arbitrage

What happened with GameStop?

PNRJ critique of neoclassical economics, current events, ethics, financial fraud, inequality, market failure, public policy , , , , , , ,

Feb 7 JDN 2459253

No doubt by now you’ve heard about the recent bubble in GameStop stock that triggered several trading stops, nearly destroyed a hedge fund, and launched a thousand memes. What really strikes me about this whole thing is how ordinary it is: This is basically the sort of thing that happens in our financial markets all the time. So why are so many people suddenly paying so much attention to it?

There are a few important ways this is unusual: Most importantly, the bubble was triggered by a large number of middle-class people investing small amounts, rather than by a handful of billionaires or hedge funds. It’s also more explicitly collusive than usual, with public statements in writing about what stocks are being manipulated rather than hushed whispers between executives at golf courses. Partly as a consequence of these, the response from the government and the financial industry has been quite different as well, trying to halt trading and block transactions in a way that they would never do if the crisis had been caused by large financial institutions.

If you’re interested in the technical details of what happened, what a short squeeze is and how it can make a hedge fund lose enormous amounts of money unexpectedly, I recommend this summary by KQED. But the gist of it is simple enough: Melvin Capital placed huge bets that GameStop stock would fall in price, and a coalition of middle-class traders coordinated on Reddit to screw them over by buying a bunch of GameStop stock and driving up the price. It worked, and now Melvin Capital lost something on the order of $3-5 billion in just a few days.

The particular kind of bet they placed is called a short, and it’s a completely routine practice on Wall Street despite the fact that I could never quite understand why it is a thing that should be allowed.

The essence of a short is quite simple: When you short, you are selling something you don’t own. You “borrow” it (it isn’t really even borrowing), and then sell it to someone else, promising to buy it back and return it to where you borrowed it from at some point in the future. This amounts to a bet that the price will decline, so that the price at which you buy it is lower than the price at which you sold it.

Doesn’t that seem like an odd thing to be allowed to do? Normally you can’t sell something you have merely borrowed. I can’t borrow a car and then sell it; car title in fact exists precisely to prevent this from happening. If I were to borrow your coat and then sell it to a thrift store, I’d have committed larceny. It’s really quite immaterial whether I plan to buy it back afterward; in general we do not allow people to sell things that they do not own.

Now perhaps the problem is that when I borrow your coat or your car, you expect me to return that precise object—not a similar coat or a car of equivalent Blue Book value, but your coat or your car. When I borrow a share of GameStop stock, no one really cares whether it is that specific share which I return—indeed, it would be almost impossible to even know whether it was. So in that way it’s a bit like borrowing money: If I borrow $20 from you, you don’t expect me to pay back that precise $20 bill. Indeed you’d be shocked if I did, since presumably I borrowed it in order to spend it or invest it, so how would I ever get it back?

But you also don’t sell money, generally speaking. Yes, there are currency exchanges and money-market accounts; but these are rather exceptional cases. In general, money is not bought and sold the way coats or cars are.

What about consumable commodities? You probably don’t care too much about any particular banana, sandwich, or gallon of gasoline. Perhaps in some circumstances we might “loan” someone a gallon of gasoline, intending them to repay us at some later time with a different gallon of gasoline. But far more likely, I think, would be simply giving a friend a gallon of gasoline and then not expecting any particular repayment except perhaps a vague offer of providing a similar favor in the future. I have in fact heard someone say the sentence “Can I borrow your sandwich?”, but it felt very odd when I heard it. (Indeed, I responded something like, “No, you can keep it.”)

And in order to actually be shorting gasoline (which is a thing that you, too, can do, perhaps even right now, if you have a margin account on a commodities exchange), it isn’t enough to borrow a gallon with the expectation of repaying a different gallon; you must also sell that gallon you borrowed. And now it seems very odd indeed to say to a friend, “Hey, can I borrow a gallon of gasoline so that I can sell it to someone for a profit?”

The usual arguments for why shorting should be allowed are much like the arguments for exotic financial instruments in general: “Increase liquidity”, “promote efficient markets”. These arguments are so general and so ubiquitous that they essentially amount to the strongest form of laissez-faire: Whatever Wall Street bankers feel like doing is fine and good and part of what makes American capitalism great.

In fact, I was never quite clear why margin accounts are something we decided to allow; margin trading is inherently high-leverage and thus inherently high-risk. Borrowing money in order to arbitrage financial assets doesn’t just seem like a very risky thing to do, it has been one way or another implicated in virtually every financial crisis that has ever occurred. It would be an exaggeration to say that leveraged arbitrage is the one single cause of financial crises, but it would be a shockingly small exaggeration. I think it absolutely is fair to say that if leveraged arbitrage did not exist, financial crises would be far rarer and further between.

Indeed, I am increasingly dubious of the whole idea of allowing arbitrage in general. Some amount of arbitrage may be unavoidable; there may always be people people who see that prices are different for the same item in two different markets, and then exploit that difference before anyone can stop them. But this is a bit like saying that theft is probably inevitable: Yes, every human society that has had a system of property ownership (which is most of them—even communal hunter-gatherers have rules about personal property), has had some amount of theft. That doesn’t mean there is nothing we can do to reduce theft, or that we should simply allow theft wherever it occurs.

The moral argument against arbitrage is straightforward enough: You’re not doing anything. No good is produced; no service is provided. You are making money without actually contributing any real value to anyone. You just make money by having money. This is what people in the Middle Ages found suspicious about lending money at interest; but lending money actually is doing something—sometimes people need more money than they have, and lending it to them is providing a useful service for which you deserve some compensation.

A common argument economists make is that arbitrage will make prices more “efficient”, but when you ask them what they mean by “efficient”, the answer they give is that it removes arbitrage opportunities! So the good thing about arbitrage is that it stops you from doing more arbitrage?

And what if it doesn’t stop you? Many of the ways to exploit price gaps (particularly the simplest ones like “where it’s cheap, buy it; where it’s expensive, sell it”) will automatically close those gaps, but it’s not at all clear to me that all the ways to exploit price gaps will necessarily do so. And even if it’s a small minority of market manipulation strategies that exploit gaps without closing them, those are precisely the strategies that will be most profitable in the long run, because they don’t undermine their own success. Then, left to their own devices, markets will evolve to use such strategies more and more, because those are the strategies that work.

That is, in order for arbitrage to be beneficial, it must always be beneficial; there must be no way to exploit price gaps without inevitably closing those price gaps. If that is not the case, then evolutionary pressure will push more and more of the financial system toward using methods of arbitrage that don’t close gaps—or even exacerbate them. And indeed, when you look at how ludicrously volatile and crisis-prone our financial system has become, it sure looks an awful lot like an evolutionary equilibrium where harmful arbitrage strategies have evolved to dominate.

A world where arbitrage actually led to efficient pricing would be a world where the S&P 500 rises a steady 0.02% per day, each and every day. Maybe you’d see a big move when there was actually a major event, like the start of a war or the invention of a vaccine for a pandemic. You’d probably see a jump up or down of a percentage point or two with each quarterly Fed announcement. But daily moves of even five or six percentage points would be a very rare occurrence—because the real expected long-run aggregate value of the 500 largest publicly-traded corporations in America is what the S&P 500 is supposed to represent, and that is not a number that should change very much very often. The fact that I couldn’t really tell you what that number is without multi-trillion-dollar error bars is so much the worse for anyone who thinks that financial markets can somehow get it exactly right every minute of every day.

Moreover, it’s not hard to imagine how we might close price gaps without simply allowing people to exploit them. There could be a bunch of economists at the Federal Reserve whose job it is to locate markets where there are arbitrage opportunities, and then a bundle of government funds that they can allocate to buying and selling assets in order to close those price gaps. Any profits made are received by the treasury; any losses taken are borne by the treasury. The economists would get paid a comfortable salary, and perhaps get bonuses based on doing a good job in closing large or important price gaps; but there is no need to give them even a substantial fraction of the proceeds, much less all of it. This is already how our money supply is managed, and it works quite well, indeed obviously much better than an alternative with “skin in the game”: Can you imagine the dystopian nightmare we’d live in if the Chair of the Federal Reserve actually received even a 1% share of the US money supply? (Actually I think that’s basically what happened in Zimbabwe: The people who decided how much money to print got to keep a chunk of the money that was printed.)

I don’t actually think this GameStop bubble is all that important in itself. A decade from now, it may be no more memorable than Left Shark or the Macarena. But what is really striking about it is how little it differs from business-as-usual on Wall Street. The fact that a few million Redditors can gather together to buy a stock “for the lulz” or to “stick it to the Man” and thereby bring hedge funds to their knees is not such a big deal in itself, but it is symptomatic of much deeper structural flaws in our financial system.

What would a game with realistic markets look like?

PNRJ experimental economics, macroeconomics, public policy , , , , , , ,

Aug 12 JDN 2458343

From Pokemon to Dungeons & Dragons, Final Fantasy to Mass Effect, almost all role-playing games have some sort of market: Typically, you buy and sell equipment, and often can buy services such as sleeping at inns. Yet the way those markets work is extremely rigid and unrealistic.

(I’m of course excluding games like EVE Online that actually create real markets between players; those markets are so realistic I actually think they would provide a good opportunity for genuine controlled experiments in macroeconomics.)

The weirdest thing about in-game markets is the fact that items almost always come with a fixed price. Sometimes there is some opportunity for haggling, or some randomization between different merchants; but the notion always persists that the item has a “true price” that is being adjusted upward or downward. This is more or less the opposite of how prices actually work in real markets.

There is no “true price” of a car or a pizza. Prices are whatever buyers and sellers make them. There is a true value—the amount of real benefit that can be obtained from a good—but even this is something that varies between individuals and also changes based on the other goods being consumed. The value of a pizza is considerably higher for someone who hasn’t eaten in days than to someone who just finished eating another pizza.

There is also what is called “The Law of One Price”, but like all laws of economics, it’s like the Pirate Code, more what you’d call a “guideline”, and it only applies to a particular good in a particular market at a particular time. The Law of One Price doesn’t even say that a pizza should have the same price tomorrow as it does today, or that the same pizza can’t be sold to two different customers at two different prices; it only says that the same pizza shouldn’t have two different prices in the same place at the same time for the same customer. (It seems almost tautological, right? And yet it still fails empirically, and does so again and again. I have seen offers for the same book in the same condition posted on the same website that differed by as much as 50%.)

In well-developed capitalist markets in large First World countries, we can lull ourselves into the illusion that there is only one price for a good, because markets are highly liquid and either highly competitive or controlled by a strong and stable oligopoly that enforces a particular price across places and times. The McDonald’s Dollar Menu is a policy choice by a massive multinational corporation; it’s not what would occur naturally if those items were sold on a competitive market.

Even then, this illusion can be broken when we are faced with a large economic shock, such as the OPEC price shock in 1973 or a natural disaster like Hurricane Katrina. It also tends to be broken for illiquid goods such as real estate.

If we consider the environment in which most role-playing games take place, it’s usually a sort of quasi-medieval or quasi-Renaissance feudal society, where a given government controls only a small region and traveling between towns is difficult and dangerous. Not only should the prices of goods differ substantially between towns, the currency used should frequently differ as well. Yes, most places would accept gold and silver; but a kingdom with a stable government will generally have a currency of significant seignorage, with coins worth considerably more than the gold used to mint them—yet the value of that seignorage will drop off as you move further away from that kingdom and its sphere of influence.

Moreover, prices should be inconsistent even between traders in the same town, and extremely volatile. When a town is mostly self-sufficient and trade is only a small part of its economy, even a small shock such as a bad thunderstorm or a brief drought can yield massive shifts in prices. Shortages and gluts will be frequent, as both supply and demand are small and ever-changing.

This wouldn’t be that difficult to implement. The simplest way would just be to institute random shocks to prices that vary by place and time. A more sophisticated method would be to actually simulate supply and demand for different goods, and then have prices respond to realistic shocks (e.g. a drought makes wheat more expensive, and the price of swords suddenly skyrockets after news of an impending dragon attack). Experiments have shown that competitive market outcomes can be achieved by simulating even a dozen or so traders using very simple heuristics like “don’t pay more than you can afford” and “don’t charge less than it cost you”.

Why don’t game designers implement this? I think there are two reasons.

The first is simply that it would be more complicated. This is a legitimate concern in many cases; I particularly think Pokemon can justify using a simple economy, given its target audience. I particularly agree that having more than a handful of currencies would be too much for players to keep track of; though perhaps having two or three (one for each major faction?) is still more interesting than only having one.

Also, tabletop games are inherently more limited in the amount of computation they can use, compared to video games. But for a game as complicated as say Skyrim, this really isn’t much of a defense. Skyrim actually simulated the daily routines of over a hundred different non-player characters; it could have been simulating markets in the background as well—in fact, it could have simply had those same non-player characters buy and sell goods with each other in a double-auction market that would automatically generate the prices that players face.

The more important reason, I think, is that game designers have a paralyzing fear of arbitrage.

I find it particularly aggravating how frequently games will set it up so that the price at which you buy and the price at which you sell are constrained so that the buying price is always higher, often as much as twice as high. This is not at all how markets work in the real world; frankly it’s only even close to true for goods like cars that rapidly depreciate. It make senses that a given merchant will not sell you a good for less than what they would pay to buy it from you; but that only requires each individual merchant to have a well-defined willingness-to-pay and willingness-to-accept. It certainly does not require the arbitrary constraint that you can never sell something for more than what you bought it for.

In fact, I would probably even allow players who specialize in social skills to short-change and bamboozle merchants for profit, as this is absolutely something that happens in the real world, and was likely especially common under the very low levels of literacy and numeracy that prevailed in the Middle Ages.

To many game designers (and gamers), the ability to buy a good in one place, travel to another place, and sell that good for a higher price seems like cheating. But this practice is call being a merchant. That is literally what the entire retail industry does. The rules of your game should allow you to profit from activities that are in fact genuinely profitable real economic services in the real world.

I remember a similar complaint being raised against Skyrim shortly after its release, that one could acquire a pickaxe, collect iron ore, smelt it into steel, forge weapons out of it, and then sell the weapons for a sizeable profit. To some people, this sounded like cheating. To me, it sounds like being a blacksmith. This is especially true because Skyrim’s skill system allowed you to improve the quality of your smithed items over time, just like learning a trade through practice (though it ramped up too fast, as it didn’t take long to make yourself clearly the best blacksmith in all of Skyrim). Frankly, this makes far more sense than being able to acquire gold by adventuring through the countryside and slaughtering monsters or collecting lost items from caves. Blacksmiths were a large part of the medieval economy; spelunking adventurers were not. Indeed, it bothers me that there weren’t more opportunities like this; you couldn’t make your wealth by being a farmer, a vintner, or a carpenter, for instance.

Even if you managed to pull off pure arbitrage, providing no real services, such as by buying and selling between two merchants in the same town, or the same merchant on two consecutive days, that is also a highly profitable industry. Most of our financial system is built around it, frankly. If you manage to make your wealth selling wheat futures instead of slaying dragons, I say more power to you. After all, there were an awful lot of wheat-future traders in the Middle Ages, and to my knowledge no actually successful dragon-slayers.

Of course, if your game is about slaying dragons, it should include some slaying of dragons. And if you really don’t care about making a realistic market in your game, so be it. But I think that more realistic markets could actually offer a great deal of richness and immersion into a world without greatly increasing the difficulty or complexity of the game. A world where prices change in response to the events of the story just feels more real, more alive.

The ability to profit without violence might actually draw whole new modes of play to the game (as has indeed occurred with Skyrim, where a small but significant proportion of players have chosen to live out peaceful lives as traders or blacksmiths). I would also enrich the experience of more conventional players and helping them recover from setbacks (if the only way to make money is to fight monsters and you keep getting killed by monsters, there isn’t much you can do; but if you have the option of working as a trader or a carpenter for awhile, you could save up for better equipment and try the fighting later).

And hey, game designers: If any of you are having trouble figuring out how to implement such a thing, my consulting fees are quite affordable.

How following the crowd can doom us all

PNRJ heuristics and biases , , , , , , , , , , , , , , , , , , , , , , , ,

JDN 2457110 EDT 21:30

Humans are nothing if not social animals. We like to follow the crowd, do what everyone else is doing—and many of us will continue to do so even if our own behavior doesn’t make sense to us. There is a very famous experiment in cognitive science that demonstrates this vividly.

People are given a very simple task to perform several times: We show you line X and lines A, B, and C. Now tell us which of A, B or C is the same length as X. Couldn’t be easier, right? But there’s a trick: seven other people are in the same room performing the same experiment, and they all say that B is the same length as X, even though you can clearly see that A is the correct answer. Do you stick with what you know, or say what everyone else is saying? Typically, you say what everyone else is saying. Over 18 trials, 75% of people followed the crowd at least once, and some people followed the crowd every single time. Some people even began to doubt their own perception, wondering if B really was the right answer—there are four lights, anyone?

Given that our behavior can be distorted by others in such simple and obvious tasks, it should be no surprise that it can be distorted even more in complex and ambiguous tasks—like those involved in finance. If everyone is buying up Beanie Babies or Tweeter stock, maybe you should too, right? Can all those people be wrong?

In fact, matters are even worse with the stock market, because it is in a sense rational to buy into a bubble if you know that other people will as well. As long as you aren’t the last to buy in, you can make a lot of money that way. In speculation, you try to predict the way that other people will cause prices to move and base your decisions around that—but then everyone else is doing the same thing. By Keynes called it a “beauty contest”; apparently in his day it was common to have contests for picking the most beautiful photo—but how is beauty assessed? By how many people pick it! So you actually don’t want to choose the one you think is most beautiful, you want to choose the one you think most people will think is the most beautiful—or the one you think most people will think most people will think….

Our herd behavior probably made a lot more sense when we evolved it millennia ago; when most of your threats are external and human beings don’t have that much influence over our environment, the majority opinion is quite likely to be right, and can often given you an answer much faster than you could figure it out on your own. (If everyone else thinks a lion is hiding in the bushes, there’s probably a lion hiding in the bushes—and if there is, the last thing you want is to be the only one who didn’t run.) The problem arises when this tendency to follow the ground feeds back on itself, and our behavior becomes driven not by the external reality but by an attempt to predict each other’s predictions of each other’s predictions. Yet this is exactly how financial markets are structured.

With this in mind, the surprise is not why markets are unstable—the surprise is why markets are ever stable. I think the main reason markets ever manage price stability is actually something most economists think of as a failure of markets: Price rigidity and so-called “menu costs“. If it’s costly to change your price, you won’t be constantly trying to adjust it to the mood of the hour—or the minute, or the microsecond—but instead trying to tie it to the fundamental value of what you’re selling so that the price will continue to be close for a long time ahead. You may get shortages in times of high demand and gluts in times of low demand, but as long as those two things roughly balance out you’ll leave the price where it is. But if you can instantly and costlessly change the price however you want, you can raise it when people seem particularly interested in buying and lower it when they don’t, and then people can start trying to buy when your price is low and sell when it is high. If people were completely rational and had perfect information, this arbitrage would stabilize prices—but since they’re not, arbitrage attempts can over- or under-compensate, and thus result in cyclical or even chaotic changes in prices.

Our herd behavior then makes this worse, as more people buying leads to, well, more people buying, and more people selling leads to more people selling. If there were no other causes of behavior, the result would be prices that explode outward exponentially; but even with other forces trying to counteract them, prices can move suddenly and unpredictably.

If most traders are irrational or under-informed while a handful are rational and well-informed, the latter can exploit the former for enormous amounts of money; this fact is often used to argue that irrational or under-informed traders will simply drop out, but it should only take you a few moments of thought to see why that isn’t necessarily true. The incentives isn’t just to be well-informed but also to keep others from being well-informed. If everyone were rational and had perfect information, stock trading would be the most boring job in the world, because the prices would never change except perhaps to grow with the growth rate of the overall economy. Wall Street therefore has every incentive in the world not to let that happen. And now perhaps you can see why they are so opposed to regulations that would require them to improve transparency or slow down market changes. Without the ability to deceive people about the real value of assets or trigger irrational bouts of mass buying or selling, Wall Street would make little or no money at all. Not only are markets inherently unstable by themselves, in addition we have extremely powerful individuals and institutions who are driven to ensure that this instability is never corrected.

This is why as our markets have become ever more streamlined and interconnected, instead of becoming more efficient as expected, they have actually become more unstable. They were never stable—and the gold standard made that instability worse—but despite monetary policy that has provided us with very stable inflation in the prices of real goods, the prices of assets such as stocks and real estate have continued to fluctuate wildly. Real estate isn’t as bad as stocks, again because of price rigidity—houses rarely have their values re-assessed multiple times per year, let alone multiple times per second. But real estate markets are still unstable, because of so many people trying to speculate on them. We think of real estate as a good way to make money fast—and if you’re lucky, it can be. But in a rational and efficient market, real estate would be almost as boring as stock trading; your profits would be driven entirely by population growth (increasing the demand for land without changing the supply) and the value added in construction of buildings. In fact, the population growth effect should be sapped by a land tax, and then you should only make a profit if you actually build things. Simply owning land shouldn’t be a way of making money—and the reason for this should be obvious: You’re not actually doing anything. I don’t like patent rents very much, but at least inventing new technologies is actually beneficial for society. Owning land contributes absolutely nothing, and yet it has been one of the primary means of amassing wealth for centuries and continues to be today.

But (so-called) investors and the banks and hedge funds they control have little reason to change their ways, as long as the system is set up so that they can keep profiting from the instability that they foster. Particularly when we let them keep the profits when things go well, but immediately rush to bail them out when things go badly, they have basically no incentive at all not to take maximum risk and seek maximum instability. We need a fundamentally different outlook on the proper role and structure of finance in our economy.

Fortunately one is emerging, summarized in a slogan among economically-savvy liberals: Banking should be boring. (Elizabeth Warren has said this, as have Joseph Stiglitz and Paul Krugman.) And indeed it should, for all banks are supposed to be doing is lending money from people who have it and don’t need it to people who need it but don’t have it. They aren’t supposed to be making large profits of their own, because they aren’t the ones actually adding value to the economy. Indeed it was never quite clear to me why banks should be privatized in the first place, though I guess it makes more sense than, oh, say, prisons.

Unfortunately, the majority opinion right now, at least among those who make policy, seems to be that banks don’t need to be restructured or even placed on a tighter leash; no, they need to be set free so they can work their magic again. Even otherwise reasonable, intelligent people quickly become unshakeable ideologues when it comes to the idea of raising taxes or tightening regulations. And as much as I’d like to think that it’s just a small but powerful minority of people who thinks this way, I know full well that a large proportion of Americans believe in these views and intentionally elect politicians who will act upon them.

All the more reason to break from the crowd, don’t you think?

No, capital taxes should not be zero

PNRJ critique of neoclassical economics, public policy , , , , , , , , , , , , , , , , , , ,

JDN 2456998 PST 11:38.

It’s an astonishingly common notion among neoclassical economists that we should never tax capital gains, and all taxes should fall upon labor income. Here Scott Sumner writing for The Economist has the audacity to declare this a ‘basic principle of economics’. Many of the arguments are based on rather esoteric theorems like the Atkinson-Stiglitz Theorem (I thought you were better than that, Stiglitz!) and the Chamley-Judd Theorem.

All of these theorems rest upon two very important assumptions, which many economists take for granted—yet which are utterly and totally untrue. For once it’s not assumed that we are infinite identical psychopaths; actually psychopaths might not give wealth to their children in inheritance, which would undermine the argument in a different way, by making each individual have a finite time horizon. No, the assumptions are that saving is the source of investment, and investment is the source of capital income.

Investment is the source of capital, that’s definitely true—the total amount of wealth in society is determined by investment. You do have to account for the fact that real investment isn’t just factories and machines, it’s also education, healthcare, infrastructure. With that in mind, yes, absolutely, the total amount of wealth is a function of the investment rate.

But that doesn’t mean that investment is the source of capital income—because in our present system the distribution of capital income is in no way determined by real investment or the actual production of goods. Virtually all capital income comes from financial markets, which are rife with corruption—they are indeed the main source of corruption that remains in First World nations—and driven primarily by arbitrage and speculation, not real investment. Contrary to popular belief and economic theory, the stock market does not fund corporations; corporations fund the stock market. It’s this bizarre game our society plays, in which a certain portion of the real output of our productive industries is siphoned off so that people who are already rich can gamble over it. Any theory of capital income which fails to take these facts into account is going to be fundamentally distorted.

The other assumption is that investment is savings, that the way capital increases is by labor income that isn’t spent on consumption. This isn’t even close to true, and I never understood why so many economists think it is. The notion seems to be that there is a certain amount of money in the world, and what you don’t spend on consumption goods you can instead spend on investment. But this is just flatly not true; the money supply is dynamically flexible, and the primary means by which money is created is through banks creating loans for the purpose of investment. It’s that I term I talked about in my post on the deficit; it seems to come out of nowhere, because that’s literally what happens.

On the reasoning that savings is just labor income that you don’t spend on consumption, then if you compute the figure W – C , wages and salaries minus consumption, that figure should be savings, and it should be equal to investment. Well, that figure is negative—for reasons I gave in that post. Total employee compensation in the US in 2014 is $9.2 trillion, while total personal consumption expenditure is $11.4 trillion. The reason we are able to save at all is because of government transfers, which account for $2.5 trillion. To fill up our GDP to its total of $16.8 trillion, you need to add capital income: proprietor income ($1.4 trillion) and receipts on assets ($2.1 trillion); then you need to add in the part of government spending that isn’t transfers ($1.4 trillion).

If you start with the fanciful assumption that the way capital increases is by people being “thrifty” and choosing to save a larger proportion of their income, then it makes some sense not to tax capital income. (Scott Sumner makes exactly that argument, having us compare two brothers with equal income, one of whom chooses to save more.) But this is so fundamentally removed from how capital—and for that matter capitalism—actually operates that I have difficulty understanding why anyone could think that it is true.

The best I can come up with is something like this: They model the world by imagining that there is only one good, peanuts, and everyone starts with the same number of peanuts, and everyone has a choice to either eat their peanuts or save and replant them. Then, the total production of peanuts in the future will be due to the proportion of peanuts that were replanted today, and the amount of peanuts each person has will be due to their past decisions to save rather than consume. Therefore savings will be equal to investment and investment will be the source of capital income.

I bet you can already see the problem even in this simple model, if we just relax the assumption of equal wealth endowments: Some people have a lot more peanuts than others. Why do some people eat all their peanuts? Well it probably has something to do with the fact they’d starve if they didn’t. Reducing your consumption below the level at which you can survive isn’t “thrifty”, it’s suicidal. (And if you think this is a strawman, the IMF has literally told Third World countries that their problem is they need to save more. Here they are arguing that in Ghana.) In fact, economic growth leads to saving, not the other way around. Most Americans aren’t starving, and could probably stand to save more than we do, but honestly it might not be good if we did—everyone trying to save more can lead to the Paradox of Thrift and cause a recession.

Even worse, in that model world, there is only capital income. There is no such thing as labor income, only the number of peanuts you grow from last year’s planting. If we now add in labor income, what happens? Well, peanuts don’t work anymore… let’s try robots. You have a certain number of robots, and you can either use the robots to do things you need (including somehow feeding you, I guess), or you can use them to build more robots to use later. You can also build more robots yourself. Then the “zero capital tax” argument amounts to saying that the government should take some of your robots for public use if you made them yourself, but not if they were made by other robots you already had.

In order for that argument to carry through, you need to say that there was no such thing as an initial capital endowment; all robots that exist were either made by their owners or saved from previous construction. If there is anyone who simply happened to be born with more robots, or has more because they stole them from someone else (or, more likely, both, they inherited from someone who stole), the argument falls apart.

And even then you need to think about the incentives: If capital income is really all from savings, then taxing capital income provides an incentive to spend. Is that a bad thing? I feel like it isn’t; the economy needs spending. In the robot toy model, we’re giving people a reason to use their robots to do actual stuff, instead of just leaving them to make more robots. That actually seems like it might be a good thing, doesn’t it? More stuff gets done that helps people, instead of just having vast warehouses full of robots building other robots in the hopes that someday we can finally use them for something. Whereas, taxing labor income may give people an incentive not to work, which is definitely going to reduce economic output. More precisely, higher taxes on labor would give low-wage workers an incentive to work less, and give high-wage workers an incentive to work more, which is a major part of the justification of progressive income taxes. A lot of the models intended to illustrate the Chamley-Judd Theorem assume that taxes have an effect on capital but no effect on labor, which is kind of begging the question.

Another thought that occurred to me is: What if the robots in the warehouse are all destroyed by a war or an earthquake? And indeed the possibility of sudden capital destruction would be a good reason not to put everything into investment. This is generally modeled as “uninsurable depreciation risk”, but come on; of course it’s uninsurable. All real risk is uninsurable in the aggregate. Insurance redistributes resources from those who have them but don’t need them to those who suddenly find they need them but don’t have them. This actually does reduce the real risk in utility, but it certainly doesn’t reduce the real risk in terms of goods. Stephen Colbert made this point very well: “Obamacare needs the premiums of healthier people to cover the costs of sicker people. It’s a devious con that can only be described as—insurance.” (This suggests that Stephen Colbert understands insurance better than many economists.) Someone has to make that new car that you bought using your insurance when you totaled the last one. Insurance companies cannot create cars or houses—or robots—out of thin air. And as Piketty and Saez point out, uninsurable risk undermines the Chamley-Judd Theorem. Unlike all these other economists, Piketty and Saez actually understand capital and inequality.
Sumner hand-waves that point away by saying we should just institute a one-time transfer of wealth to equalized the initial distribution, as though this were somehow a practically (not to mention politically) feasible alternative. Ultimately, yes, I’d like to see something like that happen; restore the balance and then begin anew with a just system. But that’s exceedingly difficult to do, while raising the tax rate on capital gains is very easy—and furthermore if we leave the current stock market and derivatives market in place, we will not have a just system by any stretch of the imagination. Perhaps if we can actually create a system where new wealth is really due to your own efforts, where there is no such thing as inheritance of riches (say a 100% estate tax above $1 million), no such thing as poverty (a basic income), no speculation or arbitrage, and financial markets that actually have a single real interest rate and offer all the credit that everyone needs, maybe then you can say that we should not tax capital income.

Until then, we should tax capital income, probably at least as much as we tax labor income.