Capital in the Twenty-First Century (64 page)

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.

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.

What is more striking when one reads Pareto’s work with the benefit of hindsight is
that he clearly had no evidence to support his theory of stability. Pareto was writing
in 1900 or thereabouts. He used available tax tables from 1880–1890, based on data
from Prussia and Saxony as well as several Swiss and Italian cities. The information
was scanty and covered a decade at most. What is more, it showed a slight trend toward
higher inequality, which Pareto intentionally sought to hide.
³⁰
In any case, it is clear that such data provide no basis whatsoever for any conclusion
about the long-term behavior of inequality around the world.

Pareto’s judgment was clearly influenced by his political prejudices: he was above
all wary of socialists and what he took to be their redistributive illusions. In this
respect he was hardly different from any number of contemporary colleagues, such as
the French economist Pierre Leroy-Beaulieu, whom he admired. Pareto’s case is interesting
because it illustrates the powerful illusion of eternal stability, to which the uncritical
use of mathematics in the social sciences sometimes leads. Seeking to find out how
rapidly the number of taxpayers decreases as one climbs higher in the income hierarchy,
Pareto discovered that the rate of decrease could be approximated by a mathematical
law that subsequently became known as “Pareto’s law” or, alternatively, as an instance
of a general class of functions known as “power laws.”
³¹
Indeed, this family of functions is still used today to study distributions of wealth
and income. Note, however, that the power law applies only to the upper tail of these
distributions and that the relation is only approximate and locally valid. It can
nevertheless be used to model processes due to multiplicative shocks, like those described
earlier.

Note, moreover, that we are speaking not of a single function or curve but of a family
of functions: everything depends on the coefficients and parameters that define each
individual curve. The data collected in the WTID as well as the data on wealth presented
here show that these Pareto coefficients have varied enormously over time. When we
say that a distribution of wealth is a Pareto distribution, we have not really said
anything at all. It may be a distribution in which the upper decile receives only
slightly more than 20 percent of total income (as in Scandinavia in 1970–1980) or
one in which the upper decile receives 50 percent (as in the United States in 2000–2010)
or one in which the upper decile owns more than 90 percent of total wealth (as in
France and Britain in 1900–1910). In each case we are dealing with a Pareto distribution,
but the coefficients are quite different. The corresponding social, economic, and
political realities are clearly poles apart.
³²

Even today, some people imagine, as Pareto did, that the distribution of wealth is
rock stable, as if it were somehow a law of nature. In fact, nothing could be further
from the truth. When we study inequality in historical perspective, the important
thing to explain is not the stability of the distribution but the significant changes
that occur from time to time. In the case of the wealth distribution, I have identified
a way to explain the very large historical variations that occur (whether described
in terms of Pareto coefficients or as shares of the top decile and centile) in terms
of the difference
r
−
g
between the rate of return on capital and the growth rate of the economy.

I come now to the essential question: Why has the inequality of wealth not returned
to the level achieved in the Belle Époque, and can we be sure that this situation
is permanent and irreversible?

Let me state at the outset that I have no definitive and totally satisfactory answer
to this question. Several factors have played important roles in the past and will
continue to do so in the future, and it is quite simply impossible to achieve mathematical
certainty on this point.

The very substantial reduction in inequality of wealth following the shocks of 1914–1945
is the easiest part to explain. Capital suffered a series of extremely violent shocks
as a result of the wars and the policies to which they gave rise, and the capital/income
ratio therefore collapsed. One might of course think that the reduction of wealth
would have affected all fortunes proportionately, regardless of their rank in the
hierarchy, leaving the distribution of wealth unchanged. But to believe this one would
have to forget the fact that wealth has different origins and fulfills different functions.
At the very top of the hierarchy, most wealth was accumulated long ago, and it takes
much longer to reconstitute such a large fortune than to accumulate a modest one.

Furthermore, the largest fortunes serve to finance a certain lifestyle. The detailed
probate records collected from the archives show unambiguously that many rentiers
in the interwar years did not reduce expenses sufficiently rapidly to compensate for
the shocks to their fortunes and income during the war and in the decade that followed,
so that they eventually had to eat into their capital to finance current expenditures.
Hence they bequeathed to the next generation fortunes significantly smaller than those
they had inherited, and the previous social equilibrium could no longer be sustained.
The Parisian data are particularly eloquent on this point. For example, the wealthiest
1 percent of Parisians in the Belle Époque had capital income roughly 80–100 times
as great as the average wage of that time, which enabled them to live very well and
still reinvest a small portion of their income and thus increase their inherited wealth.
³³
From 1872 to 1912, the system appears to have been perfectly balanced: the wealthiest
individuals passed on to the next generation enough to finance a lifestyle requiring
80–100 times the average wage or even a bit more, so that wealth became even more
concentrated. This equilibrium clearly broke down in the interwar years: the wealthiest
1 percent of Parisians continued to live more or less as they had always done but
left the next generation just enough to yield capital income of 30–40 times the average
wage; by the late 1930s, this had fallen to just 20 times the average wage. For the
rentiers, this was the beginning of the end. This was probably the most important
reason for the deconcentration of wealth that we see in all European countries (and
to a less extent in the United States) in the wake of the shocks of 1914–1945.