# Debt, deficits and fiscal arithmetic

Fiscal austerity – defined as the reduction in the structural (primary) budget deficit – might be politically popular, but is it necessary from an economic perspective?

I ask this because the current Conservative government expects to eliminate the budget deficit by the middle of the next decade. So, the deficit reduction programme, which has been in place since 2010, will continue into the 2020’s. But should it? Are balanced budgets necessary to achieve sustainability in the public finances?

No. A balanced budget, or a budget surplus for that matter, are neither necessary nor sufficient to achieve fiscal sustainability [1].

One way to approach this issue is to evaluate the math – the fiscal arithmetic. We can demonstrate that ‘balancing the books’ is unnecessary to achieve fiscal sustainability by using the following simple equation:

### d = b*[(r-g)/(1+g)]

where d is the primary budget balance, b is the public debt to GDP ratio, r is the real interest rate and g is real rate of trend growth.

The right side of the equation provides the primary budget balance (the budget balance excluding interest payments), as a proportion of national income, required to stabilise the public debt to GDP ratio.

At present, d is 85.8 percent and r (measured by the 10 year gilt yield, adjusted for inflation) is minus 1.03 percent. Now, let’s assume that the trend real rate of growth is somewhere around 1.5 percent. Then, the primary budget balance required to stabilise the ratio of public debt to national income is equal to minus 2.1% of GDP.

In other words, the current government can run a primary deficit of 2.1% of GDP whilst also observing a decline in the public debt (as a proportion of national income). This certainly does bring the governments fiscal targets into question, particularly the targets for the primary deficit. The primary budget is currently envisaged to be brought into balance by 2020/21. But we have just mathematically proven that this is unnecessary.

To understand why (from a different perspective), suppose that the primary budget is in balance. Then, with the real rate of growth above the long-term real interest rate, national income will increase more than the interest payments add to the debt so, ultimately, the ratio of government debt to GDP will decline. Therefore, the government could borrow more and still reduce the debt to GDP ratio. This is in large part because the state is able to finance its borrowing at negative real interest rates.

It is now, I hope, demonstratively clear that pursuing a balanced budget, through austerity, is currently an unnecessary endeavour – that is if the purpose is to achieve sustainability in the public finances, and stabilise or reduce the ratio of public debt to national income.

[1] There is no agreed upon, precise definition of fiscal sustainability but here I have defined it to be where the debt-to-GDP ratio is constant.