# Our Misleading Measure of Income and Wealth Inequality: The Standard Gini Coefficient

Robert H. Wade is a Professor of Political Economy, London School of Economics and a winner of the Leontief Prize in Economics for 2008. His “Governing the Market” won Best Book in Political Economy from the American Political Science Association. Originally published at Triple Crisis.

It is by now generally accepted that the sharp rise in income and wealth inequality in the US and much of Western Europe over the 1990s and 2000s was one of the bulldozer forces behind the rise in financial fragility.  And it has long been accepted that the Gini coefficient is the workhorse measure of inequality.  But it is not generally recognized that the coefficient is normally defined in a way which biases the measure in a downward direction, making inequality seem less large than another version of the coefficient would suggest.  By this alternative measure inequality is much higher than is generally thought. The standard measure is misleading us into thinking that economic growth is more “inclusive’ than it is.

Recall that the Gini coefficient is a number between zero and one that measures the degree of inequality in the distribution of income in a given society (named after an Italian statistician, Corrado Gini). The coefficient is zero for a society in which each member receives exactly the same income; it reaches its maximum value (bounded from above by 1.0) for a society in which one member receives all the income and the rest nothing.

As normally defined the Gini says that inequality remains constant—growth remains ‘inclusive’—if all individuals (or countries by average income) experience the same rate of growth, and rises only when upper incomes grow faster than lower incomes. So inequality remains constant if a two person (or two country) distribution x = (10, 40) becomes y = (20, 80). Yet the income gap has grown from 10 to 40.

It is at least as plausible to say that inequality remains constant—growth remains inclusive—when all individuals (countries) experience the same absolute addition to their incomes; say from x = (10, 40) to y* = (20, 50). If upper income individuals (countries) experience bigger absolute additions, inequality increases, and growth is not inclusive.

The normal Gini could be called the Relative Gini. The Gini based on absolute changes could be called the Absolute Gini—defined as the Relative Gini multiplied by the mean income. In the above illustration, the Relative Gini for both distributions is the same, at 0.3. But as mean income doubles from 25 to 50 in the transition from x to y, the Absolute Gini doubles, from 7.5 to 15.0.

The Absolute Gini typically rises much more frequently and by much more than than the Relative Gini, and its use would make ‘income inequality’ into a more salient political issue. For obvious reasons, the Relative Gini could be called a ‘rightist’ measure, and the Absolute Gini a ‘leftist’ measure (Kolm 1976a and 1976b).

Economists’ long-standing nonchalance about income inequality is reflected in the fact that the Absolute Gini is rarely used in empirical work. Its unpopularity also reflects the fact that cross-country comparisons of the Absolute Gini are more complicated than for the Relative Gini, because the former depends on the mean of each distribution. This requires that we convert incomes into the same currency (for example, to compare absolute inequality in India with that in the US we have to convert the two means and income distributions either into rupees or into dollars). And to perform comparisons across time we also need to correct for inflation. The choice of appropriate exchange rates and price deflators becomes crucial for making reliable comparisons of absolute inequality.

These inconveniences have often been held up as justification for sticking with relative measures of inequality. But as Kolm explains, ‘these problems are exactly the same ones which are traditionally encountered in the comparisons of national or per capita incomes…and they can be given the same traditional solutions. Anyway, convenience could not be an alibi for endorsing injustice’ (1976a: 419–20).

The bottom line is—all these technical complexities aside—that students of inequality should not ignore trends in absolute income gaps when making inequality comparisons, as most of the literature does.

Thanks to S. Subramanian, Madras Institute of Development Studies, for help on the Absolute Gini.

00007
This entry was posted in Guest Post on .

Readers, I have had a correspondent characterize my views as realistic cynical. Let me briefly explain them. I believe in universal programs that provide concrete material benefits, especially to the working class. Medicare for All is the prime example, but tuition-free college and a Post Office Bank also fall under this heading. So do a Jobs Guarantee and a Debt Jubilee. Clearly, neither liberal Democrats nor conservative Republicans can deliver on such programs, because the two are different flavors of neoliberalism (“Because markets”). I don’t much care about the “ism” that delivers the benefits, although whichever one does have to put common humanity first, as opposed to markets. Could be a second FDR saving capitalism, democratic socialism leashing and collaring it, or communism razing it. I don’t much care, as long as the benefits are delivered. To me, the key issue — and this is why Medicare for All is always first with me — is the tens of thousands of excess “deaths from despair,” as described by the Case-Deaton study, and other recent studies. That enormous body count makes Medicare for All, at the very least, a moral and strategic imperative. And that level of suffering and organic damage makes the concerns of identity politics — even the worthy fight to help the refugees Bush, Obama, and Clinton’s wars created — bright shiny objects by comparison. Hence my frustration with the news flow — currently in my view the swirling intersection of two, separate Shock Doctrine campaigns, one by the Administration, and the other by out-of-power liberals and their allies in the State and in the press — a news flow that constantly forces me to focus on matters that I regard as of secondary importance to the excess deaths. What kind of political economy is it that halts or even reverses the increases in life expectancy that civilized societies have achieved? I am also very hopeful that the continuing destruction of both party establishments will open the space for voices supporting programs similar to those I have listed; let’s call such voices “the left.” Volatility creates opportunity, especially if the Democrat establishment, which puts markets first and opposes all such programs, isn’t allowed to get back into the saddle. Eyes on the prize! I love the tactical level, and secretly love even the horse race, since I’ve been blogging about it daily for fourteen years, but everything I write has this perspective at the back of it.

1. Mark Przepiora

An absolute gini function does seem problematic. Maybe a better measure would be, the usual gini function, but instead of using income as the inputs, using something like income minus poverty level income? That way you still get numbers between 0 and 1, but you measure the inequality only of income beyond the bare minimum needed to survive.

2. ambrit

Friends;
What’s funny is that the Kolm papers cited come from the Nineteen Seventies! We’ve been farting around without thrashing out this issue, one Kolm himself describes as one of “inequity”, for a very long time.
We can see this as a strong indication that economics cannot be divorced from politics. Our values are central to our formulations. It just goes to show that businesspeople make lousy politicians, and politicians make horrendous economists.

1. psychohistorian

What this goes to show me is that agnotology (the manufacturing of ignorance) is the ongoing nuclear warhead of choice for the inherited rich running our world.

Are you sure wealth inequality is bad for you? Why don’t you starve on it for a while and get back to me…….

3. bobs

Hmm, so if I make \$1K a year and you make \$100K, what is suggested is that our inequality should be seen to “increase” if next year I make \$1billion and you make \$1billion + 100K. Really???

1. Nacho Pepe

I am afraid you are wrong. The Absolut index won´t worsen if you in absolute terms receive the same amount (1 billion as per your example) than the one with a higher income (100K).

Even if you meant that you received less (1 billion minus 1K that you already had as compared to the higher-income guy who receives 1 billion plus the 100K he already had)the mean in your example changes from 100.05K (99.05K higher than your income) to 1,000,050K, only 50K higher than your income. So your position with respect to the mean has actually improved in 49.05K.
However, in the article, I don´t understand how a distribution (10,40) has a 10 income gap and a distribution (20,80) has a 40 income gap.

1. diptherio

Ugh…the (10,40) are the two values for X, while the (20,80) are the the values for Y (before and after). There is a difference of 10 between 10 and 20, and a difference of 40 between 40 and 80. The nominal distance between X and Y has quadrupled from the first instance to the second, but our standard Gini coeff. doesn’t pick this up.

2. diptherio

Your straw man needs some more stuffing, I can see right through him.

To answer your rather flip question: yes, inequality has increased. In your two-person economy the actual difference in wealth in the first instance is \$99K. In the second instance the difference is \$100K. Assuming these are the only two people in your model (which is what you imply) inequality has indeed increased. Duh. The fact that they both “have a billion dollars now” is meaningless in your example.

1. Jim Haygood

Bob’s point is that two billionaires whose wealth differs by only \$100K (1/10,000th) are for all practical purposes equally wealthy.

If you have a billion-dollar equity portfolio, it can easily fluctuate by \$10 million (one percent) in a day. A \$100K difference between two billionaires is so small and so unstable as to be practically unmeasurable.

Wade’s arithmetic model simply doesn’t scale up. The existing geometric model is accepted and appropriate for the task.

Unbelievable that a Leontief Prize winner could scribble such tendentious nonsense. If I were taking a class from this innumerate goofball, I’d withdraw from the course.

1. craazyman

Tell us what you really think! :)

If somebody gave me a million dollars tomorrow I wouldn’t have any problem if the person giving it to me got richer by \$5 million. Unless everybody got \$5 million and I only got \$1 million.

Where does all the money come from since the world is a sealed unchanging sphere in space light years from anywhere with nothing coming in or going out except sunlight and heat?

send \$5 million to: Joe, PO Box 7, Magonia — and I’ll be happy for a few years.

4. Ed

One of the insidious effects of inequality is the ability of the elite to price out everyone else from various goods. Anyone trying to find a place to live in New York City recently can attest to this. This has arguably happened with the entire United States government. I agree that absolute changes in income and wealth matter.

If someone asked me to draw up a measure of income inequality from scratch, I would use the absolute ratio of average income to median income, with lowest inequality where average income equalled median income. The only problem with this I can see would be societies -and these are fairly rare- where the average income is lower than the median income. This would happen in societies without many wealthy people but a large slave population, like some ancient Greek city states and 18th century colonial America. But my measure would still capture the inequality in these situations by using the absolute value. Overall, I’ve never cared much for the Gini coefficient because it seems an overly complicated way to measure what it is trying to measure.

1. Min

“One of the insidious effects of inequality is the ability of the elite to price out everyone else from various goods.”

Yes. Given the ability of the rich to set prices when they want to, it amazes me that people can believe that the market knows best.

1. Massinissa

Well, remember that when people say “the market”, they really mean “the capitalist elite”.

So when people say “the market knows best”, they really mean “the capitalist elite know best”.

Hyper-capitalists are ultimately just authoritarians who like hierarchy.

5. Hugh

I am not a fan of Gini coefficients. They are a mathematical toy, and not even a very interesting one at that. If we are discussing wealth or income inequality, what does a Gini coefficient add to our understanding? It seems to me the Gini subtracts from it. When I am talking about wealth and income, I want to know what these are by quintiles, what they are for the top 10%, 1%, 0.1%. I want to know the medians. I want to know if the goals our society has set for itself, that is what kind of a society we want, are being met.

For me, the Gini coefficient does not convey meaningful information. I mean any time it gets discussed, it has to be unpacked. Which Gini are we talking about? There are a lot of them. And we have to go into their contexts and limitations. But if we are going to discuss all this anyway, why bother with the Gini? Why not just discuss these issues in the first place? Am I the only one or does it strike others how absurd it is to seek to convey in a single number an issue as complex as inequality with all of its economic, political, cultural, and societal dimensions?

1. jake chase

Well, you’ve put the Gini back in the bottle.

Incidentally, what really matters is absolute wealth inequality. Nobody has ever come close to measuring wealth accurately, and if people had any idea of the disparities they would be even more upset than they already are. The only reason 95% of the population has any wealth at all is alleged home equity. Of course, you could only capitalize it by selling the home and living in your car, or by taking one of those reverse mortgages flogged by Fred Thompson on television. And let’s not forget that for most people home equity no longer exists.

2. diptherio

While I agree with your critique, I would point out that, FWIW, the Gini has the great advantage of being a single number. All of our economic data is problematic in the calculation (as you are well aware): take GDP for example. It is a horrible measure of economic health but it’s what we’ve got and it’s what gets used. It’s simple and relatively easy to understand (or at least get the gist of). Same thing with Gini: it is flawed but we need to have a simple metric than can be pointed to, if only for rhetorical purposes.

6. Min

It is equally plausible that the Gini coefficient has an upward bias instead of a downward bias. For example, say that real incomes double, while the Gini coefficient remains the same. That might mean that a rich man can now afford twice as many yachts as before, while a middle class man can now afford a single yacht. Arguably, the doubling of income means more to the middle class man than the rich man. Lower down the class scale, maybe a lower class family can afford to send their kids to college, when they could not before. Arguably, that means more to them than getting a yacht.

1. Min

Hmmm. I see a problem with my post.

I am assuming that real incomes double. My income doubles, and so does that of my barber. Doesn’t that mean that I cannot afford twice as many haircuts as before? His prices will surely rise, in real terms, even if they do not double. It would seem that increasing real income means altering what people buy and sell.

So I cannot assume that college becomes affordable to the lower class family. Maybe they can afford a new car.

2. diptherio

Everyone’s income doubling would imply that all prices have also doubled (else how to pay the increased incomes?). Therefore, in your scenario, inequality would be remain the same, and prices for all goods would have adjusted upwards so that everyone would be exactly as well off as before (assuming that wage gains were uniform and all-inclusive0.

1. Min

You are thinking about a nominal doubling of income, not a real doubling.

In the barber example, his real income could double without his prices doubling. His rent might not double in real terms, for instance. In fact, that would pretty much be the case, since the rent might well only keep up with inflation, remaining approximately constant in real terms.

1. Calgacus

My income doubles, and so does that of my barber. Doesn’t that mean that I cannot afford twice as many haircuts as before? His prices will surely rise, in real terms, even if they do not double. It would seem that increasing real income means altering what people buy and sell.

No, it does not necessarily, logically mean that you can’t afford twice as many haircuts. (Only realistically, practicallly) Everybody’s real income doubling would be a definitely Good Thing. That is why it is so hard to achieve. Of course you are right that in the real world, prices change, and things are never equal, and consumption patterns change, and everything doesn’t become equally cheaper in real terms simultaneously.

And barbering actually is an example that Wray and other economists like to use as something that technology doesn’t improve, where the sort of real income doubling scenario of below is unrealistic, and relative prices will change. Saying that real incomes double, but (realistically) saying your barber’s real prices don’t halve means that somebody else’s real prices have to more than halve.

But one (unrealistic, but clear, tractable) way that means “real incomes double” could be when everybody pays the same dollar amount for everything, but consumes twice as much of the exact same real stuff. So you would pay the same amount, and get twice as many haircuts, etc. Nobody’s nominal income changes, the dollar just goes farther for everything. Deflationary paradise!

7. Josef

(1) While the Gini coefficient is generally accepted as a measure of inequality, I can only recommend to study its mathematical characteristics more deeply. It is in and of itself neither suitable nor intuitive. Example: How does an income distribution have to change to achieve a change in Gini index from 0.2 to 0.3? And how does it have to change for a Gini shift from 0.5 to 0.6? – It seems to be a comparable change, but it isn’t.

The only advantage the Gini coefficient has is that it’s – in mathematical terms – comparable. One can say “today, it’s biger (or smaller) than yesterday”, so it’s simple to come to conclusions. It’s only… these conclusions are meaningless and oversimplified.

(2) The trick ist that the Gini coefficient *implicitly* sets a yardstick to compare against, it assumes what our dream society looks like. That’s a bit short-sighted.

(3) All that said, when comparing two nations like US to India, it’d still be an issue to convert exchange rates. Instead (or to complement that measure), purchase power should be used.

1. Min

“How does an income distribution have to change to achieve a change in Gini index from 0.2 to 0.3? And how does it have to change for a Gini shift from 0.5 to 0.6? – It seems to be a comparable change, but it isn’t.”

My question is why does in seem to be a comparable change?

1. larry

Min, it seems to be comparable because the Gini coefficient is often treated as if it measures a linear function. Which it doesn’t except in the special when everyone is equal. The Lorentz curve, which the Gini coeffiecient represents, is non-linear in cases of inequality. It is this non-linearity that makes what looks like similar differences between a poor person and a rich person look more or less equivalent when we know in fact they are not. Differences at the so-called bottom end are “smaller” than differences at the “upper” end of the curve, the sort of thing you would see with an exponential curve. The shape of the Lorentz curve is such that fewer people get a greater share at the top income end than at the bottom income end – the differences are not comparable.

8. craazyman

I think something went horribly wrong with the algebra here. That seems to happen a lot in economic reasoning. Even when you use a calculator it doesn’t add up. It only works as a form of suggestion.

However it’s quite appropriate to use the phrase “Gini”, remarkably so, in that weird way language has of unconsciously evoking two apparently unconnected ideas that nevertheless relate profoundly through metaphor.

Consider that Ginis (Genies or Jinn or Djinn) is the Arabic term for metaphysical beings that incarnate and seek to destroy humans through forms of deceit and trickery, feeding off their life energy. Such also is the operation of some (but not all, to be fair) of the world’s elites and kleptocrats who manipulate mankind through the power of capital over labor.

So the Gini co-efficient, as a measure of economic inequality, is also the “Genie” coefficient, or the measure of the degree to which a population’s life energy is siphoned through the perpetration of the illusion that a strained dialectic of concentrated capital/diffused and atomized labor is somehow essential for species survival.

the owner of capital rubs the bottle and the “genie” appears to make his or her every wish a command, created through the life blood of the laboring masses, which appears as an effortless miracle inside the cloistered walls of the fortress in which capital lives.

9. MLS

Does the Gini coefficient look only at the asset side or does it consider liabilities too?

One can argue that an individual with a \$100k in assets and \$100k in liabilities is exactly as wealthy as someone with \$1 million in assets and \$1 million liabilities. Net worth in both cases is zero.

1. craazyman

If you have enough assets you can restructure the offsetting liabilities when things start breaking bad, and stay rich. That’s the Genie at work!

10. Glenn Condell

As a measure of income inequality the Gini may be great, but isn’t it missing something as a pointer to wealth inequality? Ie, the 32 trillion parked in Nick Shaxson’s Treasure Islands? If these proceeds of crime and tax evasion didn’t count at the point of origin they won’t show up as factors in Gini calculations.

Surely the difference between relative and absolute Gini would be dwarfed by the difference between either and a measure that included hidden assets.

11. Paul Tioxon

The Gini is out the bottle, it grants wishes of income. Income inequality would be easier to handle, if only life were lived in that one dimension that only money can buy. But, those with higher income, whether absolute or relative, do not have to live for 10 years, bound and gagged and released only to be raped or have a baby. Those 3 girls and the people dodging bullets or catching them would trade off any position in the income stratification for not having to live through what they did. The one eyed vision at least tries to express the reality of inequality. It tries to measure it in a rational way. But is anyone with listening so that it may be changed? Policy makers know there is inequality, they design the laws and implement the policies to keep it that way. And the 2nd and 3rd class citizens and all of the rest, know it without ever reading a chart. So, just who puts out studies that minimize the scale of a real problem for people who will never act on even that attenuated description to ameliorate the damage? Useless and pointless knowledge. But there is something going on, but you just don’t know what it is, do you? The people at the top, insulated and inbred, always the last to know.

12. reason

Aren’t there other problems with Gini – for instance that real changes in inequality can be mismeasured – for instance by increases in inequality at the top being offset by decreases in the middle (i.e. a move from a middle class society to a feudal one not being reflected in the measure).

13. larry

The Gini is only intended to show inequalities in income distribution in a given system. You can’t ask it to do things for which it was never designed. If a Gini Coefficient shows that the bottom 25% of the population has 5% of the national income, the next 25% has 10% of the national income, and the third 25% has 15% of the national income, this means that the top 25% has 70% of the national income. This is obviously hugely inequitable. But the Gini can’t tell why this is so. The coefficient must be incorporated into a more inclusive explanatory framework in order to be able to specify why a given Gini is the way it is.