Scalability and inequality

May 15 JDN 2459715

Why are some molecules (e.g. DNA) billions of times larger than others (e.g. H2O), but all atoms are within a much narrower range of sizes (only a few hundred)?

Why are some animals (e.g. elephants) millions of times as heavy as other (e.g. mice), but their cells are basically the same size?

Why does capital income vary so much more (factors of thousands or millions) than wages (factors of tens or hundreds)?

These three questions turn out to have much the same answer: Scalability.

Atoms are not very scalable: Adding another proton to a nucleus causes interactions with all the other protons, which makes the whole atom unstable after a hundred protons or so. But molecules, particularly organic polymers such as DNA, are tremendously scalable: You can add another piece to one end without affecting anything else in the molecule, and keep on doing that more or less forever.

Cells are not very scalable: Even with the aid of active transport mechanisms and complex cellular machinery, a cell’s functionality is still very much limited by its surface area. But animals are tremendously scalable: The same exponential growth that got you from a zygote to a mouse only needs to continue a couple years longer and it’ll get you all the way to an elephant. (A baby elephant, anyway; an adult will require a dozen or so years—remarkably comparable to humans, in fact.)

Labor income is not very scalable: There are only so many hours in a day, and the more hours you work the less productive you’ll be in each additional hour. But capital income is perfectly scalable: We can add another digit to that brokerage account with nothing more than a few milliseconds of electronic pulses, and keep doing that basically forever (due to the way integer storage works, above 2^63 it would require special coding, but it can be done; and seeing as that’s over 9 quintillion, it’s not likely to be a problem any time soon—though I am vaguely tempted to write a short story about an interplanetary corporation that gets thrown into turmoil by an integer overflow error).

This isn’t just an effect of our accounting either. Capital is scalable in a way that labor is not. When your contribution to production is owning a factory, there’s really nothing to stop you from owning another factory, and then another, and another. But when your contribution is working at a factory, you can only work so hard for so many hours.

When a phenomenon is highly scalable, it can take on a wide range of outcomes—as we see in molecules, animals, and capital income. When it’s not, it will only take on a narrow range of outcomes—as we see in atoms, cells, and labor income.

Exponential growth is also part of the story here: Animals certainly grow exponentially, and so can capital when invested; even some polymers function that way (e.g. under polymerase chain reaction). But I think the scalability is actually more important: Growing rapidly isn’t so useful if you’re going to immediately be blocked by a scalability constraint. (This actually relates to the difference between r- and K- evolutionary strategies, and offers further insight into the differences between mice and elephants.) Conversely, even if you grow slowly, given enough time, you’ll reach whatever constraint you’re up against.

Indeed, we can even say something about the probability distribution we are likely to get from random processes that are scalable or non-scalable.

A non-scalable random process will generally converge toward the familiar normal distribution, a “bell curve”:

[Image from Wikipedia: By Inductiveload – self-made, Mathematica, Inkscape, Public Domain,]

The normal distribution has most of its weight near the middle; most of the population ends up near there. This is clearly the case for labor income: Most people are middle class, while some are poor and a few are rich.

But a scalable random process will typically converge toward quite a different distribution, a Pareto distribution:

[Image from Wikipedia: By Danvildanvil – Own work, CC BY-SA 3.0,]

A Pareto distribution has most of its weight near zero, but covers an extremely wide range. Indeed it is what we call fat tailed, meaning that really extreme events occur often enough to have a meaningful effect on the average. A Pareto distribution has most of the people at the bottom, but the ones at the top are really on top.

And indeed, that’s exactly how capital income works: Most people have little or no capital income (indeed only about half of Americans and only a third(!) of Brits own any stocks at all), while a handful of hectobillionaires make utterly ludicrous amounts of money literally in their sleep.

Indeed, it turns out that income in general is pretty close to distributed normally (or maybe lognormally) for most of the income range, and then becomes very much Pareto at the top—where nearly all the income is capital income.

This fundamental difference in scalability between capital and labor underlies much of what makes income inequality so difficult to fight. Capital is scalable, and begets more capital. Labor is non-scalable, and we only have to much to give.

It would require a radically different system of capital ownership to really eliminate this gap—and, well, that’s been tried, and so far, it hasn’t worked out so well. Our best option is probably to let people continue to own whatever amounts of capital, and then tax the proceeds in order to redistribute the resulting income. That certainly has its own downsides, but they seem to be a lot more manageable than either unfettered anarcho-capitalism or totalitarian communism.

Maybe we should forgive student debt after all.

May 8 JDN 2459708

President Biden has been promising some form of student debt relief since the start of his campaign, though so far all he has actually implemented is a series of no-interest deferments and some improvements to the existing forgiveness programs. (This is still significant—it has definitely helped a lot of people with cashflow during the pandemic.) Actual forgiveness for a large segment of the population remains elusive, and if it does happen, it’s unclear how extensive it will be in either intensity (amount forgiven) or scope (who is eligible).

I personally had been fine with this; while I have a substantial loan balance myself, I also have a PhD in economics, which—theoretically—should at some point entitle me to sufficient income to repay those loans.

Moreover, until recently I had been one of the few left-wing people I know to not be terribly enthusiastic about loan forgiveness. It struck me as a poor use of those government funds, because $1.75 trillion is an awful lot of money, and college graduates are a relatively privileged population. (And yes, it is valid to consider this a question of “spending”, because the US government is the least liquidity-constrained entity on Earth. In lieu of forgiving $1.75 trillion in debt, they could borrow $1.75 trillion in debt and use it to pay for whatever they want, and their ultimate budget balance would be basically the same in each case.)

But I say all this in the past tense because Krugman’s recent column has caused me to reconsider. He gives two strong reasons why debt forgiveness may actually be a good idea.

The first is that Congress is useless. Thanks to gerrymandering and the 40% or so of our population who keeps electing Republicans no matter how crazy they get, it’s all but impossible to pass useful legislation. The pandemic relief programs were the exception that proves the rule: Somehow those managed to get through, even though in any other context it’s clear that Congress would never have approved any kind of (non-military) program that spent that much money or helped that many poor people.

Student loans are the purview of the Department of Education, which is entirely under control of the Executive Branch, and therefore, ultimately, the President of the United States. So Biden could forgive student loans by executive order and there’s very little Congress could do to stop him. Even if that $1.75 trillion could be better spent, if it wasn’t going to be anyway, we may as well use it for this.

The second is that “college graduates” is too broad a category. Usually I’m on guard for this sort of thing, but in this case I faltered, and did not notice the fallacy of composition so many labor economists were making by lumping all college grads into the same economic category. Yes, some of us are doing well, but many are not. Within-group inequality matters.

A key insight here comes from carefully analyzing the college wage premium, which is the median income of college graduates, divided by the median income of high school graduates. This is an estimate of the overall value of a college education. It’s pretty large, as a matter of fact: It amounts to something like a doubling of your income, or about $1 million over one’s whole lifespan.

From about 1980-2000, wage inequality grew about as fast as today, and the college wage premium grew even faster. So it was plausible—if not necessarily correct—to believe that the wage inequality reflected the higher income and higher productivity of college grads. But since 2000, wage inequality has continued to grow, while the college wage premium has been utterly stagnant. Thus, higher inequality can no longer (if it ever could) be explained by the effects of college education.

Now some college graduates are definitely making a lot more money—such as those who went into finance. But it turns out that most are not. As Krugman points out, the 95th percentile of male college grads has seen a 25% increase in real (inflation-adjusted) income in the last 20 years, while the median male college grad has actually seen a slight decrease. (I’m not sure why Krugman restricted to males, so I’m curious how it looks if you include women. But probably not radically different?)

I still don’t think student loan forgiveness would be the best use of that (enormous sum of) money. But if it’s what’s politically feasible, it definitely could help a lot of people. And it would be easy enough to make it more progressive, by phasing out forgiveness for graduates with higher incomes.

And hey, it would certainly help me, so maybe I shouldn’t argue too strongly against it?

Welp, I have COVID.

May 1 JDN 2459701

Tuesday night I had a fever. Wednesday morning, I tested positive.

Given how the pandemic has been going, I suppose it was more or less inevitable that this day would come. From almost the beginning, the refrain was “flatten the curve”, not “wait for a cure”. It was expected that almost all of us would get the virus eventually, and just a question of how long we could draw that out. In my case, apparently two years. For that whole time I had been scrupulous about precautions, but I did not sustain all of them all of the time, and indeed as Scotland loosened restrictions I think I became too complacent.

The good news is that I am young and reasonably healthy (migraines notwithstanding), and I had three doses of the Moderna vaccine. As a result my symptoms are relatively mild; I feel like I have a bad cold or perhaps a mild flu. Aside from the fever, which I’ve been able to keep down with NSAIDs, pretty much all my symptoms are in my sinuses. So far, I haven’t even lost my sense of taste.

It hasn’t even really interfered with my work, because my migraines were already doing a bang-up job of that. (My accent remains consistently “American broadcast standard”, but as you can see, I am gradually picking up some Britishisms, such as “bang-up job” and “sorted” with no “out”, as well as learning to put the “u” in “labour” and “behaviour”. I doubt I’ll ever start saying “aye” and “nae” though.) I am in fact even less productive than I was without COVID, but the marginal difference is relatively small. The main activity it has kept me from doing is moving and unpacking boxes (now that our shipment from California has finally arrived).

So, all things considered, if I was going to get infected with a pandemic and potentially life-threatening virus, it could have been a lot worse.