by
Marcus Miller and Lei Zhang

Variables used are defined as follows:
Parameter Definition b Level of debt/capacity output - endogenous g
θ
Government expenditure/capacity output - endogenous
Tax revenue as a fraction of capacity output r
γ
π
Cost of debt service as a fraction of capacity output
Rate of capacity growth,
Rate of inflation
2

b
B
Debt sustainability and government expenditure b
0 b*
Bond Accumulation 𝑏 = (𝑟 − 𝜋 − 𝛾)𝑏 + 𝑔 − 𝜃
𝑏 = 0
A
0
A A
1
Tax take
A
2
E r-γ-π g*
B
θ g
3

From a point such as A
1
, 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 𝑟𝑏 + 𝑔 − 𝜃 .
Let this target be chosen to be consistent with a debt target of b*; so 𝛿 ∗ = (𝛾 +𝜋)𝑏 ∗
The baseline model can then be summarised in two equations:
FC 𝑔 = −𝛼 𝑆 − 𝛿 ∗ = −𝛼 𝑟𝑏 + 𝑔 − 𝜃 − 𝛿 ∗ = −𝛼 𝑟𝑏 + 𝑔 − 𝜃 ′
B A
𝑏 = (𝑟 − 𝜋 − 𝛾)𝑏 + 𝑔 − 𝜃 where 𝜃 ′ = 𝜃 + 𝛿 ∗ .
Or in matrix form: 𝑔
𝑏
=
−𝛼 −𝛼𝑟
1 𝑟 − 𝜋 − 𝛾 𝑔 𝑏
+ 𝛼𝜃 ′
−𝜃
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b
B
Fiscal consolidation with capacity output: the baseline model
F r
𝑏 = 0 b*
A' A
Tax take
E g* r-γ-π
B
θ 𝑔 = 0
F
θ'
δ* g
6

0.36
0.7
0.8
0.9
1.0
1.1
Different speeds of consolidation
α = 0.4
α = 0.5
α = 1
0.37
0.38
0.39
0.40
0.41
0.42
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b
B
Fiscal fatigue defines an upper debt limit
“Fiscal fatigue” of Barr et al.
b
F r
𝑏 = 0 b* g
A
A'
Tax take
E g* r-γ-π
B
θ 𝑔 = 0
F
θ'
δ* g
8

Fiscal consolidation with endogenous income and taxation:
BB flatter to left of MM; equil shifts up FF.
𝑏 = 𝑟 − π − γ 𝑏 + 𝑔 − 𝜃 + 𝜑( 𝑔
0
− 𝑔) 𝑔
𝑏
=
−∝ −𝛼𝑟
1 − 𝜙 𝑟 − 𝜋 − 𝛾 𝑔 𝑏
+ 𝑔 𝛼𝜃′
0
− 𝜃
9

b
B
Fiscal stabilisation works, but with temporary recession
B′
F r
𝑏 = 0
Recession
M
No Recession
Higher debt with lower tax take
C b*
M g*
E
A r-γ-π
Tax take at capacity output
F
θ 𝑔 = 0
B
θ′
δ* g
10

Simulation results which converge to full employment in the long-run
0.80
With endogenous taxes
0.75
Not cyclically adjusted
0.70
Baseline case
0.65
0.380
0.382
0.384
0.386
0.388
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b
B
F r
Fiscal consolidation – waiting and hoping
Regime switches
D
Temporary recession
M
No recession
𝑏 = 0
E'
A'
E
C
Tax take at capacity output
A b*
D
X r-γ-π g*
M B
θ 𝑔 = 0
F
θ'
δ* g
12

Simulations during the period of waiting and hoping
0.34
With endogenous taxes
1.6
Baseline case
0.8
0.36
1.4
1.2
Not-cyclically adjusted
1.0
0.40
0.42
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b
B
Tightening fiscal policy to hit the debt target, b*
Recession
M
No Recession
B'
F
F' r b*
E'
Tax take at capacity output
E
D
E g
D
B' g*
M
θ
B F'
δ*
F
θ' g
14

Simulations showing the effect of the tightening of structural deficits
With endogenous taxes
0.90
0.85
0.80
0.75
Not cyclically adjusted
0.70
0.65
0.36
Baseline case
0.40
0.42
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b
Fiscal consolidation defeated by high interest rates
F r
B′ 𝑔 = 0
𝑏 = 0
S
U
Explosive path of debt
E
A
U
θ
δ*
F
θ′
B′
S g
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b
F
B′ 𝑏
0
𝑏 = 0
S 𝑔 = 0
Z b*
E
M
A
Z
Failed attempts to stabilise
S g*
M 𝑟 − 𝜋 − 𝛾
1 − 𝜑
F
θ
δ*
θ′ g
17

b
B
DeLong and Summers: stabilisation delays fiscal consolidation, with higher taxes to cover debt interest
M
D
𝑏 = 0
F r
C b** b*
A
E´
E
F r-γ-π g*
M B
θ 𝑔 = 0
F
θ′ θ′′
δ* g
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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
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BEFORE: Investors holds sovereign bonds - but are prone to switch
Private
Investors
Lucky
Sovereigns
“Flight to safety”
Unlucky sovereigns face high spreads
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:
(a) Plain vanilla
(b) Growth and GDP-linked
Liabilities
Euro stability bonds
Equity base
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• 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?
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