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Sovereign default
Kuala Lumpur 2016 -- Luis Servén
Kuala Lumpur 2016 -- Luis Servén2
Plan
1. Sovereign default in retrospect
2. Modeling sovereign default
3. Self-fulfilling debt crises
4. The maturity of sovereign borrowing
5. Sovereign theft
6. The timing of default
7. The cost of default
8. Financial repression
Kuala Lumpur 2016 -- Luis Servén3
Gross public debt, percent of GDP
The tables have turned.
Kuala Lumpur 2016 -- Luis Servén4
General government debt (% GDP)
Kuala Lumpur 2016 -- Luis Servén5
General government debt (% GDP)
Kuala Lumpur 2016 -- Luis Servén6
General government debt (% GDP)
Kuala Lumpur 2016 -- Luis Servén7
Kuala Lumpur 2016 -- Luis Servén8
Kuala Lumpur 2016 -- Luis Servén9
Source: Trading Economics (http://www.tradingeconomics.com/euro-area/government-debt-to-gdp)
Kuala Lumpur 2016 -- Luis Servén11
Kuala Lumpur 2016 -- Luis Servén12
Kuala Lumpur 2016 -- Luis Servén13
Kuala Lumpur 2016 -- Luis Servén14
Kuala Lumpur 2016 -- Luis Servén15
Sovereign credit events are often seen as a feature of
today’s emerging markets – but their frequency was
as high or higher in the past of today’s rich countries
(and perhaps their near future too!)
The biggest bunching of default episodes happened (i)
after the Napoleonic wars, and (ii) after World War II.
In the 19th century alone, Portugal, Germany and Austria
defaulted 5 times each.
Between 1550 and 1880 Spain defaulted 13 times.
In comparison, the emerging-market defaults of the
1980s and 1990s were sparser and affected a smaller
share of the world economy.
Kuala Lumpur 2016 -- Luis Servén16
Kuala Lumpur 2016 -- Luis Servén17
Kuala Lumpur 2016 -- Luis Servén18
Sovereign default tends to happen more frequently in the
wake of capital flow booms
Kuala Lumpur 2016 -- Luis Servén19
Defaults are more frequent at (or following) times of low
commodity prices
Kuala Lumpur 2016 -- Luis Servén20
The run-up to default is characterized by rising debt
Kuala Lumpur 2016 -- Luis Servén21
The run-up to default is characterized by rising debt
Kuala Lumpur 2016 -- Luis Servén22
Incidence of default and debt levels: all countries
Kuala Lumpur 2016 -- Luis Servén23
Incidence of default and debt levels: emerging markets
Kuala Lumpur 2016 -- Luis Servén24
Public debt, banking crises and sovereign default
Multinomial logit regressions, panel data
Source: Reinhart and Rogoff 2011
Kuala Lumpur 2016 -- Luis Servén25
Public debt, banking crises and sovereign default
Multinomial logit regressions, panel data
Source: Reinhart and Rogoff 2011
Kuala Lumpur 2016 -- Luis Servén26
Public debt, banking crises and sovereign default
Multinomial logit regressions, panel data
Kuala Lumpur 2016 -- Luis Servén27
Modeling sovereign default
Two theoretical views of sovereign default:
(1) Contingent debt: incentive-compatible contracts with state-
contingent payments. Incentives to default are greater in
good states, so default risk should be pro-cyclical.
Typically no defaults in equilibrium.
(2) Non-contingent debt (Eaton-Gersovitz 1981): default
offers a form of risk-sharing to the debtor in the absence of
state-contingent payments. Equilibrium default tends to
happen at times of economic adversity.
Kuala Lumpur 2016 -- Luis Servén28
With non-contingent debt, when is sovereign default optimal?
Cost vs benefit calculation:
Benefit: keeping the resources (for consumption and/or
investment) rather than using them for debt service.
Cost: usually taken to be exclusion form financial markets
It may take other forms too (more on this later):
Seizure of assets abroad
Disruption of trade (including curoff of trade financing)
Secondary debt markets – absent discriminatory default
Debt holdings of domestic banks
Kuala Lumpur 2016 -- Luis Servén29
Hence default is more likely to be the right choice if
-- debt service due is large (so large benefit)
-- the government is not in (much) need of new borrowing (so
small cost of losing access to markets)
e.g., a sovereign with a big debt stock but a small (or no)
deficit in the present and near future.
Kuala Lumpur 2016 -- Luis Servén30
Basic framework to study sovereign default (Arellano
2008):
• benevolent government in small open economy trading bonds
with risk-neutral foreign creditors
• Asset incompleteness: it makes lenders willing to offer
defaultable debt contracts by charging a premium.
• Bond contracts reflect default probabilities endogenous to the
borrower’s incentives to default. Hence the equilibrium
borrowing rate is linked to default.
• Default is penalized with temporary exclusion from financial
markets.
This setup delivers counter-cyclical default risk – as
intuitively expected.
Kuala Lumpur 2016 -- Luis Servén31
Model setup:
• One-period discount bond B (debt if B < 0).
• Uninsurable shocks to income y (Markov with
transition function f(y’, y))
• Risk neutral creditors: bond price incorporates default
probability. Price of B units of bond, given y, is q(B,y).
• Risk averse borrower: default provides a form of risk-
sharing, given that debt is non-contingent.
• Zero recovery: default is full, not partial.
Kuala Lumpur 2016 -- Luis Servén32
Resource constraint under repayment:
c = y + B - q(B’ ,y)B’
(B are bonds carried over from last period)
When the government chooses to default, assume old debts
are erased, and a period of financial autarky follows. In
addition, there are direct output losses.
Resource constraint under default: c = ydef
Output loss: ydef = h(y) < y, where h’ > 0.
Foreign creditors can borrow (or lend) without limit at fixed
r. They have perfect information about y and f.
Kuala Lumpur 2016 -- Luis Servén33
Risk-neutral lenders maximize expected profits choosing B’
and taking bond prices as given:
E profits = qB’ – (1- δ)B’/(1+r)
δ is the (endogenous!) probability of default. For positive
B’, δ = 0, so the equilibrium price q = 1/(1+r).
For negative B’ , default may occur, so the equilibrium price
must compensate for the possibility of default:
q = (1- δ)/(1+r)
Hence q lies in [0, 1/(1+r)].
The government starts with initial assets B, observes y, and
decides to repay or default. If it repays, it can choose B’
subject to the resource constraint, taking q(B’, y) as given.
Kuala Lumpur 2016 -- Luis Servén34
The government’s value function reflects the option to
default:
If the government chooses to repay, the value conditional
on not defaulting is
Under default, income (= consumption) falls and there is
financial autarky that ends with probability θ:
Kuala Lumpur 2016 -- Luis Servén35
In equilibrium, ( , ') reflects the government's default
probabilities (and is consistent with lenders' zero expected profits).
Define the 'stopping region' in which default is optimal, given :
q y B
B
( ) : ( , ) ( )c dD B y v B y v y
Some basic results:
• D(B) is larger the smaller B – i.e., default is more likely
with higher initial debt.
• For sufficiently low B (=sufficiently high debt), default
happens for any realization of y.
• For sufficiently high B, default does not happen for any y
(note that default can never be optimal for B>0)
Kuala Lumpur 2016 -- Luis Servén36
• If output is iid, today’s realization of y gives no
information on tomorrow’s realization. Hence bond
prices depend only on debt: q(y, B’) = q(B’)
• Default incentives then are stronger the lower output: if
y2 is in the default set, and y1< y2, then y2 is too.
• This implies the existence of an upper bound y*(B) such
that default happens for any y < y* (where y* depends
negatively on assets, or positively on debt). The
equilibrium price then depends just on the boundary and
the distribution of y:
1
( ') 1 ( *( '))1
q B F y Br
Kuala Lumpur 2016 -- Luis Servén37
Can there be default in equilibrium?
What matters for borrowers is the extra resources for
consumption they get from borrowing today, q(B)B.
Depending on the form of F, this may generate a ‘Laffer
curve’: a B* such that q(B*)B* provides the maximum
volume of resources for consumption.
The borrower will never choose B’ < B* because s/he can
get the same resources incurring a lower liability (more on
this later).
Kuala Lumpur 2016 -- Luis Servén38
Kuala Lumpur 2016 -- Luis Servén39
Contracts in the ‘risky borrowing’ region carry a default
premium.
Contracts to the right (with higher B’) are default-free.
Contracts to the left will never be taken due to the Laffer
curve.
For the ‘risky borrowing’ region to exist, the bond price
function needs to decrease slowly, so that lower asset levels
yield increasing resources for consumption.
Kuala Lumpur 2016 -- Luis Servén40
Model simulation:
equilibrium prices for a high and a low income shock
(+/- 5% from trend)
Kuala Lumpur 2016 -- Luis Servén41
To what extent can this simple framework fit the data?
The standard test in this literature is to calibrate the model
to Argentina (or some other serial defaulter!) and see if it
fits the facts.
The main finding is that the model can match the volatility
of spreads, but underpredicts their average level. It does
predict a default at the end of 2001 (as actually happened).
Kuala Lumpur 2016 -- Luis Servén42
Kuala Lumpur 2016 -- Luis Servén43
• One limitation of the basic framework is the assumption
of zero recovery. In reality, default episodes involve
partial recovery – whose extent varies a lot.
• Adding endogenous recovery rates allows studying how
renegotiation interacts with the default decision (Yue
2010). It also makes the period of exclusion from
markets endogenous.
• When default occurs, the lenders negotiate with the
country over debt reduction in a Nash bargaining game.
• The main new prediction is that recovery rates decrease
with the volume of debt – as actually observed.
Kuala Lumpur 2016 -- Luis Servén44
Kuala Lumpur 2016 -- Luis Servén45
Kuala Lumpur 2016 -- Luis Servén46
• In this extended framework, the correspondence between
default probabilities and spreads is not one-to-one because of
the endogenous recovery value.
• Still, model simulations (calibrated to Argentina) cannot match
the average level of spreads.
Kuala Lumpur 2016 -- Luis Servén47
Kuala Lumpur 2016 -- Luis Servén48
The model does predict the default of 2001.
49
Self-fulfilling debt crises
In the conventional view default is driven by (bad)
fundamentals. There is a unique equilibrium.
Then sudden shifts in risk premia, seemingly unrelated to
fundamentals (such as those seen in the Eurozone crisis in
2010-2012), are hard to explain.
“…we are in a situation now where you have large parts of the euro
area in what we call a ‘bad equilibrium’, namely an equilibrium
where you may have self-fulfilling expectations that feed upon
themselves and generate very adverse scenarios.”
ECB President Mario Draghi, September 6, 2012
Kuala Lumpur 2016 -- Luis Servén
Euro area sovereign spreads
Kuala Lumpur 2016 -- Luis Servén50
Kuala Lumpur 2016 -- Luis Servén51
Sovereign CDS spreads, basis points
Source: Bloomberg
0
200
400
600
800
1,000
1,200
1,400
1,600
0
200
400
600
800
1,000
1,200
1,400
1,600
Jan-0
8M
ar-0
8A
pr-
08
Jun-0
8Ju
l-08
Sep
-08
Nov-0
8D
ec-0
8
Feb
-09
Mar
-09
May
-09
Jun-0
9A
ug-0
9
Oct
-09
No
v-0
9Ja
n-1
0
Feb
-10
Apr-
10
May
-10
Jul-
10
Aug-1
0
Oct
-10
Dec
-10
Jan-1
1
Mar
-11
Apr-
11
Jun-1
1Ju
l-11
Sep
-11
Nov-1
1D
ec-1
1F
eb-1
2
Mar
-12
May
-12
Jun-1
2
Aug-1
2O
ct-1
2N
ov-1
2Ja
n-1
3F
eb-1
3
Ap
r-1
3M
ay-1
3
Greece Portugal Ireland Spain
52 Kuala Lumpur 2016 -- Luis Servén
Sovereign CDS spreads, basis points
Source: Bloomberg and World Bank
0
200
400
600
800
1,000
1,200
1,400
1,600
0
200
400
600
800
1,000
1,200
1,400
1,600
Jan-0
8M
ar-0
8A
pr-
08
Jun
-08
Jul-
08
Sep
-08
Nov-0
8D
ec-0
8
Feb
-09
Mar
-09
May
-09
Jun
-09
Aug-0
9
Oct
-09
No
v-0
9Ja
n-1
0
Feb
-10
Apr-
10
May
-10
Jul-
10
Aug-1
0
Oct
-10
Dec
-10
Jan-1
1
Mar
-11
Apr-
11
Jun
-11
Jul-
11
Sep
-11
Nov-1
1D
ec-1
1F
eb-1
2
Mar
-12
May
-12
Jun
-12
Aug-1
2O
ct-1
2N
ov-1
2Ja
n-1
3F
eb-1
3
Ap
r-13
May
-13
Average BRCTI (Brazil, Russia, China, Turkey, Indonesia)
Average EU-5 (Greece, Spain, Portugal, Italy, Ireland)
53 Kuala Lumpur 2016 -- Luis Servén
Self-fulfilling sovereign debt crises are analogous to
second-generation currency crises
Two kinds:
• Rollover crises: creditor runs on short-term debt – just
like bank runs.
Self-fulfilling liquidity crises (Cole and Kehoe 2000): lenders’
refuse to roll over the debt coming due because of fears of default.
This forces immediate default – even though it would not be
triggered if lenders held more optimistic expectations.
Kuala Lumpur 2016 -- Luis Servén54
Rollover crises can arise when the stock of debt coming
due is sufficiently large and economic fundamentals are
sufficiently weak (e.g., Bocola and Dovis 2015).
Role for a LOLR (the IMF?) to step in and avoid the
liquidity crisis
Standard policy advice: avoid short-term borrowing and
bunching of maturities.
Kuala Lumpur 2016 -- Luis Servén55
• Multiple equilibria through risk spreads
In standard models of sovereign debt, interest rates are high when
default probabilities are high.
But there may be conditions under which the reverse is also true:
default probabilities are high because interest rates are high.
If creditors believe the borrower is likely to default, they may
demand a large risk premium for their loans, eventually turning the
borrower insolvent (Calvo 2008)
Kuala Lumpur 2016 -- Luis Servén56
Unlike rollover crises, default need not happen immediately: “slow-
moving” debt crises may occur (Lorenzoni and Werning 2014).
(1) Under what conditions can the feedback loop between interest
rates and debt burden lead to self-fulfilling debt crises?
(2) If default can happen through self-fulfilling spread hikes, how
can policy help avoid the ‘high spread’ outcome?
Kuala Lumpur 2016 -- Luis Servén57
Simple 2-period model with multiplicity (Ayres et al 2015)
Borrower is a small open economy with preferences
U(c1) + βEU(c2)
Income process:
y1 = 1
y2 = yl with probability p
yh with probability (1 − p)
1 < yl < yh
Continuum of risk-neutral foreign lenders with alternative return R*
The expected return of lending to the country, taking default into
account, has to be equal to R*
Kuala Lumpur 2016 -- Luis Servén58
Zero initial debt.
Borrow b, at a rate R. At t = 2, two possibilities:
1. pay bR = a.
2. default. If default, output is lost and c2 = 1
Borrower’s choice variable: two possible specifications
1. b, amount received at t = 1 (as in Calvo 2008): the
government decides how much to issue at the lowest bid.
2. a = bR, amount paid at t = 2 (as in Arellano 2008): the
government decides the value of debt at maturity and adjusts
its short-term financing need.
Kuala Lumpur 2016 -- Luis Servén59
• First period
Creditor i offers limited funds at gross interest rate Ri.
The borrower moves next and borrows from the low-rate creditors:
In equilibrium, Ri = R; let bi = b.
• Second period
Output is realized. The borrower pays only if the cost of paying is
less than the benefit of paying:
bR < y2 − 1
Kuala Lumpur 2016 -- Luis Servén60
1
0
ib b di
• Supply of debt: given by creditors’ arbitrage condition
R* = R[1 − F (1 + Rb)]. This defines a locus of points (b, R) that
can be interpreted as the supply of funds.
For each b there may be more than one R that satisfies the equation
Kuala Lumpur 2016 -- Luis Servén61
Kuala Lumpur 2016 -- Luis Servén62
Debt supply
For high debt demand, there may be 2 equilibria
• Demand for debt: given by utility maximization by the borrower:
Kuala Lumpur 2016 -- Luis Servén63
1
1
(1 ) (1 ) (1) ( ) ( )
The first-order condition is
'(1 ) '( ) ( )
This defines the demand for debt.
Y
bR
Y
bR
U b F bR U U y bR f y dy
U b R U y bR f y dy
Kuala Lumpur 2016 -- Luis Servén64
Equilibrium
For high debt demand, there may be 2 equilibria
What is different in the standard model (Arellano (2008) and Aguiar
and Gopinath (2006))?
• Alternative action: does it matter (for multiplicity) whether the choice for the
borrower is b or a = Rb?
1. Calvo (1988). Schedule in b, multiple equilibria.
2. Aguiar and Gopinath (2006), Arellano (2008). Schedule in a, single
equilibrium.
[For lenders, it is clearly inessential]
• Alternative timing:
1. The borrower moves first and chooses b or a = bR (as here)
2. Given the choice b (or a), creditors move next and offer schedule R(b)
[or q(a) = 1 / R(a) as in Arellano 2008]
Kuala Lumpur 2016 -- Luis Servén65
Kuala Lumpur 2016 -- Luis Servén
(conventional case)
66
Rb
For any general density f(y) and CDF F(y),
• If the borrower chooses b, the supply schedule is
R* = R[1 − F (1 + Rb)]
• If the borrower chooses a = Rb, the supply schedule is
R* = R[1 − F (1 + a)]
• Multiplicity results from the possibility of different premia
being charged on a given amount of borrowing
• Picking a amounts to picking the future liability – inclusive of
the premium added by creditors in R.
• If the borrower moves first and chooses a, she is in effect
choosing the spread too – no room for multiplicityKuala Lumpur 2016 -- Luis Servén67
In most configurations there can be multiple equilibria and
self-fulfilling debt crises.
The standard setting assumes the government commits to a given
bond issuance a – regardless of the eventual pricing (amount
raised). In reality, the government will likely issue debt as needed
to raise its target amount b.
With multiplicity, policy may be effective in selecting the
low rate equilibrium:
Design of the policy intervention: a deep-pocket agent offers to
lend large amounts to the country at policy rate RP
The policy would be effective but costless if RP is set just above
the low-level equilibrium R.
Kuala Lumpur 2016 -- Luis Servén68
Slow-moving self-fulfilling crises
Spread feedback loop with long-term debt (Lorenzoni and Werning
2015).
(Simplified) setting: long-term debt as a perpetuity with coupon
payments that decay geometrically at rate 0 < δ < 1:
κ, κ (1-δ), κ (1-δ)2…
So a bond issued at t-s corresponds to (1-δ)s bonds issued at time t
[avoids having to keep track of how much debt was issued when]
Investors’ discount rate is R = 1+r
Smaller δ = longer maturity. Assume κ = δ+r
Kuala Lumpur 2016 -- Luis Servén69
• Budget constraint if no default: st + qt[bt+1 - (1-δ) bt] = κbt
The surplus s is uncertain. To simplify, assume all uncertainty
is concentrated at t = T.
Before T, the surplus follows
(a debt-responsive fiscal rule)
From T onward, the surplus forever equals s = rS, where S is
uncertain with CDF F(S)
Default happens at T if s < rbT. This happens with prob F(bT)
Under default, there is a recovery value ϕ
Kuala Lumpur 2016 -- Luis Servén70
1 0 1(1 ) ( )t t ts s b
• Investors’ arbitrage equation for t < T – 1:
qt = [(1-δ) qt+1+κ] / (1+r)
• Arbitrage equation at T – 1:
Multiplying both sides by bT we get a Laffer curve.
In general it is not monotonic because as bT
increases the probability of default also rises
Kuala Lumpur 2016 -- Luis Servén71
1
0
11 ( ) ( )
1
Tb
T T
T
q F b SdF Sr b
Kuala Lumpur 2016 -- Luis Servén72
A numerical example
Blue = Laffer curve
Green = qT and bT obtained solving the model for all possible values of q0
Here there are three equilibria (two stable)
Kuala Lumpur 2016 -- Luis Servén73
A numerical example: dynamics
A jump from the good to the bad equilibrium leads to a growing difference in debt
dynamics as a larger fraction of debt is issued at distressed prices
Kuala Lumpur 2016 -- Luis Servén74
More activist surplus rule increases the good-equilibrium uniqueness region (lower
red region). With passive surplus, high debt leads to immediate default.
Longer maturities also expand the good-equilibrium uniqueness region. Very low
maturities require more refinancing and expand the immediate default region.
Was this mechanism at work in the Euro crisis?
Not clear: short–run spreads jumped even more than long-run spreads.
Kuala Lumpur 2016 -- Luis Servén75
Other possible explanations
Rollover risk (Corsetti and Dedola 2014)
Currency risk (Euro exit)
Can policy help avoid self-fulfilling debt crises?
Monetary policy might help rule out the bad equilibrium – by inflating
away the debt. This is relevant with long-term debt – not for runs on
short-term debt.
This is analyzed by Bacchetta, Perazzi and van Wincoop (2015): long-
term debt in a NK model of monetary policy.
Result: Aggressive monetary policy does work – but at the cost of very
high inflation (e.g., 25% for b/y around 100%).
Kuala Lumpur 2016 -- Luis Servén76
Kuala Lumpur 2016 -- Luis Servén77
The maturity of sovereign borrowing
Borrowers can issue debt at short and long maturities. What
drives the maturity structure of public debt?
Short-term debt provides a commitment device for the debtor – it
reduces the incentive to default or inflate away (because the
penalty comes right away).
Long-term debt can be diluted by further debt issuance.
This difference is reflected in the returns required by debt
holders. Thus it is cheaper for debtors to raise short-term loans.
But also: long-term debt avoids the risk of rollover crises.
Kuala Lumpur 2016 -- Luis Servén78
The equilibrium maturity composition of debt reflects these
ingredients.
Some recent perspectives:
• Lender risk aversion: Asset holders may need to liquidate
their holdings of long-term debt prior to maturity at an
uncertain price, so they charge a risk premium to hold them
(Broner et al 2011)
The secondary-market price of long term debt is volatile
because future government revenues are uncertain.
Kuala Lumpur 2016 -- Luis Servén79
• Hedging benefit of long-term debt for (risk-neutral)
borrowers: debtors can hedge against the risk of having to
issue debt in bad times – e.g., having to roll over the debt
at high rates (Arellano and Ramanarayanan 2012).
• Optimal choice of maturity under dilution and rollover
risk (Chatterjee and Eyigungor 2012)
Kuala Lumpur 2016 -- Luis Servén80
Consider the case of risk-averse lenders who want to hedge the
risk of lending long term. (Broner et al 2011)
The government transfers part of the rollover risk to investors by
issuing some long-term debt.
The optimal maturity composition of debt results from risk-
sharing equilibrium between lenders and borrowers.
Funds supply shocks: the higher investor risk-aversion, the
higher the term premium and the shorter the maturity of debt.
Funds demand shocks: the lower expected future fiscal revenues,
the higher the term premium.
These model predictions are tested using foreign-currency bond
price and quantity data for 8 emerging markets, 1990-2003.
Kuala Lumpur 2016 -- Luis Servén81
The term premium is usually positive
Kuala Lumpur 2016 -- Luis Servén82
The term premium usually rises in crisis periods
Kuala Lumpur 2016 -- Luis Servén83
But with extreme turbulence there are reversals…
Kuala Lumpur 2016 -- Luis Servén84
…with extreme turbulence there are reversals…
Kuala Lumpur 2016 -- Luis Servén85
…with extreme turbulence there are reversals…
Kuala Lumpur 2016 -- Luis Servén86
Selected Euro Area countries 10-year
government bond spread vs Bund (basis points)
Source: Bloomberg
-500
0
500
1,000
1,500
2,000
Jan-9
5
Aug-9
5
Mar
-96
Oct
-96
May
-97
Dec
-97
Jul-
98
Feb
-99
Sep
-99
Apr-
00
Nov-0
0
Jun-0
1
Jan-0
2
Aug-0
2
Mar
-03
Oct
-03
May
-04
Dec
-04
Jul-
05
Feb
-06
Sep
-06
Apr-
07
Nov-0
7
Jun
-08
Jan-0
9
Aug-0
9
Mar
-10
Oct
-10
May
-11
Dec
-11
Jul-
12
Feb
-13
Portugal Ireland Italy Greece Spain
87 Kuala Lumpur 2016 -- Luis Servén
Selected Euro Area countries 2-year
government bond spread vs Bund (basis points)
Source: Bloomberg
-500
0
500
1,000
1,500
2,000
Jul-
97
Jan-9
8
Jul-
98
Jan-9
9
Jul-
99
Jan-0
0
Jul-
00
Jan-0
1
Jul-
01
Jan
-02
Jul-
02
Jan-0
3
Jul-
03
Jan-0
4
Jul-
04
Jan-0
5
Jul-
05
Jan-0
6
Jul-
06
Jan-0
7
Jul-
07
Jan-0
8
Jul-
08
Jan-0
9
Jul-
09
Jan-1
0
Jul-
10
Jan-1
1
Jul-
11
Jan-1
2
Jul-
12
Jan-1
3
Jul-
13
Portugal Ireland Italy Greece Spain
88 Kuala Lumpur 2016 -- Luis Servén
Kuala Lumpur 2016 -- Luis Servén89
Crises make a significant difference for the term premium – in
all cases and crisis definitions.
Kuala Lumpur 2016 -- Luis Servén90
Adding some standard controls does not change the result
Kuala Lumpur 2016 -- Luis Servén91
In turbulent periods countries issue less long-term debt (but
there is no significant effect on short-term)
Kuala Lumpur 2016 -- Luis Servén92
Kuala Lumpur 2016 -- Luis Servén93
Borrower hedging: alternative perspective highlighting the
hedging benefit of long-term borrowing for debtors
(Arellano and Ramanarayanan 2012).
Lenders are risk-neutral, and borrowers hedge against the
risk of having to issue debt at high rates in bad times.
Kuala Lumpur 2016 -- Luis Servén94
Setup: to keep thinks tractable, model long-term debt as a
perpetuity with coupon payments that decay geometrically
at rate 0 < δ < 1.
[This helps avoid having to keep track of how much debt
was issued when]
1
1
1
1
price of the perpetuity at issue
what the borrower collects
payment due in period
total payment due (=long-term debt stock) at time t
law of motion
t
t t
n
t
tj
Lt t j
j
Lt Lt t
q
q
t n
b
b b
of long-term debt
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The rest of the setup is similar to Arellano (2008):
'
'
( , , ) max ( , , ), ( )
( ) ( ) (0,0, ') (1 ) ( ') ( , ') ' default value
( , , ) max ( ) ( , , ) ( , ') ' continuation value
( ' , '
o c d
S L S L
d def o d
y
c c
S L S L
y
S L S S L
v b b y v b b y v y
v y u y v y v y f y y dy
v b b y u c v b b y f y y dy
c y b b q b b
, ) ' ( ' , ' , ) ' consumption
( , ) : ( , , ) ( ) default set
( , ) : ( , , ) ( ) repayment set
S L S L L
c d
S L S L
c d
S L S L
y b q b b y b
D b b y Y v b b y v y
R b b y Y v b b y v y
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( ' , ' )
( ' , ' )
1 Pr[ ]( ' , ' , ) ( , ') '
1 * 1 *
1( ' , ' , ) 1 ( ' , ' , '), ( ' , ' , '), ' ( , ') '
1 *
where are the policy functions characterizing debt
S L
S L
S S L
R b b
L S L L S S L L S L
R b b
j
repaymentq b b y f y y dy
r r
q b b y q b b b y b b b y y f y y dyr
b
issuance.
The pricing of debt by risk-neutral competitive lenders is :
The important thing to note is the extra item in the long-term
debt price: purchasing long debt today yields a payment of 1
tomorrow, plus remaining debt worth δq’L.
Facing these prices, the borrower’s optimal decision regarding
short- and long-term borrowing yields first-order conditions:
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1 ' '( ') '
1 ' ' '( ') '
'''( ) 1 (1 *) '( ') '
' '
'''( ) 1
' '
(1 *) '( ') ' L
L
L LS S L
S S S S
L LS S L
L L L L
E q u c R
E q R E u c R
b bb q qu c r E u c R
q b q b
b bb q qu c
q b q b
r E u c R
The LHS of both first order conditions captures the effects of
issuing debt on the incentives to repay.
• the price of S-T debt depends on incentive to repay tomorrow
• the price of L-T debt depends also on the decision to borrow again
tomorrow: if it is positively related to today’s debt, then the price of L-
T debt is more sensitive to debt volumes than the S-T price – so S-T
debt provides a stronger incentive to repay.
The RHS of the L-T FOC captures its hedging benefit.
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1 ' , '( ') ' 0LCov q u c R
The hedging benefit arises when
i.e., when across repayment states low consumption is
accompanied by low debt prices – L-T bonds are then a good
hedge because their value falls in bad times.
This does not apply to S-T debt because its future value does
not change across states.
Hence a risk-averse borrower will generally issue both types of
debt.
The optimal maturity structure of borrowing is achieved by
equating the incentive to repay of L-T debt, relative to that of
ST debt, to the hedging benefit of L-T debt.
The relative incentive benefit (higher incentive to repay) of
short-term debt reflects the fact that it cannot be ‘diluted’ by
more borrowing. In contrast, the price of L-T depends on
future borrowing.
Short-term debt has a disciplining effect – lenders can liquidate
it early in bad states, so they are willing to lend larger amounts,
at lower spreads, than L-T debt.
L-T debt allows hedging future fluctuations in consumption
coming from changes in default risk.
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The paper performs some numerical exercises calibrated to
Brazil to test its ability to replicate the maturity structure of
debt and spreads.
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The model underpredicts the average slope of the spread curve,
as well as the average level of spreads at times of high short
spreads (= turbulence).
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The model matches the comovement of duration and spreads,
but underpredicts the average duration of new debt
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In the model, the relative incentive of ST debt is higher when
spreads rise. Maturity shortens when short spreads rise more
than long spreads – same as in the data.
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Other simulations adding risk-averse lenders improve the fit of
spreads but worsen the fit of debt quantitites.
Optimal maturity choice: Chatterjee and Eyigungor (2012)
• Framework similar to Arellano and Ramanarayanan (2012).
Long-term debt is a better hedge against output shocks, but
more expensive than ST debt due to debt dilution.
In baseline model, dilution effect dominates and welfare is
decreasing in maturity!
Adding a small probability of self-fulfilling rollover crises
changes the result.
• Long-term debt limits vulnerability
• With short-term debt only, government must reduce borrowing to
limit vulnerability, and this turns around the welfare result.
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Sovereign theft
Why limit the focus to sovereign debt default? Think also of
sovereign expropriation of foreign investment: more
broadly, “sovereign theft” (Tomz and Wright 2010).
Expropriation risk affects all investments – but especially
foreign investment due to the lack of strong supranational
institutions.
Define expropriation as any of “nationalization, coerced
sale to government, intervention or requisition, or unilateral
contract renegotiation”.
Problem: data available only for countries with U.S. FDI
positions.
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Some stylized facts:
-- Like default, expropriation has tended to occur in waves.
-- Waves of default and expropriation have not coincided.
Expropriations were most common in the 1970s, and at
the end of the sample.
-- Since the 1970s were a period of boom for LDCs, this
means that expropriation does not happen more often in
bad times, unlike default (consistent with theory)
-- Across developing countries, most have either defaulted
and expropriated, or neither.
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What are the determinants of expropriation?
• Since traditional debt stipulates fixed payments, the
incentive to default is highest when resources are most
limited – in bad times.
• Equity involves payments that correlate with the
business cycle. The incentive to expropriate depends on
the relative value placed on resources at bad times:
-- if it is very high, it still leads to expropriation (out of
“desperation”) even though payments are low
-- if it is about the same as in booms, then the incentive
is to expropriate in good times when payments are
large (“opportunism”)
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Analytically, assume the foreign investor has the right to a
share α of total output, itself subject to a stochastic
shock θ. The capital stock k is chosen before the shock
is realized. Then default is optimal if
Here PE is an additional benefit (“prize”) of not defaulting –
e.g., continued access to future investment, avoidance of
sanctions, etc. Let
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Then expropriation occurs when
If the elasticity of substitution is greater than 1, the LHS
rises with the productivity shock, so expropriation is
more likely in good times (“opportunism”). The
opposite happens if it is less than 1 (“desperation”).
How does this work in practice ? Numerical simulations
comparing the expropriation model with an Arellano-
like sovereign default model.
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The probability of expropriation in bad times is lower than that of
default because of the better risk-sharing that equity provides.
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If default on one asset makes you lose both prizes, you tend to
default on both or none. But this is not what we see in the data.
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What does all this imply for the structure of foreign asset
positions ?
Because equity contracts are state-contingent, theory
implies that they should face lower probabilities of
sovereign theft by risk-averse borrowers.
Hence we should see a predominance of equity and FDI
finance over debt in international markets – which was
not the case in the past, but is changing now…
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The timing of default
Theoretical models predict that defaults should happen in
‘bad times’, and conversely for expropriation – is this right?
Tomz and Wright 2008: look at episodes of sovereign
default over 1820-2004 in 175 countries.
Defaults are taken to include reschedulings and
renegotiations, and are assumed to last until there is
agreement with a majority of creditors.
This yields 169 default episodes. Bunching especially
around the 1980s.
H-P filter to define good and bad times.
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In Argentina and Chile, bad times are neither necessary nor
sufficient for default to occur.
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Overall, default occurs more frequently in bad times – but the relationship is
not strong: more than 1/3 of defaults begin in good times.
Severe downturns are more closely tied to defaults – these are twice more
likely when output is 7% or more below trend.
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They also simulate the Aguiar-Gopinath (2006) model to
check its predictions about the timing of default.
The two versions of the model (temporary and permanent
shocks) yield a much tighter relation of default with output:
With temporary shocks, default begins with output below trend
100% of the time.
With permanent shocks, 85% of the time
In reality, it is only 62 percent.
The predicted magnitude of the output shortfall at the onset of
default is also much bigger than the 1.4% observed.
One possible reason for these discrepancies is that other
factors besides output (e.g., political conditions, world
interest rates…) also matter for default.
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Eden et al (2013): look at the correlates and timing of both
default and expropriation.
They use a large dataset covering 192 countries over 1970-
2004.
Both kinds of events tend to happen in the same countries,
but they rarely happen at (or around) the same time.
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Summarizing:
In the short run, default tends to be preceded by rapid debt
accumulation (like in Reinhart-Rogoff).
• It also tends to be preceded by slow growth.
• Defaults are not very persistent over time – i.e., (recent)
past default is not a good predictor of upcoming default.
In contrast, expropriation does not appear to be related to
the existing FDI stock.
• Nor is it systematically preceded by slow growth.
• But expropriation is strongly persistent – the best
predictor is an earlier expropriation occurring in the past
5 years.
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The cost of sovereign default
Theoretical models typically assume that default is punished
by subsequently higher borrowing costs, up to full exclusion
from financial markets.
But casual evidence suggests that countries typically regain
access to credit fairly quickly – as quickly as a couple of years
after default.
What does the less-casual evidence show?
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Cruces and Trebesch (2012): detailed analysis of a large
dataset on creditor losses (‘haircuts’) from default /
restructuring episodes.
Sovereign default is in fact a robust predictor of subsequent
borrowing conditions – once the extent of haircuts is taken
into account.
Data: all sovereign debt restructurings 1970-2010.
Haircut defined by the percentage difference between the old
and new (if any) debt obligations.
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The simplest haircut measure at the time of a restructuring is
HF = 1 – (Face value of new debt / Face value of old debt)
But this is a poor indicator because it does not capture the
haircut implied by, e.g., a lengthening of maturity.
The most common haircut measure is
HM = 1 – (PV of new debt / Face value of old debt)
with the PV computed at the post-default market rate.
This overstates haircuts by assuming the old debt was due in
full on the date of debt exchange. A better measure (used
in the paper) is
HSZ = 1 – (PV of new debt / PV of old debt)
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Haircuts show large and increasing dispersion.
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Face-value reduction has become increasingly common, and it
usually leads to larger haircuts than pure restructuring.
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Theoretical models of default typically assume 100% haircuts.
– seldom seen in reality.
To assess the effects of default, examine two questions:
(1) Do larger haircuts lead to larger yield spreads after
restructuring?
(2) Do larger haircuts lead to longer periods of exclusion from
credit markets?
For (1), look at EMBI Global spreads (relative to those of non-
defaulters). Break into two groups (haircut above and below
the median of 37%).
There is a clear difference between the spreads after low and
high haircuts – especially after 3+ years.
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Also, run regressions of EMBIG spreads on haircut size and
other variables.
If haircut size is ignored, spreads only seem to be affected for
a couple of years after restructuring – the standard finding
that ‘all is quickly forgotten’.
Putting in haircut size makes a big difference: a 1% extra
haircut raises spreads 6.75 bp after 1 year, and still 3 bp in
years 4-5.
A haircut of 40% (close to the mean) raises spreads by 140 bp
the first year and 127 bp 4-5 years after.
Adding restructuring dummies and controls does not take
away the significance of haircut size.
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For the effect of haircut size on market exclusion, define
‘reaccess’ as the first year with an international loan or
bond placement and/or international credit flows to the
public sector.
Bigger haircuts lead to longer periods of exclusion.
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A Cox hazard model confirms the adverse effect of haircut
size on reaccess.
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The cost of sovereign default and the financial system
The conventional assumption is that the defaulted sovereign
debt is held by outsiders (foreigners) whose welfare does
not matter.
In reality, much debt is held by domestic agents, and
‘discriminatory default’ is in most cases not feasible – so
default also imposes a welfare cost on them.
Locals may end up holding the debt through secondary
market transactions, in which case default hurts primarily
domestic savers (Broner et al 2010).
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Source: Broner et al (2014)
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Source: Broner et al (2014)
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Government debt held by banks, 2010
In reality, much of the outstanding sovereign debt is
typically held by banks.
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Sovereign debt holdings, by sector (% of total)
Source: Broner et al (2014)
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Sovereign debt holdings, by sector (% of total)
Source: Broner et al (2014)
Argentine banks' exposure to a default
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Greek banks' exposure to a default
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Peripheral European Banking System Exposure to their
Own Government and Private Sector, 2011 Q1(in percent of banking system equity)
0 200 400 600 800 1000 1200
Greece
Ireland
Portugal
Own Government
Own Private Sector
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155
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When domestic banks hold much of the debt, sovereign
default weakens bank balance sheets and leads to a credit
crunch – and a growth decline.
Gennaioli, Martin and Rossi (2014): these domestic costs of
default encourage debt repayment, quite aside of reputation
and/or market exclusion effects.
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Two issues to explore:
(1) The cost of default
(2) The frequency of default
Two potential drivers:
-- Banks’ public debt holdings
-- The quality of financial institutions (higher quality allows
greater leverage and a bigger role for bank credit)
Panel data of emerging and developed countries over 1980 -
2005
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Bigger holdings of public debt worsen the post-default
credit crunch
Subsequent work using bank-level data (Gennaioli et al 2016) yields
similar results.
Stronger financial institutions also worsen the crunch
because they typically result in higher leverage.
Once institutional quality and bank debt holdings are taken into account
(in interaction terms), default alone is not a significant predictor of
credit crunches.
Other regressions show that larger bank debt holdings (and better
financial institutions) ceteris paribus reduce the likelihood of sovereign
default – in line with the arguments on the cost of default.
All this is quite consistent with what we currently see in Europe…
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Bigger bank holdings of debt reduce the frequency of default
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Financial repression
Default (or restructuring) is only one way to reduce high
sovereign debt/GDP ratios. Historically there have
been others:
(1) Growth
(2) Fiscal adjustment
(3) Surprise inflation
(4) Financial repression, often along with steady
inflation
The various options are usually found in combination
But (4) and (5) only work for domestic-currency debt
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Financial repression involves the payment of below-
market rates on public debt, allowed by
– mandatory holdings of public debt by major
lenders (e.g., pension funds, banks…) often
imposed by ‘prudential regulation’
– interest rate ceilings or controls
…in general, a tight connection between government
and lenders
It played a big role to reduce the large debt stocks of rich
countries post-WWII (in contrast with the defaults
that help reduce post-WWI debts).
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Financial repression combined with inflation can lead to
negative real interest rates and ‘debt liquidation’
A transfer from lenders to borrowers (the government)
Over 1945-80 real interest rates were negative on
average in both advanced and emerging countries.
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How big was the liquidation effect of financial
repression? Think of it as an implicit tax revenue.
Source: Reinhart and Sbrancia (2011)
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Financial repression is likely to be very tempting to rich-
country governments facing massive debt stocks.
Repression may re-emerge disguised as ‘prudential
regulation’ of banks, pension funds and other
intermediaries forcing them to hold public debt.
Some argue that the decoupling of public debt prices (or
interest rates) and risk is already happening through
intervention of Central Banks and other non-market
players across the world…