ONE of the key aims of taxation and public spending is to redistribute income from rich to poor. The way most statisticians, economists and policymakers think about this is in terms of a cross-sectional snapshot: what the distribution of wealth or income is between different people in a population in a single year. But we might care more about lifetime incomes: in the modern labour market, many people now have very high incomes in certain parts of their lives, and much lower ones at other times.

A new paper by the Institute for Fiscal Studies (IFS) shines a new light on how well the British tax system redistributes incomes over people's lifetimes, in addition to using the cross-sectional approach. It presents several interesting findings. For a start, it finds that lifetime inequality in Britain has always been much lower than cross-sectional inequality (see first chart). This is because the poorest in any given year are not always poor for their entire lives; the IFS's simulations suggest that those who, over the whole of their life, are in the lowest 10%, only spend an average of a fifth of their lifetimes at the bottom.

More startlingly, policies that increased or cut welfare expenditure appear to have had very little impact on lifetime inequality. For instance, while the benefit cuts of the late 1980s reduced benefits and increased cross-sectional inequality, it had a much more muted effect on lifetime inequality. And, similarly, although Gordon Brown's massive expansion of means-tested tax credits in the 2000s reduced cross-sectional inequality, they had very little impact on cutting lifetime inequality.

The paper also finds that the redistribution performed by the British welfare state is, to a great extent, smoothing incomes over people's lifetimes rather than in a given year.Whereas 36% of individuals receive more in benefits than they pay in tax in any given year, only 7% do so over their lifetimes. Over half of all redistribution is simply across peoples' lifespans; the young pay in while they work, and take out when they retire (see second chart).

This is, perhaps, a result of the origin of Britain's welfare system. The thinkers who developed the principles behind the system, such as Seehohm Rowntree and William Beveridge, envisaged it as a mechanism more to smooth incomes over Britons' lifetimes than as a system of redistributing wealth from the rich to the poor. What the IFS's paper shows is that Britain's welfare state still acts in the same way as its founders intended, more like a forced saving scheme for retirement rather than as Robin Hood. That suggests that policymakers today need to think more about inequality on a lifetime basis—and how to reduce it—unlike their predecessors who founded the welfare state.