Scotland could lose a billion pounds a year within a decade under plans to give Holyrood greater tax and welfare powers, according to a highly respected economic think tank.

Experts called for a “public debate” around how ministers achieve greater devolution.

Earlier this week peers urged David Cameron to halt his flagship Scotland Bill, currently going through Westminster, warning that "nobody knows what is going on".

A new report by the Institute for Fiscal Studies (IFS), the University of Stirling and the Centre for Constitutional Change, funded by the Nuffield Foundation, focuses on the so-called 'fiscal framework' which will distribute money between London and Edinburgh under the plans.

The paper looked at the options for how the current arrangements could be adjusted and found that the differences could be as much as £1 billion a year after just over 10 years.

The report’s authors also warn that it is impossible to reconcile the principle that devolution of powers should cause ‘no detriment’ with the Barnett Formula, the controversial calculation which determines how money is allocated to the devolved nations.

They suggest a reassessment of the UK's finances – including of Barnett.

David Cameron committed to keep the formula last year part of the 'Vow' made by the main pro-Union party leaders in the run up to the independence referendum.

David Bell, Professor of Economics at the University of Stirling and Fellow of the Centre on Constitutional Change and a co-author of the report, said: “The options available for calculating the block grant adjustments, and other elements of the fiscal framework will have major effects on Scottish Government’s budget and the fiscal risks and incentives it faces. These issues should be part of the public and parliamentary debate, as much as the tax and welfare powers set out in the Scotland Bill itself have been.”

David Phillips, a senior research economist at the IFS and another author of the paper, adds, “It may now be time for a more fundamental reassessment of how the devolved governments are financed: including whether the Barnett Formula should be reformed.”

On Friday the influential House of Lords Economic Affairs Committee warned that the process of giving Holyrood more tax and welfare powers was being done with "undue haste" and too little assessment of the consequences.

The so-called "fiscal framework" will decide how money should be distributed after Scotland's get new powers.

A deal on the system was supposed to have been hammered out over the summer, but the two governments have been unable to agree.

Leading Scottish economist Professor Anton Muscatelli, the principal of Glasgow University, has also warned that the wrong framework could cost Scotland millions of pounds.

John Swinney, the Deputy First Minister, has said that Scottish ministers would support the Scotland Bill only “if there is a satisfactory and fair fiscal framework agreed between the Scottish and UK Governments. We will never sell the people of Scotland short.”

Last night Scotland Office Minister Andrew Dunlop said that there was no reason not to reach a deal, but rejected a rethink of the Barnett Formula.

He described negotiations between the two governments as collaborative and constructive.

He added: “There is a huge amount on which John Swinney and I, and indeed both of Scotland’s Governments, agree about on this issue, so now is the time to deliver what we have both committed to – the best possible deal for Scotland.

“As a number of Peers and academics have pointed out, there are issues which will need to be resolved, but one thing is clear - both governments want a deal which will stand the test of time. We both want to retain the Barnett Formula. And we both want the Parliamentary process which will deliver the Scotland Bill to continue.”

The framework is the mechanism which will underpin the transfer of a huge swathe of powers, including control over income tax and a significant proportion of the welfare budget, from Westminster to Holyrood, as recommended in the Smith Agreement and delivered in the Scotland Bill."