Raising the personal income tax allowance has become a totemic policy for the Liberal Democrats. They secured the promise in the coalition agreement that the government would make progress each year towards lifting the threshold to £10,000, taking a growing number of low earners out of paying tax altogether – and ever since they have repeatedly pointed to it as an example of how they've forced the hardline Tories into easing the burden on working families.

Labour has always rightly argued that the policy is not the best way of helping poorer households in tough times; today, the Institute for Fiscal Studies publishes research that reveals who really benefits most – some of the richest households in the country.

As George Osborne weighs up the competing arguments of Tory backbenchers before the budget on 21 March, his Lib Dem coalition partners and furious middle-class mums about to lose their child benefit, James Browne of the IFS lays bare the reality of focusing the Treasury's firepower on raising the tax threshold.

One third of all adults receive no benefit from the change at all, because they already earn too little to pay any income tax. Looking across families as a whole, instead of taking taxpayers as isolated individuals, it becomes clear that because both people in a two-earner household each get to claim their own personal allowance, they would do best out of the measure. Even as a percentage of their income, it is higher earners who benefit most.

As Browne puts it, "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."

One way to claw some of this gain back from wealthier households – and reduce the £5bn cost of the measure for the exchequer – would be to bring down the threshold at which higher-rate tax becomes due. But that would have a number of consequences that would be less than politically appealing. Browne points out that it would bring 600,000 more taxpayers into the higher-rate band, and since paying higher-rate tax is going to be the cut-off point for entitlement to child benefit, 200,000 more families would lose out. Far from being a progressive crusade to liberate the lowest paid from the attentions of the taxman, this policy is costly, regressive, and will offer scant help to those suffering most in austerity Britain.