Capital in the Twenty-First Century

by Thomas Piketty

  Make no mistake: I am obviously not denying that inflation can in some cases have real effects on wealth, the return on wealth, and the distribution of wealth. The effect, however, is largely one of redistributing wealth among asset categories rather than a long-term structural effect. For example, I showed earlier that inflation played a central role in virtually wiping out the value of public debt in the rich countries in the wake of the two world wars. But when inflation remains high for a considerable period of time, investors will try to protect themselves by investing in real assets. There is every reason to believe that the largest fortunes are often those that are best indexed and most diversified over the long run, while smaller fortunes—typically checking or savings accounts—are the most seriously 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 in order to achieve the best investment strategy. Again, however, there is no certainty that the largest fortunes are the ones most affected by inflation or that relying on inflation to reduce the influence of wealth accumulated in the past is the best way of attaining that goal. I will come back to this key question in the next Part Three, when I turn to the way the effective returns obtained by different investors vary with size of fortune, and in Part Four, when I compare the various institutions and policies that may influence the distribution of wealth, including primarily taxes and inflation. At this stage, let me note simply that inflation primarily plays a role—sometimes desirable, sometimes not—in redistributing wealth among those who have it. In any case, the potential impact of inflation on the average return on capital is fairly limited and much smaller than the apparent nominal effect.13

  What Is Capital Used For?

  Using the best available historical data, I have shown how the return on capital evolved over time. I will now try to explain the changes observed. How is the rate of return on capital determined in a particular society at a particular point in time? What are the main social and economic forces at work, why do these forces change over time, and what can we predict about how the rate of return on capital will evolve in the twenty-first century?

  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).

  In any case, the rate of return on capital is determined by the following two forces: first, technology (what is capital used for?), and second, the abundance of the capital stock (too much capital kills the return on capital).

  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. Yet capital might still play an important role in such a society as a pure store of value: for example, people might choose to accumulate piles of food (assuming that conditions allow for such storage) in anticipation of a possible future famine or perhaps for purely aesthetic reasons (adding piles of jewels and other ornaments to the food piles, perhaps). 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.

  Nothing prevents us from imagining such a society, but in all known human societies, including the most primitive, things have been arranged differently. 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.). Historically, the earliest forms of capital accumulation involved both tools and improvements to land (fencing, irrigation, drainage, etc.) and rudimentary dwellings (caves, tents, huts, etc.). Increasingly sophisticated forms of industrial and business capital came later, as did constantly improved forms of housing.

  The Notion of Marginal Productivity of Capital

  Concretely, the marginal productivity of capital is defined by the value of the additional production due to one additional unit of capital. Suppose, for example, that in a certain agricultural society, a person with the equivalent of 100 euros’ worth of additional land or tools (given the prevailing price of land and tools) can increase food production by the equivalent of 5 euros per year (all other things being equal, in particular the quantity of labor utilized). We then say that the marginal productivity of capital is 5 euros for an investment of 100 euros, or 5 percent a year. Under conditions of pure and perfect competition, this is the annual rate of return that the owner of the capital (land or tools) should obtain from the agricultural laborer. If the owner seeks to obtain more than 5 percent, the laborer will rent land and tools from another capitalist. And if the laborer wants to pay less than 5 percent, then the land and tools will go to another laborer. Obviously, there can be situations in which the landlord is in a monopoly position when it comes to renting land and tools or purchasing labor (in the latter case one speaks of “monopsony” rather than monopoly), in which case the owner of capital can impose a rate of return greater than the marginal productivity of his capital.

  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. In theory, this is the function of the system of financial intermediation (banks and financial markets): to find the best possible uses for capital, such that each available unit of capital is invested where it is most productive (at the opposite ends of the earth, if need be) and pays the highest possible return to the investor. 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.

  In practice, financial institutions and stock markets are generally a long way from achieving this ideal of perfection. They are often sources of chronic instability, waves of speculation, and bubbles. 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. Whatever institutional imperfections may exist, however, it is clear that systems of financial intermediation have played a central and irreplaceable role in the history of economic development. The process has always involved a
very large number of actors, not just banks and formal financial markets: for example, in the eighteenth and nineteenth centuries, notaries played a central role in bringing investors together with entrepreneurs in need of financing, such as Père Goriot with his pasta factories and César Birotteau with his desire to invest in real estate.14

  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. For example, if an owner of land and tools exploits his own capital, he probably does not account separately for the return on the capital that he invests in himself. Yet this capital is nevertheless useful, and his marginal productivity is the same as if the return were paid to an outside investor. 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. In that case, the private return is less than the “social” return on capital, but the latter is still defined as the marginal productivity of an additional unit of capital. Is it useful and just for the owners of capital to receive this marginal product as payment for their ownership of property (whether their own past savings or that of their ancestors) even if they contribute no new work? This is clearly a crucial question, but not the one I am asking here.

  Too Much Capital Kills the Return on Capital

  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. For example, if each agricultural worker already has thousands of hectares to farm, it is likely that the extra yield of an additional hectare of land will be limited. Similarly, if a country has already built a huge number of new dwellings, so that every resident enjoys hundreds of square feet of living space, then the increase to well-being of one additional building—as measured by the additional rent an individual would be prepared to pay in order to live in that building—would no doubt be very small. The same is true for machinery and equipment of any kind: marginal productivity decreases with quantity beyond a certain threshold. (Although it is possible that some minimum number of tools are needed to begin production, saturation is eventually reached.) 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 interesting question is therefore not whether the marginal productivity of capital decreases when the stock of capital increases (this is obvious) but rather how fast it decreases. In particular, the central question is how much the return on capital r decreases (assuming that it is equal to the marginal productivity of capital) when the capital/income ratio β increases. Two cases are possible. If the return on capital r falls more than proportionately when the capital/income ratio β increases (for example, if r decreases by more than half when β is doubled), then the share of capital income in national income α = r × β decreases when β increases. In other words, the decrease in the return on capital more than compensates for the increase in the capital/income ratio. Conversely, if the return r falls less than proportionately when β increases (for example, if r decreases by less than half when β is doubled), then capital’s share α = r × β increases when β increases. In that case, the effect of the decreased return on capital is simply to cushion and moderate the increase in the capital share compared to the increase in the capital/income ratio.

  Based on historical evolutions observed in Britain and France, the second case seems more relevant over the long run: the capital share of income, α, follows the same U-shaped curve as the capital income ratio, β (with a high level in the eighteenth and nineteenth centuries, a drop in the middle of the twentieth century, and a rebound in the late twentieth and early twenty-first centuries). 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.

  It is nevertheless important to emphasize that both cases are theoretically possible. 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. In thinking about these questions, economists often use the concept of a “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.

  For example, 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 put to work in any productive way.

  Conversely, if the elasticity of substitution is infinite, the marginal productivity of capital (and labor) is totally independent of the available quantity of capital and labor. In particular, the return on capital is fixed and does not depend on the quantity of capital: it is always possible to accumulate more capital and increase production by a fixed percentage, for example, 5 or 10 percent a year per unit of additional capital. 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).15 If the elasticity is greater than one, an increase in the capital/income ratio β leads instead to a drop in the marginal productivity of capital, so that the capital share α = r × β increases (again assuming that the return on capital is equal to its marginal productivity).16 If the elasticity is exactly equal to one, then the two effects cancel each other out: the return on capital decreases in exactly the same proportion as the capital/income ratio β increases, so that the product α = r × β does not change.

  Beyond Cobb-Douglas: The Question of the Stability of the Capital-Labor Split

  The case of an elasticity of substitution exactly equal to one corresponds to the so-called Cobb-Douglas production function, named for the economists Charles Cobb and Paul Douglas, who first proposed it in 1928. With a Cobb-Douglas production function, no matter what happens, and in particular no matter what quantities of capital and labor are available, the capital share of income is always equal to the fixed coefficient α, which can be taken as a purely technological parameter.17

  For example, if α = 30 percent, then no matter what the capital/income ratio is, income from capital will account for 30 percent of national income (and income from labor for 70 percent). If the savings rate and growth rate are such that the long-term capital/income ra
tio β = s / g corresponds to six years of national income, then the rate of return on capital will be 5 percent, so that the capital share of income will be 30 percent. If the long-term capital stock is only three years of national income, then the return on capital will rise to 10 percent. And if the savings and growth rates are such that the capital stock represents ten years of national income, then the return on capital will fall to 3 percent. In all cases, the capital share of income will be 30 percent.

  The Cobb-Douglas production function became very popular in economics textbooks after World War II (after being popularized by Paul Samuelson), in part for good reasons but also in part for bad ones, including simplicity (economists like simple stories, even when they are only approximately correct), but above all because the stability of the capital-labor split gives a fairly peaceful and harmonious view of the social order. In fact, the stability of capital’s share of income—assuming it turns out to be true—in no way guarantees harmony: it is compatible with extreme and untenable inequality of the ownership of capital and distribution of income. 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.