I first wrote this article 33 years ago as a young researcher at the Institute for Fiscal Studies think-tank, and have repeated it at regular intervals since.
When Ed Miliband announced last week a new flagship policy for his opposition Labour party – a reduced starting rate of income tax to help the low paid – he provided me with an opportunity to pull out the file again.
This measure has been introduced and abandoned three times in Mr Miliband’s lifetime. (The Labour leader was born in 1969.) The reason for these gyrations is that the proposals sound attractive if you think about them briefly and lose their attraction if you think about them for longer. This superficial appeal is the result of a confusion of algebra and a mistake about data.
The mathematical error confuses marginal and average rates of tax. The marginal rate is the amount of tax you would pay on an additional pound of income. The average rate is the proportion of your total income paid in tax. You can lower the marginal rate of tax on an individual without changing their average rate – and vice versa. Every politician who wants to help the low paid by reducing their income tax rate should write that sentence out 50 times.
Suppose the starting rate of tax is 20 per cent and is payable on all income over £10,000. Now compare two policies. Either raise the tax threshold to £11,000, or introduce a lower rate of tax of 10 per cent on the first £2,000 of taxable income. Both these changes are worth £200 a year to anyone who earns more than £12,000, and the reduced rate halves the tax bill of those who earn between £10,000 and £12,000.
But the higher threshold eliminates completely the tax liability of everyone earning between £10,000 and £11,000 and reduces the tax liability of everyone between £11,000 and £12,000 by more than half. A higher personal allowance is always a better way of spending money on helping the low paid than a lower initial rate.
The mistake about data is to confuse the low paid and the poor. Most individuals with very low annual earnings are not adult breadwinners in full-time employment but secondary earners. They are typically married women with part-time jobs and childcare responsibilities, retired people who engage in occasional paid work, young people, or those who for some reason worked only part of the year.
The confusion here is less serious today than it was 33 years ago, partly because the tax threshold has been raised by governments that understood the issues, such as the present one (this is a contribution of the Liberal Democrats, the junior partner in Britain’s coalition government, to better policies). This is also partly because of the increase in the number of single-parent families, many of which are poor.
But it remains true that if you want to find clusters of poor households in the tax statistics, you should be looking not at the very bottom of the annual income distribution, but a little further up.
That is why measures to help the poor are generally more effectively delivered through the benefit system, which can respond to the shape and circumstances of households, than by adjusting the tax schedules, which do not. It is also the reason why Gordon Brown‘s tax reforms of 2007, which Mr Miliband rightly regrets, were so disastrous. In one of his last acts as chancellor, Mr Brown removed the 10 per cent lower rate band, while cutting the basic rate of tax from 22 per cent to 20 per cent.
The counterintuitive properties of tax schedules mean that those who lost most from this change were those who paid tax at 22 per cent (and thus derived maximum benefit from the 10 per cent rate), but who were not paying much tax at 22 per cent (and therefore derived little benefit from seeing it fall to 20 per cent).
If Mr Brown had wanted to devise a tax measure that fell heavily on poor households, he could hardly have crafted it more skilfully. He believed he could offset this effect by tinkering with the benefit system, but if you understood that you are probably a researcher for the institute rather than a poor household.
Tax systems are delicate, complex instruments, and politicians tinker with them at their peril. But they never learn that lesson, which is why history, and this column, is so often repeated.