Capital in the Twenty-First Century

by Thomas Piketty

The law also affects stock market prices, as I noted when I discussed why stock prices in Germany are relatively low.

The market value of a company listed on the stock exchange is its stock market capitalization.

The accounting value of a firm, also called book value or net assets or own capital, is equal to the accumulated value of all assets—buildings, infrastructure, machinery, patents, majority or minority stakes in subsidiaries and other firms, vault cash, and so on—included in the firm’s balance sheet, less the total of all outstanding debt.

From a theoretical point of view, there is nothing that guarantees long-term stability of the value of land, much less of all natural resources. I will come back to this point when I analyze the dynamics of wealth and foreign asset holdings in the petroleum exporting countries.35

When a firm buys its own shares, it enables its shareholders to realize capital gains, which will generally be taxed less heavily than if the firm had used the same sum of money to distribute dividends. It is important to realize that the same is true when a firm buys the stock of other firms, so that overall the business sector allows the individual sector to realize capital gains by purchasing financial instruments.

We find that the general evolution of capital’s share of income, α, is described by the same U-shaped curve as the capital / income ratio, β, although the depth of the U is less pronounced. In other words, the rate of return on capital, r, seems to have attenuated the evolution of the quantity of capital, β: r is higher in periods when β is lower, and vice versa, which seems natural.

The overall curve and the orders of magnitude described here may be taken as reliable and significant, at least to a first approximation. Nevertheless, the limitations and weaknesses of the data should be noted immediately. First, as noted, the very notion of an “average” rate of return on capital is a fairly abstract construct. In practice, the rate of return varies widely with the type of asset, as well as with the size of individual fortunes (it is generally easier to obtain a good return if one begins with a large stock of capital), and this tends to amplify inequalities.

Obviously some people earn more than the average return and others less. Before looking at the distribution of individual returns around the mean, it is natural to begin by analyzing the location of the mean.

In classic novels of the early nineteenth century, such as those of Balzac and Jane Austen, the equivalence between capital and rent at a rate of 5 percent (or more rarely 4 percent) is taken for granted. Novelists frequently failed to mention the nature of the capital and generally treated land and public debt as almost perfect substitutes, mentioning only the yield in rent.

With real assets, everything is different. The price of real estate, like the price of shares of stock or parts of a company or investments in a mutual fund, generally rises at least as rapidly as the consumer price index. In other words, not only must we not subtract inflation from the annual rents or dividends received on such assets, but we often need to add to the annual return the capital gains earned when the asset is sold (or subtract the capital loss, as the case may be).

the potential impact of inflation on the average return on capital is fairly limited and much smaller than the apparent nominal effect.

According to the simplest economic models, assuming “pure and perfect” competition in both capital and labor markets, the rate of return on capital should be exactly equal to the “marginal productivity” of capital (that is, the additional output due to one additional unit of capital). In more complex models, which are also more realistic, the rate of return on capital also depends on the relative bargaining power of the various parties involved. Depending on the situation, it may be higher or lower than the marginal productivity of capital (especially since this quantity is not always precisely measurable).

Technology naturally plays a key role. If capital is of no use as a factor of production, then by definition its marginal productivity is zero. In the abstract, one can easily imagine a society in which capital is of no use in the production process: no investment can increase the productivity of farmland, no tool or machine can increase output, and having a roof over one’s head adds nothing to well-being compared with sleeping outdoors.

In the abstract, nothing prevents us from imagining a society in which the capital / income ratio β is quite high but the return on capital r is strictly zero. In that case, the share of capital in national income, α = r × β, would also be zero. In such a society, all of national income and output would go to labor.

In all civilizations, capital fulfills two economic functions: first, it provides housing (more precisely, capital produces “housing services,” whose value is measured by the equivalent rental value of dwellings, defined as the increment of well-being due to sleeping and living under a roof rather than outside), and second, it serves as a factor of production in producing other goods and services (in processes of production that may require land, tools, buildings, offices, machinery, infrastructure, patents, etc.).

In a more complex economy, where there are many more diverse uses of capital—one can invest 100 euros not only in farming but also in housing or in an industrial or service firm—the marginal productivity of capital may be difficult to determine.

A capital market is said to be “perfect” if it enables each unit of capital to be invested in the most productive way possible and to earn the maximal marginal product the economy allows, if possible as part of a perfectly diversified investment portfolio in order to earn the average return risk-free while at the same time minimizing intermediation costs.

To be sure, it is not a simple task to find the best possible use for each unit of capital around the world, or even within the borders of a single country.

What is more, “short-termism” and “creative accounting” are sometimes the shortest path to maximizing the immediate private return on capital.

It is important to state clearly that the notion of marginal productivity of capital is defined independently of the institutions and rules—or absence of rules—that define the capital-labor split in a given society.

Too much capital kills the return on capital: whatever the rules and institutions that structure the capital-labor split may be, it is natural to expect that the marginal productivity of capital decreases as the stock of capital increases.

Conversely, in a country where an enormous population must share a limited supply of land, scarce housing, and a small supply of tools, then the marginal product of an additional unit of capital will naturally be quite high, and the fortunate owners of that capital will not fail to take advantage of this.

The evolution of the rate of return on capital, r, significantly reduces the amplitude of this U-curve, however: the return on capital was particularly high after World War II, when capital was scarce, in keeping with the principle of decreasing marginal productivity. But this effect was not strong enough to invert the U-curve of the capital / income ratio, β, and transform it into an inverted U-curve for the capital share α.

Everything depends on the vagaries of technology, or more precisely, everything depends on the range of technologies available to combine capital and labor to produce the various types of goods and services that society wants to consume.

One characteristic of a production function is that it defines an elasticity of substitution between capital and labor: that is, it measures how easy it is to substitute capital for labor, or labor for capital, to produce required goods and services.

if the coefficients of the production function are completely fixed, then the elasticity of substitution is zero: it takes exactly one hectare and one tool per agricultural worker (or one machine per industrial worker), neither more nor less. If each worker has as little as 1/100 hectare too much or one tool too many, the marginal productivity of the additional capital will be zero.

Similarly, if the number of workers is one too many for the available capital stock, the extra worker cannot be p...

Conversely, if the elasticity of substitution is infinite, the marginal productivity of capital (and labor) is totally independent of the a...

Think of an entirely robotized economy in which one can increase production at will simply by adding more capital. Neither of these two extreme cases is really relevant: the first sins by want of imagination and the second by excess of technological optimism (or pessimism about the human race, depending on one’s point of view). The relevant question is whether the elasticity of substitution between labor and capital is greater or less than one. If the elasticity lies between zero and one, then an increase in the capital / income ratio β leads to a decrease in the marginal productivity of capital large enough that the capital share α = r × β decreases (assuming that the return on capital is determined by its marginal productivity).

This is perhaps the most important lesson of this study thus far: modern technology still uses a great deal of capital, and even more important, because capital has many uses, one can accumulate enormous amounts of it without reducing its return to zero. Under these conditions, there is no reason why capital’s share must decrease over the very long run, even if technology changes in a way that is relatively favorable to labor.

Some people think that capital has lost its importance and that we have magically gone from a civilization based on capital, inheritance, and kinship to one based on human capital and talent. Fat-cat stockholders have supposedly been replaced by talented managers thanks solely to changes in technology.

Marx did not use mathematical models, and his prose was not always limpid, so it is difficult to be sure what he had in mind. But one logically consistent way of interpreting his thought is to consider the dynamic law β = s/g in the special case where the growth rate g is zero or very close to zero.

If the savings rate s is positive, meaning the capitalists insist on accumulating more and more capital every year in order to increase their power and perpetuate their advantages or simply because their standard of living is already so high, then the capital / income ratio will increase indefinitely. More generally, if g is close to zero, the long-term capital / income ratio β = s/g tends toward infinity. And if β is extremely large, then the return on capital r must get smaller and smaller and closer and closer to zero, or else capital’s share of income, α = r × β, will ultimately devour all of national income.

Only permanent growth of productivity and population can compensate for the permanent addition of new units of capital, as the law β = s/g makes clear.

To be sure, the law β = s/g describes a growth path in which all macroeconomic quantities—capital stock, income and output flows—progress at the same pace over the long run.

As noted, it is also possible that technological changes over the very long run will slightly favor human labor over capital, thus lowering the return on capital and the capital share. But the size of this long-term effect seems limited, and it is possible that it will be more than compensated by other forces tending in the opposite direction, such as the creation of increasingly sophisticated systems of financial intermediation and international competition for capital.

My results fully confirm this view. Progress toward economic and technological rationality need not imply progress toward democratic and meritocratic rationality. The primary reason for this is simple: technology, like the market, has neither limits nor morality. The evolution of technology has certainly increased the need for human skills and competence. But it has also increased the need for buildings, homes, offices, equipment of all kinds, patents, and so on, so that in the end the total value of all these forms of nonhuman capital (real estate, business capital, industrial capital, financial capital) has increased almost as rapidly as total income from labor.

To sum up: modern growth, which is based on the growth of productivity and the diffusion of knowledge, has made it possible to avoid the apocalypse predicted by Marx and to balance the process of capital accumulation. But it has not altered the deep structures of capital—or at any rate has not truly reduced the macroeconomic importance of capital relative to labor.

The fact that Europe—and to some extent the entire world—have only just gotten over these shocks has given rise to the impression that patrimonial capitalism—which is flourishing in these early years of the twenty-first century—is something new, whereas it is in large part a repetition of the past and characteristic of a low-growth environment like the nineteenth century.

Many people believe that modern growth naturally favors labor over inheritance and competence over birth. What is the source of this widespread belief, and how sure can we be that it is correct?

In the case of unequal incomes from capital, the most important processes involve savings and investment behavior, laws governing gift-giving and inheritance, and the operation of real estate and financial markets. The statistical measures of income inequality that one finds in the writings of economists as well as in public debate are all too often synthetic indices, such as the Gini coefficient, which mix very different things, such as inequality with respect to labor and capital, so that it is impossible to distinguish clearly among the multiple dimensions of inequality and the various mechanisms at work.

Inequalities with respect to labor usually seem mild, moderate, and almost reasonable (to the extent that inequality can be reasonable—this point should not be overstated). In comparison, inequalities with respect to capital are always extreme.

I should also make it clear that the hierarchies (and therefore centiles and deciles) of income are not the same as those of wealth. The top 10 percent or bottom 50 percent of the labor income distribution are not the same people who constitute the top 10 percent or bottom 50 percent of the wealth distribution. The “1 percent” who earn the most are not the same as the “1 percent” who own the most.

In traditional societies, the correlation between the two dimensions was often negative (because people with large fortunes did not work and were therefore at the bottom of the labor income hierarchy). In modern societies, the correlation is generally positive but never perfect (the coefficient of correlation is always less than one). For example, many people belong to the upper class in terms of labor income but to the lower class in terms of wealth, and vice versa. Social inequality is multidimensional, just like political conflict.

In countries where income from labor is most equally distributed, such as the Scandinavian countries between 1970 and 1990, the top 10 percent of earners receive about 20 percent of total wages and the bottom 50 percent about 35 percent.

The inescapable reality is this: wealth is so concentrated that a large segment of society is virtually unaware of its existence, so that some people imagine that it belongs to surreal or mysterious entities. That is why it is so essential to study capital and its distribution in a methodical, systematic way.

Housing is the favorite investment of the middle class and moderately well-to-do, but true wealth always consists primarily of financial and business assets.

Indices often obscure the fact that there are anomalies or inconsistencies in the underlying data, or that data from other countries or other periods are not directly comparable (because, for example, the tops of the distribution have been truncated or because income from capital is omitted for some countries but not others). Working with distribution tables forces us to be more consistent and transparent.

Socioeconomic inequalities—disparities of income and wealth between social groups—are always both causes and effects of other developments in other spheres. All these dimensions of analysis are inextricably intertwined. Hence the history of the distribution of wealth is one way of interpreting a country’s history more generally.

Although this is a matter of degree, it is nevertheless important: there are moments when the quantitative becomes qualitative. This change also explains why the share of income going to the upper centile today is barely higher than the upper centile’s share of total wages: income from capital assumes decisive importance only in the top thousandth or top ten-thousandth. Its influence in the top centile as a whole is relatively insignificant.