Do we need a budget surplus to get the ratio of government debt to GDP down? There seems to be some confusion on this, so let me clarify.
George Osborne said today:
Government must ensure that debt continues to fall as a percentage of GDP, including using surpluses in good years for this purpose.
That word "including" is doing some work here, because surpluses are not always necessary to get the debt-GDP ratio down. A simple formula tells us this. It says the primary budget balance compatible with a stable debt-GDP ratio is equal to:
d * [(r-g)/(1+g)]
where d is the debt-GDP ratio, r is the long-term real interest rate and g the long-term real growth rate.
So, let's take d as 0.8 (the OBR's forecast for the peak ratio in 2015-16 and g as 0.02, a bit below the OBR's forecast. Long-term real interest rates are now negative, but let's assume they rise to 1%. Then our formula tells us that we can stabilize the debt-GDP ratio with a deficit of 0.78% of GDP.
To see this, imagine the primary balance were zero. Then with growth above the interest rate, GDP will rise by more than interest payments add to the debt, so the debt-GDP ratio will fall.
In this context, Richard Murphy is half-right to say:
We do not need a surplus: when the government has control of its currency it can run a deficit equivalent to debt multiplied by the interest rate and stand still.
He's right to say we don't need a surplus. But he's wrong to think the government's control of the currency matters in this context; the above formula holds, regardless of whether the government controls the currency or not.
However, the government is going far beyond this. The OBR envisages the primary balance - the balance excluding interest payments - going into surplus after 2016, and hitting 2.9% of GDP in 2018-19. There are three possible justifications for this:
1. As Tim says, a surplus might be necessary for demand management purposes, to cool the economy down. This, though, raises all sorts of questions of whether such management is best done by fiscal or monetary policy.
2. The government fears that interest rates will rise faster than I've assumed. A real rate of 4% - a return to what we have in the 80s - would require a surplus of 1.6% of GDP to stabilize the debt-GDP ratio. This, though, raises questions of whether "secular stagnation" will keep rates low or not. It's in this context that Richard's point about the government being able to print money does matter; printing money to buy government debt might be a way to hold interest rates down, if this is necessary (though this raises other issues).
3.It believes the debt-GDP ratio is too high now, and must fall faster than a primary deficit would permit. Again, though, this poses some tricky questions about whether debt is a burden on future generations and if so whether this is a bad thing.
Now, I don't want or need to take a view on these matters. All I wanted to do is clarify the maths of the relationship between debt and deficits. And this tells us that, at current interest rates, we don't need a surplus to reduce the debt-GDP ratio.