 1.977 1.882 0.197 7.802 2.857 2.629 1.122 8.537 4-YearCumulativeMultiplier 1.865 2.025 0.203 7.307 5.089 4.863 2.51 13.528 Notes: This table shows the transfer multipliers for the models under monetary and fiscal regimes when we re-calibrate the baselinemodel.Mi(X)representthecumulativetransfermultiplierofvariableXatt-horizonunderiregime.Wereportimpact t multipliersand4-yearcumulativemultiplierswhengovernmentdistributestransfersequallyover6months. AppendixTableC.10: WelfareGainswithInflationaryCost-PushShocks MonetaryRegime FiscalRegime TransferDistribution Long-run Short-run Long-run Short-run (t = 4) (t = 4) PanelA:Welfaregainswith10%InflationaryShocks RicardianHousehold -0.012 -1.45 0.011 -1.248 HTMHousehold 0.075 6.372 0.119 7.825 PanelB:Welfaregainswith20%InflationaryShocks RicardianHousehold -0.011 -1.413 0.01 -1.243 HTMHousehold 0.076 6.496 0.12 7.823 Notes: This table shows long- and short-run welfare gains resulting from the redistribution, compared to the modelswithoutredistribution. Thevaluesarethedifferenceinthewelfaremeasure(µi )betweenthetransfer t,k cases(underthetworegimes)andthebenchmarkcase(themonetaryregimewithouttransfers). 50

AppendixTableC.11: TransferMultipliersUnderTwoAlternativeCalibrations MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:Alternativecalibrationwithabovesteadystateinitialdebt(50.9%) ImpactMultipliers 1.938 1.86 0.133 7.849 6.759 5.988 4.921 12.777 4-YearCumulativeMultiplier 1.8 2.012 0.065 7.478 15.638 14.768 10.319 33.049 PanelB:Alternativecalibrationwithabovesteadystateinitialdebt(71.8%) ImpactMultipliers 1.824 1.732 0.113 7.426 5.916 5.168 4.187 11.576 4-YearCumulativeMultiplier 1.732 1.913 0.08 7.141 13.325 12.329 8.747 28.311 Notes:Thistableshowsthetransfermultipliersforthemodelsundermonetaryandfiscalregimeswhenwere-calibratethebaseline model.InPanelA,wecalibratetheCOVIDshocksinthebaselinemodelunderthemonetaryregimewithtime-0governmentdebt whichis10%higherthanthesteady-state(50.9%ofdebt-to-GDP).InPanelB,wecalibratetheCOVIDshocksinthebaseline modelunderthemonetaryregimewithtime-0governmentdebtwhichis10%higherthanthealternativesteady-state(71.8%of debt-to-GDPwhichmatchestheaverageUSdebt-to-GDPratiofrom2010Q1through2020Q1).Mi(X)representthecumulative t transfermultiplierofvariableX att-horizonunderiregime. Wereportimpactmultipliersand4-yearcumulativemultipliers whengovernmentdistributestransfersequallyover6months. AppendixTableC.12: WelfareGainsUnderTwoAlternativeCalibrations MonetaryRegime FiscalRegime TransferDistribution Long-run Short-run Long-run Short-run (t = 4) (t = 4) PanelA:Alternativecalibrationwithabovesteadystateinitialdebt(50.9%) RicardianHousehold -0.013 -1.436 0.066 -1.498 HTMHousehold 0.078 6.365 0.25 14.015 PanelB:Alternativecalibrationwithabovesteadystateinitialdebt(71.8%) RicardianHousehold -0.014 -1.646 0.094 -1.359 HTMHousehold 0.08 6.478 0.241 12.776 Notes: This table shows long- and short-run welfare gains resulting from the redistribution, compared to the modelswithoutredistribution. Thevaluesarethedifferenceinthewelfaremeasure(µi )betweenthetransfer t,k cases (under the two regimes) and the benchmark case (the monetary regime without transfers). In Panel A, wecalibratetheCOVIDshocksinthebaselinemodelunderthemonetaryregimewithtime-0governmentdebt whichis10%higherthanthesteady-state(50.9%ofdebt-to-GDP).InPanelB,wecalibratetheCOVIDshocks inthebaselinemodelunderthemonetaryregimewithtime-0governmentdebtwhichis10%higherthanthe alternativesteady-state(71.8%ofdebt-to-GDPwhichmatchestheaverageUSdebt-to-GDPratiofrom2010Q1 through2020Q1). 51

Appendix Table C.13: Transfer Multipliers with Above Steady State Initial Debt (Without COVIDShocks) MonetaryRegime FiscalRegime MM t (Y) MM t (YR) MM t (CR) MM t (CH) MF t (Y) MF t (YR) MF t (CR) MF t (CH) PanelA:ImpactMultipliers Baseline 2.670 2.464 -0.911 14.394 4.640 4.083 -0.028 19.920 Abovesteadystateinitialdebt 2.385 2.190 -0.808 12.836 3.903 3.428 -0.027 16.770 PanelB:4-YearCumulativeMultipliers Baseline 1.490 1.703 -1.107 9.991 2.696 2.805 -0.256 12.359 Abovesteadystateinitialdebt 1.426 1.608 -0.974 9.285 2.403 2.492 -0.246 11.075 Notes: Thistableshowsthethetransfermultipliersforaggregateoutput,Ricardiansectoroutput,RicardianconsumptionandHTMconsumption. Mi(X)representthecumulativetransfermultiplierofvariableX att-horizonunderiregime. Wereportimpactmultipliers t (t=0)aswellas4–year(t=24)cumulativemultipliers. AppendixTableC.14: TransferMultiplierswithDifferentDurationofBindingZLBPeriods MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:ZLBDuration:4Periods(Baseline) ImpactMultipliers 1.923 1.863 0.119 7.828 2.949 2.726 1.166 8.788 4-YearCumulativeMultiplier 1.732 2.023 -0.002 7.409 5.552 5.429 3.078 13.652 PanelB:ZLBDuration:5Periods ImpactMultipliers 1.85 1.8 0.059 7.71 3.461 3.134 1.703 9.218 4-YearCumulativeMultiplier 1.529 1.773 -0.052 6.705 6.57 6.207 4.263 14.124 PanelC:ZLBDuration:6Periods ImpactMultipliers 1.759 1.733 0 7.514 4.1 3.656 2.408 9.639 4-YearCumulativeMultiplier 1.337 1.569 -0.118 6.098 7.927 7.325 5.826 14.805 PanelD:ZLBDuration:7Periods ImpactMultipliers 1.628 1.648 -0.063 7.165 5.071 4.461 3.537 10.091 4-YearCumulativeMultiplier 1.125 1.388 -0.202 5.469 10.079 9.189 8.366 15.684 PanelE:ZLBDuration:8Periods ImpactMultipliers 1.567 1.607 -0.099 7.019 5.419 4.751 3.955 10.212 4-YearCumulativeMultiplier 1.027 1.315 -0.264 5.253 10.87 9.896 9.323 15.935 Notes:Thistableshowsthetransfermultipliersforthemodelsundermonetaryandfiscalregimeswithdifferentdifferentperiods ofZLB.WeintroducedifferentdegreesofthepersistenceinpreferenceshockstogeneratedifferentZLBduration(persistence ofpreferenceshocksinPanelA:0.0,inPanelB:0.2,inPanelC:0.4,inPanelD:0.6,inPanelE:0.65). Mi(X)representthe t cumulativetransfermultiplierofvariableX att-horizonunderiregime. Wereportimpactmultipliersand4-yearcumulative multiplierswhengovernmentdistributestransfersequallyover6months. 52

Appendix Table C.15: Transfer Multipliers Without HTM Labor Supply Shocks and HTM Sector-SpecificShocks MonetaryRegime FiscalRegime MM(Y) MM(Y )MM(CR)MM(CH) MF(Y) MF(Y ) MF(CR) MF(CH) t t R t t t t R t t PanelA:OnlyPreferenceShocks ImpactMultipliers 3.083 2.746 0.066 12.961 5.518 4.691 1.629 18.25 4-YearCumulativeMultiplier 1.791 1.703 0.094 7.348 6.453 5.768 4.085 14.205 Notes: This table shows the transfer multipliers for the models under monetary and fiscal regimes when we re-calibrate the baselinemodel.Mi(X)representthecumulativetransfermultiplierofvariableXatt-horizonunderiregime.Wereportimpact t multipliersand4-yearcumulativemultiplierswhengovernmentdistributestransfersequallyover6months. 53

0 0 10 -2 -5 0 -4 -6 -10 -10 -8 -15 -20 -10 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 4 2 -2 2 1 -4 -6 0 0 -8 -2 -1 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 2 4 6 8 10 12 6 1.5 0.3 4 1 0.2 2 0.1 0 0.5 -2 0 0 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 2 4 6 8 10 12 AppendixFigureC.1: RedistributionPolicywithInflationaryShocks 5 1 5 20 0.5 10 0 0 0 0 -0.5 -10 -5 -20 -5 -1 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 1 2 2 10 0.5 5 0 0 0 0 -0.5 -5 -2 -2 -10 -1 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 Appendix Figure C.2: Impact and Cumulative Multipliers by Different Transfer Size/Sign withoutCOVIDShocks 54