Drift-diffusion decision-making: The stock market in your brain

2015-05-302015-05-30 PNRJ cognitive science alternative, ambivalence, bias, confirmation bias, cutting-edge, decision, drift diffusion, indifference, neuroeconomics, random walk, trend

JDN 2456173 EDT 17:32.

Since I’ve been emphasizing the “economics” side of things a lot lately, I decided this week to focus more on the “cognitive” side. Today’s topic comes from cutting-edge research in cognitive science and neuroeconomics, so we still haven’t ironed out all the details.

The question we are trying to answer is an incredibly basic one: How do we make decisions? Given the vast space of possible behaviors human beings can engage in, how do we determine which ones we actually do?

There are actually two phases of decision-making.

The first phase is alternative generation, in which we come up with a set of choices. Some ideas occur to us, others do not; some are familiar and come to mind easily, others only appear after careful consideration. Techniques like brainstorming exist to help us with this task, but none of them are really very good; one of the most important bottlenecks in human cognition is the individual capacity to generate creative alternatives. The task is mind-bogglingly complex; the number of possible choices you could make at any given moment is already vast, and with each passing moment the number of possible behavioral sequences grows exponentially. Just think about all the possible sentences I could type write now, and then think about how incredibly narrow a space of possible behavioral options it is to assume that I’m typing sentences.

Most of the world’s innovation can ultimately be attributed to better alternative generation; particular with regard to social systems, but in many cases even with regard to technologies, the capability existed for decades or even centuries but the idea simply never occurred to anyone. (You can see this by looking at the work of Heron of Alexandria and Leonardo da Vinci; the capacity to build these machines existed, and a handful of individuals were creative enough to actually try it, but it never occurred to anyone that there could be enormous, world-changing benefits to expanding these technologies for mass production.)

Unfortunately, we basically don’t understand alternative generation at all. It’s an almost complete gap in our understanding of human cognition. It actually has a lot to do with some of the central unsolved problems of cognitive science and artificial intelligence; if we could create a computer that is capable of creative thought, we would basically make human beings obsolete once and for all. (Oddly enough, physical labor is probably where human beings would still be necessary the longest; robots aren’t yet very good at climbing stairs or lifting irregularly-shaped objects, much less giving haircuts or painting on canvas.)

The second part is what most “decision-making” research is actually about, and I’ll call it alternative selection. Once you have a list of two, three or four viable options—rarely more than this, as I’ll talk about more in a moment—how do you go about choosing the one you’ll actually do?

This is a topic that has undergone considerable research, and we’re beginning to make progress. The leading models right now are variants of drift-diffusion (hence the title of the post), and these models have the very appealing property that they are neurologically plausible, predictively accurate, and yet close to rationally optimal.

Drift-diffusion models basically are, as I said in the subtitle, a stock market in your brain. Picture the stereotype of the trading floor of the New York Stock Exchange, with hundreds of people bustling about, shouting “Buy!” “Sell!” “Buy!” with the price going up with every “Buy!” and down with every “Sell!”; in reality the NYSE isn’t much like that, and hasn’t been for decades, because everyone is staring at a screen and most of the trading is automated and occurs in microseconds. (It’s kind of like how if you draw a cartoon of a doctor, they will invariably be wearing a head mirror, but if you’ve actually been to a doctor lately, they don’t actually wear those anymore.)

Drift-diffusion, however, is like that. Let’s say we have a decision to make, “Yes” or “No”. Thousands of neurons devoted to that decision start firing, some saying “Yes”, exciting other “Yes” neurons and inhibiting “No” neurons, while others say “No”, exciting other “No” neurons and inhibiting other “Yes” neurons. New information feeds in, triggering some to “Yes” and others to “No”. The resulting process behaves like a random walk, specifically a trend random walk, where the intensity of the trend is determined by whatever criteria you are feeding into the decision. The decision will be made when a certain threshold is reached, say, 95% agreement among all neurons.

I wrote a little R program to demonstrate drift-diffusion models; the images I’ll be showing are R plots from that program. The graphs represent the aggregated “opinion” of all the deciding neurons; as you go from left to right, time passes, and the opinions “drift” toward one side or the other. For these graphs, the top of the graph represents the better choice.

It may actually be easiest to understand if you imagine that we are choosing a belief; new evidence accumulates that pushes us toward the correct answer (top) or the incorrect answer (bottom), because even a true belief will have some evidence that seems to be against it. You encounter this evidence more or less randomly (or do you?), and which belief you ultimately form will depend upon both how strong the evidence is and how thoughtful you are in forming your beliefs.

If the evidence is very strong (or in general, the two choices are very different), the trend will be very strong, and you’ll almost certainly come to a decision very quickly:

If the evidence is weaker (the two choices are very similar), the trend will be much weaker, and it will take much longer to make a decision:

One way to make a decision faster would be to have a weaker threshold, like 75% agreement instead of 95%; but this has the downside that it can result in making the wrong choice. Notice how some of the paths go down to the bottom, which in this case is the worse choice:

But if there is actually no difference between the two options, a low threshold is good, because you don’t spend time waffling over a pointless decision. (I know that I’ve had a problem with that in real life, spending too long making a decision that ultimately is of minor importance; my drift thresholds are too high!) With a low threshold, you get it over with:

With a high threshold, you can go on for ages:

This is the difference between indifferent about a decision and being ambivalent. If you are indifferent, you are dealing with two small amounts of utility and it doesn’t really matter which one you choose. If you are ambivalent, you are dealing with two large amounts of utility and it’s very important to get it right—but you aren’t sure which one to choose. If you are indifferent, you should use a low threshold and get it over with; but if you are ambivalent, it actually makes sense to keep your threshold high and spend a lot of time thinking about the problem in order to be sure you get it right.

It’s also possible to set a higher threshold for one option than the other; I think this is actually what we’re doing when we exhibit many cognitive biases like confirmation bias. If the decision you’re making is between keeping your current beliefs and changing them to something else, your diffusion space actually looks more like this:

You’ll only make the correct choice (top) if you set equal thresholds (meaning you reason fairly instead of exhibiting cognitive biases) and high thresholds (meaning you spend sufficient time thinking about the question). If I may change to a sports metaphor, people tend to move the goalposts—the team “change your mind” has to kick a lot further than the team “keep your current belief”.

We can also extend drift-diffusion models to changing your mind (or experiencing regret such as “buyer’s remorse“) if we assume that the system doesn’t actually cut off once it reaches a threshold; the threshold makes us take the action, but then our neurons keep on arguing it out in the background. We may hover near the threshold or soar off into absolute certainty—but on the other hand we may waffle all the way back to the other decision:

There are all sorts of generalizations and extensions of drift-diffusion models, but these basic ones should give you a sense of how useful they are. More importantly, they are accurate; drift-diffusion models produce very sharp mathematical predictions about human behavior, and in general these predictions are verified in experiments.

The main reason we started using drift-diffusion models is that they account very well for the fact that decisions become more accurate when we spend more time on them. The way they do that is quite elegant: Under harsher time pressure, we use lower thresholds, which speeds up the process but also introduces more errors. When we don’t have time pressure, we use high thresholds and take a long time, but almost always make the right decision.

Under certain (rather narrow) circumstances, drift-diffusion models can actually be equivalent to the optimal Bayesian model. These models can also be extended for use in purchasing choices, and one day we will hopefully have a stock-market-in-the-brain model of actual stock market decisions!

Drift-diffusion models are based on decisions between two alternatives with only one relevant attribute under consideration, but they are being expanded to decisions with multiple attributes and decisions with multiple alternatives; the fact that this is difficult is in my opinion not a bug but a feature—decisions with multiple alternatives and attributes are actually difficult for human beings to make. The fact that drift-diffusion models have difficulty with the very situations that human beings have difficulty with provides powerful evidence that drift-diffusion models are accurately representing the processes that go on inside a human brain. I’d be worried if it were too easy to extend the models to complex decisions—it would suggest that our model is describing a more flexible decision process than the one human beings actually use. Human decisions really do seem to be attempts to shoehorn two-choice single-attribute decision methods onto more complex problems, and a lot of mistakes we make are attributable to that.

In particular, the phenomena of analysis paralysis and the paradox of choice are easily explained this way. Why is it that when people are given more alternatives, they often spend far more time trying to decide and often end up less satisfied than they were before? This makes sense if, when faced with a large number of alternatives, we spend time trying to compare them pairwise on every attribute, and then get stuck with a whole bunch of incomparable pairwise comparisons that we then have to aggregate somehow. If we could simply assign a simple utility value to each attribute and sum them up, adding new alternatives should only increase the time required by a small amount and should never result in a reduction in final utility.

When I have an important decision to make, I actually assemble a formal utility model, as I did recently when deciding on a new computer to buy (it should be in the mail any day now!). The hardest part, however, is assigning values to the coefficients in the model; just how much am I willing to spend for an extra gigabyte of RAM, anyway? How exactly do those CPU benchmarks translate into dollar value for me? I can clearly tell that this is not the native process of my mental architecture.

No, alas, we seem to be stuck with drift-diffusion, which is nearly optimal for choices with two alternatives on a single attribute, but actually pretty awful for multiple-alternative multiple-attribute decisions. But perhaps by better understanding our suboptimal processes, we can rearrange our environment to bring us closer to optimal conditions—or perhaps, one day, change the processes themselves!

How to change the world

2015-05-23 PNRJ core principles, critique of neoclassical economics agronomy, altruism, anthropology, art, austerity, biology, Black-Scholes, CAPM, chemistry, cognitive science, earning to give, ecology, Einstein, engineering, forecasting, Hard Problem, Jonas Salk, Keynes, literature, mathematics, music, neuroscience, philosophy, physics, political science, psychology, sociology, Steve Jobs, Tomorrowland, Will Rogers

JDN 2457166 EDT 17:53.

I just got back from watching Tomorrowland, which is oddly appropriate since I had already planned this topic in advance. How do we, as they say in the film, “fix the world”?

I can’t find it at the moment, but I vaguely remember some radio segment on which a couple of neoclassical economists were interviewed and asked what sort of career can change the world, and they answered something like, “Go into finance, make a lot of money, and then donate it to charity.”

In a slightly more nuanced form this strategy is called earning to give, and frankly I think it’s pretty awful. Most of the damage that is done to the world is done in the name of maximizing profits, and basically what you end up doing is stealing people’s money and then claiming you are a great altruist for giving some of it back. I guess if you can make enormous amounts of money doing something that isn’t inherently bad and then donate that—like what Bill Gates did—it seems better. But realistically your potential income is probably not actually raised that much by working in finance, sales, or oil production; you could have made the same income as a college professor or a software engineer and not be actively stripping the world of its prosperity. If we actually had the sort of ideal policies that would internalize all externalities, this dilemma wouldn’t arise; but we’re nowhere near that, and if we did have that system, the only billionaires would be Nobel laureate scientists. Albert Einstein was a million times more productive than the average person. Steve Jobs was just a million times luckier. Even then, there is the very serious question of whether it makes sense to give all the fruits of genius to the geniuses themselves, who very quickly find they have all they need while others starve. It was certainly Jonas Salk’s view that his work should only profit him modestly and its benefits should be shared with as many people as possible. So really, in an ideal world there might be no billionaires at all.

Here I would like to present an alternative. If you are an intelligent, hard-working person with a lot of talent and the dream of changing the world, what should you be doing with your time? I’ve given this a great deal of thought in planning my own life, and here are the criteria I came up with:

You must be willing and able to commit to doing it despite great obstacles. This is another reason why earning to give doesn’t actually make sense; your heart (or rather, limbic system) won’t be in it. You’ll be miserable, you’ll become discouraged and demoralized by obstacles, and others will surpass you. In principle Wall Street quantitative analysts who make $10 million a year could donate 90% to UNICEF, but they don’t, and you know why? Because the kind of person who is willing and able to exploit and backstab their way to that position is the kind of person who doesn’t give money to UNICEF.
There must be important tasks to be achieved in that discipline. This one is relatively easy to satisfy; I’ll give you a list in a moment of things that could be contributed by a wide variety of fields. Still, it does place some limitations: For one, it rules out the simplest form of earning to give (a more nuanced form might cause you to choose quantum physics over social work because it pays better and is just as productive—but you’re not simply maximizing income to donate). For another, it rules out routine, ordinary jobs that the world needs but don’t make significant breakthroughs. The world needs truck drivers (until robot trucks take off), but there will never be a great world-changing truck driver, because even the world’s greatest truck driver can only carry so much stuff so fast. There are no world-famous secretaries or plumbers. People like to say that these sorts of jobs “change the world in their own way”, which is a nice sentiment, but ultimately it just doesn’t get things done. We didn’t lift ourselves into the Industrial Age by people being really fantastic blacksmiths; we did it by inventing machines that make blacksmiths obsolete. We didn’t rise to the Information Age by people being really good slide-rule calculators; we did it by inventing computers that work a million times as fast as any slide-rule. Maybe not everyone can have this kind of grand world-changing impact; and I certainly agree that you shouldn’t have to in order to live a good life in peace and happiness. But if that’s what you’re hoping to do with your life, there are certain professions that give you a chance of doing so—and certain professions that don’t.
The important tasks must be currently underinvested. There are a lot of very big problems that many people are already working on. If you work on the problems that are trendy, the ones everyone is talking about, your marginal contribution may be very small. On the other hand, you can’t just pick problems at random; many problems are not invested in precisely because they aren’t that important. You need to find problems people aren’t working on but should be—problems that should be the focus of our attention but for one reason or another get ignored. A good example here is to work on pancreatic cancer instead of breast cancer; breast cancer research is drowning in money and really doesn’t need any more; pancreatic cancer kills 2/3 as many people but receives less than 1/6 as much funding. If you want to do cancer research, you should probably be doing pancreatic cancer.
You must have something about you that gives you a comparative—and preferably, absolute—advantage in that field. This is the hardest one to achieve, and it is in fact the reason why most people can’t make world-changing breakthroughs. It is in fact so hard to achieve that it’s difficult to even say you have until you’ve already done something world-changing. You must have something special about you that lets you achieve what others have failed. You must be one of the best in the world. Even as you stand on the shoulders of giants, you must see further—for millions of others stand on those same shoulders and see nothing. If you believe that you have what it takes, you will be called arrogant and naïve; and in many cases you will be. But in a few cases—maybe 1 in 100, maybe even 1 in 1000, you’ll actually be right. Not everyone who believes they can change the world does so, but everyone who changes the world believed they could.

Now, what sort of careers might satisfy all these requirements?

Well, basically any kind of scientific research:

Mathematicians could work on network theory, or nonlinear dynamics (the first step: separating “nonlinear dynamics” into the dozen or so subfields it should actually comprise—as has been remarked, “nonlinear” is a bit like “non-elephant”), or data processing algorithms for our ever-growing morasses of unprocessed computer data.

Physicists could be working on fusion power, or ways to neutralize radioactive waste, or fundamental physics that could one day unlock technologies as exotic as teleportation and faster-than-light travel. They could work on quantum encryption and quantum computing. Or if those are still too applied for your taste, you could work in cosmology and seek to answer some of the deepest, most fundamental questions in human existence.

Chemists could be working on stronger or cheaper materials for infrastructure—the extreme example being space elevators—or technologies to clean up landfills and oceanic pollution. They could work on improved batteries for solar and wind power, or nanotechnology to revolutionize manufacturing.

Biologists could work on any number of diseases, from cancer and diabetes to malaria and antibiotic-resistant tuberculosis. They could work on stem-cell research and regenerative medicine, or genetic engineering and body enhancement, or on gerontology and age reversal. Biology is a field with so many important unsolved problems that if you have the stomach for it and the interest in some biological problem, you can’t really go wrong.

Electrical engineers can obviously work on improving the power and performance of computer systems, though I think over the last 20 years or so the marginal benefits of that kind of research have begun to wane. Efforts might be better spent in cybernetics, control systems, or network theory, where considerably more is left uncharted; or in artificial intelligence, where computing power is only the first step.

Mechanical engineers could work on making vehicles safer and cheaper, or building reusable spacecraft, or designing self-constructing or self-repairing infrastructure. They could work on 3D printing and just-in-time manufacturing, scaling it up for whole factories and down for home appliances.

Aerospace engineers could link the world with hypersonic travel, build satellites to provide Internet service to the farthest reaches of the globe, or create interplanetary rockets to colonize Mars and the moons of Jupiter and Saturn. They could mine asteroids and make previously rare metals ubiquitous. They could build aerial drones for delivery of goods and revolutionize logistics.

Agronomists could work on sustainable farming methods (hint: stop farming meat), invent new strains of crops that are hardier against pests, more nutritious, or higher-yielding; on the other hand a lot of this is already being done, so maybe it’s time to think outside the box and consider what we might do to make our food system more robust against climate change or other catastrophes.

Ecologists will obviously be working on predicting and mitigating the effects of global climate change, but there are a wide variety of ways of doing so. You could focus on ocean acidification, or on desertification, or on fishery depletion, or on carbon emissions. You could work on getting the climate models so precise that they become completely undeniable to anyone but the most dogmatically opposed. You could focus on endangered species and habitat disruption. Ecology is in general so underfunded and undersupported that basically anything you could do in ecology would be beneficial.

Neuroscientists have plenty of things to do as well: Understanding vision, memory, motor control, facial recognition, emotion, decision-making and so on. But one topic in particular is lacking in researchers, and that is the fundamental Hard Problem of consciousness. This one is going to be an uphill battle, and will require a special level of tenacity and perseverance. The problem is so poorly understood it’s difficult to even state clearly, let alone solve. But if you could do it—if you could even make a significant step toward it—it could literally be the greatest achievement in the history of humanity. It is one of the fundamental questions of our existence, the very thing that separates us from inanimate matter, the very thing that makes questions possible in the first place. Understand consciousness and you understand the very thing that makes us human. That achievement is so enormous that it seems almost petty to point out that the revolutionary effects of artificial intelligence would also fall into your lap.

The arts and humanities also have a great deal to contribute, and are woefully underappreciated.

Artists, authors, and musicians all have the potential to make us rethink our place in the world, reconsider and reimagine what we believe and strive for. If physics and engineering can make us better at winning wars, art and literature and remind us why we should never fight them in the first place. The greatest works of art can remind us of our shared humanity, link us all together in a grander civilization that transcends the petty boundaries of culture, geography, or religion. Art can also be timeless in a way nothing else can; most of Aristotle’s science is long-since refuted, but even the Great Pyramid thousands of years before him continues to awe us. (Aristotle is about equidistant chronologically between us and the Great Pyramid.)

Philosophers may not seem like they have much to add—and to be fair, a great deal of what goes on today in metaethics and epistemology doesn’t add much to civilization—but in fact it was Enlightenment philosophy that brought us democracy, the scientific method, and market economics. Today there are still major unsolved problems in ethics—particularly bioethics—that are in need of philosophical research. Technologies like nanotechnology and genetic engineering offer us the promise of enormous benefits, but also the risk of enormous harms; we need philosophers to help us decide how to use these technologies to make our lives better instead of worse. We need to know where to draw the lines between life and death, between justice and cruelty. Literally nothing could be more important than knowing right from wrong.

Now that I have sung the praises of the natural sciences and the humanities, let me now explain why I am a social scientist, and why you probably should be as well.

Psychologists and cognitive scientists obviously have a great deal to give us in the study of mental illness, but they may actually have more to contribute in the study of mental health—in understanding not just what makes us depressed or schizophrenic, but what makes us happy or intelligent. The 21^st century may not simply see the end of mental illness, but the rise of a new level of mental prosperity, where being happy, focused, and motivated are matters of course. The revolution that biology has brought to our lives may pale in comparison to the revolution that psychology will bring. On the more social side of things, psychology may allow us to understand nationalism, sectarianism, and the tribal instinct in general, and allow us to finally learn to undermine fanaticism, encourage critical thought, and make people more rational. The benefits of this are almost impossible to overstate: It is our own limited, broken, 90%-or-so heuristic rationality that has brought us from simians to Shakespeare, from gorillas to Godel. To raise that figure to 95% or 99% or 99.9% could be as revolutionary as was whatever evolutionary change first brought us out of the savannah as Australopithecus africanus.

Sociologists and anthropologists will also have a great deal to contribute to this process, as they approach the tribal instinct from the top down. They may be able to tell us how nations are formed and undermined, why some cultures assimilate and others collide. They can work to understand combat bigotry in all its forms, racism, sexism, ethnocentrism. These could be the fields that finally end war, by understanding and correcting the imbalances in human societies that give rise to violent conflict.

Political scientists and public policy researchers can allow us to understand and restructure governments, undermining corruption, reducing inequality, making voting systems more expressive and more transparent. They can search for the keystones of different political systems, finding the weaknesses in democracy to shore up and the weaknesses in autocracy to exploit. They can work toward a true international government, representative of all the world’s people and with the authority and capability to enforce global peace. If the sociologists don’t end war and genocide, perhaps the political scientists can—or more likely they can do it together.

And then, at last, we come to economists. While I certainly work with a lot of ideas from psychology, sociology, and political science, I primarily consider myself an economist. Why is that? Why do I think the most important problems for me—and perhaps everyone—to be working on are fundamentally economic?

Because, above all, economics is broken. The other social sciences are basically on the right track; their theories are still very limited, their models are not very precise, and there are decades of work left to be done, but the core principles upon which they operate are correct. Economics is the field to work in because of criterion 3: Almost all the important problems in economics are underinvested.

Macroeconomics is where we are doing relatively well, and yet the Keynesian models that allowed us to reduce the damage of the Second Depression nonetheless had no power to predict its arrival. While inflation has been at least somewhat tamed, the far worse problem of unemployment has not been resolved or even really understood.

When we get to microeconomics, the neoclassical models are totally defective. Their core assumptions of total rationality and total selfishness are embarrassingly wrong. We have no idea what controls assets prices, or decides credit constraints, or motivates investment decisions. Our models of how people respond to risk are all wrong. We have no formal account of altruism or its limitations. As manufacturing is increasingly automated and work shifts into services, most economic models make no distinction between the two sectors. While finance takes over more and more of our society’s wealth, most formal models of the economy don’t even include a financial sector.

Economic forecasting is no better than chance. The most widely-used asset-pricing model, CAPM, fails completely in empirical tests; its defenders concede this and then have the audacity to declare that it doesn’t matter because the mathematics works. The Black-Scholes derivative-pricing model that caused the Second Depression could easily have been predicted to do so, because it contains a term that assumes normal distributions when we know for a fact that financial markets are fat-tailed; simply put, it claims certain events will never happen that actually occur several times a year.

Worst of all, economics is the field that people listen to. When a psychologist or sociologist says something on television, people say that it sounds interesting and basically ignore it. When an economist says something on television, national policies are shifted accordingly. Austerity exists as national policy in part due to a spreadsheet error by two famous economists.

Keynes already knew this in 1936: “The ideas of economists and political philosophers, both when they are right and when they are wrong, are more powerful than is commonly understood. Indeed the world is ruled by little else. Practical men, who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back.”

Meanwhile, the problems that economics deals with have a direct influence on the lives of millions of people. Bad economics gives us recessions and depressions; it cripples our industries and siphons off wealth to an increasingly corrupt elite. Bad economics literally starves people: It is because of bad economics that there is still such a thing as world hunger. We have enough food, we have the technology to distribute it—but we don’t have the economic policy to lift people out of poverty so that they can afford to buy it. Bad economics is why we don’t have the funding to cure diabetes or colonize Mars (but we have the funding for oil fracking and aircraft carriers, don’t we?). All of that other scientific research that needs done probably could be done, if the resources of our society were properly distributed and utilized.

This combination of both overwhelming influence, overwhelming importance and overwhelming error makes economics the low-hanging fruit; you don’t even have to be particularly brilliant to have better ideas than most economists (though no doubt it helps if you are). Economics is where we have a whole bunch of important questions that are unanswered—or the answers we have are wrong. (As Will Rogers said, “It isn’t what we don’t know that gives us trouble, it’s what we know that ain’t so.”)

Thus, rather than tell you go into finance and earn to give, those economists could simply have said: “You should become an economist. You could hardly do worse than we have.”

Why the Republican candidates like flat income tax—and we really, really don’t

2015-05-17 PNRJ critique of neoclassical economics, public policy basic income, Bernie Sanders, capital, Democrat, elections, flat tax, halo effect, Hillary Clinton, investment, IRS, just world, land tax, Miles Kimball, Mitt Romney, monetary policy, money, poverty, profit, progressive, Republican, saving, tax code, tax reform, taxation, taxes, wealth

JDN 2456160 EDT 13:55.

The Republican Party is scrambling to find viable Presidential candidates for next year’s election. The Democrats only have two major contenders: Hillary Clinton looks like the front-runner (and will obviously have the most funding), but Bernie Sanders is doing surprisingly well, and is particularly refreshing because he is running purely on his principles and ideas. He has no significant connections, no family dynasty (unlike Jeb Bush and, again, Hillary Clinton) and not a huge amount of wealth (Bernie’s net wealth is about $500,000, making him comfortably upper-middle class; compare to Hillary’s $21.5 million and her husband’s $80 million); but he has ideas that resonate with people. Bernie Sanders is what politics is supposed to be. Clinton’s campaign will certainly raise more than his; but he has already raised over $4 million, and if he makes it to about $10 million studies suggest that additional spending above that point is largely negligible. He actually has a decent chance of winning, and if he did it would be a very good sign for the future of America.

But the Republican field is a good deal more contentious, and the 19 candidates currently running have been scrambling to prove that they are the most right-wing in order to impress far-right primary voters. (When the general election comes around, whoever wins will of course pivot back toward the center, changing from, say, outright fascism to something more like reactionism or neo-feudalism. If you were hoping they’d pivot so far back as to actually be sensible center-right capitalists, think again; Hillary Clinton is the only one who will take that role, and they’ll go out of their way to disagree with her in every way they possibly can, much as they’ve done with Obama.) One of the ways that Republicans are hoping to prove their right-wing credentials is by proposing a flat income tax and eliminating the IRS.

Unlike most of their proposals, I can see why many people think this actually sounds like a good idea. It would certainly dramatically reduce bureaucracy, and that’s obviously worthwhile since excess bureaucracy is pure deadweight loss. (A surprising number of economists seem to forget that government does other things besides create excess bureaucracy, but I must admit it does in fact create excess bureaucracy.)

Though if they actually made the flat tax rate 20% or even—I can’t believe this is seriously being proposed—10%, there is no way the federal government would have enough revenue. The only options would be (1) massive increases in national debt (2) total collapse of government services—including their beloved military, mind you, or (3) directly linking the Federal Reserve quantitative easing program to fiscal policy and funding the deficit with printed money. Of these, 3 might not actually be that bad (it would probably trigger some inflation, but actually we could use that right now), but it’s extremely unlikely to happen, particularly under Republicans. In reality, after getting a taste of 2, we’d clearly end up with 1. And then they’d be complaining about the debt and clamor for more spending cuts, more spending cuts, ever more spending cuts, but there would simply be no way to run a functioning government on 10% of GDP in anything like our current system. Maybe you could do it on 20%—maybe—but we currently spend more like 35%, and that’s already a very low amount of spending for a First World country. The UK is more typical at 47%, while Germany is a bit low at 44%; Sweden spends 52% and France spends a whopping 57%. Anyone who suggests we cut government spending from 35% to 20% needs to explain which 3/7 of government services are going to immediately disappear—not to mention which 3/7 of government employees are going to be immediately laid off.

And then they want to add investment deductions; in general investment deductions are a good thing, as long as you tie them to actual investments in genuinely useful things like factories and computer servers. (Or better yet, schools, research labs, or maglev lines, but private companies almost never invest in that sort of thing, so the deduction wouldn’t apply.) The kernel of truth in the otherwise ridiculous argument that we should never tax capital is that taxing real investment would definitely be harmful in the long run. As I discussed with Miles Kimball (a cognitive economist at Michigan and fellow econ-blogger I hope to work with at some point), we could minimize the distortionary effects of corporate taxes by establishing a strong deduction for real investment, and this would allow us to redistribute some of this enormous wealth inequality without dramatically harming economic growth.

But if you deduct things that aren’t actually investments—like stock speculation and derivatives arbitrage—then you reduce your revenue dramatically and don’t actually incentivize genuinely useful investments. This is the problem with our current system, in which GE can pay no corporate income tax on $108 billion in annual profit—and you know they weren’t using all that for genuinely productive investment activities. But then, if you create a strong enforcement system for ensuring it is real investment, you need bureaucracy—which is exactly what the flat tax was claimed to remove. At the very least, the idea of eliminating the IRS remains ridiculous if you have any significant deductions.

Thus, the benefits of a flat income tax are minimal if not outright illusory; and the costs, oh, the costs are horrible. In order to have remotely reasonable amounts of revenue, you’d need to dramatically raise taxes on the majority of people, while significantly lowering them on the rich. You would create a direct transfer of wealth from the poor to the rich, increasing our already enormous income inequality and driving millions of people into poverty.

Thus, it would be difficult to more clearly demonstrate that you care only about the interests of the top 1% than to propose a flat income tax. I guess Mitt Romney’s 47% rant actually takes the cake on that one though (Yes, all those freeloading… soldiers… and children… and old people?).

Many Republicans are insisting that a flat tax would create a surge of economic growth, but that’s simply not how macroeconomics works. If you steeply raise taxes on the majority of people while cutting them on the rich, you’ll see consumer spending plummet and the entire economy will be driven into recession. Rich people simply don’t spend their money in the same way as the rest of us, and the functioning of the economy depends upon a continuous flow of spending. There is a standard neoclassical economic argument about how reducing spending and increasing saving would lead to increased investment and greater prosperity—but that model basically assumes that we have a fixed amount of stuff we’re either using up or making more stuff with, which is simply not how money works; as James Kroeger cogently explains on his blog “Nontrivial Pursuits”, money is created as it is needed; investment isn’t determined by people saving what they don’t spend. Indeed, increased consumption generally leads to increased investment, because our economy is currently limited by demand, not supply. We could build a lot more stuff, if only people could afford to buy it.

And that’s not even considering the labor incentives; as I already talked about in my previous post on progressive taxation, there are two incentives involved when you increase someone’s hourly wage. On the one hand, they get paid more for each hour, which is a reason to work; that’s the substitution effect. But on the other hand, they have more money in general, which is a reason they don’t need to work; that’s the income effect. Broadly speaking, the substitution effect dominates at low incomes (about $20,000 or less), the income effect dominates at high incomes (about $100,000 or more), and the two effects cancel out at moderate incomes. Since a tax on your income hits you in much the same way as a reduction in your wage, this means that raising taxes on the poor makes them work less, while raising taxes on the rich makes them work more. But if you go from our currently slightly-progressive system to a flat system, you raise taxes on the poor and cut them on the rich, which would mean that the poor would work less, and the rich would also work less! This would reduce economic output even further. If you want to maximize the incentive to work, you want progressive taxes, not flat taxes.

Flat taxes sound appealing because they are so simple; even the basic formula for our current tax rates is complicated, and we combine it with hundreds of pages of deductions and credits—not to mention tens of thousands of pages of case law!—making it a huge morass of bureaucracy that barely anyone really understands and corporate lawyers can easily exploit. I’m all in favor of getting rid of that; but you don’t need a flat tax to do that. You can fit the formula for a progressive tax on a single page—indeed, on a single line: r = 1 – I^-p

That’s it. It’s simple enough to be plugged into any calculator that is capable of exponents, not to mention efficiently implemented in Microsoft Excel (more efficiently than our current system in fact).

Combined with that simple formula, you could list all of the sensible deductions on a couple of additional pages (business investments and educational expenses, mostly—poverty should be addressed by a basic income, not by tax deductions on things like heating and housing, which are actually indirect corporate subsidies), along with a land tax (one line: $3000 per hectare), a basic income (one more line: $8,000 per adult and $4,000 per child), and some additional excise taxes on goods with negative externalities (like alcohol, tobacco, oil, coal, and lead), with a line for each; then you can provide a supplementary manual of maybe 50 pages explaining the detailed rules for applying each of those deductions in unusual cases. The entire tax code should be readable by an ordinary person in a single sitting no longer than a few hours. That means no more than 100 pages and no more than a 7th-grade reading level.

Why do I say this? Isn’t that a ridiculous standard? No, it is a Constitutional imperative. It is a fundamental violation of your liberty to tax you according to rules you cannot reasonably understand—indeed, bordering on Kafkaesque. While this isn’t taxation without representation—we do vote for representatives, after all—it is something very much like it; what good is the ability to change rules if you don’t even understand the rules in the first place? Nor would it be all that difficult: You first deduct these things from your income, then plug the result into this formula.

So yes, I absolutely agree with the basic principle of tax reform. The tax code should be scrapped and recreated from scratch, and the final product should be a primary form of only a few pages combined with a supplementary manual of no more than 100 pages. But you don’t need a flat tax to do that, and indeed for many other reasons a flat tax is a terrible idea, particularly if the suggested rate is 10% or 15%, less than half what we actually spend. The real question is why so many Republican candidates think that this will appeal to their voter base—and why they could actually be right about that.

Part of it is the entirely justified outrage at the complexity of our current tax system, and the appealing simplicity of a flat tax. Part of it is the long history of American hatred of taxes; we were founded upon resisting taxes, and we’ve been resisting taxes ever since. In some ways this is healthy; taxes per se are not a good thing, they are a bad thing, a necessary evil.

But those two things alone cannot explain why anyone would advocate raising taxes on the poorest half of the population while dramatically cutting them on the top 1%. If you are opposed to taxes in general, you’d cut them on everyone; and if you recognize the necessity of taxation, you’d be trying to find ways to minimize the harm while ensuring sufficient tax revenue, which in general means progressive taxation.

To understand why they would be pushing so hard for flat taxes, I think we need to say that many Republicans, particularly those in positions of power, honestly do think that rich people are better than poor people and we should always give more to the rich and less to the poor. (Maybe it’s partly halo effect, in which good begets good and bad begets bad? Or maybe just world theory, the ingrained belief that the world is as it ought to be?)

Romney’s 47% rant wasn’t an exception; it was what he honestly believes, what he says when he doesn’t know he’s on camera. He thinks that he earned every penny of his $250 million net wealth; yes, even the part he got from marrying his wife and the part he got from abusing tax laws, arbitraging assets and liquidating companies. He thinks that people who live on $4,000 or even $400 a year are simply lazy freeloaders, who could easily work harder, perhaps do some arbitrage and liquidation of their own (check out these alleged “rags to riches” stories including the line “tried his hand at mortgage brokering”), but choose not to, and as a result deserve what they get. (It’s important to realize just how bizarre this moral attitude truly is; even if I thought you were the laziest person on Earth, I wouldn’t let you starve to death.) He thinks that the social welfare programs which have reduced poverty but never managed to eliminate it are too generous—if he even thinks they should exist at all. And in thinking these things, he is not some bizarre aberration; he is representing an entire class of people, nearly all of whom vote Republican.

The good news is, these people are still in the minority. They hold significant sway over the Republican primary, but will not have nearly as much impact in the general election. And right now, the Republican candidates are so numerous and so awful that I have trouble seeing how the Democrats could possibly lose. (But please, don’t take that as a challenge, you guys.)

What you need to know about tax incidence

2015-05-092015-05-09 PNRJ core principles, public policy, Top 10 things to know about economics Adam Smith, consumer surplus, deadweight loss, economic surplus, elasticity, equations, land tax, LaTeX, producer surplus, rent, rent control, supply and demand, tax incidence, taxation, taxes

JDN 2457152 EDT 14:54.

I said in my previous post that I consider tax incidence to be one of the top ten things you should know about economics. If I actually try to make a top ten list, I think it goes something like this:

Supply and demand
Monopoly and oligopoly
Externalities
Tax incidence
Utility, especially marginal utility of wealth
Pareto-efficiency
Risk and loss aversion
Biases and heuristics, including sunk-cost fallacy, scope neglect, herd behavior, anchoring and representative heuristic
Asymmetric information
Winner-takes-all effect

So really tax incidence is in my top five things you should know about economics, and yet I still haven’t talked about it very much. Well, today I will. The basic principles of supply and demand I’m basically assuming you know, but I really should spend some more time on monopoly and externalities at some point.

Why is tax incidence so important? Because of one central fact: The person who pays the tax is not the person who writes the check.

It doesn’t matter whether a tax is paid by the buyer or the seller; it matters what the buyer and seller can do to avoid the tax. If you can change your behavior in order to avoid paying the tax—buy less stuff, or buy somewhere else, or deduct something—you will not bear the tax as much as someone else who can’t do anything to avoid the tax, even if you are the one who writes the check. If you can avoid it and they can’t, other parties in the transaction will adjust their prices in order to eat the tax on your behalf.

Thus, if you have a good that you absolutely must buy no matter what—like, say, table salt—and then we make everyone who sells that good pay an extra $5 per kilogram, I can guarantee you that you will pay an extra $5 per kilogram, and the suppliers will make just as much money as they did before. (A salt tax would be an excellent way to redistribute wealth from ordinary people to corporations, if you’re into that sort of thing. Not that we have any trouble doing that in America.)

On the other hand, if you have a good that you’ll only buy at a very specific price—like, say, fast food—then we can make you write the check for a tax of an extra $5 per kilogram you use, and in real terms you’ll pay hardly any tax at all, because the sellers will either eat the cost themselves by lowering the prices or stop selling the product entirely. (A fast food tax might actually be a good idea as a public health measure, because it would reduce production and consumption of fast food—remember, heart disease is one of the leading causes of death in the United States, making cheeseburgers a good deal more dangerous than terrorists—but it’s a bad idea as a revenue measure, because rather than pay it, people are just going to buy and sell less.)

In the limit in which supply and demand are both completely fixed (perfectly inelastic), you can tax however you want and it’s just free redistribution of wealth however you like. In the limit in which supply and demand are both locked into a single price (perfectly elastic), you literally cannot tax that good—you’ll just eliminate production entirely. There aren’t a lot of perfectly elastic goods in the real world, but the closest I can think of is cash. If you instituted a 2% tax on all cash withdrawn, most people would stop using cash basically overnight. If you want a simple way to make all transactions digital, find a way to enforce a cash tax. When you have a perfect substitute available, taxation eliminates production entirely.

To really make sense out of tax incidence, I’m going to need a lot of a neoclassical economists’ favorite thing: Supply and demand curves. These things pop up everywhere in economics; and they’re quite useful. I’m not so sure about their application to things like aggregate demand and the business cycle, for example, but today I’m going to use them for the sort of microeconomic small-market stuff that they were originally designed for; and what I say here is going to be basically completely orthodox, right out of what you’d find in an ECON 301 textbook.

Let’s assume that things are linear, just to make the math easier. You’d get basically the same answers with nonlinear demand and supply functions, but it would be a lot more work. Likewise, I’m going to assume a unit tax on goods—like $2890 per hectare—as opposed to a proportional tax on sales—like 6% property tax—again, for mathematical simplicity.

The next concept I’m going to have to talk about is elasticity—which is the proportional amount that quantity sold changes relative to price. If price increases 2% and you buy 4% less, you have a demand elasticity of -2. If price increases 2% and you buy 1% less, you have a demand elasticity of -1/2. If price increases 3% and you sell 6% more, you have a supply elasticity of 2. If price decreases 5% and you sell 1% less, you have a supply elasticity of 1/5.

Elasticity doesn’t have any units of measurement, it’s just a number—which is part of why we like to use it. It also has some very nice mathematical properties involving logarithms, but we won’t be needing those today.

The price that renters are willing and able to pay, the demand price P_Dwill start at their maximum price, the reserve price P_R, and then it will decrease linearly according to the quantity of land rented Q, according to a linear function (simply because we assumed that) which will vary according to a parameter e that represents the elasticity of demand (it isn’t strictly equal to it, but it’s sort of a linearization).

We’re interested in what is called the consumer surplus; it is equal to the total amount of value that buyers get from their purchases, converted into dollars, minus the amount they had to pay for those purchases. This we add to the producer surplus, which is the amount paid for those purchases minus the cost of producing them—which is basically just the same thing as profit. Togerther the consumer surplus and producer surplus make the total economic surplus, which economists generally try to maximize. Because different people have different marginal utility of wealth, this is actually a really terrible idea for deep and fundamental reasons—taking a house from Mitt Romney and giving it to a homeless person would most definitely reduce economic surplus, even though it would obviously make the world a better place. Indeed, I think that many of the problems in the world, particularly those related to inequality, can be traced to the fact that markets maximize economic surplus rather than actual utility. But for now I’m going to ignore all that, and pretend that maximizing economic surplus is what we want to do.

You can read off the economic surplus straight from the supply and demand curves; it’s the area between the lines. (Mathematically, it’s an integral; but that’s equivalent to the area under a curve, and with straight lines they’re just triangles.) I’m going to call the consumer surplus just “surplus”, and producer surplus I’ll call “profit”.

Below the demand curve and above the price is the surplus, and below the price and above the supply curve is the profit:

I’m going to be bold here and actually use equations! Hopefully this won’t turn off too many readers. I will give each equation in both a simple text format and in proper LaTeX. Remember, you can render LaTeX here.

P_D = P_R– 1/e * Q

P_D = P_R – \frac{1}{e} Q \\

The marginal cost that landlords have to pay, the supply price P_S, is a bit weirder, as I’ll talk about more in a moment. For now let’s say that it is a linear function, starting at zero cost for some quantity Q₀ and then increases linearly according to a parameter n that similarly represents the elasticity of supply.

P_S = 1/n * (Q – Q₀)

P_S = \frac{1}{n} \left( Q – Q_0 \right) \\

Now, if you introduce a tax, there will be a difference between the price that renters pay and the price that landlords receive—namely, the tax, which we’ll call T. I’m going to assume that, on paper, the landlord pays the whole tax. As I said above, this literally does not matter. I could assume that on paper the renter pays the whole tax, and the real effect on the distribution of wealth would be identical. All we’d have to do is set P_D = P and P_S = P – T; the consumer and producer surplus would end up exactly the same. Or we could do something in between, with P’_D = P + rT and P’_S = P – (1 – r) T.

Then, if the market is competitive, we just set the prices equal, taking the tax into account:

P = P_D – T = P_R – 1/e * Q – T = P_S = 1/n * (Q – Q₀)

P= P_D – T = P_R – \frac{1}{e} Q – T= P_S = \frac{1}{n} \left(Q – Q_0 \right) \\

P_R – 1/e * Q – T = 1/n * (Q – Q₀)

P_R – \frac{1}{e} Q – T = \frac{1}{n} \left(Q – Q_0 \right) \\

Notice the equivalency here; if we set P’_D = P + rT and P’_S = P – (1 – r) T, so that the consumer now pays a fraction of the tax r.

P = P’_D – rT = P_r – 1/e*Q = P’_S + (1 – r) T + 1/n * (Q – Q₀) + (1 – r) T

P^\prime_D – r T = P = P_R – \frac{1}{e} Q = P^\prime_S = \frac{1}{n} \left(Q – Q_0 \right) + (1 – r) T\\

The result is exactly the same:

P_R – 1/e * Q – T = 1/n * (Q – Q₀)

P_R – \frac{1}{e} Q – T = \frac{1}{n} \left(Q – Q_0 \right) \\

I’ll spare you the algebra, but this comes out to:

Q = (P_R – T)/(1/n + 1/e) + (Q₀)/(1 + n/e)

Q = \frac{P_R – T}{\frac{1}{n} + \frac{1}{e}} + \frac{Q_0}{1 + \frac{n}{e}}

P = (P_R – T)/(1+ n/e) – (Q₀)/(e + n)

P = \frac{P_R – T}}{1 + \frac{n}{e}} – \frac{Q_0}{e+n} \\

That’s if the market is competitive.

If the market is a monopoly, instead of setting the prices equal, we set the price the landlord receives equal to the marginal revenue—which takes into account the fact that increasing the amount they sell forces them to reduce the price they charge everyone else. Thus, the marginal revenue drops faster than the price as the quantity sold increases.

After a bunch of algebra (and just a dash of calculus), that comes out to these very similar, but not quite identical, equations:

Q = (P_R – T)/(1/n + 2/e) + (Q₀)/(1+ 2n/e)

Q = \frac{P_R – T}{\frac{1}{n} + \frac{2}{e}} + \frac{Q_0}{1 + \frac{2n}{e}} \\

P = (P_R – T)*((1/n + 1/e)/(1/n + 2/e) – (Q₀)/(e + 2n)

P = \left( P_R – T\right)\frac{\frac{1}{n} + \frac{1}{e}}{\frac{1}{n} + \frac{2}{e}} – \frac{Q_0}{e+2n} \\

Yes, it changes some 1s into 2s. That by itself accounts for the full effect of monopoly. That’s why I think it’s worthwhile to use the equations; they are deeply elegant and express in a compact form all of the different cases. They look really intimidating right now, but for most of the cases we’ll consider these general equations simplify quite dramatically.

There are several cases to consider.

Land has an extremely high cost to create—for practical purposes, we can consider its supply fixed, that is, perfectly inelastic. If the market is competitive, so that landlords have no market power, then they will simply rent out all the land they have at whatever price the market will bear:

This is like setting n = 0 and T = 0 in the above equations, the competitive ones.

Q = Q₀

Q = Q_0 \\

P = P_R – Q₀/e

P = P_R – \frac{Q_0}{e} \\

If we now introduce a tax, it will fall completely on the landlords, because they have little choice but to rent out all the land they have, and they can only rent it at a price—including tax—that the market will bear.

Now we still have n = 0 but not T = 0.

Q = Q₀

Q = Q_0 \\

P = P_R – T – Q₀/e

P = P_R – T – \frac{Q_0}{e} \\

The consumer surplus will be:

½ (Q)(P_R – P – T) = 1/(2e)* Q₀²

\frac{1}{2}Q(P_R – P – T) = \frac{1}{2e}Q_0^2 \\

Notice how T isn’t in the result. The consumer surplus is unaffected by the tax.

The producer surplus, on the other hand, will be reduced by the tax:

(Q)(P) = (P_R – T – Q₀/e) Q₀ = P_R Q₀ – 1/e Q₀² – TQ₀

(Q)(P) = (P_R – T – \frac{Q_0}{e})Q_0 = P_R Q_0 – \frac{1}{e} Q_0^2 – T Q_0 \\

T appears linearly as TQ₀, which is the same as the tax revenue. All the money goes directly from the landlord to the government, as we want if our goal is to redistribute wealth without raising rent.

But now suppose that the market is not competitive, and by tacit collusion or regulatory capture the landlords can exert some market power; this is quite likely the case in reality. Actually in reality we’re probably somewhere in between monopoly and competition, either oligopoly or monopolistic competition—which I will talk about a good deal more in a later post, I promise.

It could be that demand is still sufficiently high that even with their market power, landlords have an incentive to rent out all their available land, in which case the result will be the same as in the competitive market.

A tax will then fall completely on the landlords as before:

Indeed, in this case it doesn’t really matter that the market is monopolistic; everything is the same as it would be under a competitive market. Notice how if you set n = 0, the monopolistic equations and the competitive equations come out exactly the same. The good news is, this is quite likely our actual situation! So even in the presence of significant market power the land tax can redistribute wealth in just the way we want.

But there are a few other possibilities. One is that demand is not sufficiently high, so that the landlords’ market power causes them to actually hold back some land in order to raise the price:

This will create some of what we call deadweight loss, in which some economic value is wasted. By restricting the land they rent out, the landlords make more profit, but the harm they cause to tenant is created than the profit they gain, so there is value wasted.

Now instead of setting n = 0, we actually set n = infinity. Why? Because the reason that the landlords restrict the land they sell is that their marginal revenue is actually negative beyond that point—they would actually get less money in total if they sold more land. Instead of being bounded by their cost of production (because they have none, the land is there whether they sell it or not), they are bounded by zero. (Once again we’ve hit upon a fundamental concept in economics, particularly macroeconomics, that I don’t have time to talk about today: the zero lower bound.) Thus, they can change quantity all they want (within a certain range) without changing the price, which is equivalent to a supply elasticity of infinity.

Introducing a tax will then exacerbate this deadweight loss (adding DWL2 to the original DWL1), because it provides even more incentive for the landlords to restrict the supply of land:

Q = e/2*(P_R – T)

Q = \frac{e}{2} \left(P_R – T\right)\\

P = 1/2*(P_R – T)

P = \frac{1}{2} \left(P_R – T\right) \\

The quantity Q₀ completely drops out, because it doesn’t matter how much land is available (as long as it’s enough); it only matters how much land it is profitable to rent out.

We can then find the consumer and producer surplus, and see that they are both reduced by the tax. The consumer surplus is as follows:

½ (Q)(P_R – 1/2(P_R – T)) = e/4*(P_R² – T²)

\frac{1}{2}Q \left( P_R – \frac{1}{2}left( P – T \right) \right) = \frac{e}{4}\left( P_R^2 – T^2 \right) \\

This time, the tax does have an effect on reducing the consumer surplus.

The producer surplus, on the other hand, will be:

(Q)(P) = 1/2*(P_R – T)*e/2*(P_R – T) = e/4*(P_R – T)²

(Q)(P) = \frac{1}{2}\left(P_R – T \right) \frac{e}{2} \left(P_R – T\right) = \frac{e}{4} \left(P_R – T)^2 \\

Notice how it is also reduced by the tax—and no longer in a simple linear way.

The tax revenue is now a function of the demand:

TQ = e/2*T(P_R – T)

T Q = \frac{e}{2} T (P_R – T) \\

If you add all these up, you’ll find that the sum is this:

e/2 * (P_R^2 – T^2)

\frac{e}{2} \left(P_R^2 – T^2 \right) \\

The sum is actually reduced by an amount equal to e/2*T^2, which is the deadweight loss.

Finally there is an even worse scenario, in which the tax is so large that it actually creates an incentive to restrict land where none previously existed:

Notice, however, that because the supply of land is inelastic the deadweight loss is still relatively small compared to the huge amount of tax revenue.

But actually this isn’t the whole story, because a land tax provides an incentive to get rid of land that you’re not profiting from. If this incentive is strong enough, the monopolistic power of landlords will disappear, as the unused land gets sold to more landholders or to the government. This is a way of avoiding the tax, but it’s one that actually benefits society, so we don’t mind incentivizing it.

Now, let’s compare this to our current system of property taxes, which include the value of buildings. Buildings are expensive to create, but we build them all the time; the supply of buildings is strongly dependent upon the price at which those buildings will sell. This makes for a supply curve that is somewhat elastic.

If the market were competitive and we had no taxes, it would be optimally efficient:

Property taxes create an incentive to produce fewer buildings, and this creates deadweight loss. Notice that this happens even if the market is perfectly competitive:

Since both n and e are finite and nonzero, we’d need to use the whole equations: Since the algebra is such a mess, I don’t see any reason to subject you to it; but suffice it to say, the T does not drop out. Tenants do see their consumer surplus reduced, and the larger the tax the more this is so.

Now, suppose that the market for buildings is monopolistic, as it most likely is. This would create deadweight loss even in the absence of a tax:

But a tax will add even more deadweight loss:

Once again, we’d need the full equations, and once again it’s a mess; but the result is, as before, that the tax gets passed on to the tenants in the form of more restricted sales and therefore higher rents.

Because of the finite supply elasticity, there’s no way that the tax can avoid raising the rent. As long as landlords have to pay more taxes when they build more or better buildings, they are going to raise the rent in those buildings accordingly—whether the market is competitive or not.

If the market is indeed monopolistic, there may be ways to bring the rent down: suppose we know what the competitive market price of rent should be, and we can establish rent control to that effect. If we are truly correct about the price to set, this rent control can not only reduce rent, it can actually reduce the deadweight loss:

But if we set the rent control too low, or don’t properly account for the varying cost of different buildings, we can instead introduce a new kind of deadweight loss, by making it too expensive to make new buildings.

In fact, what actually seems to happen is more complicated than that—because otherwise the number of buildings is obviously far too small, rent control is usually set to affect some buildings and not others. So what seems to happen is that the rent market fragments into two markets: One, which is too small, but very good for those few who get the chance to use it; and the other, which is unaffected by the rent control but is more monopolistic and therefore raises prices even further. This is why almost all economists are opposed to rent control (PDF); it doesn’t solve the problem of high rent and simply causes a whole new set of problems.

A land tax with a basic income, on the other hand, would help poor people at least as much as rent control presently does—probably a good deal more—without discouraging the production and maintenance of new apartment buildings.

But now we come to a key point: The land tax must be uniform per hectare.

If it is instead based on the value of the land, then this acts like a finite elasticity of supply; it provides an incentive to reduce the value of your own land in order to avoid the tax. As I showed above, this is particularly pernicious if the market is monopolistic, but even if it is competitive the effect is still there.

One exception I can see is if there are different tiers based on broad classes of land that it’s difficult to switch between, such as “land in Manhattan” versus “land in Brooklyn” or “desert land” versus “forest land”. But even this policy would have to be done very carefully, because any opportunity to substitute can create an opportunity to pass on the tax to someone else—for instance if land taxes are lower in Brooklyn developers are going to move to Brooklyn. Maybe we want that, in which case that is a good policy; but we should be aware of these sorts of additional consequences. The simplest way to avoid all these problems is to simply make the land tax uniform. And given the quantities we’re talking about—less than $3000 per hectare per year—it should be affordable for anyone except the very large landholders we’re trying to distribute wealth from in the first place.

The good news is, most economists would probably be on board with this proposal. After all, the neoclassical models themselves say it would be more efficient than our current system of rent control and property taxes—and the idea is at least as old as Adam Smith. Perhaps we can finally change the fact that the rent is too damn high.

What if you couldn’t own land?

2015-05-01 PNRJ core principles, public policy Adam Smith, basic income, capital gains, capitalism, corporate tax, Eddie Izzard, elasticity, inequality, Jeff Bezos, John Lennon, land, landlord, ownership, Piketty, property, real estate, tax incidence, taxation, taxes, The Guess Who, wealth

JDN 2457145 EDT 20:49.

Today’s post we’re on the socialism scale somewhere near the The Guess Who, but not quite all the way to John Lennon. I’d like to questions one of the fundamental tenets of modern capitalism, but not the basic concept of private ownership itself:

What if you couldn’t own land?

Many things that you can own were more-or-less straightforwardly created by someone. A car, a computer, a television, a pair of shoes; for today let’s even take for granted intellectual property like books, movies, and songs; at least those things (“things”) were actually made by someone.

But land? We’re talking about chunks of the Earth here. They were here billions of years before us, and in all probability will be here billions of years after we’re gone. There’s no need to incentivize its creation; the vast majority of land was already here and did not need to be created. (I do have to say “the vast majority”, because in places like Japan, Hong Kong, and the Netherlands real estate has become so scarce that people do literally build land out into the sea. But this is something like 0.0001% of the world’s land.)

What we want to incentivize is land development; we want it to be profitable to build buildings and irrigate deserts, and yes, even cut down forests sometimes (though then there should be a carbon tax with credits for forested land to ensure that there isn’t too much incentive). Yet our current property tax system doesn’t do this very well; if you build bigger buildings, you end up paying more property taxes. Yes, you may also make some profit on the buildings—but it’s risky, and you may not get enough benefit to justify the added property taxes.

Moreover, we want to allocate land—we want some way of deciding who is allowed to use what land where and when (and perhaps why). Allowing land to be bought and sold is one way to do that, but it is not the only way.

Indeed, land ownership suffers from a couple of truly glaring flaws as an allocation system:

It creates self-perpetuating inequality. Because land grows in value over time (due to population growth and urbanization, among other things), those who currently own land end up getting an ever-growing quantity of wealth while those who do not own land do not, and very likely end up having to pay ever-growing rents to the landlords. (I like calling them “landlords”; it really drives home the fact that our landholding system is still basically the same as it was under feudalism.) In fact, the recent rise in the share of income that goes to owners of capital rather than workers is almost entirely attributable to the rise in the price of real estate. As that post rightly recognizes, this does nothing to undermine Piketty’s central message of rising inequality due to capital income (pace The Washington Post); it merely tells us to focus on real estate instead of other forms of capital.
It has no non-arbitrary allocation. If we want to decide who owns a car, we can ask questions like, “Who built it? Did someone buy it from them? Did they pay a fair price?”; if we want to decide who owns a book, we can ask questions like, “Who wrote it? Did they sell it to a publisher? What was the royalty rate?” That is, there is a clear original owner, and there is a sense of whether the transfer of ownership can be considered fair. But if we want to decide who owns a chunk of land, basically all we can ask is, “What does the deed say?” The owner is the owner because they are the owner; there’s no sense in which that ownership is fair. We certainly can’t go back to the original creation of the land, because that was due to natural forces gigayears ago. If we keep tracing the ownership backward, we will eventually end up with some guy (almost certainly a man, a White man in fact) with a gun who pointed that gun at other people and said, “This is mine.” This is true of basically all the land in the world (aside from those little bits of Japan and such); it was already there, and the only reason someone got to own it was because they said so and had a bigger gun. And a flag, perhaps: “Do you have a flag?” I suppose, in theory at least, there are a few ways of allocating land which seem less arbitrary: One would be to give everyone an equal amount. But this is practically very difficult: What do you do when the population changes? If you have 2% annual population growth, do you carve off 2% of everybody’s lot each year? Another would be to let people squat land, and automatically own the land that they live on—but again practical difficulties quickly become enormous. In any case, these two methods bear about as much resemblance to our actual allocation of land as a squirrel does to a Tyrannosaurus.

So, what else might we use? The system that makes the most sense to me is that we would own all land as a society. In practical terms this would mean that all land is Federal land, and if you want to use it for something, you need to pay rent to the government. There are many different ways the government could set the rent, but the most sensible might be to charge a flat rate per hectare regardless of where the land is or what it’s being used for, because that would maximize the incentive to develop the land. It would also make the rent fall entirely on the landowner, because the rent would be perfectly inelastic—meaning that you can’t change the quantity you make based on the price, because you aren’t making it; it’s just already sitting there.

Of course, this idea is obviously politically impossible in our current environment—or indeed any foreseeable political environment. I’m just fantasizing here, right?

Well, not quite. There is one thing we could do that would be economically quite similar to government-only land ownership; it’s called a land tax. The idea is incredibly simple: you just collect a flat tax per hectare of land. Economists have known that a land tax is efficient at providing revenue and reducing inequality since at least Adam Smith. So maybe ownership of land isn’t actually foundational to capitalism, after all; maybe we’ve just never fully gotten over feudalism. (I basically agree with Adam Smith, and for doing so I am often called a socialist.) The beautiful thing about a land tax is that it has a tax incidence in which the owners of the land end up bearing the full brunt of the tax.

Tax incidence is something it’s very important to understand; it would be on my list of the top ten economic principles that people should learn. We often have fierce political debates over who will actually write the check: Should employers pay the health insurance premium, or should employees? Will buyers pay sales tax, or sellers? Should we tax corporate profits or personal capital gains?

Please understand that I am not exaggerating when I say that these sorts of questions are totally irrelevant. It simply does not matter who actually writes the check; what matters is who bears the cost. Making the employer pay the health insurance premium doesn’t make the slightest difference if all they’re going to do is cut wages by the exact same amount. You can see the irrelevance of the fact that sellers pay sales tax every time you walk into a store—you always end up paying the price plus the tax, don’t you? (I found that the base price of most items was the same between Long Beach and Ann Arbor, but my total expenditure was always 3% more because of the 9% sales tax versus the 6%.) How do we determine who actually pays the tax? It depends on the elasticity—how easily can you change your behavior in order to avoid the tax? Can you find a different job because the health insurance premiums are too high? No? Then you’re probably paying that premium, even if your employer writes the check. If you can find a new job whenever you want, your employer might have to pay it for you even if you write the check.

The incidence of corporate taxes and taxes on capital gains are even more complicated, because it could affect the behavior of corporations in many different ways; indeed, many economists argue that the corporate tax simply results in higher unemployment or lower wages for workers. I don’t think that’s actually true, but I honestly can’t rule it out completely, precisely because corporate taxes are so complicated. You need to know all sorts of things about the structure of stock markets, and the freedom of trade, and the mobility of immigration… it’s a complete and total mess.

It’s because of tax incidence that a land tax makes so much sense; there’s no way for the landowner to escape it, other than giving up the land entirely. In particular, they can’t charge more for rent without being out-competed (unless landowners are really good at colluding—which might be true for large developers, but not individual landlords). Their elasticity is so low that they’re forced to bear the full cost of the tax.

If the land tax were high enough, it could eliminate the automatic growth in wealth that comes from holding land, and thereby reducing long-run inequality dramatically. The revenue could be used for my other favorite fiscal policy, the basic income—and real estate is a big enough part of our nation’s wealth that it’s actually entirely realistic to fund an $8,000 per person per year basic income entirely on land tax revenue. The total value of US land is about $14 trillion, and an $8,000 basic income for 320 million people would cost about $2.6 trillion; that’s only 19%. You’d actually want to make it a flat tax per hectare, so how much would that be? Well, 60% of US land is privately owned at present (no sense taxing the land the government already owns), and total US land area is about 9 million square kilometers, so to raise $2.5 trillion you’d need a tax of $289,000 per square kilometer, or $2,890 per hectare. If you own a hectare—which is bigger than most single-family lots—you’d only pay $2,890 per year in land tax, well within what most middle-class families could handle. But if you own 290,000 acres like Jeff Bezos, (that’s 117,000 hectares) you’re paying $338 million per year. Since Jeff Bezos has about $38 billion in net wealth, he can actually afford to pay that ($338 million per year is about one-tenth of what Jeff Bezos makes automatically on dividends), though he might consider selling off some of the land to avoid the taxes, which is exactly the sort of incentive we wanted to create.

Indeed, when I contemplate this policy I’m struck by the fact that it has basically no downside—usually in public policy you’re forced to make hard compromises and tradeoffs, but a land tax plus basic income is a system that carries almost no downsides at all. It won’t disincentivize investment, it won’t disincentivize working, it will dramatically reduce inequality, it will save the government a great deal of money on social welfare spending, and best of all it will eliminate poverty immediately and forever. The only people it would hurt at all are extremely rich, and they wouldn’t even be hurt very much, while it would benefit millions of people including some of the most needy.

Why aren’t we doing this already!?

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Human Economics

Cognitive development economics: Understanding the mind in order to feed the world

Month: May 2015