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Sovereign Default in a Monetary Union
de Ferra, Sergio Romei, Federica
Working paper
Presented by Ruben Veiga
January 2019
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 1 / 17
Introduction
Motivation: Core vs Periphery in the EU.Sovereign default in a monetary union. Three levels:
1 Debts are too high.2 Monetary policy too tight when nominal rigidities bind.3 A coalition of the Periphery countries may want to default
strategically!Results on monetary policy:
Zero lower bound may act as a disciplining device.The Core may be willing to accept a laxer monetary policy to getpaid back.
Main ingredients:Default in 2 period model.Nominal rigidities.Different levels of government with small individual agents.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 2 / 17
Outline
1 ModelEnvironmentHouseholdsFirmsCentral BankRegional GovernmentsNational GovernmentsMarket clearing
2 DefaultRegionsCountriesPeriphery Coalition
3 Implications for monetary policy
4 Conclusions
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 3 / 17
ModelEnvironment
Two periods: t = 1,2.
Mass one of countries. Two types: H and F .National fiscal authority.Mass 1 of identical regional fiscal authorities.Continuum of households.Continuum of identical firms.
Supranational monetary authority.Two goods: tradable T (endowment) . . .
yT ,H,1 = yT ,F ,2 = yLyT ,F ,1 = yT ,H,2 = yH
. . . and non-tradable N produced with labor (and subject tonominal rigidities):
yN,i = li
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 4 / 17
ModelEnvironment
Two periods: t = 1,2.Mass one of countries. Two types: H and F .
National fiscal authority.Mass 1 of identical regional fiscal authorities.Continuum of households.Continuum of identical firms.
Supranational monetary authority.Two goods: tradable T (endowment) . . .
yT ,H,1 = yT ,F ,2 = yLyT ,F ,1 = yT ,H,2 = yH
. . . and non-tradable N produced with labor (and subject tonominal rigidities):
yN,i = li
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 4 / 17
ModelEnvironment
Two periods: t = 1,2.Mass one of countries. Two types: H and F .
National fiscal authority.Mass 1 of identical regional fiscal authorities.Continuum of households.Continuum of identical firms.
Supranational monetary authority.
Two goods: tradable T (endowment) . . .
yT ,H,1 = yT ,F ,2 = yLyT ,F ,1 = yT ,H,2 = yH
. . . and non-tradable N produced with labor (and subject tonominal rigidities):
yN,i = li
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 4 / 17
ModelEnvironment
Two periods: t = 1,2.Mass one of countries. Two types: H and F .
National fiscal authority.Mass 1 of identical regional fiscal authorities.Continuum of households.Continuum of identical firms.
Supranational monetary authority.Two goods: tradable T (endowment) . . .
yT ,H,1 = yT ,F ,2 = yLyT ,F ,1 = yT ,H,2 = yH
. . . and non-tradable N produced with labor (and subject tonominal rigidities):
yN,i = li
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 4 / 17
ModelHouseholds
Household of region j , country i .
MaxUi,j = log(
caT ,i,j,1c1−a
N,i,j,1
)+ βE
[log(
caT ,i,j,2c1−a
N,i,j,2
)]s.t. pT ,1cT ,i,j,1 + pN,i,1cN,i,j,1 +
bM,i,j
1 + i= pT ,1
(yT ,i,1 + si,j,1
)+ wi,1li,1
pT ,2cT ,i,j,2 + pN,i,2cN,i,j,2 = pT ,2(yT ,i,2 + si,j,2
)+ bM,i,j + wi,2li,2
Consume Tradable and Non-Tradable. Some endowment ofTradableWork li,t for wage.Save bM,i > 0 that pays nominal interest rate i
Transfer si , j , t from regional gov. j . Stochastic in 2nd period.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 5 / 17
ModelHouseholds
Household of region j , country i .
MaxUi,j = log(
caT ,i,j,1c1−a
N,i,j,1
)+ βE
[log(
caT ,i,j,2c1−a
N,i,j,2
)]s.t. pT ,1cT ,i,j,1 + pN,i,1cN,i,j,1 +
bM,i,j
1 + i= pT ,1
(yT ,i,1 + si,j,1
)+ wi,1li,1
pT ,2cT ,i,j,2 + pN,i,2cN,i,j,2 = pT ,2(yT ,i,2 + si,j,2
)+ bM,i,j + wi,2li,2
Consume Tradable and Non-Tradable. Some endowment ofTradable
Work li,t for wage.Save bM,i > 0 that pays nominal interest rate i
Transfer si , j , t from regional gov. j . Stochastic in 2nd period.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 5 / 17
ModelHouseholds
Household of region j , country i .
MaxUi,j = log(
caT ,i,j,1c1−a
N,i,j,1
)+ βE
[log(
caT ,i,j,2c1−a
N,i,j,2
)]s.t. pT ,1cT ,i,j,1 + pN,i,1cN,i,j,1 +
bM,i,j
1 + i= pT ,1
(yT ,i,1 + si,j,1
)+ wi,1li,1
pT ,2cT ,i,j,2 + pN,i,2cN,i,j,2 = pT ,2(yT ,i,2 + si,j,2
)+ bM,i,j + wi,2li,2
Consume Tradable and Non-Tradable. Some endowment ofTradableWork li,t for wage.
Save bM,i > 0 that pays nominal interest rate i
Transfer si , j , t from regional gov. j . Stochastic in 2nd period.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 5 / 17
ModelHouseholds
Household of region j , country i .
MaxUi,j = log(
caT ,i,j,1c1−a
N,i,j,1
)+ βE
[log(
caT ,i,j,2c1−a
N,i,j,2
)]s.t. pT ,1cT ,i,j,1 + pN,i,1cN,i,j,1 +
bM,i,j
1 + i= pT ,1
(yT ,i,1 + si,j,1
)+ wi,1li,1
pT ,2cT ,i,j,2 + pN,i,2cN,i,j,2 = pT ,2(yT ,i,2 + si,j,2
)+ bM,i,j + wi,2li,2
Consume Tradable and Non-Tradable. Some endowment ofTradableWork li,t for wage.Save bM,i > 0 that pays nominal interest rate i
Transfer si , j , t from regional gov. j . Stochastic in 2nd period.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 5 / 17
ModelHouseholds
Household of region j , country i .
MaxUi,j = log(
caT ,i,j,1c1−a
N,i,j,1
)+ βE
[log(
caT ,i,j,2c1−a
N,i,j,2
)]s.t. pT ,1cT ,i,j,1 + pN,i,1cN,i,j,1 +
bM,i,j
1 + i= pT ,1
(yT ,i,1 + si,j,1
)+ wi,1li,1
pT ,2cT ,i,j,2 + pN,i,2cN,i,j,2 = pT ,2(yT ,i,2 + si,j,2
)+ bM,i,j + wi,2li,2
Consume Tradable and Non-Tradable. Some endowment ofTradableWork li,t for wage.Save bM,i > 0 that pays nominal interest rate i
Transfer si , j , t from regional gov. j . Stochastic in 2nd period.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 5 / 17
ModelHouseholds
Intratemporal:
cN,i,j,t =1− a
apT ,t
pN,i,tcT ,i,j,t
Intertemporal:
1cT ,i,j,1
= β(1 + i)E[
pT ,1
pT ,2
1cT ,i,j,2
]+ µi,j
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 6 / 17
ModelFirms
Firm problem (firms live in Country i , no regional index j):
maxyN,i,t ,li,t
pN,i,tyN,i,t − wi,t li,t
subject to: yN,i,t = li,t
Wage=price of non-tradable.
pN,i,t = wi,t
Nominal rigidities:
wi,1 ≥ κi,1 ; wi,2 ≥ κi,2wi,1
Only a concern when T scarce=⇒ only bind in H at t = 1 and in F in t = 2.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 7 / 17
ModelFirms
Firm problem (firms live in Country i , no regional index j):
maxyN,i,t ,li,t
pN,i,tyN,i,t − wi,t li,t
subject to: yN,i,t = li,t
Wage=price of non-tradable.
pN,i,t = wi,t
Nominal rigidities:
wi,1 ≥ κi,1 ; wi,2 ≥ κi,2wi,1
Only a concern when T scarce=⇒ only bind in H at t = 1 and in F in t = 2.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 7 / 17
Central bank
Not benevolent, rules based.At t = 1, sets i to target average price:
p∗1 = exp
(∫ 1
0ψi × log
(pi,1)
di
)
where price index is pi,t = paT ,i,t × p1−a
N,i,t = paT ,t × w1−a
i,t
At t = 2 sets pT ,2 to target inflation:
π∗ = exp
(∫ 1
0ψi × log
(πi,2)
di
)where inflation is πi,2 =
pi,2pi,1
.
Zero lower bound:i ≥ 0
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 8 / 17
Central bank
Not benevolent, rules based.At t = 1, sets i to target average price:
p∗1 = exp
(∫ 1
0ψi × log
(pi,1)
di
)
where price index is pi,t = paT ,i,t × p1−a
N,i,t = paT ,t × w1−a
i,t
At t = 2 sets pT ,2 to target inflation:
π∗ = exp
(∫ 1
0ψi × log
(πi,2)
di
)where inflation is πi,2 =
pi,2pi,1
.
Zero lower bound:i ≥ 0
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 8 / 17
Regional governments
Maximize welfare of HH: sets transfers and decides if default.Final period default
Cost of default at t = 2: ζ2 =
{ζ̂ > 0 with probability ω0 with probability 1− ω
Default if cost is zero or −bi,j,2 > ζ2.
Initial period trading:H enters with some debt to F : bF ,1 = −bH,1.Choose st and b2 to maximize welfare subject to:
si,j,1 = bi,j,1 −1
1 + ri,jbi,j,2
si,j,2 = max{−ζ2,bi,j,2
}ri,j = r
(bi,j,2
)Initial period default (assume that are low compared with defaultat 2nd period)
Cost (known) : ζ1 < ζ̂ − yH + yL plus exclusion from markets and ζ2.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 9 / 17
Regional governments
Maximize welfare of HH: sets transfers and decides if default.Final period default
Cost of default at t = 2: ζ2 =
{ζ̂ > 0 with probability ω0 with probability 1− ω
Default if cost is zero or −bi,j,2 > ζ2.Initial period trading:
H enters with some debt to F : bF ,1 = −bH,1.Choose st and b2 to maximize welfare subject to:
si,j,1 = bi,j,1 −1
1 + ri,jbi,j,2
si,j,2 = max{−ζ2,bi,j,2
}ri,j = r
(bi,j,2
)Initial period default (assume that are low compared with defaultat 2nd period)
Cost (known) : ζ1 < ζ̂ − yH + yL plus exclusion from markets and ζ2.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 9 / 17
National governments
Alter regional decisions on defaultInternalize the effects of default on domestic demand (the amountof N good produced by firms subject to nominal rigidities)Cannot discriminate across regions.
Coordinated defaultForm coalition of Peryphery countriesThey internalize the the impacts of monetary policy andredistribution effects of the default-repayment decision at t = 1.
Why do we need all these levels of government?!Regions do not internalize impact of decisions on local production(nominal rigidities) and (aggregate prices) monetary policy.Nations internalize the first but not the second.Coalition of the Periphery internalizes both.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 10 / 17
National governments
Alter regional decisions on defaultInternalize the effects of default on domestic demand (the amountof N good produced by firms subject to nominal rigidities)Cannot discriminate across regions.
Coordinated defaultForm coalition of Peryphery countriesThey internalize the the impacts of monetary policy andredistribution effects of the default-repayment decision at t = 1.
Why do we need all these levels of government?!Regions do not internalize impact of decisions on local production(nominal rigidities) and (aggregate prices) monetary policy.Nations internalize the first but not the second.Coalition of the Periphery internalizes both.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 10 / 17
National governments
Alter regional decisions on defaultInternalize the effects of default on domestic demand (the amountof N good produced by firms subject to nominal rigidities)Cannot discriminate across regions.
Coordinated defaultForm coalition of Peryphery countriesThey internalize the the impacts of monetary policy andredistribution effects of the default-repayment decision at t = 1.
Why do we need all these levels of government?!Regions do not internalize impact of decisions on local production(nominal rigidities) and (aggregate prices) monetary policy.Nations internalize the first but not the second.Coalition of the Periphery internalizes both.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 10 / 17
Market Clearing
Tradable good: ∫icT ,i,ddi =
∫iyT ,i,t − ζtDi,tdi
Non Tradable good: ∫jcN,i,j,tdj = yN,i,t
Safe assets ∫ibM,idi = 0 =⇒ bM,i = 0 ∀i
Labor Market: (li,1 − l
) (wi,1 − κi,1
)= 0(
li,2 − l) (
wi,2 − κi,2wi,1)= 0
Sovereign debt: ∫ibi,2di = 0
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 11 / 17
Default by Regions
If repay, CT ,H,1 = CT ,H,2.Region ignores the contribution of good N to welfare.Same result with one good flexible price model.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 12 / 17
Default by Countries
Country i internalizes effects of nominal rigidities→ wants toalleviate the slackness in the economy by ↑ cT ,1 → Lowerthreshold.
Default→↑ cT ,1, ↓ cT ,2 →↑ cN →↑ li
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 13 / 17
Default by coalition of countries
If all H countries default:↑ PT ,1 (tradable resources go to default penalty, so less supply...)F countries cannot save though sovereign bonds =⇒ ↓ cT ,F,2
cT ,F,1
By p∗1 target, ↑ PT ,1 =⇒ ↓ PN,H,1. But if nominal rigidities bind,this cannot happen.Inter-temporal decision of F determines i:
(1 + i) =1βE[
pT ,2
pT ,1
cT ,F ,2
cT ,F ,1
]Either ↑ PT ,2 (but π will go below target) or ↓ i.Then, the CB is forced to lower i, which increases demand on N infirst period and reduce slackness.When nominal rigidities bind for H, the coalition understands howit can force expansionary monetary policy that benefits it.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 14 / 17
Default by coalition of countries
If all H countries default:↑ PT ,1 (tradable resources go to default penalty, so less supply...)F countries cannot save though sovereign bonds =⇒ ↓ cT ,F,2
cT ,F,1
By p∗1 target, ↑ PT ,1 =⇒ ↓ PN,H,1. But if nominal rigidities bind,this cannot happen.
Inter-temporal decision of F determines i:
(1 + i) =1βE[
pT ,2
pT ,1
cT ,F ,2
cT ,F ,1
]Either ↑ PT ,2 (but π will go below target) or ↓ i.Then, the CB is forced to lower i, which increases demand on N infirst period and reduce slackness.When nominal rigidities bind for H, the coalition understands howit can force expansionary monetary policy that benefits it.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 14 / 17
Default by coalition of countries
If all H countries default:↑ PT ,1 (tradable resources go to default penalty, so less supply...)F countries cannot save though sovereign bonds =⇒ ↓ cT ,F,2
cT ,F,1
By p∗1 target, ↑ PT ,1 =⇒ ↓ PN,H,1. But if nominal rigidities bind,this cannot happen.Inter-temporal decision of F determines i:
(1 + i) =1βE[
pT ,2
pT ,1
cT ,F ,2
cT ,F ,1
]Either ↑ PT ,2 (but π will go below target) or ↓ i.
Then, the CB is forced to lower i, which increases demand on N infirst period and reduce slackness.When nominal rigidities bind for H, the coalition understands howit can force expansionary monetary policy that benefits it.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 14 / 17
Default by coalition of countries
If all H countries default:↑ PT ,1 (tradable resources go to default penalty, so less supply...)F countries cannot save though sovereign bonds =⇒ ↓ cT ,F,2
cT ,F,1
By p∗1 target, ↑ PT ,1 =⇒ ↓ PN,H,1. But if nominal rigidities bind,this cannot happen.Inter-temporal decision of F determines i:
(1 + i) =1βE[
pT ,2
pT ,1
cT ,F ,2
cT ,F ,1
]Either ↑ PT ,2 (but π will go below target) or ↓ i.Then, the CB is forced to lower i, which increases demand on N infirst period and reduce slackness.When nominal rigidities bind for H, the coalition understands howit can force expansionary monetary policy that benefits it.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 14 / 17
Zero lower bound
ZLB impose a limit on expansionary monetary policy, reducing theincentives of coalition H to default.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 15 / 17
North vs South: preferences over monetary policy
H prefer higher prices in period 1 to relax nominal rigidities.F prefer lower prices in period 1, to allow for higher inflation inperiod 2, when their output will be lower.But F prefer higher prices in period 1 conditional on H defaulting.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 16 / 17
Conclusions
Neat 2 period model with default. All action happens at period 1.Nice use of different levels of government. But regionalgovernments really necessary?Not sure about robustness of some assumptions.Default-expansionary monetary policy mechanism not so obvious.
de Ferra-Romei ( Working paper Presented by Ruben Veiga )Sovereign Default in a Monetary Union January 2019 17 / 17
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