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 Series
CERGE-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) income
to achieve consumption smoothing.
2 Structural reforms to spur growth
and 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 by
costly 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 trade
see 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 to
punish a sovereign based on past actions)
3 Incomplete markets (no state-contingent debt)
Under what conditions does the
market 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 (consumption
smoothing 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 honor
debt, 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, ¯w] (“recession” and “normal times”).
A two-state Markov switching regime
pt 2 [0, 1] is the (endogenous) probability
of 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 increasing
convex function of the probability of recovery:
X0 (p) > 0 and X00 (p) > 0.
In normal times, X = 0.

(First-Best) Pareto Optimum
Consider a planner who has access to a savings
technology 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 both
consumption and e¤ort choice,
The optimal allocation:
1 Constant consumption sequence
2 Constant reform e¤ort during recession.
Note that if R < 1/β, the planner
frontloads consumption and backloads e¤ort.

Markets
A benevolent government issues one-period discount bonds
b0, 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 to
honor 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 honor
after observing the realization of w and φ.

Default and Renegotiation II
Whenever the default threat is credible, creditors
make a take-it-or-leave-it renegotiation o¤er.
The o¤er keeps the government indi¤erent between
defaulting 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 on
payo¤-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 cannot
commit to punish sovereign for past behavior.

Value Functions
V (b, φ, w) = max fW (b, w) , W (0, w) φg ,
where:
W (b, w) = max
b0
u Q b0
, w b0
+ w b + Z b0
, w ,
Z b0
, ¯w = β EV b0
, φ0
, ¯w ,
Z b0
, w = max
p
8
<
:
X (p) + β
2
4
(1 p) EV (b0, φ0, w) +
pEV (b0, φ0, ¯w)
3
5
9
=
;
.

Renegotiation Threshold
De…ne ˆb (φ, w) as the renegotiated debt
that keeps the sovereign indi¤erent
between repaying ˆb (φ, w) and outright default:
W ˆb (φ, w) , w = W (0, w) φ.
Given the realization of φ and w, the sovereign
will threaten to default if b > ˆb (φ, w) .
Or, identically, 9 ¯Φ (b) (resp. Φ (b)) such that the sovereign
will threaten to default if φ < ¯Φ (b) (resp. φ < Φ (b)).
¯Φ (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 expected
rate of return on the sovereign debt must equal R
Q b0
, ¯w =
1
R
1 F Φ b0
, ¯w
| {z }
probability full repayment
+
1
R
1
b0
Z ¯Φ(b0)
0
ˆb φ0
, ¯w f φ0
dφ0
| {z }
expected debt recovery under reneg. (φ0<F (Φ(b0, ¯w )))

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
Bondprice,Q(b',w)
Debt issued, b'
Risk-free price, 1/R
Normal time
bar(b)
Figure: Bond price function Q (b, ¯w) 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 (C0) H
=
u0 (Q (b0, ¯w) b0 + ¯w b)
u0 (Q (B (b0, ¯w) , ¯w) B (b0, ¯w) + ¯w b0)
= βR
In case of renegotiation, consumption increases
(relative to case when debt is honored)
u0 (C)
u0 (C0) R
> βR
Henceforth, set βR = 1. When debt is honored,
the CEE yields constant consumption and debt.

0 10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Time
Debt
Consumption
Figure: Debt and consumption during normal times.

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 1.8
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Bondprice,Q(b',w)
Debt issued, b'
Risk-free price, 1/R
Normal
Recession
b_bar
b: 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
= arg max
p
8
<
:
X (p) +
+β [pEV (b0, φ0, ¯w) + (1 p) EV (b0, φ0, w)]
9
=
;
.
The …rst order condition yields:
X0
Ψ b0
| {z }
marg. cost reform.
= β
Z ∞
0
V b0
, φ0
, ¯w 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 debt
increases 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 reform
in order to leave the recession.
2 Debt overhang: However, higher debt also
makes 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, b
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
ReformEffort,(b)
0.1
0.12
0.14
0.16
0.18
0.2
Figure: Reform e¤ort function

Time
1 5 T=10 15
Debt
0.6
0.8
1
1.2
1.4
1.6
Consumption
0.5
0.6
0.7
0.8
0.9
1
1.1
Debt
Consumption
Time
1 5 T=10
ReformEffort
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 debt
is 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 insure
against the continuation of the recession
However, insurance mitigates incentives to reform

GDP-linked debt (details)
Let bw and b ¯w denote recession-contingent debt
and recovery-contingent debt.
Denote their prices by Qw b0
w , b0
¯w and Q ¯w b0
w , b0
¯w .
The budget constraint in recession is:
Qw b0
w , b0
¯w b0
w +Q ¯w b0
w , b0
¯w b0
w = B (b, φ, w) +c w.

GDP-linked debt (details)
The value function is:
V (b, φ, w) =
max
fb0
w ,b0
¯w g
u
Qw b0
w , b0
¯w b0
w +
Q ¯w b0
w , b0
¯w b0
¯w + w B (b, φ, w)
X Ψ b0
w , b0
¯w + β
1 Ψ b0
w , b0
¯w EV b0
w , w +
Ψ b0
w , b0
¯w EV (b0
¯w , ¯w)
.
If the probability that the recession ends was
exogenous, Ψ0 = 0, consumption would be independent of
the realization of the aggregate state: c0jH,w = c0jH, ¯w = c.
However, due to moral hazard, consumption falls
and recession-contingent debt increases whenever
the economy remains in recession and debt is honored.

A Planning Problem
A dynamic principle-agent problem
with one-sided commitment.
Planner faces the same limited enforcement
constraint as the market, but
... can commit to future policies
... can make state-contingent promises.
There is a limit to the punishment
that 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)
+pdev W (0, ¯w) E [φ0]
1
A ,
where E [φ0] denotes the expected value of φ0 and
pdev = arg max
p
f X (p) + β ((1 p) W (0, w) + pW (0, ¯w))g
) X0
(pdev ) = β [W (0, ¯w) W (0, w)] .

Constrained Optimum (in recession)
P (v) = max
f ¯ωφ,ωφ,cφ,pφg
Z
@
2
4w cφ + β
0
@
1 pφ P(ωφ)
+pφ
¯P( ¯ωφ)
1
A
3
5 dF (φ)
subject to
Z
@
u(cφ) X(pφ) + β (1 pφ)ωφ + pφ ¯ωφ dF (φ) = v
(PKC)
u(cφ) X(pφ) + β 1 pφ ωφ + pφ ¯ωφ W (0, w) φ (PC)
X pφ + β 1 pφ ωφ + pφ ¯ωφ ζdev (IC)
1 P, ¯P can be interpreted as PV of creditors’exp. pro…ts
2 ωφ is the promised utility conditional on the state
(i.e., the realization of φ)

Optimal Contract with Slack IC
Time
1 5 T=10 15
Consumption
0.75
0.775
0.8
0.825
0.85
Time
1 5 T=10
ReformEffort
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
Time
1 5 T=10 15
Consumption
0.55
0.6
0.65
0.7
0.75
0.8
0.85
ReformEffort
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.21
Consumption
Reform Effort
Time
1 5 T=10 15
PromisedUtility,Recession
-11.2
-11.1
-11
-10.9
-10.8
PromisedUtility,Recovery
-1.55
-1.5
-1.45
-1.4
Recession
Recovery
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 is
equivalent to the laissez-faire equilibrium
(assuming planner breaks even)
Allowing for renegotiation of the bond is equivalent to
introducing 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 b0
2 sets a constant transfer (loan) per period
3 requests a repayment (bn) as soon as the recession ends
4 sweetens the deal each time the borrower gets a low φ
5 out-of-equilibrium threat: drop borrower if e¤ort deviation
Initial promise ν0 depends on the
expected pro…t of the intervention:
Here zero pro…t implies: P(ν0) = R ˆQ(b0, w)b0.

Time
1 5 T=10 15
Debt
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Consumption
0.7
0.75
0.8
0.85
0.9
Debt
Consumption
Time
1 5 T=10
ReformEffort
0.12
0.13
0.14
0.15
0.16
Figure: Implementation of constrained e¢ ciency by means of an
assistance program: simulation of consumption, e¤ort and "implicit
debt" over time.

If the Planner Cannot Observe E¤ort...
Proposition: if the planner does not observe e¤ort,
then the planning (constrained optimal) allocation is
equivalent to the laissez-faire equilibrium with
state-contingent debt.
Note: the result requires that the punishment for
deviation 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 ¯φ φ is distributed exponential, with truncation
point ¯φ and rate parameter η.

Targeted Moments
Target Data Model Par. Value
Average 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% ¯φ 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 ¯b, years)

Time
1 5 10 15 20 25 30 35 40 45 50
Consumption
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Market equilibrium, (a)
ReformEffort
0.1
0.2
0.3
0.4
0.5
Consumption
Reform Effort
Time
1 5 10 15 20 25 30 35 40 45 50
Debtaccumulation
0
0.2
0.4
0.6
0.8
1
1.2
Market equilibrium, (b)
Recession
Debt accumulation
Time
1 5 10 15 20 25 30 35 40 45 50
Consumption
0.75
0.8
0.85
0.9
Second-best, (c)
ReformEffort
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time
1 5 10 15 20 25 30 35 40 45 50
Consumption
0.7
0.8
0.9
1
1.1
First-best, (d)
ReformEffort
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 is
in 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 with
Asonuma 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 13.17 577
State-Cont. Debt 0.94 34
State-Cont. Debt & Contr. E¤ort 2.96 113
Commitment to Honor Debt 10.97 475

Quantitative Welfare E¤ects: Decomposition
Decompose total welfare gain of going from competitive
equilibrium to …rst best into a volatility e¤ect, a level e¤ect,
and a discounting e¤ect.
Discounting Volatility Level
75% 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 (debt
renegotiation 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 50
Initial debt (% of GDP)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
Consumptionequivalentwelfareloss(%)
(a) No Renegotiation
=1
=2
=3
0 20 40 60 80 100 120
Initial 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¤ort
to evaluate the welfare e¤ect of di¤erent policies.
The model is tractable: analytical characterization of the
stochastic equilibrium, including CEE, the equilibrium
price of debt and the probability of renegotiation.
We compare the competitive equilibrium with economies with
less 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 reform
falls with debt (“debt overhang”);
equilibrium outcome: an “unlucky” borrower (recession
drags on) will eventually enter the debt overhang region.

Summary III
An e¢ cient assistance program requires:
! budget support (i.e., loans) during recession
followed 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 incorporates
that a large debt increases the probability
that Greece does not repay after recovering.
The model is quantitatively consistent with realistic
(high) debt, plausible default premium, and with
the empirical haircuts after renegotiation

Sovereign debt and structural reforms

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