Fiscal consolidation: Dr Pangloss
meets Mr Keynes
Marcus Miller and Lei Zhang
19th June 2013
Debt unsustainability and measure to
correct this
Variables used may be defined as follows:
Parameter
Definition
b
Level of debt/capacity output
g
Government expenditure/capacity output
θ
Tax revenue as a fraction of capacity output
r
Real rate of interest, taken as exogenous
γ
Rate of capacity growth, taken as exogenous
2
Debt sustainability and government
expenditure
b
B
Bond Accumulation
𝑏 = (𝑟 − 𝛾)𝑏 + 𝑔 − 𝜃
𝑏=0
Tax take
b0
b*
A0
A2
A1
A
E
r-γ
B
g*
θ
g
3
From a point such as A1, where the sum of expenditure and growthadjusted interest charges exceeding the tax base, debt will grow
unsustainably unless some action is taken. Such action may include:
• reducing expenditure or raising tax rates;
• debt reduction via inflation or explicit repudiation;
• financial repression, i.e. lowering the rate of interest paid;
• increasing the growth rate
• a debt equity swap
or some combination of the above.
4
Let the plan for fiscal consolidation be to adjust the structural deficit,
S, so as to hit a target of δ*, where S is defined as 𝑟𝑏 + 𝑔 − 𝜃.
Let this target be chosen to be consistent with a debt target of b*;
so 𝛿 ∗ = 𝛾b*.
The baseline model can then be summarised in two equations:
FC
𝑔 = −𝛼 𝑆 − 𝛿 ∗ = −𝛼 𝑟𝑏 + 𝑔 − 𝜃 − 𝛿 ∗ = −𝛼 𝑟𝑏 + 𝑔 − 𝜃 ′
BA 𝑏 = (𝑟 − 𝛾)𝑏 + 𝑔 − 𝜃
where 𝜃 ′ = 𝜃 + 𝛿 ∗ .
Or in matrix form:
−𝛼
𝑔
= 1
𝑏
−𝛼𝑟 𝑔
𝛼𝜃 ′
𝑟 − 𝛾 𝑏 + −𝜃
5
Fiscal consolidation with capacity output:
the baseline model
b
B
𝑏=0
F
r
Tax take
A
A'
E
b*
r-γ
𝑔=0
F
θ'
B
g*
θ
δ*
g
6
Different speeds of consolidation
7
Fiscal fatigue defines an upper debt limit
b
B
“Fiscal fatigue” of Barr et al.
𝑏=0
b
F
Tax take
r
A'
A
E
b*
r-γ
g
𝑔=0
F
B
g*
θ
δ*
θ'
g
8
Fiscal stabilisation works, but with
temporary recession
b
B
M
Recession
B′
𝑏=0
No Recession
Higher debt
with lower
tax take
F
r
C
A
Tax take at
capacity
output
E
b*
r-γ
M
g*
𝑔=0
F
θ
δ*
B
θ′
g
9
Simulation results which converge to full
employment in the long-run
With endogenous
taxes
Non-cyclically adjusted
Baseline case
10
Fiscal consolidation with endogenous
income and taxation:
flattens BB to left of MM so
equilibrium shifts up FF.
𝑏 = 𝑟 − γ 𝑏 + 𝑔 − 𝜃 + 𝜑(𝑔0 −g)
−𝛼
−𝛼𝑟 𝑔
𝑔
𝛼𝜃 ′
= 1−φ 𝑟−𝛾
+
𝑏
φ𝑔0 − 𝜃
𝑏
11
Fiscal consolidation – waiting and hoping
b
Regime switches
B
M
D
Temporary
recession
No recession
𝑏=0
F
r
Tax take at
capacity output
A'
E'
C
A
E
b*
X
r-γ
𝑔=0
M B
D
g*
F
θ'
θ
δ*
g
12
Simulations during the period of waiting and hoping
With endogenous
taxes
Non-cyclically adjusted
Baseline case
13
b
Tightening fiscal policy to hit the debt target, b*
B
M
Recession
No Recession
B'
F
F' r
Tax take at
capacity
output
E'
E
b*
ED
B'
M
gD
g*
F
θ'
B F'
θ
δ*
g
14
Simulations showing the effect of the
tightening of structural deficits
Non-cyclically adjusted
With endogenous taxes
Baseline case
15
Fiscal consolidation defeated by high interest rates
b
U
Explosive path of debt
F
r
𝑔=0
B′
𝑏=0
S
A
E
S
F
U
θ
δ*
θ′
B′
g
16
Failed attempts to stabilise
b
F
M
𝑔=0
𝑏=0
B′
𝑏0
Z
A
S
Z
b*
E
S
𝑟−𝛾
1−𝜑
M
g*
F
θ
θ′
δ*
g
17
DeLong and Summers: stabilisation delays fiscal
consolidation
b
B
M
D
𝑏=0
C
F
r
A
E´
b**
b*
E
F
r-γ
M
g*
𝑔=0
B
θ
δ*
F
θ′
θ′′
g
18
Different types of stability bonds
Name
Euro-bonds
“Blue bonds”
“Elite” bonds
Debt retirement fund
Concept
Issue of common bonds to replace all
debt
Issue of common bonds up to 60% of
GDP
Common bonds only for AAA rated
countries
New entity that pools all debts above
60% of GDP, issues its own common
bonds. Countries have a credible
commitment to amortise the debt in a
certain time frame
19
BEFORE: Investors holds sovereign bonds - but
are prone to switch
Private
Investors
Lucky
Sovereigns
“Flight to safety”
Unlucky
Sovereigns
Unlucky sovereigns face high spreads
20
AFTER: Stability and growth fund pools sovereign
debt - and diversifies types of bond
Private
Investors
Stability
bonds
Stability and
Growth Fund
Lucky
Sovereigns
Growth bonds
Unlucky
Sovereigns
21
Balance sheet of SPV
Assets
Sovereign bonds:
Liabilities
(a)
Plain vanilla
Euro stability bonds
(b)
Growth and GDP-linked
Equity base
22