CHAPTERS IN ECONOMIC POLICY
Part. II
Unit 8
The dynamics of debt to GDP ratio
The Arithmetic of Deficits and Debt
–The budget deficit in year t equals:
deficit t  rBt 1  Gt  Tt
rBt 1 is the interest payments on the debt
Gt is government spending during year t.
Tt
is taxes minus transfers during year t.
In words: The budget deficit equals spending,
including interest payments on the debt, minus
taxes net of transfers.
- Note that we measure interest payments as real
interest payments rather than as actual interest
payments. The correct measure of the deficit is
sometimes called the inflation-adjusted deficit
The Arithmetic of Deficits and Debt
•The government budget constraint states that
the change in government debt during year t is
equal to the deficit during year t:
Bt  Bt 1 deficitt
•It is often convenient to decompose the deficit
into the sum of two terms:
 Interest payments on the debt, rBt-1
 The difference between spending and taxes,
Gt-Tt. This term is called the primary deficit
(equivalently, Tt –Gt is called the primary
surplus).
The Arithmetic of Deficits and Debt
Bt  Bt 1
change in the debt

rBt 1
interest payments

Gt  Tt
Primary deficit
Bt  (1  r ) Bt 1  Gt  Tt
The debt to GDP ratio
- In an economy in which output grows over time, it
makes sense to focus on the ratio of debt to
output
-The debt-to-GDP ratio, or debt ratio gives the
evolution of the ratio of debt to GDP.
The Arithmetic of the Debt Ratio
Bt
Bt 1
Bt 1 Gt  Tt

 (r  g )

Yt
Yt 1
Yt 1
Yt
It is possible to demonstrate that the change in
the debt ratio over time is equal to the sum of
two terms.
- The first term is the difference between the real
interest rate and the growth rate times the initial
debt ratio.
- The second term is the ratio of the primary
deficit to GDP.
The Evolution of the Debt Ratio
in OECD Countries
Bt Bt 1
Bt 1 Gt  Tt

 (r  g )

Yt Yt 1
Yt 1
Yt
This equation implies that the increase in the ratio of debt
to GDP will be larger:
- the higher the real interest rate,
- the lower the growth rate of output,
- the higher the initial debt ratio,
- the higher the ratio of the primary deficit to GDP
The Evolution of the Debt-to-GDP Ratio in OECD
Countries
Bt Bt 1
Bt 1 Gt  Tt

 (r  g )

Yt Yt 1
Yt 1
Yt
- In the 1960s, GDP growth was strong. As a
result, rg was negative. Countries were able
to decrease their debt ratios without having to
run large primary surpluses.
- In the 1970s, rg was again negative due to
very low (and even negative) real interest
rates, leading to a further decrease in the debt
ratio.
The Evolution of the Debt-to-GDP Ratio in OECD
Countries
Bt Bt 1
Bt 1 Gt  Tt

 (r  g )

Yt Yt 1
Yt 1
Yt
- In the 1980s, real interest rates increased and growth
rates decreased, thus, debt ratios increased rapidly.
- Throughout the 1990s, interest rates remained high
and growth rates low. However, most countries ran
primary surpluses sufficient to imply a steady decline
in their debt ratios.
- So far, during the 2000s, real interest rates are low,
but many countries are running primary deficits, and
their debt ratios are again going up.
- High public debt and economic policy
Let’s start from the equation:
[(Bt /Yt)  (Bt-1 /Yt-1)] = (rg)(Bt-1 /Yt-1)+(GtTt)/Yt
Let’s assume
r = 3%;
g = 2%
Bt-1 /Yt-1 = 100%
•
-In order to have a constant debt/GDP ratio, a 1% primary
surplus is sufficient
Let’s assume now that, to counteract speculation in the
currency market, the central bank is forced to increase
domestic interest rate
As a consequence, the real interest rate is likely to increase
(e.g to 5%) and the GDP growth rate to decrease (e.g.
to 1%)
In order to have a constant debt/GDP ratio, a 4% primary
surplus is now needed
This however implies a severely restrictive fiscal policy
which could bring to a recession (g0)
In this context debt to GDP ratio is likely to increase,
fuelling adverse expectations in the financial
markets
As a consequence: increase of interest rates to
compensate the investors of the risk of default
Likely outcame: default