Here are some rather raw notes on my reading of Thomas Piketty's famous book Capital in the twenty-first century.

Part one - Income and capital

Chapter 1 - Income and output

• Domestic output equals GDP less depreciation; depreciation is significant, typically around 10% of GDP.
• National income is equal to domestic output plus net income from abroad, i.e. returns on capital owned inside the country but located elsewhere. Net income is near zero for most developed nations because other countries own assets located there.
• Global income must equal global output, by definition (unless Martians are involved!).
• Capital is defined by Piketty as any form of wealth that can be owned. Capital and wealth are used interchangeably by Piketty.
• Human capital is excluded.
• National income is equal to income from capital plus income from labour.
• National wealth (or capital) can be split into as public plus private wealth, or alternatively domestic plus foreign wealth.
• The capital-income ratio is given the symbol β
• β can be thought of as the number of years of a country's income held as wealth, so β=6 means a country holds six years worth of income as its wealth.
• The income from capital as a fraction of national income is denoted by α.
• α = r × β is an accounting identity and follows from the definition of r.
• i.e. income from capital equals r times amount of capital; then divide both sides by national income to get above equation.
• Figures 1.1 and 1.2 contrast shares of world output and population respectively for each major continent.
• Europe and America's share of output greatly exceeds their population share, at expense of Asia and Africa.
• Piketty uses Purchase Power Parity dollars (PPP) to convert currencies. More stable, and gives a more realistic estimate of inequality.
• PPP accounts for what a given amount of currency can buy in a country, rather than how many dollars it can be exchanged for, e.g. 100 USD will buy much more in a poorer country than it would in the US.
• National income distribution is more unequal than output distribution because wealthy countries are more likely to own capital in poorer countries and so draw a return from that capital.
• Developing nations have caught up with richer ones because of diffusion of knowledge not because they received capital investment from rich countries; in fact, China and South Korea have protected themselves from foreign capital flows, and competition from foreign companies in order to allow native companies to grow and catch up.

Chapter 2 - Growth: Illusions and reality

• Growth can, with some difficulty, be decomposed into a demographic growth component (growth with population) and an economic growth component. Only the latter results in improved living standards.
• Global growth is about 3%, whereas population growth is 1%.
• Table 2.1 shows global growth was only demographic at 0.1% before 1700, and dramatically increased due to large economic component over the industrial revolution.
• Cumulative effect of growth over time needs to be appreciated: 1% growth over a year seems small but equates to 33% growth of thirty years (a generation).
• Demographic growth has been very high since 1700, but now shows signs of slowing.
• High demographic growth dilutes wealth-concentration effect of inheritance.
• Output per capita, called productivity, has increased dramatically since industrial revolution.
• This means purchasing power of average person is typically ten times higher now than a hundred years ago.
• Productivity gains have mainly been in production of goods due to automation, whereas it's hardly changed in services, hence latter's growth gathers an increasing share of the workforce.
• Typical growth in developed countries in 20th century was 1 to 1.5%; 3 to 4% in poor nations that are catching up.
• Growth rate of 1% must involve significant social change.
• Fig 2.3: Europe growth was high post WW2, but this ended when it caught up with US in the 1970s.
• Policies of Thatcher and Reagan in 1980s didn't seem to affect growth.
• Population growth peaked earlier in the 20th century, before economic growth.
• Fig 2.4 and 2.5 shows growth falling in 21st century.
• Growth rates quoted in Piketty are real, i.e. inflation corrected.
• Growth brings new and changing products, which makes it hard to assess changing prices, and so effect of inflation on growth.
• Price changes can drive inequality, if owners of certain items see a jump in their value.
• Inflation erodes debt.
• There was almost no inflation before WW1.
• Novels no longer refer to amounts of money due to inflation.

Part two - The dynamics of capital/income ration

Chapter 3 - The metamorphoses of capital

• Fig 3.1 Agriculture now negligible, national capital to income ratio high and climbing.
• Foreign capital owned by Britain and France fell post colonial times.
• Public net wealth is small compared to private net wealth.
• Public debt is owned (not owed) by a minority and so important to inequality
• I find the net measures in this chapter misleading. In particular, public assets cannot be sold, so what's the sense in offsetting them against debts?

Chapter 4 - From old Europe to the new world

• Fig 4.4 Germany's relatively low private capital is due to apparently lower stockmarket valuation of its firms, since it runs a stakeholder approach to firms: eg representatives for workers, community, gov and environmental groups sit on boards of directors. Rhenish capitalism/social ownership.
• Fig 4.6 USA national capital much more stable than Europe from 1790 to now.
• In fig 4.10 ownership of slaves is included and makes up about a quarter of national capital at its peak. Even though it goes to zero by 1880; it makes the profile of national capital vs time even more stable looking.

Chapter 5 - The income/capital ratio over the long runs

• Why did capital/income in Europe return to historic highs in late 20th century and why are they higher than for US?
• Net public capital is small compared to private capital in all major economies
• 2nd law β=s/g - in words: the ratio of capital to income (β) is equal to the rate of increase of capital (s for savings) divided by rate of increase of income (g for growth)
• This law is true in the long run, not necessarily precisely obeyed at any given time if rapid flucuations are occurring.
• National income = GDP - depreciation + net foreign income
• Return to higher β is due primarily to small g, but also privatisation and increase of asset prices.
• Table 5.1 Higher β in Europe vs N America is due to higher population growth in the latter.
• Table 5.3 depreciation significantly reduces gross savings.
• Table 5.4 public savings are negative because private savers having been buying government bonds.
• Fig 5.6 market value is sum of shares of company ; book value is assets - liabilities. Ratio is Tobin's Q.

Chapter 6 - The capital-labour split in the 21st century

• Britain & France have best data.
• Fig 6.1 and 2 show both countries have fairly stable split over 2 centuries with labour being 60% to 80% and a noticeable jump up at WW1. Not sure how he sees a U shape in those graphs!
• Figs 6.3 and 4 show rate of return 4 to 6% except for spikes after 2 WWs.
• The "pure" rate of return accounts for labour expended on managing investments.
• Most household wealth is in real assets, eg a house, that have a real role in the economy, unlike money which is a nominal asset, vulnerable to inflation.
• Inflation can redistribute wealth and erode debt, but has a lesser role in determining the return on capital.
• Marginal productivity is extra output from adding one unit of capital. It decreases as β increases. But since α = r x β, how α (share of income as return from capital) behaves depends on how r varies with β. This is measured by elasticity of substitution, which is when r goes as 1/β which means α stays constant ie any capital-labour split gives the same return α. If zero, labour has to be set according to capital, and α decreases with increasing β and vice versa if elasticity is large.
• Evidence is that elasticity is a bit above 1 and so α grows gradually with rising β, share of income from capital increases as ratio of capital to income grows. It was less than 1 in 18th century agricultural economy.
• Long term decrease in capital and mirrored increased in labour's share of income suggests human capital is more important, ie knowledge and skills possessed by workers. But traditional capital is still important and has not been displaced by increased human capital.
• Marx's prediction that accumulation of capital by few owners would kill the return on capital makes sense if low growth persists (then historic ownership is dominant). Ie income would mostly go to capital, workers revolt etc But he didn't account for growth from increased productivity.
• Last page of chapter: "Progress toward economic and technical rationality need not imply progress toward democratic and meritocratic rationality." Possibly true :(
• Technology and knowledge have caused increases in growth that have avoided Marx's apocalypse, but not altered the structure of capital, eg the capital-labour split.

Part three - The structure of inequality

Chapter 7 - Inequality and concentration: preliminary bearings

• Tables 7.1-3 give broad stats in different regions, at different times of inequality in labour income and capital.
• If top 10% have 20% of income, by mathematics, their average salary is twice that of whole population average.
• All figures are pre-tax here.
• In Inequalities wrt capitalism section: "wealth is so concentrated that a large segment of society is virtually unaware of its existence, so that some people imagine that it belongs to surreal and mysterious entities."
• Inequality of wealth is greater than inequality of income. Europe has "medium" inequality: top 10% has 60%, middle 40% has 35% and bottom 50% has 5%.
• Over the last century, inequality has reduced markedly creating the middle class. 100 years ago in Britain: top 1% had >60%, Middle 40% had 5% and bottom 50% had <5%.

Chapter 8 - Two worlds

French case:

• Fig 8.1 and 2 - share of income for top decile & percentile in capital dropped sharply during WW2 whereas top wage decile & percentile remained the same.
• Inequality changes in the 20th century were not gradual or planned but resulted from war crises and political shocks and changes.
• Fig 8.3 and 4 - in France, point where income from capital overtook that from labour moved from about top 1% in 1932 to top 0.5%
• In the top decile, the top 1% is different from other 9% - the latter earn their income by working. This kind of effect is not visible if relying on a single number measure of inequality like the gini coefficient.
• Share of wages going to the top centile increased significantly from the 1990s in France - high pay packages for top managers.

US case:

• Inequality was reduced by policies that froze managers pay during ww2 and boosted the lowest paid.
• Inequality remained constant until the late 1970s, after which it increased sharply, mainly due to huge pay to top managers. Spikes in income from capital gains are apparent before the dot com bubble burst in 2000 and before crash of 2008.

Chapter 9 - Inequality of labour income

• All wages in 20th century France have been lifted; wage inequality remained constant. In contrast, inequality increased in US.
• Both examples plus Scandinavia point to investment in education acting against rising inequality.
• Rhenish capitalism involves stake and stock holders, already discussed in part 2.
• Regarding imperfect competition and minimum wage: "the goal is to make sure that no employer can exploit his competitive advantage beyond a certain limit".
• Last para in minimum wage section is great! "best way to increase wages and reduce wage inequalities in the long run is to invest in education and skills."
• In Inequalities in emerging economies section: "deterioration of the tax data after 1990... due in part to... computerised records."
• Marginal productivity theory cannot explain supermanagers' pay rises.
• Pro business policies from early 1980s onwards included cuts to top rate of tax. As big business leaders/owners get wealthier, their influence over politicians grows, hence more pro business policies and tax cuts. Positive feedback for inequality growth.

Chapter 10 - Inequality of capital ownership

• Historical reduction in inequality occurred with the rise of a middle class.
• Figs 10.1-6 show wealth inequality in France, Britain, Sweden, US and Europe. All show similar pattern: big drop in inequality during mid 20th century, followed by slow rise thereafter, though US is different in that inequality started lower but ended up higher.
• Fig 10.7 shows r>g since 1820.Together with fig 10.8 which plots α and s; it's possible to verify second law of economics.
• Fig 10.8 shows r>g since 0 AD.
• Figs 10.10 and 11 show that r<g once tax and losses are accounted for, but only in mid 20th century.
• Economic models usually use time preference (e.g. whether to spend $100 today or $105 tomorrow?) to explain why r is historically 4-5% and >g. Piketty argues this is tautological and over simplistic.
• If g=1% and r=5% then wealthy person will keep pace with average growth of income if they reinvest (save) a fifth of capital income each year.
• Laws on entails - default inheritance of eldest son - ended in major economies by early 20th century
• Pareto power law distribution of weath distribution is a useful mathematical description
• Inequality hasn't returned to 19th levels despite r>g because not enough time has passed and taxation has changed.

Chapter 11 - Merit and inheritance in the long run

• Demographic growth is predicted to slow, and since r>g, inequality will rise in 21st century.
• French inheritance tax historical record is the "best known".
• Fig 11.1 shows France's inheritance was about 20% of national income before WW1; feel to 4% post WW2; now rising through 15%.
• Two alternative ways to estimate inheritance: economic (wealth and age distribution) or fiscal (tax). Both give reassuringly similar answers, though latter is less than former, probably because some inheritance avoid taxs (legally or otherwise).
• Accounting identity of inheritance: inheritance/national income = deaths per year × (average wealth at death / average wealth of all) × β.
• All three of these factors decreased to cause mid 20th century dip in French inheritance flow.
• French annual mortality of adults decreased from 2.2% in 1900 to 1.2% in 2000.
• Partly explained by baby boom introducing a large cohort of young adults in latter half of century.
• Gifts pre-death should be included with inheritance flows as this is now increasingly important.
• Older people have generally been wealthier than young adults, except for around WW2.
• Piketty predicts share of total wealth that was inherited in France will return to being between 80-90% in 21st century from a low of 45% in 1970.
• Fig 11.10 living standards of top 1% inheritors is now roughly equal to that of top 1% of those who derive income from work.
• Data for other countries on inheritance is less good, but UK and Germany exhibit similar trends over last century.
• Much harder to assess US and developing countries.

Chapter 12 - Global inequality of wealth in the 21st century

• Return on capital varies with amount owned - a fact often neglected.
• Large funds can expend huge sums on managing the fund, e.g. managing risky, high-yield investments.
• Data on individual fortunes hard to assess, or imperfectly estimated, e.g. Forbes magazine.
• Bill Gates's fortune grew as a rapidly as a non-working heiress Liliane Bettencourt of L'Oreal, and continued to grow at same rate after he stopped working.
• Entrepreneurs turn into rentiers.
• Table 12.2 shows returns on University endowments (i.e. their capital) grows most, as high as 10% per annum, for the largest funds. Best data available on such large fortunes and their returns.
• Inflation does not affect returns on capital very much.
• Sovereign wealth funds: Norway's fund worth $700 billion in 2013, and offers good data, but despite being double that of all US university endowments combined, it is not growing as fast, possibly due to public/democratic scrutiny. Middle east wealth funds comparable in size, but data is more opaque.
• Will sovereign wealth funds own the world? Will some countries own other countries?! Will China own the world? Probably not.
• Loss of democratic sovereignty as capital and its power shifts across national borders avoiding tax, and promoting a feeling of dispossession of the majority of people who have little capital. Particularly acute in Europe with many small states with no united fiscal regime.
• The net wealth (assets less debts) of some rich countries appears to be negative, and indeed the world overall appears to be in debt! "Earth owned by Mars"! The explanation is probably that some private wealth is "invisibly" held in tax havens.

Part four - Regulating capital in the 21st century

Chapter 13 - A social state for the 21st century

• Wars of 20th century wiped away past and its structure of inequality.
• Tax exposes wealth to democratic scrutiny as well redistributing it.
• 2008 crash was not as bad as 1929 because governments and central banks stepped in and ensured there was liquidity, ie money still flowed.
• Fig 13.1 - taxes were less than 10% of country income until early 20th C. Now stabilised at 30%(US) to 55% (Sweden).
• Role of governments is at an all time high in social and economic matters.
• Education & health account for 20% of developed country GDP, mix of public & private provision.
• Half national income in developed countries is spent on social issues - debate needed about how it's organised.
• Social mobility better in Europe than US.
• Average income of Harvard parents is $450k; represents top 2% of income distribution in US.
• Free access to grand ecoles in France benefits children of parents in top 10% income bracket; free tuition not good enough in itself.
• Pensions are currently pay as you go, but now growth is lower, a capitalised pension scheme is needed, but investing now would deprive current retirees.
• After 1980, ultraliberal wave from developed countries forced poor countries to cut their public sectors.
• Decline of poor countries revenue in 80s due to custom duties
• The kind of fiscal and social state emerging in developing world is of utmost importance to future.

Chapter 14 - Rethinking the progressive income tax

• Tax is not technical but social and philosophical.
• Tax can trigger social unrest eg poll tax,or war,eg American revolution.
• Globalisation leans heavily on least wealthy workers in wealthy countries, justifying progressive tax there.
• Fig 14.1 and 2 shows high tax rates of mid 20th century.
• Taxing high income or wealth at 70 or 80% does not raise much revenue, but it does curb growth of high pay and so inequality.
• US and Britain had highest tax rates and distinguished between earned and unearned income.
• In mid 20th century top managers in UK or US were less inclined to fight for big rises because 80% or more would just go to government as tax.
• Dropping top rate of tax shows no increase in productivity nor GDP growth from 1980 onwards in UK or US compared to Germany.

Chapter 15 A global tax on capital

• Global tax on capital viewed as dangerous and idealistic but so was income tax a century ago.
• Piketty proposes a progressive annual tax on global wealth.
• Tax must cover all forms of wealth, unlike current systems.
• Global tax is not about funding social state, but restraining growth of inequality and will force greater transparency of asset ownership.
• No technical difficulty to do so: USA does it for hundreds of millions, and FACTA is an attempt to extend reach outside USA
• 0.1% rate would force transparency without any inequality reduction.
• Progressive tax on capital is missing in most countries.
• Wealthy capital owners like Gates or Bettencourt cannot spend most of the capital return, so it just gets added to their capital stock and not taxed, without any evasion or breach of the law.
• Annual tax on capital of a few percent enforced across nations would be fair and provide a significant extra public revenue. 2% GDP in Europe.
• Protectionism offers a possible alternative in some situations. It is useful to protect a developing economy from established foreign competition, eg S Korea or China.
• China controls its currency and restricts outflows of capital and foreign ownership.
• Unequal distribution of petroleum resource causes wars, eg middle east.
• Redistribution through immigration is a partial solution to inequality.

Chapter 16 - The question of public debt

• Rich countries have high private wealth but poor (indebted) governments.
• Governments of poor countries are less indebted.
• Europe has high private wealth but struggles with public debt.
• Three methods to tackle public debt: tax on capital, inflation or austerity.
• Inflation worked before; austerity is the worst.
• What follows applies to Europe.
• Public assets equals public debt
• National wealth is 6 years of income, mostly owned privately, by households. Half is real estate; half is financial assets, including public debt.
• European assets owned by foreign agents equal foreign assets owned by Europeans.
• Public assets could be privatised, but then rents would still need to be paid to use them, effectively replacing debt interest, and this would have some socially and morally unacceptable consequences, eg private police.
• Simply cancelling public debt may hit the current owners of bonds unfairly; may not be those who purchased bonds during the crisis.
• Better to introduce a progressive tax on capital which could bring debt to zero in 10 years.
• Inflation can be redistributive but is difficult to control and might have unintended consequences.
• Central banks main role is to stabilise the financial system by providing liquidity in times of need.
• Central banks don't create capital, but can inject money into the economy by creating an asset and debt simultaneously.
• Europe has a currency, but no state, and a central bank, the ECB, that cannot exercise a monetary policy to satisfy 17 states with separate fiscal regimes.
• Implement tax according to location of asset rather than where owner lives?
• Cross-border agreement on data sharing, interest on debt, taxation is no more Utopian or idealistic than a stateless currency. In fact it's needed by it.
• To decide the appropriate level of public debt requires answering the question: what value of β is desirable?
• The golden rule r=g provides a theoretical upper bound on β, the amount of capital in units of income.
• To achieve this would require that capital is accumulated until r falls to g - requires an unrealistically huge stock of capital.
• There is no rational argument behind why Europe has set limits of 3% and 60% of GDP for public budget deficits and debt respectively.
• Europe needs a budgetary parliament to go with its single currency.
• Public debt is often repressively redistributive; specifically, wealthy lend money to gov and receive interest instead of paying tax.
• Debt flexibility is necessary in a crisis, so arbitrary or legislated rules are not wise.
• Public and private wealth are at record high levels - the problem is not public debt being too high, but wealth is unequally distributed.
• Funding solutions to climate change will impact public debt decisions.
• Free market with private companies vs public ownership are two polar opposites - many types of organisations/companies exist in between.
• We need more transparent accounts of big private companies if we wish to hold them to account.

Conclusion chapter

• Without government intervention our societies will revert to r>g and inequality will grow, i.e. wealth from the past (r) grows faster than the active and productive economy involving output and wages (g).
• It is possible to increase growth, investing in education, knowledge and non-polluting technologies. But this cannot raise growth to 4 to 5% per year to compete with r, except temporarily in developing economies.
• A hefty income tax may harm motor of the economy (entrepreneurs) and limit growth.
• A progressive tax on capital is needed, and this requires a high degree of cooperation between nations. European small countries are a particular challenge.
• Last 2 sentences: "...all citizens should take a serious interest in money, its measurements, the facts surrounding it, and its history. Those who have a lot of it never fail to defend their interests. Refusing to deal with numbers rarely serves the interests of the least well-off."