Reputational Effects in Sovereign Default

Reputational Effects in Sovereign Default

Konstantin Egorov¹ Michal Fabinger²

1Pennsylvania State University ²University of Tokyo

OAP-PRI Economic Workshop

Outlines

Outline of the Talk

1 Motivation

2 Model

3 Results

Motivation

Motivation

Argentina

Sources: EMBI spread data, BIS debt data, OECD gdp data

Motivation

Motivation

Barrett (2016):

Data on 27 defaults between 1980 and 2013

Conditional on observables, spreads are higher for at least two years after default

Motivation

Motivation

“Graduation” from default

Countries with low default risk today went through long periods of high default risk in the past

Qian, Reinhart, and Rogoff (2010) report that “2 decades without a relapse (falling into crisis) is an important marker... However, crisis recidivism distributions have very fat tails, so that it takes at least 50 and perhaps 100 years to meaningfully speak of “graduation”.”

Motivation

Research Question

History dependence in sovereign default Past repayment lowers current spread

“Graduation” from default

Explain and quantify with reputation model Imperfect information about cost of default

Investors infer unobserved types based on history of observable actions Debt repayment as a signal of “good” type

Country needs to earn reputation to “graduate” from default

Motivation

Related Literature

Default with imperfect information

Kletzer (1984), Atkeson (1991), Cole, Dow, and English (1995), Alfaro, Kanczuk (2005), Sandleris (2008, 2010), Catao, Fostel, Kapur (2009), Cata, Fostel, Ranciere (2011), Dovis (2014), Phan (2014), Chatterjee et al. (2015) ...

D’Erasmo (2011)

Two types of government (high and low discount rate)

Government with lowβ mimic the behavior of government with highβ Beliefs are updated in Bayesian fashion based on observable history Explains frequency of default and debt-to-GDP ratio

Barrett (2016)

Continuum of types

Exogenous consumption decision

Explains high spread after default and low frequency of default

Model

Utility; GDP without default

Small open economy, single aggregate good U =

∞

X

t=0

β^tu(c_t), u(c_t) = 1 1−γc_t^1−γ Only one-period bonds traded internationally: asset levela Risk-neutral creditors (~ idiosyncratic country GDP risk ) If not in default, GDP processyt=e^zt with AR(1) zt:

zt =ρzzt−1+εt, ρz ∈(0,1), εt ∼N(0, σ²_z)

Model

Good credit, bad credit

The country may have a good credit (G), or following default bad credit (B)

A country with bad credit can regain good credit with exogenous probability λ

Country with bad credit is considered “in default”

Model

Default

The government optimally decides each period whether to default If in default, exclusion from international financial markets

In addition, if in default, GDP reduced to (1−x)y_t

wherex ∈(0,1) represents an explicit cost of default, loosely interpreted as the “level of government responsibility”

Before default,only the government knows x

unlike in the baseline models of Aguiar and Gopinath (JIE 2006) and Arellano (AER 2008)

Note: D’Erasmo (2011) considers information asymmetry regarding the government’s discount rate. But since the hidden state can take only two values, in equilibrium information asymmetry disappears very quickly, and effectively we get a complete information model

Model

Default cost determination

The cost of defaultx is known only to the government It does not change over time unless the country defaults

Following a default, new political elite comes to power and draws a new value ofx from a known distribution with pdf ϕ(x) and support [xmin,xmax]

Model

Pooling equilibrium

Pooling equilibrium

Creditors update their beliefs aboutx in a Bayesian fashion each period

Equilibrium selection criterion: choose the equilibrium that maximizes welfare of the pool of countries (with good credit)

This eliminates unnatural equilibria

In the limit of no information asymmetry, one recovers the usual Euler equation

Model

Reputation mechanism

If the country goes through a severe recession without defaulting, creditors infer that the government’s cost of default must be high

the government is “responsible”

The lowest possible reputation level (denoted xb) consistent with past behavior goes up

The country can borrow at lower interest rates

Investors know the country better, so they know how much to lend without triggering a default

Eventually, the country may “graduate from default”

Model

Solution to the model

Four state variables:

a... asset level

z ... (potential) log GDP; or equivalently y ... (potential) GDP

x ... cost of default

x_b ... minimum cost of default consistent with past behavior

Model

Solution to the model

One value function for good credit, one value function for bad credit Set of Bellman equations

Solved numerically by:

discretizing dimensionsa andz, and

using Chebyshev polynomials for dimensionsx andx_b

Model

Solution to the model: value functions

Value function for a country having the choice to default or not:

V(a,y,x,xb) = maxⁿV^G(a,y,x,xb),V^B(y,x)^o Value function for a country with good credit:

V^G(a,y,x,x_b) = max

c,a⁰

u(c) +βE_y⁰_|yV a⁰,y⁰,x,x_b⁰ s.t. c =y+a−q a⁰,a,y,x_ba⁰

q(a⁰,a,y,x_b) is the bond price

x_b⁰ are updated beliefs of investors: x_b⁰ =x_b⁰(a,y,x_b)

Value function for a country with bad credit:

V^B(y,x) =u((1−x)y) +β(1−λ)E_y⁰_|yV^B(y⁰,x) +βλE_y⁰_,x⁰|yV 0,y⁰,x⁰,xmin

Model

Solution to the model: investors’ beliefs

Define ¯x = ¯x(a,y,xb) as

V^G(a,y,¯x,xb) =V^B(y,x)¯ Updated investors’ beliefs:

x_b⁰ (a,y,x_b) = max{x_b,¯x(a,y,x_b)}

Model

Solution to the model: pooling equilibrium

Welfare maximizing pooling equilibrium a⁰(a,y,xb) = arg max

a⁰

Z xmax

x_b⁰(a,y,xb)

u y+a−q a⁰,a,y,xb a⁰

+βE_y⁰_|yV a⁰,y⁰,x,x_b⁰ (a,y,x_b)ⁱϕ(x)dx Incentive-compatibility constraint

V^G(a,y,x,xb)≥max

a⁰

(

u y+a−1−E_y⁰_|yD˜(a⁰,y⁰,x_min)

1 +r a⁰

!

+βE_y⁰_|yV a⁰,y⁰,x,x =x_min^o Bond price

q a⁰,a,y,x_b= Rxmax

x_b⁰(a,y,xb)

h1−E_y⁰_|yD(a⁰,y⁰,x,x_b⁰ (a,y,x_b))ⁱϕ(x)dx (1 +r)^R_x^x0^max

b(a,y,xb)ϕ(x)dx

Results

Parameter values

Risk aversion γ 2

Probability of redemption λ 10%

Persistence of income ρ_z 0.9

Standard deviation of income σ_z 3.4%

Discount factor β 0.8

Risk-free interest rate r 1%

Support of distribution of cost of default [x_min,x_max] [0.5%,8%]

Results

Simulation

0 50 100 150 200 250 300 350 400

0 50 100 150

Debt, % of annual GDP

0 50 100 150 200 250 300 350 400

0.6 0.81 1.2 1.4

GDP

0 50 100 150 200 250 300 350 400

0 5

Interest Rate Spread, %

0 50 100 150 200 250 300 350 400

0 20 40

Reputation x_b, %

Results

Defaults and business cycle moments

Moment Data Model with

imperfect information

Aguiar-Gopinath (JIE 2006) -

Model I

σ(y) 4.08 5.82 4.32

σ(c) 4.85 7.37 4.37

σ(TB/y) 1.36 1.50 0.17

σ(R) 3.17 0.88 0.04

corr(c,y) 0.96 0.86 0.99

corr(TB/y,y) -0.89 -0.08 -0.33

corr(R,y) -0.59 0.02 0.51

corr(R,TB/y) 0.68 0.29 -0.21

Defaults(per 10000 quarters) 75 74 2

Debt/GDP (%) 75 27

MaxR (bp) 396 23

Results

Conclusions

In the real world, creditors have to form expectations about the nature of the debtor country government

We build a model of sovereign default that incorporates this feature Past behavior is reflected in today’s interest rates

Graduation from default

Realistic interest rate schedule, realistic default rate under natural assumptions about the GDP process