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Assessing the Appropriate Size of Relief inSovereign Debt Restructuring

The New School for Social Research, Department of Economics

Martin Guzman (Columbia-UBA-CIGI) Domenico Lombardi (CIGI)

April 18, 2017

Martin Guzman (Columbia-UBA), Domenico Lombardi (CIGI) Assessing the Appropriate Size of Relief in SDR

Motivation

What’s the “appropriate” size of relief in a sovereign debtrestructuring process?


Related literature


Related literature

Principles for sovereign debt restructuring (Guzman-Stiglitz 2015,

2016)

Must ensure proper functioning of sovereign lending markets

Ex-ante efficiency

Ex-post efficiency

The restructuring must restore the conditions for pursuing thesovereign’s development goals

The ultimate goal of a sovereign restructuring is therestoration of debt sustainability

But what does it mean?


Related literature

Edwards (2015): Inter-country comparison of market haircuts

180 restructuring episodes with private creditors from 1970 to2010 (data from Cruces-Trebesch 2013)

Actual haircuts vs. Predicted haircuts

If actual haircut >> (<<) predicted haircut =⇒ too much(too little) haircut

But the approach is flawed


Related literature

The majority of the restructurings in the sample were noteffective for achieving the necessary relief

Haircut is not a measure of debt relief but a proxy of investorlosses

Ht = 1− PV new bond(rt+ε)

PV old bond(rt+ε)


The “too little” syndrome

t 3 4 5 6 7

Frequency 0.497 0.525 0.553 0.575 0.6

Frequency: denotes fraction of restructuring with privatecreditors (bondholders and bank loans) followed by anotherrestructuring or default with the same group within t years


Relation to other literature

Empirical literature on fiscal sustainability (Bohn 1995, 2005, 2008,

Mendoza-Ostry 2008)

Commitment issues and strategic defaults (D’Erasmo-Mendoza

2013, 2014; D’Erasmo et al. 2015; Eaton-Gersovitz 1981; Aguiar-Gopinath

2006)

Excusable defaults (Grossman-Van Huyck 1988; Levy Yeyati-Panizza 2007;

Collard et al. 2015)

Strategic default is a matter of will. Excusable default is amatter of means

Effects of debt relief on economic performance (Reinhart-Trebesch

2016; LDA for West Germany)


The concept of debt sustainability



Consistency issues (Guzman-Heymann 2015)

Any borrowing can be considered ‘sustainable’ if thelending-borrower transaction is consistent, in the sense thatthe borrowing cost reflect the actual probability of default

When market participants refer to sustainability, theyintuitively refer to the risk of a country falling into a situationof debt distress (IMF 2013)



A general definition: public debt is economically sustainablewhen its repayment does not rely on a sequence of unboundedfuture borrowings

Caveat 1: Economic sustainability is a necessary but notsufficient condition for principles-based sustainability

Caveat 2: the analyst cannot know with certainty what will bethe evolution of the state variables that determine the debtrepayment capacity

Therefore, any statement on debt sustainability is by definitionprobabilistic


Empirical approach for testing debt sustainabilityAd hoc sustainability

Notation:

st : fiscal surplus to GDP ratio

1 + r = 1+R1+γ

R: constant nominal interest rate

γ: constant growth rate of output

d∗t : outstanding debt payments in period t


Empirical approach for testing debt sustainabilityAd hoc sustainability

(TC) holds iff (IBC) holds:

(IBC):

d∗t =∞∑j=0

(1 + r)−jEtst+j

(TC):limj→∞(1 + r)−jEtdt+j = 0

Definition 1

Fiscal policy satisfies ad hoc sustainability if (IBC) holds


Empirical approach for testing debt sustainabilityModel-based sustainability

Bohn (1995, 2005, 2008)

Arrow-Debreu securities

=⇒ Lenders use the same pricing kernel ut+j

(IBC’):

d∗t (zt) =∞∑j=0

Et [ut+jst+j ]

(TC’):limj→∞Et [ut+jdt+j ] = 0

Definition 2

Fiscal policy satisfies model-based sustainability if (IBC’) holds


Empirical approach for testing debt sustainabilityModel-based sustainability

=⇒(1 + r)−j = βjEt

uc(ct+j(zt+j))

uc(ct(zt))

(IBC’) can be rewritten as follows (Mendoza-Ostry 2008):

d∗t (zt) =∞∑j=0

{(1 + r)−jEtst+j + covt

[βj

uc(ct+j(zt+j))

uc(ct(zt)), st+j

]}Under complete markets, there cannot be excessive borrowing

The government trades insurance across possible states ofnature

Test: regress primary balance on outstanding debt → positive(significant) coefficient is sufficient condition for sustainability


Empirical approach for testing debt sustainability

What the test informs: assuming the past is a representativeguide for the future, would fiscal policy be sustainable?

But the course of policies could be reversed

Our question: Is there any feasible course of policies consistentwith the satisfaction of the transversality condition (plus otherconditions) with high probability?


A methodology for assessing the appropriate size ofrelief in sovereign debt restructuring


A criterion for assessing the appropriate size of debt reliefA preview of the methodology

1 Define “restructuring principles” and translate them intoeconomic terms

2 Describe the model that represents the economy underanalysis

3 For each possible economic scenario, find the trajectory offixed points {st}t that satisfies IBC

4 Classify each fixed point according to its economic and“political” feasibility

5 If there is a “sufficiently large” mass of feasible trajectories offixed points, then the state variable d∗t satisfies sustainabilitywith high probability

6 Otherwise, there is need for a debt write off large enough asto achieve a “sufficiently large” mass of trajectories of fixedpoints


A criterion for assessing the appropriate size of debt relief

Suppose (IBC) is the appropriate IBC

Suppose:

st = s(γt ,Rt ,Xst , ε

st )

γt = γ(st ,Xγt , ε

γt )

Rt = R(st ,XRt , ε

Rt )

=⇒

st = s[γ(st ,X

γt , ε

γt ),R(st ,X

Rt , ε

Rt ),X s

t , εst

]= T (st) ≡ s∗t



Definition 3

The set of economically feasible st is defined as

JE = {st : γ(st ,Xγt , ε

γt ) > −1 ∧ R(st ,X

Rt , ε

Rt ) ≥ 0

∧ R(st ,XRt , ε

Rt ) > γ(st ,X

γt , ε

γt )}

Definition 4

s∗t is an economically feasible fixed point if s∗t ∈ JE

Definition 5

s∗t is a politically feasible fixed point if s∗t ∈ JP

Definition 6

s∗t is a feasible fixed point if s∗t ∈ JF = JE ∩ JP



Definition 7

dt−1,t is x-sustainable if given the probability distributions for εit(i = s, γ,R), there are {s∗t }t ∈ JF s.t. IBC holds with probabilitymass not smaller than x

Definition 8

Suppose IBC holds with probability x ′ < x for d∗t . Then, theappropriate level of debt relief, ∆, must satisfy ∆ = d∗t − d∗

′t ,

where d∗′

t is the maximum value of d that satisfies x-sustainability


A methodology for assessing the appropriate size ofrelief in sovereign debt restructuring:

An illustration of its applicability


A criterion for assessing the appropriate size of debt reliefAn illustration: The case of constant fiscal surplus to GDP ratio

Commonly invoked object in practical episodes ofrestructuring: the debt-stabilizing constant fiscal surplus toGDP ratio

Suppose (IBC) is the relevant IBC

Suppose γt = γ, Rt,t+1 = R, both r.v. ex-ante

Let γn and Rn be any possible realization of γ and R=⇒

sn = d∗t

(Rn − γn

1 + γn

)



Suppose

γn = α0 − α1sn

Rn = β0 − β1sn

αi and βi have discrete uniform distributions:α0 ∼ unif (0.02, 0.07) with pmf = 1/6; α1 ∼ unif (0, 1) withpmf = 1/11; β0 ∼ unif (0.03, 0.07) with pmf = 0.2;β1 ∼ unif (0, 101) with pmf = 1/101



Under our distributional assumptions, N = 33, 330combination of states

Compute sn for each n, for d∗t ∈ [0.01, 1.8]

Multiple fixed points



1 Eliminate dynamically inefficient combinations

2 Count scenarios where there is at least one economicallyfeasible fixed point

3 Political feasibility: supposeJP = {st ∈ (−1, 1) : γ(st ,X

γt , ε

γt ) ≥ 0.01}

4 Count scenarios where there is at least one politically feasiblefixed point

5 Compute ratio of relevant scenarios with feasible fixed point



x-sustainability:

0

0.2

0.4

0.6

0.8

1

1.2

0.01

0.05

0.09

0.13

0.17

0.21

0.25

0.29

0.33

0.37

0.41

0.45

0.49

0.53

0.57

0.61

0.65

0.69

0.73

0.77

0.81

0.85

0.89

0.93

0.97

1.01

1.05

1.09

1.13

1.17

1.21

1.25

1.29

1.33

1.37

1.41

1.45

1.49

1.53

1.57

1.61

1.65

1.69

1.73

1.77

Fractio

n of states with

feasible fixed

points

Initial debt to GDP ratio



Appropriate relief, x = 0.95

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.01

0.05

0.09

0.13

0.17

0.21

0.25

0.29

0.33

0.37

0.41

0.45

0.49

0.53

0.57

0.61

0.65

0.69

0.73

0.77

0.81

0.85

0.89

0.93

0.97

1.01

1.05

1.09

1.13

1.17

1.21

1.25

1.29

1.33

1.37

1.41

1.45

1.49

1.53

1.57

1.61

1.65

1.69

1.73

1.77

Approp

riate deb

t relief for x=

0.95

Initial debt to GDP ratio


A criterion for assessing the appropriate size of debt reliefDiscussion

Framework can be used for identifying the “optimal” fiscalplan from the perspective of debt relief

Framework can be used for designing GDP linked exchangebonds


Conclusions

Need for clarifying what’s a sensible framework for assessinghow appropriate is a debt discount

Evidence that suggests presence of too little syndrome insovereign debt restructuring

Broad definition of concept of sustainability

Possible guide for practitioners

Framework could be the basis to codify the UN sustainabilityprinciple


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