Ahead of this week’s Budget, the chancellor looked to be facing a seemingly impossible task.

Back in June, the prime minister announced a birthday present for the NHS amounting to more than £20 billion extra in real terms by 2023−24 for frontline services in England alone.

In her party conference speech a few weeks ago, the prime minister then said that “a decade after the financial crash, people need to know that the austerity it led to is over”.

This open-ended promise to end austerity and a bumper funding settlement for the NHS, alongside the chancellor’s ongoing commitment to deficit reduction looked as though it would make Mr Hammond’s job this week that much harder.

However, the chancellor was able yesterday to find the money for the NHS without any increase in borrowing forecasts relative to March.

How did he manage to square this circle?

In short, he was rescued by better than expected public finance figures. This was driven by higher than expected tax revenues and lower than expected spending, giving the chancellor a windfall of £12bn this year and £18bn by 2022−23.

Rather than banking this windfall, Mr Hammond chose to spend it – almost entirely on the NHS. We perhaps ought not to be surprised: evidence suggests that since 2010, chancellors are more willing to spend windfall improvements than to enact a fiscal tightening when the forecast worsens, and it was perhaps too tempting for him to loosen the spending squeeze while leaving the outlook for borrowing unchanged.

But was this enough to say that “the era of austerity is finally coming to an end”, as the chancellor put it in his speech? As is so often the case when you ask economists a question, the answer is: “it depends”.

There is no one universally accepted definition of austerity, so what it means to bring it to an end is a point of contention. If we look at overall day-to-day spending on public services (as measured by resource departmental expenditure limits, or RDEL), this is now set to rise by around 8% in real terms between this year and 2023−24, outstripping growth in the population so that per capita spending is also on an upwards trend. As a share of national income, it’s set to stay broadly flat. On this measure, then, austerity for public services does indeed appear to be over.

Remember, however, that almost all of that extra spending will go to the NHS. And the government has ongoing commitments to spend 2% of national income on defence, and 0.7% of national income on overseas aid.

We might instead think that an end to austerity means keeping those promises on the NHS, aid and defence while halting cuts to other departments’ day-to-day budgets. In fact, on this minimal definition, the chancellor’s new plans do imply an end to austerity – just.

Overall spending on those unprotected areas is set to stay flat in real terms between now and 2023−24. But this wouldn’t be enough to keep pace with growth in the population or the wider economy, so unprotected departmental spending would fall in per capita terms and as a share of national income.

Spending on those areas has already fallen by 19% in real terms since 2010−11. Make no mistake, this is certainly no spending bonanza and many public services will continue to feel squeezed in the years ahead.

And then there’s social security. Despite the chancellor’s Budget giveaways relating to universal credit, there are around £4 billion of cuts to working age benefits still in the pipeline. Clearly, austerity for those benefit recipients is far from over.

Where does this leave us?

The chancellor managed to find enough money to pay for the NHS’s birthday present and ease some of the squeeze elsewhere, all without increasing borrowing or taxes. Depending on your definition, you could point to this as the end of austerity for public services.

But we shouldn’t lose sight of the bigger picture. Planned cuts to social security remain.

Budget announcements mean that health spending will continue to grow as a share of public service spending, up from 23% in 2000−01 to 29% in 2010−11, and set to reach 38% by 2023−24.

At some point, with rising costs of service delivery and an ageing population, the government will need to take some tough decisions over how to deal with longer term pressures on public spending.

This week, the chancellor ducked those questions for another year.

This article was originally published in Public Finance Magazine and is reproduced here with full permission.