Piketty Has Two Separate Income Inequality Theories

The FT has a piece critical of Thomas Piketty's wealth data in his new book "Capital in the 21st Century." I already wrote a response to that piece in which I point out that Piketty's US wealth data is entirely consistent with newer and much-improved data from Emmanuel Saez and Gabriel Zucman. Also in response to the FT piece, Mike Konczal has a post that argues FT got Piketty's argument wrong.

Building on Konczal's piece, I want to explain Piketty's two separate arguments for why income inequality will increase in the future. And there are actually two, despite what many reviewers seem to think.

1. Capital Share Effect

Piketty's first argument (and the one Konczal writes about) is that a decline in growth will cause capital's share of the national income to increase.

1a. Capital-to-Income Ratio Will Increase

The first part of this argument is that the capital-to-income ratio will increase. It goes like this:

  1. β = s/g. The capital-to-income ratio (β), i.e. a nation's capital stock divided by its national income, moves towards the nation's savings rate (s) divided by the growth rate of the national income (g).
  2. g↓. Population growth and per-capita income growth will decline. This will cause the growth rate of the national income (g) to decline.
  3. β↑. Since β = s/g and g↓, math tells us the capital-to-income ratio (β) will increase. This assumes savings rates don't fall.

1b. The Rate of Return on Capital Will Not Decrease (Enough)

The second part of the Capital Share Effect argument is that the rate of return on capital will not decrease enough, which will cause capital's share of the national income to increase. It goes like this:

  1. α = r*β. Capital's share of the national income (α), i.e what percentage of the national income goes to capital each year, is determined by the rate of return on capital (r) multiplied by the capital-to-income ratio (β).
  2. β. Recall from above the argument that the capital-to-income ratio will increase.
  3. r→. The rate of return on capital will not decrease. Or, if it does decrease, it will not decrease enough to offset the increase in the capital-to-income ratio.
  4. α. Since α = r*β and r→ and β↑, then math tells us that capital's share of the national income (α) will increase.

1c. Capital Is Very Unevenly Distributed

The final part of the Capital Share Effect argument consists of just observing that capital is very unevenly distributed. The top 10% owns around 75% of the capital. The top 1% owns around 40% of the capital. If the share of income going to capital increases, and capital is very unevenly distributed (which it is), then that means the national income is going to become more unevenly distributed. Crucially, this argument does not rely on any r > g logic and does not require capital itself to become any more unevenly distributed than it currently is.

For example, consider a nation with a 4-to-1 capital-to-income ratio, a 5% rate of return, and 50% of the nation's capital held by the top 1%. In that nation, 20% of the national income goes to capital (4 * 5). This means, from capital income alone, 10% of the national income goes to the top 1% (20% * 50%). It's actually more than that because the wealthiest people have higher rates of return than the overall rate of return, but we can leave that point aside here.

Now suppose that nation moved to a 6-to-1 capital-to-income ratio, the rate of return stayed at 5%, and 50% of the nation's capital was still held by the top 1%. Notice, wealth inequality has not increased. In this nation, 30% of the national income goes to capital (6 * 5). This means, from capital income alone, 15% of the national income goes to the top 1% (30% * 50%).

This is the Capital Share Effect argument. It is not premised upon capital (i.e. wealth) inequality going up. It is premised upon capital's share of the national income going up.

2. Capital Concentration Effect

Piketty's second argument is that capital, and therefore capital income, will become more unevenly distributed and concentrated at the top. It deserves stressing here once again that this is a separate argument from the above one. The above one does not require capital to become more unevenly distributed for income inequality to go up. This is a different point altogether from that one. The Capital Concentration Effect argument goes like this:

  1. r > g. When the rate of return on capital (r) is higher than the growth rate of the national income (g), and savings dynamics cooperate, a nation's capital stock will tend to concentrate into fewer hands. The larger the spread between r and g is, the more forcefully this dynamic pushes towards greater capital concentration
  2. g↓. Recall from above the argument that growth will decline.
  3. r→. Recall from above that Piketty doesn't think the rate of return will decrease or, if it does decrease, that it will not decrease enough.
  4. Capital Concentration. Thus, the spread between r and g will increase. And that will push strongly towards greater concentration of the capital stock in the hands of a few.

Obviously, if capital becomes concentrated in the hands of fewer people, then that means capital income will become more unevenly distributed. This means income overall will become more unevenly distributed.

As I understand it, FT's data arguments are about whether this Capital Concentration Effect argument is consistent with the data. That's an empirical question. The best data we have (Saez-Zucman) says absolutely yes:

Conclusion

Piketty thinks both the Capital Share Effect and the Capital Concentration Effect are coming. That would mean more of the national income will go to capital (something that we've already seen happening in recent years) and that the distribution of capital income will itself become more concentrated at the top (something we've also already seen happening in recent years). The combo of these two would mean significantly more income inequality.

These are two separate arguments though. Income inequality can increase through the Capital Share Effect even if the ownership of capital does not become more concentrated. Income inequality can increase through the Capital Concentration Effect even if capital's share of the national income does not increase. These are separate things. FT's piece, at best, takes a run at the Capital Concentration Effect (though Saez-Zucman checks that argument entirely). It leaves untouched the Capital Share Effect argument. This is a common problem in treatments of Piketty (probably because of the mania surrounding r > g, which only plays a part in the Capital Concentration Effect).

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