How rich are we, really?

Oct 29, JDN 2458056

The most commonly-used measure of a nation’s wealth is its per-capita GDP, which is simply a total of all spending in a country divided by its population. More recently we adjust for purchasing power, giving us GDP per capita at purchasing power parity (PPP).

By this measure, the United States always does well. At most a dozen countries are above us, most of them by a small amount, and all of them are quite small countries. (For fundamental statistical reasons, we should expect both the highest and lowest average incomes to be in the smallest countries.)

But this is only half the story: It tells us how much income a country has, but not how that income is distributed. We should adjust for inequality.

How can we do this? I have devised a method that uses the marginal utility of wealth plus a measure of inequality called the Gini coefficient to work out an estimate of the average utility, instead of the average income.

I then convert back into a dollar figure. This figure is the income everyone would need to have under perfect equality, in order to give the same real welfare as the current system. That is, if we could redistribute wealth in such a way to raise everyone above this value up to it, and lower everyone above this value down to it, the total welfare of the country would not change. This provides a well-founded ranking of which country’s people are actually better off overall, accounting for both overall income and the distribution of that income.

The estimate is sensitive to the precise form I use for marginal utility, so I’ll show you comparisons for three different cases.

The “conservative” estimate uses a risk aversion parameter of 1, which means that utility is logarithmic in income. The real value of a dollar is inversely proportional to the number of dollars you already have.

The medium estimate uses a risk aversion parameter of 2, which means that the real value of a dollar is inversely proportional to the square of the number of dollars you already have.

And then the “liberal” estimate uses a risk aversion parameter of 3, which means that the real value of a dollar is inversely proportional to the cube of the number of dollars you already have.

I’ll compare ten countries, which I think are broadly representative of classes of countries in the world today.

The United States, the world hegemon which needs no introduction.

China, rising world superpower and world’s most populous country.

India, world’s largest democracy and developing economy with a long way to go.

Norway, as representative of the Scandinavian social democracies.

Germany, as representative of continental Europe.

Russia, as representative of the Soviet Union and the Second World bloc.

Saudi Arabia, as representative of the Middle East petrostates.

Botswana, as representative of African developing economies.

Zimbabwe, as representative of failed Sub-Saharan African states.

Brazil, as representative of Latin American developing economies.
The ordering of these countries by GDP per-capita PPP is probably not too surprising:

  1. Norway 69,249
  2. United States 57,436
  3. Saudi Arabia 55,158
  4. Germany 48,111
  5. Russia 26,490
  6. Botswana 17,042
  7. China 15,399
  8. Brazil 15,242
  9. India 6,616
  10. Zimbabwe 1,970

Norway is clearly the richest, the US, Saudi Arabia, and Germany are quite close, Russia is toward the upper end, Botswana, China, and Brazil are close together in the middle, and then India and especially Zimbabwe are extremely poor.

But now let’s take a look at the inequality in each country, as measured by the Gini coefficient (which ranges from 0, perfect equality, to 1, total inequality).

  1. Botswana 0.605
  2. Zimbabwe 0.501
  3. Brazil 0.484
  4. United States 0.461
  5. Saudi Arabia 0.459
  6. China 0.422
  7. Russia 0.416
  8. India 0.351
  9. Germany 0.301
  10. Norway 0.259

The US remains (alarmingly) close to Saudi Arabia by this measure. Most of the countries are between 40 and 50. But Botswana is astonishingly unequal, while Germany and Norway are much more equal.

With that in mind, let’s take a look at the inequality-adjusted per-capita GDP. First, the conservative estimate, with a parameter of 1:

  1. Norway 58700
  2. United States 42246
  3. Saudi Arabia 40632
  4. Germany 39653
  5. Russia 20488
  6. China 11660
  7. Botswana 11138
  8. Brazil 11015
  9. India 5269
  10. Zimbabwe 1405

So far, ordering of nations is almost the same compared to what we got with just per-capita GDP. But notice how Germany has moved up closer to the US and Botswana actually fallen behind China.

Now let’s try a parameter of 2, which I think is the closest to the truth:

  1. Norway 49758
  2. Germany 32683
  3. United States 31073
  4. Saudi Arabia 29931
  5. Russia 15581
  6. China 8829
  7. Brazil 7961
  8. Botswana 7280
  9. India 4197
  10. Zimbabwe 1002

Now we have seen some movement. Norway remains solidly on top, but Germany has overtaken the United States and Botswana has fallen behind not only China, but also Brazil. Russia remains in the middle, and India and Zimbawbe remain on the bottom.

Finally, let’s try a parameter of 3.

  1. Norway 42179
  2. Germany 26937
  3. United States 22855
  4. Saudi Arabia 22049
  5. Russia 11849
  6. China 6685
  7. Brazil 5753
  8. Botswana 4758
  9. India 3343
  10. Zimbabwe 715

Norway has now pulled far and away ahead of everyone else. Germany is substantially above the United States. China has pulled away from Brazil, and Botswana has fallen almost all the way to the level of India. Zimbabwe, as always, is at the very bottom.

Let’s compare this to another measure of national well-being, the Inequality-Adjusted Human Development Index (which goes from 0, the worst, to 1 the best). This index combines education, public health, and income, and adjusts for inequality. It seems to be a fairly good measure of well-being, but it’s very difficult to compile data for, so a lot of countries are missing (including Saudi Arabia); plus the precise weightings on everything are very ad hoc.

  1. Norway 0.898
  2. Germany 0.859
  3. United States 0.796
  4. Russia 0.725
  5. China 0.543
  6. Brazil 0.531
  7. India 0.435
  8. Botswana 0.433
  9. Zimbabwe 0.371

Other than putting India above Botswana, this ordering is the same as what we get from my (much easier to calculate and theoretically more well-founded) index with either a parameter of 2 or 3.

What’s more, my index can be directly interpreted: The average standard of living in the US is as if everyone were making $31,073 per year. What exactly is an IHDI index of 0.796 supposed to mean? We’re… 79.6% of the way to the best possible country?

In any case, there’s a straightforward (if not terribly surprising) policy implication here: Inequality is a big problem.

In particular, inequality in the US is clearly too high. Despite an overall income that is very high, almost 18 log points higher than Germany, our overall standard of living is actually about 5 log points lower due to our higher level of inequality. While our average income is only 19 log points lower than Norway, our actual standard of living is 47 log points lower.

Inequality in Botswana also means that their recent astonishing economic growth is not quite as impressive as it at first appeared. Many people are being left behind. While in raw income they appear to be 10 log points ahead of China and only 121 log points behind the US, once you adjust for their very high inequality they are 19 log points behind China, and 145 log points behind the US.

Of course, some things don’t change. Norway is still on top, and Zimbabwe is still on the bottom.

Means, medians, and inequality denial

JDN 2457324 EDT 21:45

You may have noticed a couple of big changes in the blog today. The first is that I’ve retitled it “Human Economics” to emphasize the positive, and the second is that I’ve moved it to my domain which is a lot shorter and easier to type. I’ll be making two bite-sized posts a week, just as I have been piloting for the last few weeks.

Earlier today I was dismayed to see a friend link to this graph by the American Enterprise Institute (a well-known Libertarian think-tank):


Look! The “above $100,000” is the only increasing category! That means standard of living in the US is increasing! There’s no inequality problem!

The AEI has an agenda to sell you, which is that the free market is amazing and requires absolutely no intervention, and government is just a bunch of big bad meanies who want to take your hard-earned money and give it away to lazy people. They chose very carefully what data to use for this plot in order to make it look like inequality isn’t increasing.

Here’s a more impartial way of looking at the situation, the most obvious, pre-theoretical way of looking at inequality: What has happened to mean income versus median income?

As a refresher from intro statistics, the mean is what you get by adding up the total money and dividing by the number of people; the median is what a person in the exact middle has. So for example if there are three people in a room, one makes $20,000, the second makes $50,000, and the third is Bill Gates making $10,000,000,000, then the mean income is $3,333,333,356 but the median income is $50,000. In a distribution similar to the power-law distribution that incomes generally fall into, the mean is usually higher than the median, and how much higher is a measure of how much inequality there is. (In my example, the mean is much higher, because there’s huge inequality with Bill Gates in the room.) This confuses people, because when people say “the average”, they usually intend the mean; but when they say “the average person”, they usually intend the median. The average person in my three-person example makes $50,000, but the average income is $3.3 billion.

So if we look at mean income versus median income in the US over time, this is what we see:


In 1953, mean household income was $36,535 and median household income was $32,932. Mean income was therefore 10.9% higher than median income.

In 2013, mean household income was $88,765 and median income was $66,632. Mean household income was therefore 33.2% higher than median income.

That, my dear readers, is a substantial increase in inequality. To be fair, it’s also a substantial increase in standard of living; these figures are already adjusted for inflation, so the average family really did see their standard of living roughly double during that period.

But this also isn’t the whole story.

First, notice that real median household income is actually about 5% lower now than it was in 2007. Real mean household income is also lower than its peak in 2006, but only by about 2%. This is why in a real sense we are still in the Second Depression; income for most people has not retained its pre-recession peak.

Furthermore, real median earnings for full-time employees have not meaningfully increased over the last 35 years; in 1982 dollars, they were $335 in 1979 and they are $340 now:


At first I thought this was because people were working more hours, but that doesn’t seem to be true; average weekly hours of work have fallen from 38.2 to 33.6:


The main reason seems to be actually that women are entering the workforce, so more households have multiple full-time incomes; while only 43% of women were in the labor force in 1970, almost 57% are now.


I must confess to a certain confusion on this point, however, as the difference doesn’t seem to be reflected in any of the measures of personal income. Median personal income was about 41% of median family income in 1974, and now it’s about 43%. I’m not sure exactly what’s going on here.


The Gini index, a standard measure of income inequality, is only collected every few years, yet shows a clear rising trend from 37% in 1986 to 41% in 2013:


But perhaps the best way to really grasp our rising inequality is to look at the actual proportions of income received by each portion of the population.

This is what it looks like if you use US Census data, broken down by groups of 20% and the top 5%; notice how since 1977 the top 5% have taken in more than the 40%-60% bracket, and they are poised to soon take in more than the 60%-80% bracket as well:


The result is even more striking if you use the World Top Incomes Database. You can watch the share of income rise for the top 10%, 5%, 1%, 0.1%, and 0.01%:


But in fact it’s even worse than it sounds. What I’ve just drawn double-counts a lot of things; it includes the top 0.01% in the top 0.1%, which is in turn included in the top 1%, and so on. If you exclude these, so that we’re only looking at the people in the top 10% but not the top 5%, the people in the top 5% but not the top 1%, and so on, something even more disturbing happens:


While the top 10% does see some gains, the top 5% gains faster, and the gains accrue even faster as you go up the chain.

Since 1970, the top 10%-5% share grew 10%. The top 0.01% share grew 389%.


Top 10-5% share

Top 10-5% share incl. cap. gains

Top 5-1% share

Top 5-1% share incl cap. gains

Top 1-0.5% share

Top 1-0.5% share incl. cap. gains

Top 0.5-0.1% share

Top 0.5-0.1% share incl. cap. gains

Top 0.1-0.01% share

Top 0.1-0.01% share incl. cap. gains

Top 0.01% share

Top 0.01% share incl. cap. gains



























Relative gain













To be clear, these are relative gains in shares. Including capital gains, the share of income received by the top 10%-5% grew from 10.96% to 12.06%, a moderate increase. The share of income received by the top 0.01% grew from 1.00% to 4.89%, a huge increase. (Yes, the top 0.01% now receive almost 5% of the income, making them on average almost 500 times richer than the rest of us.)

The pie has been getting bigger, which is a good thing. But the rich are getting an ever-larger piece of that pie, and the piece the very rich get is expanding at an alarming rate.

It’s certainly a reasonable question what is causing this rise in inequality, and what can or should be done about it. By people like the AEI try to pretend it doesn’t even exist, and that’s not economic policy analysis; that’s just plain denial.