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.