Capital in the 21st Century: a Short Intro to Thomas Piketty's new book
A short Intro
“Capital” in a nutshell:
Structure of the book
Findings of the book
Data and methodology
Income and Capital:
Income and Output
Growth: Illusions and Realities
The dynamics of Capital/Income Ratio:
The metamorphosis of Capital
The Capital/Income Ratio of the Long Run
The Capital – Labor Split in the Twenty-First Century
• Professor of Macro-Economics at the Paris
School of Economics.
• Director of EHESS.
• Author of numerous articles (published in
journals such as the Quarterly Journal of
Economics, the Journal of Political
Economy, the American Economic Review
and the Review of Economic Studies) and of
a dozen books.
• Major historical and theoretical works on
the interplay between economic
development and the distribution of
income and wealth.
• Le capital au XXIème siècle (T. Piketty, Le seuil, 2013);
• Capital is Back: Wealth-Income Ratios in Rich Countries
1700-2010 (T. Piketty, G. Zucman, 2013);
• A Theory of Optimal Inheritance Taxation (T. Piketty, E.
Saez, Econometrica, 2013);
• World Top Incomes Database (F. Alvaredo, T. Atkinson, T.
Piketty, E.Saez, 2011-2013).
What are the grand dynamics that drive the accumulation and
distribution of capital?
How is the concentration of wealth in the long run?
Given such concentration, how is the long-term evolution of inequality?
Which are the main drivers of inequality?
What can prevent inequality?
What should we do to reduce inequality?
Relevant questions in Piketty’s literature:
Piketty tried to answer all these questions in:
Structure of the book:
The book has three main parts:
A history of inequality and wealth (Parts I &II);
A forecast of how things will evolve over the next century
Policy reccomendations, such as global tax on wealth (Part
Findings of the book:
• The history of the distribution of wealth has always been deeply political, and it
cannot be reduced to purely economic mechanisms;
• The dynamics of wealth distribution reveal powerful mechanisms pushing
alternately toward convergence and divergence;
• No matter how powerful a convergent force may be, it can be overwhelmed by
stronger forces pushing in the opposite direction, toward greater inequality;
• The fundamental force for divergence is represented by: r > g
Fundamental Force: r > g
“If the rate of return on capital remains
significantly above the growth rate for an
extended period of time (more likely when the
growth rate is low), then the risk of divergence in
the distribution of wealth is very high”.
• More precisely, when the rate of return on capital exceeds the growth rate of
economy, then the inherited wealth growth faster than output and income;
• People with inherited wealth need save only a portion of their income from
capital to see the capital growth more quickly than the economy as a whole;
• In such case, the concentration of wealth will attain extremely high levels
incompatible with meritocratic values and principles of social justice;
• Empirical evidence and historical data of XIX and XX centuries would show
such inequality pattern.
Growth of inequality as central issue!
Data and methodology:
1. Sources dealing with inequality and distribution of income:
World Top Income Database (WTID) as primary source of data;
High incomes estimated from tax data based on stated incomes;
National income and average income derived from national
Data series begin when an income tax is established (1910 – 1920).
2. Sources dealing with distribution of wealth and relation of wealth
Changes in inequality of wealth estimated from estate tax returns;
Data on wealth and inheritance;
Total stock of national wealth (lands, other real estate, ecc.) derived
from capital/income ratio: misure of wealth in terms of years of
national income required to amass it.
Reliance primarily on data of US, Japan, Germany, France, UK.
In this presentation we discuss Parts I and II of the book
We introduce the concept of national income, capital and capital/income ratio;
We discuss how the global distribution of income and wealth has evolved;
We examine the long-run evolution of the capital-income ratio;
We show the global division of income between labor and capital in 21 Century;
We examine global historical experiences of the evolution of the capital/income
ratio and the relative shares of capital and labor.
Income and Output
National income: sum of all income available to the residents of a given
country in a given year, regardless of the legal classification.
[GDP – Depreciation = (usually 90% of GDP)]
Net income from abroad
[Income received by the country from investments abroad]
National income can be decomposed as follows:
National income = capital income + labor income
Capital income: sum of all non-human assets that can be owned
and exchanged on some market (real properties, financial assets,
To Piketty the words “Capital income” and “Wealth” are perfectly
National Wealth = Private Wealth + Public Wealth
National Wealth can be broken down in:
National Wealth = Domestic Capital + Net Foreign Capital
Domestic Capital: value of the capital stock (buildings, firms, etc.)
located within the borders of a country;
Net Foreign Capital: difference between assets owned by the country’s
citizens in the rest of the world and assets of the country owned by
citizens of other countries.
Which rule ties together Income & Capital?
Income is a flow: quantity of goods produced and distributed in a given period.
Capital is a stock: total wealth owned at a given point. This stock comes from the
wealth accumulated in all prior years combined.
Then, we can measure the capital stock of a country (β) by dividing that stock by the
annual flow of income:
β = Capital/Income
[Ex.: β = 6 (or 600%) means that a country’s total capital stock is the equivalent of
six years of national income].
First Foundamental Law of Capitalism: α = r x β
r = rate of return on Capital;
This law links the Capital stock to the flow of Income from Capital;
[Ex.: if β = 600% and r = 5%, then α = r x β = 30% ]
In other words, if national wealth represents the equivalent of
six years of national income, and if the rate of return on capital
is 5 %, then capital’s share in national income is 30%.
Very important law: it expresses a simple relationship among
the 3 most important concepts of capitalist system and allow us
to analyze the importance of capital for an entire country.
How these abstract quantities can be measured?
Data on distribution of Global Production show that:
In Western Countries national income is roughly 30,000-35.000 € per capita;
Global inequality ranges from regions in which the per capita income is on order of
150-250 Euros per month to regions where it is as high as 2.500 – 3.000 Euros per
month. Global average is around 600-800 euro per month.
Global income distribution is more unequal than the output distribution:
countries with the highest per capita output are also more likely to own part of the
capital of other countries and therefore to receive a positive flow of income from
capital originating in countries with a lower level of per capita output.
Don’t forecast convergence of per capita income between rich and poor nations.
Growth: Illusions and Realities
Growth must be decomposed in two terms: population growth and per
capita output growth;
1) Population Growth:
Piketty implies that we are returning to very low level of growth, at least
insofar as the demographic component is concerned.
Demographic growth has important implications for the structure of
inequality: indeed, strong demographic growth tends to play an equalizing
role because it decreases the importance of inherited wealth;
A stagnant or decreasing population increases the influence of capital
accumulated in previous generations;
The same intuition can be applied to economic stagnation: with low growth, it’s
plausible that the rate of return on capital will be substantially higher than the
economic growth rate;
Furthermore when growth is zero, the various economic and social functions as
well as professional activities, are reproduced virtually without change from
generation to generation.
With these preliminaries what can we say about future growth?
Global Growth over the past three centuries can be pictured
as a bell curve with a very high peak.
Population growth and per capita output growth accelerated
over the course of the eighteenth and nineteenth centuries,
but now are returning to much lower levels.
According to Piketty’s data in a optimistic scenario, global
growth of per capita output would slightly exceed 2.5% per
year between 2012 and 2030 and again between 2030 and
2050, before falling below 1.5 initially and then declining to
around 1.2% in the final third of the century.
If we add the two curves (both of Population Growth and of Per
Capita Output Growth) we obtain a third curve as follow:
The growth rate of world output will drop below 3.5% in 2030-
2050 and then to roughly 1.5% during the second half of the XXIc.
The Metamorphoses of Capital
What is the evolution of capital stock as measured by the capital/income
How did the nature of the wealth change over time?
(France 1700 - 2010)
Capital/Income ratio in both countries followed similar trajectories.
National capitals fluctuated between six and seven years of national income up to
1914. Then plumbed during World Wars and began to climb afterwards (U-shaped
In the end, by 2010, the capital/income ratio had returned to its pre-World War I
What is changed then is the composition of national capital since 1700: once
mainly land, now became primarily industrial and financial assets.
[National capital = farmland + housing + other domestic capital + net foreign capital]
Piketty suggests that the structure of national capital has been transformed since
1700 while preserving the same value in terms of annual income.
(Germany 1700 - 2010)
All available sources indicate that the changes observed in Britain, France and
Germany are representative of the entire continent: although interesting
variations do exist, the overall pattern is the same.
This phenomenon affected all European Countries.
To better understand the patter: of national capital in Europe:
Capital in America: more stable than in Europe
In US capital mattered less then Europe: national capital was scarcely more
than 3 years of national income when US declared Independence. Why?
There was so much land that its market value was very low: the price effect
more than counterbalanced the volume effect.
Also other types of capital were less important: new arrivals – a large
fraction of US population, did not cross the Atlantic with their capitals; then
it took time to accumulate the equivalent of years of national income.
Net Foreign capital have also had limited importance in US. This is because US
never became a colonial power itself. They have been at times positive, at times
negative but always of relative limited importance. (less than 5%).
However, a key difference in US capital structure was the market of slaves. In
1800 slaves represented nearly 20% of population for a total market value of a
year and half of US national income.
If we add the values of slaves along with other component of wealth, we find
that the total American wealth has remained stable from the colonial era to the
present, at around four a half years of national income.
The Capital/Income Ratio over the Long Run
So far we have seen that the nature of capital was totally
transformed but the total value of capital stock, measured in
years of national income, did not change very much over a long
period of time.
However since 1950 we see in all countries a steady increase of
the capital/income ratio. Why?
What forces imply that capital in one society should be worth six
or seven years of national income?
Is there an equilibrium level for the capital/income ratio?
The Second Fundamental Law of Capitalism
A simple and transparent way to relate β (capital/income ratio), s (savings
rate) and g (growth rate):
β = s / g
[Ex. If a country saves 12% of national income every year, and the rate of growth of its national
income is 2% per year, then in the long run capital/income ratio will be 600%]
This simply means that a country that saves a lot and growth slowly will over
the long run accumulate an enormous stock of capital, which can in turn have
a significant effect on the social structure and distribution of wealth.
Then the return to high income/capital ratio in XXI c. can therefore be
explained as a return to a slow-growth regime.
Decreased growth in both its 2 components (demographic and
per capita output) is responsible for high capital accumulation.
According to Piketty’s data this law is able to give a good
account of the historical evolution of the capital/income ratio.
This law is the result if a dynamic process: it represents a state
of equilibrium toward which an economy will tend if the
savings rate s and the growth rate g.
To remember however that such law works only under certain
assumptions (ex. valid only in the long run, only valid for
accumulable capital, exc.).
Over forty years, these differences mount up to create
significant variation: if one combine variations in growth rates
with variations in savings rate, it is easy to explain why different
countries accumulate very different quantities of capital.
This mechanism that explains the capital accumulation is amplified by 2
1) The Privatization of Wealth in rich countries: the revival of private
wealth is partly due the ongoing privatization of national wealth. [Ex. In
Italy the decrease in public wealth represented between 1/5 and ¼ of the
increase in private wealth].
2) The “Catch up” of asset prices over the long term: one may see a general
tendency of Tobin Q (i.e. ratio of market value to the book value of
individual firms) to increase in rich countries since 1970. This is a
consequence of the historic rebound of asset prices.
Possible Predictions of Capital/Income ratio in XXI c.
The Capital Labor Split in the Twenty–First Century
From the analysis of the capital/income ratio to the division of national
income between labor and capital: the formula α = r x β allow us to move
transparently between the two.
[Ex. If capital stock is equal to six years of national income (β = 6), and if average return on
capital is 5% (r = 5%), then the share of income from capital α, in national income is 30%].
Yet, how to determine the rate of return r?
This average rates of return aggregates the returns of very different
types of assets and investments: the goal is in fact to measure the
average return on capital in a given society taken as a whole.
The principal conclusion of Piketty’s estimates then is that in both
France and Britain, from XVIII to XXI, the pure return on capital has
oscillated around a central value 4-5% a year, or more generally in an
interval from 3-6% a year.
However takes into account that such returns are pretax returns.
When all the taxes are taken into account, the average tax rate on
income from capital is currently around 30% in most of the rich
Furthermore, that pure return of around 3-4% is an average that hides
Finally that rates of return are real rates of return, not nominal. No
inflation rate is counted.
Piketty finds that capital’s share of income was 35-40% in both Britain
and France in the late XVIII and XIX century, before falling to 20-25% in
the middle of XX century and then rising again to 25-30% in the late of XX
This corresponds to an average rate of return on capital of around 5-6%
in XVIII and XIX centuries, rising to 7-8% in the mid-XX century and then
falling to 4-5% in late XX and XXI centuries.
How is the rate of return on capital determined in a particular society at a
particular point in time? Which social and economic forces are at work?
The rate of return on capital is primarily determined by 2 forces:
1) Technology: simply means what is capital used for;
2) The abundance of the capital stock: whatever the rules and institutions that
structure the capital-labor split may be, it is natural to expect that the marginal
productivity of capital decreases as the stock of capital increases.
Too much capital kills the return on capital!
How much the return on capital r decreases when the capital/income β increases?
2 cases are possible:
1) If r falls more than proportionally when the capital/income β increases, then
the share of capital income α = r x β decreases when β increases.
2) If r falls less than proportionally when β increases, then share of capital
income α = r x β increases when β increases.
Based on historical evolutions observed in Britain and France the second case
is more relevant over the long term: the capital share of income α, follows the
same U-shaped curve as the capital income ratio β.
Indeed, Piketty’s data indicate that capital’s share of income increased in
most rich countries between 1970 and 2010 to the extent that capital/income
To sum up let’s imagine the following scenario:
1) No structural growth, the productivity and population growth rate g is
2) Savings rate s is positive (capitalists insist to accumulate more and
more capital every year):
Then, the capital/income ratio β will increase indefinitely;
3) But if β is extremely large, capital’s share of income α = r x β, will
ultimately devour all of national income.
In stagnant societies, wealth accumulated in the past naturally takes on
What we learnt from Piketty’s work?
Similar patterns may be recognized in the evolution of Wealth and Capital
amongst rich countries;
We may link together Growth, Savings and Rate of Return on Capital by the
First and Second Law of Capitalism to understand how the dynamics of
capital/income ratio is affected by macroeconomic variations;
Piketty recognized the validity of his model by looking at an huge amount of
historical data available of rich countries.
The forecast is an increasing accumulation of capital by wealthy people in a
The result is greater inequality which required political intervention.