Sheepskin effect doesn’t prove much

Sep 20 JDN 2459113

The sheepskin effect is the observation that the increase in income from graduating from college after four years, relative going through college for three years, is much higher than the increase in income from simply going through college for three years instead of two.

It has been suggested that this provides strong evidence that education is primarily due to signaling, and doesn’t provide any actual value. In this post I’m going to show why this view is mistaken. The sheepskin effect in fact tells us very little about the true value of college. (Noah Smith actually made a pretty decent argument that it provides evidence against signaling!)

To see this, consider two very simple models.

In both models, we’ll assume that markets are competitive but productivity is not directly observable, so employers sort you based on your education level and then pay a wage equal to the average productivity of people at your education level, compensated for the cost of getting that education.

Model 1:

In this model, people all start with the same productivity, and are randomly assigned by their life circumstances to go to either 0, 1, 2, 3, or 4 years of college. College itself has no long-term cost.

The first year of college you learn a lot, the next couple of years you don’t learn much because you’re trying to find your way, and then in the last year of college you learn a lot of specialized skills that directly increase your productivity.

So this is your productivity after x years of college:

Years of collegeProductivity

We assumed that you’d get paid your productivity, so these are also your wages.

The increase in income each year goes from +7, to +5, to +3, then jumps up to +6. So if you compare the 4-year-minus-3-year gap (+6) with the 3-year-minus-2-year gap (+3), you get a sheepskin effect.

Model 2:

In this model, college is useless and provides no actual benefits. People vary in their intrinsic productivity, which is also directly correlated with the difficulty of making it through college.

In particular, there are five types of people:

TypeProductivityCost per year of college

The wages for different levels of college education are as follows:

Years of collegeWage

Notice that these are exactly the same wages as in scenario 1. This is of course entirely intentional. In a moment I’ll show why this is a Nash equilibrium.

Consider the choice of how many years of college to attend. You know your type, so you know the cost of college to you. You want to maximize your net benefit, which is the wage you’ll get minus the total cost of going to college.

Let’s assume that if a given year of college isn’t worth it, you won’t try to continue past it and see if more would be.

For a type-0 person, they could get 10 by not going to college at all, or 17-(1)(8) = 9 by going for 1 year, so they stop.

For a type-1 person, they could get 10 by not going to college at all, or 17-(1)(6) = 11 by going for 1 year, or 22-(2)(6) = 10 by going for 2 years, so they stop.

Filling out all the possibilities yields this table:

Years \ Type01234



I’d actually like to point out that it was much harder to find numbers that allowed me to make the sheepskin effect work in the second model, where education was all signaling. In the model where education provides genuine benefit, all I need to do is posit that the last year of college is particularly valuable (perhaps because high-level specialized courses are more beneficial to productivity). I could pretty much vary that parameter however I wanted, and get whatever magnitude of sheepskin effect I chose.

For the signaling model, I had to carefully calibrate the parameters so that the costs and benefits lined up just right to make sure that each type chose exactly the amount of college I wanted them to choose while still getting the desired sheepskin effect. It took me about two hours of very frustrating fiddling just to get numbers that worked. And that’s with the assumption that someone who finds 2 years of college not worth it won’t consider trying for 4 years of college (which, given the numbers above, they actually might want to), as well as the assumption that when type-3 individuals are indifferent between staying and dropping out they drop out.

And yet the sheepskin effect is supposed to be evidence that the world works like the signaling model?

I’m sure a more sophisticated model could make the signaling explanation a little more robust. The biggest limitation of these models is that once you observe someone’s education level, you immediately know their true productivity, whether it came from college or not. Realistically we should be allowing for unobserved variation that can’t be sorted out by years of college.

Maybe it seems implausible that the last year of college is actually more beneficial to your productivity than the previous years. This is probably the intuition behind the idea that sheepskin effects are evidence of signaling rather than genuine learning.

So how about this model?

Model 3:

As in the second model, there are four types of people, types 0, 1, 2, 3, and 4. They all start with the same level of productivity, and they have the same cost of going to college; but they get different benefits from going to college.

The problem is, people don’t start out knowing what type they are. Nor can they observe their productivity directly. All they can do is observe their experience of going to college and then try to figure out what type they must be.

Type 0s don’t benefit from college at all, and they know they are type 0; so they don’t go to college.

Type 1s benefit a tiny amount from college (+1 productivity per year), but don’t realize they are type 1s until after one year of college.

Type 2s benefit a little from college (+2 productivity per year), but don’t realize they are type 2s until after two years of college.

Type 3s benefit a moderate amount from college (+3 productivity per year), but don’t realize they are type 3s until after three years of college.

Type 4s benefit a great deal from college (+5 productivity per year), but don’t realize they are type 4s until after three years of college.

What then will happen? Type 0s will not go to college. Type 1s will go one year and then drop out. Type 2s will go two years and then drop out. Type 3s will go three years and then drop out. And type 4s will actually graduate.

That results in the following before-and-after productivity:

TypeProductivity before collegeYears of collegeProductivity after college

If each person is paid a wage equal to their productivity, there will be a huge sheepskin effect; wages only go up +1 for 1 year, +3 for 2 years, +5 for 3 years, but then they jump up to +11 for graduation. It appears that the benefit of that last year of college is more than the other three combined. But in fact it’s not; for any given individual, the benefits of college are the same each year. It’s just that college is more beneficial to the people who decided to stay longer.

And I could of course change that assumption too, making the early years more beneficial, or varying the distribution of types, or adding more uncertainty—and so on. But it’s really not hard at all to make a model where college is beneficial and you observe a large sheepskin effect.

In reality, I am confident that some of the observed benefit of college is due to sorting—not the same thing as signaling—rather than the direct benefits of education. The earnings advantage of going to a top-tier school may be as much about the selection of students as they are the actual quality of the education, since once you control for measures of student ability like GPA and test scores those benefits drop dramatically.

Moreover, I agree that it’s worth looking at this: Insofar as college is about sorting or signaling, it’s wasteful from a societal perspective, and we should be trying to find more efficient sorting mechanisms.

But I highly doubt that all the benefits of college are due to sorting or signaling; there definitely are a lot of important things that people learn in college, not just conventional academic knowledge like how to do calculus, but also broader skills like how to manage time, how to work in groups, and how to present ideas to others. Colleges also cultivate friendships and provide opportunities for networking and exposure to a diverse community. Judging by voting patterns, I’m going to go out on a limb and say that college also makes you a better citizen, which would be well worth it by itself.

The truth is, we don’t know exactly why college is beneficial. We certainly know that it is beneficial: Unemployment rates and median earnings are directly sorted by education level. Yes, even PhDs in philosophy and sociology have lower unemployment and higher incomes (on average) than the general population. (And of course PhDs in economics do better still.)

Glorifying superstars glorifies excessive risk

Apr 26 JDN 2458964

Suppose you were offered the choice of the following two gambles; which one would you take?

Gamble A: 99.9% chance of $0; 0.1% chance of $100 million

Gamble B: 10% chance of $50,000; 80% chance of $100,000; 10% chance of $1 million

I think it’s pretty clear that you should choose gamble B.

If you were risk-neutral, the expected payoffs would be $100,000 for gamble A and $185,000 for gamble B. So clearly gamble B is the better deal.

But you’re probably risk-averse. If you have logarithmic utility with a baseline and current wealth of $10,000, the difference is even larger:

0.001*ln(10001) = 0.009

0.1*ln(6) + 0.8*ln(11) + 0.1*ln(101) = 2.56

Yet suppose this is a gamble that a lot of people get to take. And furthermore suppose that what you read about in the news every day is always the people who are the very richest. Then you will read, over and over again, about people who took gamble A and got lucky enough to get the $100 million. You’d probably start to wonder if maybe you should be taking gamble A instead.

This is more or less the world we live in. A handful of billionaires own staggering amounts of wealth, and we are constantly hearing about them. Even aside from the fact that most of them inherited a large portion of it and all of them had plenty of advantages that most of us will never have, it’s still not clear that they were actually smart about taking the paths they did—it could simply be that they got spectacularly lucky.

Or perhaps there’s an even clearer example: Professional athletes. The vast majority of athletes make basically no money at sports. Even most paid athletes are in minor leagues and make only a modest living.

There’s certainly nothing wrong with being an amateur who plays sports for fun. But if you were to invest a large proportion of your time training in sports in the hopes of becoming a professional athlete, you would most likely find yourself gravely disappointed, as your chances of actually getting into the major leagues and becoming a multi-millionaire are exceedingly small. Yet you can probably name at least a few major league athletes who are multi-millionaires—perhaps dozens, if you’re a serious fan—and I doubt you can name anywhere near as many minor league players or players who never made it into paid leagues in the first place.

When we spend all of our time focused on the superstars, what we are effectively assessing is the maximum possible income available on a given career track. And it’s true; the maximum for professional athletes and especially entrepreneurs is extremely high. But the maximum isn’t what you should care about; you should really be concerned about the average or even the median.

And it turns out that the same professions that offer staggeringly high incomes at the very top also tend to be professions with extremely high risk attached. The average income for an athlete is very small; the median is almost certainly zero. Entrepreneurs do better; their average and median income aren’t too much worse than most jobs. But this moderate average comes with a great deal of risk; yes, you could become a billionaire—but far more likely, you could become bankrupt.

This is a deeply perverse result: The careers that our culture most glorifies, the ones that we inspire people to dream about, are precisely those that are the most likely to result in financial ruin.

Realizing this changes your perspective on a lot of things. For instance, there is a common lament that teachers aren’t paid the way professional athletes are. I for one am extremely grateful that this is the case. If teachers were paid like athletes, yes, 0.1% would be millionaires, but only 4.9% would make a decent living, and the remaining 95% would be utterly broke. Indeed, this is precisely what might happen if MOOCs really take off, and a handful of superstar teachers are able to produce all the content while the vast majority of teaching mostly amounts to showing someone else’s slideshows. Teachers are much better off in a world where they almost all make a decent living even though none of them ever get spectacularly rich. (Are many teachers still underpaid? Sure. How do I know this? Because there are teacher shortages. A chronic shortage of something is a surefire sign that its price is too low.) And clearly the idea that we could make all teachers millionaires is just ludicrous: Do you want to pay $1 million a year for your child’s education?

Is there a way that we could change this perverse pattern? Could we somehow make it feel more inspiring to choose a career that isn’t so risky? Well, I doubt we’ll ever get children to dream of being accountants or middle managers. But there are a wide range of careers that are fulfilling and meaningful while still making a decent living—like, well, teaching. Even working in creative arts can be like this: While very few authors are millionaires, the median income for an author is quite respectable. (On the other hand there’s some survivor bias here: We don’t count you as an author if you can’t get published at all.) Software engineers are generally quite satisfied with their jobs, and they manage to get quite high incomes with low risk. I think the real answer here is to spend less time glorifying obscene hoards of wealth and more time celebrating lives that are rich and meaningful.

I don’t know if Jeff Bezos is truly happy. But I do know that you and I are more likely to be happy if instead of trying to emulate him, we focus on making our own lives meaningful.

The real cost of high rent

Jan 26 JDN 2458875

The average daily commute time in the United States is about 26 minutes each way—for a total of 52 minutes every weekday. Public transit commute times are substantially longer in most states than driving commute times: In California, the average driving commute is 28 minutes each way, while the average public transit commute is 51 minutes each way. Adding this up over 5 workdays per week, working 50 weeks per year, means that on average Americans spend over 216 hours each year commuting.

Median annual income in the US is about $33,000. Assuming about 2000 hours of work per year for a full-time job, that’s a wage of $16.50 per hour. This makes the total cost of commute time in the United States over $3500 per worker per year. Multiplied by a labor force of 205 million, this makes the total cost of commute time over $730 billion per year. That’s not even counting the additional carbon emissions and road fatalities. This is all pure waste. The optimal commute time is zero minutes; the closer we can get to that, the better. Telecommuting might finally make this a reality, at least for a large swath of workers. Already over 40% of US workers telecommute at least some of the time.

Let me remind you that it would cost about $200 billion per year to end world hunger. We could end world hunger three times over with the effort we currently waste in commute time.

Where is this cost coming from? Why are commutes so long? The answer is obvious: The rent is too damn high. People have long commutes because they can’t afford to live closer to where they work.

Almost half of all renter households in the US pay more than 30% of their income in rent—and 25% pay more than half of their income. The average household rent in the US is over $1400 per month, almost $17,000 per year—more than the per-capita GDP of China.

Not that buying a home solves the problem: In many US cities the price-to-rent ratio of homes is over 20 to 1, and in Manhattan and San Francisco it’s as high as 50 to 1. If you already bought your home years ago, this is great for you; for the rest of us, not so much. Interestingly, high rents seem to correlate with higher price-to-rent ratios, so it seems like purchase prices are responding even more to whatever economic pressure is driving up rents.

Overall about a third of all US consumer spending is on housing; out of our total consumption spending of $13 trillion, this means we are spending over $4 trillion per year on housing, about the GDP of Germany. Of course, some of this is actually worth spending: Housing costs a lot to build, and provides many valuable benefits.

What should we be spending on housing, if the housing market were competitive and efficient?

I think Chicago’s housing market looks fairly healthy. Homes there go for about $250,000, with prices that are relatively stable; and the price-to-rent ratio is about 20 to 1. Chicago is a large city with a population density of about 6,000 people per square kilometer, so it’s not as if I’m using a tiny rural town as my comparison. If the entire population of the United States were concentrated at the same density as the city of Chicago, we’d all fit in only 55,000 square kilometers—less than the area of West Virginia.
Compare this to the median housing price in California ($550,000), New York ($330,000), or Washington, D.C. ($630,000). There are metro areas with housing prices far above even this: In San Jose the median home price is $1.1 million. I find it very hard to believe that it is literally four times as hard to build homes in San Jose as it is in Chicago. Something is distorting that price—maybe it’s over-regulation, maybe it’s monopoly power, maybe it’s speculation—I’m not sure what exactly, but there’s definitely something out of whack here.

This suggests that a more efficient housing market would probably cut prices in California by 50% and prices in New York by 25%. Since about 40% of all spending in California is on housing, this price change would effectively free up 20% of California’s GDP—and 20% of $3 trillion is $600 billion per year. The additional 8% of New York’s GDP gets us another $130 billion, and we’re already at that $730 billion I calculated for the total cost of commuting, only considering New York and California alone.

This means that the total amount of waste—including both time and money—due to housing being too expensive probably exceeds $1.5 trillion per year. This is an enormous sum of money: We’re spending an Australia here. We could just about pay for a single-payer healthcare system with this.

A more nuanced “Carousel of Progress”

Aug 11 JDN 2458707

I recently got back from a trip to Disney World; while most of the attractions are purely fictional and designed only to entertain, a few are factual and designed to inform and persuade. One of these is the “Carousel of Progress”.

The Carousel of Progress consists of a series of animatronic stages, each representing the lifestyle of a particular historical era. They follow the same family over time, showing what their life is like in each era. When it was originally built, the eras shown were 1900s, 1920s, 1940s, and 1960s; but over time they have updated the “present day” stage, and now they are 1900s, 1920s, 1940s, and 1990s. The aim of the attraction is to show how technology has made our lives better.

The family they show is upper-middle class; this makes sense, as most of the audience probably is as well. But to really understand the progress we have made, we need to also consider the full range of incomes.

In this post I will go through a similar sequence of eras, comparing the lifestyles of not just the middle class, but also the rich and the poor.

In what follows, I’ve tried to create that, using the best approximate figures on standard of living I could find from each era. The numbers are given in my best guess of the inflation-adjusted standard of living; obviously they’re much more precise in the 1980s to today than they are for earlier eras.

I’ve summarized all these income estimates in the graph below (note the log scale):



This means that, after a bumpy ride through the Middle Ages and the Industrial Revolution, we did actually raise the floor—the poor today are about as well off as the middle class in ancient times. But we raised the ceiling an awful lot faster; the rich today are something like a thousand times as rich as the rich in ancient times.


50 AD: Roman Empire

Rich: Patrician

Life is good! My seaside villa is one of the finest in Rome, and my industrious slaves fulfill my every need. At my personal zoo I recently acquired a lion and an elephant. I dine on only the finest foods, including wine from my personal vineyard. An aqueduct feeds directly into my personal baths. The war in Gallia seems to be going well; I look forward to my share of the spoils.

Wealth: $4 million

Income: $200,000

Middle class: Plebeian

Things could be worse. My family has a roof over our heads and bread on our table, so I’m grateful for that. But working all day on the farm is exhausting, and we can’t afford servants to help. My oldest son is a gladiator, though so far he has not attained the highest ranks of the profession. My youngest son was recently drafted into military service in Gallia; I pray for his safety.

Wealth: $10,000

Income: $10,000

Poor: Proletarian

Wealth: $0

Income: $1,000

Living in a hovel I don’t even own with my four children and begging on the streets isn’t an easy life, but at least I’m not a slave. Most of our food is provided by public services. With the war raging in Gallia, one of our small blessings is that we are actually too poor to be drafted into service.

1000 AD: Medieval England

Rich: Duke

While living in a castle is nice, I sometimes wish an end to the frequent raids and border skirmishes that made these high walls necessary. Still, I can’t complain; I own plenty of land, and have plenty of serfs to work it. I am in good favor with the king, and so His Majesty’s army has helped protect my lands against invasion. I have all the feasts, wine, and women a man could ask for.

Wealth: $2 million

Income: $100,000

Middle class: Knight

I can’t complain. It is an honor to be a knight in His Majesty’s army, and I am proud that my family was able to earn enough wealth to buy me a horse, a sword, and the training necessary to reach this rank. I own a little bit of land, but my lord has called upon me for a new campaign, I’m hoping to buy a larger estate with the spoils I earn from it. My family has plenty of food to eat, though if the well runs dry I’m not sure where we’ll get more water.

Wealth: $5,000

Income: $5,000

Poor: Serf

Live grows harder by the day, it seems. My lord keeps demanding more and more work from us, but already the land is producing as much as it can bear. Though we are responsible for planting and harvesting the wheat, often the bread never makes it to my family’s table.

Wealth: $0

Income: $500

1600 AD: Renaissance Venice

Rich: Noble

With the advent of global trade and colonization, wealth has flooded into Venice, and I have had the chance to claim some portion of that flood. I dress in the finest silks, and eat exotic foods from lands as distant as India and China. Servants fulfill my every need. How could life be better?

Wealth: $10 million

Income: $1 million

Middle class: Merchant

I am a proud member of the trader’s guild. Though it our trade ships that carry wealth from across the seas, we often find that wealth passing on up to the nobles, leaving little for ourselves. Still, I have my own land, my own house, and plenty of food for my family.

Wealth: $10,000

Income: $10,000

Poor: The Pebbles

I had a good job working in construction until recently, but I was laid off. I could no longer afford my rent, so now I live on the streets. I feel as though I work constantly but never can find a way to get ahead.

Wealth: $0

Income: $2,000

1750 AD: Pre-Revolutionary France

Rich: Noble

Viva la France! Life is better than ever. Servants do all my work, while the wealth produced by my fields and factories all goes to me. I barely even pay any taxes on my grand estates.

Wealth: $20 million

Income: $2 million

Middle class: Bourgeoisie

I live reasonably well, all things considered. My family has a home and enough food to eat. Still, taxes are becoming increasingly onerous even as the nobles become increasingly detached from the needs of common people like us. Still, we may as well accept it; I doubt things will change any time soon.

Wealth: $15,000

Income: $15,000

Poor: Peasant

Life is hard. I work all day on the farm to make wheat, and then the nobles tax it all away. We have to make our own clothes even as the nobles luxuriate in silks from around the world.

Wealth: $0

Income: $500

1900 AD: United States


My coal mine has been a roaring success! I am now one of the richest men who has ever lived. I even have my own horseless carriage. Servants are getting more expensive these days, though; even though I’m richer than my grandfather I can’t afford as many servants.

Wealth: $1 billion

Income: $100 million

Middle class

“Well, the robins are back. That’s a sure sign of spring. What year is it? Oh, just before the turn of the century. And believe me, things couldn’t be any better than they are today. Yes sir, we got all the latest things: gas lamps, a telephone, and the latest design in cast iron stoves. That reservoir keeps five gallons of water hot all day on just three buckets of coal. Sure beats chopping wood! And isn’t our new ice box a beauty. Holds 50 pounds of ice. Milk doesn’t sour as quick as is used to. Our dog Rover here keeps the water in the drip pan from overflowing. You know, it wasn’t too long ago we had to carry water from a well. But thanks to progress, we’ve got a pump right here in the kitchen. ‘Course we keep a bucket of water handy to prime it with. Yes sir, we’ve got everything to make life easier. Mother! I was reading about a fellow named Tom Edison, who’s working on an idea for snap on electric lights.”

Wealth: $18,000

Income: $18,000


I live on the streets most of the time. I eat food out of the garbage. What little money I have is earned by begging. I’m not proud, but it’s all I can do to survive.

Wealth: $0

Income: $2,000

1920 AD: United States


Life is sweet. My electric company is raking in the dough these days; seems they can hardly find enough copper to lay all the new cables we need to supply all the folks buying into our grid. I have four automobiles now—all top of the line of course. The times, they are a-changin’: Can you believe they gave women the vote? Eh, well, I suppose they can hardly vote worse than us men do already.

Wealth: $5 billion

Income: $500 million

Middle class

“Whew! Hottest summer we’ve had in years. Well, we’ve progressed a long way since the turn of the century 20 years ago. But no one realized then that this would be the age of electricity. Everyone’s using it: farmers, factories, whole towns. With electric streetlights we don’t worry so much about the youngsters being out after dark. And what a difference in our home. We can run as many wires as we need in any direction for Mother’s new electrical servants: electric sewing machine, coffee percolator, toaster, waffle iron, refrigerator, and they all go to work at the click of a switch. Take it easy! You’ll blow a fuse! Queenie! Leave ’em alone. Well, the days of lugging heavy irons from the old cookstove to an ironing board are gone forever. With an electric iron and electric lights, Mother now has time to enjoy her embroidery in the cool of the evening. Right, Mother?”

Wealth: $20,000

Income: $20,000


Life on the streets is still hard, but at least they’ve got these new soup kitchens to feed me and my family, and with running water in the city we can sometimes get clean water to drink. That newfangled electricity stuff is supposed to be the bee’s knees, but we sure can’t afford it.

Wealth: $0

Income: $4,000

1940 AD: United States


My steel company is doing extremely well, particularly with the war in Europe raising the price of steel. We just bought our very own airplane; isn’t that marvelous? With Britain under siege and France already fallen to the Krauts, I think we’re gonna end up in the war soon—FDR certainly has been making noises to that effect. If I were poor, I’d be worried about my sons getting drafted; but I’m sure we won’t have to worry about that. No, I’m just looking forward to my stock returns when they start churning out tanks instead of cars in Detroit!

Wealth: $2 billion

Income: $200 million

Middle class

“Well it’s autumn again and the kids are back in school. Thank goodness! Here we are in the frantic forties and the music is better than ever. And it’s amazing how our new kitchen wonders are helping to take over the hard work. Everything is improving. Electric range is better. Refrigerators are bigger and make lots more ice cubes. But my favorite is the electric dishwasher. Now Mother spends less time in the kitchen and I don’t have to dry the dishes anymore. Oh, I spend a lot of time here. Have to. Now that television has arrived, Grandma and Grandpa have taken over my den. Television has changed our lives. It’s brought a whole new world of culture into our home.”

Wealth: $24,000

Income: $24,000


The Depression was hard on everybody, but I think it was hardest on us poors. This New Deal business seems to be helping out a lot, though; on one of the new construction projects I was able to find work for the first time in months. I’m worried we’re going to be brought into the war soon, but if I get drafted at least that means three squares a day.

Wealth: $0

Income: $4,000

1960 AD: United States


Running an oil company is not for the faint of heart; they keep adding more onerous regulations every year. Still, profits are bigger than ever. I just wish Uncle Sam would stop taking such a big cut; Commies, all of them. I can barely afford upkeep on my yacht these days with all the taxes.

Wealth: $2 billion

Income: $200 million

Middle class

We just got a color TV at home, and we’ve been watching around the clock. We get all four channels! And my new T-bird is a real beauty; paid a fortune for her, but worth every penny. Society is improving, too; with Rosa Parks and whatnot, I’m guessing things are about to get a lot better for colored folks especially. After that, I’m thinking it’ll be the gays’ turn next; I wonder how long that will take.

Wealth: $30,000

Income: $30,000


Life is still hard, but I think it’s better now than it’s ever been, even for poor folks like me. Thanks to Welfare, I’m not even as poor as I could be. It’s tough to make ends meet, but at least I can afford a place to live and food to eat. And I’m pretty healthy too: Antibiotics and vaccines mean that we are finally safe from some terrible diseases, like polio. It seems crazy: Just a generation ago the President had a disease that now even folks like me are protected from.

Wealth: $0

Income: $6,000

1980 AD: United States


They told me I was crazy to invest in these “personal computing machines”, but I saw the writing on the wall. Computers are the future, man. They’re gonna be everywhere, and do everything. We’re gonna have robots and flying cars, and if I have anything to say about it, I’m gonna own the factories that make them.

Wealth: $5 billion

Income: $500 million

Middle class

We have our own PC now. I use it for work, but my kids use it mostly for computer games. I still can’t beat my daughter at Pong, but I can at least hold my own at Pac-Man these days. I hear that programming skills are going to be in high demand soon, so I’ve been trying to teach the kids BASIC.

Wealth: $50,000

Income: $50,000


Nixon’s Welfare “reform” really hit my family hard. If I don’t find work soon, they’re going to cut my benefits; but if I could find work, what would I need benefits for? Jimmy Carter made some things better, but it doesn’t look like he’ll be re-elected. Can you believe that old actor Ronald Reagan is running?

Wealth: $0

Income: $8,000

2000 AD: United States


I sure played my cards right in the stock market, buying those tech firms just before the Internet boom really hit. Now I have my own jet and I’m thinking of buying a yacht. Maybe I’ll diversify into real estate; it looks like housing prices are heading north.

Wealth: $10 billion

Income: $1 billion

Middle class

Our home has almost doubled in value since we bought it; we took some of that out as a home equity loan, which helped us buy laptops for our kids. It’s amazing what they can do now; we used to have a big clunky desktop, and these little laptops would run circles around it. We also installed a 56k modem; I’m a little worried about what effect the Internet will have on the kids, but it seems like that’s where everything is going.

Wealth: $60,000

Income: $60,000


I hate working in fast food, but it beats not working at all. I really wish they’d raise minimum wage though; once you figure in inflation, we’re actually making less than people did ten years ago. I think I qualify for Welfare or something, but the paperwork has gotten so crazy I couldn’t even deal with it. I’m just trying to get by on what I make at the burger joint.

Wealth: $0

Income: $10,000

2020 AD: United States, Present Day


I knew my app startup would be a success, but even I couldn’t have predicted we’d make it this far. Bought out by Apple for $40 billion? I could hardly have dreamed it myself. I am living the high life; I’ve got my own helicopter now, and a yacht 50 feet long (#lifestyle #swag!). I just upgraded my Google Glass to the new model; it is awesome AF. I think I might move out of the Bay Area and get myself a mansion in Beverly Hills.

Wealth: $20 billion

Income: $2 billion

Middle class

Why is rent so expensive? And how am I ever going to pay off these student loans? After college I managed to land an office job because I’m pretty good with Excel, but it’s still tough to make ends meet. Smartphones are cool and all, but it would be nice to actually own my own home. I think my parents had planned for me to inherit theirs, but we lost it in the subprime crash. Eh, things could be worse. #FirstWorldProblems.

Wealth: $62,000

Income: $62,000


Things were really bad a few years ago, but they seem to be picking up a little now; I’ve been able to find a job, at least. But it doesn’t pay well; I can’t barely afford rent. I don’t have what they call “marketable skills”, I guess. I should have gone back to school, probably, but I didn’t want to have to deal with student loans. Maybe things will be better once Trump finally gets out of office.

Wealth: $0

Income: $12,000

2040 AD: United States, Cyberpunk Future


I guess I picked out the right crypto to buy, because it gave me enough to buy my own AI company and now I’m rolling in it. My new helicopter is one of those twin-turbofan models that runs on fuel cells—I was sick of paying carbon tax to fuel up the old kerosene model. I just got cybernetic implants: No phone to carry around, nothing to get lost! I hear they’re working on going to neural interface soon, so we won’t even need to wave our hands around to use them.

Wealth: $40 billion

Income: $4 billion


I used to have a nice job in data analysis, but they automated most of it and outsourced the rest. Now I work for a different corp doing customer service, because that’s the only thing humans seem to still be good for. I have to admit the corps have done some good things for us, though; my daughter was born blind but now she’s got artificial eyes. (Of course, how will we ever pay off those medical debts?) And I really wish someone had done something about climate change sooner; summers these days are absolutely unbearable.

Wealth: $65,000

Income: $65,000


Wealth: $0

Income: $15,000

I lost my trucking job to a robot, can you believe that? But how am I supposed to compete with 22 hours of daily uptime? Basic income is just about all the money I have. I haven’t been able to find steady work in years. I should have gone to college and studied CS, probably; it seems like salaries in AI get higher every year.

Why do we need “publish or perish”?

June 23 JDN 2458658

This question may seem a bit self-serving, coming from a grad student who is struggling to get his first paper published in a peer-reviewed journal. But given the deep structural flaws in the academic publishing system, I think it’s worth taking a step back to ask just what peer-reviewed journals are supposed to be accomplishing.

The argument is often made that research journals are a way of sharing knowledge. If this is their goal, they have utterly and totally failed. Most papers are read by only a handful of people. When scientists want to learn about the research their colleagues are doing, they don’t read papers; they go to conferences to listen to presentations and look at posters. The way papers are written, they are often all but incomprehensible to anyone outside a very narrow subfield. When published by proprietary journals, papers are often hidden behind paywalls and accessible only through universities. As a knowledge-sharing mechanism, the peer-reviewed journal is a complete failure.

But academic publishing serves another function, which in practice is its only real function: Peer-reviewed publications are a method of evaluation. They are a way of deciding which researchers are good enough to be hired, get tenure, and receive grants. Having peer-reviewed publications—particularly in “top journals”, however that is defined within a given field—is a key metric that universities and grant agencies use to decide which researchers are worth spending on. Indeed, in some cases it seems to be utterly decisive.

We should be honest about this: This is an absolutely necessary function. It is uncomfortable to think about the fact that we must exclude a large proportion of competent, qualified people from being hired or getting tenure in academia, but given the large number of candidates and the small amounts of funding available, this is inevitable. We can’t hire everyone who would probably be good enough. We can only hire a few, and it makes sense to want those few to be the best. (Also, don’t fret too much: Even if you don’t make it into academia, getting a PhD is still a profitable investment. Economists and natural scientists do the best, unsurprisingly; but even humanities PhDs are still generally worth it. Median annual earnings of $77,000 is nothing to sneeze at: US median household income is only about $60,000. Humanities graduates only seem poor in relation to STEM or professional graduates; they’re still rich compared to everyone else.)

But I think it’s worth asking whether the peer review system is actually selecting the best researchers, or even the best research. Note that these are not the same question: The best research done in graduate school might not necessarily reflect the best long-run career trajectory for a researcher. A lot of very important, very difficult questions in science are just not the sort of thing you can get a convincing answer to in a couple of years, and so someone who wants to work on the really big problems may actually have a harder time getting published in graduate school or as a junior faculty member, even though ultimately work on the big problems is what’s most important for society. But I’m sure there’s a positive correlation overall: The kind of person who is going to do better research later is probably, other things equal, going to do better research right now.

Yet even accepting the fact that all we have to go on in assessing what you’ll eventually do is what you have already done, it’s not clear that the process of publishing in a peer-reviewed journal is a particularly good method of assessing the quality of research. Some really terrible research has gotten published in journals—I’m gonna pick on Daryl Bem, because he’s the worst—and a lot of really good research never made it into journals and is languishing on old computer hard drives. (The term “file drawer problem” is about 40 years obsolete; though to be fair, it was in fact coined about 40 years ago.)

That by itself doesn’t actually prove that journals are a bad mechanism. Even a good mechanism, applied to a difficult problem, is going to make some errors. But there are a lot of things about academic publishing, at least as currently constituted, that obviously don’t seem like a good mechanism, such as for-profit publishers, unpaid reviewiers, lack of double-blinded review, and above all, the obsession with “statistical significance” that leads to p-hacking.

Each of these problems I’ve listed has a simple fix (though whether the powers that be actually are willing to implement it is a different question: Questions of policy are often much easier to solve than problems of politics). But maybe we should ask whether the system is even worth fixing, or if it should simply be replaced entirely.

While we’re at it, let’s talk about the academic tenure system, because the peer-review system is largely an evaluation mechanism for the academic tenure system. Publishing in top journals is what decides whether you get tenure. The problem with “Publish or perish” isn’t the “publish”; it’s the perish”. Do we even need an academic tenure system?

The usual argument for academic tenure concerns academic freedom: Tenured professors have job security, so they can afford to say things that may be controversial or embarrassing to the university. But the way the tenure system works is that you only have this job security after going through a long and painful gauntlet of job insecurity. You have to spend several years prostrating yourself to the elders of your field before you can get inducted into their ranks and finally be secure.

Of course, job insecurity is the norm, particularly in the United States: Most employment in the US is “at-will”, meaning essentially that your employer can fire you for any reason at any time. There are specifically illegal reasons for firing (like gender, race, and religion); but it’s extremely hard to prove wrongful termination when all the employer needs to say is, “They didn’t do a good job” or “They weren’t a team player”. So I can understand how it must feel strange for a private-sector worker who could be fired at any time to see academics complain about the rigors of the tenure system.

But there are some important differences here: The academic job market is not nearly as competitive as the private sector job market. There simply aren’t that many prestigious universities, and within each university there are only a small number of positions to fill. As a result, universities have an enormous amount of power over their faculty, which is why they can get away with paying adjuncts salaries that amount to less than minimum wage. (People with graduate degrees! Making less than minimum wage!) At least in most private-sector labor markets in the US, the market is competitive enough that if you get fired, you can probably get hired again somewhere else. In academia that’s not so clear.

I think what bothers me the most about the tenure system is the hierarchical structure: There is a very sharp divide between those who have tenure, those who don’t have it but can get it (“tenure-track”), and those who can’t get it. The lines between professor, associate professor, assistant professor, lecturer, and adjunct are quite sharp. The higher up you are, the more job security you have, the more money you make, and generally the better your working conditions are overall. Much like what makes graduate school so stressful, there are a series of high-stakes checkpoints you need to get through in order to rise in the ranks. And several of those checkpoints are based largely, if not entirely, on publication in peer-reviewed journals.

In fact, we are probably stressing ourselves out more than we need to. I certainly did for my advancement to candidacy; I spent two weeks at such a high stress level I was getting migraines every single day (clearly on the wrong side of the Yerkes-Dodson curve), only to completely breeze through the exam.

I think I might need to put this up on a wall somewhere to remind myself:

Most grad students complete their degrees, and most assistant professors get tenure.

The real filters are admissions and hiring: Most applications to grad school are rejected (though probably most graduate students are ultimately accepted somewhere—I couldn’t find any good data on that in a quick search), and most PhD graduates do not get hired on the tenure track. But if you can make it through those two gauntlets, you can probably make it through the rest.

In our current system, publications are a way to filter people, because the number of people who want to become professors is much higher than the number of professor positions available. But as an economist, this raises a very big question: Why aren’t salaries falling?

You see, that’s how markets are supposed to work: When supply exceeds demand, the price is supposed to fall until the market clears. Lower salaries would both open up more slots at universities (you can hire more faculty with the same level of funding) and shift some candidates into other careers (if you can get paid a lot better elsewhere, academia may not seem so attractive). Eventually there should be a salary point at which demand equals supply. So why aren’t we reaching it?

Well, it comes back to that tenure system. We can’t lower the salaries of tenured faculty, not without a total upheaval of the current system. So instead what actually happens is that universities switch to using adjuncts, who have very low salaries indeed. If there were no tenure, would all faculty get paid like adjuncts? No, they wouldn’tbecause universities would have all that money they’re currently paying to tenured faculty, and all the talent currently locked up in tenured positions would be on the market, driving up the prevailing salary. What would happen if we eliminated tenure is not that all salaries would fall to adjunct level; rather, salaries would all adjust to some intermediate level between what adjuncts currently make and what tenured professors currently make.

What would the new salary be, exactly? That would require a detailed model of the supply and demand elasticities, so I can’t tell you without starting a whole new research paper. But a back-of-the-envelope calculation would suggest something like the overall current median faculty salary. This suggests a median salary somewhere around $75,000. This is a lot less than some professors make, but it’s also a lot more than what adjuncts make, and it’s a pretty good living overall.

If the salary for professors fell, the pool of candidates would decrease, and we wouldn’t need such harsh filtering mechanisms. We might decide we don’t need a strict evaluation system at all, and since the knowledge-sharing function of journals is much better served by other means, we could probably get rid of them altogether.

Of course, who am I kidding? That’s not going to happen. The people who make these rules succeeded in the current system. They are the ones who stand to lose high salaries and job security under a reform policy. They like things just the way they are.

Green New Deal Part 3: Guaranteeing education and healthcare is easy—why aren’t we doing it?

Apr 21 JDN 2458595

Last week was one of the “hard parts” of the Green New Deal. Today it’s back to one of the “easy parts”: Guaranteed education and healthcare.

“Providing all people of the United States with – (i) high-quality health care; […]

“Providing resources, training, and high-quality education, including higher education, to all people of the United States.”

Many Americans seem to think that providing universal healthcare would be prohibitively expensive. In fact, it would have literally negative net cost.
The US currently has the most bloated, expensive, inefficient healthcare system in the entire world. We spend almost $10,000 per person per year on healthcare, and get outcomes no better than France or the UK where they spend less than $5,000.
In fact, our public healthcare expenditures are currently higher than almost every other country. Our private expenditures are therefore pure waste; all they are doing is providing returns for the shareholders of corporations. If we were to simply copy the UK National Health Service and spend money in exactly the same way as they do, we would spend the same amount in public funds and almost nothing in private funds—and the UK has a higher mean lifespan than the US.
This is absolutely a no-brainer. Burn the whole system of private insurance down. Copy a healthcare system that actually works, like they use in every other First World country.
It wouldn’t even be that complicated to implement: We already have a single-payer healthcare system in the US; it’s called Medicare. Currently only old people get it; but old people use the most healthcare anyway. Hence, Medicare for All: Just lower the eligibility age for Medicare to 18 (if not zero). In the short run there would be additional costs for the transition, but in the long run we would save mind-boggling amounts of money, all while improving healthcare outcomes and extending our lifespans. Current estimates say that the net savings of Medicare for All would be about $5 trillion over the next 10 years. We can afford this. Indeed, the question is, as it was for infrastructure: How can we afford not to do this?
Isn’t this socialism? Yeah, I suppose it is. But healthcare is one of the few things that socialist countries consistently do extremely well. Cuba is a socialist country—a real socialist country, not a social democratic welfare state like Norway but a genuinely authoritarian centrally-planned economy. Cuba’s per-capita GDP PPP is a third of ours. Yet their life expectancy is actually higher than ours, because their healthcare system is just that good. Their per-capita healthcare spending is one-fourth of ours, and their health outcomes are better. So yeah, let’s be socialist in our healthcare. Socialists seem really good at healthcare.
And this makes sense, if you think about it. Doctors can do their jobs a lot better when they’re focused on just treating everyone who needs help, rather than arguing with insurance companies over what should and shouldn’t be covered. Preventative medicine is extremely cost-effective, yet it’s usually the first thing that people skimp on when trying to save money on health insurance. A variety of public health measures (such as vaccination and air quality regulation) are extremely cost-effective, but they are public goods that the private sector would not pay for by itself.
It’s not as if healthcare was ever really a competitive market anyway: When you get sick or injured, do you shop around for the best or cheapest hospital? How would you even go about that, when they don’t even post most of their prices and what prices they post are often wildly different than what you’ll actually pay?
The only serious argument I’ve heard against single-payer healthcare is a moral one: “Why should I have to pay for other people’s healthcare?” Well, I guess, because… you’re a human being? You should care about other human beings, and not want them to suffer and die from easily treatable diseases?
I don’t know how to explain to you that you should care about other people.

Single-payer healthcare is not only affordable: It would be cheaper and better than what we are currently doing. (In fact, almost anything would be cheaper and better than what we are currently doing—Obamacare was an improvement over the previous mess, but it’s still a mess.)
What about public education? Well, we already have that up to the high school level, and it works quite well.
Contrary to popular belief, the average public high school has better outcomes in terms of test scores and college placements than the average private high school. There are some elite private schools that do better, but they are extraordinarily expensive and they self-select only the best students. Public schools have to take all students, and they have a limited budget; but they have high quality standards and they require their teachers to be certified.
The flaws in our public school system are largely from it being not public enough, which is to say that schools are funded by their local property taxes instead of having their costs equally shared across whole states. This gives them the same basic problem as private schools: Rich kids get better schools.
If we removed that inequality, our educational outcomes would probably be among the best in the world—indeed, in our most well-funded school districts, they are. The state of Massachusetts which actually funds their public schools equally and well, gets international test scores just as good as the supposedly “superior” educational systems of Asian countries. In fact, this is probably even unfair to Massachusetts, as we know that China specifically selects the regions that have the best students to be the ones to take these international tests. Massachusetts is the best the US has to offer, but Shanghai is also the best China has to offer, so it’s only fair we compare apples to apples.
Public education has benefits for our whole society. We want to have a population of citizens, workers, and consumers who are well-educated. There are enormous benefits of primary and secondary education in terms of reducing poverty, improving public health, and increased economic growth.
So there’s my impassioned argument for why we should continue to support free, universal public education up to high school.
When it comes to college, I can’t be quite so enthusiastic. While there are societal benefits of college education, most of the benefits of college accrue to the individuals who go to college themselves.
The median weekly income of someone with a high school diploma is about $730; with a bachelor’s degree this rises to $1200; and with a doctoral or professional degree it gets over $1800. Higher education also greatly reduces your risk of being unemployed; while about 4% of the general population is unemployed, only 1.5% of people with doctorates or professional degrees are. Add that up over all the weeks of your life, and it’s a lot of money.
The net present value of a college education has been estimated at approximately $1 million. This result is quite sensitive to the choice of discount rate; at a higher discount rate you can get the net present value as “low” as $250,000.
With this in mind, the fact that the median student loan debt for a college graduate is about $30,000 doesn’t sound so terrible, does it? You’re taking out a loan for $30,000 to get something that will earn you between $250,000 and $1 million over the course of your life.
There is some evidence that having student loans delays homeownership; but this is a problem with our mortgage system, not our education system. It’s mainly the inability to finance a down payment that prevents people from buying homes. We should implement a system of block grants for first-time homeowners that gives them a chunk of money to make a down payment, perhaps $50,000. This would cost about as much as the mortgage interest tax deduction which mainly benefits the upper-middle class.
Higher education does have societal benefits as well. Perhaps the starkest I’ve noticed is how categorically higher education decided people’s votes on Donald Trump: Counties with high rates of college education almost all voted for Clinton, and counties with low rates of college education almost all voted for Trump. This was true even controlling for income and a lot of other demographic factors. Only authoritarianism, sexism and racism were better predictors of voting for Trump—and those could very well be mediating variables, if education reduces such attitudes.
If indeed it’s true that higher education makes people less sexist, less racist, less authoritarian, and overall better citizens, then it would be worth every penny to provide universal free college.
But it’s worth noting that even countries like Germany and Sweden which ostensibly do that don’t really do that: While college tuition is free for Swedish citizens and Germany provides free college for all students of any nationality, nevertheless the proportion of people in Sweden and Germany with bachelor’s degrees is actually lower than that of the United States. In Sweden the gap largely disappears if you restrict to younger cohorts—but in Germany it’s still there.
Indeed, from where I’m sitting, “universal free college” looks an awful lot like “the lower-middle class pays for the upper-middle class to go to college”. Social class is still a strong predictor of education level in Sweden. Among OECD countries, education seems to be the best at promoting upward mobility in Australia, and average college tuition in Australia is actually higher than average college tuition in the US (yes, even adjusting for currency exchange: Australian dollars are worth only slightly less than US dollars).
What does Australia do? They have a really good student loan system. You have to reach an annual income of about $40,000 per year before you need to make payments at all, and the loans are subsidized to be interest-free. Once you do owe payments, the debt is repaid at a rate proportional to your income—so effectively it’s not a debt at all but an equity stake.
In the US, students have been taking the desperate (and very cyberpunk) route of selling literal equity stakes in their education to Wall Street banks; this is a terrible idea for a hundred reasons. But having the government have something like an equity stake in students makes a lot of sense.
Because of the subsidies and generous repayment plans, the Australian government loses money on their student loan system, but so what? In order to implement universal free college, they would have spent an awful lot more than they are losing now. This way, the losses are specifically on students who got a lot of education but never managed to raise their income high enough—which means the government is actually incentivized to improve the quality of education or job-matching.
The cost of universal free college is considerable: That $1.3 trillion currently owed as student loans would be additional government debt or tax liability instead. Is this utterly unaffordable? No. But it’s not trivial either. We’re talking about roughly $60 billion per year in additional government spending, a bit less than what we currently spend on food stamps. An expenditure like that should have a large public benefit (as food stamps absolutely, definitely do!); I’m not convinced that free college would have such a benefit.
It would benefit me personally enormously: I currently owe over $100,000 in debt (about half from my undergrad and half from my first master’s). But I’m fairly privileged. Once I finally make it through this PhD, I can expect to make something like $100,000 per year until I retire. I’m not sure that benefiting people like me should be a major goal of public policy.
That said, I don’t think universal free college is a terrible policy. Done well, it could be a good thing. But it isn’t the no-brainer that single-payer healthcare is. We can still make sure that students are not overburdened by debt without making college tuition actually free.

What we could, what we should, and what we must

May 27 JDN 2458266

In one of the most famous essays in all of ethical philosophy, Peter Singer famously argued that we are morally obligated to give so much to charity that we would effectively reduce ourselves to poverty only slightly better than what our donations sought to prevent. His argument is a surprisingly convincing one, especially for such a radical proposition. Indeed, one of the core activities of the Effective Altruism movement has basically been finding ways to moderate Singer’s argument without giving up on its core principles, because it’s so obvious both that we ought to do much more to help people around the world and that there’s no way we’re ever going to do what that argument actually asks of us.

The most cost-effective charities in the world can save a human life for an average cost of under $4,000. The maneuver that Singer basically makes is quite simple: If you know that you could save someone’s life for $4,000, you have $4,000 to spend, and instead you spend that $4,000 on something else, aren’t you saying that whatever you did spend it on was more important than saving that person’s life? And is that really something you believe?

But if you think a little more carefully, it becomes clear that things are not quite so simple. You aren’t being paid $4,000 to kill someone, first of all. If you were willing to accept $4,000 as sufficient payment to commit a murder, you would be, quite simply, a monster. Implicitly the “infinite identical psychopath” of neoclassical rational agent models would be willing to do such a thing, but very few actual human beings—even actual psychopaths—are that callous.

Obviously, we must refrain from murdering people, even for amounts far in excess of $4,000. If you were offered the chance to murder someone for $4 billion dollars, I can understand why you would be tempted to do such a thing. Think of what you could do with all that money! Not only would you and everyone in your immediate family be independently wealthy for life, you could donate billions of dollars to charity and save as much as a million lives. What’s one life for a million? Even then, I have a strong intuition that you shouldn’t commit this murder—but I have never been able to find a compelling moral argument for why. The best I’ve been able to come up with a sort of Kantian notion: What if everyone did this?

Since the most plausible scenario is that the $4 billion comes from existing wealth, all those murders would simply be transferring wealth around, from unknown sources. If you stipulate where the wealth comes from, the dilemma can change quite a bit.

Suppose for example the $4 billion is confiscated from Bashar Al-Assad. That would be in itself a good thing, lessening the power of a genocidal tyrant. So we need to add that to the positive side of the ledger. It is probably worth killing one innocent person just to undermine Al-Assad’s power; indeed, the US Air Force certainly seems to think so, as they average more than one civilian fatality every day in airstrikes.

Now suppose the wealth was extracted by clever financial machinations that took just a few dollars out of every bank account in America. This would be in itself a bad thing, but perhaps not a terrible thing, especially since we’re planning on giving most of it to UNICEF. Those people should have given it anyway, right? This sounds like a pretty good movie, actually; a cyberpunk Robin Hood basically.

Next, suppose it was obtained by stealing the life savings of a million poor people in Africa. Now the method of obtaining the money is so terrible that it’s not clear that funneling it through UNICEF would compensate, even if you didn’t have to murder someone to get it.

Finally, suppose that the wealth is actually created anew—not printed money from the Federal Reserve, but some new technology that will increase the world’s wealth by billions of dollars yet requires the death of an innocent person to create. In this scenario, the murder has become something more like the inherent risk in human subjects biomedical research, and actually seems justifiable. And indeed, that fits with the Kantian answer, for if we all had the chance to kill one person in order to create something that would increase the wealth of the world by $4 billion, we could turn this planet into a post-scarcity utopia within a generation for fewer deaths than are currently caused by diabetes.

Anyway, my point here is that the detailed context of a decision actually matters a great deal. We can’t simply abstract away from everything else in the world and ask whether the money is worth the life.

When we consider this broader context with regard to the world’s most cost-effective charities, it becomes apparent that a small proportion of very dedicated people giving huge proportions of their income to charity is not the kind of world we want to see.

If I actually gave so much that I equalized my marginal utility of wealth to that of a child dying of malaria in Ghana, I would have to donate over 95% of my income—and well before that point, I would be homeless and impoverished. This actually seems penny-wise and pound-foolish even from the perspective of total altruism: If I stop paying rent, it gets a lot harder for me to finish my doctorate and become a development economist. And even if I never donated another dollar, the world would be much better off with one more good development economist than with even another $23,000 to the Against Malaria Foundation. Once you factor in the higher income I’ll have (and proportionately higher donations I’ll make), it’s obviously the wrong decision for me to give 95% of $25,000 today rather than 10% of $70,000 every year for the next 20 years after I graduate.

But the optimal amount for me to donate from that perspective is whatever the maximum would be that I could give without jeopardizing my education and career prospects. This is almost certainly more than I am presently giving. Exactly how much more is actually not all that apparent: It’s not enough to say that I need to be able to pay rent, eat three meals a day, and own a laptop that’s good enough for programming and statistical analysis. There’s also a certain amount that I need for leisure, to keep myself at optimal cognitive functioning for the next several years. Do I need that specific video game, that specific movie? Surely not—but if I go the next ten years without ever watching another movie or playing another video game, I’m probably going to be in trouble psychologically. But what exactly is the minimum amount to keep me functioning well? And how much should I be willing to spend attending conferences? Those can be important career-building activities, but they can also be expensive wastes of time.

Singer acts as though jeopardizing your career prospects is no big deal, but this is clearly wrong: The harm isn’t just to your own well-being, but also to your productivity and earning power that could have allowed you to donate more later. You are a human capital asset, and you are right to invest in yourself. Exactly how much you should invest in yourself is a much harder question.
Such calculations are extremely difficult to do. There are all sorts of variables I simply don’t know, and don’t have any clear way of finding out. It’s not a good sign for an ethical theory when even someone with years of education and expertise on specifically that topic still can’t figure out the answer. Ethics is supposed to be something we can apply to everyone.

So I think it’s most helpful to think in those terms: What could we apply to everyone? What standard of donation would be high enough if we could get everyone on board?

World poverty is rapidly declining. The direct poverty gap at the UN poverty line of $1.90 per day is now only $80 billion. Realistically, we couldn’t simply close that gap precisely (there would also be all sorts of perverse incentives if we tried to do it that way). But the standard estimate that it would take about $300 billion per year in well-targeted spending to eliminate world hunger is looking very good.

How much would each person, just those in the middle class or above within the US or the EU, have to give in order to raise this much?
89% of US income is received by the top 60% of households (who I would say are unambiguously “middle class or above”). Income inequality is not as extreme within the EU, so the proportion of income received by the top 60% seems to be more like 75%.

89% of US GDP plus 75% of EU GDP is all together about $29 trillion per year. This means that in order to raise $300 billion, each person in the middle class or above would need to donate just over one percent of their income.

Not 95%. Not 25%. Not even 10%. Just 1%. That would be enough.

Of course, more is generally better—at least until you start jeopardizing your career prospects. So by all means, give 2% or 5% or even 10%. But I really don’t think it’s helpful to make people feel guilty about not giving 95% when all we really needed was for everyone to give 1%.

There is an important difference between what we could do, what we should do, and what we must do.

What we must do are moral obligations so strong they are essentially inviolable: We must not murder people. There may be extreme circumstances where exceptions can be made (such as collateral damage in war), and we can always come up with hypothetical scenarios that would justify almost anything, but for the vast majority of people the vast majority of time, these ethical rules are absolutely binding.

What we should do are moral obligations that are strong enough to be marks against your character if you break them, but not so absolutely binding that you have to be a monster not to follow them. This is where I put donating at least 1% of your income. (This is also where I put being vegetarian, but perhaps that is a topic for another time.) You really ought to do it, and you are doing something wrongful if you don’t—but most people don’t, and you are not a terrible person if you don’t.

This latter category is in part socially constructed, based on the norms people actually follow. Today, slavery is obviously a grave crime, and to be a human trafficker who participates in it you must be a psychopath. But two hundred years ago, things were somewhat different: Slavery was still wrong, yes, but it was quite possible to be an ordinary person who was generally an upstanding citizen in most respects and yet still own slaves. I would still condemn people who owned slaves back then, but not nearly as forcefully as I would condemn someone who owned slaves today. Two hundred years from now, perhaps vegetarianism will move up a category: The norm will be that everyone eats only plants, and someone who went out of their way to kill and eat a pig would have to be a psychopath. Eating meat is already wrong today—but it will be more wrong in the future. I’d say the same about donating 1% of your income, but actually I’m hoping that by two hundred years from now there will be no more poverty left to eradicate, and donation will no longer be necessary.

Finally, there is what we could do—supererogatory, even heroic actions of self-sacrifice that would make the world a better place, but cannot be reasonably expected of us. This is where donating 95% or even 25% of your income would fall. Yes, absolutely, that would help more people than donating 1%; but you don’t owe the world that much. It’s not wrong for you to contribute less than this. You don’t need to feel guilty for not giving this much.

But I do want to make you feel guilty if you don’t give at least 1%. Don’t tell me you can’t. You can. If your income is $30,000 per year, that’s $300 per year. If you needed that much for a car repair, or dental work, or fixing your roof, you’d find a way to come up with it. No one in the First World middle class is that liquidity-constrained. It is true that half of Americans say they couldn’t come up with $400 in an emergency, but I frankly don’t believe it. (I believe it for the bottom 25% or so, who are actually poor; but not half of Americans.) If you have even one credit card that’s not maxed out, you can do this—and frankly even if a card is maxed out, you can probably call them and get them to raise your limit. There is something you could cut out of your spending that would allow you to get back 1% of your annual income. I don’t know what it is, necessarily: Restaurants? Entertainment? Clothes? But I’m not asking you to give a third of your income—I’m asking you to give one penny out of every dollar.

I give considerably more than that; my current donation target is 8% and I’m planning on raising it to 10% or more once I get a high-paying job. I live on a grad student salary which is less than the median personal income in the US. So I know it can be done. But I am very intentionally not asking you to give this much; that would be above and beyond the call of duty. I’m only asking you to give 1%.

Why is redistribution of wealth so difficult to achieve in the US?

Jan 28 JDN 2458147

Income and wealth in equality is much higher in the US than in other First World countries. Within the OECD, only Mexico, Turkey, and Chile have higher income inequality than we do. Over 60% of Americans agree that the distribution of wealth in the US is unfair. Furthermore, the majority of Americans support the use of taxes and transfers to directly redistribute wealth from the rich to the poor.

Why, then, is it so hard to actually get any meaningful wealth redistribution in the United States?

Part of it is surely partisan differences: While about 70% of Democrats favor redistributive taxes, about 70% of Republicans oppose them. So one would not expect a move toward redistribution when Republicans control all three branches of government, and indeed we have seen quite the opposite. (Then again, one would also not expect a government shutdown under one-party rule, and yet that is what we have.)

But even most Republicans say they would like to see a much more equal distribution of wealth than the one we actually have. In fact, when I as an inequality economist look at the distribution of wealth people say they want, it looks a little too equal! Even Denmark and Sweden aren’t that egalitarian! I know more or less how to get from here to Denmark; but from here to “Equalden” looks like an awful long way. So if this is really the distribution of wealth people want, we need to be doing a huge amount of wealth redistribution—but we’re hardly doing any at all.

Indeed, we didn’t actually see all that much redistribution of wealth when Democrats more or less controlled all three branches in the period from 2008-2010. We may have seen a little bit shortly thereafter, and tax policy typically does come with a delay of a year or two. But as you can see in this graph, the Great Recession did more to reduce the top 1% income share than any tax policy changes:


The biggest changes made to our tax code under Obama were actually the handling of capital gains; the increase of the top rate on capital gains from 15% to 20%, plus the 3.8% capital surtax from the Affordable Care Act raised the tax bill for the top 0.1% by tens of billions of dollars. Surprisingly, Trump’s tax cuts don’t actually remove these provisions, though they did dramatically cut the corporate tax rate, which will probably have a similar effect on the income distribution.

To be honest, I’m not as disappointed with Trump’s tax cuts as I thought I would be. Some genuinely good ideas (like the reduction of the mortgage interest deduction, tighter restrictions on carried interest, and increase of the personal standard deduction) and some reasonable but debatable ideas (like cuts to the corporate tax rate, switching to a territorial corporate tax system, limits to deductions on corporate debt payments, removal of the deduction of state taxes, and extensions of 529 savings plans to private primary and secondary schools) were mixed in with the absolutely ludicrous and terrible ideas (like eliminating the Obamacare mandate, doubling the estate tax threshold, cutting the alcohol tax, and allowing offshore drilling in Alaska [One of these things is not like the other ones….]). Some of the terrible ideas, like ending the deduction of student loan interest and tuition waivers, were actually removed in the final version of the bill. Of course, you won’t be surprised when I tell you that the overall US tax system became a lot less progressive as a result of this bill. And even if cutting the corporate tax while raising the capital gains tax is probably a good idea (as I and many economists believe), cutting the corporate tax without raising the capital gains tax probably isn’t.

(An aside: For how much they claim to be “tough on crime”, it’s always kind of baffling to see how often Republicans like to cut alcohol taxes and pollution regulations, which are pretty much the only things that have ever been empirically shown to actually reduce crime. There is some evidence that maybe more policing also helps, but if so, it does so in a far less cost-effective way—indeed, the direct cost of alcohol taxes and pollution taxes is negative. Even if they didn’t work at all, they’d still be worth it just because they raise revenue. I begin to suspect that Republicans don’t actually want to reduce crime, because they know they can use the fear of crime to win votes; they simply want to appear tough on crime, and so they press as hard as they can for more policing and incarceration in the country that already has the highest incarceration rate in the world. This may be a more general phenomenon: While Democrats want to actually solve problems, Republicans want to appear to solve problems while actually exacerbating them, thus insuring their own job security. Compare how Bush kept talking about Osama bin laden while invading Iraq, and Obama actually killed Osama bin Laden. Is this too cynical? Can anything be too cynical in the era of Trump? There were 50,000 Russian bots on Twitter trying to tilt our election! Mueller’s FBI investigation is already implicating several of Trump’s top officials! Everything that seemed like paranoia or cynicism just a few years ago is turning out to be entirely true.)

This is what seems to happen: Year after year, we raise some taxes, then we cut some taxes. Then when raise some taxes, then we cut some taxes. The tax system gets a little more progressive for a few years and inequality begins to fall, and then those changes are removed and inequality begins to rise again. Back and forth and round and round we go.

Is there some way to lock in these tax changes for a longer period of time? The only way I can see would be a change in voter behavior: Keep voting in Democrats to all branches of government consistently for 20 years, and then maybe we would see a serious reduction in income and wealth inequality. Or at least stop voting in Republicans; aside from the Democrats, there are some third parties that would also support redistribution, like the Green Party. And yes, it really is about voting behavior: As prevalent as gerrymandering has become, as terrible as the Electoral College is, as widespread as voter suppression has gotten, Trump only won because 63 million Americans voted for him. Even after everything he’s done, Trumps’ approval rating is still about 39%. As long as there are enough people in this country whose partisan loyalty so strongly outweighs any rational assessment of policy, we are going to continue to see such travesties continue.

It would certainly help if our voting system were fairer, so that third parties had a better chance at taking seats. But it’s also difficult to see how that could happen any time soon. For now, the best I can come up with is trying to show people two things:

First, most Americans favor redistribution of wealth. You’re not alone in wanting that. It’s not some fringe opinion.

Second, there is a real difference between Democrats and Republicans on this issue. The canard “The two parties are the same” is the most untrue it has been in at least twenty years.

I would even understand if there are other issues you consider more important than wealth redistribution. Ecological sustainability is the most defensible—you can’t eat GNP—though that would push you even harder toward the left. Among things that might push you right, I can understand being concerned about higher taxes hurting economic growth, and while I think the view that abortion is murder is ludicrous, given that as your belief I can understand why you would want to prioritize fighting abortion. (If I thought we were murdering millions of babies every year, I’d be pretty mad too! Of course, you should be glad, then, that the US abortion rate has been falling. Right? You know about that, right?)

What I don’t get, however, is people who thought that voting for Donald Trump would help working people. I don’t understand how you can see someone who epitomizes everything that is wrong with the billionaire rentier class and think, “Yeah, he seems like he’s definitely a populist. That guy who was born insanely rich and made even more mind-boggling amounts of money by lying and screwing people over is definitely going to look out for folks like me.”

If I understood that, maybe I would know where to go from here. But people’s political beliefs can be astonishingly intransigent to evidence. Politics is the mind-killer.

Think of this as a moral recession

August 27, JDN 2457993

The Great Depression was, without doubt, the worst macroeconomic event of the last 200 years. Over 30 million people became unemployed. Unemployment exceeded 20%. Standard of living fell by as much as a third in the United States. Political unrest spread across the world, and the collapsing government of Germany ultimately became the Third Reich and triggered the Second World War If we ignore the world war, however, the effect on mortality rates was surprisingly small. (“Other than that, Mrs. Lincoln, how was the play?”)

And yet, how long do you suppose it took for economic growth to repair the damage? 80 years? 50 years? 30 years? 20 years? Try ten to fifteen. By 1940, the US, US, Germany, and Japan all had a per-capita GDP at least as high as in 1930. By 1945, every country in Europe had a per-capita GDP at least as high as they did before the Great Depression.

The moral of this story is this: Recessions are bad, and can have far-reaching consequences; but ultimately what really matters in the long run is growth.

Assuming the same growth otherwise, a country that had a recession as large as the Great Depression would be about 70% as rich as one that didn’t.

But over 100 years, a country that experienced 3% growth instead of 2% growth would be over two and a half times richer.

Therefore, in terms of standard of living only, if you were given the choice between having a Great Depression but otherwise growing at 3%, and having no recessions but growing at 2%, your grandchildren will be better off if you chose the former. (Of course, given the possibility of political unrest or even war, the depression could very well end up worse.)

With that in mind, I want you to think of the last few years—and especially the last few months—as a moral recession. Donald Trump being President of the United States is clearly a step backward for human civilization, and it seems to have breathed new life into some of the worst ideologies our society has ever harbored, from extreme misogyny, homophobia, right-wing nationalism, and White supremacism to outright Neo-Nazism. When one of the central debates in our public discourse is what level of violence is justifiable against Nazis under what circumstances, something has gone terribly, terribly wrong.

But much as recessions are overwhelmed in the long run by economic growth, there is reason to be confident that this moral backslide is temporary and will be similarly overwhelmed by humanity’s long-run moral progress.

What moral progress, you ask? Let’s remind ourselves.

Just 100 years ago, women could not vote in the United States.

160 years ago, slavery was legal in 15 US states.

Just 3 years ago, same-sex marriage was illegal in 14 US states. Yes, you read that number correctly. I said three. There are gay couples graduating high school and getting married now who as freshmen didn’t think they would be allowed to get married.

That’s just the United States. What about the rest of the world?

100 years ago, almost all of the world’s countries were dictatorships. Today, half of the world’s countries are democracies. Indeed, thanks to India, the majority of the world’s population now lives under democracy.

35 years ago, the Soviet Union still ruled most of Eastern Europe and Northern Asia with an iron fist (or should I say “curtain”?).

30 years ago, the number of human beings in extreme poverty—note I said number, not just rate; the world population was two-thirds what it is today—was twice as large as it is today.

Over the last 65 years, the global death rate due to war has fallen from 250 per million to just 10 per million.

The global literacy rate has risen from 40% to 80% in just 50 years.

World life expectancy has increased by 6 years in just the last 20 years.

We are living in a golden age. Do not forget that.

Indeed, if there is anything that could destroy all these astonishing achievements, I think it would be our failure to appreciate them.

If you listen to what these Neo-Nazi White supremacists say about their grievances, they sound like the spoiled children of millionaires (I mean, they elected one President, after all). They are outraged because they only get 90% of what they want instead of 100%—or even outraged not because they didn’t get what they wanted but because someone else they don’t know also did.

If you listen to the far left, their complaints don’t make much more sense. If you didn’t actually know any statistics, you’d think that life is just as bad for Black people in America today as it was under Jim Crow or even slavery. Well, it’s not even close. I’m not saying racism is gone; it’s definitely still here. But the civil rights movement has made absolutely enormous strides, from banning school segregation and housing redlining to reforming prison sentences and instituting affirmative action programs. Simply the fact that “racist” is now widely considered a terrible thing to be is a major accomplishment in itself. A typical Black person today, despite having only about 60% of the income of a typical White person, is still richer than a typical White person was just 50 years ago. While the 71% high school completion rate Black people currently have may not sound great, it’s much higher than the 50% rate that the whole US population had as recently as 1950.

Yes, there are some things that aren’t going very well right now. The two that I think are most important are climate change and income inequality. As both the global mean temperature anomaly and the world top 1% income share continue to rise, millions of people will suffer and die needlessly from diseases of poverty and natural disasters.

And of course if Neo-Nazis manage to take hold of the US government and try to repeat the Third Reich, that could be literally the worst thing that ever happened. If it triggered a nuclear war, it unquestionably would be literally the worst thing that ever happened. Both these events are unlikely—but not nearly as unlikely as they should be. (Five Thirty Eight interviewed several nuclear experts who estimated a probability of imminent nuclear war at a horrifying five percent.) So I certainly don’t want to make anyone complacent about these very grave problems.

But I worry also that we go too far the other direction, and fail to celebrate the truly amazing progress humanity has made thus far. We hear so often that we are treading water, getting nowhere, or even falling backward, that we begin to feel as though the fight for moral progress is utterly hopeless. If all these centuries of fighting for justice really had gotten us nowhere, the only sensible thing to do at this point would be to give up. But on the contrary, we have made enormous progress in an incredibly short period of time. We are on the verge of finally winning this fight. The last thing we want to do now is give up.

Why “marginal productivity” is no excuse for inequality

May 28, JDN 2457902

In most neoclassical models, workers are paid according to their marginal productivity—the additional (market) value of goods that a firm is able to produce by hiring that worker. This is often used as an excuse for inequality: If someone can produce more, why shouldn’t they be paid more?

The most extreme example of this is people like Maura Pennington writing for Forbes about how poor people just need to get off their butts and “do something”; but there is a whole literature in mainstream economics, particularly “optimal tax theory”, arguing based on marginal productivity that we should tax the very richest people the least and never tax capital income. The Chamley-Judd Theorem famously “shows” (by making heroic assumptions) that taxing capital just makes everyone worse off because it reduces everyone’s productivity.

The biggest reason this is wrong is that there are many, many reasons why someone would have a higher income without being any more productive. They could inherit wealth from their ancestors and get a return on that wealth; they could have a monopoly or some other form of market power; they could use bribery and corruption to tilt government policy in their favor. Indeed, most of the top 0.01% do literally all of these things.

But even if you assume that pay is related to productivity in competitive markets, the argument is not nearly as strong as it may at first appear. Here I have a simple little model to illustrate this.

Suppose there are 10 firms and 10 workers. Suppose that firm 1 has 1 unit of effective capital (capital adjusted for productivity), firm 2 has 2 units, and so on up to firm 10 which has 10 units. And suppose that worker 1 has 1 unit of so-called “human capital”, representing their overall level of skills and education, worker 2 has 2 units, and so on up to worker 10 with 10 units. Suppose each firm only needs one worker, so this is a matching problem.

Furthermore, suppose that productivity is equal to capital times human capital: That is, if firm 2 hired worker 7, they would make 2*7 = $14 of output.

What will happen in this market if it converges to equilibrium?

Well, first of all, the most productive firm is going to hire the most productive worker—so firm 10 will hire worker 10 and produce $100 of output. What wage will they pay? Well, they need a wage that is high enough to keep worker 10 from trying to go elsewhere. They should therefore pay a wage of $90—the next-highest firm productivity times the worker’s productivity. That’s the highest wage any other firm could credibly offer; so if they pay this wage, worker 10 will not have any reason to leave.

Now the problem has been reduced to matching 9 firms to 9 workers. Firm 9 will hire worker 9, making $81 of output, and paying $72 in wages.

And so on, until worker 1 at firm 1 produces $1 and receives… $0. Because there is no way for worker 1 to threaten to leave, in this model they actually get nothing. If I assume there’s some sort of social welfare system providing say $0.50, then at least worker 1 can get that $0.50 by threatening to leave and go on welfare. (This, by the way, is probably the real reason firms hate social welfare spending; it gives their workers more bargaining power and raises wages.) Or maybe they have to pay that $0.50 just to keep the worker from starving to death.

What does inequality look like in this society?
Well, the most-productive firm only has 10 times as much capital as the least-productive firm, and the most-educated worker only has 10 times as much skill as the least-educated worker, so we might think that incomes would vary only by a factor of 10.

But in fact they vary by a factor of over 100.

The richest worker makes $90, while the poorest worker makes $0.50. That’s a ratio of 180. (Still lower than the ratio of the average CEO to their average employee in the US, by the way.) The worker is 10 times as productive, but they receive 180 times as much income.

The firm profits vary along a more reasonable scale in this case; firm 1 makes a profit of $0.50 while firm 10 makes a profit of $10. Indeed, except for firm 1, firm n always makes a profit of $n. So that’s very nearly a linear scaling in productivity.

Where did this result come from? Why is it so different from the usual assumptions? All I did was change one thing: I allowed for increasing returns to scale.

If you make the usual assumption of constant returns to scale, this result can’t happen. Multiplying all the inputs by 10 should just multiply the output by 10, by assumption—since that is the definition of constant returns to scale.

But if you look at the structure of real-world incomes, it’s pretty obvious that we don’t have constant returns to scale.

If we had constant returns to scale, we should expect that wages for the same person should only vary slightly if that person were to work in different places. In particular, to have a 2-fold increase in wage for the same worker you’d need more than a 2-fold increase in capital.

This is a bit counter-intuitive, so let me explain a bit further. If a 2-fold increase in capital results in a 2-fold increase in wage for a given worker, that’s increasing returns to scale—indeed, it’s precisely the production function I assumed above.
If you had constant returns to scale, a 2-fold increase in wage would require something like an 8-fold increase in capital. This is because you should get a 2-fold increase in total production by doubling everything—capital, labor, human capital, whatever else. So doubling capital by itself should produce a much weaker effect. For technical reasons I’d rather not get into at the moment, usually it’s assumed that production is approximately proportional to capital to the one-third power—so to double production you need to multiply capital by 2^3 = 8.

I wasn’t able to quickly find really good data on wages for the same workers across different countries, but this should at least give a rough idea. In Mumbai, the minimum monthly wage for a full-time worker is about $80. In Shanghai, it is about $250. If you multiply out the US federal minimum wage of $7.25 per hour by 40 hours by 4 weeks, that comes to $1160 per month.

Of course, these are not the same workers. Even an “unskilled” worker in the US has a lot more education and training than a minimum-wage worker in India or China. But it’s not that much more. Maybe if we normalize India to 1, China is 3 and the US is 10.

Likewise, these are not the same jobs. Even a minimum wage job in the US is much more capital-intensive and uses much higher technology than most jobs in India or China. But it’s not that much more. Again let’s say India is 1, China is 3 and the US is 10.

If we had constant returns to scale, what should the wages be? Well, for India at productivity 1, the wage is $80. So for China at productivity 3, the wage should be $240—it’s actually $250, close enough for this rough approximation. But the US wage should be $800—and it is in fact $1160, 45% larger than we would expect by constant returns to scale.

Let’s try comparing within a particular industry, where the differences in skill and technology should be far smaller. The median salary for a software engineer in India is about 430,000 INR, which comes to about $6,700. If that sounds rather low for a software engineer, you’re probably more accustomed to the figure for US software engineers, which is $74,000. That is a factor of 11 to 1. For the same job. Maybe US software engineers are better than Indian software engineers—but are they that much better? Yes, you can adjust for purchasing power and shrink the gap: Prices in the US are about 4 times as high as those in India, so the real gap might be 3 to 1. But these huge price differences themselves need to be explained somehow, and even 3 to 1 for the same job in the same industry is still probably too large to explain by differences in either capital or education, unless you allow for increasing returns to scale.

In most industries, we probably don’t have quite as much increasing returns to scale as I assumed in my simple model. Workers in the US don’t make 100 times as much as workers in India, despite plausibly having both 10 times as much physical capital and 10 times as much human capital.

But in some industries, this model might not even be enough! The most successful authors and filmmakers, for example, make literally thousands of times as much money as the average author or filmmaker in their own country. J.K. Rowling has almost $1 billion from writing the Harry Potter series; this is despite having literally the same amount of physical capital and probably not much more human capital than the average author in the UK who makes only about 11,000 GBP—which is about $14,000. Harry Potter and the Philosopher’s Stone is now almost exactly 20 years old, which means that Rowling made an average of $50 million per year, some 3500 times as much as the average British author. Is she better than the average British author? Sure. Is she three thousand times better? I don’t think so. And we can’t even make the argument that she has more capital and technology to work with, because she doesn’t! They’re typing on the same laptops and using the same printing presses. Either the return on human capital for British authors is astronomical, or something other than marginal productivity is at work here—and either way, we don’t have anything close to constant returns to scale.

What can we take away from this? Well, if we don’t have constant returns to scale, then even if wage rates are proportional to marginal productivity, they aren’t proportional to the component of marginal productivity that you yourself bring. The same software developer makes more at Microsoft than at some Indian software company, the same doctor makes more at a US hospital than a hospital in China, the same college professor makes more at Harvard than at a community college, and J.K. Rowling makes three thousand times as much as the average British author—therefore we can’t speak of marginal productivity as inhering in you as an individual. It is an emergent property of a production process that includes you as a part. So even if you’re entirely being paid according to “your” productivity, it’s not really your productivity—it’s the productivity of the production process you’re involved in. A myriad of other factors had to snap into place to make your productivity what it is, most of which you had no control over. So in what sense, then, can we say you earned your higher pay?

Moreover, this problem becomes most acute precisely when incomes diverge the most. The differential in wages between two welders at the same auto plant may well be largely due to their relative skill at welding. But there’s absolutely no way that the top athletes, authors, filmmakers, CEOs, or hedge fund managers could possibly make the incomes they do by being individually that much more productive.