Capital in the Twenty-First Century

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Thomas Piketty. 2014. Capital in the Twenty-First Century. Translated by Arthur Goldhammer. Cambridge, MA: The Belknap Press of Harvard University Press.

As John Maynard Keynes was the economist of economic depression and government stimulus, Thomas Piketty may be the economist of sluggish growth and growing economic inequality. This is the strongest argument I’ve seen against the notion that the rising tide of economic growth lifts all the boats, the yachts and the little rowboats alike. That notion has the most truth to it when the economy is growing at an exceptionally high rate. Piketty explains why it can’t work when the growth rate is reverting to a lower level. Then the income going to investors increases faster than the income going to wage earners. If the growth rate remains persistently low, the share of national income received by investors may eventually stabilize, but it will stabilize at a very high level. If left to its own devices, a capitalist economy will then tend to create a capitalist class living off of large inherited fortunes, a situation not conducive to political equality and democracy.

Piketty reaches his conclusions by studying the fundamental relationships among several economic variables: the rate of economic growth (g), the rate of return on capital (r), the savings rate (s), the share of national income going to capital (alpha), and the ratio of capital to national income (beta). At the heart of the argument is the observation that r is usually greater than g. This difference explains why people who live off of investments get a disproportionate share of national income, and also how that share will grow whenever r increases or g falls.

Some commentators have oversimplified the economics by saying that inequality automatically gets worse just because r > g, and Piketty himself makes statements that contribute to that impression. That would be true if capital always grew at the rate of return r. But as any investor should know, an investment doesn’t actually compound at the rate of return unless all returns are reinvested. If you save only some returns and spend the rest, as many investors do, then your capital actually grows less than r.  For the economy as a whole, the rate of capital expansion is not r, but a lower value that takes the national savings rate into account, and that actually approaches g if the relevant rates remain stable for a long time. The following example should clarify these dynamics.

Imagine a two-class society consisting of capitalists and workers. The capitalists get their income primarily from investments, and the workers get their income primarily from wages. Imagine that national output and income are growing at a real sustained rate of 2%, but the average rate of return on investments is 5%. Capital has the potential to grow over twice as fast as average income, but that potential isn’t normally realized because some income from capital is spent rather than reinvested. Suppose that the national savings rate is 10% of income, a rate that is five times the growth rate of national income. The growth in capital will reach a limit when amount of capital is also five times as much as annual income. At that point the savings rate of 10% of income can only add 2% to capital, since capital is 5 times income. So the growth rate of capital stabilizes at g, not r. Multiply the 5% rate of return by 5, the ratio of capital to income, and you get the share of income derived from capital (25%). But the savings rate is only 10%, so the savings added to capital each year are only 40% of the income from capital. So it makes sense that capital will actually grow at g (2%), instead of r (5%). A household living entirely from investment income needs to invest only 40% of its income to increase both its capital and its income by 2% a year.

These relationships can be summarized by two equations given by Piketty:

Capital-to-income ratio Beta = s/g = 10%/2% = 5

Capital’s share of income Alpha = r x Beta  = 5% x 5 = 25%

Now we are in a better position to see why r is normally greater than g. This difference enables some people to derive their income from capital, save and invest a portion of that income while spending the rest, and still see their income grow as fast as the general growth rate of the economy. It’s hard to see how capitalism could work if r weren’t greater than g, because then it wouldn’t pay to be a capitalist.

This example also illustrates that as long as the rates are stable and the difference between r and g is not too large, capital’s share of income is not extreme, although it is usually disproportionate to the size of the group that gets most of it. And although a superficial reading of Piketty might lead one to conclude that general inequality will keep increasing as long as r > g, the math says that capital’s share of income does approach stability as long as r, g and s are constant. What may not approach stability is the size of large inherited fortunes, since their owners can live off a small portion of the income and maintain a savings rate much higher than the national average. Their capital can grow as fast as r, or even more than that if they receive superior investment advice.

But now let’s get to the heart of Piketty’s argument by looking at what happens when the growth rate falls. Suppose that the growth rate slows from 2% to a sustained 1%. One might expect the return on capital to be cut in half as well, but that has not been the the historical experience. The rate of return r has fluctuated in a narrow range of about 4 to 5% whether economic growth g is high or low. (Maybe that’s why it’s called capitalism: the capitalists get richer more consistently than the workers!) So let’s suppose that the return on capital remains 5%, allowing capital to grow faster than income and output. If growth remains 1% for some time, the ratio of capital to income will grow from 5 to 10, and capital’s share of income will grow from 25% to 50%:

Beta = s/g = 10%/1% = 10

Alpha = r x Beta = 5% x 10 = 50%

Just a 1% decline in the growth rate has produced a huge transfer of income from labor to capital.

What Piketty establishes is that the difference between the return on capital and the growth rate is the crucial determinant of the division of income between capital and labor. The fact that r is greater than g is what makes it pay to be a capitalist. And the greater the gap between r and g, the more it pays to be a capitalist. Since r has usually varied within a narrower range than g, variations in g are more crucial. With a return on capital of 5% and a savings rate of 10%, it takes a sustained growth rate of at least 1% to keep capital from receiving over 50% of the national income. With a high growth rate, getting ahead through labor compares favorably with getting ahead through investment, but with a low growth rate, it becomes much more important to have capital to invest. With sustained growth at 0.7%, capital gets 71% of the income, and with growth of only 0.5%, capital theoretically takes all the income! (With growth below that, no equilibrium point can be calculated.)

Piketty drives the point home:

In a society where output per capita grows tenfold every generation, it is better to count on what one can earn and save from one’s own labor: the income of previous generations is so small compared with current income that the wealth accumulated by one’s parents and grandparents doesn’t amount to much….

When the rate of return on capital significantly exceeds the growth rate of the economy (as it did through much of history until the nineteenth century and as is likely to be the case again in the twenty-first century), then it logically follows that inherited wealth grows faster than output and income. People with inherited wealth need save only a portion of their income from capital to see that capital grow more quickly than the economy as a whole. Under such conditions, it is almost inevitable that inherited wealth will dominate wealth amassed from a lifetime’s labor by a wide margin, and the concentration of capital will attain extremely high levels— levels potentially incompatible with the meritocratic values and principles of social justice fundamental to modern democratic societies.

Are there any natural economic limits on the gap between r and g, or can it increase until the lion’s share of the national income goes to capital? One limit could be that as capital accumulation becomes too extreme, the rate of return on capital has to come down a bit. It becomes too hard to invest all that capital productively in a slow-growth economy, and imprudent investments just produce asset bubbles that eventually burst (sound familiar?). Decline in g may be offset partly by decline in r, so that capital’s share of income doesn’t increase as much as if r were constant. In the previous example, if the return on capital falls to 4% (with g = 1%), capital’s share of income becomes 40% instead of 50%. But in practice, fluctuations in r are not usually enough to keep fluctuations in g from producing substantial redistributions of income.

Piketty believes that limits on economic inequality have to come primarily from noneconomic factors, either through unwanted “shocks” to capital like war, or deliberate public policies like progressive taxation. For most of capitalism’s history, the growth rate has not been high enough to prevent capitalists from hogging a large share of the income and accumulating vast fortunes. The biggest exception was during the postwar economic boom, fueled both by recovery from a period of depression and war and by a baby boom. Piketty expects economic growth in the twenty-first century to be much lower. His projection is for 1.2% per-capita growth in the richest countries (with population growth providing a small but declining boost to output in some countries). Capital’s share of income, which was in the range of 15-25% for rich countries in 1970, has already increased to 25-30%, and would be expected to rise to at least 40% if growth remains this low. To make matters worse, disparities in pay between top managers and ordinary workers have risen to unprecedented levels, and taxes have declined on high incomes and estates, with the US leading both these trends. Welcome to the twenty-first century!

Piketty’s book has already started a global conversation, and may well frame the debate over economics and public policy for years to come.


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