The Liberal Democrats propose to increase the income tax personal allowance to £10,000 while keeping the level of income at which people start to pay the higher rate of tax unchanged. They say this giveaway would cost £16.8 billion in 2011-12. They also propose a set of significant tax-raising measures:

• Reforming air passenger duty to operate per flight instead of per passenger and introducing additional tax for some domestic flights, to raise £3.3 billion
• Introducing an annual 1% tax on domestic property values above £2m, to raise £1.7 billion
• Introducing an additional 10% tax on the profits of UK banks (with no offset for losses) until bank regulation is fundamentally reformed, to raise £2.2 billion
• Restricting tax relief on pension contributions to the basic rate, to raise £5.5 billion
• Reducing the capital gains tax allowance from £10,100 to £1,000 and taxing capital gains above this at marginal income tax rates, to raise £1.9 billion
• Introducing anti-avoidance and anti-evasion measures to raise £4.6 billion

In total, the Liberal Democrats estimate that these tax increases would raise £19.2 billion in 2011-12, £2.4 billion more than the cost of their income tax cut. We will be releasing a full analysis of this package - and all of the main parties' tax and benefit proposals - in the coming days. But what can we say by way of an initial assessment of whether the sums add up?

Increasing the personal allowance to £10,000 does indeed look like it would cost around £16.8 billion (or at most a billion or so more), assuming that people do not change their behaviour in response to the tax cut. In practice it would encourage more families to have someone in paid work (and paying taxes), thereby reducing the cost.

Whether the tax raising proposals would raise what the Liberal Democrats expect is much more uncertain. They could raise more or less.

For the reforms to aviation taxation, the Liberal Democrats suggest that they would set the rate as high as is necessary to achieve the £3.3 billion extra revenue they want. That is perfectly feasible.

On the taxation of 'mansions', banks, pensions and capital gains, the data that are publicly available do not allow us to give a definitive costing. To arrive at their figures, the Liberal Democrats have had to make numerous assumptions. Some of these assumptions are questionable, and there are some mistakes, but while in some cases that implies raising less revenue than the Liberal Democrats estimate, in other cases it implies raising more. Their estimates for the mansion tax, the bank tax and the restriction of pensions tax relief do not seem unduly optimistic, while the reforms to capital gains tax would probably raise substantially more than the £1.9 billion they suggest. But there is a great deal of uncertainty around all these costings, given the paucity of relevant data available.

The estimate that £4.6 billion would be raised from their anti-avoidance and anti-evasion measures looks highly speculative. The Liberal Democrats have not attempted to estimate directly the impact of most of the measures they specify; they simply assume particular proportions of the total 'tax gap' attributable to evasion and avoidance that they think they could fill. Whether their approach would really raise so much more than the Government's continuing strenuous efforts must be open to question. For example:

• In estimating the revenue that a General Anti-Avoidance Principle (GAAP) would generate, they assume that they can recover a percentage of the revenue the Government thinks it loses from both 'avoidance' and differences in 'legal interpretation'. Yet a GAAP of the kind they describe would do little to address the latter, and so the fraction of 'avoidance' alone that a GAAP would need to eliminate to raise the same total is much larger than the Liberal Democrats assume.
• Resources to tackle evasion are supposed to be freed up by the 'simplification' of the tax system implied by their other reforms and from a new commercial arm of HMRC set up to provide a pre-clearance service to underpin the GAAP. But it is not clear that their other reforms would reduce the cost of administering the tax system: there would be fewer income tax payers, but more capital gains tax payers, and it is far from clear that the pensions tax reform would reduce the demands on HMRC as the Liberal Democrats suggest. And the proposed new commercial arm of HMRC has to meet the costs of a pre-clearance mechanism before having anything left over to spend tackling evasion. To assume that a combination of profitable pre-clearance activities and 'simplification' would generate enough spare resources to stop £1.4 billion of evasion seems optimistic.

Beyond these concerns, the fractions of evasion and avoidance that the Liberal Democrats claim their measures would eliminate are assumed arbitrarily (though in fairness we have no way to estimate them more accurately). They may be too high or too low. The Liberal Democrats acknowledge this uncertainty and describe their £4.6 billion figure as a 'target', but they are relying on the revenue to fund their income tax cut.

So what is the overall picture?

We can be pretty confident that the Liberal Democrats' headline giveaway would cost roughly what they claim. Whether the revenue raising measures would yield what they expect is much more uncertain - and we cannot even say with confidence whether they are more likely to raise too much revenue or too little. On the one hand, their estimates of the revenue to be raised from tackling avoidance and evasion seem optimistic; on the other hand, the estimates of the revenue to be raised from the rest of the package if anything look pessimistic. The only way to find out for sure would be to suck it and see.