After three years of the most intense debate about Scotland's future, could the sum total be a restoration of the Barnett Formula?

The present deadlock between the UK and Scottish governments over the “fiscal framework” for tax devolution, we are told, is to be broken by the reinvention of the much-derided calculus devised on the back of an envelope by the former Labour treasury secretary Lord Barnett in 1978.

If reports are accurate, the UK and Scottish governments are approaching a deal under which the underlying principle of the Barnett formula – that Scotland should not lose out in terms of spending relative to England simply because of economic and population factors beyond its immediate control – is to be restored.

Except that this can't be the case. There are very complex mathematics involved and incomprehensible formulas relating to “per capita index deduction”. But, ultimately, there is no way of taking the risk out of a system that is intended to devolve risk. And there is no way short of full tax devolution to resolve the anomalies arising from devolving one tax – income tax – in isolation.

As this column has argued since the Scotland Bill first emerged, the Barnett Formula will be effectively phased out by the new tax powers originally proposed by the Smith Commission.

Barnett is a fixed formula based on per capita increases in spending in UK departments. Under a system in which taxation is being devolved, this fixed parity can no longer exist.

Some people argue that Barnett still exists for the “bit that isn't devolved”: the residual block grant. But the principle that increases in Scottish spending per head should more or less match increases in UK spending could not possibly continue when half of all the revenue raised in Scotland becomes variable.

As economists such as Professor Anton Muscatelli rightly point out, because Scotland's population is falling relative to England's there is every likelihood that Scotland could lose out in public spending.

Indeed, this was exactly what many Tory critics of Barnett wanted to see. They are convinced that English taxpayers have been subsidising Scotland's free tuition fees, free prescriptions and free personal care. They haven't, of course, precisely because Barnett was not variable.

The Scottish Government did not have the power to increase the Barnett cash to pay for what some Labour politicians call the “free stuff”. It had to meet the cost of elderly care and free higher education from economies elsewhere.

This was a hard task, but the Scottish Government managed to make the sums work because the Barnett allocations in the early years of this century have been quite generous. This was in part because so much of the Scottish budget was composed of health spending: around one third of it.

The steady increases in spending – Barnett consequentials – gave Scottish governments a heap of cash, some of which they discreetly diverted to other purposes. This is why spending on health did not rise in real terms as fast as it did in England.

But all good things must come to an end and the UK has changed. The Scotland Bill came up with a wizard wheeze: reduce UK welfare spending and then give the Scottish Government powers to raise income tax to compensate benefit claimants. This would hoist the Scots on their own social democratic petard.

The supposed “no detriment” clause could never work, because Scotland only has powers to raise or lower income tax – not national insurance, corporation tax, excise duties or any of the other major sources of revenue. It can't increase wealth taxes.

You can't overcome this fatal imbalance through mathematics. Nor can you factor out changes in the UK immigration policy that fundamentally affect population growth. Come to that, you can't counter the fundamental imbalances of wealth and opportunity that arise from the increasing centralisation of economic life in London and the south east.

The fiscal framework can be made fairer – marginally. But the Scottish Government has landed itself in a fiscal trap, and no amount of algebra will get it out. The “no detriment” rule can in theory work on day one but not thereafter.

Barnett was never perfect: in fact it served over time to erode Scotland's legitimate spending differential over England. But I'm afraid it was better than anything the incomprehensible fiscal framework can deliver. And once it's gone, it's gone.