Capital in the Twenty-First Century (109 page)

10
. See for example the interesting data on the distribution of land in Roger S. Bagnall,
“Landholding in Late Roman Egypt: The Distribution of Wealth,”
Journal of Roman Studies
82 (November 1992): 128–49. Other work of this type yields similar results. See the
online technical appendix.

11
. Bibliographic and technical details can be found in the online technical appendix.

12
. Some estimates find that the top centile in the United States as a whole owned less
than 15 percent of total national wealth around 1800, but that finding depends entirely
on the decision to focus on free individuals only, which is obviously a controversial
choice. The estimates that are reported here refer to the entire population (free
and unfree). See the online technical appendix.

13
. See Willford I. King,
The Wealth and Income of the People of the United States
(New York: MacMillan, 1915). King, a professor of statistics and economics at the
University of Wisconsin, relied on imperfect but suggestive data from several US states
and compared them with European estimates, mainly based on Prussian tax statistics.
He found the differences to be much smaller than he initially imagined.

14
. These levels, based on official Federal Reserve Bank surveys, may be somewhat low
(given the difficult of estimate large fortunes), and the top centile’s share may
have reached 40 percent. See the online technical appendix.

15
. The European average in
Figure 10.6
was calculated from the figures for France, Britain, and Sweden (which appear to
have been representative). See the online technical appendix.

16
. For land rent, the earliest data available for antiquity and the Middle Ages suggest
annual returns of around 5 percent. For interest on loans, we often find rates above
5 percent in earlier periods, typically on the order of 6–8 percent, even for loans
with real estate collateral. See, for example, the data collected by S. Homer and
R. Sylla,
A History of Interest Rates
(New Brunswick, NJ: Rutgers University Press, 1996).

17
. If the return on capital were greater than the time preference, everyone would prefer
to reduce present consumption and save more (so that the capital stock would grow
indefinitely, until the return on capital fell to the rate of time preference). In
the opposite case, everyone would sell a portion of her capital stock in order to
increase present consumption (and the capital stock would decrease until the return
on capital rose to equal
θ
). In either case we are left with
r
=
θ
.

18
. The infinite horizon model implies an infinite elasticity of saving—and thus of
the supply of capital—in the long run. It therefore assumes that tax policy cannot
affect the supply of capital.

19
. Formally, in the standard infinite horizon model, the equilibrium rate of return
is given by the formula
r
=
θ
+
γ
×
g
(where
θ
is the rate of time preference and
γ
measures the concavity of the utility function. It is generally estimated that
γ
lies between 1.5 and 2.5. For example, if
θ
=
5% and
γ
=
2, then
r
=
5% for
g
=
0% and
r
=
9% for
g
=
2%, so that the gap
r
−
g
rises from 5% to 7% when growth increases from 0% to 2%. See the online technical
appendix.

20
. A third for parents with two children and a half for those with only one child.

21
. Note that in 1807 Napoleon introduced the
majorat
for his imperial nobility. This allowed an increased share of certain landed estates
linked to titles of nobility to go the eldest males. Only a few thousand individuals
were concerned. Moreover, Charles X tried to restore
substitutions héréditaires
for his own nobility in 1826. These throwbacks to the Ancien Régime affected only
a small part of the population and were in any case definitively abolished in 1848.

22
. See Jens Beckert,
Inherited Wealth
(Princeton: Princeton University Press, 2008).

23
. In theory, women enjoyed the same rights as men when it came to dividing estates,
according to the Civil Code. But a wife was not free to dispose of her property as
she saw fit: this type of asymmetry, in regard to opening and managing bank accounts,
selling property, etc., did not totally disappear until the 1970s. In practice, therefore,
the new law favored (male) heads of families: younger sons acquired the same rights
as elder sons, but daughters were left behind. See the online technical appendix.

24
. See Pierre Rosanvallon,
La société des égaux
(Paris: Le Seuil, 2011), 50.

25
. The equation relating the Pareto coefficient to
r
−
g
is given in the online technical appendix.

26
. Clearly, this does not imply that the
r
>
g
logic is necessarily the only force at work. The model and related calculations are
obviously a simplification of reality and do not claim to identify the precise role
played by each mechanism (various contradictory forces may balance each other). It
does show, however, that the
r
>
g
logic is by itself sufficient to explain the observed level of concentration. See
the online technical appendix.

27
. The Swedish case is interesting, because it combines several contradictory forces
that seem to balance one another out: first, the capital/income ratio was lower than
in France or Britain in the nineteenth and early twentieth centuries (the value of
land was lower, and domestic capital was partly owned by foreigners—in this respect,
Sweden was similar to Canada), and second, primogeniture was in force until the end
of the nineteenth century, and some entails on large dynastic fortunes in Sweden persist
to this day. In the end, wealth was less concentrated in Sweden in 1900–1910 than
in Britain and close the French level. See
Figures 10.1
–
4
and the work of Henry Ohlsson, Jesper Roine, and Daniel Waldenström.

28
. Recall that the estimates of the “pure” return on capital indicated in
Figure 10.10
should be regarded as minimums and that the average observed return rose as high
as 6–7 percent in Britain and France in the nineteenth century (see
Chapter 6
).

29
. Fortunately, Duchesse and her kittens ultimately meet Thomas O’Malley, an alley
cat whose earthy ways they find more amusing than art classes (a little like Jack
Dawson, who meets young Rose on the deck of
Titanic
two years later, in 1912).

30
. For an analysis of Pareto’s data, see my
Les hauts revenus en France au 20e siècle: Inégalités et redistribution 1901–1998
(Paris: Grasset, 2001), 527–30.

31
. For details, see the online technical appendix.

32
. The simplest way to think of Pareto coefficients is to use what are sometimes called
“inverted coefficients,” which in practice vary from 1.5 to 3.5. An inverted coefficient
of 1.5 means that average income or wealth above a certain threshold is equal to 1.5
times the threshold level (individuals with more than a million euros of property
own on average 1.5 million euros’ worth, etc., for any given threshold), which is
a relatively low level of inequality (there are few very wealthy individuals). By
contrast, an inverted coefficient of 3.5 represents a very high level of inequality.
Another way to think about power functions is the following: a coefficient around
1.5 means that the top 0.1 percent are barely twice as rich on average as the top
1 percent (and similarly for the top 0.01 percent within the top 0.1 percent, etc.).
By contrast, a coefficient around 3.5 means that they are more than five times as
rich. All of this is explained in the online technical appendix. For graphs representing
the historical evolution of the Pareto coefficients throughout the twentieth century
for the various countries in the WTID, see Anthony B. Atkinson, Thomas Piketty, and
Emmanuel Saez, “Top Incomes in the Long Run of History,”
Journal of Economic Literature
49, no. 1 (2011): 3–71.

33
. That is, they had something like an income of 2–2.5 million euros a year in a society
where the average wage was 24,000 euros a year (2,000 a month). See the online technical
appendix.

34
. Paris real estate (which at the time consisted mainly of wholly owned buildings
rather than apartments) was beyond the reach of the modestly wealthy, who were the
only ones for whom provincial real estate, including especially farmland, still mattered.
César Birotteau, who rejected his wife’s advice to invest in some good farms near
Chinon on the grounds that this was too staid an investment, saw himself as bold and
forward-looking—unfortunately for him. See Table S10.4 (available online) for a more
detailed version of
Table 10.1
showing the very rapid growth of foreign assets between 1872 and 1912, especially
in the largest portfolios.

35
. The national solidarity tax, instituted by the ordinance of August 15, 1945, was
an exceptional levy on all wealth, estimated as of June 4, 1945, at rates up to 20
percent for the largest fortunes, together with an exceptional levy on all nominal
increases of wealth between 1940 and 1945, at rates up to 100 percent for the largest
increases. In practice, in view of the very high inflation rate during the war (prices
more than tripled between 1940 and 1945), this levy amounted to a 100 percent tax
on anyone who did not sufficiently suffer during the war, as André Philip, a Socialist
member of General de Gaulle’s provisional government, admitted, explaining that it
was inevitable that the tax should weigh equally on “those who did not become wealthier
and perhaps even those who, in monetary terms, became poorer, in the sense that their
fortunes did not increase to the same degree as the general increase in prices, but
who were able to preserve their overall fortunes at a time when so many people in
France lost everything.” See André Siegfried,
L’Année Politique 1944–1945
(Paris: Editions du Grand Siècle, 1946), 159.

36
. See the online technical appendix.

37
. See in particular my
Les hauts revenus en France,
396–403. See also Piketty, “Income Inequality in France, 1901–1998,”
Journal of Political Economy
111, no. 5 (2003): 1004–42.

38
. See the simulations by Fabien Dell, “L’allemagne inégale: Inégalités de revenus
et de patrimoine en Allemagne, dynamique d’accumulation du capital et taxation de
Bismarck à Schröder 1870–2005,” Ph.D. thesis, Paris School of Economics, 2008. See
also F. Dell, “Top Incomes in Germany and Switzerland Over over the Twentieth Century,”
Journal of the European Economic Association
3, no. 2/3 (2005): 412–21.

1
. I exclude theft and pillage, although these are not totally without historical significance.
Private appropriation of natural resources is discussed in the next chapter.

2
. In order to focus on long-term evolutions, I use averages by decade here. The annual
series are available online. For more detail on techniques and methods, see Thomas
Piketty, “On the Long-Run Evolution of Inheritance: France 1820–2050,” Paris School
of Economics, 2010; a summary version was published in the
Quarterly Journal of Economics
126, no. 3 (August 2011): 1071–131. These documents are available in the online technical
appendix.

3
. The discussion that follows is a little more technical than previous discussions
(but necessary to understand what is behind the observed evolutions), and some readers
may wish to skip a few pages and go directly to the implications and the discussion
of what lies ahead in the twenty-first century, which can be found in the sections
on Vautrin’s lecture and Rastignac’s dilemma.

4
. The term
μ
is corrected to take account of gifts (see below).

5
. In other words, one of every fifty adults dies each year. Since minors generally
own very little capital, it is clearer to write the decomposition in terms of adult
mortality (and to define
μ
in terms of adults alone). A small correction is then necessary to take account of
the wealth of minors. See the online technical appendix.

6
. On this subject, see Jens Beckert, trans. Thomas Dunlop,
Inherited Wealth
(Princeton: Princeton University Press, 2008), 291.

7
. Becker never explicitly states the idea that the rise of human capital should eclipse
the importance of inherited wealth, but it is often implicit in his work. In particular,
he notes frequently that society has become “more meritocratic” owing to the increasing
importance of education (without further detail). Becker has also proposed theoretical
models in which parents can bequeath wealth to less gifted children, less well endowed
with human capital, thereby reducing inequality. Given the extreme vertical concentration
of inherited wealth (the top decile always owns more than 60 percent of the wealth
available for inheritance, while the bottom half of the population owns nothing),
this potential horizontal redistribution effect within groups of wealthy siblings
(which, moreover, is not evident in the data, of which Becker makes almost no use)
is hardly likely to predominate. See the online technical appendix.