Who will gain from the council tax freeze?

The decision to freeze council tax across Scotland next year might have been a crowd-pleasing vote-winner at the SNP conference.

A week later, it's not looking quite so clever. The proposal can be expected to go ahead, but with collateral damage to other budgets, probably to public services, relations with local councils and with Scottish Green ministers.

The policy process that led to that announcement may also have caused some damage to Humza Yousaf's relations with senior SNP ministers.

The first minister was in splurging mood when he addressed his conference in Aberdeen. This uncosted promise was in addition to £300m to reduce hospital waiting lists and £500m to anchor the green energy supply chain in Scotland.

All laudable, you might think, but with no visible means of funding them. They either involve a raid on other budgets or they're old money.

And in the case of council tax, that is money that will not now be coming into council coffers to fund public services.

The finance secretary, Shona Robison, says councils will be able to recoup the lost revenue on the council tax increase they might have introduced next April. How? By negotiation, she says.

But they have become used to being the bit of Holyrood's budget that gets squeezed hardest. Recent history suggests the outcome of these "negotiations" will mean a further squeeze.

It was pointed out to Ms Robison in the Scottish Parliament on Tuesday that she had said on 3 October to MSPs in committee that the Verity House Agreement, intended to reset bruised and battered relations with local authorities, would mean more flexibility for councils.

That flexibility was taken away from local authorities in the first minister's announcement. Ms Robison now says that she had been referring to flexibility in increasing bills on second and empty homes.

But under pressure about the way this decision was reached, she was keen instead to press her political opponents on whether they support the council tax freeze, or oppose it.

New analysis of the numbers at the Fraser of Allander Institute suggest that, in doing so, they will be supporting a policy that gives a tax break to those who already have most wealth. It favours those who live in the most valuable homes, where the top council tax bands mean the highest bills.

If your bill is frozen on what might have been say, a 5% increase, the amount that the Scottish government and councils are foregoing through this freeze is clearly bigger on the biggest bills than it is on the smallest ones.

The poorest households, on benefits, don't pay council tax, or don't pay much of it. These Strathclyde economists point out that of the 10% highest-income households, 100% will benefit from the freeze.

Only 70% among the 10% lowest income will benefit. And even less of the second-to-bottom 10%, or decile.

In cash terms, the poorest 10% of households will see savings of less than £50 next year from avoiding a 5% increase in council tax bills. The highest-income tenth of households will save around £150.

And if you assume that bills might have gone up by more than 5% next year to close the gap in council budgets, that would mean an even bigger giveaway to high income homes.

But, goes the argument, it will matter more to lower income households, as council tax is a bigger part of their outgoings? That is true, according to this analysis.

The saving made by the poorest decile, or tenth of households, averages £1 in every £400 of their budget. For the top-earning decile, a bigger cash sum can be a smaller proportion of higher income, at an average of £1 saved in every £1,600 of income.

For the 80% of people in between, the saving is much less varied, at around £1 in every £900 of income.

But this way of looking at it serves to expose two glaring problems with all this. One is that any discussion of more or less valuable homes is based on a valuation that is now 32 years old.

That's when council tax was introduced, as a sticking plaster response to the revolt over the notorious poll tax, or 'community charge'.

Now, no government is brave enough to order a revaluation. While that would surely mean many homes moving up a band or even two, resulting in higher bills, it also means some homes would be valued in lower bands.

People living in them are currently paying too much, but they don't know it, so they aren't complaining.

If you assume any revaluation would lead to the same amount of money being raised, and that all that changes would be the share of that total raised from each home, the losers would be roughly equal to the number of gainers. For every pound added somewhere, it's taken away somewhere else.

The other problem: council tax is regressive, in that it hits those on low incomes harder, as a proportion of income, than it hits those on high incomes.

That was one reason why the SNP said the council tax was "hated" when it first won office at Holyrood some 16 years ago. Its replacement was the most prominent pledge of the party's campaign in 2007. The promise was to replace it with a local income tax.

That proved to be too difficult for the first SNP government. And even when it had a majority, after the 2011 election, the party chose to freeze council tax instead of reforming it. That freeze continued for nine years, for which local authorities accumulated £70m each year.

Those were in the days of much lower price inflation. With prices now rising more steeply, the cost of compensating local councils looks much more expensive.

The calculation at the Fraser of Allander Institute is that a freeze on council tax that might have gone up 5% will require £148m in extra grant to councils. And if the councils can negotiate a deal that compensates them for an 8% increase, they would get £417m.

But that's not all they've lost. This was a special kind of giveaway to those in the big houses, because there was a plan, until Humza Yousaf's conference speech, to alter the ratio of payments between the different bands - for the second time, raising the proportion of revenue raised from the most valuable properties.

If you add the income foregone by not applying that increase, councils can claim they should get at least £180m more.

Scottish Green MSPs, and others, want this to be "fully funded".

What that means, of course, is raiding other public service, or raising other taxes. That would likely mean income tax, which is the main lever the Scottish government can pull.

So watch out for Shona Robison funding the council tax freeze with higher income tax on higher earners. Indeed, this may be a long, slow process which, deliberately or not, is gradually replacing council tax by making it less and less of the total revenue raised, to the point that it could be axed. Instead of being replaced by locally set income tax, it would be an extension of the Scotland-wide income tax regime.

The Scottish government's second big revenue earner is Land and Buildings Transactions Tax, and there is some discussion of whether the equivalent Stamp Duty Land Tax could be cut at Westminster - leaving a wider gap between Scottish and English home-moving bills.

That differential in personal and property taxes is becoming more of an issue for business groups. Recruiting high earners into Scotland becomes less attractive with higher tax bills, and that is a tax base that the Scottish government needs, both to retain and to grow.

Neither government has much room for manoeuvre, when the chancellor sets out the Autumn Statement at Westminster next month and Shona Robison publishes her draft budget just before Christmas.

The Scottish Fiscal Commission has already warned of a £1bn funding gap opening up for Holyrood's finance minister, while several public services are deemed to have unsustainable finances, most notably the health service.