The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Federal Reserve Bank of Chicago
Monetary and Fiscal Policies in Times of
Large Debt: Unity is Strength
Francesco Bianchi, Renato Faccini, and
Leonardo Melosi
REVISED
May 11, 2020
WP 2020-13
https://doi.org/10.21033/wp-2020-13
*
Working papers are not edited, and all opinions and errors are the
responsibility of the author(s). The views expressed do not necessarily
reflect the views of the Federal Reserve Bank of Chicago or the Federal
Reserve System.
Monetary and Fiscal Policies in Times of Large Debt:
Unity is Strength
Francesco Bianchi
Renato Faccini
Leonardo Melosi
Duke University
Danmarks Nationalbank
FRB Chicago
CEPR and NBER
Queen Mary, University of London
EUI and CEPR
Centre for Macroeconomics (LSE)
May 11, 2020
Abstract
The COVID pandemic found policymakers facing constraints on their ability to react to an exceptionally large negative shock. The current low interest rate environment
limits the tools the central bank can use to stabilize the economy, while the large public
debt curtails the e¢ cacy of …scal interventions by inducing expectations of costly …scal adjustments. Against this background, we study the implications of a coordinated
…scal and monetary strategy aiming at creating a controlled rise of in‡ation to wear
away a targeted fraction of debt. Under this coordinated strategy, the …scal authority
introduces an emergency budget with no provisions on how it will be balanced, while
the monetary authority tolerates a temporary increase in in‡ation to accommodate the
emergency budget. In our model the coordinated strategy enhances the e¢ cacy of the
…scal stimulus planned in response to the COVID pandemic and allows the Federal
Reserve to correct a prolonged period of below-target in‡ation. The strategy results
in only moderate levels of in‡ation by separating long-run …scal sustainability from a
short-run policy intervention.
JEL Codes: E50, E62, E30.
Keywords: Monetary policy, …scal policy, emergency budget, shock speci…c rule, COVID.
Emails: francesco.bianchi@duke.edu, rmmf@nationalbanken.dk, and lmelosi@frbchi.org. We thank
Jonas Fisher and Federico Ravenna for their very helpful suggestions. The views in this paper are solely those
of the authors and should not be interpreted as re‡ecting the views of the Federal Reserve Bank of Chicago,
Danmarks Nationalbank, or any person associated with the Federal Reserve System or the European System
of Central Banks.
1
Introduction
The COVID pandemic found policymakers facing constraints on their ability to react to an
exceptionally large negative shock. The current low interest rate environment limits the
tools the central bank can use to stabilize the economy following adverse shocks. The US
economy has experienced a prolonged period of below-target in‡ation and it is now back to
the zero lower bound as a result of the COVID shock. At the same time, the record high
debt level may curtail the e¢ cacy of …scal interventions by inducing expectations of costly
…scal adjustments. In January 2020, the Congressional Budget O¢ ce (CBO) estimated that,
under current law, Federal debt at the end of this decade would be higher as a percentage
of GDP than at any time since 1946. If no …scal adjustment is made, debt will continue to
increase and in 2050 will be higher than the highest level ever recorded in the United States.
High and increasing federal debt would reduce national saving and income, limit the ability
of policymakers to respond to unforeseen events, and increase the likelihood of a …scal crisis.
The recent …scal stimulus of $2.6 trillion dollars and the recession caused by the restrictive measures taken by authorities in many states to contrast the spreading of COVID-19
are exacerbating this already strained …scal situation. The debate over widening …scal imbalances, and what to do about them, is likely to move toward the center of the political
agenda after the pandemic crisis is over. Expectations of …scal corrections and of diminished
…scal space in the next recession could be a heavy drag on economic activity. In fact, such
expectations may diminish the e¤ectiveness of the recent …scal stimulus.
In this paper, we analyze a policy that involves coordination between the monetary and
…scal authorities to in‡ate away a fraction of the large public debt. In the coordinated
policy, the …scal authority ascribes the …scal interventions in response to COVID-19 to an
emergency budget, and the monetary authority replaces its perfectly symmetric strategy
of in‡ation stabilization with a temporary increase in the in‡ation target. We …nd that
this policy enhances the e¤ectiveness of …scal stimulus and correct a two-decade-long period
of below-target in‡ation, thereby expanding the limited leeway that …scal and monetary
authorities have when acting in isolation.
An important historical precedent that shares some similarities with the approach studied
in this paper is President Roosevelt’s New Deal. In 1933, President Roosevelt openly argued
that there were two separate budgets. A regular federal budget for which a pledge was made
to cut speci…c outlays to guarantee its …scal backing. An emergency budget, which was
needed to defeat the depression and which was unbalanced. In April of the same year, the
United States abandoned the gold standard, delinking the value of the dollar to gold and
reclaiming autonomous monetary policy.
2
We introduce the notion of emergency budget into an otherwise state-of-the-art dynamic
general equilibrium model to illustrate the e¤ects of adopting this new monetary and …scal
setting. The model features a rich …scal block with distortionary taxation on labor and capital income. Unlike a typical model, the …scal authority has two budgets. A regular budget,
backed by future …scal adjustments, and an emergency budget. The …scal authority is committed to repay the debt ascribed to the regular budget following the orthodox approach –by
increasing tax rates on labor, capital and consumption and by cutting government spending.
Yet, the …scal and monetary authorities agree on working together to stabilize the jump in
the emergency budget resulting from the $2.6 trillion stimulus package. The introduction of
a time-varying short-term in‡ation goal clari…es to the public that the monetary authority
is willing to coordinate its policy with the …scal authority and tolerate in‡ation above the
long-run two-percent target for some time. The exact amount of tolerated in‡ation is the
one that is needed to wear away the desired amount of debt. The concerted actions of the
two authorities make such path for in‡ation credible because needed to stabilize the amount
of debt in excess of the regular budget.
This new setting causes a rapid stabilization of the debt-to-GDP ratio mainly because it
generates an economic boom. Thus, while the $2.6 trillion 2020 stimulus bill is the largest
U.S. …scal stimulus on record, we …nd that the decision of ascribing it to the emergency
budget results in just a modest increase in in‡ation. A general equilibrium e¤ect explains
this result: the economic boom ensuing the introduction of the new regime signi…cantly
contributes to lowering the debt-to-GDP ratio and hence in‡ation does not have to rise
exorbitantly to wear away the debt ascribed to the emergency budget. Indeed, after a rapid
but contained increase, in‡ation falls, remaining slightly heightened for several years. Such a
persistent e¤ect on in‡ation raises nominal interest rates reducing the risk for the economy to
fall into a liquidity trap. In the short run, the rapid increase in in‡ation lowers real interest
rates and improves the ability of policymakers to shore up the economy from the COVID
recession.
We then discuss the implications of two alternative scenarios, in which the Central Bank
refuses to share any responsibility in ensuring the stability of debt. First, we compare
the outcome of our policy proposal to the one in which policymakers follow the orthodox
approach of raising taxes and cutting expenditures to reduce the debt-to-GDP ratio. The
orthodox approach dwarfs the expansionary e¤ects of the …scal stimulus on output and
has very long-lasting contractionary e¤ects, depressing economic activity for a considerable
number of years. This economic slowdown partially de…es the government’s e¤ort to reduce
the debt-to-GDP ratio, resulting in a much longer period of …scal consolidation compared to
the approach analyzed in this paper.
3
Alternatively, inaction could result in expectations of high in‡ation if agents become
convinced that the …scal authority will not be able to rein in debt via …scal adjustments and
might be tempted to coerce the central bank to create in‡ation to stabilize the entirety of
debt. In this scenario, the central bank e¤ectively loses control of in‡ation and any attempt
to stabilize it could back…re. The economy experiences high in‡ation and a substantial
increase in macroeconomic volatility because the economy is no longer insulated with respect
to …scal imbalances. By adopting a coordinated strategy based on the introduction of an
emergency budget instead, policymakers would remove uncertainty about the future and limit
the in‡ationary consequences of the policy intervention. This is the result of separating the
issue of long-run …scal sustainability from a stabilization policy. In fact, policy coordination
might be the only way to preserve central bank independence in the long run.
This paper is connected to the vast literature on monetary-…scal policy interaction (Sargent and Wallace 1981; Leeper 1991; Sims 1994; Woodford 1994, 1995, 2001; Cochrane
1998, 2001; Schmitt-Grohe and Uribe 2000; Bassetto 2002; Reis 2016; among many others).
Monetary-…scal policy interaction is modelled based on monetary and …scal policy rules as
in Leeper (1991). Bianchi and Melosi (2019) introduced the concept of shock speci…c rules
as a way to resolve a con‡ict between the monetary and …scal authorities in presence of a
high …scal burden that the …scal authority is reluctant or unable to stabilize. This notion
of shock-speci…c rules proves to be useful to solve models in which monetary and …scal authorities adopt state-dependent targets, like in the case of the emergency budget studied in
this paper. In this paper, we introduce an emergency budget into a state-of-the-art DSGE
model with a rich …scal block as a solution to a situation of impasse due to high distortionary taxation and a low interest rate environment. We highlight that absent coordination
between the two authorities, a large …scal stimulus might result in a disappointing economic
performance. This is because distortionary taxation and the inability of the central bank to
operate smoothly once at the zero lower bound represent a drag on the economy, even if no
con‡ict between the two authorities arise.
Our work is also related to Woodford (2003) and Benhabib, Schmitt-Grohe, and Uribe
(2002) who show that liquidity traps can be made …scally unsustainable. Furthermore, the
shock-speci…c rule that we investigate shares some features with the policy interventions that
Chris Sims has advocated at the 2016 Jackson Hole meeting to replace ine¤ective monetary
policy at the zero lower bound (Sims 2016). Concisely, Sims argues that policymakers should
make clear that …scal policy also aims at achieving a certain level of in‡ation. Unlike Sims’
proposal, our shock speci…c rule outlines the amount of debt that policymakers are planning
to stabilize with in‡ation and links such amount to one particular event, the …scal stimulus
in response to the COVID-19 pandemic. This is an important distinction that limits the
4
amount of in‡ation generated by the coordinated policy strategy analyzed in this paper.
Once the shock is reabsorbed, the economy naturally reverts back to the pre-crisis policy
framework.
Hall and Sargent (2011) show that historically most of US debt stabilization has been
achieved through a combination of growth, revaluation e¤ects, and low real interest rates,
while changes in primary surpluses played a relatively modest role. Bianchi and Ilut (2017)
link the high in‡ation of the 1970s to a Fiscally-led regime in which the monetary authority
accommodates the behavior of the …scal authority. Bianchi and Melosi (2017) argue that
the possibility of a return to such regime can explain the lack of de‡ation in the aftermath
of the Great Recession. Leeper, Traum, and Walker (2017) …nd that monetary-led and
Fiscally-led regimes return similar …t when a DSGE model is estimated on post-WWII US
data. Thus, there is evidence that the post-Volcker monetary-led policy mix characterized
by ample central bank independence has not always been the norm. The shock-speci…c rule
studied in this paper can be thought as a way to remove the risk of a tout court return
to a Fiscally-led strategy, in which the monetary authority is required to systematically
create in‡ation to stabilize government debt.1 Such change would lead to very high levels of
in‡ation and macroeconomic volatility.
The paper is organized as follows. Section 2 and Section 3 present the model and its calibration, respectively. Section 4 lays out the strategy of our quantitative analysis and presents
the main results. In Section 5, we compare the economic implications of the emergency budget strategy with a tout court switch to a Fiscally-led regime, a scenario in which the central
bank loses its independence and create in‡ation to stabilize the large post-COVID-19 public
debt. Section 6 contains our concluding remarks.
2
The Model
We extend a version of the medium scale general equilibrium model estimated by Leeper,
Traum, and Walker (2017) to account for shock speci…c rules along the lines of Bianchi and
Melosi (2019). Namely, the environment consists of an economy a la Christiano, Eichenbaum,
and Evans (2005), augmented with distortionary taxes on labor, capital and consumption,
and a rich …scal block. With respect to a typical model, both monetary and …scal policy rules
are speci…ed with respect to a regular budget and an emergency budget. In what follows,
we outline the model in detail.
1
See Bassetto (2002) for a seminal study of the game theoretical aspects of the interactation between the
monetary and …scal authorithies.
5
2.1
Households
The economy is populated by a unit measure of households, of which a fraction are handto-mouth consumers. The remaining fraction, 1
, are savers and we indicate them with
an S superscript. Hand-to-mouth households are assumed in the model as a simple way of
breaking the Ricardian equivalence, making transfers relevant for a fraction of the population.
Savers A household of optimizing saving agents, indexed by j, derives utility from the
consumption of a composite good, Ct S (j), which comprises private consumption CtS (j) and
government consumption Gt such that Ct S (j) = CtS (j) + G Gt . The parameter G governs the substitutability between private and government consumption. When negative, the
goods are complements; when positive, they are substitute. External habits in consumption imply that utility is derived relative to the previous period value of aggregate savers’
consumption of the composite good Ct S1 , where 2 [0; 1] is the habit parameter. Saver
households also derive disutility from the supply of di¤erentiated labor services from all
R1
its members, indexed by l, LSt (j) = 0 LSt (j; l) dl. The period utility function is given by
LSt (j)1+ = (1 + ) , where is the Frisch elasticity.
Ct S1
UtS = ln Ct S (j)
Households accumulate wealth in the form of physical capital KtS . The stock of capital
depreciates at rate and accrues with investment ItS , net ofh adjustment costs.
The law of
i
S (j)
I
) KtS 1 (j) + 1 s I St (j) ItS (j), where s
motion for physical capital is: KtS (j) = (1
t 1
denotes a standard investment adjustment cost function that satis…es the properties s (e ) =
s0 (e ) = 0 and s00 (e ) s > 0.
Households derive income from renting e¤ective capital KtS (j) to the intermediate …rms.
E¤ective capital is related to physical capital according to KtS (j) = t (j) KtS 1 (j), where
t (j) is the capital utilization rate. The cost of utilizing one unit of physical capital is given
by the function ( t (j)). Given the steady-state utilization rate (j) = 1, the function
00 (1)
satis…es the following properties: (1) = 0, and 0 (1)
= 1 , where 2 [0; 1). We further
denote the gross rental rate of capital as Rtk and the tax rate on capital rental income as K
t .
The household can also invest in the …nancial market by purchasing two types of zerocoupon bonds, which di¤er in their maturity. One-period bonds promising a nominal payo¤
Bs;t at time t + 1 can be purchased at the present discounted value Rt 1 Bs;t , where Rt is the
gross nominal interest rate set by the central bank. Long-term government bond Bt with a
maturity decaying at constant rate 2 [0; 1] and duration(1
) 1 , can be purchased at
price PtB .
Each period, the household receives after-tax nominal labor income, after-tax revenues
from renting capital to the …rms, lump-sum transfers from the government ZtS and dividends
from the …rms Dt . These resources can be spent to consume and to invest in physical capital
6
and bonds. The nominal budget constraint for the saver household is:
C
t
Pt 1
=
1 + PtB
K
t
+ 1
CtS (j) + Pt ItS (j) + PtB Bt (j) + Rt 1 Bs;t
R1
L
Wt (l) LSt (j; l) dl
Bt 1 (j) + Bs;t 1 (j) + 1
t
0
Rtk
t
(1)
( t ) KtS 1 (j) + Pt ZtS (j) + Dt (j) ;
(j) KtS 1 (j)
L
where Wt (l) denotes the wage rate that applies to all household members, and C
t and t
denote the tax rates on consumption and labor income, respectively. The household maxiP
t S
mizes lifetime discounted utility 1
Ut subject to the sequence of budget constraints in
t=0
Eq.(1).
Hand-to-Mouth Households Every period, hand-to-mouth households consume all of
their disposable, after-tax income, which comprises revenues from labor supply and government transfers. It is assumed that the hand-to-mouth households supply di¤erentiated
labor services, and set their wage to be equal to the average wage that is optimally chosen by the savers, as described below. Using the superscript N to indicate the non-saving,
hand-to-mouth households, their budget constraint can be written as follows:
1+
C
t
Pt CtN
(j) = 1
L
t
Z
1
N
Wt (l) LN
t (j; l) dl + Pt Zt (j) ;
0
where it is assumed that both savers and non savers face the same tax rates on consumption
and labor income.
2.2
Firms and Price Setting
Final good producers A perfectly competitive sector of …nal good …rms produces the
homogeneous good Yt at time t by combining a unit pmeasure of intermediate di¤erentiated
1+
R1
1
inputs using the technology Yt = 0 Yt (i) 1+ p di
; where p denotes the mark-up to the
prices of intermediate goods. Pro…t maximization yields the demand function for intermedip
p
ate goods Yt (i) = Yt (Pt (i) =Pt ) (1+ )= , where Pt (i) is the price of the di¤erentiated good
i and Pt is the aggregate price of the …nal good.
Intermediate good producers Intermediate …rms produce using the technology Yt (i) =
Kt (i) (At Lt (i))1
At , where is a …xed cost of production that grows with the rate
of labor-augmenting technological progress At and 2 [0; 1] a parameter. It is assumed
that technological progress At grows at the constant rate e . Intermediate …rms rent capital
and labor in perfectly competitive factor markets. It is assumed that Lt is a bundle of
7
all the di¤erentiated labor services supplied in the economy, which are aggregated into a
homogeneous input by a labor agency, as described below. The nominal rental rate of
capital is denoted by RtK and the wage rate by Wt . Cost minimization implies that all …rms
Rtk Wt1 At 1+ :
incur the same nominal marginal cost M Ct = (1
) 1
When setting prices, intermediate producers face frictions à la Calvo, i.e., at time t
a …rm i can optimally reset its price with probability ! p . Otherwise it adjusts the price
with partial indexation to the previous period in‡ation rate according to the rule Pt (i) =
( t 1 ) p ( )1 p Pt 1 (i), where p 2 [0; 1] is a parameter, t 1 = PPtt 12 and denotes the
aggregate rate of in‡ation at steady state.
Intermediate producers that are allowed to reset their price maximize the expected discounted stream of nominal pro…ts:
max Et
1
X
s=0
( ! p )s
S
t+s
S
t
"
s
Y
p
1
t+k 1
k=1
p
!
Pt (i) Yt+s (i)
subject to the demand function from the …nal good sector, where
utility of the savers.
2.3
M Ct+s Yt+s (i)
S
#
denotes the marginal
Wages
We assume that both savers and hand-to-mouth households are monopoly suppliers of a unit
measure of di¤erentiated labor service, indexed by l. Each period, a saver household gets
an opportunity to optimally readjust the wage rate that applies to all of its workers, Wt (l),
with probability ! w . If the wage cannot be reoptimized, it will be increased at the geometric
average of the steady state rate of in‡ation and of last period in‡ation t 1 , according
to the rule Wt (l) = Wt 1 (l) ( t 1 e ) w ( e )1 w , where w 2 [0; 1] captures the degree of
nominal wage indexation. It is assumed that the hand-to-mouth households set their wage
to be equal to the average wage that is optimally chosen by the savers.
All households, including both savers and non savers, sell their labor service to a representative, competitive agency that transforms
it into an aggregate labor input, according
1+ w
R1
1
, where w is the wage mark-up. The agency
to the technology Lt = 0 Lt (l) 1+ w dl
rents labor type Lt (l) at price Wt (l) and sells a homogeneous labor input to the intermediate
producers at price Wt . The static pro…t maximization problem yields the demand function
w
w
Lt (l) = Lt (Wt (l) =Wt ) (1+ )= .
8
2.4
Government Budget Constraint
Assuming that one-period government bonds are in zero net supply, the government nominal
budget constraint can be written as:
PtB Bt +
K k
t Rt Kt
+
L
t W t Lt
+
C
t P t Ct
= 1 + PtB Bt
1
+ Pt Gt + Pt Zt ;
(2)
R1
) CtS denotes aggregate consumption and Zt = 0 Zt (j) dj = Z S =
where Ct = CtN + (1
Z N , following the assumption that lump-sum transfers are identical across households. The
budget constraint in Eq. (2) implies that the …scal authority …nances government expenditures, transfers, and the rollover of expiring long-term debt by raising taxes on consumption,
labor and capital, and by issuing new long-term debt obligations.
2.5
Monetary and Fiscal Policy
We rescale the variables entering the …scal rules by de…ning gt = Gt =At , zt = Zt =At and
we denote the debt-to-GDP ratio as the market value of outstanding debt divided by GDP
PB B
sb;t 1 = Ptt 11 Ytt 11 . In what follows, for each variable x, we use x
b to denote the percentage
deviation from its own steady state.
We consider two cases. In the …scal orthodoxy case, the …scal authority is committed to
repay the entirety of public debt with future …scal adjustments and the monetary authority
is engaged in responding aggressively to deviations of in‡ation from its …xed target. In
the emergency budget case, the …scal authority creates and emergency budget that is not
expected to be balanced with future surpluses and the central bank adopts a rule with a
temporary in‡ation target meant to accommodate the emergency budget.
Fiscal Orthodoxy Under …scal orthodoxy, the …scal authority adjusts government spending g^t , transfers z^t , and tax rates on capital income, labor income, and consumption ^J ,
J 2 fK; L; Cg as follows:
g^t = G g^t 1 (1
^b;t 1 ;
(3)
G)
Gs
z^t =
^t 1
Zz
^Jt =
(1
J
J ^t 1
Z)
+ (1
^b;t 1
Zs
J)
+ "Zt ;
^b;t 1 ;
Js
(4)
(5)
where s^b;t 1 denotes the debt-to-GDP ratio and "Zt
N (0; 2z ) the shock to transfers. The
…scal authority is credibly committed to repay its obligations by raising taxes and cutting
expenditures and this behavior is captured by the values for the reaction parameters G , Z ,
and J > 0 that are consistent with Ricardian …scal policy.
9
Under …scal orthodoxy the central bank is fully committed to respond strongly to in‡ation
^ t , on one-period
deviations from its …xed target ^ t = ln t with the nominal rate of interest, R
bond. The monetary rule is
^t =
R
where the parameter
active.
^
r Rt 1
+ (1
r)
^t +
^t
yy
;
(6)
> 1 so that the Taylor principle is satis…ed and monetary policy is
Emergency Budget Under the emergency budget strategy, the …scal authority is committed to repay only a fraction of debt s^Tb;t < s^b;t by raising taxes and cutting expenditures.
No provision is made about how the residual part of debt, s^b;t s^Tb;t , the emergency budget,
will be stabilized:
g^t =
z^t =
^t 1
Gg
^t 1
Zz
^Jt =
(1
(1
J
J ^t 1
G)
Z)
+ (1
^Tb;t 1 ;
Gs
^Tb;t 1
Zs
J)
+ "Zt ;
^Tb;t 1 ;
Js
(7)
(8)
(9)
where J 2 fK; L; Cg and "Zt
N (0; 2z ). The parameters G > 0, Z > 0, and J > 0 are
consistent with Ricardian …scal policy. The restrictions on these parameters imply that the
government is committed to raise enough …scal resources to cover the amount of debt s^Tb;t 1 .
On the other hand, the …scal authority is not committed to move primary surpluses to cover
the amount of debt exceeding the target amount s^Tb;t 1 .
The …scal stimulus is captured by a large shock to transfers ("Zt > 0). This can be
interpreted as a situation in which the …scal authority introduces an emergency budget to
…nance the debt-to-GDP resulting from the …scal stimulus. The …scal authority is committed
to raise primary surpluses to cover its pre-COVID debt as Ricardian policy prescribes. Below
we will explain how the level of debt sTb;t that the …scal authority is committed to repay is
determined.
The monetary authority fully cooperates with the …scal authority by allowing in‡ation
to temporary increase above the long-term target. This can be done by introducing a temporary time-varying in‡ation target ^ Tt to accommodate the in‡ation needed to stabilize the
emergency budget (^
sb;t s^Tb;t ), i.e., the fraction of the debt-to-GDP ratio that is not …scally
backed. The monetary authority responds to deviations of in‡ation from this temporarily
^ t will be commensurated
higher target ^ Tt : Thus, movements in the nominal interest rate R
to the deviations of in‡ation from the temporary in‡ation target, and not to the deviations
10
from the …xed long-term target as in the …scal orthodoxy case. This leads us to a Taylor
rule modi…ed to account for the presence of the emergency budget:
^t =
R
^
r Rt 1
+ (1
r)
^t
^ Tt +
^t
yy
;
(10)
where
> 1 implies active monetary policy. This monetary rule implies that the central
bank reacts only to in‡ation deviations from the time-varying target ^ Tt . In equilibrium, this
target is larger than the …xed in‡ation objective used in the …scal orthodoxy case, implying
that on average the central bank will tolerate a higher level of in‡ation. This strategy is
justi…ed by the need to let in‡ation rise by the exact amount necessary to stabilize the debt
ascribed to the emergency budget s^b;t s^Tb;t . At the same time, the central bank retains
the commitment to …ght excessively high levels of in‡ation and to return to the long-term
target once the emergency budget is reabsorbed. In the next section, we will discuss how to
characterize these temporary in‡ation targets.
The idea of the emergency budget presents some similarities with President Roosevelt’s
New Deal. President Roosevelt ran his Presidential campaign as …scally conservative, but in
1933, he openly argued that there were two separate budgets. A regular federal budget for
which a pledge was made to cut speci…c outlays. An emergency budget, which was needed
to defeat the depression and which was unbalanced. In April of the same year, the United
States abandoned the gold standard, disanchoring the value of the dollar from gold in a way
to gain leeway in the conduct of monetary policy. Eggertsson (2008) and Jacobson, Leeper,
and Preston (2019) argue that these policy decisions played a key role in ending the Great
Depression.
Temporary Targets of Debt-to-Output Ratio and In‡ation The …scal and monetary rules under the emergency-budget strategy require policymakers to provide temporary
targets for the debt-to-GDP ratio and in‡ation, which we denoted with sTb;t and Tt . These
targets de…ne the amount of the debt-to-GDP ratio not backed by future …scal adjustments
and the amount of in‡ation that the central bank needs to forgo to stabilize such amount.
We construct a shadow economy to characterize these targets.
The same equations that characterize the equilibrium of the actual economy also govern
the shadow economy. The only point of departure is that the initial $2.6-trillion dollars
shock to transfers does not a¤ect the shadow economy. All other shocks, including the
shock that have started the recession, would hit both the actual economy and the shadow
economy. Furthermore, in the shadow economy …scal and monetary policies are Ricardian
and respond to in‡ation and previous period’s debt-to-GDP ratio of the shadow economy.
11
Hence, by construction, the shadow economy returns the dynamics of in‡ation and debt-toGDP ratio in the counterfactual scenario in which the …scal stimulus was not undertaken
and so the monetary- and …scal-policy mix would be Ricardian.
It also follows that the debt-to-GDP ratio in the shadow economy precisely isolates the
portion of debt that does not depend on the …scal stimulus and hence is not …nanced with the
emergency budget. To balance that portion of the debt-to-GDP ratio, the …scal authority is
fully committed to raise future surpluses. Thus, the target debt-to-GDP ratio s^Tb;t 1 in the
…scal rules (7)-(9) corresponds to the debt-to-GDP ratio in the shadow economy, which we
denote by s^b;t .
The …scal authority will not be responsible to adjust taxes or expenditures to stabilize the
remaining fraction of debt, which is given by the di¤erence s^b;t 1 s^Tb;t 1 , where sb;t 1 is the
debt-to-GDP ratio in the actual economy. It should be noted that the size of the emergency
budget to …nance the debt-to-GDP ratio resulting from the $2.6-trillion …scal stimulus is
endogenous, as the actual size of the debt-to-GDP ratio to be stabilized depends on the
e¤ects of the stimulus on the equilibrium outcome (e.g., output, tax revenues, transfers, etc.)
in the actual economy. This makes the fraction of debt that the government is not committed
to stabilize with future …scal adjustments to vary over time. In other words, policymakers
are not committed to repay the increase in the debt-to-GDP ratio resulting from the …scal
stimulus. However, they remain committed to raise taxes and lower expenditures to stabilize
the pre-existing amount of the debt-to-GDP ratio.
We now turn our attention to the temporary state-dependent in‡ation target in the monetary rule (10). The central bank needs to choose this temporary target so that in‡ation can
rise just by the amount necessary to stabilize the emergency budget, (^
sb;t 1 s^Tb;t 1 ). Again,
the shadow economy we have de…ned in this section comes handy. Indeed, the di¤erence
between the equilibrium in‡ation in the actual economy and the equilibrium in‡ation in
the shadow economy can be shown to give us the right amount of in‡ation needed to wear
away the fraction of the debt …nanced with the emergency budget. Therefore, we write the
temporary in‡ation target Tt in the rule of the actual economy as the di¤erence between
the two equilibrium in‡ation rates in the two economies; that is, ^ Tt
^ t ^ t , where t
denotes the equilibrium in‡ation rate in the shadow economy.
Endowed with these intuitions, we then can rewrite the monetary and …scal rules (7)-(10)
as follows
(11)
g^t = G g^t 1 (1
^b;t 1 ;
G) Gs
z^t =
^t 1
Zz
^Jt =
(1
J
J ^t 1
Z)
+ (1
12
^b;t 1
Zs
J)
+ "Zt ;
^b;t 1 ;
Js
(12)
(13)
with J 2 fK; L; Cg and
^t =
R
^
r Rt 1
+ (1
r)
^t +
^t
yy
;
(14)
where the starred variables are de…ned in the shadow economy described earlier.
Note that these rules belong to the broader class of shock-speci…c rules introduced by
Bianchi and Melosi (2019). To see this, note that policymakers respond with di¤erent
strength to the changes in debt, in‡ation, and output resulting from the large …scal stimulus shock. Following a positive transfer shock to be …nanced with the emergency budget
strategy, the temporary in‡ation target of the central bank will increase, as we shall show.
Such increase in the target would lead the central bank to respond more aggressively when
in‡ation is below the …xed long-term target and to be more accommodative when in‡ation
runs above the …xed long-term in‡ation target. Interestingly, the FOMC has discussed the
suitability of a similar asymmetric approach to in‡ation stabilization in its meeting of 28 and
29 January 2020 as reported by the minutes of that meeting on page 10. Bianchi, Melosi,
and Rottner (2019) show that this type of asymmetric monetary rules re-anchor in‡ation
expectations to the long-term in‡ation objective and correct the de‡ationary bias arising in
a low interest rate environment.
Loglinear Approximation and Model Solution The model is log-linearized around the
steady state (transfers and primary surplus are linearized). Once the equations of the shadow
economy are added to the equations of the actual economy, including the rules expressed
as shock-speci…c rules as in equation (11)-(14), the model can be solved using o¤-the-shelf
methods for linear rational expectations models. Appendix A presents the complete set of
linearized equations.
3
Calibration
The model is calibrate to the U.S. economy at quarterly frequency, relying largely on the
estimates by Leeper, Traum, and Walker (2017) over the period 1955Q1 through 2014Q2.
Calibrated parameter values, along with their description and source are reported in Table
1. Starting with the parameters that characterize household preferences, we follow Leeper,
Traum, and Walker (2017) in setting the inverse Frish elasticity to 1:77, the external habit
parameter to 0:99 and the coe¢ cient governing the substitutability between private and
public consumption G to 0:24. The discount factor is set to 0:999 in order to match a
real interest rate of 1.1%. We follow Kaplan, Violante, and Weidner (2014) and we set the
13
Calibration
Parameters
Preferences
Description
Discount factor
Inverse Frisch elasticity
Habit formation
G
Substitutability of private vs. gov. consumption
Frictions and technology
100
Steady-state log growth rate of technology
Share of hand-to-mouth households
Elasticity in production function
Capital depreciation rate
s
Investment adjustment cost
Capital utilization cost
!p
Price Calvo parameter
!w
Wage Calvo parameter
Price indexation
p
Wage
indexation
w
Price
markup
p
Wage markup
w
Monetary authority
Interest rate response to in‡ation
Interest rate response to output
y
Interest
rate smoothing
r
Fiscal authority
Debt maturity decay rate
L
Steady-state tax rate on labor
K
Steady-state tax rate on capital
C
Steady-state tax rate on consumption
Persistence
of G, and tax rates i = G; K; L
i
Persistence
of transfers rule
Z
Debt
response
with G
G
Debt
response
with transfers
Z
Debt
response,
for i = K , L
i
Debt response with consumption taxes
C
Steady state calibration targets
sgc
Government expenditures to GDP ratio
sb
Debt to annualized GDP ratio
Value
Target/source
0:999
1:770
0:990
0:240
Real rate 1.4%. (FOMC SEP)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
0:250
0:11
0:330
0:025
5:460
0:160
0:920
0:910
0:060
0:180
0:140
0:140
Leeper et al. (2017)
Kaplan et al. (2014)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
2:000
0:100
0:710
See Section 3
See Section 3
Leeper et al. (2017)
0:959
0:186
0:218
0:023
0:980
0:500
0:260
0:220
0:220
0:000
CBO (2020)
Leeper et al. (2017)
Leeper et al. (2017)
Leeper et al. (2017)
Estimated
Calibrated
Leeper et al. (2017)
Calibrated
Calibrated
See Section 3
0:110
0:600
Leeper et al. (2017)
Leeper et al. (2017)
Table 1: Calibrated values for model parameters and steady-state targets.
share of hand-to-mouth household to match the poor hand-to-mouth consumers 0:11.2
The values of all parameters governing technology and the frictions in price and wage
setting are also taken from Leeper, Traum, and Walker (2017). Namely, with regards to the
technological parameters, the steady state quarterly growth rate of technology 100 e is set
to 0:25, the elasticity of output to capital in the production function takes the value of 0:33,
the rate of capital depreciation is set to 0:025, and the parameters governing the convexity
2
As shown in that paper, including the wealthy hand-to-mouth consumers, who are people owning illiquid
assets and short of cash, would increase this parameter to 0:33%. Results would not qualitatively change if
we used this larger number.
14
of the investment adjustment cost function and of the capital utilization cost function are
set to 5:46, and 0:16, respectively. As for the parameters related to the pricing frictions, the
Calvo parameters for prices and wages are set to 0:92 and 0:91, respectively, the steady state
markups are both set to 0:14, and the parameters governing indexation are set to 0:06 for
prices and 0:18 for wages, respectively.
Steady-state …scal variables are also implied by the same parameterization as in Leeper,
Traum, and Walker (2017). Speci…cally, the decay rate of the maturity of long-term bonds,
, is set to 0.9593 to match an average duration of six years estimated by Congressional
Budget O¢ ce (2020). We also assume a steady state debt to GDP ratio of 60% (240% with
respect to quarterly GDP). This number is above the historical average. The conclusions
of our paper would not be a¤ected by lower values because the emergency budget does not
apply to the pre-existing debt. The share of government consumption in GDP is set to the
value of 0:11. The steady-state tax rates on capital, labor and consumption are set to 0.218,
0.186 and 0.023, respectively.
Moving to the coe¢ cients that characterize the behavior of the monetary authority, we
set the interest rate response to in‡ation in the monetary regime
to the conventional value
of 2, the response to output y to 0:1 and the smoothing coe¢ cient r to 0.71 as estimated
by Leeper, Traum, and Walker (2017).
The debt responses of transfers, as well as capital and income tax rates, Z ; K ; and
L , are set so as to drive the debt-to-GDP ratio to its steady state value of 60% in twenty
years in the case of …scal orthodoxy.3 In doing this, we assume that the adjustment (in
deviation from the steady-state value) to achieve this objective is the same across these
three …scal tools. This yields a coe¢ cient for Z ; K ; and L equal to 0:22. The response
of government consumption to the evolution of the debt-to-GDP ratio, G , is set to equal
the value estimated by Leeper, Traum, and Walker (2017). The consumption tax rate C
is assumed to be constant. We estimate the serial correlation coe¢ cients in the …scal rule
using the time series constructed by Leeper, Traum, and Walker (2017) and described in
their online appendix.
4
Policy Evaluation
We initialize the economy with the value of the debt-to-GDP ratio estimated by the CBO for
year 2019. We then calibrate the 2020 transfer shock using the CARES act …scal stimulus
3
After twenty years, the debt-to-GDP ratio is very similar across both policy strategies.
15
package as shown below.4 We then trace the response of the model economy under …scal
orthodoxy and the emergency budget scenarios. Recall that the two cases only di¤er with
respect to the way policymakers …nance the increase in the debt-to-GDP resulting from
the $2.6-trillion …scal stimulus. Technically, this implies that under the emergency budget
scenario, the debt-to-GDP ratio in the shadow economy corresponds to the pre-shock debtto-GDP ratio in the actual economy as policymakers address the pre-existing level of debt
with Ricardian policies. In what follows, we are interested in taking into account how the
initial stock of debt a¤ects the macroeconomic outlook in the two scenarios. Thus, we are
not plotting simple impulse response functions to the large transfer shock but we also take
into consideration the sizable pre-existing government debt that policymakers aim to repay
with higher distortionary taxes or transfers, which lowers the non savers’consumption.
We do not take a stand on the size of the recession due to the COVID-19 outbreak, given
that there is still considerable uncertainty around the exact magnitude and duration of the
shock. Introducing the COVID-19 shock would not alter our analysis below, which is focused on the di¤erence between the …scal orthodoxy and emergency budget policy strategies.
This is because we assume that the increase of the debt-to-GDP ratio due to the contraction in GDP following the COVID-19 shock will not be …nanced by the emergency budget.
Therefore, policymakers will follow Ricardian policies with respect to this additional debt.
Designing an emergency budget to …nance the whole …scal consequences of the COVID-19
shock would require policymakers to fully understand the economic e¤ects of the pandemic
as the emergency budget is introduced. We think that at this stage, this is not a plausible
assumption.
4.1
Calibration of Shocks and Initial Conditions
To calibrate the shock "z;t to transfers in 2020, we start from the equation that characterizes
the direct e¤ect of transfer shocks on the log deviations of the debt-to-GDP ratio from its
own steady state:
z
zt
@b
sb;t
1 @b
= (1
(15)
Z)
@"z;t
b
@"z;t
where sbb;t denotes the log-deviations of the debt-to-GDP ratio from its steady state level, z
and b denote the steady-state detrended transfers and debt, z^t denotes transfers in deviations
from steady state and Z denotes the serial correlation in the transfers rule. Since transfers
1 @b
zt
follow an exogenous AR(1) process in our model, (1
equals the total change in
Z)
@"z;t
transfers from time t to in…nity owing to the time-t shock "z;t .
4
Although this package also includes an increase in government consumption, most of the …scal stimulus
results in an increase in transfers.
16
We use the increase in the debt-to-GDP ratio due to the stimulus to calibrate the lefthand side of equation (15) and with the knowledge of z and b we calibrate the magnitude of
the shock to transfers as follows:
@b
zt
b
= (1
@"z;t
z
Z)
@b
sb;t
@"z;t
(16)
According to the CBO, the U.S. government debt was equal to 16.8 trillions in 2019; 79
percent of the U.S. GDP of the same year. If we add the $2.6 trillion stimulus to the 2019
stock of debt, the U.S. debt-to-GDP ratio rises to 89 percent of 2019 GDP.
We use the associated log increase in the debt-to-GDP ratio due to the …scal stimulus to
calibrate the derivative @b
sb;t =@"z;t , which we plug into equation (16) to get the initial size of
the shocks to transfers.
We denote the initial debt-to-GDP ratio in both the actual economy and the shadow
economy with sbb0 . We initialize this debt as follows:
sbb0 = ln
sb;CBO
;
sb
(17)
where sb;CBO is the CBO estimate of the 2019 U.S. debt-to-GDP ratio (i.e., before the 2020
…scal stimulus) and sb denotes the steady-state debt-to-GDP ratio, which we set to be equal
to 60%. The debt in deviation from its trend is initialized consistently (^b0 = sbb;0 and ^b0 = sbb;0
as y^0 is assumed to be zero).
4.2
Fiscal Space
We present the results of our empirical exercise by plotting the path of key macroeconomic
variables as they revert to their stationary equilibrium following a shock to government transfers and starting from an initial condition of government debt that is 19 percentage points
above its steady-state equilibrium. Figure 1 represents the dynamics of key macroeconomic
aggregates: output, consumption, and investment in the …rst row, the real interest rate,
in‡ation, and the nominal interest rate in the second row. Figure 2 reports the behavior of
the …scal variables, which include the debt-to-GDP ratio, the primary surplus, and government consumption in the …rst row, and the tax rate on labor income, the tax rate on capital
income, and transfers as a fraction of GDP in the second row. In both …gures and for each
panel, the dashed black line represents the path under …scal orthodoxy, that is, assuming
that all debt is stabilized by the …scal authority appropriately raising taxes and cutting on
government expenditures. The solid blue line represents instead the case in which the …scal
authority does not take an explicit responsibility for balancing the $2.6-trillion emergency
17
Output
Consumption
Fiscal Orthodoxy
Emergency Budget
2.00
Investment
3.00
2.00
2.00
1.00
1.00
1.00
0.00
0.00
0.00
10
20
30
40
10
Real Interest Rate
20
30
40
Inflation Rate
3.60
2.6
1.60
10
2.4
20
30
40
Nominal Interest Rate
3.40
1.40
2.2
3.20
1.20
2
10
20
30
40
10
20
30
40
10
20
30
40
Figure 1: Transitional Dynamics of Key Macroeconomic Aggregates: Fiscal Orthodoxy vs. Emergency Budget. Under the
Fiscal Orthodoxy scenario (black dashed line), the entirety of the debt-to-GDP ratio is stabilized by the …scal authority. In
the Emergency budget scenario (solid blue line), the COVID …scal stimulus is assigned to an emergency budget with no …scal
backing.
budget, in a coordinated attempt with the central bank to use monetary policy to stabilize
this fraction of public debt.
Fiscal orthodoxy We …rst describe the response of the model economy in the case of
…scal orthodoxy (black dashed line). Starting from the behavior of the real macroeconomic
aggregates in Figure 1, we observe that the massive …scal stimulus only produces a shortlived increase in output with a peak impact of about 2%. The expansionary e¤ects of the
stimulus persist for three quarters re‡ecting the rise in consumption from the hand-to-mouth
households. The central bank’s commitment to …ght in‡ation implies a higher real interest
rate and investment falls, as capital taxes rise (see Figure 2).
The main take-away from this exercise is that the …scal space to respond to the COVID
shock is limited. Under …scal orthodoxy, expectations of future tax rises generate a negative
wealth e¤ect which bears negatively on the consumption decision of savers. As a result, the
positive impact of the expansionary …scal policy dies out as the direct e¤ect of transfers on
hand-to-mouth consumption fades away. We note that the expansionary e¤ects of the …scal
stimulus in Figure 1 should be considered as an upper-bound to the short-run e¤ects of …scal
transfers, as our environment abstracts from the speci…c features of the spreading of the
18
Primary Surplus (% of GDP) Government Consumption (% of GDP)
Debt/GDP
2.75
0.00
85.00
-1.00
2.70
-2.00
80.00
Fiscal Orthodoxy
Emergency Budget
-3.00
2.65
75.00
10
20
30
40
10
Tax Rate on Labor
20
30
10
40
20
30
40
Transfers (% of GDP)
Tax Rate on Capital
19.20
6.00
22.40
5.00
19.00
22.20
4.00
18.80
22.00
3.00
18.60
21.80
10
20
30
40
10
20
30
40
10
20
30
40
Figure 2: Transitional Dynamics of Fiscal Variables: Fiscal Orthodoxy vs. Emergency Budget. Under the Fiscal Orthodoxy
scenario (black dashed line), the entirety of the debt-to-GDP ratio is stabilized by the …scal authority. In the Emergency budget
scenario (solid blue line), the COVID …scal stimulus is assigned to an emergency budget with no …scal backing.
COVID-19, such as the lockdown in several sectors of the economy, which would decrease
the short-run impact of …scal multipliers.
Emergency budget In the case where the …scal and monetary authorities coordinate to
stabilize the amount of government debt that directly relates to the emergency budget, the
real interest rate falls, as in‡ation rises. In turn, the persistent fall in real interest rates
induces a sharp increase in consumption and investment, which stimulates production for
over …ve years, with a peak on impact of about 2.3%. Figure 3 illustrates the targets of
the coordinated monetary- and …scal-policy mix that produces an escape from the limited
room that the …scal and the monetary authorities have in isolation. The right panel of
the …gure plots the actual behavior of the debt-to-GDP ratio in the case of a coordinated
response (solid blue line), together with the debt-to-GDP ratio which the …scal authority is
committed to cover with future …scal adjustments (black dashed line). As explained above,
this corresponds to the debt-to-GDP ratio the shadow economy. The di¤erence between the
two lines is the amount of debt in the emergency budget which at any point in time remains
to be stabilized by the concerted action of the monetary authority. The monetary strategy
that achieves this goal is plotted in the left panel of the …gure, which depicts the actual
rate of in‡ation (solid blue line) along with the announced temporary time-varying target
19
Debt-to-GDP Rate
Inflation
85.00
2.60
80.00
2.50
2.40
75.00
2.30
70.00
2.20
65.00
Inflation
Temporary Time-Varying Inflation Target
Long-Term Fixed Inflation Target
2.10
2.00
Debt-to-GDP Ratio
Regular Budget Debt-to-GDP ratio
Long-Term Target
60.00
0
10
20
30
0
40
10
20
30
40
Figure 3: Monetary and Fiscal Policy Targets Under an Emergency Budget. Under the Emergency budget scenario, the COVID
…scal stimulus is ascribed to an emergency budget with no …scal backing. The emergency budget is given by the di¤erence
between the total debt-to-GDP ratio (solid blue line) and the amount of debt-to-GDP ratio backed by future primary surpluses
(dashed-dotted red line). The red dashed-dotted line in the left panel corresponds to the temporary state-dependent in‡ation
target.
(dotted-dashed red line).
It is important to notice that the temporary target is less than 50 basis point above the
two-percent long-term in‡ation target and converges to the long-term two-percent goal very
sluggishly. This result can be e¤ectively be interpreted as a modest increase in the in‡ation
objective. By raising the target in combination with the adoption of the emergency budget
by the …scal side authority, the central bank achieves the joint objective of enhancing the
e¤ectiveness of the …scal stimulus and correcting a two-decade-long period of below-target
in‡ation. Arguably, the fact that the increase in in‡ation is necessary in order to stabilize
the emergency budget adds credibility to the coordinated policy, unlike an unilateral decision
of the central bank that agents might see as easily revertible.
While our model economy features only the initial shock to transfers, we could introduce
the standard battery of business cycle shocks (e.g., discount factor shocks, technology shock
etc.). So long as policymakers are credibly committed to address any …scal imbalances
generated by these business cycle shocks with Ricardian policies, the temporary in‡ation
target Tt in the rule (10) would not be a¤ected by the realization of any of these shocks.5
Comparing Fiscal Orthodoxy and Emergency Budget As illustrated in Figure 2,
the tax rates on labor, capital and consumption, do not have to rise as much in the case of
an emergency budget, as the production boom generated by the coordinated …scal-monetary
policy mix induces a boom in …scal revenues that contributes to keep the debt-to-GDP ratio
5
Technically, this happens as both the economy and the subeconomy are linear economies and their
equilibrium outcomes are equally a¤ected by these shocks.
20
Fiscal Orthodoxy
Debt-to-GDP Ratio
Debt-to-GDP Ratio
6.00
Real Cost of Servicing Debt
Primary Surplus
GDP growth
Changes in Debt-to-GDP Ratio
4.00
2.00
2.00
0.00
-2.00
-2.00
-4.00
-4.00
-6.00
-6.00
10
20
30
40
85.00
85.00
80.00
80.00
75.00
75.00
0
10
20
30
Real Cost of Servicing Debt
Primary Surplus
GDP growth
Changes in Debt-to-GDP Ratio
4.00
0.00
0
Emergency Budget
6.00
40
0
10
20
30
0
10
20
30
40
40
Figure 4: Contributions to Changes in Debt-to-GDP Ratios. The upper panels show the changes in public debt as de…ned on
the left-hand-side of equation (18) following the $2.6 trillion …scal shock. The lower panels show the implied dynamics of the
debt-to-GDP ratio.
in check. To further elucidate the underlying mechanism, we consider a decomposition of the
per-period change in the debt-to-GDP ratio based on the loglinearized budget constraint:
sbb;t
1
sbb;t
1
=
h
|e
P^tB
1
PtB 1 + ^ t
i
{z
}
service cost of debt
h
i
"
K kk
k
^t +
r b ^K
+
r
^
+
k
t
t
|
+
Cc
b
^C
^t
t +c
{z
1
y^t
|
{z
y^t
GDP growth
L
1
}
h
i #
^t
^t + L
w Lb ^Lt + w
Primary surplus
g
g^
b t
z
z^
b t
}
(18)
where on the right hand side the …rst term within square brackets captures the e¤ect of the
real cost of servicing debt on the change in the debt-to-GDP ratio, the second term captures
the e¤ects of output growth, and the last …ve terms de…ne the contribution of the primary
surplus.
Figure 4 provides the decomposition for the …scal orthodoxy (left plot) and the emergency
budget (right plot) scenarios. In both cases, the enormous increase in primary de…cits
dominates the initial increase in the debt-to-GDP ratio as captured by the teal bars lying
21
in the positive territory for the …rst four quarters. Note that the height of these bars is
fairly close across the two policy strategies as the transfers dominate the (negative) change
in the primary budget in these early periods. However, the initial increase in the debt-toGDP ratio is very di¤erent across the two scenarios. This is due to two reasons. First, the
boom is stronger and more prolonged under the emergency budget (see the yellow bars).
Second, the dramatic fall in the real cost of the debt (the blue bars) is more pronounced
when policymakers adopt the emergency-budget approach, which contributes to lowering the
debt-to-GDP ratio in the …rst period and to reduce its growth rate over the following three
periods. This e¤ect is a combination of low real interest rates and the jump in the long term
nominal interest rate that reduces the prices of long term bonds. The …gure shows that when
the emergency budget is adopted, the debt-to-GDP ratio reaches a peak value of about 86%
compared to a value of about 89% in the case of orthodoxy. The di¤erence is due to the
improved ability by policymakers to lower the real interest rate, with bene…cial e¤ects on
growth and in‡ation, in the case of the emergency budget.
In the long run, across both scenarios policymakers are raising primary surpluses to
stabilize the pre-existing stock of debt, for which they are committed to repay through …scal
adjustments. These actions are captured by the teal bars lying in the negative territory from
period 5 and on. These …scal adjustments are costly and lower output as shown in Figure
1. It is important to notice that the better economic performance and the slightly higher
in‡ation in the …rst four quarters under the emergency budget case leaves policymakers with
a slimmer debt-to-GDP ratio in period 5. As a result, the …scal adjustment is less drastic,
which is re‡ected in shorter teal bars in the right graph. In Figure 1, the more gentle
…scal consolidation was shown to improve output. Even though the …scal adjustment is less
severe, the fact that the emergency-budget policy mix allows policymakers to tidy up the
…scal situation early on implies that debt converges faster to the long-term target when the
emergency budget is adopted.
4.3
Helicopter Money
In the case of the emergency budget depicted in Figure 1, the coordinated action of the …scal
and monetary authorities wears away a well-de…ned and limited portion of the debt-to-GDP
ratio by causing a gradual rise in in‡ation that the central bank accommodates. What sparks
in‡ation is the announcement of a new …scal and monetary policy mix, which is re‡ected
in the projected paths of the …scal instruments, i.e. tax rates, transfers and government
expenditures, and of the temporarily asymmetric in‡ation target. In‡ation expectations
jump upon the implementation of the coordinated policy mix, leading to an immediate
22
decline in real interest rates.
The model abstracts from money, as the monetary policy rule is de…ned in terms of
an interest rate policy. Nevertheless, it can be interesting to understand how our analysis
relates to the discussion on helicopter money, i.e., the assumption of a …scal transfer of cash
to households …nanced by an increase in money growth. The policy we analyze clearly shares
some elements of commonality with the discussion on helicopter money. However, whatever
happens to money in equilibrium is not necessary to pinpoint the source of in‡ation, which
lies in the agreement between the …scal and the monetary authorities about how to …nance an
existing …scal burden. Money is a tool, and its equilibrium behavior that is consistent with a
given policy mix can be made explicit and traced, with no consequences for the equilibrium
dynamics reported in the previous sections.
The simplest way to introduce money in the model, is to assume it in the utility function.
For instance, we could postulate the function
UtS =
ln Ct S (j)
LSt (j)1+ = (1 + ) + ln
Ct S1
Mt
Pt
;
where Mt denotes money and > 0. At the same time, seigniorage revenues derived from
money creation would need to be added to the government budget constraint, yielding:
K k
t Rt Kt
+
L
t Wt Lt
+
C
t Pt C t
+ PtB Bt
1 + PtB Bt
1
+ Mt
Mt
1
= Pt Gt + Pt Zt ; (19)
which implies that nominal government expenditures or transfers can be …nanced by an
increase in the stock of money. Assuming for simplicity that no utility is derived from
government consumption such that Ct S = CtS , that there are no habits in consumption
( = 0), that there is no growth in steady state ( = 0), utility maximization yields the
following demand function for real money balances, after substituting for the Euler equation:
Mt
=
Pt
1
Ct
1
1
Rt
1
;
(20)
which shows the standard result that real money demand is positively related to consumption
and negatively related to the interest rate. Equation (20) implies that for a given interest
rate set by the central bank, and for a given level of aggregate consumption and prices at
time t, the supply of money Mt has to adjust to satisfy the demand for real money balances.
In the case of the emergency budget depicted in Figure 1, the path of the price level and
of consumption relative to the case of …scal orthodoxy, implies that the supply of money
has to increase to satisfy the demand function in Eq. (20). This increase in the stock of
money generates seigniorage revenue for the government, which can be used to …nance cash
23
transfers to the households in Eq.(19) or alleviate the …scal burden. In both cases, the
analysis presented above would not signi…cantly change given that the equilibrium path is
pinned down by the interaction between the …scal rules and the Taylor rule, and not by the
precise path of money supply.
In a related paper, Galí (2019) compares the e¤ectiveness of …scal policy under debt
…nancing vs. money …nancing, …nding larger multipliers in the latter case. Galí (2019)
also …nds that the relative e¤ectiveness of money …nancing relative to debt …nancing is
reduced in the presence of the zero lower bound (ZLB). In our analysis of the emergency
budget reported in Figure 1 the presence of the ZLB is not a constraint to the e¤ectiveness
of the coordinated policy mix analyzed in this paper. Rather, the coordination between
the …scal and the monetary authorities could in principle be helpful to escape the ZLB by
creating expectations of higher in‡ation, which is immediately re‡ected in higher nominal
interest rates. The di¤erence stems from the assumption in Galí (2019), that while dropping
money from the helicopter, the monetary authority keeps the in‡ation target at zero. In our
analysis instead, the in‡ation target is temporarily raised with the explicit intent of reducing
the burden of the debt.
5
Post-COVID Environment and Central Bank Independence
The coronavirus outbreak will have important consequences for the US economy. One important legacy will certainly be a further increase in the amount of government debt. As
shown in the previous sections, a large debt-to-GDP ratio reduces the ability of the …scal
authority to stabilize the economy during downturns. Thus, it is fair to expect that in the
years ahead, the …scal space to contrast recessions will be greatly reduced. This is particularly problematic in a low interest rate environment that limits the tools available for the
Federal Reserve to provide accommodation in a recession.
In this section, we consider a post-COVID scenario in which the U.S. debt-to-GDP ratio
reaches a record high level, a quite likely outcome absent the coordinated policies discussed
above. This large value of debt would only exacerbate the policy impasse analyzed in the
previous sections. If the policy standstill reaches the point where the public loses con…dence
in the ability of the central bank to e¤ectively stabilize the economy in a recession, the central
bank could get under further scrutiny, which could threaten its independence. Furthermore,
if the private sector also loses con…dence about the …scal authority’s ability or willingness to
raise su¢ cient primary surpluses to back the large stock of debt, in‡ationary pressure would
24
Debt/GDP
Inflation Rate
145.00
5
Fiscal Orthodoxy
Emergency Budget
Lost Central Bank Independence
140.00
135.00
4.5
130.00
4
125.00
120.00
3.5
115.00
3
110.00
105.00
2.5
100.00
2
5
10
15
20
25
30
35
40
5
10
15
20
25
30
35
40
Figure 5: Post-COVID scenario: In‡ation and Debt Dynamics under the assumption that the large post-COVID recession
public debt will be addressed with (i) Fiscal Orthodoxy, (ii) an Emergency Budget 20% of the pre-existing debt will be ascribed
to, and a Tout Court Switch to Fiscally-Led Regime, implying a sudden loss of central bank’s independence (Lost Central Bank
Independence).
arise, as agents turn to the central bank for a possible solution.
Under these circumstances, the central bank would be left with the following two options.
One possibility is that it tries to reign in in‡ation by aggressively raising interest rates.
Bianchi and Melosi (2019) show that this choice might in fact back…re if agents expect that
the central bank will lose its independence. In this case the economy could enter a vicious
spiral of stag‡ation and further debt accumulation. This happens as tightening monetary
policy raises the debt-to-GDP ratio both directly, by increasing the cost of servicing the debt,
and indirectly, by driving the economy into a recession. If agents expect that eventually the
central bank will have to follow the directives of the …scal authority, the increased …scal
burden would generate a further increase in in‡ation, as opposed to a decline.
The second possibility is that the central bank forgoes the goal of in‡ation stabilization.
We contrast this scenario with the case in which the monetary and …scal authorities coordinate to create an emergency budget, which implicitly circumscribes the increase of in‡ation
that the central bank needs to accommodate. By delimitating the amount of debt that is
not …scally backed, this plan e¤ectively preserves the central bank’s long-run goals and independence. We consider a post-COVID scenario, assuming that the initial stock of debt will
reach 150% of GDP. The underlying assumption is that policymakers have not implemented
the coordinated strategy yet. Consistently with this assumption, the emergency budget rule
now consists of assigning a certain fraction of the existing, larger debt to the emergency
budget.
The results of this exercise are shown in Figure 5. The solid red line with square markers
indicates the dynamics of in‡ation and the debt-to-DGP ratio if the central bank is no
25
In‡ation
Output
Fiscal Orthodoxy
0.1561
0.7641
Unconditional Volatility
Emergency Budget
0.1561
0.7641
Lost Central Bank Independence
0.2605
2.0778
Table 2: Unconditional standard deviation of in‡ation and output under the assumption that the …scal and monetary policy
mix is monetary led (Fiscal Orthodoxy), is coordinated over an emergency budget (Emergency Budget), and …scally led (Lost
Central Bank Independence). We add the shocks estimated by Leeper, Traum, and Walker (2017) to the model.
longer independent from the …scal authority, which is modeled as a tout-court switch to the
Fiscally-led regime (left and right panels, respectively). In this case, the …scal authority
is not expected to implement the …scal adjustments that are required to head back to the
60% steady-state debt-to-GDP target, and all adjustments of the debt-to-GDP ratio are
due to the in‡ation created by the monetary authority.6 The cost of such policy is a large
and persistent rise of in‡ation, with a peak of 6% in the second quarter. After 10 years,
in‡ation is still around 4:5%; well above 3%; the peak of in‡ation observed in the case of
the emergency budget (blue line). The larger rate of in‡ation and the associated drop in
real interest rates imply a faster convergence of the debt-to-GDP ratio to its long run target
under the Fiscally-led policy mix.
The high and persistent increase in in‡ation is not the most damaging outcome of the
loss of central bank independence. A tout court switch to the Fiscally-led policy mix also
implies a change in the way future shocks will be handled. Table 2 reports the unconditional
standard deviation for in‡ation and output for three cases: Fiscal Orthodoxy, Emergency
Budget, and Lost Central Bank Independence when the full set of shocks in the estimated
model by Leeper, Traum, and Walker (2017) are added. It is immediate to see that this
last scenario implies a drastic increase in macroeconomic volatility with respect to Fiscal
orthodoxy. This is because now the monetary authority is supposed to accommodate all
‡uctuations in the debt-to-GDP ratio. Instead, the emergency budget rule preserves longrun macroeconomic stability because it separates an exceptional policy intervention from
the problem of long-run …scal stability. Once the initial shock is reabsorbed, the economy
naturally returns to the pre-crisis policy mix in which the …scal burden is responsibility of
the …scal authority.
Policymakers could also decide to adopt the emergency budget framework to systematically intervene during those recessions that are large enough to push the economy to the
zero lower bound. For example, policymakers could decide to ascribe the expenses incurred
during these exceptionally large recessions to the emergency budget. In this case, macroeconomic volatility under the emergency budget policy framework would be even lower than
6
Technically, we restrict the interest rate response to in‡ation, as well as the policy parameters governing
the response of all …scal instruments to lagged debt-GDP to zero.
26
under Fiscal orthodoxy. This is because the emergency budget would act as an automatic
stabilizer, increasing in‡ation expectations every time that the central bank loses its ability
to act. The increase in in‡ation expectations would determine a drop in the real interest rate
and, consequently, a smaller recession and no de‡ation. Thus, the emergency budget would
compensate the limits of monetary policy in a low interest rate environment and reduce the
overall volatility of the economy in response to very large shocks. At the same time, when the
economy is not at the zero lower bound, debt would be fully backed by …scal interventions,
retaining the advantages of …scal discipline. These two mechanisms combined would lead to
lower macroeconomic volatility.
In the analysis above, we abstracted from two considerations that would arguably make
a switch to the Fiscally-led regime even more damaging. First, we have not considered the
political economy implications of such a policy change. In a nutshell, it is easy to imagine
that once the …scal authority becomes the leading authority, there might be incentives to
increase spending, given that the …scal authority would not bear the cost of the necessary
adjustments. This would arguably cause an in‡ationary bias with roots due to the lack
of …scal discipline (see Persson and Tabellini 2002 for seminal contributions on this topic).
Second, while the emergency-budget coordinated strategy causes only a moderate increase
in in‡ation and no increase in long-run volatility, a tout court switch to the Fiscally-led
policy mix would have much more important consequences, as shown above. Thus, it is
quite possible that …rms would react to such an important policy change by increasing the
frequency of price adjustment, resulting in an even larger increase of in‡ation.
Finally, we analyzed the e¤ects of an immediate change to the Fiscally-led policy mix,
resulting in a sudden jump in in‡ation. The large increase in in‡ation could also materialize more gradually if agents slowly revise their expectations about the ability of the …scal
authority to stabilize debt. In that case, in‡ation could experience a run-up and accelerating behavior similar to what was observed in the 1970s (Bianchi and Melosi 2013). Once
in‡ation is out of control, only a drastic change in the monetary-…scal policy mix like the
one experienced by the US economy in the early 1980s would succeed in bringing in‡ation
down. This would be a costly adjustment, as agents would take time to revise their beliefs
about the monetary-…scal policy mix. The coordinated strategy would help in avoiding such
a scenario by separating a short-run …scal intervention from the problem of long-run …scal
stability.
27
6
Conclusions
We studied a coordinated …scal and monetary strategy aiming at creating a controlled rise
of in‡ation and an increase in …scal space in response to the COVID shock. This policy
alleviates the constraints currently faced by the two authorities. Record-low long-term nominal interest rates limit the tools of the central bank to stabilize the economy. The large
public debt curtails the e¢ cacy of …scal interventions by inducing expectations of costly
…scal adjustments. Under our coordinated strategy, the …scal authority ascribes the large
…scal stimulus to an emergency budget with no provisions on how it will be balanced, while
the monetary authority allows a temporary increase in in‡ation. The coordinated strategy
enhances the e¢ cacy of the …scal stimulus planned in response to the COVID pandemic. The
strategy results in only moderate levels of in‡ation and preserves long-run macroeconomic
stability by separating long-run …scal sustainability from a short-run policy intervention.
We show that a coordinated action that delimits the amount of debt that requires central
bank intervention may be the lesser of two evils for those concerned about preserving central
independence. In fact, the coordinated strategy might be even desirable in and of itself
because it would bring about a controlled re‡ation of the US economy, rendering the central
bank the necessary room of maneuver to stabilize the economy in the years ahead.
References
Bassetto, M. (2002): “A Game-Theoretic View of the Fiscal Theory of the Price Level,”
Econometrica, 70(6), 2167–2195.
Benhabib, J., S. Schmitt-Grohe, and M. Uribe (2002): “Avoiding Liquidity Traps,”
Journal of Political Economy, 110(3), 535–563.
Bianchi, F., and C. Ilut (2017): “Monetary/Fiscal Policy Mix and Agents’ Beliefs,”
Review of Economic Dynamics, 26, 113–139.
Bianchi, F., and L. Melosi (2013): “Dormant Shocks and Fiscal Virtue,” in NBER
Macroeconomics Annual 2013, Volume 28, NBER Chapters, pp. 1–46. National Bureau of
Economic Research, Inc.
(2017): “Escaping the Great Recession,”American Economic Review, 107(4), 1030
–58.
(2019): “The dire e¤ects of the lack of monetary and …scal coordination,”Journal
of Monetary Economics, 104, 1–22.
Bianchi, F., L. Melosi, and M. Rottner (2019): “Hitting the Elusive In‡ation Target,”
NBER working paper.
28
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): “Nominal Rigidities and
the Dynamic E¤ects of a Shock to Monetary Policy,”Journal of Political Economy, 113(1),
1–45.
Cochrane, J. H. (1998): “A Frictionless Model of U.S. In‡ation,” in NBER Macroeconomics Annual 1998, ed. by B. S. Bernanke, and J. J. Rotemberg, pp. 323–384. MIT
Press, Cambridge, MA.
(2001): “Long Term Debt and Optimal Policy in the Fiscal Theory of the Price
Level,”Econometrica, 69, 69–116.
Congressional Budget Office (2020): “Federal Debt: a Primer,” (CBO Publication
No. 56165). Washington, DC: Congressional Budget O¢ ce.
Eggertsson, G. B. (2008): “Great Expectations and the End of the Depression,”American
Economic Review, 98(4), 1476–1516.
Galí, J. (2019): “The e¤ects of a money-…nanced …scal stimulus,” Journal of Monetary
Economics, forthcoming.
Hall, G. J., and T. J. Sargent (2011): “Interest Rate Risk and Other Determinants
of Post-WWII U.S. Government Debt/GDP Dynamics,” American Economic Journal:
Macroeconomics, 3(3), 192–214.
Jacobson, M. M., E. M. Leeper, and B. Preston (2019): “Recovery of 1933,”NBER
Working Papers 25629, National Bureau of Economic Research, Inc.
Kaplan, G., G. Violante, and J. Weidner (2014): “The Wealthy Hand-to-Mouth,”
Brookings Papers on Economic Activity, 44(1), 77–138.
Leeper, E. M. (1991): “Equilibria Under Active and Passive Monetary and Fiscal Policies,”
Journal of Monetary Economics, 27, 129–147.
Leeper, E. M., N. Traum, and T. B. Walker (2017): “Clearing Up the Fiscal Multiplier
Morass,”American Economic Review, 107(8), 2409–2454.
Persson, T., and G. Tabellini (2002): Political Economics: Explaining Economic Policy.
The MIT Press.
Reis, R. (2016): “QE in the future: the central bank’s balance sheet in a …nancial crisis,”
Discussion Papers 1620, Centre for Macroeconomics (CFM).
Sargent, T., and N. Wallace (1981): “Some Unpleasant Monetarist Arithmetic,” Federal Reserve Bank of Minneapolis Quarterly Review, Fall, 1–17.
Schmitt-Grohe, S., and M. Uribe (2000): “Price level determinacy and monetary policy
under a balanced-budget requirement,”Journal of Monetary Economics, 45(1), 211–246.
Sims, C. A. (1994): “A Simple Model for Study of the Determination of the Price Level
and the Interaction of Monetary and Fiscal Policy,”Economic Theory, 4, 381–399.
Sims, C. A. (2016): “Fiscal policy, monetary policy and central bank independence,” in
29
Kansas Citi Fed Jackson Hole Conference.
Woodford, M. (1994): “Monetary Policy and Price Level Determinacy in a Cash-inAdvance Economy,”Economic Theory, 4, 345–389.
(1995): “Price Level Determinacy without Control of a Monetary Aggregate,”
Carnegie-Rochester Series of Public Policy, 43, 1–46.
(2001): “Fiscal Requirements of Price Stability,” Journal of Money, Credit, and
Banking, 33, 669–728.
(2003): Interest and prices: Foundations of a theory of monetary policy. Princeton
University Press, Princeton, New Jersey.
30
A
The Log-Linear Model
The model features a trend in the state of labor-augmenting technological progress. In order
Ct S
Yy
S
=
,
c
; cSt =
to make the model stationary, we de…ne the following variables: yt = A
t
At
t
CtS
; cN
t
At
CN
P BB
Zt
t
t
t
= Att ; kt = K
; gt = G
; zt = A
; bt = Ptt Att ; wt = PW
, and St = St At . We list
At
At
t
t At
below the equations of the log-linear model, starting with those that characterize the actualeconomy block.
Production function:
i
y+ h ^
^t :
y^t =
kt + (1
)L
(21)
y
Capital-labor ratio:
k^t :
^t
w^t = L
r^tK
(22)
Marginal cost:
m
d
ct = r^tk + (1
Phillips curve:
^t =
Et ^ t+1 +
1+
where p = [(1
! p ) (1 ! p )] = ! p 1 +
Saver household’s FOC for consumption:
e
^S =
t
e
p
1+
p
(23)
) w^t :
^t
1
+
p
:
p
d
ct ;
pm
(24)
^C
t :
(25)
C
ct S +
ct S 1
e
1+
C
Public/private consumption in utility:
c^t =
cS
cS +
Gg
c^St +
Gg
cS
+
Gg
g^t :
(26)
Euler equation:
^S = R
^ t + Et ^ S
t
t+1
Et ^ t+1 :
(27)
Maturity structure of debt:
^ t + P^ B =
R
t
R
B
Et P^t+1
:
(28)
Saver household’s FOC for capacity utilization:
K
rtk
1
K
K
t
31
=
1
^t :
(29)
Saver household’s FOC for capital:
q^t = Et ^ t+1
^t + e
R
K
1
k
rk Et r^t+1
r Et ^K
t+1 + e
K k
e
) Et q^t+1 : (30)
(1
Saver household’s FOC for investment:
^{t +
1
q^t
(1 + ) se2
1+
Et^{t+1 =
1
^{t 1 :
1+
(31)
E¤ective capital:
k^t = ^t + b
kt 1:
Law of motion for capital:
b
k t = (1
)e b
kt
+ 1
1
(32)
(1
)e
(33)
^{t :
Hand-to-mouth household’s budget constraint:
C N C
c ^t
+ 1+
C
1
w^t
1+
1
cN c^N
t = 1
L
^t
wL w^t + L
L
wL^Lt + z z^t :
(34)
Wage equation:
w^t =
+
w
+
^t
1+
1
Et w^t+1
1+
1+
1+
w
w^t
^ t + ^ St
L
L
1
L
^Lt
w
^t +
1+
(35)
Et ^ t+1 :
Aggregate households’consumption
c^
ct = cS (1
) c^St + cN c^N
t :
(36)
Aggregate resource constraint:
y y^t = c^
ct + i^{t + g^
gt +
0
(37)
(1) k^t :
Government budget constraint:
b^
bt +
y
1 b h^
bt
=
y
K kk
r
1
y
h
^t
i
Lh L
^
+
w
^ +w
^ t + Lt +
y t
i b
g
z
P^tB 1 +
P^tB + g^t + z^t :
ye
y
y
^K
t
r^tk
i
^
+ kt +
L
32
C
c C
^ + c^t
y t
(38)
Monetary policy rule under …scal orthodoxy:
^ t = (1
R
r)
^t +
^t
yy
:
(39)
In the case of the emergency budget instead, the rule above is replaced by:
^ t = (1
R
r)
^t +
^t
yy
;
where ^ t refers to the rate of in‡ation in the shadow economy, which is characterized below.
The …scal rules under the case of orthodoxy are:
g^t =
z^t =
^t 1
Gg
^t 1
Zz
^Jt =
(1
(1
J
J ^t 1
G)
Z)
+ (1
^b;t 1 ;
Gs
^b;t 1
Zs
J)
+ "Zt ;
^b;t 1 :
Js
(40)
(41)
(42)
In the case of the emergency budget they are replaced by
g^t =
z^t =
^t 1
Gg
^t 1
Zz
^Jt =
(1
(1
J
J ^t 1
G)
Z)
+ (1
^b;t 1 ;
Gs
^b;t 1
Zs
J)
+ "Zt ;
^b;t 1 :
Js
(43)
(44)
(45)
The block of equations that characterize the shadow economy consists in an additional set
of equations (21) to (38) plus the rule for the monetary authority (39) and the rules for
the …scal authority (40) to (42), where any variables that refers to the actual economy xt is
replaced by the same variable in the shadow economy xt :
33
@FedFRASER