UK Regional Inequality: Is the UK Still a Coherent Sample?

The previous piece (UK - The Curse of Regional Inequalities) ended by warning that if regional income inequalities continue to widen, at some point the UK loses coherence as a statistical sample. Or, to put it plain English, the inequalities can become so great that in economic terms we're no longer really talking about a single integrated society.

For better or worse, these judgements need not be made on the basis of prejudice or political outlook. Rather, it is the data which does the talking. The underlying premise is that many social and economic phenomena show a Zipfian pattern of distribution. (How to describe Zipfian distributions? It is a mathematical pattern which was first observed in the frequency of words in a language. Wikipedia to the rescue:'Zipf's law states that given a large sample of words used, the frequency of any word is inversely proportional to its rank in the frequency table. So word number n has a frequency proportional to 1/n. Thus the most frequent word will occur about twice as often as the second most frequent word, three times as often as the third most frequent word, etc.'

Zipfian distributions are also regularly observed in economic geography, most famously in the size/frequency distribution of cities within a nation (which, by the way, is how you can tell that London is the capital of Europe, rather than the UK).

We can use it to test whether the rising regional inequality in the UK is threatening its coherence as a society. As before, I am using the ONS's exemplary survey of household per capita disposable income, available annually from 1997 to 2016. In this case, I am using the NUTS3 breakdown of the UK into 179 different regions (NUTS stands for Nomenclature of Territorial Units for Statistics and is based on areas of local government). Basically, I am counting the number of NUTS3 units which fall into per capita annual income bands, stepping with increments of £500. The chart then logs both the frequency and the income (income along the x-axis, frequency along the y-axis).

In a single society one would expect the relationship between per capita income and frequence to be very regular - in fact, one would expect it to be roughly Zipfian. So how's it looking? First, this is the distribution pattern in 1997:

1997 coherence.jpg

There are three, maybe four, outliers of significant poverty, and three, maybe four, outliers of significant wealth. But these are comparatively rare, with the income/frequency of most of the regions clearly cleaving to a strong log/log trend. You might (or might not) be worried about the outliers at either end, but overall the sample looks strongly coherent.

And so on to 2007.

2007 coherence.jpg

The pattern hasn't changed much. The positive outliers are perhaps a little more obvious, and the negative outliers slightly more frequent, but the chart is still dominated by a very clear and strong trend linking income and frequency in a predictable relationship. The centre, we might say, is holding.

You cannot say the same thing for 2016's data-set.

2016 coherence.jpg

One can still see a rough sort of relationship at work, but it takes an uncomfortable effort of will. Had you not seen the pattern of 1997 and 2016, one would be tempted to see two conflicting trendlines at work here: one sloping upward and to the right, and the other sloping downward and to the left. Or one might see, perhaps four bands of frequency (at roughly 2.5, 2, 0.7 and zero).

I think the 2016 chart is very unsettling. Not primarily because of the evidence of inequality, but because it suggests that the complicated and extended network of economic relationships which normally result in a coherent pattern of economic activity and hence income distribution are looking extremely frayed. That suggests that the economic fortunes of different parts of the country no longer have the same impact or implication (positive or negative) on other parts that they used to. A rise of income in, say, Hounslow, no longer means much to, say, Wolverhampton or Leicester. Conversely, even a dramatic fall in fortunes in, say, Southampton, may not longer have any noticeable implications for Oxfordshire. So why should either region have any interest in the economic welfare of the other? Once again, putting things horribly simply, if the society no longer expresses (among other things) a complicated chain of commercial co-dependence, what does it express?