Capital in the Twenty-First Century

by Thomas Piketty

  The problem with the theory is that it is too simplistic and systematic: it is impossible to encapsulate all savings behavior and all attitudes toward the future in a single inexorable psychological parameter. If we take the most extreme version of the model (called the “infinite horizon” model, because agents calculate the consequences of their savings strategy for all their descendants until the end of time as though they were thinking of themselves, in accordance with their own rate of time preference), it follows that the net rate of return on capital cannot vary by even as little as a tenth of a percent: any attempt to alter the net return (for example, by changing tax policy) will trigger an infinitely powerful reaction in one sense or another (saving or dissaving) in order to force the net return back to its unique equilibrium. Such a prediction is scarcely realistic: history shows that the elasticity of saving is positive but not infinite, especially when the rate of return varies within moderate and reasonable limits.18

  Another difficulty with this theoretical model (in its strictest interpretation) is that it implies that the rate of return on capital, r, must, in order to maintain the economy in equilibrium, rise very rapidly with the growth rate g, so that the gap between r and g should be greater in a rapidly growing economy than in one that is not growing at all. Once again, this prediction is not very realistic, nor is it compatible with historical experience (the return on capital may rise in a rapidly growing economy but probably not enough to increase the gap r − g significantly, to judge by observed historical experience), and it, too, is a consequence of the infinite horizon hypothesis. Note, however, that the intuition here is again partially valid and in any case interesting from a strictly logical point of view. In the standard economic model, based on the existence of a “perfect” market for capital (in which each owner of capital receives a return equal to the highest marginal productivity available in the economy, and everyone can borrow as much as he or she wants at that rate), the reason why the return on capital, r, is systematically and necessarily higher than the growth rate, g, is the following. If r were less than g, economic agents, realizing that their future income (and that of their descendants) will rise faster than the rate at which they can borrow, will feel infinitely wealthy and will therefore wish to borrow without limit in order to consume immediately (until r rises above g). In this extreme form, the mechanism is not entirely plausible, but it shows that r > g is true in the most standard of economic models and is even more likely to be true as capital markets become more efficient.19

  To recap: savings behavior and attitudes toward the future cannot be encapsulated in a single parameter. These choices need to be analyzed in more complex models, involving not only time preference but also precautionary savings, life-cycle effects, the importance attached to wealth in itself, and many other factors. These choices depend on the social and institutional environment (such as the existence of a public pension system), family strategies and pressures, and limitations that social groups impose on themselves (for example, in some aristocratic societies, heirs are not free to sell family property), in addition to individual psychological and cultural factors.

  To my way of thinking, the inequality r > g should be analyzed as a historical reality dependent on a variety of mechanisms and not as an absolute logical necessity. It is the result of a confluence of forces, each largely independent of the others. For one thing, the rate of growth, g, tends to be structurally low (generally not much more than 1 percent a year once the demographic transition is complete and the country reaches the world technological frontier, where the pace of innovation is fairly slow). For another, the rate of return on capital, r, depends on many technological, psychological, social, and cultural factors, which together seem to result in a return of roughly 4–5 percent (in any event distinctly greater than 1 percent).

  Is There an Equilibrium Distribution?

  Let me now turn to the consequences of r > g for the dynamics of the wealth distribution. The fact that the return on capital is distinctly and persistently greater than the growth rate is a powerful force for a more unequal distribution of wealth. For example, if g = 1 percent and r = 5 percent, wealthy individuals have to reinvest only one-fifth of their annual capital income to ensure that their capital will grow faster than average income. Under these conditions, the only forces that can avoid an indefinite inegalitarian spiral and stabilize inequality of wealth at a finite level are the following. First, if the fortunes of wealthy individuals grow more rapidly than average income, the capital/income ratio will rise indefinitely, which in the long run should lead to a decrease in the rate of return on capital. Nevertheless, this mechanism can take decades to operate, especially in an open economy in which wealthy individuals can accumulate foreign assets, as was the case in Britain and France in the nineteenth century and up to the eve of World War I. In principle, this process always comes to an end (when those who own foreign assets take possession of the entire planet), but this can obviously take time. This process was largely responsible for the vertiginous increase in the top centile’s share of wealth in Britain and France during the Belle Époque.

  Furthermore, in regard to the trajectories of individual fortunes, this divergent process can be countered by shocks of various kinds, whether demographic (such as the absence of an heir or the presence of too many heirs, leading to dispersal of the family capital, or early death, or prolonged life) or economic (such as a bad investment or a peasant uprising or a financial crisis or a mediocre season, etc.). Shocks of this sort always affect family fortunes, so that changes in the wealth distribution occur even in the most static societies. Note, moreover, the importance of demographic choices (the fewer children the rich choose to have, the more concentrated wealth becomes) and inheritance laws.

  Many traditional aristocratic societies were based on the principle of primogeniture: the eldest son inherited all (or at any rate a disproportionately large share) of the family property so as to avoid fragmentation and to preserve or increase the family’s wealth. The eldest son’s privilege concerned the family’s primary estate in particular and often placed heavy constraints on the property: the heir was not allowed to diminish its value and was obliged to live on the income from the capital, which was then conveyed in turn to the next heir in the line of succession, usually the eldest grandson. In British law this was the system of “entails” (the equivalent in French law being the system of substitution héréditaire under the Ancien Régime). It was the reason for the misfortune of Elinor and Marianne in Sense and Sensibility: the Norland estate passed directly to their father and half-brother, John Dashwood, who decided, after considering the matter with his wife, Fanny, to leave them nothing. The fate of the two sisters is a direct consequence of this sinister conversation. In Persuasion, Sir Walter’s estate goes directly to his nephew, bypassing his three daughters. Jane Austen, herself disfavored by inheritance and left a spinster along with her sister, knew what she was talking about.

  The inheritance law that derived from the French Revolution and the Civil Code that followed rested on two main pillars: the abolition of substitutions héréditaires and primogeniture and the adoption of the principle of equal division of property among brothers and sisters (equipartition). This principle has been applied strictly and consistently since 1804: in France, the quotité disponible (that is, the share of the estate that parents are free to dispose of as they wish) is only a quarter of total wealth for parents with three or more children,20 and exemption is granted only in extreme circumstances (for example, if the children murder their stepmother). It is important to understand that the new law was based not only on a principle of equality (younger children were valued as much as the eldest and protected from the whims of the parents) but also on a principle of liberty and economic efficiency. In particular, the abolition of entails, which Adam Smith disliked and Voltaire, Rousseau, and Montesquieu abhorred, rested on a simple idea: this abolition allowed the free circulation of goods and the possibility of reallocating prope
rty to the best possible use in the judgment of the living generation, despite what dead ancestors may have thought. Interestingly, after considerable debate, Americans came to the same conclusion in the years after the Revolution: entails were forbidden, even in the South. As Thomas Jefferson famously put it, “the Earth belongs to the living.” And equipartition of estates among siblings became the legal default, that is, the rule that applied in the absence of an explicit will (although the freedom to make one’s will as one pleases still prevails in both the United States and Britain, in practice most estates are equally divided among siblings). This was an important difference between France and the United States on the one hand, where the law of equipartition applied from the nineteenth century on, and Britain on the other, where primogeniture remained the default in 1925 for a portion of the parental property, namely, landed and agricultural capital.21 In Germany, it was not until the Weimar Republic that the German equivalent of entails was abolished in 1919.22

  During the French Revolution, this egalitarian, antiauthoritarian, liberal legislation (which challenged parental authority while affirming that of the new family head, in some case to the detriment of his spouse) was greeted with considerable optimism, at least by men—despite being quite radical for the time.23 Proponents of this revolutionary legislation were convinced that they had found the key to future equality. Since, moreover, the Civil Code granted everyone equal rights with respect to the market and property, and guilds had been abolished, the ultimate outcome seemed clear: such a system would inevitably eliminate the inequalities of the past. The marquis de Condorcet gave forceful expression to this optimistic view in his Esquisse d’un tableau historique des progrès de l’esprit humain (1794): “It is easy to prove that fortunes tend naturally toward equality, and that excessive differences of wealth either cannot exist or must promptly cease, if the civil laws do not establish artificial ways of perpetuating and amassing such fortunes, and if freedom of commerce and industry eliminate the advantage that any prohibitive law or fiscal privilege gives to acquired wealth.”24

  The Civil Code and the Illusion of the French Revolution

  How, then, are we to explain the fact that the concentration of wealth increased steadily in France throughout the nineteenth century and ultimately peaked in the Belle Époque at a level even more extreme than when the Civil Code was introduced and scarcely less than in monarchical and aristocratic Britain? Clearly, equality of rights and opportunities is not enough to ensure an egalitarian distribution of wealth.

  Indeed, once the rate of return on capital significantly and durably exceeds the growth rate, the dynamics of the accumulation and transmission of wealth automatically lead to a very highly concentrated distribution, and egalitarian sharing among siblings does not make much of a difference. As I mentioned a moment ago, there are always economic and demographic shocks that affect the trajectories of individual family fortunes. With the aid of a fairly simple mathematical model, one can show that for a given structure of shocks of this kind, the distribution of wealth tends toward a long-run equilibrium and that the equilibrium level of inequality is an increasing function of the gap r − g between the rate of return on capital and the growth rate. Intuitively, the difference r − g measures the rate at which capital income diverges from average income if none of it is consumed and everything is reinvested in the capital stock. The greater the difference r − g, the more powerful the divergent force. If the demographic and economic shocks take a multiplicative form (i.e., the greater the initial capital, the greater the effect of a good or bad investment), the long-run equilibrium distribution is a Pareto distribution (a mathematical form based on a power law, which corresponds fairly well to distributions observed in practice). One can also show fairly easily that the coefficient of the Pareto distribution (which measures the degree of inequality) is a steeply increasing function of the difference r − g.25

  Concretely, what this means is that if the gap between the return on capital and the growth rate is as high as that observed in France in the nineteenth century, when the average rate of return was 5 percent a year and growth was roughly 1 percent, the model predicts that the cumulative dynamics of wealth accumulation will automatically give rise to an extremely high concentration of wealth, with typically around 90 percent of capital owned by the top decile and more than 50 percent by the top centile.26

  In other words, the fundamental inequality r > g can explain the very high level of capital inequality observed in the nineteenth century, and thus in a sense the failure of the French Revolution. Although the revolutionary assemblies established a universal tax (and in so doing provided us with a peerless instrument for measuring the distribution of wealth), the tax rate was so low (barely 1–2 percent on directly transmitted estates, no matter how large, throughout the nineteenth century) that it had no measurable impact on the difference between the rate of return on capital and the growth rate. Under these conditions, it is no surprise that inequality of wealth was as great in nineteenth-century France and even during the republican Belle Époque as in monarchical Britain. The formal nature of the regime was of little moment compared with the inequality r > g.

  Equipartition of estates between siblings did have some effect, but less than the gap r − g. Concretely, primogeniture (or, more precisely, primogeniture on agricultural land, which accounted for a decreasing share of British national capital over the course of the nineteenth century), magnified the effects of demographic and economic shocks (creating additional inequality depending on one’s rank in the sibling order) and thus increased the Pareto coefficient and gave rise to a more concentrated distribution of wealth. This may help to explain why the top decile’s share of total wealth was greater in Britain than in France in 1900–1910 (slightly more than 90 percent, compared with slightly less in France), and especially why the top centile’s share was significantly greater on the British side of the Channel (70 percent v. 60 percent), since this appears to have been based on the preservation of a small number of very large landed estates. But this effect was partly compensated by France’s low demographic growth rate (cumulative inequality of wealth is structurally greater when the population is stagnant, again because of the difference between r and g), and in the end it had only a moderate effect on the overall distribution, which was fairly close in the two countries.27

  In Paris, where the Napoleonic Civil Code came into effect in 1804 and where inequality cannot be laid at the door of British aristocrats and the queen of England, the top centile owned more than 70 percent of total wealth in 1913, even more than in Britain. The reality was so striking that it even found expression in an animated cartoon, The Aristocats, set in Paris in 1910. The size of the old lady’s fortune is not mentioned, but to judge by the splendor of her residence and by the zeal of her butler Edgar to get rid of Duchesse and her three kittens, it must have been considerable.

  In terms of the r > g logic, the fact that the growth rate increased from barely 0.2 percent prior to 1800 to 0.5 percent in the eighteenth century and then to 1 percent in the nineteenth century does not seem to have made much of a difference: it was still small compared to a return on capital of around 5 percent, especially since the Industrial Revolution appears to have slightly increased that return.28 According to the theoretical model, if the return on capital is around 5 percent a year, the equilibrium concentration of capital will not decrease significantly unless the growth rate exceeds 1.5–2 percent or taxes on capital reduce the net return to below 3–3.5 percent, or both.

  Note, finally, that if the difference r − g surpasses a certain threshold, there is no equilibrium distribution: inequality of wealth will increase without limit, and the gap between the peak of the distribution and the average will grow indefinitely. The exact level of this threshold of course depends on savings behavior: divergence is more likely to occur if the very wealthy have nothing to spend their money on and no choice but to save and add to their capital stock. The Aristocats calls attention to the
problem: Adélaïde de Bonnefamille obviously enjoys a handsome income, which she lavishes on piano lessons and painting classes for Duchesse, Marie, Toulouse, and Berlioz, who are somewhat bored by it all.29 This kind of behavior explains quite well the rising concentration of wealth in France, and particularly in Paris, in the Belle Époque: the largest fortunes increasingly belonged to the elderly, who saved a large fraction of their capital income, so that their capital grew significantly faster than the economy. As noted, such an inegalitarian spiral cannot continue indefinitely: ultimately, there will be no place to invest the savings, and the global return on capital will fall, until an equilibrium distribution emerges. But that can take a very long time, and since the top centile’s share of Parisian wealth in 1913 already exceeded 70 percent, it is legitimate to ask how high the equilibrium level would have been had the shocks due to World War I not occurred.

  Pareto and the Illusion of Stable Inequality

  It is worth pausing a moment to discuss some methodological and historical issues concerning the statistical measurement of inequality. In Chapter 7, I discussed the Italian statistician Corrado Gini and his famous coefficient. Although the Gini coefficient was intended to sum up inequality in a single number, it actually gives a simplistic, overly optimistic, and difficult-to-interpret picture of what is really going on. A more interesting case is that of Gini’s compatriot Vilfredo Pareto, whose major works, including a discussion of the famous “Pareto law,” were published between 1890 and 1910. In the interwar years, the Italian Fascists adopted Pareto as one of their own and promoted his theory of elites. Although they were no doubt seeking to capitalize on his prestige, it is nevertheless true that Pareto, shortly before his death in 1923, hailed Mussolini’s accession to power. Of course the Fascists would naturally have been attracted to Pareto’s theory of stable inequality and the pointlessness of trying to change it.