Sovereign Default in a Monetary Unionmkredler/ReadGr/VeigaOnDeFerraRomei18.pdf · Presented by Ruben Veiga January 2019 de Ferra-Romei ( Working paperSovereign Default in a Monetary

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.


Outline

1 ModelEnvironmentHouseholdsFirmsCentral BankRegional GovernmentsNational GovernmentsMarket clearing

2 DefaultRegionsCountriesPeriphery Coalition

3 Implications for monetary policy

4 Conclusions


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


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.




yN,i = li


ModelEnvironment



Supranational monetary authority.

Two goods: tradable T (endowment) . . .



yN,i = li


ModelEnvironment






yN,i = li


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.


ModelHouseholds


MaxUi,j = log(

caT ,i,j,1c1−a

N,i,j,1

)+ βE

[log(

caT ,i,j,2c1−a

N,i,j,2


bM,i,j

1 + i= pT ,1

(yT ,i,1 + si,j,1

)+ wi,1li,1



Consume Tradable and Non-Tradable. Some endowment ofTradable

Work li,t for wage.Save bM,i > 0 that pays nominal interest rate i



ModelHouseholds


MaxUi,j = log(

caT ,i,j,1c1−a

N,i,j,1

)+ βE

[log(

caT ,i,j,2c1−a

N,i,j,2


bM,i,j

1 + i= pT ,1

(yT ,i,1 + si,j,1

)+ wi,1li,1



Consume Tradable and Non-Tradable. Some endowment ofTradableWork li,t for wage.

Save bM,i > 0 that pays nominal interest rate i



ModelHouseholds


MaxUi,j = log(

caT ,i,j,1c1−a

N,i,j,1

)+ βE

[log(

caT ,i,j,2c1−a

N,i,j,2


bM,i,j

1 + i= pT ,1

(yT ,i,1 + si,j,1

)+ wi,1li,1






ModelHouseholds


MaxUi,j = log(

caT ,i,j,1c1−a

N,i,j,1

)+ βE

[log(

caT ,i,j,2c1−a

N,i,j,2


bM,i,j

1 + i= pT ,1

(yT ,i,1 + si,j,1

)+ wi,1li,1






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


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.


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.


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


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


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.


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.


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.












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


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.


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


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.




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





cT ,F,1


(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.




cT ,F,1


(1 + i) =1βE[

pT ,2

pT ,1

cT ,F ,2

cT ,F ,1



Zero lower bound

ZLB impose a limit on expansionary monetary policy, reducing theincentives of coalition H to default.


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.


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.


Documents

Sovereign Default in a Monetary Unionmkredler/ReadGr/VeigaOnDeFerraRomei18.pdf · Presented by Ruben Veiga January 2019 de Ferra-Romei ( Working paperSovereign Default in a Monetary