Capital in the Twenty-First Century (29 page)

In any case, it is clear that this type of calculation makes sense only in a slave
society, where human capital can be sold on the market, permanently and irrevocably.
Some economists, including the authors of a recent series of World Bank reports on
“the wealth of nations,” choose to calculate the total value of “human capital” by
capitalizing the value of the income flow from labor on the basis of a more or less
arbitrary annual rate of return (typically 4–5 percent). These reports conclude with
amazement that human capital is the leading form of capital in the enchanted world
of the twenty-first century. In reality, this conclusion is perfectly obvious and
would also have been true in the eighteenth century: whenever more than half of national
income goes to labor and one chooses to capitalize the flow of labor income at the
same or nearly the same rate as the flow of income to capital, then by definition
the value of human capital is greater than the value of all other forms of capital.
There is no need for amazement and no need to resort to a hypothetical capitalization
to reach this conclusion. (It is enough to compare the flows.).
¹⁸
Attributing a monetary value to the stock of human capital makes sense only in societies
where it is actually possible to own other individuals fully and entirely—societies
that at first sight have definitively ceased to exist.

{FIVE}

The Capital/Income Ratio over the Long Run

In the previous chapter I examined the metamorphoses of capital in Europe and North
America since the eighteenth century. Over the long run, the nature of wealth was
totally transformed: capital in the form of agricultural land was gradually replaced
by industrial and financial capital and urban real estate. Yet the most striking fact
was surely that in spite of these transformations, the total value of the capital
stock, measured in years of national income—the ratio that measures the overall importance
of capital in the economy and society—appears not to have changed very much over a
very long period of time. In Britain and France, the countries for which we possess
the most complete historical data, national capital today represents about five or
six years of national income, which is just slightly less than the level of wealth
observed in the eighteenth and nineteenth centuries and right up to the eve of World
War I (about six or seven years of national income). Given the strong, steady increase
of the capital/income ratio since the 1950s, moreover, it is natural to ask whether
this increase will continue in the decades to come and whether the capital/income
ratio will regain or even surpass past levels before the end of the twenty-first century.

The second salient fact concerns the comparison between Europe and the United States.
Unsurprisingly, the shocks of the 1914–1945 period affected Europe much more strongly,
so that the capital/income ratio was lower there from the 1920s into the 1980s. If
we except this lengthy period of war and its aftermath, however, we find that the
capital/income ratio has always tended to be higher in Europe. This was true in the
nineteenth and early twentieth centuries (when the capital/income ratio was 6 to 7
in Europe compared with 4 to 5 in the United States) and again in the late twentieth
and early twenty-first centuries: private wealth in Europe again surpassed US levels
in the early 1990s, and the capital/income ratio there is close to 6 today, compared
with slightly more than 4 in the United States (see
Figures 5.1
and
5.2
).
¹

FIGURE 5.1.
   Private and public capital: Europe and America, 1870–2010

The fluctuations of national capital in the long run correspond mostly to the fluctuations
of private capital (both in Europe and in the United States).

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

FIGURE 5.2.
   National capital in Europe and America, 1870–2010

National capital (public and private) is worth 6.5 years of national income in Europe
in 1910, versus 4.5 years in America.

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

These facts remain to be explained. Why did the capital/income ratio return to historical
highs in Europe, and why should it be structurally higher in Europe than in the United
States? What magical forces imply that capital in one society should be worth six
or seven years of national income rather than three or four? Is there an equilibrium
level for the capital/income ratio, and if so how is it determined, what are the consequences
for the rate of return on capital, and what is the relation between it and the capital-labor
split of national income? To answer these questions, I will begin by presenting the
dynamic law that allows us to relate the capital/income ratio in an economy to its
savings and growth rates.

In the long run, the capital/income ratio
β
is related in a simple and transparent way to the savings rate
s
and the growth rate
g
according to the following formula:

β
=
s
/
g

For example, if
s
=
12% and
g
=
2%, then
β
=
s
/
g
=
600%.
²

In other words, if a country saves 12 percent of its national income every year, and
the rate of growth of its national income is 2 percent per year, then in the long
run the capital/income ratio will be equal to 600 percent: the country will have accumulated
capital worth six years of national income.

This formula, which can be regarded as the second fundamental law of capitalism, reflects
an obvious but important point: a country that saves a lot and grows slowly will over
the long run accumulate an enormous stock of capital (relative to its income), which
can in turn have a significant effect on the social structure and distribution of
wealth.

Let me put it another way: in a quasi-stagnant society, wealth accumulated in the
past will inevitably acquire disproportionate importance.

The return to a structurally high capital/income ratio in the twenty-first century,
close to the levels observed in the eighteenth and nineteenth centuries, can therefore
be explained by the return to a slow-growth regime. Decreased growth—especially demographic
growth—is thus responsible for capital’s comeback.

The basic point is that small variations in the rate of growth can have very large
effects on the capital/income ratio over the long run.

For example, given a savings rate of 12 percent, if the rate of growth falls to 1.5
percent a year (instead of 2 percent), then the long-term capital/income ratio
β
=
s
/
g
will rise to eight years of national income (instead of six). If the growth rate
falls to 1 percent, then
β
=
s
/
g
will rise to twelve years, indicative of a society twice as capital intensive as
when the growth rate was 2 percent. In one respect, this is good news: capital is
potentially useful to everyone, and provided that things are properly organized, everyone
can benefit from it. In another respect, however, what this means is that the owners
of capital—for a given distribution of wealth—potentially control a larger share of
total economic resources. In any event, the economic, social, and political repercussions
of such a change are considerable.

On the other hand if the growth rate increases to 3 percent, then
β
=
s
/
g
will fall to just four years of national income. If the savings rate simultaneously
decreases slightly to
s
=
9 percent, then the long-run capital/income ratio will decline to 3.

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.

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.