The deficit and the debt: a flow and a stock

Overview

How a fiscal deficit differs from the national debt, budget surplus and identity of the holders of government debt matter.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Explain how a fiscal deficit differs from the national debt.

   Model answer

   A fiscal deficit is the amount by which government spending exceeds government revenue over a period, normally a financial year, so it measures how much the government has to borrow during that year. The national debt is the total amount the government owes at a moment in time, accumulated from all past borrowing that has not yet been repaid. The deficit is therefore a flow, measured in pounds per year, and the debt is a stock, measured in pounds. Each year's deficit adds to the debt, and each year's surplus subtracts from it, so the two are related as an addition is related to a total, not as two versions of the same thing.

2. 2

   Why is it useful to think of a deficit as a flow and debt as a stock, and what everyday comparison makes the distinction clear?

   Model answer

   A flow has a time dimension and only means something when a period is attached to it, while a stock is a quantity existing at an instant. The comparison that makes it clearest is a bath: the rate at which water runs from the tap is a flow, and the amount of water in the bath is a stock. Reducing the flow of new borrowing still adds water to the bath, so the debt continues to rise; only turning the tap off entirely, which means balancing the budget, stops the total growing, and only draining water, which means running a surplus, reduces it. The same logic explains why a government can truthfully announce that it has halved the deficit while the debt has grown throughout.

3. 3

   Government spending in a year is £900 billion and revenue is £820 billion, and nominal GDP is £2,000 billion. Calculate the fiscal deficit in pounds and as a percentage of GDP.

   Model answer

   The deficit is spending minus revenue, which is £900 billion minus £820 billion, giving £80 billion. As a share of GDP that is 80 divided by 2,000, which is 0.04, or 4% of GDP. Expressing it as a percentage matters because it measures the borrowing against the size of the economy that must ultimately service it, so a deficit of £80 billion means something quite different in an economy of £2,000 billion from what it would mean in one of £500 billion.

4. 4

   A country starts a year with a national debt of £2,000 billion and runs a deficit of £100 billion. Calculate the debt at the end of the year, and state what would have to happen for the debt to fall.

   Model answer

   The deficit is added to the existing stock, so the debt at the end of the year is £2,000 billion plus £100 billion, which is £2,100 billion. For the cash value of the debt to fall, the government would have to run a surplus, meaning revenue greater than spending, and use the excess to repay maturing debt. Merely reducing the deficit, from £100 billion to £40 billion for example, still adds £40 billion to the stock, so the debt would continue to rise, only more slowly.

5. 5

   Can the national debt fall as a share of GDP while the government is still running a deficit? Illustrate with figures.

   Model answer

   Yes, provided nominal GDP grows faster than the debt. Take a debt of £2,000 billion and GDP of £2,500 billion, so the ratio is 80%. Suppose the deficit is £80 billion, taking the debt to £2,080 billion, and nominal GDP grows by 4% to £2,600 billion. The new ratio is 2,080 divided by 2,600, which is exactly 80%, so the deficit of £80 billion, equal to 3.2% of GDP, is precisely the deficit that holds the ratio steady. Any deficit smaller than that would let the ratio fall even though the cash debt was still rising. This is why the growth rate of nominal income matters so much to the sustainability of public debt.

6. 6

   A country has debt of £2,000 billion and GDP of £2,500 billion. It runs a deficit of £100 billion and nominal GDP grows by 4%. Calculate the debt ratio before and after and comment.

   Model answer

   Before, the ratio is 2,000 divided by 2,500, which is 80.0%. The debt becomes £2,100 billion and GDP becomes £2,500 billion multiplied by 1.04, which is £2,600 billion. The new ratio is 2,100 divided by 2,600, which is 80.77%, so the ratio has risen by about 0.8 percentage points. The deficit of 4% of GDP was larger than the 3.2% that growth of 4% would have supported at an 80% ratio, so the debt burden increased even though the economy grew. It shows that whether a deficit is sustainable cannot be judged from its size alone; it depends on the existing debt ratio and on the growth rate of nominal income.

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