Several of the world’s largest banks are known to have committed large-scale fraud. Why have we done so little about it?

July 16, JDN 2457951

In 2014, JPMorgan Chase paid a settlement of $614 million for fraudulent mortgage lending contributing to the crisis; but this was spare change compared to the $16.5 billion Bank of America paid in settlements for their fradulent mortgages.

In 2015, Citibank paid $700 million in restitution and $35 million in penalties for fraudulent advertising of “payment protection” services.

In 2016, Wells Fargo paid $190 in settlements for defrauding their customers with fake accounts.

Even PayPal has paid $25 million in settlements over abuses of their “PayPal Credit” system.
In 2016, Goldman Sachs paid $5.1 billion in settlements over their fraudulent sales of mortgage-backed securities.
But the worst offender of course is HSBC, which has paid $2.5 billion in settlements over fraud, as well as $1.9 billion in settlements for laundering money for terrorists. The US Justice Department has kept their money-laundering protections classified because they’re so bad that simply revealing them to the public could result in vast amounts of criminal abuse.
These are some of the world’s largest banks. JPMorgan Chase alone owns 8.0% of all investment banking worldwide; Goldman Sachs owns 6.6%; Citi owns 4.9%; Wells Fargo 2.5%; and HSBC 1.8%. That means that between them, these five corporations—all proven to have engaged in large-scale fraud—own almost one-fourth of all the world’s investment banking assets.

What shocks me the most about this is that hardly anyone seems to care. It’s seen as “normal”, as “business as usual” that a quarter of the world’s investment banking system is owned by white-collar criminals. When the issue is even brought up, often the complaint seems to be that the government is being somehow overzealous. The Economist even went so far as to characterize the prosecution of Wall Street fraud as a “shakedown”. Apparently the idea that our world’s most profitable companies shouldn’t be able to launder money for terrorists is just ridiculous. These are rich people; you expect them to follow rules? What is this, some kind of democracy?

Is this just always how it has been? Has corruption always been so thoroughly infused with finance that we don’t even know how to separate them? Has the oligarchy of the top 0.01% become so strong that we can’t even bring ourselves to challenge them when they commit literal treason? For, in case you’ve forgotten, that is what money-laundering for terrorists is: HSBC gave aid and comfort to the enemies of the free world. Like “freedom” and “terrorism”, the word “treason” has been so overused that we begin to forget its meaning; but one of the groups that HSBC gladly loaned money to is an organization that has financed Hezbollah and Al-Qaeda. These are people that American and British soldiers have died fighting against, and when a British bank was found colluding with them, the penalty was… a few weeks of profits, no personal responsibility, and not a single day of prison time. The settlement was in fact less than the profits gained from the criminal enterprise, so this wasn’t even a fine; it was a tax. Our response to treason was to impose a tax.

And this of course was not the result of some newfound leniency in American government in general. No, we are still the nation that imprisons 700 out of every 100,000 people, the nation with more prisoners than any other nation on Earth. Our police officers still kill young Black men with impunity, including at least three dozen unarmed Black men every year, many of them for no apparent reason at all. (The precise number is still unknown, as the police refuse to keep an official database of all the citizens they kill.) Decades of “law and order” politicians promising to stop the “rising crime” (that is actually falling) have made the United States very close to a police state, especially in poor neighborhoods that are primarily inhabited by Black and Hispanic people. We don’t even have an especially high crime rate, except for gun homicides (and that because we have so many guns, also more than any other nation on Earth). We are, if anything, an especially vindictive society, cruel, unforgiving, and violent towards those we perceive as transgressors.

Except, that is, when the criminals are rich. Even the racial biases seem to go away in such circumstances; there is no reasonable doubt as to the guilt of O.J. Simpson or Bill Cosby, but Simpson only ended up in prison years later on a completely unrelated offense, and after Cosby’s mistrial it’s unclear if he’ll ever see any prison time. I don’t see how either man could have been less punished for his crimes had he been White; but can anyone seriously doubt that both men would be punished more had they not been rich?

I do not think that capitalism is an irredeemable system. I think that, in themselves, free markets are very useful, and we should not remove or restrict them unnecessarily. But capitalism isn’t supposed to be a system where the rich can do whatever they want and the poor have to accept it. Capitalism is supposed to be a system where everyone is free to do as they choose, unless they are harming others—and the rules are supposed to be the same for everyone. A free market is not one where you can buy the right to take away other people’s freedom.

Is this just some utopian idealism? It would surely be utopian to imagine a world where fraud never happens, that much is true. Someone, somewhere, will always be defrauding someone else. But a world where fraud is punished most of the time? Where our most powerful institutions are still subject to the basic rule of law? Is that a pipe dream as well?

What we lose by aggregating

Jun 25, JDN 2457930

One of the central premises of current neoclassical macroeconomics is the representative agent: Rather than trying to keep track of all the thousands of firms, millions of people, and billions of goods and in a national economy, we aggregate everything up into a single worker/consumer and a single firm producing and consuming a single commodity.

This sometimes goes under the baffling misnomer of microfoundations, which would seem to suggest that it carries detailed information about the microeconomic behavior underlying it; in fact what this means is that the large-scale behavior is determined by some sort of (perfectly) rational optimization process as if there were just one person running the entire economy optimally.

First of all, let me say that some degree of aggregation is obviously necessary. Literally keeping track of every single transaction by every single person in an entire economy would require absurd amounts of data and calculation. We might have enough computing power to theoretically try this nowadays, but then again we might not—and in any case such a model would very rapidly lose sight of the forest for the trees.

But it is also clearly possible to aggregate too much, and most economists don’t seem to appreciate this. They cite a couple of famous theorems (like the Gorman Aggregation Theorem) involving perfectly-competitive firms and perfectly-rational identical consumers that offer a thin veneer of justification for aggregating everything into one, and then go on with their work as if this meant everything were fine.

What’s wrong with such an approach?

Well, first of all, a representative agent model can’t talk about inequality at all. It’s not even that a representative agent model says inequality is good, or not a problem; it lacks the capacity to even formulate the concept. Trying to talk about income or wealth inequality in a representative agent model would be like trying to decide whether your left hand is richer than your right hand.

It’s also nearly impossible to talk about poverty in a representative agent model; the best you can do is talk about a country’s overall level of development, and assume (not without reason) that a country with a per-capita GDP of $1,000 probably has a lot more poverty than a country with a per-capita GDP of $50,000. But two countries with the same per-capita GDP can have very different poverty rates—and indeed, the cynic in me wonders if the reason we’re reluctant to use inequality-adjusted measures of development is precisely that many American economists fear where this might put the US in the rankings. The Human Development Index was a step in the right direction because it includes things other than money (and as a result Saudi Arabia looks much worse and Cuba much better), but it still aggregates and averages everything, so as long as your rich people are doing well enough they can compensate for how badly your poor people are doing.

Nor can you talk about oligopoly in a representative agent model, as there is always only one firm, which for some reason chooses to act as if it were facing competition instead of rationally behaving as a monopoly. (This is not quite as nonsensical as it sounds, as the aggregation actually does kind of work if there truly are so many firms that they are all forced down to zero profit by fierce competition—but then again, what market is actually like that?) There is no market share, no market power; all are at the mercy of the One True Price.

You can still talk about externalities, sort of; but in order to do so you have to set up this weird doublethink phenomenon where the representative consumer keeps polluting their backyard and then can’t figure out why their backyard is so darn polluted. (I suppose humans do seem to behave like that sometimes; but wait, I thought you believed people were rational?) I think this probably confuses many an undergrad, in fact; the models we teach them about externalities generally use this baffling assumption that people consider one set of costs when making their decisions and then bear a different set of costs from the outcome. If you can conceptualize the idea that we’re aggregating across people and thinking “as if” there were a representative agent, you can ultimately make sense of this; but I think a lot of students get really confused by it.

Indeed, what can you talk about with a representative agent model? Economic growth and business cycles. That’s… about it. These are not minor issues, of course; indeed, as Robert Lucas famously said:

The consequences for human welfare involved in questions like these [on economic growth] are simply staggering: once one starts to think about them, it is hard to think about anything else.

I certainly do think that studying economic growth and business cycles should be among the top priorities of macroeconomics. But then, I also think that poverty and inequality should be among the top priorities, and they haven’t been—perhaps because the obsession with representative agent models make that basically impossible.

I want to be constructive here; I appreciate that aggregating makes things much easier. So what could we do to include some heterogeneity without too much cost in complexity?

Here’s one: How about we have p firms, making q types of goods, sold to n consumers? If you want you can start by setting all these numbers equal to 2; simply going from 1 to 2 has an enormous effect, as it allows you to at least say something about inequality. Getting them as high as 100 or even 1000 still shouldn’t be a problem for computing the model on an ordinary laptop. (There are “econophysicists” who like to use these sorts of agent-based models, but so far very few economists take them seriously. Partly that is justified by their lack of foundational knowledge in economics—the arrogance of physicists taking on a new field is legendary—but partly it is also interdepartmental turf war, as economists don’t like the idea of physicists treading on their sacred ground.) One thing that really baffles me about this is that economists routinely use computers to solve models that can’t be calculated by hand, but it never seems to occur to them that they could have started at the beginning planning to make the model solvable only by computer, and that would spare them from making the sort of heroic assumptions they are accustomed to making—assumptions that only made sense when they were used to make a model solvable that otherwise wouldn’t be.

You could also assign a probability distribution over incomes; that can get messy quickly, but we actually are fortunate that the constant relative risk aversion utility function and the Pareto distribution over incomes seem to fit the data quite well—as the product of those two things is integrable by hand. As long as you can model how your policy affects this distribution without making that integral impossible (which is surprisingly tricky), you can aggregate over utility instead of over income, which is a lot more reasonable as a measure of welfare.

And really I’m only scratching the surface here. There are a vast array of possible new approaches that would allow us to extend macroeconomic models to cover heterogeneity; the real problem is an apparent lack of will in the community to make such an attempt. Most economists still seem very happy with representative agent models, and reluctant to consider anything else—often arguing, in fact, that anything else would make the model less microfounded when plainly the opposite is the case.


What is the point of democracy?

Apr 9, JDN 2457853

[This topic was chosen by Patreon vote.]

“Democracy” is the sort of word that often becomes just an Applause Light (indeed it was the original example Less Wrong used). Like “freedom” and “liberty” (and for much the same reasons), it’s a good thing, that much we know; but it’s often unclear what is even meant by the word, much less why it should be so important to us.

From another angle, it is strangely common for economists and political scientists to argue that democracy is not all that important; they at least tend to use a precise formal definition of “democracy”, but are oddly quick to dismiss it as pointless or even harmful when it doesn’t line up precisely with their models of an efficient economy or society. I think the best example of this is the so-called “Downs paradox”, where political scientists were so steeped in the tradition of defining all rationality as psychopathic self-interest that they couldn’t even explain why it would occur to anyone to vote. (And indeed, rumor has it that most economists don’t bother to vote, much less campaign politically—which perhaps begins to explain why our economic policy is so terrible.)

Yet especially for Americans in the Trump era, I think it is vital to understand what “democracy” is supposed to mean, and why it is so important.

So, first of all, what is democracy? It is nothing more or less than government by popular vote.

This comes in degrees, of course: The purest direct democracy would have the entire population vote on even the most mundane policies and decisions. You could actually manage something like a monastery or a social club in such a fashion, but this is clearly unworkable on any large scale. Even once you get to hundreds of people, much less thousands or millions, it becomes unviable. The closest example I’ve seen is Switzerland, where there are always numerous popular referenda on ballots that are voted on by entire regions or the entire country—and even then, Switzerland does have representatives that make many of the day-to-day decisions.

So in practice all large-scale democratic systems are some degree of representative democracy, or republic, where some especially decisions may be made by popular vote, but most policies are made by elected representatives, staff appointed by those representatives, or even career civil servants who are appointed in a nominally apolitical process not so different from private-sector hiring. In the most extreme cases such civil servants can become so powerful that you get a deep state, where career bureaucrats exercise more power than elected officials—at that point I think you have actually lost the right to really call yourself a “democracy” and have become something more like a technocracy.
Yet of course a country can get even more undemocratic than that, and many are, governed by an aristocracy or oligarchy that vests power in a small number of wealthy and powerful individuals, or monarchy or autocracy that gives near-absolute power to a single individual.

Thus, there is a continuum of most to least democratic, with popular vote at one end, followed by elected representatives, followed by appointed civil servants, followed by a handful of oligarchs, and ultimately the most undemocratic system is an autocracy controlled by a single individual.

I also think it’s worth mentioning that constitutional monarchies with strong parliamentary systems, like the United Kingdom and Norway, are also “democracies” in the sense I intend. Yes, technically they have these hereditary monarchs—but in practice, the vast majority of the state’s power is vested in the votes of its people. Indeed, if we separate out parliamentary constitutional monarchy from presidential majoritarian democracy and compare them, the former might actually turn out to be better. Certainly, some of the world’s most prosperous nations are governed that way.

As I’ve already acknowledge, the very far extreme of pure direct democracy is unfeasible. But why would we want to get closer to that end? Why be like Switzerland or Denmark rather than like Turkey or Russia—or for that matter why be like California rather than like Mississippi?
Well, if you know anything about the overall welfare of these states, it almost seems obvious—Switzerland and Denmark are richer, happier, safer, healthier, more peaceful, and overall better in almost every way than Turkey and Russia. The gap between California and Mississippi is not as large, but it is larger than most people realize. Median household income in California is $64,500; in Mississippi it is only $40,593. Both are still well within the normal range of a highly-developed country, but that effectively makes California richer than Luxembourg but Mississippi poorer than South Korea. But perhaps the really stark comparison to make is life expectancy: Life expectancy at birth in California is almost 81 years, while in Mississippi it’s only 75.

Of course, there are a lot of other differences between states besides how much of their governance is done by popular referendum. Simply making Mississippi decide more things by popular vote would not turn it into California—much less would making Turkey more democratic turn it into Switzerland. So we shouldn’t attribute these comparisons entirely to differences in democracy. Indeed, a pair of two-way comparisons is only in the barest sense a statistical argument; we should be looking at dozens if not hundreds of comparisons if we really want to see the effects of democracy. And we should of course be trying to control for other factors, adjust for country fixed-effects, and preferably use natural experiments or instrumental variables to tease out causality.

Yet such studies have in fact been done. Stronger degrees of democracy appear to improve long-run economic growth, as well as reduce corruption, increase free trade, protect peace, and even improve air quality.

Subtler analyses have compared majoritarian versus proportional systems (where proportional seems, to me, at least, more democratic), as well as different republican systems with stronger or weaker checks and balances (stronger is clearly better, though whether that is “more democratic” is at least debatable). The effects of democracy on income distribution are more complicated, probably because there have been some highly undemocratic socialist regimes.

So, the common belief that democracy is good seems to be pretty well supported by the data. But why is democracy good? Is it just a practical matter of happening to get better overall results? Could it one day be overturned by some superior system such as technocracy or a benevolent autocratic AI?

Well, I don’t want to rule out the possibility of improving upon existing systems of government. Clearly new systems of government have in fact emerged over the course of history—Greek “democracy” and Roman “republic” were both really aristocracy, and anything close to universal suffrage didn’t really emerge on a large scale until the 20th century. So the 21st (or 22nd) century could well devise a superior form of government we haven’t yet imagined.
However, I do think there is good reason to believe that any new system of government that actually manages to improve upon democracy will still resemble democracy, because there are three key features democracy has that other systems of government simply can’t match. It is these three features that make democracy so important and so worth fighting for.

1. Everyone’s interests are equally represented.

Perhaps no real system actually manages to represent everyone’s interests equally, but the more democratic a system is, the better it will conform to this ideal. A well-designed voting system can aggregate the interests of an entire population and choose the course of action that creates the greatest overall benefit.

Markets can also be a good system for allocating resources, but while markets represent everyone’s interests, they do so highly unequally. Rich people are quite literally weighted more heavily in the sum.

Most systems of government do even worse, by completely silencing the voices of the majority of the population. The notion of a “benevolent autocracy” is really a conceit; what makes you think you could possibly keep the autocrat benevolent?

This is also why any form of disenfranchisement is dangerous and a direct attack upon democracy. Even if people are voting irrationally, against their own interests and yours, by silencing their voice you are undermining the most fundamental tenet of democracy itself. All voices must be heard, no exceptions. That is democracy’s fundamental strength.

2. The system is self-correcting.

This may more accurately describe a constitutional republican system with strong checks and balances, but that is what most well-functioning democracies have and it is what I recommend. If you conceive of “more democracy” as meaning that people can vote their way into fascism by electing a sufficiently charismatic totalitarian, then I do not want us to have “more democracy”. But just as contracts and regulations that protect you can make you in real terms more free because you can now safely do things you otherwise couldn’t risk, I consider strong checks and balances that maintain the stability of a republic against charismatic fascists to be in a deeper sense more democratic. This is ultimately semantic; I think I’ve made it clear enough that I want strong checks and balances.

With such checks and balances in place, democracies may move slower than autocracies; they may spend more time in deliberation or even bitter, polarized conflict. But this also means that their policies do not lurch from one emperor’s whim to another, and they are stable against being overtaken by corruption or fascism. Their policies are stable and predictable; their institutions are strong and resilient.

No other system of government yet devised by humans has this kind of stability, which may be why democracies are gradually taking over the world. Charismatic fascism fails when the charismatic leader dies; hereditary monarchy collapses when the great-grandson of the great king is incompetent; even oligarchy and aristocracy, which have at least some staying power, ultimately fall apart when the downtrodden peasants ultimately revolt. But democracy abides, for where monarchy and aristocracy are made of families and autocracy and fascism are made of a single man, democracy is made of principles and institutions. Democracy is evolutionarily stable, and thus in Darwinian terms we can predict it will eventually prevail.

3. The coercion that government requires is justified.

All government is inherently coercive. Libertarians are not wrong about this. Taxation is coercive. Regulation is coercive. Law is coercive. (The ones who go on to say that all government is “death threats” or “slavery” are bonkers, mind you. But it is in fact coercive.)

The coercion of government is particularly terrible if that coercion is coming from a system like an autocracy, where the will of the people is minimally if at all represented in the decisions of policymakers. Then that is a coercion imposed from outside, a coercion in the fullest sense, one person who imposes their will upon another.

But when government coercion comes from a democracy, it takes on a fundamentally different meaning. Then it is not they who coerce us—it is we who coerce ourselves. Now, why in the world would you coerce yourself? It seems ridiculous, doesn’t it?

Not if you know any game theory. There are in fall all sorts of reasons why one might want to coerce oneself, and two in particular become particularly important for the justification of democratic government.

The first and most important is collective action: There are many situations in which people all working together to accomplish a goal can be beneficial to everyone, but nonetheless any individual person who found a way to shirk their duty and not contribute could benefit even more. Anyone who has done a group project in school with a couple of lazy students in it will know this experience: You end up doing all the work, but they still get a good grade at the end. If everyone had taken the rational, self-interested action of slacking off, everyone in the group would have failed the project.

Now imagine that the group project we’re trying to achieve is, say, defending against an attack by Imperial Japan. We can’t exactly afford to risk that project falling through. So maybe we should actually force people to support it—in the form of taxes, or even perhaps a draft (as ultimately we did in WW2). Then it is no longer rational to try to shirk your duty, so everyone does their duty, the project gets done, and we’re all better off. How do we decide which projects are important enough to justify such coercion? We vote, of course. This is the most fundamental justification of democratic government.

The second that is relevant for government is commitment. There are many circumstances in which we want to accomplish something in the future, and from a long-run perspective it makes sense to achieve that goal—but then when the time comes to take action, we are tempted to procrastinate or change our minds. How can we resolve such a dilemma? Well, one way is to tie our own hands—to coerce ourselves into carrying out the necessary task we are tempted to avoid or delay.

This applies to many types of civil and criminal law, particularly regarding property ownership. Murder is a crime that most people would not commit even if it were completely legal. But shoplifting? I think if most people knew there would be no penalty for petty theft and retail fraud they would be tempted into doing it at least on occasion. I doubt it would be frequent enough to collapse our entire economic system, but it would introduce a lot of inefficiency, and make almost everything more expensive. By having laws in place that punish us for such behavior, we have a way of defusing such temptations, at least for most people most of the time. This is not as important for the basic functioning of government as is collective action, but I think it is still important enough to be worthy of mention.

Of course, there will always be someone who disagrees with any given law, regardless of how sensible and well-founded that law may be. And while in some sense “we all” agreed to pay these taxes, when the IRS actually demands that specific dollar amount from you, it may well be an amount that you would not have chosen if you’d been able to set our entire tax system yourself. But this is a problem of aggregation that I think may be completely intractable; there’s no way to govern by consensus, because human beings just can’t achieve consensus on the scale of millions of people. Governing by popular vote and representation is the best alternative we’ve been able to come up with. If and when someone devises a system of government that solves that problem and represents the public will even better than voting, then we will have a superior alternative to democracy.

Until then, it is as Churchill said: “Democracy is the worst form of government, except for all the others.”

Markets value rich people more

Feb 26, JDN 2457811

Competitive markets are optimal at maximizing utility, as long as you value rich people more.

That is literally a theorem in neoclassical economics. I had previously thought that this was something most economists didn’t realize; I had delusions of grandeur that maybe I could finally convince them that this is the case. But no, it turns out this is actually a well-known finding; it’s just that somehow nobody seems to care. Or if they do care, they never talk about it. For all the thousands of papers and articles about the distortions created by minimum wage and capital gains tax, you’d think someone could spare the time to talk about the vastly larger fundamental distortions created by the structure of the market itself.

It’s not as if this is something completely hopeless we could never deal with. A basic income would go a long way toward correcting this distortion, especially if coupled with highly progressive taxes. By creating a hard floor and a soft ceiling on income, you can reduce the inequality that makes these distortions so large.

The basics of the theorem are quite straightforward, so I think it’s worth explaining them here. It’s extremely general; it applies anywhere that goods are allocated by market prices and different individuals have wildly different amounts of wealth.

Suppose that each person has a certain amount of wealth W to spend. Person 1 has W1, person 2 has W2, and so on. They all have some amount of happiness, defined by a utility function, which I’ll assume is only dependent on wealth; this is a massive oversimplification of course, but it wouldn’t substantially change my conclusions to include other factors—it would just make everything more complicated. (In fact, including altruistic motives would make the whole argument stronger, not weaker.) Thus I can write each person’s utility as a function U(W). The rate of change of this utility as wealth increases, the marginal utility of wealth, is denoted U'(W).

By the law of diminishing marginal utility, the marginal utility of wealth U'(W) is decreasing. That is, the more wealth you have, the less each new dollar is worth to you.

Now suppose people are buying goods. Each good C provides some amount of marginal utility U'(C) to the person who buys it. This can vary across individuals; some people like Pepsi, others Coke. This marginal utility is also decreasing; a house is worth a lot more to you if you are living in the street than if you already have a mansion. Ideally we would want the goods to go to the people who want them the most—but as you’ll see in a moment, markets systematically fail to do this.

If people are making their purchases rationally, each person’s willingness-to-pay P for a given good C will be equal to their marginal utility of that good, divided by their marginal utility of wealth:

P = U'(C)/U'(W)

Now consider this from the perspective of society as a whole. If you wanted to maximize utility, you’d equalize marginal utility across individuals (by the Extreme Value Theorem). The idea is that if marginal utility is higher for one person, you should give that person more, because the benefit of what you give them will be larger that way; and if marginal utility is lower for another person, you should give that person less, because the benefit of what you give them will be smaller. When everyone is equal, you are at the maximum.

But market prices don’t actually do this. Instead they equalize over willingness-to-pay. So if you’ve got two individuals 1 and 2, instead of having this:

U'(C1) = U'(C2)

you have this:

P1 = P2

which translates to:

U'(C1)/U'(W1) = U'(C2)/U'(W2)

If the marginal utilities were the same, U'(W1) = U'(W2), we’d be fine; these would give the same results. But that would only happen if W1 = W2, that is, if the two individuals had the same amount of wealth.

Now suppose we were instead maximizing weighted utility, where each person gets a weighting factor A based on how “important” they are or something. If your A is higher, your utility matters more. If we maximized this new weighted utility, we would end up like this:

A1*U'(C1) = A2*U'(C2)

Because person 1’s utility counts for more, their marginal utility also counts for more. This seems very strange; why are we valuing some people more than others? On what grounds?

Yet this is effectively what we’ve already done by using market prices.
Just set:
A = 1/U'(W)

Since marginal utility of wealth is decreasing, 1/U'(W) is higher precisely when W is higher.

How much higher? Well, that depends on the utility function. The two utility functions I find most plausible are logarithmic and harmonic. (Actually I think both apply, one to other-directed spending and the other to self-directed spending.)

If utility is logarithmic:

U = ln(W)

Then marginal utility is inversely proportional:

U'(W) = 1/W

In that case, your value as a human being, as spoken by the One True Market, is precisely equal to your wealth:

A = 1/U'(W) = W

If utility is harmonic, matters are even more severe.

U(W) = 1-1/W

Marginal utility goes as the inverse square of wealth:

U'(W) = 1/W^2

And thus your value, according to the market, is equal to the square of your wealth:

A = 1/U'(W) = W^2

What are we really saying here? Hopefully no one actually believes that Bill Gates is really morally worth 400 trillion times as much as a starving child in Malawi, as the calculation from harmonic utility would imply. (Bill Gates himself certainly doesn’t!) Even the logarithmic utility estimate saying that he’s worth 20 million times as much is pretty hard to believe.

But implicitly, the market “believes” that, because when it decides how to allocate resources, something that is worth 1 microQALY to Bill Gates (about the value a nickel dropped on the floor to you or I) but worth 20 QALY (twenty years of life!) to the Malawian child, will in either case be priced at $8,000, and since the child doesn’t have $8,000, it will probably go to Mr. Gates. Perhaps a middle-class American could purchase it, provided it was worth some 0.3 QALY to them.

Now consider that this is happening in every transaction, for every good, in every market. Goods are not being sold to the people who get the most value out of them; they are being sold to the people who have the most money.

And suddenly, the entire edifice of “market efficiency” comes crashing down like a house of cards. A global market that quite efficiently maximizes willingness-to-pay is so thoroughly out of whack when it comes to actually maximizing utility that massive redistribution of wealth could enormously increase human welfare, even if it turned out to cut our total output in half—if utility is harmonic, even if it cut our total output to one-tenth its current value.

The only way to escape this is to argue that marginal utility of wealth is not decreasing, or at least decreasing very, very slowly. Suppose for instance that utility goes as the 0.9 power of wealth:

U(W) = W^0.9

Then marginal utility goes as the -0.1 power of wealth:

U'(W) = 0.9 W^(-0.1)

On this scale, Bill Gates is only worth about 5 times as much as the Malawian child, which in his particular case might actually be too small—if a trolley is about to kill either Bill Gates or 5 Malawian children, I think I save Bill Gates, because he’ll go on to save many more than 5 Malawian children. (Of course, substitute Donald Trump or Charles Koch and I’d let the trolley run over him without a second thought if even a single child is at stake, so it’s not actually a function of wealth.) In any case, a 5 to 1 range across the whole range of human wealth is really not that big a deal. It would introduce some distortions, but not enough to justify any redistribution that would meaningfully reduce overall output.

Of course, that commits you to saying that $1 to a Malawian child is only worth about $1.50 to you or I and $5 to Bill Gates. If you can truly believe this, then perhaps you can sleep at night accepting the outcomes of neoclassical economics. But can you, really, believe that? If you had the choice between an intervention that would give $100 to each of 10,000 children in Malawi, and another that would give $50,000 to each of 100 billionaires, would you really choose the billionaires? Do you really think that the world would be better off if you did?

We don’t have precise measurements of marginal utility of wealth, unfortunately. At the moment, I think logarithmic utility is the safest assumption; it’s about the slowest decrease that is consistent with the data we have and it is very intuitive and mathematically tractable. Perhaps I’m wrong and the decrease is even slower than that, say W^(-0.5) (then the market only values billionaires as worth thousands of times as much as starving children). But there’s no way you can go as far as it would take to justify our current distribution of wealth. W^(-0.1) is simply not a plausible value.

And this means that free markets, left to their own devices, will systematically fail to maximize human welfare. We need redistribution—a lot of redistribution. Don’t take my word for it; the math says so.

The real crisis in education is access, not debt

Jan 8, JDN 2457762

A few weeks ago I tried to provide assurances that the “student debt crisis” is really not much of a crisis; there is a lot of debt, but it is being spent on a very good investment both for individuals and for society. Student debt is not that large in the scheme of things, and it more than pays for itself in the long run.

But this does not mean we are not in the midst of an education crisis. It’s simply not about debt.

The crisis I’m worried about involves access.

As you may recall, there are a substantial number of people with very small amounts of student debt, and they tend to be the most likely to default. The highest default rates are among the group of people with student debt greater than $0 but less than $5000.

So how is it that there are people with only $5,000 in student debt anyway? You can’t buy much college for $5,000 these days, as tuition prices have risen at an enormous rate: From 1983 to 2013, in inflation-adjusted dollars, average annual tuition rose from $7,286 at public institutions and $17,333 at private institutions to $15,640 at public institutions and $35,987 at private institutions—more than doubling in each case.

Enrollments are much higher, but this by itself should not raise tuition per student. So where is all the extra money going? Some of it is due to increases in public funding that have failed to keep up with higher enrollments; but a lot of it just seems to be going to higher pay for administrators and athletic coaches. This is definitely a problem; students should not be forced to subsidize the millions of dollars most universities lose on funding athletics—the NCAA, who if anything are surely biased in favor of athletics, found that the total net loss due to athletics spending at FBS universities was $17 million per year. Only a handful of schools actually turn a profit on athletics, all of them Division I. So it might be fair to speak of an “irresponsible college administration crisis”, administrators who heap wealth upon themselves and their beloved athletic programs while students struggle to pay their bills, or even a “college tuition crisis” where tuition keeps rising far beyond what is sustainable. But that’s not the same thing as a “student debt crisis”—just as the mortgage crisis we had in 2008 is distinct from the slow-burning housing price crisis we’ve been in since the 1980s. Making restrictions on mortgages tighter might prevent banks from being as predatory as they have been lately, but it won’t suddenly allow people to better afford houses.

And likewise, I’m much more worried about students who don’t go to college because they are afraid of this so-called “debt crisis”; they’re going to end up much worse off. As Eduardo Porter put it in the New York Times:

And yet Mr. Beltrán says he probably wouldn’t have gone to college full time if he hadn’t received a Pell grant and financial aid from New York State to defray the costs. He has also heard too many stories about people struggling under an unbearable burden of student loans to even consider going into debt. “Honestly, I don’t think I would have gone,” he said. “I couldn’t have done four years.”

And that would have been the wrong decision.

His reasoning is not unusual. The rising cost of college looms like an insurmountable obstacle for many low-income Americans hoping to get a higher education. The notion of a college education becoming a financial albatross around the neck of the nation’s youth is a growing meme across the culture. Some education experts now advise high school graduates that a college education may not be such a good investment after all. “Sticker price matters a lot,” said Lawrence Katz, a professor of Harvard University. “It is a deterrent.”




And the most perplexing part of this accounting is that regardless of cost, getting a degree is the best financial decision a young American can make.

According to the O.E.C.D.’s report, a college degree is worth $365,000 for the average American man after subtracting all its direct and indirect costs over a lifetime. For women — who still tend to earn less than men — it’s worth $185,000.

College graduates have higher employment rates and make more money. According to the O.E.C.D., a typical graduate from a four-year college earns 84 percent more than a high school graduate. A graduate from a community college makes 16 percent more.

A college education is more profitable in the United States than in pretty much every other advanced nation. Only Irish women get more for the investment: $185,960 net.

So, these students who have $5,000 or less in student debt; what does that mean? That amount couldn’t even pay for a single year at most universities, so how did that happen?

Well, they almost certainly went to community college; only a community college could provide you with a nontrivial amount of education for less than $5,000. But community colleges vary tremendously in their quality, and some have truly terrible matriculation rates. While most students who start at a four-year school do eventually get a bachelor’s degree (57% at public schools, 78% at private schools), only 17% of students who start at community college do. And once students drop out, they very rarely actually return to complete a degree.

Indeed, the only way to really have that little student debt is to drop out quickly. Most students who drop out do so chiefly for reasons that really aren’t all that surprising: Mostly, they can’t afford to pay their bills. “Unable to balance school and work” is the number 1 reported reason why students drop out of college.

In the American system, student loans are only designed to pay the direct expenses of education; they often don’t cover the real costs of housing, food, transportation and healthcare, and even when they do, they basically never cover the opportunity cost of education—the money you could be making if you were working full-time instead of going to college. For many poor students, simply breaking even on their own expenses isn’t good enough; they have families that need to be taken care of, and that means working full-time. Many of them even need to provide for their parents or grandparents who may be poor or disabled. Yet in the US system it is tacitly assumed that your parents will help you—so when you need to help them, what are you supposed to do? You give up on college and you get a job.

The most successful reforms for solving this problem have been comprehensive; they involved working to support students directly and intensively in all aspects of their lives, not just the direct financial costs of school itself.

Another option would be to do something more like what they do in Sweden, where there is also a lot of student debt, but for a very different reason. The direct cost of college is paid automatically by the government. Yet essentially all Swedish students have student debt, and total student debt in Sweden is much larger than other European countries and comparable to the United States; why? Because Sweden understands that you should also provide for the opportunity cost. In Sweden, students live fully self-sufficient on student loans, just as if they were working full-time. They are not expected to be supported by their parents.

The problem with American student loans, then, is not that they are too large—but that they are too small. They don’t provide for what students actually need, and thus don’t allow them to make the large investment in their education that would have paid off in the long run. Panic over student loans being too large could make the problem worse, if it causes us to reduce the amount of loanable funds available for students.

The lack of support for poor students isn’t the only problem. There are also huge barriers to education in the US based upon race. While Asian students do as well (if not better) than White students, Black and Latino students have substantially lower levels of educational attainment. Affirmative action programs can reduce these disparities, but they are unpopular and widely regarded as unfair, and not entirely without reason.

A better option—indeed one that should be a no-brainer in my opinion—is not to create counter-biases in favor of Black and Latino students (which is what affirmative action is), but to eliminate biases in favor of White students that we know exist. Chief among these are so-called “legacy admissions”, in which elite universities attract wealthy alumni donors by granting their children admission and funding regardless of whether they even remotely deserve it or would contribute anything academically to the university.

These “legacy admissions” are frankly un-American. They go against everything our nation supposedly stands for; in fact, they reek of feudalism. And unsurprisingly, they bias heavily in favor of White students—indeed, over 90 percent of legacy admits are White and Protestant. Athletic admissions are also contrary to the stated mission of the university, though their racial biases are more complicated (Black students are highly overrepresented in football and basketball admits, for example) and it is at least not inherently un-American to select students based upon their athletic talent as opposed to their academic talent.

But this by itself would not be enough; the gaps are clearly too large to close that way. Getting into college is only the start, and graduation rates are much worse for Black students than White students. Moreover, the education gap begins well before college—high school dropout rates are much higher among Black and Latino studentsas well.

In fact, even closing the education gap by itself would not be enough; racial biases permeate our whole society. Black individuals with college degrees are substantially more likely to be unemployed and have substantially lower wages on average than White individuals with college degrees—indeed, a bachelor’s degree gets a Black man a lower mean wage than a White man would get with only an associate’s degree.

Fortunately, the barriers against women in college education have largely been conquered. In fact, there are now more women in US undergraduate institutions than men. This is not to say that there are not barriers against women in society at large; women still make about 75% as much income as men on average, and even once you adjust for factors such as education and career choice they still only make about 95% as much. Moreover, these factors we’re controlling for are endogenous. Women don’t choose their careers in a vacuum, they choose them based upon a variety of social and cultural pressures. The fact that 93% of auto mechanics are men and 79% of clerical workers are women might reflect innate differences in preferences—but it could just as well reflect a variety of cultural biases or even outright discrimination. Quite likely, it’s some combination of these. So it is not obvious to me that the “adjusted” wage gap is actually a more accurate reflection of the treatment of women in our society than the “unadjusted” wage gap; the true level of bias is most likely somewhere in between the two figures.

Gender wage gaps vary substantially across age groups and between even quite similar countries: Middle-aged women in Germany make 28% less than middle-aged men, while in France that gap is only 19%. Young women in Latvia make 14% less than young men, but in Romania they make 1.1% more. This variation clearly shows that this is not purely the effect of some innate genetic difference in skills or preferences; it must be at least in large part the product of cultural pressures or policy choices.

Even within academia, women are less likely to be hired full-time instead of part-time, awarded tenure, or promoted to administrative positions. Moreover, this must be active discrimination in some form, because gaps in hiring and wage offers between men and women persist in randomized controlled experiments. You can literally present the exact same resume and get a different result depending on whether you attached a male name or a female name.

But at least when it comes to the particular question of getting bachelor’s degrees, we have achieved something approaching equality across gender, and that is no minor accomplishment. Most countries in the world still have more men than women graduating from college, and in some countries the difference is terrifyingly large. I found from World Bank data that in the Democratic Republic of Congo, only 3% of men go to college—and less than 1% of women do. Even in Germany, 29% of men graduate from college but only 19% of women do. Getting both of these figures over 30% and actually having women higher than men is a substantial achievement for which the United States should be proud.

Yet it still remains the case that Americans who are poor, Black, Native American, or Latino are substantially less likely to ever make it through college. Panic about student debt might well be making this problem worse, as someone whose family makes $15,000 per year is bound to hear $50,000 in debt as an overwhelming burden, even as you try to explain that it will eventually pay for itself seven times over.

We need to instead be talking about the barriers that are keeping people from attending college, and pressuring them to drop out once they do. Debt is not the problem. Even tuition is not really the problem. Access is the problem. College is an astonishingly good investment—but most people never get the chance to make it. That is what we need to change.

No, Scandinavian countries aren’t parasites. They’re just… better.

Oct 1, JDN 2457663

If you’ve been reading my blogs for awhile, you likely have noticed me occasionally drop the hashtag #ScandinaviaIsBetter; I am in fact quite enamored of the Scandinavian (or Nordic more generally) model of economic and social policy.

But this is not a consensus view (except perhaps within Scandinavia itself), and I haven’t actually gotten around to presenting a detailed argument for just what it is that makes these countries so great.

I was inspired to do this by discussion with a classmate of mine (who shall remain nameless) who emphatically disagreed; he actually seems to think that American economic policy is somewhere near optimal (and to be fair, it might actually be near optimal, in the broad space of all possible economic policies—we are not Maoist China, we are not Somalia, we are not a nuclear wasteland). He couldn’t disagree with the statistics on how wealthy and secure and happy Scandinavian countries are, so instead he came up with this: “They are parasites.”

What he seemed to mean by this is that somehow Scandinavian countries achieve their success by sapping wealth from other countries, perhaps the rest of Europe, perhaps the world more generally. On this view, it’s not that Norway and Denmark aren’t rich because they economic policy basically figured out; no, they are somehow draining those riches from elsewhere.

This could scarcely be further from the truth.

But first, consider a couple of countries that are parasites, at least partially: Luxembourg and Singapore.

Singapore has an enormous trade surplus: 5.5 billion SGD per month, which is $4 billion per month, so almost $50 billion per year. They also have a positive balance of payments of $61 billion per year. Singapore’s total GDP is about $310 billion, so these are not small amounts. What does this mean? It means that Singapore is taking in a lot more money than they are spending out. They are effectively acting as mercantilists, or if you like as a profit-seeking corporation.

Moreover, Singapore is totally dependent on trade: their exports are over $330 billion per year, and their imports are over $280 billion. You may recognize each of these figures as comparable to the entire GDP of the country. Yes, their total trade is 200% of GDP. They aren’t really so much a country as a gigantic trading company.

What about Luxembourg? Well, they have a trade deficit of 420 million Euros per month, which is about $560 million per year. Their imports total about $2 billion per year, and their exports about $1.5 billion. Since Luxembourg’s total GDP is $56 billion, these aren’t unreasonably huge figures (total trade is about 6% of GDP); so Luxembourg isn’t a parasite in the sense that Singapore is.

No, what makes Luxembourg a parasite is the fact that 36% of their GDP is due to finance. Compare the US, where 12% of our GDP is finance—and we are clearly overfinancialized. Over a third of Luxembourg’s income doesn’t involve actually… doing anything. They hold onto other people’s money and place bets with it. Even insofar as finance can be useful, it should be only very slightly profitable, and definitely not more than 10% of GDP. As Stiglitz and Krugman agree (and both are Nobel Laureate economists), banking should be boring.

Do either of these arguments apply to Scandinavia? Let’s look at trade first. Denmark’s imports total about 42 billion DKK per month, which is about $70 billion per year. Their exports total about $90 billion per year. Denmark’s total GDP is $330 billion, so these numbers are quite reasonable. What are their main sectors? Manufacturing, farming, and fuel production. Notably, not finance.

Similar arguments hold for Sweden and Norway. They may be small countries, but they have diversified economies and strong production of real economic goods. Norway is probably overly dependent on oil exports, but they are specifically trying to move away from that right now. Even as it is, only about $90 billion of their $150 billion exports are related to oil, and exports in general are only about 35% of GDP, so oil is about 20% of Norway’s GDP. Compare that to Saudi Arabia, of which has 90% of its exports related to oil, accounting for 45% of GDP. If oil were to suddenly disappear, Norway would lose 20% of their GDP, dropping their per-capita GDP… all the way to the same as the US. (Terrifying!) But Saudi Arabia would suffer a total economic collapse, and their per capita-GDP would fall from where it is now at about the same as the US to about the same as Greece.

And at least oil actually does things. Oil exporting countries aren’t parasites so much as they are drug dealers. The world is “rolling drunk on petroleum”, and until we manage to get sober we’re going to continue to need that sweet black crude. Better we buy it from Norway than Saudi Arabia.

So, what is it that makes Scandinavia so great? Why do they have the highest happiness ratings, the lowest poverty rates, the best education systems, the lowest unemployment rates, the best social mobility and the highest incomes? To be fair, in most of these not literally every top spot is held by a Scandinavian country; Canada does well, Germany does well, the UK does well, even the US does well. Unemployment rates in particular deserve further explanation, because a lot of very poor countries report surprisingly low unemployment rates, such as Cambodia and Laos.

It’s also important to recognize that even great countries can have serious flaws, and the remnants of the feudal system in Scandinavia—especially in Sweden—still contribute to substantial inequality of wealth and power.

But in general, I think if you assembled a general index of overall prosperity of a country (or simply used one that already exists like the Human Development Index), you would find that Scandinavian countries are disproportionately represented at the very highest rankings. This calls out for some sort of explanation.

Is it simply that they are so small? They are certainly quite small; Norway and Denmark each have fewer people than the core of New York City, and Sweden has slightly more people than the Chicago metropolitan area. Put them all together, add in Finland and Iceland (which aren’t quite Scandinavia), and all together you have about the population of the New York City Combined Statistical Area.

But some of the world’s smallest countries are also its poorest. Samoa and Kiribati each have populations comparable to the city of Ann Arbor and per-capita GDPs 1/10 that of the US. Eritrea is the same size as Norway, and 70 times poorer. Burundi is slightly larger than Sweden, and has a per-capita GDP PPP of only $3.14 per day.

There’s actually a good statistical reason to expect that the smallest countries should vary the most in their incomes; you’re averaging over a smaller sample so you get more variance in the estimate. But this doesn’t explain why Norway is rich and Eritrea is poor. Incomes aren’t assigned randomly. This might be a reason to try comparing Norway to specifically New York City or Los Angeles rather than to the United States as a whole (Norway still does better, in case you were wondering—especially compared to LA); but it’s not a reason to say that Norway’s wealth doesn’t really count.

Is it because they are ethnically homogeneous? Yes, relatively speaking; but perhaps not as much as you imagine. 14% of Sweden’s population is immigrants, of which 64% are from outside the EU. 10% of Denmark’s population is comprised of immigrants, of which 66% came from non-Western countries. Immigrants are 13% of Norway’s population, of which half are from non-Western countries.

That’s certainly more ethnically homogeneous than the United States; 13% of our population is immigrants, which may sound comparable, but almost all non-immigrants in Scandinavia are of indigenous Nordic descent, all “White” by the usual classification. Meanwhile the United States is 64% non-Hispanic White, 16% Hispanic, 12% Black, 5% Asian, and 1% Native American or Pacific Islander.

Scandinavian countries are actually by some measures less homogeneous than the US in terms of religion, however; only 4% of Americans are not Christian (78.5%), atheist (16.1%), or Jewish (1.7%), and only 0.6% are Muslim. As much as In Sweden, on the other hand, 60% of the population is nominally Lutheran, but 80% is atheist, and 5% of the population is Muslim. So if you think of Christian/Muslim as the sharp divide (theologically this doesn’t make a whole lot of sense, but it seems to be the cultural norm in vogue), then Sweden has more religious conflict to worry about than the US does.

Moreover, there are some very ethnically homogeneous countries that are in horrible shape. North Korea is almost completely ethnically homogeneous, for example, as is Haiti. There does seem to be a correlation between higher ethnic diversity and lower economic prosperity, but Canada and the US are vastly more diverse than Japan and South Korea yet significantly richer. So clearly ethnicity is not the whole story here.

I do think ethnic homogeneity can partly explain why Scandinavian countries have the good policies they do; because humans are tribal, ethnic homogeneity engenders a sense of unity and cooperation, a notion that “we are all in this together”. That egalitarian attitude makes people more comfortable with some of the policies that make Scandinavia what it is, which I will get into at the end of this post.

What about culture? Is there something about Nordic ideas, those Viking traditions, that makes Scandinavia better? Miles Kimball has argued this; he says we need to import “hard work, healthy diets, social cohesion and high levels of trust—not Socialism”. And truth be told, it’s hard to refute this assertion, since it’s very difficult to isolate and control for cultural variables even though we know they are important.

But this difficulty in falsification is a reason to be cautious about such a hypothesis; it should be a last resort when all the more testable theories have been ruled out. I’m not saying culture doesn’t matter; it clearly does. But unless you can test it, “culture” becomes a theory that can explain just about anything—which means that it really explains nothing.

The “social cohesion and high levels of trust” part actually can be tested to some extent—and it is fairly well supported. High levels of trust are strongly correlated with economic prosperity. But we don’t really need to “import” that; the US is already near the top of the list in countries with the highest levels of trust.

I can’t really disagree with “good diet”, except to say that almost everywhere eats a better diet than the United States. The homeland of McDonald’s and Coca-Cola is frankly quite dystopian when it comes to rates of heart disease and diabetes. Given our horrible diet and ludicrously inefficient healthcare system, the only reason we live as long as we do is that we are an extremely rich country (so we can afford to pay the most for healthcare, for certain definitions of “afford”), and almost no one here smokes anymore. But good diet isn’t so much Scandinavian as it is… un-American.

But as for “hard work”, he’s got it backwards; the average number of work hours per week is 33 in Denmark and Norway, compared to 38 in the US. Among full-time workers in the US, the average number of hours per week is a whopping 47. Working hours in the US are much more intensive than anywhere in Europe, including Scandinavia. Though of course we are nowhere near the insane work addiction suffered by most East Asian countries; lately South Korea and Japan have been instituting massive reforms to try to get people to stop working themselves to death. And not surprisingly, work-related stress is a leading cause of death in the United States. If anything, we need to import some laziness, or at least a sense of work-life balance. (Indeed, I’m fairly sure that the only reason he said “hard work” is that it’s a cultural Applause Light in the US; being against hard work is like being against the American Flag or homemade apple pie. At this point, “we need more hard work” isn’t so much an assertion as it is a declaration of tribal membership.)

But none of these things adequately explains why poverty and inequality is so much lower in Scandinavia than it is in the United States, and there’s really a quite simple explanation.

Why is it that #ScandinaviaIsBetter? They’re not afraid to make rich people pay higher taxes so they can help poor people.

In the US, this idea of “redistribution of wealth” is anathema, even taboo; simply accusing a policy of being “redistributive” or “socialist” is for many Americans a knock-down argument against that policy. In Denmark, “socialist” is a meaningful descriptor; some policies are “socialist”, others “capitalist”, and these aren’t particularly weighted terms; it’s like saying here that a policy is “Keynesian” or “Monetarist”, or if that’s too obscure, saying that it’s “liberal” or “conservative”. People will definitely take sides, and it is a matter of political importance—but it’s inside the Overton Window. It’s not almost unthinkable as it is here.

If culture has an effect here, it likely comes from Scandinavia’s long traditions of egalitarianism. Going at least back to the Vikings, in theory at least (clearly not always in practice), people—or at least fellow Scandinavians—were considered equal participants in society, no one “better” or “higher” than anyone else. Even today, it is impolite in Denmark to express pride at your own accomplishments; there’s a sense that you are trying to present yourself as somehow more deserving than others. Honestly this attitude seems unhealthy to me, though perhaps preferable to the unrelenting narcissism of American society; but insofar as culture is making Scandinavia better, it’s almost certainly because this thoroughgoing sense of egalitarianism underlies all their economic policy. In the US, the rich are brilliant and the poor are lazy; in Denmark, the rich are fortunate and the poor are unlucky. (Which theory is more accurate? Donald Trump. I rest my case.)

To be clear, Scandinavia is not communist; and they are certainly not Stalinist. They don’t believe in total collectivization of industry, or complete government control over the economy. They don’t believe in complete, total equality, or even a hard cap on wealth: Stefan Persson is an 11-figure billionaire. Does he pay high taxes, living in Sweden? Yes he does, considerably higher than he’d pay in the US. He seems to be okay with that. Why, it’s almost like his marginal utility of wealth is now negligible.

Scandinavian countries also don’t try to micromanage your life in the way often associated with “socialism”–in fact I’d say they do it less than we do in the US. Here we have Republicans who want to require drug tests for food stamps even though that literally wastes money and helps no one; there they just provide a long list of government benefits for everyone free of charge. They just held a conference in Copenhagen to discuss the possibility of transitioning many of these benefits into a basic income; and basic income is the least intrusive means of redistributing wealth.

In fact, because Scandinavian countries tax differently, it’s not necessarily the case that people always pay higher taxes there. But they pay more transparent taxes, and taxes with sharper incidence. Denmark’s corporate tax rate is only 22% compared to 35% in the US; but their top personal income tax bracket is 59% while ours is only 39.6% (though it can rise over 50% with some state taxes). Denmark also has a land value tax and a VAT, both of which most economists have clamored for for generations. (The land value tax I totally agree with; the VAT I’m a little more ambivalent about.) Moreover, filing your taxes in Denmark is not a month-long stress marathon of gathering paperwork, filling out forms, and fearing that you’ll get something wrong and be audited as it is in the US; they literally just send you a bill. You can contest it, but most people don’t. You just pay it and you’re done.

Now, that does mean the government is keeping track of your income; and I might think that Americans would never tolerate such extreme surveillance… and then I remember that PRISM is a thing. Apparently we’re totally fine with the NSA reading our emails, but God forbid the IRS just fill out our 1040s for us (that they are going to read anyway). And there’s no surveillance involved in requiring retail stores to incorporate sales tax into listed price like they do in Europe instead of making us do math at the cash register like they do here. It’s almost like Americans are trying to make taxes as painful as possible.

Indeed, I think Scandanavian socialism is a good example of how high taxes are a sign of a free society, not an authoritarian one. Taxes are a minimal incursion on liberty. High taxes are how you fund a strong government and maintain extensive infrastructure and public services while still being fair and following the rule of law. The lowest tax rates in the world are in North Korea, which has ostensibly no taxes at all; the government just confiscates whatever they decide they want. Taxes in Venezuela are quite low, because the government just owns all the oil refineries (and also uses multiple currency exchange rates to arbitrage seigniorage). US taxes are low by First World standards, but not by world standards, because we combine a free society with a staunch opposition to excessive taxation. Most of the rest of the free world is fine with paying a lot more taxes than we do. In fact, even using Heritage Foundation data, there is a clear positive correlation between higher tax rates and higher economic freedom:
Graph: Heritage Foundation Economic Freedom Index and tax burden

What’s really strange, though, is that most Americans actually support higher taxes on the rich. They often have strange or even incoherent ideas about what constitutes “rich”; I have extended family members who have said they think $100,000 is an unreasonable amount of money for someone to make, yet somehow are totally okay with Donald Trump making $300,000,000. The chant “we are the 99%” has always been off by a couple orders of magnitude; the plutocrat rentier class is the top 0.01%, not the top 1%. The top 1% consists mainly of doctors and lawyers and engineers; the top 0.01%, to a man—and they are nearly all men, in fact White men—either own corporations or work in finance. But even adjusting for all this, it seems like at least a bare majority of Americans are all right with “redistributive” “socialist” policies—as long as you don’t call them that.

So I suppose that’s sort of what I’m trying to do; don’t think of it as “socialism”. Think of it as #ScandinaviaIsBetter.

“The cake is a lie”: The fundamental distortions of inequality

July 13, JDN 2457583

Inequality of wealth and income, especially when it is very large, fundamentally and radically distorts outcomes in a capitalist market. I’ve already alluded to this matter in previous posts on externalities and marginal utility of wealth, but it is so important I think it deserves to have its own post. In many ways this marks a paradigm shift: You can’t think about economics the same way once you realize it is true.

To motivate what I’m getting at, I’ll expand upon an example from a previous post.

Suppose there are only two goods in the world; let’s call them “cake” (K) and “money” (M). Then suppose there are three people, Baker, who makes cakes, Richie, who is very rich, and Hungry, who is very poor. Furthermore, suppose that Baker, Richie and Hungry all have exactly the same utility function, which exhibits diminishing marginal utility in cake and money. To make it more concrete, let’s suppose that this utility function is logarithmic, specifically: U = 10*ln(K+1) + ln(M+1)

The only difference between them is in their initial endowments: Baker starts with 10 cakes, Richie starts with $100,000, and Hungry starts with $10.

Therefore their starting utilities are:

U(B) = 10*ln(10+1)= 23.98

U(R) = ln(100,000+1) = 11.51

U(H) = ln(10+1) = 2.40

Thus, the total happiness is the sum of these: U = 37.89

Now let’s ask two very simple questions:

1. What redistribution would maximize overall happiness?
2. What redistribution will actually occur if the three agents trade rationally?

If multiple agents have the same diminishing marginal utility function, it’s actually a simple and deep theorem that the total will be maximized if they split the wealth exactly evenly. In the following blockquote I’ll prove the simplest case, which is two agents and one good; it’s an incredibly elegant proof:

Given: for all x, f(x) > 0, f'(x) > 0, f”(x) < 0.

Maximize: f(x) + f(A-x) for fixed A

f'(x) – f'(A – x) = 0

f'(x) = f'(A – x)

Since f”(x) < 0, this is a maximum.

Since f'(x) > 0, f is monotonic; therefore f is injective.

x = A – x


This can be generalized to any number of agents, and for multiple goods. Thus, in this case overall happiness is maximized if the cakes and money are both evenly distributed, so that each person gets 3 1/3 cakes and $33,336.66.

The total utility in that case is:

3 * (10 ln(10/3+1) + ln(33,336.66+1)) = 3 * (14.66 + 10.414) = 3 (25.074) =75.22

That’s considerably better than our initial distribution (almost twice as good). Now, how close do we get by rational trade?

Each person is willing to trade up until the point where their marginal utility of cake is equal to their marginal utility of money. The price of cake will be set by the respective marginal utilities.

In particular, let’s look at the trade that will occur between Baker and Richie. They will trade until their marginal rate of substitution is the same.

The actual algebra involved is obnoxious (if you’re really curious, here are some solved exercises of similar trade problems), so let’s just skip to the end. (I rushed through, so I’m not actually totally sure I got it right, but to make my point the precise numbers aren’t important.)
Basically what happens is that Richie pays an exorbitant price of $10,000 per cake, buying half the cakes with half of his money.

Baker’s new utility and Richie’s new utility are thus the same:
U(R) = U(B) = 10*ln(5+1) + ln(50,000+1) = 17.92 + 10.82 = 28.74
What about Hungry? Yeah, well, he doesn’t have $10,000. If cakes are infinitely divisible, he can buy up to 1/1000 of a cake. But it turns out that even that isn’t worth doing (it would cost too much for what he gains from it), so he may as well buy nothing, and his utility remains 2.40.

Hungry wanted cake just as much as Richie, and because Richie has so much more Hungry would have gotten more happiness from each new bite. Neoclassical economists promised him that markets were efficient and optimal, and so he thought he’d get the cake he needs—but the cake is a lie.

The total utility is therefore:

U = U(B) + U(R) + U(H)

U = 28.74 + 28.74 + 2.40

U = 59.88

Note three things about this result: First, it is more than where we started at 37.89—trade increases utility. Second, both Richie and Baker are better off than they were—trade is Pareto-improving. Third, the total is less than the optimal value of 75.22—trade is not utility-maximizing in the presence of inequality. This is a general theorem that I could prove formally, if I wanted to bore and confuse all my readers. (Perhaps someday I will try to publish a paper doing that.)

This result is incredibly radical—it basically goes against the core of neoclassical welfare theory, or at least of all its applications to real-world policy—so let me be absolutely clear about what I’m saying, and what assumptions I had to make to get there.

I am saying that if people start with different amounts of wealth, the trades they would willfully engage in, acting purely under their own self interest, would not maximize the total happiness of the population. Redistribution of wealth toward equality would increase total happiness.

First, I had to assume that we could simply redistribute goods however we like without affecting the total amount of goods. This is wildly unrealistic, which is why I’m not actually saying we should reduce inequality to zero (as would follow if you took this result completely literally). Ironically, this is an assumption that most neoclassical welfare theory agrees with—the Second Welfare Theorem only makes any sense in a world where wealth can be magically redistributed between people without any harmful economic effects. If you weaken this assumption, what you find is basically that we should redistribute wealth toward equality, but beware of the tradeoff between too much redistribution and too little.

Second, I had to assume that there’s such a thing as “utility”—specifically, interpersonally comparable cardinal utility. In other words, I had to assume that there’s some way of measuring how much happiness each person has, and meaningfully comparing them so that I can say whether taking something from one person and giving it to someone else is good or bad in any given circumstance.

This is the assumption neoclassical welfare theory generally does not accept; instead they use ordinal utility, on which we can only say whether things are better or worse, but never by how much. Thus, their only way of determining whether a situation is better or worse is Pareto efficiency, which I discussed in a post a couple years ago. The change from the situation where Baker and Richie trade and Hungry is left in the lurch to the situation where all share cake and money equally in socialist utopia is not a Pareto-improvement. Richie and Baker are slightly worse off with 25.07 utilons in the latter scenario, while they had 28.74 utilons in the former.

Third, I had to assume selfishness—which is again fairly unrealistic, but again not something neoclassical theory disagrees with. If you weaken this assumption and say that people are at least partially altruistic, you can get the result where instead of buying things for themselves, people donate money to help others out, and eventually the whole system achieves optimal utility by willful actions. (It depends just how altruistic people are, as well as how unequal the initial endowments are.) This actually is basically what I’m trying to make happen in the real world—I want to show people that markets won’t do it on their own, but we have the chance to do it ourselves. But even then, it would go a lot faster if we used the power of government instead of waiting on private donations.

Also, I’m ignoring externalities, which are a different type of market failure which in no way conflicts with this type of failure. Indeed, there are three basic functions of government in my view: One is to maintain security. The second is to cancel externalities. The third is to redistribute wealth. The DOD, the EPA, and the SSA, basically. One could also add macroeconomic stability as a fourth core function—the Fed.

One way to escape my theorem would be to deny interpersonally comparable utility, but this makes measuring welfare in any way (including the usual methods of consumer surplus and GDP) meaningless, and furthermore results in the ridiculous claim that we have no way of being sure whether Bill Gates is happier than a child starving and dying of malaria in Burkina Faso, because they are two different people and we can’t compare different people. Far more reasonable is not to believe in cardinal utility, meaning that we can say an extra dollar makes you better off, but we can’t put a number on how much.

And indeed, the difficulty of even finding a unit of measure for utility would seem to support this view: Should I use QALY? DALY? A Likert scale from 0 to 10? There is no known measure of utility that is without serious flaws and limitations.

But it’s important to understand just how strong your denial of cardinal utility needs to be in order for this theorem to fail. It’s not enough that we can’t measure precisely; it’s not even enough that we can’t measure with current knowledge and technology. It must be fundamentally impossible to measure. It must be literally meaningless to say that taking a dollar from Bill Gates and giving it to the starving Burkinabe would do more good than harm, as if you were asserting that triangles are greener than schadenfreude.

Indeed, the whole project of welfare theory doesn’t make a whole lot of sense if all you have to work with is ordinal utility. Yes, in principle there are policy changes that could make absolutely everyone better off, or make some better off while harming absolutely no one; and the Pareto criterion can indeed tell you that those would be good things to do.

But in reality, such policies almost never exist. In the real world, almost anything you do is going to harm someone. The Nuremburg trials harmed Nazi war criminals. The invention of the automobile harmed horse trainers. The discovery of scientific medicine took jobs away from witch doctors. Inversely, almost any policy is going to benefit someone. The Great Leap Forward was a pretty good deal for Mao. The purges advanced the self-interest of Stalin. Slavery was profitable for plantation owners. So if you can only evaluate policy outcomes based on the Pareto criterion, you are literally committed to saying that there is no difference in welfare between the Great Leap Forward and the invention of the polio vaccine.

One way around it (that might actually be a good kludge for now, until we get better at measuring utility) is to broaden the Pareto criterion: We could use a majoritarian criterion, where you care about the number of people benefited versus harmed, without worrying about magnitudes—but this can lead to Tyranny of the Majority. Or you could use the Difference Principle developed by Rawls: find an ordering where we can say that some people are better or worse off than others, and then make the system so that the worst-off people are benefited as much as possible. I can think of a few cases where I wouldn’t want to apply this criterion (essentially they are circumstances where autonomy and consent are vital), but in general it’s a very good approach.

Neither of these depends upon cardinal utility, so have you escaped my theorem? Well, no, actually. You’ve weakened it, to be sure—it is no longer a statement about the fundamental impossibility of welfare-maximizing markets. But applied to the real world, people in Third World poverty are obviously the worst off, and therefore worthy of our help by the Difference Principle; and there are an awful lot of them and very few billionaires, so majority rule says take from the billionaires. The basic conclusion that it is a moral imperative to dramatically reduce global inequality remains—as does the realization that the “efficiency” and “optimality” of unregulated capitalism is a chimera.