3.2 Evolution of Debt/GDP, cases of Debt/GDP

Question 1

What was the pattern of debt-GDP ratio?

Answer 1

Between 1974 and 1990 - explosive path towards affordable

Constant ratio 1990-2007

Explosive path towards unaffordable post 2007

Question 2

What is the relationship between deficits and debt?

Answer 2

Smaller deficit means less debt, bigger deficit means more debt
- The fact they aren’t the same suggests other factors play an important role

Question 3

WHat is government debt? How is the budget deficit modelled?

Answer 3

Accumulation of current and past deficits - debt owed by the government (= stock of bonds Bt)

Budget deficit is difference between government expenditures (incl. interest on debt), and its receipts (mostly from tax):

Model is shown on week 3 page 3

Deficit = real interest paid on bonds + government spending - taxes

(G - T) known as the primary deficit

deficitt = rBt-1 + Gt - Tt

rBt-1 = interest paid on bonds
Gt = government spending
Tt = taxes transfers in year t

Question 4

How does the debt/GDP ratio evolve? What does this tell us?

Answer 4

Bt/Yt - Bt-1/Yt-1 = (r-g) ((Bt-1)/ (Y-1)) + (Gt - Tt / Yt)

1. Tells us the change in debt ratio is equal to the sum of two terms:
2. Difference between real interest rate (r) and growth of GDP (g), multiplied by the debt ratio at the end of the previous period
   - The growth rate of the economy and interest rate are other factors
3. The second term is the ratio of the primary deficit to GDP

Question 5

How do we capture trends in the debt?

Answer 5

We study the evolution holding r, g and primary deficit constant:

Bt/Yt = (1+r - g)*(Bt-1)/(Yt-1) + (Gt-Tt)/Yt

1 + r - g is parameter B

Bt/Yt is debt ratio

Gt - Tt / Yt is the exongeous variable or the linear equiation

Assumption:
- Government runs primary deficits (or surplus) in relation to GDP that are constant over time, namely that Gt - Tt / Yt is constant

• Also that r and g are constant

Question 6

What is the graph we use to show the debt/GDP cases

Answer 6

The x axis is debt at t-1, the debt ratio Bt/Yt

The y axis is debt at t, the debt ratio holding r,g and primary deficit constant Bt/Yt = (1+r-G)*(Bt-1)/(Yt-1) + (Gt-Tt)/Yt

The slope is 1+r-g

A line at 45 degrees is also presented on the line

Question 7

What is the case of explosive unaffordable debt?

Answer 7

• If initial debt zero, the debt (amount of bonds, B, needed) equals Gt-Tt/Yt - exogenous variable / linear equaiton - also the Y intercept which is positive

When the lines intersect, the debt/GDP ratio isan equilibrium where debt ratio is constant - that equilibrium may not be stable

Dynamics of debt/GDP in the long run:
- If growth < interest rate (the slope is steep), and the country runs a primary deficit, the debt ratio increases over time

Question 8

What is the effect of explosive unaffordable debt in the long run?

Answer 8

• Worst case to be in - fears government could go bankrupt

In the long run, if growth < interest rate (steep slope), and the country runs a primary deficit - the debt ratio increases over time

Question 9

What is the case of explosive debt, but affordable? What are the dynamics of this in the long run

Answer 9

On debt/GDP ratio moving downwards

The Y intercept is negative:

g < r and Gt-Tt < 0

The points intersect with the 45 degree curve. At the point of intersection there is a constant ratio of GDP
- Not stable in this case - if moves 1 pence away from this debt ratio will never return to the point

Long run dynamics:
- Even if g < r (steep), the debt ratio decreases over time because the govenrment runs an ‘adequate’ primary surplus (intercept is negative)

• If you want to reduce the ratio then run a surplus to achieve this

Question 10

What is the case of stable debt - but is it affordable?

Answer 10

Y intercept positive
- Government has a deficit
- GDP increasing quickly, expanding capacity of the government to generate revenues through taxes
- MAkes debt to GDP ratio grow more slowly

Dynamics in long run:
- If g>r, debt ratio converges to equilibrium level despite presence of primary deficits (Gt>Tt > 0)

The debt is stable - converges to constant value of GDP

Is it affordable? - 40% of the time yes, 100% no

Question 11

What is the case of stable debt when it is affordable?

Answer 11

• Intersect is at a negative rate - savings
• Y intercept negative - in primary deficit

Dynamics in long run:
- If g > r and government runs primary surplus, then debt ratio always converges to its equilibrium level - means government has savings

Question 12

How can we simplify the diagram of affordable stable debt?

Answer 12

We use a diagram with 3 lines:

1. Debt/GDP
2. Deficit/GDP
3. Bank rate - Growth rate of nominal GDP

Graph shown on page 4 of week 3