UNIVERSITÀ CATTOLICA DEL SACRO CUORE

Dipartimento di Economia e Finanza

Working Paper Series

The Redistributive Effects of a Money-Financed Fiscal Stimulus

Chiara Punzo, Lorenza Rossi

Working Paper n. 76

January 2019

The Redistributive Effects of a Money-Financed Fiscal Stimulus

Chiara Punzo Università Cattolica del Sacro Cuore

Lorenza Rossi Università degli studi di Pavia

Working Paper n. 76 January 2019

Dipartimento di Economia e Finanza Università Cattolica del Sacro Cuore

Largo Gemelli 1 - 20123 Milano – Italy tel: +39.02.7234.2976 - fax: +39.02.7234.2781

e-mail: dip.economiaefinanza@unicatt.it

The Working Paper Series promotes the circulation of research results produced by the members and affiliates of the Dipartimento di Economia e Finanza, with the aim of encouraging their dissemination and discussion. Results may be in a preliminary or advanced stage. The Dipartimento di Economia e Finanza is part of the Dipartimenti e Istituti di Scienze Economiche (DISCE) of the Università Cattolica del Sacro Cuore.

The Redistributive Effects of a Money-FinancedFiscal Stimulus

Chiara Punzo and Lorenza Rossi ∗

December 2018

Abstract

This paper analyzes the redistributive channel of a money financedfiscal stimulus (MFFS). It shows that the way in which this regime isimplemented is crucial to determine its redistributive effects and conse-quently its effectiveness. In normal times, the most effective regime is aMFFS with no additional intervention by the Central Bank to stabilizethe real public debt using inflation, whereas a MFFS accompanied by realdebt stabilization - through the adjustment of seigniorage - is the mosteffective one in a ZLB scenario. In a TANK model this regime is so effec-tive to avoid the recessionary effects implied by the ZLB. This result doesnot hold in a RANK model, where the redistributive channel is absent.Remarkably, contrary to the common wisdom a MFFS is followed by amoderate increase of inflation, which is only temporarily higher than thetarget.

KEYWORDS: Money-Financed fiscal stimulus, seignorage, govern-ment spending, redistribution, borrower-saver, fiscal multipliers, welfare,RANK versus TANK.

JEL CODES: E32, E52, E62

∗Chiara Punzo, Department of Economics and Finance, Università Cattolica del SacroCuore, via Necchi, 5, 20123 Milan, Italy, e-mail: chiara.punzo@unicatt.it and Lorenza Rossi,Department of Economics and Management, University of Pavia, via San Felice, 5, 27100Pavia, Italy, e-mail: lorenza.rossi@unipv.it (correspoding author). The authors thank GuidoAscari, Fabrice Collard, Davide De Bortoli, Jordi Galì, Tommaso Monacelli and SalvatoreNisticò for very helpful feedback and discussions. We are also grateful to all the participantsin the 22nd Conference on "Theories and Methods in Macroeconomics", the 24th Conferenceon "Computing in Economics and Finance", the 5th Macro, Banking and Finance Workshop,the Conference on "Finance and Economic Growth in the Aftermath of the Crisis", the 22ndAnnual Workshop on Economic Science with Heterogeneous Interacting Agents held at theUniversità Cattolica del Sacro Cuore, the Catalan Economic Society Conference, the 8thRCEA Macro-Money-Finance Workshop and the XXV Rome Conference on Money, Bankingand Finance.

1

1 Introduction

This paper contributes to the literature on the redistributive effects of monetaryand fiscal policies. In particular, it analyzes the redistributive channel of amoney-financed fiscal stimulus (MFFS - henceforth) compared to that of a debtfinanced fiscal stimulus (DFFS) in a borrowers-savers framework. It looks atthe strength of these alternative fiscal financing regimes and investigates howtheir redistributive effects influence the effectiveness of the stimulus itself.By considering a Two-Agents New-Keynesian model - henceforth, TANK

model - in a Borrower-Saver framework, this paper argues that redistribution is akey channel through which the fiscal financing regimes affect the macroeconomicaggregates. Usually, the debate about money financing is burdened by thedeep fear of hyperinflation. The idea that a future inflation tax can reduce theability of money to stimulate the aggregate demand has been central in theeconomic debate that followed the recent crisis. However, in a borrowers-saversmodel, the inflation tax can be used to redistribute from one household to theother one further amplifying or reducing the effect of the stimulus. For thisreason, in this paper we consider two types of MFFS: i) a MFFS in which theincrease in government purchases are entirely financed through money creationwithout any additional intervention by the Central Bank (our benchmark MFFS,hereinafter); ii) a MFFS in which, though the increase in government spendingis financed through money, the seigniorage is adjusted in each period to keepunchanged the real value of public debt using the inflation, as in Galì (2017)(alternative MFFS, hereinafter). In this respect, this paper shows that, theway in which a MFFS is implemented is crucial to determine the redistributiveeffects of the stimulus and consequently its effectiveness. It also results crucialto determine whether the stimulus is welfare improving with respect to a DFFSor not. Overall, we show that consumption and output multipliers are larger ina MFFS than in a DFFS. This occurs because the stimulus redistributes morefrom savers to borrowers, that is to the households with the higher marginalpropensity to consume. However, we show that the effectiveness of a MFFS isstate dependent. In normal times the most effective regime is the benchmarkMFFS, whereas it is the alternative MFFS that becomes the most effectivefinancing scheme in a ZLB scenario. In a TANK model this regime is so effectiveto avoid the recessionary effects of the ZLB. Remarkably, this result does nothold in a RANK model, where the redistributive channel is absent. Further,contrary to the common wisdom we show that a MFFS is followed by a moderateincrease of inflation which is only temporarily higher than the target.In this paper, Borrowers and Savers are modeled as in Bilbiie, Monacelli

and Perotti (2013 - BMP henceforth). The two agents differ in their degreeof impatience, they are both intertemporal maximizers, so that borrowing andlending take place in equilibrium, and financial markets are imperfect. Bor-rowers face a suitable defined borrowing limit, and it is important to highlightthat, differently from the standard rule-of-thumb framework, the distribution ofdebt/saving across agents is endogenous. In this context, the paper studies thedynamics of the model in response to an exogenous increase in government pur-

2

chases under the two types of MFFS. The results obtained under a MFFS arecompared with those implied by a DFFS, with the central bank implementinga standard inflation targeting interest rate rule. To better understand the roleplayed by the redistribution channel, the results obtained in the TANK modelare then compared with the ones characterizing a representative agent model(RANK henceforth).In details, the contribution of the paper can be summarized in five main

results.First, in normal times, all the regimes imply a redistributive effect from

savers to borrowers. However, thanks to the accommodative monetary policy,borrowers gains are much larger under the benchmark MFFS than under thealternative one and the DFFS. This is due to the fact that borrowers, who arethe households with the higher marginal propensity to consume, increase theirconsumption by a larger amount than savers. The consumption ratio betweenborrowers and savers is indeed five times higher under the benchmark MFFSthan under a DFFS. As a consequence, the aggregate demand increases by alarger amount and the benchmark MFFS is followed by a stronger expansionaryeffect on output than a DFFS. Further, thanks to the redistribution channelthe benchmark MFFS strongly amplifies the impact of the fiscal interventionwith respect to a RANK model, increasing the effectiveness of the MFFS. Re-markably, the amplification is obtained at the cost of a mild increase of inflation,which is only temporarily higher than the target. The alternative MFFS insteadonly mildly amplifies the effect of the policy with respect to a DFFS. In thiscase, the transmission mechanism is indeed less effective since the redistributivechannel of public bonds and that of inflation are muted to stabilize the realvalue of the debt.Second, we compute consumption and output fiscal multipliers associated

to the three different financing regimes and we find that, under our benchmarkMFFS fiscal multipliers are largely higher than one in normal times. Inter-estingly, these multipliers increase exponentially as the share of borrowers in-creases. The reason is the following. Given that borrower’s consumption reactsmore than saver’s consumption to an increase in public spending, the higher isthe share of borrowers the higher is the contribution of the redistribution chan-nel to the fiscal multipliers under both financing regimes. Also, we find thatfiscal multipliers are an increasing function of the borrowing limit. By relaxingthe borrowing constraint, the amount of private debt obtained by borrowersincreases and the implied wealth effects become larger, so that borrower’s con-sumption increases by a larger amount. This reflects on higher fiscal multipliers.On the contrary fiscal multipliers associated to the alternative MFFS are closeto the ones implied by a DFFS. They become instead lower than those impliedby a DFFS for suffi ciently high values of the share of borrowers, larger than40%, that is largely higher than what found in the data.Third, in terms of consumption equivalent welfare, we find that borrowers

are better off under our benchmark MFFS than under a DFFS, whereas saversare worse off. Fourth, our benchmark MFFS is preferable in terms of aggregatewelfare only in the TANK model. In the RANK model it is instead welfare

3

detrimental.Overall, we can state that in normal times our benchmark MFFS results

more effective than the other two regimes, it implies larger multipliers and iswelfare improving. Our benchmark MFFS is preferable in a TANK model sincethe expansionary effects of government spending are larger, thanks to very highfiscal multipliers.The key economic drivers of these results are the following. Under the

benchmark MFFS, government spending shocks are entirely financed throughmoney, with the real debt free to change. In this case, the decline in the real ratebrought about by the injection of new liquidity implies a consumption crowding-in for both agents. Inflation increases more than under a DFFS and the declinein the real interest rate is much bigger. Though a consumption crowding-incharacterizes also the standard RANK model, in a TANK model the redistrib-ution channel affects significantly the dynamics of aggregate variables. Indeed,the increase in inflation erodes the real value of debt, with savers losing andborrowers gaining. The marginal value of one unit of debt decreases inducingborrowers, which represent the households with the higher marginal propensityto consume, to increase their demand. Borrowers’consumption increases morethan savers’consumption. As a result, the aggregate demand increases morethan in a RANK model and so does the aggregate output. In normal times, aDFFS is less inflationary than the benchmark MFFS, implying a lower erosionof the real value of debt and thus a less expansionary effect on output. On thecontrary, when the MFFS is accompanied by a seigniorage adjusted in everyperiod to keep real value of the debt unchanged as in Galì (2017), the redistrib-ution channels due to higher inflation and lower real debt are not effective andthe policy results much less expansionary in normal times.Fifth, this paper shows the alternative MFFS becomes the most effective

financing regime in a ZLB scenario. It redistributes from savers to borrowersand, by sustaining higher level of inflation than in normal times, is able toavoid the economy to enter into a recession. The intuition for this last result israther simple. As soon as an adverse demand shock pushes the economy into aZLB scenario, the real GDP falls down bringing about an increase of the realvalue of public debt, both under a DFFS and under the benchmark MFFS. Onthe contrary, under the alternative MFFS the seigniorage is adjusted to keepunchanged the real value of public debt by generating higher inflation than inthe benchmark MFFS. The stronger inflationary effect of the alternative MFFSpushes the real interest rate down more than under the benchmark one and thepolicy redistributes from savers to borrowers, so that borrowers consumptionincreases and so does aggregate consumption. As a result, the policy pushes upthe aggregate demand and results so effective to avoid the economy to enter intoa recession. On the contrary, under the DFFS and the benchmark MFFS, thereal value of debt increases so that savers who are the owners of the public debtare better off, while borrowers are worse off. The substitution effect, due tothe decrease of the real interest rate under the benchmark MFFS, is more thancompensated by the income effect. Both consumption of borrowers and that ofsavers decreases on impact and the policy results less effective than in normal

4

times. Last but not the least, it is rather important to notice that the strongeffectiveness of the alternative MFFS does not hold in a RANK model, wherethe redistributive channel is absent. Again, this suggests that the redistributivechannel is very important and that it cannot be neglected by policy makers.The Technical Appendix of this paper considers an economy characterized by

a non-competitive labor market. In this case wage-setting decisions are made bylabor type specific unions. Each union pools the labor income of agents, leadingborrowers and savers to work for the same amount of time. This implies thatthe redistribution channel does not affects differently labor supply decisions ofthe two agents, which is in line with the evidence that wealthy households donot work an amount of hours lower than that of poorer households. We showthat our results are even reinforced under the alternative labor market.The last Great Recession has opened a wide spectrum of policy tools. A

more moderate example of money creation has already been implemented bycentral banks, as quantitative easing operations. The latter has been accompa-nied by expansive fiscal policies at least in the US. On this last issue, Giavazziand Tabellini (2014) argue that measures as quantitative easing should alwaystake place together with fiscal easing. In a recent paper, Galì (2017) comparesthe effectiveness of a MFFS defined as in ii) and of a DFFS, in a standard Rep-resentative Agent New Keynesian model (RANK), with and without bindingzero lower bound (ZLB). By considering a simple RANK model with perfectfinancial markets, the paper voluntary ignores the possible redistributive effectsof the two alternative regimes associated to the fiscal stimulus. However, in aneconomy where a fraction of agents is financially constrained, the way of financ-ing fiscal stimula matters, since it can redistribute away from some agents toothers. The redistribution channel originated from a stimulus may then interactwith the stimulus itself by reducing or increasing its effectiveness, significantlyaffecting the dynamics of aggregate variables and the aggregate welfare. Ourpaper goes in this direction by investigating the redistributive effects of moneyfinanced spending policies and the role played by the redistribution channel inaffecting aggregate dynamics in normal times as well as in bad times.The remainder of this paper is organized as follows. Section 2 briefly presents

the related literature, Section 3 spells out the model economy, while Section 4analyzes the effect of a money-financed fiscal stimulus in a NK-DSGEmodel withsavers and borrowers. Section 5 summarizes the main findings and concludes.

2 Related Literature

Our paper is closely related to the literature of heterogeneous households mod-els. The latest generation of models with heterogeneous agents and financialfrictions, the so called Heterogeneous Agent New Keynesian models (HANKhenceforth) are characterized by multi-agents and thus they are particularlysuitable to study redistributive issues, however at the cost of being computa-tional more complex. In these models the effects of any aggregate shock will beamplified or dampened depending on the way the shock affects the distribution

5

of income and wealth across households. Among many others, Oh and Reis(2012), McKay and Reis (2016) were the first contributions to this literature.More recent contributions are Guerrieri and Lorenzoni (2017), Auclert (2017),Kaplan et al. (2017), Ravn and Sterk (2017), Farhi and Werning (2017), Kaplanand Violante (2018) and Galí and Debortoli (2017), among many others. Guer-rieri and Lorenzoni (2017) focus for example on the effects of credit crunches.Auclert (2017) considers a Bewley-Hugget-Aiyagari model calibrated on the U.S.economy and provides a careful analysis of the redistributive effects of monetarypolicy, showing that redistribution works through three main channels. Thesechannels may amplify the effects of monetary policy on aggregate consumption.Similarly, Kaplan et al. (2017) argue that the aggregate effects of monetarypolicy shocks will depend on the type of the fiscal policy in response to them.Kaplan and Violante (2018) present an updated survey of the HANK literatureand analyze the role of households’heterogeneity for the response of the macro-economic to aggregate shocks. They find that monetary shocks are weaker andfiscal shocks are stronger in HANK than in RANK, so that they conclude thatdegree of equivalence between HANK and RANK models crucially depends onthe shock being analyzed. They also recognize that the development of HANKmodels is still in its infancy, mostly because of the computational complexityin dealing with the equilibrium distribution as a state variable, which limitsthe development of more structured models. Importantly, none of these papercompares the effects of a MFFS to a DFFS.A very recent paper of Debortoli and Galì (2017) shows that TANK models

can provide a good and tractable approximation of the HANK models. Theyshow that a TANK model approximates well, both quantitatively and qualita-tively the dynamics of an HANK model in response to aggregate shocks. Alsoin this case they do not investigate the effects of a MFFS. The Borrower-Saverframework used in our paper goes in the same direction of showing that thepresence of borrowers in a TANK setup is suffi cient to introduce a strong re-distribution channel generating non negligible effects on the dynamics of theaggregate variables. Importantly, differently from previous papers our paperconsiders the effects of a MFFS both in normal times and in bad times.Our paper is also related to the recent DSGE literature which has shown a

renewed interest in monetary and fiscal policy interactions under a ZLB scenario.For example, Woodford (2011) shows analytically that in a simple NK modelfiscal multipliers are larger than one when monetary policy is constrained by theZLB.1 Christiano, Eichenbaum and Rebelo (2011), Eggertsson and Woodford(2011) also point to the existence of very large government spending multiplierswhen the ZLB is binding. Galì (2017) analyzes the effects of an alternativeand not conventional monetary policy to recover the economy: a fiscal stimulus,in the forms of both a temporary increase in government purchases and a taxcut, financed entirely through money creation both in normal times and at theZLB. He finds that when the ZLB is not binding, a MFFS has much largermultipliers than a DFFS. That difference in effectiveness persists, but is much

1Eggerson and Woodford (2003) previously study the optimal monetary policy at the ZLB.

6

smaller, under a binding ZLB.2 All these papers on monetary and fiscal policyinteraction at the ZLB however consider a representative agent economy andthus they do not investigate the possible redistributive effects of these policieswhich are instead the main objective of our paper. Differently from these papers,we show that how the redistribution channel interacts with the stimulus is statedependent and crucial to determine the effectiveness of the stimulus itself.Finally, a number of recent empirical papers substantiate our interest in

studying the redistributive effects of the two stimula. In particular, Doepke andSchneider (2006) show that inflationary episodes can cause significant revalu-ations of assets and redistributive effects from wealthy, middle age, and oldhouseholds towards the government (the main debtor) and poor, young house-holds. Notice that, while wealthy and middle age households are usually netsavers, poor and young households are instead net borrowers in the US economy.Similar evidence is documented by Adam and Zhu (2014) for European coun-tries and Canada. An additional paper motivating our analysis is Coibion et al.(2012), who, relying on the CEX survey, find that monetary expansions reduceinequality, as measured by Gini coeffi cients, suggesting a redistribution awayfrom wealthier individuals (savers). In Sterk and Tenreyro (2016), monetarypolicy expansions cause a redistribution of income from retirees, who rely moreheavily on their nominal wealth as source of finance for consumption, to work-ing agents and future tax payers. The consumption of goods by working agentsincreases relative to that of retired agents following a monetary expansion.With these evidence in mind, in the remainder of the paper, we present the

Borrower-Saver setup of our model and we study the strength of the two regimesand how their redistributive effects influence the effectiveness of the policy itself.

3 The Model

The model considered is a closed economy composed by four agents: households,firms, the fiscal authority and the monetary authority.

3.1 Households

All households have preferences defined over private consumption, Cι,t, realbalances, mι,t = Mι,t/Pt, and labor services, Nι,t, according to the followingseparable period utility function,

ln (Cι,t)− χ

(x− mι,t

Cι,t

)1+σ

1 + σ−N1+ϕι,t

1 + ϕ, with χ > 0, σ > 0 and ϕ ≥ 0 (1)

2 In a very similar framework, English et al (2017) find that money-financed fiscal programs,if communicated successfully and seen as credible by the public, could provide significantstimulus. Conversely, such a program would be ineffective in providing stimulus if the publicdoubted the central bank’s commitment to a such extreme.

7

where mι,t =Mι,t

Pt, x is a satiation level of money and Cι,t is the aggregate level

of consumption for each type of household (ι = b, s, respectively borrowers andsavers).3

SaversSavers’problem becomes:

U0 = E0

∞∑t=0

βtι

ln (Cι,t)− χ

(x− mι,t

Cι,t

)1+σ

1 + σ−N1+ϕι,t

1 + ϕ

, (2)

s.t.

the budget constraint

PtCs,t +BHs,t +Ans,t +Ms,t + Ωs,tPtVt ≤ (1 + it−1)BHs,t−1 + (1 + it−1)Ans,t

Ms,t−1 + Ωs,t−1Pt (Vt−1 + Γt)

+WtNs,t − PtTs,t, (3)

where Wt is the nominal wage, Ans,t−1 is the nominal value at beginning ofperiod t of total private assets held in period t, a portfolio of one-period bondsissued in t−1 on which the household receives the nominal interest it−1. Vt−1 isthe real market value at time t of shares in intermediate good firms, Γt are realdividend payoffs of these shares, Ωs,t are share holdings, Ts,t is the lump-sumtax, BHs,t are the savers’holdings of nominally riskless one-period governmentbonds (paying an interest it). The nominal debt BHt pays one unit in nominalterms in period t+ 1.Given prices, policies and transfers Pt (z) ,Wt, it, Gt, Ts,t, Vt,Γt, Ttt≥0 , the

saver chooses the set of processesCs,t (z) , Cs,t, Ns,t,Ms,t, As,t, B

Hs,t,Ωs,t

t≥0

,soas to maximize (2) subject to (3) , the usual Cs,t ≥ 0, Ns,t ≥ 0,Ms,t ≥ 0 andthe no-Ponzi game conditions.

After defining the aggregate price level as Pt =[∫ 1

0Pt (z)

1−εdz] 11−ε

, as

well as real debt as, bHt ≡ Bt/Pt,optimality is characterized by the followingfirst-order conditions for savers:

βsEt

Cs,t (1 + it)

Cs,t+1πt+1

= 1, (4)

βsEt

Cs,tCs,t+1

Vt+1 + Γt+1

Vt

= 1, (5)

Ns,tCs,t = wt, (6)

3Our assumption of the utility function for real balances is borrowed from English et al.(2017).

8

χ

(x− ms,t

Cs,t

)σ=

(it

1 + it

). (7)

Equation (4) is the standard Euler equation for bond holdings, while equation(5) is the Euler equation for share holdings. Equation (6) is the savers’laborsupply, whereas equation (7) is their demand for real balances. Notice that,under log-utility of consumption, real money balances vary directly with con-sumption with a unitary coeffi cient. Also notice that for it > 0, it

1+it> 0, so

that the opportunity cost of holding money always guarantees that demand formoney will be ms,t

Cs,t< x. When it = 0, then the RHS of the money demand will

be zero, implying that the money is equal to its satiation level x.BorrowersIn each period t ≥ 0 and under all contingencies, the rest of households on

the [0, λ] interval is impatient (and will borrow in equilibrium, hence we indexthem by b for borrowers). They face the following budget constraint in nominalterms:

PtCb,t + PtAnb,t +Mb,t ≤ (1 + it−1)Anb,t−1 +Mb,t−1 +WtNb,t − PtTb,t,

the borrowing constraint (on borrowing in real terms) at all times t:

−Ab,t ≤ D, (8)

the usual Cb,t ≥ 0, Nb,t ≥ 0, and

Mb,t ≥ 0. (9)

The constraint (9), as we will show, becomes particularly important whenthe borrowing constraint is binding.Given prices, policies and transfers Pt (z) ,Wt, φt, it, Gt, Tb,t, Ttt≥0, the

borrower chooses the set of processesCb,t (z) , Cb,t, Nb,t,Mb,t, A

nb,t

t≥0

, so as

to maximize (2) subject to (8) , Cb,t ≥ 0, Nb,t ≥ 0 and (9). Optimality is char-acterized by the first-order conditions:

C−1b,t = βbEt

(1 + itπt+1

C−1b,t+1

)+ φt, (10)

Nϕb,tCb,t = wt, (11)

Mb,t = 0 (12)

implying that

χxσ =

(it

1 + it

)− φM

b

t (13)

Notice that, in (10), φt takes a positive value whenever the constraint is binding.Indeed, because of BMP assumptions on the relative size of the discount factors,

9

the borrowing constraint will always bind. As shown in the technical Appendix,this implies that borrowers are net borrowers and that their demand isMb,t = 0,

and equation (13) is the equation that determines the value of φMb

t . Notice that

at the ZLB, with it = 0, φMb

t = 1− χxσ is constant.

3.2 Firms

The economy is characterized by an infinite number of firms indexed by z on theunit interval [0, 1] . Each firm produces a differentiated variety with a constantreturn to scale technology,

Yt (z) = Nt (z) , (14)

where Nt (z) denotes the quantity of labor hired by firm z in period t. Fol-lowing Rotemberg (1982), we assume that firms face quadratic price adjustment

costs θ2

(Pt(z)Pt−1(z) − 1

)2

and θ ≥ 0. Nominal profits read as:

Et

∞∑i=0

Qt,t+i (z)

[Pt+i (z)Yt+i (z)−Wt+iNt+i (z)

−Pt+i θ2(

Pt+i(z)Pt+i−1(z) − 1

) ], (15)

where Qt,t+i is the discount factor in period t for nominal profits i periodsahead.Assuming that firms discount at the same rate as savers implies Qt,t+i =

βisCs,t

Cs,t+iπt+i, each firm faces the following demand function:

Yt (z) =

(Pt (z)

Pt

)−εY dt , (16)

where Y dt is aggregate demand and it is taken as given by any firm z.Cost minimization, taking the wage as given, implies that the real marginalcost is wt. Firms choose processes Pt (z) , Nt (z) , Yt (z)t≥0 so as to maximize(15) subject to (14) and (16), taking as given aggregate prices and quantitiesPt,Wt, Y

dt

t≥0

. Let the real marginal cost be denoted by

mct = wt (17)

Then, at a symmetric equilibrium where Pt (z) = Pt for all z ∈ [0, 1], profitmaximization and the definition of the discount factor imply:

πt (πt − 1) = βEt

[Cs,tCs,t+1

πt+1 (πt+1 − 1)

]+εNtγ

(mct −

ε− 1

ε

), (18)

where (18) is the standard Phillips curve according to which current inflationdepends positively on future inflation and current marginal cost. The aggregatereal profits are:

Γt = (1−mct)Yt −γ

2(πt − 1)

2. (19)

10

3.3 Fiscal Authority and Monetary Authority

The fiscal authority provides the public good Gt (z) for any z ∈ [0, 1] and weaggregate them according to:

Gt =

[∫ 1

0

Gt (z)ε−1ε dz

] εε−1

, (20)

so that total government expenditures in nominal terms is PtGt and thepublic demand of any variety is:

Gt (z) =

(Pt (z)

Pt

)−εGt. (21)

Expenditures are financed by levying a lump-sum tax or by issuing one pe-riod, risk-free, non state contingent nominal bonds. Hence, the fiscal authority’speriod budget constraint is given by

PtGt +Bt−1 (1 + it−1) = (1− λ)Ts,t + λTb,t + PtSGt +Bt, (22)

where Gt and Tι,t denote government purchases and lump-sum taxes in nom-inal terms, Bt is the stock of one-period nominally riskless government debtissued in period t yielding a nominal return it, and SGt denotes a real transferfrom the central bank to the fiscal authority. Equivalently, and after lettingbt = Bt/Pt we can write:

Gt + bt−1(1 + it−1)

πt= (1− λ) τs,t + λτ b,t + SGt + bt. (23)

where τ ι,t denotes lump-sum taxes (in real terms).The central bank’s budget constraint is given by

BMt + PtSGt = BMt−1 (1 + it−1) + ∆Mt,

where BMt denotes the central bank’s holdings of government debt at theend of period t, and Mt is the quantity of money in circulation4 . Equivalently,in real terms

bMt + SGt = bMt−1

(1 + it−1)

πt+

∆Mt

Pt, (24)

where bMt ≡ BMt /Pt and∆Mt

Ptis the amount of seigniorage generated in

period t.The amount of government debt held by households (expressed in real terms),

and denoted by bHt ≡ BHt /Pt, is given by4The balance sheet of the central bank is given by

BMt =Mt.

11

bHt = bt − bMt (25)

In what follows we often refer to bHt as net government debt, for short.Combining (23) , (24) and (25) one can derive the government’s consolidatedbudget constraint

Gt + bHt−1

(1 + it−1)

πt= (1− λ) τs,t + λτ b,t + bHt +

∆Mt

Pt(26)

which may also be interpreted as a difference equation describing the evolu-tion of net government debt over time. Below, following Galì (2017), we considerequilibria near a steady state with zero inflation, no trend growth, and constantgovernment debt bH , government purchases G, and taxes τ 5 . On the otherhand, constancy of real balances requires that ∆M = 0 in the steady state. Itfollows from (26) that

τ b =G+ ibH − (1− λ) τs

λ, (27)

and

τs =G+ ibH − λτ b

(1− λ). (28)

Note that (24)implies

SG = ibM , (29)

i.e. in that steady state the central bank’s transfer to the fiscal authorityequals the interest revenue generated by its holdings of government debt. In par-ticular, the level of seigniorage (expressed as a fraction of steady state output)can be approximated as

(∆Mt

Pt

)(1

Y

)=

(∆Mt

Mt−1

)(Mt−1

Pt−1

)(Pt−1

Pt

)(1

Y

)∼=

(1

V

)∆mt (30)

where mt = logMt and V ≡ PYM is the steady state income velocity of

money. Equation (30) implies that the level of seigniorage is proportional tomoney growth up to a first order approximation.

Also, as in Galì (2016) bHt ≡(bHt −b

H)Y , gt = (Gt−G)

Y and τ ι,t ≡ (τι,t−τι)Y are

the deviations of net government debt, government purchases and taxes fromtheir steady state values, expressed as a fraction of steady state output. Finally,assume that the fiscal authority implements the following feedback rule

5The constancy of the net government debt in the steady state implicitly assumes a taxrule designed to stabilize that variable about some target bH .

12

τ ι,t = ΦB bHt . (31)

This tax rule is general enough to allow taxes on each agent to react tostabilize government debt (ΦB = 0.02 is the debt feedback coeffi cient). Theplan prescribes a tax path that depends on public debt. We think that this isan interesting case, even though it is a simple one, because an endogenous taxresponse to public debt roughly agrees with the intentions declared by most ofpublic debt-targeting governments.Importantly, in our benchmark model the definition of a MFFS is different

from the one used in Galì (2017), since the temporary increase in governmentpurchases is entirely financed through money, and the fiscal authority does notfully stabilize public debt.6 The adoption of this definition is particularly rel-evant in a TANK model, since public debt reduces in real terms implying anadditional redistributive effect, which amplifies the effects of the stimulus.

3.4 Money-Financed vs. Debt-Financed Fiscal Stimulus

We now define deviations of government purchases from that "normal" level G,as. Gt = Gt −G. We refer to those deviations as "fiscal stimulus". Further, weassume that such fiscal stimulus, expressed as a fraction of steady state outputand denoted by gt ≡ (Gt−G)

Y , follows the following exogenous AR(1) process

gt = ρg gt−1 + εgt , (32)

where ρg ∈ [0, 1) indexes the persistence of the government spending shock.Our baseline policy experiment consists of an increase in government purchasesfinanced entirely through seigniorage. Formally,

∆Mt

Pt= Gt, (33)

or, equivalently, using (30),

∆mt = V gt, (34a)

i.e., the growth rate of the money supply is proportional to the fiscal stimulus,inheriting the latter’s exogeneity.As an alternative to the benchmark MFFS, we consider an alternative MFFS

(Galì, 2016) in which seigniorage is adjusted every period in order to keep realdebt unchanged. In terms of the notation, it requires to replace equation (34a)with:

bHt = 0 (35)

As an alternative to the two types of MFFS, we analyze the effects of a DFFSin which the central bank follows a simple interest rate rule of the following type

6This is the definition used by Galì (2014), which is a previous version of the (2017) paper.

13

log

(1 + it1 + i

)= φππt, (36)

where πt = log πtπ and φπ > 1 determines the strength of the central bank’s

response of inflation deviations from the zero long-term target. Notice that,in contrast with the money-financing regime, ∆mt is no longer determined bygt.The interest rate rule requires that the central bank injects or withdrawsmoney from circulation by means of open market operations (in exchange forgovernment debt) in order to accommodate whatever money is demanded byhouseholds at the targeted interest rate.As discussed below, an interest rate rule like (36) gives the central bank a

tight control over inflation in response to a fiscal stimulus, through its choice ofcoeffi cient φπ.Yet, that tighter control comes at the price of a smaller impact ofthe fiscal stimulus on economic activity (i.e. a smaller "fiscal multiplier").

3.5 Equilibrium

The equilibrium allocation Yt = Ct + Gt + θ2 (πt − 1)2 is based on additional

markets clearing conditions,

Ct = λCb,t + (1− λ)Cs,t; (37)

Mt = λMb,t + (1− λ)Ms,t; (38)

Nt = λNb,t + (1− λ)Ns,t; (39)

respectively, aggregate consumption, money market clearing condition andlabor market clearing condition.

4 Model Dynamics and Welfare: Normal Times

This section is divided in four parts. First, it reports the quarterly calibrationused. Second, it shows the IRFs to government spending shocks comparing themodel dynamics implied by the benchmark MFFS with those implied by theother two financing schemes, that are the alternative MFFS and the DFFS.Then, it computes the implied fiscal multipliers and the welfare implication ofthe three regimes.The Technical Appendix of this paper describes a TANK model under the

assumption of an alternative non-competitive labor market. In this case, wage-setting decisions are made by labor type specific unions. Each union poolsthe labor income of agents, leading borrowers and savers to work for the sameamount of time. This implies that the redistribution channel does not affectsdifferently labor supply decision of the two consumers type, which is in linewith the evidence that wealthy households do not work an amount of hours

14

lower than that of poorer households. We show (Figures 9−13) that our resultsare robust and even reinforced under this alternative labor market.

4.1 Calibration

We solve the model by taking a first order approximation around the steadystate. Before showing our results, we briefly describe the baseline calibrationof the parameters. That calibration is summarized in the top panel of Table(1) . We assume the following settings for the household related parameters inline to those of BMP (2013): discount factors of borrowers and savers are setrespectively βb = 0.95 and βs = 0.99. Analogously, as in BMP, we set theborrowing constraint D = 0.5. Parameter λ, denoting the share of impatientagents, is set to 0.25.The remaining parameters are kept at their baseline values, as in Gali (2017).

We assume the elasticity of substitution among goods ε = 6 and the curvature oflabor disutility ϕ = 1. The model’s main frictions are given by price stickinessand market power in goods market. We assume a baseline setting of α = 0.75,an average price duration of four quarters, a value consistent with much ofthe empirical micro and macro evidence. The focus on direct financing of thefiscal stimulus through money creation by the central bank calls for choosingthe monetary base (M0) as that empirical counterpart. Average (quarterly) M0income velocity in the U.S. over the 1960-2015 period is 3.6. The correspondingvalue fro the euro area over the period 1999-2015 is 2.7. We take a middle groundand set V = 3 as the steady state inverse velocity in the baseline calibration.Further, we assume the following setting for the parameters related to moneydemand in utility function. The weight of real balances in utility function is setχ = 0.018, in line with Annicchiarico et al. (2012). The specification of moneydemand implies a unitary long-run elasticity with respect to consumption. Weimpose a short run interest rate semi-elasticity of money demand equal to 2.5(when expressed at an annual rate), in line with English et al. (2017). Finally,the money satiation level x is calibrated so that x > ms

Cs.

We calibrate the fiscal parameters so that the value of the tax adjustmentparameter, ΦB , is set so that one-twentieth of the deviation from target in thedebt ratio is corrected over four periods (i.e. one year), in the absence of furtherdeficits. This requires ΦB equal to 0.02. That calibration can be seen as a roughapproximation to the fiscal adjustment speed required for euro area countries,as established by the so called "fiscal compact" adopted in 2012. In additionwe assume the following fiscal policy settings: γ = 0.2 (steady state share ofgovernment purchases in output), bH = 2.4 (corresponding to a 60 percent ratioof debt to annual output) and, for the persistence parameter ρg, we choose 0.5as a baseline setting.

15

Description ValueNK Modelβb Borrower’s discount factor 0.95βs Saver’s discount factor 0.99D Borrowing Constraint 0.5λ Share of impatient agents 0.25χ Weight of money in utility function 0.018x Money satiation level 1σ short run interest rate semi-elasticity of money demand 2.5V Velocity (quarterly) 3γ Government spending share 1/5ρg Fiscal stimulus persistence 0.5bH Steady state debt ratio (quarterly) 2.4ε Elasticity of substitution (goods) 6η Elasticity of money demand to output 7α Index of price rigidities 0.75ΦB Debt feedback coeffi cient 0.02

Table 1: Baseline Calibration

4.2 Money-Financed vs. Debt-Financed Fiscal Stimulus

Figures 1 and 2 compare the impulse response functions (IRFs) implied by ourTANK model under the two types of MFFS (red solid line and pink dotted line)with those obtained under a DFFS accompanied by a monetary policy describedby the simple interest rate Taylor rule (blue dotted line). In particular, thered solid line indicates a MFFS defined as an increase in government purchasesentirely financed through the emission of new liquidity by the Central bank, withthe real value of debt free to change consequently and tax changes correspondingto real debt changes according to a fiscal rule (31). We label this stimulus asour benchmark MFFS. The pink dotted line indicates instead a MFFS in which,though the increase in government purchases is entirely financed through money,the seigniorage is adjusted in each period to keep real debt unchanged. In otherwords, it avoids that inflation erodes the real value of the debt. We labelthis stimulus as our alternative MFFS. Figure 1 displays the IRFs of selectedaggregate variables to a one percent increase in government purchases, whileFigure 2 shows the redistributive effects of the alternative financing regimes.To quantify the importance of the redistribution channel in the transmission ofthe fiscal stimulus to the aggregate economy, Figure 3 compares the aggregateresponses of output and consumption of our TANK model with those obtainedin a RANK model7 .As shown in Figure 1, the initial shock consists in a one percent increase of

government expenditure. First of all, notice that under the benchmark MFFS,

7We consider an economy with a representative household which is equivalent to the saverin our benchmark TANK model.

16

the creation of new money strongly reduces the real value of public debt dueto the increase in inflation that the injection of new liquidity provokes. On thecontrary, by construction, under the alternative MFFS the real value of publicdebt remains unchanged. Notice that the benchmark MFFS implies an higherinflationary effect. The lower increase results from the behavior of the mon-etary authority which starts reducing money creation from the second periodon in order to to keep real value of debt unchanged. As a consequence, thereal interest rate decreases less under the alternative MFFS. The dynamics ofinflation, together with that of the real interest rate and the real debt, is keyto understand the stronger expansionary effect of the benchmark MFFS withrespect to the alternative one and the role played by the redistribution channel.In both models, the decline in real rates brought about by the increase in infla-tion due to the injection of new liquidity implies a consumption crowding-in forboth agents, though for the reasons stated above the crowding-in effect is muchstronger under the benchmark MFFS. Finally, the gradualism in the price re-sponse, implied by staggered price setting amplifies the transmission mechanismof a MFFS.8 Remarkably and contrary to the common wisdom, in both cases aMFFS is followed by a moderate increase of inflation which is only temporarilyhigher than the target.The blue dotted line shows the case in which the fiscal stimulus is financed

through the issuance of public debt. In this case the Central Bank withdrawsmoney from circulation in order to satisfy the reduction of the money demanddue to higher targeted interest rate. The presence of an inflation targetinginterest rate rule - which accompanies a DFFS - implies that the nominal interestrate increases more than one to one with inflation, leading to an increase in thereal interest rate, that triggers a smaller real expansion than in a MFFS.

- Figure 1 about here -

Figure 2 underlines the redistributive effects of the fiscal policy under the dif-ferent financing regimes. We can observe how the redistributive effects influencethe effectiveness of the three financing schemes, particularly of our benchmarkMFFS. First of all notice that, under the benchmark MFFS, the resulting in-crease in inflation erodes the real value of debt, with savers losing and borrowersgaining. The marginal value of one unit of debt decreases, inducing borrowersto consume more. Overall, borrowers’consumption increases more than savers’consumption. Remarkably, under the benchmark MFFS, the consumption ratiobetween the consumption of borrowers and that of savers is three times higherthan under the alternative MFFS and the DFFS which, in turn, are more similaramong them. This underlines the key role of inflation in affecting the redistrib-ution channel which strongly amplifies the effects of the benchmark MFFS onaggregate consumption. As shown in Figure 3, the redistribution channel playsa key role in amplifying the effect of the stimulus with respect to a RANK

8As in Galì (2016), our model implies an upward response of the nominal interest ratewhich suggests that the existence of a zero lower bound on that variable (whether currentlybinding or not) should not be an impediment to the implementation.

17

model. Indeed, the difference in consumption is of the order of 2 percentagepoints under the benchmark MFFS, while it is almost 0.5 percentage pointsunder the alternative MFFS and under the DFFS. Differently from a MFFS, aDFFS implies a standard crowding-out effect on saver’s consumption. Also inthis case the stimulus implies a redistribution from savers to borrowers (mea-sured in terms of consumption ratio), so that such the redistribution channelamplifies also the effects of the DFFS on aggregate output. However, the lowerconsumption ratio implies a lower effect on aggregate consumption, and thus onaggregate output, than under our benchmark MFFS. The response of output isinstead only slightly higher under the alternative MFFS than under the DFFS,both in the RANK and in the TANK model.

- Figure 2 about here -

Overall, our analysis confirms that the effects a MFFS, which leaves the realvalue of debt free to change in a NK monetary economy should be preferableto a DFFS and to a MFFS that keep the real value of debt unchanged, due tothe much stronger redistributive effects implied by the baseline MFFS. Last butnot the least, private debt results in a strong reduction. While the impact oninflation is very limited, a DFFS, accompanied by a simple interest rate rule,has instead the disadvantage of a smaller impact on aggregate activity, at thecost of higher debt.

- Figure 3 about here -

Our results on the dynamic effects of the two regimes in normal times canbe summarized as follows.

Result 1: In normal times, all the regimes considered imply a redistribu-tive effect from savers to borrowers. The redistribution is much larger underthe benchmark MFFS, so that policy results highly effective and expansionary,though being only slightly inflationary. Last but not the least under the bench-mark MFFS the real debt decreases. The redistribution channel significantlyincreases the effectiveness of the fiscal stimulus under all financing regimes withrespect to a RANK model, however it is particularly strong under the benchmarkMFFS.

4.3 Multipliers

In this section, we firstly compute the fiscal multipliers of output and con-sumption associated to an increase in government purchases, under the threealternative fiscal financing regimes. We will compute the multipliers changingλ, corresponding to changing the fraction of borrowers in the economy. Then,in order to understand the role played by the financial constraint, we evaluatethe same multipliers under different values of the borrowing limit, D.To differentiate between the immediate impact of a change in fiscal spending

and its long-run implications for the economy, we compute both the instanta-neous and the cumulative fiscal multiplier, following Uhlig (2010).

18

The Instantaneous Fiscal Multiplier (ICF, hereinafter) measures, in eachperiod, the percentage deviation of a generic variable Xt from its steady statein response to a change in government purchases that, on impact, amounts toone percent of the SS value of output. That is:

IFM (x) ≡ xt

gTGY

,∀t ≥ T (40)

where xt = Xt−XX

, gT = GT−GG

with t being the time index for the periods

following the initial fiscal shock in period T . G and Y are, respectively, thesteady state values of government spending and output. In particular, we willconsider the impact multipliers associated to t = T, and we refer to them asImpact Multipliers of x.As stressed by Uhlig (2010), policy makers cannot solely rely on the instan-

taneous multiplier since it can be misleading as it ignores the cumulated impactof the initial fiscal policy measure on the economy over time. Thus, in order tocapture the cumulative impact on the variable of interest of the fiscal shock, weconsider also the cumulative fiscal multiplier in analogy to Uhlig (2010).The Cumulative Fiscal Multiplier (CFM, hereinafter) identifies, in each pe-

riod, the discounted cumulative change of a variable Xt measured in terms ofpercentage deviation from its steady state relative to the discounted cumulativechange of government spending from its steady state value. That is

CFM (x) ≡∑ts=T R

−(s−t)xs

GY

∑ts=T R

−(s−t)gs,∀t ≥ T (41)

with R being the steady state of the nominal interest rate used as discount rate.Figure 4 shows the IFM and CFM for consumption and output, under the

three financing schemes, as λ changes from 0.1 to 0.45. As expected, consump-tion and output multipliers (both the impact and the cumulative ones) are muchhigher under the benchmark MFFS, being the monetary authority more accom-modative. In this case, the multipliers of consumption and output are alwaysgreater than one. Further, they increase exponentially as the share of borrow-ers, λ, increases, particularly the impact multipliers. As expected under thealternative MFFS the multipliers are much lower, but they also increase withλ. Under a DFFS, the multipliers of output are always above one and they alsoincrease with λ. The multipliers of consumption take a value, instead, largerthan one only for values of λ ≥ 0.35 for the IFM(C), and for λ ≥ 0.37 in thecase of CFM(C). Remarkably, notice that the multipliers associated to a DFFSbecome largely higher than that implied by a MFFS with debt stabilization forvalues of λ larger than 0.4. As the share of borrowers increases the inflationaryeffect of both the stimula becomes higher than under our baseline calibrationwith λ = 0, 25. This, in turn, implies that from the second period on, the mone-tary authority has to increase the real rate by a much larger amount under thealternative MFFS than under a DFFS (which follows a standard Taylor rule)

19

to stabilize the real debt. As a consequence, from the second period two on thereal interest rate becomes positive and higher than under a DFFS. This impliesa lower effect on both savers and borrowers consumption.

- Figure 4 about here -

Finally, Figure 5 shows the CFM multipliers for three different values ofthe borrowing limit, that are D = 0.1;D = 0.5;D = 1, under the alternativefinancing schemes. Notice that, in all cases, fiscal multipliers increase as Dincreases. By relaxing the borrowing constraint, the borrower’s consumptioncan increase more, and it generates higher fiscal multipliers.

- Figure 5 about here -

Our results on fiscal multipliers can be summarized as follows.

Result 2: Under the benchmark MFFS, consumption and output multipliersare largely higher than one. The benchmark MFFS implies higher fiscal multipli-ers than the DFFS and the alternative MFFS. Under all the financing schemes,fiscal multipliers are an increasing function of the share of borrowers λ, and ofthe borrowing limit, D. However, multipliers associated to DFFS become largelyhigher than that implied by the alternative MFFS for values of λ larger than0.4 and for suffi ciently high value of D.

To further understand the contribution of the borrowing limit, we now com-pute the cumulative multipliers of output and consumption under the threeregimes for D increasing from 0.1 to 7 and for λ respectively equal to 0.3 and0.4. Figure 8 shows the results.Notice that, overall, a DFFS implies multipliers higher than the other regimes

only for values of λ and D larger than what reported by the empirical evidence.

4.4 Welfare

To assess the normative implications of the two stimula, we numerically evaluatethe welfare. To do it, we solve the model using a second-order approximationof the structural equations, for each regime. We compute the individual welfarefor savers and borrowers, respectively, as follows:

Ws,t = (1− βs)Et∞∑k=0

βks

(ln (Cs,k)−

N1+ϕs,k

1 + ϕ+ χV (ms,t)

)(42)

Wb,t = (1− βb)Et∞∑k=0

βkb

(ln (Cb,k)−

N1+ϕb,k

1 + ϕ+ χV (mb,t)

)(43)

Notice that we assume that real balances have a negligible weight in utilityrelative to consumption or employment, so that they do not affect welfare re-sults.9 As in Mendicino and Pescatori (2007), Rubio and Carrasco-Gallego

9We do not want that welfare results on MFFS are driven by the presence of real balancesin the utility function. In respect of it, our assumption is conservative.

20

(2014), Forlati and Lambertini (2014) and Notarpietro et al. (2015), amongothers, it implies that each type of agent receives the same level of utility froma constant consumption stream. The social welfare is, then, a weighted sum ofthe individual welfare of each different kind of household

Wt = ωsWs,t + ωbWb,t (44)

where ωs = 1 − λ and ωb = λ. Given that the utility function is not cardinal,a welfare measure based on the value function is not revealing. For this reason,we convert the welfare measures in consumption equivalent units, defined asthe constant fraction of consumption under a MFFS, that households shouldgive away in each period to equate the value function under a DFFS.10 Then,whenever a MFFS implies welfare gains, households would be willing to payin consumption units for the policy to be implemented. The derivation of thewelfare equivalent units for savers and borrowers implies that:

CEs = exp[(1− βs)

(WMFFSs,t −WDFFS

s,t

)]− 1 (45)

CEb = exp[(1− βb)

(WMFFSb,t −WDFFS

b,t

)]− 1 (46)

are respectively consumption equivalent measures of savers and borrowers, wherethe superscripts in the welfare values denote the benchmark MFFS (and thealternative MFFS) and the DFFS. Positive values of consumption equivalentwelfare imply that the agent is better under a MFFS than a DFFS, whereasnegative values of consumption equivalent imply that the agent is worse off un-der a MFFS than under a DFFS. The consumption equivalent derived from thesocial welfare is instead given by,

CE = exp(WMFFSt −WDFFS

t

)− 1 (47)

thus, a positive value of CE implies that a MFFS is preferable in terms ofaggregate welfare than a DFFS, whereas a negative value of CE means thataggregate welfare is higher under a DFFS than under a MFFS.Table 2 shows the values of the consumption equivalent welfare implied by

the benchmark MFFS with respect to a DFFS. In particular, it shows the twoagents consumption equivalent measures (CEb and CEs) and that of aggregateconsumption equivalent welfare, CE, in percentage terms. We compute thesemeasures under the three different values of the borrowing constraint parameter,D, that is D = 0.1; 0.5; 1.

Table 2: Consumption Equivalent Measure in % terms

Borrowing Limit CEb CEs CE

D = 0.1 2.7862 −0.4460 0.3524D = 0.5 2.8979 −0.4635 0.3664D = 1 3.0162 −0.4858 0.3784

10Notice that the MFFS and the DFFS are characterized by the same steady state andtherefore the two stimulus are comparable in terms of consumption equivalent units.

21

Notice that, in all the three cases considered, borrowers get welfare gains, interms of consumption equivalent measures, when the fiscal stimulus is accompa-nied by money injection. On the contrary, savers incurs in welfare losses. Thismeans that borrowers are better off under our benchmark MFFS than under aDFFS, while savers are worse off. Borrowers consumption equivalent is around2.9%, whereas that of savers is negative and close to -0.46% in the benchmarkmodel with D = 0.5. Consumption equivalent units derived from the socialwelfare are positive, implying welfare gains from the MFFS of about 0.37% interms of consumption equivalent measure. Remarkably, notice that when theborrowing limit passes from D = 0.1 to the baseline calibration of D = 0.5 andto D = 1, meaning that borrowers are less financially constrained, both thewelfare gains for borrowers and the welfare losses for savers increase and alsoaggregate welfare gets higher11 .

Our results on welfare can be summarized as follows.

Result 3: In terms of consumption equivalent welfare, borrowers are betteroff while savers are worse off under a MFFS than under a DFFS. The aggregatewelfare is higher under the benchmark MFFS than under the DFFS.

To better understand the role played by the redistribution channel, we nowcompare the consumption equivalent welfare implied by our baseline TANKmodel with those implied by a RANK model characterized by the same stimula.Table 3 reports the results obtained using our benchmark MFFS (first column)and those of a MFFS accompanied by a fiscal authority that, as in Galì (2017),fully stabilizes real debt, that where bHt = 0 (second column). In both casesthe value of the borrowing limit is set to 0.5 as in our baseline calibration. Re-markably, notice that our benchmark MFFS is preferable in terms of aggregatewelfare only in the TANK model. In the RANK model a MFFS is welfare detri-mental, unless the monetary contemporary stabilize the real debt by increasingthe real interest rate from the second period on.

Table 3: Consumption Equivalent Measure in % terms

Benchmark MFFS, D = 0.5 MFFS with bHt = 0, D = 0.5

CETANK 0.3664 0.0463CEb 2.8979 0.1994CEs −0.4635 −0.0047CERANK −14.1443 0.8198

The intuition behind this result is the following. Under the benchmark model,public debt decreases in real terms when the stimulus is money financed throughthe benchmark MFFS. This is due to the inflationary effect of the policy thatreduces the real value of debt. As a consequence, savers which are the owners

11The values of D equal to 0.1, 0.5 and 1 correspond respectively to SS borrowing to bor-rower’s labor income ratios, D

wNb, equal to 0, 1, 0.5 and 1.

22

of public assets are worse off. Also, the real value of private debt reduces asinflation increases, so that borrowers are better off. This brings about a positivewealth effect on borrowers and a negative one on savers, which reflects into alarger increase in borrowers consumption relatively to that of savers. Despitethis, savers consumption increases under a MFFS while it decreases under aDFFS. The positive reaction of savers consumption is due to the decrease ofthe real interest rate brought about by monetary injection and the increasedaggregate demand. In the RANK model all agents are savers and thus thecrowding-in effect on consumption is still present though lower than in a TANKmodel, where aggregate consumption mostly increase because of the presence ofborrowers. Further, the RANK model is also characterized by a negative effecton welfare triggered by the labor supply. Savers labor supply decreases in theDFFS by a larger amount than under a MFFS. The overall effect implies a higherincrease in welfare under a DFFS than under a MFFS and the consumptionequivalent welfare is then negative.In the TANK model the positive effects on borrowers welfare dominate the

negative ones on savers and the benchmark MFFS is preferable in terms of ag-gregate welfare than the DFFS. If instead the monetary authority fully stabilizesthe public debt savers are better off under a MFFS than under a DFFS, both inthe RANK and in the TANK model. In this case, in fact, the negative wealtheffect of the debt are absent.To sum up, we can state the following.

Result 4: The benchmark MFFS is preferable in terms of aggregate welfareonly in the benchmark TANK model. When the MFFS is accompanied by amonetary authority which fully stabilizes the debt a MFFS implies an higherwelfare than a DFFS both in the RANK and in the TANK model.

5 Model Dynamics in a ZLB scenario

In this section, as in Galì (2017), we analyze the effectiveness of the fiscal stim-ulus in stabilizing the economy in the face of an adverse demand shock, underboth a money-financed and a debt-financed regime. The shock is large enoughto push the nominal interest rate on the ZLB. The ZLB constraint can be in-corporated formally in the set of the log-linearized equilibrium conditions aboveby replacing savers’money demand with(

it − log (βs))(

ms,t − Cs,t + ηit

)= 0 (48)

for all t, where

it ≥ log (β) (49)

is the nominal interest rate bounded to zero and

ms,t ≥ Cs,t + ηit

23

represents savers’demand for real balances.In addition, in the case of debt financing, condition (36) must be replaced

with: (it − log (βs)

) (it − φπ

(log(

πtπ

)))

= 0 (50)

for all t, which guarantees that the Taylor rule is met as long as the ZLBconstraint is not binding.Next we analyze several scenarios, each defined by a specific combination of

monetary and fiscal policy responses to the demand shock. In particular, as inGalì (2017), we assume that the demand shock ρt = −γ for t = 0, 1, 2, ...T andρt = 0 for t = T + 1, T + 2, ... This can be interpreted as a temporary adversedemand shock that causes the drop of the natural interest rate up to period T ,vanishing thereafter. In particular, we assume γ = 0.06 and T = 5. We assumethat the shock is unanticipated, however once it is realized, the trajectory ofthe shock and corresponding policy responses are known with certainty.We start by considering the benchmark case of no fiscal response to the

shock (gt = 0, for t = 0, 1, 2, ...) with the central bank implementing the Taylorrule subject to the ZLB constraint. As discussed in Galì (2015, chapter 5) andGalì(2017), that policy lowers the nominal rate to zero for the duration of theshock (i.e. up to T ), and then it reverts back to a simple stabilizing rule12 .Formally,

it = max[log (βs) , ρt + φπ

(log(

πtπ

))]

where φπ > 1.

- Figures 6 about here -

Figure 6 shows the responses of the economy to the adverse demand shock.Under all regimes, public expenditure increases by 1 percent and the fiscal stim-ulus lasts for the duration of the adverse demand shock.Figure 6 shows that the benchmark MFFS is the most effective only in

normal times. In a ZLB scenario instead the benchmark MFFS redistributesfrom borrowers to savers and implies a strong recession, though less persistentthan under the DFFS. On the contrary, the alternative MFFS becomes themost effective financing regime in a ZLB scenario. It redistributes from saversto borrowers and, by sustaining higher level of inflation, is able to avoid theeconomy to enter into a recession. The intuition for this last result is rathersimple. An adverse demand shock pushes the economy into a ZLB scenario.As a consequence of the negative demand shock, as shown in Figure 6, thereal GDP falls down bringing about an increase of the real value of public

12See, e.g. Eggertsson and Woodford (2003). Following Galì (2017), our goal is to charac-terize the effect of different fiscal interventions. The case of discretionary monetary policy inthe absence of fiscal response is just a useful benchmark with respect to which we measurethe effectiveness of different fiscal interventions.

24

debt, not only under a DFFS, but also under the benchmark MFFS. Thus,savers who are the owners of the public debt are better off, while borrowersare worse off. Though the real interest rate falls down under the benchmarkMFFS, it is not suffi cient to bring about a consumption crowding-in. Bothconsumption of borrowers and savers decreases on impact and the policy resultsless effective than in normal times. On the contrary, the alternative MFFS ismuch more effective in ZLB than in normal times. In fact, under this alternativeregime the seigniorage is adjusted to keep unchanged the real value of publicdebt, by generating higher inflation than in the benchmark MFFS. The strongerinflationary effect of the alternative MFFS pushes the real interest rate downmore than under the benchmark one and the policy redistributes from saversto borrowers, so that borrowers consumption increases and so does aggregateconsumption (as shown in Figure 7). As a result, the policy pushes up theaggregate demand and results so effective to avoid the economy to enter into arecession.Finally, Figure 8 shows the responses of output and consumption under the

three financing schemes compared to those of a RANK model. It is ratherimportant to notice that the strong effectiveness of the alternative MFFS doesnot hold in a RANK model, where the redistributive channel is absent. Again,this suggests that the redistributive channel is very important and that it cannotbe neglected by policy makers.To sum up, we can state the following.

Result 5: The alternative MFFS is the most effective regime in a ZLBscenario. In a TANK model this regime is so effective to avoid the recessionaryeffects implied by the ZLB. Remarkably, this result does not hold in a RANKmodel, where the redistributive channel is absent.

6 Conclusion

By considering a Two-Agents New-Keynesian model in a Borrower-Saver frame-work, this paper argues that redistribution is a key channel through which thefiscal financing regimes affect the macroeconomic aggregates. In particular, itanalyzes the redistributive channel of a MFFS compared to that of a DFFS.The idea that a future inflation tax can reduce the ability of money to stimulatethe aggregate demand has been central in the economic debate that followedthe recent crisis. However, in a borrowers-savers model, the inflation tax canbe used to redistribute from one household to the other one further amplifyingor reducing the effect of the stimulus. For this reason, in this paper we con-sider two types of MFFS: if the seigniorage is adjusted in each period to keepunchanged the real value of public debt and to avoid a prolonged inflationaryeffect of the policy (Galì, 2017) or not.We show that the effectiveness of a MFFS is state dependent - due to the

redistribution channel. In normal times, the most effective regime is a MFFSwith no additional intervention by the Central Bank to stabilize real public debt

25

using inflation, whereas in a ZLB scenario, a MFFS accompanied by real debtstabilization - through the adjustment of seigniorage - is the most effective one.The contribution of the paper can be summarized in five main results.First, in normal times, all the regimes imply a redistributive effect from

savers to borrowers. However, thanks to the accommodative monetary policy,borrowers gains are much larger under our a MFFS without public debt sta-bilization. The consumption ratio between borrowers and savers is indeed fivetimes higher under the MFFS without real public debt stabilization than undera DFFS, so that the first one is followed by a stronger expansionary effect on out-put than the latter one. As a consequence, the redistribution channel stronglyamplifies the impact of the fiscal intervention with respect to a RANK model,increasing the effectiveness of the MFFS. Public debt stabilization instead onlymildly amplifies the effect of a MFFS with respect to a DFFS. In this case, thetransmission mechanism is indeed less effective since the redistributive channelof public bonds and that of inflation are muted to stabilize the real value of thedebt.Second, we compute consumption and output fiscal multipliers associated

to the three different financing regimes and we find that, under our benchmarkMFFS fiscal multipliers are largely higher than one. Interestingly, these multi-pliers increase exponentially as the share of borrowers increases. Also, we findthat fiscal multipliers are an increasing function of the borrowing limit.Third, our benchmark MFFS is preferable in a TANK model since the ex-

pansionary effects of government spending are larger, thanks to very high fiscalmultipliers. Fourth, in a RANK model it is instead welfare detrimental withrespect to a DFFS.Fifth, while in normal times, the most effective regime is the benchmark

MFFS, in a ZLB scenario the most effective one is a MFFS accompanied by thestabilization of real public debt - through the adjustment of seigniorage. In aTANK model this regime is so effective to avoid the recessionary effects impliedby the ZLB. Remarkably, this result does not hold in a RANK model, wherethe redistributive channel is absent.Finally, we show that contrary to the common wisdom a MFFS is followed

by a moderate increase of inflation which is only temporarily higher than thetarget. This suggests that the redistribution channel cannot be neglected bypolicy makers.

References

[1] Adam, K. and Zhu, J. (2016). Price-Level Changes And The Redistribu-tion Of Nominal Wealth Across The Euro Area, Journal of the EuropeanEconomic Association, European Economic Association, vol. 14(4), pages871-906, August.

26

[2] Annicchiarico, B, Giammarioli, N. and Piergallini, A. (2012). BudgetaryPolicies in a DSGE Model with Finite Horizons, Research in Economics,66(2).

[3] Auclert, A. (2017). Monetary Policy and the Redistribution Channel,NBER Working Papers 23451, National Bureau of Economic Research, Inc.

[4] Bilbiie, F.O., Monacelli, T. and Perotti, R. (2013). Public Debt and Re-distribution with Borrowing Constraints, The Economic Journal, vol. 123,pp. F64-F98.

[5] Bilbiie Florin O., Monacelli Tommaso and Perotti Roberto, (2014). Is Gov-ernment Spending at the Zero Lower Bound Desirable?, NBER WorkingPapers 20687, National Bureau of Economic Research.

[6] Christiano, L., Eichenbaum, M. and Rebelo, S. (2011): When is the Gov-ernment Spending Multiplier Large? Journal of Political Economy, 119(1),78-121.

[7] Coibion, O., Gorodnichenko, Y., Kueng, L. and Silvia, J., (2017). Inno-cent Bystanders? Monetary policy and inequality, Journal of MonetaryEconomics, Elsevier, vol. 88(C), pages 70-89.

[8] Debortoli, D. and Galì, J. (2017). Monetary Policy with HeterogeneousAgents: Insights from TANK models, mimeo.

[9] Del Negro Marco, Giannoni Marc, Christina Patterson, 2016. The ForwardGuidance Puzzle, 2016 Meeting Papers 143, Society for Economic Dynam-ics.

[10] Di Bartolomeo, G. and Rossi, L. (2007). Effectiveness of monetary pol-icy and limited asset market participation: Neoclassical versus keynesianeffects, International Journal of Economic Theory, vol. 3, pp. 213-218.

[11] Doepke, M. and Schneider, M. (2006). Aggregate Implications of WealthRedistribution: The Case of Inflation, Journal of the European EconomicAssociation, MIT Press, vol. 4(2-3), pages 493-502, 04-05.

[12] English W. B., Erceg C. J. and Lopez-Salido D. (2017). Money-FinancedFiscal Programs: A Cautionary Tale. FEDS Working Paper No. 2017-060.

[13] Eggertsson, G. and Woodford, M. (2003): Zero bound on interest rates andoptimal monetary policy. Brookings papers on economic activity 2003(1),139-233

[14] Eggertsson, Gauti (2011): What Fiscal Policy is Effective at Zero InterestRates? NBER Macroeconomics Annual 2010, 59-112.

[15] Farhi Emmanuel, Werning Iván, Monetary Policy, Bounded Rationality,and Incomplete Markets, (2017), NBER Working Paper No. 23281

27

[16] Galì, J. (2017). The Effects of a Money-Financed Fiscal Stimulus, mimeo.

[17] Galì, J., Lòpez-Salido, J. D. and Vallés, J. (2007). Understanding the ef-fects of government spending on consumption, Journal of the EuropeanEconomic Association,. vol. 5(1), pp. 227-270.

[18] Giavazzi, F. and Tabellini, G. (2014). How to Jumpstart the EurozoneEconomy, www.voxeu.org.

[19] Guerrieri, Veronica and Guido Lorenzoni (2017): Credit Crises, Precau-tionary Savings, and the Liquidity Trap, Quarterly Journal of Economics132(3), 1427-1467.

[20] Kaplan, Greg, Benjamin Moll, and Giovanni L.Violante (2017): MonetaryPolicy according to HANK, American Economic Review, vol. 18(3), March2108, 697-743.

[21] Kirsanova, T., Leith C. and Wren-Lewis, S. (2009). Monetary and fiscalpolicy interaction: the current consensus assignment in the light of recentdevelopments, Economic Journal, vol. 119(541), pp. 482-496.

[22] Mendicino, C. and Pescatori, A. (2005). Credit Frictions, Housing Pricesand Optimal Monetary Policy Rules, Money Macro and Finance (MMF)Research Group Conference 2005 67, Money Macro and Finance ResearchGroup.

[23] Notarpietro, A. and Siviero, S. (2015). Optimal Monetary Policy Rules andHouse Prices: The Role of Financial Frictions, Journal of Money, Creditand Banking, vol. 47(S1), pages 383-410, March.

[24] Oh, Hyunseung and Ricardo Reis (2012): Targeted Transfers and the FiscalResponse to the Great Recession, Journal of Monetary Economics 59, S50-S64.

[25] Pataracchia, B., Raciborski, R., Ratto, M., Roeger, W. (2013). Endoge-nous housing risk in an estimated DSGE model of the Euro Area, Euro-pean Economy - Economic Papers 2008 - 2015 505, Directorate GeneralEconomic and Financial Affairs (DG ECFIN), European Commission.

[26] Rubio, M. and Carrasco-Gallego,J. A. (2015). Macroprudential and Mon-etary Policy Rules: a Welfare Analysis, Manchester School, University ofManchester, vol. 83(2), pages 127-152, March.

[27] Rubio, M. and Carrasco-Gallego, J. A. (2014). "Macroprudential and mon-etary policies: Implications for financial stability and welfare," Journal ofBanking & Finance, vol. 49(C), pages 326-336.

[28] Sterk, V. and Tenreyro, S. (2016). The Transmission of Monetary Pol-icy through Redistributions and Durable Purchases, Working Papers 1601,Council on Economic Policies.

28

[29] Turner, A. (2013). Debt, Money and Mephistopheles: How do we Get Outof this Mess? lecture delivered at the Cass Business School.

[30] Uhlig, H. (2010). Some Fiscal Calculus, American Economic Review, Amer-ican Economic Association, vol. 100(2), pages 30-34, May.

[31] Woodford, M. (2011). Simple analytics of the government expenditure mul-tiplier, American Economic Journal: Macroeconomics, vol. 3(1), pp. 1-35.

29

A The money demand for borrowers

We now show that borrowers’optimal money demand is always zero. Supposethat Mb,t > 0, in this case borrowers will consume less today, - implying a lossin utility of consumption and a gain in terms of utility of money balances today.Money saved today will be consumed tomorrow. In other words, borrowers willchoose Mb,t > 0 if and only if:

−UCbt + Umbt + βbUCbt+1 = 0 (51)

which can be rewritten as

Umbt

∣∣∣mbt>0

= UCbt − βUCbt+1 (52)

This means that borrowers will optimally choose M bt = 0, every time

Umbt

∣∣∣mbt=0

< UCbt − βUCbt+1 (53)

Further, since the borrower is constrained in terms of bond, we know from theEuler equation that

UCbt = (1 + it)βbUCbt+1 + φt, (54)

and thus that

βbUCbt+1 =UCbt

1 + it− φt

1 + it(55)

which can be substituted into (53) implying that

Umbt

∣∣∣mbt=0

< UCbtit

1 + it+

φt1 + it

(56)

Now, remember that if M bt = 0, the constraint on money demand is binding

and then

UmbtUCb

=

(it

1 + it

)− φM

b

t (57)

or

Umbt =

(it

1 + it

)UCb − φM

b

t UCb (58)

equation (58) can be substituted into (56) so that

Umbt

∣∣∣mbt=0

=

(it

1 + it

)UCbt − φ

Mb

t UCbt < UCbtit

1 + it+

φt1 + it

(59)

simplifying

−φMb

t UCbt <φt

1 + it(60)

30

Notice that since the borrowing constraint is always binding φt > 0 for each

t, since with M bt = 0, φM

b

t > 0 this equation is always satisfied, implying thatborrowers do not save either in terms of bonds nor in terms of money.Similarly we now show that savers will always choose a demand for money

with Mst > 0 and thus implying that φM

s

t = 0. Since φt = 0 for savers, equation(59) for savers will be:

Umst∣∣mst>0

=

(it

1 + it

)UCst = UCbt

it1 + it

(61)

which is always satisfied.

B Robustness

B.1 Alternative Labor Market Structures

B.1.1 Households

There is a continuum of households indexed by i ∈ [0, 1]. Households in theinterval [0, λ] consume their available labor income and borrow in each period.Households in the interval (λ, 1] hold assets and smooth consumption. Theperiod utility function is common across households and it has the followingseparable form:

Ut = ln (Cι,t)− χ

(x− mι,t

Cι,t

)1+σ

1 + σ− N1+ϕ

t

1 + ϕ. (62)

We assume a continuum of differentiated labor inputs indexed by j ∈ [0, 1]. Asin Schmitt-Grohe and Uribe (2006), agent i supplies each possible type of laborinput. Wage-setting decisions are made by labor type specific unions indexedby j ∈ [0, 1]. Given the wage W j

t fixed by union j, agents stand ready tosupply as many hours to the labor market j, N j

t , as required by firms, that

is: N jt =

(W jt

Wt

)−θwNdt , where θw is the elasticity of substitution between labor

inputs. Here Ndt is aggregate labor demand and Wt is an index of the wages

prevailing in the economy at time t. Formal definitions of labor demand andof the wage index can be found in the section devoted to firms. Agents aredistributed uniformly across unions; hence aggregate demand for labor type j isspread uniformly across the households.13 It follows that the individual quantityof hours worked, Nt (i), is common across households, and we denote it as Nt.This must satisfy the time resource constraint Nt =

∫ 1

0N jt dj. Combining the

latter with labor demand we obtain Nt = Ndt

∫ 1

0

(W jt

Wt

)−θwdj. The labor market

structure rules out differences in labor income between households without the13Thus a share λ of the members of each union are borrowers, while the remaining portion

is composed of Ricardian agents.

31

need to resort to contingent markets for hours. The common labor income is

given by Ldt∫ 1

0W jt

(W jt

Wt

)−θwdj. Notice that each union pools the labor income

of agents, leading borrowers and savers to work for the same amount of time.

Savers Savers face the following flow budget constraint in nominal terms :

PtCs,t +BHs,t + PtAs,t +Ms,t + Ωs,tPtVt ≤ (1 + it−1)BHs,t−1 + (1 + it−1)PtAs,t

Ms,t−1 + Ωs,t−1Pt (Vt−1 + Γt) (63)

+Ndt

∫ 1

0

N jt

(W jt

Wt

)−θw− Ts,t.

A saver has labor income Ndt

∫ 1

0W jt

(W jt

Wt

)−θwdj. As,t−1 is the real value

at beginning of period t of total private assets held in period t, a portfolio ofone-period bonds issued in t − 1 on which the household receives the nominalinterest it−1. Vt−1 is the real market value at time t of shares in intermediategood firms, Γt are real dividend payoffs of these shares, Ωs,t are share holdings,Ts,t is the lump-sum tax, BHs,t are the savers’holdings of nominally riskless one-period government bonds (paying an interest it). The nominal debt BHt paysone unit in nominal terms in period t+ 1.

After defining the aggregate price level as Pt =[∫ 1

0Pt (z)

1−εdz] 11−ε

, as

well as real debt as, bHt ≡ Bt/Pt,optimality is characterized by the followingfirst-order conditions for savers:

βsEt

Cs,t (1 + it)

Cs,t+1πt+1

= 1, (64)

βsEt

Cs,tCs,t+1

Vt+1 + Γt+1

Vt

= 1, (65)

χ

(x− ms,t

Cs,t

)σ=

(it

1 + it

). (66)

Borrowers Borrowers (indicated with the subscript b) face a borrowing con-straint at all times. They face the following budget constraint:

PtCb,t+PtAb,t+Mb,t = (1 + it−1)PtAb,t−1−Mb,t−1+Ndt

∫ 1

0

W jt

(W jt

Wt

)−θwdj−Tb,t,

(67)and, the borrowing constraint (on borrowing in real terms) at all times t :

−Ab,t ≤ D

32

the usual Cb,t ≥ 0 and

Mb,t ≥ 0.

Agents belonging to this group consume disposable income and borrow ineach period and delegate wage decisions to unions. For these reasons there is nofirst order condition with respect to labor supply but optimality is characterizedby the first-order conditions:

C−1b,t = βbEt

(1 + itπt+1

C−1b,t+1

)+ φt

and,

Mb,t = 0.

B.1.2 Wage Setting

As in Galì and Lopez-Salido (2007) the nominal wage newly reset at t, Wt, ischosen to maximize a weighted average of agents’lifetime utilities. The weightsattached to the utilities of savers and borrowers are (1− λ) and λ, respectively.The union problem is

maxWt

[(1− λ) ln (Cs,t) + λ ln (Cb,t)]−

(1− λ)χ

(x− ms,t

Cs,t

)1+σ

1 + σ+ λχ

(x− mb,t

Cb,t

)1+σ

1 + σ

− [N1+ϕt

1 + ϕ

]subject to Nt =

∫ 1

0N jt dj, (63) and (67). The FOC with respect to Wt is[

λ1

MRSb,t+ (1− λ)

1

MRSb,t

]Wt

Pt− µw = 0

orWt

Pt= µw

[λ

1

CbtLϕt

+ (1− λ)1

CstLϕt

]−1

(68)

substituting for MRSb,t = CbtNϕt and MRSs,t = CstN

ϕt

B.1.3 Aggregation and Market Clearing

The equilibrium allocation Yt = Ct + Gt + θ2 (πt − 1)2 is based on additional

markets clearing conditions,

Ct = λCb,t + (1− λ)Cs,t; (69)

Mt = λMb,t + (1− λ)Ms,t; (70)

respectively, aggregate consumption and money market clearing condition.

33

The clearing of labor markets requires:

N jt =

(W jt

Wt

)−θwNdt ∀j Nt =

∫ 1

0N jt dj (71)

where Y dt = Ct represents aggregate demand, Njt =

∫ 1

0N jt (z) dz is total aggre-

gate demand of labor input j and Ndt =

∫ 1

0Nt (z) dz denotes firms’aggregate

demand of the composite labor input Nt.Figures 9-13 compare the impulse response functions (IRFs) implied by our

TANK model in presence of wage-setting by unions under a MFFS with thoseobtained under a DFFS accompanied by a monetary policy described by thesimple interest rate Taylor rule. As shown, there are no qualitative differenceswith respect to the benchmark model neither at aggregate level nor at disaggre-gate level. However, the presence of unions amplifies the redistribution channelfrom savers to borrowers, leading to a larger expansion under both regimes.This is due to the fact that the income effect on borrowers cannot be absorbedby decreasing their labor supply, but only by their consumption boom. And, itexplains also why, under both regimes, the expansionary effect of a fiscal stim-ulus in a TANK model is larger than in a RANK one, as Figures 11 shows.Finally Figures 12 ad 13 show the implied fiscal multipliers. Again, the resultsof the baseline model are reinforced in a unionized labor market economy.

Figures

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1government spending

0 2 4 6 8 10­15

­10

­5

0

5debt

0 2 4 6 8 100

1

2

3inflation

0 2 4 6 8 10­1.5

­1

­0.5

0real interest rate

0 2 4 6 8 100

2

4

6consumption

0 2 4 6 8 100

2

4

6output

M­financed M­financed(b h=0) Debt­financed

Figure 1: The effects of a Fiscal Stimulus

34

0 5 100

2

4

6consumption

0 5 100

5

10

15borr.consumption

0 5 10­1

0

1

2

3

4saver consumption

0 5 100

2

4

6

8

10c­ratio

0 5 100

2

4

6hours

0 5 10­3

­2

­1

0borr.labor supply

0 5 100

2

4

6

8

10saver labor supply

0 5 10­15

­10

­5

0labor ratio

M­financed M­financed(b h=0) Debt­financed

Figure 2: The redistributive effects of a Fiscal Stimulus

0 2 4 6 8 100

2

4

6Output ­ M­financed

0 2 4 6 8 100

0.5

1

1.5

2Output ­ M­financed(bh=0)

RANK TANK

0 2 4 6 8 100

0.5

1

1.5Output ­ Debt­financed

RANK TANK0 2 4 6 8 10

0

2

4

6Consumption ­ M­financed

RANK TANK0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1Consumption ­ M­financed(bh=0)

0 2 4 6 8 10­0.1

0

0.1

0.2

0.3

0.4Consumption ­ Debt­financed

Figure 3: RANK vs TANK in Normal times

35

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

5

10

15

20

25

Istanteneous Fiscal Multiplier of Consumption IFMC

M­financed M­financed (b h=0) Debt­financed =1

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

5

10

15Cumulative Fiscal Multiplier of Consumption CFMC

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

5

10

15

20

Impact Fiscal Multiplier of Output IFMY

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

2

4

6

8

10

12

Cumulative Fiscal Multiplier of Output CFMY

Figure 4. Fiscal Multipliers of Output and Consumption.

0.1 0.2 0.3 0.4

8

10

12

14

16CFM Consumption ­ M­financed

D=0.1 D=0.5 D=1

0.1 0.2 0.3 0.4

8

10

12

CFM Output ­ M­financed

0.1 0.2 0.3 0.4

1

1.5

2

2.5

3

CFM Consumption ­ M­financed(bh=0)

0.1 0.2 0.3 0.41.5

2

2.5

3

3.5

CFM Output ­ M­financed(bh=0)

D=0.1 D=0.5 D=1

0.1 0.2 0.3 0.4

2

4

6

8

10CFM Consumption ­ Debt­financed

0.1 0.2 0.3 0.4

2

4

6

8

CFM Output ­ Debt­financed

D=0.1 D=0.5 D=1

Figure 5. Cumulative Fiscal Multipliers: changing the borrowing limit

36

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1govt purchases

0 2 4 6 8 10­20

0

20

40

60

80debt

0 2 4 6 8 10­10

­5

0

5

10inflation

0 2 4 6 8 10­5

0

5

10real rate

0 2 4 6 8 10­30

­20

­10

0

10consumption

0 2 4 6 8 10­10

0

10

20output

M­financed M­financed (b h=0) Debt­financed

Figure 6: Dynamic Effects of an increase of government expenditurein a liquidity trap

0 5 10­30

­20

­10

0

10consumption

0 5 10­40

­20

0

20borr.consumption

0 5 10­30

­20

­10

0

10saver consumption

0 5 10­20

­10

0

10

20

30c­ratio

0 5 10­10

0

10

20hours

M­financed M­financed(b h=0) Debt­financed

0 5 10­5

0

5

10

15

20borr.labor supply

0 5 10­20

­10

0

10

20

30saver labor supply

0 5 10­40

­20

0

20

40l­ratio

Figure 7: Redistributive Effects of an increase of governmentexpenditure in a liquidity trap

37

0 2 4 6 8 10­10

­5

0

5

Output ­ M­financed

RANK TANK

0 2 4 6 8 10­10

0

10

20Output ­ M­financed(bh=0)

RANK TANK

0 2 4 6 8 10­10

­5

0

5Output ­ Debt­financed

0 2 4 6 8 10­10

­5

0

5Consumption ­ M­financed

0 2 4 6 8 10­15

­10

­5

0

5Consumption ­ M­financed(bh=0)

0 2 4 6 8 10­30

­20

­10

0Consumption ­ Debt­financed

RANK TANK

Figure 8: RANK vs TANK in a ZLB scenario

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1government spending

0 2 4 6 8 10­15

­10

­5

0

5

10debt

0 2 4 6 8 100

2

4

6inflation

0 2 4 6 8 10­1

­0.8

­0.6

­0.4

­0.2

0

real interest rate

0 2 4 6 8 10­5

0

5

10

15

20consumption

0 2 4 6 8 100

5

10

15

20output

M­financed M­financed(b h=0) Debt­financed

Figure 9: The effects of a Fiscal Stimulus (in presence of unions)

38

0 2 4 6 8 10 12­5

0

5

10

15

20consumption

0 2 4 6 8 10 120

20

40

60

80

100borr.consumption

0 2 4 6 8 10 12­0.5

0

0.5

1saver consumption

0 2 4 6 8 10 120

20

40

60

80c­ratio

M­financed M­financed(b h=0) Debt­financed

Figure 10: The redistributive effects of a Fiscal Stimulus (in presenceof unions)

0 2 4 6 8 100

5

10

15

20Output ­ M­financed

RANK TANK

0 2 4 6 8 100

1

2

3

4

Output ­ M­financed(bh=0)

RANK TANK

0 2 4 6 8 100

2

4

6Output ­ Debt­financed

0 2 4 6 8 100

5

10

15

20Consumption ­ M­financed

0 2 4 6 8 10

0

1

2

3

4

Consumption ­ M­financed(bh=0)

0 2 4 6 8 100

2

4

6Consumption ­ Debt­financed

RANK TANK

Figure 11: RANK vs TANK (in presence of unions)

39

0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26

5

10

15

20

Istanteneous Fiscal Multiplier of Consumption IFMC

M­financed M­financed (b h=0) Debt­financed =1

0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26

2

4

6

8

10

12Cumulative Fiscal Multiplier of Consumption CFMC

0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26

5

10

15

20Impact Fiscal Multiplier of Output IFMY

0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26

2

4

6

8

10

Cumulative Fiscal Multiplier of Output CFMY

Figure 12: Fiscal Multipliers of Output and Consumption (inpresence of unions)

0.12 0.14 0.16 0.18 0.2 0.22

7

8

9

10

CFM Consumption ­ M­financed

D=0.1 D=0.5 D=1

0.12 0.14 0.16 0.18 0.2 0.22

7

8

9

CFM Output ­ M­financed

0.12 0.14 0.16 0.18 0.2 0.22

1

1.5

2CFM Consumption ­ M­financed(bh=0)

D=0.1 D=0.5 D=10.12 0.14 0.16 0.18 0.2 0.22

1.6

1.8

2

2.2

2.4

2.6CFM Output ­ M­financed(bh=0)

0.12 0.14 0.16 0.18 0.2 0.22

1

2

3

CFM Consumption ­ Debt­financed

0.12 0.14 0.16 0.18 0.2 0.22

1.5

2

2.5

3

3.5

CFM Output ­ Debt­financed

D=0.1 D=0.5 D=1

Figure 13: Cumulative Fiscal Multipliers: changing the borrowinglimit (in presence of unions)

40

Working Paper del Dipartimento di Economia e Finanza

1. L. Colombo, H. Dawid, Strategic Location Choice under Dynamic Oligopolistic

Competition and Spillovers, novembre 2013.

2. M. Bordignon, M. Gamalerio, G. Turati, Decentralization, Vertical Fiscal Imbalance, and

Political Selection, novembre 2013.

3. M. Guerini, Is the Friedman Rule Stabilizing? Some Unpleasant Results in a Heterogeneous

Expectations Framework, novembre 2013.

4. E. Brenna, C. Di Novi, Is caring for elderly parents detrimental to women’s mental health?

The influence of the European North-South gradient, novembre 2013.

5. F. Sobbrio, Citizen-Editors' Endogenous Information Acquisition and News Accuracy,

novembre 2013.

6. P. Bingley, L. Cappellari, Correlation of Brothers Earnings and Intergenerational

Transmission, novembre 2013.

7. T. Assenza, W. A. Brock, C. H. Hommes, Animal Spirits, Heterogeneous Expectations and

the Emergence of Booms and Busts, dicembre 2013.

8. D. Parisi, Is There Room for ‘Fear’ as a Human Passion in the Work by Adam Smith?,

gennaio 2014.

9. E. Brenna, F. Spandonaro, Does federalism induce patients’ mobility across regions?

Evidence from the Italian experience, febbraio 2014.

10. A. Monticini, F. Ravazzolo, Forecasting the intraday market price of money, febbraio 2014.

11. Tiziana Assenza, Jakob Grazzini, Cars Hommes, Domenico Massaro, PQ Strategies in

Monopolistic Competition: Some Insights from the Lab, marzo 2014.

12. R. Davidson, A. Monticini, Heteroskedasticity-and-Autocorrelation-Consistent

Bootstrapping, marzo 2014.

13. C. Lucifora, S. Moriconi, Policy Myopia and Labour Market Institutions, giugno 2014.

14. N. Pecora, A. Spelta, Shareholding Network in the Euro Area Banking Market, giugno 2014.

15. G. Mazzolini, The economic consequences of accidents at work, giugno 2014.

16. M. Ambrosanio, P. Balduzzi, M. Bordignon, Economic crisis and fiscal federalism in Italy,

settembre 2014.

17. P. Bingley, L. Cappellari, K. Tatsiramos, Family, Community and Long-Term Earnings

Inequality, ottobre 2014.

18. S. Frazzoni, M. L. Mancusi, Z. Rotondi, M. Sobrero, A. Vezzulli, Innovation and export in

SMEs: the role of relationship banking, novembre 2014.

19. H. Gnutzmann, Price Discrimination in Asymmetric Industries: Implications for

Competition and Welfare, novembre 2014.

20. A. Baglioni, A. Boitani, M. Bordignon, Labor mobility and fiscal policy in a currency union,

novembre 2014.

21. C. Nielsen, Rational Overconfidence and Social Security, dicembre 2014.

22. M. Kurz, M. Motolese, G. Piccillo, H. Wu, Monetary Policy with Diverse Private

Expectations, febbraio 2015.

23. S. Piccolo, P. Tedeschi, G. Ursino, How Limiting Deceptive Practices Harms Consumers,

maggio 2015.

24. A.K.S. Chand, S. Currarini, G. Ursino, Cheap Talk with Correlated Signals, maggio 2015.

25. S. Piccolo, P. Tedeschi, G. Ursino, Deceptive Advertising with Rational Buyers, giugno

2015.

26. S. Piccolo, E. Tarantino, G. Ursino, The Value of Transparency in Multidivisional Firms,

giugno 2015.

27. G. Ursino, Supply Chain Control: a Theory of Vertical Integration, giugno 2015.

28. I. Aldasoro, D. Delli Gatti, E. Faia, Bank Networks: Contagion, Systemic Risk and

Prudential Policy, luglio 2015.

29. S. Moriconi, G. Peri, Country-Specific Preferences and Employment Rates in Europe,

settembre 2015.

30. R. Crinò, L. Ogliari, Financial Frictions, Product Quality, and International Trade,

settembre 2015.

31. J. Grazzini, A. Spelta, An empirical analysis of the global input-output network and its

evolution, ottobre 2015.

32. L. Cappellari, A. Di Paolo, Bilingual Schooling and Earnings: Evidence from a Language-

in-Education Reform, novembre 2015.

33. A. Litina, S. Moriconi, S. Zanaj, The Cultural Transmission of Environmental Preferences:

Evidence from International Migration, novembre 2015.

34. S. Moriconi, P. M. Picard, S. Zanaj, Commodity Taxation and Regulatory Competition,

novembre 2015.

35. M. Bordignon, V. Grembi, S. Piazza, Who do you blame in local finance? An analysis of

municipal financing in Italy, dicembre 2015.

36. A. Spelta, A unified view of systemic risk: detecting SIFIs and forecasting the financial cycle

via EWSs, gennaio 2016.

37. N. Pecora, A. Spelta, Discovering SIFIs in interbank communities, febbraio 2016.

38. M. Botta, L. Colombo, Macroeconomic and Institutional Determinants of Capital Structure

Decisions, aprile 2016.

39. A. Gamba, G. Immordino, S. Piccolo, Organized Crime and the Bright Side of Subversion of

Law, maggio 2016.

40. L. Corno, N. Hildebrandt, A. Voena, Weather Shocks, Age of Marriage and the Direction of

Marriage Payments, maggio 2016.

41. A. Spelta, Stock prices prediction via tensor decomposition and links forecast, maggio 2016.

42. T. Assenza, D. Delli Gatti, J. Grazzini, G. Ricchiuti, Heterogeneous Firms and International

Trade: The role of productivity and financial fragility, giugno 2016.

43. S. Moriconi, Taxation, industry integration and production efficiency, giugno 2016.

44. L. Fiorito, C. Orsi, Survival Value and a Robust, Practical, Joyless Individualism: Thomas

Nixon Carver, Social Justice, and Eugenics, luglio 2016.

45. E. Cottini, P. Ghinetti, Employment insecurity and employees’ health in Denmark, settembre

2016.

46. G. Cecere, N. Corrocher, M. L. Mancusi, Financial constraints and public funding for eco-

innovation: Empirical evidence on European SMEs, settembre 2016.

47. E. Brenna, L. Gitto, Financing elderly care in Italy and Europe. Is there a common vision?,

settembre 2016.

48. D. G. C. Britto, Unemployment Insurance and the Duration of Employment: Theory and

Evidence from a Regression Kink Design, settembre 2016.

49. E. Caroli, C.Lucifora, D. Vigani, Is there a Retirement-Health Care utilization puzzle?

Evidence from SHARE data in Europe, ottobre 2016.

50. G. Femminis, From simple growth to numerical simulations: A primer in dynamic

programming, ottobre 2016.

51. C. Lucifora, M. Tonello, Monitoring and sanctioning cheating at school: What works? Evidence from a national evaluation program, ottobre 2016.

52. A. Baglioni, M. Esposito, Modigliani-Miller Doesn’t Hold in a “Bailinable” World: A New

Capital Structure to Reduce the Banks’ Funding Cost, novembre 2016.

53. L. Cappellari, P. Castelnovo, D. Checchi, M. Leonardi, Skilled or educated? Educational

reforms, human capital and earnings, novembre 2016.

54. D. Britto, S. Fiorin, Corruption and Legislature Size: Evidence from Brazil, dicembre 2016.

55. F. Andreoli, E. Peluso, So close yet so unequal: Reconsidering spatial inequality in U.S.

cities, febbraio 2017.

56. E. Cottini, P. Ghinetti, Is it the way you live or the job you have? Health effects of lifestyles

and working conditions, marzo 2017.

57. A. Albanese, L. Cappellari, M. Leonardi, The Effects of Youth Labor Market Reforms:

Evidence from Italian Apprenticeships; maggio 2017.

58. S. Perdichizzi, Estimating Fiscal multipliers in the Eurozone. A Nonlinear Panel Data

Approach, maggio 2017.

59. S. Perdichizzi, The impact of ECBs conventional and unconventional monetary policies on

European banking indexes returns, maggio 2017.

60. E. Brenna, Healthcare tax credits: financial help to taxpayers or support to higher income

and better educated patients? Evidence from Italy, giugno 2017.

61. G. Gokmen, T. Nannicini, M. G. Onorato, C. Papageorgiou, Policies in Hard Times:

Assessing the Impact of Financial Crises on Structural Reforms, settembre 2017.

62. M. Tettamanzi, E Many Pluribus Unum: A Behavioural Macro-Economic Agent Based

Model, novembre 2017.

63. A. Boitani, C. Punzo, Banks’ leverage behaviour in a two-agent New Keynesian model,

gennaio 2018.

64. M. Bertoni, G. Brunello, L. Cappellari, Parents, Siblings and Schoolmates. The Effects of

Family-School Interactions on Educational Achievement and Long-term Labor Market

Outcomes, gennaio 2018.

65. G. P. Barbetta, G. Sorrenti, G. Turati, Multigrading and Child Achievement, gennaio 2018.

66. S. Gagliarducci, M. G. Onorato, F. Sobbrio, G. Tabellini, War of the Waves: Radio and

Resistance During World War II, febbraio 2018.

67. P. Bingley, L. Cappellari, Workers, Firms and Life-Cycle Wage Dynamics, marzo 2018.

68. A. Boitani, S. Perdichizzi, Public Expenditure Multipliers in recessions. Evidence from the

Eurozone, marzo 2018.

69. M. Le Moglie, G. Turati, Electoral Cycle Bias in the Media Coverage of Corruption News,

aprile 2018.

70. R. Davidson, A. Monticini, Improvements in Bootstrap Inference, aprile 2018.

71. R. Crinò, G. Immordino, S. Piccolo, Fighting Mobile Crime, giugno 2018.

72. R. Caminal, L. Cappellari, A. Di Paolo, Linguistic skills and the intergenerational

transmission of language, agosto 2018.

73. E. Brenna, L. Gitto, Adult education, the use of Information and Communication

Technologies and the impact on quality of life: a case study, settembre 2018.

74. M. Bordignon, Y. Deng, J. Huang, J. Yang, Plunging into the Sea: Ideological Change,

Institutional Environments and Private Entrepreneurship in China, settembre 2018.

75. M. Bordignon, D. Xiang, L. Zhan, Predicting the Effects of a Sugar Sweetened Beverage

Tax in a Household Production Model, settembre 2018.

76. C. Punzo, L. Rossi, The Redistributive Effects of a Money-Financed Fiscal Stimulus,

gennaio 2019.