Quick Note on Piketty, Savings Rates, and Rates of Return

Earlier, I explained the way that Piketty's "r > g" (the rate of return on capital is greater than the rate of the growth in national income) is mediated through savings rates, or s. Many commentators have behaved as if they scored some point against Piketty to point out that not all capital income is saved (some if it is consumed each year) and therefore returns on investments don't all turn into new wealth. But Piketty's point regarding "r > g" does not require all capital income to be saved. So long as savings dynamics cooperate (something that's easier to do when the spread between r and g is bigger), wealth inequality will grow and grow.

One of the overlooked parts of the Saez-Zucman data that came out after Piketty's book actually addresses this very issue. For "r > g" to result in growing wealth inequalities, it has to be the case that the wealthy have somewhat higher savings rates than the non-wealthy. This seems like it would be obviously true insofar as it's easy to save a higher percentage of your income when you have a ton of it. But is it true empirically? Saez-Zucman say yes, at least in periods that are not World War II:

Though this is not necessary, it also is apparently the case that as wealth increases, so too does average rates of return:

These are the pre-tax returns. When you switch to post-tax, they are actually all smoothed out and equal. Though, in the past, taxes used to do more than even out rates of return. They actually caused rates of return to be lower for wealthier people than less wealthier people.

By putting rates of return and savings rates together, you can actually directly address the question of concentration. Is wealth growing faster at the top than the bottom? Again, Saez-Zucman says yes. From 1986-2012, the wealth of the top 1% grew at 4.9%, the wealth of the top 10% grew at 3.9%, and the wealth of the bottom 90% grew at 2.1%. In the 60 or so years prior to 1986, the reverse ordering was true: the wealth of the bottom 90% grew the fastest, then the top 10%, then the top 1%.

The most important point to take away here is the savings point reflected in the first graph. Piketty's wealth inequality divergence theory requires the wealthy to save somewhat more than the non-wealthy, and it appears that they do that pretty consistently across time.

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