Capital in the Twenty-First Century

by Thomas Piketty

Their farmland was not worth very much, but since they had the bright idea of owning not just the land but also the labor force needed to work that land, their total capital was even greater.

The Second Fundamental Law of Capitalism: β = s/g In the long run, the capital / income ratio β is related in a simple and transparent way to the savings rate s and the growth rate g according to the following formula: β = s/g

the overall rate of growth of national income, that is, the sum of the per capita growth rate and the population growth rate.3 In other words, for a savings rate on the

order of 10–12 percent and a growth rate of national income per capita on the order of 1.5–2 percent a year, it follows immediately that a country that has near-zero demographic growth and therefore a total growth rate close to 1.5–2 percent, as in Europe, can expect to accumulate a capital stock worth six to eight years of national income, whereas a country with demographic growth on the order of 1 percent a year and therefore a total growth rate of 2.5–3 percent, as in the United States, will accumulate a capital stock worth only three to four years of national income.

levels. It also enables us to understand why Europe tends for structural reasons to accumulate more capital than the United States (or at any rate will tend to do so as long as the US demographic growth rate remains higher than the European, which probably will not be forever). But before I can explain this phenomenon, I must make several conceptual and theoretical points more precise.

First, it is important to be clear that the second fundamental law of capitalism, β = s/g, is applicable only if certain crucial assumptions are satisfied. First, this is an asymptotic law, meaning that it

is valid only in the long run: if a country saves a proportion s of its income indefinitely, and if the rate of growth of its national income is g permanently, then its capital / income ratio will tend closer and closer to β = s/g and stabilize at that level. This won’t happen in a day, however: if a country saves a proportion s of its income for only a few years, it will not be enough to achieve a capital / income ratio of β = s/g.

Now we can understand why it took so much time for the shocks of 1914–1945 to fade away, and why it is so important to take a very long historical view when studying these questions. At the individual level, fortunes are sometimes amassed very quickly, but at the country level, the movement of the capital / income ratio described by the law β = s/g is a long-run phenomenon.

At the beginning of the 1970s, the total value of private wealth (net of debt) stood between two and three and a half years of national income in all the rich countries, on all continents.6 Forty years later, in 2010, private wealth represented between four and seven years of national income in all the countries under study.7

patrimonial capitalism.

Between 1970 and 2010, the average annual rate

of growth of per capita national income ranged from 1.6 to 2.0 percent in the eight most developed countries and more often than not remained between 1.7 and 1.9 percent. Given the imperfections of the available statistical measures (especially price indices), it is by no means certain that such small differences are statistically significant.

1970. One particularly clear case is that of Japan: with a savings rate close to 15 percent a year and a growth rate barely above 2 percent, it is hardly surprising that Japan has over the long run accumulated a capital stock worth six to seven years of national income. This is an automatic consequence of the dynamic law of accumulation, β = s/g. Similarly, it is not surprising that the United States, which saves much less than Japan and is growing faster, has a significantly lower capital / income ratio.

(to repair a hole in the roof or a pipe or to replace a worn-out automobile, computer, machine, or what have you). The difference is important, because annual capital depreciation in the developed economies is on the order of 10–15 percent of national income and absorbs nearly half of total savings, which generally run around 25–30 percent of national income, leaving net savings of 10–15 percent of national income (see Table 5.3).

Available historical sources indicate that the total value of church-owned property in eighteenth-century France

amounted to about 7–8 percent of total private wealth, or approximately 50–60 percent of national income (some of this property was confiscated and sold during the French Revolution to pay off debts incurred by the government of the Ancien Régime).17 In other words, the Catholic Church owned more property in Ancien Régime France (relative to the total private wealth of the era) than prosperous US foundations own today. It is interesting to observe that the two levels are nevertheless fairly close.

Instead of paying taxes to balance the government’s budget, the Italians—or at any rate those who had the means—lent money to the government by buying government bonds or public assets, which increased their private wealth without increasing the national wealth.

That is why, in practice, one always observes enormous variations in the ratio of the market value to the book value of individual firms. This ratio, which is also known as “Tobin’s Q” (for the economist James Tobin, who was the first to define it),

farmland is worth less than 10 percent of national income in both France and Britain.

More precisely: we find that capital’s share of income was on the order of 35–40 percent in both Britain and France in the late eighteenth century and throughout the nineteenth, before falling to 20–25 percent in the middle of the twentieth century and then rising again to 25–30 percent in the late twentieth and early twenty-first centuries (see Figures 6.1 and 6.2). This corresponds to an average rate of return on capital of around 5–6 percent in the eighteenth and nineteenth centuries, rising to 7–8 percent in the mid-twentieth century, and then falling to 4–5 percent in the late twentieth and early twenty-first centuries (see Figures 6.3 and 6.4).

FIGURE 6.3. The pure rate of return on capital

The pure rate of return to capital is roughly stable around 4–5 percent in the long run. Sources and series: see piketty.pse.ens.fr/capital21c.

Despite these caveats, my estimates for capital’s share of national income in this period (at least 40 percent) appear to be valid: in both Britain and France, the rents paid to landlords alone accounted for 20 percent of national income in the eighteenth and early nineteenth centuries, and all signs are that the return on farmland (which accounted for about half of national capital) was slightly less than the average return on capital and significantly less than the return on industrial capital, to judge by the very high level of industrial profits, especially during the first half of the nineteenth century.

It is likely that such high returns also include a nonnegligible portion of remuneration for informal entrepreneurial labor. (Similar returns are also observed in emerging economies such as China today, where growth rates are also very rapid.)

When all taxes are taken into account, the average tax rate on income from capital is currently around 30 percent in most of the rich countries. This is the primary reason for the large gap between the pure economic return on capital and the return actually accruing to individual owners.

Non-interest-bearing checking accounts currently represent only about 10–20 percent of national income, or at most 3–4 percent of total wealth (which, as readers will recall, is 500–600 percent of national income).

“nominal” rate of interest, that is, the rate of interest prior to deduction of the inflation rate, will rise to a high level, usually greater than the inflation rate. But the investor’s results depend on when the investment was made, how the parties to the transaction anticipated future inflation at that point in time, and so on: the “real”

affected by inflation. To be sure, one could argue that the transition from virtually zero inflation in the nineteenth century to 2 percent inflation in the late twentieth and early twenty-first centuries led to a slight decrease in the pure return on capital, in the sense that it is easier to be a rentier in a regime of zero inflation (where wealth accumulated in the past runs no risk of being whittled away by rising prices), whereas today’s investor must spend more time reallocating her wealth among different asset categories

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.).

The same is true if the economic system chooses to collectivize all or part of the capital stock, and in extreme cases (the Soviet Union, for example) to eliminate all private return on capital.

Too Much Capital Kills the Return on Capital

“production function,” which is a mathematical formula reflecting the technological possibilities that exist in a given society.

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.

which can be taken as a purely technological parameter.17

The Cobb-Douglas production function became very popular in economics textbooks after World War II (after being popularized by Paul Samuelson),

Contrary to a widespread idea, moreover, stability of capital’s share of national income in no way implies stability of the capital / income ratio, which can easily take on very different values at different times and in different countries, so that, in particular, there can be substantial international imbalances in the ownership of capital.

By the same token, Marxist economists liked to show that capital’s share was always increasing while wages stagnated, even if believing this sometimes required twisting the data.

From the 1990s on, however, numerous studies mention a significant increase in the share of national income in the rich countries going to profits and capital after 1970, along with the concomitant decrease in the share going to wages and labor.

The universal stability thesis thus began to be questioned, and in the 2000s several official reports published by the Organisation for Economic Cooperation and Development (OECD) and International Monetary Fund (IMF) took note of the phenomenon (a sign that the question was being taken seriously).23

existence of many opportunities to substitute capital for labor.

“Cambridge capital controversy”

First, the return to a historic regime of low growth, and in particular zero or even negative demographic growth, leads logically to the return of capital. This tendency for low-growth societies to reconstitute very large stocks of capital is expressed by the law β = s/g and can be summarized as follows: in stagnant

importance. In Europe today, the capital / income ratio has already risen to around five to six years of national income, scarcely less than the level observed in the eighteenth and nineteenth centuries and up to the eve of World War I. At the global level, it is entirely possible that the capital / income ratio will attain or even surpass this level during the twenty-first century. If the savings rate is now around 10 percent and the growth rate stabilizes at around 1.5 percent in the very long run, then the global stock of capital will logically rise to six or seven years of income. And if growth falls to 1 percent, the capital stock could rise as high as ten years of income.

The Caprices of Technology The principal lesson of this second part of the book is surely that there is no natural force that inevitably reduces the importance of capital and of income flowing from ownership of capital over the course of history.

In the decades after World War II, people began to think that the triumph of human capital over capital in the traditional sense (land, buildings, and financial capital) was a natural and irreversible process, due perhaps to technology and to purely economic forces. In fact, however, some people were already saying that political forces were central.

toward economic and technological rationality need not imply progress toward democratic an...

How much has the structure of inequality with respect to both labor and capital actually changed since the nineteenth century?

There was nothing natural or spontaneous about this process, in contrast to the optimistic predictions of Kuznets’s theory.

I begin by noting that in all societies, income inequality can be decomposed into three terms: inequality in income from labor; inequality in the ownership of capital and the income to which it gives rise; and the interaction between these two terms. Vautrin’s famous lesson to Rastignac in Balzac’s Père Goriot is perhaps the clearest introduction to these issues.

The Key Question: Work or Inheritance?