April 14th, 2010

Beem-Ur the Destructor


I asserted on a friend's Facebook status today that flat taxes are a bad idea for anyone except the very rich, because income has a power-law distribution, so if you want to maintain the same level of revenue (and you do*), if you switch from our current progressive tax-bracket system to a comparatively regressive flat tax system, tax rates go up for everyone except those out in the high-income tail.

(*Revenue can't drop because only about 5% of the federal budget is what you'd call discretionary; the vast bulk of it goes to things like medicare and national defense, which have not, historically, been especially popular areas to make drastic cuts in spending. See http://washingtonindependent.com/81684/the-futility-of-budget-cuts for some lovely graphs.)

So, of course, having said that, I then had to go and prove to myself that I was right. And I am (yay dinking about with spreadsheets!), but the nifty thing is that I found a very interesting paper on Temporal evolution of the “thermal” and “superthermal” income classes in the USA during 1983–2001.

What it shows is that only the top 3% of individual incomes follow a Pareto (power-law) distribution; the other 97% follow a Boltzmann-Gibbs (exponential) distribution. The exponential bulk is in thermal equilibrium (if you correct for inflation), while the power-law tail is "superthermal" and fluctuates with the stock market. There's a cutoff point (about 4 times the normalized "income temperature") where the distribution switches over; in 2001 it was around $150k.

Which is all quite fascinating, but what does it mean? There must be some reason why the rules are different for part of the populace than they are for the other part; it's not as if you were making $149k and got a $2k raise that your bank account would suddenly magically work differently. So I was pondering this, and I think I came up with an answer.

It has to do with where your money comes from.

Most people's income derives from wages, or something equivalent: there's some thing that you do, and other people give you money for doing it. But! If you have a lot of money, enough that you have a decent pile of it sitting around after you've paid all your bills, you can invest it, and get more of it just for having it. And investment is a positive feedback loop: the more you've got, the faster it grows. Take a bunch of investments, apply exponential growth and some noise, and quite naturally you will get a power-law distribution.

Basically everyone who can invest money does so, and there's only so much you can increase your cost of living as your income increases. So as people get more wage-type income, pretty universally they'll start to get investment income as well, and eventually that can grow to matter more than wages. Which means that 4*T = $150k crossover point isn't anything special, it's just the statistical average of the point where any individual's investments start to dominate the kinetics of his income stream.

So I thought that was interesting. It has significant implications for how a society should structure its tax code to achieve various goals. And I'm psyched that I was able to figure it out.