Income distribution in the UK

Background

Is someone in receipt of an annual income of £60,000 rich? This question emerged after a Labour party politician recently claimed that a £60k p.a. income does not make someone rich. The issue arose in relation to whether the income tax rate on such incomes should rise. The politician claimed that the tax rate on such incomes should not rise because someone with this income is not rich. Of course, for many UK citizens someone with this annual income is rich, even very rich. To others, an annual income of £60k makes someone well-heeled, but not rich.

Separation point

But is there a point on the income scale that incontrovertibly separates the rich from the merely well-heeled? If there is, given the recent controversy, the £60k point is not it. Here is a graph of pre-tax income in the UK in 2011.

The most obvious point to notice is how skewed incomes are in the UK. Most incomes are clustered at the low end.  As incomes rise, so do the numbers in receipt of them fall. The highest income shown is £140k. However, there are incomes higher than this which are not shown on the graph. These unshown incomes belong to the top 1% and range up to an unspecified upper limit from the £140k+ lower limit. These unshown incomes are not contained in the data set supplied by HMRC. Given the skew in the data it seems reasonable to suppose that this top 1% can safely be designated as rich.

But is there a lower income threshold still that marks out the rich from the well-heeled? There exists no absolute definition of affluence as far as I am aware. So to answer the question, perhaps consideration of relative affluence might be helpful.

Skew

Skew is a measure of symmetry. The chart of income distribution shows emphatically that income in the UK is not distributed symmetrically. It shows that income distribution is positively skewed, that is, there are more people receiving low incomes than receive high incomes  A plot of a symmetric distribution would typically follow either a bell shape or a rectangle.

A robust and simple measure of skew is

(Highest value – median value)  /  (Median value – lowest value)

A value above unity denotes positive skew.

By progressively truncating the distribution by one percentile point simultaneously at each end, the above measure can be adapted to determine skew at all percentile points of the distribution.  Here is a chart that shows how skew increases with UK income.

The data and calculations are shown as a note at the bottom of this page.

What the chart shows very emphatically is that UK income distribution is very skewed, that incomes are very high the further one moves to the right of the median income (the 50th percentile). Might skew therefore give us an indication of the level of income at which someone becomes “rich”?

Post-tax income

To what extent does the UK’s mildly progressive income tax system modify the skew? The following chart shows that income tax modifies the skew to some extent but that a lot of skew at the top remains after tax. So perhaps even higher income tax rates on high incomes are needed to reduce the extreme skew that exists at the top end of the post-tax  income distribution.

An alternative to tax increases

Another way of reducing skew would be to increase the median pre-tax income. This would enable income tax rates to be  left as they currently are while simultaneously increasing the government’s tax take.  An increased median income would also provide incentive for low paid workers who, within the current income distribution, appear to be confined to an inescapable income trap. The incentive effects would extend to job seekers who, according to research, are unemployed for shorter periods of time when attractive incomes are on offer. Formulating a politically and legally feasible policy to achieve an increase in median income and a move towards a less skewed income distribution may be difficult, but hopefully not insurmountable.

Appendix

Calculation of income skew by income percentile, sourced from HMRC data.