The Gini coefficient
Note: non-sports post.
Income inequality is rising in the United States. If you measure inequality by the Gini Coefficient, which I guess is as good as a measure as any, you get a fairly steady increase from 0.399 in 1967 to 0.466 in 2001. (A higher number means a more unequal distribution; 0.000 means everyone has the same income; 1.000 means one person has all the income.)
Inequality has increased in Canada, too; in fact, what got me interested in this topic was a recent newspaper article complaining about the rise in Canadian income dispersion. These kinds of articles come around all the time, in discussions about how the rich are getting richer.
The stated or unstated assumption is that more inequality is worse, and more equality is better. I don't think that's true. Rather, I think that rising inequality can indeed be worse, but it can also be neutral, or it might actually be a sign of improvement for everyone.
The problem isn't with the measurement itself; as I said above, the Gini Coefficient is a reasonable way to measure what it's supposed to measure. The problem is with the interpretation of movement in the measurement. Even if you think that, all things being equal, more equality is better than less equality, it doesn't necessarily follow that a higher Gini is bad, -- because all things are never equal.
A baseball analogy, perhaps a mediocre one, might be stolen bases. Yes, stolen bases are good for an offense; every additional steal creates about 0.2 runs. But it doesn't follow that an increase in the number of steals is good for offense (in the 60s, steals were up but offense was down.). It doesn't follow that bad offensive teams should try to steal more (they'll just get caught stealing more and score even fewer runs). And it doesn't mean that teams with more steals are somehow better than teams with fewer steals (stolen bases don't correlate well to winning).
The number of steals is just a measurement of – the number of steals. If you want to go beyond that, and draw conclusions from changes in the stolen base rate, you have to justify those conclusions. The naive view -- steals are good so it's bad when teams steal less! -- just isn't true.
It's the same for measures of income inequality. There are dozens of reasons why an increase in income inequality can be a neutral thing, or even a good thing, and you don't have to think very hard to come up with them. I have thirty of them here. I could probably think of ten more. (Some of them, of course, have been thought of before; this Wikipedia page includes several.)
1. First, absolute income matters a lot more than relative income. Would you rather live in the USA where the Gini is 0.46, or in a country where the Gini is zero but everyone earns exactly $5? That's a contrived example, but there are real-life examples too. Albania has a Gini of 0.27, but a per-capita income only one-eighth of the USA. Would you be willing to sacrifice 87% of your pay in order to be more equal to everyone else?
Obviously, other factors can be more important than income inequality. If you think it would be bad for the USA's Gini to go from 0.46 to (say) 0.48, would you change your mind if a 10% increase in income came with it? How about 20%, or 50%?
The Gini rose from 0.42 in 1991 to 0.47 in 2001. But per-capita income, in inflation-adjusted 2006 dollars, rose 23%, from $21,102 to $26,024. Is that a fair trade-off? If you think it is -- and even if you think it isn't -- then complaining about income inequality without mentioning the trade-off isn't very reasonable.
2. The above argument wouldn't be all that persuasive if there weren't a link between the level of equality and the level of income. And there is. If you want to lower the Gini, you have to take income from the rich and give it to the poor. (You could raise income to the poor in other ways, but if those ways were easy, the poor would be doing it themselves already.) Taking income from the rich reduces the incentive to get rich, which in turn reduces overall wealth. Economists could probably tell you what the trade-off actually is -- how much an increase in upper-income tax rates would slow down economic growth. But I think they'd all tell you that there *is* a significant trade-off. More on this later.
3. Suppose that tomorrow, someone comes up with a cure for an untreatable cancer. He sells a million cures at $1,000 each, and makes a billion dollars. Inequality goes up. But everyone is better off! Everyone has just as much income as before, but now we have the opportunity to buy a cure for cancer -- should we ever get it -- for only $1000.
So it's good when inequality goes up for reasons like this ... and I don't think it's that contrived an example. Bill Gates got rich creating Windows ... which costs only, what, about $40 a copy? I get way more than my $40 worth, and I'm happy that Microsoft succeeded and increased inequality on my behalf. The same is true for most of the products I use. I hope that there are more breakthroughs that make other people rich, even if I don't get richer at all.
4. As a general principle, the way you earn a high income is by doing things that benefit other people. You can cure cancer or create an operating system, but you can also perform appendectomies or write computer programs quickly or give a better haircut. A higher Gini might just mean that more people are figuring out better ways to benefit more other people. Or, it could just be a matter of population growth. Fifty years ago, movies played to only millions of people. Now, a movie of the same quality would be seen by billions. That means directors who would have merely been millionnaires in 1970 might be billionnaires now. That's a good thing, not a bad thing, that those who enrich others' lives have many more "others" to benefit. I'm glad that someone in China can now enjoy "Airplane!", the greatest movie ever made, even if it means that the Zucker brothers get a little richer and the US gets a little more unequal.
5. What's the right value for the Gini coefficient? Is .46 too high? Too low? What should it be?
We know that for incomes, higher is better. We know that for golf scores, lower is better. We know that for room temperature, the closer to 72 degrees Fahrenheit, the better.
What's ideal for the Gini? It's not zero; if everyone had to have equal incomes, that would be more Marxist than Marx -- nobody would want to work, and everyone's income would be very low. It's not 1 -- that means one person has all the income, and the rest of us starve.
So what's the point we're shooting for? Nobody knows. And if nobody knows, how can you draw any conclusions at all about whether 0.46 is too high or too low?
In fairness, there is a counterargument here: that we don't know what the Gini should be, but we know there's too much inequality, so we need to go lower. To which I have two answers: first, suppose we reduce inequality. How will you know when we're done? If there's a way to tell, why not tell us now? And, second, some people may *not* think there's too much inequality now. To those people, the fact that the Gini is rising is irrelevant -- you have to convince them that more equality is essential, in order that they see the rise as a bad thing.
The issue shouldn't be that inequality is rising -- the issue should be that inequality is too high. Is it?
6. The Gini doesn't consider that people could be equal over a lifetime, but temporarily unequal due to age differences. Even if everyone had exactly equal income patterns -- say, zero for the first three years of adulthood while they're in school, then escalating equal salaries until retirement, then equal pensions in old age -- the Gini would be non-zero, because, in any given year, you'd be looking at some zeroes, some low-income, some high-income,and some retirees.
Part of the Gini is simply the effect of differing lifetime income among any given individual. If it turns out that people are voluntarily changing their work patterns to have fewer low-income years and more high-income years, the Gini increases even if inequality hasn't.
7. There's a trend to more years of higher education, which would cause part of that increase. If the long-term trend is for more schooling (meaning more years at zero income) and higher incomes after, that would increase within-lifetime inequality, and therefore the Gini, even if everyone remains exactly equal over their lifetime.
Look at it this way: suppose everyone has three years of school at $0, then forty years of work at $50K. They're all equal over their lifetime. But what happens any given year? Of every 43 people, then, three have $0 and forty have $50K, which looks unequal.
Now, suppose everyone decides to go to school for five years to make more money: now you have five people at $0 and thirty-eight people at $70K. This is more unequal, resulting in a higher Gini -- but it's actually better for everyone.
8. People are living longer. If the trend is to make lots of money between 25 and 65, and take a low pension later, then adding more low-pension years will appear to reduce inequality, even if everyone is still the same.
To oversimplify: the trend used to be that you start work at 18, then earn a fairly low salary until you die (because you can't afford a retirement pension). Now, the trend is: make no money for five years while you're at school. Then make good money until 65. Then get a lower pension. The old way, everyone is fairly equal each year. The new way, everyone is still fairly equal over a lifetime, but income varies considerably each year. The new way is less equal when comparing individuals during any given year, but just as equal over a lifetime. And, of course, more desirable.
9. People have different propensities to work; that's just human nature.
Co-workers Bob and Joe are each offered 50 hours of overtime work. Bob accepts, and makes $60K that year. Joe declines, preferring more time with his family, and makes $50K that year. Inequality of income has increased, but that's because inequality of WORK has increased. That's perfectly fair and desirable.
Shouldn't inequality of income be fair to match the inequality of work or effort that created it? And isn't it good that Bob and Joe both have more choices, even though the Gini goes up?
10. People have different ambitions. Ann and Cathy both make $40K a year and are of equal proficiency at their job. Ann makes an extra effort to climb the corporate ladder into management. Cathy doesn't -- she doesn't like kissing butt and prefers to avoid the hassles of supervising other people. Ann jumps to $60K a year; Cathy stays at $40K. Both are happy. Inequality of income goes up, but, again, this is a good thing, as both Ann and Cathy got what they wanted.
11. People have different propensities for risk-taking. Right now, T-bills are paying less than 1%, while other, riskier investments yield 10% and more. Suppose Tom and Jerry have equal jobs and salaries, but Tom is more conservative than Jerry. Tom invests in a CD paying 1.5%, while Jerry invests in real estate yielding 10%. Their incomes suddenly become unequal, but, again, both Tom and Jerry got what they wanted, so the increase in inequality is again a good thing.
12. Even when people have the same propensity for risk-taking, they might just get different results. Jerry and Kevin might be the same in every other respect, but if Jerry invests in mutual fund A, and Kevin invests in mutual fund B, their returns will be different, and their incomes will start to become unequal. Why is that necessarily bad?
Or, take lottery tickets. Everyone who buys a lottery ticket knows that the distribution of incomes among ticket-buyers will be unequal. But they don't mind, and they do it anyway. Is it a bad thing when lotteries increase the Gini? Ticket-buyers probably don't think so.
13. There are other ways to buy security. I work in the IT field, and several of my co-workers, who were on contract, voluntarily took a large pay cut, in some cases close to 50%, to become government employees. Other of my co-workers did not. That created income inequality between the two groups. But did it really make us unequal? Government jobs are very secure. Isn't it reasonable to assume that my friends who took the pay cut simply bought their security, and we're just as equal as we were before? Half of us take our pay in money, and the other half take it in security.
The moral: you can't just consider monetary income; you have to consider things that money can "buy" in the non-traditional sense.
14. There are lots of examples of non-traditional income-substitutes. Suppose you have two identical couples who are neighbors. Helen works, earns $40,000 a year, and takes her kids to day care. Iris quit her $40,000 job to take care of her kids at home. Again, is this unequal? I don't think so. It looks unequal to the Gini, which only measures monetary income. But if Iris chose to stay home and forgo her $40,000 a year, she's obviously benefiting by at least $40,000 -- or she wouldn't stay home! To me, Helen and Iris are exactly equal, despite what the paychecks say.
15. Here's another one: home ownership. Kevin and Laura both make $50,000 a year, but Kevin owns his home, and Laura pays $1,000 a month to rent an identical one. They are equal in money income, but, really, Kevin has more total income -- he "earns" an extra $12,000 a year by having the use of his home rent-free. In this particular Kevin-and-Laura case, the Gini actually *underestimates* inequality, unlike all the previous examples, where it *overestimates* it. However, for the country as a whole, it might again overestimate it, if low-income earners are more likely to own their homes outright. And retirees are likely to have paid-off mortgages.
16. Here's still another one: children. Oscar has two kids, and has to accept a lower income in order to stay in their town and raise them in a stable environment. Paul has no kids, and can move around looking for higher-paying jobs. Their incomes are unequal, but are they really? Oscar has chosen to have kids and pay the price; he values being a father more than he values the bit of extra money he could earn if he were childless. While it's politically incorrect to compare children to money, the fact remains that children are hugely important to people, and they're not free -- there are real costs and opportunity costs to having children. It seems weird to feel sorry for Oscar because he chose children over money, just as it would be weird to feel sorry for someone who was poorer because they chose to buy a fancier car. You have to count everything that affects income, not just the actual income.
These cases of trading money for non-money might be more frequent now then ever, because, as we get richer, they become more affordable -- it's easier to stay home with the kids when your spouse makes $80K a year as a computer programmer in 2009 than when she made $40K (inflation-adjusted) as a programmer back in 1974. As overall wealth increases, the ability to choose to earn less increases. In turn, the diversity of choices increases, and the distribution of monetary income gets wider. Again, this is a most excellent development, in my opinion, and I hope it continues.
17. I quit full-time work a couple of years ago. Right now, I'm not working much, just occasional jobs. If I go back to work, I will earn an above-average income and increase the Gini coefficient. Is that really a bad thing?
18. Small-business owners have incomes that fluctuate from year to year. This year, Al might make $100K and Bruce $20K, but the next year it's reversed. Since the Gini is calculated per year, it looks like Al and Bruce are unequal, even though they had exactly the same income over a two-year span.
19. Part of what's measured by "income" is capital gains. But the stock market has up years and down years. If inequality fell last year because of all the capital losses realized in the stock-market collapse, is that a good thing? Should we rejoice because Warren Buffett is poorer, even if we're poorer too? If that's not worth celebrating, then why is it worth complaining when the reverse happens, when Warren Buffett gets richer but inequality goes up?
20. Do the measurements of income inequality take taxes into account? I don't think they do. That defeats the purpose, doesn't it? A large part of what we expect government to do is help out the poor who need it. And they do that by disproportionately taking money from the rich.
So if the point of the Gini is to measure how much money people actually have to spend -- which is the number that actually means something -- you certainly have to adjust for taxes! It's very possible that the pre-tax Gini is up but the after-tax Gini is down.
21. It's not just cash benefits that we get from government; it's services too. Suppose it costs $10 million to run the public library, and that works out to $10 per person. Since everyone has equal access to the library, shouldn't we add $10 to everyone's (after-tax) income before we calculate the Gini? I think we should. (You could argue that the poor don't benefit as much from the library as the rich (or that hungry poor people can't eat books!), but I'm not sure that's the case. Because, if it were, we'd give the library tax to the poor, and pay for the library with membership fees. That would make everyone better off. Since we don't, it's fair to assume that giving the poor free access to the library benefits them more.)
It's not just libraries -- it's police, and fire protection, too -- the poor are served just as well as the rich by police protection. And don't forget public transit (which certainly *does* benefit the poor more than the rich), and all the other services that government provides.
Part of the reason we pay for these services out of taxes is that they're so essential that we want to make sure even the poorest members of society benefit from them. But in that case, we need to figure them into the calculation.
My perception is that the level government services has exploded over the last few decades, while the Gini has increased only moderately. Figure in the value of those services -- and taxation, if you haven't already done so -- and the increase would be substantially lower.
22. It's spending that matters, not income. If I gave you an income of $1,000,000, but told you you could never spend it, it would be useless. And if I let you have a million dollars worth of merchandise (of your choice), instead of cash, the merchandise would be just as good.
And it's a principle of economics that people work to smooth out their consumption (spending) over their lifetime. That means they borrow money when they're young, to pay for cars and TVs and houses, and pay it back when they're older. And so, consumption is much less unequal than income. (It's theoretically possible for everyone to consume exactly the same, despite differing incomes over time; imagine an insurance company that offers you $50,000 worth of consumption every year in exchange for your salary every year. That would make everyone equal. Then, imagine doing this yourself -- you borrow in years where you're below $50,000, and pay back the debt in years when you're above $50,000.)
I remember seeing a few articles that mentioned that low-income people actually spend a lot more than their income, almost twice as much in some cases. (This might be through tax credits, or welfare, or such.) In that case, measuring income inequality is a pretty crappy way of measuring the differences in how people actually live. We should measure *consumption* inequality.
23. And if we DO measure inequality of consumption, the number goes way, way down. The way the Gini index is constructed, the more money you make, the more effect you have on the Gini. But suppose a highest-income earner makes $1 billion per year. There's no way that person can, or would, spend that much money. If he's really good at spending, he might consume (say) $10 million. (I couldn't consume anything close to $10 million in a year, but let's be conservative.) So if you want to measure spending, rather than income, the Gini is going to be overestimated by the effect of that $990 million.
As the very-rich get very-richer, they have the potential to stretch the Gini way out of proportion; but, in the most meaningful sense, consumption, inequality won't have changed much at all.
24. The super-rich, the ones that account for so much of the Gini, are also the biggest charitable donors. Bill Gates gives a lot of money to philanthropic causes. Even if they're in Africa, rather than the US, that actually increases worldwide equality, doesn't it? If you gave a million dollars to 100 random people, they'd spend it on themselves. If you give $100 million to Bill Gates, he'd spend it on some of the poorest people in the world. So greater inequality among the super-rich becomes greater equality overall!
25. Bernie Madoff lowered the Gini a little bit last year.
26. A substantial portion of income comes from savings and investments. And, because of the power of compounding, a small increase in savings today can add up to a huge difference in income in the future.
Ruth orders a pizza every week for a year, at $1,000. Sarah, having seen those commercials about saving money and living better, buys her pizza at Wal-Mart, for $400. She invests the $600 difference at 5% after inflation.
Forty years later, her $600 has grown into about $4200. She now pulls in an extra $300 or so in income from that $4200. The Gini rises, but there was never any inequality there, just differences in saving patterns.
And differences in savings are HUGE. I know older couples who made incomes I couldn't live on myself, who managed to save enough that they make more in retirement than they did when they were working. And I know people with six-figure incomes who are deep in debt and can't afford to pay their bills. The difference is not inequality of opportunity to earn income -- it's inequality of savings rates.
27. As we get richer and richer, it becomes easier to save. A 20" (tube) color TV now costs $100; I bought one thirteen years ago for my Dad at $500. In terms of TVs, you can save $400 with no change of lifestyle from 1996.
Or, of course, you could use the $400 to upgrade to a flat panel LCD, which many people do. But there's a choice there now that wasn't there only a few years ago. And because people are different, they make different choices. More choices means more diversity. More diversity means more dispersion in savings rates. More dispersion in savings rates means higher income inequality.
I think all this is a good thing.
28. Again because of the power of compounding, the effect of savings grows the more years you can save. So as life expectancies rise, you'd expect income inequality to rise. Imagine saving $1000 at age 25, again at 5%. By 65, you'll have $7,040. But if you can live to 95, you'll have $30,426. So it follows that the Gini should rise as people live longer and save longer.
If people lived to 200, inequality would be absolutely huge: save $1000 at 25 and you'll have $1.5 million by age 175. It wouldn't mean that society was unequal, just that it naturally takes time to build wealth. We don't worry about "inequality of knowledge" between a 25-year-old doctor and a 65-year-old doctor -- why should it be any different for savings?
Or, looked at another way: a 65-year-old has worked, over his lifetime, 40 times as much as a 25-year-old. Why would you expect their incomes to be equal?
29. It's pretty much accepted that we could create more equal incomes if we wanted to, by increasing tax rates on the rich. And it's also accepted that it would slow down economic growth -- say, by reducing it from 3% a year to 1.5% a year -- because of reduced incentive to work or take risks.
Now, suppose that country A decides to follow that route, and grow by 1.5% a year. Country B decides to let the inequality be, and grow by 3% a year.
100 years later, average income in country A has grown from $30,000 a year to $132,961. In country B, income has grown from $30,000 to $576,559.
So B is four times richer than A.
If you were to combine country A and B into one country, you'd almost certainly measure more inequality than in B alone! Now, if there was a moral obligation in A to increase equality even at the expense of total wealth, then is there also a moral obligation to increase equality *between A and B*? If there is, how would you do it? By force? And wouldn't that be unfair to B, whose population decided that the trade-off favored higher incomes over equal incomes?
30. Suppose that we -- the US and Canada -- had decided to increase equality back in 1908, and raised tax rates on the rich. And suppose that had lowered our growth rate by 1.5 percentage points over the last century. Then, we'd have only 23% as much income as we have now.
Would it have been worth it? Would you be willing, in retrospect, to take a 75% pay cut (and a 75% cut in government services, and probably a huge cut in medical advances) so that previous generations would have been more equal?
I wouldn't, and I doubt if anyone else would.
So then, don't you also have to think it would be a bad thing to make your great-great-grandchildren take a 75% pay cut 100 years into the future? Because that's the trade-off. At 1.5 percentage points difference, we'd seriously be costing the next generations hundreds of thousands of dollars each.
Now, 1.5 percentage points might be a bit high. If we assume only 1.0 percentage points, then instead of a 75% pay cut, it's a 60% pay cut. If we assume 0.5 percentage points, it's a 39% pay cut. At what point are we happy with the trade-off?
It's a legitimate question, but I don't think the Gini coefficient factors into the answer very easily. At least not unless you have an argument about what the Gini *should* be, and how much it's worth paying to get it there.
Absent that, the Gini is not very useful at all.
Brian Burke reminds me in the comments of another problem with the Gini, an important one.
31. New immigrants to Canada and the US tend to be poorer than average, if only because most countries in the world are poorer than we are. This distorts the Gini. To paraphrase Brian's theatre analogy in the comments:
Suppose that there are five people in the country, with incomes of $10K, $20K, $30K, $40K, and $50K. Over the next 10 years, everyone's salary rises $10K, substantially reducing inequality. But a new immigrant arrives, who earns $10K.
What do we now have? Six people, earning $10K, $20K, $30K, $40K, $50K, and $60K. This is a higher Gini than before -- but only because of the new immigrant! Within the country, equality is actually increasing.
This is huge, and I'm kicking myself for forgetting to include it. I remember several economists mentioning it in the context of income -- that the reason lower-quintile income hasn't seemed to increase is simply because new immigrants replace the lower-income people who moved up and out of the low-income group. (Here's a post by Arnold Kling, as an example.)
UPDATE: I'm just going to add more as I think of them.
32. Immigration, which mostly brings in people who start out at low incomes, increases the Gini, as I noted above. However, it *reduces* inequality for the world as a whole -- immigrants usually do much better here than they would in their home countries. Doesn't that suggest that looking at the Gini for a particular country, in isolation, could be misleading?
33. Activists decry the low wages American firms pay employees in poor countries. But if those US companies paid higher wages, they would be well above-market for those countries, increasing inequality there. Does that mean a higher Gini in a poorer country is OK?