Capital in the Twenty-First Century

by Thomas Piketty

  The Law of Cumulative Growth

  In order to understand this argument better, it may be helpful to pause a moment to consider what might be called “the law of cumulative growth,” which holds that a low annual growth rate over a very long period of time gives rise to considerable progress.

  Concretely, the population of the world grew at an average annual rate of barely 0.8 percent between 1700 and 2012. Over three centuries, however, this meant that the global population increased more than tenfold. A planet with about 600 million inhabitants in 1700 had more than 7 billion in 2012 (see Figure 2.1). If this pace were to continue for the next three centuries, the world’s population would exceed 70 billion in 2300.

  To give a clear picture of the explosive effects of the law of cumulative growth, I have indicated in Table 2.2 the correspondence between the annual growth rate (the figure usually reported) and the long-term growth multiplier. For example, a growth rate of 1 percent per year will multiply the population by a factor of 1.35 after thirty years, 3 after one hundred years, 20 after three hundred years, and more than 20,000 after one thousand years. The simple conclusion that jumps out from this table is that growth rates greater than 1–1.5 percent a year cannot be sustained indefinitely without generating vertiginous population increases.

  FIGURE 2.1. The growth of world population, 1700–2012

  World population rose from 600 million inhabitants in 1700 to 7 billion in 2012.

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

  We see clearly how different choices of time frame lead to contradictory perceptions of the growth process. Over a period of one year, 1 percent growth seems very low, almost imperceptible. People living at the time might not notice any change at all. To them, such growth might seem like complete stagnation, in which each year is virtually identical to the previous one. Growth might therefore seem like a fairly abstract notion, a purely mathematical and statistical construct. But if we expand the time frame to that of a generation, that is, about thirty years, which is the most relevant time scale for evaluating change in the society we live in, the same growth rate results in an increase of about a third, which represents a transformation of quite substantial magnitude. Although this is less impressive than growth of 2–2.5 percent per year, which leads to a doubling in every generation, it is still enough to alter society regularly and profoundly and in the very long run to transform it radically.

  The law of cumulative growth is essentially identical to the law of cumulative returns, which says that an annual rate of return of a few percent, compounded over several decades, automatically results in a very large increase of the initial capital, provided that the return is constantly reinvested, or at a minimum that only a small portion of it is consumed by the owner of the capital (small in comparison with the growth rate of the society in question).

  The central thesis of this book is precisely that an apparently small gap between the return on capital and the rate of growth can in the long run have powerful and destabilizing effects on the structure and dynamics of social inequality. In a sense, everything follows from the laws of cumulative growth and cumulative returns, and that is why the reader will find it useful at this point to become familiar with these notions.

  The Stages of Demographic Growth

  I return now to the examination of global population growth.

  If the rhythm of demographic growth observed between 1700 and 2012 (0.8 percent per year on average) had started in antiquity and continued ever since, the world’s population would have been multiplied by nearly 100,000 between 0 and 1700. Given that the population in 1700 is estimated to have been approximately 600 million, we would have to assume a ridiculously small global population at the time of Christ’s birth (fewer than ten thousand people). Even a growth rate of 0.2 percent, extended over 1700 years, would imply a global population of only 20 million in year 0, whereas the best available information suggests that the figure was actually greater than 200 million, with 50 million living in the Roman Empire alone. Regardless of any flaws that may exist in the historical sources and global population estimates for these two dates, there is not a shadow of a doubt that the average demographic growth rate between 0 and 1700 was less than 0.2 percent and almost certainly less than 0.1 percent.

  Contrary to a widely held belief, this Malthusian regime of very low growth was not one of complete demographic stagnation. The rate of growth was admittedly quite slow, and the cumulative growth of several generations was often wiped out in a few years by epidemic and famine.2 Still, world population seems to have increased by a quarter between 0 and 1000, then by a half between 1000 and 1500, and by half again between 1500 and 1700, during which the demographic growth rate was close to 0.2 percent. The acceleration of growth was most likely a very gradual process, which proceeded hand in hand with growth in medical knowledge and sanitary improvements, that is to say, extremely slowly.

  Demographic growth accelerated considerably after 1700, with average growth rates on the order of 0.4 percent per year in the eighteenth century and 0.6 percent in the nineteenth. Europe (including its American offshoot) experienced its most rapid demographic growth between 1700 and 1913, only to see the process reverse in the twentieth century: the rate of growth of the European population fell by half, to 0.4 percent, in the period 1913–2012, compared with 0.8 percent between 1820 and 1913. Here we see the phenomenon known as the demographic transition: the continual increase in life expectancy is no longer enough to compensate for the falling birth rate, and the pace of population growth slowly reverts to a lower level.

  In Asia and Africa, however, the birth rate remained high far longer than in Europe, so that demographic growth in the twentieth century reached vertiginous heights: 1.5–2 percent per year, which translates into a fivefold or more increase in the population over the course of a century. Egypt had a population of slightly more than 10 million at the turn of the twentieth century but now numbers more than 80 million. Nigeria and Pakistan each had scarcely more than 20 million people, but today each has more than 160 million.

  It is interesting to note that the growth rates of 1.5–2 percent a year attained by Asia and Africa in the twentieth century are roughly the same as those observed in America in the nineteenth and twentieth centuries (see Table 2.3). The United States thus went from a population of less than 3 million in 1780 to 100 million in 1910 and more than 300 million in 2010, or more than a hundredfold increase in just over two centuries, as mentioned earlier. The crucial difference, obviously, is that the demographic growth of the New World was largely due to immigration from other continents, especially Europe, whereas the 1.5–2 percent growth in Asia and Africa is due entirely to natural increase (the surplus of births over deaths).

  As a consequence of this demographic acceleration, global population growth reached the record level of 1.4 percent in the twentieth century, compared with 0.4–0.6 percent in the eighteenth and nineteenth centuries (see Table 2.3).

  It is important to understand that we are just emerging from this period of open-ended demographic acceleration. Between 1970 and 1990, global population was still growing 1.8 percent annually, almost as high as the absolute historical record of 1.9 percent achieved in the period 1950–1970. For the period 1990–2012, the average rate is still 1.3 percent, which is extremely high.3

  According to official forecasts, progress toward the demographic transition at the global level should now accelerate, leading to eventual stabilization of the planet’s population. According to a UN forecast, the demographic growth rate should fall to 0.4 percent by the 2030s and settle around 0.1 percent in the 2070s. If this forecast is correct, the world will return to the very low-growth regime of the years before 1700. The global demographic growth rate would then have followed a gigantic bell curve in the period 1700–2100, with a spectacular peak of close to 2 percent in the period 1950–1990 (see Figure 2.2).

  Note, moreover, that the demographic growth anticipated for the second
half of the twenty-first century (0.2 percent in the period 2050–2100) is entirely due to the continent of Africa (with annual growth of 1 percent). On the three other continents, the population will probably either stagnate (0.0 percent in America) or decrease (−0.1 percent in Europe and −0.2 percent in Asia). Such a prolonged period of negative demographic growth in peacetime would be unprecedented (see Table 2.3).

  FIGURE 2.2. The growth rate of world population from Antiquity to 2100

  The growth rate of world population was above 1 percent per year from 1950 to 2012 and should return toward 0 percent by the end of the twenty-first century.

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

  Negative Demographic Growth?

  These forecasts are obviously rather uncertain. They depend first on the evolution of life expectancy (and thus in part on advances in medical science) and second on the decisions that future generations will make in regard to childbearing. If life expectancy is taken as given, the fertility rate determines the demographic growth rate. The important point to bear in mind is that small variations in the number of children couples decide to have can have significant consequences for society writ large.4

  What demographic history teaches us is that these childbearing decisions are largely unpredictable. They are influenced by cultural, economic, psychological, and personal factors related to the life goals that individuals choose for themselves. These decisions may also depend on the material conditions that different countries decide to provide, or not provide, for the purpose of making family life compatible with professional life: schools, day care, gender equality, and so on. These issues will undoubtedly play a growing part in twenty-first-century political debate and public policy. Looking beyond the general schema just outlined, we find numerous regional differences and stunning changes in demographic patterns, many of them linked to specific features of each country’s history.5

  The most spectacular reversal no doubt involves Europe and America. In 1780, when the population of Western Europe was already greater than 100 million and that of North America barely 3 million, no one could have guessed the magnitude of the change that lay ahead. By 2010, the population of Western Europe was just above 410 million, while the North American population had increased to 350 million. According to UN projections, the catch-up process will be complete by 2050, at which time the Western European population will have grown to around 430 million, compared with 450 million for North America. What explains this reversal? Not just the flow of immigrants to the New World but also the markedly higher fertility rate there compared with old Europe. The gap persists to this day, even among groups that came originally from Europe, and the reasons for it remain largely a mystery to demographers. One thing is sure: the higher fertility rate in North America is not due to more generous family policies, since such policies are virtually nonexistent there.

  Should the difference be interpreted as reflecting a greater North American faith in the future, a New World optimism, and a greater propensity to think of one’s own and one’s children’s futures in terms of a perpetually growing economy? When it comes to decisions as complex as those related to fertility, no psychological or cultural explanation can be ruled out in advance, and anything is possible. Indeed, US demographic growth has been declining steadily, and current trends could be reversed if immigration into the European Union continues to increase, or fertility increases, or the European life expectancy widens the gap with the United States. United Nations forecasts are not certainties.

  We also find spectacular demographic turnarounds within each continent. France was the most populous country in Europe in the eighteenth century (and, as noted, both Young and Malthus saw this as the reason for French rural poverty and even as the cause of the French Revolution). But the demographic transition occurred unusually early in France: a fall in the birth rate led to a virtually stagnant population as early as the nineteenth century. This is generally attributed to de-Christianization, which also came early. Yet an equally unusual leap in the birth rate took place in the twentieth century—a leap often attributed to pronatal policies adopted after the two world wars and to the trauma of defeat in 1940. France’s wager may well pay off, since UN forecasts predict that the population of France will exceed that of Germany by 2050 or so. It is difficult, however, to distinguish the various causes of this reversal: economic, political, cultural, and psychological factors all play a part.6

  On a grander scale, everyone knows the consequences of the Chinese policy to allow only one child per family (a decision made in the 1970s, when China feared being condemned to remain an underdeveloped country, and now in the process of being relaxed). The Chinese population, which was roughly 50 percent greater than India’s when this radical policy was adopted, is now close to being surpassed by that of its neighbor. According to the United Nations, India will be the most populous country in the world by 2020. Yet here, too, nothing is set in stone: population history invariably combines individual choices, developmental strategies, and national psychologies—private motives and power motives. No one at this point can seriously claim to know what demographic turnarounds may occur in the twenty-first century.

  It would therefore be presumptuous to regard the official UN predictions as anything other than a “central scenario.” In any case, the United Nations has also published two other sets of predictions, and the gaps between these various scenarios at the 2100 horizon are, unsurprisingly, quite large.7

  The central scenario is nevertheless the most plausible we have, given the present state of our knowledge. Between 1990 and 2012, the population of Europe was virtually stagnant, and the population of several countries actually decreased. Fertility rates in Germany, Italy, Spain, and Poland fell below 1.5 children per woman in the 2000s, and only an increase in life expectancy coupled with a high level of immigration prevented a rapid decrease of population. In view of these facts, the UN prediction of zero demographic growth in Europe until 2030 and slightly negative rates after that is by no means extravagant. Indeed, it seems to be the most reasonable forecast. The same is true for UN predictions for Asia and other regions: the generations being born now in Japan and China are roughly one-third smaller than the generations born in the 1990s. The demographic transition is largely complete. Changes in individual decisions and government policies may slightly alter these trends: for example, slightly negative rates (such as we see in Japan and Germany) may become slightly positive (as in France and Scandinavia), which would be a significant change, but we are unlikely to see anything more than that, at least for the next several decades.

  Of course the very long-run forecasts are much more uncertain. Note, however, that if the rate of population growth observed from 1700 to 2012—0.8 percent per year—were to continue for the next three centuries, the world’s population would be on the order of 70 billion in 2300. To be sure, this cannot be ruled out: childbearing behavior could change, or technological advances might allow growth with much less pollution than is possible to imagine now, with output consisting of new, almost entirely nonmaterial goods and services produced with renewable energy sources exhibiting a negligible carbon footprint. At this point, however, it is hardly an exaggeration to say that a world population of 70 billion seems neither especially plausible nor particularly desirable. The most likely hypothesis is that the global population growth rate over the next several centuries will be significantly less than 0.8 percent. The official prediction of 0.1–0.2 percent per year over the very long run seems rather plausible a priori.

  Growth as a Factor for Equalization

  In any case, it is not the purpose of this book to make demographic predictions but rather to acknowledge these various possibilities and analyze their implications for the evolution of the wealth distribution. Beyond the consequences for the development and relative power of nations, demographic growth also has important implications for the structure of inequality. Other things being equal, strong demographic growth
tends to play an equalizing role because it decreases the importance of inherited wealth: every generation must in some sense construct itself.

  To take an extreme example, in a world in which each couple has ten children, it is clearly better as a general rule not to count too much on inherited wealth, because the family wealth will be divided by ten with each new generation. In such a society, the overall influence of inherited wealth would be strongly diminished, and most people would be more realistic to rely on their own labor and savings.

  The same would be true in a society where the population is constantly replenished by immigration from other countries, as was the case in America. Assuming that most immigrants arrive without much wealth, the amount of wealth passed down from previous generations is inherently fairly limited in comparison with new wealth accumulated through savings. Demographic growth via immigration has other consequences, however, especially in regard to inequality between immigrants and natives as well as within each group. Such a society is thus not globally comparable to a society in which the primary source of population growth is natural increase (that is, from new births).

  I will show that the intuition concerning the effects of strong demographic growth can to a certain extent be generalized to societies with very rapid economic (and not just demographic) growth. For example, 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.

  Conversely, a stagnant or, worse, decreasing population increases the influence of capital accumulated in previous generations. The same is true of economic stagnation. With low growth, moreover, it is fairly plausible that the rate of return on capital will be substantially higher than the growth rate, a situation that, as I noted in the introduction, is the main factor leading toward very substantial inequality in the distribution of wealth over the long run. Capital-dominated societies in the past, with hierarchies largely determined by inherited wealth (a category that includes both traditional rural societies and the countries of nineteenth-century Europe) can arise and subsist only in low-growth regimes. I will consider the extent to which the probable return to a low-growth regime, if it occurs, will affect the dynamics of capital accumulation and the structure of inequality. In particular, inherited wealth will make a comeback—a long-term phenomenon whose effects are already being felt in Europe and that could extend to other parts of the world as well. That is why it is important for present purposes to become familiar with the history of demographic and economic growth.