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 213 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 1 / 1
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 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 2 / 1
Existing Theory Quantitative models of sovereign default have countries either repaying or defaulting in full (Aguiar and Gopinath 26, Arellano 28) With countries restructuring all of its debt after default (Yue 21, Benjamin and Wright 29, D Erasmo 212) Default as state contingent assets does not sit well with the evidence that default is costly (Trade costs, Rose 22; financial crises, Reinhart and Rogoff 21; lawsuits and sanctions, Hatchondo & Martinez 213) The theory is Non-Markovian It requires coordination among existing and prospective lenders Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 3 / 1
This paper 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 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 4 / 1
DATA Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 5 / 1
Defaults in the Data Panel data for 99 developing countries from 197-21 Public debt data from World Development Indicators: debt in arrears and new loans Default events from Standard & Poor and Trebesch and Cruces (212) Debt in Arrears Partial Default= Debt Service + Debt in Arrears Debt in Arrears= Interest and principals due this period but in arrears Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 6 / 1
2 4 6 8 Defaulted Debt / Payments Due Defaults in the Data: 1 Sovereign Default is Partial Def ault in Brazil 197 198 199 2 21 year Default events are associated with large arrears but default is partial Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 7 / 1
2 4 6 8 Defaulted Debt / Payments Due Defaults in the Data: 1 Sovereign Default is Partial Def aults in Ecuador 197 198 199 2 21 year Defaults can be very small as in 28 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 8 / 1
2 4 6 8 Defaulted Debt / Payments Due 1 Sovereign Default is Partial Defaults in Indonesia 199 1995 2 25 21 year Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 9 / 1
2 4 6 8 1 Defaulted Debt / Payments Due Defaults in the Data: 1 Sovereign Default is Partial Def aults in Argentina 197 198 199 2 21 year Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 1 / 1
Defaults in the Data: 1 Sovereign Default is Partial 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 CHL CHL CHL CHL CHL CHL CHL CHL CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR CMR 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 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 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 J AM J AM J AM J AM J AM J AM J AM J AM J AM J AM J AM J AM J AM J AM J AM JOR JOR JOR JOR JOR KEN KEN KEN KEN KEN KEN 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 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 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 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 Defaulted Debt / Payments Due 197 198 199 2 21 year Partial Def aults Across all S&P default : countries default on average on 59% of what is due Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 11 / 1
2 2 4 6 8 Defaults in Data: 2 Borrowing during Sovereign Default Defaults in Indonesia 199 1995 2 25 21 year sdef/low New Loans / Payments Due Defaulted Debt / Payments Due During default countries continue to borrow Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 12 / 1
1 2 3 Fraction 1 2 3 4 Fraction Defaults in Data: 2 Borrowing during Sovereign Default Defaults Non Defaults 1 1 2 New Loans / GNI 1 1 2 New Loans / GNI 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 () Partial Default Macro Borders 13 / 1
2 4 6 8 1 Defaulted Debt / Payments Due Defaults in Data: 3 Larger Default in Downturns Partial Default and GDP Growth GDP Growth and Partial Defaults ETH MMR GNB ZWE MOZ SLE SLE RUS ZMB GIN PER MDG BGR MKD MRT VNM RUS ARG SLB SLE TGO PAN GRD IDN GTMSYC CMR IRN TGO CRI BFA GRD JOR ARG GAB PRY IDN GAB ECU MDA SEN CPV MDA MMR GMB IDN BRA BOL MARJAM NGA GTM MNG NER BOL CMR GHA DMA GHA KEN GHA NGA MWI JAM UKR ECU PAK MWI NGA VEN VEN PRY PHL KEN SLV SEN MAR VENTUR BLZ TGO URY CHLDZA SEN MEX PERJAM URYURY ROMROM PER TURMMR VENECUURY 2 1 1 2 GDP growth VEN ZWE Defaulted Debt / Payments Due Fitted values Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 14 / 1
THEORY Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 15 / 1
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 25) or renegotiated (with a wide range of haircuts- -1%) 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 (6)) 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 () Partial Default Macro Borders 16 / 1
Model Dynamic model of borrowing and default Small open economy with stochastic endowment z which is Markov with transition Γ z,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 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 17 / 1
Borrower 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 > 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 () Partial Default Macro Borders 18 / 1
Recursive Problem: Borrower State: (z, A, y) Nature, what it owes, what it has Choose consumption, new loans, and default st V (z, A, y) = max c,b,d u(c) + βe { V (z, A, y ) z } c = y (A D) + q(z, A, D) B A = δ A + B + R D y = z ψ(d), D A Resulting policy functions: B(z, A, y), and D(z, A, y) Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 19 / 1
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) = ( 1 ) D(z, A, y) A Today Tomorrow + 1 ( ) D(z, A, y) δ + ( R δ) E {H(z, A, y ) z} 1 + r A A and y are determined by borrower s functions Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 2 / 1
Bond Price and Equilibrium 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 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 21 / 1
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 = 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) Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 22 / 1
Budget Constraint C t+1 1 Borrow Risk Free C 5 1 t
Budget Constraint C t+1 1 Borrow 5 1 C t
Budget Constraint C t+1 1 Default Borrow 5 1 C t
Budget Constraint C t+1 1 Default Both Borrow 5 1 C t
Variety of Examples 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 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 23 / 1
Numerical settings Default cost y = z ψ(d) decreasing and concave with lower bound { } ψ(d) = (D D) ψ max 2 (γ D+D) ( D) 2 (γ D+), ψ Explore 3 experiments: High debt, low debt, and persistent shocks Common parameters: σ = 2, r = 17%, δ =, R = 8, γ = 5, ψ= 9 Description Parameter Example 1 Example 2 Example 2 High Debt Low Debt Persistent Shock process z iid with σ H iid with σ H Argentina Penalty slope D 5 7 6 Fixed cost ψ 99 99 995 Discount β 85 85 94 Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 24 / 1
Average statistics Data Partial default 59% Frequency of default 51% Debt /Output 49% Spread During defaults: Debt/GDP 87% Spreads Arrears/Output 62% New loans/output 17% Output relt to Mean -14% Large frequency of partial defaults During defaults debt is large, output is low, countries continue to borrow Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 25 / 1
Average statistics Data Examples High Debt Low Debt Persistent Partial default 59% 18% 1% 76% Frequency of default 51% 11% 3% 74% Debt /Output 49% 3% 1% 19% Spread 5% 17% 15% During defaults: Debt/GDP 87% 41% 55% 13% Spreads 15% 43% 18% Arrears/Output 62% 36% 55% 53% New loans/output 17% 73% 2% 86% Output relt to Mean -14% -15% -8% -4% Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 26 / 1
Tomorrow: cash in hand Examples confirm partial default is alternative credit Intertemporal frontier: Only B 55 5 45 4 35 3 5 1 15 2 25 3 Today: consumption cash in hand Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 27 / 1
Tomorrow: cash in hand Intertemporal frontier: Only B D= risk free 55 5 45 4 35 3 5 1 15 2 25 3 Today: consumption cash in hand Concave frontier via q() due to increasing default risk Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 28 / 1
Tomorrow: cash in hand Intertemporal frontier: Only D D= B= 55 5 45 4 35 3 5 1 15 2 25 3 Today: consumption cash in hand Shape of frontier depends on ψ(d) and R Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 29 / 1
Tomorrow: cash in hand Intertemporal frontier: B and D 55 D= B= D opt 5 45 4 35 3 5 1 15 2 25 3 Today: consumption cash in hand Smaller transfers with B, intermediate with B + D, large with D Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 3 / 1
Default D Loan B Policy Functions: Borrow and Default 6 5 4 Prod= 4162774 6 5 4 3 3 2 2 1 1 1 1 2 2 2 4 6 Debt A 2 2 2 4 6 Debt A Small debt: B >, and D = Large debt: B =, D = A Endogenously borrow less due to bad price Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 31 / 1
price Q Policy functions: Prices 1 Q D= Q D> Q D>> 8 6 4 2 1 2 3 4 5 6 Debt next A` Price decreases with larger debt and is worse when default D > Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 32 / 1
175 18 185 19 195 2 Defaulted Debt / Payments Due Implication 1: Partial Default Partial Defaults (High Debt) 3 35 4 45 5 period Default is always partial Narrow range Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 33 / 1
2 4 6 8 1 Defaulted Debt / Payments Due Implication 1: Partial Default Partial Defaults (Persistent) 3 35 4 45 5 period Wide range of partial default Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 34 / 1
5 1 15 2 Implication 2 Borrowing during Sovereign Default Defaults and Loans (High Debt) 45 41 415 period Defaulted Debt / Payments Due Loans / Payments Due New loans are used much more actively than defaults Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 35 / 1
5 1 15 2 25 Implication 2 Borrowing during Sovereign Default Defaults and Loans (Persistent) 45 41 415 period Defaulted Debt / Payments Due Loans / Payments Due New loans and defaults actively used Large substitution between two Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 36 / 1
5 1 15 2 Defaulted Debt / Payments Due Implication 3: Larger Default in Downturns Partial Defaults (High Debt) 4 45 5 55 6 Output Defaulted Debt / Payments Due Fitted values Defaults only with the lowest income Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 37 / 1
5 5 1 15 Defaulted Debt / Payments Due Implication 3: Larger Default in Downturns Partial Defaults (Persistent) 4 45 5 55 6 Output Defaulted Debt / Payments Due Fitted values Larger defaults with lower income Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 38 / 1
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 () Partial Default Macro Borders 39 / 1
price Q (D=) Loan B Default D Policy Functions: Persistent Case 8 6 4 2 2 Prod= 4162774 5 1 15 8 6 4 2 2 Prod= 4562222 5 1 15 8 6 4 2 2 Prod= 5 5 1 15 8 6 4 2 2 Prod= 5479786 5 1 15 8 6 4 2 2 Prod= 6561 5 1 15 8 6 4 2 2 5 1 15 Debt A 8 6 4 2 2 5 1 15 Debt A 8 6 4 2 2 5 1 15 Debt A 8 6 4 2 2 5 1 15 Debt A 8 6 4 2 2 5 1 15 Debt A 1 1 1 1 1 5 5 5 5 5 5 1 15 Debt next A` 5 1 15 Debt next A` 5 1 15 Debt next A` 5 1 15 Debt next A` 5 1 15 Debt next A` Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 4 / 1
consumption cash in hand (today) Persistent case: Frontier low shock Pr od= 4162774 D= B= D opt 25 2 15 1 5 3 35 4 45 5 55 6 cash in hand tomorrow Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 41 / 1
consumption cash in hand (today) Persistent case: Frontier high shock Prod= 5 D= B= D opt 25 2 15 1 5 3 35 4 45 5 55 6 cash in hand tomorrow Arellano, Mateos-Planas, Rios-Rull () Partial Default Macro Borders 42 / 1