Tax incidence revisited, part 4: Surplus and deadweight loss

JDN 2457355

I’ve already mentioned the fact that taxation creates deadweight loss, but in order to understand tax incidence it’s important to appreciate exactly how this works.

Deadweight loss is usually measured in terms of total economic surplus, which is a strange and deeply-flawed measure of value but relatively easy to calculate.

Surplus is based upon the concept of willingness-to-pay; the value of something is determined by the maximum amount of money you would be willing to pay for it.

This is bizarre for a number of reasons, and I think the most important one is that people differ in how much wealth they have, and therefore in their marginal utility of wealth. $1 is worth more to a starving child in Ghana than it is to me, and worth more to me than it is to a hedge fund manager, and worth more to a hedge fund manager than it is to Bill Gates. So when you try to set what something is worth based on how much someone will pay for it, which someone are you using?

People also vary, of course, in how much real value a good has to them: Some people like dark chocolate, some don’t. Some people love spicy foods and others despise them. Some people enjoy watching sports, others would rather read a book. A meal is worth a lot more to you if you haven’t eaten in days than if you just ate half an hour ago. That’s not actually a problem; part of the point of a market economy is to distribute goods to those who value them most. But willingness-to-pay is really the product of two different effects: The real effect, how much utility the good provides you; and the wealth effect, how your level of wealth affects how much you’d pay to get the same amount of utility. By itself, willingness-to-pay has no means of distinguishing these two effects, and actually I think one of the deepest problems with capitalism is that ultimately capitalism has no means of distinguishing these two effects. Products will be sold to the highest bidder, not the person who needs it the most—and that’s why Americans throw away enough food to end world hunger.

But for today, let’s set that aside. Let’s pretend that willingness-to-pay is really a good measure of value. One thing that is really nice about it is that you can read it right off the supply and demand curves.

When you buy something, your consumer surplus is the difference between your willingness-to-pay and how much you actually did pay. If a sandwich is worth $10 to you and you pay $5 to get it, you have received $5 of consumer surplus.

When you sell something, your producer surplus is the difference between how much you were paid and your willingness-to-accept, which is the minimum amount of money you would accept to part with it. If making that sandwich cost you $2 to buy ingredients and $1 worth of your time, your willingness-to-accept would be $3; if you then sell it for $5, you have received $2 of producer surplus.

Total economic surplus is simply the sum of consumer surplus and producer surplus. One of the goals of an efficient market is to maximize total economic surplus.

Let’s return to our previous example, where a 20% tax raised the original wage from $22.50 and thus resulted in an after-tax wage of $18.

Before the tax, the supply and demand curves looked like this:

equilibrium_notax

Consumer surplus is the area below the demand curve, above the price, up to the total number of goods sold. The basic reasoning behind this is that the demand curve gives the willingness-to-pay for each good, which decreases as more goods are sold because of diminishing marginal utility. So what this curve is saying is that the first hour of work was worth $40 to the employer, but each following hour was worth a bit less, until the 10th hour of work was only worth $35. Thus the first hour gave $40-$20 = $20 of surplus, while the 10th hour only gave $35-$20 = $15 of surplus.

Producer surplus is the area above the supply curve, below the price, again up to the total number of goods sold. The reasoning is the same: If the first hour of work cost $5 worth of time but the 10th hour cost $10 worth of time, the first hour provided $20-$5 = $15 in producer surplus, but the 10th hour only provided $20-$10 = $10 in producer surplus.

Imagine drawing a little 1-pixel-wide line straight down from the demand curve to the price for each hour and then adding up all those little lines into the total area under the curve, and similarly drawing little 1-pixel-wide lines straight up from the supply curve.

surplus

The employer was paying $20 * 40 = $800 for an amount of work that they actually valued at $1200 (the total area under the demand curve up to 40 hours), so they benefit by $400. The worker was being paid $800 for an amount of work that they would have been willing to accept $480 to do (the total area under the supply curve up to 40 hours), so they benefit $320. The sum of these is the total surplus $720.

equilibrium_notax_surplus

After the tax, the employer is paying $22.50 * 35 = $787.50, but for an amount of work that they only value at $1093.75, so their new surplus is only $306.25. The worker is receiving $18 * 35 = $630, for an amount of work they’d have been willing to accept $385 to do, so their new surplus is $245. Even when you add back in the government revenue of $4.50 * 35 = $157.50, the total surplus is still only $708.75. What happened to that extra $11.25 of value? It simply disappeared. It’s gone. That’s what we mean by “deadweight loss”. That’s why there is a downside to taxation.

equilibrium_tax_surplus

How large the deadweight loss is depends on the precise shape of the supply and demand curves, specifically on how elastic they are. Remember that elasticity is the proportional change in the quantity sold relative to the change in price. If increasing the price 1% makes you want to buy 2% less, you have a demand elasticity of -2. (Some would just say “2”, but then how do we say it if raising the price makes you want to buy more? The Law of Demand is more like what you’d call a guideline.) If increasing the price 1% makes you want to sell 0.5% more, you have a supply elasticity of 0.5.

If supply and demand are highly elastic, deadweight loss will be large, because even a small tax causes people to stop buying and selling a large amount of goods. If either supply or demand is inelastic, deadweight loss will be small, because people will more or less buy and sell as they always did regardless of the tax.

I’ve filled in the deadweight loss with brown in each of these graphs. They are designed to have the same tax rate, and the same price and quantity sold before the tax.

When supply and demand are elastic, the deadweight loss is large:

equilibrium_elastic_tax_surplus

But when supply and demand are inelastic, the deadweight loss is small:

equilibrium_inelastic_tax_surplus

Notice that despite the original price and the tax rate being the same, the tax revenue is also larger in the case of inelastic supply and demand. (The total surplus is also larger, but it’s generally thought that we don’t have much control over the real value and cost of goods, so we can’t generally make something more inelastic in order to increase total surplus.)

Thus, all other things equal, it is better to tax goods that are inelastic, because this will raise more tax revenue while producing less deadweight loss.

But that’s not all that elasticity does!

At last, the end of our journey approaches: In the next post in this series, I will explain how elasticity affects who actually ends up bearing the burden of the tax.

Tax incidence revisited, part 3: Taxation and the value of money

JDN 2457352

Our journey through the world of taxes continues. I’ve already talked about how taxes have upsides and downsides, as well as how taxes directly affect prices and “before-tax” prices are almost meaningless.

Now it’s time to get into something that even a lot of economists don’t quite seem to grasp, yet which turns out to be fundamental to what taxes truly are.

In the usual way of thinking, it works something like this: We have an economy, through which a bunch of money flows, and then the government comes in and takes some of that money in the form of taxes. They do this because they want to spend money on a variety of services, from military defense to public schools, and in order to afford doing that they need money, so they take in taxes.

This view is not simply wrong—it’s almost literally backwards. Money is not something the economy had that the government comes in and takes. Money is something that the government creates and then adds to the economy to make it function more efficiently. Taxes are not the government taking out money that they need to use; taxes are the government regulating the quantity of money in the system in order to stabilize its value. The government could spend as much money as they wanted without collecting a cent in taxes (not should, but could—it would be a bad idea, but definitely possible); taxes do not exist to fund the government, but to regulate the money supply.

Indeed—and this is the really vital and counter-intuitive point—without taxes, money would have no value.

There is an old myth of how money came into existence that involves bartering: People used to trade goods for other goods, and then people found that gold was particularly good for trading, and started using it for everything, and then eventually people started making paper notes to trade for gold, and voila, money was born.

In fact, such a “barter economy” has never been documented to exist. It probably did once or twice, just given the enormous variety of human cultures; but it was never widespread. Ancient economies were based on family sharing, gifts, and debts of honor.

It is true that gold and silver emerged as the first forms of money, “commodity money”, but they did not emerge endogenously out of trading that was already happening—they were created by the actions of governments. The real value of the gold or silver may have helped things along, but it was not the primary reason why people wanted to hold the money. Money has been based upon government for over 3000 years—the history of money and civilization as we know it. “Fiat money” is basically a redundancy; almost all money, even in a gold standard system, is ultimately fiat money.

The primary reason why people wanted the money was so that they could use it to pay taxes.

It’s really quite simple, actually.

When there is a rule imposed by the government that you will be punished if you don’t turn up on April 15 with at least $4,287 pieces of green paper marked “US Dollar”, you will try to acquire $4,287 pieces of green paper marked “US Dollar”. You will not care whether those notes are exchangeable for gold or silver; you will not care that they were printed by the government originally. Because you will be punished if you don’t come up with those pieces of paper, you will try to get some.

If someone else has some pieces of green paper marked “US Dollar”, and knows that you need them to avoid being punished on April 15, they will offer them to you—provided that you give them something they want in return. Perhaps it’s a favor you could do for them, or something you own that they’d like to have. You will be willing to make this exchange, in order to avoid being punished on April 15.
Thus, taxation gives money value, and allows purchases to occur.

Once you establish a monetary system, it becomes self-sustaining. If you know other people will accept money as payment, you are more willing to accept money as payment because you know that you can go spend it with those people. “Legal tender” also helps this process along—the government threatens to punish people who refuse to accept money as payment. In practice, however, this sort of law is rarely enforced, and doesn’t need to be, because taxation by itself is sufficient to form the basis of the monetary system.

It’s deeply ironic that people who complain about printing money often say we are “debasing” the currency; when you think carefully about what debasement was, it clearly shows that the value of money never really resided in the gold or silver itself. If a government can successfully extract revenue from its monetary system by changing the amount of gold or silver in each coin, then the value of those coins can’t be in the gold and silver—it has to be in the power of the government. You can’t make a profit by dividing a commodity into smaller pieces and then selling the pieces. (Okay, you sort of can, by buying in bulk and selling at retail. But that’s not what we’re talking about. You can’t make money by buying 100 50-gallon barrels of oil and then selling them as 125 40-gallon barrels of oil; it’s the same amount of oil.)

Similarly, the fact that there is such a thing as seignioragethe value of currency in excess of its cost to create—shows that governments impart value to their money. Indeed, one of the reasons for debasement was to realign the value of coins with the value of the metals in the coins, which wouldn’t be necessary if those were simply by definition the same thing.

Taxation serves another important function in the monetary system, which is to regulate the supply of money. The government adds money to the economy by spending, and removes it by taxing; if they add more than they remove—a deficit—the money supply increases, while if they remove more than they add—a surplus—the money supply decreases. In order to maintain stable prices, you want the money supply to increase at approximately the rate of growth; for moderate inflation (which is probably better than actual price stability), you want the money supply to increase slightly faster than the rate of growth. Thus, in general we want the government deficit as a portion of GDP to be slightly larger than the growth rate of the economy. Thus, our current deficit of 2.8% of GDP is actually about where it should be, and we have no particular reason to want to decrease it. (This is somewhat oversimplified, because it ignores the contribution of the Federal Reserve, interest rates, and bank-created money. Most of the money in the world is actually not created by the government, but by banks which are restrained to greater or lesser extent by the government.)

Even a lot of people who try to explain modern monetary theory mistakenly speak as though there was a fundamental shift when we fully abandoned the gold standard in the 1970s. (This is a good explanation overall, but it makes this very error.) But in fact a gold standard really isn’t money “backed” by anything—gold is not what gives the money value, gold is almost worthless by itself. It’s pretty and it doesn’t corrode, but otherwise, what exactly can you do with it? Being tied to money is what made gold valuable, not the other way around. To see this, imagine a world where you have 20,000 tons of gold, but you know that you can never sell it. No one will ever purchase a single ounce. Would you feel particularly rich in that scenario? I think not. Now suppose you have a virtually limitless quantity of pieces of paper that you know people will accept for anything you would ever wish to buy. They are backed by nothing, they are just pieces of paper—but you are now rich, by the standard definition of the word. I can even make the analogy remove the exchange value of money and just use taxation: if you know that in two days you will be imprisoned if you don’t have this particular piece of paper, for the next two days you will guard that piece of paper with your life. It won’t bother you that you can’t exchange that piece of paper for anything else—you wouldn’t even want to. If instead someone else has it, you’ll be willing to do some rather large favors for them in order to get it.

Whenever people try to tell me that our money is “worthless” because it’s based on fiat instead of backed by gold (this happens surprisingly often), I always make them an offer: If you truly believe that our money is worthless, I’ll gladly take any you have off of your hands. I will even provide you with something of real value in return, such as an empty aluminum can or a pair of socks. If they truly believe that fiat money is worthless, they should eagerly accept my offer—yet oddly, nobody ever does.

This does actually create a rather interesting argument against progressive taxation: If the goal of taxation is simply to control inflation, shouldn’t we tax people based only on their spending? Well, if that were the only goal, maybe. But we also have other goals, such as maintaining employment and controlling inequality. Progressive taxation may actually take a larger amount of money out of the system than would be necessary simply to control inflation; but it does so in order to ensure that the super-rich do not become even more rich and powerful.

Governments are limited by real constraints of power and resources, but they they have no monetary constraints other than those they impose themselves. There is definitely something strongly coercive about taxation, and therefore about a monetary system which is built upon taxation. Unfortunately, I don’t know of any good alternatives. We might be able to come up with one: Perhaps people could donate to public goods in a mutually-enforced way similar to Kickstarter, but nobody has yet made that practical; or maybe the government could restructure itself to make a profit by selling private goods at the same time as it provides public goods, but then we have all the downsides of nationalized businesses. For the time being, the only system which has been shown to work to provide public goods and maintain long-term monetary stability is a system in which the government taxes and spends.

A gold standard is just a fiat monetary system in which the central bank arbitrarily decides that their money supply will be directly linked to the supply of an arbitrarily chosen commodity. At best, this could be some sort of commitment strategy to ensure that they don’t create vastly too much or too little money; but at worst, it prevents them from actually creating the right amount of money—and the gold standard was basically what caused the Great Depression. A gold standard is no more sensible a means of backing your currency than would be a standard requiring only prime-numbered interest rates, or one which requires you to print exactly as much money per minute as the price of a Ferrari.

No, the real thing that backs our money is the existence of the tax system. Far from taxation being “taking your hard-earned money”, without taxes money itself could not exist.

The Prisoner’s Dilemma

JDN 2457348
When this post officially goes live, it will have been one full week since I launched my Patreon, on which I’ve already received enough support to be more than halfway to my first funding goal. After this post, I will be far enough ahead in posting that I can release every post one full week ahead of time for my Patreon patrons (can I just call them Patreons?).

It’s actually fitting that today’s topic is the Prisoner’s Dilemma, for Patreon is a great example of how real human beings can find solutions to this problem even if infinite identical psychopaths could not.

The Prisoner’s Dilemma is the most fundamental problem in game theory—arguably the reason game theory is worth bothering with in the first place. There is a standard story that people generally tell to set up the dilemma, but honestly I find that they obscure more than they illuminate. You can find it in the Wikipedia article if you’re interested.

The basic idea of the Prisoner’s Dilemma is that there are many times in life when you have a choice: You can do the nice thing and cooperate, which costs you something, but benefits the other person more; or you can do the selfish thing and defect, which benefits you but harms the other person more.

The game can basically be defined as four possibilities: If you both cooperate, you each get 1 point. If you both defect, you each get 0 points. If you cooperate when the other player defects, you lose 1 point while the other player gets 2 points. If you defect when the other player cooperates, you get 2 points while the other player loses 1 point.

P2 Cooperate P2 Defect
P1 Cooperate +1, +1 -1, +2
P2 Defect +2, -1 0, 0

These games are nonzero-sum, meaning that the total amount of benefit or harm incurred is not constant; it depends upon what players choose to do. In my example, the total benefit varies from +2 (both cooperate) to +1 (one cooperates, one defects) to 0 (both defect).

The answer which is “neat, plausible, and wrong” (to use Mencken’s oft-misquoted turn of phrase) is to reason this way: If the other player cooperates, I can get +1 if I cooperate, or +2 if I defect. So I should defect. If the other player defects, I can get -1 if I cooperate, or 0 if I defect. So I should defect. In either case I defect, therefore I should always defect.

The problem with this argument is that your behavior affects the other player. You can’t simply hold their behavior fixed when making your choice. If you always defect, the other player has no incentive to cooperate, so you both always defect and get 0. But if you credibly promise to cooperate every time they also cooperate, you create an incentive to cooperate that can get you both +1 instead.

If there were a fixed amount of benefit, the game would be zero-sum, and cooperation would always be damaging yourself. In zero-sum games, the assumption that acting selfishly maximizes your payoffs is correct; we could still debate whether it’s necessarily more rational (I don’t think it’s always irrational to harm yourself to benefit someone else an equal amount), but it definitely is what maximizes your money.

But in nonzero-sum games, that assumption no longer holds; we can both end up better off by cooperating than we would have been if we had both defected.
Below is a very simple zero-sum game (notice how indeed in each outcome, the payoffs sum to zero; any zero-sum game can be written so that this is so, hence the name):

Player 2 cooperates Player 2 defects
Player 1 cooperates 0, 0 -1, +1
Player 1 defects +1, -1 0, 0

In that game, there really is no reason for you to cooperate; you make yourself no better off if they cooperate, and you give them a strong incentive to defect and make you worse off. But that game is not a Prisoner’s Dilemma, even though it may look superficially similar.

The real world, however, is full of variations on the Prisoner’s Dilemma. This sort of situation is fundamental to our experience; it probably happens to you multiple times every single day.
When you finish eating at a restaurant, you could pay the bill (cooperate) or you could dine and dash (defect). When you are waiting in line, you could quietly take your place in the queue (cooperate) or you could cut ahead of people (defect). If you’re married, you could stay faithful to your spouse (cooperate) or you could cheat on them (defect). You could pay more for the shoes made in the USA (cooperate), or buy the cheap shoes that were made in a sweatshop (defect). You could pay more to buy a more fuel-efficient car (cooperate), or buy that cheap gas-guzzler even though you know how much it pollutes (defect). Most of us cooperate most of the time, but occasionally are tempted into defecting.

The “Prisoner’s Dilemma” is honestly not much of a dilemma. A lot of neoclassical economists really struggle with it; their model of rational behavior is so narrow that it keeps putting out the result that they are supposed to always defect, but they know that this results in a bad outcome. More recently we’ve done experiments and we find that very few people actually behave that way (though typically neoclassical economists do), and also that people end up making more money in these experimental games than they would if they behaved as neoclassical economics says would be optimal.

Let me repeat that: People make more money than they would if they acted according to what’s supposed to be optimal according to neoclassical economists. I think that’s why it feels like such a paradox to them; their twin ideals of infinite identical psychopaths and maximizing the money you make have shown themselves to be at odds with one another.

But in fact, it’s really not that paradoxical: Rationality doesn’t mean being maximally selfish at every opportunity. It also doesn’t mean maximizing the money you make, but even if it did, it still wouldn’t mean being maximally selfish.

We have tested experimentally what sort of strategy is most effective at making the most money in the Prisoner’s Dilemma; basically we make a bunch of competing computer programs to play the game against one another for points, and tally up the points. When we do that, the winner is almost always a remarkably simple strategy, called “Tit for Tat”. If your opponent cooperated last time, cooperate. If your opponent defected last time, defect. Reward cooperation, punish defection.

In more complex cases (such as allowing for random errors in behavior), some subtle variations on that strategy turn out to be better, but are still basically focused around rewarding cooperation and punishing defection.
This probably seems quite intuitive, yes? It may even be the strategy that it occurred to you to try when you first learned about the game. This strategy comes naturally to humans, not because it is actually obvious as a mathematical result (the obvious mathematical result is the neoclassical one that turns out to be wrong), but because it is effective—human beings evolved to think this way because it gave us the ability to form stable cooperative coalitions. This is what gives us our enormous evolutionary advantage over just about everything else; we have transcended the limitations of a single individual and now work together in much larger groups. E.O. Wilson likes to call us “eusocial”, a term formally applied only to a very narrow range of species such as ants and bees (and for some reason, naked mole rats); but I don’t think this is actually strong enough, because human beings are social in a way that even ants are not. We cooperate on the scale of millions of individuals, who are basically unrelated genetically (or very distantly related). That is what makes us the species who eradicate viruses and land robots on other planets. Much more so than intelligence per se, the human superpower is cooperation.

Indeed, it is not a great exaggeration to say that morality exists as a concept in the human mind because cooperation is optimal in many nonzero-sum games such as these. If the world were zero-sum, morality wouldn’t work; the immoral action would always make you better off, and the bad guys would always win. We probably would never even have evolved to think in moral terms, because any individual or species that started to go that direction would be rapidly outcompeted by those that remained steadfastly selfish.

What does correlation have to do with causation?

JDN 2457345

I’ve been thinking of expanding the topics of this blog into some basic statistics and econometrics. It has been said that there are “Lies, damn lies, and statistics”; but in fact it’s almost the opposite—there are truths, whole truths, and statistics. Almost everything in the world that we know—not merely guess, or suppose, or intuit, or believe, but actually know, with a quantifiable level of certainty—is done by means of statistics. All sciences are based on them, from physics (when they say the Higgs discovery is a “5-sigma event”, that’s a statistic) to psychology, ecology to economics. Far from being something we cannot trust, they are in a sense the only thing we can trust.

The reason it sometimes feels like we cannot trust statistics is that most people do not understand statistics very well; this creates opportunities for both accidental confusion and willful distortion. My hope is therefore to provide you with some of the basic statistical knowledge you need to combat the worst distortions and correct the worst confusions.

I wasn’t quite sure where to start on this quest, but I suppose I have to start somewhere. I figured I may as well start with an adage about statistics that I hear commonly abused: “Correlation does not imply causation.”

Taken at its original meaning, this is definitely true. Unfortunately, it can be easily abused or misunderstood.

In its original meaning, the formal sense of the word “imply” meaning logical implication, to “imply” something is an extremely strong statement. It means that you logically entail that result, that if the antecedent is true, the consequent must be true, on pain of logical contradiction. Logical implication is for most practical purposes synonymous with mathematical proof. (Unfortunately, it’s not quite synonymous, because of things like Gödel’s incompleteness theorems and Löb’s theorem.)

And indeed, correlation does not logically entail causation; it’s quite possible to have correlations without any causal connection whatsoever, simply by chance. One of my former professors liked to brag that from 1990 to 2010 whether or not she ate breakfast had a statistically significant positive correlation with that day’s closing price for the Dow Jones Industrial Average.

How is this possible? Did my professor actually somehow influence the stock market by eating breakfast? Of course not; if she could do that, she’d be a billionaire by now. And obviously the Dow’s price at 17:00 couldn’t influence whether she ate breakfast at 09:00. Could there be some common cause driving both of them, like the weather? I guess it’s possible; maybe in good weather she gets up earlier and people are in better moods so they buy more stocks. But the most likely reason for this correlation is much simpler than that: She tried a whole bunch of different combinations until she found two things that correlated. At the usual significance level of 0.05, on average you need to try about 20 combinations of totally unrelated things before two of them will show up as correlated. (My guess is she used a number of different stock indexes and varied the starting and ending year. That’s a way to generate a surprisingly large number of degrees of freedom without it seeming like you’re doing anything particularly nefarious.)

But how do we know they aren’t actually causally related? Well, I suppose we don’t. Especially if the universe is ultimately deterministic and nonlocal (as I’ve become increasingly convinced by the results of recent quantum experiments), any two data sets could be causally related somehow. But the point is they don’t have to be; you can pick any randomly-generated datasets, pair them up in 20 different ways, and odds are, one of those ways will show a statistically significant correlation.

All of that is true, and important to understand. Finding a correlation between eating grapefruit and getting breast cancer, or between liking bitter foods and being a psychopath, does not necessarily mean that there is any real causal link between the two. If we can replicate these results in a bunch of other studies, that would suggest that the link is real; but typically, such findings cannot be replicated. There is something deeply wrong with the way science journalists operate; they like to publish the new and exciting findings, which 9 times out of 10 turn out to be completely wrong. They never want to talk about the really important and fascinating things that we know are true because we’ve been confirming them over hundreds of different experiments, because that’s “old news”. The journalistic desire to be new and first fundamentally contradicts the scientific requirement of being replicated and confirmed.

So, yes, it’s quite possible to have a correlation that tells you absolutely nothing about causation.

But this is exceptional. In most cases, correlation actually tells you quite a bit about causation.

And this is why I don’t like the adage; “imply” has a very different meaning in common speech, meaning merely to suggest or evoke. Almost everything you say implies all sorts of things in this broader sense, some more strongly than others, even though it may logically entail none of them.

Correlation does in fact suggest causation. Like any suggestion, it can be overridden. If we know that 20 different combinations were tried until one finally yielded a correlation, we have reason to distrust that correlation. If we find a correlation between A and B but there is no logical way they can be connected, we infer that it is simply an odd coincidence.

But when we encounter any given correlation, there are three other scenarios which are far more likely than mere coincidence: A causes B, B causes A, or some other factor C causes A and B. These are also not mutually exclusive; they can all be true to some extent, and in many cases are.

A great deal of work in science, and particularly in economics, is based upon using correlation to infer causation, and has to be—because there is simply no alternative means of approaching the problem.

Yes, sometimes you can do randomized controlled experiments, and some really important new findings in behavioral economics and development economics have been made this way. Indeed, much of the work that I hope to do over the course of my career is based on randomized controlled experiments, because they truly are the foundation of scientific knowledge. But sometimes, that’s just not an option.

Let’s consider an example: In my master’s thesis I found a strong correlation between the level of corruption in a country (as estimated by the World Bank) and the proportion of that country’s income which goes to the top 0.01% of the population. Countries that have higher levels of corruption also tend to have a larger proportion of income that accrues to the top 0.01%. That correlation is a fact; it’s there. There’s no denying it. But where does it come from? That’s the real question.

Could it be pure coincidence? Well, maybe; but when it keeps showing up in several different models with different variables included, that becomes unlikely. A single p < 0.05 will happen about 1 in 20 times by chance; but five in a row should happen less than 1 in 1 million times (assuming they’re independent, which, to be fair, they usually aren’t).

Could it be some artifact of the measurement methods? It’s possible. In particular, I was concerned about the possibility of Halo Effect, in which people tend to assume that something which is better (or worse) in one way is automatically better (or worse) in other ways as well. People might think of their country as more corrupt simply because it has higher inequality, even if there is no real connection. But it would have taken a very large halo bias to explain this effect.

So, does corruption cause income inequality? It’s not hard to see how that might happen: More corrupt individuals could bribe leaders or exploit loopholes to make themselves extremely rich, and thereby increase inequality.

Does inequality cause corruption? This also makes some sense, since it’s a lot easier to bribe leaders and manipulate regulations when you have a lot of money to work with in the first place.

Does something else cause both corruption and inequality? Also quite plausible. Maybe some general cultural factors are involved, or certain economic policies lead to both corruption and inequality. I did try to control for such things, but I obviously couldn’t include all possible variables.

So, which way does the causation run? Unfortunately, I don’t know. I tried some clever statistical techniques to try to figure this out; in particular, I looked at which tends to come first—the corruption or the inequality—and whether they could be used to predict each other, a method called Granger causality. Those results were inconclusive, however. I could neither verify nor exclude a causal connection in either direction. But is there a causal connection? I think so. It’s too robust to just be coincidence. I simply don’t know whether A causes B, B causes A, or C causes A and B.

Imagine trying to do this same study as a randomized controlled experiment. Are we supposed to create two societies and flip a coin to decide which one we make more corrupt? Or which one we give more income inequality? Perhaps you could do some sort of experiment with a proxy for corruption (cheating on a test or something like that), and then have unequal payoffs in the experiment—but that is very far removed from how corruption actually works in the real world, and worse, it’s prohibitively expensive to make really life-altering income inequality within an experimental context. Sure, we can give one participant $1 and the other $1,000; but we can’t give one participant $10,000 and the other $10 million, and it’s the latter that we’re really talking about when we deal with real-world income inequality. I’m not opposed to doing such an experiment, but it can only tell us so much. At some point you need to actually test the validity of your theory in the real world, and for that we need to use statistical correlations.

Or think about macroeconomics; how exactly are you supposed to test a theory of the business cycle experimentally? I guess theoretically you could subject an entire country to a new monetary policy selected at random, but the consequences of being put into the wrong experimental group would be disastrous. Moreover, nobody is going to accept a random monetary policy democratically, so you’d have to introduce it against the will of the population, by some sort of tyranny or at least technocracy. Even if this is theoretically possible, it’s mind-bogglingly unethical.

Now, you might be thinking: But we do change real-world policies, right? Couldn’t we use those changes as a sort of “experiment”? Yes, absolutely; that’s called a quasi-experiment or a natural experiment. They are tremendously useful. But since they are not truly randomized, they aren’t quite experiments. Ultimately, everything you get out of a quasi-experiment is based on statistical correlations.

Thus, abuse of the adage “Correlation does not imply causation” can lead to ignoring whole subfields of science, because there is no realistic way of running experiments in those subfields. Sometimes, statistics are all we have to work with.

This is why I like to say it a little differently:

Correlation does not prove causation. But correlation definitely can suggest causation.

Tax incidence revisited, part 2: How taxes affect prices

JDN 2457341

One of the most important aspects of taxation is also one of the most counter-intuitive and (relatedly) least-understood: Taxes are not externally applied to pre-existing exchanges of money. Taxes endogenously interact with the system of prices, changing what the prices will be and then taking a portion of the money exchanged.

The price of something “before taxes” is not actually the price you would pay for it if there had been no taxes on it. Your “pre-tax income” is not actually the income you would have had if there were no income or payroll taxes.

The most obvious case to consider is that of government employees: If there were no taxes, public school teachers could not exist, so the “pre-tax income” of a public school teacher is a meaningless quantity. You don’t “take taxes out” of a government salary; you decide how much money the government employee will actually receive, and then at the same time allocate a certain amount into other budgets based on the tax code—a certain amount into the state general fund, a certain amount into the Social Security Trust Fund, and so on. These two actions could in principle be done completely separately; instead of saying that a teacher has a “pre-tax salary” of $50,000 and is taxed 20%, you could simply say that the teacher receives $40,000 and pay $10,000 into the appropriate other budgets.

In fact, when there is a conflict of international jurisdiction this is sometimes literally what we do. Employees of the World Bank are given immunity from all income and payroll taxes (effectively, diplomatic immunity, though this is not usually how we use the term) based on international law, except for US citizens, who have their taxes paid for them by the World Bank. As a result, all World Bank salaries are quoted “after-tax”, that is, the actual amount of money employees will receive in their paychecks. As a result, a $120,000 salary at the World Bank is considerably higher than a $120,000 salary at Goldman Sachs; the latter would only (“only”) pay about $96,000 in real terms.

For private-sector salaries, it’s not as obvious, but it’s still true. There is actually someone who pays that “before-tax” salary—namely, the employer. “Pre-tax” salaries are actually a measure of labor expenditure (sometimes erroneously called “labor costs”, even by economists—but a true labor cost is the amount of effort, discomfort, stress, and opportunity cost involved in doing labor; it’s an amount of utility, not an amount of money). The salary “before tax” is the amount of money that the employer has to come up with in order to pay their payroll. It is a real amount of money being exchanged, divided between the employee and the government.

The key thing to realize is that salaries are not set in a vacuum. There are various economic (and political) pressures which drive employers to set different salaries. In the real world, there are all sorts of pressures that affect salaries: labor unions, regulations, racist and sexist biases, nepotism, psychological heuristics, employees with different levels of bargaining skill, employers with different concepts of fairness or levels of generosity, corporate boards concerned about public relations, shareholder activism, and so on.

But even if we abstract away from all that for a moment and just look at the fundamental economics, assuming that salaries are set at the price the market will bear, that price depends upon the tax system.

This is because taxes effectively drive a wedge between supply and demand.

Indeed, on a graph, it actually looks like a wedge, as you’ll see in a moment.

Let’s pretend that we’re in a perfectly competitive market. Everyone is completely rational, we all have perfect information, and nobody has any power to manipulate the market. We’ll even assume that we are dealing with hourly wages and we can freely choose the number of hours worked. (This is silly, of course; but removing this complexity helps to clarify the concept and doesn’t change the basic result that prices depend upon taxes.)

We’ll have a supply curve, which is a graph of the minimum price the worker is willing to accept for each hour in order to work a given number of hours. We generally assume that the supply curve slopes upward, meaning that people are willing to work more hours if you offer them a higher wage for each hour. The idea is that it gets progressively harder to find the time—it eats into more and more important alternative activities. (This is in fact a gross oversimplification, but it’ll do for now. In the real world, labor is the one thing for which the supply curve frequently bends backward.)

supply_curve

We’ll also have a demand curve, which is a graph of the maximum price the employer is willing to pay for each hour, if the employee works that many hours. We generally assume that the demand curve slopes downward, meaning that the employer is willing to pay less for each hour if the employee works more hours. The reason is that most activities have diminishing marginal returns, so each extra hour of work generally produces less output than the previous hour, and is therefore not worth paying as much for. (This too is an oversimplification, as I discussed previously in my post on the Law of Demand.)

demand_curve

Put these two together, and in a competitive market the price will be set at the point at which supply is equal to demand, so that the very last hour of work was worth exactly what the employer paid for it. That last hour is just barely worth it to the employer, and just barely worth it to the worker; any additional time would either be too expensive for the employer or not lucrative enough for the worker. But for all the previous hours, the value to the employer is higher than the wage, and the cost to the worker is lower than the wage. As a result, both the employer and the worker benefit.

equilibrium_notax

But now, suppose we implement a tax. For concreteness, suppose the previous market-clearing wage was $20 per hour, the worker was working 40 hours, and the tax is 20%. If the employer still offers a wage of $20 for 40 hours of work, the worker is no longer going to accept it, because they will only receive $16 per hour after taxes, and $16 isn’t enough for them to be willing to work 40 hours. The worker could ask for a pre-tax wage of $25 so that the after-tax wage would be $20, but then the employer will balk, because $25 per hour is too expensive for 40 hours of work.

In order to restore the balance (and when we say “equilibrium”, that’s really all we mean—balance), the employer will need to offer a higher pre-tax wage, which means they will demand fewer hours of work. The worker will then be willing to accept a lower after-tax wage for those reduced hours.

In effect, there are now two prices at work: A supply price, the after-tax wage that the worker receives, which must be at or above the supply curve; and a demand price, the pre-tax wage that the employer pays, which must be at or below the demand curve. The difference between those two prices is the tax.

equilibrium_tax

In this case, I’ve set it up so that the pre-tax wage is $22.50, the after-tax wage is $18, and the amount of the tax is $4.50 or 20% of $22.50. In order for both the employer and the worker to accept those prices, the amount of hours worked has been reduced to 35.

As a result of the tax, the wage that we’ve been calling “pre-tax” is actually higher than the wage that the worker would have received if the tax had not existed. This is a general phenomenon; it’s almost always true that your “pre-tax” wage or salary overestimates what you would have actually gotten if the tax had not existed. In one extreme case, it might actually be the same; in another extreme case, your after-tax wage is what you would have received and the “pre-tax” wage rises high enough to account for the entirety of the tax revenue. It’s not really “pre-tax” at all; it’s the after-tax demand price.

Because of this, it’s fundamentally wrongheaded for people to complain that taxes are “taking your hard-earned money”. In all but the most exceptional cases, that “pre-tax” salary that’s being deducted from would never have existed. It’s more of an accounting construct than anything else, or like I said before a measure of labor expenditure. It is generally true that your after-tax salary is lower than the salary you would have gotten without the tax, but the difference is generally much smaller than the amount of the tax that you see deducted. In this case, the worker would see $4.50 per hour deducted from their wage, but in fact they are only down $2 per hour from where they would have been without the tax. And of course, none of this includes the benefits of the tax, which in many cases actually far exceed the costs; if we extended the example, it wouldn’t be hard to devise a scenario in which the worker who had their wage income reduced received an even larger benefit in the form of some public good such as national defense or infrastructure.

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To truly honor veterans, end war

JDN 2457339 EST 20:00 (Nov 11, 2015)

Today is Veterans’ Day, on which we are asked to celebrate the service of military veterans, particularly those who have died as a result of war. We tend to focus on those who die in combat, but actually these have always been relatively uncommon; throughout history, most soldiers have died later of their wounds or of infections. More recently as a result of advances in body armor and medicine, actually relatively few soldiers die even of war wounds or infections—instead, they are permanently maimed and psychologically damaged, and the most common way that war kills soldiers now is by making them commit suicide.

Even adjusting for the fact that soldiers are mostly young men (the group of people most likely to commit suicide), military veterans still have about 50 excess suicides per million people per year, for a total of about 300 suicides per million per year. Using the total number, that’s over 8000 veteran suicides per year, or 22 per day. Using only the excess compared to men of the same ages, it’s still an additional 1300 suicides per year.

While the 14-years-and-counting Afghanistan War has killed 2,271 American soldiers and the 11-year Iraq War has killed 4,491 American soldiers directly (or as a result of wounds), during that same time period from 2001 to 2015 there have been about 18,000 excess suicides as a result of the military—excess in the sense that they would not have occurred if those men had been civilians. Altogether that means there would be nearly 25,000 additional American soldiers alive today were it not for these two wars.

War does not only kill soldiers while they are on the battlefield—indeed, most of the veterans it kills die here at home.

There is a reason Woodrow Wilson chose November 11 as the date for Veterans’ Day: It was on this day in 1918 that World War 1, up to that point the war that had caused the most deaths in human history, was officially ended. Sadly, it did not remain the deadliest war, but was surpassed by World War 2 a generation later. Fortunately, no other war has ever exceeded World War 2—at least, not yet.

We tend to celebrate holidays like this with a lot of ritual and pageantry (or even in the most inane and American way possible, with free restaurant meals and discounts on various consumer products), and there’s nothing inherently wrong with that. Nor is there anything wrong with taking a moment to salute the flag or say “Thank you for your service.” But that is not how I believe veterans should be honored. If I were a veteran, that is not how I would want to be honored.

We are getting much closer to how I think they should be honored when the White House announces reforms at Veterans’ Affairs hospitals and guaranteed in-state tuition at public universities for families of veterans—things that really do in a concrete and measurable way improve the lives of veterans and may even save some of them from that cruel fate of suicide.

But ultimately there is only one way that I believe we can truly honor veterans and the spirit of the holiday as Wilson intended it, and that is to end war once and for all.

Is this an ambitious goal? Absolutely. But is it an impossible dream? I do not believe so.

In just the last half century, we have already made most of the progress that needed to be made. In this brilliant video animation, you can see two things: First, the mind-numbingly horrific scale of World War 2, the worst war in human history; but second, the incredible progress we have made since then toward world peace. It was as if the world needed that one time to be so unbearably horrible in order to finally realize just what war is and why we need a better way of solving conflicts.

This is part of a very long-term trend in declining violence, for a variety of reasons that are still not thoroughly understood. In simplest terms, human beings just seem to be getting better at not killing each other.

Nassim Nicholas Taleb argues that this is just a statistical illusion, because technologies like nuclear weapons create the possibility of violence on a previously unimaginable scale, and it simply hasn’t happened yet. For nuclear weapons in particular, I think he may be right—the consequences of nuclear war are simply so catastrophic that even a small risk of it is worth paying almost any price to avoid.

Fortunately, nuclear weapons are not necessary to prevent war: South Africa has no designs on attacking Japan anytime soon, but neither has nuclear weapons. Germany and Poland lack nuclear arsenals and were the first countries to fight in World War 2, but now that both are part of the European Union, war between them today seems almost unthinkable. When American commentators fret about China today it is always about wage competition and Treasury bonds, not aircraft carriers and nuclear missiles. Conversely, North Korea’s acquisition of nuclear weapons has by no means stabilized the region against future conflicts, and the fact that India and Pakistan have nuclear missiles pointed at one another has hardly prevented them from killing each other over Kashmir. We do not need nuclear weapons as a constant threat of annihilation in order to learn to live together; political and economic ties achieve that goal far more reliably.

And I think Taleb is wrong about the trend in general. He argues that the only reason violence is declining is that concentration of power has made violence rarer but more catastrophic when it occurs. Yet we know that many forms of violence which used to occur no longer do, not because of the overwhelming force of a Leviathan to prevent them, but because people simply choose not to do them anymore. There are no more gladiator fights, no more cat-burnings, no more public lynchings—not because of the expansion in government power, but because our society seems to have grown out of that phase.

Indeed, what horrifies us about ISIS and Boko Haram would have been considered quite normal, even civilized, in the Middle Ages. (If you’ve ever heard someone say we should “bring back chivalry”, you should explain to them that the system of knight chivalry in the 12th century had basically the same moral code as ISIS today—one of the commandments Gautier’s La Chevalerie attributes as part of the chivalric code is literally “Thou shalt make war against the infidel without cessation and without mercy.”) It is not so much that they are uniquely evil by historical standards, as that we grew out of that sort of barbaric violence awhile ago but they don’t seem to have gotten the memo.

In fact, one thing people don’t seem to understand about Steven Pinker’s argument about this “Long Peace” is that it still works if you include the world wars. The reason World War 2 killed so many people was not that it was uniquely brutal, nor even simply because its weapons were more technologically advanced. It also had to do with the scale of integration—we called it a single war even though it involved dozens of countries because those countries were all united into one of two sides, whereas in centuries past that many countries could be constantly fighting each other in various combinations but it would never be called the same war. But the primary reason World War 2 killed the largest raw number of people was simply because the world population was so much larger. Controlling for world population, World War 2 was not even among the top 5 worst wars—it barely makes the top 10. The worst war in history by proportion of the population killed was almost certainly the An Lushan Rebellion in 8th century China, which many of you may not even have heard of until today.

Though it may not seem so as ISIS kidnaps Christians and drone strikes continue, shrouded in secrecy, we really are on track to end war. Not today, not tomorrow, maybe not in any of our lifetimes—but someday, we may finally be able to celebrate Veterans’ Day as it was truly intended: To honor our soldiers by making it no longer necessary for them to die.