Discusses the sustainability of the federal debt using debt dynamics and the structural primary balance

1. Another slideshow from
Ed Dolan’s Econ Blog
http://dolanecon.blogspot.com/
Structural Primary Balance
and Debt Dynamics
November 28, 2012
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look at my textbook, Introduction to Economics, from BVT Publishers.
Please go to the new version
of this slideshow, posted on
November 30, 2015
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orial-is-the-government-debt-out-of-control

2. November 28, 2012 Ed Dolan’s Econ Blog http://dolanecon.blogspot.com/
Sustainable Fiscal Policy
What does it mean for fiscal policy to be sustainable?
Possible answers:
1.Policy is sustainable as long as the government is
solvent, that is, it can meet its financial obligations as
they come due
2.It is sustainable if the ratio of debt to GDP does not
grow without limit
3.Fiscal policy is sustainable if it follows rules and
procedures that serve a rational public purpose
This slideshow is concerned with the second meaning of
sustainability, sometimes called “mathematical
sustainability.” See Ed Dolan’s Econ Blog for Nov. 28,
2011 for a discussion of all three meanings
Photo source: John Cummings,
http://commons.wikimedia.org/wiki/File:US_Capitol_Buildin
g,_sunset.JPG

3. Variables of the Model
Let . . .
 GRO = growth rate of GDP
 EXP = government expenditures1
 REV = total tax revenue
 PGMEXP = program expenditures, that
is, all expenditures except interest
 DEBT = government financial liabilities2
 R = rate of interest on the debt
 INT = interest expenditures = R*DEBT
 OBAL = overall budget balance
= (EXP-REV)
 PBAL = primary budget balance
 SPB = structural primary budget balance
Notes:
1 All variables except R expressed as ratios to GDP
2 DEBT includes all of the government’s net financial liabilities to the
private sector, including interest-bearing debt and monetary liabilities
(currency plus bank reserve deposits at the central bank)
Definition: The primary budget
balance is the budget balance
excluding interest expense
PBAL = REV - PGMEXP
PBAL = OBAL + R*DEBT

4. Automatic fiscal stabilizers
 During a cyclical downturn, the
economy is said to have a negative
output gap
 Automatic stabilizers are budget
elements that automatically move
the budget toward deficit curing a
cyclical downturn, for example:
Income taxes
Unemployment benefits
 By adding to aggregate demand
during downturns, automatic
stabilizers moderate the business
cycle

5. Current vs. Structural Budget Balance
 The current balance of the budget
is the measured value each year of
taxes minus expenditures
 The structural balance (sometimes
called the cyclically adjusted
balance) is the current balance
minus the contribution of automatic
stabilizers
 The structural balance shows what
the current balance would be under
current laws in force if the output
gap were zero

6. Structural Primary Balance
 A country’s Structural primary
balance (SPB) is the primary
budget balance that would exist
given current tax and expenditure
laws if there were no output gap
 The chart shows structural primary
balances for 2011 for selected
OECD members

7. Structural Primary Balance as an Indicator of Sustainability
 The structural primary balance is a
useful indicator of the mathematical
sustainability of fiscal policy
 The equilibrium value of SPB
required to maintain the debt-to-GDP
ratio at a constant value on average
over the business cycle depends on
the initial debt-to-GDP ratio (DEBT),
the rate of interest (R), and the rate
of growth of GDP (GRO)
To hold the debt ratio constant
over the business cycle, the
structural primary balance
must equal the debt ratio times
the difference between the
interest rate on the debt and
the rate of GDP growth
SPB = DEBT*(R-GRO)

8. Interest Rate vs. Growth Rate
 Typically (but not always) interest
rates on government debt run a
little higher than the rate of growth
of GDP
 When that is the case, the
structural primary balance must be
held to a slight surplus to maintain
a constant debt to GDP ratio

9. What Happens when Interest Rate > Growth Rate
If the interest rate R exceeds the
growth rate GRO, and assuming a
constant value for PBAL, the ratio of
debt to GDP
Remains constant if
SPB=(DEBT*(R-GRO))
Grows without limit if
SPB>(DEBT*(R-GRO))
Decreases without limit if
SPB<(DEBT*(R-GRO))
Note: Negative value of debt indicates
accumulation of assets in a sovereign
wealth fund
SPB=.005
SPB=.01
SPB=.015

10. Examples: Interest Rate < Growth Rate
If the interest rate R is less than the
growth rate GRO, then the ratio of
debt to GDP
Remains constant if
PBAL=DEBT*(R-GRO)
Grows to a new limit if
PBAL>(DEBT*(R-GRO))
Decreases to a new limit if
PBAL<(DEBT*(R-GRO))
SPB= -.015
SPB= -.01
SPB= -.005

11. Conclusions
 For any initial ratio of debt to GDP (DEBT), interest rate (R), and GDP growth
rate GRO, there is an equilibrium value of the structural primary balance SPB =
(DEBT*(R-GRO)). If SPB begins at the equilibrium value and remains there, the
debt-to-GDP ratio will remain constant
 If the interest rate on government debt exceeds the growth rate:
 The debt grows without limit if SPB is held at less than its equilibrium value
 The debt eventually falls to zero and the government accumulates net assets if SPB
is held above its equilibrium value,
 If the interest rate is below the growth rate and SPB is held at a constant value ,
the debt ratio eventually reaches an equilibrium regardless of the starting values
of the variables