Capital is Back:
Wealth-Income Ratios in Rich Countries 1700-2010
Thomas Piketty
Paris School of Economics

Gabriel Zucman
Paris School of Economics

July 26, 2013⇤

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 eightdeveloped economies. For the U.S., U.K., Germany, and France, we are able to extend ouranalysis 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 e↵ect, today’s
ratios appear to be returning to the high values observed in Europe in the eighteenth andnineteenth 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 slowdownof productivity and population growth, in line with the= s/g Harrod-Domar-Solow
formula. That is, for a given net saving rate s = 10%, the long run wealth-income ratio
is about 300% if g = 3% and 600% if g = 1.5%. Our results have important 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.

⇤

Thomas Piketty: piketty@pse.ens.fr; Gabriel Zucman: zucman@pse.ens.fr. We are grateful to seminar participants at the Paris School of Economics, Sciences Po, the International Monetary Fund, Columbia University,
University of Pennsylvania, the European Commission, the University of Copenhagen, and the NBER summer
institute for their comments and reactions. A detailed Data Appendix supplementing the present working paper is available online: http://piketty.pse.ens.fr/capitalisback and http://www.gabriel-zucman.eu/
capitalisback.

1

Introduction

This paper addresses what is arguably one the most basic economic questions: how do wealthincome and capital-output ratios evolve in the long run, and why?
Until recently it was difficult to properly address this question, for one simple reason: 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 ofcapital stocks were typically obtained by cumulating past flows of saving and investment. Thisis fine for some purposes, but 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 thestocks 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 that we havein order to study wealth accumulation – a question that is so important that we cannot wait
for perfect data before we start addressing it, and that has indeed been addressed in the pastby 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 aconceptually coherent manner, so as to better identify their limitations. Our paper, therefore,
can also be viewed as an attempt to evaluate 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 wealthand income, available online, whose main characteristics are summarized in Table 1. To ourknowledge, it is the first international database to include long-run, homogeneous information
on national wealth. 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
1the 1970-2010 period. Through to the world wars, there was a lively tradition of national wealthaccounting in many countries. By combining numerous historical estimates in a systematic andconsistent 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 – and most important – contribution is to exploit the database in order toestablish a number of new striking results. Looking first at the recent period, we document that
wealth-income ratios have been gradually rising in each of the top eight developed countries overthe last four decades, from about 200-300% in 1970 to 400-600% in 2010 (Figure 1). Taking
a long-run perspective, we find that 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 2 and 3). In the U.S., the wealth-income
ratio has also followed a U-shaped pattern, but less marked (Figure 4).
In order to understand these dynamics, we provide detailed decompositions of wealth accumulation into volume e↵ects (saving) and relative price e↵ects (real capital gains and losses).
The results show that the U-shaped evolution of the European wealth-income ratios can be explained by two main factors. The first is a long-run swing in relative asset prices, itself largely
driven by changes in capital policies in the course of the twentieth century. Before World WarI, 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 ofproductivity and population growth. According to the Harrod-Domar-Solow formula, in thelong run the wealth-income ratio

is equal to the net saving rate s divided by the income

growth rate g. So for a given saving rate s =10%, the long-run

is about 300% if g = 3% andabout 600% if g = 1.5%. In short: capital is back because low growth is back.
The= s/g formula is simple, yet as we show in the paper surprisingly powerful. It canaccount for a significant part of the 1970-2010 rise in the wealth-income ratios of Europe andJapan, two economies where population and productivity growth have slowed markedly. It2can also explain why wealth-income ratios are lower in the U.S., where population growth has
been historically much larger than in Europe – and still continues to be to some extent – butwhere saving rates are not higher. Last, the Harrod-Domar-Solow formula seems to accountreasonably well for the very long-run dynamics of wealth accumulation. Over a few years andeven a few decades, valuation e↵ects and war destructions are of paramount importance. But inthe main developed economies, we find that today’s wealth levels are reasonably well explainedby 1870-2010 saving and income growth rates, in line with the workhorse one-good model ofcapital accumulation. In the long run, assuming a significant divergence between the price ofconsumption and capital goods seems unnecessary.
Our findings have a number of implications for the future and for policy-making. First, thelow wealth-income ratios of the mid-twentieth century were due to very special circumstances.
The world wars and anti-capital policies destroyed a large fraction of the world capital stockand reduced the market value of private wealth, which is unlikely to happen again with freemarkets. By contrast, the= s/g logic will in all likelihood matter a great deal in theforeseeable future. 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 . For thetime being, this e↵ect is strong in Europe and Japan. To the extent that growth will ultimately
slow everywhere, wealth-income ratios may well ultimately rise in the whole world.
The return of high wealth-income ratios is certainly not bad in itself, but it raises new issues
about capital taxation and regulation. Because wealth is always very concentrated (due inparticular to the cumulative and multiplicative processes governing wealth inequality dynamics),
highimplies than the inequality of wealth, and potentially the inequality of inherited wealth, islikely to play a bigger role for the overall structure of inequality in the twenty first century thanit did in the postwar period. This evolution might reinforce the need for progressive capital andinheritance taxation (Piketty, 2011; Piketty and Saez, 2013). If international tax competition
prevents this policy change from happening, one cannot exclude the development of a new waveof anti-globalization and anti-capital policies.
Further, because s and g are largely determined by di↵erent forces, wealth-income ratios
can vary a lot between countries. This fact has important implications for financial regulation.
With perfect capital markets, large di↵erences in wealth-income ratios potentially imply large
net foreign asset positions, which can create political tensions between countries. With imperfect3

capital markets and home portfolios bias, structurally high wealth-income ratios can contributeto 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 2008-2009.1
Housing and financial bubbles are potentially more devastating when the total stock of wealthamounts to 6-8 years of national income rather than 2-3 years only. The fact that the Japaneseand Spanish bubbles are easily identifiable in our dataset also suggests that monitoring wealthincome ratios may help designing appropriate financial and monetary policy. In Japan andSpain, most observers had noticed that asset price indexes were rising fast. But in the absenceof 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. We believe that 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 18th and early 19th century,
capital was mostly land (Figure 3), so that there was limited scope for substituting labor tocapital. In the 20th and 21st centuries, by contrast, capital takes many forms, to an extent suchthat the elasticity of substitution between labor and capital might well be larger than 1. Withan elasticity even moderately larger than 1, rising capital-output ratios can generate substantial
increases in capital shares, similar to those that have occurred in most rich countries since the1970s. Looking forward, with low growth and high wealth-income ratios, one cannot exclude afurther increase in capital shares.
The paper is organized as follows. Section 2 relates our work to the existing literature. In
section 3 we present the conceptual framework and accounting equations used in this research.
Section 4 is devoted to the decomposition of wealth accumulation in rich countries over the 19702010 period. In section 5, 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 6 in which we discuss the changing nature of wealth in the U.K., France and the
U.S. since the 18th century. In section 7, 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 8 presents some possible directions for
1

See Appendix figure A8. We do not include Spain in our main sample of countries because the Bank of
Spain balance sheets that are currently available only start in 1987, and we want to be able to decompose wealthaccumulation over a longer period (at least 1970-2010).

4

future research. The main sources and concepts are presented in the main text, and we leave
the complete methodological details to an extensive online Data Appendix.

2

Related literature

2.1

Literature on national wealthAs far as we know, 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 inthis 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 mostrich countries, the publication of time series of national wealth only began in the 1990s and2000s. In a key country like Germany, the first official balance sheets were released in 2010.
It is worth stressing, however, that the recent emphasis on national wealth largely represents
a return to older practice. Until the early twentieth century, economists, statisticians and social
arithmeticians 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 earlyeighteenth 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), Gi↵en (1889) and Bowley (1920)
in the U.K., Foville (1893) and Colson (1903) in France, Hel↵erich (1913) in Germany, King(1915) in the U.S., and dozens of other economists from all industrialized nations. Althoughthese historical balance sheets are far from perfect, their methods are well documented and they
are usually internally consistent. One should also keep in mind that it was in many ways easierto estimate national wealth around 1900-1910 than it is today: the structure of property wasmuch simpler, with far less financial intermediation and cross-border positions.
Following the 1914-1945 capital shocks, the long tradition of research on national wealthlargely 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 theinterwar 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 e↵ort to put together historical balance sheets in recent decades, most notably by Goldsmith (1985, 1991), todate no systematic attempt has been made to relate the evolution of wealth-income ratios to the5magnitude of saving flows.2 The reason is probably that it is only recently that official balance
sheets have become sufficiently widespread to make the exercise meaningful.

2.2

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 growthmodel 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= s/g formula was

first derived by Harrod (1939) and Domar (1947) using fixed-coefficient production functions, inwhich caseis entirely given by technology – hence the knife-edge conclusions about growth.3

The classic derivation of the formula with a flexible production function Y = F (K, L) involving
capital-labor substitution, thereby making

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

= 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 for instance Denison, 1962; Jorgenson and Griliches, 1967; Feinstein, 1978) and it waslater on extended to human capital (Mankiw, Romer and Weil, 1992; Barro, 1991). The maindi↵erence 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 computedby cumulating past investment flows and attempting to adjust for changes in price – what is
known as the perpetual inventory method. By contrast, we measure capital by using nationalbalance sheets in which we observe the actual evolution of the market value of most types ofassets: real estate, equities (which capture the market value of corporations), bonds, and soon. We are essentially interested in what non-human private capital is worth for households
2

In particular, Goldsmith does not relate his wealth estimates to saving and investment flows. He is mostlyinterested 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 Gi↵en and Foville were fascinated by the huge accumulation of private capital, but did not havemuch estimates of income, saving and investment, so they were not able to properly analyze the evolution of thewealth-income ratio. Surprisingly enough, socialist authors like Karl Marx – who were obviously much interested
in the rise of capital and the possibility that reaches very high levels – largely ignored the literature on national
wealth.
3Harrod emphasized the inherent instability of the growth process, while Domar stressed the possibility thatand s can adjust in case the natural growth rate g di↵ers from s/ .

6

at each point in time – and in what public capital would be worth if it was privatized. This
notion is precisely what the economists of the eighteenth and nineteenth century aimed tocapture. We believe it is a useful, meaningful, and well defined starting point.4 There are
two additional advantages to using balance sheets: first, they include data for a large numberof assets, including non-produced assets such as land which by definition cannot be measured
by cumulating past investment flows. Second, they rely for the most part on observed market
prices – such as actual real estate transactions and financial market quotes – contrary to theprices used in the perpetual inventory method, which tend not to be well defined.5
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 notthat robust. The constancy of the capital-output ratio, in particular, is simply 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 a lot of confusion about what
the level of the capital-output ratio is supposed to be (see, e.g., Kaldor, 1961; Samuelson, 1970;
Simon, 1990; Jones and Romer, 2010). The data we presently have suggest that the ratio isoften closer to 5-6 in most rich countries today than to the values of 3-4 typically used in macromodels and textbooks.6
Our results also suggest that the focus on the possibility of a balanced growth path thathas long characterized academic debates on capital accumulation (most notably during theCambridge controversy of the 1960s-1970s) has been somewhat misplaced. It is fairly obviousthat there can be a lot of capital-labor substitution in the long-run, and that many di↵erent
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
4
By contrast, in the famous Cambridge controversy, the proponent of the U.K. view argued that the notionof capital used in neoclassical growth models is not well defined. In our view much of the controversy owes tothe lack of balance sheet data, and to the difficulty of making comparisons with pre-World War 1 estimates ofnational capital stocks.
5
As we discuss in details in Appendix A.1.2, the price estimates used in the perpetual inventory method raise
all sorts of difficulties (depreciation, quality improvement, aggregation bias, etc.). Even when these difficulties
can be overcome, PIM estimates of the capital stock at current price need not be equal to the current market
value of wealth. For instance, the current value of dwellings obtained by the PIM is essentially equal to past
investments in dwellings adjusted for the evolution of the relative price of construction. This has no reason tobe equal to the current market value of residential real estate – which in practice is often higher.
6
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, completely disregards the large stock of housing capital, as well as
non-corporate businesses and government capital.

7

with large instability, asset price bubbles and high degrees of inequality – all plausible scenarios
in mature, low-growth economies.

2.3

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). To some extent, what we are doing in this paper is to extend thisline of work to domestic wealth and to longer time periods. We document the changing natureof domestic capital over time, and we investigate the extent to which the observed aggregate
dynamics can be accounted for by saving flows and valuation e↵ects. A key di↵erence is that ourinvestigation 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 inthe dynamics of the national wealth of a number of countries, more spectacularly the U.S. The
reason is that gross foreign positions are much bigger than net positions, thereby potentiallygenerating large capital gains or losses at the country level.7 One of the things we attempt to
do is to put the study of external wealth into the broader perspective of national wealth.8

2.4

Literature on rising capital shares

Our work is also closely related to the growing literature establishing that capital shares havebeen rising in most countries over the last decades (Ellis and Smith, 2007; Azmat, Manningand Van Reenen, 2011; Karabarbounis and Neiman, 2013). The fact that we find rising wealthincome and capital-output ratios in the leading rich economies reinforces the presumption that
capital shares are indeed rising globally. We believe that this confirmation is important in itself,
because computing factor shares raises all sorts of issues. In many situations, what accrues tolabor and to capital is unclear – both in the non-corporate sector and in the corporate sector,
where profits and dividends recorded in the national accounts sometimes include labor income
components that are impossible to isolate. Wealth-income and capital-output ratios provide an
7

See Obstfeld (2013) and Gourinchas and Rey (2013) for recent papers surveying the literature on this issue.
Eisner (1980), Babeau (1983), Greenwood and Wol↵ (1992), Wol↵ (1999), and Gale and Sabelhaus (1999)
study the dynamics of U.S. aggregate household wealth using official balance sheets and survey data. With apure household perspective, however, one is bound to attribute an excessively large role to capital gains, because
a lot of private saving takes the form corporate retained earnings.
88

indication of the relative importance of capital in production largely immune to these issues,
although they are themselves not perfect. They usefully complement measures of factor shares.
More generally, we attempt to make progress in the measurement of three fundamentallyinter-related macroeconomic variables: the capital share, the capital-output ratio, and themarginal product of capital (see also Caselli and Feyrer, 2007). As we discuss in section 7,
rising capital-output ratios together with rising capital shares and declining returns to capital
imply an elasticity of substitution between labor and capital higher than 1 – consistent withthe results obtained by Karabarbounis and Neiman (2013) over the same period of time.

2.5

Literature on income and wealth inequalities

Last, this paper is to a large extent the continuation of the study of the long run evolution ofprivate 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 tostudy 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 global distributional trends in the analysis. Any
study of wealth inequality requires reliable estimates of aggregate wealth to start with. Plugging
distributions into our data set would make it possible to analyze the dynamics of the global
distribution of wealth.9 The resulting series could then be used to improve the top income sharesestimates that were recently constructed for a number of countries (see Atkinson, Piketty, Saez2011). We see the present research as an important step in this direction.

3

Conceptual framework and methodology

3.1

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
9

See Davies et al. (2010) for a study of the world distribution of wealth using national balance sheet data.

9

international guidelines (SNA, 1993, 2008). For the previous periods, we have collected a large
number of historical balance sheets and income series, which we have homogenized using thesame concepts and definitions as those used in the most recent official accounts.10 Here we
provide the main definitions.
Private wealth Wt is the net wealth (assets minus liabilities) of households and non-profit
institutions serving households.11 Following SNA guidelines, assets include all the non-financial
assets – land, buildings, machines, etc. – and financial assets – including life insurance andpensions 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 allother claims on future government expenditures and transfers (like education expenses for one’s
children and health benefits). Durable goods owned by households, such as cars and furniture,are excluded as well.12 As a general rule, all assets and liabilities are valued at their prevailingmarket prices. Corporations are included in private wealth through the market value of equities.
Unquoted shares are typically valued on the basis of observed market prices for comparable,
publicly traded companies.
We similarly define public (or government) wealth Wgt as the net wealth of public administrations and government agencies. In available balance sheets, public non-financial assets likeadministrative 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 Wnt as the sum of private and public wealth:Wnt = Wt + Wgt
National wealth can also be decomposed into domestic capital and net foreign assets:
Wnt = Kt + N F At
10

Section A of the Data Appendix provides a detailed description of the concepts and definitions used by the
1993 and 2008 SNA. Country-specific information on historical balance sheets are provided in Data Appendix
sections B (devoted to the U.S.), D (Germany), E (France), and F (U.K.).
11
The main reason for including non-profit institutions serving households (NPISH) in private wealth is thatthe frontier between individuals and private foundations is not always entirely 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. Note also that the household sector includes allunincorporated businesses.
12
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 the long-run evolution of durable
goods in the U.S.

10

And domestic capital Kt 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 othernon-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 Wct as the di↵erence between the book-value of corporations and their market
value (which is the value of their equities). By definition, Wct 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 di↵erent from 1, so that residual corporate wealth is at times positive, attimes negative. We define book-value national wealth Wbt as the sum of market-value national
wealth and residual corporate wealth: Wbt = Wnt + Wct = Wt + Wgt + Wct . Although we prefer
our market-value concept of national wealth (or national capital), both definitions have somemerit, as we shall see.13
Balance sheets are constructed by national statistical institutes and central banks usinga large number of census-like sources, in particular reports from financial and non-financial
corporations about their balance sheet and o↵-balance sheet positions, and housing surveys.
The perpetual inventory method usually plays a secondary role. The interested reader is referredto 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 Yt is the sum of net domestic
output and net foreign income: Yt = Ydt +rt ·N F At .14 Domestic output can be thought as comingfrom some production function that uses domestic capital and labor as inputs: Ydt = F (Kt , Lt ).
We are particularly interested in the evolution of the private wealth-national income ratio
t = Wt /Yt and of the (market-value) national wealth-national income ratio

nt = Wnt /Yt .

In

a closed economy – and more generally in an open economy with a zero net foreign position– the national wealth-national income rationt

13

is the same as the domestic capital-output

Wbt corresponds to the concept of “national net worth” in the SNA (see Data Appendix A.4.2). In thispaper, we propose to use “national wealth” and “national capital” interchangeably (and similarly for “domestic
wealth” and “domestic capital”, and “private wealth” and “private capital”), and to specify whether one uses
“market-value” or “book-value” aggregates. Note that 19th century authors such as Gi↵en and Foville also used“national wealth” and “national capital” interchangeably. The di↵erence 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).
14
National income also includes net foreign labor income and net foreign production taxes – both of which areusually negligible.

11

ratiokt = Kt /Ydt .

15

In case public wealth is equal to zero, then both ratios are also equal

to the private wealth-national income ratio:

t

=

nt

=

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 ↵t = rt · t . With imperfect capital
markets, the average rate of return rt can substantially vary across assets. In particular, it canbe di↵erent for domestic and foreign assets. With perfect capital markets, the rate of returnrt is the same for all assets and is equal to the marginal product of capital. With a CobbDouglas production function F (K, L) = K ↵ L1 ↵ , and a closed economy setting, the capitalshare is entirely set by technology: ↵t = rt ·t = ↵. A higher capital-output ratio

t is exactlycompensated by a lower capital return rt = ↵/ t , so that the product of the two is constant.
In an open economy setting, the world capital share is also constant and equal to ↵, and theworld rate of return is also given by rt = ↵/ t , but the countries with higher-than-average
wealth-income ratios invest part of their wealth in other countries, so that for them the shareof capital in national income is larger than ↵. With a CES production function, much depends
on whether the capital-labor elasticity of substitution
then asis larger or smaller than one. If> 1,

t rises, the fall of the marginal product of capital rt is smaller than the rise oft , sothat the capital share ↵t = rt ·fall of rt is bigger than the rise oft is an increasing function oft.

Conversely, if< 1, thet , so that the capital share is a decreasing function oft.

16

Because we include all forms of capital assets into our aggregate capital concept K (including
housing), the aggregate elasticity of substitution

should really be interpreted as resulting fromboth supply forces (producers shift between technologies with di↵erent capital intensities) anddemand forces (consumers shift between goods and services with di↵erent capital intensities,
including housing services vs. other goods and services).17
15

In principle, one can imagine a country with a zero net foreign asset position (so that Wnt = Kt ) but
non-zero net foreign income flows (so that Yt 6= Ydt ). In this case the national wealth-national income ratio nt
will slightly di↵er from the domestic capital-output ratio kt . In practice today, di↵erences between Yt and Ydt
are very small – national income Yt is usually between 97% and 103% of domestic output Ydt (see Appendix
Figure A57). Net foreign asset positions are usually small as well, so that kt turns out to be usually close to
nt in the 1970-2010 period (see Appendix Figure A67).
1
1
16
A CES production function is given by: F (K, L) = (a·K+(1 a)·L) 1 . As ! 1, 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 ! 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.
17
Excluding housing from wealth strikes us an inappropriate, first because it typically represents about halfof the capital stock, and next because the frontier with other capital assets is not always entirely 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

12

3.2

The one-good wealth accumulation model:= s/g

Generally speaking, wealth accumulation between time t and t + 1 can always be decomposed
into a volume e↵ect and a relative price e↵ect:

Wt+1 = Wt + St + KGt
where:
Wt is the market value of aggregate wealth at time t
St is the net saving flow between time t and t + 1 (volume e↵ect)
KGt is the capital gain or loss between time t and t + 1 (relative price e↵ect)
In the one-good model of wealth accumulation, and more generally in a model with a constantrelative price between capital and consumption goods, there is no relative price e↵ect (KGt = 0).
The wealth-income ratio

t = Wt /Yt is simply given by the following transition equation:

t+1 =1 + gwst·
1 + gttwhere:
1 + gwst = 1 + st / t = saving-induced wealth growth rate
1 + gt = Yt+1 /Yt = growth rate of national income
st = St /Yt = net saving rate.
In the long run, with a fixed saving rate st = s and growth rate gt = g, the steady-state
wealth-income ratio is given by the well-known Harrod-Domar-Solow formula:

t !

= s/g

Should we use gross-of-depreciation saving rates rather than net rates, the steady-state
formula would be= s/(g+ ) with s the gross saving rate, and the depreciation rate expressed

as a proportion of the wealth stock. We find it more transparent to express everything in termsof net saving rates and use the= s/g formula, so as to better concentrate on the saving versus

capital gain decomposition. Both formulations are equivalent and require the same data.18
capital assets.
18
Appendix Table A84 provides cross-country data on private 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

13

3.3

The

= s/g formula is independent of saving motives

It is worth stressing that the steady-state formula= s/g is a pure accounting equation. By

definition, it holds in the steady-state of any micro-founded model, independently of the exact
nature of saving motives. If the saving rate is s = 10%, and if the economy grows at rateg = 2%, then in the long run the wealth income ratio has to be equal to= 500%, because itis the only ratio such that wealth rises at the same rate as income: gws = s/ = 2% = g.
In the long run, income growth g is the sum of productivity and population growth. Amongother things, it depends on the pace of innovation and on fertility behavior (which is notoriously
difficult to predict, as the large variations between rich countries illustrate).19 The saving rate salso depends on many forces: s measures the strength of the various psychological and economic
motives for saving and wealth accumulation (dynastic, lifecycle, precautionary, prestige, taste forbequests, etc.). The motives and tastes for saving vary a lot across individuals and potentiallyacross countries.20
One simple way to see this is the “bequest-in-the-utility-function” model. Consider a dynamic economy with a discrete set of generations 0, 1, .., t, ..., zero population growth, andexogenous labor productivity growth at rate g > 0. Each generation has measure Nt = N ,lives one period, and is replaced by the next generation. Each individual living in generationt receives bequest bt = wt

0 from generation t

1 at the beginning of period t, inelasticallysupplies one unit of labor during his lifetime (so that labor supply Lt = Nt = N ), and earns
labor income yLt . At the end of period, he then splits lifetime resources (the sum of labor income and capitalized bequests received) into consumption ct and bequests left bt+1 = wt+10,

according to the following budget constraint:
ct + bt+1  yt = yLt + (1 + rt )bt
The simplest case is when the utility function is defined directly over consumption ct andthe increase in wealthbt = bt+1

bt and takes a simple Cobb-Douglas form: V (c, b) =one writes down the decomposition of wealth accumulation using gross or net saving, one needs depreciation
series.
19
The speed of productivity growth could also be partly determined by the pace of capital accumulation (likein AK-type endogenous growth models). Here we take as given the many di↵erent reasons why productivity
growth and population growth vary across countries.
20
For estimates of the distribution of bequest motives between individuals, see, e.g., Kopczuk and Lupton(2007). On cross-country variations in saving rates due to habit formation (generating a positive s(g) relationship), see Carroll, Overland and Weil (2000). On the importance of prestige and social status motives for wealthaccumulation, see Carroll (2000).

14c1 s bs .21 Utility maximization then leads to a fixed saving rate at the level of each dynasty:
wt+1 = wt + syt . By multiplying per capita values by population Nt = N we have the same
linear transition equation at the aggregate level: Wt+1 = Wt + sYt .
Assume a closed economy and no government wealth. Domestic output is given by a standard
constant returns to scale production function Ydt = F (Kt , Ht ) where Ht = (1 + g)t · Lt is the
supply of efficient labor. The wealth-income ratio

t = Wt /Yt is the same as the capital-output

ratio Kt /Ydt . With perfectly competitive markets, the rate of return is given by the marginal
product of capital: rt = FK . Now assume a small open economy taking the world rate of
return as given (rt = r). The domestic capital stock is set by r = FK . National income
Yt = Ydt + r(WtKt ) can be larger or smaller than domestic output depending on whether the

net foreign asset position N F At = Wt

Kt is positive or negative. Whether we consider theclosed or open economy case, the long-run wealth-income ratio is given by the same formula:t !

= s/g. It depends on the strength of the bequest motive on the one hand, and on therate of productivity growth on the other.22
With other functional forms for the utility function, e.g. with V = V (c, b), or with heterogenous labor productivities and/or saving tastes across individuals, one simply needs to replace
the parameter s by the properly defined average bequest taste parameter. In any case we keep
the same general formula= s/g.23

If we introduce overlapping generations and lifecycle saving into the “bequest-in-the-utilityfunction” model, then one can show that the saving rate parameter s in the= s/g formula now

depends not only on the strength of the bequest taste, but also on the magnitude of the lifecycle
saving motive. Typically, following the Modigliani triangle logic, the saving rate s = s( ) is anincreasing function of the fraction of one’s lifetime that is spent in retirement ( ). The long-run
21

Intuitively, this corresponds to a form of “moral” preferences where individuals feel that they cannot possibly
leave less wealth to their children than what they have received from their parents, and derive utility from theincrease in wealth (maybe because this is a signal of their ability or virtue). Of course the strength of this saving
motive might well vary across individuals and countries.
22
In addition, with a Cobb-Douglas production function F (K, H) = K ↵ H 1 ↵ , the domestic capital-output
ratio is given by: Kt /Ydt = ↵/r. Depending on whether this is smaller or larger than = s/g, the long run net
foreign asset position is positive or negative. In the closed-economy case, rt ! r = ↵/ = ↵ · g/s.
23
For instance, with V (c, b) = c1 s bs , we get wt+1 = s(wt + yt ) and t ! = s/(g + 1 s) = se/g (withse = s(1 + )). In a model with general heterogenous labor incomes yLti and utility functions V ti (c, b), one
simply needs to replace s by the properly defined weighted average si (see Piketty and Saez, 2013). Note alsothat if one interprets each period 0, 1, ..., t, ... as a generation lasting H years, then the = s/g formula is better
viewed as giving a ratio of wealth over generational income b = s/G, where G = (1 + g)H 1 is the generational
growth rate and g is the corresponding yearly growth rate. For g small, the corresponding wealth-yearly income
ratio H · b is approximately equal to = s/g.

15

now depends on demographic parameters, life expectancy, and the generosity of the publicsocial security system.24
Last, the= s/g formula also applies in the infinite-horizon, dynastic model, whereby eachPdynasty maximizes V = t 0 U (ct )/(1+✓)t . One well-known, unrealistic feature of this model isthat the long run rate of return is entirely determined by preference parameters and the growth
rate: rt ! r = ✓ + g.25 In e↵ect, the model assumes an infinite long-run elasticity of capital
supply with respect to the net-of-tax rate of return. It mechanically entails extreme consequences
for optimal capital tax policy (namely, zero tax). The “bequest-in-the-utility-function” model
provides a less extreme and more flexible conceptual framework in order to analyze the wealthaccumulation process.26 But from a purely logical standpoint, it is important to realize thatthe Harrod-Domar-Solow also holds in the dynastic model. The steady-state saving rate in thedynastic model is equal to s = ↵·g/r = ↵·g/(✓ + g).27 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= s/g is again a decreasing function of the growth rate.28

3.4

The two-good model: volume vs. relative price e↵ects

Wherever savings come from, the key assumption behind the one-good model of wealth accumulation and the= s/g formula is that there is no change in the relative price between capitaland consumption goods. This is a strong assumption. In practice, relative asset price e↵ects
often vastly dominate volume e↵ects in the short run, and sometimes in the medium run as
well. One key issue addressed in this paper is whether relative price e↵ects also matter for the
analysis of long-run wealth accumulation.
There are many theoretical reasons why they could matter, particularly if the speed oftechnical progress is not the same for capital and consumption goods. One extreme case would
24

For a simple model along those lines, see Appendix K.4.
10 is the curvature of the utility function: U (c) = c1
( > 1 is usually assumed to be more realistic).
26
Depending upon the exact functional form of the utility function V (c, b) (or V (c, b)), one can generate any
elasticity of saving behavior s(r) with respect to the net-of-tax rate of return. The elasticity could be positiveor negative, large or small, leaving it to empirical studies to settle the issue. Available estimates tend to suggest
a low positive long run elasticity (Piketty and Saez, 2013). It is unclear whether increased tax competition andcuts in capital tax rates over the recent decades have a↵ected saving rates and have contributed to the rise of
wealth-income ratios.
27↵ = r · is the capital share. Intuitively, a fraction g/r of capital income is saved in the long-run, so thatdynastic wealth grows at the same rate g as national income.
28
With a Cobb-Douglas production function (fixed capital share), the wealth-income ratio is simply given by= ↵/r = ↵/(✓ + · g) and takes its maximum value = ↵/✓ for g = 0.
25

16

be a two-good model where the capital good is in fixed supply: Vt = V (say, fixed land supply).
The market value of wealth if given by Wt = qt V , where qt is the price of the capital good(say, land price) relative to the consumption good. Assume fixed population and labor supply
Lt = Nt = N0 , positive labor productivity growth g > 0 and the same utility function U (c, b) =c1 s bs as that described above, wherebt = bt+1

bt = wt+1

wt is the di↵erence (in value)

between left and received bequests. Then one can easily see that the relative price qt will riseat the same pace as output and income in the long run, so that the market value of wealth rises
as fast as output and income. By construction, there is no saving at all in this model (since thecapital good is by assumption in fixed supply), and the rise in the value of wealth is entirely
due to a relative price e↵ect.29 This is the opposite extreme of the one-good model, whereby
the rise in the value of wealth is entirely due to a volume e↵ect.
In practice, there are all sorts of intermediate cases between these two polar cases: in thereal world, volume e↵ects matter, but so do relative price e↵ects. Our approach is to let thedata speak. We decompose the evolution of the wealth-income ratio into two multiplicative
components (volume and relative price) using the following accounting equation:

t+1 =(1 + gwst )(1 + qt )t
1 + gtwhere:
1 + gwst = 1 + st / t = saving-induced wealth growth rate
1 + qt = capital-gains-induced wealth growth rate
1 + gt = Yt+1 /Yt = growth rate of national income
1 + qt is the real rate of capital gain or loss (i.e., the excess of asset price inflation overconsumer price inflation) and can be estimated as a residual. We do not try to specify whereqt comes from (one can think of stochastic production functions for capital and consumption
goods, with di↵erent rates of technical progress in the two sectors), and we infer it from the dataat our disposal ont , ...,

t+n , st , ..., st+n , and gt , ...gt+n . In e↵ect, if we observe that the wealth-

income ratios rises too fast as compared to recorded saving, we record positive real capital gains
qt . Although we tend to prefer the multiplicative decomposition of wealth accumulation (which29

For instance with a Cobb-Douglas production function Y = V ↵ N 1 ↵ , we have: Yt = Y0 (1 + g)t (withY0 = V ↵ N01 ↵ and 1+g = (1+g)1 ↵ ; if g small, g ⇡ (1 ↵)g); qt = q0 (1+g)t (with t = Wt /Yt = qt V /Yt = s/g,
i.e. qt = (s/g)(Yt /V )); and YKt = rWt = ↵Yt , i.e. r = ↵g/s. In e↵ect, the relative capital price rises as fast as
income and output, and the level of the relative capital price is set by the taste for wealth.

17

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. The exact equations and detailed decomposition results are provided inAppendix K. In the next two sections, we will present the main decomposition results, startingwith the 1970-2010 period, before moving to longer periods of time.

4

Wealth-income ratios in rich countries 1970-2010

4.1

The rise of private wealth-income ratios

The first fact that we want to understand is the gradual rise of private wealth-national income
ratios in rich countries over the 1970-2010 period – from about 200-300% in 1970 to about
400-600% (Figure 1 above). We begin with a discussion of the basic descriptive statistics.
Private wealth-national income ratios have risen in every developed economy since 1970, butthere are interesting cross-country variations. Within Europe, the French and U.K. trajectories
are relatively close: in both countries, private wealth rose from 300-310% of national income in1970 to 540-560% 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 ofGerman wealth at market value is an interesting puzzle, on which we will return. At this stage,
we simply note that we are unable to identify any methodological or conceptual di↵erence inthe work of German statisticians (who apply the same SNA guidelines as everybody else) that
could explain the gap with other European countries.30
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 welook at the Japanese trajectory from a longer run, cross-country perspective, it is yet another30

See Appendix D on Germany. We made sure that the trend is una↵ected by German unification in 1990.
The often noted di↵erence 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 di↵erent typesof assets, and there is no obvious reason in general why housing assets should deliver higher capital gains thanfinancial assets. We return to this issue below.

18

example of the 1970-2010 rise of wealth-income ratios – fairly close to Italy in terms of total
magnitude over the 40 years period.
In the U.S., private wealth rose from slightly more than 300% of national income in 1970 toalmost 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 thismight change in the near future). In other countries the wealth-income ratio stabilized or fell
relatively little during the 2008-2010 financial crisis.31 In Canada, private wealth rose from250% of national income in 1970 to 420% in 2010 – a trajectory that is comparable to Germany,
but a with a somewhat larger starting point.
The general rise in private wealth-national income ratios would be even more spectacularshould 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, thendeclined to about 80% in 1970 and to 75%-80% in 2010, in particular because of the riseof freely provided public services and in-kind transfers such as health and education. As aconsequence, the private wealth-disposable income ratio is well above 700% in a number ofcountries in 2010, while it was below 400% in every country in 1970.32 Whether one should
use national or disposable income as denominator is a matter of perspective. If one aims tocompare 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 study the wealth accumulation process and to compare wealth-income ratios
over long periods of time, it seems more justified to look at economic values and therefore tofocus on the private wealth-national income ratio, as we do in the present paper.33
31

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).
32
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 a↵ect the upward trend.
33
In the end it really depends on how one views government-provided services. If one assumes that government
expenditures are useless, and that the rise of government during the 20th century has limited the ability of private
individuals to accumulate and transmit 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 healthand 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 of using national income is that it
tends to be better measured. Disposable income can display large time-series and cross-country variations forpurely definitional reasons. In European countries disposable income typically jumps from 70% to about 80% ofnational income if one includes in-kind health transfers (such as insurance reimbursements), and to about 90%
of national income if one includes all in-kind transfers (education, housing, etc.). See Appendix Figure A65.

19

4.2

Private wealth vs. national wealth

We now move from private to national wealth – the sum of private and government wealth.
In rich countries, net government wealth has always been relatively small compared to private
wealth, and it has declined since 1970, as Figure 5 illustrates. This decline is due both toprivatization policies – leading to a reduction in government assets – and to the gradual increasein public debt.
In the U.S., as well as in Germany, France, and the U.K., net government wealth wasaround 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. In Canada, the government turned strongly negativein the late 1980s – with a trough of -60% in 1995, like Italy in 2010 – but is now back tozero. 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 definitely appears tobe quantitatively 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 6).34 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.

4.3

Growth rates vs. saving rates

How can we account for the general rise of wealth-income ratio, as well as for the cross country
variations? According to the one-good capital accumulation model and the Harrod-DomarSolow formula= s/g, the two key forces driving wealth-income ratios are the saving rate s

and the income growth rate g. So before we present our decomposition results, it is useful tohave in mind the magnitude of growth and saving rates in rich countries over the 1970-2010
period. The basic fact is that there are important variations across countries, for both growth34

Note that national wealth is una↵ected by the treatment of future government spending such as pay-as-yougo pensions. Should we include claims on future spendings spending in wealth, private wealth would be higher
and government wealth lower, leaving national wealth unchanged.

20and saving rates, and that they seem largely unrelated (Table 2).35
Variations in income growth rates are mostly due to variations in population growth. Over1970-2010, average per capita growth rates have been virtually the same in all rich countries:
they are always between 1.6% and 2.0%, and for most countries between 1.7% and 1.9%. Given
the data imperfections we face, it is unclear whether di↵erences of 0.1%-0.2% are statisticallysignificant. 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.36
In contrast, variations in population growth are large and significant. Over 1970-2010,average population growth rates vary from less than 0.2% per year in Germany to over 1.4%
in Australia. Population growth is over 1% per year in New World countries (U.S., Canada,
Australia), and less than 0.5% in Europe and Japan. As a consequence, total growth rates areabout 2.5%-3% in the former group, and closer to 2% in the latter. Di↵erences in population
growth are due to di↵erences in both migration and fertility. Within Europe, for example, there
is a well known gap between high fertility countries such as France (with population growthequal to 0.5% per year) and low fertility countries like Germany (less than 0.2% per year, witha sharp fall at the end of the period).37
Variations in saving rates are also large. Average net-of-depreciation private saving rates
vary from 7%-8% in the U.S. and the U.K. to 14%-15% in Japan and Italy, with a large groupof countries around 10%-12% (Germany, France, Canada, Australia). In theory, one could
imagine that low population growth, aging countries have higher saving rate, because theyneed to accumulate more wealth for their old days. Maybe it is not a coincidence if the twocountries 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 di↵erences in tastes for saving and/or wealth accumulation and35
Here we focus upon the long run picture, so we mostly comment about the 40-year averages. Complete
breakdowns of growth and saving rates by decades are available in the Appendix country tables.
36
In particular, the U.S. and Japan both fall last in the ranking if we deflate income by the CPI rather thanthe GDP deflator (see Appendix Table A165). Di↵erences 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 di↵erences 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.
37
Population growth in Japan over the 1970-2010 period appears to be relatively large (0.5%), but it is actuallymuch higher in 1970-1990 (0.8%) than in 1990-2010 (0.2%). Japan is also the country with the largest fall inper capita growth rates, from 3.6% in 1970-1990 to 0.5% in 1990-2010. See Appendix Table JP.3.

21

transmission,38 as well as di↵erences in psychological perceptions of the need for saving (i.e.,di↵erent levels of trust and confidence in the future).39 As a result, there is only a weakly
significant negative relationship between private saving and growth rates at the country level.
And when we consider national rather than private saving (see Table 3), we find no relationshipat all between saving and growth.40
In brief: as a first approximation, productivity growth is the same everywhere in the richworld, but fertility decisions, migration policy and saving behavior vary widely and are largely
unrelated to one another. This potentially creates a lot of room for wide, multi-dimensionalvariations in wealth-income ratios

4.4= s/g.

Basic decomposition: volume vs. price e↵ects

Table 4 presents our results on the decomposition of 1970-2010 national wealth accumulation
into saving and capital gains e↵ects.41 The main finding is that new savings explain the largest
part of wealth accumulation, but that 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 to431% of national income in 2010. National wealth has grown at an average real rate gw = 3.0%
per year. On the basis of national saving flows alone, we find that wealth would have grown
at rate gws = 2.1% per year only. We conclude that the residual capital-gains-induced wealthgrowth rate q = (1 + gw )/(1 + gws )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, while
residual capital gains explain 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%. Capitalgains are larger in the U.K., Italy, and Australia.
38

See, e.g., Hayashi (1986) on Japanese tastes for bequest.
The e↵ect 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 berelatively 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.
40
See Appendix Figures A122 and A123. Note that in some countries a large fraction of private savings isabsorbed by government deficits (more than one third in Italy over the 1970-2010 period).
41
Here we only show the multiplicative decompositions of national wealth. The additive decompositions yield
similar conclusions; see Appendix Table A101. Additive and multiplicative decompositions of private wealth arepresented in Appendix Table A111b.
39

22

The capital gains we compute are obtained as a residual, and so may reflect measurement
errors in addition to real valuation e↵ects.42 There are two main possible issues. First, it
is entirely possible that national saving flows are substantially under-estimated because they
do not include research and development expenditure. To address this concern, we have recomputed our wealth accumulation equations using saving flows that include R&D. Even after
we include generous estimates of R&D expenditure, in many countries the 2010 observed levelsof national wealth are still significantly larger than those predicted by 1970 wealth levels and1970-2010 saving flows alone (Figure 7a).43 Take the case of France: predicted national wealthin 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 national wealth is equal
to 605%. We have the equivalent of over 100% of national income in “excess wealth”.44
Second, we might somewhat underestimate the value of public assets at the beginning of theperiod 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 stillslightly 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 total 1970-2010 increase in , and42

In the Appendix, we have checked that the pattern of capital gains residuals we find is highly correlatedwith capital gains on listed equities and housing coming from available asset price indexes (see Figures A143 toA157). Note that the capital gains inferred from our wealth decomposition exercises are structurally lower thanthose coming from equity price indexes, for a good reason. A substantial fraction of national saving takes theform of corporate retained earnings (see Table 3) 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). Such capital gains, however, would
be spurious, in the sense that they correspond to the accumulation of earnings retained within corporations tofinance new investment (thereby leading to rising stock prices), rather than to a true relative price e↵ect.
43
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 7a-7b 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).
44
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 certainly cannot completely be ruled out. One would need, however, large and systematic
errors to account for the amount of excess wealth we find.

23

saving for about 60%, with a lot of heterogeneity across countries.45
How can we explain the substantial capital gains we find? As we shall see below, housing
and stock market capital gains in the U.K. and France since the 1970s-1980s can be understoodas the outcome of a long run asset price recovery. Asset prices fell substantially during the
1910-1950 period, and have been rising regularly ever since 1950. There might, however, havebeen some overshooting in the recovery process, particularly in housing prices. Four of thecountries 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 it is tempting to conclude that part of the capital gains
we measure owe to abnormally high real estate prices in 2010.
To a large extent, the housing bubble explanation for the rise of wealth-income ratios iscomplementary to the real explanation. In countries like France and Italy, savings are sufficiently
large relative to growth to generate a significant increase in the wealth-income ratio. Given thevalues taken by s and g over the 1970-2010 period, and given the steady-state formula
the wealth-income ratios= s/g,

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(and/or do not want to diversify their portfolio internationally as much as they could) thenmaybe it is not too surprising if this generates high upward pressure on housing prices.
There is one interesting exception to the general pattern of positive capital gains: Germany.
Given the relatively large saving flows and low growth rates in 1970-2010, we should observe
more wealth in 2010 than 400% of national income. According to our estimate that includes
R&D expenditure in saving flows, “missing wealth” in Germany is of the order of 50-100% ofnational income (Figure 7a). German statisticians might over-estimate saving and investment
flows, or under-estimate the current stock of private 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 themarket value of corporations.46 Germans might also have less taste for expensive capital goods
45
46

See Appendix A.5.2 and Appendix Table A99.
Whether this is good or bad for productive efficiency is a complex issue which we do not address in this24

(particularly housing goods) 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 we have at our disposal, we are not able toput a precise number on each explanation.
Last, it is worth noting that when we compute a European average wealth accumulation
equation – by taking a weighted average of Germany, France, U.K. and Italy – then capitalgains and losses seem to partly wash out (Figure 7b). 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 di↵erent from those we find in Europe. So one possibility is that
substantial relative asset price movements happens permanently within relatively small nationalor regional economic units, but tend to correct themselves at more aggregate levels. German
asset prices might rise in the near future and fall in other European countries.

4.5

Domestic capital vs. foreign wealth

So far we analyzed the accumulation of wealth without paying attention to the composition of
wealth portfolios, and in particular irrespective of whether wealth is invested domestically or
abroad. National wealth, as we have seen, can be written as the sum of domestic capital and net
foreign wealth.47 The basic fact to have in mind is that net foreign wealth – whether positiveor negative – has been a relatively small part of national wealth in rich countries throughout
the 1970-2010 period (see Figure 6).
Despite this fact, external wealth has turned out to play an important role in the generalevolution of wealth-income ratios. First, 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 the equivalent of between 40% and 70% of national income in net foreign
assets. Although Japan’s and Germany’s net foreign positions are still substantially smaller
paper (at first sight, low equity values do not seem to prevent German firms from producing good products). In
this “stakeholder” view of the firm, the market value of corporations can be interpreted as the value for capitalowners, while the book value can be interpreted as the value for all stakeholders. Both views have their merits.
See Appendix for further discussion.
47
Remember that a country’s net foreign wealth is equal to its gross foreign assets (assets owned by residents
in the rest of the world) minus its gross foreign liabilities (domestic assets owned by rest-of-the-world residents).
Domestic capital is national wealth minus net foreign wealth, i.e. is equal to the market value of all domestic
capital assets located in the home country, whether they are owned by the personal, government, or corporate
sector, or by the rest of the world (see below for a decomposition between housing and other capital goods).

25

than the positions reached by the U.K. and France around 1900-1910, they are starting to be
substantial. And the German position is rising fast. As a result, in Japan and Germany, therise in net foreign assets represents more than a quarter of the total rise of the national wealthnational income ratio (Table 5). In most of the other countries in our database, by contrast, net
foreign positions are currently slightly negative – typically between -10% and -30% of national
income – and have been declining. For those countries, the rise in the domestic capital-output
ratio has been larger than the rise in the national wealth-income ratio. One caveat is thatthe official net foreign asset positions do not include the sizable assets held by a number ofrich country residents in tax havens. In all likelihood, including these assets would turn therich world’s total net foreign asset position from negative to positive. The improvement would
probably be particularly large for Europe (Zucman, 2013).
Second, there has been a huge rise in the gross foreign positions of countries since the 1970s.
A significant share of each country’s domestic capital is now owned by other countries. The
rise in cross-border positions is highly significant everywhere – it is spectacular in Europe, a
bit less so in the world’s largest economies, the U.S. and Japan.48 One implications is that
capital gains and losses on foreign portfolios can be large and volatile over time and acrosscountries. And indeed, we find that foreign portfolios have generated large capital gains in the
U.S. (but also the U.K. and Australia) and significant capital losses in some other countries(Japan, Germany, France). Strikingly, in Germany virtually all capital losses at the national
level can be attributed to foreign assets (Table 6). In the U.S., net capital gains on cross-border
portfolios represent one third of total capital gains at the national level, and the equivalent of
the total rise in the U.S. national wealth-national income ratio since 1970.49

4.6

Housing vs. other domestic capital goods

Last, we present decomposition results for housing versus other domestic capital assets.
48

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., gross foreign assets amount to about 120%of national income, and gross liabilities to about 100% of national (hence a negative position equal to about-20%). For detailed series, see Appendix figures A39-A42.
49
Our results on the net capital gains on U.S. external wealth 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 accumulationof 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.

26

The accumulation of housing wealth has played a large role in the total accumulation ofdomestic capital, but with significant variations between countries. In the U.K., France and
Italy, the rise in domestic capital-national income ratios (or domestic capital-output ratios) isalmost entirely due to the rise of housing (Table 7). In Japan, housing represents less than halfof the total rise of domestic capital – and an even smaller proportion of the total rise of national
wealth, given the large accumulation of net foreign assets.50
In most countries, other domestic capital goods have also contributed to the rise of national
wealth, in particular because their market value has tended to increase. Tobin’s Q ratios
between market and book value of corporations were much below 1 in the 1970s and are closer
to 1 (and at times above 1) in the 1990s-2000s.51 But there are again interesting cross-country
variations. Tobin’s Q is very low in Germany: is has remained well below 1 (typically around0.5), contrary to the U.K. and the U.S. One interpretation is the “stakeholder e↵ect” describedabove: shareholders of German companies do not have full control of company assets – they share
their voting rights with workers’ representatives and sometime regional governments – whichmight push Q below 1.52 Yet another possibility is that some of the variations in Q reflect data
limitations. Quite puzzlingly, indeed, in most countries Q appears to be structurally below 1,
although intangible capital is imperfectly accounted for, which in principle should push it above
1. Part of the explanation may be that the book-value of corporations – corporate assets asmeasured by statisticians using the perpetual inventory method – tends to be over-estimated innational accounts. This is another area in which existing statistics might need to be improved.

5

Wealth-income ratios in rich countries 1870-2010

It is impossible to properly understand the rise of wealth-income ratios in rich countries in the
recent decades without putting the 1970-2010 period into a longer historical perspective. As we50

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 byhotels 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 areasin which we believe national accounts could be improved.
51
See Appendix Figure A92. Note, however, that because of the general increase in corporate capital, bookvalue national wealth (expressed as a fraction of national income) has increased almost as much as market-value
national wealth (see Appendix figure A25).
52
In Germany, book-value national wealth is substantially above market-value national wealth (about 5 yearsof national income instead of 4 years). The opposite occurs in the U.K.

27

have seen, a significant part of the rise ofsince the 1970s is due to capital gains: about 40%

on average, with large di↵erences between countries. The key question is the following: is thisdue to a structural, long-run rise in the relative price of assets (caused for instance by uneventechnical progress), or is it a recovery e↵ect? Our conclusion is that it is mostly a recoverye↵ect. The capital gains observed during the 1970-2010 period largely seem to compensate thecapital losses observed during earlier parts of the 20th century.
We have reached this conclusion by analyzing 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 wealthnational income ratios appear to be returning to the high values observed in 1870-1910, namely
about 600%-700% (Figure 2 above). For the U.S., the U-shaped pattern is much less strong(Figure 4 above). In addition, European public wealth-national income ratios have followed aninverted U-curve over the past century.53 But the magnitude of the pattern for public wealthis 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 helda 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. (Figure 8).
Starting from 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 8 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 forGermany. But in all cases saving flows account for the bulk of wealth accumulation: capitalgains seem to wash out in the long run.54
Looking at each sub-period, we find in every European country a strong U-shaped relative
53

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 eveof World War 1.
54
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 multiplicativemodels.

28

capital price e↵ect. In the U.K., for example, we find a negative rate of real capital losses equalto -1.9% per year between 1910 and 1950, followed by real gains of +0.9% per year between 1950
and 1980 and 2.4% between 1980 and 2010 (Table 9). The pattern is similar for France. In thesetwo countries, there seems to have been a slight over-shooting in the recovery process, in thesense that the total cumulated relative asset price e↵ect over the 1910-2010 period appears tobe somewhat positive (+0.2% per year in the U.K., +0.3% in France). In Germany, by contrast,
the recovery is yet too 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 capitalgains/losses we estimate might also reflect measurement issues: 1870-2010 saving flows might besomewhat underestimated in the U.K. or 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 areroughly consistent with one another – a result we already find quite remarkable.
Table 10 decomposes the huge decline in 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 . Low national saving during this period accounts for 46% of the fall inand negative valuation e↵ects (including losses on foreign portfolios) for the remaining 50%. In
France and Germany, cumulated physical war destructions account for about one quarter of thefall in . 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).55
The U.S. case is again fairly di↵erent from that of Europe. The fall ofduring the 1910-1950

period was more modest, and so was the recovery since 1950. Regarding capital gains, we findin every sub-period a small but positive relative price e↵ect. The capital gain e↵ect becomesbigger 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.
55

U.K. net public wealth then turned positive during the 1950s-1960s. See Appendix figure A16 and A22.

29

6

The changing nature of national wealth, 1700-2010

6.1

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. – thecountry with the most comprehensive historical balance sheets – the national wealth-national
income ratios appears to have been approximately stable during the 18th and 19th centuries– around 600-700%, or possibly somewhat higher (Figure 3 above). In France, where a large
number of historical national wealth estimates were also established during those two centuries,
the picture is similar (Figure 9).
We should make clear that the raw data sources available for the 18th -19th 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 definitely seems to be robust.
All available estimates, coming from many di↵erent authors using independent methodologies,
provide the same orders of magnitude. National wealth always seems to be between 6 and 8
years of national income (usually around 7 years) from 1700 to 1914 in two countries, with no
obvious trend in the long run.
Strikingly, the wealth-income ratio around 2010 is now relatively close to what it was in
the 18th centuries in both the U.K. and France, in spite of considerable changes in the natureof wealth. The general picture is relatively straightforward. The value of agricultural land –including land improvement of all sorts – was between 4 and 5 years of national income in the
U.K. and the France in the early 18th centuries, and is now less than 10% national income
in both countries. But land has been replaced by other forms of capital – housing and otherdomestic capital (offices, machines, patents, etc.) – to such an extent that the wealth-income
ratio appears to be almost as high today as three hundred years ago. In the long run, the declineof the share of agricultural land in national capital mirrors that of the share of agriculture innational income, from over two thirds in the 18th century to a few percent today – with a fasterand earlier historical decline in the U.K. The huge variations in the share of net foreign assets
in national wealth are also striking. Net foreign assets were virtually zero in the 18th century.
They reached very high levels in the late 19th and early 20th century – almost 2 years of national
income in the U.K. around 1910, over 1 year in France. Following the wars and the collapse of
the British and French colonial empires, they came back to virtually zero around 1950.

30

Why is it that wealth-income ratios were so high in the 18th -19th centuries, and why do they
seem to be approaching these levels again in the 21st century? A natural explanation lies in the= s/g steady-state formula. With slow growth, even moderate saving rates naturally lead tolarge wealth-income ratios. Growth was low until the 18th -19th centuries, and is likely to be low
again in the 21st century as population growth vanishes, thereby potentially generating highwealth-income ratios again.
This is probably an important part of the explanation. Unfortunately, data limitations
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 (un-accumulated wealth).
The main difficulty is that pre-1870 estimates of saving and investment flows appear to be too
fragile to be used in wealth accumulation decompositions. Also, with very low growth – annual
growth rates were typically much less than 1% until the 18th century – it is clear than any small
error in the net-of-depreciation saving rate s can make a huge di↵erence in terms of predicted
steady-state wealth-income ratio= s/g. In preindustrial societies where g ⇡ 0.5

1%,

whether the net saving rate is s = 5% or s = 8% is going to matter a lot. Historical estimatessuggest that there was substantial investment going on in traditional societies, including in therural sector. Annual spendings on land improvement (drainage, irrigation, a↵orestation etc.)
alone could be as large as 3-4% of national income. This suggests that a large fraction of total
agricultural land value in 18th century U.K. and France actually derived from past investment.
In all likelihood, the “pure land value” (i.e., the value of the pure natural resource broughtby land, before any investment or improvement, as it was discovered thousands of years ago,at prehistoric times) was much less than 4 years of national income. Some estimates made in
the 18th century tend to suggest that it was around 1 year of national income.56 Saving andinvestment series are unfortunately not sufficiently reliable to definitively address the question.
The residual “pure land” value could be less than 0.5 year, or up to 2 years of national income.

6.2

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
56

See in particular the famous estimates by Thomas Paine (1795), who suggested in front of the French
National Assembly to confiscate the “pure land” component of inheritance, which he estimated to be about 1
year of national income. On saving and investment series covering the 18th -19th centuries, particularly for the
U.K. and France, see data Appendix.

31

together historical balance sheets starting around 1770 (Figure 10). The robust finding, which
we also obtain with Canada, is that the value of agricultural land in the late 18th and early
19th centuries is much less in the New World – 1 to 2 years of national income – than in Old
Europe – 3 to 4 years.57 Part of the explanation could well be lower accumulated investment
and land improvement relative to economic and population growth in the New World (i.e., alower cumulated s/g ratio). However, available evidence suggests that the relatively low New
World wealth-income ratios can also be explained by a “land abundance” e↵ect. Land was soabundant in the New word that its price per acre was low. The right model to think about
this e↵ect involves a production function with an elasticity of substitution lower than 1 between
land and labor – a necessary condition for the price e↵ect to dominate the volume e↵ect.
To see this, think of a two-good model of the form introduced in section 3.4 above. That is,
assume that the capital good solely consists of land and is in fixed supply: Vt = V . For the sakeof 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 input (land) V and labor input L into output Y .
Assume that F (V, L) is a CES function with elasticity , and that there is zero productivity
and population growth.
Consider two countries 0 and 1 with similar technology and preferences. Assume that country
1 (America) has more land relative to labor than country 0 (Old Europe): V1 /L1 > V0 /L0 . Then
one can easily see that country 1 will end up with lower land value (relative to income) thancountry 0 (i.e.,

1 <0 , withthe elasticity of substitution

1 = K1 /Y1 = q1 ·V1 /Y1 and

0 = K0 /Y0 = q0 ·V0 /Y0 )if and only if

is less than one. This result directly follows from the fact that thecapital share ↵ is smaller in country 1 than in country 0 (i.e., ↵1 = FV ·V1 /Y1 < ↵0 = FV ·V0 /Y0 )if and only if

is less than one. The capital share is lower in the land-abundant country. Under

standard assumptions on preferences and equilibrium rates of return, this also implies that land
value is lower in the land-abundant country:

1 <

57

0.

58

For the long run evolution of wealth composition in Germany and Canada, see Appendix figures A46 andA47. The German pattern is close to that of the U.K. and France (except that the net foreign asset position ofGermany around 1900-1910 is less strongly positive than in the two colonial powers). The Canadian pattern isclose to that of the U.S. (except that net foreign asset position is strongly negative throughout the 19th century
and much of the 20th century).
58
With a dynastic utility model, the rate of return is set by the rate of time preference (r = ✓), so that
1 s s
b , then the wealth-income
1 = ↵1 /r < 0 = ↵0 /r. With a bequest-in-the-utility-function model U (c, b) = c
ratio is set by = s/(1 s) (see section 3.4 above), so that the di↵erence in capital share entirely translates into adi↵erence in rates of return: r1 = ↵1 / < r0 = ↵0 / . However to the extent that the interest elasticity of saving

32

Intuitively, an elasticity of substitution< 1 means that there is not much that one can dowith 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 e↵ect dominates the volumee↵ect. 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. At the opposite extreme, in a hightech economy where there are lots of alternative uses and forms for capital (a robot economy),
it is natural to expect higher elasticities of substitution, either closer to 1 (Cobb-Douglas) oreven larger than one (as we shall see below).
To summarize: part of the initial di↵erence inbetween Europe and America in the 18th -19th centuries seems to be due to a relative price e↵ect (due to land abundance) rather than toa pure saving e↵ect (via the= s/g formula). Both logic actually tend to reinforce each other:

the lower land prices and higher wage rates attract labor to the New World, implying very large
population growth rates and relatively low steady-state= s/g ratios.59

The lower land values prevailing in America during the 1770-1860 period were to someextent 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
be rich and control a large share of national income by owning the labor force. In the extreme
case where a tiny elite owns the entire labor force, the total value of the slave stock can inprinciple be very large, say as large as 20 years of national income (assuming the labor shareis 100% of output and the rate of return is equal to 5%).60 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 haves = s(r) is positive, this also implies 1 < 0 . A similar intuition applies to the case with U (c, b) = c1 s bs
(assuming positive population or productivity growth so as to obtain a well-defined steady-state = s/g).
59
There is a large historical literature on the factor flows that characterized the 19th 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 di↵erences in land value (rural, urban and suburban) still matter today. However
they go together with di↵erent tastes over housing in city centers versus suburban areas, so that it is difficult
to disentangle the various e↵ects. The fact that the bulk of 1870-2010 wealth accumulation is well explained byvolume e↵ects – both in Europe and in the U.S. – suggests that today’s di↵erences in pure land values are lesscentral than they used to be.
60
With a one-good model and a Cobb-Douglas production function F (K, L) = K ↵ L1 ↵ , the market value Hof the human capital stock (i.e., the value of the labor force from the viewpoint of a potential slave owner) isalways equal to (1 ↵)/↵ times the non-human capital stock. If ↵ = 1/3, then H = 2 . This is assumingthat the slave owner equates returns across all human and non-human assets. With a CES production function
1
1
F (K, L) = (a · K+ (1 a) · L) 1 , we have H = a1 · 1/.

33

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 thevalue of slaves and the value of land, we obtain wealth-income ratios in the U.S. South which
are relatively close to those of the Old World. Slaves approximately compensate the lower land
values (Figures 11 and 12).
Needless to say, this peculiar form of wealth has little to do with “national” wealth and isbetter analyzed in terms of appropriation and power relationship than in terms of saving andaccumulation. We view these “augmented” national balance sheets as a way to illustrate theambiguous relationship of the New world with wealth and inequality. To some extent, America
is the land of equal opportunity, the place where wealth accumulated in the past does not mattertoo much. But at the same time, America is also the place where a new form of wealth and classstructure – arguably more extreme and violent than the class structure prevailing in Europe –flourished, whereby part of the population owned another part.61

7

Capital-output ratios vs. capital shares

So far we have mostly focused on the evolution of wealth-income and capital-output ratios.
We now compare the long-run evolution of capital-output ratios and capital shares in order tobriefly discuss the changing nature of technology and the pros and cons of the Cobb-Douglas
approximation in the very long run.
The first basic fact is that capital shares did rise in rich countries during the 1970-2010
period, from about 15%-25% in the 1970s to 25%-35% in the 2000s-2010s, with large variations
over time and across countries (Figure 13). However they did not rise as much as national
wealth-national income and domestic capital-output ratios, so that the average of return towealth – which can be computed as rt = ↵t / t – declined somewhat (Figure 14).62 Of course,
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
61

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.
62
The results 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 13 are net of depreciation.

34

with imperfect competition and an increase in the bargaining power of capital (e.g., due toglobalization and increasing capital mobility). One can also think of a production function withthree factors – capital, high skill labor and low skill labor – where capital is more strongly
complementary with skilled than with unskilled labor. With a rise in skills, and possibly withskill-biased technical change, it can easily generate a rising capital share.
Yet another – and more parsimonious – way to obtain the same result is a standard twofactor, CES production function F (K, L) with an elasticity of substitution> 1.63 Importantly,

the elasticity does not need to be hugely superior to one in order to account for the observed
trends. With an elasticity

around 1.2-1.6, a doubling of capital-output ratio

can lead to alarge rise in the capital share ↵. With large changes in , one can obtain substantial movementsin the capital share with a production function that is only moderately more flexible than thestandard Cobb-Douglas function. For instance, with

= 1.5, the capital share rises from↵ = 28% to ↵ = 36% if the wealth-income ratio jumps from= 2.5 to= 5, which is roughly

what has happened in rich countries since the 1970s. The capital share would reach ↵ = 42%
in case further capital accumulation takes place and the wealth-income ratio attains
case the production function becomes even more flexible over time (say,= 8. In= 1.8), the capitalshare would then be as large as ↵ = 53%.64
We do not claim that this scenario will necessarily happen. Our point is simply that it
cannot be excluded. Constant capital-output ratios and capital shares are more of a belief thana well-grounded fact. Capital-output ratios have no strong reason to stay constant: s and g vary
for all sorts of reasons over time and across countries, so it is natural to expect
63= s/g to vary

One can of course combine the various possible explanations. Karabarbounis and Neiman (2013) for instanceuse a two-goods model in which there is a decline in the relative price of investment. As a result, firms shift awayfrom labor toward capital, and with an elasticity of substitution larger than 1 the capital share ↵ increases.
As the two-goods model we apply in section 6.2. to 19th century U.S. and Europe illustrates, when the relative
price of investment is lower (e.g., lower land values) and> 1, the wealth-income ratio has to be higher.
Thus, the explanation for the rise in ↵ put forward by Karabarbounis and Neiman (2013) is consistent with ourfindings of rising . The di↵erence is that we do not need a two-goods model to account for the rise in ↵: inany one-good model, when g decreases (while s remains the same so that increases) and > 1, ↵ has to rise.
In the real world, both forces (lower g and declining relative price of some capital goods) probably play a rolein the dynamics of ↵, 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 e↵ect over 1970-2010(see section 4). This could be due to a positive price e↵ect for land, foreign, and R&D assets, which are notincluded in standard measures of the relative price of capital.
1
164
In a perfectly competitive model with Y = F (K, L) = (a · K+ (1 a) · L) 1 , the rate of return is
1
1/
given by r = FK = a ·(with = K/Y ), and the capital share is given by ↵ = r · = a ·. Witha = 0.21 and = 1.5, ↵ goes from 28% to 36% and 42% as rises from 2.5 to 5 and 8. With = 1.8, ↵ rises to
53% if = 8.

35

widely. Relatively small departures from standard Cobb-Douglas assumptions then imply thatthe capital share ↵ = r ·can also vary substantially. In our view, it is natural to imagine thatwas possibly much less than 1 in the 18th -19th centuries and became significantly larger than

1 in the 20th -21st centuries. One expects a higher elasticity of substitution in more diversified
economies where capital can take many forms.65
Taking a very long run perspective on the evolution of factor shares, there seems to beevidence – both in the U.K. and France – that the capital share was somewhat larger in the
18th -19th centuries (say, around 40%) than it is in the early 21st century (about 30%), despite
the recent rise. Will capital shares return to their 18th -19th century levels? The capital-output
ratio

is still somewhat lower today than what it used to be in the distant past. So one

possibility is that the capital share ↵ will slowly return to about 40% as

keeps increasingin the coming decades – consistent with an elasticity of substitution larger than 1. However,it could also be that the labor exponent in the production function has declined structurally
since the 18th -19th centuries, because of the rise of human capital. Over time, human inputs
may have become relatively more important than non-human 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 “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 capitalshares ↵ than wealth-income ratios . The measurement of ↵ – and therefore of the averagerate of return r = ↵/ – is complicated by self-employment and tax optimization behavior 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 formalintermediation services (provided by banks and real estate agents), but do not deduct the timespent by capital owners to manage their portfolios, to spot the right investment opportunities,
and so on. Such costs are difficult to measure, and might well vary over time. In particular,
they might be larger in fast growing economies rather than in the stagnant, rural economies
65

The fact that the capital share ↵ was historically low in the mid-20th century (when was also low) can
also be viewed as evidence for > 1. Indeed, ↵ and move in the same direction if > 1, and in opposite
directions if < 1.

36

of the 18th century. For this reason, we may tend to over-estimate average rates of returnto capital when we compute them using national accounts capital income flow series (via ther = ↵/ formula), especially in high-growth economies. In this paper, we have tried to showthat an alternative way to address the issue of the relative importance of capital and labor in
the economy is to study the evolution ofrather than the evolution of ↵ – which so far has

been the focus of most of the attention. Ideally, both evolutions need to be analyzed together.

8

Directions for future research

Our analysis could be extended in various ways. First, it would be interesting to study wealthincome ratios at the world level. Throughout the 1870-2010 period, the top eight developed
economies analyzed in this paper represent between one half and three quarters of world output.
By making plausible assumptions about the evolution of other countries’ wealth-income ratios,
we have estimated the evolution of the world wealth-income ratio between 1870 and 2010.
Unsurprisingly, we find a spectacular U-shaped pattern (Figure 16).66 The exact levels areapproximate, but the general shape appears to be robust. Prior to World War 1, the world
wealth-income ratio was high and rising. Europe made about half of world output around 19001910 and had a high wealth-income ratio;

was rising in the U.S. and other parts of the world.

The world ratio then fell abruptly during the 1910-1950 period. According to our estimates,
it has been recovering since then and is currently approaching its 1910 nadir. Around 75% of
the 1990-2010 rise in the world wealth-income ratio (from about 400% to about 450%) is due
to Europe and Japan, while China only accounts for about 15%. From a global perspective,
therefore, capital accumulation in rich countries is probably a much more important determinantof the decline in the global return to capital than the large Chinese savings.67
We also report on Figure 16 one possible evolution of the wealth-income ratio in 2010-2100.
This projection is based upon specific and uncertain assumptions about the future. We take theprojected population growth rates from the U.N. central scenario (with near zero or negative66

See Appendix Table A8 for the detailed computations and assumptions behind Figure 16. Note that thenational wealth-national income ratio is less strongly U-shaped than the private wealth-national income ratio,
due to the high level of global public assets in the 1950s-1970s.
67
The increase in the net foreign asset position of China (from 0 to about 30% of national income) has beeneven smaller than the rise of China’s (from about 200% to 400% of national income). However, to the extent
that China’s foreign saving is mostly invested in the U.S. and that national capital markets are segmented, theChina-U.S. capital flows might account for a substantial fraction of the decline in the U.S. return to capital.

37

population growth pretty much everywhere after 2050, except in Africa). We assume rapid
convergence of emerging countries (at current pace) and stabilization of per capita growth rates
at relatively low levels in frontier economies (1.4%). Last, we assume that saving rates willstabilize around 10-12% of national income. If this happens, then the world wealth-income
ratio

will keep rising to about 600-700% by 2070-2100, i.e. approximately the same level as

Europe in the 18th-19th centuries. Needless to say, this is only one possible scenario. Much
will depend on the evolution of fertility behavior, life expectancy, innovation, the shape of the
production function ( > 1 or < 1), and the various psychological and economic motives forsaving.68 Our bottom line is simply that with low growth there are strong and powerful economic
forces pushing toward high wealth-income ratios in the global economy of the 21st century, justlike in the low growth societies of the past.
Next, it would be interesting to include individual-level wealth inequality in the analysis.
In this paper, we have emphasized the importance of aggregate wealth-income ratios and net
foreign wealth positions, i.e. inequality of wealth between countries. However there is evidence –for example from Forbes’ global billionaires list – that the evolution of wealth inequality between
individuals is also quite spectacular (possibly even more). Over the past 20-30 years, the very
top of the world wealth distribution seems to have been rising at a rate that is substantiallyabove that of average wealth – which is itself substantially above the growth rate of per capita
income and output, given the rise in global . One explanation could be that the slowdown ofgrowth can contribute to both a rise of the aggregate wealth-income ratio and to an increase of
wealth inequality. Indeed, in any dynamic wealth accumulation model with heterogeneity andrandom multiplicative shocks, the steady-state variance and inverted Pareto coefficient is anincreasing function of the rg di↵erential between the net-of-tax rate of return and the growthrate of the economy (see, e.g., Atkinson, Piketty and Saez, 2011).
Last, we plan to extend our analysis to investigate the evolution of the share of inherited
wealth in aggregate wealth. The return of high wealth-income ratios does not necessarily imply
the return of inheritance. In case wealth is distributed in a relatively egalitarian manner andmostly derives from lifecycle saving, then one can have high and rising68

with no corresponding

Private saving rates around s =10-12% are in line with what we observe in rich countries – particularly
Europe and Japan – in recent decades, so it makes sense to use such values in our benchmark scenario. However
if we include government dissaving then national saving rates in rich countries are substantially lower than 1012% and are on a declining trend, see Appendix Figures A96 to A103. It is also possible that saving rates will
eventually react more strongly than expected to a decline in rates of return.

38

rise in inheritance. To see this, observe that the annual flow of inheritance, expressed as aproportion of national income, which we note byt , can be decomposed as the product of threeterms: byt = µt ·mt · t (wheret is the aggregate-wealth income ratio, mt is the annual mortality

rate, and µt is the ratio between average wealth at death and the average wealth of the living).
With pure lifecycle wealth, µt = 0, so that byt = 0, irrespective of how large

t might be.

In the case of France, the long-run U-shaped pattern for the inheritance flow byt actuallyturns out to be even more spectacular than the U-shaped pattern observed fort , due to the factthat µt has also followed a marked U-curve. The relative wealth of the elderly was historically
low in the postwar period, so that there was not much to inherit in the 1950s-1960s (Piketty,2011). However this certainly does not imply that the same evolution applies everywhere.
As we have seen, there are large variations in the quantity of wealth that di↵erent countries
accumulate, so it is natural to expect large di↵erences in the importance of inherited wealth.
The historical series available so far regarding the inheritance flow are too scarce to reachfirm conclusions on this important issue. Existing estimates suggest that the French U-shaped
pattern also applies to Germany (Schinke, 2012), and to a lesser extent to the U.K. (Atkinson,2012) and the U.S. (see Piketty and Zucman, 2013, for a survey). Cross-country variations
could be due to di↵erences in pension systems and the share of private wealth that is annuitizedand therefore non transmissible. From a theoretical perspective, however, it is unclear why
there should be much crowding out between lifecycle wealth and transmissible wealth in an
open economy: any extra pension wealth should be invested abroad. It could be that there aredi↵erences in tastes for wealth transmission across countries. Wealthy individuals in the U.K.
and in the U.S. may have less taste for bequest than in France and Germany.69 But there arealso important data problems that could partly explain why the rise of the inheritance flow
appears to be more limited in some countries than in others. Wealth surveys tend to vastly
underestimate inheritance receipts, not to mention inter vivos gifts, which play a large rolein the recent French and German evolution (and which can only be properly measured withadministrative data). All of this raises important challenges for future research.

69

One can interpret the lower = s/g in the U.S. in terms of lower bequest taste: with higher population
growth and the same bequest taste (per children) as in Europe, the U.S. should save more. However a large partof U.S. population growth historically comes from migration, so this interpretation cannot be fully accurate.

39

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42

Figure 1: Private wealth / national income ratios 1970-2010
800%
700%
600%

USA

Japan

Germany

FranceUK

Italy

CanadaAustralia

500%
400%
300%
200%
100%
1970

1975

1980

1985

1990

1995

2000

2005

2010

Authors' computations using country national accounts. Private wealth = non-financial assets + financial assets - financial liabilities(household & non-profit sectors)

Figure 2: Private wealth / national income ratios in Europe
1870-2010
800%
Germany

700%

France
600%

UK

500%
400%
300%
200%
100%
1870

1890

1910

1930

1950

1970

1990

2010

Authors' computations using country national accounts. Private wealth = non-financial assets + financial assets - financial liabilities(household & non-profit sectors). Data are decennial averages (1910-1913 averages for 1910)

Figure 3: The changing nature of national wealth: UK
1700-2010
800%
Net foreign assets

700%% national income

600%

Other domestic capital
Housing
Agricultural land

500%
400%
300%
200%
100%
0%
1700 1750 1810 1850 1880 1910 1920 1950 1970 1990 2010
National wealth = agricultural land + housing + other domestic capital goods + net foreign assets

Figure 4: Private wealth / national income ratios 1870-2010:
Europe vs. USA
800%
700%
USA

600%

Europe

500%
400%
300%
200%
100%
1870

1890

1910

1930

1950

1970

1990

2010

Authors' computations using country national accounts. Private wealth = non-financial assets + financial assets - financial liabilities(household & non-profit sectors). Data are decennial averages (1910-1913 averages for Europe)

800%
700%

% of national income

600%

Figure 5: Private vs. governement wealth 1970-2010
USA

Japan

Germany

FranceUK

Italy

CanadaAustralia

500%
400%
300%
Privatewealth200%

Government
wealth

100%
0%
-100%
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 6: National vs. foreign wealth, 1970-2010% of national income

900%

USA

Japan

800%

Germany

France

700%

UK

Italy

CanadaAustralia

600%
500%
400%
300%
200%

Net foreign
wealthNational
wealth

100%
0%
-100%
1970

1975

1980

1985

1990

1995

2000

2005

Authors' computations using country national accounts. Net foreign wealth = net foreign assets owned by country residents in rest of
the world (all sectors)

2010

Observed national wealth / income ratio 2010

Figure 7a: Observed vs. predicted national wealth / national
income ratios (2010)
700%
650%
600%
550%

Italy

Japan

FranceAustralia
U.K.

500%
450%

U.S.

400%

CanadaGermany

350%
300%
300%

350%

400%

450%

500%

550%

600%

650%

Predicted national wealth / income ratio 2010 (on the basis of 1970 initial wealth and1970-2010 cumulated saving flows) (additive decomposition, incl. R&D)

700%

Observed national wealth / income ratio 2010

Figure 7b: Observed vs. predicted national wealth / national
income ratios (2010)
700%
650%
Japan

600%
550%

Europe500%
450%

North America

400%
350%
300%
300%

350%

400%

450%

500%

550%

600%

650%

Predicted national wealth / income ratio 2010 (on the basis of 1970 initial wealth and1970-2010 cumulated saving flows) (additive decomposition, incl. R&D)

700%

800%

Figure 8: National and foreign wealth 1870-2010: Europe vs.
USA

700%
USA

% of national income

600%

Europe

500%
400%
300%

National
wealthNet foreign
wealth

200%
100%
0%
-100%
1870

1890

1910

1930

1950

1970

1990

2010

Figure 9: The changing nature of national wealth: France
1700-2010
800%
Net foreign assets
700%% national income

600%

Other domestic capital
Housing
Agricultural land

500%
400%
300%
200%
100%
0%
1700 1750 1780 1810 1850 1880 1910 1920 1950 1970 1990 2000 2010
National wealth = agricultural land + housing + other domestic capital goods + net foreign assets

700%

Figure 10: The changing nature of national wealth: US
1770-2010
Net foreign assets
Other domestic capital600%% national income

Housing

500%

Agricultural land

400%
300%
200%
100%
0%
1770

1810

1850

1880

1910

1920

1930

1950

1970

National wealth = agricultural land + housing + other domestic capital goods + net foreign assets

1990

2010

700%

Figure 11: The changing nature of wealth: US 1770-2010 (incl.
slaves)Net foreign assets

Other domestic capital

600%

Housing% national income

Slaves500%

Agricultural land

400%
300%
200%
100%
0%
1770

1810

1850

1880

1910

1920

1930

1950

1970

National wealth = agricultural land + housing + other domestic capital goods + net foreign assets

1990

2010

800%

Figure 12: National wealth in 1770-1810: Old vs. New world
Other domestic capital

700%

Housing% national income

600%

Slaves500%

Agricultural Land
400%
300%
200%
100%
0%
UK

FranceUS South

US North40%

Figure 13: Capital shares in factor-price national income
1975-2010

35%
30%
25%
20%
15%
10%
1975

1980

1985

USA

Japan

Germany

FranceUK

CanadaAustralia

Italy

1990

1995

2000

2005

2010

Figure 14: Average return on private wealth 1975-2010
12%
10%
8%
6%
4%
2%
0%
1975

1980

USA

Japan

Germany

FranceUK

CanadaAustralia

Italy

1985

1990

1995

2000

2005

2010

100%
90%

Figure 15: Factor shares in factor-price national income 1820-2010:
UK and France

UK

France

80%
70%
60%

Labor
share

50%

Capital
share

40%
30%
20%
10%
0%
1820

1840

1860

1880

1900

1920

1940

1960

1980

2000

Figure 16: World private wealth / national income ratio
1870-2100
800%
700%
600%
500%
400%
300%
200%
100%
1870 1890 1910 1930 1950 1970 1990 2010 2030 2050 2070 2090
Authors' computations and simulations using country national accounts and UN growth projections. Private wealth = non-financial
assets + financial assets - financial liabilities (household & non-profit sectors)

Table 1: A new macro database on income and wealth

Total period
covered indatabase

Annual series

Decennial
estimates

U.S.

1770-2010

1869-2010

1770-2010Japan

1960-2010

1960-2010

Germany

1870-2010

1870-2010

France1700-2010

1896-2010

1700-2010

U.K.

1700-2010

1855-2010

1700-2010

Italy

1965-2010

1965-2010

Canada1970-2010

1970-2010

Australia

1970-2010

1970-2010

Income and wealth database constructed by the authors using country national
accounts (official series and balance sheets and non-official historical estimates). See
country appendices for sources, methods and detailed series.

Table 2: Growth rate vs private saving rate in rich countries, 1970-2010

Real growth rate
Real growth rate ofPopulation growthof national
per capita nationalrateincomeincomeNet private
saving rate
(personal +corporate)(% national income)

U.S.

2.8%

1.0%

1.8%

7.7%

Japan

2.5%

0.5%

2.0%

14.6%

Germany

2.0%

0.2%

1.8%

12.2%

France

2.2%

0.6%

1.6%

11.1%

U.K.

2.2%

0.3%

1.9%

7.3%

Italy

1.9%

0.3%

1.6%

15.0%

Canada

2.8%

1.1%

1.7%

12.1%

Australia

3.2%

1.4%

1.7%

9.9%

Authors' computations using country national accounts. Growth rates are geometric averages and for income use chainweighted GDP deflators. For alternative deflators, see Appendix Table A3 and Country Tables US.3, JP.3, etc. 1970-2010
average saving rates are obtained by weighting yearly saving rates by real national income.

Table 3: Saving rates 1970-2010: national vs. private

Average saving
rates 1970-2010(% national
income)Net national
Net privateincl. personalsaving (private + savings (personalsavings
government)+ corporate)incl. corporatesavings(retained
earnings)

4.6%

3.1%

60%

40%

6.8%

7.8%

47%

53%

9.4%

2.9%

76%

24%

9.0%

2.1%

81%

19%

2.8%

4.6%

38%

62%

14.6%

0.4%

97%

3%

12.1%

7.2%

4.9%

60%

40%

9.9%

5.9%

3.9%

60%

40%

U.S.

5.2%

7.7%

Japan

14.6%

14.6%

Germany

10.2%

12.2%

France

9.2%

11.1%

U.K.

5.3%

7.3%

Italy

8.5%

15.0%

Canada10.1%

Australia

8.9%

Net government
saving
-2.4%
0.0%
-2.1%
-1.9%
-2.0%
-6.5%
-2.0%
-0.9%

Authors' computations using country national accounts. 1970-2010 averages are obtained by weighthing yearly saving rates by real
national income.

Table 4: Accumulation of national wealth in rich countries, 1970-2010
Decomposition of 1970-2010 wealth growth rate
National wealth-national
income ratios

Real growth
SavingsCapital-gainsrate of national induced wealth induced wealthwealth
growth rate
growth rate

β (1970)β (2010)gw

gws = s/β
2.1%

q
0.8%

U.S.

404%

431%

3.0%

72%

28%

Japan

359%

616%

3.9%

3.1%

0.8%

78%

22%

Germany

313%

416%

2.7%

3.1%

-0.4%

114%

-14%

France

351%

605%

3.6%

2.7%

0.9%

75%

25%

U.K.

314%

523%

3.5%

1.5%

2.0%

42%

58%

Italy

259%

609%

4.1%

2.6%

1.5%

63%

37%

Canada

284%

412%

3.8%

3.4%

0.4%

89%

11%

Australia

391%

584%

4.2%

2.5%

1.6%

61%

39%

Table 5: Accumulation of national wealth in rich countries, 1970-2010: domestic
capital vs foreign wealth

U.S.
Japan
Germany
FranceU.K.
Italy
CanadaAustralia

1970 national wealth /national income ratio2010 national wealth /national income ratioincl. Domestic
capitalincl. Domestic
capitalincl. Foreign
wealth

404%
399%

456%

359%
313%

189%

-31%

422%

391%

392%

655%

-42%

128%
-10%

97%

584%
-20%

-26%

350%

412%
-41%

-24%

163%
-20%

640%

284%

410%

278%

609%
12%

31%

254%
-13%

548%

259%

325%

71%

527%
6%

64%

102%
39%

618%

365%

247%

192%

605%
11%

-30%

256%
67%

377%

351%

359%

57%

416%
8%

340%

-25%

548%

incl. Foreign
wealth

27%

616%
3%

305%

incl. Domestic
capital

431%
4%

356%

incl. Foreign
wealth1970-2010 rise innational wealth /national income ratio

31%

194%
-70%

244%

-50%

Table 6: National wealth accumulation in rich countries: domestic
vs. foreign capital gains
1970-2010 capitalgains on national
wealth (% of 2010
national income)

Decomposition of 1970-2010 capitalgains
Domestic wealthForeign wealth

U.S.

105%

72%

33%

Japan

27%

45%

-18%

Germany

-25%

-3%

-22%

France

164%

179%

-15%

U.K.

235%

217%

18%

Italy

213%

240%

-27%

Canada

63%

55%

7%

Australia

220%

178%

41%

Authors' computations using country national accounts. Other volume changes were put insaving flows and thus excluded from capital gains.

Table 7: Domestic capital accumulation in rich countries, 1970-2010: housing vsother domestic capital
1970 domestic capital / 2010 domestic capital /national income ratio
national income ratioincl. Housing

U.S.
Japan
Germany
FranceU.K.
Italy
CanadaAustralia

incl. Other
domestic
capitalincl. Housing

399%
142%

182%

356%
305%

202%

254%

208%

410%

279%

364%

113%

97%
213%

101%

655%
239%

-13%

392%

422%
217%

11%

189%
248%

386%

325%

172%

267%

640%
141%

-41%

278%
247%

300%

247%

108%

112%

548%
261%

103%

71%
136%

371%

359%

107%

89%

618%
236%

17%

192%
328%

241%

340%

98%

41%

377%
177%

104%

274%

220%

incl. Other
domestic
capital

57%

548%
225%

129%

incl. Housing

456%
257%

131%

incl. Other
domestic
capital1970-2010 rise indomestic capital /national income ratio

-4%

244%
291%

193%

52%

Table 8: Accumulation of national wealth in rich countries, 1870-2010Market-value national
wealth-national income
ratiosReal growth Decomposition of 1870-2010 wealth growth rate
rate of
SavingsCapital-gainsReal growthnational
induced wealth induced wealthrateofwealthincomegrowth rate
growth rate

β (1870)β (2010)

g

gw

U.S.

413%

431%

3.4%

3.4%

Germany

745%

416%

2.3%

2.0%

France

689%

605%

2.1%

2.0%

U.K.

656%

523%

1.9%

1.8%

gws = s/β
2.6%

q
0.8%

76%

24%

2.6%

-0.6%

128%

-28%

1.8%

0.2%

91%

9%

1.6%

0.2%

89%

11%

The real growth rate of national wealth has been 3.4% per year in the U.S. between 1870 and 2010. This can be decomposed into a 2.6%
savings-induced growth rate and a 0.8% residual term (capital gains and/or measurement errors).
Authors' computations using country national accounts. War destructions & other volume changes were included in savings-induced
wealth growth rate. For full decomposition, see Appendix Country Tables US.4c, DE.4c, etc.

Table 9: Accumulation of national wealth: US, UK, Germany, France, 1870-2010Market-value national
wealth-national income
ratiosβtβt+nReal growthrate ofnational
wealthgw

Savings-induced Capital-gainsinduced
wealth growth
wealthrate (incl. war
growth rate
destructions)
gws = s/βqPanel A: United States
1870-2010

413%

431%

1870-1910

413%

469%

1910-2010

469%

431%

1910-1950

469%

380%

1950-1980

380%

434%

1980-2010

434%

431%

3.4%
4.3%
3.1%
2.7%
4.0%
2.7%

2.6%

0.8%

76%

24%

2.9%

1.4%

68%

32%

2.5%

0.6%

80%

20%

2.2%

0.5%

82%

18%

3.7%

0.2%

94%

6%

1.6%

1.1%

58%

42%

Panel B: United Kingdom
1870-2010

656%

527%

1870-1910

656%

694%

1910-2010

719%

527%

1910-1950

719%

241%

1950-1980

241%

416%

1980-2010

416%

527%

1.8%
2.1%
1.6%
-1.3%
4.0%
3.4%

1.5%

0.3%

83%

17%

1.7%

0.4%

79%

21%

1.4%

0.2%

86%

14%

0.6%

-1.9%

-43%

143%

3.0%

0.9%

76%

24%

1.0%

2.4%

28%

72%

2.6%

-0.6%

128%

-28%

2.3%

-0.1%

107%

-7%

2.8%

-0.8%

137%

-37%

Panel C: Germany
1870-2010

745%

416%

1870-1910

745%

637%

1910-2010

637%

416%

2.0%
2.1%
2.0%

1910-1950

637%

223%

1950-1980

223%

330%

1980-2010

330%

416%

-1.4%
6.3%
2.5%

0.0%

-1.5%

-3%

103%

6.8%

-0.5%

108%

-8%

2.5%

0.0%

101%

-1%

1.8%

0.2%

91%

9%

1.4%

0.0%

103%

-3%

2.0%

0.3%

89%

11%

-0.1%

-1.1%

8%

92%

4.7%

1.2%

80%

20%

2.2%

1.2%

65%

35%

Panel D: France
1870-2010

689%

605%

1870-1910

689%

747%

1910-2010

747%

605%

1910-1950

747%

261%

1950-1980

261%

383%

1980-2010

383%

605%

2.0%
1.3%
2.2%
-1.2%
5.9%
3.4%

The real growth rate of national wealth has been 3.1% per year in the U.S. between 1910 and 2010. This can be
decomposed into a 2.5% savings-induced growth rate and a 0.6% residual term (capital gains and/or
measurement errors).
Authors' computations using country national accounts. War destructions & other volume changes were included insavings-induced wealth growth rate. For full decomposition, see Appendix Country Tables US.4c, DE.4c, etc.

Table 10: Accumulation of national wealth in rich countries, 1910-1950

U.S.

Decomposition of 1950 national wealth-national income
National wealthratio
national income ratios
Cumulated
Initial wealth Cumulated
Capital gains
war
effectnew savings
or losses
destructionsβ (1910) β (1950)
132%
193%
0%
55%
469%
380%

Germany

637%

223%

France

747%

261%

U.K.

719%

208%

400%
421%
409%

109%

-120%

-165%

31%

29%

40%

144%

-132%

-172%

38%

27%

35%

75%

-19%

-256%

46%

4%

50%

Germany's national wealth-income ratio fell from 637% to 223% between 1910 and 1950. 31% of the fall can be attributed toinsufficient saving, 29% to war destructions, and 40% to real capital losses.