Sunday, March 25, 2012

Concentration of Wealth Simulation

I've been exploring the question of how the super-rich get so rich.  You may have heard that the top 1% controls over 35% of the wealth.  Robert Lenzner recently ran a piece in Forbes noting that the top 0.1% earn half of all capital gains income.

There are two basic ways to make money in a capitalist economy.  One way is through labor -- you can trade your time for money.  The other is through investment -- you can trade your money for more money.  There are plenty of ways to do this -- stocks, finance, hedge funds, but they all share the feature that, if you start with twice as much money, without any more work or skill you make twice as much money.

I made a simple economic simulation to see the range of possible distributions of wealth that can naturally arise from a capitalist economy.  I thought about writing it in Python and sharing the source code, but it occurred to me that now that IE9 has been out for a while, the world ought to be safe for HTML5 and computationally intensive JavaScript, so I've embedded the code for everyone to play with.  Caution: may be painfully slow on your phone.

This tool requires HTML 5. Please upgrade your browser.

Each round of the simulation, everyone spends money, then the money is divided between labor (think employees) and capital (owners/shareholders, lenders) with wages and return rates varying randomly.  Money not spent is invested so that returns to capital are distributed in proportion to wealth.  For spending, a certain amount is considered "necessity," by which I merely mean the minimum amount of spending that will be done by someone who isn't living paycheck-to-paycheck.  Luxury spending rises in proportion to wealth. 

What can you learn from a model obviously far simpler than reality?  One is that the mere fact that money can be used to make more money is sufficient to explain the sort of extreme concentration of wealth seen in our economy.  Conservatives often suggest differing degrees of talent or education as a reason for inequality; protesters in the Occupy Wall Street movement note that the rich use money to buy influence to further rig the system in their favor.  (And both claims may have some merit though neither is incorporated in my model.)  In both cases they are trying to make a moral case for or against inequality by arguing whether the wealth of the superrich is deserved.  I have more practical concerns.  I want to know whether a capitalist society that neither does anything to create inequality nor prevent its growth to extreme levels is sustainable over the long term.

The main question I wanted to answer with this model is: is inequality self-stabilizing?  That is, should we expect that, given no major changes in the economy, the super-rich will get a little richer but then stop seeing their share of the wealth grow, or is it more likely that wealth will continue to be concentrated in fewer hands if nothing fundamentally changes?  The latter case is familiar to anyone who's played Monopoly; the rich keep getting richer until there is no money left in anyone else's pocket.

What I've found is that just about any balance between capital and labor that give the top 1% 35% of the wealth will eventually give them 90% of the wealth or more.  So am I missing any important stabilizing processes? 

For decades following World War 2, tax rates on the wealthiest were kept at 90%, making it quite difficult for the rich to get richer.  As this tax rate dropped, inequality took off and it has shown no signs of stopping.  As globalization and automation shift the balance of power further toward capital at labor's expense, it's hard to see what would stop the continuing growth of inequality unless we decide once again that we will deliberately stop it.


  1. I'm not sure I entirely understand the luxuries/necessities slider. Is it the share of income that is spent on each by the actors in this simulation, or is it something else? Does the income spent on necessities stay with the poor and the income spent on luxuries transfer from the wealthy to the poor? How does this exactly work in this simulation?

    Also; on the capital-labor ratio; obviously having a higher share of income go to capital means more inequality growth. In my macro class, I learned about 3/10 of long-run output goes to capital and about 7/10 goes to labor, or wages, so I used that as my baseline.

  2. It is the share of total spending in the economy that goes to each. It does not affect who gets the money; it only affects how spending varies with wealth. If you slide it all the way to necessity, then there is a certain amount of money that everyone who can afford to spends, no one spends more and those who spend less are spending everything they have. If you slide it all the way to luxury, everyone consumes proportionally to their wealth. In between you get a linear combination of the two. I suspect this model deviates most from reality at the high end where it's approximately proportional in most cases -- I doubt that a billionaire spends at 1000 times the rate of a millionaire, but playing around with other consumption models just made it more prone to create extreme inequality (not to mention slower).

  3. Wish I had discovered this site before I coded this up! Their basic "why wealth trickles up" model is essentially the same as mine, with the consumption model being 100% luxury/0% necessity. So I'll take it as validation of my approach. But their simple consumption model, where consumption is linearly proportional to wealth, results in low inequality for realistic profit ratios -- they show an economy with 30% of earnings going to capital having a Gini coefficient of 8%, whereas the lowest Gini coefficient in the US over the past century was 38.6%. According the ecodynamics model (page 35), that happens if only 30% of returns go to labor. So it seems to get realistic results you do need to account for the fact that people with low incomes spend a higher fraction of their wealth. Which makes it seem that much more naive to me when they use their model to show that if the government forced the poor/lower middle class to spend a smaller fraction of their wealth than whatever fraction everyone else is spending, poverty would be eliminated!

    It occurs to me that a simple way to explain the percentage in my consumption model is that a percentage of 30% means anyone earning less than 30% of GDP per capita will live paycheck-to-paycheck and not accumulate wealth, whereas those making more than that will spend 30% of GDP per capita + a constant * their wealth.

  4. "There are two basic ways to make money in a capitalist economy. One way is through labor -- you can trade your time for money. The other is through investment -- you can trade your money for more money."

    There's also a third way: RENTS.

  5. This is great! Thanks for the link from CEPR. But I'm having trouble understanding it. Could you do a few bullet points on what's happening here?

    I built a (technically) less sophisticated model in excel, looking at inequality a different way. Once I've got a handle on yours I'd like to think about them in tandem, see what it teaches me.

    Would love to hear feedback.

    Have you looked at Steve Keen's Minsky modeler?

  6. You can look at the page source, specifically the doRound function. The velocity of money is fixed in this model.

    We start with 10,000 people, each with $100,000. On each step up to 5% of the money supply is spent. So if you do entirely "necessity" consumption, everyone will spend $5,000 (unless they have less than that), whereas if you do entirely "luxury" consumption, everyone will spend 5% of their wealth, whereas if you do 50/50, everyone will spend 2.5% of their wealth + $2,500. The money spent is divided into labor income and capital income. For the labor income, everyone is assigned a uniform random number between 0 and 1, which is then normalized to sum to total labor income. For capital income, everyone gets a random number times their wealth, normalized to sum to total capital income. Repeat indefinitely.

    The Minsky modeler looks neat, though for me I'm not sure I find those diagrams any more intuitive than just writing code.

    If I ever get around to it I'd love to expand this into a business cycle model along the lines of yours or Keen's. Many models, like yours, look at inequality by assuming there are two types of people. I assume there is one, and get a very broad distribution of wealth.

    Your model is very simple in the sense of having few moving parts, with the downside of having to make non-obvious assumptions about how growth and investment and other aspects of the economy work. So the result is plausible (I suspect correct) but not convincing. Personally I'd prefer a model with a production function and capital accumulation.

  7. Just wandering back around to this, don't really have time to go deeper right now but I keep thinking about it.

    I *really* like this:

    "It occurs to me that a simple way to explain the percentage in my consumption model is that a percentage of 30% means anyone earning less than 30% of GDP per capita will live paycheck-to-paycheck and not accumulate wealth, whereas those making more than that will spend 30% of GDP per capita + a constant * their wealth."

    I've always thought the standard Keynesian consumption function was crazy, not incorporating spending from wealth, only income.

    But I think the constant should actually be a function, incorporating marginal propensity to spend out of *wealth.* So two interacting functions (interacting via wealth accumulation/dis-accumulation), one relative to income, one relative to wealth.

    A sort-of aside, I much prefer the notion of marginal propensity to spend rather than marginal propensity to consume. Because people and especially businesses (which we're sort of conflating here, or just ignoring businesses, with the missing production function) can spend on goods that they will only consume over very long periods.

    It seems that MPS can work in a model if we continue to conflate households and businesses, and just assume that production produces a surplus (materialized labor?), which is monetized by the financial system (Treasury, Fed, Banks) constantly producing new financial assets ("money").

    I think Minsky has the advantage that people can see how the model's working, without parsing code. A Minsky model should be accompanied by a written explanation listing all the formulas in clearly worded form, and animations of the resulting graphs with clearly labeled axes etc.

    Sorry for the semi-randomness, just sharing some of my thinking on this.