Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable...
Transcript of Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable...
![Page 1: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/1.jpg)
Political Economy of Sovereign DebtCycles of Debt Crisis and Inequality Overhang
Alessandro Dovis, Mikhail Golosov, and Ali Shourideh
Penn State, Princeton & Wharton
August 21, 2015
ITAM-PIER Conference
DGS Political Economy of Sovereign Debt
![Page 2: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/2.jpg)
Introduction
• Fiscal consolidations have unequal effect across the population:
◦ Ponticelli and Voth (2012): Lead to social unrest, often to reversalCyclical behavior of fiscal policies
• Populist policy cycles (Dornbusch and Edwards (1991), Sachs (1989))
◦ Latin american economies in the 20th century:Argentina under Peron, Chile under Allende, Brazil under Sarney
◦ Typical dynamics:
- Large redistributive programs, accumulation of foreign debt- Eventually country got into trouble- Repayment of foreign debt and reversal of redistributive policies
• Theory of fiscal policy cycles in open economy based on
◦ Redistributive motive◦ Lack of commitment
DGS Political Economy of Sovereign Debt
![Page 3: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/3.jpg)
Introduction
• Fiscal consolidations have unequal effect across the population:
◦ Ponticelli and Voth (2012): Lead to social unrest, often to reversalCyclical behavior of fiscal policies
• Populist policy cycles (Dornbusch and Edwards (1991), Sachs (1989))
◦ Latin american economies in the 20th century:Argentina under Peron, Chile under Allende, Brazil under Sarney
◦ Typical dynamics:
- Large redistributive programs, accumulation of foreign debt- Eventually country got into trouble- Repayment of foreign debt and reversal of redistributive policies
• Theory of fiscal policy cycles in open economy based on
◦ Redistributive motive◦ Lack of commitment
DGS Political Economy of Sovereign Debt
![Page 4: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/4.jpg)
What We Do
• Small open economy
• OLG and heterogenous income/skill
• Government with redistributive motive
◦ Redistribution within and across generations◦ Set income taxes, transfers and pensions→ Efficiency-equality trade-off◦ Issues debt: domestically and abroad
• Gov’t cannot commit to
◦ Repay government debt◦ Future income taxes, transfers and pensions
• Two ways to determine policies:
◦ Fictitious planner that cares about current and future generations◦ Outcome of probabilistic voting (Lindbeck and Weibull, 1987)
DGS Political Economy of Sovereign Debt
![Page 5: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/5.jpg)
Main Results
When government highly (external) indebted:
• Overshooting: Drastic adjustment in external indebtedness
◦ External debt reduced below its long-run sustainable level◦ Allow for large inequality
• Repatriation: Foreign debt is substituted with domestic debt
If gov’t more impatient than foreign lenders (or probabilistic voting):
• Cyclical fiscal policy
DGS Political Economy of Sovereign Debt
![Page 6: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/6.jpg)
Main Results
When government highly (external) indebted:
• Overshooting: Drastic adjustment in external indebtedness
◦ External debt reduced below its long-run sustainable level◦ Allow for large inequality
• Repatriation: Foreign debt is substituted with domestic debt
If gov’t more impatient than foreign lenders (or probabilistic voting):
• Cyclical fiscal policy
Time
External Debt
B∗
t
bLow Inequality
DGS Political Economy of Sovereign Debt
![Page 7: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/7.jpg)
Main Results
When government highly (external) indebted:
• Overshooting: Drastic adjustment in external indebtedness
◦ External debt reduced below its long-run sustainable level◦ Allow for large inequality
• Repatriation: Foreign debt is substituted with domestic debt
If gov’t more impatient than foreign lenders (or probabilistic voting):
• Cyclical fiscal policy
Time
External Debt
B∗
t t+ 1
b
bHigh Inequality
Low Inequality
DGS Political Economy of Sovereign Debt
![Page 8: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/8.jpg)
Main Results
When government highly (external) indebted:
• Overshooting: Drastic adjustment in external indebtedness
◦ External debt reduced below its long-run sustainable level◦ Allow for large inequality
• Repatriation: Foreign debt is substituted with domestic debt
If gov’t more impatient than foreign lenders (or probabilistic voting):
• Cyclical fiscal policy
Time
External Debt
B∗
t t+ 1
b
b
b
High Inequality
Low InequalityLow Inequality
t+ 2
DGS Political Economy of Sovereign Debt
![Page 9: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/9.jpg)
Inequality Overhang
• Two incentives to default:
◦ Foreign: Reduce payments to foreigners◦ Domestic: Consumption inequality among the old is undesirable;
always desirable 100% tax on assets for the current old andredistribute via pension
• If wealth inequality among old is large:
◦ There is a strong domestic motive to default◦ Government can support low amount of foreign debt
• Consistent with Berg-Sachs (1988), Aizenman-Jinjarak (2012)
DGS Political Economy of Sovereign Debt
![Page 10: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/10.jpg)
Inequality Overhang
• Two incentives to default:
◦ Foreign: Reduce payments to foreigners◦ Domestic: Consumption inequality among the old is undesirable;
always desirable 100% tax on assets for the current old andredistribute via pension
• If wealth inequality among old is large:
◦ There is a strong domestic motive to default◦ Government can support low amount of foreign debt
• Consistent with Berg-Sachs (1988), Aizenman-Jinjarak (2012)
DGS Political Economy of Sovereign Debt
![Page 11: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/11.jpg)
Related Literature
• Optimal Fiscal Policy: Barro (1979), Lucas and Stokey(1983),Werning (2007), Bhandari, Evans, Golosov, and Sargent (2013)
• Optimal Fiscal Policy without Commitment:
◦ Open economy: Amador, Aguiar and Gopinath(2009), Aguiar andAmador (2014)◦ Closed economy: Farhi, Sleet, Werning and Yeltekin (2012),
D’Erasmo and Mendoza (2014), Scheuer and Wolitzky (2014)
DGS Political Economy of Sovereign Debt
![Page 12: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/12.jpg)
Environment
DGS Political Economy of Sovereign Debt
![Page 13: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/13.jpg)
Environment
• Time is discrete: t = 0, 1, 2, · · ·
• Small open economy
◦ International interest rate 1 + r∗
• OLG structure:
◦ Continuum of households; live for two periods
• Government
DGS Political Economy of Sovereign Debt
![Page 14: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/14.jpg)
Households
• Preferencesu(ct,0,yt; θ) + βu(ct,1)
where θ ∈ Θ ={θ1, · · · , θN
}is individual specific labor
productivity and Pr(θ = θi) = µi.
• Analytical results for log-log preferences
u(c,y; θ) = log c+ψ log(
1 −y
θ
)u(c) = log c
• GDP: Yt =∑i µiyit
◦ Normalization∑Ni=1 µ
iθi = 1;
DGS Political Economy of Sovereign Debt
![Page 15: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/15.jpg)
Households
• Households have access to complete domestic asset markets;No access to international credit market
◦ Without loss of generality: equivalent to households access to int’lcredit market + capital control
• Taxes and transfers:
◦ Linear tax on labor income: τl,t◦ Linear tax on assets: τa,t+1
◦ Receive transfers when young and old: Tt and Pt+1
• Budget constraint:
ci0,t + qtait+1 6 (1 − τl,t)y
it + Tt
cit,1 6 (1 − τa,t+1)ait+1 + Pt+1
DGS Political Economy of Sovereign Debt
![Page 16: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/16.jpg)
Government
• Government can issue debt to
◦ International lenders: B∗t◦ Households: Bt
• Government budget constraint
δtB∗t + (1 − τa,t)Bt + Tt + Pt +Gt = τlt
∑i
µiyit
+qtBt+1 + q∗tB∗t+1
• Credit market clearing:
Bt+1 =∑i
µiait+1
• If B∗t+1 > 0 then q∗t =δt+1
1+r∗
DGS Political Economy of Sovereign Debt
![Page 17: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/17.jpg)
Government
• Government can issue debt to
◦ International lenders: B∗t◦ Households: Bt
• Government budget constraint
δtB∗t + (1 − τa,t)Bt + Tt + Pt +Gt = τlt
∑i
µiyit
+qtBt+1 + q∗tB∗t+1
• Credit market clearing:
Bt+1 =∑i
µiait+1
• If B∗t+1 > 0 then q∗t =δt+1
1+r∗
DGS Political Economy of Sovereign Debt
![Page 18: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/18.jpg)
Government Preferences
• βtαi: Pareto weight of agent of type i in generation t
• Government objective
W =1
βU1,−1 +
∞∑t=0
βtUt
where
◦ U1,−1: Aggregate welfare among initial old◦ Ut: Aggregate welfare of generation born at t:
• Assumption – Inequality aversion: α1 > α2 > · · · > αN◦ Utilitarian: αi = αj
◦ Rawlsian: α1 = 1,αi = 0, i > 1
• Assumption: β(1 + r∗) 6 1
DGS Political Economy of Sovereign Debt
![Page 19: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/19.jpg)
Government Preferences
• βtαi: Pareto weight of agent of type i in generation t
• Government objective
W =1
βU1,−1 +
∞∑t=0
βtUt
where
◦ U1,−1: Aggregate welfare among initial old◦ Ut: Aggregate welfare of generation born at t:
• Assumption – Inequality aversion: α1 > α2 > · · · > αN◦ Utilitarian: αi = αj
◦ Rawlsian: α1 = 1,αi = 0, i > 1
• Assumption: β(1 + r∗) 6 1
DGS Political Economy of Sovereign Debt
![Page 20: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/20.jpg)
Optimal Policy Problem
maxpolicy, all’n, prices
W =1
βU−1,1 +
∞∑t=0
βtUt
subject to
• Policy, all’n, prices constitute a competitive equilibrium
◦ Given an initial value of external government debt: B∗0◦ Given an initial distribution of assets:
{ai0}i=1,··· ,I
• Sustainability constraint
1
βUt−1,1 +
∞∑s=t
βs−tUs >W
DGS Political Economy of Sovereign Debt
![Page 21: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/21.jpg)
Government Value of Default
• W:
◦ The government is in financial autarky forever◦ No saving by households (expect 100% tax on assets)◦ No consumption inequality among the old
• Cost of default: Disruption of asset markets
◦ Cannot borrow from foreign to smooth (relevant with shocks)◦ No saving by households ⇒ worse efficiency-equality trade-off
• W: value of the limit of the finite horizon game
Details
DGS Political Economy of Sovereign Debt
![Page 22: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/22.jpg)
Characterization of Competitive Equilibrium
• To characterize equilibrium, sufficient to focus on aggregates(Ct,0,Ct,1, Yt) that satisfies inter temporal budget constraint
◦ determines τl,t, Tt,Pt+1
◦ determines distribution of allocations through Negishi weights Φt
• With log-log preferences:
ϕit = 1 + κθi − 1
1 − Yt
◦ ϕit: the fraction of consumption by individual of type iconsumption and wealth inequality◦ As Yt increases, Φt increases in SOSD.◦ intuition: Higher taxes ⇒ lower inequality ⇒ lower GDP
DGS Political Economy of Sovereign Debt
![Page 23: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/23.jpg)
Government Preferences
• Value for the government as function of C0,C1, Y with log-log:
Up(C0,C1, Y) = logC0 +ψ log(1 − Y) + β logC1
+(1 +ψ+ β)∑i
αiµi logϕi
Up1 (C1, Y) = β logC1 + β
∑i
αiµi logϕi
DGS Political Economy of Sovereign Debt
![Page 24: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/24.jpg)
Optimal Policy Problem
Government chooses {Ct,0,Ct−1,1, Yt}∞t=0 to
maxβ
β
[∑i
µiαi log(ai0 + P)
]+
∞∑t=0
βtUp(Ct,0,Ct,1, Yt)
subject to
B∗0 +∞∑t=0
1
(1 + r∗)t[Ct−1,1 + Ct,0 +Gt] 6
∞∑t=0
1
(1 + r∗)tYt
1
βUp1 (Ct−1,1; Yt−1) +
∞∑s=t
βs−tUp(Cs,0,Cs,1, Ys) >W
given(B∗0 , {ai0}
)
DGS Political Economy of Sovereign Debt
![Page 25: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/25.jpg)
Optimal Policy with Commitment
DGS Political Economy of Sovereign Debt
![Page 26: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/26.jpg)
Optimal Policy with Commitment and β(1 + r∗) = 1
• Constant consumption and output over time
• Constant inequality - except among initial old
• Roll over external debt; no repayment, CAt =r∗
1+r∗B∗0
DGS Political Economy of Sovereign Debt
![Page 27: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/27.jpg)
Optimal Policy with Commitment and β(1 + r∗) = 1
B∗
Inequality∂ϕi
∂θi
Steady Statewith commitment
DGS Political Economy of Sovereign Debt
![Page 28: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/28.jpg)
Optimal Policy with Commitment and β(1 + r∗) = 1
B∗
Inequality∂ϕi
∂θi
Steady Stateb
with commitment
(B∗t , Ineqt)
DGS Political Economy of Sovereign Debt
![Page 29: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/29.jpg)
Optimal Policy with Commitment and β(1 + r∗) = 1
B∗
Inequality∂ϕi
∂θi
Steady Stateb
with commitment
b
(B∗t , Ineqt)
(B∗t+1, Ineqt+1)
DGS Political Economy of Sovereign Debt
![Page 30: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/30.jpg)
Optimal Policy without Commitment
DGS Political Economy of Sovereign Debt
![Page 31: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/31.jpg)
Two Incentives to Default
• Foreign: Reduce payments to foreigners
• Domestic: Consumption inequality among the old is undesirable;always desirable 100% tax on assets for the current old andredistribute via pension
Higher incentive to default if:
• High foreign debt
• Wealth inequality is high (inequality overhang)
β
β[logC−1,1+
∑i
µiαi logϕit−1]+
∞∑t=0
βtUp(C0,t,C1,t, Yt;Φt) >W
DGS Political Economy of Sovereign Debt
![Page 32: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/32.jpg)
Best Sustainable Allocations with β(1 + r∗) = 1
B∗
Inequality∂ϕi
∂θi
Steady StateNot Sustainable
with commitment
Sustainable
DGS Political Economy of Sovereign Debt
![Page 33: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/33.jpg)
Best Sustainable Allocations with β(1 + r∗) = 1
B∗
Inequality∂ϕi
∂θi
Steady StateNot Sustainable
with commitment
Sustainable
b
b
DGS Political Economy of Sovereign Debt
![Page 34: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/34.jpg)
Best Sustainable Allocations with β(1 + r∗) = 1
B∗
Inequality∂ϕi
∂θi
Steady Statewith commitment
b
b
No Repayment
B∗
b
DGS Political Economy of Sovereign Debt
![Page 35: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/35.jpg)
Best Sustainable Allocations with β(1 + r∗) = 1
B∗
Inequality∂ϕi
∂θi
Steady Statewith commitment
b
b
No Repayment
Repayment
B∗
b
DGS Political Economy of Sovereign Debt
![Page 36: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/36.jpg)
Solution
• Problem has many dimensional states(B∗, {ai}
)• For t > 1, aggregates and inequality for generations born at s > t
are recursive in B∗
• Problem at t = 0 choses aggregates for t = 0, foreign debt andinequality for current generation given
(B∗0 , {ai0}
)
DGS Political Economy of Sovereign Debt
![Page 37: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/37.jpg)
Recursive Problem
• State variable: Value of foreign debt B∗
V(B∗) = maxC0,C1,Y,V ′
β
βlogC1 + logC0 +ψ log(1 − Y)
+(1 +ψ+ β)∑i µiαi logϕi(Y) + βV(B∗
′)
subject to
C0 + C1 +G+ B∗ 6 Y +1
1 + r∗B∗′
1
β
∑i
µiαi logϕi(Y) + V(B∗′) > W
• Value for current gov’t is
W(B∗, Y−) =β
β
∑i
µiαi logϕi(Y−) + V(B∗)
DGS Political Economy of Sovereign Debt
![Page 38: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/38.jpg)
Recursive Problem
• State variable: Value of foreign debt B∗
V(B∗) = maxC,Y,V ′
κlogC+ψ log(1 − Y)
+(1 +ψ+ β)∑i µiαi logϕi(Y) + βV(B∗
′)
subject to
C+G+ B∗ 6 Y +1
1 + r∗B∗′
1
β
∑i
µiαi logϕi(Y) + V(B∗′) > W
• Value for current gov’t is
W(B∗, Y−) =β
β
∑i
µiαi logϕi(Y−) + V(B∗)
DGS Political Economy of Sovereign Debt
![Page 39: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/39.jpg)
Main Result: B∗ ′(B∗) is Inverted U-shaped
TheoremThere exists B∗ such that:
• for all B∗ < B∗, B∗′(B∗) is increasing in B∗ and the sustainability
constraint is slack
• for all B∗ > B∗, B∗′(B∗) is decreasing in B∗ and the sustainability
constraint is binding
b
45o
B∗
B∗′
B∗
β(1 + r∗) = 1
DGS Political Economy of Sovereign Debt
![Page 40: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/40.jpg)
Main Result: B∗ ′(B∗) is Inverted U-shaped
TheoremThere exists B∗ such that:
• for all B∗ < B∗, B∗′(B∗) is increasing in B∗ and the sustainability
constraint is slack
• for all B∗ > B∗, B∗′(B∗) is decreasing in B∗ and the sustainability
constraint is binding
b
45o
B∗
B∗′
B∗
β(1 + r∗) < 1
DGS Political Economy of Sovereign Debt
![Page 41: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/41.jpg)
Idea of Proof: Low Foreign Debt
• Low foreign debt ⇒ sustainability constraint is slack
◦ Euler Equation:
V ′(B∗) = β(1 + r∗)V ′(B∗′)
◦ V(·): concave and decreasing → B∗′
increasing in B∗.
DGS Political Economy of Sovereign Debt
![Page 42: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/42.jpg)
Idea of Proof: High Foreign Debt
• Low promised values ⇒ sustainability constraint is binding
◦ Sustainability with equality
β
β
∑i
µiαi logϕi + V(B∗′) =W
◦ As B∗ increases: consumption, leisure and “equality” decrease
◦ “Equality” is a normal good
◦ Φ increases (SOSD) ⇒ to satisfy sustainability must decrease B∗′
DGS Political Economy of Sovereign Debt
![Page 43: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/43.jpg)
Overshooting
Inequality∂ϕi
∂θi
b
B∗
⇐⇒ Y{(B∗, Y ) : W (B∗, Y ) = W}
B∗
B∗
{(B∗′, Y ) : u(B∗′, Y ;B∗) = U}
B∗
u(B∗′, Y;B∗) = κlogC+ψ log(1−Y)+(1+ψ+β)
∑i µiαi logϕi(Y)+ βV(B∗
′)
DGS Political Economy of Sovereign Debt
![Page 44: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/44.jpg)
Overshooting
B∗
Inequality∂ϕi
∂θi
b
B∗
B∗
⇐⇒ Y{(B∗, Y ) : W (B∗, Y ) = W}
B∗
B∗
{(B∗′, Y ) : u(B∗′, Y ;B∗) = U}
B∗ ↑
u(B∗′, Y;B∗) = κlogC+ψ log(1−Y)+(1+ψ+β)
∑i µiαi logϕi(Y)+ βV(B∗
′)
DGS Political Economy of Sovereign Debt
![Page 45: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/45.jpg)
Overshooting
B∗
Inequality∂ϕi
∂θi
b
B∗
B∗
⇐⇒ Y{(B∗, Y ) : W (B∗, Y ) = W}
B∗
B∗
{(B∗′, Y ) : u(B∗′, Y ;B∗) = U}
B∗ ↑
u(B∗′, Y;B∗) = κlogC+ψ log(1−Y)+(1+ψ+β)
∑i µiαi logϕi(Y)+ βV(B∗
′)
DGS Political Economy of Sovereign Debt
![Page 46: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/46.jpg)
Why Gradual Adjustment is not Optimal?
Different government’s perspective:
• Current government
◦ Equality is a normal good: Willing to tolerate high inequality◦ Output gains come with increase in inequality
• Future government:
◦ Cost of inequality among old lower than cost of extra unit of debt◦ Sustainability constraint more sensitive to B∗ than Y
Gov’t better off by
• Allowing for larger inequality (and so increase output)
• Reducing further foreign debt (to ensure credibility of plan)
Gap in gov’t budget made up by issuing more domestic debt
• Easier to sustain because held by domestic citizens
• Repatriation
DGS Political Economy of Sovereign Debt
![Page 47: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/47.jpg)
Why Gradual Adjustment is not Optimal?
Different government’s perspective:
• Current government
◦ Equality is a normal good: Willing to tolerate high inequality◦ Output gains come with increase in inequality
• Future government:
◦ Cost of inequality among old lower than cost of extra unit of debt◦ Sustainability constraint more sensitive to B∗ than Y
Gov’t better off by
• Allowing for larger inequality (and so increase output)
• Reducing further foreign debt (to ensure credibility of plan)
Gap in gov’t budget made up by issuing more domestic debt
• Easier to sustain because held by domestic citizens
• Repatriation
DGS Political Economy of Sovereign Debt
![Page 48: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/48.jpg)
Who is Paying for the Adjustment?
• Burden of adjustment is on current generations:
◦ Old receive low pensions◦ Young receive low consumption, high income inequality
• Compensated by higher future values:
◦ Young promised high pension payments◦ Low income inequality for future generations◦ Front-loading of consumption if β(1 + r∗) < 1→ Accumulation of external gov’t debt
⇒ This gives rise to cycles
DGS Political Economy of Sovereign Debt
![Page 49: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/49.jpg)
Who is Paying for the Adjustment?
• Burden of adjustment is on current generations:
◦ Old receive low pensions◦ Young receive low consumption, high income inequality
• Compensated by higher future values:
◦ Young promised high pension payments◦ Low income inequality for future generations◦ Front-loading of consumption if β(1 + r∗) < 1→ Accumulation of external gov’t debt⇒ This gives rise to cycles
DGS Political Economy of Sovereign Debt
![Page 50: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/50.jpg)
Cycles when β(1 + r∗) < 1
b
45o
B∗
B∗′
B∗0 B∗
ss
DGS Political Economy of Sovereign Debt
![Page 51: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/51.jpg)
Summing-up
In best outcome when government cannot commit and hasredistributive motives, fiscal consolidations are characterized by
• Large adjustment in foreign debt position
• Increase in inequality
• Repatriation of gov’t debt
• Burden on current generation (even if β(1 + r∗) < 1)
• Cyclical policy is optimal if β(1 + r∗) < 1
DGS Political Economy of Sovereign Debt
![Page 52: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/52.jpg)
Assumptions
• Imperfect redistribution Details
◦ Absence of type-specific transfers critical
• Preferences
◦ Results robust to different preferences◦ Analytical results for GHH GHH
◦ Numerical results for BGP preferences
DGS Political Economy of Sovereign Debt
![Page 53: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/53.jpg)
Extensions
• Economy with shocks Details
◦ Same logic◦ Justification for β(1 + r∗) < 1◦ Difference wrt RA economy a la Thomas-Worrall:
Repayment can happen also in bad fiscal time
• Political economy model Details
◦ Consider two equilibria:
- Best SPE- Selection in spirit of Eaton-Gersovitz
◦ So far policies are set by fictitious gov’t that attaches weights tofuture generations◦ Results survive if policies are set in best interest of generations
currently alive only
DGS Political Economy of Sovereign Debt
![Page 54: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/54.jpg)
Conclusion
• Fiscal and Redistributive policies when gov’t lacks commitment
◦ Interaction between domestic and foreign motive to default
• Optimal fiscal consolidation involves cyclical behavior of externaldebt and austerity type adjustments
DGS Political Economy of Sovereign Debt
![Page 55: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/55.jpg)
Populist Cycles
Juan Peron in 1952:
The justicialista [i.e. Peronist] economy asserts that theproduction of the economy should first satisfy the needs of itsinhabitants and only export the surplus; the surplus, nothingmore. With this theory the boys here, of course, eat moreevery day and consume more, so that the surplus is smaller.But these poor guys have been submerged for fifty years; forthis reason I have let them spend and eat and wasteeverything they wanted to for five years . . . but now weundoubtedly must begin to reorder things so as not to wasteany more.
DGS Political Economy of Sovereign Debt
![Page 56: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/56.jpg)
Extra Slides
DGS Political Economy of Sovereign Debt
![Page 57: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/57.jpg)
Government Value of Default
(1 − β)W = maxpolicy, all’n, prices
1
β
∑i
αiµiβu(ci1) +∑i
αiµiu(ci0,yi; θi)
subject to
• Policy, all’n, prices constitute a competitive equilibrium with noassets trade:
◦ Default on government debt: B∗0 = 0, ai0 = 0 ⇒ ci1 = P for all i◦ Young households do not save anticipating default next period:ai1 = 0
Back
DGS Political Economy of Sovereign Debt
![Page 58: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/58.jpg)
Government Value of Default
(1 − β)W = maxpolicy, all’n, prices
1
β
∑i
αiµiβu(ci1) +∑i
αiµiu(ci0,yi; θi)
subject toci1 = P
the static implementability constraint:
uicci0 + u
iyyi = T
and the resource constraint∑i
µici1 +∑i
µici0 +G 6∑i
yi
Back
DGS Political Economy of Sovereign Debt
![Page 59: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/59.jpg)
Period-0 Problem
W0(B∗0 , {ai0}) = max
β
β
∑i
µiαi log((1 − τa)ai0 + P) + V
subject to
1
βUp1 (C1,−;Φ−1) + V >W
B(V) − P − (1 − τa)∑i
µiai0 = B∗0
• Initial external Gov’t Debt: B∗0 Back
DGS Political Economy of Sovereign Debt
![Page 60: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/60.jpg)
Role of Imperfect Redistribution
• Inability to perfectly redistribute resources across householdscritical
• Suppose gov’t had access to type-dependent transfers {T i}
• In this case αiuic = αjujc → {ϕi∗}
• Sustainability constraint is
β
β[logC1 +
∑i
µiαi logϕi∗] + V ′ >W
→ once sustainability binds C1 and V ′ independent of state(as in Thomas-Worrall, 1998)
Back
DGS Political Economy of Sovereign Debt
![Page 61: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/61.jpg)
Role of Preferences
• With log-log preferences:
◦ Wealth effect: Y(V) is decreasing in V◦ Key factor: inequality is decreasing in V
• Can prove the same result for GHH:
log(c0 − v
(yθ
))+ β log c1
◦ Y(V) is increasing in V◦ Key factor: inequality is decreasing in V
Policies Back
DGS Political Economy of Sovereign Debt
![Page 62: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/62.jpg)
Numerical Example with GHH: Allocations
−4.6 −4.4 −4.2 −4 −3.8 −3.6 −3.4 −3.2 −3 −2.8−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
B ∗(V )
V
GH
GL
−4.6 −4.4 −4.2 −4 −3.8 −3.6 −3.4 −3.2 −3 −2.8−5
−4.5
−4
−3.5
−3
−2.5
V ‘(V )
V
GH
GL
45o
−4.6 −4.4 −4.2 −4 −3.8 −3.6 −3.4 −3.2 −3 −2.80.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
C0(V )
V−4.6 −4.4 −4.2 −4 −3.8 −3.6 −3.4 −3.2 −3 −2.8
0.18
0.2
0.22
0.24
0.26
0.28
0.3
C1(V )
V
C1H
G1L
−4.6 −4.4 −4.2 −4 −3.8 −3.6 −3.4 −3.2 −3 −2.80.85
0.9
0.95
1
1.05
1.1
Y (V )
V−4.6 −4.4 −4.2 −4 −3.8 −3.6 −3.4 −3.2 −3 −2.80
0.5
1
1.5
2
2.5
3
{ϕ i(V ) }
VBack DGS Political Economy of Sovereign Debt
![Page 63: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/63.jpg)
Fiscal Consolidation Dynamics with GHH
1 2 3 41
1.0005
1.001
1.0015
1.002
Output
time
1 2 3 41
1.002
1.004
1.006
1.008
1.01
1.012
Consumption Young
time
1 2 3 41
1.005
1.01
1.015
1.02
1.025
Consumption Old
time
1 2 3 4−0.5
0
0.5
1
1.5
Domestic and Foreign Debt
time
Foreign
Domestic
BackDGS Political Economy of Sovereign Debt
![Page 64: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/64.jpg)
Stochastic Economy
DGS Political Economy of Sovereign Debt
![Page 65: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/65.jpg)
Shocks
• Suppose Gt: i.i.d. where Gt ∈ {GL < GH}
• Worst equilibrium is the same as before: WL > WH.
• Complete market for households and government
• Assumption: β(1 + r∗) < 1
• Why impatience?
◦ Continuum of identical countries◦ Lack of commitment in each country◦ Market clearing interest rate is low:
- Countries oversave to avoid default/reneging on tax policies- Alvarez and Jermann (2000), Aiyagari(1994)
DGS Political Economy of Sovereign Debt
![Page 66: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/66.jpg)
V ′(V,G) is U-Shaped
−5.4 −5.2 −5 −4.8 −4.6 −4.4 −4.2 −4 −3.8−5.6
−5.4
−5.2
−5
−4.8
−4.6
−4.4
−4.2
−4
−3.8
−3.6
V‘(V )
V
GH
GL
45o
DGS Political Economy of Sovereign Debt
![Page 67: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/67.jpg)
Overshooting More Pronounced When G Low
−5.4 −5.2 −5 −4.8 −4.6 −4.4 −4.2 −4 −3.8−5.6
−5.4
−5.2
−5
−4.8
−4.6
−4.4
−4.2
−4
−3.8
−3.6
V‘(V )
V
GH
GL
45o
In general equilibrium: Transition from highest value of external debtto negative external debt
DGS Political Economy of Sovereign Debt
![Page 68: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/68.jpg)
But Can Happen Also When G High
−5.4 −5.2 −5 −4.8 −4.6 −4.4 −4.2 −4 −3.8−5.6
−5.4
−5.2
−5
−4.8
−4.6
−4.4
−4.2
−4
−3.8
−3.6
V‘(V )
V
GH
GL
45o
Not true in standard Thomas-Worrall type model (RA economy)Back
DGS Political Economy of Sovereign Debt
![Page 69: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/69.jpg)
Net Repayment Also When G High
−5.4 −5.2 −5 −4.8 −4.6 −4.4 −4.2 −4−0.3
−0.25
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1Public Current Account
V
GH
GL
When government is highly indebted: Positive public current accountalso when G is high Back
DGS Political Economy of Sovereign Debt
![Page 70: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/70.jpg)
Allocations with Log-Log
−5 −4.5 −40.2
0.25
0.3
0.35
0.4
C0(V )
V−5 −4.5 −4
0.22
0.225
0.23
0.235
0.24
0.245
C1(V )
V
CH
GL
−5 −4.5 −40.45
0.5
0.55
0.6
Y (V )
V−5 −4.5 −4
0
0.5
1
1.5
2
2.5
{ϕi(V )}
V
DGS Political Economy of Sovereign Debt
![Page 71: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/71.jpg)
Policies with Log-Log
−5 −4.5 −40.35
0.4
0.45
0.5
0.55
τℓ(V )
V
−5 −4.5 −4−0.4
−0.3
−0.2
−0.1
0
τa(V )
V
GH
GL
−5 −4.5 −4−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
T (V )
V
−5 −4.5 −40.048
0.05
0.052
0.054
0.056
0.058
0.06
P (V )
V
DGS Political Economy of Sovereign Debt
![Page 72: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/72.jpg)
Repatriation of Government Debt
−5.4 −5.2 −5 −4.8 −4.6 −4.4 −4.2 −40.172
0.174
0.176
0.178
0.18
0.182
0.184
0.186Domestic Debt Next Period
V
GH
GL
−5.4 −5.2 −5 −4.8 −4.6 −4.4 −4.2 −4−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
Foreign Debt Next Period
V
Total Debt and Shares Details
DGS Political Economy of Sovereign Debt
![Page 73: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/73.jpg)
Fiscal Consolidation Dynamics
1 2 3 40.99
0.992
0.994
0.996
0.998
1
1.002
Output
time
1 2 3 41
1.01
1.02
1.03
1.04
Consumption Young
time
1 2 3 41
1.01
1.02
1.03
1.04
Consumption Old
time
1 2 3 4−0.5
0
0.5
1
1.5
Domestic and Foreign Debt
time
Foreign
Domestic
DGS Political Economy of Sovereign Debt
![Page 74: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/74.jpg)
Repatriation of Government Debt
−5 −4.5 −4
0.15
0.16
0.17
0.18
0.19
0.2
Total Gov’t Debt
Next Period
V
GH
GL
−5 −4.5 −40.9
0.95
1
1.05
1.1
1.15
1.2
1.25Domestic Share
V
−5 −4.5 −4−0.25
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
Foreign Share
V
Back
DGS Political Economy of Sovereign Debt
![Page 75: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/75.jpg)
Repatriation of Government Debt
When there is repayment:
• Gov’t debt held by foreign investors goes from high to low
• Gov’t debt held domestically goes from low to high
◦ Under our preferred decentralization:
B(V,G) =∑i
µiai(V,G) =∑i
µi[ci(V,G) − P(V,G)]
= C1(V,G) − c11(V,G) = [1 −ϕ1(V,G)]C1(V,G)
◦ C1 ↑ and ϕ1 ↓ ⇒ B ↑Back
DGS Political Economy of Sovereign Debt
![Page 76: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/76.jpg)
Political Economy Model
DGS Political Economy of Sovereign Debt
![Page 77: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/77.jpg)
Political Economy Model
• Policies are set in best interest of generations currently alive
• Policies outcome of political game between two short livedparties: Probabilistic Voting a la Lindbeck and Weibull (1987) Details
• Everything the same as before except sustainability constraint:
ωUp1 (Ct,1, Yt) + vt+1 > v
wherevt = U
p(Ct,0,Ct,1, Yt)
and v is the value of worst equilibrium for current government
DGS Political Economy of Sovereign Debt
![Page 78: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/78.jpg)
Political Economy Model: Results
Consider two SPE outcomes:
• Selection in spirit of Eaton-Gersovitz
◦ If gov’t reneges on debt or pension payments reversion to worstequilibrium
• Best SPE
For both:
• Burden of adjustment on current young
◦ Even if current gov’t attaches zero weight on future generations
• Total debt is cyclical
• Foreign debt is cyclical when ω is large enough
DGS Political Economy of Sovereign Debt
![Page 79: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/79.jpg)
Political Economy Model
• Policies outcome of political game between two short livedparties:Probabilistic Voting a la Lindbeck and Weinbull (1987)
◦ Stage 1: Each party proposes a policy: default, taxes, transfers,pensions
◦ Stage 2: households receive ideological bias shock and vote.winner: majority of votes
◦ Stage 3: Policies are implemented
DGS Political Economy of Sovereign Debt
![Page 80: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/80.jpg)
Political Equilibrium
• Utility of agent i from policy by party j: uit,j + εt,jεit,j uniform
• Probability of winning for party j:∑i
µiFio(uit−1,1,j − u
it−1,1,−j) +
∑i
µiFiy(uit,j − u
it,−j)
• Symmetric equilibrium + uniformity assumption: Governmentmaximizes:
ω∑i
αiµiuit−1,1 +∑i
αiµiuit
• Strategic interaction: pensions chosen by government at t+ 1affect government’s choice at t
DGS Political Economy of Sovereign Debt
![Page 81: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/81.jpg)
Subgame Perfect Equilibria
• Everything the same as before except sustainability constraint:
ωUp1 (Ct,1, Yt) + vt+1 > v
wherevt = U
p(Ct,0,Ct,1, Yt)
and v is the value of worst equilibrium for current government
• Consider two SPE outcomes:◦ Selection in spirit of Eaton-Gersovitz
- If gov’t reneges on debt or pension payments reversion to worstequilibrium
◦ Best SPE
DGS Political Economy of Sovereign Debt
![Page 82: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/82.jpg)
Eaton-Gersovitz Equilibrium
• State: (B, z) where B = (B∗, {ai},Pe), z indicator of past default
• If z = 1: value for the current government is V
• If z = 0: V (B, 0) = max {v (B) ,V} where
v (B) = max(P,C0,Y,B′)
ω∑i
µiαi log(ai + P
)+Up(C0,C1, Y)
subject to∑i
µi(ai + P
)+ C0 + B
∗ +G 6 Y +1
1 + r∗B∗′
v(B′)> V, P > Pe
C1 =
(∑i
µiai′ + P(B′))
, ai′ + P(B′)= ϕi (Y)C1
For t > 1 outcomes recursive in “total debt”: B = B∗ +∑i µiai + Pe
DGS Political Economy of Sovereign Debt
![Page 83: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/83.jpg)
Eaton-Gersovitz Equilibrium
• State: (B, z) where B = (B∗, {ai},Pe), z indicator of past default
• If z = 1: value for the current government is V
• If z = 0: V (B, 0) = max {v (B) ,V} where
v (B) = max(P,C0,Y,B′)
ω∑i
µiαi log(ai + P
)+Up(C0,C1, Y)
subject to∑i
µi(ai + P
)+ C0 + B
∗ +G 6 Y +1
1 + r∗B∗′
v(B′)> V, P > Pe
C1 =
(∑i
µiai′ + P(B′))
, ai′ + P(B′)= ϕi (Y)C1
For t > 1 outcomes recursive in “total debt”: B = B∗ +∑i µiai + Pe
DGS Political Economy of Sovereign Debt
![Page 84: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/84.jpg)
Auxiliary Problem
• For t > 1
w(B)= maxC0,Y,C′1,B
∗′Up(C0,C1, Y)
subject to
B+ C0 +G 6 Y +B∗′
1 + r∗
ω[H (Y) + log
(C′1)]
+w(B∗′ + C′1
)> V
• At t = 0
v (B) = maxP>Pe
ω∑i
µiαi log(ai + P
)+w(B∗ +
∑i
µiai + P)
• Sustainability constraint similar to normative benchmark
DGS Political Economy of Sovereign Debt
![Page 85: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/85.jpg)
Main Result: Overshooting and Cycles
TheoremB′(B) is decreasing.
The theorem implies that:
• Burden of adjustment on current young
◦ Even if current gov’t attaches zero weight on future generations
• Total debt is cyclical
• Foreign debt is cyclical when ω is large enough
Similar result can be proven for best SPE Details Back
DGS Political Economy of Sovereign Debt
![Page 86: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/86.jpg)
Best SPE
max1
βUp1 (C1,−1,Φ−1) +
∞∑t=0
βtUp(Ct,0,Ct,1, Yt)
subject to
B∗0 +∞∑t=0
1
(1 + r∗)t[Ct−1,1 + Ct,0 +Gt] 6
∞∑t=0
1
(1 + r∗)tZYt
ωUp1 (Ct−1,1, Yt−1) +U
p(Ct,0,Ct,1, Yt) > v
given Φ−1,B∗0
DGS Political Economy of Sovereign Debt
![Page 87: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/87.jpg)
Main Result
• Problem is recursive in vt
TheoremSuppose that β(1 + r∗) 6 1. Then there exists v∗
1. When v > v∗, v ′(v) is increasing
2. When v < v∗, v ′(v) is decreasing
• Total debt is cyclical in v
• Foreign debt is cyclical only when ω is large enough
• Similar property holds for a class of Markov equilibria:
◦ Assumption: future governments cannot renege on pensions(triggers punishment)
Back
DGS Political Economy of Sovereign Debt
![Page 88: Political Economy of Sovereign Debt€¦ · External debt reduced below its long-run sustainable level Allow for large inequality ... If wealth inequality among old is large: There](https://reader034.fdocuments.us/reader034/viewer/2022050407/5f83f64e7b79ed15c26ad2f7/html5/thumbnails/88.jpg)
Main Result
• Problem is recursive in vt
TheoremSuppose that β(1 + r∗) 6 1. Then there exists v∗
1. When v > v∗, v ′(v) is increasing
2. When v < v∗, v ′(v) is decreasing
• Total debt is cyclical in v
• Foreign debt is cyclical only when ω is large enough
• Similar property holds for a class of Markov equilibria:
◦ Assumption: future governments cannot renege on pensions(triggers punishment)
Back
DGS Political Economy of Sovereign Debt