In an interview with BBC Radio 4’s Today programme on Thursday, the shadow chancellor was asked “about servicing the national debt, which costs about £48bn a year at the moment. How much would it cost under Labour every year?”

He said: “We would ensure that day to day spending was not paid for by borrowing, that we would only invest for our infrastructure and that investment would pay for itself through the growth that’s achieved, and that’s a one-for-one return.”

Later he was asked: “We all know that you would borrow to invest. The question that I’ve asked you a couple of times now is how much it would add to the servicing costs every year?”

He said that because interest rates were low, the cost in terms of the national debt would be “minimal”.

Mr McDonnell added: “We’re talking about it paying for itself. A one-to-one multiplier; that’s the standard analysis by the OBR and others.”

He went on to say: “Immediately that infrastructure [investment] puts more people back into work, they pay their taxes and as a result of that you recover your costs.”

Can borrowing more money really pay for itself immediately?

GDP growth vs tax revenue

Mr McDonnell has cited “one-for-one multipliers” to help explain his answer. These are the kind of economicky words that would impress even Michael Gove.

“Multipliers” are measures that help the government to work out how much the national wealth will grow as a result of spending.

For example, a multiplier of one-to-four means that for every pound of government spending, GDP will grow by four pounds. Different types of spending will have different multipliers.

Mr McDonnell is right to say that many economists think spending to invest in the economy has a multiplier of about one-for-one.

In fact, the Office for Budget Responsibility puts it at slightly more than that: it estimates that if the government invests an extra £1 in the economy, GDP will grow by £1.10.

So in that sense, Mr McDonnell is right that Labour’s planned investment would “pay for itself in terms of growth.”

He’s also right that interest rates are low, and so the cost of servicing the national debt would only go up slightly from extra borrowing under Labour’s plans.

But what he didn’t mention is how much Labour’s plans would add to the underlying national debt.

And the key to answering that is working out how much their investment would yield in tax revenue.

Mr McDonnell said investing in infrastructure “puts more people back into work, they pay their taxes and as a result of that you recover your costs”.

At first glance, that seems plausible.

It’s true that as GDP rises, the government can expect to receive more in taxes as consumers spend more (which provides VAT revenue) and as workers earn more (and pay more income tax).

But for every pound added to GDP, the government only gets about 35p more in tax revenue.

The chief economist at the Institute of Economic Affairs, Julian Jessop, pointed out this problem in an article earlier this year.

He says that for increased government spending to fund itself through taxes, “the fiscal multiplier would have to be implausibly high”. He estimates that the multiplier would have to be about one-to-three, “assuming a tax/GDP ratio of 35 per cent”.

Put simply, you might take Mr McDonnell’s claim that the planned investment would “pay for itself” to mean that:

£1 of government investment = £1 of GDP growth = £1 tax revenue

When in fact, the formula looks like this:

£1 of government investment = £1 of GDP growth = £0.35 of tax revenue

So it’s possible for Labour to claim that tax revenue might offset the interest on the additional debt.

But there’s no way that enough revenue could be raised to cover the additional debt itself.

Does it matter if we have more debt?

The Institute of Fiscal Studies carried out a detailed analysis of Labour’s spending plans before the last election.

They said Labour’s extra spending on infrastructure “could still be consistent with debt falling as a share of national income”.

But they said the national debt would fall much more slowly than under Conservative plans.

And Labour would have to raise taxes substantially too.

FactCheck verdict

John McDonnell said that Labour’s planned investment in the economy would “pay for itself through the growth that’s achieved”.

That part of his claim is correct: for every £1 of government investment, GDP will grow by £1 (or even slightly more).

He also said: “Immediately that infrastructure [investment] puts more people back into work, they pay their taxes and as a result of that you recover your costs.”

Mr McDonnell added that the increase in debt interest payments under Labour would be “minimal”.

But when he talks about Labour’s planned investment “paying for itself”, he’s only talking about the interest on the debt – not the debt itself.

In fact, for every £1 of additional investment, the government can only expect about 35p more in tax revenue.

So the national debt would inevitably grow under Labour plans, and take longer to pay off.

A Labour spokesman said: “As this article clearly states, John McDonnell was asked about the costs of servicing the debt on Labour’s borrowing for investment.

“The accusation that John McDonnell was not telling the ‘whole story’ is entirely unfounded and inaccurate because he was not asked and did not discuss repaying the debt – a totally different question. It is clear that John McDonnell answered the question which he was asked truthfully and factually.

“The repayment of principal is accounted for within Labour’s Fiscal Credibility Rule which mandates the next Labour government to reduce debt over the course of a Parliament.

“It is ironic and deeply disappointing that a self-styled fact check blog is factually inaccurate and seems to have misunderstood the distinction between the costs of servicing government borrowing as opposed to the repayment of the principal. ”

[Amendments were made to this article on November 25 to clarify the difference between paying the interest on the national debt and paying the debt off. The headline was changed and an incorrect figure was removed.]