Fiscal rules and the sovereign default premium

Fiscal Rules and the Sovereign Default Premium
Juan Carlos Hatchondo Leonardo Martinez Francisco Roch
Indiana University IMF CEMLA
and U. of Wisconsin
The views expressed herein are those of the authors and should not be attributed to
the IMF, its Executive Board, or its management.
1 / 112

MISSPECIFICATION, ANCHORS, AND “PRICES VS.
QUANTITIES”
...1 Policy recommendations that are robust to model
misspeciﬁcation (Hansen and Sargent, 2008).
...2 Fiscal policy frameworks do not have an anchor that improves
commitment to future policies (unlike frameworks used for
monetary analysis; Leeper, 2010).
...3 Are prices or quantities the best planning instrument under
heterogeneity and uncertainty/risk (Weitzman, 1974; Poole, 1970,
for monetary policy)?
3 / 112

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 / 112

MOST FISCAL RULES TARGET DEBT LEVELS
1985
1987
1989
1991
1993
1995
1999
2001
2003
2005
2007
2009
2010
2012
2014
0
20
40
60
80
Debt rule
No debt rule and budget balance rule
No debt rule and no budget balance rule
And even if they don’t, they do: E.g., Colombia’s MTFF.
5 / 112

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 / 112

DEBT INTOLERANCE (REINHART ET AL., 2003)
A…
ZAF
BRA
CHL
COL
MEX
PAN
PER
LBN
MYS
PHL
THA
CIV
MAR
NGA
BGR
RUS
CHN
HUN
CRO
POL
0
100
200
300
400
500
600
700
800
0 20 40 60 80 100 120 140 160
EMBIGSpreads(basispoints)
General government gross debt/GDP
VEN
7 / 112

DEBT INTOLERANCE IN THE EU (2010, 2016)
CZE
DEU
FRA
IRL
BEL
DNK
ESP
SWE
NLD
AUT
BGR
HRV
CYP
EST
HUN
ITA
LVALTU
MLT
POL
PRT
SVN
ROU
SVK
GBR
FIN
0
50
100
150
200
250
300
350
400
0 30 60 90 120
CDSSpreads(basispoints)
General government gross debt/GDP
8 / 112

THIS PAPER
Debt brake vs. spread brake: a debt (spread) brake imposes a
limit on the fiscal balance when the sovereign debt (spread) is
above a threshold.
The sovereign spread outperforms the debt level as the fiscal
anchor.
...1 More robust anchor/policy advice (Croatia? Portugal? Greece?
Spain? Peru? Brazil?).
...2 Better common anchor (EU).
...3 Could improve ownership/credibility/commitment.
Substantial gains from anchoring fiscal expectations.
9 / 112

...2
Three-period model
10 / 112

ENVIRONMENT
Government’s income in period t = yt. With t ∈ {1, 2, 3}.
y1 = y2 = 0, y3 > 0 and stochastic with cdf F.
The government maximizes utility of a representative consumer
with discount factor β > 0.
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)
11 / 112

OPTIMAL POLICIES
Ramsey borrowing: sequence of borrowing that maximizes the
government’s expected utility in period 1, given the default rule
of the period 3 government.
Markov borrowing: sequence of borrowing chosen sequentially
by the governments in periods 1 and 2.
12 / 112

TIME INCONSISTENCY (DEBT DILUTION)
.
Proposition
..
......
Suppose δ < 1; i.e., the government issues long-term debt in period 1.
Then, Markov policies and Ramsey policies do not coincide.
13 / 112

WHY?
The period 2 Ramsey policy satisﬁes
u′
(
cR
2
) [
q2(bR
1 , bR
2 ) + bR
2
∂q2(bR
1 , bR
2 )
∂b2
]
=
β
∫ ∞
bR
1
(1−δ)+bR
2
ϕ
u′
(
cR
3
)
f(y3)dy3−u′
(
cR
1
)
bR
1
∂q1(bR
1 , bR
2 )
∂b2
.
But the period 2 Markov strategy satisﬁes
u′
(
cM
2 (b1)
) [
q2(b1, bM
2 (b1)) + bM
2 (b1)
∂q2(b1, bM
2 (b1))
∂b2
]
=
β
∫ ∞
b1(1−δ)+bM
2 (b1)
ϕ
u′
(
cM
3 (b1, y3)
)
f(y3)dy3.
14 / 112

(NO MODEL UNCERTAINTY OR HETEROGENEITY)
PRICES = QUANTITIES
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 / 112

LESS INTOLERANCE => HIGHER RAMSEY DEBT
.
Proposition
..
......
Suppose u(c) = c, δ = 0,
ζq(b) =
b
ϕ
f
(
b
ϕ
)
1 − F
(
b
ϕ
)
is increasing with respect to b, and limb→∞ ζq(b) ≥ 1. Consider any set
of economies that are different only in the value of the cost of
defaulting ϕ. Then, Ramsey policies are given by {bR
1 = ηϕ, bR
2 = 0},
where η ∈ R++ satisﬁes
1 − η
f (η)
1 − F (η)
= β2
.
16 / 112

CONSTRAINED RAMSEY
...1 Robust rule under risk/uncertainty: planner needs to chose a
idiosyncratic non-contingent rule for one economy, before
knowing value of ϕ.
...2 Common rule under heterogeneity: planner needs to choose the
same rule for every economy in a set of economies that are
different only in the value of the cost of defaulting ϕ.
17 / 112

COMMON SPREAD BRAKE ≻ COMMON DEBT BRAKE
Note that q2(b1, b2) = 1 − F
(
b1(1−δ)+b2
ϕ
)
and {bR
1 = ηϕ, bR
2 = 0}.
Therefore, the price limit consistent with Ramsey borrowing does not
depend on ϕ.
.
Proposition
..
......
Suppose u(c) = c, δ = 0, ζq(b) is increasing with respect to b, and
limb→∞ ζq(b) ≥ 1. Consider any set of economies that are different
only in the value of the cost of defaulting ϕ. The optimal common
spread-brake threshold for any such set is Q∗
= 1 − F(η) and achieves
the Ramsey allocation in every economy of the set. Furthermore, Q∗
generates larger welfare gains than any common debt brake ¯B.
18 / 112

...3
Quantitative model
19 / 112

THE MODEL
Because of long-term debt, expectations about future debt levels
determine the endogenous sovereign spread.
20 / 112

DEBT BRAKE
b′
≤ max{¯b, (1 − δ)b}
Find the optimal value for ¯b.
We ﬁrst assume an initial state with mean TFP and no debt (other
initial states are also investigated in the paper).
21 / 112

SPREAD BRAKE
q(b′
, s)
Price at which
bonds are issued
≥ q if b′
> b.
Find the optimal value for q.
We ﬁrst assume an initial state with mean TFP and no debt (other
initial states are also investigated in the paper).
22 / 112

MODEL UNCERTAINTY/HETEROGENEITY
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
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
Avg. spread without rules
23 / 112

OPTIMAL THRESHOLDS WITHOUT
UNCERTAINTY/HETEROGENEITY
1 2 3 4 5
20
30
40
50
60
70
80
Debtas%oftrendGDP
Optimal idiosyncratic debt threshold
1 2 3 4 5
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
Optimal idiosyncratic spread threshold
The optimal debt threshold without uncertainty/heterogeneity changes almost one
to one with the average debt level in the no-rule economy.
24 / 112

MAXMIN DEBT BRAKE (23%)
1 2 3 4 5
-1.5
-1
-0.5
0
0.5Welfaregain(%CE)
Optimal common debt brake
25 / 112

MAXMIN SPREAD BRAKE (0.5%) ≻ MAXMIN 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
Welfaregain(%CE)
Optimal common spread brake
The optimal MaxMin spread brake is binding in
high-debt-intolerance economies without imposing an excessive
constraint in low-debt-intolerance economies.
26 / 112

PENALTY NEEDED TO ENFORCE THE MAXMIN DEBT
BRAKE
1 2 3 4 5
-5
0
5
10
15
20
25
Enforcementcost(%oftrendGDP)
Rawlsian debt brake
27 / 112

PENALTY NEEDED TO ENFORCE THE MAXMIN
SPREAD BRAKE
1 2 3 4 5
−5
0
5
10
15
20
25
Enforcementcost(%oftrendGDP)
Rawlsian debt brake
Rawlsian spread brake
28 / 112

NEGATIVE SHOCKS WITHOUT A FISCAL ANCHOR
Quarter
0 20 40 60 80
%
-10
-5
0
5
10
15
20
LogTFP
Spread without rule
29 / 112

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
30 / 112

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
31 / 112

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
0
10
20
30
40
50
60
Debtmarketvalue/GDP(in%)
Without rules
32 / 112

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
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
0
10
20
30
40
50
60
Debtmarketvalue/GDP(in%) Without rules
33 / 112

...7
Conclusions and extensions
34 / 112

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) 35 / 112

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)?
36 / 112

a. The no-rule environment
38 / 112

EQUILIBRIUM CONCEPT
...1
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.
Limit of ﬁnite-horizon economy.
39 / 112

TECHNOLOGY
Linear technology in labor
y = ez
l
TFP shock z follows a Markov process.
40 / 112

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.
41 / 112

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
42 / 112

IF THE GOVERNMENT DEFAULTS
Chooses g and labor tax τ while in default.
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
43 / 112

LENDERS
Foreign.
Risk-neutral (same results with shock to the lenders’ risk
aversion)
Opportunity cost of lending: risk-free bonds paying r.
44 / 112

b. Recursive formulation (without rule)
45 / 112

VALUE FUNCTIONS
...1
Repay/default decision
V(b, z) = max
{
VR
(b, z), VD
(b, z)
}
Value of repaying
VR
(b, z) = max
b′≥0,c≥0,g≥0,τ≥0
{
u (c, g, 1 − l) + βEz′|zV(b′
, z′
)
}
,
subject to
g = τez
l − b + q(b′
, z)
[
b′
− (1 − δ)b
]
,
c = (1 − τ)ez
l,
l = ˆl (z, τ, g) ,
q
(
b′
, z
)
≥ q if b′
> b.
46 / 112

VALUE OF DEFAULTING
VD
(b, z) = max
c≥0,g≥0,τ≥0
u (c, g, 1 − l)
+ βEz′|z
[
(1 − ξ)VD
(b(1 + r), z′
) + ξV(αb(1 + r), z′
)
]
,
subject to
g = τ [ez
− ϕ(z)] l,
c = (1 − τ) [ez
− ϕ(z)] l,
l = ˆl (log(ez
− ϕ(z)), τ, g) .
47 / 112

BOND PRICE
q(b′
, z)(1 + r) = Ez′|z
[
ˆd
(
b′
, z′
)
(1 + r)qD
((1 + r)b′
, z′
)
+
[
1 − ˆd
(
b′
, z′
)] [
1 + (1 − δ) q(ˆb(b′
, z′
), z′
)
]]
,
qD
(b′
, z)(1 + r) = Ez′|z
[
(1 − ξ)(1 + r)qD
(b′
(1 + r), z′
)
+ξα
[
d′
qD
(
αb′
, z′
)
+
(
1 − d′
) [
1 + (1 − δ) q(b′′
, z′
)
]]]
,
where d′ = ˆd (αb′, z′), and b′′ = ˆb(αb′, z′).
48 / 112

c. Calibration (without rule)
49 / 112

CALIBRATION STRATEGY
...1
Preference parameters for private consumption and leisure
decisions: taken from prior literature.
Remaining parameters: based on data from a small-open
economy that pays a default premium (Spain).
(δ, β, λ0, λ1, π, γg) chosen to match: (i) average duration of
government debt, (ii) average spread, (iii) average level of
government debt, (iv) volatility of c, (v) average level of g, and (vi)
volatility of g.
50 / 112

FUNCTIONAL FORMS
Preferences: u(c, g, l) = π
g1−γg
1−γg
+ (1 − π)
[c−ψl1+ω/(1+ω)]
1−γ
1−γ
TFP process: zt = (1 − ρ) µz + ρzt−1 + εt, with εt ∼ N
(
0, σ2
ϵ
)
.
Output loss while in default: ϕ (z) = max
{
λ0ez + λ1e2z, 0
}
1 period = 1 quarter
51 / 112

CALIBRATED WITHOUT THE SIMULATIONS
Domestic income ρ 0.97 1960Q1-2013Q1
Domestic income σϵ 1.04% 1960Q1-2013Q1
Mean productivity µy (-1/2)σ2
ϵ Mean productivity = 1
Risk aversion γ 2 Prior literature
Inverse of labor elasticity ω 0.6 Neumeyer and Perri
Weight of labor hours ψ 2.48/(1 + ω) Neumeyer and Perri
Risk-free rate r 0.01 Prior literature
Recovery rate α 0.35 Cruces and Trebesch
Duration of defaults ξ 0.083 Dias and Richmond
Minimum issuance price q 0.3¯q Never binding
52 / 112

CALIBRATED WITH THE SIMULATIONS
Duration of long-term bond δ 0.0275
Discount factor β 0.97
Income loss while in default λ0 -0.731
Income loss while in default λ1 0.9
Risk aversion for public consumption γg 3
Weight of public consumption π 0.182
53 / 112

d. Quantitative results
55 / 112

SIMULATIONS MATCH TARGETS
...1
Data No-rule benchmark
Annual spread (in %) 2.0 2.0
Mean debt-to-income ratio (in %) 61.8 61.5
Debt duration (years) 6.0 6.0
Mean g/c (in %) 36.5 36.5
σ(g)/σ(y) 0.9 0.9
σ(c)/σ(y) 1.1 1.1
56 / 112

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
57 / 112

COUNTRIES WITH SUPRANATIONAL FISCAL RULES
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
Countries with only national rules
Countries with only supranational rules
Countries with both rules
58 / 112

...5
Global factors and spread brakes
59 / 112

SHOCKS TO THE LENDERS’ RISK AVERSION
Potential concern of using interest rates to anchor ﬁscal policy:
they move for reasons that are beyond the government’s control.
We assume that the stochastic discount factor M(z′, z, p) satisﬁes
M(z′
, z, p) = exp(−r − pε′
+ 0.5p2
σ2
ϵ )
p ∈ {0, pH} denotes the risk-premium shock.
Parametrization based on the EMBI global spread: Three
high-risk-premium episodes every twenty years (πLH = 0.0375).
Each episode lasts on average for two years (πHL = 0.125).
Increase in spread during high-premium episode = 2.2%
(pH = 70).
Recalibrate cost of default to get average debt level of 62%. 60 / 112

DEBT BRAKE SIMILAR TO SPREAD BRAKE (p)
Without rule Debt brake Spread brake
(50%) (1%)
Spread increase with pH 2.1 1.0 1.6
Mean g/c (in %) 36.6 37.3 36.9
σ(g)/σ(y) 1.0 0.9 1.0
σ(c)/σ(y) 1.1 1.1 1.1
Welfare gain (in %) 0.3 0.3
61 / 112

¯B∗
< Q∗
(p)
Exclusion Recovery β
¯B∗ 0.50 0.58 0.50
Q∗
(spread, in %) 1.00 1.00 1.20
Welfare gains with ¯B∗
Average (in %) 0.20 0.18 0.35
Maximum (in %) 0.39 0.40 0.80
Minimum (in %) 0.00 0.00 0.09
Welfare gains with Q∗
Average (in %) 0.28 0.29 0.37
Maximum (in %) 0.36 0.42 0.91
Minimum (in %) 0.20 0.17 0.08
62 / 112

WELFARE GAINS ACROSS DEBT INTOLERANCE (p)
1 2 3 4 5
Exclusion (years)
0
0.1
0.2
0.3
0.4
0.5
0.6
Welfaregain(%CE)
0.1 0.2 0.3 0.4 0.5 0.6
Recovery rate
0
0.1
0.2
0.3
0.4
0.5
0.6
Welfaregain(%CE)
Optimal common debt spread
63 / 112

OPTIMAL INDIVIDUAL DEBT THRESHOLDS (p)
Optimal debt threshold changes almost one to one with the average debt level in the
no-rule economy.
1 2 3 4 5 6
20
30
40
50
60
70
80
90
Debtas%oftrendGDP
Optimal debt limit
0.1 0.2 0.3 0.4 0.5 0.6
30
40
50
60
70
80
90
Recovery rate
Debtas%oftrendGDP
Optimal debt limit
64 / 112

OPTIMAL INDIVIDUAL SPREAD THRESHOLDS (p)
Optimal spread threshold is less sensitive to debt intolerance.
1 2 3 4 5 6
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
Optimal spread limit
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.5
1
1.5
2
2.5
3
Recovery rate
Annualspread(in%)
65 / 112

SIMILAR WELFARE GAINS ACROSS β (p)
0.95 0.96 0.97 0.98 0.99
β
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6Welfaregain(%CE)
66 / 112

OPTIMAL INDIVIDUAL THRESHOLDS ACROSS β (p)
0.95 0.96 0.97 0.98 0.99
β
30
40
50
60
70
80
90
Debtas%oftrendGDP
Optimal debt limit
0.95 0.96 0.97 0.98 0.99
β
0
1
2
3
4
5
6
Annualspread(in%)
67 / 112

...6
Political myopia
68 / 112

POLITICAL MYOPIA
Stricter ﬁscal rules and larger welfare gains.
0.95 0.96 0.97 0.98 0.99
β
0
1
2
3
4
5
6
Annualspread(in%)
0.95 0.96 0.97 0.98 0.99
β
20
30
40
50
60
70
80
90
Debtas%oftrendGDP
69 / 112

POLITICAL MYOPIA AND DEBT INTOLERANCE
USAGBR AUT
BEL
DNK
FRA
DEU
ITA
NLDNORSWE
JPNFIN
ISL
IRL
MLT
PRT
ESP
TUR
NZL
ZAF
BRA
CHL
COL
CRI
DOM
SLV
GTM
MEX
PAN PER
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,bps
0 25 50 75
Political Risk
USA
GBR AUT
BEL
DNK
FRA
DEU
ITA
NLD
NOR
SWE
JPN
FIN
GRC
ISL
IRL
MLT
PRT
ESP
TURNZL
ZAF
ARG
BRA
CHL
COL
CRI
DOM
SLV
GTM
MEX
PAN
PER
URY
JAM
BHR
CYP
IRQISR
LBN
QAT
HKG
IDN
KOR
MYS
PHL
SGP
THA
MAR
TUN
KAZBGR
RUS
CHN
UKR
CZE
SVK
EST
LVA
SRBHUN
LTU
HRVSVN
POL
ROM
050100150200250
Publicdebt,%GDP
0 25 50 75
Political Risk
70 / 112

...7
Fiscal rules and the cyclicality of ﬁscal
policy
71 / 112

STATE-CONTINGENT ¯b
Debt limit ¯b(z) = ¯y[a0 + a1(ez − eµz )]
a0 determines mean debt threshold.
If a1 < 0 debt limit increases in bad times.
Optimal slope (a1) = 0.
Optimal debt threshold = 52.5% of mean output.
72 / 112

SIMULATIONS WITH A STATE-CONTINGENT ¯b
Trade-off: Countercyclical policy is good for insurance (lowers
volatility of g) but increases default risk.
a1 = −1 a1 = 0 a1 = 1
Mean g/c (in %) 37.0 37.1 37.2
σ(g)/σ(y) 0.8 0.9 1.1
σ(c)/σ(y) 1.0 1.1 1.1
Welfare gain (in %) 0.2 0.5 0.4
73 / 112

...8
Optimal rules for indebted governments
74 / 112

INDEBTED GOVERNMENTS
Debt threshold ¯b to be imposed in every period after T.
Initial debt level = 62% of ¯y
¯b∗ = 60% of ¯y
T∗ between 5 and 8 quarters
welfare gains between 0.6% and 0.8%
75 / 112

POSSIBILITY OF A FREE LUNCH
0 10 20 30 40
0
2
4
6
8
10
12
Quarters
Annualspread(in%)
No rule and low ini. tfp
No rule and mean ini. tfp
No rule and high ini. tfp
Debt rule and low ini. tfp
Debt rule and mean ini. tfp
Debt rule and high ini. tfp
76 / 112

...8
The no-default rule
77 / 112

NO-DEFAULT RULE
Gain from abandoning the rule between 11 and 12% of ¯y
78 / 112

IMPULSE RESPONSE
One-standard-deviation TFP fall
0 2 4 6 8 10 12 14
Years
0
50
100
150
200
250
300
350
Basispoints
Without rules
With opt. debt brake
With opt. spread brake
0 2 4 6 8 10 12 14
Years
0
0.05
0.1
0.15
%Change
Without rules
With opt. debt brake
With opt. spread brake
79 / 112

VOX
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
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Std deviation of income (in %)
Welfaregain(%cons.)
With common debt rule
With common spread rule
With best idiosyncratic rule
80 / 112

VOX
0.1 0.2 0.3 0.4 0.5 0.6
Recovery rate
30
40
50
60
70
80
90
100
Debtas%oftrendGDP
0.95 0.96 0.97 0.98 0.99
β
0
1
2
3
4
5
6
Annualspread(in%)
81 / 112

The sovereign spread as a common and robust
ﬁscal anchor
Juan Carlos Hatchondo Leonardo Martinez Francisco Roch
Indiana University RESMF WHDS1
The views expressed herein are those of the authors and should not be attributed to
the IMF, its Executive Board, or its management.
82 / 112

1 2 3 4 5
20
30
40
50
60
70
80
Debtas%oftrendGDP
1 2 3 4 5
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
0.95 0.96 0.97 0.98 0.99
β
30
40
50
60
70
80
90
Debtas%oftrendGDP
0.95 0.96 0.97 0.98 0.99
β
0
1
2
3
4
5
6
Annualspread(in%)
83 / 112

CORE SPREAD
2,000
EMBI Global - spread
1,500
1,000
500
0
-500
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Uruguay Median Uruguay Core Embi
Source: Datastream and staff calculationSource: Datastream and staff calculation
84 / 112

CALIBRATION
Discipline the endogenous spread function
Match features of the data:
Average levels of debt and spread.
Spread volatility and countercyclicality.
Spread increase due to adverse global shocks.
Volatility of public and private consumption.
85 / 112

WHY DOES THE SPREAD BRAKE WORK BETTER?
A common spread brake allows for more borrowing in economies with
less debt intolerance.
A common debt brake doesn’t.
Both allow for more borrowing in economies that need to borrow more.
86 / 112

OPTIMAL IDIOSYNCRATIC SPREAD THRESHOLDS
0.95 0.96 0.97 0.98 0.99
β
0
1
2
3
4
5
6
Annualspread(in%)
1 2 3 4 5
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
Optimal idiosyncratic spread threshold is less sensitive to parameter values.
87 / 112

OPTIMAL IDIOSYNCRATIC DEBT THRESHOLDS
1 2 3 4 5
20
30
40
50
60
70
80
Debtas%oftrendGDP
0.1 0.2 0.3 0.4 0.5 0.6
Recovery rate
30
40
50
60
70
80
90
100
Debtas%oftrendGDP
The optimal idiosyncratic debt threshold changes almost one to one with the average
debt level in the no-rule economy.
88 / 112

OUTLINE
...1 Motivation
...2 Three-period model
...3 Quantitative model
...4 Conclusions
89 / 112

EQUILIBRIUM DEFAULT DECISION
bt = number of bonds issued by the government in period t.
Default rule in period 3:
ˆd(b1, b2, y3) =



1 if y3 < b1(1−δ)+b2
ϕ ,
0 otherwise.
90 / 112

BOND PRICING EQUATIONS
Bond price menu at t = 2:
q2(b1, b2) = 1 − F
(
b1(1 − δ) + b2
ϕ
)
Bond price menu at t = 1:
q1(b1, b2) = δ
Sure repayment
at t = 2
+(1 − δ)
[
1 − F
(
b1(1 − δ) + b2
ϕ
)]
Repayment prob. at t = 3
91 / 112

ONE-PERIOD DEBT: NO NEED FOR FISCAL RULE
.
Proposition
..
......
Suppose δ = 1; i.e., bonds issued in period 1 pay off in period 2 alone.
Then, the government’s expected utility in period 1 cannot be
improved with a ﬁscal rule that limits debt choices in period 2.
The period-2 government chooses the borrowing level b∗
2 that
maximizes the government’s expected utility in period 1.
92 / 112

QUANTITATIVE MODEL OUTLINE
...1 Motivation
...2 Three-period model
...3 Quantitative model
...1 The no-rule environment
...2 Recursive formulation (without rule)
...3 Fiscal rules
...4 Calibration (without rule)
...5 Results
...4 Conclusions
93 / 112

COMMITMENT TO THE SPREAD (DEBT) BRAKE
Automatic budget corrections when the spread-brake threshold
is bridged
E.g., frozen (real) current expenditures or public wages
Maybe only with positive output gap
Independent fiscal councils
Focusing on the more transparent benefits from lower interest
rates instead of on the more controversial effects of lower debt
levels may improve a country’s ownership of the its fiscal rule.
Conceptually, it may be easier to commit to a spread brake than to
an inflation target.
94 / 112

ENHANCED COMMITMENT TO FISCAL RULES
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
Countries with fiscal rules
Fiscal councils
95 / 112

RESULTS OUTLINE
...1 Simulations without a fiscal rule
...2 Idiosyncratic fiscal rules
...3 Commitment to fiscal rules
...4 Common and robust fiscal rules
...5 Political myopia
...6 Global factors and spread brakes
...7 Fiscal rules and the cyclicality of fiscal policy
...8 Optimal rules for indebted governments
...9 The no-default rule
96 / 112

...1
Simulations without a ﬁscal rule
97 / 112

PROCYCLICAL FISCAL POLICY
0.8 0.9 1 1.1 1.2 1.3 1.4
0.26
0.27
0.28
0.29
0.3
0.31
0.32
Current income / mean income
Taxrate
0.8 0.9 1 1.1 1.2 1.3
0.2
0.25
0.3
Current income / mean income
Publicconsumption/meanincome
98 / 112

...2
Idiosyncratic ﬁscal rules
99 / 112

ACROSS β
.
Proposition
..
......
For any set of economies that differ only in the value of β, the optimal
common debt-brake threshold ¯B∗ generates the same welfare gain than
the optimal common spread-brake threshold Q∗
= 1 − F
(
¯B∗
ϕ
)
in every
economy in the set.
q2(b1, b2) = 1 − F
(
b1(1 − δ) + b2
ϕ
)
100 / 112

IMPULSE RESPONSE
One-standard-deviation TFP fall
Private consumption Public consumption
0 2 4 6 8 10 12 14
Years
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
%Change
Without rules
0 2 4 6 8 10 12 14
Years
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
%Change
Without rules
101 / 112

...3
Commitment to the optimal ﬁscal rule
102 / 112

COMMITMENT TO THE OPTIMAL SPREAD BRAKE
For all states of the economy, the expected utility of the
representative household is higher in the economy with the
optimal spread brake than in the no-rule benchmark.
103 / 112

...4
Common and robust ﬁscal rules
104 / 112

COMMON DEBT BRAKE ≺ COMMON SPREAD BRAKE
Exclusion Recovery β
¯B∗ 0.60 0.60 0.50
Q∗
(spread, in %) 0.45 0.40 0.50
Welfare gains with ¯B∗
Average (in %) 0.24 0.23 0.16
Maximum (in %) 0.55 0.48 0.41
Minimum (in %) 0.00 0.00 0.00
Welfare gains with Q∗
Average (in %) 0.34 0.34 0.17
Maximum (in %) 0.36 0.45 0.45
Minimum (in %) 0.28 0.20 0.01
105 / 112

WELFARE GAINS ACROSS DEBT INTOLERANCE
1 2 3 4 5
0
0.1
0.2
0.3
0.4
0.5
0.6
Welfaregain(%CE)
0.1 0.2 0.3 0.4 0.5 0.6
Recovery rate
0
0.1
0.2
0.3
0.4
0.5
0.6
Welfaregain(%CE)
Optimal common debt spread
106 / 112

OPTIMAL IDIOSYNCRATIC DEBT THRESHOLDS
1 2 3 4 5
20
30
40
50
60
70
80
Debtas%oftrendGDP
0.1 0.2 0.3 0.4 0.5 0.6
Recovery rate
30
40
50
60
70
80
90
100
Debtas%oftrendGDP
The optimal idiosyncratic debt threshold changes almost one to one with the average
debt level in the no-rule economy.
107 / 112

OPTIMAL IDIOSYNCRATIC SPREAD THRESHOLDS
0.1 0.2 0.3 0.4 0.5 0.6
Recovery rate
0
0.5
1
1.5
2
2.5
3
Annualspread(in%)
1 2 3 4 5
0
0.5
1
1.5
2
2.5
3
3.5
4
Annualspread(in%)
108 / 112

SIMILAR WELFARE GAINS ACROSS β
0.95 0.96 0.97 0.98 0.99
β
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6Welfaregain(%CE)
109 / 112

OPTIMAL IDIOSYNCRATIC BRAKE THRESHOLDS (β)
0.95 0.96 0.97 0.98 0.99
β
0
1
2
3
4
5
6
Annualspread(in%)
0.95 0.96 0.97 0.98 0.99
β
30
40
50
60
70
80
90
Debtas%oftrendGDP
110 / 112

WE SHOW THAT
A “common spread-brake” fiscal rule mitigates the deficit bias in
economies with different levels of debt intolerance.
A “common debt-brake” fiscal rule does not.
Why? The spread incorporates information about debt
intolerance.
It may be much easier to enforce a spread brake than to enforce a
debt brake.
Overall, the sovereign spread may work better than the debt level
as a common and robust fiscal anchor.
111 / 112

OPTIMAL “COMMON AND ROBUST” FISCAL
ANCHOR
Consider a set of heterogenous economies indexed by the value of
the parameter θ ∈ {ϕ, σy, β}.
v(x; θ) = period 1 expected utility in an economy with a Ramsey
planner that chooses instrument x.
h(θ) = density function for θ in the set.
112 / 112

Fiscal rules and the sovereign default premium

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