Why Prices Don’t Respond Sooner to a Prospective
Sovereign Debt Crisis
R. Anton Braun1
1

Tomoyuki Nakajima2

Federal Reserve Bank of Atlanta
2

Kyoto University

May 28, 2012
Canon Institute for Global Studies
Preliminary. Comments Welcome. These are our own personal views.

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Introduction

Fiscal problems
Govt. Debt/GDP

Govt. Debt/GDP

Govt. Debt/GDP

70
60

100
50

50

Percentage

150

Percentage

Percentage

200

40
30
20
10

0

0

Korea

USA

10

10

8

8

Percentage

6
4

Short-Term Interest Rate

Percentage

10.0005.000

Germany

Canada

14
12

30

10

25

8
6
4

0.000

Germany

Canada

10

6

8

20

5

4
2

4
3
2

0

1

-2

0

Korea

Percentage

25

6GreeceCore Inflation

Core Inflation
7

Percentage

Percentage

10

12

Japan

Braun and Nakajima

15

0

USA

Core Inflation

20

5

0

Korea

GreeceShort-Term Interest Rate
35

2

Japan

4

Short-Term Interest Rate

20.00015.000

6

0

USA

Korea

Greece20Percentage

Percentage

GermanyLong-term Bond Yields

12

2

Japan

Percentage

CanadaLong-term Bond Yields

Long-term Bond Yields
18
16
14
12
10
8
6
4
2
0

Percentage

Japan

160
140
120
100
80
60
40
20
0

15
10
5
0

USA

CanadaWhy Prices Don’t Respond Sooner to a Prospective Sovereign Debt Crisis

Germany

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Introduction

Resolutions
It seems fairly obvious that the current level of deficit spending in Japan and
U.S. cannot be sustained for ever.
Possible resolutions:1
2

Increase taxes (or reduce spending);
fail to increase taxes (sovereign debt crisis):
inflation?
payment suspension?

Is the second scenario a realistic possibility?
If so, how can we explain the current state of Japan or the U.S. withstable or declining prices;high government-bond prices;high yen rate, etc?

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Introduction

Our message

The fact that inflation and bond yields are low today does not mean that therisk of a debt crisis is low.
The current situations in Japan and the U.S. are perfectly consistent with theview that there is a non-negligible probability of a sovereign debt crisis.

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Introduction

How we make our point
Consider two types of default (separately):
1Implicit default via inflation (fiscal theory of the price level);

2

Explicit default on long-term government debt.

Compare two specifications:1

Frictionless asset markets (complete markets);2

Financial frictions.

Agents have heterogenous beliefs about the probability of default.
Financial frictions are modeled as in Geanakoplos (2003,2010):
no contingent claims are traded;agents can borrow to purchase govt debt;
govt debt cannot be short sold.

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Introduction

Properties of the model
Complete markets:
Prices respond instantly to news about the possibility of a debt crisis.
Inflation smoothing.

Financial frictions:
No response of price to news about the possibility of a debt crisis.
Price responses are concentrated in states immediately prior to default state.

Key in our model with financial frictions:
Some individuals want to use leverage to purchase govt debt;
Others do not want to purchase govt debt by themselves, but are willing tolend to those who buy it.

In reality, a large proportion of sovereign debt is held by leveraged financial
institutions.
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Introduction

Related literature

Our model builds on the following two strands of literature:
1

Fiscal theory of the price level (FTPL):
Leeper (1991); Sims (1994); Woodford (1994); Cochrane (2001); Bassetto(2002); etc.

2

Collateral, beliefs, and leverage:
Geanakoplos (1997, 2003, 2010); Fostel and Geanakoplos (2008); Geanakoplos
and Zame (2009), Simsek (2010),etc.

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Introduction

Fiscal theory of the price level“Naive” assumptions made in the standard FTPL:
The government commits to a fixed sequence of real tax revenues, {Tt }.
Such a commitment is made both in and out of the equilibrium path.
The price level “adjusts” so that the govt budget constraint holds.

Criticism against the FTPL by Bassetto (2002):
It is impossible to consider “out of the equilibrium path” in the Walrasianframework assumed in the FTPL.
Bassetto (2002) considers a market game and finds that a version of the
FTPL holds.

For simplicity, here we follow the naive version of the FTPL, but it isstraightforward to build a market game similar to Bassetto’s for our model.

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Introduction

Theory of leverage by Geanakoplos
Conditions of loans:interest rate;
collateral;collateral rate.

How can the interest rate and the collateral rate be determined in markets
simultaneously?
That is, how can one demand-equals-supply equation for a loan determine twovariables — the interest rate and the collateral rate?

Geanakoplos has developed a competitive-equilibrium framework determining
the interest rate and the collateral rate for loans simultaneously.
The key is to consider loans with different collateral rates as different assets.

In our model only one type of loans are traded in equilibrium, whose
collateral rate is given by the ‘no-default constraint.’
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Introduction

Some evidence
Rheinhart and Rogoff (2010) find that the probability of sovereign debt crises
goes up following:banking crises;
sharp increases in government and external debt.

Nieto Parra (2008):
Investment banks demand higher underwriting fees 1 to 3 years before debt
crisis.
bond spreads do not respond to the news and remain stable up to the crisis.

Lau (2003): Argentine CDS only increase about 2 months prior to IMF
package and 15 months prior to default.
Greek sovereign debt spread first increased to 2 percent in December 2008
about 16 months before their request for funds from EU/IMF.
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Introduction

Plan of the talk1

Introduction

2

Implicit default: 2 period model3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks

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Implicit default: 2 period model

1

Introduction

2

Implicit default: 2 period model3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks

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Implicit default: 2 period model

Model
Two periods: t = 0, 1.
Two states at date 1: s1 ∈ {U, D}.

Notation: s 0 ∈ S 0 = {0} and s 1 = s1 ∈ S 1 = {U, D}.

More generally, st denotes the shock realized in period t and s t denotes thehistory of shocks.
States are distinguished by the amount of taxes:(
TH ,if s1 = U,
T1 =
TL ,
if s1 = D (debt crisis).
where TL  TH .

A continuum of agents h ∈ [0, 1].
At date 0, agent h believes that s1 = U with probability h.
Agents are identical except for their beliefs.

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Implicit default: 2 period model

Event tree

T1 = THUh
T0 = 0D
1−h
T1 = TL

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Implicit default: 2 period model

Individuals
Preferences:c0 +X

γ h (s 1 )c(s 1 )s 1 ∈S 1

where γ h (s 1 ) = subjective probabilities given by(h,for s1 = U,
h 1
γ (s ) =1 − h,
for s1 = D.
Endowments:
y0 at date 0, and y1 at date 1 (for all s 1 ∈ S 1 ).

Storage technology:
Gross real rate of return = R (riskfree).
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Implicit default: 2 period model

Government
Flow budget constraint:B̄ = P0 T0 + q0 B0 ,B0 = P(s 1 )T (s 1 ),for s 1 ∈ S 1 .

where B̄ = initial amount of govt debt (nominal); B0 = amount of govt
bonds issued at date 0; P(s t ) = price level at date-event s t ; q0 = nominal
price of govt bonds at date 0.
Monetary policy: the nominal interest rate, q10 .
Fiscal policy: real amount of taxes collected in each period:
T0 = 0,(T (s 1 ) =Braun and NakajimaTH ,if s1 = U,TL ,if s1 = D.

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Implicit default: 2 period model

Three market structures
1“complete markets”
asset markets without frictions.
complete set of contingent claims with a “natural debt limit.”2“no borrowing”
two assets:
govt bonds, and storage.

frictions:no borrowing;
no short sales of govt bonds.
3“leverage”
three assets:
govt bonds, storage, and loans.

frictions:
agents can borrow to purchase govt debt;
borrowing is limited by the “no-default constraint.”
no short sales of govt debt.
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Implicit default: 2 period model

1

Introduction

2

Implicit default: 2 period model

Complete markets

Complete markets
Financial frictions: no borrowing
Financial frictions: leverage
Numerical example
3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks
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Implicit default: 2 period model

Complete markets

Complete Markets
frictionless asset markets:complete set of contingent claims (Arrow securities) are traded under the
mildest possible debt limit (natural debt limit).

Arrow security (s 1 |s 0 ):traded at s 0 and pays off one unit of account in period 1 iff s 1 occurs.
b h (s 1 |s 0 ) = quantity of Arrow security (s 1 |s 0 ) purchased by individual h.
q(s 1 |s 0 ) = price of Arrow security (s 1 |s 0 ).

Govt bonds pay one unit of account at every state in period 1.
No arbitrage condition:
q0 =X

q(s 1 |s 0 ).

s 1 ∈S 1

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Implicit default: 2 period model

Complete markets

Individual hUtility maximization problem of agent h:
max c0 +X

γ h (s 1 )c(s 1 )s 1 ∈S 1

subject toc 0 + k0 +X
s 1 ∈S 1

q(s 1 |s 0 )c(s 1 ) ≤ y1 − T (s 1 ) +b(s 1 |s 0 )
b0
B̄
+ q0
≤
+ y0 ,
P0
P0
P0b(s 1 |s 0 )b0++ Rk0 ,1
P(s )P(s 1 )

s 1 ∈ S 1,

c0 , k0 , b0 , c(s 1 ) ≥ 0.

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Implicit default: 2 period model

Complete markets

Equilibrium with complete markets
c0h = 0 for all h ∈ [0, 1].

“Marginal agent”: h0 = 12 .
Pessimistic agents, h ≤ h0 ,(c h (s 1 ) =Optimistic agents, h > h0 ,(c h (s 1 ) =0,for s 1 = U,

1
(Ry0 + y1 ),h0

for s 1 = D.

1
(Ry0 + y1 ),1−h0

for s 1 = U,0,

for s 1 = D.

Equilibrium prices:
o
1n
B̄
=
h0 TH + (1 − h0 )TL ,P0R
B0= T (s 1 ),P(s 1 )
Braun and Nakajima

for s 1 ∈ S 1 .

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Implicit default: 2 period model

Complete markets

Equilibrium Trading Strategies

Optimistic and pessimistic agents hold ‘symmetric’ portfolios:
Optimistic agents purchase Arrow security U, and sell Arrow security D.
Pessimistic agents do the opposite.

The equilibrium price level will equally reflect the views of optimists andpessimists.

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Implicit default: 2 period model

1

Introduction

2

Implicit default: 2 period model

Financial frictions: no borrowing

Complete markets
Financial frictions: no borrowing
Financial frictions: leverage
Numerical example
3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks
Braun and Nakajima

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Implicit default: 2 period model

Financial frictions: no borrowing

Market structure
Two assets:
govt bonds and storage.

Frictions:no short sales of govt bonds;
no borrowing.

Budget set for each individual:b0
B̄≤+ y0 ,
P0
P0
b0
c(s 1 ) ≤ Rk0 +− T (s 1 ) + y1 ,P(s 1 )
c0 + k0 + q0

for s 1 ∈ S 1 ,c0 , k0 , b0 , c(s 1 ) ≥ 0.
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Implicit default: 2 period model

Financial frictions: no borrowing

Utility maximization
h0 = marginal buyer of govt bonds.
Pessimistic agents only invest in storage: For h ≤ h0 ,c0h = b0h = 0,
k0h =

B̄
+ y0 ,P0c h (s 1 ) = Rk0h + y1 − T (s 1 )Optimistic agents only invest in govt bonds: For h > h0 ,c0h = k0h = 0,


P0 B̄
h
b0 =
+ y0 ,
q0 P0
1
b h + y1 − T (s 1 )c h (s 1 ) =P(s 1 ) 0
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Implicit default: 2 period model

Financial frictions: no borrowing

Equilibrium without borrowing
h0 = marginal buyer of govt bonds:


q0
1
1
1
=
h0 +
(1 − h0 ) ,P0R P(U)
P(D)Market clearing condition for govt bonds:


q0
B̄
B0 = (1 − h0 )+ y0 ,P0
P0
Equilibrium prices at date 1:
P(s 1 ) =B0,
T (s 1 )for s 1 ∈ S 1 ,Evolution of the govt debt:
B̄ = q0 B0 .
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Implicit default: 2 period model

1

Introduction

2

Implicit default: 2 period model

Financial frictions: leverage

Complete markets
Financial frictions: no borrowing
Financial frictions: leverage
Numerical example
3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks
Braun and Nakajima

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Implicit default: 2 period model

Financial frictions: leverage

Market structure
Three kinds of assets:
govt bonds, storage and loans.

Frictions:
govt bonds cannot be short sold;agents can borrow to purchase govt bonds using those bonds as collateral;loans are limited by collateral requirements.

Use Geanakoplos’s (2003, 2010) theory of collateral contracts.
Loans with different collateral rates are traded.

In this model, only one type of loans are traded in equilibrium.
It is the loan contract with the lowest collateral rate sufficient to avoid default.
Thus, we need to consider only one type of loans, which is characterized by
the risk-free interest rate R, and the ‘no-default constraint.’
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Implicit default: 2 period model

Financial frictions: leverage

Budget constraint with loans
The budget set for each agent can be defined byb0
B̄≤+ y0 + φ0 ,P0
P0
b0
c(s 1 ) ≤ y1 − T (s 1 ) ++ Rk0 − Rφ0 ,P(s 1 )b0
Rφ0 ≤, (no-default condition),P(D)c0 + k0 + q0

for s 1 ∈ S 1 ,c0 , k0 , b0 , c(s 1 ) ≥ 0.
Loan contract with one unit of govt bond b0 as collateral:1= (real) amount of borrowing;
RP(D)q0= (real) value of the bond (collateral) at date 0;
P0

collateral rate = value of the bond/ amount of borrowing = q0 P(D)R.
P0
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Implicit default: 2 period model

Financial frictions: leverage

Utility maximization
Equilibrium leverage:
Optimistic agents borrow as much as they can and use the proceeds topurchase government debt.
Pessimistic agents lend to optimistic agents.

Asymmetry between optimists and pessimists:
Optimistic agents can bet on their beliefs.
Indeed, borrowing to purchase govt debt is effectively equivalent to purchasing
Arrow security U.

Pessimistic agent cannot bet on their beliefs.
Short selling of government debt is ruled out so that there is no trading strategy
mimicking Arrow security D.

The price level will reflect the optimists’ view more than the pessimists’.
This generates deflationary pressure.
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Implicit default: 2 period model

Financial frictions: leverage

Equilibrium with leverage

Utility maximization:c0h = 0, h ∈ [0, 1],
 
−1 

 q0 − 1
B̄
+
y
,
0
h
P0
RP(D)
P0
b0 =
 0,
(
b0h
,
h > h0 ,− R1 P(D)hhk0 − φ0 =B̄h ≤ h0P0 + y 0 ,h ≤ h0c h (s 1 ) = y1 − T (s 1 ) +h ∈ [0, 1]

Braun and Nakajimab0h+ R(k0h − φh0 ),P(s 1 )

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Implicit default: 2 period model

Financial frictions: leverage

Equilibrium with leverageh0 = marginal buyer of govt bonds:
1
1
P(U) − P(D)h0 q0
1
P0 − RP(D)= R,

Market clearing condition for govt bonds:




q0
1
B̄
−
B0 = (1 − h0 )+ y0 ,P0
RP(D)P0
Equilibrium prices at date 1:
P(s 1 ) =B0,
T (s 1 )for s 1 ∈ S 1 ,Evolution of the govt debt:
B̄ = q0 B0 .
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Implicit default: 2 period model

1

Introduction

2

Implicit default: 2 period model

Numerical example

Complete markets
Financial frictions: no borrowing
Financial frictions: leverage
Numerical example
3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks
Braun and Nakajima

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Implicit default: 2 period model

Numerical example

Two Period model: numerical example

Inflation rates (%) at t = 0 and s 1 = D, and marginal buyers
π−1

π0

π(D)

h0

(1) complete markets

-1.96

30.72

47.06

0.5

(2) no borrowing

-1.96

25.57

53.09

0.56

(3) leverage

-1.96

9.46

75.62

0.79

At t = −1, everyone believes Pr(s1 = U) = 1.
At t = 0, news arrives so that agents start to hold different views.
Parameters: B̄ = 1, y0 = 1, q0 = 1, R = 1.02, TH = 1, TL = 0.5.
Because q0 = 1 and R > 1, there is deflation in period -1 (π−1 < 0).
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Implicit default: T -period model

1

Introduction

2

Implicit default: 2 period model3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks

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Implicit default: T -period model

Environment
Shocks: st ∈ {U, D}, t = 1, . . . , T .
Endowments:ty (s ) = y0 ,

for t = 0,T

for all s T .

0,


 y ,

for all s t with t = 1, . . . , T − 1,




 0,

for all s t with t = 0, . . . , T − 1,

Taxes:T (s t ) =

TL ,


 T ,
H

Braun and Nakajima

for s T = D T ,for all s T 6= D T .

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Implicit default: T -period model

Example: Event tree in three period model

T1 = 0

U
h

U
h

D
1−h

D
1−h

U
h

T2 = THT2 = THT0 = 0T1 = 0Braun and NakajimaD1−hT2 = THT2 = TL

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Implicit default: T -period model

Numerical example: Three period model

Inflation rates and marginal buyers
π−1

π0

π(D)

π(D 2 )h0h(D)(1) complete markets

-1.96

17.65

22.55

30.72

0.50

0.33

(2) with leverage

-1.96

-1.09

10.86

71.89

0.94

0.75

At t = −1, everyone believes Pr(st = U) = 1.
At t = 0, news arrives so that agents start to hold different views.
B̄ = 1, y0 = 1, q0 = q(D) = q(U) = 1, R = 1.02, TH = 1, TL = 0.5.

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Implicit default: T -period model

Inflation rates at s t = D t when T = 5
inflation rate

8070

leveraged
complete

60
50
40
30
20
10
0
-10
-1
Braun and Nakajima

0

1

2

3

4

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Implicit default: T -period model

Properties of the equilibrium

Complete Markets
Inflation rate jumps on the news in period 0
Smoothing. Inflation is smooth along the path to a debt crisis.
Along path to crisis, marginal buyer is falling at the rate 1/(t+2)

Financial frictions
No response of inflation rate to news.
Concentration: Inflation rate is low except in states near and during the debt
crisis.
Marginal buyer is much higher (above 0.74 in all periods)

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Explicit default

1

Introduction

2

Implicit default: 2 period model3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks

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Explicit default

Setup with long-term bonds and explicit default
Shock U, D is realized in each period.
Price levels, {P(s t )}, are exogenously given.
Govt debt:
B̄ = amount of government debt in period 0.
No new debt issued in any other period.
All debt is long-term and matures in period T.

Sovereign debt crisis:
Govt defaults in period T only if S T = D T .
When the govt defaults, it repays only a fraction α ∈ (0, 1) of B̄.

Govt only collects taxes in final period.
 B̄ ,
if s T 6= D T ,P(s T )T (s T ) = α B̄T ,if s T = D T . (debt crisis)P(s )Braun and Nakajima

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Explicit default

Numerical example
Look at the evolution of the log yield of the govt debt in s t :11
ρ(s t ) ≡ln,
T −tq(s t )
where q(s t ) = price of govt debt in s t , which matures in period T .
parameter values:
Constant price levels: P(s t ) = P for all s t and t.
Real interest rate: R = 1.02.
Default rate: α = 0.2.

Prior to period 0, everyone believes that there is not govt default, i.e.,α(s T ) = 1 with probability one.
Under this assumption, the log yield of govt debt in period -1 isρ−1 = ln(1.02) = 1.98%.
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Explicit default

Yields on long-term bond at s t = D t when T = 5
Log yields in the five-period model (%)
ρ−1

ρ0

ρ(D)

ρ(D 2 )

ρ(D 3 )

(1) complete markets

1.98

6.34

14.84

34.68

104.15(2) financial frictions

1.98

1.98

2.05

5.04

38.70

Complete markets
bond yield responds to news
yield rises along the path towards default

Financial frictions
bond yield does not respond to news
Bond yield response is delayed.
Magnitude of the increase in bond yield is smaller along path to default.
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Discussion

1

Introduction

2

Implicit default: 2 period model3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks

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Government
Discussion
Individuals and non-financial companies
Domestic Financial Institutions
PrivatePublicCentral Bank
Foreign sector

6.17
1.41
5.38
1.82
2.44
1.11
4.44

12.4
47.2
16.0
21.4
9.8
38.9

Who holds Japanese govt debt?
Holdings of Japanese Government Debt
End of fiscal year 2008

Total
Government
Individuals and non-financial companies
Domestic Financial Institutions
PrivatePublicCentral Bank
Foreign sector

Amount(trillion yen)936.63114.0475.88
687.45354.27268.06
65.12
59.26

Fraction(%, net of govt)

9.2
83.6
43.1
32.6
7.9
7.2

financial sector: accepts deposits and holds government debt
individual holdings of government debt are small.
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Discussion

Who holds US debt?
Table 4
Holdings of U.S. Government Debt
End of Calendar year 2010

Total
Government
Individuals and non-financial companies
Domestic Financial Institutions
PrivatePublicCentral Bank
Foreign sector

Amount(trillion $)
14.03
6.17
1.41
5.38
1.82
2.44
1.11
4.44

Fraction(%, net of govt)

12.4
47.2
16.0
21.4
9.8
38.9

Holdings of Japanese Government Debt
End of fiscal year 2008

Financial sector also holds a lot of government debt.
AmountFraction(trillion yen) (%, net of govt)
Total
936.63Government
Our result
is robust to the introduction of a 114.04
foreign sector.
Individuals and non-financial companies
75.88
9.2
Domestic Financial Institutions
687.45
83.6
Braun and Nakajima
Why Prices Don’t Respond Sooner toa Prospective Sovereign
Debt Crisis

Foreign sector is also important.

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Discussion

Discussion:Restrictions on short selling govt debt.
A cheap way to finance a mortgage: short government debt.
1

Borrow government debt today.

2

Sell it. Use proceeds to purchase a home.

3

Repay at the interest rate on government debt.

Mortgage rates are higher than the yield on government debt.
Table 5Spreads on Mortgage Rates over
Government Debt in U.S. and Japan
Data collected on October 24, 2011*
U.S.
Japan
(Percentage) (Percentage)
1- Year ARM
2.84
0.86
5/1-year ARM
1.92
1.22
15-Year Fixed
0.5125n.a.
20-Year Fixed
n.a.
0.47
30-Year Fixed
1.06
0.46
*Government debt yields andU.S. Mortgage rates are from Bloomberg.
Japan Mortgage rates are from Shinsei Bank.

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Discussion

Government restrictions

Basel I and II induce banks to take long leveraged positions in government
debt.
Governments take actions to restrict short selling in states where the risk ofdefault is high.
Our model suggests that banning short sales of government debt is effective
in reducing price pressure!

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Concluding remarks

1

Introduction

2

Implicit default: 2 period model3

Implicit default: T -period model

4

Explicit default

5Discussion

6

Concluding remarks

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Concluding remarks

Summary
We have presented a model in which deflation/low yields can persist evenwhen people recognize that a debt fiscal crisis is not a negligible possibility.
Crucial features of our model:
asset markets are imperfect:borrowing is limited by the no-default constraint;

individuals hold heterogeneous portfolios:
some agents want to purchase govt debt;
others do not want to purchase it by themselves, but are willing to lend to those
who buy it.

Compared to the case with frictionless asset markets, our model implies:
the inflation rate is much lower before the crisis, but it gets much higher oncethe crisis occurs.
In the model with long-term govt debt, the yield on govt debt behaves
similarly.
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Concluding remarks

Robustness
Here we have assumed that individuals have different beliefs on how likely thedebt crisis occurs.
Any other assumption that leads to the same type of heterogeneity inportfolios would work too.
Example: different degrees of risk aversion.

We have also assumed that loans are risk-free.
If we interpret “loans” in our model as “demand deposits” in banks, this may
sound odd, because they are also subject to the risk of inflation.
In reality, govt bonds offer higher interest rates than demand deposits.
Any other assumption that generates this type of rate-of-return differentials
would work too.
Example: difference in maturity.

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Concluding remarks

Some directions for future researchother forms of heterogeneity (e.g., degrees of risk aversion).
allowing some agents to short-sell government debt (arbitrageurs) as in e.g.
Vayanos and Gromb (2010), Chen et al. (2001), but impose limits onarbitrage.
Endogenous default
normative analysis.
more traditional DSGE framework.
open economy.

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