Partial Default Cristina Arellano, Xavier Mateos-Planas and - - PowerPoint PPT Presentation
Partial Default Cristina Arellano, Xavier Mateos-Planas and Jose-Victor Rios-Rull Mpls Fed, Univ of Minnesota, Queen Mary University of London Macro Within and Across Borders NBER Summer Institute July 2013 Arellano, Mateos-Planas, Rios-Rull
Cristina Arellano, Xavier Mateos-Planas and Jose-Victor Rios-Rull
Mpls Fed, Univ of Minnesota, Queen Mary University of London
Macro Within and Across Borders NBER Summer Institute July 2013
Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro · · · Borders 1 / 1
Sovereign defaults are somewhat frequent in developing countries. Defaults are commonly thought as discrete events: country either repays or defaults on all its debt.
(As if they filed for bankruptcy like people.)
But defaults are very heterogeneous events.
▶ Some defaults have costly and lengthy resolutions. ▶ Others defaults are minor with fast resolutions. Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro · · · Borders 2 / 1
Quantitative models of sovereign default have countries either repaying or defaulting in full.
(Aguiar and Gopinath 2006, Arellano 2008).
With countries restructuring all of its debt after default.
(Yue 2010, Benjamin and Wright 2009, D’Erasmo 2012).
Default as state contingent assets does not sit well with the evidence that default is costly.
(Trade costs, Rose 2002; financial crises, Reinhart and Rogoff 2010; lawsuits and sanctions, Hatchondo & Martinez 2013).
The theory is Non-Markovian. It requires coordination among existing and prospective lenders.
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We document the properties across heterogeneous sovereign defaults.
. .
1
Sovereign defaults are partial. . .
2
During defaults sovereigns continue to receive foreign credit. . .
3
Larger defaults in downturns.
We develop a Markovian model of partial default.
▶ The model promising for explaining the heterogeneity across defaults. ▶ The environment requires output loses when debt is in arrears, and
partial recovery of those debts.
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Panel data for 99 developing countries from 1970-2010. Public debt data from World Development Indicators: debt in arrears and new loans. Default events from Standard & Poor and Trebesch and Cruces (2012). Partial Default= Debt in Arrears Debt Service + Debt in Arrears Debt in Arrears= Interest and principals due this period but in arrears.
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. 2 . 4 . 6 . 8 D e f a u l t e d D e b t / P a y m e n t s D u e 1970 1980 1990 2000 2010 year
Def ault in Brazil
Default events are associated with large arrears but default is partial
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.2 .4 .6 .8 Defaulted Debt / Payments Due 1970 1980 1990 2000 2010 year
Defaults in Ecuador
Defaults can be very small as in 2008.
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.2 .4 .6 .8 Defaulted Debt / Payments Due 1990 1995 2000 2005 2010 year
Defaults in Indonesia
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.2 .4 .6 .8 1 Defaulted Debt / Payments Due 1970 1980 1990 2000 2010 year
Def aults in Argentina
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AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO AGO ALB ALB ALB ALB ALB ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG ARG BFA BFA BFA BFA BFA BFA BFA BFA BFA BFA BFA BFA BFA BFA BGR BGR BGR BGR BGR BLZ BLZ BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BOL BRA BRA BRA BRA BRA BRA BRA BRA BRA BRA BRA BRA CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CAF CHL CHL CHL CHL CHL CHL CHL CHL CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CIV CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG COG CPV CPV CPV CPV CPV CPV CPV CPV CPV CPV CPV CPV CPV CPV CPV CPV CRI CRI CRI CRI CRI CRI CRI CRI CRI CRI DMA DMA DMA DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DOM DZA DZA DZA DZA DZA DZA ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ECU ETH ETH ETH ETH ETH ETH ETH ETH ETH GAB GAB GAB GAB GAB GAB GAB GAB GAB GAB GAB GAB GAB GAB GAB GAB GHA GHA GHA GIN GIN GIN GIN GIN GIN GIN GIN GIN GIN GIN GMB GMB GMB GMB GMB GNB GNB GNB GNB GNB GNB GNB GNB GNB GNB GNB GNB GNB GNB GRD GRD GRD GRD GTM GTM GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY GUY HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HND HTI HTI HTI HTI HTI HTI HTI HTI HTI HTI HTI HTI HTI IDN IDN IDN IDN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN IRN JAM JAM JAM JAM JAM JAM JAM JAM JAM JAM JAM JAM JAM JAM JAM JOR JOR JOR JOR JOR KEN KEN KEN KEN KEN KEN LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR LBR MAR MAR MAR MAR MAR MAR MDA MDA MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MDG MEX MEX MEX MEX MEX MEX MEX MEX MEX MKD MKD MKD MKD MKD MKD MMR MMR MMR MMR MMR MMR MMR MMR MMR MMR MMR MMR MNG MNG MNG MNG MOZ MOZ MOZ MOZ MOZ MOZ MOZ MOZ MOZ MOZ MRT MRT MRT MRT MRT MWI MWI NER NER NER NER NER NER NER NER NER NGA NGA NGA NGA NGA NGA NGA NGA NGA NGA NGA NGA NGA NGA NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC NIC PAK PAK PAN PAN PAN PAN PAN PAN PAN PAN PAN PAN PAN PAN PAN PAN PER PER PER PER PER PER PER PER PER PER PER PER PER PER PER PER PER PER PHL PHL PHL PHL PHL PHL PHL PHL PHL PHL PRY PRY PRY PRY PRY PRY PRY PRY PRY ROM ROM ROM ROM RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RWA SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SDN SEN SEN SEN SEN SEN SEN SEN SEN SEN SEN SEN SLB SLB SLB SLB SLB SLB SLB SLB SLB SLB SLB SLE SLE SLE SLE SLE SLE SLE SLE SLE SLE SLE SLE SLE SLE SLV SLV SLV SLV SLV SLV SLV SLV SLV SLV SLV SLV SLV SLV SLV SLV SRB SRB SRB SRB SRB SRB SRB SRB SRB SRB SRB SRB SRB STP STP STP STP STP STP STP STP SYC SYC SYC TGO TGO TGO TGO TGO TGO TGO TGO TGO TGO TGO TGO TGO TUR TUR TUR TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA TZA UGA UGA UGA UGA UGA UGA UGA UGA UGA UGA UGA UGA UGA UGA UKR UKR UKR URY URY URY URY URY URY URY VEN VEN VEN VEN VEN VEN VEN VEN VEN VEN VEN VEN VEN VNM VNM VNM VNM VNM VNM VNM VNM VNM VNM VNM VNM VNM VNM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM YEM ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZAR ZMB ZMB ZMB ZMB ZMB ZMB ZMB ZMB ZMB ZMB ZMB ZMB ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE ZWE
. 2 . 4 . 6 . 8 1 D e f a u l t e d D e b t / P a y m e n t s D u e 1970 1980 1990 2000 2010 year
Partial Def aults
Across all S&P default : countries default on average on 59% of what is due.
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.2 .4 .6 .8 1990 1995 2000 2005 2010 year sdef/low Defaulted Debt / Payments Due New Loans / Payments Due
Defaults in Indonesia
During default countries continue to borrow
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.1 .2 .3 Fraction
.1 .2 New Loans / GNI
Defaults
.1 .2 .3 .4 Fraction
.1 .2 New Loans / GNI
Non Defaults
Countries get new loans during defaults almost as much as in normal times, Caveat: Data on new government loans contains many missing observations.
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Partial Default and GDP Growth
ARG ARG BFA BGR BLZ BOL BOL BRA CAF CAF CHL CIV CIV CMR CMR COG CPV CRI DMA DOM DOM DZA ECU ECU ECU ETH GAB GAB GHA GHA GHA GIN GMB GNB GRD GRD GTM GTM GUY GUY HND IDN IDN IDN IRN JAM JAM JAM JOR KEN KEN LBR MAR MAR MDA MDA MDG MEX MKD MMR MMR MMR MNG MOZ MRT MWI MWI NER NGA NGA NGA PAK PAN PER PER PER PER PHL PRY PRY ROM ROM RUS RUS SDN SEN SEN SEN SLB SLE SLE SLE SLV SYC TGO TGO TGO TGO TUR TUR UKR URY URY URY URY VEN VEN VEN VEN VEN VNM ZAR ZMB ZWE ZWE
.2 .4 .6 .8 1 Defaulted Debt / Payments Due
10 20 GDP growth Defaulted Debt / Payments Due Fitted values
GDP Growth and Partial Defaults
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Limited, but not inexistent, legal system in the world allows for sovereign default. However,
▶ Creditors of defaulted debt create some havoc. Costs increasing in the
level of defaulted debt.
▶ Defaulted Debt does not disappear, it remains in the balance sheet
until repayment (like Venezuela 2005) or renegotiated (with a wide range of haircuts- 0-100%). Today a constant fraction of debt in arrears survives.
Inability of lenders to coordinate to exclude further future lending (free entry in lending markets (Krueger and Uhlig (06)). Markov Equilibria (when non multiple equilibria in the static counterpart, it is the
limit of equilibria in finite horizon economies).
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Dynamic model of borrowing and default
Small open economy with stochastic endowment z which is Markov with transition Γz,z′. The small open economy trades bonds with international lenders (often, but not always, borrows, hence borrower) and can default on them. Cost of defaulting reduces next period output and is increasing with the level of defaulted debt. Lenders are risk neutral.
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Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B. c = y − (A − D) + q(z, A′, D) B D ≤ A Total coupon obligations tomorrow. A′ = δ A + B + ( ¯ R − δ ) D D remains as future obligations annuitized at rate ¯ R. D > 0 has direct costs on endowment with y ′ = z′ψ(D). Price functions q(z, A′, D) describe access to credit.
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State: (z, A, y). Nature, what it owes, what it has. Choose consumption, new loans, and default. V (z, A, y) = max
c,B,D u(c) + βE
{ V ′(z′, A, y ′)|z } s.t. c = y − (A − D) + q(z, A′, D) B A′ = δ A + B + ¯ R D y ′ = z′ ψ(D), 0 ≤ D ≤ A. Resulting policy functions: B(z, A, y), and D(z, A, y).
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Take as given policy functions and discount at world’s interest rate r. Value to a claim of one unit. H(z, A, y) = ( 1 − D(z, A, y) A ) Today Tomorrow + 1 1 + r ( δ + ( ¯ R − δ)D(z, A, y) A ) E{H(z′, A′, y ′)|z}. A′ and y ′ are determined by borrower’s functions.
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Zero profit condition determines price functions q(z, A′, D) = 1 1 + r E{H(z′ψ(D), A′, z′)|z}. Compensates for expected loss in default. Partial defaults give price of debt a long-term component. Markov equilibrium is the obvious thing. The small country maximizes given prices and the free entry condition given the expected return of loans.
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Transfer future resources towards present with B or D. Let w = y − A denote cash in hand. Standard consumption-savings trade-off:
▶ Increase in consumption with B or D
c − w = q(A′, D, z)B + D
▶ By reduction in cash on hand tomorrow
w′ = z′ψ(D) − A′ with A′ = B − ¯ RD, D < A
B is restricted by q(A′, D, z). D is restricted by A and carries additional cost through ψ(D).
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. .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. .
Ct+1 Ct
Risk Free
1 0.5 1.0
Borrow
. .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. .
Ct+1 Ct 1 0.5 1.0
Borrow Default Both
. .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. .
Ct+1 Ct 1 0.5 1.0
Borrow Default Both
. .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. .
Ct+1 Ct 1 0.5 1.0
Borrow Default Both
Explore the numerical properties of these economies. We look for the properties in the data that we documented
.
1
Sovereign defaults are partial. . .
2
During defaults sovereigns continue to receive foreign credit. . .
3
Larger defaults in downturns.
Designed to resemble developing countries with a year.
▶ There is a fixed cost to default. ▶ Various economies that differ in the size of debt and persistency of
shocks.
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Default cost y = z′ψ(D) decreasing and concave with lower bound
ψ(D) = ψ0 max {
(D− ¯ D)2(γ ¯ D+D) (0− ¯ D)2(γ ¯ D+0) , ψ
}
Explore 3 experiments: High debt, low debt, and persistent shocks Common parameters: σ = 2, r = 1.7%, δ = 0, ¯
R = 0.80, γ = 0.5, ψ= 0.9.
Description Parameter Example 1 Example 2 Example 2 High Debt Low Debt Persistent Shock process
z
iid with σH iid with σH Argentina Penalty slope
¯ D
0.5 0.7 0.6 Fixed cost
ψ0
0.99 0.99 0.995 Discount
β
0.85 0.85 0.94
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Data Partial default 59% Frequency of default 51% Debt /Output 49% Spread – During defaults: Debt/GDP 87% Spreads – Arrears/Output 6.2% New loans/Output 1.07% Output relt. to Mean
Large frequency of partial defaults During defaults debt is large, output is low, countries continue to borrow
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Data Examples High Debt Low Debt Persistent Partial default 59% 18% 100% 76% Frequency of default 51% 11% 30% 74% Debt /Output 49% 30% 1% 19% Spread – 0.5% 17% 1.5% During defaults: Debt/GDP 87% 41% 5.5% 13% Spreads – 1.05% 43% 1.8% Arrears/Output 6.2% 36% 5.5% 5.3% New loans/Output 1.07% 7.3% 2% 8.6% Output relt. to Mean
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Intertemporal frontier: Only B
0.05 0.1 0.15 0.2 0.25 0.3 0.3 0.35 0.4 0.45 0.5 0.55 T
r
: c a s h i n h a n d Today: consumption - cash in hand
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0.05 0.1 0.15 0.2 0.25 0.3 0.3 0.35 0.4 0.45 0.5 0.55 Tomorrow: cash in hand Today: consumption - cash in hand D=0 risk free
Concave frontier via q(.) due to increasing default risk
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0.05 0.1 0.15 0.2 0.25 0.3 0.3 0.35 0.4 0.45 0.5 0.55 Tomorrow: cash in hand Today: consumption - cash in hand D=0 B=0
Shape of frontier depends on ψ(D) and ¯
R
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0.05 0.1 0.15 0.2 0.25 0.3 0.3 0.35 0.4 0.45 0.5 0.55 Tomorrow: cash in hand Today: consumption - cash in hand D=0 B=0 D opt
Smaller transfers with B, intermediate with B + D, large with D
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0.2 0.4 0.6
0.1 0.2 0.3 0.4 0.5 0.6 Debt A D e f a u l t D Prod= 0.4162774
0.2 0.4 0.6
0.1 0.2 0.3 0.4 0.5 0.6 Debt A L
n B
Small debt: B > 0, and D = 0 Large debt: B = 0, D = A. Endogenously borrow less due to bad price.
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0.1 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 Debt next A` price Q Q D=0 Q D>0 Q D>>0
Price decreases with larger debt and is worse when default D > 0.
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. 1 7 5 . 1 8 . 1 8 5 . 1 9 . 1 9 5 . 2 D e f a u l t e d D e b t / P a y m e n t s D u e 3000 3500 4000 4500 5000 period
Partial Defaults (High Debt)
Default is always partial. Narrow range
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.2 .4 .6 .8 1 Defaulted Debt / Payments Due 3000 3500 4000 4500 5000 period
Partial Defaults (Persistent)
Wide range of partial default
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.5 1 1.5 2 4050 4100 4150 period Defaulted Debt / Payments Due Loans / Payments Due
Defaults and Loans (High Debt)
New loans are used much more actively than defaults
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.5 1 1.5 2 2.5 4050 4100 4150 period Defaulted Debt / Payments Due Loans / Payments Due
Defaults and Loans (Persistent)
New loans and defaults actively used. Large substitution between two
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.05 .1 .15 .2 Defaulted Debt / Payments Due .4 .45 .5 .55 .6 Output Defaulted Debt / Payments Due Fitted values
Partial Defaults (High Debt) Defaults only with the lowest income
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.5 1 1.5 Defaulted Debt / Payments Due .4 .45 .5 .55 .6 Output Defaulted Debt / Payments Due Fitted values
Partial Defaults (Persistent)
Larger defaults with lower income
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Sovereign default is partial and countries continue to borrow during defaults. Propose new (Markovian) theory consistent with these facts . Continuing work: .
▶ Take model to data. Move a bit out of examples. ▶ Model as laboratory for recovering costs of default.
Link it with partial individual default (Herkenhoff and Ohanian (13)).
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0.5 1 1.5
0.2 0.4 0.6 0.8 D e f a u l t D P rod= 0.4162774 0.5 1 1.5
0.2 0.4 0.6 0.8 P rod= 0.4562222 0.5 1 1.5
0.2 0.4 0.6 0.8 P rod= 0.5000000 0.5 1 1.5
0.2 0.4 0.6 0.8 P rod= 0.5479786 0.5 1 1.5
0.2 0.4 0.6 0.8 P rod= 0.6005610 0.5 1 1.5
0.2 0.4 0.6 0.8 Debt A L
n B 0.5 1 1.5
0.2 0.4 0.6 0.8 Debt A 0.5 1 1.5
0.2 0.4 0.6 0.8 Debt A 0.5 1 1.5
0.2 0.4 0.6 0.8 Debt A 0.5 1 1.5
0.2 0.4 0.6 0.8 Debt A 0.5 1 1.5 0.5 1 Debt next A ` p r i c e Q ( D = ) 0.5 1 1.5 0.5 1 Debt next A ` 0.5 1 1.5 0.5 1 Debt next A ` 0.5 1 1.5 0.5 1 Debt next A ` 0.5 1 1.5 0.5 1 Debt next A ` Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro · · · Borders 40 / 1
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.05 0.1 0.15 0.2 0.25 cash in hand tomorrow consumption - cash in hand (today) Prod= 0.4162774 D=0 B=0 D opt
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0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.05 0.1 0.15 0.2 0.25 cash in hand tomorrow consumption - cash in hand (today) Prod= 0.5000000 D=0 B=0 D opt
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