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
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Motivation
Sovereign defaults are somewhat frequent in developing countries.
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Motivation
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.)
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Motivation
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.
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Motivation
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.
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Motivation
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.
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Existing Theory Quantitative models of sovereign default have countries either repaying or defaulting in full. (Aguiar and Gopinath 2006, Arellano 2008).
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Existing Theory 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).
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Existing Theory 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).
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Existing Theory 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. Arellano, Mateos-Planas, Rios-Rull ()
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This paper We document the properties across heterogeneous sovereign defaults.
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This paper We document the properties across heterogeneous sovereign defaults. . Sovereign defaults are partial.
1
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This paper We document the properties across heterogeneous sovereign defaults. . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
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This paper We document the properties across heterogeneous sovereign defaults. . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
Arellano, Mateos-Planas, Rios-Rull ()
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This paper We document the properties across heterogeneous sovereign defaults. . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
We develop a Markovian model of partial default.
Arellano, Mateos-Planas, Rios-Rull ()
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This paper We document the properties across heterogeneous sovereign defaults. . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
We develop a Markovian model of partial default. ▶
The model promising for explaining the heterogeneity across defaults.
Arellano, Mateos-Planas, Rios-Rull ()
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This paper We document the properties across heterogeneous sovereign defaults. . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
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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DATA
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Defaults in the Data Panel data for 99 developing countries from 1970-2010.
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Defaults in the Data Panel data for 99 developing countries from 1970-2010. Public debt data from World Development Indicators: debt in arrears and new loans.
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Defaults in the Data 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).
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Defaults in the Data 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=
Arellano, Mateos-Planas, Rios-Rull ()
Debt in Arrears Debt Service + Debt in Arrears
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Defaults in the Data 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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Defaults in the Data: 1. Sovereign Default is Partial
0
Defaulted Debt / Payments Due .2 .4 .6
.8
Def ault in Brazil
1970
1980
1990 year
2000
2010
Default events are associated with large arrears but default is partial Arellano, Mateos-Planas, Rios-Rull ()
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Defaults in the Data: 1. Sovereign Default is Partial
0
Defaulted Debt / Payments Due .2 .4 .6
.8
Def aults in Ecuador
1970
1980
1990 year
2000
2010
Defaults can be very small as in 2008. Arellano, Mateos-Planas, Rios-Rull ()
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1. Sovereign Default is Partial
0
Defaulted Debt / Payments Due .2 .4 .6
.8
Defaults in Indonesia
1990
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1995
2000 year
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2010
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Defaults in the Data: 1. Sovereign Default is Partial
0
Defaulted Debt / Payments Due .2 .4 .6
.8
1
D ef aults in Argentina
1970
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1990 year
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2010
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Defaults in the Data: 1. Sovereign Default is Partial 1
Partial Def aults SDN
MMR
SRB ETH
ZWE SLE
RUS GIN ALB MRT MKD BGR
RWA SLB RUS ARG CIV
GIN SLE HTI TGO UGA PAN GTM CIV CMR TGO TGO IRN CRI BFA PRY GAB JOR ARG ECU DOM HND SEN GUYCPV MMR GMB JAM BOL BRA MAR GTM GHA NER BOL GHA NGA JAM GHA MWI ZWE
0
Defaulted Debt / Payments Due .2 .4 .6
.8
ZAR
LBR GNB TZA SLE STP CAF MOZ NIC ZMB YEM CAF MDG GUY COGAGO VNM PER
1970
MWI VEN PHL SLV TUR SEN MAR TGO TUR MEX MMRROM DZA PER PER JAM PER ROM CHL URY URY SEN URY VEN
1980
1990 year
SYC IDN IDN
GRD GRD
GAB MDA MDA NGA MNG IDN CMR DMA KEN UKR VEN
PAK ECU NGAPRY
JAM
DOM
KEN VEN VEN URY
2000
BLZ
ECU
2010
Across all S&P default : countries default on average on 59% of what is due. Arellano, Mateos-Planas, Rios-Rull ()
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Defaults in Data: 2. Borrowing during Sovereign Default
-.2
0
.2
.4
.6
.8
Defaults in Indonesia
1990
1995
2000 year
sdef/low New Loans / Payments Due
2005
2010
Defaulted Debt / Payments Due
During default countries continue to borrow Arellano, Mateos-Planas, Rios-Rull ()
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Defaults in Data: 2. Borrowing during Sovereign Default
Fraction .2 0
0
.1
.1
Fraction
.2
.3
.4
Non Defaults
.3
Defaults
-.1
0 .1 N ew Loans / GN I
.2
-.1
0 .1 N ew Loans / GN I
.2
Countries get new loans during defaults almost as much as in normal times, Caveat: Data on new government loans contains many missing observations. Arellano, Mateos-Planas, Rios-Rull ()
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Defaults in Data: 3. Larger Default in Downturns Partial Default and GDP Growth
1
GDP Growth and Partial Defaults MMR ETH SDN LBR GNB ZWE SLE CAF SLE ZMB ZAR RUS GIN CAF MDG GUY COG PER MRT VNM MKD BGR RUS SLB ARG SLE CIV TGO PAN GRD IDN GTMSYCCMR CIV TGO TGO GRD IRN BFA CRI PRY IDN JOR GAB ARG ECUSEN HND DOM MDA CPV GAB MDA MMR GUYGMB NGA MAR JAM MNG BRA BOLGTM IDN CMR DMA GHA NER BOL KEN GHA NGA GHA MWIUKR JAM DOM VEN NGA PAK ECU MWI PRY VEN PHL KEN SLV TUR SEN MARVEN BLZ TGO ECU MEX MMR DZA URY CHLSEN PERJAM PER URY ROM PER UTUR RY ROM VEN URY
Defaulted Debt / Payments Due 0 .2 .4 .6 .8
MOZ
-20
-10
0 GDP growth
Defaulted Debt / Payments Due
Arellano, Mateos-Planas, Rios-Rull ()
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ZWE
VEN
10
20
Fitted values
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THEORY
Arellano, Mateos-Planas, Rios-Rull ()
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Ingredients of our theory Limited, but not inexistent, legal system in the world allows for sovereign default. However,
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Ingredients of our theory 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.
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Ingredients of our theory 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.
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Ingredients of our theory 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)).
Arellano, Mateos-Planas, Rios-Rull ()
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Ingredients of our theory 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). Arellano, Mateos-Planas, Rios-Rull ()
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Model Dynamic model of borrowing and default
Small open economy with stochastic endowment z which is Markov with transition Γz,z ′ .
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Model 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.
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Model 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.
Arellano, Mateos-Planas, Rios-Rull ()
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Model 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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Borrower Trades perpetuity bonds that decay at rate δ.
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B.
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B. c
Arellano, Mateos-Planas, Rios-Rull ()
= y − (A − D ) + q (z, A′ , D ) B
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B.
= y − (A − D ) + q (z, A′ , D ) B D ≤ A c
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B.
= y − (A − D ) + q (z, A′ , D ) B D ≤ A c
Total coupon obligations tomorrow.
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B.
= y − (A − D ) + q (z, A′ , D ) B D ≤ A c
Total coupon obligations tomorrow. A′ = δ A + B + ( R¯ − δ ) D
Arellano, Mateos-Planas, Rios-Rull ()
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B.
= y − (A − D ) + q (z, A′ , D ) B D ≤ A c
Total coupon obligations tomorrow. A′ = δ A + B + ( R¯ − δ ) D ¯ D remains as future obligations annuitized at rate R.
Arellano, Mateos-Planas, Rios-Rull ()
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B.
= y − (A − D ) + q (z, A′ , D ) B D ≤ A c
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 ).
Arellano, Mateos-Planas, Rios-Rull ()
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Borrower Trades perpetuity bonds that decay at rate δ. Has coupons A, defaults on D, borrows B.
= y − (A − D ) + q (z, A′ , D ) B D ≤ A c
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. Arellano, Mateos-Planas, Rios-Rull ()
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Recursive Problem: Borrower State: (z, A, y ). Nature, what it owes, what it has.
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Recursive Problem: Borrower State: (z, A, y ). Nature, what it owes, what it has. Choose consumption, new loans, and default.
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Recursive Problem: Borrower State: (z, A, y ). Nature, what it owes, what it has. Choose consumption, new loans, and default. { } V (z, A, y ) = max u (c ) + βE V ′ (z ′ , A, y ′ )|z c,B,D
s.t.
Arellano, Mateos-Planas, Rios-Rull ()
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Recursive Problem: Borrower State: (z, A, y ). Nature, what it owes, what it has. Choose consumption, new loans, and default. { } V (z, A, y ) = max u (c ) + βE V ′ (z ′ , A, y ′ )|z c,B,D
s.t. c
Arellano, Mateos-Planas, Rios-Rull ()
= y − (A − D ) + q (z, A′ , D ) B
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Recursive Problem: Borrower State: (z, A, y ). Nature, what it owes, what it has. Choose consumption, new loans, and default. { } V (z, A, y ) = max u (c ) + βE V ′ (z ′ , A, y ′ )|z c,B,D
s.t. c A′
Arellano, Mateos-Planas, Rios-Rull ()
= y − (A − D ) + q (z, A′ , D ) B = δ A + B + R¯ D
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Recursive Problem: Borrower State: (z, A, y ). Nature, what it owes, what it has. Choose consumption, new loans, and default. { } V (z, A, y ) = max u (c ) + βE V ′ (z ′ , A, y ′ )|z c,B,D
s.t. c A′ y′
Arellano, Mateos-Planas, Rios-Rull ()
= y − (A − D ) + q (z, A′ , D ) B = δ A + B + R¯ D = z ′ ψ (D ), 0 ≤ D ≤ A.
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Recursive Problem: Borrower State: (z, A, y ). Nature, what it owes, what it has. Choose consumption, new loans, and default. { } V (z, A, y ) = max u (c ) + βE V ′ (z ′ , A, y ′ )|z c,B,D
s.t. c A′ y′
= y − (A − D ) + q (z, A′ , D ) B = δ A + B + R¯ D = z ′ ψ (D ), 0 ≤ D ≤ A.
Resulting policy functions: B (z, A, y ), and D (z, A, y ).
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r .
Arellano, Mateos-Planas, Rios-Rull ()
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r . Value to a claim of one unit.
Arellano, Mateos-Planas, Rios-Rull ()
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r . Value to a claim of one unit. ( H (z, A, y ) =
Arellano, Mateos-Planas, Rios-Rull ()
D (z, A, y ) 1− A
)
Partial Default
Today
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r . Value to a claim of one unit. ( H (z, A, y ) =
Tomorrow
D (z, A, y ) 1− A
+
Arellano, Mateos-Planas, Rios-Rull ()
) Today
1 1+r
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r . Value to a claim of one unit. ( H (z, A, y ) =
Tomorrow
D (z, A, y ) 1− A
1 + 1+r
Arellano, Mateos-Planas, Rios-Rull ()
) Today
( δ
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r . Value to a claim of one unit. ( H (z, A, y ) =
Tomorrow
D (z, A, y ) 1− A
1 + 1+r
Arellano, Mateos-Planas, Rios-Rull ()
(
) Today
D (z, A, y ) δ + (R¯ − δ) A
Partial Default
)
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r . Value to a claim of one unit. ( H (z, A, y ) =
Tomorrow
D (z, A, y ) 1− A
1 + 1+r
Arellano, Mateos-Planas, Rios-Rull ()
(
) Today
D (z, A, y ) δ + (R¯ − δ) A
Partial Default
)
E {H (z ′ , A′ , y ′ )|z }.
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Recursive Problem: Lenders Take as given policy functions and discount at world’s interest rate r . Value to a claim of one unit. ( H (z, A, y ) =
Tomorrow
D (z, A, y ) 1− A
1 + 1+r
(
) Today
D (z, A, y ) δ + (R¯ − δ) A
)
E {H (z ′ , A′ , y ′ )|z }.
A′ and y ′ are determined by borrower’s functions.
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Bond Price and Equilibrium Zero profit condition determines price functions q (z, A′ , D ) =
Arellano, Mateos-Planas, Rios-Rull ()
1 E {H (z ′ ψ(D ), A′ , z ′ )|z }. 1+r
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Bond Price and Equilibrium Zero profit condition determines price functions q (z, A′ , D ) =
1 E {H (z ′ ψ(D ), A′ , z ′ )|z }. 1+r
Compensates for expected loss in default.
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Bond Price and Equilibrium Zero profit condition determines price functions q (z, A′ , D ) =
1 E {H (z ′ ψ(D ), A′ , z ′ )|z }. 1+r
Compensates for expected loss in default. Partial defaults give price of debt a long-term component.
Arellano, Mateos-Planas, Rios-Rull ()
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Bond Price and Equilibrium Zero profit condition determines price functions q (z, A′ , D ) =
1 E {H (z ′ ψ(D ), A′ , z ′ )|z }. 1+r
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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Default as Expensive Debt Transfer future resources towards present with B or D.
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Default as Expensive Debt Transfer future resources towards present with B or D. Let w = y − A denote cash in hand.
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Default as Expensive Debt Transfer future resources towards present with B or D. Let w = y − A denote cash in hand. Standard consumption-savings trade-off:
Arellano, Mateos-Planas, Rios-Rull ()
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Default as Expensive Debt 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
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Default as Expensive Debt 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
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
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Default as Expensive Debt 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′
Arellano, Mateos-Planas, Rios-Rull ()
= z ′ ψ (D ) − A′
Partial Default
Macro · · · Borders
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Default as Expensive Debt 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
with
Arellano, Mateos-Planas, Rios-Rull ()
w′ A′
= z ′ ψ (D ) − A′ ¯ = B − RD, D
Partial Default
Macro · · · Borders
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Default as Expensive Debt 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
with
w′ A′
= z ′ ψ (D ) − A′ ¯ = B − RD, D
B is restricted by q (A′ , D, z ).
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
22 / 42
Default as Expensive Debt 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
with
w′ A′
= z ′ ψ (D ) − A′ ¯ = B − RD, D
B is restricted by q (A′ , D, z ). D is restricted by A and carries additional cost through ψ(D ). Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Ct+1
Budget Constraint 1
Borrow 0
0
Risk Free
0.5
1.0 ..
. ..
. ..
.
Ct
. . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. ..
. ..
.
..
. ..
. ..
.
Ct+1
Budget Constraint 1
Borrow 0
0
0.5
1.0 ..
. ..
. ..
.
Ct
. . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. ..
. ..
.
..
. ..
. ..
.
Ct+1
Budget Constraint 1
Default
Borrow 0
0
0.5
1.0 ..
. ..
. ..
.
Ct
. . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. ..
. ..
.
..
. ..
. ..
.
Ct+1
Budget Constraint 1
Default Both Borrow 0
0
0.5
1.0 ..
. ..
. ..
.
Ct
. . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. ..
. ..
.
..
. ..
. ..
.
Variety of Examples Explore the numerical properties of these economies.
Arellano, Mateos-Planas, Rios-Rull ()
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Variety of Examples Explore the numerical properties of these economies. We look for the properties in the data that we documented
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
23 / 42
Variety of Examples Explore the numerical properties of these economies. We look for the properties in the data that we documented . Sovereign defaults are partial.
1
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
23 / 42
Variety of Examples Explore the numerical properties of these economies. We look for the properties in the data that we documented . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
23 / 42
Variety of Examples Explore the numerical properties of these economies. We look for the properties in the data that we documented . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
23 / 42
Variety of Examples Explore the numerical properties of these economies. We look for the properties in the data that we documented . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
Designed to resemble developing countries with a year.
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
23 / 42
Variety of Examples Explore the numerical properties of these economies. We look for the properties in the data that we documented . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
Designed to resemble developing countries with a year. ▶
There is a fixed cost to default.
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
23 / 42
Variety of Examples Explore the numerical properties of these economies. We look for the properties in the data that we documented . Sovereign defaults are partial.
1
. During defaults sovereigns continue to receive foreign credit.
2
. Larger defaults in downturns.
3
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.
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Numerical settings Default cost y = z ′ ψ(D ) decreasing and concave with lower bound
ψ(D ) = ψ0 max
Arellano, Mateos-Planas, Rios-Rull ()
{
(D −D¯ )2 (γD¯ +D ) ,ψ (0−D¯ )2 (γD¯ +0)
Partial Default
}
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Numerical settings Default cost y = z ′ ψ(D ) decreasing and concave with lower bound
ψ(D ) = ψ0 max
{
(D −D¯ )2 (γD¯ +D ) ,ψ (0−D¯ )2 (γD¯ +0)
}
Explore 3 experiments: High debt, low debt, and persistent shocks
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
24 / 42
Numerical settings Default cost y = z ′ ψ(D ) decreasing and concave with lower bound
ψ(D ) = ψ0 max
{
(D −D¯ )2 (γD¯ +D ) ,ψ (0−D¯ )2 (γD¯ +0)
}
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.
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Numerical settings Default cost y = z ′ ψ(D ) decreasing and concave with lower bound
ψ(D ) = ψ0 max
{
(D −D¯ )2 (γD¯ +D ) ,ψ (0−D¯ )2 (γD¯ +0)
}
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
Shock process Penalty slope Fixed cost Discount Arellano, Mateos-Planas, Rios-Rull ()
z D¯ ψ0 β
Example 1 High Debt iid with σH 0.5 0.99 0.85 Partial Default
Example 2 Low Debt iid with σH 0.7 0.99 0.85
Example 2 Persistent Argentina 0.6 0.995 0.94 Macro · · · Borders
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Average statistics Data Partial default Frequency of default Debt /Output Spread During defaults: Debt/GDP Spreads Arrears/Output New loans/Output Output relt. to Mean
59% 51% 49% – 87% – 6.2% 1.07% -1.4%
Large frequency of partial defaults During defaults debt is large, output is low, countries continue to borrow Arellano, Mateos-Planas, Rios-Rull ()
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Average statistics Data Partial default Frequency of default Debt /Output Spread During defaults: Debt/GDP Spreads Arrears/Output New loans/Output Output relt. to Mean
Arellano, Mateos-Planas, Rios-Rull ()
59% 51% 49% –
High Debt 18% 11% 30% 0.5%
Examples Low Debt 100% 30% 1% 17%
Persistent 76% 74% 19% 1.5%
87% – 6.2% 1.07% -1.4%
41% 1.05% 36% 7.3% -15%
5.5% 43% 5.5% 2% -8%
13% 1.8% 5.3% 8.6% -4%
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Examples confirm partial default is alternative credit Intertemporal frontier: Only B
0.55
Tomor row: cash in hand
0.5
0.45
0.4
0.35
0.3 0
0.05
Arellano, Mateos-Planas, Rios-Rull ()
0.1 0.15 0.2 Today : c ons umption - c as h in hand
Partial Default
0.25
0.3
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Intertemporal frontier: Only B D =0 ris k free 0.55
Tomorrow: cash in hand
0.5
0.45
0.4
0.35
0.3 0
0.05
0.1 0.15 0.2 Today : c ons umption - c as h in hand
0.25
0.3
Concave frontier via q (.) due to increasing default risk Arellano, Mateos-Planas, Rios-Rull ()
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Intertemporal frontier: Only D D=0 B=0 0.55
Tomorrow: cash in hand
0.5
0.45
0.4
0.35
0.3 0
0.05
0.1 0.15 0.2 Today : c ons umption - c as h in hand
0.25
0.3
Shape of frontier depends on ψ(D ) and R¯ Arellano, Mateos-Planas, Rios-Rull ()
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Intertemporal frontier: B and D D =0 B=0 D opt 0.55
Tomorrow: cash in hand
0.5
0.45
0.4
0.35
0.3 0
0.05
0.1 0.15 0.2 Today : c ons umption - c as h in hand
0.25
0.3
Smaller transfers with B, intermediate with B + D, large with D Arellano, Mateos-Planas, Rios-Rull ()
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Policy Functions: Borrow and Default 0.4162774 0.6
0.5
0.5
0.4
0.4
0.3
0.3
Loan B
Default D
Prod= 0.6
0.2
0.2
0.1
0.1
0
0 -0.1
-0.1 -0.2 -0.2
0
0.2 Debt A
0.4
0.6
-0.2 -0.2
0
0.2 Debt A
0.4
0.6
Small debt: B > 0, and D = 0 Large debt: B = 0, D = A. Endogenously borrow less due to bad price. Arellano, Mateos-Planas, Rios-Rull ()
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Policy functions: Prices Q D=0 Q D>0 Q D>>0
1
price Q
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3 Debt next A`
0.4
0.5
0.6
Price decreases with larger debt and is worse when default D > 0. Arellano, Mateos-Planas, Rios-Rull ()
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Implication 1: Partial Default
.175
Defaulted Debt / Payments Due .18 .185 .19 .195
.2
Partial Defaults (High Debt)
3000
3500
4000 period
4500
5000
Default is always partial. Narrow range Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Implication 1: Partial Default
Defaulted Debt / Payments Due .2 .4 .6 .8
1
Partial Defaults (Persistent)
3000
3500
4000 period
4500
5000
Wide range of partial default Arellano, Mateos-Planas, Rios-Rull ()
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Implication 2. Borrowing during Sovereign Default
0
.5
1
1.5
2
Defaults and Loans (High Debt)
4050
4100 period Defaulted Debt / Payments Due
4150 Loans / Payments Due
New loans are used much more actively than defaults Arellano, Mateos-Planas, Rios-Rull ()
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Implication 2. Borrowing during Sovereign Default
0
.5
1
1.5
2
2.5
Defaults and Loans (Persistent)
4050
4100 period Defaulted Debt / Payments Due
4150 Loans / Payments Due
New loans and defaults actively used. Large substitution between two Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Implication 3: Larger Default in Downturns
Defaulted Debt / Payments Due 0 .05 .1 .15
.2
Partial Defaults (High Debt)
.4
.45
.5 Output
Defaulted Debt / Payments Due
.55
.6
Fitted values
Defaults only with the lowest income Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Implication 3: Larger Default in Downturns
Defaulted Debt / Payments Due -.5 0 .5 1
1.5
Partial Defaults (Persistent)
.4
.45
.5 Output
Defaulted Debt / Payments Due
.55
.6
Fitted values
Larger defaults with lower income Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
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Conclusion Sovereign default is partial and countries continue to borrow during defaults.
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Conclusion Sovereign default is partial and countries continue to borrow during defaults. Propose new (Markovian) theory consistent with these facts .
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
Macro · · · Borders
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Conclusion Sovereign default is partial and countries continue to borrow during defaults. Propose new (Markovian) theory consistent with these facts . Continuing work: .
Arellano, Mateos-Planas, Rios-Rull ()
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Conclusion 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.
Arellano, Mateos-Planas, Rios-Rull ()
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Conclusion 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.
Arellano, Mateos-Planas, Rios-Rull ()
Partial Default
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Conclusion 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)).
Arellano, Mateos-Planas, Rios-Rull ()
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Policy Functions: Persistent Case
0 0.5
0.8 0.6 0.4 0.2 0 -0.2
price Q (D=0)
Loan B
Default D
Prod= 0.4162774 0.8 0.6 0.4 0.2 0 -0.2
1 1.5
0 0.5 1 1.5 Debt A
Prod= 0.4562222 0.8 0.6 0.4 0.2 0 -0.2
0 0.5
0.8 0.6 0.4 0.2 0 -0.2
1 1.5
0 0.5 1 1.5 Debt A
Prod= 0.5000000 0.8 0.6 0.4 0.2 0 -0.2
0 0.5
0.8 0.6 0.4 0.2 0 -0.2
1 1.5
0 0.5 1 1.5 Debt A
Prod= 0.5479786 0.8 0.6 0.4 0.2 0 -0.2
0 0.5
0.8 0.6 0.4 0.2 0 -0.2
1 1.5
0 0.5 1 1.5 Debt A
Prod= 0.6005610 0.8 0.6 0.4 0.2 0 -0.2
0.8 0.6 0.4 0.2 0 -0.2
1
1
1
1
1
0.5
0.5
0.5
0.5
0.5
0
0
0.5 1 1.5 Debt next A`
0
0
0.5 1 1.5 Debt next A`
Arellano, Mateos-Planas, Rios-Rull ()
0
0
0.5 1 1.5 Debt next A`
Partial Default
0
0
0.5 1 1.5 Debt next A`
0 0.5
0
1 1.5
0 0.5 1 1.5 Debt A
0
0.5 1 1.5 Debt next A`
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Persistent case: Frontier low shock Pr od=
0.4162774 D =0 B=0 D opt
consumption - cash in hand (today)
0.25
0.2
0.15
0.1
0.05
0
0.3
Arellano, Mateos-Planas, Rios-Rull ()
0.35
0.4
0.45 c as h in hand tomorrow
Partial Default
0.5
0.55
0.6
Macro · · · Borders
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Persistent case: Frontier high shock Prod=
0.5000000 D=0 B=0 D opt
consumption - c as h in hand (today)
0.25
0.2
0.15
0.1
0.05
0
0.3
Arellano, Mateos-Planas, Rios-Rull ()
0.35
0.4
0.45 cash in hand tomorrow
Partial Default
0.5
0.55
0.6
Macro · · · Borders
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