Are the UK and US really as unequal as the statistics seem to show?

This is one of those slight puzzlers that comes from my long running thought that not all is quite as it seems with respect to official statistics. I'm not entirely convinced that the UK and US are as unequal as looking at the official inequality statistics (the Gini Index for example) would have us believe.

Have a look at this:

But he faces a Herculean task – a recent government study estimated that Italy's black economy, which includes evasion of income tax and VAT, amounts to 275 billion euros a year, or 17.5 per cent of GDP.

In a country where restaurants continue to do a brisk trade and smart new cars ply the motorways, only 72,000 Italians last year declared a gross annual income of more than 200,000 euros – representing just 0.17 per cent of all tax payers.

And then have a look at the Italian Gini, which is apparently 32, and thus lower than the UK's (and much lower than the US). However, casting an eyeball over the difference in living standards between a poor peasant in the South of Italy and the glory of an upper middle class lifestyle in Milan this doesn't really seem quite right.

I have a feeling that these numbers are influenced by the way they are calculated (well, obviously they are but bear with me). We know that the Italian grey economy is larger than the UK's or the US one. We have World Bank statistics on that. We also have semi-official evidence that what those with low grey economies have managed to do is stop the rich, the high income people, from having untaxed incomes. Note please, here I mean tax evasion, not avoidance. That is, incomes entirely unrecorded by the tax office. This isn't entirely true of course, but as a generality it holds.

The grey economy is that which would be legal if everyone was paying tax: we are not talking about the black economy where the activities themselves are illegal regardless of tax payments. We are also talking about tax evasion, people who simply do not declare income, not tax avoidance where clever accountants and the provisions of the law are used to reduce tax bills on declared incomes. We also know that the grey economy in the UK is not in fact rich bankers just kissing off the taxman. It's small traders dodging income tax and VAT. Largely so that is: something which that Italian story shows is not quite so true of that country.

Which leads me to this thought about the inequality figures, the Gini indexes for various countries. These are calculated from the official declared incomes: they have to be, there is no other possible source. But if the grey economy in some places is largely the rich not declaring incomes, while in other places it is largely the poor not doing so, then we're going to see those Ginis, calculated from the official data, diverging from the actual distribution of incomes in the country.

Here is where we get into a difficulty with this idea. It's obviously and clearly true, if there is a difference in who is evading taxes then inequality figures calculated without accounting for that difference are not going to be comparable. The difficulty though is that we don't know how important this is. If it shifts the Gini by 0.1 of a percentage point then it's not really an issuie we need to worry about. If it shifts the Gini by 5 percentage points then obviously it is: Italy would be, for example, more unequal than the UK.

Further, my problem now becomes that I've not the technical skills to go and work this out. This is just a specific example of what I am sure is something of a more general rule. Some of the things we are told about the world around us are a result of the way the statistics are constructed, not actually a reflection of the real world. I've quite a long list of such anomalies that perhaps should be written up as research papers: hmm, maybe I should get myself a research student or two? You know, people who can actually use Excel?