# 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 Brexit means for you, Britain, and the world

July 6, JDN 2457576

It’s a stupid portmanteau, but it has stuck, so I guess I’ll suck it up and use the word “Brexit” to refer to the narrowly-successful referendum declaring that the United Kingdom will exit the European Union.

In this post I’ll try to answer one of the nagging questions that was the most googled question in the UK after the vote was finished: “What does it mean to leave the EU?”

First of all, let’s answer the second-most googled question: “What is the EU?”

The European Union is one of those awkward international institutions, like the UN, NATO, and the World Bank, that doesn’t really have a lot of actual power, but is meant to symbolize international unity and ultimately work toward forming a more cohesive international government. This is probably how people felt about national government maybe 500 years ago, when feudalism was the main system of government and nation-states hadn’t really established themselves yet. Oh, sure, there’s a King of England and all that; but what does he really do? The real decisions are all made by the dukes and the earls and whatnot. Likewise today, the EU and NATO don’t really do all that much; the real decisions are made by the UK and the US.

The biggest things that the EU does are all economic; it creates a unified trade zone called the single market that is meant to allow free movement of people and goods between countries in Europe with little if any barrier. The ultimate goal was actually to make it as unified as internal trade within the United States, but it never quite made it that far. More realistically, it’s like NAFTA, but more so, and with ten times as many countries (yet, oddly enough, almost exactly the same number of people). Starting in 1999, the EU also created the Euro, a unified national currency, which to this day remains one of the world’s strongest, most stable currencies—right up there with the dollar and the pound.

Wait, the pound? Yes, the pound. While the UK entered the EU, they did not enter the Eurozone, and therefore retained their own national currency rather than joining the Euro. One of the first pieces of fallout from Brexit was a sudden drop in the pound’s value as investors around the world got skittish about the UK’s ability to support its current level of trade.
There are in fact several layers of “EU-ness”, if you will, several levels of commitment to the project of the European Union. The strongest commitment is from the Inner Six, the six founding countries (Belgium, France, the Netherlands, Luxembourg, Italy, and Germany), followed by the aforementioned Eurozone, followed by the Schengen Area (which bans passport controls among citizens of member countries), followed by the EU member states as a whole, followed by candidate states (such as Turkey), which haven’t joined yet but are trying to. The UK was never all that fully committed to the EU to begin with; they aren’t even in the Schengen Area, much less the Eurozone. So by this vote, the UK is essentially saying that they’d dipped their toes in the water, and it was too cold, so they’re going home.

Despite the fear of many xenophobic English people (yes, specifically English—Scotland and Northern Ireland overwhelmingly voted against leaving the EU), the EU already had very little control over the UK. Though I suppose they will now have even less.

Countries in the Eurozone were subject to a lot more control, via the European Central Bank controlling their money supply. The strong Euro is great for countries like Germany and France… and one of the central problems facing countries like Portugal and Greece. Strong currencies aren’t always a good thing—they cause trade deficits. And Greece has so little influence over European monetary policy that it’s essentially as if they were pegged to someone else’s currency. But the UK really can’t use this argument, because they’ve stayed on the pound all along.

The real question is what’s going to happen to the UK’s participation in the single market. I can outline four possible scenarios, from best to worst:

1. Brexit doesn’t actually happen: Parliament could use (some would say “abuse”) their remaining authority to override the referendum and keep the UK in the EU. After a brief period of uncertainty, everything returns to normal. Probably the best outcome, but fairly unlikely, and rather undemocratic. Probability: 10%
2. The single market is renegotiated, making Brexit more bark than bite: At this point, a more likely way for the UK to stop the bleeding would be to leave the EU formally, but renegotiate all the associated treaties and trade agreements so that most of the EU rules about free trade, labor standards, environmental regulations, and so on actually remain in force. This would result in a brief recession in the UK as policies take time to be re-established and markets are overwhelmed by uncertainty, but its long-term economic trajectory would remain the same. The result would be similar to the current situation in Norway, and hey, #ScandinaviaIsBetter. Probability: 40%
3. Brexit is fully carried out, but the UK remains whole: If UKIP attains enough of a mandate and a majority coalition in Parliament, they could really push through their full agenda of withdrawing from European trade. If this happens, the UK would withdraw from the single market and could implement any manner of tariffs, quotas, and immigration restrictions. Hundreds of thousands of Britons living in Europe and Europeans living in Britain would be displaced. Trade between the UK and EU would dry up. Krugman argues that it won’t be as bad as the most alarmist predictions, but it will still be pretty bad—and he definitely should know, since this is the sort of thing he got a Nobel for. The result would be a severe recession, with an immediate fall in UK GDP of somewhere between 2% and 4%, and a loss of long-run potential GDP between 6% and 8%. (For comparison, the Great Recession in the US was a loss of about 5% of GDP over 2 years.) The OECD has run a number of models on this, and the Bank of England is especially worried because they have little room to lower interest rates to fight such a recession. Their best bet would probably be to print an awful lot of pounds, but with the pound already devalued and so much national pride wrapped up in the historical strength of the pound, that seems unlikely. The result would therefore be a loss of about \$85 billion in wealth immediately and more like \$200 billion per year in the long run—for basically no reason. Sadly, this is the most likely scenario. Probability: 45%
4. Balkanization of the UK: As I mentioned earlier, Scotland and Northern Ireland overwhelmingly voted against Brexit, and want no part of it. As a result, they have actually been making noises about leaving the UK if the UK decides to leave the EU. The First Minister of Scotland has proposed an “independence referendum” on Scotland leaving the UK in order to stay in the EU, and a grassroots movement in Northern Ireland is pushing for unification of all of Ireland in order to stay in the EU with the Republic of Ireland. This sort of national shake-up is basically unprecedented; parts of one state breaking off in order to stay in a larger international union? The closest example I can think of is West Germany and East Germany splitting to join NATO and the Eastern Bloc respectively, and I think we all know how well that went for East Germany. But really this is much more radical than that. NATO was a military alliance, not an economic union; nuclear weapons understandably make people do drastic things. Moreover, Germany hadn’t unified in the first place until Bismark in 1871, and thus was less than a century old when it split again. Scotland joined England to form the United Kingdom in 1707, three centuries ago, at a time when the United States didn’t even exist—indeed, George Washington hadn’t even been born. Scotland leaving the UK to stay with the EU would be like Texas leaving the US to stay in NAFTA—nay, more like Massachusetts doing that, because Scotland was a founding member of the UK and Texas didn’t become a state until 1845. While Scotland might actually be better off this way than if they go along with Brexit (and England of course even worse), this Balkanization would cast a dark shadow over all projects of international unification for decades to come, at a level far beyond what any mere Brexit could do. It would essentially mean declaring that all national unity is up for grabs, there is no such thing as a permanently unified state. I never thought I would see such a policy even being considered, much less passed; but I can’t be sure it won’t happen. My best hope is that Scotland can use this threat to keep the UK in the EU, or at least in the single market—but what if UKIP calls their bluff? Probability: 5%

Options 2 and 3 are the most likely, and actually there are intermediate cases between them; they could only implement immigration restrictions but not tariffs, for example, and that would lessen the economic fallout but still displace hundreds of thousands of people. They could only remove a few of the most stringent EU regulations, but still keep most of the good ones; that wouldn’t be so bad. Or they could be idiots and remove the good regulations (like environmental sustainability and freedom of movement) while keeping the more questionable ones (like the ban on capital controls).

Only time will tell, and the most important thing to keep in mind here is that trade is nonzero-sum. If and when England loses that \$200 billion per year in trade, where will it go? Nowhere. It will disappear. That wealth—about enough to end world hunger—will simply never be created, because xenophobia reintroduced inefficiencies into the global market. Yes, it might not all disappear—Europe’s scramble for import sources and export markets could lead to say \$50 billion per year in increased US trade, for example, because we’re the obvious substitute—but the net effect on the whole world will almost certainly be negative. The world will become poorer, and Britain will feel it the most.

Still, like most economists there is another emotion I’m feeling besides “What have they done!? This is terrible!”; there’s another part of my brain saying, “Wow, this is an amazing natural experiment in free trade!” Maybe the result will be bad enough to make people finally wake up about free trade, but not bad enough to cause catastrophic damage. If nothing else, it’ll give economists something to work on for years.

# 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.