# Inequality-adjusted GDP and median income

Dec 11 JDN 2459925

There are many problems with GDP as a measure of a nation’s prosperity. For one, GDP ignores natural resources and ecological degradation; so a tree is only counted in GDP once it is cut down. For another, it doesn’t value unpaid work, so caring for a child only increases GDP if you are a paid nanny rather than the child’s parents.

But one of the most obvious problems is the use of an average to evaluate overall prosperity, without considering the level of inequality.

Consider two countries. In Alphania, everyone has an income of about \$50,000. In Betavia, 99% of people have an income of \$1,000 and 1% have an income of \$10 million. What is the per-capita GDP of each country? Alphania’s is \$50,000 of course; but Betavia’s is \$100,990. Does it really make sense to say that Betavia is a more prosperous country? Maybe it has more wealth overall, but its huge inequality means that it is really not at a high level of development. It honestly sounds like an awful place to live.

A much more sensible measure would be something like median income: How much does a typical person have? In Alphania this is still \$50,000; but in Betavia it is only \$1,000.

Yet even this leaves out most of the actual distribution; by definition a median is only determined by what is the 50th percentile. We could vary all other incomes a great deal without changing the median.

A better measure would be some sort of inequality-adjusted per-capita GDP, which rescales GDP based on the level of inequality in a country. But we would need a good way of making that adjustment.

I contend that the most sensible way would be to adopt some kind of model of marginal utility of income, and then figure out what income would correspond to the overall average level of utility.

In other words, average over the level of happiness that people in a country get from their income, and then figure out what level of income would correspond to that level of happiness. If we magically gave everyone the same amount of money, how much would they need to get in order for the average happiness in the country to remain the same?

This is clearly going to be less than the average level of income, because marginal utility of income is decreasing; a dollar is not worth as much in real terms to a rich person as it is to a poor person. So if we could somehow redistribute all income evenly while keeping the average the same, that would actually increase overall happiness (though, for many reasons, we can’t simply do that).

For example, suppose that utility of income is logarithmic: U = ln(I).

This means that the marginal utility of an additional dollar is inversely proportional to how many dollars you already have: U'(I) = 1/I.

It also means that a 1% gain or loss in your income feels about the same regardless of how much income you have: ln((1+r)Y) = ln(Y) + ln(1+r). This seems like a quite reasonable, maybe even a bit conservative, assumption; I suspect that losing 1% of your income actually hurts more when you are poor than when you are rich.

Then the inequality adjusted GDP Y is a value such that ln(Y) is equal to the overall average level of utility: E[U] = ln(Y), so Y = exp(E[U]).

This sounds like a very difficult thing to calculate. But fortunately, the distribution of actual income seems to quite closely follow a log-normal distribution. This means that when we take the logarithm of income to get utility, we just get back a very nice, convenient normal distribution!

In fact, it turns out that for a log-normal distribution, the following holds: exp(E[ln(Y)]) = median(Y)

The income which corresponds to the average utility turns out to simply be the median income! We went looking for a better measure than median income, and ended up finding out that median income was the right measure all along.

This wouldn’t hold for most other distributions; and since real-world economies don’t perfectly follow a log-normal distribution, a more precise estimate would need to be adjusted accordingly. But the approximation is quite good for most countries we have good data on, so even for the ones we don’t, median income is likely a very good estimate.

The ranking of countries by median income isn’t radically different from the ranking by per-capita GDP; rich countries are still rich and poor countries are still poor. But it is different enough to matter.

Luxembourg is in 1st place on both lists. Scandinavian countries and the US are in the top 10 in both cases. So it’s fair to say that #ScandinaviaIsBetter for real, and the US really is so rich that our higher inequality doesn’t make our median income lower than the rest of the First World.

But some countries are quite different. Ireland looks quite good in per-capita GDP, but quite bad in median income. This is because a lot of the GDP in Ireland is actually profits by corporations that are only nominally headquartered in Ireland and don’t actually employ very many people there.

The comparison between the US, the UK, and Canada seems particularly instructive. If you look at per-capita GDP PPP, the US looks much richer at \$75,000 compared to Canada’s \$57,800 (a difference of 29% or 26 log points). But if you look at median personal income, they are nearly equal: \$19,300 in the US and \$18,600 in Canada (3.7% or 3.7 log points).

On the other hand, in per-capita GDP PPP, the UK looks close to Canada at \$55,800 (3.6% or 3.6 lp); but in median income it is dramatically worse, at only \$14,800 (26% or 23 lp). So Canada and the UK have similar overall levels of wealth, but life for a typical Canadian is much better than life for a typical Briton because of the higher inequality in Britain. And the US has more wealth than Canada, but it doesn’t meaningfully improve the lifestyle of a typical American relative to a typical Canadian.

# What really happened in Greece

JDN 2457506

I said I’d get back to this issue, so here goes.

Their per-capita GDP PPP has fallen from a peak of over \$32,000 in 2007 to a trough of just over \$24,000 in 2013, and only just began to recover over the last 2 years. That’s a fall of 29 log points. Put another way, the average person in Greece has about the same real income now that they had in the year 2000—a decade and a half of economic growth disappeared.

Their unemployment rate surged from about 7% in 2007 to almost 28% in 2013. It remains over 24%. That is, almost one quarter of all adults in Greece are seeking jobs and not finding them. The US has not seen an unemployment rate that high since the Great Depression.

Most shocking of all, over 40% of the population in Greece is now below the national poverty line. They define poverty as 60% of the inflation-adjusted average income in 2009, which works out to 665 Euros per person (\$756 at current exchange rates) per month, or about \$9000 per year. They also have an absolute poverty line, which 14% of Greeks now fall below, but only 2% did before the crash.

So now, let’s talk about why.

There’s a standard narrative you’ve probably heard many times, which goes something like this:

The Greek government spent too profligately, heaping social services on the population without the tax base to support them. Unemployment insurance was too generous; pensions were too large; it was too hard to fire workers or cut wages. Thus, work incentives were too weak, and there was no way to sustain a high GDP. But they refused to cut back on these social services, and as a result went further and further into debt until it finally became unsustainable. Now they are cutting spending and raising taxes like they needed to, and it will eventually allow them to repay their debt.

Here’s a fellow of the Cato Institute spreading this narrative on the BBC. Here’s ABC with a five bullet-point list: Pension system, benefits, early retirement, “high unemployment and work culture issues” (yes, seriously), and tax evasion. Here the Telegraph says that Greece “went on a spending spree” and “stopped paying taxes”.

That story is almost completely wrong. Almost nothing about it is true. Cato and the Telegraph got basically everything wrong. The only one ABC got right was tax evasion.

Here’s someone else arguing that Greece has a problem with corruption and failed governance; there is something to be said for this, as Greece is fairly corrupt by European standards—though hardly by world standards. For being only a generation removed from an authoritarian military junta, they’re doing quite well actually. They’re about as corrupt as a typical upper-middle income country like Libya or Botswana; and Botswana is widely regarded as the shining city on a hill of transparency as far as Sub-Saharan Africa is concerned. So corruption may have made things worse, but it can’t be the whole story.

First of all, social services in Greece were not particularly extensive compared to the rest of Europe.

Before the crisis, Greece’s government spending was about 44% of GDP.

That was about the same as Germany. It was slightly more than the UK. It was less than Denmark and France, both of which have government spending of about 50% of GDP.

Greece even tried to cut spending to pay down their debt—it didn’t work, because they simply ended up worsening the economic collapse and undermining the tax base they needed to do that.

Europe has fairly extensive social services by world standards—but that’s a major part of why it’s the First World. Even the US, despite spending far less than Europe on social services, still spends a great deal more than most countries—about 36% of GDP.

Second, if work incentives were a problem, you would not have high unemployment. People don’t seem to grasp what the word unemployment actually means, which is part of why I can’t stand it when news outlets just arbitrarily substitute “jobless” to save a couple of syllables. Unemployment does not mean simply that you don’t have a job. It means that you don’t have a job and are trying to get one.

The word you’re looking for to describe simply not having a job is nonemployment, and that’s such a rarely used term my spell-checker complains about it. Yet economists rarely use this term precisely because it doesn’t matter; a high nonemployment rate is not a symptom of a failing economy but a result of high productivity moving us toward the post-scarcity future (kicking and screaming, evidently). If the problem with Greece were that they were too lazy and they retire too early (which is basically what ABC was saying in slightly more polite language), there would be high nonemployment, but there would not be high unemployment. “High unemployment and work culture issues” is actually a contradiction.

Before the crisis, Greece had an employment-to-population ratio of 49%, meaning a nonemployment rate of 51%. If that sounds ludicrously high, you’re not accustomed to nonemployment figures. During the same time, the United States had an employment-to-population ratio of 52% and thus a nonemployment rate of 48%. So the number of people in Greece who were voluntarily choosing to drop out of work before the crisis was just slightly larger than the number in the US—and actually when you adjust for the fact that the US is full of young immigrants and Greece is full of old people (their median age is 10 years older than ours), it begins to look like it’s we Americans who are lazy. (Actually, it’s that we are studious—the US has an extremely high rate of college enrollment and the best colleges in the world. Full-time students are nonemployed, but they are certainly not unemployed.)

But Greece does have an enormously high debt, right? Yes—but it was actually not as bad before the crisis. Their government debt surged from 105% of GDP to almost 180% today. 105% of GDP is about what we have right now in the US; it’s less than what we had right after WW2. This is a little high, but really nothing to worry about, especially if you’ve incurred the debt for the right reasons. (The famous paper by Rogart and Reinhoff arguing that 90% of GDP is a horrible point of no return was literally based on math errors.)

So… what did happen? If it wasn’t their profligate spending that put them in this mess, what was it?

Well, first of all, there was the Second Depression, a worldwide phenomenon triggered by the collapse of derivatives markets in the United States. (You want unsustainable debt? Try 20 to 1 leveraged CDO-squareds and one quadrillion dollars in notional value. Notional value isn’t everything, but it’s a lot.) So it’s mainly our fault, or rather the fault of our largest banks. As far as us voters, it’s “our fault” in the way that if your car gets stolen it’s “your fault” for not locking the doors and installing a LoJack. We could have regulated against this and enforced those regulations, but we didn’t. (Fortunately, Dodd-Frank looks like it might be working.)

Greece was hit particularly hard because they are highly dependent on trade, particularly in services like tourism that are highly sensitive to the business cycle. Before the crash they imported 36% of GDP and exported 23% of GDP. Now they import 35% of GDP and export 33% of GDP—but it’s a much smaller GDP. Their exports have only slightly increased while their imports have plummeted. (This has reduced their “trade deficit”, but that has always been a silly concept. I guess it’s less silly if you don’t control your own currency, but it’s still silly.)

Once the crash happened, the US had sovereign monetary policy and the wherewithal to actually use that monetary policy effectively, so we weathered the crash fairly well, all things considered. Our unemployment rate barely went over 10%. But Greece did not have sovereign monetary policy—they are tied to the Euro—and that severely limited their options for expanding the money supply as a result of the crisis. Raising spending and cutting taxes was the best thing they could do.

But the bank(st?)ers and their derivatives schemes caused the Greek debt crisis a good deal more directly than just that. Part of the condition of joining the Euro was that countries must limit their fiscal deficit to no more than 3% of GDP (which is a totally arbitrary figure with no economic basis in case you were wondering). Greece was unwilling or unable to do so, but wanted to look like they were following the rules—so they called up Goldman Sachs and got them to make some special derivatives that Greece could use to continue borrowing without looking like they were borrowing. The bank could have refused; they could have even reported it to the European Central Bank. But of course they didn’t; they got their brokerage fee, and they knew they’d sell it off to some other bank long before they had to worry about whether Greece could ever actually repay it. And then (as I said I’d get back to in a previous post) they paid off the credit rating agencies to get them to rate these newfangled securities as low-risk.

In other words, Greece is not broke; they are being robbed.

Like homeowners in the US, Greece was offered loans they couldn’t afford to pay, but the banks told them they could, because the banks had lost all incentive to actually bother with the question of whether loans can be repaid. They had “moved on”; their “financial innovation” of securitization and collateralized debt obligations meant that they could collect origination fees and brokerage fees on loans that could never possibly be repaid, then sell them off to some Greater Fool down the line who would end up actually bearing the default. As long as the system was complex enough and opaque enough, the buyers would never realize the garbage they were getting until it was too late. The entire concept of loans was thereby broken: The basic assumption that you only loan money you expect to be repaid no longer held.

And it worked, for awhile, until finally the unpayable loans tried to create more money than there was in the world, and people started demanding repayment that simply wasn’t possible. Then the whole scheme fell apart, and banks began to go under—but of course we saved them, because you’ve got to save the banks, how can you not save the banks?

Honestly I don’t even disagree with saving the banks, actually. It was probably necessary. What bothers me is that we did nothing to save everyone else. We did nothing to keep people in their homes, nothing to stop businesses from collapsing and workers losing their jobs. Precisely because of the absurd over-leveraging of the financial system, the cost to simply refinance every mortgage in America would have been less than the amount we loaned out in bank bailouts. The banks probably would have done fine anyway, but if they didn’t, so what? The banks exist to serve the people—not the other way around.

We can stop this from happening again—here in the US, in Greece, in the rest of Europe, everywhere. But in order to do that we must first understand what actually happened; we must stop blaming the victims and start blaming the perpetrators.