```Fiscal consolidation:
Dr Pangloss meets Mr Keynes
by
Marcus Miller and Lei Zhang
Debt unsustainability and measure to
correct this
Variables used are defined as follows:
Parameter
Definition
b
Level of debt/capacity output - endogenous
g
Government expenditure/capacity output - endogenous
θ
Tax revenue as a fraction of capacity output
r
Cost of debt service as a fraction of capacity output
γ
Rate of capacity growth,
π
Rate of inflation
2
Debt sustainability and government
expenditure
b
B
Bond Accumulation  = ( −  − ) +  −
=0
Tax take
b0
b*
A0
A2
A1
A
E
r-γ-π
B
g*
θ
g
3
From a point such as A1, where the sum of expenditure and interest
charges (adjusted for growth and inflation) exceeds 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  +  − .
Let this target be chosen to be consistent with a debt target of b*;
so  ∗ = ( +) ∗
The baseline model can then be summarised in two equations:
FC
= −  −  ∗ = −  +  −  −  ∗ = −  +  −  ′
BA  = ( −  − ) +  −
where  ′ =  +  ∗ .
Or in matrix form:
−

= 1

−

′
−  −   + −
5
Fiscal consolidation with capacity output:
the baseline model
b
B
=0
F
r
Tax take
A
A'
E
b*
r-γ-π
=0
F
θ'
B
g*
θ
δ*
g
6
Different speeds of consolidation
1.1
α = 0.4
1.0
α = 0.5
α=1
0.9
0.8
0.7
0.36
0.37
0.38
0.39
0.40
0.41
0.42
7
Fiscal fatigue defines an upper debt limit
b
B
“Fiscal fatigue” of Barr et al.
=0
b
F
Tax take
r
A'
A
E
b*
r-γ-π
=0
g
F
B
g*
θ
δ*
θ'
g
8
Fiscal consolidation with endogenous
income and taxation:
BB flatter to left of MM; equil shifts up FF.
=  − π − γ  +  −  + (0 − )
−∝

= 1−

−

′
+
−−
0 −
9
Fiscal stabilisation works, but with
temporary recession
b
B
M
Recession
B′
=0
No Recession
Higher debt
with lower
tax take
F
r
C
A
Tax take at
capacity
output
E
b*
r-γ-π
=0
M
g*
F
θ
δ*
B
θ′
g
10
Simulation results which converge to full
employment in the long-run
0.80
With endogenous
taxes
0.75
0.70
Baseline case
0.65
0.380
0.382
0.384
0.386
0.388
11
Fiscal consolidation – waiting and hoping
b
Regime switches
B
M
D
Temporary
recession
No recession
=0
F
r
Tax take at
capacity output
A'
E'
C
A
E
b*
X r-γ-π
=0
M B
D
g*
F
θ'
θ
δ*
g
12
Simulations during the period of waiting and hoping
1.6
With endogenous
taxes
1.4
1.2
1.0
Baseline case
0.34
0.36
0.8
0.40
0.42
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
0.90
0.85
With endogenous taxes
0.80
0.75
0.70
0.65
Baseline case
0.36
0.40
0.42
15
Fiscal consolidation defeated by high interest rates
b
U
Explosive path of debt
F
r
=0
B′
=0
S
A
E
S
F
U
θ
δ*
θ′
B′
g
16
Failed attempts to stabilise
b
F
M
=0
=0
B′
0
Z
A
S
Z
b*
E
S
−−
1−
M
g*
F
θ
θ′
δ*
g
17
DeLong and Summers: stabilisation delays fiscal
consolidation, with higher taxes to cover debt
interest
b
B
M
D
=0
C
F
r
A
E´
b**
b*
E
F
r-γ-π
=0
M
g*
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
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)
Equity base
22
Conclusion
• Have used simple multiplier to capture private
sector reaction to public sector consolidation.
• Far preferable explicitly to model private and
public sector behaviour as they engage in a
dance of deleveraging, but…
• Koo warns of balance sheet recession that will
result.
• Is it true that credibility rules out state
contingent policy?
23
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