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Sovereign Default: The Role of Expectations

Joao Ayres, Gaston Navarro, Juan Pablo Nicolini, Pedro Teles

Discussion by Wouter Den Haan

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Punchline

•  This paper makes some (to me) surprising points in a simple model

•  What are those points?

•  Multiplicity in sovereign debt model depends crucially on •  Small changes in timing

•  Borrower choosing “amount borrowed” or “amount to be paid back” (inlcuding interest payments)

•  Whether the distribution of GDP has multiple peaks

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The big question

What is behind (the fear of) sovereign default?

1.  Fundamentals?

2.  Self-fulfilling beliefs

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0

5

10

15

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25

30

Jan-

1990

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ct-1

990

Jul-1

991

Apr

-199

2 Ja

n-19

93

Oct

-199

3 Ju

l-199

4 A

pr-1

995

Jan-

1996

O

ct-1

996

Jul-1

997

Apr

-199

8 Ja

n-19

99

Oct

-199

9 Ju

l-200

0 A

pr-2

001

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2002

O

ct-2

002

Jul-2

003

Apr

-200

4 Ja

n-20

05

Oct

-200

5 Ju

l-200

6 A

pr-2

007

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2008

O

ct-2

008

Jul-2

009

Apr

-201

0 Ja

n-20

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Oct

-201

1 Ju

l-201

2 A

pr-2

013

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2014

O

ct-2

014

Jul-2

015

10 yr gov't bond yields (%)

Greece

Ireland

Italy

Spain

Portugal

Germany

Fundamental or Sustainable Problem?

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Mario Draghi (2012)

“The assessment of the Governing Council is that we are in … a ‘bad equilibrium’, namely

an equilibrium where you may have self-fulfilling expectations that feed upon themselves and generate very adverse

scenarios. So, there is a case for intervening, in a sense, to ‘break’ these expectations …”

Do Self-fulfilling Equilibria exist?

ECB Press conference, transcript from the Q&A, September 6 2012

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Self-Fulfilling Debt Crisis

Source: De Grauwe and Ji (2013)

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Gross Government Debt (%GDP)

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10-year sovereign debt yield

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The model

Standard ingredients:

1.  Relation between supply for funds and interest rate

•  Risk neutral lender

2.  Relation between demand for funds and interest rate

•  Default has output cost

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What is the twist here?

1.  Careful about what the borrower chooses

2.  Careful about timing

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What does borrower choose?

1.  Borrower chooses amount borrowed: b

⇒ supply curve is R* = R (1 – F(1+bR))

2.  Borrower chooses amount due at maturiy: a = bR

⇒ supply curve is R* = R (1 – F(1+a))

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Model implies standard figures

0.75 0.80 0.85 0.901.0

1.1

1.2

1.3

1.4

1.5

1.6

0.9 1.0 1.1 1.21.0

1.1

1.2

1.3

1.4

1.5

1.6

Figure 6: Choosing value of debt at maturity a or amount borrowed b

ically increasing function. Since the borrower can choose a, the borrower is always

going to choose in the low R/low a part of the schedule. The borrower is also going

to take into account the monopoly power in choosing the level of a. These are the

assumptions in Aguiar and Gopinath (2006) and Arellano (2008). The equilibrium is

unique.

Suppose now that the borrower faces the full supply curve as depicted in Figure

2 with an increasing low rate schedule and a decreasing high rate schedule. Then

by picking b, the borrower is not able to select the equilibrium outcome.14 There

are multiple possible interest rates that make creditors equally happy. The way this

can be formalized, as in Calvo (1988),15 is with multiple interest rate functions R (b),

which can be the low rate increasing schedule or the high rate decreasing one. Any

other combination of those two schedules is also possible. The borrower is o§ered one

schedule of the interest rate as a function of the debt level b and chooses debt optimally

given the schedule.

In summary, the assumption on the timing of moves is a key assumption to have

14Trivially, it is still possible to obtain uniqueness in the case in which the borrower faces thesupply curve in R and b defined by (1). If the borrower picks R, then it is able to select the low rateequilibrium directly. That is essentially what happens when the borrower faces the schedule R (a)and picks a.15In Calvo (1988), debt is exogenous.

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Why does borrower choice matter?

1.  Borrower chooses amount borrowed, b,

⇒ choice is not directly related to default probability

2.  Borrower chooses amount due at maturity, bR,

⇒ choice is related to default probability through R

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Why does timing matter?

•  Creditors move first ⇒ Borrower takes R as given

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Why does timing matter?

0.75 0.80 0.85 0.901.0

1.1

1.2

1.3

1.4

1.5

1.6

0.9 1.0 1.1 1.21.0

1.1

1.2

1.3

1.4

1.5

1.6

Figure 6: Choosing value of debt at maturity a or amount borrowed b

ically increasing function. Since the borrower can choose a, the borrower is always

going to choose in the low R/low a part of the schedule. The borrower is also going

to take into account the monopoly power in choosing the level of a. These are the

assumptions in Aguiar and Gopinath (2006) and Arellano (2008). The equilibrium is

unique.

Suppose now that the borrower faces the full supply curve as depicted in Figure

2 with an increasing low rate schedule and a decreasing high rate schedule. Then

by picking b, the borrower is not able to select the equilibrium outcome.14 There

are multiple possible interest rates that make creditors equally happy. The way this

can be formalized, as in Calvo (1988),15 is with multiple interest rate functions R (b),

which can be the low rate increasing schedule or the high rate decreasing one. Any

other combination of those two schedules is also possible. The borrower is o§ered one

schedule of the interest rate as a function of the debt level b and chooses debt optimally

given the schedule.

In summary, the assumption on the timing of moves is a key assumption to have

14Trivially, it is still possible to obtain uniqueness in the case in which the borrower faces thesupply curve in R and b defined by (1). If the borrower picks R, then it is able to select the low rateequilibrium directly. That is essentially what happens when the borrower faces the schedule R (a)and picks a.15In Calvo (1988), debt is exogenous.

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What do borrowing governments actually do?

19-7-2016 press release for 10-year Spanish bond auction •  Following the announcement strong Indications of Interest (“IOI’s”)

were received which surpassed EUR 15 billion (including EUR 3.1 billion of Joint Lead Manager interest) on Tuesday morning when the Initial Pricing Thoughts (“IPTs”) of mid swaps +102 area were released at 09:30 CET.

•  Given the strength of the IPT process with interest in excess of EUR 25 billion (including EUR 3.65 billion of JLM interest), the orderbook officially opened within the hour, at the guidance of mid swaps +99 area.

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Another reason for multiplicity

•  Distribution of output has multiple humps

•  For example, related to “recession” and “expansion” regime

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Another reason for multiplicity

1 1.5 2 2.5 31

1.5

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2.5

Figure 5: Supply and demand for the bimodal distribution

If the debt level is relatively large, multiple equilibria are more likely to arise. This

is the case with the bimodal distribution analyzed earlier, but it is particularly so

when the value of the debt is close to the maximum and any single mode distribution

is perturbed by adding a nonmonotonic transformation. The details are in Appendix

2.

2.2 Policy

To illustrate the e§ects of policy, the case of the bimodal distribution depicted in Figure

5 is considered. The extensions to other cases are straightforward.

Consider there is a new agent, a foreign creditor that can act as a large lender, with

deep pockets.11 This large lender can o§er to lend to the country, at a policy rate RP ,

any amount lower than or equal to a maximum level bP . It follows that there cannot

be an equilibrium with an interest rate larger than RP .

Now, let us imagine that bP and RP are the debt level and interest rate correspond-

to have multiplicity with low levels of debt arising simply from the discontinuity of the demand. Thisnever happened in our simulations, however.

11If the borrower was a small agent rather than a sovereign, any creditor could possibly play thisrole.

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Other points/questions

1.  What are qualitative assumptions on F(Y) needed?

•  Especially for supply curve with multiple upward-slopping parts

2.  Quantitatively convincing?

3.  How robust are the results?

•  When default doesn’t mean lender gets nothing

•  Senior debt

4.  Are implications the same if monetary policy is considered (unexpected deflation of debt)