sovereign debt and structural reforms

Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion

Sovereign Debt and Structural Reforms

A. Müller K. Storesletten F. Zilibotti

ADEMU Seminar SeriesCERGE-EI Prague, March 20, 2017

Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti


The Debt Dilemma

� The Great Recession hit some Euro countries hard(Portugal, Ireland, Italy, Greece, Spain).

� Natural policy response to a negative income shock:1 Borrow against future (higher) incometo achieve consumption smoothing.

2 Structural reforms to spur growthand speed up recovery

� Problem: sovereign lacks commitment to honor debt� Additional debt increases default risk premia� Incentives to reform might be a¤ected by debt burden



Building Blocks

� A sovereign country has fallen in a recession.� Recovery can be accelerated bycostly structural reforms.

� Debt repayment is subject to limited enforcement(the Troika cannot bomb Athens).

� Renegotiation can avert (mitigate) the cost of default.� Stochastic default costs determine the terms of renegotiation

- e.g., internal politics, international sympathy, value of tradesee evidence in Sturzenegger&Zettelmeyer (JIMF2011),Reinhart&Trebesch (JEEA2016).



Questions

� Study interaction of three frictions in a dynamic model:1 Limited enforcement (debt can be reneged on)2 Limited commitment (market cannot commit topunish a sovereign based on past actions)

3 Incomplete markets (no state-contingent debt)

� Under what conditions does themarket attain/fail to attain e¢ ciency?

� Quantitative questions:1 How large are the potential welfare gains?2 Would ruling out renegotiation improve welfare?3 How large are gains from introducing GDP-linked bonds?



Related Literature

� Model is related to Bulow&Rogo¤ (1989)� Renegotiation entails no cost;� (Potential) default cost de�nes threat point for renegotiation;� Repeated renegotiation is equilibrium outcome.

� Add to B&R: risk aversion, a borrowing motive (consumptionsmoothing in recess.), reform e¤ort, and quantitative analysis

� Quantitative models with costly default and renegotiation� Arellano (2008), Aguiar and Gopinath (2006), etc.

� Models of sovereign debt restructuring� Ex-post ine¢ cient restructuring improves incentives to honordebt, e.g., Yue (2011), Benjamin&Wright (2008),Bolton&Jeanne (2007), Dovis (2016), Amador&al. (2015).

� Debt a¤ects incentives to undertake productive investments:Krugman (1988), Atkeson (1991).



Environment: Technology

� Stochastic aggregate endowments,w 2 [w , w̄ ] (�recession�and �normal times�).

� A two-state Markov switching regime� pt 2 [0, 1] is the (endogenous) probabilityof leaving the low state (w);

� "normal" is an absorbing state (relaxed later).



Environment: Preferences

� Representative in�nitely-lived agent with preferences:

E0 ∑ βt�u (ct )� φt Ifdefault in tg � X (pt )

�.

� X is the cost of reform, assumed to be an increasingconvex function of the probability of recovery:X 0 (p) > 0 and X 00 (p) > 0.

� In normal times, X = 0.



(First-Best) Pareto Optimum

� Consider a planner who has access to a savingstechnology with return R = 1/β.

� Maximize agent�s utility subject to lifetime budget constraint� expected PV of income equals expected PV of consumption.

� Assume that the planner can dictate bothconsumption and e¤ort choice,

� The optimal allocation:1 Constant consumption sequence2 Constant reform e¤ort during recession.

� Note that if R < 1/β, the plannerfrontloads consumption and backloads e¤ort.



Markets

� A benevolent government issues one-period discount bondsb0, i.e., claims to one unit of next-period consumption.

� The bond price is denoted by Q.� Small open economy:

� Bonds are purchased by risk neutral foreign investors;� Risk-free world interest rate: R.



Default and Renegotiation I

� Every period, the government decides whether tohonor the outstanding debt, repudiate it(�inexcusable default�), or renegotiate it.

� Default is subject to a stochastic (i.i.d.) cost, φ,drawn from a p.d.f. f (φ) (c.d.f. F (φ)).

� The realization of the default cost is common knowledge.� The government decides whether to honorafter observing the realization of w and φ.



Default and Renegotiation II

� Whenever the default threat is credible, creditorsmake a take-it-or-leave-it renegotiation o¤er.

� The o¤er keeps the government indi¤erent betweendefaulting and honoring the renegotiated debt level.

� No cost is due under renegotiation (for simplicity).� When the risk of renegotiation is positive, Q < 1/R.



Equilibrium Concept: Markov Equilibrium

� Focus on Markov equilibria� Equilibrium functions only depend onpayo¤-relevant state variables, i.e., b, φ, and w .

� Rules out reputational equilibria(e.g. equilibria conditional on e¤ort previous period)

� Direct default cost vs. reputation (B&R 2015).

� Captures assumption that the market cannotcommit to punish sovereign for past behavior.



Value Functions

V (b, φ,w) = max fW (b,w) ,W (0,w)� φg ,where:

W (b,w) = maxb 0

�u�Q�b0,w

�� b0 + w � b

�+ Z

�b0,w

�,

Z�b0, w̄

�= β� EV

�b0, φ0, w̄

�,

Z�b0,w

�= max

p

8<:�X (p) + β�

24 (1� p)EV (b0, φ0,w) +pEV (b0, φ0, w̄)

359=; .



Renegotiation Threshold

� De�ne b̂ (φ,w) as the renegotiated debtthat keeps the sovereign indi¤erentbetween repaying b̂ (φ,w) and outright default:

W�b̂ (φ,w) ,w

�= W (0,w)� φ.

� Given the realization of φ and w , the sovereignwill threaten to default if b > b̂ (φ,w) .

� Or, identically, 9Φ̄ (b) (resp. Φ (b)) such that the sovereignwill threaten to default if φ < Φ̄ (b) (resp. φ < Φ (b)).

� Φ̄ (b) < Φ (b) (default is more likely in recession).



Normal Times and Recession

� Characterize equilibrium in two steps

� Normal times (after recession ends)

� Recession (with endogenous reform e¤ort)



Normal Time: Debt Price

� Since investors are risk neutral, the expectedrate of return on the sovereign debt must equal R

Q�b0, w̄

�=

1R��1� F

�Φ�b0, w̄

��| {z }probability full repayment

+1R� 1

b0

Z Φ̄(b 0)

0b̂�φ0, w̄

�� f

�φ0�dφ0| {z }

expected debt recovery under reneg. (φ0<F (Φ(b 0,w̄ )))



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0.8

0.85

0.9

0.95

Bond

pric

e, Q

(b',w

)

Debt issued, b'

Riskfree price, 1/RNormal timebar(b)

Figure: Bond price function Q (b, w̄) during normal times



Normal Times: Conditional Euler Equation

� Conditional on no renegotiation (H="honor debt"),a version of the Euler equation (CEE) holds:

u0 (C )u0 (C 0)

��H=

u0 (Q (b0, w̄)� b0 + w̄ � b)u0 (Q (B (b0, w̄) , w̄)� B (b0, w̄) + w̄ � b0) = βR

� In case of renegotiation, consumption increases(relative to case when debt is honored)

u0 (C )u0 (C 0)

��R> βR

� Henceforth, set βR = 1. When debt is honored,the CEE yields constant consumption and debt.



0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

Time

DebtConsumption

Figure: Debt and consumption during normal times.



Normal Times and Recession

� Characterize equilibrium in two steps

� Normal times (after recession ends)

� Recession (with endogenous reform e¤ort)



Timing

1 Aggregate state w is observed;

2 Outside option φ is observed;

3 Sovereign decides whether to honor outstanding debt(in case not, renegotiation game is played);

4 Sovereign issues new debt and consumes;

5 Sovereign exerts reform e¤ort.



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.65

0.7

0.75

0.8

0.85

0.9

0.95

1Bo

nd p

rice,

Q(b

',w)

Debt issued, b'

Riskfree price, 1/RNormalRecessionb_barb: F( Φ(b,w l))=1

Figure: Bond price function in normal time and recession



Reform E¤ort I� Recall timing: the government chooses b0 �rst, and then p.� Investors have rational expectations over p.� The reform e¤ort solves:

Ψ�b0�= argmax

p

8<:�X (p) +

+β [pEV (b0, φ0, w̄) + (1� p)EV (b0, φ0,w)]

9=; .

� The �rst order condition yields:

X 0�Ψ�b0��| {z }

marg. cost reform.

= β

�Z ∞

0

�V�b0, φ0, w̄

�� V

�b0, φ0,w

��dF�φ0��

| {z }expected bene�t of leaving the recession

.



Reform E¤ort II

� Note: If recession ends, then the price of debtincreases because the set of defaults states shrinks.

� Problem:� reform e¤ort is chosen by the debtor after debt is issued.� part of the gains from reform accrue to creditors.

� RESULT: Reform e¤ort is underprovided:

� it would be larger if this period�s e¤ort were contractible.



Reform E¤ort III

� Two opposite forces regulate incentives to reform over time:

1 E¢ ciency: When debt is high, consumption is low,so the marginal utility of consumption is high !! a higher debt strengthens the incentive to reformin order to leave the recession.

2 Debt overhang: However, higher debt alsomakes the moral hazard problem more severe !! debt overhang (Krugman 1988).

� The e¢ ciency e¤ect dominates for a range of low b.� The debt-overhang e¤ect dominates for a range of high b.� RESULT: Equilibrium reform e¤ort is hump-shaped in b.



Debt, b0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Ref

orm

Effo

rt,(b

)

0.1

0.12

0.14

0.16

0.18

0.2

Figure: Reform e¤ort function



Time1 5 T=10 15

Deb

t

0.6

0.8

1

1.2

1.4

1.6

Con

sum

ptio

n

0.5

0.6

0.7

0.8

0.9

1

1.1

DebtConsumption

Time1 5 T=10

Ref

orm

Effo

rt

0.15

0.16

0.17

0.18

0.19

0.2

Figure: Simulation of debt, consumption and e¤ort.Note: debt increases into the debt-overhang area in equilibrium



GDP-linked debt

� We have exogenously assumed that the interest rate on debtis the same irrepective of the realization of the income shock(in the literature, �non-state-contingent debt�)

� The analysis can be extended to allow for GDP-linked debt.� Market for GDP-linked debt cannot restore e¢ ciency.

� Culprit: moral hazard problem and limited commitment.

� Key insight: state-contingent debt is of limited use� State-contingent debt would allow the country to insureagainst the continuation of the recession

� However, insurance mitigates incentives to reform



GDP-linked debt (details)

� Let bw and bw̄ denote recession-contingent debtand recovery-contingent debt.

� Denote their prices by Qw�b0w , b

0w̄

�and Qw̄

�b0w , b

0w̄

�.

� The budget constraint in recession is:

Qw�b0w , b

0w̄

��b0w +Qw̄

�b0w , b

0w̄

��b0w = B (b, φ,w)+ c�w .



GDP-linked debt (details)� The value function is:

V (b, φ,w) =

maxfb 0w ,b 0w̄g

�u�

Qw�b0w , b

0w̄

�� b0w+

Qw̄�b0w , b

0w̄

�� b0w̄ + w �B (b, φ,w)

��X

�Ψ�b0w , b

0w̄

��+ β

� �1�Ψ

�b0w , b

0w̄

��EV

�b0w ,w

�+

Ψ�b0w , b

0w̄

�EV (b0w̄ , w̄)

��.

� If the probability that the recession ends wasexogenous, Ψ0 = 0, consumption would be independent ofthe realization of the aggregate state: c 0jH ,w = c 0jH ,w̄ = c .

� However, due to moral hazard, consumption fallsand recession-contingent debt increases wheneverthe economy remains in recession and debt is honored.



A Planning Problem

� A dynamic principle-agent problemwith one-sided commitment.

� Planner faces the same limited enforcementconstraint as the market, but

� ... can commit to future policies� ... can make state-contingent promises.

� There is a limit to the punishmentthat the planner can in�ict to the agent

� ! send her to the market equilibrium.

� Promised utility approach,following Thomas and Worrall (1988).



Two cases

1 Planner can observe reform e¤ort (as can markets).

2 Planner cannot observe reform e¤ort.



Constrained Optimum: E¤ort Deviation

� Contract speci�es e¤ort & maximizes punishment for dev.� Max punishment: terminate contract and impose default cost.� More formally, continuation utility from a deviation is given by

ζdev � �X (pdev ) + β

0@ (1� pdev )W (0,w)

+pdevW (0, w̄)� E [φ0]

1A ,� where E [φ0] denotes the expected value of φ0 and

pdev = argmaxpf�X (p) + β ((1� p)W (0,w) + pW (0, w̄))g

) X 0 (pdev ) = β [W (0, w̄)�W (0,w)] .



Constrained Optimum (in recession)

P (v) = maxfω̄φ,ωφ,cφ,pφg

Z@

24w � cφ + β

0@�1� pφ

�P(ωφ)

+pφP̄(ω̄φ)

1A35 dF (φ)subject toZ

@

�u(cφ)� X (pφ) + β

�(1� pφ)ωφ + pφω̄φ

��dF (φ) = v

(PKC)

u(cφ)�X (pφ)+ β��1� pφ

�ωφ + pφω̄φ

�� W (0,w)� φ (PC)

�X�pφ

�+ β

��1� pφ

�ωφ + pφω̄φ

�� ζdev (IC)

1 P, P̄ can be interpreted as PV of creditors�exp. pro�ts2 ωφ is the promised utility conditional on the state(i.e., the realization of φ)



Optimal Contract with Slack IC

Time1 5 T=10 15

Con

sum

ptio

n

0.75

0.775

0.8

0.825

0.85

Time1 5 T=10

Ref

orm

Effo

rt

0.12

0.13

0.14

0.15

0.16

Figure: Cons. and e¤ort in the planning problem with slack IC



Optimal Contract with Initially Binding IC

Time1 5 T=10 15

Con

sum

ptio

n

0.55

0.6

0.65

0.7

0.75

0.8

0.85

Ref

orm

Effo

rt0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

ConsumptionReform Effort

Time1 5 T=10 15

Pro

mis

ed U

tility

, Rec

essi

on

11.2

11.1

11

10.9

10.8

Pro

mis

ed U

tility

, Rec

over

y

1.55

1.5

1.45

1.4RecessionRecovery

Figure: Cons., e¤ort, and promised util. when the IC is initially binding



Normal Times and Value of Commitment

� Proposition: if the economy starts in normal times,then the constrained optimal allocation isequivalent to the laissez-faire equilibrium(assuming planner breaks even)

� Allowing for renegotiation of the bond is equivalent tointroducing a full set of state-contingent securities.

� This equivalence does not extend to recessions� with moral hazard in reform e¤ort,the lack of commitment imposes an e¢ ciency loss.



Assistance Plan

� An agency (e.g., the IMF)...1 Buys the outstanding initial debt b02 sets a constant transfer (loan) per period3 requests a repayment (bn) as soon as the recession ends4 sweetens the deal each time the borrower gets a low φ5 out-of-equilibrium threat: drop borrower if e¤ort deviation

� Initial promise ν0 depends on theexpected pro�t of the intervention:

� Here zero pro�t implies: P(ν0) = RQ̂(b0,w)b0.



Time1 5 T=10 15

Deb

t

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Con

sum

ptio

n

0.7

0.75

0.8

0.85

0.9

DebtConsumption

Time1 5 T=10

Ref

orm

Effo

rt

0.12

0.13

0.14

0.15

0.16

Figure: Implementation of constrained e¢ ciency by means of anassistance program: simulation of consumption, e¤ort and "implicitdebt" over time.



If the Planner Cannot Observe E¤ort...

� Proposition: if the planner does not observe e¤ort,then the planning (constrained optimal) allocation isequivalent to the laissez-faire equilibrium withstate-contingent debt.

� Note: the result requires that the punishment fordeviation is to go to the mkt with state-contingent debt.



Recurrent recessions

� Exogenous (low) probability of falling into recession� βR < 1 (to have a stationary debt distribution)

� during normal times debt (wealth) tends to a target level� during recessions debt increases

� IC constraint binds recurrently



Parameters calibrated externally

� A period corresponds to one year� Recession causes a 40% income fall (Greece 2007-13)

� Probability of falling back into a recession: 1%� Annual real gross interest rate: R = 1.02� CRRA-utility with risk aversion of 2� E¤ort cost is iso-elastic: X (p) = ξ � p1+ϕ

� Assume that φ̄� φ is distributed exponential, with truncationpoint φ̄ and rate parameter η.



Targeted Moments

Target Data Model Par. ValueAverage debt: 54.9% 54.0% β 0.972(% GDP, GIIPS, 1950-2015)Bond spread: 4.04% 3.99% η 1.804(GIIPS, at 100% debt-output ratio, 2008-2012)Maximum debt level: 178% 176% φ̄ 2.134(% of normal output, Collard et al. 2015)Expected recession duration: 5 4.95 ϕ 14.24(at max. reform e¤ort, years)Expected recession duration: 10 9.99 ξ 14.55(at the debt limit b̄, years)



Time1 5 10 15 20 25 30 35 40 45 50

Con

sum

ptio

n

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Market equilibrium, (a)

Ref

orm

Effo

rt

0.1

0.2

0.3

0.4

0.5

ConsumptionReform Effort

Time1 5 10 15 20 25 30 35 40 45 50

Deb

t acc

umul

atio

n

0

0.2

0.4

0.6

0.8

1

1.2Market equilibrium, (b)

RecessionDebt accumulation

Time1 5 10 15 20 25 30 35 40 45 50

Con

sum

ptio

n

0.75

0.8

0.85

0.9Secondbest, (c)

Ref

orm

Effo

rt

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time1 5 10 15 20 25 30 35 40 45 50

Con

sum

ptio

n

0.7

0.8

0.9

1

1.1Firstbest, (d)

Ref

orm

Effo

rt

0

0.025

0.05

0.075

0.1

0.125

0.15

Figure: Simulation of market equilibrium, second-best, and �rst-best.



Non-Targeted Moments

� Calibration yields an average bond spread of 3%,in line with data for GIIPS-vs-Germany 1992-2015 (2.5%).

� Renegotiation probability is 6.5%,in line with Tomz and Wright (2013).

� Average haircut conditional on renegotiation is 41%,in line with Tomz and Wright (2013).

� Variation in haircuts isin line with Cruces and Trebesch (2013).

� Average debt relief (market value) 21%,in line with Reinhart and Trebesch (2016).

� Debt-GDP ratio�s are higher in renegotiation periods (89.7%)compared to the average debt-GDP ratio (53.7%), in line withAsonuma and Trebesch (2016).



Quantitative Welfare E¤ects

� Compute welfare gain of going from benchmark economy(competitive equilibrium) to an alternative economy,measured as equivalent variation (in % of consumption).

� Evaluated at 100% debt-GDP ratio during recession

Experiment Total Debt Equivalent (% of Rec. GDP)First Best 13.17 577State-Cont. Debt 0.94 34State-Cont. Debt & Contr. E¤ort 2.96 113Commitment to Honor Debt 10.97 475



Quantitative Welfare E¤ects: Decomposition

� Decompose total welfare gain of going from competitiveequilibrium to �rst best into a volatility e¤ect, a level e¤ect,and a discounting e¤ect.

Discounting Volatility Level75% 21% 4%



Choking Renegotiation

� Experiments:1 disallow renegotiation (New York versus Argentina)

� either honor debt or outright default (Arellano, 2008)

2 assistance program, but commit to punish any deviation (debtrenegotiation or reforms) with termination of contract

� E¤ects:� default occurs in equilibrium� larger default premium� less borrowing (and less risk sharing) in equilibrium



0 10 20 30 40 50Initial debt (% of GDP)

3.5

3

2.5

2

1.5

1

0.5

Con

sum

ptio

n eq

uiva

lent

wel

fare

loss

(%)

(a) No Renegotiation

=1=2=3

0 20 40 60 80 100 120Initial debt (% of GDP)

2.5

2

1.5

1

0.5

0(b) Grexit

=1=2=3



Summary I

� A simple model of sovereign debt and reform e¤ortto evaluate the welfare e¤ect of di¤erent policies.

� The model is tractable: analytical characterization of thestochastic equilibrium, including CEE, the equilibriumprice of debt and the probability of renegotiation.

� We compare the competitive equilibrium with economies withless frictions.



Summary II

� For an economy in recession, the market(laissez-faire equilibrium) yields

� excessive consumption (and reform) volatility;� suboptimal reform e¤ort;� for large debt levels, incentive to reformfalls with debt (�debt overhang�);

� equilibrium outcome: an �unlucky�borrower (recessiondrags on) will eventually enter the debt overhang region.



Summary III

� An e¢ cient assistance program requires:

! budget support (i.e., loans) during recessionfollowed by settling the sovereign country with a(large) debt on market terms upon recovery;

& monitoring of reform e¤ort;& �scal austerity.

� When faced by a credible default threat,the �agency�gives in and sweetens the deal:higher consumption, lower reform e¤ort.

! no Grexit.



Summary IV

� Time consistent? Yes, our model incorporatesthat a large debt increases the probabilitythat Greece does not repay after recovering.

� The model is quantitatively consistent with realistic(high) debt, plausible default premium, and withthe empirical haircuts after renegotiation


sovereign debt and structural reforms

Economy & Finance