The authors of the report that claims that inequality costs the UK £39 billion a year (see yesterday’s post) say that rates of imprisonment would fall by 37 per cent in a ‘more equal’ UK. If one takes the leap of faith that inequality causes more imprisonment, their figures roughly add up, but there is no reason to believe any such relationship exists. The only plausible mechanism would be if inequality caused crime. The authors explicitly state that this is the case, but even The Spirit Level does not make that claim. The truth is that the crime rate does not rise in line with the imprisonment rate – the UK currently has a relatively high rate of imprisonment and a relatively low crime rate. Rates of imprisonment are not the result of crime per se, let alone of inequality, but are the result of political and judicial decisions on sentencing.

It could be argued that governments which prioritise income redistribution are less likely to favour incarceration and long prison sentences (as in Scandinavia). In this scenario, smaller prison populations and lower inequality would be the twin results of a single factor (government policy). It would be foolish to infer from this that one effect (inequality) causes the other effect (imprisonment). This is a basic correlation/causation fallacy.

The largest part of the £39 billion figure comes from the savings that a reduction in income inequality would supposedly bring in the field of mental health. The authors claim that ‘reducing inequality would improve people’s mental health by five per cent’. Since this does not make any sense, I can only assume that they mean it would reduce the number of people who suffer from mental health problems by five percentage points. Once again, this is based on a scatterplot from The Spirit Level which mixes and matches several different surveys which even Wilkinson and Pickett admit are not comparable. Only twelve countries are included in their graph. If they had cast their net wider, they would have found no correlation between inequality and mental health.

Nevertheless, the authors from the Equality Trust say that a reduction in inequality would save the country no less than £25 billion per year. As usual in this six page report, they provide few details or sources to explain how they arrive at this estimate. It seems that they simply took an estimate of the cost of mental illness (£105 billion) and divided it by four. £105 billion is roughly the entire budget of the NHS, so the actual cost to the taxpayer of mental illness is clearly only a fraction of that. Sure enough, the authors acknowledge that the ‘wider costs’ that they base their figure on include ‘lost productivity’, ‘social costs’ and ‘quality of life’ estimates. These costs are not picked up by the taxpayer. Once again, they are internal costs to the individual and many of the ‘costs’ are not economic in any meaningful sense. The lack of citations in the report makes it difficult to pass further comment.

Only once do the authors hint at the fact that the bulk of their cost estimates refer to non-financial and/or internal costs. They write that inequality in the UK ‘could cost the equivalent of over £39 billion every single year’. The use of the word ‘equivalent’ might alert somebody who is familiar with these kind of studies to the fact that they are not costs to either the economy or the taxpayer, but few people would go beyond the Observer article (which gives no such clue). Having made this small admission, the authors go on to strongly imply that their estimate is a direct burden on the taxpayer by comparing it to ‘total government spending on defence’, asserting that a ‘more equal’ UK would be a ‘financially richer society’, and claiming that the cost to ‘every man, woman and child’ is £622 a year.

There is a wider problem with these estimates (and The Spirit Level in general) in that the authors make a basic statistical error in not only assuming that correlation is proof of causation, but in assuming that any difference between countries is entirely due to the variable on the x-axis (in this case, income inequality). For example, they assume that a 33 per cent difference between the murder rate in the UK and the ‘more equal’ countries (which does not actually exist) means that adjusting a single variable will result in a commensurate decline in murders. This is quite wrong.

Statisticians use the coefficient of determination (the r-squared) to judge what percentage of the variation is due to the factor on the x-axis. So, for example, an r-squared of 0.35 suggests that the factor is responsible for 35 per cent of the variation. Wilkinson and Pickett do not provide this information in The Spirit Level, but the r-squareds are almost invariably small and almost never imply that inequality is the cause of the majority of the variation (ie. it is not the main ‘cause’). Although this may seem a technical point, the authors’ failure to follow rudimentary statistical practice suggests that this is not a serious effort to find the ‘cost’ of anything. Even if the original correlations were robust (which they are not) and even if the ‘costs’ listed were costs to the taxpayer/government (which most of them are not), the weakness of the coefficients of determination mean that the ‘costs’ should be more than halved.

Finally, the authors use data from as back as 1990 to make their case. There is no acknowledgement that inequality has declined in the UK in recent years. The decline has been significant, with the Gini coefficient (the standard measure of inequality) falling from 36.2 in 2001 to 32.3 in 2011.2 It is now lower than at any time since 1986 and is only slightly higher than the rich world average of 31.0. By the logic of The Spirit Level, we should have already seen substantial improvements in the criteria they examine, with commensurate savings to the taxpayer. There is no evidence that any such miracle has taken place.