GEORGE OSBORNE, the Conservative chancellor, is in a bind. What seemed like a piece of clever politics in his July budget partially unravelled on October 26th, when the House of Lords rejected his plan to lop £4.4 billion ($6.7 billion) off the bill for tax credits, income top-ups for the low-paid. After the vote, Mr Osborne emerged from the Treasury to report through gritted teeth that he would “listen” to criticism and find ways to soften the blow. He has no good options; barring a U-turn the policy will do damage to some of Britain’s most vulnerable, and to his reputation.

Back in July the government claimed the budget was a boon for “strivers”, whom it has previously contrasted with non-working “skivers”. Iain Duncan Smith, the work and pensions minister, pumped his fists with delight as Mr Osborne revealed a big rise in the minimum wage. But closer inspection revealed a harsher settlement. After the government failed to publish its usual distributional analysis, the Institute for Fiscal Studies (IFS), a think-tank, helpfully obliged. Its figures revealed huge losses for the poorest, inadequately offset by the minimum wage and other tax tweaks (see chart).

Tax credits are designed to bust poverty, while nudging people into work. The government supplements low wages, then gradually teases the benefits away as income rises. Mr Osborne had two options for reducing the system’s cost: cutting the initial benefit payment; or increasing the rate at which it is yanked back.

In his summer budget, the chancellor pulled every lever he had. He announced a freeze on the generosity of tax-credit payments until 2020, and new rules to take them away more quickly. But whereas the freeze would creep in gradually, the faster withdrawals would wallop people all at once next April. The Resolution Foundation, a think-tank, estimated that 3.3m families would lose on average £1,100 a year, throwing 200,000 children into poverty. A single mother of two working 40 hours a week on the minimum wage would see her weekly income drop from £417 in March to £391 in April. The Lords balked, and pushed back this proposal.

Back-pedalling, Mr Osborne has vowed to help those families affected. But for this delicate task he has only blunt instruments. A faster increase in the minimum wage might force employers to soften the blow of benefit cuts. But whereas tax credits and minimum wages have similar income-boosting effects, they have opposite effects on employers’ eagerness to hire. The official independent forecaster already says the higher minimum wage will mean 4m fewer hours of work per week will be offered by 2020; raising it or bringing it forward would do more harm still.

An alternative would be to try to cushion the families through the tax system. But this would be both ineffective and very costly. Whereas income taxes and national-insurance contributions are designed to squeeze most from the rich, tax credits target poor families (43% of households receiving them have earnings below £10,000, meaning they already pay no income tax). The mismatch means that any tax cut that got close to compensating the tax-credit losers would also be a huge, expensive giveaway to the well-off.

Mr Osborne could delay the pain by phasing it in gradually or inflicting it only on new claimants. Wage growth in the meantime might make the cuts a fraction easier to bear. But it would make little difference in the end—and drawing out the cuts over two or three years would leave them dangerously fresh in voters’ minds come the general election in 2020.

Nor would these sticking plasters solve a more fundamental problem with the proposal: its effect on incentives to work. By clawing back tax credits more quickly as income rises, the government risks encouraging shirking rather than working. Currently, families earning between £3,850 and £6,420 a year can keep every extra £1 they earn. The reform would claw back 48p of every extra £1. A lone parent earning above £11,000 and still receiving tax credits would face an effective tax rate of 80%.

The government is on a broader mission to simplify welfare, removing some of its perverse incentives. But the new plans undermine that aim. Under earlier proposals, a single mother of two would have been able to work for 22 hours on the minimum wage before her benefits started falling. With Mr Osborne’s changes this would fall to ten hours. “There is a pretty big risk that because of these changes people are going to cut their hours,” says Torsten Bell of the Resolution Foundation.

Pain with no gain

Are the cuts worth all this pain and distortion? Mr Osborne’s motive for taking the axe to tax credits was that they had become too costly. In his budget speech he noted that they cost £1.1 billion in 1999 and will cost £30 billion this year. Although his figures are misleading (£1.1 billion covers only half a year’s spending and ignores other benefits that tax credits gradually replaced), on a fair comparison real-terms spending has quadrupled since 1999. As a share of GDP, tax credits cost more than three times as much as America’s Earned Income Tax Credit (EITC), which inspired them. In all, Britain spent 4.3% of GDP on family benefits in 2011, far more than the rich-country OECD average of 2.6%.

Yet it is not quite the mindless splurge the government makes out. Herwig Immervoll, an employment expert at the OECD, points out that spending in Britain is closely means-tested and therefore sensitive to the economic cycle: in 2011 tax credits cushioned the hit to wages from the recession. And tax credits have broader ambitions in mitigating child poverty than America’s EITC. The IFS reckons that in 1997-2010 changes to Britain’s tax and benefits system, of which tax credits were the centrepiece, kept 1.8m children out of poverty and raised the household income of the poorest half of children by 28%.

Moreover, Mr Osborne has £11.6 billion of fiscal wriggle-room to play with. Reining in the policy or, more sensibly, abandoning it altogether, would not be difficult. Even without the blocked reforms, the chancellor will have chiselled the cost of the system down from 1.8% of GDP in 2010–11 to 1.4% by 2020-21. Cynics suggest that the promise to cut £12 billion from the welfare bill was only included in the Conservative manifesto as a chip to be bargained away in coalition negotiations. In the absence of a coalition partner, the House of Lords might just have to do.