Presented at part of the ADEMU Project at the Macroeconomic and Financial Imbalances and Spillovers Workshop June 2017

1. Fiscal Rules and the Sovereign Default Premium
Juan Carlos Hatchondo Leonardo Martinez Francisco Roch
The views expressed herein are those of the authors and should not be attributed to
the IMF, its Executive Board, or its management.
1 / 83

2. ...1
Motivation
2 / 83

3. FISCAL ANCHORS
Fiscal policy frameworks do not have an anchor to manage
expectations about future policies (unlike frameworks used for
monetary analysis; Leeper 2010).
This paper:
Having a fiscal anchor could be important.
The sovereign spread (and not the debt level) should be the anchor.
...1 Better common anchor (SGP).
...2 More robust anchor/policy advice (Spain?).
...3 Better ownership/more credible/easier to commit too.
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4. FISCAL RULES COULD PROVIDE FISCAL ANCHORS
A large and increasing number of countries have fiscal rules with
numerical targets.
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
0
10
20
30
40
50
60
70
80
90
Numberofcountrieswithfiscalrules
4 / 83

5. MOST FISCAL RULES TARGET DEBT LEVELS
1985
1987
1989
1991
1993
1995
1999
2001
2003
2005
2007
2009
2010
2012
2014
Numberofcountrieswithfiscalrules
0
20
40
60
80
Debt rule
No debt rule and budget balance rule
No debt rule and no budget balance rule
5 / 83

6. WHAT IS THE OPTIMAL DEBT LEVEL?
Blanchard (IMFdirect 2011): “Are old rules of thumb, such as
trying to keep the debt-to-GDP ratio below 60 percent in
advanced countries, still reliable?”
The Fiscal Monitor (2013): “The optimal-debt concept has
remained at a fairly abstract level... adjustment needs scenario
has used benchmark debt ratios of 60 percent of GDP... But the
appropriate debt target need not be the same for all countries...”
Eberhardt and Presbitero (JIE 2015): impossibility of finding
common debt thresholds across countries for the relationship
between debt levels and long-run growth.
6 / 83

7. DEBT INTOLERANCE
USAGBRAUT
BEL
DNK
FRA
DEU
ITA
NLDNOR SWE
JPNFIN
ISL
IRL
MLT
PRT
ESP
TUR
NZL
ZAF
BRA
CHL
COL
CRI
DOM
SLV
GTM
MEX
PANPER
URY
JAM
BHR
CYP
IRQ
ISR
LBN
QAT
HKG
IDN
KOR
MYS
PHL
SGP
THA
MAR
TUN
KAZ
BGR
RUS
CHN
UKR
CZESVK
EST
LVA
SRB
HUN
LTU
HRV
SVN
POL
ROM
0200400600
SovereignCDSspread(2015),bps
0 50 100 150 200 250
Public debt (2015), % GDP
More debt intolerance ⇒ higher spreads for lower debt (Reinhart et
al., 2003).
7 / 83

8. A COMMON, ROBUST, AND CREDIBLE ANCHOR
...1 Political constraints lead to common fiscal anchors for several
governments (e.g. SGP) that may face different levels of debt
intolerance.
...2 For one government, the level of debt intolerance changes over time
and is difficult to identify.
What is the debt level consistent with acceptable fiscal risk in
Greece? Brazil? Spain?
We would like policy advice to be robust to this uncertainty.
...3 The anchor should be credible: governments would not gain from
deviating from the fiscal rule.
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9. SPREAD BRAKE VS. DEBT BRAKE
A spread (debt) brake imposes a limit on the fiscal balance when
the sovereign spread (debt) is above a threshold.
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10. ...2
Three-period model
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11. ENVIRONMENT
Government’s income in period t = yt. With t ∈ {1, 2, 3}.
y1 = y2 = 0, y3 > 0 and stochastic.
The government maximizes utility of a representative consumer.
A bond issued at t = 1 promises the payment sequence {δ, 1 − δ}.
A bond issued at t = 2 promises a payment of 1 at t = 3.
Foreign risk-neutral lenders’ discount factor = 1.
Lenders are atomistic and bond market is competitive.
Cost of defaulting: Lose fraction ϕ of y3 (no default in first two
periods)
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12. OPTIMAL POLICIES
Ramsey policies: sequence of borrowing that maximizes the
government’s expected utility in period 1, given the default rule
of the period 3 government.
Markov policies: sequence of borrowing chosen sequentially by
the governments in periods 1 and 2.
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13. (WITH LONG-TERM DEBT) WE NEED A FISCAL RULE
.
Proposition
..
......
Suppose δ < 1; i.e., the government issues long-term debt in period 1.
Then, only with a fiscal rule limiting the government’s choices in
period 2, Markov policies coincide with Ramsey policies.
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14. WHY IS A FISCAL RULE NEEDED?
The period 2 Ramsey policy satisfies
u′
(
c2(bR
1 , bR
2 )
) [
q2(bR
1 , bR
2 ) + bR
2
∂q2(bR
1 , bR
2 )
∂b2
]
=
βE
[
u′
(
c3(bR
1 , bR
2 , y3)
) [
1 − ˆd(bR
1 , bR
2 , y3)
]]
−u′
(
c1(bR
1 , bR
2 )
)
bR
1
∂q1(bR
1 , bR
2 )
∂b2
.
But the period 2 Markov strategy satisfies
u′
(
c2(b1, bM
2 (b1))
) [
q2(b1, bM
2 (b1)) + bM
2 (b1)
∂q2(b1, bM
2 (b1))
∂b2
]
= βE
[
u′
(
c3(b1, bM
2 (b1), y3)
) [
1 − ˆd(b1, bM
2 (b1), y3)
]]
.
14 / 83

15. IDIOSYNCRATIC DEBT BRAKE = IDIOSYNCRATIC
SPREAD BRAKE
Idiosyncratic debt brake imposes a ceiling on the debt level,
(1 − δ)b1 + b2 ≤ ¯b.
Idiosyncratic spread brake imposes a ceiling on the spread paid
by the government and thus a floor on the sovereign bond price,
q2(b1, b2) ≥ q.
.
Proposition
..
......
If the government’s choices in period 2 are limited with either a debt
brake with threshold ¯b∗ = (1 − δ)bR
1 + bR
2 or a spread brake with
threshold q∗ = q2(bR
1 , bR
2 ), Markov policies coincide with Ramsey
policies. 15 / 83

16. OPTIMAL “COMMON” FISCAL RULES
Consider a set of heterogenous economies indexed by the value of
the parameter θ ∈ {ϕ, σy, β}.
v(x; θ) = expected utility in period 1 of an economy with a fiscal
rule with threshold x.
h(θ) = density function for θ in the set.
The optimal common fiscal rule threshold X∗ maximizes
max
x
∫
v(x; θ)h(θ)dθ.
16 / 83

17. WHY A “COMMON AND ROBUST” FISCAL RULE?
X∗ would be chosen by a planner that maximizes the expected
utility in period 1 of
...1 a set of different economies while giving weight h(θ) to economies
with parameter value θ.
...2 a single economy when the planner is uncertain about the value of
the parameter θ and assigns the likelihood h(θ) to θ.
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18. ASSUMPTION 1
The function
ζq(b) =
b
ϕ
f
(
b
ϕ
)
1 − F
(
b
ϕ
)
is increasing with respect to b and limb→∞ ζq(b) ≥ 1.
18 / 83

19. COMMON SPREAD BRAKE ≻ COMMON DEBT BRAKE
.
Proposition
..
......
Suppose δ = 0, u(c) = c, and Assumption 1 holds. Then, for any
economy with cost of defaulting ϕ, the optimal debt brake threshold is
¯b∗ = ηϕ and the optimal spread brake threshold is q∗ = 1 − F(η), with
η > 0. Therefore, for any set of economies that differ in the level of
debt intolerance (i.e., for economies with different values of ϕ), the
optimal common spread-brake threshold is Q∗
= 1 − F(η), and
generates larger welfare gains than any common debt-brake threshold
¯B.
19 / 83

20. NUMERICAL EXAMPLE
Assume:
u (c) = −c−1
β = 1,
log(y3) ∼ N
(
0, σy
)
,
δ = 0.
If σy = 0.1, debt levels between 25 and 169 percent of average
period 3 income, spreads between 1 and 12 percent.
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21. WELFARE GAINS FROM IDIOSYNCRATIC RULE
0 0.2 0.4 0.6 0.8 1
Default cost (φ)
0
0.5
1
1.5
2
Welfaregain(%cons.)
Idiosyncratic rule
0 5 10 15
0
0.5
1
1.5
2
Std deviation of income (in %)
Welfaregain(%cons.)
Idiosyncratic rule
Same welfare gains with either optimal idiosyncratic debt brake or
optimal idiosyncratic spread brake
21 / 83

22. COMMON DEBT BRAKE DOESN’T WORK WELL
0 0.2 0.4 0.6 0.8 1
Default cost (φ)
0
0.5
1
1.5
2
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
0 5 10 15
0
0.5
1
1.5
2
Std deviation of income (in %)
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
The optimal common debt brake does not impose an excessive
constraint in low-debt-intolerance economies and thus is not binding
in most economies.
22 / 83

23. COMMON SPREAD BRAKE IS BETTER
0 0.2 0.4 0.6 0.8 1
Default cost (φ)
0
0.5
1
1.5
2
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
Common spread brake
0 5 10 15
0
0.5
1
1.5
2
Std deviation of income (in %)
Welfaregain(%cons.)
Idiosyncratic rule
Common debt brake
Common spread brake
A relatively low spread threshold still does not impose an excessive
constraint in low-debt-intolerance economies but imposes a welfare
improving constraint in high-debt-intolerance economies.
23 / 83

24. ...3
Quantitative model
24 / 83

25. LITERATURE
Eaton and Gersovitz (RESTUD 1981), Aguiar and Gopinath (JIE
2006), Arellano (AER 2008), Hatchondo and Martinez (JIE 2009,
EQ 2012, IEJ 2013), Hatchondo, Martinez, and Sosa-Padilla (JME
2014, JPE 2016), Hatchondo, Martinez, and Onder (JIE 2017),
Hatchondo, Martinez, and Sapriza (EQ 2007, IER 2009, RED 2010),
Arellano and Ramanarayanan (JPE 2012), Chatterjee and
Eyigungor (AER 2012, AER 2016), Cuadra and Sapriza (JIE 2008),
Cuadra, Sanchez, and Sapriza (RED 2010), Boz (JIE 2011), Durdu,
Nunes, and Sapriza (JIE 2013).
25 / 83

26. ...1
The no-rule environment
26 / 83

27. EQUILIBRIUM CONCEPT
Markov Perfect Equilibrium.
Each period the government decides taking as given bond prices
and future defaulting, spending, taxing, and borrowing strategies.
Current optimal choices are consistent with future government
strategies.
Bond holders make zero expected profits.
Limit of finite-horizon economy.
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28. TECHNOLOGY
Linear technology in labor
y = ez
l
TFP shock z follows a Markov process.
28 / 83

29. PREFERENCES
Benevolent government
max Et
[
∞
∑
j=0
βj
u
(
ct+j, gt+j, lt+j
)
]
taking into account private consumption and labor decisions.
g =public consumption.
29 / 83

30. IF THE GOVERNMENT PAYS ITS DEBT OBLIGATIONS
Issues long-term debt.
Bonds are perpetuities with geometrically decreasing coupon
obligations
Important for the quantitative performance of the model
(Hatchondo and Martinez 2009; Chatterjee and Eyigungor 2012).
Chooses provision of public good: g
Chooses labor tax: τ
30 / 83

31. DEFAULTS
Two costs of defaulting:
...1 Exclusion from credit market for a stochastic number of periods.
...2 Fall in TFP in every period in which the government is in default.
With constant probability, the government can exit the default by
exchanging α new bonds per bond in default (debt restructuring).
1 − α = haircut
Chooses g and labor tax τ while in default.
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32. LENDERS
Foreign.
Risk-neutral (later, same results with shock to the lenders’ risk
aversion)
Opportunity cost of lending: risk-free bonds paying r.
32 / 83

33. SIMULATIONS MATCH TARGETS
Data No-rule benchmark
Mean debt-to-income ratio (in %) 61.8 61.5
Debt duration (years) 6.0 6.0
Annual spread (in %) 2.0 2.0
Mean g/c (in %) 36.5 36.5
σ(g)/σ(y) 0.9 0.9
σ(c)/σ(y) 1.1 1.1
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34. ...5
Fiscal rules
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35. DEBT BRAKE
b′
≤ max{¯b, (1 − δ)b}
Find the optimal value for ¯b.
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36. SPREAD BRAKE
Find the optimal value for q in the constraint under repayment:
q(b′
, z)
Price at which
bonds are issued
≥ q if b′
> b.
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37. ...6
Quantitative results
37 / 83

38. IDIOSYNCRATIC DEBT BRAKE ≃ IDIOSYNCRATIC
SPREAD BRAKE
Without rule Debt brake Spread brake
(52.5%) (0.45%)
Mean debt-to-income ratio 61.5 54.9 59.4
Annual spread (in %) 2.0 0.5 1.0
Mean g/c (in %) 36.5 37.1 36.9
σ(g)/σ(y) 0.9 0.9 1.0
σ(c)/σ(y) 1.1 1.1 1.1
Defaults per 100 years 2.9 0.8 1.1
Welfare gain (in %) 0.5 0.4
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39. BORROWING WITHOUT A FISCAL ANCHOR
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
0.5
1
1.5
2
2.5
3
Annualspread(in%)
Without rules
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
10
20
30
40
50
60
Debtmarketvalue/GDP(in%)
Without rules
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40. BORROWING WITH A FISCAL ANCHOR
The fiscal anchor allow for less debt (lower face value) but may allow
for more borrowing (because of the higher interest rate)
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
0.5
1
1.5
2
2.5
3
Annualspread(in%)
Without rules
With optimal spread brake
0 10 20 30 40 50 60 70
End-of-period debt / GDP (in %)
0
10
20
30
40
50
60
Debtmarketvalue/GDP(in%) Without rules
With optimal spread brake
40 / 83

41. NEGATIVE SHOCKS WITHOUT A FISCAL ANCHOR
Quarter
0 20 40 60 80
%
-10
-5
0
5
10
15
20
LogTFP
Spread without rule
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42. NEGATIVE SHOCK WITH A FISCAL ANCHOR
Quarter
0 20 40 60 80
%
-10
-5
0
5
10
15
20
LogTFP
Spread without rule
Spread with optimal spread brake
42 / 83

43. CONSUMPTION IS NOT MORE VOLATILE WITH THE
SPREAD BRAKE
Quarter
0 20 40 60 80
%
-10
-5
0
5
10
15
20
LogTFP
Spread without rule
Spread with optimal spread brake
0 10 20 30 40 50 60 70 80
Quarter
20
30
40
50
60
70
80
90
%
-5
0
5
10
15
%
Log private consumption without rule
Log private consumption with optimal spread brake
Log public consumption without rule
Log public consumption with optimal spread brake
Debt without rule
Debt with optimal spread brake
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44. COMMON RULES
Longer exclusion ⇒ ↑ cost of defaulting ⇒ more debt.
Higher recovery ⇒ ↓ benefit of defaulting ⇒ more debt.
More impatient borrower ⇒ ↑ benefit of borrowing ⇒ more debt.
We assume exclusions between 1 and 5 years (benchmark = 3), recovery
rates between 10% and 60% (benchmark = 35%), and discount factor
between 0.96 and 0.985 (benchmark = 0.97).
Thus, we study economies with average debt levels between 30% and
90%, and average spreads between 0.5% and 5.5%.
44 / 83

45. HETEROGENOUS ECONOMIES
1 2 3 4 5
Exclusion duration (years)
20
30
40
50
60
70
80
Debtas%oftrendGDP
Avg. debt without rules
1 2 3 4 5
Exclusion duration (years)
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
Avg. spread without rules
45 / 83

46. OPTIMAL IDIOSYNCRATIC THRESHOLDS
1 2 3 4 5
Exclusion duration (years)
20
30
40
50
60
70
80
Debtas%oftrendGDP
Avg. debt without rules
Optimal idiosyncratic debt threshold
1 2 3 4 5
Exclusion duration (years)
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
Avg. spread without rules
Optimal idiosyncratic spread threshold
The optimal idiosyncratic debt threshold changes almost one to one with the average
debt level in the no-rule economy.
46 / 83

47. RAWLSIAN DEBT BRAKE GENERATES WELFARE
LOSSES
1 2 3 4 5
Exclusion duration (years)
-1.5
-1
-0.5
0
0.5
Welfaregain(%CE)
Optimal common debt brake
0.1 0.2 0.3 0.4 0.5 0.6
Recovery rate
-0.5
0
0.5
Welfaregain(%CE)
Optimal common debt brake
To be binding in high-debt-intolerance economies, the optimal
common Rawlsian debt brake imposes an excessive constraint in
low-debt-intolerance economies.
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48. RAWLSIAN SPREAD BRAKE ≻ RAWLSIAN DEBT
BRAKE
1 2 3 4 5
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Exclusion duration (years)
Welfaregain(%CE)
Optimal common debt brake
Optimal common spread brake
0.1 0.2 0.3 0.4 0.5 0.6
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Recovery rateWelfaregain(%CE)
Optimal common debt brake
Optimal common spread brake
The optimal common Rawlsian spread brake is binding in
high-debt-intolerance economies without imposing an excessive
constraint in low-debt-intolerance economies.
48 / 83

49. PENALTY NEEDED TO ENFORCE THE RAWLSIAN
DEBT BRAKE
1 2 3 4 5
Exclusion duration (years)
-5
0
5
10
15
20
25
Enforcementcost(%oftrendGDP)
Rawlsian debt brake
49 / 83

50. PENALTY NEEDED TO ENFORCE THE RAWLSIAN
SPREAD BRAKE
1 2 3 4 5
−5
0
5
10
15
20
25
Exclusion duration (years)
Enforcementcost(%oftrendGDP)
Rawlsian debt brake
Rawlsian spread brake
50 / 83

51. ...7
Conclusions and extensions
51 / 83

52. CONCLUSIONS
Maybe sovereign spreads should play a more prominent role in
anchoring discussions of fiscal policy
Economies that suffer less debt intolerance should be allowed to
issue more debt.
It may be much easier to enforce a spread brake than to enforce a
debt brake.
Also
a market-determined fiscal anchor could be less susceptible to
creative accounting
more comprehensive measure of fiscal risks (e.g., debt maturity,
currency composition, implicit or contingent liabilities) 52 / 83

53. NEED FOR FUTURE WORK?
What should the spread-brake threshold be? Should it be reduced
gradually (mimicking disinflation periods)?
Which interest rates should fiscal rules use?
The average spread over which period should be used to trigger
the spread brake?
How should a spread brake be complemented with other
numerical targets?
How fast should the fiscal adjustment triggered by the brake be?
Would the spread limit help with other shocks (bailout
probability, multiple equilibria, political shocks, debt shocks)?
53 / 83