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On the International Dimension of Fiscal Policy
Gianluca Benigno and Bianca De Paoli
London School of Economics and Bank of England
February 2010
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Motivation
How should …scal policy be conducted in an open economy?
- Is the prescription di¤erent than the case of closed economies?
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
2 / 24
Motivation
How should …scal policy be conducted in an open economy?
- Is the prescription di¤erent than the case of closed economies?
What is the optimal level of tax smoothing?
- Does the answer depend on the optimal level of exchange rate volatility?
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
2 / 24
Motivation
How should …scal policy be conducted in an open economy?
- Is the prescription di¤erent than the case of closed economies?
What is the optimal level of tax smoothing?
- Does the answer depend on the optimal level of exchange rate volatility?
From a positive perspective, transmission mechanism of …scal shocks
might depend on exchange rate ‡uctuations.
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Motivation (2):
Complementing the literature
Neoclassical literature on optimal …scal policy has focused mainly on
closed economy models
- when taxes are distortionary, taxes should be smoothed over time and
across states of nature
- If possible, taxes would be essentially invariant (see Lucas and Stokey,
1983 and Chari, Christiano and Kehoe, 1991) or would follow a random walk
(see Barro, 1979, Aiyagari et al. 2002).
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
3 / 24
Motivation (2):
Complementing the literature
Neoclassical literature on optimal …scal policy has focused mainly on
closed economy models
- when taxes are distortionary, taxes should be smoothed over time and
across states of nature
- If possible, taxes would be essentially invariant (see Lucas and Stokey,
1983 and Chari, Christiano and Kehoe, 1991) or would follow a random walk
(see Barro, 1979, Aiyagari et al. 2002).
Open economy models have concentrated in the analysis of monetary
policy
- Obstfeld and Rogo¤ (2002), Gali and Monacelli (2005) isomorphism result
between optimal policy in open and closed economy
- Corsetti&Pesenti (2001)/Benigno&Benigno (2003)/De Paoli (2008)presence of terms of trade externality eliminates the result
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
3 / 24
Motivation (2):
Complementing the literature
Neoclassical literature on optimal …scal policy has focused mainly on
closed economy models
- when taxes are distortionary, taxes should be smoothed over time and
across states of nature
- If possible, taxes would be essentially invariant (see Lucas and Stokey,
1983 and Chari, Christiano and Kehoe, 1991) or would follow a random walk
(see Barro, 1979, Aiyagari et al. 2002).
Open economy models have concentrated in the analysis of monetary
policy
- Obstfeld and Rogo¤ (2002), Gali and Monacelli (2005) isomorphism result
between optimal policy in open and closed economy
- Corsetti&Pesenti (2001)/Benigno&Benigno (2003)/De Paoli (2008)presence of terms of trade externality eliminates the result
Bridging the gap...
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
3 / 24
Approach
Theoretical, normative analysis of …scal policy
Formalize a small open economy with endogenous …scal policy
Characterize a utility based loss function each speci…cation
Derive the optimal …scal policy (also look at the planner’s problem)
Analyse the implication for tax and exchange rate volatility
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
4 / 24
Anticipating the results
..
Our analysis shows that in a small open economy optimal policy departs from
tax smoothing.
As emphasised in the optimal monetary policy literature policymakers in open
economies are in‡uenced by a “terms of trade externality”.
- E.g. In an open economy that is a monopolist producer of its own goods, a real
exchange rate appreciation can lead to higher welfare by allowing domestic agents to
consume more for lower levels of domestic production.
- Thus, policymakers have an incentive to use …scal policy to exploit this externality.
- As a result, distortionary taxes vary over time and across states of nature.
When we consider the joint …scal and monetary policy problem, there is a
trade-o¤ between price stability and tax-smoothing that arises from the terms of
trade externality. Quantitatively cost of in‡ation are high and optimal in‡ation
volatility is low.
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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The Model:
overview
2-country DSGE model ) small open economy
Home bias ) deviations from PPP
Monopolistic competition and nominal rigidities a la Calvo ) Role
for monetary policy
Preferences ) allow for trade imbalances
Fiscal authority issues nominal debt and set income taxes (extension
includes the case of indexed linked debt)
Stochastic environment: domestic and foreign productivity shocks,
markup and …scal shocks
Benigno & De Paoli (LSE&BoE)
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February 2010
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The model:
Preferences
Utility (country H – measure n)
∞
U t = Et
∑ βs
s =t
∞
U t = Et
∑ βs
t
s =t
t
"
[U (Cs )
log Cs
V (y (h)s , εY ,s )]
1
n
Z n ε η y h 1 +η
Y ,s ( )s
1+η
0
#
Home bias (Sutherland 2001)
1
θ
θ 1
θ
C = v CH
(1
v ) = (1
+ (1
1
θ
θ 1
θ
θ
θ 1
v ) CF
n)λ and v = nλ
"
# σσ 1
1 Z
σ 1
1 σ n
CH =
c (z ) σ dz
n
0
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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The model:
Relative prices and demand
Law of one price: p (z ) = S p (z ).
Home bias ) PPP does not hold: Qt
SOE demand
yt (h) =
pt (h)
PH ,t
σ
PH ,t
Pt
St Pt /Pt
θ
RoW demand
yt ( f ) =
Benigno & De Paoli (LSE&BoE)
λ) Ct + λ
(1
pt (f )
Pt
1
Qt
Ct
σ
Ct
International Dimension of Fiscal Policy
February 2010
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The model:
Asset markets
Complete markets
UC Ct +1
U (Ct +1 ) Qt +1
= C
UC (Ct )
UC (Ct ) Qt
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
9 / 24
The model:
Fiscal Policy
Government issues one period nominal risk free bonds expressed in local
currency units, collects taxes and faces exogenous expenditure streams.
Government debt Dtn , expressed in nominal terms, follows the law of
motion:
Dtn = Dtn 1 (1 + it 1 ) PH ,t st
where st is the real primary budget surplus:
st
τ t Yt
Gt
Trt
The case real bonds:
Dtr = Dtr
Benigno & De Paoli (LSE&BoE)
r
1 (1 + it 1 ) +
PH ,t
st
Pt
International Dimension of Fiscal Policy
(1)
February 2010
10 / 24
The model:
Monopolistic competitive …rms
Firms’behavior (‡exible prices)
Set prices as a markup over marginal costs
pH ,t =
Benigno & De Paoli (LSE&BoE)
(1
σmut
τ t )(σ
Vy (Yt , εY ,t )
1) Uc (CT )
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February 2010
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Social planner vs. competitive allocation
Understanding the policy incentive:
Planner problem (maximizes agents’utility subject to resourse
constraint and complete markets assumption):
pH ,t Uc (Ct ) = Q (RSt )Vy (Yt , εY ,t )
Competitive equilibrium:
(1
σmut
τ t )(σ
σmut
τ t )(σ
1)
pH ,t Uc (Ct ) =
1)
Vy (Yt , εY ,t )
E¢ ciency condition
(1
Q (RSt ) = 1
) Movements in the tax rate, in the real exchange rate, and markup
shocks generate ine¢ ciencies (i.e. competitive equilibrium departs
from planner’s problem)
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Social planner vs. competitive allocation (2)
E¢ ciency condition
(1
σmut
τ t )(σ
1)
Q (RSt ) = 1
Closed economy
σmut
=1
(1 τ t )(σ 1)
Tax smoothing is optimal when there are no markup shocks
Steady state tax subsidy eliminates steady-state distortion
1
τ̄ =
σ 1
(assuming mu = 1)
Open economy tax smoothing no longer optimal
Steady state optimal tax depends on degree of openness and
substitutability between goods
Q̄ (λ, ρ, θ )
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Understanding the ToT externality
θρ > 1 : real exchange rate appreciation (or ToT improvement)
increases welfare/ reduces loss
Substitute goods: appreciation decreases CH but increases CF reduction in U (C ) smaller than in V (Y )
Complement goods: appreciation cannot divert consumption towards
foreign goods (decrease in CH accompanied by decrease in CF )
θρ < 1: depreciation improve welfare ) leads to higher CH that
increases marginal utility of CF : U (C ) "> V (Y ) "
Externality only eliminated only when the economy is closed (λ = 0)
or when θρ = 1 - in this case marginal utility of CH independent of
CF , and vice-versa
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Linear Quadratic Approach:
Motivation
E¢ ciency condition can pin down the optimal level of taxes in the
case of nominal bonds
) Set taxes to eliminate di¤erence between social planner and
competitive equilibrium
) Government solvency condition satis…ed given in‡ation can
replicate state contingent debt
But in the case of real bonds this is not the case
Have to solve system of non-linear equations
Linear quadratic loss function can also help policy implementation
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
15 / 24
Linear Quadratic Approach:
Loss function
Agent´ s Utility ) Welfare metric
Method of Benigno&Woodford (2003), Sutherland (2002)
min Uc C̄ Et0 ∑ βt
Closed economy
1
Φτ (b
τt
2
min Uc C̄ Et0 ∑ βt
1
b
τ Tt )2 + ΦRS rs
b 2t + t.i.p + O (jjξ jj3 ),
2
1
Φτ (b
τt
2
b
τ Tt )2 + t.i.p + O (jjξ jj3 ),
Open economy: ΦRS rs
b 2t arises given the terms of trade externality
Corsetti and Pesenti (2001): improvements in ToT ) allow larger
consumption for a given level of labour e¤ort (or domestic production)
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Optimal Policy:
The case of nominal debt
Optimal targeting rule
ΦRS rs
bt +
Closed economy:
(1 + l )
Φτ (b
τt
ρ (1 λ )
b
τt
0
0
0
b
τ Tt ) = 0.
b
τ Tt = 0.
Taxes are constant when b
τ Tt = 0 ) when there are no markup
shocks and the steady state is e¢ cient
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Optimal Policy:
Closed economy with nominal debt
Sdv tax rate relative to output
0.5
0.4
0.3
0.2
0.1
0
0.5
1
1.5
Steady state markup
2
2.5
1
1.5
Steady state markup
2
2.5
With Markup Shocks
1.2
1
0.8
0.6
0.4
0.2
0
0.5
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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Optimal Policy:
Open economy with nominal debt
-3
x 10 Sdv Planner/Comp. Wedge
Sdv tax rate relative to output
2
1
1.5
1
0.5
0.5
0
1
1.5
2
2.5
Steady state markup
3
0
1
1.5
2
2.5
Steady state markup
3
-3
x 10
With Markup Shocks
2
5
1.5
4
3
1
2
0.5
0
1
0
1.5
2
2.5
3
1
1.5
2
2.5
3
Steady state markup
Steady state markup
Benigno & De Paoli (LSE&BoE)
International Dimension of Fiscal Policy
February 2010
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19 / 24
Optimal Policy:
Open economy with nominal debt (e¢ cient steady state and no markup shocks)
Sdv tax rate relative to output
Sdv Planner/Comp. Wedge
0.05
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
-0.05
0.4
λ
0
0.1
0.2
0.4
2
2.5
λ
0.05
1
0.8
0.6
0.4
0.2
0.3
0
1
1.5
2
2.5
3
-0.05
θ
Benigno & De Paoli (LSE&BoE)
1
1.5
3
θ
International Dimension of Fiscal Policy
February 2010
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Optimal Policy:
Open economy with real debt (e¢ cient steady state and no markup shocks)
Stv of taxes relative to output
Sdv Planner/Comp. wedge
1.5
0.05
1
0
0.5
0
0
0.1
0.2
0.3
0.4
0.5
-0.05
0
0.1
0.2
λ
0.3
0.4
0.5
λ
Stv of taxes relative to output
Sdv Planner/Comp. wedge
1.5
0.05
1
0
0.5
0
0.5
1
1.5
Benigno & De Paoli (LSE&BoE)
2
θ
2.5
3
-0.05
0.5
International Dimension of Fiscal Policy
1
1.5
2
θ
2.5
February 2010
3
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Optimal Policy: Sticky prices targeting rules
Firms set prices following partial adjustment rule a la Calvo
Loss function now depends also on domestic producer in‡ation
General forms of targeting rules
(1 + l ) Φy
∆b
yt + ΦRS ∆rs
bt +
(1 λ ) ρ
(1
kΦπ
bH
(γb
πH
t + dss (a + 1) π
t 1) = 0
τ ) + bdss k
bH
Et π
t +1 = 0,
Benigno & De Paoli (LSE&BoE)
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February 2010
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Optimal Policy: Sticky prices targeting rules
Figure: Figure 5
Benigno & De Paoli (LSE&BoE)
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Concluding remarks
Simple framework for …scal policy in open economy
Normative analysis: Fiscal policy problem in an open economy 6=
closed economy
Optimal tax variability in an open economy 6= closed economy
Optimal steady state tax in an open economy 6= closed economy
Reason: incentive to use taxes to a¤ect the terms of trade
Fiscal policy e¢ ciency depends on the type of debt.
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February 2010
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