Default and Interest Rate Shocks:
Renegotiation Matters
Victor Almeida
Carlos Esquivel
Timothy J. Kehoe
Juan Pablo Nicolini

February 2024

Default status and US real interest rate
25Countries in default

820
615

4
210

Percentage points

Number of countries in default(left axis)100
5US real interest rate0(right axis)-2-41959 1964 1969 1974 1979 1984 1989 1994 1999 2004
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This paper▶ Did the Volcker Shock cause the defaults?
▶ Direct mechanism: higher r =⇒ higher borrowing costs▶ Our paper: Version of the model with endogenous renegotiation▶ Renegotiation mechanism: higher r =⇒ higher expected haircut

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Renegotiation mechanism▶ High interest rates while bargaining makes lenders more impatient.
▶ Key: interest rate still high when bargaining.
▶ Race between▶ Persistency of interest rate shock▶ How fast a renegotiation opportunity arrives.

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Quantitative results▶ Direct is small▶ 6% of defaults only triggered if interest-rate is high▶ Renegotiation mechanism is larger▶ 22% of defaults only triggered if interest-rate are high

▶ Lower bound?

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Related literature▶ Sovereign default model▶ Aguiar and Gopinath (2006), Arellano (2008)▶ Long-term debt
▶ Hatchondo and Martinez (2009), Chatterjee and Eyigungor (2012), Arellano andRamanarayanan (2012)▶ Debt renegotiation▶ Yue (2010), Hatchondo, Martinez, and Sosa-Padilla (2014)▶ Varying risk free interest rates▶ Guimaraes (2011), Johri, Khan, and Sosa-Padilla (2016), Tourre (2017)
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Simple model, environment▶ Risk-free interest rate: r▶ We then do comparative statics▶ Output shock: y , with E [y ] = 1 and CDF F (y )▶ Lenders: risk neutral, discount future at rate r▶ Short-term debt only

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Simple model, environment▶ Government: preferences described by u (c) with standard properties▶ Inherits debt b, observes (y , r ), and decides to default or repay▶ If repay: pay b, issue b ′ at price q P▶ If default: output is λ, 0 < λ < 1

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Simple model, environment▶ A renegotiation opportunity arrives with probability θ▶ Nash bargaining solution▶ After renegotiation, output is 1 forever and government pays a constant coupon ρ tothe lenders

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Simple model, timeline

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Renegotiation Solution▶ PROPOSITION: A higher interest rate implies better negotiating terms for thecountry, so V R (r ), the value after renegotiation, is increasing on r
▶ Thus,hi
V D (r ) = u(λ) + β (1 − θ)V D (r ) + θV R (r )orV D (r ) =hi
1u(λ) + βθV R (r )[1 − β(1 − θ)]is increasing in r

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Value while good standing▶ The problem while the government repays can be written as:nh D ioP′ ′V P (b, y ; r ) = max
u(c)+βEmax
Vb,y;r, V (r )′bs.t.

c +b =y + i1 h1 − F y T b′1+r

where y T is defined by:
V P b ′ , y T ; r = V D (r )▶ Increases in r reduce the possibility set and increase both V D (r ) and y T

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Model without renegotiation▶ In the model with no renegotiation:nh D ioP′ ′b,y,VV P (b, y ) = max
u(c)+βEmaxV′bs.t.

 i1 h1 − F y T b′c +b =y +1+r

where y T is defined by:
V P b′ , y T = V D

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Full model, environment▶ Small open economy, stochastic income ytlog yt = ρ log yt−1 + ϵt , ϵt ∼ N 0, σϵ21−σ▶ Preferences for consumption each period u (ct ) = ct 1−σ−113 / 24

Full model, environment▶ Long-term bonds bt , price qt , mature at rate γ, law of motion:
bt+1 = (1 − γ) bt + it
▶ Quadratic default costs▶ In default, income is h (yt ) = yt − max 0, ϕ0 yt + ϕ1 yt2 , ϕ0 < 0 < ϕ1

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Full model, new features▶ Volcker Shock: rt ∈ r H , r L Markov chain, transition matrix πi,j , i, j ∈ {H, L}▶ An opportunity to renegotiate arrives with probability θ:▶ Face value of debt changes to btR▶ Sovereign gains access to financial markets▶ Output is still stochastic after renegotiation

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Calibration: We follow standard practice!

Parameterlow r

ValueDetails

rL

1.2%

1955–1980high rrH

6.2%

1981–1985

Pr(low to high r)

πL,H

1%

Duration of 100 years

Pr(high to low r)

πH,L

20%

Duration of 5 years

bond maturity

γ0.75

Sixteen-month bonds

Pr(renegotiation)

θ19.2%

5.2 years exclusion (Gelos et al. (2011))

risk aversion

σ2Standardρ

0.705

AR(1) estimation with

σϵ0.040

annual data 1933-1983

income process

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Internal Calibration

Parameter

Value

MomentData

Modellenders’ bargaining

α0.11

average haircut

0.24

0.24

default costϕ0-0.20

default probability

0.03

0.03

default cost

ϕ10.23average spreads

0.03

0.02

discount factor

β0.82

debt-to-GDP ratio

0.19

0.19

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Shocks that trigger default: Renegotiation vs. No renegotiation▶ 20,000 simulations▶ Look at first default after 500 periods▶ Count defaults with high r and such that the country would not default if small r .
▶ Without renegotiation: 6% of Volcker shocks trigger a default▶ With renegotiation: 22% of Volcker shocks trigger a default

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Renegotiation failure in 1980s▶ Renegotiation attempts every two years▶ Unsuccessful until Brady Plan in 1989/1990▶ Potential explanation: US regulators did not allow banks to write down the debt
"Had these institutions been required to mark their sometimes substantial holdings ofunderwater debt to market or to increase loan-loss reserves to levels close to theexpected losses on this debt, then ... Manufacturers Hanover, Bank of America, andperhaps Citicorp would have been insolvent."(Lewis William Seidman (2000), Full Faith and Credit)

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History of lost decade“The entire Ford administration, including me, told the large banks that the process ofrecycling petrodollars to the less developed countries was beneficial, and perhaps apatriotic duty.” (Seidman 2000),▶ 1979 reinterpretation of law▶ Loans to a single borrower could not exceed 10 percent of bank’s capital: different
government agencies in foreign countries are different borrowers▶ Regulation during 1980s▶ No reserves provisions for delinquent LDCs loans

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Renegotiation failure in 1980s▶ Dooley 1995 (Pg. 271):“...the events following the debt crisis cannot be adequately modeled as a gameinvolving only debtors (developing-country governments) and creditors (commercialbanks). By leaving out the interested and relatively wealthy third parties (industrial
country governments), this framework fails to capture the basic nature of the problems
generated by the crisis.”“Neither the banks nor the creditor governments, however, saw any advantage topresenting their position with excessive clarity. Banks were winning the game as it wasbeing played, and governments that had asserted they would not “bail out the banks”
were not anxious to concede that they were doing slowly what they would not doquickly.”
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Shocks that trigger default: Renegotiation vs. No renegotiation

Defaults Triggered by High r
no renegotiation renegotiation
θ = 1/5
6%22%
θ = 1/2
8%
47%

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US Banks and Volcker▶ The risk of bank failures affected policy decisions by the Fed▶ Volcker addressed the FOMC:‘There is a substantive need for a relaxation of pressures in the private markets in
the United States... Extraordinary things may have to be done. We haven’t had aparallel to this situation historically except to the extent that 1929 is a parallel.”(Transcript, FOMC Meeting, October 5th, 1982, pg 19.)23 / 24

Empirical evidenceSZhi,e,j,t= α + βrt + ΓZi,e + uj + ϵi,e,j,tWithout controls(1)real risk-free rate

(2)

With controls(3)7.030**(2.951)7.015**(3.039)0.0960(0.0813)6.510*(3.609)-0.232**(0.106)
0.939***(0.168)37.06***(5.196)36.53***(5.367)36.36***(6.284)

6.329*(3.800)-0.225**(0.107)
1.091***(0.377)
1.914(4.254)35.29***(6.965)

78
14
Yes

78
14
Yes

maturity of instrument (years)
coupon rate (fixed, percent)coupon rate (float, dummy)
constant
Observations
Number of episodes
Episode random effects

(4)

139
139
17
17
Yes
Yes
Standard errors in parentheses

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Calibration with fixed b R backParameter

Value

Moment

Data

Model

Restructuring terms

bR

0.07

average haircut

0.24

0.24

default cost

ϕ0-0.16

default probability

0.030.04

default cost

ϕ10.18average spreads

0.03

0.02

discount factor

β0.78

debt-to-GDP ratio

0.19

0.10

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Shocks that trigger default: Renegotiation vs. Fixed bR▶ Average paths around default:▶ 20,000 simulations▶ Look at periods before and after first default after 500 periods▶ With fixed b R : 7% of defaults triggered with high r▶ With renegotiation: 12% of defaults triggered with high r
Average paths around default episodesback

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Distribution of haircuts back

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Model, equilibrium
An equilibrium is value and policy functions, a bond price schedule q, an outside option
Q, and a renegotiation rule b R such that:
1. Given q, Q, and b R , the value and policy functions solve the sovereign’s problem
2. Given q, Q, and the value and policy functions, b R solves the bargaining problem
3. The bond price schedule is consistent with zero profits in expectation
E [{1 − d (b ′ , y ′ , r ′ )} {(γ + (1 − γ) q (b ′′ , y ′ , r ′ ))}] b ′q b′ , y , r b′ =1+rE [d (b ′ , y ′ , r ′ ) Q (y ′ , r ′ )]+1+rwhere b ′′ = b P (b ′ , y ′ , r ′ )24 / 24

Characterization of the renegotiation game
▶ From the F.O.C. of the bargaining problem, we getS SOV b R , y , rLEN
Rα ′=(1−α)
Sb,y,ru (y − (γ + (1 − γ) q (b ′ , y , r )) b R + q (b ′ , y , r ) b ′ )where b ′ = b P b R , y , r▶ If α = 0, lenders have no bargaining power S LEN b R , y , r = γ + (1 − γ) q b ′ , y , r b R − Q (y , r ) = 0
which implies b R = 0 (i.e., the standard model)

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Characterization of the renegotiation game
▶ For the case of one-period debt (γ = 1), i.i.d. income shocks, r fixed at r L or r H ,and steady state after default and renegotiation:▶ Proposition: For α ∈ [0, 1], a solution b R exists in every state and is unique▶ Proposition: For any α ∈ [0, 1], high risk-free interest rate implies:▶ borrowing is more expensive q b ′ , y , r H ≤ q b ′ , y , r L▶ lenders’ outside option is lower Q y , r H ≤ Q y , r L▶ sovereign gets higher debt relief b R y , r H ≤ b R y , r L

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High interest rates and default incentives
The sovereign defaults if
V P (b, y , r ) < V D (y , r )Standard mechanism:▶ V P b, y , r H < V P b, y , r L (higher borrowing costs)
Our mechanism (with persistent r ):
▶ V D y , r H > V D y , r L (lower expected renegotiated debt)

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High interest rates and borrowing costsq b′ , y , r =1+ r}|1 {zE  1 − d b′ , y ′ , r ′γ + (1 − γ) q b ′′ , y ′ , r ′Standard mechanism

+1+ r}|1 {zStandard mechanism Q (y ′ , r ′ ) ′ ′ ′Edb,y,r
′b| {z }Our mechanism

Standard mechanism:▶ Higher r reduces q because of higher discounting
Our mechanism (with persistent r ):▶ Higher r reduces expected b R −→ reduces value of holding defaulted debt Q
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