Virtually all economic forecasters expect that a no-deal Brexit will be economically harmful for the UK, at least in the short to medium term. If you believe what you have seen written on the sides of buses, it might seem like the UK’s public finances would at least benefit from no longer being obliged to contribute to the EU’s budget. But IFS researchers have found that the long-term picture for borrowing and government debt appears more complicated, and less promising.

The no-deal scenario we have analysed is a relatively benign one, based on work done by the Office for Budget Responsibility (OBR) and the International Monetary Fund (IMF) earlier this year. It assumes – unlike the government's own Operation Yellowhammer papers – that the immediate disruption can be kept to a minimum and that trade barriers between the UK and the EU will rise only gradually.

Even so, there is evidence that the direct benefit to the public finances of leaving the EU – £12bn a year that would no longer be sent to Brussels – will not make up for the economic contraction that will occur. We predict that wages and profits would be lower across much of the economy, reducing tax revenues. This will also affect the housing market – which is particularly sensitive to the economic cycle, and which contributed £12.9bn in tax revenues last year – with fewer properties being sold, and at lower prices.

A smaller economy means that even borrowing the same amount, in cash terms, adds up to an increase in borrowing as a percentage of national income – which makes that borrowing less sustainable. After adjusting the OBR’s forecast for recent developments, we've calculated a rise in annual borrowing to a peak of £92bn a year, or 4 per cent of national income, following a no-deal Brexit. This is more than double the share of national income that the government borrowed last year. These large deficits then feed through to debt. At the end of August, debt as a share of national income (excluding the Bank of England) stood at 72.7 per cent. Following a no-deal Brexit, we would expect this to rise, by 2024, to 83 per cent – the highest level of government debt since the mid-1960s.

It's possible and indeed likely that the government would react to a no-deal exit with a stimulus package. A stimulus of 1 per cent of national income – or about £22bn in today’s cash terms – in tax cuts and spending rises, deployed for two years, would increase debt by less than 1 per cent of national income. A well-aimed temporary stimulus package could smooth the transition to a smaller post-no-deal economy; it would be up to policymakers to weigh the potential benefits against the moderate increase in debt. The case for a stimulus would be strongest if it were targeted at the regions (such as the West Midlands or Northern Ireland) or industries (such as car manufacturing) that will be hit hardest by a no-deal Brexit.

And while this stimulus would add to the national debt, it would be dwarfed by the debt impact of a no-deal Brexit itself. Since 2007 debt has doubled as a share of national income, but the government’s debt interest spending has actually fallen. This is due to low interest rates, which might also strengthen the case for borrowing to invest in projects that boost economic growth or improve quality of life down the road – although identifying these projects and getting that value from them is another matter.

So, is it only ideologues who would still worry about public sector debt? Ultimately, the long-run sustainability of public sector debt – that is, whether it tends to rise or fall as a share of national income – depends on the relationship between growth and the interest rate. Policymakers might expect growth to pick up again after an anaemic decade following a no-deal exit, and they might expect interest rates to remain low. But unwinding large increases in debt as a share of national income is the work of decades. Betting on no-deal now, then, is not only a short-term risk, but a gamble on the relationship between growth and interest rates remaining favourable 30, 40 or 50 years into the future.

We also should not forget that Brexit is far from the only challenge facing the UK’s public finances. Past experience suggests that the UK goes into recession about once a decade, which might push up borrowing by another 1.75 per cent of national income for a couple of years. Longer-term pressures on the public finances from an ageing population could require spending on health, social care, and pensions to rise by another 2 per cent of national income by the end of the coming decade – and 2 per cent more by the end of the 2030s.

After almost a decade of austerity, Chancellor Sajid Javid claims to have opened the spending taps. But this doesn’t get rid of the difficult trade-offs on taxes and spending that the government, and voters, will face in the coming decades. A no-deal Brexit, by reducing the size of the pie, can only make those choices starker.

Isabel Stockton is a research economist at the Institute for Fiscal Studies.