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## A Conversation with GoD

Can Putanumonit put a number on the divine itself?

The following is an inexact transcript of a conversation that happened exactly like this. The scene: a wine bar in Manhattan, on my second (and final) date with a Jewish girl. We’ll call her “Jewish Girl on Date”, or J-GoD for short.

J-GoD: You’ve changed your OKCupid religion status from “Jewish” to “atheist” since last week. What happened this weekend that proved to you that God doesn’t exist?

Jacob’s inner voice: Actually, I switched it to optimize my dating profile and avoid Jewish girls that give me grief about not being as Jewish as their moms expect me to be.

Jacob’s mouth: I don’t think that anything can really prove that God doesn’t exist. That’s partly because the definition of God will usually shift to accommodate any evidence.

J-GoD: So why do you call yourself an atheist if you can’t prove that God doesn’t exist?

Jacob: I give the existence of any specific god a low enough probability that I functionally behave as if I was sure no god existed.

J-GoD: Probability?!

Jacob: I give about a 1 in 10 chance for the existence of any popularly conceived supernatural beings, including humanity’s descendants simulating our reality. For some specific religion’s god, like the Old Testament Jewish God (we’ll call him J-God for short), something like 1 in 1,000,000.

J-GoD: How can you put a number on the existence of J-God?

Jacob: Umm, I have this blog about how you can put a number on almost anything… Anyway, probability numbers are how I represent how confident I am that something is true or not.

J-GoD: How the hell can you be exactly one in a million confident that God exists?

Jacob: I wish I could say that I calculated the prior of the Kolmogorov complexity implied by the description of J-God and updated on all available evidence. In reality, I just picked a really low number that matches how confident I allow myself to be on complex metaphysical questions.

J-GoD: So you’re just making up a number to say that you think that God doesn’t exist?

Jacob: No, no, the exact number is important. For example, if I was walking down the street and suddenly saw a bush burst in flames, and the bush burned but wasn’t consumed, and I heard a voice from the sky saying: “I am the God of your father, God of Abraham of Isaac and of Jacob“, I would definitely update my belief.

It’s possible that I could see a divine bush in a godless world as the result of hallucinogenic drugs or a convoluted prank involving VR, but I’m much more likely to see it in a universe in which J-God exists. In J-God’s universe pranksters and drugs still exist, but so does a divinity that is known for using burning bushes to impress people. Let’s say that a burning bush is one hundred times more likely in a J-God universe. So, I would update my belief in J-God by a factor of one hundred, from 1 in 1,000,000 to 1 in 10,000. That’s a high enough probability of J-God watching over me that I would at least make sure to never again boil a goat in its mother’s milk.

A second miracle would bring my posterior belief in J-God from 1/10,000 to 1/100, far above any other single supernatural being and high enough to give some real bite to Pascal’s wager. At three independently observed miracles, I will switch to living a life of humble devotion to J-God.

J-GoD: You think that people should only believe in a God after they see him perform exactly three miracles? That’s a perverse notion of belief! Belief in God has nothing to do with seeing miracles!

Jacob: Actually, the great medieval rationalist rabbi Moses Maimonides discusses in great detail the question of miracle-based belief in God. In Guide for the Perplexed, chapter LXIII he says:

You know how widespread were in those days the opinions of the Sabeans: all men, except a few individuals, were idolaters, that is to say, they believed in spirits, in man’s power to direct the influences of the heavenly bodies, and in the effect of talismans. Any one who in those days laid claim to authority, based it either [on reasoning and proof] or that some spiritual power was conferred upon him by a star, by an angel, or by a similar agency.

He basically says that for people who see magic in every charlatan and miracles every other Tuesday, a miracle should not constitute strong evidence. This is sound Bayesian reasoning. However, we are no longer “in those days”. As an educated rationalist in 2016, I don’t believe that supernatural wonders are common at all. Seeing a true miracle with my own eyes would provide solid grounds for changing my belief.

In Mishne Torah, Maimonides agrees that the performance of miracles should at least make you consider that you’re dealing with a genuine, Twitter-verified, message from the divine, i.e. a prophet:

Just as we are commanded to render a [legal] judgment based on the testimony of two witnesses, even though we do not know if they are testifying truthfully or falsely, similarly, it is a mitzvah to listen to this prophet even though we do not know whether the wonder is true or performed by magic or sorcery.

By “magic and sorcery” Maimonides means illusions and tricks, as opposed to true divine intervention. For example, hallucinogenic drugs and VR count as “magic and sorcery”. Now of course, Maimonides knows that 0 and 1 aren’t probabilities, so Bayesian updating on evidence cannot bring a man to absolute and total belief. As long as drugs or VR are a possibility, they cannot be completely discounted as the source of the observed miracle.

From Mishne Torah again:

The Jews did not believe in Moses, our teacher, because of the wonders that he performed. Whenever anyone’s belief is based on wonders, the commitment of his heart has shortcomings, because it is possible to perform a wonder through magic or sorcery.

Here’s a great (atheist) Jew explaining how a great (deeply religious) Jew proved that two smart Jews shouldn’t disagree on their picture of reality. Maimonides and I don’t have the shared knowledge required to reach consensus, but we are in complete agreement regarding the proper epistemology of miracle-based belief in J-God.

We differ in our moral value judgment on less-than-absolute belief: I believe that it is a virtue, Maimonides that it is a shortcoming. However, I am a moral anti-realist: I believe that moral value judgments are a fact about (my and Maimonides’) minds, not about external reality. Thus, our moral disagreement isn’t cause for concern for me that I am irrational on the subject.

J-GoD: What kind of atheist are you that you analyze in minute detail the biblical commentary of medieval rabbis?

Jacob: What kind of Jew would I be if I didn’t?

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## Welcome to Put A Num On It!

#### What’s Putanumonit?

People see some things as quantifiable, e.g. tax rates, and unquantifiable, e.g. love, charity, happiness, feminism and Chinese soccer. Personally, I have no idea how the American tax system works, but everything else seems quite easy to put a number on if you try.

For example, a simple mathematical fact can explain why the Chinese soccer team sucks  despite China’s huge population. I write often about other sports as well. Love and dating is also a popular subject, from guides on leveraging or “hacking” OkCupid to musings on feminism and Nice Guys. My best received post is Shopping for Happiness, one of my essays on the best ways to use money to make yourself happier and to improve the worldI call out people who use bullshit numbers, whether by mistake or with intent to mislead. Those include bad scientists, good scientists, and even FiveThirtyEightI fully encourage you to call me out in turn when I get something wrong. I occasionally dive into economics and public policy, I wrote about voting (bad idea), basic income (good idea, maybe) and inequality (complicated idea). My writing, in fact my entire life, is informed by the rationality community and the writings on LessWrong.com. A few of my posts address.

I also wrote a post about Pokémon. I hope that doesn’t become a category.

Putanumonit is a personal labor of love, free of ads and affiliations. The chronological archive is here, new posts arrive 3-4 times a month on a schedule unknown even to me. Please subscribe on the right sidebar, leave comments on any old or new post and write putanumonit at gmail dot com with personal missives, datasets you want me to analyze and invitations to beer.

Enjoy,

Jacob

## What this overpaid man has to say about the gender wage gap is shocking!

How come women make 79 cents on the dollar? Here are two prominent explanations that are clearly wrong, and two uncommon explanations that are possibly true.

A couple months ago, Vox tried to explain economic inequality using cartoons. That article was so deficient and misleading that it inspired me to write a whole rant on how reporting about inequality is often deficient and misleading. The income gap between the rich and the poor struck me as a subject that is actually amenable to an intelligent and balanced analysis. That’s in contrast, just to throw a random example, to the income gap between men and women.

So of course, this week Vox decided to explain the gender wage gap using cartoons. And guess what? It’s excellent. It’s well researched (by Claudia Goldin, a woman economist), well written (by Sarah Kliff, a woman editor), and describes an interesting explanation of the gender wage gap – the differing value of specific work hours.

Actually, I should say “factor that plays into” instead of “explanation of” the wage gap – it’s a complex effect that is driven by many causes that also interact with each other. The best we can do is identify several such factors and see if they fit data to build a better understanding of what’s going on. So, emboldened by Vox, I will offer two more possible developments contributing to the wage gap that neither invoke nor employ sexism. Also, unlike Mesdames Goldin and Kliff, I will not make a single penny from writing this. Thus I will be counteracting the gender wage gap through personal effort and example.

#### What’s wrong with arguments from sexism?

The two “arguments from sexism” regarding the gender wage come from the two ends of the gender-politics horseshoe,  and are thus pleasingly symmetrical and equally wrong. The argument from the RadFem-left side of the horseshoe is that women are paid less because oppressive men conspire to pay them less. The argument from the MRA-right is that women are just naturally less talented then men, with some allusion to evolutionary psychology accounting for the talent gap. Prior to collecting any data, we should notice the first argument contradicts basic economic math and the second argument contradicts… evolutionary psychology.

Economics tells us that if a wage gap existed, smart companies would profit by hiring women, driving the sexist companies out of business. People often dismiss this argument because of its simplicity, but it’s much more powerful than they realize. The average profit margins for businesses in the US are a mere 9%, while wages and benefits make up more than 60% of employer costs. If the wage gap of 79 cents on the dollar was for equal labor, employers hiring women would save 21% on labor costs, or more than 12% on total costs. This would more than double their profits ,while employers hiring men would go bankrupt. Overpaying for equal labor even by 5% increases your costs by 3%, that’s one third of an average company’s profits. In a competitive economy with high costs of labor, any sexist discrimination in wages large enough to be noticeable is also too costly to survive.

The evo psych talent argument seems to me like a classic fake explanation: it fails to predict the very effect it purports to explain. Consider this story:

Lacking the ability to resolve conflicts in their favor using brute strength, women have evolved to manage conflicts through interpersonal skills. Thus, women are less aggressive but better at persuasion, empathy and cooperation. These talents lead women to dominate occupations that require talking people over to your side, such as: politics, education, sales, entertainment, humanities academia, marketing, law, and all managerial positions in large corporations. This list of occupations covers every single highly paid career except for STEM and medicine. As a result, we see few women wasting their time trying to become doctors but otherwise most women earning higher incomes than men.

– Falkovich et al. Why men make 79 cents on a woman’s dollar (2016)

Now compare that, backed by the fact that women outpace men in educational attainment, to whichever just-so evo-psych story you heard about how women make less because evolved to be less assertive/analytical/hardworking. Which story sounds more reasonable?. Of course,  the plausibility of explanations should matter little if we have data. So what does the data say? It says that apparently you can find bias against women, bias against men or no bias at all depending on chance, researcher attitudes and whether Mercury is in retrograde.

If these arguments are supported by neither theory nor practice, why do so many people tout them passionately? (Just trust me, you don’t want to see links for this claim, they’re all horrible). I think that these are “beliefs as attire“, they are used mainly to signal loyalty to the RadFem/MRA political group that unifies around blaming the patriarchy/feminism for all its problems.

It’s important to remember that reversed stupidity isn’t intelligence: the explanations from sexism aren’t wrong because people believe them for dumb political reasons, they’re independently wrong. 5,000 years ago in Egypt someone proclaimed the crazy idea that the sun is larger than the earth just to curry political favor with the priests of Ra, and was correct by accident.

So, here are my two stories, and the data that backs them up:

#### It’s not all about the money

Jobs offer many different things besides compensation, Vox mentions only the obvious one that women trade-off for money: flexible hours needed to raise children. But a job isn’t just the hours and the wages.

Plumbers make almost 50% more than teachers, because the latter job is rewarding, high status and lets you work with children, while the former is boring, low status, and lets you work with sewage. This is also true at the higher end of the pay scale: MBA graduate women are likelier to work for non-profits, men likelier to work in corporate finance. Corporate finance isn’t cool, but it pays.

Also among MBAs, women are much likelier to work in marketing for big corporations like Coca Cola or Kraft: a very stable job but one with lower wage growth. Men are much likelier to work for hedge funds, where the salary is higher on average but also very volatile, as is the survival of entire company. Remember, when a hedge fund blows up and its male employees find themselves on the street, they immediately drop out of the wage-gap calculation which only includes the fully employed.

In happy-nomics terms, women are making the much smarter trade off. The effects on happiness of job security and finding purpose and meaning at work far outweigh the effects of salary increases beyond a certain point. So why do men value money more than flexibility, fun, coolness and stability?

There are likely many reasons, one of them is that 72% of women think that men should pay for the first date, and 82% of men agree. More broadly, men’s income correlates very strongly with being married, while women’s income barely does (raw data here). The fact is, both men and women care much more about a man’s salary than a woman’s, and that can be both a cause and an effect of men trading off other benefits for money.

It’s hard for men to earn little

Let’s imagine a simple economy consisting of three kinds of jobs. Half the men in our fantasy economy are fighters and make \$20,000 a year. Half the women are rogues and also make \$20,000. Finally, half of all men and women are wizards, and wizards make \$100,000. The average wages for full time employees are \$60,000, the same for men and women.

Now let’s imagine that the economy outsources all the fighter jobs to orcs/skeletons/China and the fighter men are fired. These men drop out of the employment statistics, and the average wage for employed men shoots to \$100,000 since only male wizards have jobs. “Fie the gender wage gap, women make 60 cents on the dollar!” cry the newspapers, even as men face a much worse economic employment situation than the women.

There’s some evidence that this is actually happening in our world (the male employment shift, not the orcs).

Here’s a gender-composition breakdown of various job categories, and here are the occupations with the largest employment changes. The occupations doing the worst are carpenters, laborers, freight movers and construction workers. These sectors are losing hundreds of thousands of (mostly male) jobs a year. It’s becoming harder and harder for men to find year round, low-paying jobs that would count against the average male wage in the statistics. Some of the men who are laid off from low paying jobs count as unemployed, but many give up on working full-time again and drop out of the labor force entirely. From 1994 to 2014, women’s labor force participation fell by 1.8%, while men’s dropped by a whopping 5.9%.

The fastest growing occupations are nurses and personal care aides (and also nursing aides and medical assistants, which is apparently a completely different occupation). These latter jobs also have a constant year-round demand. If you’re a “personal aide to a home nursing assistant” you definitely count in the fully employed statistics.

Basically, if you’re doing any sort of assisting or aiding in a medical or home setting, you have no trouble finding stable employment and your wages are slowly rising but still low. Also, you’re probably a woman, which means that you’re contributing to the gender wage gap. Shame on you.

#### So, is there sexist discrimination or not?

If that’s the question you’re still asking, you haven’t paid attention. Asking “is there discrimination or not?” is only important for recruiting soldier-arguments in support of your political position. The useful question is: “what should we do to allow men and women thrive in their jobs?” and the answer is: “it’s hard”.

My two proposals, that women choose different trade-offs and that the stats are skewed by there being less low-paying jobs for men, are just two of the myriad ways in which the desires, opportunities and paths to employment are different for each gender. The policy takeaway isn’t that there’s no discrimination so we shouldn’t do anything. The takeaway is that we should be careful about proposing solutions to issues that result from a dozen complex developments happening in parallel, until we really understand what’s going on.

Understanding this complexity and working to untangle it one piece of data at a time is the fox approach. Unfortunately, the more politically polarizing a subject is, the less patience people have for complexity, and the foxes (and Voxes) are rarely heard over the din. But we can’t make progress on a fox issue with hedgehog answers, we have to keep untangling. But it’s worth it: just look how cute these foxes are!

## Pokemonumber On It

It’s time to turn my data modeling skills to the one question that matters: how long will you need to play to catch every Pokémon?

Rob Wiblin is the research director of 80000 Hours. His writings about philanthropy, economics, and life advice are read by thousands of people. Last week, Rob tweeted:

This tweet was read by 4 million people.

Let it not be said that I can’t take a hint. I’ve written extensively about philanthropy, economics and life advice, so it’s time I switched to writing about what really matters: Pokémon. Specifically, let’s answer the main question on the nation’s mind these days: how long will it take to, in fact, catch ’em all.

This isn’t a trifling matter to be addressed by guesstimating a few numbers and tossing them in an equation. In my quest for the ultimate pokemonumber I observed the best hunters, counted every single pokemon in my own deck, sourced the wisdom of the internet, estimated a Bayesian parametric model, programmed a simulation, and braved the stormy seas of GitHub for the first time so you can play with the program yourself. And of course, it all took twice as long as it should have because I frequently had to stop writing and go on a pokewalk in my neighborhood. All in the name of research.

The first thing we know about catching ’em all is that one guy out of the 20 million Americans with Pokemon Go on their phones has indeed done so, and that 19,999,999 still haven’t. It took Nick Johnson about 100-120 hours over two weeks to complete the American pokedex. That’s high but not uniquely so, there were probably several thousand people who played as many hours and Nick turned out to be the luckiest among them.

There’s a limit to how much we can extrapolate from a single data point, but it gives us a useful edge case: our simulation should catch ’em all in as little as 100 hours about once every several thousand tries. The average result should be in the order of magnitude of several hundred hours.

To get better detail, I looked at my own play two weeks after installing the app. IGN’s wiki informs us that Pokemon Go uses 4-8 MB of cellular data per hour. I’m using LTE so my own usage is probably on the high end, let’s say 7 MB/hr. I think I play for about an hour a day so my Pokemon data usage should be around 100 MB for 14 hours of play.

Holy crap this  game is hard to put down! Ok, so that makes it 30 hours of play. During these 30 hours I have captured 502 pokemon, but I ignore about every third pokemon I see so that means that I’ve seen around 753, or 25 pokemon sightings per hour of play.

The next thing to figure out is the rarity of each specific pokemon. Here’s the best chart the internet currently has to offer:

This is a really useful chart, but there are three things missing from it:

1. It only has one pokemon from each of the 69 evolutionary lines (66 that are available on each continent). I couldn’t find information on the chances of seeing an evolved pokemon, so we’ll start by estimating how long it will take to catch one pokemon in each genus and extrapolate from there.
2. As people have commented on Reddit, the rarity of pokemon is very location-dependent. Drowzees overrun Toronto at night, but there are hardly any in Queens in daytime. The chart has zubats outside the most common category, this sounds crazy to anyone in Pittsburgh where every other pokemon is a zubat. This means that  the general structure of this chart is useful, but we won’t rely on the specific types of pokemon in each category.
3. The main thing missing from this chart is numbers. That’s where I come in.

What we need is a numerical rarity table for each pokemon. What we have is the chart above and the 753 pokemon I have meticulously recorded like Darwin on The Beagle. Our challenge lies in creating a general and broadly applicable model from very limited and specific data. The art and science of model selection consists in finding the right balance between applicability and precision, or equivalently between variance and bias, or parsimony and fit to the data.

Out of the 753 pokemon that I have seen, 37 have been pidgeys, 31 weedles and 4 ponytas. An overly specific model would say that the probability of seeing a pidgey is thus exactly 37/753 = 4.9%, for weedles it’s 4.1% and 0.53% for ponytas. This fits my observations perfectly, but it’s unlikely to generalize. A priori, it’s much likelier that I have simply lucked into more pidgeys than that Niantic programming pidgeys to show up exactly 4.9137% of the time for every player. This approach would use the data too much, and overfit the model. In model selection language, we estimate too many parameters: 66 of them if we’re picking a unique probability for each pokemon type.

On the other hand, saying that every pokemon has the same 1/66 chance of appearing is too general a model. It may be a reasonable guess ahead of time, but it doesn’t fit the data at all. The chance of seeing 10 times as many pidgeys as ponytas if they were equally likely is one in 20 million.

A balanced model tries to get close enough to the observed data, while using the least number of parameters, in accordance with Occam’s Razor. For example, we can assume that pidgeys and weedles fall in some category with other types that all have a roughly 4-5% chance of appearing, while ponyta is in another category that has a different, lower probability.

The reddit chart has 9 rarity categories plus “special”, but I’m not sure what’s special about the latter except that some of them are available as starter pokemon. We’ll stick with 9 groups. Each category has a different number of pokemon in it, and that strikes me as an unnecessary complication. I haven’t seen any of the 3 mythical pokemon yet so I’ll take the chart’s word on 6 and 3 pokemon in epic and mythical. On the everywhere side, there are 4 pokemon that show up much more often for me than any others: zubats, rattatas, drowzees and doduos. I will assume that the remaining 53 pokemon are evenly spread among the 6 categories in the middle: 9 in each (one group will have 8). That’s because there’s no reasonable amount of data the chart maker could have gathered that will show that there are exactly 7 pokemon in common and 9 in uncommon and not 8 and 8 or 9 and 7. In the absence of evidence, we should assume that the groups are equally sized to be parsimonious.

Now the tricky part: how to assign a probability to each pokemon type without “using up” too many parameters? Here, the edge cases are useful. The four everywhere pokemon account for about on third of all the ones I see, so I’ll give every pokemon in that category around 8% (1/4 of 33%). I have seen 3 of the 6 epic pokemon, so the chance that a single pokemon I come across is epic is roughly 3/753, or 0.4%, and each of the 6 epic pokemon has around .06%. Epic is 7 categories away from everywhere, and .06% * 27 ≈ 8%. Hmm. Could the per-pokemon probability in each successive category differ by a factor of 2? That would certainly be elegant, let’s see if it fits.

If each category has half the probability per pokemon as the one above it, each pokemon the virtually everywhere category will have 4% of showing up. 4% * 753 = 30, so if that’s the case I’ll expect that the 8 or 9 most common pokemon after the first 4 will show up around 30 times each. Here’s what I’ve actually seen:

 Spearow 40 Pidgey 37 Weedle 31 Caterpie 26 Voltorb 25 Krabby 20 Magnemite 18 Tentacool 15

Not perfect, but not unreasonable as an approximation. The fit gets better as I look at the other categories. For example, the common pokemon are ranked 31-39 based on rarity and I expect to see each of the common pokemon 4 times out of 753 (0.5%). Looking at my records, I have in fact seen each pokemon in places 31-39 between 3-5 times. If my model is correct, one of the three mystical pokemon will show up once every 1000 tries or so, since 3 (mystical types) * 8% * 2-8 ≈ 1/1000. The fact that I haven’t seen any in 753 tries yet fits the data. It also means that I’m frickin’ due to find one soon.

This then is my best guess at the probability distribution of pokemon of each type:

 Group name N in Group Examples (where the chart and I agree) P(each) Everywhere 4 Zubat, drowzee, pidgey 8% Virt. Everywhere 8 Oddish, weedle 4% Very Common 9 Magikarp, krabby 2% Common 9 Nidoran, clefairy 1% Uncommon 9 Geodude, jigglypuff 0.5% Rare 9 Tangela, koffing 0.25% Very Rare 9 Rhyhorn, scyther 0.125% Epic 6 Electabuzz, hitmonlee 0.063% Mystical 3 Snorlax, porygon 0.031%

I like this model: it matches both the chart and my own pokecounts, and instead of sixty six parameters we described the data using only nine: 9 categories; equal probability within each category; 4, 8, 6, 3 pokemon in some categories, 9 in the rest; 8% for the probability of each everywhere pokemon and 1/2 probability drop for each consecutive category. And wouldn’t you know it, when you add the probabilities of each pokemon appearing it all adds up to 100%.

Who’s the boss of Bayesian data analysis? I’m the boss.

(Just kidding, Andrew Gelman is the boss.)

OK, one more step to go: given the probabilities of coming across each pokemon type, how many pokemon will you see before seeing one of each? This question is too difficult for my puny brain to calculate using algebra, but it’s not too difficult for my laptop to calculate using brute force. Ladies and gentlemen, welcome to the Putanumonit simulations Github repository.

pokemon.py is a small Python program simulating Pokémon Go games. Each game consists of turns in which you see a single pokemon based on a given probability distribution. The function counts the turn on which you saw each pokemon for the first time. The sim function allows you to simulate many games and calculate aggregate statistics. Here’s what I got from running the simulation 10,000 times with the probability distribution I estimated above:

• The median number of turns before seeing each of the 66 pokemon types is 5,800, or 232 hours of play (at 25 pokemon/hour).
• The mean is higher, at 6,600 turns. That’s because the “unlucky” simulations do much worse (~20,000 turns) than the “lucky” ones do well (~2,000). The “unluckies” skew the mean upwards, but not the median.
• The quickest any of my 10,000 sims did was 1,150 turns, or 46 hours. We can assume that Nick Johnson is about 1-in-10,000 lucky himself, and it took him 100-120 hours. This means that catching all 142 distinct pokemon takes 2-3 times as long as catching just the 66 evolutionary types. This is a very rough estimate based on a single data point, but it doesn’t sound utterly unreasonable. Whatever the real ratio is, it’s probably closer to 2 or 3 than to 1.01 or to 30.
• So, my best estimate is that catching all 142 pokemon, if you aren’t as lucky as Nick, will take at least 500-700 hours, or about a year of your life if you play for 2 hours a day.
• Yes, that sounds like a lot, but what else were you really going to do with the rest of 2016-2017?
• In 65% of simulations the last pokemon caught was one of the three mysticals, and these simulations took 7,460 turns on average. In 30% the last pokemon caught was epic, these took 5,310 turns. In only 5% of the simulations the last pokemon caught was one of the 57 types that aren’t in the rarest two groups; these were the quickest games of all at 3,740 turns on average. This means that the length of the game is mostly determined by how long it takes you to catch the 3-6 pokemon that are rarest in your area. The amount of time to complete the other 60 common types in the pokedex is relatively fixed.

You can play around with the program and see how the games play out under different assumptions. You’re also welcome to comment with the data you gathered on your own hunts and other questions you want answered. From now on, this blog will forego any economical, philanthropic, political, or scientific distractions and focus exclusively on Pokémon until the madness subsides. Or until we catch ’em all.

## The Price is Always Right

In the 17th century, John Locke described an immutable law of nature regarding the prices of goods. So why do we keep raging against it in vain to this day?

Last night I dreamt that I lived in a world parallel to ours, in Old Cork City in the Stated Unions of Columbia. The Columbians are an affluent and enlightened lot, but they suffer from a very peculiar madness: they consider Newton’s laws of motion and gravity to be ethically unjust and refuse to abide by them. It is clear to every Columbian that light objects soar while heavy objects must crash to the ground. Yes, scientists at Old Cork College have repeatedly shown that feathers and a bowling ball fall at the same speed in the absence of air resistance, but Columbians figure that gravity works differently in a perfect academic setting than it does in real life.

Since it is unfair for heavy things to fly while lighter objects are earthbound, heavier than air flight is banned in the SUC. Airlines are allowed to increase the weight of their zeppelins by no more than 5% from year to year, an arbitrary number arrived at after consultation with astrologers.

There are physicists in the Stated Unions, and their journals are full of lift equations and orbit calculations. Columbians have learned to ignore their physicist’s incessant calls for airplane and rocketry development, and their admonitions that starvation will not help man to soar. It’s quite obvious that a physicist’s job is to argue over string theory and quantum interpretations, flight is a simple, common sense issue, one that the public can handle quite well without the aid of experts. A few Columbians each year diet to near starvation and then jump off cliffs hoping to fly, but their numbers are small enough not to put any politician’s career in jeopardy.

In 1903, two Columbian bicycle repairmen named Orville and Wilbur Rong built an illegal airplane in secret. From a field outside the town of Puppy Eagle the brothers soared into the cold December air. For three seconds the only sound heard was the whine of the propeller and the rush of wind on the wings. Then, the sound of gunfire filled the air as state police promptly shot the Rong Flyer from the sky. The gathered public erupted in applause at the resolute reaction of law enforcement.

In my dream, I wondered at my countrymen’s reluctance to acquiesce to the simple laws of nature. Perhaps people rebel against the idea of a system beyond any person’s design, one that doesn’t follow any person’s wishes but imposes its implacable rules on all men. Perhaps the Columbians just need more time to come to grips with Newton’s formulas. After all, they were only published as late as 1687, barely three centuries prior.

In 1695, eight years after Newton’s Principia, English philosopher John Locke published a very short essay called Venditio, concerning pricing and the ethics thereof. Wasting no time, Locke kicks off by explaining the Law of One Price in an open market (emphasis mine):

Upon demand what is the measure that ought to regulate the price for which anyone sells so as to keep it within the bounds of equity and justice, I suppose it in short to be this: the market price at the place where he sells. Whosoever keeps to that in whatever he sells I think is free from cheat, extortion and oppression, or any guilt in whatever he sells, supposing no fallacy in his wares.

To explain this a little: A man will not sell the same wheat this year under 10 Shillings per bushel which the last year he sold for 5S. This is no extortion by the above said rule, because it is this year the market price, and if he should sell under that rate he would not do a beneficial thing to the consumers, because others then would buy up his corn at this low rate and sell it again to others at the market rate, and so they make profit off his weakness and share a part of his money. […]

But if it be said ’tis unlawful to sell the same corn for 10S this week which I sold the last year for week for 5s because it is worth no more now than it was then, having no new qualities put into it to make it better, I answer it is worth no more, ’tis true, in its natural value, because it will not feed more men nor better feed them than it did last year, but yet it is worth more in its political or marchand value, as I may so call it which lies in the proportion of the quantity of wheat to the proportion of money in that place and the need of one and the other.

Locke understood that when you come to a city with many buyers and sellers, and they all sell and buy wheat from each other at 10S, the only price you can sell (or buy) wheat at is 10S. Moved by some intuition of fairness you may want to sell it at last year’s price of 5S, but you can’t. Whoever buys it for 5S will immediately resell it for 10S to those who will actually consume it, you have simply given your profit away to an unproductive third party. You may want to sell your wheat for 20S because you’re greedy, but you can’t. No one will buy for 20S what they can get next door for 10S.

A single market will have the same price across it for a single good or service. What defines a single market is a group of buyers and sellers that are easily replaced by one another. That’s why the price of wheat in a shop down the street matters: the buyer can easily go there and get that price. That also why last year’s, or even yesterday’s, price in the same shop doesn’t matter: neither the buyer nor the seller can travel to yesterday and buy yesterday’s tomatoes at yesterday’s price. The price of tomatoes on Mars is more relevant to the tomato market in London than the price of tomatoes a week before; Mars is at least in principle available to trade tomatoes with.

Like Newton’s first law, which states that an object will not change its motion unless acted upon by a force, the Law of One Price is counterintuitive for the first 10 minutes of pondering it. At that point, it becomes so deeply obvious that one is shocked at how humans have lived for millennia without grasping it. Unfortunately, 10 minutes of thought are beyond the abilities of journalists and politicians to this very day.

Burning Man tickets will be even more expensive this year thanks to a new Nevada entertainment tax that the state is requiring the festival to impose.

The price for the majority of tickets to the massive summer event in the Black Rock Desert, three hours north of Reno, has climbed from \$390 to \$424 for an individual ticket due to a 9% state tax that organizers have unsuccessfully tried to fight over the past month.

Quick, children, what’s the real price for Burning Man 2016 tickets, \$390 or \$424? The answer, of course, is that the only price of Burning Man tickets is exactly \$840, that’s the price at which they are resold to the actual festival attendees. Burning Man organizers can keep a larger or smaller chunk of the \$840 to themselves by raising or lowering the price, the state of Nevada can keep more or less of the \$840 by changing the tax, but neither of them sets the price of \$840.

Without nitpicking, let’s say that there are 70,000 tradable tickets available for Burning Man. The price of \$840 is the only one at which exactly 70,000 people want to buy a ticket. Without changing the capacity or desirability of the festival, the only thing Burning Man organizers do by moving the price is deciding how much money to donate to Stub Hub and the resellers. They could have donated that money to poor attendees by giving some of them non-transferrable free admission (they do a little of it). They could have donated that money to charity. Instead, they simply donate 70,000 * \$400 = \$28,000,000 to ticket resellers for no good reason whatsoever. Hamilton on Broadway is donating \$12,500,000 a year.

Jumping off a cliff and hoping to fly.

Of course, you may say, there are free markets and then there are hurricanes. When hurricane Sandy hit the tri-state area in 2012, many gas stations lost power and people at first were willing to pay \$20 for a gallon of gas that cost \$4 the week prior. This is such a novel and unusual situation… that John Locke described it with perfect precision 317 years prior:

To have a fuller view of this matter, let us suppose a merchant of Danzig sends two ships laden with corn, whereof the one puts into Dunkirk, where there is almost a famine for want of corn, and there he sells his wheat for 20S a bushel, whilst the other ship sells his at Ostend just by for 5s. Here it will be demanded whether it be not oppression and injustice to make such an advantage of their necessity at Dunkirk as to sell to them the same commodity at 20s per bushel which he sells for a quarter the price but twenty miles off? I answer no, because he sells at the market rate at the place where he is, but sells there no dearer to Thomas than he would to Richard. And if there he should sell for less than his corn would yield, he would only throw his profit into other men’s hands, who buying of him under the market rate would sell it again to others at the full rate it would yield. […]

Dunkirk is the market which the English merchant has carried his corn, and by reason of their necessity it proves a good one, and there he may sell his corn as it will yield at the market rate, for 20s per bushel.

Locke is correct that on a first order analysis, selling the corn (grain) at 5S in Ostend or 20S in Dunkirk are morally equivalent. If we also consider the effects of supply and demand, we can see that the ethical obligation is for the merchant to take his grain to Dunkirk, as his arrival there will help the neediest and immediately reduce wheat prices. The price of 20S is driven by the tiny supply of wheat available, even a single ship will increase that amount enough for the price to drop.

If New Jersey gas stations were allowed to sell gas at \$20, the price would have stayed at that level for at most 3 or 4 hours. That’s how long it takes to fill up a tanker in Pennsylvania or Maryland and drive to Jersey. Who would be the suckers buying at \$20 in the first few hours? Perhaps a doctor who must commute to a hospital where a single hour of her work is worth hundreds of dollars and the lives of patients.

New Jersey law prohibits “unreasonably excessive” raising of prices. In a state where fashion boutiques change the prices of jackets by 80% day to day on a whim, “unreasonably excessive” increases in the price of gas in a once-a-decade storm turned out to be 5%-10%. That number was arrived by lawyers setting precedents in courts, no one bothered to consult economists. Everyone knows that the job economists is to debate the impact of monetary policy on labor productivity in obscure journals. Prices are obviously a common sense issue that the public can handle quite well without the aid of experts.

Professor Locke, can you predict what happens when price “gouging” is capped at 5 or 10 percent:

Besides, as there can be no other measure set to a merchant’s gain but the market price where he comes, so if there were any other measure, as 5 or 10 per cent as the utmost justifiable profit, there would be no commerce in the world, and mankind would be deprived of the supply of foreign mutual conveniences of life. For the buyer, not knowing what the commodity cost the merchant to purchase and bring thither, could be under no tie of giving him the profit of 5 or 10 per cent, and so can have no other rule but of buying as cheap as he can, which turning often to the merchant’s downright loss when he comes to a bad market, if he has not the liberty on his side to sell as dear as he can when he comes to a good market. This obligation to certain loss often, without any certainty of reparation, will quickly put an end to merchandising.

What does it look it like when the “obligation to certain loss puts an end to merchandising”? It looks like a state where gas stations have gas in the ground, but no power in the grid to run the pumps. Many gas stations had generators that would power the pumps, but running the generators costs more than electricity from the grid does, and without raising prices by more than 10% that gas stations couldn’t break even while running generators. In case this isn’t clear: there is gas in the ground, there are pumps to pump the gas, there are generators to power the pumps, there are people desperate to buy the gas, there is a law that prevents them from doing so, there is someone dying in a hospital because their doctor can’t get there to help them.

But, it turns out that there weren’t enough people dying in hospitals to put governor Christie’s career in jeopardy.

A lot of people when they read The Rationality Sequences are rankled by Eliezer’s insistence that irrationality isn’t an inconsequential issue, but that almost everybody in the world is insane almost all of the time. A counterargument to Eliezer is that people have crazy beliefs when they don’t actually pay for having them. A person who disbelieves the multiple world interpretation of quantum mechanics suffers no worse harm than Eliezer’s stern disapproval. Holding crazy political views doesn’t cost a single person on the margin, since one person’s vote never counts.

The counterexample to that argument is this: they clapped.

Hurricane Fran hit North Carolina in September 1996, leaving part of the state without power in 92 degree heat. Food, baby formula and insulin were spoiling in idle refrigerators, and there was no ice to be found within 30 miles of Raleigh, NC. Fortunately, there was ice to be found 50 miles away from Raleigh in the city of Goldsboro, where four young entrepreneurs loaded two trucks with \$1.75 bags of ice and drove to Raleigh. On the way, they used chainsaws to clear the road of fallen trees for themselves and for other grateful drivers.

The trucks parked in downtown Raleigh and began selling the bags of ice at \$8 a pop, which almost no one refused to pay. As the line of Raleighites yearning for ice lengthened, the local police arrived at the scene to arrest the ice sellers and take the ice away, at gunpoint, from the people who desperately needed it, who had food and baby formula and insulin spoiling in the fridge. And many of these same people erupted in applause at the resolute reaction of law enforcement.

This morning, I woke up from my dream, and for the few seconds before I remembered I lived in New York and not Old Cork, I was smiling. Zeppelins aren’t so bad: the drinks on board are better and there’s more legroom. But when people fight the law of prices, there are no winners, only losers.

## Making the Rich Work for You

The rich are just like us, except they have more money. Should we try and grab some?

Whether you measure inequality in silly and deceitful ways, or whether you do it with emojis, economic inequality definitely exists. Some people have more of what all people want to have more of; some have less. Okay, so what?

Almost everyone agrees that economic inequality is bad. Almost nobody agrees why. Depending on whom you ask, you’ll hear that the main problem is:

1. The poor are too poor.
2. The rich are too rich.
3. What’s lacking isn’t equality of outcomes, but of opportunity, meritocracy, and social mobility.
4. It just ain’t fair.

A cynic would posit that you care about (1) if you’re poor, (2) if you’re a middle class liberal, (3) if a middle class conservative, (4) if you’re a prioritarian-egalitarian ethicist or a rhesus monkey. I’m half cynic: I’ll agree that all four issues merit discussion, and will do so from an economist-utilitarian perspective, starting with these pesky rich people.

## Grabbing your stuff

Robin Hanson probably doesn’t call himself an economist-utilitarian (abbreviated econut), but he knows more about both these topics than almost all. How does he explain the fact that so much of inequality talk is focused on the very rich?

He notes that inequality between households within a single country is much smaller than inequality between species, between humans of different eras, nations and talents, even between siblings in the same household. So why do we focus so much on it? Because we can envision successfully doing something about it, i.e. grabbing some of the money from the rich in our country and taking it for ourselves. We can’t effectively grab the money of people in a richer future, or from someone in a richer country across the world. If the rich had actual super powers that protected them from grabbers, for example if the richest group in the US were the X-Men or the Avengers, we wouldn’t rush to complain about the 1% as quickly. If the super powers of the richest 1% are things like “knowing how to consistently allocate venture capital to achieve above-market returns”, we feel safe going after their dollars.

Even if complaining about the inequality of the rich is hypocritical, it may still be useful to an economist-utilitarian. The economist side will check whether there are detrimental effects on the economy as a whole from either the concentration of money in the hands of the very rich, or the attempts to tax them. Whether there are or not, the utilitarian side will recognize that redistributing some money from the rich to everyone else may still be positive because of the diminishing marginal utility of money. Someone with a lot of dollars doesn’t get as much enjoyment out of every additional dollar – there’s only so much good soap one can use. The economist will want to make sure that the redistribution is effective, and doesn’t distort incentives in a harmful way.

Let’s put our econut hats on and see if we should try to grab some money from the rich, and if so what’s the best way to go about it.

## Do we all grow slow when the rich have mo’ dough?

Probably no. It’s easy to find people proclaiming that it’s the case that concentration of income hurts growth, but the actual case is hard to find. Forbes magazine, not normally a bastion of socialism, offers an article entitled “Increasing Inequality Hurts Economic Growth“. For evidence, the article links only to this research by the OECD. The only chart in the OECD piece with actual data (and not speculation) shows inequality rising fastest in Finland, Sweden, New Zealand, Israel and the USA, while falling in Turkey and Greece. I know which of these groups I want to be in. Even if the correlation is in the correct direction, I couldn’t find a reason why slow growth is caused by inequality rather than the other way around.

Forbes explains that “Growth happens when lots of people spend money. In the U.S., for example, the small number of people at the top of the economic ladder can’t consume and spend at the rate that the broader population can.” The rich indeed save more and spend less of their income, but their savings are (presumably) invested in productive assets like stocks and not kept in the form of a gold-coin swimming pool to dive in. Macroeconomists have debated for a century whether consumption or investment is better for the economy, it’s far from obvious that consumption is the answer. The Forbes article also claims that “The distribution of income means that there are many more in the bottom 40 percent by income than there are in the top 40 percent by income.” which is either a silly typo or an entirely new way to do math.

The Economist also chimes in and suggests a mechanism by which insufficient spending can hurt the economy:

[The] governor of the Reserve Bank of India, argued that governments often respond to inequality by easing the flow of credit to poorer households. Other recent research suggests American households borrowed heavily prior to the crisis to prop up their consumption. But for this rise in household debt, consumption would have stagnated as a result of poor wage growth. Economic eminences such as Ben Bernanke and Larry Summers argue that inequality may also contribute to the world’s “savings glut”, since the rich are less likely to spend an additional dollar than the poor. As savings pile up, interest rates fall, boosting asset prices, encouraging borrowing and making it more difficult for central banks to manage the economy.

So the rich spending less money makes it hard for central banks to respond to how non-rich people react to government policies? It’s hard to find any coherent cause or effect in that paragraph, let alone see how “inequality” is either of those. I am not an economist, but to a layman this paragraph sounds roughly like:

The CEO of Haagen Dazs argued that ice cream makers respond to inequality by making vanilla ice cream cheaper. Other research suggests that Americans ate more vanilla ice cream to prop up their sweet tooth. But for the rise in vanilla ice cream sales, consumption of ice cream would have stagnated. Ice cream eminences such as Ben and Jerry argue that inequality may also contribute to the world’s “ice cream in fridges glut” since rich people are skinnier and eat less ice cream. As sales of vanilla ice cream pile up, it makes it more difficult for Ben and Jerry’s to sell chocolate ice cream.

Maybe there’s good evidence on concentration slowing growth that my Google-fu didn’t turn up. Maybe I misunderstood the fine points of Forbes’ and Economist’s arguments because I’m not actually an economist (very different from an economist-utilitarian). But just maybe, there’s just no good reason to believe that the average does worse when the rich do better.

## The working wealthy

If letting the rich keep their money isn’t destructive, maybe taxing them is. Just for lulz, I went back to Forbes for a different article, this time arguing that taking money away from the rich people who earned it  is what hurts the economy:

When the top marginal rate was 90 percent, actor Ronald Reagan worked just half the year. As soon as he made enough money such that every additional dollar was taxed at 90 percent, he stopped working and went off to ride horses.

Before I drop my two cents on taxation and work incentives, I want to note that giving people more time to ride horses seems like a net benefit in my book.

The way Americans whose parents aren’t rich get to the 1% is with an advanced professional degree. Med school is hard and law school is risky, the path of least resistance to being rich is one of the top 50 MBA programs. Practically all of these have placement rates above 90% and starting salaries north of \$100k. All it takes to get on an MBA track is a GMAT score above 650 (roughly correlates with an IQ above 120), and ability to grind a corporate career without fucking up too bad. Basically, you need above average (but not exceptional) intelligence, ambition, grit and political acumen.

The interesting question is, what would today’s MBAs be doing in a different system, with different taxes, incentives and power structures? I know hundreds of these kinds of people from around the world, and the answer is almost certainly never “sit at home and wait for welfare”. After all, the diminishing utility of money should have roughly the same effect as a progressive tax rate (you get less and less from each dollar you earn) and yet richer Americans work more hours than anyone.

The four qualities are quite general, and by themselves leave a lot of room for vastly different career paths. In the current US economic system, they will get you a six figure income in the private sector. Countries like Israel or India are focused more on technology, so people with the above skillset study engineering instead of finance. In a country like Chile where public servants earn much more than average, you’ll find more of them in the public sector. What were smart, ambitious people who work hard and get along with bosses doing in a place like the Soviet Union? They probably joined the Communist Party and worked their way up the party ranks. In America you go into business to be able to party, in Soviet Russia…

Like electrons in a parallel circuit, people with the potential to rich the economic top will get there by whatever path offers the least resistance. If the circuit is broken (for example if a country is broke or distributes money solely based on heredity), these people will be the first to leave. Short of reverting to feudalism, changing incentives will mostly affect where talented people work (industry or country), it probably won’t make them stay home.

I’m all for shutting down the crooked ways to get rich. But that won’t eliminate great variations in wealth, because as long as you leave open the option of getting rich by creating wealth, people who want to get rich will do that instead.

Most people who get rich tend to be fairly driven. Whatever their other flaws, laziness is usually not one of them. Suppose new policies make it hard to make a fortune in finance. Does it seem plausible that the people who currently go into finance to make their fortunes will continue to do so but be content to work for ordinary salaries? The reason they go into finance is not because they love finance but because they want to get rich. If the only way left to get rich is to start startups, they’ll start startups. They’ll do well at it too, because determination is the main factor in the success of a startup. And while it would probably be a good thing for the world if people who wanted to get rich switched from playing zero-sum games to creating wealth, that would not only not eliminate great variations in wealth, but might even exacerbate them. In a zero-sum game there is at least a limit to the upside. Plus a lot of the new startups would create new technology that further accelerated variation in productivity.

Graham also notes the importance of incentives in directing where productive people choose to apply themselves. In the last three decades more and more of America’s 1% make their money in finance. I know quite a few people with truly outstanding, 1-in-10,000 mathematical talent. A disconcertingly high percentage of them work in hedge funds, where it can be argued (in great technical detail) that they contribute nothing productive to the economy, do nothing useful for the clients, and basically waste their incredible talents competing with each other in a pointless zero-sum game. They are not bad people, hedge funds just pay mathematicians more than saving humanity does.

Ok, so we can probably grab some money from the rich without destroying the economy, but we need to do it in a clever way that will not incentivize them do anything harmful. That’s one benefit of dealing with the rich: almost by definition they respond better to economic incentives than other people (*cough* Brexit *cough*).

Different tax systems have their own benefits and drawback, and a discussion of all of them will take a while. Unfortunately, I have a flight to Iceland in two hours and that discussion will have to wait until I return in two weeks. I’m sorry to leave you on a tax-policy cliffhanger, but I really need to go.

## We Are the 100 Percentiles

No table of income distribution tells the whole story, so I had to make up one.

In the previous post we saw the many ways that reports about economic inequality can mislead, either by accident or in service of a political agenda. It’s crucial to get the right numbers when writing about inequality or poverty, but it’s also important to tell an instructive story. These stories usually come in two flavors: personal tales of struggle or triumph whose scope is limited to a tiny group, or dry pamphlets full of charts and statistics with some attempt at a narrative hastily attached at the end.

Neither approach answers well the basic question: who is rich and poor in America? What kind of people actually live here, and how much do they make? Is the 57th percentile of Americans by income made up of single moms with college degrees working full-time jobs, or retired couples living off social security? For the best chance of improving income, should you marry a rich spouse or go to grad school? Does income tax hurt the rich or do they make their money from capital gains? Will minimum wage help the poor or are the poorest not working anyway? We can’t draw 318 million Americans on a chart, but we can draw 100 of them and get an idea of the actual people making up the income distribution of the US. We’ll draw them using emojis.

## Factorizing America

Like any complex phenomenon, there are a million factors correlating with income. Like any attempt to analyze a complex phenomenon, I will ignore 999,993 of them. But I won’t ignore 999,999. Any economic chart you see will divide people along a single characteristic (like gender or education), or two at most. To break a population down by 7 factors would require a 7-dimensional chart. That doesn’t fit on your favorite magazine’s two-dimensional page and it doesn’t fit your favorite magazine’s single dimensional narrative.

There is no source that breaks down income, taxes and transfers by age, gender, marital status, children, education, employment and net worth. So, I’ll have to make one. I let 100 avatars stand in for all American adults, assign them values for all 7 characteristics in a way that matches the distribution of each characteristic, and calculate how rich they are. Then, I can use my 100 avatars to get an idea of the distributions I can’t find, such as those that combine multiple factors.

For example: I know that 21% of US women have a 4-year college degree, 47% live with their spouses, 16% are in their fifties. All three of these correlate with higher earnings than average, but no source will tell me exactly how much a married 55-year-old woman with a Bachelor’s earns. In my model there are two women who fit all three conditions, they average an after-tax income of \$63,000 a year (about 1.5x the median) and are both in the 9th decile.

I don’t know how far off that \$63,000 number is from the real life average income of married, educated women in their fifties, but I’ll defend it as a reasonable guess. My 100 people are made up, but they’re made up to match as closely as possible the statistics that are available, so it’s a good bet that they match reasonably well the statistics that aren’t. This sort of educated guesswork could never be published in an economics journal, but my  goal is understanding and illumination, not citations. Without further ado, here’s the full table of 100 made up American adults who are economically distributed like 242,470,820 actual American adults for 2014.

And here’s the summary in emoji form:

 Percentile Characteristics Adjusted Income Randomized Income 1 15 👩🚶💊🎮🎅 10,340 5,185 2 59 👩💔💊📄🎅💸 9,071 5,845 3 16 👨🚶💊🎮🎅 10,829 6,309 4 46 👨💔👶📄🎅 7,848 7,185 5 56 👩💑👶🎮🎅 8,843 7,444 6 15 👨🚶💊🎮🎅 10,536 7,645 7 21 👨🚶💊📜🎅 9,559 7,701 8 17 👩🚶💊🎮🎅💵 11,610 7,787 9 46 👩💑👶👶👶👶🎮👔💵 12,796 8,036 10 31 👩💑👶👶📖🎅 8,626 8,081 11 85 👩💑💊📜🎅 17,518 9,131 12 36 👩💑💊📖🎅💵 12,428 9,223 13 35 👨💔💊📄👕💸 13,685 9,530 14 26 👩💑💊🎓🎅💸 8,949 9,627 15 23 👩💑👶📜🎅 9,441 9,746 16 33 👨🚶💊🎮👕💵 14,040 9,912 17 21 👩🚶💊📜🎅 10,731 9,934 18 28 👨💑👶👶📜👕💵 15,787 11,028 19 24 👩🚶💊🎮👕 11,300 11,504 20 19 👩🚶💊📄🎅 10,047 11,550 21 40 👩🚶👶👶👶🎮🎅💵 7,919 11,646 22 61 👨💑💊📄🎅💵 12,098 11,707 23 38 👨🚶👶👶📜👔💸 12,951 12,777 24 18 👨🚶💊📄🎅 11,317 12,903 25 20 👩🚶💊📄👔💵 16,173 12,995 26 18 👩🚶💊📄👔💵💵 25,752 13,027 27 86 👨💑💊👑🎅💵 19,349 13,268 28 34 👩💑👶👶👶📜👔💵 15,947 13,668 29 31 👨💑👶📖👔 24,910 14,065 30 53 👨💑💊🎮🎅💵 12,538 14,540 31 66 👨💔💊📄🎅💵 20,009 14,619 32 44 👩💔👶👶👶📄🎅💵💵 10,800 14,776 33 52 👩💑👶👶📄🎅💵 10,956 14,975 34 30 👨🚶💊📄🎅💵 11,512 15,021 35 49 👩💔💊📜🎅 10,243 15,146 36 23 👨🚶💊📖👔💸 15,710 15,531 37 58 👩💑💊📜👔💵 28,109 15,662 38 30 👩🚶💊📜👔💸 16,603 15,802 39 17 👨🚶💊📄👔 15,178 16,124 40 74 👩💑💊👑🎅💵💵 23,524 16,792 41 65 👩🚶💊📄🎅 17,616 17,053 42 64 👩💑👶🎓🎅💵💵 13,567 17,979 43 25 👩🚶👶📄👔💵 14,279 18,429 44 29 👩💑👶📄👕💵 14,424 18,642 45 54 👨💑💊📄👔💵 34,405 18,722 46 38 👩💔👶👶🎓👔💵 23,813 18,729 47 50 👨🚶💊📄👔💵💵 31,093 20,025 48 71 👩💑💊📄🎅 16,127 20,077 49 74 👨💑💊📄🎅 17,372 20,304 50 41 👩💑👶👶👑👕 23,932 20,356 51 83 👩💔💊📄🎅💵 19,423 20,630 52 20 👨💑👶📄👔💵 16,305 21,112 53 80 👩💔💊📖🎅💵💵 24,257 22,101 54 45 👩🚶💊📄👔💵 23,503 22,113 55 33 👩💔💊📄🎅💵💵 20,106 22,602 56 55 👨🚶💊📖👔💸 25,115 22,856 57 26 👨🚶💊📜👔 18,255 23,351 58 28 👩🚶💊📖👔💵 21,074 23,991 59 43 👨🚶💊📄👔💵💵 30,577 24,269 60 44 👨💑💊🎮👔💵 22,243 24,562 61 34 👨💑👶👶📜👔💸 21,122 25,747 62 24 👨🚶💊📄👔💵 17,891 26,069 63 48 👩💑💊🎓👔💵 46,938 28,770 64 63 👩💔💊📖👔💵 29,422 29,468 65 77 👩💑💊📄🎅💵 20,228 29,754 66 67 👩💑💊📖🎅💵💵 23,158 31,799 67 49 👨💑💊📄👔💵💵 39,023 32,864 68 59 👨💑💊📜👔💵💵💵 58,888 33,211 69 36 👨💑👶📖👔 26,962 33,620 70 72 👨💔💊📖🎅💵💵 28,651 34,230 71 58 👨🚶💊📄👔💵💵💵 60,156 35,056 72 39 👩💑💊👑👔💸 58,255 37,925 73 29 👨💔💊🎓👔💸 30,880 40,563 74 54 👩🚶💊👑👔💵💵 77,598 43,043 75 51 👩💑💊🎓👔💵💵💵 57,471 45,249 76 81 👨💔💊📜🎅💵💵💵 31,581 46,227 77 35 👩🚶💊🎓👔💸 32,560 47,088 78 40 👨💑💊🎓👔💵💵 62,077 47,200 79 25 👨💑💊🎓👔💸 36,779 47,648 80 50 👩💑👶👶👑👔💵💵💵 62,861 48,617 81 70 👨💑💊📜🎅💵💵💵 42,567 51,960 82 60 👩💑💊🎓👔💵💵💵 79,630 54,939 83 64 👨💑👶📖👔💵💵💵 49,644 55,016 84 43 👩💑💊🎓👔💸 39,430 57,697 85 73 👩💔💊📄🎅💰 95,058 59,311 86 51 👨💑💊🎓👔 59,835 67,887 87 56 👨💑👶👶🎓👔💵 47,139 69,739 88 55 👩💑💊🎓👔💵💵💵 61,539 73,034 89 69 👩💔💊🎓👔💵💵 58,647 73,826 90 60 👨💔💊🎓👔💵💵 57,876 79,235 91 39 👨💑👶👶👶👑👔💵💵💵 66,408 85,320 92 48 👨🚶💊👑👔💸 62,660 91,752 93 63 👨💑💊🎓👔💵💵 70,339 101,386 94 61 👩💑💊👑👔💰💰 176,685 108,026 95 45 👨💑👶👶👶👶👑👔💵💵💵 82,884 117,090 96 41 👨💑👶👶👑👔💵💵💵 82,893 117,525 97 88 👩💔💊📜🎅💰💰 114,590 145,687 98 77 👨💑💊🎓👔💰 149,195 161,626 99 53 👩💔👶📜👔💰💰💰 190,059 227,166 100 68 👨💑💊👑👔💰💰💰 701,586 703,604

Ok, let’s break down the breakdown and see what these numbers (and emojis) mean and how I got them.

#### Two people to a house

The US Census counts 242 million adults living in 123 million households, almost exactly 2 adults to a household on average. Most aggregate data is at the household level, so I divide household values by 2 to get the numbers for individuals. For example, according to the Congressional Budget Office the average household makes \$80,000 in market income so I adjusted the model such that each person averages \$40,000.

#### Measures of income

I calculate four components of income: (labor income) + (wealth income) + (transfers) – (taxes), to match the breakdown used by the CBO.

Labor income depends on age, gender, family status, education and employment; we’ll address each factor in turn.

Wealth income depends on net worth, more specifically – it’s 5% of each individual’s wealth. The 5% number is a surprisingly common return on capital in many different scenarios. If your wealth is in stocks, you can reasonably hope for a long-term return of 4-5% above inflation. If your wealth is in the form of a house, the median price-to-rent ratio in US cities is around 20, so you can collect 5% of the house’s value in rent each year. Conversely, if your wealth is negative (aka debt), you’ll pay about 5% in interest on mortgages, student loans and the like.

I got the distribution of net worth from the paper by Wolff 2012, tables 1 and 4. 23% of people have negative net worth and the bottom 40% average just under -\$10,000, so I gave the bottom 40 wealth amounts evenly distributed between -\$50,000 and +\$30,000. The third quintile goes from \$30,000-\$90,000, the fourth to \$300,000 and the wealthiest 5% have over a million each. I multiplied the (positive or negative) net worth of every married person by 0.75, to reconcile household numbers with individual numbers, and because sharing is caring. The average individual net worth in my table is \$355,000, consistent with \$86.8 trillion total wealth divided among 242 million people.

Emoji-wise, 💸 is for negative net worth below -\$20k, 💵 for \$20-\$99k, 💵💵 for \$100-\$299k, 💵💵💵 for \$300-\$999k, 💰 for \$1-\$2 million, 💰💰 up to \$5 million and 💰💰💰 for the two people who own more than \$5 million each.

Transfers comprise social security and the rest of welfare. I gave \$5,700 to every person over 65 and spread the rest based on number of children and distance from the poverty line. This simplification gets the model close to the actual numbers (average transfers are only \$6,700 per person, so being off isn’t a big deal) but the distribution method doesn’t accurately mirror how the government actually spreads money around to the needy.

The reason for that is that the more I studied the actual distribution of transfers in the US, the more gin and tonics I had to drink to keep my sanity. Not only is the assignment of transfers so arbitrarily complex as to be unmodelable, but it seems designed mostly to benefit lower-middle class people (21-50 percentile) at the expense of actual poor people (1-15). The third quintile by income (41-60) receive twice as much in government transfers as the bottom quintile (page 6).The bottom 15 are almost all out of the labor force (🎅), mostly unmarried (🚶, 💔), with no capability of going to college or buying a house. Policies like minimum wage, earned income tax credit, marriage tax breaks, mortgage tax breaks and college subsidies don’t help them one cent. Every policy that doesn’t help the poor ends up hurting the poor, by increasing the gap between them and the other 85%, and by blocking their social mobility and reducing their purchasing power. One of my upcoming posts will basically be a long rant about how American policies and politics are stacked against the bottom 15% to a depressing degree.

Taxes in my model are 25% of labor income plus 15% of wealth income. This doesn’t capture the monstrous complexities of the American tax system but lands the model very close to the amount of taxes actually paid by each quintile of income.

#### Factors affecting labor income

Most of the information below comes from the US Census data on families and living arrangements, and from the Census data on income and poverty. Wherever I don’t specify a source for the data, it’s one of those.

I. Age is represented as a number in each cell. I aggregated the employed Americans by age and earnings group. Earnings grow quickly in people’s twenties and thirties, reach a peak in the early fifties and decline gradually after that, perhaps because people at the highest paying jobs can afford to retire. Here’s how this income curve looks by decile, courtesy of Townhall Finance:

A U-shaped curve (upside down in our case) is a sign to try a quadratic regression, tracking how income changes with age and age squared. The regression fits very well, showing a salary increase of 5% per year of age (this describes the sharp rise for young people) and a salary decrease of 0.05% per age squared. The ratio of these coefficient is 100. What does that tell us? Above the age of 50, adding 1 year to age adds at least 100 to the square of age (51^2 – 50^2 = 101) so the negative impact of age^2 becomes stronger than the positive impact of age after 50, and earnings go down.

It’s important to note that throughout this exercise I’m using correlations, not looking for causation. I want my model to include the fact that 50-year-old people earn a lot of money, I don’t care why that is so. It’s hard to think of “age squared” as an explanatory variable, and it isn’t. It’s just a tool to account for the fact that earnings start slowly dipping past a certain point.

II. I really want to emphasize the correlations-not-explanation point when talking about gender (👩 / 👨). If you’ve seen a single income statistic in your life, it’s probably the one about women earning 79 cents on a man’s \$1. And if you’ve seen that number, you’ve seen in taken out of context in a dazzling variety of ways. Here’s the actual context: out of 242 million adults, the census counts 62 million men (about half of all men) who are employed year-round, and 46 million women (only a third). The average salary of these women is 79% that of the men. This number doesn’t control for industry, occupation, hours worked, qualification, extra-salary benefits, or the 133 million people who aren’t included in the statistic. The only thing from the above that I include in my model is education: women achieve slightly higher education attainment on average, but I also know that there are less women in business schools than in nursing schools. I decided to just use 79% as the gender adjustment for employed workers with no modification.

I am making no claim about the causes of this disparity. Maybe there’s a conspiracy of sexist men to underpay women and send them back to the kitchen. Maybe there’s a conspiracy of lazy women to mooch off their husbands. No one knows, no matter how many people claim that they do. One of my readers, herself a highly intelligent woman earning a high salary in a quantitative field, asked me to write about possible explanations for the wage gap. I can only assume that she wants to get me fired so that she can take over this blogging corner. My impression from a cursory glance at wage gap studies is that the amount of useful data is swamped by politically motivated researchers on both sides finding exactly the numbers that support their positions, time after time. I refuse to even venture close to this field, for fear of catching some nasty infection of my reasoning faculties.

III. I look at three types of marital status: married and living with your spouse (💑), never married (🚶) and everyone who was previously married but is now divorced/widowed/separated (💔). Married people tend to be older (and thus richer), so I controlled for age by looking only at the incomes of people between the ages of 35-65. Marriage rates in this age range are basically stable.

Getting hitched has little impact on the earnings of employed women: they make about 6% more than single ladies. For men, however, the effect is huge: previously married men make 74% of what cohabiting husbands do, and bachelors make less than 68%. Why? Your guess is as good as mine. OK, it’s not as good as mine: my guess is that men with a wife waiting at home find reasons to stay an extra hour or two at work and are rewarded accordingly. But your guess is probably as reasonable as mine.

IV. I used the statistics of educational attainment from the census and from Pew Research, aggregated into 6 levels: advanced degrees (👑), Bachelor’s (🎓), Associate’s (📖), some college (📜), high school diploma (📄) and no high school (🎮).

The incomes of each group relative to the median are provided by the Bureau of Labor Statistics. Instead of using ratios like I did for gender, age and marriage, I added the absolute difference of each group’s earnings to median, since each level of education opens up a new layer of available jobs. People with advanced degrees work at jobs that pay \$41,600 more than the median, Bachelor’s jobs pay \$14,820 more and jobs for high school dropout pay \$18,460 less.

V. Finally, you don’t make a labor income if you ain’t got a job (👔). 40% of Americans 15+ are out of the labor force (🎅): retirees, students and some people in between like housewives. Of the remaining 60%, about 5% are unemployed (👕) at any given time and the average unemployment duration is half a year. Since we’re looking at income over a year, I picked 6 people (10% of 60) to be unemployed based on education and family status and divided their yearly labor income by half. To be precise, I multiplied it by half. Or divided by two. You get my drift.

#### Children

The average American adult is responsible for 0.3 children, a unit of measure usually called “a dog”. I used the CBO adjustment for household size, and assumed that a cohabiting spouse takes care of half the children in the house. Long story short, if you’re raising two kids by yourself (👶👶) you have about half the effective income of someone who isn’t (💊).

#### Luck (and the other 999,992 factors)

When you try to explain real world income data with a limited set of variables, you inevitably end up with unexplained variance: all the factors behind why one person is richer than another that you didn’t account for. These can either be the variables you didn’t include (for example, I didn’t want to get into race and geography). Or, it can be the effect of random shit happening. So if I’m generating fake world data based on a limited set of variables, I also included a random-shit-happens component: multiplying the expected income by a number between 0.5 and 1.5.

To summarize: adjusted income is what each person should be making based on age, gender, family status, education and employment. Randomized income is that income, only randomized. Got it? Because these income numbers are for individuals (not households) and include wealth, transfers and taxes, they won’t look quite like what you’ll see in other tables. But, they match the macro-characteristics: the distance between the percentiles and the types of people in each one.

It’s fun (at least for me) to make up narratives about these people. Is the lady at #99 with no college degree but a decent income and a lot of wealth the widow of a millionaire? Or is she an actress who was famous in her youth and saved up some cash? Did the guy at #52 forego college because he had a kid at 19 or because he enjoys his job in a car repair shop? Is the working mother of four at #9 an immigrant in El Paso or a religious farmer in Idaho? These are 100 fake Americans, and together they’re the real America.

 Percentile Characteristics Adjusted Income Randomized Income 1 15 👩🚶💊🎮🎅 10,340 5,185 2 59 👩💔💊📄🎅💸 9,071 5,845 3 16 👨🚶💊🎮🎅 10,829 6,309 4 46 👨💔👶📄🎅 7,848 7,185 5 56 👩💑👶🎮🎅 8,843 7,444 6 15 👨🚶💊🎮🎅 10,536 7,645 7 21 👨🚶💊📜🎅 9,559 7,701 8 17 👩🚶💊🎮🎅💵 11,610 7,787 9 46 👩💑👶👶👶👶🎮👔💵 12,796 8,036 10 31 👩💑👶👶📖🎅 8,626 8,081 11 85 👩💑💊📜🎅 17,518 9,131 12 36 👩💑💊📖🎅💵 12,428 9,223 13 35 👨💔💊📄👕💸 13,685 9,530 14 26 👩💑💊🎓🎅💸 8,949 9,627 15 23 👩💑👶📜🎅 9,441 9,746 16 33 👨🚶💊🎮👕💵 14,040 9,912 17 21 👩🚶💊📜🎅 10,731 9,934 18 28 👨💑👶👶📜👕💵 15,787 11,028 19 24 👩🚶💊🎮👕 11,300 11,504 20 19 👩🚶💊📄🎅 10,047 11,550 21 40 👩🚶👶👶👶🎮🎅💵 7,919 11,646 22 61 👨💑💊📄🎅💵 12,098 11,707 23 38 👨🚶👶👶📜👔💸 12,951 12,777 24 18 👨🚶💊📄🎅 11,317 12,903 25 20 👩🚶💊📄👔💵 16,173 12,995 26 18 👩🚶💊📄👔💵💵 25,752 13,027 27 86 👨💑💊👑🎅💵 19,349 13,268 28 34 👩💑👶👶👶📜👔💵 15,947 13,668 29 31 👨💑👶📖👔 24,910 14,065 30 53 👨💑💊🎮🎅💵 12,538 14,540 31 66 👨💔💊📄🎅💵 20,009 14,619 32 44 👩💔👶👶👶📄🎅💵💵 10,800 14,776 33 52 👩💑👶👶📄🎅💵 10,956 14,975 34 30 👨🚶💊📄🎅💵 11,512 15,021 35 49 👩💔💊📜🎅 10,243 15,146 36 23 👨🚶💊📖👔💸 15,710 15,531 37 58 👩💑💊📜👔💵 28,109 15,662 38 30 👩🚶💊📜👔💸 16,603 15,802 39 17 👨🚶💊📄👔 15,178 16,124 40 74 👩💑💊👑🎅💵💵 23,524 16,792 41 65 👩🚶💊📄🎅 17,616 17,053 42 64 👩💑👶🎓🎅💵💵 13,567 17,979 43 25 👩🚶👶📄👔💵 14,279 18,429 44 29 👩💑👶📄👕💵 14,424 18,642 45 54 👨💑💊📄👔💵 34,405 18,722 46 38 👩💔👶👶🎓👔💵 23,813 18,729 47 50 👨🚶💊📄👔💵💵 31,093 20,025 48 71 👩💑💊📄🎅 16,127 20,077 49 74 👨💑💊📄🎅 17,372 20,304 50 41 👩💑👶👶👑👕 23,932 20,356 51 83 👩💔💊📄🎅💵 19,423 20,630 52 20 👨💑👶📄👔💵 16,305 21,112 53 80 👩💔💊📖🎅💵💵 24,257 22,101 54 45 👩🚶💊📄👔💵 23,503 22,113 55 33 👩💔💊📄🎅💵💵 20,106 22,602 56 55 👨🚶💊📖👔💸 25,115 22,856 57 26 👨🚶💊📜👔 18,255 23,351 58 28 👩🚶💊📖👔💵 21,074 23,991 59 43 👨🚶💊📄👔💵💵 30,577 24,269 60 44 👨💑💊🎮👔💵 22,243 24,562 61 34 👨💑👶👶📜👔💸 21,122 25,747 62 24 👨🚶💊📄👔💵 17,891 26,069 63 48 👩💑💊🎓👔💵 46,938 28,770 64 63 👩💔💊📖👔💵 29,422 29,468 65 77 👩💑💊📄🎅💵 20,228 29,754 66 67 👩💑💊📖🎅💵💵 23,158 31,799 67 49 👨💑💊📄👔💵💵 39,023 32,864 68 59 👨💑💊📜👔💵💵💵 58,888 33,211 69 36 👨💑👶📖👔 26,962 33,620 70 72 👨💔💊📖🎅💵💵 28,651 34,230 71 58 👨🚶💊📄👔💵💵💵 60,156 35,056 72 39 👩💑💊👑👔💸 58,255 37,925 73 29 👨💔💊🎓👔💸 30,880 40,563 74 54 👩🚶💊👑👔💵💵 77,598 43,043 75 51 👩💑💊🎓👔💵💵💵 57,471 45,249 76 81 👨💔💊📜🎅💵💵💵 31,581 46,227 77 35 👩🚶💊🎓👔💸 32,560 47,088 78 40 👨💑💊🎓👔💵💵 62,077 47,200 79 25 👨💑💊🎓👔💸 36,779 47,648 80 50 👩💑👶👶👑👔💵💵💵 62,861 48,617 81 70 👨💑💊📜🎅💵💵💵 42,567 51,960 82 60 👩💑💊🎓👔💵💵💵 79,630 54,939 83 64 👨💑👶📖👔💵💵💵 49,644 55,016 84 43 👩💑💊🎓👔💸 39,430 57,697 85 73 👩💔💊📄🎅💰 95,058 59,311 86 51 👨💑💊🎓👔 59,835 67,887 87 56 👨💑👶👶🎓👔💵 47,139 69,739 88 55 👩💑💊🎓👔💵💵💵 61,539 73,034 89 69 👩💔💊🎓👔💵💵 58,647 73,826 90 60 👨💔💊🎓👔💵💵 57,876 79,235 91 39 👨💑👶👶👶👑👔💵💵💵 66,408 85,320 92 48 👨🚶💊👑👔💸 62,660 91,752 93 63 👨💑💊🎓👔💵💵 70,339 101,386 94 61 👩💑💊👑👔💰💰 176,685 108,026 95 45 👨💑👶👶👶👶👑👔💵💵💵 82,884 117,090 96 41 👨💑👶👶👑👔💵💵💵 82,893 117,525 97 88 👩💔💊📜🎅💰💰 114,590 145,687 98 77 👨💑💊🎓👔💰 149,195 161,626 99 53 👩💔👶📜👔💰💰💰 190,059 227,166 100 68 👨💑💊👑👔💰💰💰 701,586 703,604