Download Efficient Sovereign Default Alessandro Dovis October 12, 2013 Penn State and Princeton IES

Efficient Sovereign Default
Alessandro Dovis
Penn State and Princeton IES
October 12, 2013
Sovereign Defaults in the Data
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Sovereign defaults (suspension of payments) are recurrent
but infrequent events
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Associated with:
Data
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Severe output and consumption losses
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Large fall in imports of intermediate goods
Maturity of debt shortens as default is more likely
Conventional Approach
Incomplete market approach to sovereign debt:
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Sovereign borrower can issue only non-contingent debt
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Sovereign borrower cannot commit to fully repay its debt
Typically:
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Exogenous maturity composition of debt
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Exogenous cost of default
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Markov equilibrium
Conventional View of Debt Crises
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Pervasive inefficiencies
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Defaults due to incomplete contracts
Excessive reliance on short-term debt causes crises
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Roll-over risk: Cole and Kehoe (2000), Rodrik and Velasco
(1999)
My Approach
As in conventional approach:
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Sovereign borrower can issue only non-contingent debt
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Sovereign borrower cannot commit to fully repay its debt
Extend by allowing for:
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Endogenous maturity composition of debt
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Endogenous cost of default (Production economy)
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Best equilibrium
My View of Debt Crises
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Best equilibrium outcome is constrained efficient
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Solution to an optimal contracting problem with:
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Lack of commitment by sovereign borrower
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Private information
Non-contingent defaultable debt of multiple maturities
sufficient to implement efficient outcome
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High reliance on short-term when default is likely part of
the efficient arrangement
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Symptom, not cause
Features of the Best Outcome
Recurrent but infrequent defaults associated with:
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Output and consumption losses
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Fall in imports of intermediate goods
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Maturity of debt shortens as indebtedness increases before
default
Contribution to the Literature
Incomplete market literature on sovereign default:
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Eaton and Gersovitz (1981), Aguiar and Gopinath (2006),
Arellano (2008), Benjamin and Wright (2009), Chatterjee and
Eyigungor (2012), Mendoza and Yue (2012), Arellano and
Ramanarayanan (2012)
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Cole and Kehoe (2000), Conesa and Kehoe (2012)
Extend by allowing for:
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Endogenous maturity composition of debt
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Endogenous cost of default (Production economy)
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Best equilibrium
Develop efficiency benchmark useful for policy analysis
Contribution to the Literature, cont.
Optimal dynamic contracting literature:
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Private Information: Green (1987), Thomas and Worrall (1990),
Atkeson and Lucas (1992)
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Lack of Commitment: Thomas and Worrall (1994), Kocherlakota
(1996), Kehoe and Perri (2002), Alburquerque and Hopenhayn
(2004), Aguiar, Amador and Gopinath (2009)
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Atkeson (1991) and Ales, Maziero, and Yared (2012)
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Quadrini (2004), Clementi and Hopenhayn (2006), DeMarzo and
Fishman (2007), DeMarzo and Sannikov (2006), Hopenhayn and
Werning (2008)
Implementation: Relate efficient outcome to data on default,
bond prices, maturity composition of debt
Outline
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Physical Environment
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Sovereign Debt Game
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Best Equilibrium Outcome is Efficient
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Characterization of Efficient Allocation
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Implementation
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Default, Bond Prices, and Maturity Composition of Debt
PHYSICAL ENVIRONMENT
Taste Shock Economy
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t = 0, 1, ..., ∞
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2 types of agents:
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Domestic agents (government)
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Foreign lenders
2 goods:
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Final good
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Intermediate good
Foreign Lenders
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Risk neutral, discount factor q ∈ (0, 1)
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Value consumption of the final good
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Large endowment of the intermediate good
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Technology of the foreign lenders is such that relative price
between intermediate and final good is one
Domestic Agents
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Preferences over final good:
∞ X
X
β t Pr(θt )θt U (c(θt ))
t=0 θt
with U strictly increasing, strictly concave and β ≤ q
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Taste shock: θt ∈ {θL , θH } distributed according to µ, iid
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Endowed with 1 unit of labor
Domestic Technology
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Final good produced using
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`: domestic labor
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m: foreign intermediate good
Y = F (m, `)
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F CRS, F (0, 1) > 0, limm→0 Fm (m, `) = ∞
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Let f (m) = F (m, 1)
SOVEREIGN DEBT GAME
Timing
Public History
ht−1
Foreign
Firms
exporters choose
choose pt
θt is
Gov’t chooses
Foreign
realized
policy, πt
lenders
gov’t private
choose
history
debt
(htg , θt )
prices, qt
mt (private info)
Government Policy, π = (τ, bS , bL , δ)
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Government taxes payment by firms to foreign exporters at
rate τ
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Government issues two non-contingent defaultable bonds
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Short-term: 1 period, bS
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Long-term: Consol, bL
Government can choose three levels of payment for existing
debt:
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δ = 1: Full payment
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δ = r ∈ (0, 1): Partial payment
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δ = 0: Suspension of payments in current period
Government Budget Constraint
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If there is full payment, δ = 1:
bS + bL + c ≤ Y (τ ) + qS (htπ , πt )b0S + qL (htπ , πt )(b0L − bL )
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If there is partial payment, δ = r ∈ (0, 1):
rbS +
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r
bL + c ≤ Y (τ ) + qS (htπ , πt )b0S + qL (htπ , πt )b0L
1−q
If there is suspension of payments, δ = 0:
c ≤ Y (τ )
and
(b0S , b0L ) = (bS , bL )
where Y (τ ) = f (mt ) − (1 − τ )pt mt
and htπ is the public history when the government acts
Definition of Sustainable Equilibrium
A sustainable equilibrium is (σ, p, m, qS , qL ) such that for all
histories
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Given private strategies, the government’s strategy, σ,
maximizes domestic agents utility subject to budget
constraints
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Given the government’s strategy:
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p and m are consistent with foreign exporters and firms
optimality conditions
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p and m
qS and qL are consistent with lenders’ no-arbitrage
condition
qS
qL
BEST SUSTAINABLE EQUILIBRIUM OUTCOME IS
CONSTRAINED EFFICIENT
Incentive Compatibility and Sustainability Constraint
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In any sustainable equilibrium outcome the government
must have no incentive to conduct undetectable deviations
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Incentive Compatibility Constraint
θt U (c(θt )) + βv(θt ) ≥ θt U (c(θt−1 , θ0 )) + βv(θt−1 , θ0 ) (IC)
where v(θt ) = continuation value for the domestic agent
Incentive Compatibility and Sustainability Constraint
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In any sustainable equilibrium outcome the government
must have no incentive to conduct detectable deviations
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Sustainability Constraint
θt U (c(θt )) + βv(θt ) ≥ θt U (f (m(θt−1 )) + βva
where va = value of autarky (worst equilibrium)
(SUST)
Best Equilibrium Outcome is Constrained Efficient
Main Proposition of the Paper
The best sustainable equilibrium outcome is such that
x = {m(θt−1 ), c(θt )}∞
t=0 solves the following optimal contracting
problem:
J(v0 ) = max
x
∞ X
X
q t Pr(θt ) −m(θt−1 ) + f m(θt−1 ) − c(θt )
t=0 θt
subject to (IC), (SUST) and
∞ X
X
t=0 θt
β t Pr(θt )θt U (c(θt )) ≥ v0
(PC)
CHARACTERIZATION OF THE CONSTRAINED
EFFICIENT ALLOCATION
Efficient Allocation Solves Recursive Problem for t ≥ 1
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B: Lenders’ value (total market value of debt)
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v: Borrower’s value
The efficient allocation solves
X
B(v) =
max
µs −m + f (m) − cs + qB(vs0 )
m,{cs ,vs0 }s=H,L
s∈{L,H}
subject to
0
µH θH U (cH ) + βvH
+ µL θL U (cL ) + βvL0 = v
0
θL U (cL ) + βvL0 ≥ θL U (cH ) + βvH
0
θH U (cH ) + βvH
≥ θH U (f (m)) + βva
0
vH
, vL0 ≥ va
(PKC)
(IC)
(SUST)
(SUST’)
PROPERTIES
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Region with ex-post inefficiencies
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Transit in and out of the region with ex-post inefficiencies
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Lack of commitment plays critical role
Private information plays critical role
Low borrower values are associated with low imports of
intermediates and low output
Lenders’ Value
Region of Ex-Post Inefficiencies
Region with
Ex-Post
Inefficiencies
Efficient
Region
B
0
va
ṽ
Borrower’s Value
When borrower’s value is low, can make both borrower and
lenders better off ex-post
Lenders’ Value
Any Efficient Allocation Starts on the Efficient Region
Region with
Ex-Post
Inefficiencies
Efficient
Region
B
0
va
ṽ
Borrower’s Value
Lenders’ Value
Transits to the Region with Ex-Post Inefficiencies
Region with
Ex-Post
Inefficiencies
Efficient
Region
B
0
va
v3
v2
v1
v0
Borrower’s Value
Starting from v0 , a sequence of high taste shocks pushes the
economy to the region with ex-post inefficiencies
Borrower’s Value
Next Period
Borrower’s Value Decreases After High Taste Shock
vH
(v)
vL
(v)
45o
va
va
ṽ
Borrower’s Value
Today
After the realization of a high taste shock, the continuation
0 (v) < v
value is lower than the current one: vH
Two Countervailing Forces
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Incentive force: Want to spread continuation values
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Cheapest way to provide utility
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Make cH large and cL small
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Spread out continuation values
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Desirable to make vH
low
Commitment force: Want to back-load borrower payoff
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By back-loading, relax future sustainability constraint
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Low production distortions in the future
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0
Want high vH
Two Countervailing Forces
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Incentive force: Want to spread continuation values
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I
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Cheapest way to provide utility
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Make cH large and cL small
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Spread out continuation values
0
Desirable to make vH
low
Commitment force: Want to back-load borrower payoff
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By back-loading, relax future sustainability constraint
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Low production distortions in the future
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0
Want high vH
If either (i) θH − θL sufficiently high or (ii) µH sufficiently low
0 (v) < v
the incentive force outweighs commitment force ⇒ vH
Borrower’s Value
Next Period
Transits to the Region with Ex-Post Inefficiencies
vH
(v)
vL
(v)
45o
va
v4
va
v1
ṽ
v0
Borrower’s Value
Today
Starting from v0 , a sequence of high taste shocks pushes the
economy to the region with ex-post inefficiencies
Borrower’s Value
Next Period
What Happens When Reach Autarky?
vH
(v)
vL
(v)
45o
va
va
ṽ
Borrower’s Value
Today
Bounce up the first time θL is realized
Low v Associated with Low Output and Intermediates
Output
Intermediate Imports
 (∗ )
∗

̃
 ∗ Borrower’s
Value

̃
 ∗ Borrower’s
Value
m∗ = statically efficient amount of intermediates, f 0 (m∗ ) = 1
Recap
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A sequence of high taste shocks pushes the economy to the
region with ex-post inefficiencies
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This path is associated with falling imports of
intermediates and output
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Autarky is a reflecting point, not absorbing
IMPLEMENTATION:
DEFAULTS, BOND PRICES, AND MATURITY
COMPOSITION
Equilibrium Payment Policy
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If v > va : Full payment, δ = 1
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If v = va :
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If θ = θH : Suspension of payments, δ = 0
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If θ = θL : Partial payment, δ = r
Equilibrium Bond Prices
Given the equilibrium payment policy, prices consistent with
lenders’ arbitrage


qS (v) =



qL (v) =

conditions
q
if v ∈ (va , v̄]
qr̄
if v = va
P
q s=L,H µj [1 + qL (vs0 (v))] if v ∈ (va , v̄]
r̄
q 1−q
if v = va
where r̄ is the expected recovery rate
LT bond price increasing in borrower continuation value
Equilibrium Maturity Composition of Debt
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From the contracting problem, total value of debt is:
b(v, θs ) ≡ f (m(v)) − m(v) − cs (v) + qB(vs0 (v))
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When δ = 1, given prices, bL (v) and bS (v) must solve
b(v, θL ) = bS (v) + bL (v) 1 + qL vL0 (v)
0
b(v, θH ) = bS (v) + bL (v) 1 + qL vH
(v)
How is Insurance Provided?
When there is default (only when v = va ):
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Suspension and partial payments provide insurance
When there is no default:
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After θH : Debt dilution
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Borrower’s continuation value decreases
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Higher probability of default in the near future
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Long-term debt price falls ⇒ capital loss for lenders
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Wealth transfer from lender to the borrower
After θL : Debt buyback
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Borrower’s continuation value increases
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Lower probability of default in the near future
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Long-term debt price rises ⇒ capital gain for lenders
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Wealth transfer from the borrower to the lenders
Default On-Path is Necessary
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Variation in price of long-term debt from variation in
future default probability
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Not from variation in equilibrium SDF
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Idiosyncratic shocks (SOE)
Different from Kreps (1982), Angeletos (2004),
Buera-Nicolini (2004)
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Aggregate shocks
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Variation in equilibrium SDF
MATURITY OF DEBT SHORTENS AS
DEFAULT IS MORE LIKELY
Maturity of Debt Shortens as Default is More Likely
Recall: bL (v) and bS (v) solve
bS (v) + bL (v) 1 + qL vL0 (v) = b(v, θL )
0
(v) = b(v, θH )
bS (v) + bL (v) 1 + qL vH
When indebtedness is high (future default is likely):
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Long-term bond prices more sensitive to shocks
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Can obtain needed insurance with small amount of
long-term debt
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Overall indebtedness is high so short-term debt must be
high
Conclusion
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Key aspects of sovereign debt and default rationalized as
best outcome of a sovereign debt game
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Best outcome is constrained efficient
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It solves optimal contracting problem with informational
and commitment frictions
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Default is not driven by
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Market incompleteness
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The high reliance on short-term debt
But by the underlying frictions
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Method to implement efficient allocation likely generalize
to other contracting problems
Dynamics Around Default Episodes
10
% deviation from trend
% deviation from trend
Consumption
GDP
15
10
5
0
-5
-10
-15
-3
-2
-1
0
Back
1
2
3
Year after Default
5
0
-5
-10
-3
-2
-1
0
1
Year after Default
Intermediate Imports
40
Mean
Mean +/- std
% deviation from trend
30
20
10
Sample of Defaults
Episodes from
Mendoza and Yue (2012)
0
-10
-20
-30
-40
-3
-2
-1
0
1
Year after Default
2
3
Source: WDI,
UN Comtrade and
Feenstra
2
3
Pricing Function: Short-Term Bond
Consistent with lenders’ arbitrage condition
qS (ht ) = qE χS (ht+1 )|ht
where
χS (ht+1 ) =







Back
1
r
if δt+1 = 1
if δt+1 = r
qE χS (ht+2 )|ht+1 if δt+1 = 0
Pricing Function: Long-Term Bond
Consistent with lenders’ arbitrage condition
qL (ht ) = qE χL (ht+1 )|ht
where
χL (ht+1 ) =
Back




1 + qL (ht+1 )



qE χL
r
1−q
(ht+2 )|ht+1
if δt+1 = 1
if δt+1 = r
if δt+1 = 0
Trade: Private Agent’s Optimality
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Foreign exporters no-arbitrage condition:
1 = E pt (ht−1 ) 1 − τ (htg , θt ) |ht−1
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Firms’ optimality:
f 0 (m(htm )) = p(ht−1 )
Back
Equilibrium Capital Controls and Imports Price
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From the contracting problem, I get m(v)
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Construct p(v) and τ (v) consistent with firms optimality
and foreign exporters no-arbitrage conditions:
f 0 (m(v)) = p(v)
1 = p(v)(1 − τ (v))
Back