1) The document discusses how sovereign governments can engage in "desperate deals" when faced with a failed bond auction, such as obtaining alternative financing at high interest rates or occasionally defaulting. 2) It presents a model where self-fulfilling debt crises occur in a "crisis zone" when a government would repay under normal pricing but default if faced with prices of zero for any positive debt issuance. 3) The model allows for "desperate deal" pricing during crises that makes the government indifferent between repaying and defaulting, and can generate crises with high but variable spreads like in the data.

1. Self-Fulfilling Debt Crises, Revisited: The
Art of the Desperate Deal
Mark Aguiar Satyajit Chatterjee
Harold L. Cole Zachary Stangebye
September 2, 2016
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2. Desperate Deals
What does a sovereign do when faced with the prospect of a
failed auction?
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3. Desperate Deals
What does a sovereign do when faced with the prospect of a
failed auction?
In Cole-Kehoe they default
In practice, they look for alternative financing
Often tolerating high spreads.
Occasionally ending up defaulting.
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4. Portugal
Difficulty in raising funds through auctions starting in 2011
Private placement of bonds in January 2011 (reported as
purchased by China)
Official 78 billion package in May 2011
34.2 billion dispersed in 2011 and 28.5 in 2012
Dual auction in October 2012
Bought “September 2013” bonds
Sold “October 2015” bonds
Goal: Clear “space” for auctions in 2013/2014
Launched new issue in early 2013
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5. Self-Fulfilling Debt Crises, Revisited
What is a self-fulfilling debt crisis?
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6. Self-Fulfilling Debt Crises, Revisited
What is a self-fulfilling debt crisis?
Cole-Kehoe: Failed auction today generates default today
Zero price for any amount of bonds issued
Choose to default - hence self-fulfilling.
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7. Self-Fulfilling Debt Crises, Revisited
What is a self-fulfilling debt crisis?
Cole-Kehoe: Failed auction today generates default today
Zero price for any amount of bonds issued
Choose to default - hence self-fulfilling.
Our model generates less extreme rollover crises than in C-K.
Keeps C-K’s “static” rollover-crisis multiplicity but considers a
richer notion of “failed” auctions.
Generate spikes in spreads without defaults, like the data.
Our model has some surprising welfare implications.
(Buybacks not all bad.)
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8. Framework
Endowment: Stochastic Growth as in Aguiar-Gopinath
Small open economy
Discrete time
Markov process for endowment growth
yt ≡ ln Yt =
t
s=0
gs + zt
= yt−1 + gt + zt − zt−1
gt follows an AR(1) process and zt is iid
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9. Framework
Bonds: Random Maturity as in Chatterjee-Eyigungor
Sovereign issues non-contingent “random-maturity” bonds
Bonds mature with Poisson probability λ
Assume that in a non-degenerate portfolio of bonds, a fraction
λ matures with probability 1
Perpetual-youth bonds allow for tractably incorporating
maturity without adding separate state variables for each
cohort of bond issuances
Bonds pay coupon r∗ each period up to and including maturity
Payments due in period t: (r∗ + λ)Bt
New issuances: Bt+1 − (1 − λ)Bt
Bt+1
Yt
≤ ¯b prevents Ponzi schemes.
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10. Framework
Lenders
Risk averse OLG lenders (risk aversion not conceptually
important)
Financial markets are segmented: Finite wealth available to
participate in bond market
Tractability: Period t’s set of investors hold bonds for one
period and then sell them to a new cohort of investors at start
of t + 1
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11. Timing
Modification of Cole-Kehoe
Initial State:
s
Auction
B − (1 − λ)B
at price
q(s, B )
Settlement
No Default
Default
V R(s, B )
V D(s)
Next Pe-
riod: s
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12. Settlement
Auction Revenue:
x(s, B ) ≡ max q(s, B )(B − (1 − λ)B), 0
Proceeds from auction are held in escrow until government
makes repayment decision
If government repays, can draw on settlement funds for
repayment and consumption
If government defaults, auction revenue disbursed to
bondholders in proportion to face value of claims:
RD
(s, B ) =
x(s, B )
B + (r∗ + λ)B
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13. Settlement
Auction Revenue:
x(s, B ) ≡ max q(s, B )(B − (1 − λ)B), 0
Proceeds from auction are held in escrow until government
makes repayment decision
If government repays, can draw on settlement funds for
repayment and consumption
If government defaults, auction revenue disbursed to
bondholders in proportion to face value of claims:
RD
(s, B ) =
x(s, B )
B + (r∗ + λ)B
If B < (1 − λ)B: Buyback funds are paid out and gone.
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14. Settlement
No Default:
Old lenders receive (r∗
+ λ)B
New lenders hold B into next period
Default:
Old lenders receive RD
(s, B )(r∗
+ λ)B
New lenders receive RD
(s, B )B
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15. The Government’s Problem
Preferences
Sovereign government makes all consumption-savings-default
decisions
Sovereign’s preferences over sequence of aggregate
consumption {Ct}∞
t=0:
E
∞
t=0
βt
u(Ct)
with
u(C) =
C1−σ
1 − σ
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16. Value Functions
V (s) denotes start-of-period value of government
V R(s, B ) denotes value if having auctioned B − (1 − λ)B
the government decides to repay (r∗ + λ)B at settlement
V D(s) denotes the value of defaulting at settlement
(independent of amount auctioned) ⇒ lose fraction φ of
endowment until “redemption” from default status
Strategic default implies:
V (s) = max max
B ≤¯bY
V R
(s, B ), V D
(s)
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17. Bellman Equations
If repay...
V R
(s, B ) = u(C) + βE V (s )|s, B ,
with
C = Y + q(s, b )(B − (1 − λ)B) − (r∗
+ λ)B.
If default...
V D
(s) = u(Y D
) + βEV E
(s )
V E
(s) = u((1 − φ)Y ) + β(1 − ξ)E V E
(s ) s
+ βξE V (s ) s, B = 0
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18. Equilibrium
Markov Equilibrium
States s ∈ S elements of s are:
Endowment: (Y , g, z)
Bonds: B
Beliefs: ρ
Policy Functions:
Bond-issuance: B(s)
Default: D(s, b ) ∈ [0, 1]
Bond-demand: µ∗
(s, b )
Price function: q(s, B ) ∈ [0, 1]
Market clearing: µ∗(s, B )W = q(s, B )B .
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19. Multiplicity of Equilibria
There is a “static” multiplicity in a given period
Arises because of timing convention: Failed auction even for
small levels of bond issuances can be supported in equilibrium
Suppose the continuation equilibrium is held constant and we
consider alternative price schedules for the current period’s
auction
Consider two scenarios for today’s auction, holding constant
equilibrium behavior going forward
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20. Cole-Kehoe Crisis
Zero price for any B ≥ (1 − λ)B:
V R
(s, (1 − λ)B)
= u (Y − (r∗
+ λ)B) + βE V (s )|s, B = (1 − λ)B
< V D
(s).
Non-Crisis
A pair (˜q, ˜B) such that:
V R
(s, B ) =
u Y − (r∗
+ λ)B + ˜q[ ˜B − (1 − λ)B] + βE V (s )|s, ˜B
> V D
(s).
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21. Constructing Equilibria
For a given state s and equilibrium policy functions, we can
price a bond conditional on no-default at settlement this
period
Such within-period commitment is the assumption of
Eaton-Gersovitz models
Our exercise assumes only commit for the current period, and
then no commitment going forward
Let qEG (s, B ) denote this price
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22. Crisis Zone
Define a “Crisis Zone” by evaluating V R(s, B ) under qEG :
C ≡ s ∈ S max
B ≤(1−λ)B
V R
(s, B ) ≤ V D
(s) &
max
B ≥(1−λ)B
V R
(s, B ) ≥ V D
(s) .
This set identifies states in which:
Faced with qEG
, the government would have no reason to
default
Faced with q = 0 for B > (1 − λ)B, it will default
Crisis zone combination of high B and low (Y , g, z)
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23. Self-Fulfilling Crises
In Cole-Kehoe equilibrium, a rollover crisis is an equilibrium in
which prices are zero for any positive amount of debt issuance
We relax this and consider a broader set of crisis equilibria
Build on the mixed strategy equilibria of Aguiar and Amador
(2014)
That model had potential buybacks and randomization off the
equilibrium path
We now bring this onto the equilibrium path and consider crisis
issuances
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24. Desperate Deals
Rethinking Failed Auctions
Desperate Deal Price Schedule: An Indifference Condition
qD
(s, B ) = ˜q V D
(s) = u Y − (r∗
+ λ)B + ˜q[B − (1 − λ)B]
+ βE V (s )|s, B .
Support as mixed-strategy equilibrium with appropriate choice
of D(s, B ) ∈ [0, 1]
Feasible for 0 ≤ qD
(s, B ) ≤ qEG
(s, B )
Government indifferent over feasible B so make selection.
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25. Crisis Price Schedule
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
B0
Y
qD
qEG
Desperate deals (indifference) prices in black. EG (good)
prices in red. CK price is 0 for issuances.
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26. Evolution of Beliefs
iid probability of crisis if s ∈ C
q = qD
Assume B(s) = B /Y = B−1/Y−1 (prior debt-output ratio
equals new ratio)
Contrast with “No Desperate Deals” model
Just original Cole-Kehoe Eq.
q = 0 for any positive issuance in a crisis
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27. Calibration
Pre-Set Parameters
Calibrate endowment to Mexico 1980Q1-2001Q4
Set risk aversion coefficient for sovereign and lenders at 2
Set quarterly risk free rate to 1%
Set average maturity to 8 quarters
Set average exclusion to 8 quarters
Probability ρ = rC is 1
4
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28. The Role of Desperate Deals
Target Moment Data Benchmark No Deals
B
Y 65.6% 66.6% 64.5%
r − r∗ 3.4% 3.4% 3.4%
σ(r − r∗) 2.5% 2.5% 0.1 %
Default Freq 2.0% 2.0% 2.1%
Massive increase in volatility relative to No Deals
(and without deterministic growth, nonlinear default costs and
volatility output).
Lower debt level with No Deals reduces difference in defaults.
(Desperate deals reduces borrowing discipline.)
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29. Crises and Default
Crises:
Fraction of quarters in crisis zone: 8.0%
Rollover crises occur 2% of the time
Defaults:
Default rate 2% per annum (targeted)
97% of defaults coincide with negative growth
70% of defaults coincide with rollover crisis
Conditional on rollover crisis, default on average 15% of time
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30. Distribution of r − r∗
Conditional on Crisis
Frequency
0 .1 .2 .3 .4
Spread
Default Unrealized Default Realized
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31. Equilibrium Price Schedule
With and Without Crisis Issuances
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
B0
Y
q
Benchmark
No Deals
Better price schedule from lenders’ anticipation of better
treatment with desperate deals.
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32. Welfare Results
some surprises
Desperate Deals equilibrium slightly dominates No Deals
Prices better conditional on crisis
Government captures this through ex ante price schedule
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33. Welfare Results
some surprises
Desperate Deals equilibrium slightly dominates No Deals
Prices better conditional on crisis
Government captures this through ex ante price schedule
Off-setting effect: Higher debt and more defaults due to more
favorable spreads
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34. Welfare Results
some surprises
Desperate Deals equilibrium slightly dominates No Deals
Prices better conditional on crisis
Government captures this through ex ante price schedule
Off-setting effect: Higher debt and more defaults due to more
favorable spreads
Buybacks during rollover crises raises welfare
Counters Bulow-Rogoff’s Buyback Boondoggle
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35. Conclusion
Models based upon Eaton-Gersovitz environment struggle
with matching spread volatility.
Cole-Kehoe environment also generates limited volatility in
spreads and extreme outcome conditional on a crisis
In our approach, self-fulfilling crises generate a mixture of
fundamental and belief-driven defaults, and desperate deals
Crises now look more like what we see in the data.
Extreme spreads look like we see in the data.
Interesting welfare implications (relative to classic
Bulow-Rogoff).
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