On inequality of wealth

Note: Non-sports post.

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In the United States, the top 10% of the population earns 30% of the income. And the top 10% of the population owns 70% of the wealth.

Statistics like these seem to be popping up all over the place lately ... someone I know posted one on Facebook a few days ago, and there was a newspaper article or two in the last month. I'm not sure what happened to bring all this up. (If anyone has links from the last week or two, let me know. I can't find them at the moment.)

A couple of years ago, taking about the Gini Coefficient, I made a bunch of arguments about why the distribution of income doesn't matter much. I think it matters a bit, but not much.

Here, I'm going to concentrate on the distribution of *wealth*. For wealth, I'm going to argue that, given a particular distribution of income, the distribution of wealth is almost completely meaningless as a moral issue, or an issue of people's well being. That is: criticize, if you want, the fact that the top 10% get 30% of the income. But given that income distribution, *it doesn't matter* how much of the wealth the top 10% own: whether it's 10%, 30%, 70%, or 99%.

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The difference between income and wealth is that income is a rate, how much you earn in a particular year. Wealth is the total amount that you possess at a specific time.

How does anyone gain wealth? Other than inheritance (which we'll disregard here), you have to save or invest some of your income. You can earn ten million dollars one year, but if you blow it all on cocaine and hookers, your wealth will be zero.

So your wealth is a result of three things: (1) your income, (2) the amount you save, and (3) rate of return on the amount you save. As I said, if you hold (1) as fixed, wealth is affected by only (2) and (3).

Suppose you have two people, John and Mary. They have exactly the same education, and they graduate into exactly the same job, paying $50,000 a year. John spends all his money every year. Mary saves an annual $6,000 in a retirement fund, earning 5%, and spends the rest.

What happens? After 40 years, John has $0 in wealth. Mary has $725,000.

Is it fair to complain about that? I don't think so. Sure, Mary is now (fairly) wealthy while John has to live on just Social Security. But, in the past, John lived much better than Mary, to the tune of $240,000 -- $6,000 a year for 40 years. Some people's tendency would be to take some of Mary's money and give it to John. But that wouldn't be fair. It would actually be quite an injustice. Mary deliberately lived significantly worse than John for 40 years, just so she could have a better retirement. Giving that money to John would *compound* the inequality, wouldn't it? It would take from the (formerly) poor lifestyle and give to the (formerly) rich lifestyle. It would compensate for the future where Mary spends more than John, but not compensate for the past, when John spent more than Mary.

Really, even though Mary has more money than John, over their lifetimes, they're equal. Thirty-five years ago, John spent $4,000 on a new state-of-the-art TV. He knew, when he bought the TV, that $4,000 then would be the equivalent of $22,000 at retirement. He bought the TV anyway. Nothing wrong with that. He chose, freely, to live $4,000 richer than Mary back then, in exchange for living $22,000 poorer than Mary later. Mary also knew the terms of the trade, and made the other choice.

But, over their lifetime, they are exactly equal. $4,000 can buy a lot of things: a vacation, a TV, a boat, a motorcycle, or a retirement fund of $22,000. If John had bought a TV, and Mary had bought a boat, could anyone argue that Mary is richer than John because she has a boat? Of course not -- because, by the same token, John has a TV of equal value.

The same thing applies here: if John has a TV that costs $4,000, and Mary has a $22,000 retirement fund, which also costs $4,000 ... they must be equally rich, right?

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When you talk about the distribution of wealth, what you're really talking about, for the most part, is the distribution of a desire to save. And there is no "proper" distribution for that, any more than there's a "proper" distribution of religious beliefs. People are diverse, and they have different tendencies. Some people like to spend, and some people are compulsive savers. Humans choose differently from each other.

Suppose the 1% of the population that owns the most rare baseball cards happens to own 70% of the rare baseball cards. It just means that the other 99% don't care as much about baseball cards. If they have the same income, they just own more other things instead.

Now, you can still argue that the reason it's a problem that the top 10% has 70% of the wealth is that the bottom 90% doesn't earn enough money to be able to save. But that argument is better made by arguing about the *income* distribution. Because, otherwise, you're combining two issues: having money, and choosing to save it. If you were to complain that the top 1% own 70% of the baseball cards *because they have a higher income*, you'd be mostly wrong. Yes, the top 1% of baseball card owners probably DO have a higher income. But that's not the main reason they own 70% of the baseball cards. The *main* reason they own 70% of the baseball cards is because they really, really like baseball cards.

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Here's a model, for a numerical example.

Start by assuming a population of 10,000 people. They all have exactly the same education, and they all graduate at age 25 into a job that pays $40,000 a year. They work until they're 65, at which point we measure their wealth.

But they're not all the same, because they have different personalities, and characteristics, and desires. Specifically:

1. They vary in how much money they like to spend. The mean of the population is to spend 90% of their salary and save 10%, but with a standard deviation of 15 points. Nobody saves more than 50% of their salary, or spends more than 115%.

2. They vary in how many children they want, and when. 20% of them want no kids. 20% of them want one kid early in life (age 27), and 20% want one kid later in life (age 35). 20% of them want two kids early, and 20% want two kids late. Kids cost $5,000 a year in expenses to age 18, and then $20,000 annually for the next four years, all of which comes out of saving.

3. They vary in how good they are at investing their money. Some play it safe, and some are more aggressive. Some study investing, and some don't. The average annual return is 4%, with an SD of 1.5 percentage points.

4. They vary in how much effort they put into their job, which affects their annual salary increases. The mean increase is 2% a year, with a standard deviation of 0.5%. Nobody ever gets fired or earns less than $40,000.

5. Nobody goes into debt more than $50,000. Once they reach $50,000, they cut their spending to keep the debt at $50K. All debt is paid off in the year before retirement. Debt earns interest of 10%.

Under these conditions, I ran a random simulation of the 10,000 people.

So, at age 65, what percentage of total wealth will the top 10% own? Take a guess before reading on. I'll write it cryptically so you don't see it by accident when you're thinking.

Ready?

The top 10% of these graduates own (7 * 9 - 22)% of the total wealth.

Got that? It's not as big as the real-life answer of 70%, but it's pretty big nonetheless. And it's *completely* due to the decisions of the individuals themselves. There is no inequality, no racism, no bad schools, no corruption, no government favors, no explotation by greedy employers. It's just natural variation in how human beings choose to live their lives.

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Some of the other results:

The top 1% had 7% of the wealth.

The top 10% had 41% of the wealth.

The top 50% had 99% of the wealth.

As you would expect, the wealthiest people were the ones who saved the most and got the highest rates of return. The wealthiest, person number 7,490, wound up with just over $4,000,000 in wealth. She saved 41% of her salary and earned 8.3% per annum. In case you think 41% is a lot ... it's not, really. There are a lot of misers in the world. At retirement, this person earned $55,551, which means she was living on around $33,000 per year. That's not unreasonable for an outlier, just over 2 SD from the mean.

Overall, it turned out that number and timing of children didn't matter much. Neither did salary (although the salaries were all pretty close). Some of the richest people earned below-average salary increases.

So what mattered is how much they saved, and how well they invested it. Of course, my model is way oversimplified, but that does correspond to my perception of how wealth happens in real life, where my sample of friends earns around the same as I do.

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One thing I should note is how the "top 1%" figure of 7% is way, way off the real life figure of 38%. Why is that? Well, the main reason is probably that the model didn't consider the possibility of enterpreneurs who can occasionally create a multi-billion-dollar company out of nothing. If Bill Gates and Warren Buffett were in the model, the figure would jump substantially from 7%.

What's more surprising, I think, is that the top 10% number was so high, at 41%. I expected it to be much lower, considering that there's so much less variation here than in the real model:

1. Here, everyone had roughly the same income, between $40,000 and $60,000. Real life, on the other hand, includes sports stars, CEOs, and other people with high productivity.

2. Here, everyone was 65. Older people are obviously wealthier, since they've had much more time to earn and save. If you take these 10,000 retired people, and combine them with 10,000 babies, then the distribution is much more unequal, since you've added a bunch of zeroes. Then, the top 10% jump to from 41% of the wealth to 64%.

The age thing is a big issue. Even if everyone were exactly equal in every way, following the same career path and the same wealth accumulation path, the distribution would be unequal if you take a snapshot in time. You'd be combining 65 year olds who are rich because they've been saving, to 25 year olds who WILL be just as rich, but aren't yet. (That, by the way, is why it's best to look at lifetime income, or at least age-adjusted income, instead of snapshot income or snapshot wealth.)

Oh, and by the way ... I built a certain amount of progressive taxation into the model. I assumed all salary above $40K is taxed at 30%. I also assumed that the savings rate is based on after-tax salary. And finally, I assumed that if you save more than 30% of your after-tax salary, any excess is taxed *again* at 30%. (This was easier than trying to compute tax on investment income.) The numbers above are *after* all this progressive taxation.

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So, my argument boils down to something like this (directed at a random skeptic):

You say that the top 10% owns 70% of the wealth, and that's too much. Why is that too much? It can't be just inequality, because here I have a model where everyone is equal, and the top 10% still owns more than 41%. Why do you think 70% is wrong, and what should the number be, and what are your assumptions?

And suppose I cornered you, and asked you to tell me exactly what your policy prescriptions are -- how much to tax the rich, what to do with the money, how to tax investment income, what loopholes to close, how to get the poor to save more, and so on. Then I would ask you, "after all that, how much of the wealth would the top 1% own?"

I'd bet you couldn't answer that. And if you don't know what the distribution of wealth would be in your ideal world, how can you possibly argue that it's the wrong number now?