Despite the planned net fiscal tightening of £123bn per year by 2016-17, the coalition government has sought to cut income tax for low-income individuals by increasing the income tax personal allowance to £10,000 by 2015-16. Significant increases to this allowance - the amount of income that is not subject to income tax - have already been implemented or announced, at a combined cost to the government of nearly £5 billion per year: it increased by £1,000 in 2011-12 to £7,475, and it will increase by a further £630 in 2012-13 to £8,105 (£700 and £210 more than it would have gone up by under default indexation rules in those years respectively).

How much more would it cost the government to meet its target of reaching a £10,000 personal allowance by 2015-16? Normal price indexation of the personal allowance (the assumption underlying the Office for Budget Responsibility's forecasts for the public finances) would mean that it would reach £8,885 in 2015-16 without any discretionary policy changes given current inflation forecasts. Compared to this baseline of £8,885, a personal allowance of £10,000 in 2015-16 would mean that tax revenues were £5.3 billion lower in that year. To reach that ambition earlier, as several Liberal Democrat and Conservative politicians have recently advocated, would reduce income tax revenues by more than this, as shown in the table below:

Note: Costs are for the year in question: if the personal allowance were subsequently increased in line with inflation (the default indexation policy), the cost would remain roughly the same. Alternatively, if the personal allowance were frozen at £10,000, the cost would fall as shown in the table.

Source: Author's calculations using the IFS tax and benefit microsimulation model, TAXBEN, run on uprated data from the 2009-10 Family Resources Survey.

These figures all assume that the threshold at which the higher 40p rate of income tax starts to be applied is unaffected. This means that higher-rate taxpayers get the same benefit from the higher personal allowance as those who remain basic-rate taxpayers. If the government wanted to lower the cost of achieving a £10,000 personal allowance, it could prevent higher-rate taxpayers from benefiting at all by reducing the threshold at which the 40p rate starts to be applied: this would reduce the cost to the Exchequer from £5.3 billion to £3.3 billion in 2015-16. This approach would lead to a significant increase, of around 600,000 in the number of higher-rate taxpayers. Under current policy proposals this would also mean that about 200,000 more families with children would lose their Child Benefit because an adult in that family would become a higher rate taxpayer after the lowering of the higher rate threshold (these Child Benefit savings would account for about £300 million of the reduced cost to government of meeting its £10,000 target in this way).

The gain from increasing the personal allowance to £10,000 in 2012-13 (without changing the higher rate income tax threshold) would be £379 a year to each individual taxpayer aged under 65 with an annual income between £10,000 and £116,210. There are three groups of individuals who would not benefit: those aged 65 or over, who already have tax allowances exceeding £10,000 (other than those with incomes above around £29,000 who see their allowance reduced to the level of the allowance for those aged under 65); those who do not have incomes high enough to pay income tax anyway (more than a third of the adult population); and those who have the personal allowance fully withdrawn as their income exceeds £120,000. Those with incomes between £8,105 and £10,000 would see their income tax liabilities fall from less than £379 to zero. A gain of £379 is of course larger as a percentage of income to a low-income individual than someone with a higher income, although it is important to remember that the poorest third of adults do not benefit at all because their incomes are already below the personal allowance.

But if we examine the distributional impact at the family level (which is normal for this sort of analysis, since we would expect at least some degree of income sharing within families) we get a different pattern to the one we might expect. This arises because two-earner couples, who tend to have higher family incomes, can benefit twice over from the increase in the personal allowance because both members of the couple would see their income tax liabilities fall by £379, meaning that they would gain £758 in total. Thus, the highest average cash gain occurs in the second-richest tenth of the income distribution (some of the richest tenth would not benefit because of the withdrawal of the personal allowance above £100,000, lowering the average gain for this group). As a percentage of income, the gain is roughly the same from just below the middle to just below the top of the income distribution, with the bottom and the very top gaining by less than this.

To summarise, the common assertion that increasing the personal allowance is progressive is true if one considers the gains across individual income taxpayers. It is not true if one considers the gains across all families as relatively few of the poorest families contain a taxpayer and two-earner couples gain twice as much in cash terms as one-earner families.

Distributional impact of increasing personal allowance to £10,000 in 2012-13, by income decile group

Notes: Income decile groups are derived by dividing all families into 10 equally-sized groups according to income adjusted for household size using the McClements equivalence scale. Decile group 1 contains the poorest tenth of the population, decile group 2 the second poorest, and so on up to decile group 10, which contains the richest tenth.

Source: Author's calculations using the IFS tax and benefit microsimulation model, TAXBEN, run on uprated data from the 2009-10 Family Resources Survey.

Some have argued that a higher income tax allowance would be a good way of introducing a short-term fiscal stimulus for the economy. In our annual Green Budget, we argued that the case for a fiscal stimulus was not clear cut, but said that if the government did choose to introduce one, it should be timely, targeted and temporary. Increasing the personal allowance does not seem to meet any of these criteria. An increase in the allowance would not be especially timely: individuals would not see the effect in their pay packets until the Autumn. It would not be well targeted: the Office for Budget Responsibility suggests that increased investment spending or spending on benefits (or indeed cuts to the main rate of VAT) would deliver a larger direct boost to the economy in the near-term. And being a long term government ambition it would not, of course, be temporary.

Increasing the income tax allowance takes low income people out of income tax. Therefore, it is the best way of focusing income tax cuts on those with lower incomes. And it will strengthen work incentives, especially for low earners. But it is important not to claim too much for a policy which, especially in the current fiscal climate, is expensive. By definition it will not help those on the lowest incomes, who do not pay income tax anyway. And in the current context it is clearly not the best way of delivering a short term fiscal stimulus - and it should not be pursued for that reason. Any stimulus needs to be timely, targeted and temporary.