Emergent Inequality, and Random Handouts · Avy Faingezicht

It does not take greed, genius, or exploitation for a society to become unequal; randomness can be enough.

Eight years ago, I wrote a quick model at a conference to simulate a thought experiment from Uri Wilensky: a closed economy of one hundred people starting with the same amount of money. At each tick everyone who still has money gives a dollar to someone else chosen at random. I liked the setup partly because it was so stripped down, and its conclusion surprising. Nobody is more talented, better connected, or more disciplined than anybody else. This world only has random movements, with a floor at zero.

And yet, even under equal starting conditions, the distribution spreads out. Some drift downward and stay near the floor for long stretches. Others accumulate more than their fair share for a while and, given enough time, wind up with surprisingly large piles. Counterintuitively, but by definition, the average never changes. Wealth in the economy is conserved, but that does not translate into symmetry or equality at the individual level. Lives diverge as contingency does its thing.

Let the simulation below run for a few thousand ticks, and see for yourself:

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No question, this is a toy model. The agents in the simulation are dumb, with no goals or strategy to achieve them. Real economies are shaped by institutions, law, culture, family structures, market power, migration, and the rest of the machinery of social life that's too complex to model well in a few hundred lines of Javascript. But toys can illuminate something small and real. Equal starting conditions are not enough to keep outcomes equal in a world that is stochastic and path-dependent, like ours.

Many conversations about inequality are confused by the simple stories we'd like to believe. In his podcast EconTalk, Russ Roberts often argues against the recurring but wrong idea of comparing snapshots of the income distribution at two points in time, and then weaving a story as though those points were the same people. In his essay "Do the Rich Capture All the Gains from Economic Growth?," he writes:

"[...] researchers look at the median income of the middle quintile in 1975 and compare that to the median income of the median quintile in 2014, say. When they find little or no change, they conclude that the average American is making no progress.

But the people in the snapshots are not the same people. You can't use two snapshots to conclude that only the rich have made progress. It's possible that everyone from the earlier snapshot has actually gotten richer and then been replaced by different people whose incomes will also rise. [...]

What the snapshots show is that the rich today are richer than the rich of yesterday. If the rich people are the same people as yesterday, then one's class determines one's fate. But if they are not the same people, the snapshots tell you that the dispersion of income has increased. That may or may not bother you, but it doesn't necessarily mean that there is a distinct group called "the rich" who are capturing all the gains while the rest of us tread water.

My little simulation above does not try to prove Roberts's broader argument. His note is way more nuanced. He includes the effects of immigration and changes in household composition on these metrics, and discusses an economy with participants who live and die, and have creative ideas, or who can decide to extract themselves and exit to other economies as the population grows and shrinks. But my toy does point in the same direction: the story is more complicated than most people think, and equality is not a stable equilibrium. Achieving equality, or starting from equality, does not mean we'll stay there. Once you allow for randomness and path dependence, it becomes much harder to treat inequality as a static picture with an obvious moral or causal interpretation.

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