Capital in the Twenty-First Century (30 page)

Hence there is a crucial difference between this law and the law
α
=
r
×
β
, which I called the first fundamental law of capitalism in
Chapter 1
. According to that law, the share of capital income in national income,
α
, is equal to the average rate of return on capital,
r
, times the capital/income ratio,
β
. It is important to realize that the law
α
=
r
×
β
is actually a pure accounting identity, valid at all times in all places, by construction.
Indeed, one can view it as a definition of the share of capital in national income
(or of the rate of return on capital, depending on which parameter is easiest to measure)
rather than as a law. By contrast, the law
β
=
s
/
g
is the result of a dynamic process: it represents a state of equilibrium toward which
an economy will tend if the savings rate is
s
and the growth rate
g
, but that equilibrium state is never perfectly realized in practice.

Second, the law
β
=
s
/
g
is valid only if one focuses on those forms of capital that human beings can accumulate.
If a significant fraction of national capital consists of pure natural resources (i.e.,
natural resources whose value is independent of any human improvement and any past
investment), then
β
can be quite high without any contribution from savings. I will say more later about
the practical importance of nonaccumulable capital.

Finally, the law
β
=
s
/
g
is valid only if asset prices evolve on average in the same way as consumer prices.
If the price of real estate or stocks rises faster than other prices, then the ratio
β
between the market value of national capital and the annual flow of national income
can again be quite high without the addition of any new savings. In the short run,
variations (capital gains or losses) of relative asset prices (i.e., of asset prices
relative to consumer prices) are often quite a bit larger than volume effects (i.e.,
effects linked to new savings). If we assume, however, that price variations balance
out over the long run, then the law
β
=
s
/
g
is necessarily valid, regardless of the reasons why the country in question chooses
to save a proportion
s
of its national income.

This point bears emphasizing: the law
β
=
s
/
g
is totally independent of the reasons why the residents of a particular country—or
their government—accumulate wealth. In practice, people accumulate capital for all
sorts of reasons: for instance, to increase future consumption (or to avoid a decrease
in consumption after retirement), or to amass or preserve wealth for the next generation,
or again to acquire the power, security, or prestige that often come with wealth.
In general, all these motivations are present at once in proportions that vary with
the individual, the country, and the age. Quite often, all these motivations are combined
in single individuals, and individuals themselves may not always be able to articulate
them clearly. In
Part Three
I discuss in depth the significant implications of these various motivations and
mechanisms of accumulation for inequality and the distribution of wealth, the role
of inheritance in the structure of inequality, and, more generally, the social, moral,
and political justification of disparities in wealth. At this stage I am simply explaining
the dynamics of the capital/income ratio (a question that can be studied, at least
initially, independently of the question of how wealth is distributed). The point
I want to stress is that the law
β
=
s
/
g
applies in all cases, regardless of the exact reasons for a country’s savings rate.

This is due to the simple fact that
β
=
s
/
g
is the only stable capital/income ratio in a country that saves a fraction
s
of its income, which grows at a rate
g
.

The argument is elementary. Let me illustrate it with an example. In concrete terms:
if a country is saving 12 percent of its income every year, and if its initial capital
stock is equal to six years of income, then the capital stock will grow at 2 percent
a year,
⁴
thus at exactly the same rate as national income, so that the capital/income ratio
will remain stable.

By contrast, if the capital stock is less than six years of income, then a savings
rate of 12 percent will cause the capital stock to grow at a rate greater than 2 percent
a year and therefore faster than income, so that the capital/income ratio will increase
until it attains its equilibrium level.

Conversely, if the capital stock is greater than six years of annual income, then
a savings rate of 12 percent implies that capital is growing at less than 2 percent
a year, so that the capital/income ratio cannot be maintained at that level and will
therefore decrease until it reaches equilibrium.

In each case, the capital/income ratio tends over the long run toward its equilibrium
level
β
=
s
/
g
(possibly augmented by pure natural resources), provided that the average price of
assets evolves at the same rate as consumption prices over the long run.
⁵

To sum up: the law
β
=
s
/
g
does not explain the short-term shocks to which the capital/income ratio is subject,
any more than it explains the existence of world wars or the crisis of 1929—events
that can be taken as examples of extreme shocks—but it does allow us to understand
the potential equilibrium level toward which the capital/income ratio tends in the
long run, when the effects of shocks and crises have dissipated.

In order to illustrate the difference between short-term and long-term movements of
the capital/income ratio, it is useful to examine the annual changes observed in the
wealthiest countries between 1970 and 2010, a period for which we have reliable and
homogeneous data for a large number of countries. To begin, here is a look at the
ratio of private capital to national income, whose evolution is shown in
Figure 5.3
for the eight richest countries in the world, in order of decreasing GDP: the United
States, Japan, Germany, France, Britain, Italy, Canada, and Australia.

FIGURE 5.3.
   Private capital in rich countries, 1970–2010

Private capital is worth between two and 3.5 years of national income in rich countries
in 1970, and between four and seven years of national income in 2010.

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

Compared with
Figures 5.1
and
5.2
, as well as with the figures that accompanied previous chapters, which presented
decennial averages in order to focus attention on long-term trends,
Figure 5.3
displays annual series and shows that the capital/income ratio in all countries varied
constantly in the very short run. These erratic changes are due to the fact that the
prices of real estate (including housing and business real estate) and financial assets
(especially shares of stock) are notoriously volatile. It is always very difficult
to set a price on capital, in part because it is objectively complex to foresee the
future demand for the goods and services generated by a firm or by real estate and
therefore to predict the future flows of profit, dividends, royalties, rents, and
so on that the assets in question will yield, and in part because the present value
of a building or corporation depends not only on these fundamental factors but also
on the price at which one can hope to sell these assets if the need arises (that is,
on the anticipated capital gain or loss).

Indeed, these anticipated future prices themselves depend on the general enthusiasm
for a given type of asset, which can give rise to so-called self-fulfilling beliefs:
as long as one can hope to sell an asset for more than one paid for it, it may be
individually rational to pay a good deal more than the fundamental value of that asset
(especially since the fundamental value is itself uncertain), thus giving in to the
general enthusiasm for that type of asset, even though it may be excessive. That is
why speculative bubbles in real estate and stocks have existed as long as capital
itself; they are consubstantial with its history.

As it happens, the most spectacular bubble in the period 1970–2010 was surely the
Japanese bubble of 1990 (see
Figure 5.3
). During the 1980s, the value of private wealth shot up in Japan from slightly more
than four years of national income at the beginning of the decade to nearly seven
at the end. Clearly, this enormous and extremely rapid increase was partly artificial:
the value of private capital fell sharply in the early 1990s before stabilizing at
around six years of national income from the mid-1990s on.

I will not rehearse the history of the numerous real estate and stock market bubbles
that inflated and burst in the rich countries after 1970, nor will I attempt to predict
future bubbles, which I am quite incapable of doing in any case. Note, however, the
sharp correction in the Italian real estate market in 1994–1995 and the bursting of
the Internet bubble in 2000–2001, which caused a particularly sharp drop in the capital/income
ratio in the United States and Britain (though not as sharp as the drop in Japan ten
years earlier). Note, too, that the subsequent US real estate and stock market boom
continued until 2007, followed by a deep drop in the recession of 2008–2009. In two
years, US private fortunes shrank from five to four years of national income, a drop
of roughly the same size as the Japanese correction of 1991–1992. In other countries,
and particularly in Europe, the correction was less severe or even nonexistent: in
Britain, France, and Italy, the price of assets, especially in real estate, briefly
stabilized in 2008 before starting upward again in 2009–2010, so that by the early
2010s private wealth had returned to the level attained in 2007, if not slightly higher.

The important point I want to emphasize is that beyond these erratic and unpredictable
variations in short-term asset prices, variations whose amplitude seems to have increased
in recent decades (and we will see later that this can be related to the increase
in the potential capital/income ratio), there is indeed a long-term trend at work
in all of the rich countries in the period 1970–2010 (see
Figure 5.3
). At the beginning of the 1970s, the total value of private wealth (net of debt)
stood between two and three and a half years of national income in all the rich countries,
on all continents.
⁶
Forty years later, in 2010, private wealth represented between four and seven years
of national income in all the countries under study.
⁷
The general evolution is clear: bubbles aside, what we are witnessing is a strong
comeback of private capital in the rich countries since 1970, or, to put it another
way, the emergence of a new patrimonial capitalism.

This structural evolution is explained by three sets of factors, which complement
and reinforce one another to give the phenomenon a very significant amplitude. The
most important factor in the long run is slower growth, especially demographic growth,
which, together with a high rate of saving, automatically gives rise to a structural
increase in the long-run capital/income ratio, owing to the law
β
=
s
/
g
. This mechanism is the dominant force in the very long run but should not be allowed
to obscure the two other factors that have substantially reinforced its effects over
the last few decades: first, the gradual privatization and transfer of public wealth
into private hands in the 1970s and 1980s, and second, a long-term catch-up phenomenon
affecting real estate and stock market prices, which also accelerated in the 1980s
and 1990s in a political context that was on the whole more favorable to private wealth
than that of the immediate postwar decades.

I begin with the first mechanism, based on slower growth coupled with continued high
saving and the dynamic law
β
=
s
/
g
. In
Table 5.1
I have indicated the average values of the growth rates and private savings rates
in the eight richest countries during the period 1970–2010. As noted in
Chapter 2
, the rate of growth of per capita national income (or the virtually identical growth
rate of per capita domestic product) has been quite similar in all the developed countries
over the last few decades. If comparisons are made over periods of a few years, the
differences can be significant, and these often spur national pride or jealousy. But
if one takes averages over longer periods, the fact is that all the rich countries
are growing at approximately the same rate. Between 1970 and 2010, the average annual
rate of growth of per capita national income ranged from 1.6 to 2.0 percent in the
eight most developed countries and more often than not remained between 1.7 and 1.9
percent. Given the imperfections of the available statistical measures (especially
price indices), it is by no means certain that such small differences are statistically
significant.
⁸