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\author{Thomas \textsc{Piketty} \\
%EndAName
Paris School of Economics \and Gabriel \textsc{Zucman} \\
%EndAName
London School of Economics and UC Berkeley}
\date{\today \thanks{%
Thomas Piketty: piketty@pse.ens.fr; Gabriel Zucman: zucman@berkeley.edu. We
are grateful to numerous seminar participants for their reactions. This
revised and shortened version also benefited from the comments of the editor
and three anonymous referees. A detailed database and Data Appendix
supplementing this article are available online: %
\url{http://piketty.pse.ens.fr/capitalisback} and %
\url{http://www.gabriel-zucman.eu/capitalisback}.} }
\uppercase{\title{Capital is Back:\\
Wealth-Income Ratios in Rich Countries 1700-2010}}\maketitle

\begin{abstract}
How do aggregate wealth-to-income ratios evolve in the long run and why? We
address this question using 1970-2010 national balance sheets recently
compiled in the top eight developed economies. For the U.S., U.K., Germany,
and France, we are able to extend our analysis as far back as 1700. We find
in every country a gradual rise of wealth-income ratios in recent decades,
from about 200-300\% in 1970 to 400-600\% in 2010. In effect, today's ratios
appear to be returning to the high values observed in Europe in the
eighteenth and nineteenth centuries (600-700\%). This can be explained by a
long run asset price recovery (itself driven by changes in capital policies
since the world wars) and by the slowdown of productivity and population
growth, in line with the $\beta =s/g$ Harrod-Domar-Solow formula. That is,
for a given net saving rate $s=$ 10\%, the long run wealth-income ratio $%
\beta $ is about 300\% if $g=$ 3\% and 600\% if $g=$ 1.5\%. Our results have
implications for capital taxation and regulation and shed new light on the
changing nature of wealth, the shape of the production function, and the
rise of capital shares.
\end{abstract}



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\section{Introduction}

This paper addresses what is arguably one the most basic economic questions:
how do wealth-income and capital-output ratios evolve in the long run, and
why?

Until recently it was difficult to properly address this question, because
national accounts were mostly about flows, not stocks. Economists had at
their disposal a large body of historical series on flows of output, income
and consumption -- but limited data on stocks of assets and liabilities.
When needed, for example for growth accounting exercises, estimates of
capital stocks were typically obtained by cumulating past flows of saving
and investment. While fine for some purposes, this procedure severely limits
the set of questions one can ask.

In recent years, the statistical institutes of nearly all developed
countries have started publishing retrospective national stock accounts
including annual and consistent balance sheets. Following new international
guidelines, the balance sheets report on the market value of all the
non-financial and financial assets and liabilities held by each sector of
the economy (households, government, and corporations) and by the rest of
the world. They can be used to measure the stocks of private and national
wealth at current market value.

This paper makes use of these new balance sheets in order to establish a
number of facts and to analyze whether standard capital accumulation models
can account for these facts. We should stress at the outset that we are well
aware of the deficiencies of existing balance sheets. In many ways these
series are still in their infancy. But they are the best data we have in
order to study wealth accumulation -- a question so important that we cannot
wait for perfect data before we start addressing it, and which has indeed
been addressed in the past by many authors using far less data than we
presently have. In addition, we feel that the best way for scholars to
contribute to future data improvement is to use existing balance sheets in a
conceptually coherent manner, so as to better identify their limitations.
Our paper, therefore, can also be viewed as an attempt to assess the
internal consistency of the flow and stock sides of existing national
accounts, and to pinpoint the areas in which progress needs to be made.

Our contribution is twofold. First, we put together a new macro-historical
data set on wealth and income, whose main characteristics are summarized in
Table I. To our knowledge, it is the first international database to include
long-run, homogeneous information on national wealth. The database is
available online, along with a comprehensive Data Appendix that precisely
documents the data construction process. For the eight largest developed
economies in the world -- the U.S., Japan, Germany, France, the U.K., Italy,
Canada, and Australia -- we have official annual series covering the
1970-2010 period. Through to the world wars, there was a lively tradition of
national wealth accounting in many countries. By combining numerous
historical estimates in a systematic and consistent manner, we are able to
extend our series as far back as 1870 (Germany), 1770 (U.S.), and 1700 (U.K.
and France). The resulting database provides extensive information on the
structure of wealth, saving, and investment. It can be used to study core
macroeconomic questions -- such as private capital accumulation, the
dynamics of the public debt, and patterns in net foreign asset positions --
altogether and over unusually long periods of time.

Our second contribution is to exploit the database in order to establish a
number of new results. We first document that wealth-income ratios have been
gradually rising in each of the top eight developed countries over the last
four decades, from about 200-300\% in 1970 to 400-600\% in 2010 (Figure I).
Taking a long-run perspective, today's ratios appear to be returning to the
high values observed in Europe in the eighteenth and nineteenth centuries,
namely about 600-700\%, despite considerable changes in the nature of wealth
(Figure II and III). In the U.S., the wealth-income ratio has also followed
a U-shaped pattern, but less marked (Figure IV).

In order to understand these dynamics, we provide detailed decompositions of
wealth accumulation into volume effects (saving) and relative price effects
(real capital gains and losses). The results show that the U-shaped
evolution of European wealth-income ratios can be explained by two main
factors. The first is a long-run swing in relative asset prices, which, we
argue, was itself largely driven by changes in capital policies in the
course of the 20$^{th}$ century. Before World War I, capital markets ran
unfettered. A number of anti-capital policies were then put into place,
which depressed asset prices through to the 1970s. These policies were
gradually lifted from the 1980s on, contributing to an asset price recovery.

The second key explanation for the return of high wealth-income ratios is
the slowdown of productivity and population growth. According to the
Harrod-Domar-Solow formula, in the long run the wealth-income ratio $\beta $
is equal to the net-of-depreciation saving rate $s$ divided by the income
growth rate $g$. So for a given saving rate $s=$10\%, the long-run $\beta $
is about 300\% if $g=$ 3\% and about 600\% if $g=$ 1.5\%. In a broad class
of general equilibrium models with endogenous saving, the steady-state
wealth-income ratio is also a decreasing function of the income growth rate $%
g$.

This mechanism sheds light on the rise in the wealth-income ratios of Europe
and Japan, two economies where population and productivity growth has slowed
markedly: capital is back because low growth is back. It also helps
understand why wealth-income ratios are lower in the U.S., where population
growth -- but not saving -- is larger than in Europe. Last, the $\beta =s/g$
steady-state formula seems to account reasonably well for the very long-run
dynamics of wealth accumulation. Over a few years and even a few decades,
valuation effects are of paramount importance. But in the main developed
economies, we find that today's wealth levels are reasonably well explained
by 1870-2010 saving and income growth rates, in line with the workhorse
one-good model of capital accumulation. In the long run, there seems to be
no significant divergence between the price of consumption and capital goods.

We stress, however, that despite our efforts we still face data limitations
when decomposing wealth accumulation in the very long run. Our
interpretations are subject to these limitations, and we hope our findings
will motivate new research on the historical dynamics of asset prices.
Further, in some countries capital gains -- particularly on housing --
explain a large part of the recent rise of wealth-income ratios. It is only
in the very long run or at a very aggregate level (i.e., at a European
rather than country level) that relative price effects seem to wash out.

Our findings have implications for the future and for policy-making. First,
the low wealth-income ratios of the mid-twentieth century were due to
special circumstances. The world wars and anti-capital policies destroyed a
large fraction of the world capital stock and reduced the market value of
private wealth, which is unlikely to happen again with free markets. By
contrast, if income growth slows down in the decades ahead, then
wealth-income ratios may become high pretty much everywhere. As long as they
keep saving sizable amounts (due to a mixture of bequest, life-cycle and
precautionary reasons), countries with low $g$ are bound to have high $\beta$%
.

The return of high wealth-income ratios is not bad in itself, but it raises
new issues about capital taxation and regulation. Because wealth is always
very concentrated (due in particular to the cumulative and multiplicative
processes governing wealth inequality dynamics), high $\beta $ implies than
the inequality of wealth, and potentially the inequality of inherited
wealth, is likely to play a bigger role for the overall structure of
inequality in the twenty first century than it did in the postwar period.
This evolution might reinforce the need for progressive capital taxation
(Piketty, 2011, 2014; Piketty and Saez, 2013), which in turn would require a
high degree of international cooperation in order to prevent wealth from
hiding in offshore tax havens (Zucman, 2013). If international tax
competition prevents these policy changes from happening, one cannot exclude
the development of a new wave of anti-globalization and anti-capital
policies.

Further, because $s$ and $g$ are largely determined by different forces,
wealth-income ratios can vary a lot between countries. The implications for
financial regulation are important. With perfect capital markets, large
differences in wealth-income ratios potentially imply large net foreign
asset positions, which can create political tensions between countries. With
imperfect capital markets and home portfolios bias, structurally high
wealth-income ratios can contribute to domestic asset price bubbles.
According to our computations, the wealth-income ratio reached 700\% at the
peak of the Japanese bubble of the late 1980s, and 800\% in Spain in
2008-2009.\footnote{%
See Appendix figure A8. We do not include Spain in our main sample of
countries because the Bank of Spain balance sheets currently available only
start in 1987, and we want to be able to decompose wealth accumulation over
a longer period (at least 1970-2010).} Housing and financial bubbles are
potentially more devastating when the total stock of wealth amounts to 6-8
years of national income rather than 2-3 years only. The fact that the
Japanese and Spanish bubbles are easily identifiable in our dataset also
suggests that monitoring wealth-income ratios may help designing appropriate
financial and monetary policy. In Japan and Spain, most observers had
noticed that asset price indexes were rising fast. But in the absence of
well-defined reference points, it is always difficult for policy makers to
determine when such evolutions have gone too far and whether they should
act. Wealth-income ratios and wealth accumulation decompositions provide
useful if imperfect reference points.

Last, our findings shed new light on the long run changes in the nature of
wealth, the shape of the production function and the recent rise in capital
shares. In the 18$^{th}$ and early 19$^{th}$ century, capital was mostly
land, so that there was limited scope for substituting labor to capital. In
the 20$^{th}$ and 21$^{st}$ centuries, by contrast, capital takes many
forms, to an extent such that the elasticity of substitution between labor
and capital might well be larger than 1. With an elasticity even moderately
larger than 1, rising capital-output ratios can generate substantial
increases in capital shares, similar to those that have occurred in rich
countries since the 1970s.

The paper is organized as follows. Section II relates our work to the
existing literature. In section III we define the key ratios and present the
accounting framework. We describe the 1970-2010 evolution of wealth-income
ratios in Section IV, before decomposing the accumulation of wealth into
volume and price effects (Section V). In section VI, we present
decomposition results over a longer period (1870-2010) for a subset of
countries (U.S., Germany, France, U.K.). We take an even longer perspective
in section VII in which we discuss the changing nature of wealth in the
U.K., France and the U.S. since the 18$^{th}$ century. In section VIII, we
compare the long-run evolution of capital-output ratios and capital shares
in order to discuss the changing nature of technology and the pros and cons
of the Cobb-Douglas approximation. Section IX concludes.

\section{Related literature}

\subsection{Literature on national wealth}

To the best of our knowledge, this paper is the first attempt to gather a
large set of national balance sheets in order to analyze the long-run
evolution of wealth-income ratios. For a long time, research in this area
was impeded by a lack of data. It is only in 1993 that the System of
National Accounts, the international standard for national accounting, first
included guidelines for wealth. In most rich countries, the publication of
time series of national wealth only began in the 1990s and 2000s. In a key
country like Germany, the first official balance sheets were released in
2010.

The recent emphasis on national wealth, however, largely represents a return
to older practice. Until the early twentieth century, economists and
statisticians were much more interested in computing national wealth than
national income and output. The first national balance sheets were
established in the late seventeenth and early eighteenth centuries by Petty
(1664) and King (1696) in the U.K., Boisguillebert (1695) and Vauban (1707)
in France. National wealth estimates then became plentiful in the nineteenth
and early twentieth century, with the work of Colqhoun (1815), Giffen (1889)
and Bowley (1920) in the U.K., Foville (1893) and Colson (1903) in France,
Helfferich (1913) in Germany, King (1915) in the U.S., and dozens of other
economists from all industrialized nations. Although these historical
balance sheets are far from perfect, their methods are well documented and
they are usually internally consistent. In many ways, it was also easier to
estimate national wealth around 1900 than it is today: the structure of
property was simpler, with less financial intermediation and cross-border
positions.

Following the 1914-1945 capital shocks, the long tradition of research on
national wealth largely disappeared, partly because of the new emphasis on
short run output fluctuations following the Great Depression, and partly
because the chaotic asset price movements of the interwar made the
computation of the current market value of wealth and the comparison with
pre-World War I estimates much more difficult. While there has been some
effort to put together historical balance sheets in recent decades, most
notably by Goldsmith (1985, 1991), to date no systematic attempt has been
made to relate the evolution of wealth-income ratios to the magnitude of
saving flows.\footnote{%
In particular, Goldsmith does not relate his wealth estimates to saving and
investment flows. He is mostly interested in the rise of financial
intermediation, that is the rise of gross financial assets and liabilities
(expressed as a fraction of national income), rather than in the evolution
of the net wealth-income ratio. Nineteenth century authors like Giffen and
Foville were fascinated by the huge accumulation of private capital, but did
not have much estimates of income, saving and investment, so they were not
able to properly analyze the evolution of the wealth-income ratio.
Surprisingly enough, authors like Karl Marx -- who were much interested in
the rise of capital and the possibility that $\beta $ reaches very high
levels -- largely ignored the literature on national wealth.} The reason is
probably that it is only recently that official balance sheets have become
sufficiently widespread to make the exercise meaningful.

\subsection{Literature on capital accumulation and growth}

The lack of data on wealth in the aftermath of the 1914-1945 shocks did not
prevent economists from studying capital accumulation. In particular, Solow
developed the neoclassical growth model in the 1950s. In this model, the
long-run capital-output ratio is equal to the ratio between the saving rate
and the growth rate of the economy. As is well-known, the $\beta =s/g$
formula was first derived by Harrod (1939) and Domar (1947) using
fixed-coefficient production functions, in which case $\beta $ is entirely
given by technology -- hence the knife-edge conclusions about growth.%
\footnote{%
Harrod emphasized the inherent instability of the growth process, while
Domar stressed the possibility that $\beta $ and $s$ can adjust in case the
natural growth rate $g$ differs from $s/\beta $.} The classic derivation of
the formula with a flexible production function $Y=F(K,L)$ involving
capital-labor substitution, thereby making $\beta $ endogenous and balanced
growth possible, is due to Solow (1956). Authors of the time had limited
national accounts at their disposal to estimate the parameters of the
formula. In numerical illustrations, they typically took $\beta =400\%$, $%
g=2\%$, and $s=8\%$. They were not entirely clear about the measurement of
capital, however.

Starting in the 1960s, the Solow model was largely applied for empirical
studies of growth (see Denison, 1962; Jorgenson and Griliches, 1967;
Feinstein, 1978) and it was later on extended to human capital (Mankiw,
Romer and Weil, 1992; Barro, 1991). The main difference between our work and
the growth accounting literature is how we measure capital. Because of the
lack of balance sheet data, in the growth literature capital is typically
measured indirectly by cumulating past investment flows and attempting to
adjust for changes in relative prices -- what is known as the perpetual
inventory method. By contrast, we measure capital directly by using country
balance sheets in which we observe the actual market value of most types of
assets: real estate, equities (which capture the market value of
corporations), bonds, and so on. We are interested in what non-human private
capital is worth for households and in what public capital would be worth if
privatized. This notion is precisely what the economists of the 18$^{th}$
and 19$^{th}$ century aimed to capture. We believe it is a useful and well
defined starting point.\footnote{%
In the famous Cambridge controversy, the proponent of the U.K. view argued
that the notion of capital used in neoclassical growth models is not well
defined. In our view much of the confusion in this controversy owes to the
lack of balance sheet data and to the difficulty of making comparisons with
pre-World War 1 capital stock estimates. It is natural to use relative
market prices to aggregate the various capital assets into national capital,
just as it is natural to use relative market prices to aggregate the various
goods and services into national output.}

Compared to the capital stock estimates obtained by the perpetual inventory
method, country balance sheets have four important advantages. First, they
include non-produced assets such as land which cannot be measured by
cumulating past investment flows. It is critical to consistently account for
non-produced assets if one wants to conduct Solow-type growth accounting
exercises and compute the marginal product of capital (Caselli and Feyrer,
2007). Second, balance sheets rely for the most part on observed market
prices -- obtained from real estate and financial market transactions --
while perpetual inventory method capital stocks rely on estimated prices
that suffer from a number of pitfalls.\footnote{%
Appendix Section A.1.2 provides a detailed discussion of the many issued
faced by the price estimates used in the perpetual inventory method: the
accounting of depreciation, quality improvement, aggregation bias, etc.
Equity market prices are themselves not perfect; they can be very volatile
in the short run. But in the long run they are arguably the best data we
have to capture the market value of corporations' capital stocks.} Third,
our measure of country capital stocks includes most forms of intangible
capital, contrary to older estimates. Last and most important, country
balance sheets now follow standardized international definitions and are
available for many countries and over long periods of time. Market-value
balance sheets have their own deficiencies, but as we argue in this paper
their advantages vastly exceed their limitations. In our view, they ought to
be used more extensively in economic research.

In particular, now that national balance sheets are available, we can see
that some of the celebrated stylized facts on capital -- established when
there was actually little data on capital -- are not that robust. The
constancy of the capital-output ratio is not a fact for Europe and Japan and
is quite debatable for the U.S. Although this constancy is often seen as one
of the key regularities in economics, there has always been some confusion
about what the level of the capital-output ratio is supposed to be (see
Kaldor, 1961; Samuelson, 1970; Simon, 1990; Jones and Romer, 2010). The data
we now have suggest that the ratio is closer to 5-6 in most rich countries
today than to the values of 3-4 often used in macro models and textbooks.%
\footnote{%
Many estimates in the literature only look at the capital-output ratio in
the corporate sector (i.e., corporate capital divided by corporate product),
in which case ratios of 3 or even 2 are indeed in line with the data (see
Figures A70-A71). This, however, disregards the large stock of housing
capital (as well as non-corporate businesses and government capital), which
we feel is inappropriate (more on this below).}

Our results also suggest that the focus on the possibility of a balanced
growth path that has long characterized academic debates on capital
accumulation (most notably during the Cambridge controversy of the
1960s-1970s) has been somewhat misplaced. It is fairly obvious that there
can be a lot of capital-labor substitution in the long-run, and that many
different $\beta$ can occur in steady-state. But this does not imply that
the economy is necessarily in a stable or optimal state in any meaningful
way. High steady-state wealth-income ratios can go together with large
instability, asset price bubbles and high degrees of inequality -- all
plausible scenarios in mature, low-growth economies.

\subsection{Literature on external balance sheets}

Our work is close in spirit to the recent literature that documents and
attempts to understand the dynamics of the external balance sheets of
countries (Lane and Milesi-Ferretti, 2007; Gourinchas and Rey, 2007; Zucman,
2013). We extend this line of work to domestic wealth and to longer time
periods: we document the changing nature of domestic capital over time, and
we investigate the extent to which the observed aggregate dynamics can be
accounted for by saving flows and valuation effects. A key difference is
that our investigation is broader in scope: as we shall see, domestic
capital typically accounts for 90\%-110\% of the total wealth of rich
countries today, while the net foreign asset position accounts for -10\% to
+10\% only. Nevertheless, external wealth will turn out to play an important
role in the dynamics of national wealth, more spectacularly in the U.S. The
reason is that gross foreign positions are much bigger than net positions,
thereby potentially generating large capital gains or losses at the country
level.\footnote{%
See Obstfeld (2013) and Gourinchas and Rey (2013) for recent papers
surveying the literature on this issue.}

\subsection{Literature on income and wealth inequalities}

Last, this paper is to a large extent the continuation of the study of the
long run evolution of private wealth in France undertaken by one of us
(Piketty, 2011). We extend Piketty's analysis to many countries, to longer
time periods, and to public and foreign wealth. However, we do not decompose
aggregate wealth accumulation into an inherited and dynastic wealth
component on the one hand and a lifecycle and self-made wealth component on
the other (as Piketty does for France). Instead, we take the structure of
saving motives and the overall level of saving as given. In future research,
it would be interesting to extend our decompositions in order to study the
evolution of the relative importance of inherited versus life-cycle wealth
in as many countries as possible. Ultimately, the goal is also to introduce
distributional trends in the analysis.\footnote{%
See Davies et al. (2010) for a study of the world distribution of personal
wealth.}

\section{Conceptual framework and methodology}

\subsection{Concepts and definitions}

The concepts we use are standard: we strictly follow the U.N. System of
National Accounts (SNA). For the 1970-2010 period, we use official national
accounts that comply with the latest international guidelines (SNA, 1993,
2008). We take the data exactly as published, except in the rare cases where
the balance sheets deviate from the SNA, in which case we correct the data
to ensure consistency across countries.\footnote{%
For example, U.S. Flow of Funds balance sheets include durable goods,
contrary to other countries (see below), so to ensure consistency we
subtract durables.} For the previous periods, we have gathered a large
number of historical balance sheets and income series, which we have
homogenized using the same concepts and definitions as those used in the
most recent official accounts. Section A of the Data Appendix provides a
thorough discussion of the concepts and definitions used by the 1993 and
2008 SNA. All the details on how we have used available historical estimates
to construct our own pre-1970 wealth series are provided in the
country-specific sections of the Data Appendix; see in particular sections B
(devoted to the U.S.), D (Germany), E (France), and F (U.K.). Here we
provide the main definitions.

Private wealth $W_{t}$ is the net wealth (assets minus liabilities) of
households and non-profit institutions serving households.\footnote{%
The main reason for including non-profit institutions serving households
(NPISH) in private wealth is that the frontier between individuals and
private foundations is not always clear. The net wealth of NPISH is usually
small, and always less than 10\% of total net private wealth: currently it
is about 1\% in France, 3\%-4\% in Japan, and 6\%-7\% in the U.S., see
Appendix Table A65. The household sector also includes unincorporated
businesses.} Following SNA guidelines, assets include all the non-financial
assets -- land, buildings, machines, etc. -- and financial assets --
including life insurance and pensions funds -- over which ownership rights
can be enforced and that provide economic benefits to their owners.
Pay-as-you-go social security pension wealth is excluded, just like all
other claims on future government expenditures and transfers (like education
expenses for one's children and health benefits).\footnote{%
In any case, such claims would wash out for the computation of national
wealth -- which we view as a more meaningful concept than private wealth --
since they would count as assets for households and liabilities for the
government.} Durable goods owned by households, such as cars and furniture,
are excluded as well.\footnote{%
The value of durable goods appears to be relatively stable over time (about
30\%-50\% of national income, i.e. 5\%-10\% of net private wealth). See for
instance Appendix Table US.6f for durable goods in the U.S.} As a general
rule, all assets and liabilities are valued at their prevailing market
prices. Corporations are included in private wealth through the market value
of equities and corporate bonds. Unquoted shares are typically valued on the
basis of observed market prices for comparable, publicly traded companies.

We similarly define public (or government) wealth $W_{gt}$ as the net wealth
of public administrations and government agencies. In available balance
sheets, public non-financial assets like administrative buildings, schools
and hospitals are valued by cumulating past investment flows and upgrading
them using observed real estate prices.

We define market-value national wealth $W_{nt}$ as the sum of private and
public wealth:

\begin{equation*}
W_{nt}=W_{t}+W_{gt}
\end{equation*}

National wealth can also be decomposed into domestic capital and net foreign
assets: 
\begin{equation*}
W_{nt}=K_{t}+NFA_{t}
\end{equation*}

And domestic capital $K_{t}$ can in turn be decomposed as the sum of
agricultural land, housing, and other domestic capital (including the market
value of corporations, and the value of other non-financial assets held by
the private and public sectors, net of their liabilities).

An alternative measure of the wealth of corporations is the total value of
corporate assets net of non-equity liabilities, what we call the
corporations' book value. We define residual corporate wealth $W_{ct}$ as
the difference between the book-value of corporations and their market value
(which is the value of their equities). By definition, $W_{ct}$ is equal to
0 when Tobin's $Q$ -- the ratio between market and book values -- is equal
to 1. In practice there are several reasons why Tobin's $Q$ can be different
from 1, so that residual corporate wealth is at times positive, at times
negative. We define book-value national wealth $W_{bt}$ as the sum of
market-value national wealth and residual corporate wealth: $%
W_{bt}=W_{nt}+W_{ct}=W_{t}+W_{gt}+W_{ct}$. Although we prefer our
market-value concept of national wealth (or national capital), both
definitions have some merit, as we shall see.\footnote{$W_{bt}$ corresponds
to the concept of \textquotedblleft national net worth" in the SNA (see Data
Appendix A.4.2). In this paper, we propose to use \textquotedblleft national
wealth" and \textquotedblleft national capital" interchangeably (and
similarly for \textquotedblleft domestic wealth" and \textquotedblleft
domestic capital", \textquotedblleft foreign wealth" and \textquotedblleft
foreign capital", and \textquotedblleft private wealth" and
\textquotedblleft private capital"), and to specify whether one uses
\textquotedblleft market-value" or \textquotedblleft book-value" aggregates
(unless specified otherwise, we use \textquotedblleft market-value"
concepts). 19$^{th}$ century authors such as Giffen and Foville also used
\textquotedblleft national wealth" and \textquotedblleft national capital"
interchangeably. The difference is that they viewed market values as the
only possible value, while we recognize that both definitions have some
merit (see below the discussion on Germany).}

Balance sheets are constructed by national statistical institutes and
central banks using a large number of census-like sources, in particular
reports from financial and non-financial corporations about their balance
sheet and off-balance sheet positions, and housing surveys. The perpetual
inventory method usually plays a secondary role. The interested reader is
referred to the Appendix for a a precise discussion of the methods used by
the leading rich countries.

Regarding income, the definitions and notations are standard. Note that we
always use net-of-depreciation income and output concepts. National income $%
Y_{t}$ is the sum of net domestic output and net foreign income: $%
Y_{t}=Y_{dt}+r_{t} NFA_{t}$.\footnote{%
National income also includes net foreign labor income and net foreign
production taxes -- both of which are usually negligible.} Domestic output
can be thought as coming from some production function that uses domestic
capital and labor as inputs: $Y_{dt}=F(K_{t},L_{t})$.

We are particularly interested in the evolution of the private
wealth-national income ratio $\beta _{t}=W_{t}/Y_{t}$ and of the
(market-value) national wealth-national income ratio $\beta
_{nt}=W_{nt}/Y_{t}$. In a closed economy -- and more generally in an open
economy with a zero net foreign position -- the national wealth-national
income ratio $\beta _{nt}$ is the same as the domestic capital-output ratio $%
\beta _{kt}=K_{t}/Y_{dt}$.\footnote{%
In principle, one can imagine a country with a zero net foreign asset
position (so that $W_{nt}=K_{t}$) but non-zero net foreign income flows (so
that $Y_{t} \neq Y_{dt}$). In this case the national wealth-national income
ratio $\beta_{nt}$ will slightly differ from the domestic capital-output
ratio $\beta_{kt}$. In practice today, differences between $Y_{t}$ and $%
Y_{dt}$ are very small -- national income $Y_{t}$ is usually between 97\%
and 103\% of domestic output $Y_{dt}$ (see Appendix Figure A57). Net foreign
asset positions are usually small as well, so that the capital-output ratio $%
\beta_{kt}$ turns out to be usually close to the national wealth-income
ratio $\beta_{nt}$ in the 1970-2010 period (see Appendix Figure A67).} In
case public wealth is equal to zero, then both ratios are also equal to the
private wealth-national income ratio: $\beta _{t}=\beta _{nt}=\beta _{kt}$.
At the global level, the world wealth-income ratio is always equal to the
world capital-output ratio.

We are also interested in the evolution of the capital share $\alpha
_{t}=r_{t}K_{t}/Y_{dt}=r_{t}\beta _{kt}$, where $r_{t}$ is the average rate
of return on domestic capital. With imperfect capital markets, $r_{t}$ can
substantially vary across assets. With perfect capital markets and no
aggregate uncertainty, $r_{t}$ is the same for all assets and is equal to
the marginal product of capital. With a Cobb-Douglas production function $%
F(K_{t},L_{t})=K_{t}^{\alpha }L_{t}^{1-\alpha }$, and a closed economy
setting, the capital share is entirely set by technology: $\alpha
_{t}=r_{t}\beta _{kt}=\alpha $. A higher capital-output ratio $\beta _{kt}$
is exactly compensated by a lower capital return $r_{t}=\alpha /\beta _{kt}$%
, so that the product of the two is constant. In an open economy setting,
the world capital share is also constant and equal to $\alpha $, and the
world rate of return is also given by $r_{t}=\alpha /\beta _{kt}$, but the
countries with higher-than-average wealth-income ratios invest part of their
wealth in other countries, so that for them the share of capital in national
income $r_{t}W_{t}/Y_{t}=r_{t}\beta _{t}$ is larger than $\alpha $.

With a CES production function, much depends on whether the capital-labor
elasticity of substitution $\sigma $ is larger or smaller than one. If $%
\sigma >1$, then as $\beta _{kt}$ rises, the fall of the marginal product of
capital $r_{t}$ is smaller than the rise of $\beta _{kt}$, so that the
capital share $\alpha _{t}=r_{t}\beta _{kt}$ is an increasing function of $%
\beta _{kt}$. Conversely, if $\sigma <1$, the fall of $r_{t}$ is bigger than
the rise of $\beta _{kt}$, so that the capital share is a decreasing
function of $\beta _{kt}$.\footnote{%
A CES production function is given by: $F(K,L)=(aK^{\frac{\sigma -1}{\sigma }%
}+(1-a)L^{\frac{\sigma -1}{\sigma }})^{\frac{\sigma }{\sigma -1}}$. As $%
\sigma \rightarrow \infty $, the production function becomes linear, i.e.
the return to capital is independent of the quantity of capital (this is
like a robot economy where capital can produce output on its own). As $%
\sigma \rightarrow 0$, the production function becomes putty-clay, i.e. the
return to capital falls to zero if the quantity of capital is slightly above
the fixed proportion technology. We return to this discussion in Section VII.%
} Because we include all forms of capital assets into our aggregate capital
concept $K$ (including housing), the aggregate elasticity of substitution $%
\sigma $ should be interpreted as resulting from both supply forces
(producers shift between technologies with different capital intensities)
and demand forces (consumers shift between goods and services with different
capital intensities, including housing services vs. other goods and
services).\footnote{%
Excluding housing from wealth strikes us an inappropriate, first because it
typically represents about half of the capital stock, and next because the
frontier with other capital assets is not always clear. In particular, the
same assets can be reallocated between housing and business uses. Note also
that official balance sheets treat housing assets owned by corporations (and
sometime those rented by households) as corporate capital assets.}

\subsection{The one-good wealth accumulation model: $\protect \beta =s/g$}

Wealth accumulation between time $t$ and $t+1$ can always be decomposed into
a volume effect and a relative price effect: $W_{nt+1}=W_{nt}+S_{t}+KG_{t}$,
where $W_{nt}$ is the market value of national wealth at time $t$, $S_{t}$
is the net-of-depreciation national saving flow between time $t$ and $t+1$
(volume effect), and $KG_{t}$ is the capital gain or loss between time $t$
and $t+1$ (relative price effect). In the one-good model of wealth
accumulation, and more generally in a model with a constant relative price
between capital and consumption goods, there is no relative price effect ($%
KG_{t}=0$). The national wealth-income ratio $\beta _{nt}=W_{nt}/Y_{t}$ is
given by the following equation:

\bigskip

\begin{equation*}
\beta _{nt+1}=\frac{1+g_{wst}}{1+g_{t}} \beta _{nt}
\end{equation*}

where: $1+g_{wst}=1+s_{t}/\beta _{nt}$ = saving-induced wealth growth rate;

$1+g_{t}=Y_{t+1}/Y_{t}$ = growth rate of national income;

$s_{t}=S_{t}/Y_{t}$ = net-of-depreciation national saving rate (domestic +
net foreign saving).

In the long run, with a fixed saving rate $s_{t}=s$ and growth rate $g_{t}=g$%
, the steady-state national wealth-income ratio is given by the
Harrod-Domar-Solow formula:

\begin{equation*}
\beta _{nt}\rightarrow \beta_{n} =s/g
\end{equation*}

Should we use gross-of-depreciation saving rates rather than net rates, the
steady-state formula would be $\beta _{n}=s/(g+\delta )$ with $s$ the gross
saving rate, and $\delta $ the depreciation rate expressed as a proportion
of the wealth stock. We find it more transparent to express everything in
terms of net saving rates and use the $s/g$ formulation, so as to better
focus on the saving versus capital gain decomposition. Both formulas are
equivalent and require the same data.\footnote{%
Appendix Table A84 provides cross-country data on depreciation. Detailed
series on gross saving, net saving, and depreciation, by sector of the
economy, are in Appendix Tables US.12c, JP.12c, etc. Whether one writes down
the decomposition of wealth accumulation using gross or net saving, one
needs depreciation series.}

The $s/g$ formulation also applies to the capital-output ratio $\beta_{k}$,
with the only difference that for $\beta_{k}$ the saving rate $s$ to take
into consideration is the domestic saving rate (i.e., national saving minus
net foreign saving\footnote{%
Net foreign saving equals the current account balance plus net foreign
capital transfers (which are usually negligible) minus net errors and
omissions in the balance of payments.}) and $g$ is the growth rate of
domestic output (i.e., national income minus net foreign income).

The steady-state formula $\beta =s/g$ is a pure accounting equation. If the
saving rate is $s=10\%$, and if the economy grows at rate $g=2\%$, then in
the long run the wealth-income ratio has to be equal to $\beta =500\%$,
because it is the only ratio such that wealth rises at the same rate as
income: $g_{ws}=s/\beta =2\%=g$. The formula holds in the steady-state of
any micro-founded model, independently of the nature of saving motives. In
models where saving is exogenous, the long run wealth-income ratio is
obviously a decreasing function of $g$. Importantly, however, the negative
relationship between steady-state $\beta $ and $g$ also holds true in a very
large class of models in which $s$ is endogenous.\footnote{%
For more details, see the working paper version of this article, Piketty and
Zucman (2013, section 3).} It holds true, in particular, in different
variants of the \textquotedblleft bequest-in-the-utility-function" model,%
\footnote{%
In such models, the saving rate parameter $s$ follows directly from the
strength of the taste for bequest or wealth in the utility function.} in OLG
models,\footnote{%
The saving rate $s$ is then determined -- among other things -- by the
number of years spent in retirement and the generosity of the public pension
system.} in the dynastic, infinite-horizon model\footnote{%
In this model, each dynasty maximizes $\sum_{t\geq 0}U(c_{t})/(1+\theta
)^{t} $. The long run rate of return is entirely determined by preference
parameters and the growth rate: $r_{t}\rightarrow r=\theta +\gamma g$, where 
$\gamma \geq 0$ is the curvature of the utility function $U(c)=c^{1-\gamma
}/(1-\gamma )$ ($\gamma >1$ is usually assumed to be more realistic). The
steady-state saving rate is equal to $s=\alpha g/r=\alpha g/(\theta +\gamma
g)$, where $\alpha =r\beta $ is the capital share. Intuitively, a fraction $%
g/r$ of capital income is saved in the long-run, so that dynastic wealth
grows at the same rate $g$ as national income. The saving rate $s=s(g)$ is
an increasing function of the growth rate, but rises less fast than $g$, so
that the steady-state wealth-income ratio $\beta =s/g$ decreases with $g$.
With a Cobb-Douglas production function (fixed capital share), the
wealth-income ratio is given by $\beta =\alpha /r=\alpha /(\theta +\gamma g)$
and takes its maximum value $\overline{\beta }=\alpha /\theta $ for $g=0$.}
and in most endogenous growth models.\footnote{%
In endogenous growth models with imperfect international capital flows, the
growth rate might rise with the saving rate, but it will usually rise less
than proportionally. It is only in the AK closed-economy model that the
growth rate rises proportionally with the saving rate.} In all those models,
a growth slowdown -- due to a decrease in population growth, productivity
growth, or both -- leads to higher capital-output and wealth-income ratios
in the long run.

\subsection{The two-good model: volume vs. relative price effects}

The steady-state $\beta=s/g$ formula only relies on the assumption that
there is no change in the relative price between capital and consumption
goods over time. In practice, relative asset price effects often vastly
dominate volume effects in the short run, and sometimes in the medium run as
well. One key issue addressed in this paper is whether relative price
effects also matter for the analysis of long-run wealth accumulation. There
are many reasons why they could matter, particularly if the speed of
technical progress is not the same for capital and consumption goods.

One extreme case would be a two-goods model in which the volume of capital
is fixed: $V_{t}=V$ (say, fixed land supply). The market value of capital if
given by $K_{t}=q_{t}V$ , where $q_{t}$ is the price of the capital good
(say, land price per acre) relative to the consumption good. Assume fixed
population and labor supply and positive labor productivity growth $g>0$.
Then one can easily see that the relative price $q_{t}$ will rise at the
same pace as output and income in the long run, so that the market value of
capital rises as fast as output and income: there are positive capital gains
in the steady-state. By construction, there is no saving at all in this
model (since the capital good is in fixed supply), and the rise in the value
of capital is entirely due to a relative price effect.\footnote{%
See the working paper version of this article, Piketty and Zucman (2013),
sections 3.3. and 3.4.} This is the opposite extreme of the one-good model,
whereby the rise in the value of capital is entirely due to a volume effect.

In practice, there are all sorts of intermediate cases between these two
polar cases: in the real world, volume effects matter, but so do relative
price effects. Our approach is to let the data speak. We decompose the
evolution of the national wealth-income ratio into two multiplicative
components (volume and relative price) using the following accounting
equation:

\begin{equation*}
\beta _{nt+1}=\frac{(1+g_{wst}) (1+q_{t})}{1+g_{t}} \beta _{nt}
\end{equation*}

where: $1+g_{wst}=1+s_{t}/\beta _{nt}$ = saving-induced wealth growth rate

$1+q_{t}$ = capital-gains-induced wealth growth rate

$1+g_{t}=Y_{t+1}/Y_{t}$ = growth rate of national income

$1+q_{t}$ is the real rate of capital gain or loss (i.e., the excess of
asset price inflation over consumer price inflation) and can be estimated as
a residual. We do not try to specify where $q_{t}$ comes from (one can think
of stochastic production functions for capital and consumption goods, with
different rates of technical progress in the two sectors), and we infer it
from the data at our disposal on $\beta _{nt},...,\beta _{nt+n}$, $%
s_{t},...,s_{t+n}$, and $g_{t},...g_{t+n}$. In effect, if we observe that
the wealth-income ratio rises too fast compared to recorded saving, we
record positive real capital gains $q_{t}$. Although we tend to prefer the
multiplicative decomposition of wealth accumulation (which is more
meaningful over long time periods), we also present additive decomposition
results. The disadvantage of additive decompositions (which are otherwise
simpler) is that they tend to overweight recent years. By construction, our
residual capital gains $q$ are the same as those found in the income-wealth
reconciliation accounts published by a growing number of statistical
agencies, with the only difference that $q$ is net of consumer price
inflation.\footnote{%
In the U.S. for example, the Bureau of Economic Analysis publishes a set of
integrated macroeconomic accounts that combine BEA's national income and
product accounts (for income) and the Federal Reserve Board's Flow of Funds
(for wealth). For the recent decades, all the U.S. series in our database
come from the integrated macro accounts, so that by construction the
residual capital gains we report are consistent with those presented in
these accounts.}

In the next sections, we present the main descriptive statistics for private
wealth, national wealth, and domestic capital, as well as the decomposition
results for national wealth (additional decomposition results are in
Appendix K). We start with the 1970-2010 period before moving to longer
periods of time.

\section{The rise of wealth-income ratios 1970-2010}

\subsection{Private wealth-income ratios}

Private wealth-income ratios have gradually increased in rich countries
since 1970, from about 200-300\% in 1970 to about 400-600\% today (Figure I
above). In top of this general trend, there are interesting cross-country
variations. Within Europe, the French and U.K. trajectories are comparable:
in both countries, private wealth rose from about 300\% of national income
in 1970 to about 550\% in 2010. In Italy, the rise was even more
spectacular, from less than 250\% in 1970 to more than 650\% today. In
Germany, the rise was proportionally larger than in France and the U.K., but
the levels of private wealth appear to be significantly lower than
elsewhere: 200\% of national income in 1970, little more than 400\% in 2010.
The relatively low level of German wealth at market value is an interesting
puzzle, on which we will return. At this stage, we note that we are unable
to identify any methodological or conceptual difference in the work of
German statisticians (who apply the same SNA guidelines as everybody else)
that could explain the gap with other European countries.\footnote{%
See Appendix D on Germany. We made sure that the trend is unaffected by
German unification in 1990. The often noted difference in home ownership
rates between Germany and other European countries is not per se an
explanation for the lower wealth-income ratio. For a given saving rate, one
can purchase different types of assets, and there is no general reason why
housing should deliver higher capital gains than financial assets..}

Outside Europe, national trajectories also display interesting variations.
In Japan, private wealth rose sharply from less than 300\% of national
income in 1970 to almost 700\% in 1990, then fell abruptly in the early
1990s and stabilized around 600\%. The 1990 Japanese peak is widely regarded
as the archetype of an asset price bubble, and probably rightly so. But if
we look at the Japanese trajectory from a longer run, cross-country
perspective, it is yet another example of the 1970-2010 rise of
wealth-income ratios -- fairly close to Italy in terms of magnitude. In the
U.S., private wealth rose from slightly more than 300\% of national income
in 1970 to almost 500\% in 2007, but then fell abruptly to about 400\% in
2010 -- so that the total 1970-2010 rise is the smallest in our sample. (The
U.S. wealth-income ratio is now rising again, so this might change in the
near future). In other countries the wealth-income ratio stabilized or fell
relatively little during the 2008-2010 financial crisis.\footnote{%
With the interesting exception of Spain, where private wealth fell with a
comparable magnitude as in the U.S. since 2007 (i.e., by the equivalent of
about 50\%-75\% of national income, or 10\%-15\% of initial wealth).}

The rise in private wealth-national income ratios would be even more
spectacular should we use disposable personal income -- i.e., national
income minus taxes plus cash transfers -- at the denominator. Disposable
income was over 90\% of national income until 1910, then declined to about
80\% in 1970 and to 75\%-80\% in 2010, in particular because of the rise of
freely provided public services and in-kind transfers such as health and
education. As a consequence, the private wealth-disposable income ratio is
well above 700\% in a number of countries in 2010, while it was below 400\%
everywhere in 1970.\footnote{%
See Appendix Figure A9. Should we include durable goods in our wealth
definition, then wealth-income ratios would be even higher -- typically by
the equivalent about 50\% of national income. However the value of durable
goods seems to be approximately constant over time as a fraction of national
income, so this would not significantly affect the upward trend.} Whether
one should divide private wealth by national or disposable income is a
matter of perspective. If one aims to compare the monetary amounts of income
and wealth that individuals have at their disposal, then looking at the
ratio between private wealth and disposable income seems more appropriate.
But in order to compare private wealth-income ratios over long periods of
time and across countries, it is more justified to look at economic values
and therefore to divide private wealth by national income.\footnote{%
In the end it really depends on how one views government-provided services
(and in our database, we provide both ratios). If one assumes that
government expenditures are useless, and that the rise of government during
the 20$^{th}$ century has limited the ability of private individuals to
accumulate private wealth, then one should use disposable income as
denominator. But to the extent that government expenditures are mostly
useful (in the absence of public spending in health and education,
individuals would have to had to pay at least as much to buy similar
services on the market), it seems more justified to use national income. One
additional advantage is that national income tends to be better measured.
Disposable income can display large time-series and cross-country variations
for purely definitional reasons. In European countries disposable income
typically jumps from 70\% to about 80\% of national income if one includes
in-kind health transfers (such as insurance reimbursements), and to about
90\% if one includes all in-kind transfers (education, housing, etc.). See
Appendix Figure A65.}

\subsection{From private to national wealth}

We now move from private to national wealth -- the sum of private and
government wealth - which in our view is a more meaningful and comprehensive
concept of wealth. In rich countries, net government wealth has always been
relatively small compared to private wealth, and it has declined since 1970,
as Figure V illustrates. This decline is due both to privatizations --
leading to a reduction in government assets -- and to an increase in public
debt.

For example, in the U.S., as well as in Germany, France, and the U.K., net
government wealth was around 50\%-100\% of national income in the
1970s-1980s, and is now close to zero. In Italy, net government wealth
became negative in the early 1980s, and is now below -50\%; in Japan, it was
historically larger -- up to about 100\% of national income in 1990 -- but
fell sharply during the 1990s-2000s and is now close to zero. Australia is
the only country in our sample with persistently and significantly positive
net government wealth.

Although there are data imperfections, the fall in government wealth appears
to be much smaller than the rise of private wealth. As a result, national
wealth has increased a lot, from 250-400\% of national income in 1970 to
400-650\% in 2010 (Figure VI).\footnote{%
Should we include claims on future government spending in wealth, private
wealth would be higher and government wealth lower, leaving national wealth
unchanged.} In Italy, for instance, net government wealth fell by the
equivalent of about one year of national income, but net private wealth rose
by over four years of national income, so that national wealth increased by
the equivalent of over three years of national income.

\subsection{From national wealth to domestic capital}

Last, our database provides evidence on the evolution of the structure of
national wealth. National wealth is the sum of domestic capital and net
foreign wealth. The first basic fact is that net foreign wealth -- whether
positive or negative -- has generally been a relatively small part of
national wealth in rich countries throughout the 1970-2010 period (see
Figure VI). However, Japan and Germany have accumulated sizable positive net
foreign positions in the 1990s-2000s, due to their large trade surpluses. In
the early 2010s, both countries own between 40\% and 70\% of national income
in net foreign assets. Although Japan's and Germany's net foreign positions
are still substantially smaller than the positions reached by the U.K. and
France around 1910, they are starting to be substantial. And the German
position is rising fast. As a result, in Japan and Germany, the rise in net
foreign assets represents more than a quarter of the total rise of the
national wealth-income ratio.

In most of the other countries in our database, by contrast, recorded net
foreign positions are currently slightly negative -- typically between -10\%
and -30\% of national income -- and have been declining.\footnote{%
However, the official net foreign asset positions do not include the sizable
assets held by rich country residents in tax havens. In all likelihood,
including these assets would turn the rich world's total net foreign asset
position from negative to positive. The improvement would be particularly
large for Europe (Zucman, 2013).} So for those countries, the rise in the
domestic capital-output ratio $\beta _{k}$ has been larger than the rise in
the national wealth-income ratio $\beta _{n}$. For example, the
capital-output ratio was about 400\% in the U.S. in 1970 and reached 460\%
in 2010.\footnote{%
See Appendix Table A51 and Appendix Figure A67.}

As we already noted, our measure of the capital-output ratio $\beta _{k}$
based on balance sheet data differs from (and is arbuably more comparable
over time and across countries than) previously available estimates obtained
by the perpetual inventory method (PIM). There are two main reasons for this
discrepancy: different valuations of housing capital and of corporations'
assets.\footnote{%
Section A.4.5 of the Data Appendix provides a detailed reconciliation on the
basis of the US case. A third and less important reason is that balance
sheets include inventories and valuables, following international
guidelines, while PIM estimates of the capital stock generally do not.}

In balance sheets, real estate is measured at its current market value,
using censuses and observed market prices. By contrast, PIM estimates only
capture the value of \textquotedblleft structures\textquotedblright , and
this value is obtained indirectly by cumulating past real estate
investments, adjusting for the evolution of the relative price of
construction (in a way that makes it difficult to properly account for
changes in quality). This procedure misses a large fraction of the value of
the housing stock.\footnote{%
The gap between the balance sheet and the PIM-based measures of real estate
includes the value of land underlying buildings, as well as any measurement
error on any side, and all cumulated changes in market-value real estate
prices that cannot be attributed to the evolution of construction costs. In
the U.S., the gap amounts to about 60\% of domestic output in 2010. Whether
this should be interpreted as the value of land is unclear, given the
imperfections of the price data used in PIM estimates and the fact that the
distinction between structures and land is somewhat arbitrary.} It fails to
capture the large increase in housing wealth that has happened since 1970
(with notable variations across countries). As Table II shows, the rise of
housing at market value accounts for virtually all of the increase in $\beta
_{k}$ in the U.K., France and Canada, for about two-thirds of the increase
in the U.S., and about half in Japan.\footnote{%
One caveat is that the frontier between housing and other capital goods is
not always entirely clear. Sometimes the same buildings are reallocated
between housing and offices, and housing services can be provided by hotels
and real estate companies. Also, the various countries do not always use the
same methods and concepts (e.g., in Japan, tenant-occupied housing is partly
counted in other domestic capital, and we could not fully correct for this).
This is an area where progress still needs to be made. Appendix A.9
pinpoints the key areas in which we believe national accounts could be
improved.}

Second, in our benchmark measure of the capital-output ratio, corporate
capital is measured through the market value of equities, while in older
estimates corporate capital is at book-value (i.e., based on PIM-estimates
of corporations' nonfinancial assets). Tobin's $Q$ ratios between market and
book values were much below 1 in the 1970s and are closer to 1 (and at times
above 1) in the 1990s-2000s.\footnote{%
See Appendix Figure A92 and Appendix Table A78. For example, in 2010, the
value of the U.S. corporate capital stock is approximately the same whether
one looks at equity market prices or at the current cost of corporate
capital goods as estimated by BEA statisticians. That is, Tobin's $Q$ is
around 1.} As a result, measured at market value, domestic capital goods
other than housing have significantly contributed to the rise of $\beta_{k}$
in a number of countries, most spectacularly Japan and Italy (Table II).

Which measure of the corporate capital stock, market or book, is more
appropriate? Both have their merits. Take the case of Germany. Tobin's $Q$
is low: it has remained around 0.5 since the 1970s, contrary to the U.K. and
the U.S. One interpretation is a ``stakeholder effect": shareholders of
German companies do not have full control of company assets -- they share
their voting rights with workers' representatives and sometime regional
governments -- which might push $Q$ below 1.\footnote{%
In Germany, book-value national wealth is substantially above market-value
national wealth (about 5 years of national income instead of 4 years). The
opposite occurs in the U.K.} If that is true, measuring corporate capital
stocks at book value might be desirable for some purposes (e.g., for growth
accounting), so in our database we also report series with corporate capital
at book value. There are, however, issues with book-value estimates (one of
which being that intangible capital is imperfectly accounted for) that lead
us to view market values as probably more informative in the long run.%
\footnote{%
See Appendix Section A.1.2. The fact that intangible capital is not fully
accounted tends to bias PIM-corporate capital stocks downwards. Other
measurement issues, however, tend to bias them upwards, in particular errors
in price deflators and problems in accounting for the assets of firms going
out of business (which sometimes incorrectly continue to be counted in the
capital stock). Overall, it seems that PIM estimates of corporations'
capital stocks have historically tended to be over-estimated. Quite
puzzlingly, indeed, in most countries Tobin's $Q$ appears to be structurally
below 1, although intangible capital is imperfectly accounted for, which in
principle should push it above 1. This is an area in which existing
statistics might need to be improved.} Whether one uses book- or
market-values for corporate capital, the capital-output ratio has increased
markedly in all rich countries since the 1970s.\footnote{%
In particular, book-value national wealth (expressed as a fraction of
national income) has increased almost as much as market-value national
wealth (see Appendix figure A25), despite the increase in Tobin's $Q$.}

\section{Decompositions of 1970-2010 wealth accumulation}

\subsection{Growth rates versus saving rates}

How can we account for the rise and cross-country variations of national
wealth-income ratio? According to the one-good capital accumulation model,
wealth-income ratios are driven by two key forces: the saving rate $s$ and
the income growth rate $g$. So it is useful to have in mind the magnitude of
1970-2010 growth and saving rates. The basic fact is that both rates vary
widely across countries and seem largely unrelated (Tables III-IV), which
creates room for wide, multi-dimensional variations in wealth-income ratios
across countries.

Variations in income growth rates are mostly due to variations in population
growth. Over 1970-2010, average per capita growth rates have been virtually
the same in all rich countries. In most cases they fall between 1.7\% and
1.9\% per year, and given the data imperfections we face, it is unclear
whether differences of 0.1\%-0.2\% are statistically significant. For
instance, the rankings of countries in terms of per capita growth are
reversed if one uses consumer price indexes rather than GDP deflators, or if
one looks at per-worker rather than per-capita growth.\footnote{%
In particular, the U.S. and Japan both fall last in the ranking if we
deflate income by the CPI rather than the GDP deflator (see Appendix Table
A165). Differences in total factor productivity (TFP) growth also appear to
be relatively small across most rich countries. A more complete treatment of
TFP growth variations should also include differences in growth rates of
work hours, human capital investment (such as higher education spendings),
etc. It is far beyond the scope of the present work.}

In contrast, variations in population growth are large and significant, as
shown in Table III. Since 1970, population growth has exceeded 1\% per year
in New World countries (U.S., Canada, Australia), and has been less than
0.5\% in Europe and Japan. As a consequence, total growth rates are about
2.5\%-3\% in the former group, and closer to 2\% in the latter. Differences
in population growth are due to differences in both migration and fertility.
Within Europe, for example, there is a well known gap between high fertility
countries such as France (with population growth equal to 0.5\% per year)
and low fertility countries like Germany (less than 0.2\% per year, with a
sharp fall at the end of the period).\footnote{%
Population growth in Japan over the 1970-2010 period appears to be
relatively large (0.5\%), but it is actually much higher in 1970-1990
(0.8\%) than in 1990-2010 (0.2\%). Japan is also the country with the
largest fall in per capita growth rates, from 3.6\% in 1970-1990 to 0.5\% in
1990-2010. See Appendix Table JP.3.}

Average net-of-depreciation private saving rates also vary widely, from
7\%-8\% in the U.S. and the U.K. to 14\%-15\% in Japan and Italy, with a
large group of countries around 10\%-12\%. In theory, one could imagine that
low population growth, aging countries have higher saving rate, because they
need to accumulate more wealth for their old days. Maybe it is not a
coincidence if the two countries with the highest private saving rate (Japan
and Italy) also have low population growth. In practice, however, saving
rates seem to vary for all sorts of reasons other than life-cycle motives,
probably reflecting differences in tastes for saving, wealth accumulation
and transmission,\footnote{%
See, e.g., Hayashi (1986) on Japanese tastes for bequest.} as well as
differences in levels of trust and confidence in the future.\footnote{%
The effect of the rise of life expectancy on saving behavior is unclear. In
theory, rising life expectancy may have contributed to pushing saving rates
upward, but in practice the level of annuitized wealth seems to be
relatively low in a number of rich countries. In France for instance,
annuitized wealth represents less than 3\% of aggregate private wealth (see
Piketty 2011, Appendix A p.37-38), suggesting that this channel does not
play an important role in the rise of the wealth-income ratio. In countries
with less generous pay-as-you-go pension systems, annuitized wealth can be
as large as 10\%-20\% of aggregate private wealth.} As a result, there is
only a weakly significant negative relationship between private saving and
growth rates at the country level, and no relationship at all when one
considers national rather than private saving (see Table IV).\footnote{%
See also Appendix Figures A122 and A123. Note that in some countries a large
fraction of private saving is in effect absorbed by government deficits
(more than one third in Italy in 1970-2010). Whether private saving responds
to public deficits is an important issue (e.g., it could be that Italian
households would have saved less without rising public deficits and the fear
of future public finance crisis). However, it is far beyond the scope of the
present paper: here we take saving behavior -- private, public and national
-- as given and attempt to analyze the extent to which these volume effects
account for the evolution of wealth.}

Thus, as a first approximation, productivity growth is the same everywhere
in the rich world, but fertility decisions, migration policy and saving
behavior vary widely and are largely unrelated to one another. These facts
help understand why national wealth-income ratios vary so much across
countries, and in particular why high-population growth New World countries
tend to have lower ratios than low-growth Europe and Japan.

\subsection{Volume versus price effects}

Table V presents our results on the decomposition of 1970-2010 national
wealth accumulation into saving and capital gains effects.\footnote{%
Here we only show the multiplicative decompositions of national wealth. The
additive decompositions yield similar conclusions; see Appendix Table A101.}
New savings explain the largest part of wealth accumulation, but there is
also a clear pattern of positive capital gains. Take the U.S. case. National
wealth was equal to 404\% of national income in 1970, and is equal to 431\%
of national income in 2010. National wealth has grown at an average real
rate $g_{w}=$ 3.0\% per year. On the basis of national saving flows alone,
wealth would have grown at rate $g_{ws}=$ 2.1\% per year only. We conclude
that the residual capital-gains-induced wealth growth rate $%
q=(1+g_{w})/(1+g_{ws})-1$ has been equal to 0.8\% per year on average. New
savings explain 72\% of the accumulation of national wealth in the U.S.
between 1970 and 2010, and residual capital gains 28\%.

Just like in the U.S., new savings also appear to explain around 70-80\% of
1970-2010 national wealth accumulation in Japan, France, and Canada, and
residual capital gains 20-30\%. Capital gains are larger in the U.K., Italy,
and Australia.

The capital gains we compute are obtained as a residual, and so may reflect
measurement errors in addition to real valuation effects.\footnote{%
In the Appendix, we check that the pattern of capital gains residuals is
highly correlated with capital gains on listed equities and housing coming
from available asset price indexes (see Figures A143 to A157). Note that the
capital gains inferred from our wealth decomposition exercises are
structurally lower than those coming from equity price indexes, for a good
reason. A substantial fraction of national saving takes the form of
corporate retained earnings (see Table IV) and these earnings generate
structural capital gains in equity markets. Should we exclude retained
earnings from saving in the wealth accumulation equation, then we would
similarly find much larger residual capital gains (see Appendix Table A105,
and studies by Eisner (1980), Babeau (1983), Greenwood and Wolff (1992),
Wolff (1999), and Gale and Sabelhaus (1999)). Such capital gains, however,
would be spurious, in the sense that they correspond to the accumulation of
earnings retained within corporations to finance new investment (thereby
leading to rising stock prices), rather than to a true relative price effect.%
} There are two main possible issues. First, it is possible that national
saving flows are under-estimated because they do not include R\&D
expenditure. To address this concern, we have re-computed our wealth
accumulation equations using saving flows that include R\&D. Even after we
include generous R\&D estimates, in many countries the 2010 observed levels
of national wealth are still significantly larger than those predicted by
1970 wealth levels and 1970-2010 saving flows alone (Figure VII).\footnote{%
R\&D has been included in investment in the latest SNA guidelines (2008),
but this change has so far only been implemented in Australia. The
computations reported in Figures VII and VIII include generous estimates of
R\&D investment based on the level of R\&D expenditure observed in the U.S.
satellite account over the 1970-2010 period (see Appendix A.5.2 for a
detailed discussion).} Take the case of France. Predicted national wealth in
2010 -- on the basis of 1970 initial national wealth and cumulated 1970-2010
national saving including R\&D -- is equal to 491\% of national income,
while observed wealth is 605\%. There is over 100\% of national income in
\textquotedblleft excess wealth".\footnote{%
Saving flows might be under-estimated for reasons other than R\&D. Given the
limitations of national accounts (in particular regarding the measurement of
depreciation, which is discussed in Appendix Section A.1.2.), this
possibility cannot completely be ruled out. One would need, however, large
and systematic errors to account for the amount of excess wealth we find.}

Second, we might somewhat underestimate the value of public assets in the
1970s in countries like the U.K., France and Italy. Part of the capital
gains we measure might simply correspond to the fact that private agents
have acquired privatized assets at relatively cheap prices. From the
viewpoint of households this is indeed a capital gain, but from a national
wealth perspective it is a pure transfer from public to private hands, and
it should be neutralized by raising the level of 1970 wealth. Whenever
possible, we have attempted to count government assets at equivalent market
values throughout the period (including in 1970), but we might still
slightly under-estimate 1970 government wealth levels.

In the end, in our preferred specification that includes generous R\&D
expenditure in saving flows, capital gains account for about 40\% on average
of the 1970-2010 increase in national wealth-income ratios $\beta_{n}$, and
saving for about 60\%, with a lot of heterogeneity across countries.%
\footnote{%
See Appendix A.5.2 and Appendix Table A99.} The only exception to the
general pattern of positive capital gains is Germany. Given the large
1970-2010 saving flows and low growth rates, we should observe more wealth
in 2010 than 400\% of national income. There is the equivalent of 50-100\%
of national income in ``missing wealth''.

\subsection{Domestic versus foreign capital gains}

How can we explain the substantial capital gains we find on national wealth,
and the losses in the case of Germany? To address this question, it is
useful to distinguish capital gains/losses on domestic assets and on net
external wealth (Table VI). Our series suggest a number of interpretations,
but we stress that data limitations make it impossible to rigorously
estimate the exact role played by each of them.

All countries (except Germany) have experienced positive capital gains on
domestic wealth. These gains have been particularly large in Europe and
mostly (though not entirely) driven by housing. One hypothesis -- which, as
we shall see, is consistent with the historical data -- is that countries
like the U.K. and France have benefitted from a long run asset price
recovery. Asset prices fell substantially between 1910 and 1950, and have
been rising ever since. There might, however, have been some overshooting in
the recovery process, particularly in housing prices. The four countries
with the largest capital gains -- UK, France, Italy, Australia -- have by
far the largest level of housing wealth in our sample: over 300\% of
national income in 2010, a level that was only attained by Japan around
1990. So part of the capital gains we measure might owe to abnormally high
real estate prices in 2010.

To a large extent, the housing bubble explanation for the rise of
wealth-income ratios is complementary to the real explanation. In countries
like France and Italy, savings are sufficiently large relative to growth to
generate a significant increase in the national wealth-income ratio: given
the values taken by $s$ and $g$ over the 1970-2010 period and the
steady-state formula $\beta_{n} =s/g$, the $\beta_{n} $ observed in 1970
were too low and had to increase. If in addition households in these
countries have a particularly strong taste for domestic assets like real
estate (or do not want to diversify their portfolio internationally as much
as they could) then maybe it is not too surprising if this generates upward
pressure on housing prices.

Regarding the atypical German capital losses, German statisticians might
over-estimate saving flows, under-estimate the current stock of wealth, or
both. Yet another possibility is that Germany has not experienced any asset
price recovery so far because the German legal system still today gives
important control rights over private assets to stakeholders other than
private property owners. Rent controls, for instance, may have prevented the
market value of real estate from increasing as much as in other countries.
Voting rights granted to employee representatives in corporate boards may
similarly reduce the market value of corporations.\footnote{%
Whether this is good or bad for productive efficiency is a complex issue
which we do not address in this paper (at first sight, low equity values do
not seem to prevent German firms from producing good products). In this
\textquotedblleft stakeholder" view of the firm, the market value of
corporations can be interpreted as the value for capital owners, while the
book value can be interpreted as the value for all stakeholders. Both views
have their merits.} Germans might also have less taste for expensive capital
goods (particularly housing) than the French, the British and the Italians,
maybe because they have less taste for living in a large centralized capital
city and prefer a more polycentric country, for historical and cultural
reasons. With the data at our disposal, we are not able to put a precise
number on each explanation.

It is interesting to note, however, that when we compute a European average
wealth accumulation equation -- by taking a weighted average of Germany,
France, U.K. and Italy -- then capital gains and losses seem to partly wash
out (Figure VIII). Europe as a whole has less residual capital gains than
the U.K., France, and Italy, thanks to Germany. Had we regional U.S. balance
sheets at our disposal, maybe we would find regional asset price variations
within the U.S. that would not be too different from those we find in
Europe. So one possibility is that substantial relative asset price
movements happens permanently within small national or regional economic
units, but tend to correct themselves at more aggregate levels. If that is
the case, German asset prices might rise in the near future and fall in
other European countries.

Turning now to net foreign assets, we find that capital gains and losses on
external portfolios have played a large role in the overall dynamics of
national wealth (Table VI). The U.S. and German cases are particularly
striking. In the U.S., net capital gains on cross-border portfolios
represent one third of total capital gains at the national level. Absent net
foreign gains, the U.S. wealth-income ratio would not have increased at all
since 1970.\footnote{%
Our results on U.S. external wealth capital gains are consistent with the
findings of Gourinchas and Rey (2007). What we add to this line of work is a
global macro perspective that includes the accumulation of both domestic and
foreign capital. Note that we include all ``other volume changes'' in saving
flows but exclude R\&D from saving. We provide detailed accumulation results
isolating saving, ``other volume changes'', and capital gains in the
country-specific tables of the Appendix.} In Germany virtually all capital
losses at the national level can be attributed to foreign assets.

The reason why capital gains on foreign portfolios matter so much is that
the gross foreign positions of countries have massively increased since the
1970s -- the rise has been spectacular in Europe, a bit less so in the
world's largest economies, the U.S. and Japan.\footnote{%
In 2010, gross assets held in France by the rest of the world amount to
about 310\% of national income, while gross assets held by French residents
in the rest of the world amount to about 300\% of national (hence a negative
position of about -10\%, in the official data). For the U.S., recorded gross
foreign assets amount to about 120\% of national income, and gross
liabilities to about 100\% of national. See Appendix figures A39-A42.} A
significant share of each country's domestic capital is now owned by other
countries. With huge gross positions, even moderate returns differential on
cross-border assets and liabilities are enough to generate large and
volatile gains and losses on net foreign wealth over time and across
countries.

\section{Wealth-income ratios in rich countries 1870-2010}

It is impossible to properly understand the recent rise of wealth-income
ratios in rich countries without putting the 1970-2010 period into a longer
historical perspective. As we have seen, on average about 40\% of the rise
of $\beta_{n}$ since the 1970s is due to capital gains, with large
differences between countries. The key question is the following: is this
due to a structural, long-run rise in the relative price of assets (caused
for instance by uneven technical progress), or is it a recovery effect? We
argue that it is mostly a recovery effect: the 1970-2010 capital gains
largely seem to compensate the capital losses observed during earlier parts
of the 20$^{th}$ century.

The argument relies on the analysis of the evolution of wealth-income ratios
over the 1870-2010 period. Due to data limitations, our long term analysis
is restricted to four countries: the U.S., the U.K., Germany and France. The
key descriptive statistics are the following. For the three European
countries, we find a similar U-shaped pattern: today's private
wealth-national income ratios appear to be returning to the high values
observed in 1870-1910, namely about 600\%-700\% (Figure II above). For the
U.S., the U-shaped pattern is much less strong (Figure IV above). In
addition, European public wealth-national income ratios have followed an
inverted U-curve over the past century.\footnote{%
Net public wealth was significantly positive (around 100\% of national
income) during the 1950s-1970s, due to large public assets and low debt.
Since then, public wealth has returned to the low level observed on the eve
of World War 1.} But the magnitude of the pattern for public wealth is very
limited compared to the U-shape evolution of private wealth, so that
European national wealth-income ratios are strongly U-shaped too. Last, in
1900-1910, European countries held a very large positive net foreign asset
position -- around 100\% of national income on average. Interestingly, the
net foreign position of Europe has again turned (slightly) positive in
2000-2010, when the national wealth-income ratio again exceeded that of the
U.S.

Starting with this set of facts, and using the best historical estimates of
saving and growth rates, we have estimated detailed 1870-2010 wealth
accumulation equations. As Table VII shows, the total accumulation of
national wealth over this 140-year-long period seems to be well accounted
for by saving flows. In order to fully reconcile the stock and flow data, we
need a small residual capital gain for the U.S., France and the U.K., and a
small residual capital loss for Germany. But in all cases saving flows
account for the bulk of wealth accumulation: capital gains seem to wash out
in the long run.\footnote{%
These results are robust to a wide range of specifications. Appendix Tables
A108 to A137 present the complete decomposition results, for each country
and sector of the economy, for both the additive and multiplicative models.}

Looking at each sub-period, we find a strong U-shaped relative capital price
effect in European countries. The U.K., for example, experienced real
capital losses at a rate of -1.9\% per year between 1910 and 1950, followed
by real gains of +0.9\% between 1950 and 1980 and +2.4\% between 1980 and
2010. The pattern is similar for France. In these two countries, there seems
to have been a slight over-shooting in the recovery process, in the sense
that the total cumulated relative asset price effect over the 1910-2010
period appears to be somewhat positive (+0.2\% per year in the U.K., +0.3\%
in France). In Germany, by contrast, the recovery is yet to come (-0.8\%
between 1910 and 2010).

We emphasize that the imperfections of our data do not allow us to put a
precise number on asset over- or undervaluation in 2010. In any multi-sector
model with uneven technical change between capital and consumption goods,
one should expect capital gains and losses that could vary between countries
(for instance depending on comparative advantage). The residual capital
gains we estimate might also reflect measurement issues: 1870-2010 saving
flows might be somewhat underestimated in the U.K. and France and
overestimated in Germany. At a modest level, our point is simply that the
one-good capital accumulation model seems to do a relatively good job in the
long run, and that the stock and flow sides of historical national accounts
are roughly consistent with one another.

Table VIII decomposes the huge decline in national wealth-income ratios that
occurred in Europe between 1910 and 1950. In the U.K., war destructions play
a negligible role -- an estimated 4\% of the total decline in $\beta_{n}$.
Low national saving accounts for 46\% of the fall in $\beta_{n}$ and
negative valuation effects (including losses on foreign portfolios) for the
remaining 50\%. In France and Germany, cumulated physical war destructions
account for about one quarter of the fall in $\beta_{n}$. Low national
saving and real capital losses each explain about half of the remaining
three quarters. Interestingly, the private wealth-national income ratio has
declined less in the U.K. than in France and Germany between 1910 and 1950,
but the reverse holds for the national wealth-income ratio (due to the large
negative U.K. public wealth around 1950).\footnote{%
U.K. net public wealth then turned positive during the 1950s-1960s. See
Appendix figure A16 and A22.}

The U.S. case is again fairly different from that of Europe. The fall of $%
\beta_{n}$ during the 1910-1950 period was more modest, and so was the
recovery since 1950. Regarding capital gains, we find in every sub-period a
small but positive relative price effect. The capital gain effect becomes
bigger in the recent decades and largely derives from the U.S. foreign
portfolio -- it seems too big to be accounted for by underestimated saving
and investment flows.

\section{The changing nature of national wealth, 1700-2010}

\subsection{The changing nature of wealth in Old Europe}

What do we know about the evolution of wealth-income ratios prior to 1870?
In the U.K. -- the country with the most comprehensive historical balance
sheets -- the national wealth-income ratio appears to have been roughly
stable around 650-700\% during the 18$^{th}$ and 19$^{th}$ centuries (Figure
III above). In France, where a large number of historical national wealth
estimates were also established, the picture is similar (Figure IX).

We should make clear that the raw data sources available for the 18$^{th}$-19%
$^{th}$ centuries are insufficient to precisely compare the levels of
wealth-income ratios between the two countries or between the various
sub-periods. But the general pattern seems robust: all estimates, coming
from many different authors using independent methodologies, provide the
same orders of magnitude. National wealth always seems to be between 6 and 8
years of national income from 1700 to 1914 in both countries, with no
obvious long-run trend.

Strikingly, today's wealth-income ratios in the U.K. and France seem
relatively close to their 18$^{th}$ century levels, in spite of considerable
changes in the nature of wealth. Agricultural land -- including land
improvement of all sorts -- was between 4 and 5 years of national income
around 1700; it is now negligible and has been replaced by housing and other
domestic capital (offices, machines, patents, etc.). In the long run, the
decline of the share of agricultural land in national wealth mirrors that of
the share of agriculture in national income, from over two thirds in the 18$%
^{th}$ century to a few percent today -- with a faster and earlier decline
in the U.K. The variations in the share of net foreign assets in national
wealth are also striking. Net foreign assets were virtually zero in the 18$%
^{th}$ century. They reached very high levels in the late 19$^{th}$ and
early 20$^{th}$ century -- almost 2 years of national income in the U.K. in
1910, over 1 year in France. Following the wars and the collapse of the
colonial empires, they came back to virtually zero around 1950.

Why were wealth-income ratios so high in the 18$^{th}$-19$^{th}$ centuries,
and why do they seem to be approaching these levels again in the 21$^{st}$
century? A natural explanation lies in the $\beta =s/g$ steady-state
formula. With slow growth, even moderate saving rates lead to large
wealth-income ratios. Growth was low until the 18$^{th}$-19$^{th}$
centuries, and is likely to be low again in the 21$^{st}$ century as
population growth vanishes, thereby potentially generating high ratios again.

That is probably an important part of the explanation. Unfortunately, data
limitations again make it difficult to evaluate the exact role played by
alternative explanations, such as structural capital gains and losses and
changes in the value of natural resources.

The main difficulty is that pre-1870 estimates of saving and investment
flows are too fragile to be used in wealth accumulation decompositions. With
very low growth, any error in the net-of-depreciation saving rate $s$ can
make a big difference in terms of predicted steady-state wealth-income ratio 
$\beta =s/g$. In preindustrial societies where $g\approx 0.5-1\%$, whether
the net saving rate is $s=5\%$ or $s=8\%$ is going to matter a lot.
Historical estimates suggest that there was substantial investment going on
in traditional societies, including in the rural sector. Annual spendings on
land improvement (drainage, irrigation, afforestation, etc.) alone could be
as large as 3-4\% of national income. This suggests that a large fraction of
total agricultural land value in 18$^{th}$ century U.K. and France actually
derived from past investment. In all likelihood, the \textquotedblleft pure
land value" (i.e., the value of land before any improvement, as it was
discovered at prehistoric times) was much less than 4 years of national
income. Some 18$^{th}$ century estimates tend to suggest that it was around
1 year of national income.\footnote{%
See in particular the famous estimates by Thomas Paine (1795), who suggested
in front of the French National Assembly to confiscate the \textquotedblleft
pure land" component of inheritance, which he estimated to be about 1 year
of national income. On saving and investment series covering the 18$^{th}$-19%
$^{th}$ centuries, particularly for the U.K. and France, see Data Appendix.}
Saving and investment series are unfortunately not sufficiently reliable to
definitively address the question. The residual \textquotedblleft pure land"
value could be less than 0.5 year, or up to 1.5 years of national income.

\subsection{The nature of wealth: Old Europe vs. the New World}

In order to make some progress on this question, it is useful to compare the
value of land in Old Europe (U.K., France, Germany) and in the New World.
For the U.S., we have put together historical balance sheets starting around
1770 (Figure X). We find that the value of agricultural land in the late 18$%
^{th}$ and early 19$^{th}$ centuries was much less in the U.S. (1 to 2 years
of national income) than in Old Europe (3 to 4 years).\footnote{%
For the long run evolution of wealth composition in Germany and Canada, see
Appendix figures A46 and A47. The German pattern is close to that of the
U.K. and France (except that the net foreign asset position of Germany
around 1900-1910 is less strongly positive than in the two colonial powers).
The Canadian pattern is close to that of the U.S. (except that net foreign
asset position is strongly negative throughout the 19$^{th}$ century and
much of the 20$^{th}$ century).} Part of the explanation could well be lower
accumulated investment relative to economic and population growth in the New
World (i.e., a lower cumulated $s/g$ ratio). However, available evidence
suggests that the relatively low New World wealth-income ratios can also be
explained by a \textquotedblleft land abundance" effect. Land was so
abundant in America that its price per acre was low. The right model to
think about this effect involves a production function with an elasticity of
substitution between land and labor lower than 1 -- a necessary condition
for the price effect to dominate the volume effect.

To see this, think of a two-good model of the form introduced in section
III.B. That is, assume that the capital good solely consists of land and
that land volume $V_{t}$ (measured in acres) is in fixed supply: $V_{t}=V$.
For the sake of simplicity, assume that no land improvement is possible. The
market value of land if given by $K=qV$ , where $q$ is the price of land
relative to the consumption good. The production function $Y=F(V,L)$
transforms capital (land volume) $V$ and labor $L$ into output $Y$. Assume
that $F(V,L)$ is a CES function with elasticity $\sigma $, and that there is
zero productivity and population growth.

Consider two countries $0$ and $1$ with similar technology and preferences.
Assume country $1$ (America) has more land volume relative to labor than
country 0 (Old Europe): $V_{1}/L_{1}>V_{0}/L_{0}$. Then country $1$ will end
up with lower land value (relative to income) than country $0$ (i.e., $\beta
_{1}<\beta _{0}$, with $\beta _{1}=K_{1}/Y_{1}=q_{1}V_{1}/Y_{1}$ and $\beta
_{0}=K_{0}/Y_{0}=q_{0}V_{0}/Y_{0}$) \ if and only if the elasticity of
substitution $\sigma $ is less than one. This result directly follows from
the fact that the capital share $\alpha $ is smaller in the land-abundant
country (i.e., $\alpha _{1}=F_{V}V_{1}/Y_{1}<\alpha _{0}=F_{V}V_{0}/Y_{0}$)
if and only if $\sigma $ is less than one. Under standard assumptions on
preferences and equilibrium rates of return, this in turn implies that land
value is lower in the land-abundant country: $\beta _{1}<\beta _{0}$.%
\footnote{%
In a dynastic utility model with zero growth, the rate of return is set by
the rate of time preference ($r=\theta $), so that $\beta _{1}=\alpha
_{1}/r<\beta _{0}=\alpha _{0}/r$. With a bequest-in-the-utility-function
model $U(c,b)=c^{1-s}b^{s}$, then the wealth-income ratio is set by $\beta
=s/(1-s)$, so that the difference in capital share entirely translates into
a difference in rates of return: $r_{1}=\alpha _{1}/\beta <r_{0}=\alpha
_{0}/\beta $. However to the extent that the interest elasticity of saving $%
s=s(r)$ is positive, this also implies $\beta _{1}<\beta _{0}$. A similar
intuition applies to the case with $U(c,b)=c^{1-s}\Delta b^{s}$ (assuming
positive population or productivity growth so as to obtain a well-defined
steady-state $\beta =s/g$). See the working paper version, Piketty and
Zucman (2013).}

Intuitively, an elasticity of substitution $\sigma <1$ means that there is
not much that one can do with capital when there is too much of it. The
marginal product of land falls to very low levels when a few million
individuals own an entire continent. The price effect dominates the volume
effect. It is exactly what one should expect to happen in a relatively
low-tech economy where there is a limited set of things that one can do with
capital.

Thus, part of the initial difference in $\beta $ between Europe and America
in the 18$^{th}$-19$^{th}$ centuries seems to be due to a relative price
effect (due to land abundance) rather than to a pure saving effect (via the $%
\beta =s/g$ formula). Both logic actually tend to reinforce each other: the
lower land prices and higher wage rates attracted labor to the New World,
implying large population growth rates and relatively low steady-state $%
\beta =s/g$ ratios.\footnote{%
There is a large historical literature on the factor flows that
characterized the 19$^{th}$ Atlantic economy. In order to explain why both
labor and capital flew to the New World, one needs to introduce a
three-factor production function (see, e.g., Taylor and Williamson, 1994,
and O'Rourke and Williamson, 2005). One could also argue that transatlantic
differences in land value (rural, urban and suburban) still matter today.
However they go together with different tastes over housing in city centers
versus suburban areas, so that it is difficult to disentangle the various
effects. The fact that the bulk of 1870-2010 wealth accumulation is well
explained by volume effects -- both in Europe and in the U.S. -- suggests
that today's differences in pure land values are less central than they used
to be.}

The lower land values prevailing in America during the 1770-1860 period were
to some extent compensated by the slavery system. Land was so abundant that
it was almost worthless, implying that it was difficult to be really rich by
owning land. However, the landed elite could control a large share of
national income by owning the labor force. Should a tiny elite own the
entire labor force, the total value of the slave stock could in principle be
very large, say as large as 20 years of national income (assuming the labor
share is 100\% of output and the rate of return is equal to 5\%).\footnote{%
With a one-good model and a Cobb-Douglas production function $%
F(K,L)=K^{\alpha }L^{1-\alpha }$, the market value $\beta _{H}$ of the human
capital stock (i.e., the value of the labor force from the viewpoint of a
potential slave owner) is always equal to $(1-\alpha )/\alpha $ times the
non-human capital stock. If $\alpha =1/3$, then $\beta _{H}=2\beta $. This
is assuming that the slave owner equates returns across all human and
non-human assets. With a CES production function $F(K,L)=(a K^{\frac{\sigma
-1}{\sigma }}+(1-a) L^{\frac{\sigma -1}{\sigma }})^{\frac{\sigma }{\sigma -1}%
}$, we have $\beta _{H}=\frac{1}{a} \beta ^{1/\sigma }-\beta $.} In the case
of antebellum U.S., the situation was less extreme, but the value of the
slave stock was still highly significant. By putting together the best
available estimates of slave prices and the number of slaves, we have come
to the conclusion that the market value of slaves was between 1 and 2 years
of national income for the entire U.S., and up to 3 years of income in
Southern states. When we add up slaves and land values, wealth-income ratios
in the U.S. South are relatively close to those of the Old World. Slaves
approximately compensate the lower price of land (Figure XI).

Needless to say, this peculiar form of wealth has little to do with
\textquotedblleft national" wealth and is better analyzed in terms of
appropriation and power relationship than in terms of saving and
accumulation. We view these \textquotedblleft augmented" national balance
sheets as a way to illustrate the ambiguous relationship of the New world
with wealth and inequality. To some extent, antebellum America is the land
of equal opportunity, the place where past wealth does not matter much. But
it is also the place where a new form of class structure -- even more
extreme than Europe's -- flourished, whereby part of the population owned
another part.\footnote{%
During the 1770-1860 period, slaves made as much as 15\%-20\% of total U.S.
population (up to 40\% in Southern states). See Appendix Table US.3b.}

\section{Capital shares and the changing nature of technology}

In this section we attempt a brief look at the implications of our new data
on capital for understanding the evolution of factor shares and of the shape
of the production function. The results should be taken with caution,
because measuring factor shares raises many difficulties. But this question
is so important that we feel it deserves a few words.

Starting first with the recent decades, Figure XII shows that capital shares
have increased in all rich countries from about 15\%-25\% in the 1970s to
25\%-35\% in 2010, with large variations over time and across countries.%
\footnote{%
Our results are consistent with a growing literature on the global rise of
capital shares since the 1970s (Ellis and Smith, 2007; Azmat, Manning and
Van Reenen, 2011; Karabarbounis and Neiman, 2014).} By our estimates,
however, capital-output ratios $\beta _{k}$ have risen even more than
capital shares $\alpha $, so that the average return to domestic capital $r$
-- which can be computed as $\alpha /\beta _{k}$ -- has declined somewhat
(Figure XIII).\footnote{%
Remember that domestic capital $K$ is national wealth $W$ minus the net
foreign asset position. The capital-output ratio $\beta _{k}$ is the ratio
of domestic capital $K$ to domestic output $Y_{d}$. The capital share $%
\alpha $ is equal to the output $Y_{K}$ generated by domestic capital
divided by $Y_{d}$. So it is pure accounting that the average return to
domestic capital, $r=Y_{K}/K$, is equal to the capital share $Y_{K}/Y_{d}$
divided by the capital-output ratio $K/Y_{d}$. Note that the results on
Figure XII are robust to the various ways of taking into account government
capital and interest payment in these computations, which are discussed in
Appendix A.7.5. The reader should have in mind that like all our income
series, the capital shares displayed in Figure XII are net of depreciation.}
This decline is what one would expect in any model: when there is more
capital, the rate of return to capital must go down. The interesting
question is whether it falls more or less than the quantity of capital.
According to our data it has fallen less, implying a rising capital share.

There are several ways to think about this piece of evidence. One can think
of a model with imperfect competition and an increase in the bargaining
power of capital (e.g., due to globalization and increasing capital
mobility). A production function with three factors -- capital, high-skill
and low-skill labor -- where capital is more strongly complementary with
skilled than with unskilled labor would also do, if there is a rise in
skills or skill-biased technical change. Yet another -- and more
parsimonious -- way to explain the rise in $\alpha $ is a standard
two-factor CES production function $F(K,L)$ with an elasticity of
substitution $\sigma >1$.\footnote{%
One can of course combine the various possible explanations. Karabarbounis
and Neiman (2014) for instance use a two-goods model in which there is a
decline in the relative price of investment. As a result, firms shift away
from labor toward capital, and with an elasticity of substitution $\sigma $
larger than 1 the capital share $\alpha $ increases. As the two-goods model
we apply in section VII.B to 19$^{th}$ century U.S. and Europe illustrates,
when the relative price of investment is lower (e.g., lower land values) and 
$\sigma >1$, the wealth-income ratio has to be higher. Thus, the explanation
for the rise in $\alpha $ put forward by Karabarbounis and Neiman (2014) is
consistent with our findings of rising $\beta $. The difference is that we
do not need a two-goods model to account for the rise in $\alpha $: in a
broad class of one-good general equilibrium models, when $g$ decreases $\beta
$ increases, and when in addition $\sigma >1$, $\alpha $ has to rise. In the
real world, both forces (lower $g$ and declining relative price of some
capital goods) probably play a role in the dynamics of $\alpha $, so that
the two explanations should be seen as complementary. One problem, however,
with the declining relative price of capital story is that while the price
of corporate tangible fixed assets may have declined, taking a broader view
of capital we actually find a positive relative price effect over 1970-2010
(see section V). This could be due to a positive price effect for land and R$%
\&$D assets, which are not included in standard measures of the relative
price of capital.} Importantly, with large changes in the capital-output
ratio $\beta _{k}$ (which in the long-run seem to be mostly due to volume
rather relative price effects),\footnote{%
Our market-value domestic capital stock $K$ can be viewed as $%
K=q_{1}V_{1}+...+q_{n}V_{n}$, where $V_{1},...,V_{n}$ are the volumes of the
various capital assets (land, housing, structures, machines, patents, ...)
and $q_{1},...,q_{n}$ their market prices (relatively to the consumption
price index). With a single capital good in fixed supply (e.g., pure land),
it makes more sense to view the production function as $Y=F(V,L)$ (see
section VII.B above). With many capital goods, the market-value concept of
capital stock $K$ is the most natural definition, especially given that the
aggregate relative capital price $q$ seems to be close to $1$ in the very
long-run; otherwise one might want to use $V=K/q$. In any case, for reasons
explained above, the best way to use available data is to start from
market-value balance sheets and compute the implicit $q$ from wealth
decomposition equations.} one can obtain substantial movements in the
capital share with a production function that is only moderately more
flexible than the standard Cobb-Douglas. For instance, with $\sigma =1.5$,
the capital share rises from $\alpha =28\%$ to $\alpha =36\%$ if $\beta _{k}$
jumps from 2.5 to 5, which is roughly what has happened in rich countries
since the 1970s. The capital share would reach $\alpha =42\%$ in case
further capital accumulation takes place and $\beta _{k}$ attains 8. In case
the production function becomes even more flexible over time (say, $\sigma
=1.8$), the capital share would then be as large as $\alpha =53\%$.\footnote{%
In a perfectly competitive model with $Y=F(K,L)=(aK^{\frac{\sigma -1}{\sigma 
}}+(1-a)L^{\frac{\sigma -1}{\sigma }})^{\frac{\sigma }{\sigma -1}}$, the
rate of return is given by $r=F_{K}=a\beta ^{-1/\sigma }$ (with $\beta =K/Y$%
), and the capital share is given by $\alpha =r\beta =a\beta ^{\frac{\sigma
-1}{\sigma }}$. With $a=0.21$ and $\sigma =1.5$, $\alpha $ goes from $28\%$
to $36\%$ and $42\%$ as $\beta $ rises from $2.5$ to $5$ and $8$. With $%
\sigma =1.8$, $\alpha $ rises to $53\%$ if $\beta =8$.}

This scenario will not necessarily happen, but it cannot be entirely
excluded either. Capital-output ratios and capital shares have no strong
reason to be constant. Since domestic saving rates $s$ and output growth
rates $g$ vary for all sorts of reasons over time and across countries, it
is natural to expect $\beta _{k}$ to vary widely. Small departures from
standard Cobb-Douglas assumptions then imply that the capital share $\alpha
=r\beta _{k}$ can also vary substantially. It is natural to imagine that $%
\sigma $ was much less than 1 in the 18$^{th}$-19$^{th}$ centuries and
became larger than 1 in the 20$^{th}$-21$^{st}$ centuries. One expects a
higher elasticity of substitution in high-tech economies where there are
lots of alternative uses and forms for capital.\footnote{%
The fact that the capital share $\alpha $ was low in the mid-20$^{th}$
century (when $\beta _{k}$ was also low) can also be viewed as evidence for $%
\sigma >1$. Indeed, $\alpha $ and $\beta _{k}$ move in the same direction if 
$\sigma >1$, and in opposite directions if $\sigma <1$.}

Taking now a very long run perspective on the evolution of factor shares,
there seems to be evidence -- both in the U.K. and France -- that the
capital share was somewhat larger in the 18$^{th}$-19$^{th}$ centuries
(around 40\%) than it is in the early 21$^{st}$ century (about 30\%),
despite the recent rise (Figure XIV). Will capital shares return to their 18$%
^{th}$-19$^{th}$ century levels? The capital-output ratio $\beta_{k} $ is
still somewhat lower today than in the distant past. So one possibility is
that the capital share $\alpha $ will slowly return to about 40\% as $%
\beta_{k} $ keeps increasing in the coming decades. However, it could also
be that the labor exponent in the production function has declined since the
18$^{th}$-19$^{th}$ centuries, because of the rise of human capital. Over
time, human inputs may have become relatively more important than capital
inputs in the production process. With the data we have at our disposal, we
are not able to say. The long-run U.K. and French data, however, suggest
that if such a \textquotedblleft rise of human capital" happened, it was
probably relatively modest.

We stress that our discussion of capital shares and production functions
should be viewed as merely exploratory and illustrative. In many ways, it is
more difficult to measure capital shares $\alpha $ than capital-output
ratios $\beta _{k}$. The measurement of $\alpha $ -- and therefore of the
average rate of return to capital -- is complicated by self-employment and
tax optimization behaviors of business owners (a growing concern in a number
of countries), by the measurement of housing product (which is not fully
homogenous internationally), and also by the problem of informal financial
intermediation. National accounts deduct from the return to capital the
costs of intermediation services provided by banks and real estate agents,
but not the time spent by capital owners to manage their portfolios. Such
costs might well vary over time. They might be larger in fast growing
economies rather than in the stagnant, rural economies of the 18$^{th}$
century. So we may over-estimate average rates of return when using national
accounts capital income flow series (and the $r=\alpha /\beta _{k}$
formula), especially in high-growth economies. In this paper, we have tried
to show that an alternative way to study the relative importance of capital
and labor in the economy is to study the evolution of $\beta $ rather than
the evolution of $\alpha $ -- which so far has been the focus of most of the
attention. Ideally, both evolutions need to be analyzed together.

\section{Conclusion}

The new wealth-income database introduced in this paper reveals some
striking facts. Capital is making a comeback: in the top eight developed
economies, aggregate wealth has risen from about 200\%-300\% of national
income in 1970 to a range of 400\%-600\% today. In effect, today's
wealth-income ratios appear to be returning to the high values observed in 18%
$^{th}$ and 19$^{th}$ Europe -- namely, 600-700\% -- in spite of
considerable changes in the nature of wealth. The low European ratios of the
post-war decades thus appear to be a historical anomaly. With low growth and
substantial saving, long run $\beta $ can naturally be very high --
600-700\%, or even more.

A full understanding of the implications of the return of high-wealth income
ratios calls for at least three extensions. It would be good to study
wealth-income ratios at the world level, to include individual-level wealth
inequality in the analysis, and to decompose wealth into an inherited
component on the one hand and a self-made component on the other. All of
this raises important challenges for future research.\\\

\noindent \textsc{Paris School of Economics}\\\
\textsc{London School of Economics and UC Berkeley}

\renewcommand{\baselinestretch}{1.16}\normalfont

\clearpage

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\clearpage

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\begin{table}[tbp]
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\includegraphics[scale=0.95]{KTable7.pdf}
\end{table}

\begin{table}[tbp]
\centering
\begin{minipage}[top]{1\linewidth}

   \centering
   \includegraphics[scale=0.6]{KTable8.pdf}


\end{minipage}
\end{table}

\end{document}
