Income Inequality

[Lionel Mandrake]

By now it's common knowledge that inequality in wealth and income has been increasing it the US over recent decades. While wealth inequality is hard to measure, income inequality is relatively easy to measure by such statistics as the percentage of income going to the top or bottom X percentage of households.

A problem with this sort of statistic is that X is arbitrary. We often hear about the bottom 10% and the top 1% or 0.1% or 0.01%, etc. No single value of X captures the whole economic picture.

There's a better way: the Gini index is familiar to people who study income inequality, but not to the general public. The Gini index is obscure because its definition is too mathematical for most people to understand. But for those who know a little calculus, it's simple and it's something well worth knowing about. If this is new to you, please take a look at

http://en.wikipedia.org/wiki/Gini_coefficient

While the Gini index is generally considered the best single measure of inequality, various refinements have been considered to describe other aspects of inequality. For example, here is an article about a way to define separate Gini indices for the poor and the rich:

http://www.maa.org/sites/default/files/pdf/upload_library/2/Jantzen-2013.pdf

[F4lconF16]

1. This is only income, correct?

Unfortunately, that is a very good measure for income inequality, but it falls short of describing inequality in total. Is there something similar for wealth distribution as well?

[muriel_volestrangler]

2. You can produce a Gini figure for wealth distribution as well

Because some people have net debt, this means you can end up with a Gini wealth index greater than 1 - as I noticed Denmark ended up with, in a 2013 survey:

By the time the 2013 Credit Suisse Global Wealth Databook was published, they reckoned Denmark's Gini index for wealth was above 1 (1.077 - Table 3.1)), because so many people had a negative net wealth - they reckoned the top 20% of the population had 92.9% of the net wealth (Table 1.5) (compared to 86.7% for the USA), and the bottom third or so of families are all in net debt - the bottom 40% of families collectively owe 20% of the country's wealth to the rest, while for the USA, the bottom 40% have a collective net wealth of 0 (again, see table 1.5).

I actually wrote to them, because I found that Gini index of more than 1 so strange, and this was the reply of a professor who was one of the authors:

The Danish wealth distribution data is strange because so many people are recorded with negative wealth, most likely because student debts are high and are kept well into middle age. Last year we had old data with which we were not comfortable, so we dropped it altogether and estimated the distribution as we do for countries without distribution data. This year we substituted the data for 2009 which became available to us.

The total wealth of the bottom 70% of Danish wealth holders is approximately zero according to these data. Hence the very large Gini, which even exceeds the normal upper bound of 100% which would apply if all wealth holdings were non-negative. It does not indicate that wealth is especially unequal at the top end, but is reflected in the Gini value which takes account of the bottom wealth holders as well as the top.

Other countries also record significant negative wealth holdings, but the Danish data is exceptional (see Databook table 1-5). The survey data appear to be valid, but are probably not produced in a way that is comparable to other countries. We are investigating how to align the numbers with other countries, but in the meantime report the best information available to us.

http://metamorphosis.democraticunderground.com/?com=view_post&forum=1002&pid=5143022

[Lionel Mandrake]

4. Very interesting, but I'm confused.

How do you define the Gini index if some people (or households) have negative wealth?

Could the total wealth conceivably be negative, e.g., if every household owed gobs of money to banks? Then what, if anything, would the Gini index mean?

[muriel_volestrangler]

5. In the '2 Ginis' paper you linked, it explains how the Gini index is actually worked out

Basically, you plot the cumulative income of the population from poorest to richest. If everyone had the same income, this would be a straight line from (0,0) (no people, no income) to (1,1) (all the people, all the income) because each person adds the same income to the total. If all the income belonged to just 1 person, it would be a flat line at the bottom followed by a vertical line. The Gini index compares the area under the graph with these two versions, which are an index of 0 and 1 respectively.

With negative wealth, the area under part of the graph is negative, and so that can drive it beyond the value of 1.

(Yes, total wealth of a population could conceivably be negative, if a huge debt was ultimately owed to people outside the population (eg if it is to banks, some of it must be to foreign-owned banks, and more than the population has in assets such as property). )

Actually, thinking about it, I'm not sure how a Gini index would be calculated if the population as a whole was in debt, because the right hand end of the graph represents 'all the wealth combined', and if that's negative it would make it difficult to say what '1' on the Y axis should be. Perhaps that means that external debt shouldn't be considered.

[Lionel Mandrake]

6. Thanks, I now understand how the Gini index can be greater than 1.

IMHO external debt is real and should be subtracted from wealth.

Also IMHO the expectation of support from the social safety net should be counted as wealth, since it's a kind of negative debt. This is especially important in countries (unlike the USA) with high taxes on the rich and generous support for those who need it. If personal wealth were computed this way, the probability of any country having negative total wealth would be negligible. (Maybe it's negligible anyway.)

[muriel_volestrangler]

7. It's hard to translate a safety net into wealth, though

because when it kicks in, its income. They do produce Gini figures both before, and after, taxes and benefits - and it's notable that the pre-tax figure for the USA isn't that different from western European ones, but the European ones drop a lot more because of the transfers.

[Lionel Mandrake]

3. Yes.

There is something similar for wealth distribution, but it is problematic. First of all, the wealth of many individuals is unknown, because they have real estate and other assets which they have no intention of selling, so the value of these assets is anyone's guess. (Only when a house is sold is its value known.) Secondly, as Muriel Volestrangler points out in her post, some individuals have negative wealth, which makes it less than obvious how to define the Gini index.