Capital in the Twenty-First Century

by Thomas Piketty

  These effects are all the more significant because the growth rate that figures in the law β = s / g is 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. And if the latter country tends to save a little less than the former, perhaps because its population is not aging as rapidly, this mechanism will be further reinforced as a result. In other words, countries with similar growth rates of income per capita can end up with very different capital/income ratios simply because their demographic growth rates are not the same.

  This law allows us to give a good account of the historical evolution of the capital/income ratio. In particular, it enables us to explain why the capital/income ratio seems now—after the shocks of 1914–1945 and the exceptionally rapid growth phase of the second half of the twentieth century—to be returning to very high 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.

  A Long-Term Law

  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.

  For example, if a country starts with zero capital and saves 12 percent of its national income for a year, it obviously will not accumulate a capital stock worth six years of its income. With a savings rate of 12 percent a year, starting from zero capital, it will take fifty years to save the equivalent of six years of income, and even then the capital/income ratio will not be equal to 6, because national income will itself have increased considerably after half a century (unless we assume that the growth rate is actually zero).

  The first principle to bear in mind is, therefore, that the accumulation of wealth takes time: it will take several decades for the law β = s / g to become true. 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.

  Hence there is a crucial difference between this law and the law α = r × β, which I called the first fundamental law of capitalism in Chapter 1. According to that law, the share of capital income in national income, α, is equal to the average rate of return on capital, r, times the capital/income ratio, β. It is important to realize that the law α = r × β is actually a pure accounting identity, valid at all times in all places, by construction. Indeed, one can view it as a definition of the share of capital in national income (or of the rate of return on capital, depending on which parameter is easiest to measure) rather than as a law. By contrast, the law β = s / g is the result of a dynamic process: it represents a state of equilibrium toward which an economy will tend if the savings rate is s and the growth rate g, but that equilibrium state is never perfectly realized in practice.

  Second, the law β = s / g is valid only if one focuses on those forms of capital that human beings can accumulate. If a significant fraction of national capital consists of pure natural resources (i.e., natural resources whose value is independent of any human improvement and any past investment), then β can be quite high without any contribution from savings. I will say more later about the practical importance of nonaccumulable capital.

  Finally, the law β = s / g is valid only if asset prices evolve on average in the same way as consumer prices. If the price of real estate or stocks rises faster than other prices, then the ratio β between the market value of national capital and the annual flow of national income can again be quite high without the addition of any new savings. In the short run, variations (capital gains or losses) of relative asset prices (i.e., of asset prices relative to consumer prices) are often quite a bit larger than volume effects (i.e., effects linked to new savings). If we assume, however, that price variations balance out over the long run, then the law β = s / g is necessarily valid, regardless of the reasons why the country in question chooses to save a proportion s of its national income.

  This point bears emphasizing: the law β = s / g is totally independent of the reasons why the residents of a particular country—or their government—accumulate wealth. In practice, people accumulate capital for all sorts of reasons: for instance, to increase future consumption (or to avoid a decrease in consumption after retirement), or to amass or preserve wealth for the next generation, or again to acquire the power, security, or prestige that often come with wealth. In general, all these motivations are present at once in proportions that vary with the individual, the country, and the age. Quite often, all these motivations are combined in single individuals, and individuals themselves may not always be able to articulate them clearly. In Part Three I discuss in depth the significant implications of these various motivations and mechanisms of accumulation for inequality and the distribution of wealth, the role of inheritance in the structure of inequality, and, more generally, the social, moral, and political justification of disparities in wealth. At this stage I am simply explaining the dynamics of the capital/income ratio (a question that can be studied, at least initially, independently of the question of how wealth is distributed). The point I want to stress is that the law β = s / g applies in all cases, regardless of the exact reasons for a country’s savings rate.

  This is due to the simple fact that β = s / g is the only stable capital/income ratio in a country that saves a fraction s of its income, which grows at a rate g.

  The argument is elementary. Let me illustrate it with an example. In concrete terms: if a country is saving 12 percent of its income every year, and if its initial capital stock is equal to six years of income, then the capital stock will grow at 2 percent a year,4 thus at exactly the same rate as national income, so that the capital/income ratio will remain stable.

  By contrast, if the capital stock is less than six years of income, then a savings rate of 12 percent will cause the capital stock to grow at a rate greater than 2 percent a year and therefore faster than income, so that the capital/income ratio will increase until it attains its equilibrium level.

  Conversely, if the capital stock is greater than six years of annual income, then a savings rate of 12 percent implies that capital is growing at less than 2 percent a year, so that the capital/income ratio cannot be maintained at that level and will therefore decrease until it reaches equilibrium.

  In each case, the capital/income ratio tends over the long run toward its equilibrium level β = s / g (possibly augmented by pure natural resources), provided that the average price of assets evolves at the same rate as consumption prices over the long run.5

  To sum up: the law β = s / g does not explain the sh
ort-term shocks to which the capital/income ratio is subject, any more than it explains the existence of world wars or the crisis of 1929—events that can be taken as examples of extreme shocks—but it does allow us to understand the potential equilibrium level toward which the capital/income ratio tends in the long run, when the effects of shocks and crises have dissipated.

  Capital’s Comeback in Rich Countries since the 1970s

  In order to illustrate the difference between short-term and long-term movements of the capital/income ratio, it is useful to examine the annual changes observed in the wealthiest countries between 1970 and 2010, a period for which we have reliable and homogeneous data for a large number of countries. To begin, here is a look at the ratio of private capital to national income, whose evolution is shown in Figure 5.3 for the eight richest countries in the world, in order of decreasing GDP: the United States, Japan, Germany, France, Britain, Italy, Canada, and Australia.

  FIGURE 5.3. Private capital in rich countries, 1970–2010

  Private capital is worth between two and 3.5 years of national income in rich countries in 1970, and between four and seven years of national income in 2010.

  Sources and series: see piketty.pse.ens.fr/capital21c.

  Compared with Figures 5.1 and 5.2, as well as with the figures that accompanied previous chapters, which presented decennial averages in order to focus attention on long-term trends, Figure 5.3 displays annual series and shows that the capital/income ratio in all countries varied constantly in the very short run. These erratic changes are due to the fact that the prices of real estate (including housing and business real estate) and financial assets (especially shares of stock) are notoriously volatile. It is always very difficult to set a price on capital, in part because it is objectively complex to foresee the future demand for the goods and services generated by a firm or by real estate and therefore to predict the future flows of profit, dividends, royalties, rents, and so on that the assets in question will yield, and in part because the present value of a building or corporation depends not only on these fundamental factors but also on the price at which one can hope to sell these assets if the need arises (that is, on the anticipated capital gain or loss).

  Indeed, these anticipated future prices themselves depend on the general enthusiasm for a given type of asset, which can give rise to so-called self-fulfilling beliefs: as long as one can hope to sell an asset for more than one paid for it, it may be individually rational to pay a good deal more than the fundamental value of that asset (especially since the fundamental value is itself uncertain), thus giving in to the general enthusiasm for that type of asset, even though it may be excessive. That is why speculative bubbles in real estate and stocks have existed as long as capital itself; they are consubstantial with its history.

  As it happens, the most spectacular bubble in the period 1970–2010 was surely the Japanese bubble of 1990 (see Figure 5.3). During the 1980s, the value of private wealth shot up in Japan from slightly more than four years of national income at the beginning of the decade to nearly seven at the end. Clearly, this enormous and extremely rapid increase was partly artificial: the value of private capital fell sharply in the early 1990s before stabilizing at around six years of national income from the mid-1990s on.

  I will not rehearse the history of the numerous real estate and stock market bubbles that inflated and burst in the rich countries after 1970, nor will I attempt to predict future bubbles, which I am quite incapable of doing in any case. Note, however, the sharp correction in the Italian real estate market in 1994–1995 and the bursting of the Internet bubble in 2000–2001, which caused a particularly sharp drop in the capital/income ratio in the United States and Britain (though not as sharp as the drop in Japan ten years earlier). Note, too, that the subsequent US real estate and stock market boom continued until 2007, followed by a deep drop in the recession of 2008–2009. In two years, US private fortunes shrank from five to four years of national income, a drop of roughly the same size as the Japanese correction of 1991–1992. In other countries, and particularly in Europe, the correction was less severe or even nonexistent: in Britain, France, and Italy, the price of assets, especially in real estate, briefly stabilized in 2008 before starting upward again in 2009–2010, so that by the early 2010s private wealth had returned to the level attained in 2007, if not slightly higher.

  The important point I want to emphasize is that beyond these erratic and unpredictable variations in short-term asset prices, variations whose amplitude seems to have increased in recent decades (and we will see later that this can be related to the increase in the potential capital/income ratio), there is indeed a long-term trend at work in all of the rich countries in the period 1970–2010 (see Figure 5.3). 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 The general evolution is clear: bubbles aside, what we are witnessing is a strong comeback of private capital in the rich countries since 1970, or, to put it another way, the emergence of a new patrimonial capitalism.

  This structural evolution is explained by three sets of factors, which complement and reinforce one another to give the phenomenon a very significant amplitude. The most important factor in the long run is slower growth, especially demographic growth, which, together with a high rate of saving, automatically gives rise to a structural increase in the long-run capital/income ratio, owing to the law β = s / g. This mechanism is the dominant force in the very long run but should not be allowed to obscure the two other factors that have substantially reinforced its effects over the last few decades: first, the gradual privatization and transfer of public wealth into private hands in the 1970s and 1980s, and second, a long-term catch-up phenomenon affecting real estate and stock market prices, which also accelerated in the 1980s and 1990s in a political context that was on the whole more favorable to private wealth than that of the immediate postwar decades.

  Beyond Bubbles: Low Growth, High Saving

  I begin with the first mechanism, based on slower growth coupled with continued high saving and the dynamic law β = s / g. In Table 5.1 I have indicated the average values of the growth rates and private savings rates in the eight richest countries during the period 1970–2010. As noted in Chapter 2, the rate of growth of per capita national income (or the virtually identical growth rate of per capita domestic product) has been quite similar in all the developed countries over the last few decades. If comparisons are made over periods of a few years, the differences can be significant, and these often spur national pride or jealousy. But if one takes averages over longer periods, the fact is that all the rich countries are growing at approximately the same rate. 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.8

  In any case, these differences are very small compared with differences in the demographic growth rate. In the period 1970–2010, population grew at less than 0.5 percent per year in Europe and Japan (and closer to 0 percent in the period 1990–2010, or in Japan even at a negative rate), compared with 1.0–1.5 percent in the United States, Canada, and Australia (see Table 5.1). Hence the overall growth rate for the period 1970–2010 was significantly higher in the United States and the other new countries than in Europe or Japan: around 3 percent a year in the former (or perhaps even a bit more), compared with barely 2 percent in the latter (or even just barely 1.5 percent in the most recent subperiod). Such differences may seem small, but over the long run they mount up, so that in fact they are quite significant. The new point I want to stress here
is that such differences in growth rates have enormous effects on the long-run accumulation of capital and largely explain why the capital/income ratio is structurally higher in Europe and Japan than in the United States.

  Turning now to average savings rates in the period 1970–2010, again one finds large variations between countries: the private savings rate generally ranges between 10 and 12 percent of national income, but it is as low as 7 to 8 percent in the United States and Britain and as high as 14–15 percent in Japan and Italy (see Table 5.1). Over forty years, these differences mount up to create significant variation. Note, too, that the countries that save the most are often those whose population is stagnant and aging (which may justify saving for the purpose of retirement and bequest), but the relation is far from systematic. As noted, there are many reasons why one might choose to save more or less, and it comes as no surprise that many factors (linked to, among other things, culture, perceptions of the future, and distinctive national histories) come into play, just as they do in regard to decisions concerning childbearing and immigration, which ultimately help to determine the demographic growth rate.

  If one now combines variations in growth rates with variations in savings rate, it is easy to explain why different countries accumulate very different quantities of capital, and why the capital/income ratio has risen sharply since 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.