E cient Sovereign Default - Alessandro Dovis · 2019-12-03 · DeMarzo and Sannikov (2006),...
Transcript of E cient Sovereign Default - Alessandro Dovis · 2019-12-03 · DeMarzo and Sannikov (2006),...
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Efficient Sovereign Default
Alessandro Dovis
University of Minnesota
February 27, 2013
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Sovereign Defaults in the Data
I Sovereign defaults (suspension of payments) are recurrent
but infrequent events
I Associated with: Data
I Severe output and consumption losses
I Large fall in imports of intermediate goods
I Maturity of debt shortens as default is more likely
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Conventional Approach
Incomplete market approach to sovereign debt:
I Sovereign borrower can issue only non-contingent debt
I Sovereign borrower cannot commit to fully repay its debt
Typically:
I Exogenous maturity composition of debt
I Exogenous cost of default
I Markov equilibrium
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Conventional View of Debt Crises
I Pervasive inefficiencies
I Defaults due to incomplete contracts
I Excessive reliance on short-term debt causes crises
I Roll-over risk: Cole and Kehoe (2000), Rodrik and Velasco
(1999)
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My Approach
As in conventional approach:
I Sovereign borrower can issue only non-contingent debt
I Sovereign borrower cannot commit to fully repay its debt
Extend by allowing for:
I Endogenous maturity composition of debt
I Endogenous cost of default (Production economy)
I Best equilibrium
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My View of Debt Crises
I Best equilibrium outcome is constrained efficient
I High reliance on short-term when default is likely part of
the efficient arrangement
I Symptom, not cause
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Best Equilibrium Outcome is Constrained Efficient
I The best equilibrium outcome is the solution to an optimal
contracting problem with two frictions:
I Lack of commitment by sovereign borrower
I Private information
I Non-contingent defaultable debt of multiple maturities
sufficient to implement efficient outcome
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Features of the Best Outcome
Recurrent but infrequent defaults associated with:
I Output and consumption losses
I Fall in imports of intermediate goods
I Maturity of debt shortens as indebtedness increases before
default
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Policy Implications
Defaults and associated costs (trade disruption) not driven by
I Market incompleteness
I The high reliance on short-term debt
But by the underlying informational and commitment frictions.
Therefore:
I Adding assets is irrelevant
I Policies that penalize short-term debt are welfare reducing
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Contribution to the Literature
Incomplete market literature on sovereign default:
I 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)
I Cole and Kehoe (2000), Conesa and Kehoe (2012)
Extend by allowing for:
I Endogenous maturity composition of debt
I Endogenous cost of default (Production economy)
I Best equilibrium
Develop efficiency benchmark useful for policy analysis
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Contribution to the Literature, cont.
Optimal dynamic contracting literature:
I Private Information: Green (1987), Thomas and Worrall (1990),
Atkeson and Lucas (1992)
I Lack of Commitment: Thomas and Worrall (1994), Kocherlakota
(1996), Kehoe and Perri (2002), Alburquerque and Hopenhayn
(2004), Aguiar, Amador and Gopinath (2009)
I Atkeson (1991) and Ales, Maziero, and Yared (2012)
I 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
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Outline
I Physical Environment
I Baseline economy
I Isomorphic taste shock formulation
I Sovereign Debt Game
I Best Equilibrium Outcome is Efficient
I Characterization of Efficient Allocation
I Implementation
I Default, Bond Prices, and Maturity Composition of Debt
I Relate to Evidence
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PHYSICAL ENVIRONMENT
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Baseline Economy
I t = 0, 1, ...,∞
I 2 types of agents:
I Foreign lenders
I Domestic agents (government)
I 3 types of goods:
I Intermediate good, m
I Domestic consumption good, y (Non-Tradable)
I Export good, y∗
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Foreign Lenders
I Risk neutral, discount factor q ∈ (0, 1)
I Value consumption of the export good
I Large endowment of the intermediate good
I Technology of the foreign lenders is such that relative price
between intermediate and export good is one
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Domestic Agents
I Preferences over domestic consumption good
E0
∞∑t=0
βtU(yt)
with U strictly increasing and concave, and β ≤ q
I Endowed with 1 unit of labor
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Domestic Technology
I Domestic consumption and export good produced using
I `: domestic labor
I m: imported intermediate good
y = zF (m1, `1) y∗ = F (m2, `2)
m1 +m2 ≤ m `1 + `2 ≤ 1
I z is the productivity of domestic sector:
z ∈ {zL, zH} iid according to π
I F CRS, F (0, 1) > 0, limm→0 Fm(m, `) =∞
I Let f(m) = F (m, 1)
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Observables in the Baseline Economy
I Domestic consumption and export good produced using
I `: domestic labor
I m: imported intermediate good
y = zF (m1, `1) y∗ = F (m2, `2)
m1 +m2 ≤ m `1 + `2 ≤ 1
I Foreign lenders observe inputs devoted to domestic
consumption, m1, `1
I Cannot observe z or y, only y/z
I Let c ≡ y/z be “consumption” of resources devoted to
domestic good production
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Observables in the Baseline Economy
I Domestic consumption and export good produced using
I `: domestic labor
I m: imported intermediate good
y = zF (m1, `1) y∗ = F (m2, `2)
m1 +m2 ≤ m `1 + `2 ≤ 1
I The technological restrictions boil down to
y
z+ y∗ = c+ y∗ ≤ f(m)
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Rewrite as a Taste Shock Economy
If U(y) = y1−γ
1−γ , let c = yz and θ = z1−γ
With this change of variable:
I Domestic agent preferences
∞∑t=0
∑θt
βt Pr(θt)θtU(c(θt))
I Domestic resource constraint
c+ y∗ ≤ f(m)
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Rest of the Talk
I Present the results using the taste shock notation
I Under the assumption γ > 1:
High taste shock corresponds to low productivity shock
θH = z1−γL > θL = z1−γ
H
With either low productivity or high taste shock, marginal
utility of imported intermediates is high
I Refer to c = y/z as consumption
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SOVEREIGN DEBT GAME
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Players
I Benevolent domestic government
I Private domestic firms
I Foreign exporters
I Foreign lenders (debt-holders)
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Timing
Public History
ht−1
Foreign
exporters
choose pt
Firms
choose
mt
θt is
realized
(private info)
Gov’t chooses
policy
gov’t private
history
(htg, θt)
Foreign
lenders
choose
debt
prices, qt
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Timing
Public History
ht−1
Foreign
exporters
choose pt
Firms
choose
mt
θt is
realized
(private info)
Gov’t chooses
policy
gov’t private
history
(htg, θt)
Foreign
lenders
choose
debt
prices, qt
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Timing
Public History
ht−1
Foreign
exporters
choose pt
Firms
choose
mt
θt is
realized
(private info)
Gov’t chooses
policy
gov’t private
history
(htg, θt)
Foreign
lenders
choose
debt
prices, qt
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Timing
Public History
ht−1
Foreign
exporters
choose pt
Firms
choose
mt
θt is
realized
(private info)
Gov’t chooses
policy
gov’t private
history
(htg, θt)
Foreign
lenders
choose
debt
prices, qt
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Timing
Public History
ht−1
Foreign
exporters
choose pt
Firms
choose
mt
θt is
realized
(private info)
Gov’t chooses
policy
gov’t private
history
(htg, θt)
Foreign
lenders
choose
debt
prices, qt
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Gov’t Policies: Capital Controls and Debt Policies
I Government taxes payment by firms to foreign exporters at
rate τt
I Interpret as capital controls
I Revenue = τtptmt
I Government issues two non-contingent defaultable bonds
I Short-term: 1 period
I bS,t+1: amount issued
I Promise to pay bS,t+1 next period
I Long-term: Consol
I bL,t+1: amount issued
I Promise to pay bL,t+1 in every subsequent period
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Gov’t Policy: Default and Payment of Debt
Three levels of payment at t, δt ∈ {1, r, 0}
I δt = 1: Full payment
I δt = r ∈ (0, 1): Partial payment
I Pay r to each short-term debt holder
I Pay r1−q to each long-term debt holder
I δt = 0: Suspension of payments in current period
The government is in default whenever δt < 1
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Timing
Public History
ht−1
Foreign
exporters
choose pt
Firms
choose
mt
θt is
realized
(private info)
Gov’t chooses
gt = (τt, δt, bt+1)
gov’t private
history
(htg, θt)
Foreign
lenders
choose
debt
prices, qt
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Timing
Public History
Foreign
exporters
choose pt
ht−1
Firms
choose
mt
(ht−1, pt)
θt is
realized
(private info)
htg = (ht−1, pt,mt)
Gov’t chooses
gt = (τt, δt, bt+1)
gov’t private
history
(htg, θt)
Foreign
lenders
choose
debt
prices, qt
ht = (htg, gt)
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Pricing Function: Short-Term Bond
Consistent with lenders’ arbitrage condition
qS(ht) = qE[χS(ht+1)|ht
]where
χS(ht+1) =
1 if δt+1 = 1
r if δt+1 = r
qE[χS(ht+2)|ht+1
]if δt+1 = 0
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Pricing Function: Long-Term Bond
Consistent with lenders’ arbitrage condition
qL(ht) = qE[χL(ht+1)|ht
]where
χL(ht+1) =
1 + qL(ht+1) if δt+1 = 1
r1−q if δt+1 = r
qE[χL(ht+2)|ht+1
]if δt+1 = 0
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Government Budget Constraint
I If there is full payment, δ = 1:
c+ bS + bL ≤ Y (τ) + qS(htg, g)b′S + qL(htg, g)(b′L − bL)
I If there is partial payment, δ = r:
c+
(bS +
bL1− q
)r ≤ Y (τ) + qS(htg, g)b′S + qL(htg, g)b′L
I If there is suspension of payments, δ = 0:
c ≤ Y (τ) and (b′S , b′L) = (bS , bL)
where Y (τ) = f(mt)− (1− τ)ptmt
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Trade: Private Agent’s Optimality
I Foreign exporters no-arbitrage condition:
1 = E[pt(h
t−1)(1− τ(htg, θt)
)|ht−1
]I Firms’ optimality:
f ′(m(htm)) = p(ht−1)
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Definition of Sustainable Equilibrium
A sustainable equilibrium is (σ, p,m, q) such that for all histories
I The government’s strategy, σ, maximizes domestic agents
utility subject to budget constraints given private strategies
I Given the government’s strategy, private strategies are such
that:
I p is consistent with foreign exporters’ arbitrage condition
I m satisfies firms’ optimality
I q is consistent with foreign lenders’ arbitrage condition
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Worst Equilibrium
I Assumption: Lenders can deny access to foreign savings
I Autarky is the worst equilibrium for the government
I Value associated with autarky is
va =E(θ)U(f(0))
1− β
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Sustainable Equilibrium Outcome
I Focus on outcomes:
I What happens along the equilibrium path
I Denote outcomes as y = (x,g,p) where
x = {m(θt−1), c(θt), y∗(θt)}∞t=0
g = {τ(θt), δ(θt), bS(θt), bL(θt)}∞t=0
p = {pt(θt−1), qS(θt), qL(θt)}∞t=0
and v(θt) = continuation value for the domestic agent
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BEST SUSTAINABLE EQUILIBRIUM OUTCOME IS
CONSTRAINED EFFICIENT
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Incentive Compatibility and Sustainability Constraint
Any sustainable equilibrium outcome must satisfy
I Incentive Compatibility Constraint
θtU(c(θt)) + βv(θt) ≥ θtU(c(θt−1, θ′)) + βv(θt−1, θ′) (IC)
Government must have no incentive to conduct
undetectable deviations
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Incentive Compatibility and Sustainability Constraint
Any sustainable equilibrium outcome must satisfy
I Sustainability Constraint
θtU(c(θt)) + βv(θt) ≥ θtU(f(m(θt−1)) + βva (SUST)
Government must have no incentive to conduct detectable
deviations
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Best Equilibrium Outcome is Constrained Efficient
Main Proposition of the Paper
The best sustainable equilibrium outcome solves the following
optimal contracting problem:
J(v0) = maxx
∞∑t=0
∑θt
qt Pr(θt)[−m(θt−1) + f
(m(θt−1)
)− c(θt)
]subject to (IC), (SUST) and
∞∑t=0
∑θt
βt Pr(θt)θtU(c(θt)) ≥ v0 (PC)
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CHARACTERIZATION OF THE CONSTRAINED
EFFICIENT ALLOCATION
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Efficient Allocation Solves Nearly Recursive Problem
I Problem at t = 0
I Problem for t ≥ 1 where
I Efficient allocation
I Lenders’ value (total value of debt), B
are recursive in borrower’s value, v
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Recursive Problem for t ≥ 1
The efficient allocation solves
B(v) = maxm,{cs,v′s}s=H,L
∑s∈{L,H}
πs[−m+ f(m)− cs + qB(v′s)
]subject to
θLU(cL) + βv′L ≥ θLU(cH) + βv′H (IC)
θHU(cH) + βv′H ≥ θHU(f(m)) + βva (SUST)
v′H , v′L ≥ va (SUST’)
πH[θHU(cH) + βv′H
]+ πL
[θLU(cL) + βv′L
]= v (PKC)
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Problem at t = 0
The efficient allocation solves
J(v) = maxm,{cs,v′s}s=H,L
∑s∈{L,H}
πs[−m+ f(m)− cs + qB(v′s)
]subject to (IC), (SUST), (SUST’) and
πH[θHU(cH) + βv′H
]+ πL
[θLU(cL) + βv′L
]≥v (PC)
where J is the Pareto Frontier
Asymmetry between t = 0 and t ≥ 1 because:
I (PKC) is an equality constraint
I (PC) is an inequality constraint
I If B(v) is increasing then (PC) is slack and J(v) > B(v)
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Problem at t = 0
The efficient allocation solves
J(v) = maxm,{cs,v′s}s=H,L
∑s∈{L,H}
πs[−m+ f(m)− cs + qB(v′s)
]subject to (IC), (SUST), (SUST’) and
πH[θHU(cH) + βv′H
]+ πL
[θLU(cL) + βv′L
]≥v (PC)
where J is the Pareto Frontier
Asymmetry between t = 0 and t ≥ 1 because:
I (PKC) is an equality constraint
I (PC) is an inequality constraint
I If B(v) is increasing then (PC) is slack and J(v) > B(v)
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PROPERTIES
I Region with ex-post inefficiencies
I Lack of commitment plays critical role
I Transit to the region with ex-post inefficiencies
I Private information plays critical role
I Low borrower values are associated with low imports of
intermediates and low output
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Region of Ex-Post Inefficiencies
0
Lenders’Value
J
Borrower’s Valueva
B
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Region of Ex-Post Inefficiencies
0
Lenders’Value
J
Efficient
Region
Borrower’s Value
Region with
Ex-Post
Inefficiencies
va v
B
When borrower’s value is low, can make both borrower and
lenders better off ex-post
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B(v) has the Depicted Shape
Proposition (Region with Ex-Post Inefficiencies Exists)
∃ v > va such that there exist
I Region with ex-post inefficiencies:
B is increasing for v ∈ [va, v)
I Efficient region
B is decreasing for v ∈ [v, v)
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Any Efficient Allocation Starts on the Efficient Region
0
Lenders’Value
J
Efficient
Region
Borrower’s Value
Region with
Ex-Post
Inefficiencies
va v
B
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Transits to the Region with Ex-Post Inefficiencies
0
Lenders’Value
J
va v0v3 v2 v1
Efficient
Region
Borrower’s Value
Region with
Ex-Post
Inefficiencies B
Starting from v0, a sequence of high taste shocks pushes the
economy to the region with ex-post inefficiencies
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Borrower’s Value Decreases After High Taste Shock
Borrower’sValue
NextPeriod
v′
L(v)
va
va
v
45o
v′
H(v)
Borrower’s ValueToday
After the realization of a high taste shock, the continuation
value is lower than the current one: v′H(v) < v
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Two Countervailing Forces
I Incentive force: Want to spread continuation values
I Cheapest way to provide utility
I Make cH large and cL small
I Spread out continuation values
I Desirable to make v′H low
I Commitment force: Want to back-load borrower payoff
I By back-loading, relax future sustainability constraint
I Low production distortions in the future
I Want high v′H
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Optimality of Ex-Post Inefficiencies
Proposition (Transit to Region with Ex-Post Inefficiencies)
If either (i) θH − θL sufficiently high or (ii) πH sufficiently low,
then any efficient allocation transits to and out of the region
with ex-post inefficiencies with strictly positive probability.
Lemma
If either (i) or (ii) then ∀ v ∈ [v, v]
v′H(v) < v
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Intuition for the Sufficient Conditions in the Lemma
(i) θH − θL large: Incentive force large
I Insurance motive is large
I Incentive compatibility makes v′H(v) lower than v
(ii) πH low: Small cost of not back-loading
I Low probability of reaching state in which future (SUST) is
tight and production is highly distorted
Incentive force outweighs commitment force ⇒ v′H(v) < v
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Transits to the Region with Ex-Post Inefficiencies
Borrower’sValue
NextPeriod
v′
L(v)
va
va
v
v0v1v4
45o
v′
H(v)
Borrower’s ValueToday
Starting from v0, a sequence of high taste shocks pushes the
economy to the region with ex-post inefficiencies
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What Happens When Reach Autarky?
Borrower’sValue
NextPeriod
v′
L(v)
va
va
v
45o
v′
H(v)
Borrower’s ValueToday
Bounce up the first time θL is realized
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Is There a Stationary Distribution?
Borrower’sValue
NextPeriod
v′
L(v)
va
va
v
45o
v′
H(v)
Borrower’s ValueToday
If q > β there exists a non-degenerate limiting distribution
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Low v Associated with Low Output and Intermediates
Intermediate ImportsOutput
∗ Borrower’sValue
∗ Borrower’sValue
∗
(∗)
m∗ = statically efficient amount of intermediates, f ′(m∗) = 1
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Recap
I A sequence of high taste shocks pushes the economy to the
region with ex-post inefficiencies
I This path is associated with falling imports of
intermediates and output
I Autarky is a reflecting point, not absorbing
I If q > β there exists a stationary distribution
Next:
I Implementation: interpret ex-post inefficient outcomes as
debt crises
I Implications for maturity composition (and interest rates)
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IMPLEMENTATION:
DEFAULTS, BOND PRICES, AND MATURITY
COMPOSITION
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Construct Equilibrium Outcome
I Allocation and total value of debt from contracting problem
I p and τ are immediate
Next, construct:
I Payment policy, δ
I Bond prices, qS and qL
I Debt holdings, bS and bL
Using v as a state variable
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Equilibrium Payment Policy
I If v > va: Full payment, δ = 1
I If v = va:
I If θ = θH : Suspension of payments, δ = 0
I If θ = θL: Partial payment, δ = r
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Equilibrium Bond Prices
Given the equilibrium payment policy, prices consistent with
lenders’ arbitrage conditions
qS(v) =
q if v ∈ (va, v]
qr if v = va
qL(v) =
q∑
s=L,H πj [1 + qL(v′s(v))] if v ∈ (va, v]
q r1−q if v = va
where r is the expected recovery rate:
r = πLr + πH [0 + qr] =πLr
1− qπH
LT bond price strictly increasing in borrower continuation value
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Equilibrium Maturity Composition of Debt
I From the contracting problem, total value of debt is:
b(v, θs) ≡ f(m(v))−m(v)− cs(v) + qB(v′s(v))
I When δ = 1, given prices, bL(v) and bS(v) must solve
b(v, θL) = bS(v) + bL(v)[1 + qL
(v′L(v)
)]b(v, θH) = bS(v) + bL(v)
[1 + qL
(v′H(v)
)]
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How is Insurance Provided?
When there is default (only when v = va):
I Suspension and partial payments provide insurance
When there is no default:
I After θH : Debt dilution
I Borrower’s continuation value decreases
I Higher probability of default in the near future
I Long-term debt price falls ⇒ capital loss for lenders
I Wealth transfer from lender to the borrower
I After θL: Debt buyback
I Borrower’s continuation value increases
I Lower probability of default in the near future
I Long-term debt price rises ⇒ capital gain for lenders
I Wealth transfer from the borrower to the lenders
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On-Path Default and Off-Path Punishment
I On-path: When there is a default
I After a partial repayment regain access to credit market
I Do not trigger autarky
I Off-path: Autarky to deter detectable deviations
I Can use less severe punishment to deter detectable
deviations
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CHARACTERIZING BEST OUTCOME
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RELATION TO THE EVIDENCE:
I Sovereign debt crises are associated with:
I Output and consumption losses
I Fall in imports of intermediate goods
I Maturity of debt shortens as default is more likely
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Sample Path Leading Toward Default
Sample Path for Productivity Shock, = 1
Enter theregion withex-postinefficiencies
= 1
Default
= 1
Time
PartialRepayment
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Defaults are Associated with Output Losses
Output
Time
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Defaults are Associated with Drop in Imports
Intermediate Imports
Time
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Maturity of Debt Shortens as Default is More Likely
ST Debt to LT Debt Ratio
Time
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Maturity of Debt Shortens as Default is More Likely
Recall: bL(v) and bS(v) solve
b(v, θL) = bS(v) + bL(v)[1 + qL
(v′L(v)
)]b(v, θH) = bS(v) + bL(v)
[1 + qL
(v′H(v)
)]When indebtedness is high (future default is likely):
I Long-term bond prices more sensitive to shocks
I Can obtain needed insurance with small amount of
long-term debt
I Overall indebtedness is high so short-term debt must be
high
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Recap
Recurrent but infrequent defaults associated with:
I Output and consumption losses
I Fall in imports of intermediate goods
I Shortening of maturity of debt as default approaches
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Conclusion
I Key aspects of sovereign debt and default rationalized as
best outcome of a sovereign debt game
I Best outcome is constrained efficient
I It solves optimal contracting problem with informational
and commitment frictions
I Default is not driven by
I Market incompleteness
I The high reliance on short-term debt
But by the underlying frictions
I Method to implement efficient allocation likely generalize
to other contracting problems
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Dynamics Around Default Episodes Back
-3 -2 -1 0 1 2 3-15
-10
-5
0
5
10
15GDP
% d
evia
tio
n fro
m tre
nd
Year after Default-3 -2 -1 0 1 2 3
-10
-5
0
5
10
Consumption
% d
evia
tio
n fro
m tre
nd
Year after Default
-3 -2 -1 0 1 2 3-40
-30
-20
-10
0
10
20
30
40
Intermediate Imports
Year after Default
% d
evia
tio
n fro
m tre
nd
Mean
Mean +/- std
Sample of DefaultsEpisodes fromMendoza and Yue (2012)
Source: WDI,UN Comtrade andFeenstra
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importsi,t = β0 + β1GDPi,t +
3∑j=0
δj1{defaulti,t−j = 1}+ εi,t
Variable Coefficient Estimate Standard Error
Constant 0.007 0.960
GDP 1.810 0.145
Default at t -0.119 0.044
Default at t− 1 -0.108 0.044
Default at t− 2 -0.040 0.044
Default at t− 3 -0.005 0.043
Back
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Equilibrium Capital Controls and Imports Price
I From the contracting problem, I get m(v)
I Construct p(v) and τ(v) consistent with firms optimality
and foreign exporters no-arbitrage conditions:
f ′(m(v)) = p(v)
1 = p(v)(1− τ(v))
Back
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Defaults are Asssociated with Consumption Losses
Consumption
Time
(0)
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Recovery Driven by Exports
Trade Balance
∗()−()
Borrower’s Value ∗0
∗()−()
From autarky, once the economy recovers, large trade surplus