Redistribution and the Monetary Fiscal Policy Mix

Finance and Economics Discussion Series

Divisions of Research & Statistics and Monetary Aﬀairs

Federal Reserve Board, Washington, D.C.

Redistribution and the Monetary–Fiscal Policy Mix

Saroj Bhattarai, Jae Won Lee, Choongryul Yang

2021-013

Please cite this paper as:

Bhattarai, Saroj, Jae Won Lee, and Choongryul Yang (2021). “Redistribu-

tion and the Monetary–Fiscal Policy Mix,” Finance and Economics Discussion Se-

ries 2021-013. Washington: Board of Governors of the Federal Reserve System,

https://doi.org/10.17016/FEDS.2021.013.

NOTE: Staﬀ working papers in the Finance and Economics Discussion Series (FEDS) are preliminary

materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth

are those of the authors and do not indicate concurrence by other members of the research staﬀ or the

Board of Governors. References in publications to the Finance and Economics Discussion Series (other than

acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Redistribution and the Monetary–Fiscal Policy Mix

∗

Saroj Bhattarai

†

Univ. of Texas-Austin

and CAMA

Jae Won Lee

‡

Univ. of Virginia

Choongryul Yang

Federal Reserve Board

Abstract

We show that the effectiveness of redistribution policy in stimulating the economy

and improving welfare is directly tied to how much inﬂation it generates, which in

turn hinges on monetary-ﬁscal adjustments that ultimately ﬁnance the transfers. We

compare two distinct types of monetary-ﬁscal adjustments: In the monetary regime, the

government eventually raises taxes to ﬁnance transfers, while in the ﬁscal regime, in-

ﬂation rises, effectively imposing inﬂation taxes on public debt holders. We show ana-

lytically in a simple model how the ﬁscal regime generates larger and more persistent

inﬂation than the monetary regime. In a quantitative application, we use a two-sector,

two-agent New Keynesian model, situate the model economy in a COVID-19 reces-

sion, and quantify the effects of the transfer components of the Coronavirus Aid, Re-

lief, and Economic Security (CARES) Act. We ﬁnd that the transfer multipliers are sig-

niﬁcantly larger under the ﬁscal regime—which results in a milder contraction—than

under the monetary regime, primarily because inﬂationary pressures of this regime

counteract the deﬂationary forces during the recession. Moreover, redistribution pro-

duces a Pareto improvement under the ﬁscal regime.

JEL classiﬁcation: E53; E62; E63

Keywords: Household heterogeneity, Redistribution, Monetary-ﬁscal policy mix, Trans-

fer multiplier, Welfare evaluation, COVID-19, CARES Act

∗

We thank Woong Yong Park for helpful comments. The views expressed here are those of the authors

and do not necessarily reﬂect those of the Federal Reserve Board or the Federal Reserve System. First

version: Dec 2020. This version: Jan 2021.

†

Department of Economics, University of Texas at Austin and CAMA, 2225 Speedway, Stop C3100,

Austin, TX 78712, U.S.A. Email: [email protected].

‡

Department of Economics, University of Virginia, PO BOX 400182, Charlottesville, VA 22904, U.S.A.

Email: [email protected].

Federal Reserve Board of Governors, 20th Street and Constitution Avenue NW, Washington, DC 20551,

U.S.A. Email: [email protected].

1 Introduction

What are the macroeconomic effects of redistribution policies that transfer resources from

one set of agents in the economy to another? What are the determinants of the transfer

multiplier? When is the transfer multiplier large? What are the welfare implications of

such redistribution policies?

Recently, the U.S. experienced the two largest contractions after World War II—the

Great Recession and the COVID-19 recession. The government responded to these con-

tractions with unprecedented ﬁscal measures—namely the American Recovery and Rein-

vestment Act of 2009 and the Coronavirus Aid, Relief, and Economic Security (CARES)

Act of 2020. These ﬁscal responses included signiﬁcant transfer components, and they

have renewed interest in the effectiveness of transfer policies in terms of rebooting the

economy and improving household welfare.

In a dynamic general equilibrium model, one would have to take numerous factors

into account to answer the above questions.

In this paper, we focus on the source of

ﬁnancing and show how the government ﬁnances transfers has a ﬁrst-order importance

for their effectiveness. Our focus is motivated by the ongoing rapid increase in public

debt caused by the large-scale transfer programs. This eventually requires ﬁscal and/or

monetary adjustments, which would ultimately ﬁnance current transfers.

We compare two distinct ways to ﬁnance transfers in a two-agent New Keynesian

(TANK) model. In the model, a set of households are unable to borrow and lend to smooth

consumption over time. A transfer policy redistributes resources toward such "hand-to-

mouth" (HTM) households and away from "Ricardian" households that own government

bonds.

In the ﬁrst policy regime, the government raises taxes. Inﬂation is then stabilized

in the usual way by the central bank. We call this case the "monetary regime." In the

second regime, the government commits itself to no adjustments in taxes, and the central

bank allows inﬂation to rise to stabilize the real value of debt, thereby imposing "inﬂation

taxes" on households that hold nominal government debt. In this "ﬁscal regime," the ﬁscal

theory of the price level operates.

We ﬁnd that the effectiveness of transfer policy is directly tied to how much inﬂation

it generates. A transfer policy is inﬂationary irrespective of the policy regimes in the

model. It is, however, more inﬂationary in the ﬁscal regime than in the monetary regime.

We discuss previous ﬁndings in more detail later. Some well-known determinants of the ﬁscal mul-

tiplier are the marginal propensity to consume of targeted households and whether the economy is in a

liquidity trap.

As we describe in further detail later, in our application, we think of these HTM households as working

in the service sector that is affected by a large negative sectoral shock.

Therefore, inﬂation-ﬁnanced transfers can be used to ﬁght deﬂationary pressures during

recessions, thereby preventing output and consumption of both types of households from

dropping signiﬁcantly. As a result, the welfare of both household types is higher when

transfers are inﬂation-ﬁnanced than when they are tax-ﬁnanced.

Furthermore, somewhat surprisingly, inﬂation-ﬁnanced transfers can produce a Pareto

improvement relative to the no-transfer case. Notice that, since the model features stag-

gered Calvo-type price setting, inﬂation is not a free lunch: it generates, ceteris paribus,

signiﬁcant resource misallocation, which leads to a decrease in labor productivity and

in welfare. These negative effects of inﬂation are, however, outweighed by the positive

effects of inﬂation in the low-inﬂation environment considered in this paper. In fact, with-

out an inﬂationary intervention, the economy would experience deﬂation, so there is little

cost of inﬂation.

Our paper starts with a simpliﬁed ﬂexible-price version of the model that permits

analytical results, thereby allowing us to illuminate the mechanism of the ﬁscal theory

in a heterogeneous-household framework. This model also serves as a useful reference

point, as the two policy regimes produce exactly the same multipliers for output and

consumption and an identical level of household welfare, even if inﬂation dynamics are

different. This is due to two features. First, both conventional taxes, which are assumed

to be lump sum, and inﬂation taxes are non-distortionary. Second, price ﬂexibility shuts

down any feedback effects from inﬂation on real variables.

For inﬂation, the ﬁscal regime gives rise to higher and more persistent inﬂation than

the monetary regime. In particular, transfers affect inﬂation through two channels in

this regime. First, an increase in transfers leads directly to an increase in public debt,

which accumulates over time. Consequently, inﬂation rises to stabilize the real value of

debt. Second, an increase in transfers may indirectly raise future public debt through an

interest rate channel. Redistribution changes Ricardian household consumption, which in

turn affects real interest rates and thus outstanding public debt in the following periods.

That is, redistribution generates a new valuation effect through real interest rate changes,

an effect that is absent in the standard one-agent model often used to analyze the ﬁscal

regime. This interest rate channel may lead to a further increase in inﬂation. Showing

these two effects explicitly in a nonlinear two-agent model is a contribution of our paper.

We then build on the analytical results and proceed to a quantitative analysis employ-

ing a two-sector TANK model. Relative to the simpliﬁed version, the quantitative model

The transfer multiplier for output is small yet still positive due to the classical labor supply channel.

Redistribution causes Ricardian household consumption to fall, creating a negative “wealth effect” on labor

supply. The households thus supply more hours for a given wage rate, which in turn raises output.

includes several realistic features that break the uniformity of the two regimes in terms of

the multipliers. The two most important are nominal rigidities and the "COVID shocks."

Sticky prices are important, as transfers now can increase output through the usual New

Keynesian channel by generating inﬂation—on top of the classical labor supply channel.

Introducing shocks is also consequential as the multipliers are generally state-dependent.

In particular, the COVID shocks cause the economy to fall into what we refer to as a

"COVID recession" as well as a liquidity trap, in which the effects of redistribution can be

different quantitatively. Finally, another difference from the analytical model is that the

government raises (gradually) labor taxes, rather than lump-sum taxes, in the monetary

regime, which, through distortionary effects, inﬂuences the transfer multipliers.

Speciﬁcally, in order to capture the salient characteristics of the COVID recession, we

suppose that the COVID shocks consist of adverse aggregate and sector-speciﬁc demand

shocks and sector-speciﬁc labor supply shocks. The sector-speciﬁc shocks intend to cap-

ture the observation that "locked out" of work and fear of "unsafe consumption" features

are more pronounced in certain sectors of the economy. We decompose the U.S. economy

into two sectors—(1) transportation, recreation, and food service sector and (2) the rest of

the economy—and let the HTM households work in the former sector in our model.

For

convenience, we call this sector the HTM sector.

Figure 1 presents dynamics of employment, hours, inﬂation, and consumption based

on such a two-sector decomposition of the U.S. economy. As is clear, there was a sharp ad-

verse effect on employment/hours in the HTM sector following the COVID crisis. More-

over, inﬂation in this sector also fell. Finally, while the HTM sector was disproportionately

affected, there was also an aggregate, economy-wide contraction and fall in inﬂation as

well. We calibrate the COVID shocks to perfectly re-produce the dynamics of hours in

the two sectors and that of inﬂation in the HTM sector, thereby situating the model econ-

omy in a COVID-recession-like environment. We then calibrate the size of transfers to

match the transfer amount in the CARES Act and study how the economy responds to

the redistribution policy under several alternative scenarios.

We ﬁnd that the transfer multipliers are signiﬁcantly larger under the ﬁscal regime

than under the monetary regime, primarily because of the difference in inﬂation dynam-

ics as mentioned above. For instance, the four-year cumulative multiplier for aggregate

output is 1.126 in the monetary regime while it is 7.739 in the ﬁscal regime. Notice that

this multiplier is greater than unity even under the monetary regime, thanks to nom-

We assume that the Ricardian households work in the other sectors that are less affected by the COVID

pandemic.

We also show with the vertical dashed line in Figure 1 when transfer payments from the CARES Act

started to get mailed.

−−> CARES Act (Apr. 15)

−40

−30

−20

−10

Percent Deviation from Jan. 2020

1 2 3 4 5 6 7 8

2020

Total

Retail, Transportation,

Leisure and Hospitality

Others

Panel A: Employment

−40

−30

−20

−10

Percent Deviation from Jan. 2020

1 2 3 4 5 6 7 8

2020

Total

Retail, Transportation,

Leisure and Hospitality

Others

Panel B: Total Hours

−70

−60

−50

−40

−30

−20

−10

Percent Deviation from Jan. 2020

1 2 3 4 5 6 7 8

2020

Total

Transportation, Recreation,

and Food Services

Others

Panel C: Real PCE

−2

−1.5

−1

−.5

Percent Deviation from Jan. 2020

1 2 3 4 5 6 7 8

2020

Total

Transportation, Recreation,

and Food Services

Others

Panel D: PCE Inflation

Figure 1: Aggregate and Sectoral Effects of COVID Crisis

Notes: This ﬁgure shows the dynamics of key variables from January 2020. Panels A and B show employ-

ment and total hours dynamics in U.S. Bureau of Labor Statistics, respectively. Black lines are dynamics

of total variable and red lines represent retail, transportation, leisure, and hospitality sector, and blue

lines represent all other sectors. Panels C and D present real personal consumption expenditure and

PCE inﬂation in U.S. Bureau of Economic Analysis, respectively. Black lines are dynamics of total vari-

able and red lines represent transportation, recreation and food services sector, and blue lines represent

all other sectors.

Sources: U.S. Bureau of Economic Analysis, U.S. Bureau of Labor Statistics

inal rigidities and the binding zero lower bound (ZLB). Just as strikingly different are

the four-year cumulative consumption multipliers. For the Ricardian households, it is

negative 0.244 in the monetary regime and 6.036 in the ﬁscal regime, while for the HTM

households, it is 5.609 in the monetary regime and 13.311 in the ﬁscal regime.

We isolate the role played by various model elements in driving our quantitative re-

The positive consumption multiplier for the Ricardian household is unique, even qualitatively so, in

the ﬁscal regime.

sults using counterfactual exercises. The unusually large multipliers reported above, es-

pecially under the ﬁscal regime, result from the economy being situated in the historically

severe COVID-recession with large deﬂationary pressures. For example, shutting down

the COVID shocks, the four-year cumulative multiplier for aggregate output is 0.96 in the

monetary regime, while it is 1.475 in the ﬁscal regime. This result underscores the state-

dependency of policy effects. Importantly, the difference in the multipliers for output

and consumption between the two regimes gets larger in the presence of COVID shocks,

which implies that while both labor-tax-ﬁnanced transfers and inﬂation-ﬁnanced trans-

fers are more effective in the COVID recession than in a normal environment, the latter is

even more so. In addition, we also ﬁnd that relying on labor taxes rather than lump-sum

taxes in the monetary regime plays a role.

Overall, as a consequence, the contraction in output and consumption is much more

muted when transfers are ﬁnanced by inﬂation taxes. Speciﬁcally, transfers, when inﬂation-

ﬁnanced, would reduce the output loss caused by the COVID shocks by roughly 5 per-

centage points at the trough compared to no-intervention case. We also ﬁnd that the

expansionary effects of inﬂation-ﬁnanced transfers are so large that such redistribution

policy generates a Pareto improvement: It increases the welfare of both the recipients and

sources of transfers, even taking into account the resources taken away from the Ricar-

dian household and the fact that the Ricardian household’s leisure decreases as a result

of output increases and distortions generated by high and persistent inﬂation.

Our paper builds on several strands of the literature. It is related to the ﬁscal-monetary

interactions literature as originally developed in Leeper (1991), Sims (1994), Woodford

(1994), Cochrane (2001), Schmitt-Grohé and Uribe (2000), and Bassetto (2002).

Sims

(2011) introduced long-term debt under this regime in a sticky price model, while Cochrane

(2018) developed it further to analyze the inﬂation implications following the Great Re-

cession. Analytical characterization of the ﬁscal regime in a linearized sticky price model

is in Bhattarai, Lee and Park (2014).

Our additional analytical contribution here is to derive the fully nonlinear results of

this ﬁscal regime in a tractable two-agent model. Motivated by the COVID crisis and the

CARES Act, we then assess the quantitative effects of redistribution policy as well as its

welfare implications in a two-sector, two-agent nonlinear model.

We build on two-agent models as originally developed in Campbell and Mankiw

(1989), Galí, López-Salido and Vallés (2007), and Bilbiie (2018). Moreover, Bilbiie, Mona-

celli and Perotti (2013), closely related to this paper, show that different ﬁnancing schemes

affect the size of the output transfer multiplier in a TANK model. However, they only

Canzoneri, Cumby and Diba (2010) and Leeper and Leith (2016) are recent surveys of this literature.

consider the monetary regime. Our main contribution is in assessing the effects of redis-

tribution policy in such an environment and showing how it depends critically on the

monetary-ﬁscal policy mix.

Recently there have been several contributions to an analysis of macroeconomic ef-

fects of the COVID crisis. Our quantitative two-sector, two-agent model is closest to the

important work of Guerrieri, Lorenzoni, Straub and Werning (2020). In assessing the

quantitative effects of ﬁscal policy during the pandemic using a model with household

heterogeneity, we are also related to Faria-e-Castro (2020) and Bayer, Born, Luetticke and

Müller (2020). Our relative contribution is in showing how the effects of redistribution

depend on the monetary-ﬁscal policy regime and then assessing both quantitative effects

and welfare implications by matching some important aggregate and sectoral aspects of

the U.S. data.

Our paper is also related to recent papers that analyze monetary-ﬁscal policy interac-

tions in TANK models—in particular, Bhattarai, Lee, Park and Yang (2020), Bianchi, Fac-

cini and Melosi (2020), and Motyovszki (2020). Bhattarai, Lee, Park and Yang (2020) study

the effects of one-time permanent capital tax rate changes in a model that also features

capital-skill complementarity. Bianchi, Faccini and Melosi (2020) and Motyovszki (2020)

are motivated by the COVID crisis and are closely related to our analysis.

Our relative

contribution analytically is a nonlinear solution of the simple TANK model under the two

regimes. On the quantitative side, while these studies focus on the positive implications

of transfers under the different regimes, we additionally provide welfare implications for

different types of households. We also emphasize that the positive and normative im-

plications of redistribution are state-dependent and that inﬂation-ﬁnanced transfers are

disproportionately more effective than tax-ﬁnanced transfers in a COVID-recession-like en-

vironment in which both sector-speciﬁc and aggregate shocks hit the economy.

Finally, our paper is also related to the government spending multiplier literature, as

the effects of transfer policy in two-agent models share some common elements with the

effects of government spending policy in representative agent models. Thus, in connect-

ing the effects to the nature of monetary policy, the binding ZLB, and the monetary-ﬁscal

policy regime, our work builds on important contributions in the government spend-

ing multiplier literature by Woodford (2011), Christiano, Eichenbaum and Rebelo (2011),

Eggertsson (2011), Leeper, Traum and Walker (2017), and Jacobson, Leeper and Preston

(2019).

Bianchi, Faccini and Melosi (2020) show that inﬂating away a targeted fraction of debt will increase

the effectiveness of the ﬁscal stimulus in a rich medium-scale model while Motyovszki (2020) considers a

small-open economy environment.

2 Simple Model and Redistribution Policy

We present a simple model that yields analytical results on effects of redistribution policy.

2.1 Model

There are two types of households: Ricardian and HTM. The Ricardian household makes

optimal labor supply and consumption/savings decisions, while the HTM household

simply consumes government transfers every period. In this setup, we analytically show

the effects on inﬂation of transferring resources away from the Ricardian households to

the HTM households and point out that these effects depend critically on how the transfer

policy is ﬁnanced.

2.1.1 Households

Ricardian Households. There are Ricardian households of measure 1 − λ. These house-

holds, taking prices as given, choose {C

, L

, B

} to maximize

∞

∑

t=0

log C

− χ





1+ϕ

1 + ϕ

subject to a standard No-ponzi-game constraint and a sequence of ﬂow budget constraints

= R

t−1

+ w

+ Ψ

− τ

where C

is consumption, L

is hours, B

is nominal government debt, Ψ

is real proﬁts,

is lump-sum taxes, P

is the price level, w

is the real wage, and R

is the nominal gross

interest rate. The discount factor and the inverse of the Frisch elasticity are denoted by

β ∈ ( 0, 1) and ϕ ≥ 0 respectively. The superscript, R, represents “Ricardian”. The ﬂow

budget constraints can be written as

+ b

= R

t−1

+ w

+ Ψ

− τ

where b

is the real value of debt, and Π

t−1

is the gross rate of inﬂation.

Optimality conditions are given by the Euler equation, the intra-termporal labor sup-

ply condition, and the transversality condition (TVC):

t+1

= β

t+1

, (2.1)





= w

, (2.2)

lim

t→∞







= 0. (2.3)

Hand-to-Mouth Households. The hand-to-mouth (HTM) households, of measure λ,

simply consume government transfers, s

, every period

= s

and have no optimization problem to solve. The superscript, H, represents “HTM”.

2.1.2 Firm

A representative ﬁrm in the competitive product market chooses hours, L

, in each period

to maximize proﬁts:

= Y

− w

subject to the production function

= L

. (2.4)

Zero proﬁt condition implies

= 1. (2.5)

2.1.3 Government

The government issues one-period nominal debt, B

. Its budget constraint (GBC) is

= R

t−1

− τ

+ s

where s

is transfers and τ

is taxes. It can be re-written as

t−1

− τ

+ s

, (2.6)

where b

is the real value of debt. Transfer, s

, is exogenous and deterministic.

Monetary and tax policy rules are





, (2.7)

(

−

)

= ψ(b

t−1

−

b), (2.8)

where φ and ψ determine the responsiveness of the policy instruments to inﬂation and

government indebtedness respectively. The steady-state values of inﬂation, debt, and

transfers,



Π,



, are set by policymakers and given exogenously.

2.1.4 Aggregation and the Resource Constraint

Aggregating the variables over the households yields s

= λs

, τ

(

1 − λ

)

, b

(

1 − λ

)

, L

(

1 − λ

)

, and Ψ

(

1 − λ

)

. Combining household and govern-

ment budget constraints gives:

(1 − λ)C

+ λC

= Y

The resource constraint above, together with the HTM household budget constraint, im-

plies that output is simply divided between the two types of households as:

, C

1 − λ

−

1 − λ

. (2.9)

2.2 Effects of Redistribution Policy

We now show the effects of transferring resources away from the Ricardian households

to the HTM households. The government can ﬁnance such a transfer program in two

distinct ways. In the ﬁrst policy regime, the government raises taxes sufﬁciently. Inﬂation

is then stabilized in the usual way by the central bank. In the second regime, the govern-

ment does not raise taxes, and the central bank allows inﬂation to rise to stabilize the real

value of debt, thereby imposing “inﬂation taxes” on the Ricardian households that hold

nominal government debt. The ﬁscal theory of the price level operates in this case.

We solve for the equilibrium time path of



, C

, Π

, R

, b

, τ



given exogenous

{

}

. Output and consumption of the two households, and thus their welfare, are in-

dependent of whether the government relies on conventional or inﬂation taxes.

ﬁrst consider those policy-invariant variables in Section 2.2.1. The alternative ﬁnancing

schemes, however, generate quite different inﬂation dynamics, which is the main focus

of this simple model. The rise of inﬂation tends to be greater and more persistent in the

second regime. The determination of the rate of inﬂation is detailed in Section 2.2.2.

This “neutrality” result does not hold in a model with nominal rigidities, as discussed in detail later.

2.2.1 Output and Consumption

We start with output. Equation (2.2) can be written as

= χ

−1

(

1 − λ

)

1+ϕ

−ϕ

+ s

(2.10)

using Equations (2.4), (2.5), and (2.9). Equation (2.10) implicitly deﬁnes output as a func-

tion of transfers: Y

= Y

(

)

. Then, one can obtain the “transfer multiplier” as

(

)

1 +

(

1 − λ

)

1+ϕ

−

(

1+ϕ

)

Notice that 0 ≤

≤ 1.

An increase in transfers raises output not for the Keynesian demand-side reason. The

channel here instead is purely classical and supply-side: An increase in s

causes Ricar-

dian household consumption to fall, creating a negative “wealth effect” on labor supply.

The households supply more hours for a given wage rate, which in turn raises output.

The multiplier is maximized (dY

/ds

= 1) when labor supply is perfectly elastic (ϕ = 0)

while it is minimized (dY

/ds

= 0) when the Ricardian household does not value leisure

(χ = 0), which shuts down the wealth effect.

The Ricardian household consumption is obtained from Equation (2.9) as

= C

(

)

≡

1 − λ

[

(

)

− s

]

. (2.11)

The derivative is

(

)

1 − λ



(

)

− 1



≤ 0.

As will be clear below, how Ricardian household consumption depends on transfers mat-

ter for inﬂation dynamics as it affects the real interest rate. That is, there is a valuation

effect on government debt due to changes in the real interest rate. This interest rate channel

of transfers is absent in the model with a representative household, where transfers have

no redistributive role, or with a perfectly elastic labor supply.

Notice that both tax types are non-distorting in this model. Consequently, for given

{

}

, the alternative ways to ﬁnance transfers (i.e., the policy regimes) have no effect on

output and consumption, as seen above.

The channel thus is the same as the effect of government spending in a one-agent model.

2.2.2 Inﬂation

We now turn to the rest of the variables,

{

, R

, b

, τ

}

∞

t=0

, with a focus on inﬂation de-

termination, given a path of

{

}

∞

t=0

. The equilibrium time path of

{

, R

, b

, τ

}

satisﬁes

the following conditions:

• Difference Equations from (2.1), (2.6), (2.7) and (2.8):

t+1

βR

, b

= R

t−1

− τ

+ s





(

−

)

= ψ(b

t−1

−

b).

• Terminal condition, as given by TVC from Equation (2.3):

lim

t→∞





= 0.

• Initial conditions:

−1

and R

−1

We ﬁrst solve for the deterministic steady state. When s

s ∀t, the system of differ-

ence equations simpliﬁes to

R = β

−1

Π,

τ =



−1

− 1



b +

with the TVC trivially satisﬁed. Given

Π and

b, which we assume exogenously deter-

mined by policymakers, the equations above determine

R and

τ. We set R

−1

R and

−1

b, without loss of generality.

The system of difference equations can be simpliﬁed as



t+1



t+1





, (2.12)



−



−1

t−1

− ψ

t−1

−

b) +

(

−

)

−1

t−1

− β

−1

∀t ≥ 1 (2.13)



−



= β

−1



− 1



b +

(

−

)

at t = 0, (2.14)

which determines

{

, b

}

given

{

}

and





, where note that from Equation (2.11),

the latter is a simple function of transfers.

The online appendix provides detail.

Equation (2.12), obtained by combining the Euler equation and the monetary policy

rule, shows how future inﬂation (Π

t+1

) depends on current inﬂation (Π

) and the real

rate captured by C

t+1

. Equation (2.13) is the GBC for t ≥ 1 after we substitute out the

nominal interest rate (R

t−1

) and taxes (τ

) using the Euler equation and the ﬁscal policy

rule. Equation (2.14) is the GBC at t = 0. This looks different from Equation (2.13) because

−1

is exogenous, and thus cannot be replaced by the Euler equation.

Equation (2.13) describes how the deviation of the real value of debt from the steady

state,



−



, evolves over time. An increase in transfers over its steady state value

(s >

s) affect debt dynamics directly and indirectly. First, ceteris paribus, such an increase

causes b

, debt carried over to the next period, to rise above

b. This direct effect is captured

by the second term,

(

−

)

, on the right hand side of Equation (2.13). Second, a change

in transfers affects Ricardian household consumption as shown in Equation (2.11) and

hence the real interest rate, which in turn inﬂuences debt dynamics. This indirect effect is

reﬂected by r

t−1

≡ β

−1

t−1

in Equation (2.13), and operates even when the current period

debt stays at the steady state (i.e. b

t−1

b). The reason is a change in interest payments

for a given amount of debt—as shown in the last term,



−1

t−1

− β

−1



In solving the system, we consider a redistribution program in which

{

}

∞

t=0

can have

arbitrary values greater than

s until a time period T, and then s

s for t ≥ T + 1. In this

case, regardless of the history until time T + 1, starting T + 2, Equation (2.13) becomes



−





−1

− ψ



t−1

−

b).

How the TVC is satisﬁed depends on the ﬁscal policy parameter ψ. When ψ > 0, debt

dynamics satisﬁes the TVC regardless of the value of b

T+1

When ψ ≤ 0, however, the

TVC requires b

T+1

b, which can be achieved when monetary policy allows inﬂation to

adjust by the required amount. Below, we discuss each case in turn.

Inﬂation under the Monetary Regime. When ψ > 0, , inﬂation is solely determined by

Equation (2.12) which becomes



t+1







for t ≥ T + 1,

as C

, Ricardian household consumption, is constant. In this case, if we were to consider

φ < 1, the system of Equations (2.12)–(2.14) does not pin down initial inﬂation Π

, and

the model permits multiple non-explosive solutions.

In addition, ψ should not be too big. We do not explicitly consider such empirically irrelevant cases.

We therefore, instead consider the standard case, φ > 1, which we call the monetary

regime. This regime produces multiple equilibria in which inﬂation is unbounded and a

unique bounded equilibrium.

Here we focus on the bounded equilibrium. In this case,

it is necessary that

T+1

= 1.

Given this “stability” condition on inﬂation, one can pin down Π

from t = 0 to T along

the saddle path. In particular, inﬂation before T + 1 can be solved backward using Equa-

tion (2.12). The initial inﬂation is given by

= C

(

)

T+1



(

)

(

T−1

)

· · · C

(

)



∏

t=0



(

)

(

)



. (2.15)

Inﬂation in the following periods is then determined by Equation (2.12).

Equation (2.15) shows that an increase in transfers is inﬂationary as the Ricardian

household consumption declines below the pre-transfer level. The magnitude of the ef-

fect depends on the response of monetary policy (measured by φ), the size of transfer

increases, and the duration of the redistribution program. Most importantly, the effect

is transitory: When the redistribution program ends, inﬂation returns immediately to the

steady-state value. Finally, redistribution programs with the same value of total transfer

payments, but with different payment schedules, have different implications for the real

interest rate and inﬂation dynamics. We discuss this in more detail below.

Inﬂation under the Fiscal Regime. We now consider the ﬁscal regime where ψ ≤ 0 and

φ < 1. Solving for inﬂation involves a similar procedure as in the monetary regime. We

ﬁrst identify a terminal condition and follow the saddle path to pin down initial inﬂation.

As mentioned above, when ψ ≤ 0, the TVC requires b

T+1

b. Given this terminal

condition, debt in preceding periods can be solved backward using Equation (2.13). Fi-

nally, given the solved b

, the time-0 GBC Equation (2.14) determines initial inﬂation Π

after which Equation (2.12) produces a non-explosive time path of inﬂation.

Before presenting the general solution, we consider a simple example that is helpful

to develop the intuition. Suppose transfers increase only for one period: s

s and

s afterwards. In the single-period redistribution program, it is necessary that b

We rule out the case in which the price level approaches zero by the TVC.

otherwise, the TVC would be violated. The GBC at t = 1 is then given as



−



| {z }







−1

(

)

(

)

| {z }

− ψ







−

b) +

(

−

)

| {z }







−1

(

)

(

)

| {z }

− β

−1







, (2.16)

from which we can obtain the initial debt level b

ensuring that b

equals

b −



−1

(

)

(

)

− ψ



−1



−1

(

)

(

)

− β

−1



The terminal condition (b

b) requires b

to decline below

b. For this to happen, Π

adjusts according to Equation (2.14):

1 −

(

−

)

− β

−1

(

)

(

)

− ψ

−1

(

)

(

)

− β

−1

. (2.17)

The redistribution policy is more inﬂationary under the ﬁscal regime than under the

monetary regime. Inﬂation rises by more on impact: Π

in Equation (2.17) is greater than

in Equation (2.15) even under the most dovish monetary regime (i.e. when φ → 1.)

More importantly, the one-time transitory increase in transfers has persistent effects on

inﬂation here, while the effect lasts only for one period under the monetary regime.

The result above holds without the interest rate channel. The presence of the third term

in the denominator, −β

[

− ψ

]

−1

[

−

]

, however, does cause Π

to increase by more

than it would in an analogous model with a representative household where transfer

changes have no effect on the real interest rate.

This term results from increased interest

payments that exert an upward pressure on b

(see Equation (2.16)). The upward pressure

is offset by a further decrease in b

, which is generated by a greater increase in Π

The effects of the interest rate channel on inﬂation, however, is subtler in a multi-

period redistribution program. The initial inﬂation in the general case is given by

1 −

∑

k=0

Ω

(

−

)

− β

∑

T+1

k=1

Ω

−1

(

)

(

k−1

)

− β

−1

, (2.18)

In that model, the term would drop because

= 1.

The online appendix provides detail.

where the “discount factor” Ω

is deﬁned as:

Ω

≡ Ω

k−1



−1

(

)

(

k−1

)

− ψ



−1

(

∏

j=1

−1







j−1



− ψ

−1

, Ω

≡ 1.

The solution (2.18) reveals that the interest rate channel can in principle, work in both

directions. On the one hand, as shown in the one-period transfer increase case, a redistri-

bution program that raises the real interest rate leads to an increase in interest payments

and a larger rise in inﬂation—as captured by the last term in the denominator. On the

other hand, such redistribution decreases the discount factor Ω

. The economy thus dis-

counts future primary surplus/deﬁcits more heavily, which causes inﬂation to adjust by

less when future transfers rise.

Therefore, generally, the net effect on inﬂation through

the interest rate channel of a multi-period redistribution program is difﬁcult to isolate

analytically, without further restrictions on the path of transfers.

In this paper, we focus on programs with constant s

for 0 ≤ t ≤ T. In such a case,

the interest rate channel works in the same way as described in the simple example, and

leads to a larger response of inﬂation. To show this, we use the property that the real

interest rate is constant throughout except for the last period of a program; that is, r

for 0 ≤ t ≤ T − 1 and r

r, if s

= s

s for 0 ≤ t ≤ T. Equation (2.18) simpliﬁes to

1 −

(

−

)

∑

k=0

(

−1

− ψ

)

−k

− β

(

− ψ

)

−1

(

−

) (

−1

− ψ

)

−T

which looks similar to Equation (2.17).

2.3 Summary and an Extension to Nominal Rigidities

To summarize, transferring resources from Ricardian to HTM households is inﬂationary

regardless of the ﬁnancing schemes considered. The ﬁscal regime, in which the govern-

ment effectively imposes “inﬂation taxes” on Ricardian households that hold nominal

government debt, however, generates greater and more persistent inﬂation than the mone-

tary regime that ﬁnances transfers raising “conventional taxes.”

Equation (2.16) also provides intuition: To achieve a target level of b

, b

needs not decrease as much

when the coefﬁcient (which is increasing in the real rate) is greater; consequently, inﬂation increases by less.

Moreover, there is a signiﬁcant ﬂexibility in the schedule of transfer payments when studying a multi-

period redistribution program. The time path of transfers

{

}

t=0

can be constant, (weakly) monotonic, or

neither. Depending on the time path, the real interest rate, β

−1

(

)

(

t−1

)

, need not be greater than or equal to

its steady-state value β

−1

for the entire duration of a redistribution program. Interest payments thus can be

lower than the pre-program level in some periods. Generally, different transfer schedules would result in

different dynamics of the real interest rate. A constant or monotonic schedule is however, most commonly

used in quantitative models.

When it comes to output, consumption, and hours, the policy regimes are “neutral.”

As we mentioned before, this result does not carry over to a model with nominal rigidi-

ties. In the online appendix, we provide a simple sticky-price model that permits some

analytical results with simplifying assumptions. The model nests the ﬂexible-price model

presented so far as a special case.

The result on inﬂation is essentially the same in that

model. A redistribution program generates greater and more persistent inﬂation under

the ﬁscal regime. Analytical results on inﬂation are more difﬁcult to obtain, as Ricar-

dian household consumption now also depends on inﬂation. Thus, the solution involves

ﬁnding a ﬁxed point in an equation analogous to Equation (2.17). Nevertheless, the mech-

anisms discussed in Sections 2.2.1 and 2.2.2 still apply.

The policy regimes are no longer neutral for output, consumption, and hours with

sticky prices because of the short-run relationship between output and inﬂation. Abusing

the notation, and in comparison to output in Equation (2.10), it is convenient to regard

output now as a function of transfers and inﬂation, where inﬂation in turn is also a func-

tion of the entire schedule of transfers:

= Y



, Π



{

}

t=0



Therefore, output would increase not only through the (labor) supply channel. When

wealth redistribution is inﬂationary, output would increase further due to the demand-

side channel. Consequently, Ricardian household consumption in Equation (2.9) would

not decrease as much as in the ﬂexible-price case, while HTM household consumption

would still be unaffected.

Since inﬂation generally increases by more under the ﬁscal regime compared to the

monetary regime, alternative ﬁnancing schemes now have different welfare implications.

With inﬂation taxes, Ricardian household consumption would not decrease as much,

which would increase their welfare. At the same time, the Ricardian households would

have to work more not only to produce more output but in addition, high and persistent

inﬂation in the ﬁscal regime produces resource misallocations, which increase labor hours

required to produce the same amount of ﬁnal output. Therefore, it is unclear a priori that

inﬂation taxes are a better or worse way to ﬁnance a redistribution program compared to

other taxes. We explore this question in a quantitative model in the next section.

The next section presents a quantitative sticky-price model. In addition, the role of nominal rigidities

(in this simple model) is relatively easy to understand as discussed below. Therefore, for brevity, we do not

present this sticky price extension of the simple model in the main text.

3 Quantitative Model and COVID Application

We now present a quantitative version of the model with an application focused on the

economic crisis induced by COVID, modeled by introducing demand and supply shocks,

and subsequent transfer policy, as embedded in the CARES Act. Compared to the simple

model, the main extension is a development of a two-sector production structure with

sticky prices, as well as the introduction of distortionary taxes such that the trade-off be-

tween different sources of ﬁnancing government debt is meaningful. We then analyze

how the implications of increasing transfers to HTM households, which are hit dispro-

portionately in a COVID crisis, depend on the monetary-ﬁscal policy mix.

3.1 Model

There are two distinct sectors where the two types of households work. Each sector pro-

duces a distinct good, which is in turn produced in differentiated varieties. Firms in both

sectors are owned by the Ricardian household. The government ﬁnances transfers to the

HTM household by levying distortionary labor taxes on the Ricardian household. In the

ﬁscal regime, partial ﬁnancing also happens by inﬂating away nominal debt.

3.1.1 Ricardian Sector

Households. Ricardian (R) households, of measure 1 − λ, solve the problem

max

}

∞

∑

t=0

exp(η

)





1−σ

1 − σ

− χ





1+ϕ

1 + ϕ

subject to a standard No-ponzi-game constraint and sequence of ﬂow budget constraints

+ b

= R

t−1



1 − τ

L,t



+ Ψ

where σ is the coefﬁcient of relative risk aversion, η

is a preference shock, C

is con-

sumption, L

is labor supply, b

is the real value of government issued debt, Π

inﬂation, R

t−1

is the nominal interest rate, w

is the real wage, and Ψ

is real proﬁts (this

household owns ﬁrms in both sectors). Labor tax, (1 − τ

L,t

), constitutes one way in which

the government ﬁnances transfers to the Hand-to-mouth household.

Consumption good C

is a CES aggregator (ε > 0) of the consumption goods pro-

duced in the two sectors



(

)



R,t



ε−1

(

1 − α

)



exp(ζ

H,t



ε−1



ε−1

where C

R,t

and C

H,t

are R-household’s demand for R-sector and for HTM-sector goods,

respectively. α is Ricardian households’ consumption weight on R-sector goods and ζ

H,t

is a demand shock that is speciﬁc for HTM goods. Let us deﬁne for future use, one of the

relative prices, S

R,t

≡



R,t



, where P

R,t

is the R-sector’s good price while P

is the CPI

price index of the R-household.

Within each sector, differentiated varieties are produced under monopolistic competi-

tion. Thus, C

R,t

and C

H,t

are Dixit-Stiglitz aggregates of a continuum of varieties. That is,

with θ > 1,

R,t





R,t

(i)



θ−1



θ−1

, C

H,t





H,t

(i)



θ−1



θ−1

Firms. Firms produce differentiated varieties using the linear production function

R,t

(

)

= L

(i) ,

and set prices according to the Calvo friction, where ω

is the probability of not getting a

chance to adjust prices. Firms that get to adjust prices solve the maximization problem

max

R∗

R,t

(i)}

∞

∑

s=0





t+s

−σ

R∗

R,t

(

)

R,t+s

− w

t+s

R∗

R,t

(

)

R,t+s

−θ

R,t+s

where P

R∗

R,t

(

)

denotes the optimally chosen price. There is no price discrimination across

sectors for varieties and we impose the law of one price. Thus, we write demand directly

in terms of Y

R,t

(i) =



R,t

(i)

R,t



−θ

R,t

, which is derived from the household’s expenditure

minimization problem across varieties.

3.1.2 Hand-to-Mouth Sector

Households. There are Hand-to-mouth (HTM) households of measure λ. HTM house-

hold’s labor endowment is exogenously ﬁxed and can change with a shock. The HTM

household then consumes, every period, wage income and government transfers

= w

(1 + η

) + s

where η

is HTM labor supply shock.

The utility function of the HTM is (again, labor supply is inelastic)





1−σ

1 − σ

where the aggregate consumption C

is a CES aggregator of sector-speciﬁc goods



(

1 − α

)



exp

(

H,t

)

H,t



ε−1

(

)



R,t



ε−1



ε−1

and where 1 − α is HTM households’ consumption weight on HTM-sector goods while

H,t

is a demand shock speciﬁc for HTM-sector goods.

Let us deﬁne for future use one

of the relative prices, S

H,t

≡

H,t

, where P

H,t

is the HTM sector’s good price while P

the CPI price index of the HTM household. C

HH,t

and C

HR,t

are Dixit-Stiglitz aggregates

of a continuum of varieties. That is, with θ > 1,

H,t





H,t

(

)



θ−1



θ−1

, C

R,t





R,t

(

)



θ−1



θ−1

Firms. Firms produce differentiated varieties using the linear production function

H,t

(

)

= L

(i)

and set prices according to the Calvo friction, where ω

is the probability of not getting

a chance to adjust prices. Firms that get to adjust prices solve the maximization problem

max

H∗

H,t

(i)}

∞

∑

s=0





t+s

−σ

H∗

H,t

(

)

H,t+s

t+s

H,t+s

−

t+s

H∗

H,t

(

)

H,t+s

−θ

H,t+s

where P

H∗

H,t

(

)

denotes the optimally chosen price.

3.1.3 Government

The government ﬂow budget constraint is

+ T

= R

t−1

+ P

where tax revenues T

(

1 − λ

)

L,t

. Transfer (deﬂated by CPI of the Ricardian

household), s

, is exogenous and deterministic. Note that, s

= λs

and b

(

1 − λ

)

Monetary and tax policy rules are of the feedback types given by

= max

(



(

1 − λ

)

+ λΠ



)

, τ

L,t

−

= ψ

t−1

−

b),

where the zero lower bound on the nominal rate applies. As in the simple model, the

monetary regime will feature a large enough monetary and tax rule response coefﬁcients,

Our modeling choice of the same consumption basket for the two types of households is driven by the

data, as we discuss later. This implies that CPI of the two households is the same.

φ and ψ

, such that government debt sustainability is not ensured via inﬂation. In con-

trast, in the ﬁscal regime, a low enough tax rule coefﬁcient, ψ

, implies that monetary

policy has to be accommodative via a low enough φ, such that debt is (at least partly)

ﬁnanced via inﬂation.

3.1.4 Market Clearing, Aggregation, Resource Constraints

We now discuss market clearing conditions as well as some key aggregate relationships.

Labor market clearing conditions are

(

1 − λ

)

R,t

(

)

di, λL

(1 + η

) =

H,t

(

)

di,

while the goods market clearing conditions, imposing law of one price, are

j,t

(

)

(

1 − λ

)

j,t

(

)

+ λC

j,t

(

)

j,t

(

)

j,t

−θ

j,t

where Y

j,t

(

1 − λ

)

j,t

+ λC

j,t

for j ∈ {R, H}.

Deﬁne economy-wide consumption as C

(

1 − λ

)

+ λC

. To derive an aggre-

gate resource constraint, we combine households’ budget constraints, government bud-

get constraint, and goods market clearing condition to obtain

= S

R,t

+ S

H,t

To derive aggregate sectoral outputs, we aggregate ﬁrms’ product functions and get

(

1 − λ

)

= Y

R,t

, λL

(1 + η

) = Y

H,t

, (3.1)

where Ξ

j,t

for j ∈ {R, H} is price dispersion term given by

j,t



1 − ω



∗

j,t

−θ

+ ω



j,t



j,t−1

3.2 Data and Calibration

Our parameterization strategy is to pick values based on long-run averages or from the

literature for the structural and policy parameters while calibrating the shocks to match

employment and inﬂation dynamics during the COVID crisis. Table 1 presents our cali-

bration. The data are described in detail in Appendix Section A.

All equilibrium conditions are derived in detail in the online appendix.

Table 1: Calibration

Value Description Sources

Households

β 0.9932 Time preference 2-month frequency

σ 1.7 Inverse of EIS Del Negro et al. (2015)

ϕ 2.2 Inverse of Frisch elasticity Del Negro et al. (2015)

χ 94.6 Labor supply disutility parameter Steady-state

= 0.3

λ 0.23 Fraction of HTM households

Employment share of retail,

transportation, leisure/hospitality

α 0.72

Consumption weight

Consumer Expenditure Surveys data

on Ricardian goods

Firms

θ 6.0 Elasticity of substitution across ﬁrms Steady-state markup: 20% (Hall, 2018)

ε 0.8

Elasticity of substitution between

Assigned

Ricardian and HTM goods

0.833 Calvo parameter for Ricardian sector Del Negro et al. (2015)

0.0 Calvo parameter for HTM sector Assigned

Government

0.509 Steady-state debt to GDP Data (1990Q1–2020Q1)

0.122 Steady-state labor tax revenue to GDP Data (1990Q1–2020Q1)

0.127 Steady-state transfers to GDP Data (1990Q1–2020Q1)

Monetary and Fiscal Policy Rules

φ (1.3, 0.0) Interest rate response to inﬂation Del Negro et al. (2015)

(0.6, 0.0) Labor tax rate response to debt Assigned

Shocks

(-17%, -19%, -13%) Size of HTM labor supply shock

Total hours for retail,

transportation, leisure/hospitality

(-41%, -42%, -17%) Size of preference shock

Total hours excluding retail,

transportation, leisure/hospitality

H,t

(-21%, -16%, 4.7%) Size of HTM sector demand shock

PCE Inﬂation for recreation,

transportation, food services

26.8% Size of transfer distribution 2020 CARES Act

Notes: This table shows model parameter values we use for our baseline model simulation. See Section 3.2 for details.

Our benchmark model is calibrated at a two-month frequency with a time discount

factor of β = 0.9932. We set the inverse of the Frisch elasticity (ϕ) to be 2.2 and the inverse

of the elasticity of intertemporal substitution (σ) to be 1.7, which are the estimates in Del

Negro, Giannoni and Schorfheide (2015). We set the elasticity of substitution across ﬁrms

to be six (θ = 6), which corresponds to a recent estimate of average markup of 20 percent

(Hall, 2018). We assume that the Ricardian and HTM goods are complements by setting

the elasticity (e ) as 0.8, which is broadly consistent with the estimates in Hobijn and Ne-

chio (2018).

We assume ﬂexible prices in the HTM sector for simplicity, while we set

Hobijn and Nechio (2018) estimate the elasticity to be 1 at a level of aggregation that distinguishes

the Calvo parameter for the Ricardian sector to be 0.833, which implies a 12-month dura-

tion of price changes, consistent with estimates in Del Negro, Giannoni and Schorfheide

(2015). Finally, the steady-state gross inﬂation is 1.

We set the fraction of HTM households (λ) to be 0.23, based on employment share of

retail trade, transportation and warehousing, and leisure and hospitality sectors in the

U.S. Bureau of Labor Statistics (BLS). We use the 2019 Consumer Expenditure Surveys

(CEX) data to calibrate α, the share parameters in the consumption baskets. We assume

households in the top 80 percentile of the income distribution as Ricardian households

and set 1 − α as 0.28 to match their consumption share for transportation, entertainment,

and food away from home.

For the steady-state of ﬁscal variables, we use federal debts, federal receipts, and gov-

ernment current transfer payments data from 1990:Q1 through 2020:Q1. We set the Taylor

rule parameter under the monetary regime to be 1.3, as estimated in Del Negro, Giannoni

and Schorfheide (2015). We set the tax rule parameter (ψ

) to be 0.6 under the monetary

regime, and we perform a sensitivity analysis later. We assume both the Taylor rule (φ)

and tax rule parameters (ψ

) to be zero under the ﬁscal regime, which is the parameteri-

zation often used in the literature.

To examine the dynamic effects of transfer policy, we calibrate the size of transfer

distribution using the transfer amounts speciﬁed in the CARES Act, which came into

operation in mid-April. In particular, we target the sum of three key components of the

Act: $293 billion to provide one-time tax rebates to individuals; (ii) $268 billion to expand

unemployment beneﬁts; and (iii) $150 billion in transfers to state and local governments.

These three components of the CARES Act consist of around 3.4 percent of GDP. Given

our calibration of steady-state government transfers, this in turn amounts to an increase

in transfers of 26.8 percent.

In our baseline exercise of transfer policy, we assume that

the total amount of transfer is equally distributed over six months—that is, three periods.

A key component of our calibration is how we choose the shock sizes. The size of

the three shocks (η

, η

, ξ

H,t

) are estimated to match the dynamics, under the monetary

regime without transfer policy, of total hours for both the HTM and Ricardian sectors

and inﬂation for the HTM sector, as given in our motivating Figure 1. In our baseline

calibration, we assume that the three shocks in the model are over after three periods.

across 10 categories of goods and services. Since we only have two sectors in the model, we set an elasticity

slightly below 1 as the baseline. Then, in a sensitivity analysis, we do an alternate calibration of 1.2.

This value of α is the same if we assume households in the bottom 20 percentile of the income distribu-

tion as HTM households and target their consumption share for these sectors. For this reason, we modeled

the same consumption basket for the two households.

In a sensitivity analysis we drop the tax rebate component of the CARES Act while calibrating the

transfer increase.

In particular, we set the size of HTM sector labor supply shocks to match BLS total

hours changes from April through August in HTM sectors (retail trade, transportation

and warehousing, and leisure and hospitality sectors). We then calibrate the size of the

preference shocks to match BLS total hours changes for sectors excluding HTM sectors,

also from April through August. Finally, we set the size of HTM sector-speciﬁc demand

shocks to match the PCE inﬂation for recreation, transportation, and food services sectors

from the U.S. Bureau of Economic Analysis. The three shocks series can perfectly match

the dynamics of total hours and inﬂation from April through August, as reported in detail

in Panel A of Appendix Table B.1.

Moreover, Panel B of Table B.1 shows that our calibration is also reasonable at match-

ing several non-targeted moments. For example, our model-implied dynamics of aggre-

gate output is quite close to the data, even though we did not use any output data in our

calibration. Moreover, model dynamics of consumption in the HTM sector is also fairly

close to the dynamics of the real PCE data, even though our calibration only targets the

dynamics of PCE inﬂation for the HTM sector.

3.3 Quantitative Results

We now present quantitative results on positive and normative implications of redistri-

bution policy during a crisis.

3.3.1 Dynamic Effects of Transfer Policy

We show how key variables evolve over time in response to the COVID shocks—a com-

bination of aggregate and sector-speciﬁc demand and supply shocks as discussed above.

We then illustrate the effects of an increase in transfers for the two regimes. These re-

sults are in Figure 2, which presents four different scenarios: the monetary regime with

and without transfers to the HTM households and the ﬁscal regime with and without

transfers. As mentioned before, we calibrate the COVID shocks to match the targeted

moments under the monetary regime in the absence of transfers. This case thus serves as

our baseline. Throughout, the duration of the redistribution policy is three periods (six

months), which coincides with the duration of the shocks.

Since the transfer payments from the CARES Act started in mid-April while our calibration strategy

matches model dynamics without transfer policy to the data, there is a slight mismatch between the data

and model counterparts, especially for August.

We solve the model non-linearly under perfect foresight. All the model variables converge back to the

steady state in the long run.

0 2 4 6 8 10 12

-20

-15

-10

-5

0 2 4 6 8 10 12

-8

-6

-4

-2

0 2 4 6 8 10 12

-15

-10

-5

0 2 4 6 8 10 12

-10

-5

0 2 4 6 8 10 12

-6

-4

-2

0 2 4 6 8 10 12

-5

0 2 4 6 8 10 12

0.002

0.004

0.006

0.008

0.01

0 2 4 6 8 10 12

Figure 2: Redistribution Policy with Different Policy Regimes

Notes: This ﬁgure shows dynamics of key variables in response to the COVID shocks under different

regimes. Blue solid lines represent the baseline case: the monetary regime without transfers. Red dashed

lines, green dotted lines, and orange dashed lines represent respectively the ﬁscal regime without trans-

fers, the monetary regime with transfers, and the ﬁscal regime with transfers.

In the baseline, where the policymakers just stick to the usual policy, the COVID

shocks generate signiﬁcant short-run contractions in aggregate output and household

consumption of both types, as shown by the solid blue lines in the ﬁrst row of the ﬁg-

ure. The contraction leads to a decline in inﬂation (as shown in the second row) and

in labor tax revenues, both of which in turn increase the real value of government debt.

The government responds by increasing the tax rate to stabilize debt under this standard

monetary regime. Meanwhile, the central bank decreases the nominal interest rate in re-

sponse to the decline in inﬂation. These policy responses are shown in the bottom row of

the ﬁgure. Notice that the ZLB binds in our model during the pandemic.

Now, let us introduce the redistribution program to the monetary regime baseline

case, the results of which are shown by the dotted green lines in Figure 2.

Overall, the

As we discussed in the calibration section, transfers increase by 26.8 percent in total, and here, they are

effects of the redistribution program are largely in line with what we have shown using

the simple model in Section 2. One major difference from the simple model is that the

redistribution program is more expansionary here because both the classical labor supply

channel and the Keynesian channel operate thanks to nominal rigidities, as we discussed

in Section 2.3.

Clearly, transfers increase HTM household consumption and decrease Ricardian house-

hold consumption (due to the resulting increase in the tax rate) relative to the baseline.

These are the direct effects of the redistribution. As discussed in Section 2, however, the

redistribution program is inﬂationary, as shown by the difference between the solid blue

lines and the dotted green lines in the second row. This indirectly has a positive effect on

household consumption of both types through general equilibrium. In particular, the de-

cline of Ricardian household consumption caused by the redistribution is very small, and

in fact in this parameterization it is nearly indistinguishable visually from the baseline

case.

Let us now turn to the ﬁscal regime where neither the tax rate nor the nominal inter-

est rate changes. The results for this case are shown by the red (without transfers) and

orange (with transfers) lines in Figure 2. The COVID shocks are also contractionary in

this regime, and, moreover, redistribution leads to an increase in HTM consumption as

well as aggregate output.

In this ﬁscal regime, the main aspect we want to highlight

is that aggregate output and consumption of both types do not drop as much as in the

monetary regime. There are three main reasons, which all also help us understand how

the transmission of shocks and transfer policy is different in this regime.

First, irrespective of whether there is redistribution or not, the ﬁscal regime generates

greater and more persistent inﬂation than the monetary regime, as that stabilizes the real

value of government debt without relying on labor taxes. Due to nominal rigidities, this

in turn has larger and longer-lasting positive effects on output and consumption of both

types, as presented in the ﬁrst row of Figure 2. Second, as shown in the simple model

in Section 2.2.2, the redistribution program is more inﬂationary in the ﬁscal regime than

in the monetary regime. This result is illustrated in the second row of the ﬁgure. The

ﬁfth and sixth panels reveal that the gap between the orange and red lines is greater than

that between the green and blue lines. Finally, the ZLB binds in the monetary regime

as we discussed above, which prevents the central bank from decreasing the policy rate

according to the monetary policy rule, and leads to a bigger drop in the monetary regime

evenly distributed over three periods.

In contrast to the monetary regime, redistribution actually increases Ricardian consumption in the ﬁscal

regime as the aforementioned indirect effect on consumption through inﬂation dominates the direct effect

in our calibration. This result, however, is difﬁcult to see in the ﬁgure. We revisit it in Section 3.3.2.

with the shocks. This mechanism is not relevant for the ﬁscal regime.

3.3.2 Transfer Multipliers

As a way to summarize these dynamic responses with and without redistribution policy,

we now present results in terms of transfer multipliers for output and consumption.

The transfer multiplier for output, for instance, under regime i ∈ {M, F} is deﬁned as

(Y) =

∑

h=0

(

− Y

)

∑

h=0

where

is output at horizon h under i-regime with transfers, Y

is output at horizon

h under the monetary regime without transfers (i.e. the baseline), and s

is transfers at

horizon h. The multipliers for Ricardian sector output and the two consumption under i-

regime—denoted respectively by M

), M

) and M

)—are similarly deﬁned.

Following the government spending multiplier literature, we consider impact multiplier

(t = 0) as well as 2–year (t = 12) and 4–year (t = 24) cumulative multipliers, which

allows for a consideration of dynamic effects in the model.

Note that in calculating these multipliers, our baseline case, as in Section 3.3.1, is al-

ways the monetary regime without transfers. This is the most interesting case to study, as

we want to study the following question: Given a transfer policy we want to implement,

what are the differences if conventional labor taxes or inﬂation taxes are used to ﬁnance

the resulting increase in government debt?

Table 2: Transfer Multipliers

Monetary Regime Fiscal Regime

(Y) M

) M

(Y) M

) M

)

Impact Multipliers 1.175 1.538 -0.205 5.692 3.983 5.272 2.418 9.105

2-Year Cumulative Multipliers 1.154 1.450 -0.217 5.641 7.289 8.884 5.607 12.796

4-Year Cumulative Multipliers 1.126 1.417 -0.244 5.609 7.739 9.408 6.036 13.311

Notes: This table shows the transfer multipliers under the monetary and ﬁscal regimes. M

(X) represent the cumulative

transfer multiplier of variable X at t-horizon under i regime. We report impact multipliers (t = 0) as well as 2–year

(t = 12) and 4–year (t = 24) cumulative multipliers when the government distributes transfers evenly over 6 months.

Table 2 shows that aggregate output and Ricardian sector output multipliers are both

above 1 in the monetary regime. The binding ZLB and sticky prices play an important

role in this result.

Moreover, the C

multiplier is above the simple model benchmark of

(1/λ), which would be 4.35 according to our calibration.

In the simple model, we showed analytically that the Ricardian sector output multiplier is below 1.

Table 2 also shows that those multipliers are even higher in the ﬁscal regime, even

though the ZLB is binding in our simulations under the monetary regime. In fact, uniquely,

even the C

multiplier is now positive in the ﬁscal regime, which is different from the

monetary regime.

The persistent inﬂation dynamics in this regime lead to persistent

real effects due to sticky prices, which contributes to these higher multipliers. Later, in

Section 3.4.1, we delve more deeply into the mechanisms that produce such large differ-

ences in the multipliers between the two regimes.

3.3.3 Welfare Effects of Transfer Policy

We ﬁnally show the effects on household welfare of the recession created by the COVID

shocks under the four different scenarios discussed above. In particular, we consider

both short- and long-run welfare effects. To this end, we implicitly deﬁne our measure of

welfare gain for household of type i ∈ {R, H} , µ

t,k

, as

∑

j=0



, L



∑

j=0



1 + µ

t,k



where





is the steady-state level of type-i household’s consumption and hours,

and

, L

are the time path of type-i household’s consumption and hours under the

different transfer duration policies (indexed by k). In this way, µ

t,k

measures welfare gains

from period 0 till (arbitrary) period t in units of a percentage of the steady-state (or pre-

COVID) level of consumption—when the redistribution program lasts for k periods.

The lifetime (total) welfare gain is then measured by µ

∞,k

≡ lim

t→∞

t,k

, often the focus

of the business cycle literature. Recall that, unless otherwise noted, we report the case in

which k=3; that is, the duration of the redistribution coincides with the duration of the

shocks.

We ﬁnd that whether the government introduces the redistribution program and how

it is ﬁnanced make a very small difference for the lifetime welfare for both types of house-

holds. This result is presented in Table 3. For example, the redistribution program ﬁ-

nanced by inﬂation taxes, that is the ﬁscal regime, increases the HTM households’ life-

time welfare by 0.198 percentage point and increases the Ricardian households’ lifetime

welfare by 0.070 percentage point, compared to the baseline. This result is expected be-

cause the COVID shocks under consideration are short-lived, which implies the recession

In the simple model where inﬂation is neutral for real variables, we showed analytically that this mul-

tiplier is negative.

It thus measures welfare gains at the point when the agents are t periods, or 2xt months, old since the

initial COVID shocks.

Table 3: Welfare Gains

Monetary Regime Fiscal Regime

Transfer Distribution Long-run Short-run

(t = 4)

Long-run Short-run

(t = 4)

Ricardian Household -0.012 -0.819 0.070 1.131

HTM Household 0.074 3.386 0.198 5.600

Notes: This table shows long- and short-run welfare gains resulting from the redistribution, compared to

the baseline. The values are the difference in the welfare measure (µ

t,k

) between the transfer cases (under

the two regimes) and the baseline case (the monetary regime without transfers). In the latter case, the

long-run welfare gains for the Ricardian households and for the HTM households are -0.439 and -0.202

percent of the steady-state level of consumption respectively.

is only a small bump in the lifetime.

What is more interesting are the welfare effects in the short run, which are presented

in detail in Figure 3. We ask two different, yet related questions. First, taking as given the

redistribution program enacted, what is the better way to ﬁnance it? Second, should the

government enact the redistribution policy at all?

On the ﬁrst question, we ﬁnd that, taking the redistribution program as given, inﬂa-

tion taxes, as used in the ﬁscal regime, produce far better welfare outcomes than labor

taxes, as used in the monetary regime. For example, at the point when the pandemic is

over (at t = 4), as given in Table 3, the redistribution program, ﬁnanced by inﬂation taxes

(i.e., the ﬁscal regime), would have increased the welfare of the HTM households and

that of the Ricardian households by 5.6 percentage points and 1.131 percentage points,

respectively, compared to the baseline. This result on the welfare gains under the ﬁscal

regime can be inferred from the second and third panels of Figure 3.

In contrast, if

the government relied on labor taxes, the HTM households’ welfare gain resulting from

the redistribution would amount to 3.386 percentage points of the steady-state level of

consumption at the end of the pandemic. Therefore, labor-tax ﬁnanced transfers are less

effective. Moreover, the redistribution now decreases the welfare of the Ricardian house-

holds by 0.819 percentage point, as these households work more hours with little change

in consumption.

We now consider the second question—that is, whether the redistribution policy is de-

sirable at all. The answer is obviously that it depends. Figure 3 shows that the inﬂation-

ﬁnanced redistribution program under the ﬁscal regime beneﬁts the HTM households the

We shut down all shocks other than the three-period COVID shocks over the lifetime. Therefore, this

exercise is different from the usual ones in the business cycle literature.

Speciﬁcally, the welfare improvements over the baseline case can be obtained by taking the difference

between the orange lines and the blue lines (the baseline).

0 2 4 6 8 10 12

-20

-15

-10

-5

0 2 4 6 8 10 12

-20

-15

-10

-5

0 2 4 6 8 10 12

-20

-15

-10

-5

Figure 3: Short-Run Welfare Gains Comparison

Notes: This ﬁgure presents the short-run welfare gains under the four different scenarios, showing µ

t,k

as a function of t. The numbers are in units of a percentage of the steady-state level of consumption.

most, but it is not the best option for the Ricardian households. But if the policy objec-

tive was simply to maximize the aggregate welfare, which is not likely the most realistic

case, the redistribution program by itself would do very little given the policy regime in

this model, as shown in the ﬁrst panel of Figure 3. With transfer payments, in either

policy regime, the HTM households would consume more, which would also lead to an

increase in aggregate output. At the same time, the Ricardian households would have to

work more for two reasons. The ﬁrst reason is to produce more output. The second rea-

son is that inﬂation created by the redistribution generates resource misallocation, which

increases labor hours required to produce a given amount of output, as shown in Equa-

tion (3.1). In our calibration here, these two welfare effects almost cancel each other out

in both regimes.

3.4 Extensions and Sensitivity Analysis

We now consider some important extensions and sensitivity analysis.

3.4.1 Inspecting the Mechanisms of Transfer Multipliers

As our main extension, we do several exercises to inspect the mechanisms that drive

transfer multipliers across the two regimes. First, we decompose the transfer multiplier

into three different components in Table 4, where in this decomposition, the output mul-

tiplier, for instance, under regime i ∈ {M, F} is

(Y) =

∑

h=0

(

−

no shock,h

)

∑

h=0

| {z }

COVID Effect with Transfer

∑

h=0

(

no shock,h

−

∑

h=0

| {z }

Transfer Effect without COVID Shocks

−

∑

h=0

−

∑

h=0

| {z }

COVID Effect without Transfer

(3.2)

where

is output at horizon h under i-regime with both transfers and COVID shocks,

no shock,h

is output at horizon h under i-regime with transfers, but without COVID shocks,

is output at horizon h under the monetary regime with COVID shocks, but without

transfers,

Y is output at steady-state, and s

is transfers at horizon h. Note that the third

effect is the same across regimes, while the ﬁrst two are different as they compute the

effect for a given regime.

Table 4: Transfer Multipliers Decomposition

Monetary Regime Fiscal Regime

(Y) M

) M

(Y) M

) M

)

Panel A: Impact Multipliers

Total Effect 1.175 1.538 -0.205 5.692 3.983 5.272 2.418 9.105

COVID Effect with Transfer -14.982 -6.446 -16.435 -10.226 -12.920 -3.589 -14.523 -7.671

Transfer Effect without COVID 0.742 0.867 -0.597 5.125 1.488 1.743 0.115 5.984

COVID Effect without Transfer -15.415 -7.117 -16.827 -10.793 -15.415 -7.117 -16.827 -10.793

Panel B: 2-Year Cumulative Multipliers

Total Effect 1.154 1.450 -0.217 5.641 7.289 8.884 5.607 12.796

COVID Effect with Transfer -14.161 -8.455 -15.090 -11.123 -8.493 -1.568 -9.711 -4.504

Transfer Effect without COVID 1.007 1.178 -0.344 5.430 1.474 1.725 0.101 5.967

COVID Effect without Transfer -14.308 -8.727 -15.217 -11.333 -14.308 -8.727 -15.217 -11.333

Panel C: 4-Year Cumulative Multipliers

Total Effect 1.126 1.417 -0.244 5.609 7.739 9.408 6.036 13.311

COVID Effect with Transfer -14.655 -9.030 -15.561 -11.688 -8.557 -1.643 -9.773 -4.578

Transfer Effect without COVID 0.960 1.123 -0.389 5.376 1.475 1.727 0.103 5.968

COVID Effect without Transfer -14.821 -9.324 -15.707 -11.921 -14.821 -9.324 -15.707 -11.921

Notes: This table shows the decomposition of the transfer multipliers for aggregate output, Ricardian sector output, Ricardian

consumption and HTM consumption, as given in Equation (3.2). M

(X) represent the cumulative transfer multiplier of variable

X at t-horizon under i regime. We report impact multipliers (t = 0) as well as 2–year (t = 12) and 4–year (t = 24) cumulative

multipliers.

As Table 4 shows, even without the COVID shocks, the transfer multipliers are higher

in the ﬁscal regime. This result is captured by the second component in Equation (3.2).

For example, this component of the impact multiplier for output is 1.488 under the ﬁscal

regime, while it is only 0.742 under the monetary regime. Moreover, uniquely in the ﬁscal

regime, the Ricardian consumption multiplier is positive (e.g. 0.115 on impact). The main

reason for these results is the high and persistent effects on inﬂation in the ﬁscal regime

induced by an increase in transfer, as shown in our analytical analysis.

We now consider the state-dependence of the transfer multipliers, ﬁrst within and

then across the regimes. First, in each of the two regimes, the transfer multipliers condi-

tional on no COVID shocks (i.e. the second component) are less than the total multipliers.

In the absence of the COVID shocks—that is, if the economy were in the steady state—

transfer-induced inﬂation, while boosting the economy, would also generate inefﬁcient

price dispersion, which in turn would lead to resource misallocations and decrease labor

productivity. However, if the economy were already in a COVID-recession, inﬂation-

ary pressures resulting from redistribution would actually counteract deﬂation due to the

COVID shocks, thereby decreasing, rather than increasing, the extent of such price dis-

persion. In addition, in the case of monetary regime, the ZLB is irrelevant with no COVID

shocks, which means that transfer-induced inﬂationary pressures do not lead to as strong

a boost in consumption as the real interest rate does not decrease strongly.

Second, comparing the two regimes, the transfer multipliers are more state-dependent

in the ﬁscal regime than in the monetary regime. That is, transfers are disproportionately

more effective in the ﬁscal regime than in the monetary regime when the economy falls

into a COVID-recession. The reason is that the aforementioned "counteracting" force is

much stronger in the ﬁscal regime that produces higher and more persistent inﬂation.

Table 4 shows that the large difference in the multipliers between the two regimes is

driven quantitatively by the ﬁrst component, which captures how the effectiveness of

transfers depends on the presence of COVID shocks. This is a measure of state depen-

dence.

Besides the state dependence, our quantitative model includes two additional features

that break the uniformity—obtained in the simple, analytical model—of the two regimes

in terms of the multipliers. They are nominal rigidities and distortionary labor taxes. In

order to isolate the role of these two features, we delve more into the second component

of the transfer multipliers in Equation (3.2) through counterfactual exercises.

For reference, Panel A of Table 5 ﬁrst re-reports the second component in the presence

of the two features.

We then remove nominal rigidities (in Panel B) and further remove

distortionary labor taxes (in Panel C). The last version then is quite close to our simple,

analytical model. This exercise thus progressively allows an analysis of which elements

are responsible for differences between the simple and the quantitative model results—

besides the COVID shocks.

Panel B of Table 5 shows that the multipliers decrease substantially with ﬂexible prices,

We can see this in the ﬁfth panel of Figure 2. Without transfer, as shown by the blue line, the COVID

shocks generate a signiﬁcant deﬂation, which can be undone by inﬂation-ﬁnanced transfers (shown by the

orange line).

The values in the panel are thus the same as those in the third row of each panel of Table 4

Table 5: Transfer Multipliers without COVID Shocks

Monetary Regime Fiscal Regime

(Y) M

) M

(Y) M

) M

)

Panel A: Without COVID Shocks under sticky price

Impact Multipliers 0.742 0.867 -0.597 5.125 1.488 1.743 0.115 5.984

2-Year Cumulative Multipliers 1.007 1.178 -0.344 5.430 1.474 1.725 0.101 5.967

4-Year Cumulative Multipliers 0.960 1.123 -0.389 5.376 1.475 1.727 0.103 5.968

Panel B: Without COVID Shocks under ﬂexible price

Impact Multipliers 0.465 0.543 -0.861 4.807 0.465 0.543 -0.861 4.807

2-Year Cumulative Multipliers 0.214 0.251 -1.101 4.520 0.465 0.543 -0.861 4.807

4-Year Cumulative Multipliers 0.095 0.111 -1.215 4.383 0.465 0.543 -0.861 4.807

Panel C: Without COVID Shocks under ﬂexible price and lump-sum tax adjustment

Impact Multipliers 0.465 0.543 -0.861 4.807 0.465 0.543 -0.861 4.807

2-Year Cumulative Multipliers 0.465 0.543 -0.861 4.807 0.465 0.543 -0.861 4.807

4-Year Cumulative Multipliers 0.465 0.543 -0.861 4.807 0.465 0.543 -0.861 4.807

Notes: This table shows the transfer multipliers without COVID shocks. Panel A reports multipliers under sticky prices

and distortionary labor taxes. Panels B reports multipliers under ﬂexible prices and distortionary labor taxes. Panels

C reports multipliers under ﬂexible prices and non-distortionary lump-sum taxes. M

(X) represent the cumulative

transfer multiplier of variable X at t-horizon under i regime. We report impact multipliers (t = 0), 2–year (t = 12), and

4–year (t = 24) cumulative multipliers.

as is often also found in the government spending multiplier literature. In fact, now

the impact multipliers are the same across the regimes, as was the case in our simple,

analytical model, as different inﬂation dynamics do not affect real allocations. Moreover,

output multipliers are now below 1, the Ricardian consumption multiplier is negative,

and the HTM consumption multiplier is close to 4.35, the analytical model solution.

The

cumulative multipliers are different from the impact multiplier in the monetary regime—

unlike the simple, analytical model—due to dynamics of distortionary labor taxes.

To make this clear, Panel C of Table 5 shows the case where the increase in transfers

are ﬁnanced by lump-sum taxes on the Ricardian household. Then, all the multipliers are

the same across the regimes and over horizons, as in the simple, analytical model.

3.4.2 Sensitivity Analysis

As our ﬁrst sensitivity exercise, we do additional analysis related to the length of the

transfer policy. So far, transfer policy duration coincided with the length of the COVID

shocks—that is, six months. We now show results for three different durations of redistri-

The solution for multipliers in the simple model that we derive would predict a Ricardian sector output

multiplier of 0.644 and Ricardian consumption multiplier of -0.464. Note that the simple model imposes

log utility and is also a one-sector environment.

bution policy: The program lasts for 2, 6, and 12 months. This exercise can be important,

as our model features HTM households. Moreover, the timing of transfers can also matter

because there are distortionary labor taxes in the model and also when the economy is at

ZLB under the monetary regime. For the different durations of the program, we ﬁx the

present value of transfers to be the same, which implies that the amount of transfers each

period is smaller when the program lasts longer.

Appendix Figures B.1 and B.2 present the responses of the variables with different du-

ration of the redistribution program under the monetary and ﬁscal regimes, respectively.

We ﬁnd that the results are overall quite similar across different lengths of the redistribu-

tion policy, except for the responses of HTM household consumption. The second panel

of the ﬁgures shows that the difference in HTM household consumption between the no-

transfer and transfer cases, for obvious reasons, is more evenly distributed across time

periods when the duration of the program is longer. Appendix Table B.2 presents the

multiplier results under different duration of transfer policy. The multipliers are higher

under the monetary regime when transfer is distributed over a longer duration. For the

ﬁscal regime, the cumulative multipliers, which capture dynamics in the model, are rela-

tively insensitive to the duration of transfer policy.

We next do sensitivity analysis with respect to two assigned parameters. We ﬁrst con-

sider a cross-sector elasticity of substitution (ε) greater than 1, equal to 1.2. Our baseline

parameterization was 0.8. Next, we consider a different parameterization of the tax rule

response coefﬁcient (ψ

) under the M regime. Compared to our baseline choice of 0.6,

we now set it at 0.1, such that labor tax rates respond less strongly to debt.

In these

exercises, we keep the rest of the parameters the same as the baseline.

Appendix Figure B.3 presents the responses of the variables with and without transfer

policy when ε = 1.2, while Table B.4 presents the transfer multipliers when ε = 1.2.

Overall, the results are similar to our baseline results. One noticeable difference is that as

the sectoral goods are more substitutable now, the consumption multiplier for the HTM

household is lower while that for the Ricardian household is higher.

Appendix Figure B.4 present the responses of the variables with and without transfer

policy when ψ

= 0.1 under the monetary regime, while Appendix Table B.5 presents

the transfer multipliers when ψ

= 0.1. The results are very similar to our baseline re-

sults. One noticeable difference is that as labor tax rates increase less strongly, under the

Appendix Table B.3 presents welfare results. Consistent with the multiplier results, in the monetary

regime, the longer duration transfer policy leads to welfare improvement for both the households.

This is in line with the estimates in Bhattarai, Lee and Park (2016), which however did not have distor-

tionary labor taxes.

These different sensitivity analysis exercises thus will not match the targeted moments anymore.

monetary regime, the multipliers are somewhat higher.

Finally, Appendix Table B.6 presents the transfer multipliers when we exclude $600

individual tax rebates in the CARES Act from our transfer experiment. The main motiva-

tion is the survey ﬁnding in Coibion, Gorodnichenko and Weber (2020) that on average,

only about 40% of tax rebates appears to have been spent by households. The size of

transfer change decreases from 26.8% to 15.7% when we exclude the individual tax re-

bates.

Table B.6 shows that the multipliers are essentially the same as before under the

monetary regime. For the ﬁscal regime however, the multipliers are even bigger. This is

another example of state dependence of multipliers, where the results differ by the size

of the change in transfers. The decomposition shows that this is driven by the higher

marginal effectiveness of transfers with COVID shocks in this regime.

4 Conclusion

Our paper makes clear that how transfers are ultimately ﬁnanced is a ﬁrst-order issue for

their effectiveness. It arguably matters more than other factors identiﬁed in the literature,

which typically reports moderate transfer multipliers. We show that inﬂation-ﬁnanced

transfers are signiﬁcantly more effective than tax-ﬁnanced transfers in boosting the econ-

omy and improving welfare. Such an inﬂation-ﬁnanced transfer program can be imple-

mented by a ﬁscal authority committing itself to no tax adjustments in the foreseeable fu-

ture, coupled with an accommodative monetary authority. We call such a ﬁscal-monetary

policy mix the ﬁscal regime—in contrast to the (conventional) monetary regime where

monetary policy stabilizes inﬂation.

We ﬁrst consider a simple two-agent model that permits analytical results and illumi-

nates the mechanism through which redistribution generates inﬂation in the two policy

regimes. In particular, the ﬁscal regime produces high and persistent inﬂation through

the direct and the indirect (that we also called the interest rate or valuation) channels. In

comparison, inﬂation is lower and shorter lived in the monetary regime. We then build

on the analytical results and proceed to a quantitative analysis in a two-sector extension.

Our quantitative exercise shows that inﬂation-ﬁnanced transfers ﬁght deﬂationary pres-

sures in a COVID-recession-like environment, thereby preventing output and consump-

tion from dropping signiﬁcantly. Such inﬂation-induced expansionary effects are so large

For the ﬁscal regime, the only reason the multiplier results are different from our baseline is that the

monetary regime under no transfers now has different dynamics.

Other than changing the size of the transfer increase, this does not affect our parameterization as we

calibrate the economy in the absence of transfer policy.

that redistribution can in fact produce a Pareto improvement.

In future work, we can take additional steps in several directions. First, the model may

be extended to feature a richer form of heterogeneity across sectors as well as households

and, in addition, more elaborate matching between sectors and households. Although

we expect that our main argument will hold in such a complex environment, it will be

interesting to see whether such an extension affects the quantitative results signiﬁcantly.

Second, while our analysis suggests a clear path for the success of a redistribution policy,

the Great Recession taught policymakers that generating inﬂation during, and in the after-

math of, a severe recession is easier said than done, possibly due to credibility problems.

Relatedly, implementation would not be as straightforward in an environment where eco-

nomic agents take into account the possibility of regime switching by policymakers when

the recession is over, as suggested in this paper. We leave a more comprehensive analysis

of such interesting issues for future research.

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APPENDIX

A Data Appendix

Employment and Total Hours. We use total employment and total hours data from

U.S. Bureau of Labor Statistics. We deﬁne HTM sector as the sum of the following three

sectors: Retail Trade (NAICS 44–45), Transportation and Warehousing (NAICS 48–49),

and Leisure and Hospitality (NAICS 71–72).

Consumption and Inﬂation. We use real Personal Consumption Expenditure (PCE)

data and PCE inﬂation from U.S. Bureau of Economic Analysis. We deﬁne HTM sec-

tor as the sum of the following three sectors: Transportation services, Recreation services,

and Food services and accommodations.

We also use 2019 Consumer Expenditure Surveys (CEX) data to calibrate both Ricar-

dian and HTM households’ share parameters in the consumption baskets. We assume

households in the top 80 percentile income distribution as Ricardian households and

match their consumption share for transportation, entertainment, and food away from

home. Similarly, we assume households in bottom 20 percentile income distribution as

HTM households and match their consumption share for these three sectors.

Fiscal Variables. We use government current transfer payments (A084RC1Q027SBEA

in FRED) to calibrate steady-state transfers to GDP ratio. We also use federal debt held

by the public data (FYGFDPUN in FRED) to calibrate debt to GDP ratio. Finally, we

use compensation of employees, paid: wages and salaries (A4102C1Q027SBEA in FRED),

proprietors’ income (PROPINC in FRED), and federal government current receipts: con-

tributions for government social insurance (W780RC1Q027SBEA in FRED) data to cali-

brate steady-state labor tax revenue to GDP ratio. The sample period for these variables

is from 1990Q1 through 2020Q1.

Transfer Distribution from CARES Act. We calibrate the size of transfer distribution

using the transfer amounts speciﬁed in Coronavirus Aid, Relief and Economy Security

Act (CARES Act), which came into operation in mid–April. In particular, we target the

sum of three key components of the Act: $293 billion to provide one-time tax rebates to

individuals; (ii) $268 billion to expand unemployment beneﬁts; (iii) $150 billion in trans-

fers to state and local governments. These three components of the CARES Act consist of

around 3.4 percent of GDP. In a sensitivity analysis, we count only components (ii) and

(iii) above.

B Appendix Tables and Figures

Appendix Table B.1: Data and Model Moments

Time Data Model

Panel A: Targeted moments (percent deviation from January)

Total Hours for retail, transportation, leisure/hospitality April -16.7% -16.7%

June -18.8% -18.8%

August -13.2% -13.2%

Total Hours excluding retail, transportation, leisure/hospitality April -6.58% -6.58%

June -8.57% -8.57%

August -6.13% -6.13%

PCE Inﬂation for recreation, transportation, food services April -0.99% -0.99%

June -0.39% -0.39%

August -0.37% -0.37%

Panel B: Non-targeted moments (percent deviation from January)

PCE Inﬂation excluding recreation, transportation, food services April -0.14% -6.30%

June -0.06% -2.29%

August 0.74% -0.12%

Real PCE for recreation, transportation, food services April -41.1% -16.7%

June -37.6% -18.8%

August -25.2% -13.2%

Real PCE excluding recreation, transportation, food services April -7.74% -9.98%

June -3.78% -11.6%

August -1.06% -8.69%

Real GDP (percent deviation from Q1) Q2 -8.99% -12.8%

Q3 -2.25% -0.07%

Notes: This table shows moments of the data and simulated series from the baseline model parameterized at the

values in Table 1. Panel A shows targeted moments and Panel B shows non-targeted moments. Data moments are

expressed as the percent deviation from the average values of outcome variables in January and February.

Appendix Table B.2: Multipliers with Different Transfer Distribution

Monetary Regime Fiscal Regime

Transfer Duration k = 1 k = 3 k = 6 k = 1 k = 3 k = 6

Panel A: Impact multiplier

(Y) 1.074 1.175 1.862 2.047 3.983 6.799

) 1.417 1.538 2.434 2.732 5.272 8.979

) -0.301 -0.205 0.439 0.606 2.418 5.053

) 5.575 5.692 6.520 6.766 9.105 12.514

Panel B: 2-year cumulative multiplier

(Y) 1.072 1.154 1.718 7.323 7.289 7.121

) 1.414 1.450 2.080 8.998 8.884 8.629

) -0.303 -0.217 0.326 5.630 5.607 5.453

) 5.572 5.641 6.277 12.865 12.796 12.578

Panel C: 4-year cumulative multiplier

(Y) 1.035 1.126 1.749 7.778 7.739 7.550

) 1.371 1.417 2.116 9.528 9.408 9.130

) -0.338 -0.244 0.355 6.065 6.036 5.863

) 5.530 5.609 6.312 13.386 13.311 13.070

Notes: This table shows the transfer multipliers with different duration of transfer distribution under

different regimes (monetary and ﬁscal regimes). M

(X) represent the cumulative transfer multiplier of

variable X at t-horizon under i regime. Panel A shows impact multipliers and Panels B and C present

two-year and four-year cumulative multipliers, respectively. We consider three cases of different dura-

tion of transfer distribution: 2-month (k = 1), 6-month (k = 3), and 12-month (k = 6).

Appendix Table B.3: Long-run Welfare Gains

Monetary Regime Fiscal Regime

Transfer Duration k = 1 k = 3 k = 6 k = 1 k = 3 k = 6

Ricardian Household -0.011 -0.012 -0.002 0.079 0.070 0.063

HTM Household 0.048 0.074 0.090 0.172 0.198 0.202

Notes: This table shows the long-run welfare gains for the models with different regimes and horizons of

transfer distributions. The numbers represent the percentage point deviations from the welfare gains

under monetary regime without transfers. We consider three cases of different duration of transfer

distribution: 2-month (T = 1), 6-month (T = 3), and 12-month (T = 6).

Appendix Table B.4: Transfer Multipliers (k = 3, ε = 1.2)

Monetary Regime Fiscal Regime

(Y) M

) M

(Y) M

) M

)

Impact Multipliers 1.086 1.262 -0.105 4.983 5.222 6.119 4.474 7.671

2-Year Cumulative Multipliers 1.072 1.220 -0.123 4.983 9.306 10.475 8.951 10.469

4-Year Cumulative Multipliers 1.044 1.189 -0.153 4.964 9.885 11.112 9.588 10.859

Notes: This table shows the transfer multipliers for the models under monetary and ﬁscal regimes when ε = 1.2. M

(X)

represent the cumulative transfer multiplier of variable X at t-horizon under i regime. We report impact multipliers,

two-year, and four-year cumulative multipliers when government distributes transfers equally over 6 months.

Appendix Table B.5: Transfer Multipliers (k = 3, ψ

= 0.1 )

Monetary Regime Fiscal Regime

(Y) M

) M

(Y) M

) M

)

Impact Multipliers 1.184 1.549 -0.196 5.703 4.023 5.324 2.456 9.154

2-Year Cumulative Multipliers 1.262 1.577 -0.114 5.766 6.957 8.497 5.290 12.415

4-Year Cumulative Multipliers 1.262 1.577 -0.114 5.766 7.363 8.971 5.677 12.881

Notes: This table shows the transfer multipliers for the models under monetary and ﬁscal regimes when ψ

= 0.1. M

(X)

represent the cumulative transfer multiplier of variable X at t-horizon under i regime. We report impact multipliers, two-

year, and four-year cumulative multipliers when government distributes transfers equally over 6 months.

Appendix Table B.6: Transfer Multipliers (k = 3, Excluding $600 Individual Tax Rebates)

Monetary Regime Fiscal Regime

(Y) M

) M

(Y) M

) M

)

Panel A: Impact Multipliers

Total Effect 1.173 1.532 -0.206 5.689 5.775 7.625 4.096 11.272

COVID Effect with Transfer -25.878 -11.478 -28.329 -17.855 -22.039 -6.278 -24.755 -13.148

Transfer Effect without COVID 0.738 0.862 -0.601 5.120 1.500 1.754 0.127 5.996

COVID Effect without Transfer -26.314 -12.149 -28.724 -18.423 -26.314 -12.149 -28.724 -18.423

Panel B: 2-Year Cumulative Multipliers

Total Effect 1.154 1.448 -0.216 5.641 11.376 13.807 9.490 17.549

COVID Effect with Transfer -24.280 -14.629 -25.850 -19.139 -14.546 -2.840 -16.610 -7.790

Transfer Effect without COVID 1.010 1.180 -0.341 5.433 1.498 1.751 0.124 5.993

COVID Effect without Transfer -24.424 -14.897 -25.975 -19.346 -24.424 -14.897 -25.975 -19.346

Panel C: 4-Year Cumulative Multipliers

Total Effect 1.127 1.415 -0.242 5.609 12.172 14.735 10.251 18.463

COVID Effect with Transfer -25.136 -15.627 -26.668 -20.12 -14.631 -2.939 -16.691 -7.887

Transfer Effect without COVID 0.963 1.125 -0.386 5.379 1.504 1.758 0.130 6.000

COVID Effect without Transfer -25.299 -15.917 -26.811 -20.350 -25.299 -15.917 -26.811 -20.350

Notes: This table shows the transfer multipliers for the models under monetary and ﬁscal regimes when we exclude $600 individual

tax rebates from our transfer experiment. The total value of transfer distribution to GDP ratio decreases from 26.8% to 15.7% when we

exclude the individual tax rebates. M

(X) represent the cumulative transfer multiplier of variable X at t-horizon under i regime. We

report impact multipliers, 2-year, and 4-year cumulative multipliers when government distributes transfers equally over 6 months.

0 2 4 6 8 10 12

-20

-15

-10

-5

0 2 4 6 8 10 12

-8

-6

-4

-2

0 2 4 6 8 10 12

-15

-10

-5

0 2 4 6 8 10 12

-10

-8

-6

-4

-2

0 2 4 6 8 10 12

-6

-4

-2

0 2 4 6 8 10 12

-5

0 2 4 6 8 10 12

0.005

0.01

0 2 4 6 8 10 12

Appendix Figure B.1: Monetary Regime: Different Duration of Redistribution Policy

Notes: This ﬁgure shows dynamics of key variables in response to the COVID shocks under monetary

regime with different duration of transfer distribution. Blue solid lines represent the baseline model

without transfers. Red dashed lines represent the case of one-time transfer distribution. Green dotted

lines represent the case where the transfers are distributed over three-period (6 months) and orange

dashed lines represent the case where the transfers are distributed over six-period (12 months). We set

the total present value of transfer amounts are the same across different duration of distribution policy.

0 2 4 6 8 10 12

-20

-15

-10

-5

0 2 4 6 8 10 12

-5

0 2 4 6 8 10 12

-15

-10

-5

0 2 4 6 8 10 12

-6

-4

-2

0 2 4 6 8 10 12

-0.5

0.5

1.5

0 2 4 6 8 10 12

-5

0 2 4 6 8 10 12

-0.5

0.5

0 2 4 6 8 10 12

-1

-0.5

0.5

Appendix Figure B.2: Fiscal Regime: Different Duration of Redistribution Policy

Notes: This ﬁgure shows dynamics of key variables in response to the COVID shocks under ﬁscal regime

with different duration of transfer distribution. Blue solid lines represent the baseline model without

transfers. Red dashed lines represent the case of one-time transfer distribution. Green dotted lines

represent the case where the transfers are distributed over three-periods (6 months) and orange dashed

lines represent the case where the transfers are distributed over six-periods (12 months). We set the total

present value of transfer amounts are the same across different duration of distribution policy.

0 2 4 6 8 10 12

-20

-15

-10

-5

0 2 4 6 8 10 12

-10

-5

0 2 4 6 8 10 12

-15

-10

-5

0 2 4 6 8 10 12

-15

-10

-5

0 2 4 6 8 10 12

-6

-4

-2

0 2 4 6 8 10 12

-15

-10

-5

0 2 4 6 8 10 12

0.01

0.02

0.03

0.04

0 2 4 6 8 10 12

Appendix Figure B.3: Redistribution Policy with Different Policy Regimes (ε = 1.2)

Notes: This ﬁgure shows dynamics of key variables in response to the COVID shocks under different

regimes when ε = 1.2. Blue solid lines represent the baseline case: the monetary regime without trans-

fers. Red dashed lines, green dotted lines, and orange dashed lines represent respectively the ﬁscal

regime without transfers, the monetary regime with transfers, and the ﬁscal regime with transfers.

0 2 4 6 8 10 12

-20

-15

-10

-5

0 2 4 6 8 10 12

-8

-6

-4

-2

0 2 4 6 8 10 12

-15

-10

-5

0 2 4 6 8 10 12

-10

-5

0 2 4 6 8 10 12

-6

-4

-2

0 2 4 6 8 10 12

-5

0 2 4 6 8 10 12

0.002

0.004

0.006

0.008

0.01

0 2 4 6 8 10 12

Appendix Figure B.4: Redistribution Policy with Different Policy Regimes (ψ

= 0.1)

Notes: This ﬁgure shows dynamics of key variables in response to the COVID shocks under different

regimes when ψ

= 0.1. Blue solid lines represent the baseline case: the monetary regime without

transfers. Red dashed lines, green dotted lines, and orange dashed lines represent respectively the ﬁscal

regime without transfers, the monetary regime with transfers, and the ﬁscal regime with transfers.