THE UK, as First Minister Alex Salmond is right to point out, is one of the most unequal societies in the developed world.

The 1980s and 90s saw the gulf between haves and have-nots widen hugely and, though the pace has slowed since then, the gap is still widening. The UK has the seventh highest level of income inequality in a league table of 35 developed countries. That position owes much to the extremes of wealth and poverty found in London though Scotland, on its own, would only be mid-table, with significantly higher levels of inequality than Nordic countries such as Iceland, Denmark and Norway which the First Minister admires so much.

The study published today by economists from Stirling University, part of the Economic and Social Research Council's Future of the UK and Scotland project, is important because of what the First Minister has said about inequality in the UK and our Nordic neighbours. Tackling the UK's deep-rooted equality problem and creating a fairer society more like Denmark's, he says, would be one of the great prizes of independence. Today's report does not shatter that dream. Indeed, it supports the SNP's claim in so far as it recognises that the present devolved administration (even taking income tax-raising powers, due to come into effect in 2016, into account) has only "relatively blunt tools" to tackle inequality. However the report does suggest that even an independent Scotland, with the full fiscal tool kit at its disposal, would find it extremely difficult to reduce inequality to Nordic levels. Such a shift, it says, would require fundamental economic reforms beyond simply raising taxes for the better off and establishing a more generous welfare regime for those who are struggling.

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A key factor identified by the Stirling team is the mobility of labour. If high earners faced seriously higher taxes, significant numbers would move, the study argues, reducing the effect of raising taxes in the first place. Independence would not discourage migration, at least not in the first few decades, as the economies of Scotland the UK remained closely bound together; very closely indeed, if the Scottish Government was to secure its proposed currency union. The study warns that the kind of progressive tax and welfare policies voters might expect in an independent Scotland would, on their own, fail to recreate a Scandinavian-style society.

Put a penny on the upper rate of income tax, for example, and the inequality gap between Scotland and the Nordic countries shrinks by just 1%. Even a 10% hike in Jobseeker's Allowance and Income Support - if that could be afforded - would only close the gap by 3.2%.

The study highlights the fact that the most equal societies start off without the extreme, often grotesque differences in income we are used to in the UK. To match the likes of Denmark, Iceland or Norway, an independent Scotland would have to rebalance its economy along similar lines. That's not impossible. But it would require truly radical action, over a considerable period of time, to achieve the SNP's goals.