# The Dismal Science

This is the story of how Economics came to be called the Dismal Science. It is a story I choose to begin with Piano wire…

Piano wire is known for producing beautiful sounds from Turning Point by Nina Simone, to Changing Opinions by Phillip Glass, to the Goldberg Variations of J.S. Bach. The sound made by piano wire when threaded into a whip and used to rend flesh from the backs of plantation slaves is presumably not among them. But it was this sound of piano wire on flesh, or news of it, that caused uproar in London during the year 1865. The whipping of slaves with piano wire had occurred in Jamaica on the orders of the Governor George Eyre. Among those who came to his defence, arguing that the whippings had been an important part of suppressing a rebellion, was Thomas Carlyle.

Over a period of many years prior to this event Thomas Carlyle had often made the case that while slavery itself may not be strictly desirable it was a reflection of an innate superiority of whites over blacks. He had a long running and public feud with John Stuart Mill on precisely this topic, including an 1849 essay entitled “Occasional Discourse on the Negro Question” in which he described Economics — “the Social Science […] which finds the secret of this universe in ‘supply-and-demand’ ” — as the Dismal Science. This was the coining of the term Dismal Science to describe Economics.

Economics was a dismal science, indeed “a dreary, desolate, and indeed quite abject and distressing one” because it denied the superiority of certain men. This was in direct contrast to Carlyle who held that some men, mostly White ones, were innately better than others, namely “Black Quashee”.  Addressing himself to Blacks in the West Indies he advised, “You are not ‘slaves’ now; nor do I wish, if it can be avoided, to see you slaves again: but decidedly you will have to be servants to those that are born wiser than you, that are born lords of you, — servants to the whites, if they are (as what mortal can doubt they are?) born wiser than you.”

Carlyle felt that “Black Quashee” was “indolent” and that if left to his own devices would simply choose to sit around eating “Pumpkin”, which would be against his “sacred appointment to labour”. To save “Black Quashee” from his own indolence he had an “indisputable and perpetual right to be compelled” to work. Economists, in a most dismal fashion, denied that certain men were inferior and should be compelled to work. Instead they suggested that a wage be offered for work and the “poor indolent blockhead, black or white” simply be left to decided for themselves whether or not to work at that wage.

While Carlyle’s essay certainly has racial undertones — less undertones than blaringly loud tones — his point was also part of a larger argument. Part of the essay and an opinion Carlyle shared with his contemporary supporters, among them John Ruskin and Charles Dickens, was the idea that some men are simply Great Men who are from birth simply destined for great things. It was the opposition of Economists to such ideas of innate superiority and their insistence on a more egalitarian view of mankind to which Carlyle objected.

A denial that some men may be innately better than others lead Economics to be known as the Dismal Science. Dismal was to insist that all men and women be treated equally. If only Economists were more Dismal today!

———-
If you decide to read Carlyle’s essay it will help to know that Exeter Hall was the home of the anti-slavery movement. It would also help to know what Carlyle’s obsession with Pumpkins is all about, but on this point I have no idea. Among Thomas Carlyle’s main opponents on the issue of slavery was the Economist and Moral Philosopher John Stuart Mill. The trial of George Eyre, the Jamacian Governor, led John Stuart Mill together with Charles Darwin and others to form the Jamaica Committee to push for the prosecution of George Eyre. Thomas Carlyle formed a rival committee for the defence, with supporters including Charles Dickens and John Ruskin.

Carlyle’s argument in the Occasional Discourse is, strictly speaking, made not in favour of slavery, merely of compelling people to work. However Carlyle was certainly not averse to the idea; “Quashee, if he will not help in bringing out the spices, will get himself made a slave again (which state will be a little less ugly than his present one), and with beneficent whip, since other methods avail not, will be compelled to work.”

A nice quote from Adam Smith’s Wealth of Nations that captures this egalitarian view of early Economists is,

The difference of natural talents in different men is, in reality, much less than we are aware of; and the very different genius which appears to distinguish men of different professions, when grown up to maturity, is not upon many occasions so much the cause, as the effect of the division of labour. The difference between the most dissimilar characters, between a philosopher and a common street porter, for example, seems to arise not so much from nature, as from habit, custom, and education. When they came into the world, and for the first six or eight years of their existence, they were perhaps, very much alike, and neither their parents nor playfellows could perceive any remarkable difference. About that age, or soon after, they came to be employed in very different occupations. The difference of talents comes then to be taken notice of, and widens by degrees, till at last the vanity of the philosopher is willing to acknowledge scarce any resemblance.

• In addition to Carlyle’s essay as linked above there are a series of modern essays examining the racial context in which the term the Dismal Science first arose in the book of essays How the Dismal Science got its Name by David Levy, this was my own introduction to the topic. A good book, but dense.
• A contemporary report from The Spectator on the Jamaica Affair.
• For more on Britain’s anti-slavery movement, one of the world’s first international humanitarian rights campaigns, try Bury the Chains: Prophets and Rebels in the Fight to Free an Empire’s Slaves by Adam Hothschild. Britain did not just ban slavery within its own borders (and colonies), it actively protested the trading of slaves by other countries, and by the end was patrolling the waters off Zanzibar to blockade the shipping of slaves to the Arabic Peninsula.
• Hard Times by Charles Dickens, a book he dedicated to Thomas Carlyle, argues against a narrow conception of behaving in a rationalist utilitarian fashion in which all actions should be based in facts while imagination and compassion are foreign concepts.
• What happened to the egalitarian views of the earlier Economists? Try The “Vanity of the Philosopher”: From Equality to Hierarchy in Post-Classical Economics by David Levy and Sandra Pearl. As with the other Levy book mentioned, this is not light reading.

# Summary of Piketty: Criticisms

[This is the fifth of five posts on Capital in the 21st Century. The first is here.]

The following are mini-summaries of some of the main criticisms of Piketty’s Capital in the 21st Century that relate to his descriptions of the historical changes in inequality and their current trends. I do not consider criticisms of Piketty’s policy prescriptions (a global wealth tax). I put some that I would describe as more substantive first, and the less important ones later. A good summary of criticisms is provided by Wolfers.

• Global growth (eg. Rogoff): The global income distribution has become more equal over the last decades. It is possible, perhaps even likely, that this is related to the lack of growth in median income in the rich countries. This has happened alongside the large increases in the shares of Income and Wealth of the top percentile, which is Piketty’s main focus. It is something worth remembering, but has no direct bearing on Piketty’s arguments about inequality in developed countries, expect perhaps putting them in the broader context. In short, while globalization may account for the increasing equality of the global income distribution, the stagnation of lower and middle incomes in developed countries, and the rising returns to higher education, it does not appear to explain the rising income share of the top percentile. (Global income growth. For global wealth distributions similar data simply does not exist (yet))
• Inequality within the 99% (eg. Autor):
• US after-tax vs pre-tax incomes (BL&S and Burtless), and changing US households (BL&S and GGKS): Piketty’s income inequality numbers are based on pre-tax incomes. One criticism of his numbers is thus that what really matters is after-tax incomes. Using after-tax incomes the top percentile still hugely increases it’s share of (after-tax) income. The main thing that looks different using after-tax incomes is that median US household incomes no longer look stagnant over the last few decades, they have increased (albeit not nearly as fast as those of top percentile). Another criticism of Piketty’s income inequality numbers for the US is that the ‘average’ US household has changed over time, it used to be the nuclear family (Mum, Dad, Two Children), but there are now many more households with only one parent. It also used to be case that only the Husband would work, this is no longer true and nowadays high income husbands tend to have high income wives. Accounting for changing households makes the increases in income inequality “less severe” (quotation marks as the increase is still the ‘same’, just changes how one sees the causes), although the trends are in the same direction. It does however change the story of stagnant median US incomes, which do grow, albeit still by less than the US economy.
• Wealth versus Capital (eg., Blume & Durlauf): Piketty does not really measure Capital, but rather Wealth. The distinction is that Wealth is the market value of all assets (ie. houses are valued by the price of houses), while Capital is only assets that are used in production and are valued by their marginal product. Among the criticisms this leads to are that Piketty measures aggregate Wealth by asset value as his numbers are susceptible to house price movements (hence BBCW and Rognlie criticisms below). Also since the inequality ‘share of income’ measures are based on marginal product there is an inconsistency between how Piketty measures aggregates and shares. They also observe that many of Piketty’s ideas about drivers of inequality — negotiating power of managers, ability of large funds to get better rates of return on assets — imply that the marginal product measures of inequality used will be invalid (validity of the marginal product measures assumes perfect competition).

Some less important criticisms are,

• Acemoglu & Robinson – The Rise and Fall of General Laws of Capitalism: Their first point is that there are no such thing as inescapable laws of capitalism (except accounting identities!). They provide some preliminary cross-country evidence on the relationship between income inequality and $$r-g$$ which, while too weak to convince anyone not already convinced, does provide a useful starting point (also has weakness that it is income inequality, while argument is really about wealth inequality). Using examples of Sweden and South Africa they point out importance of looking at many different measures of inequality, not just focusing on the one percent.
• Krussell & Smith (VoxEU): Criticize the “theory” in Piketty’s book. The objection is essentially the following. Piketty uses the formula $$K/L = s/g$$ (capital/output ratio=savings rate/growth rate) when he should use the formula $$K/Y = s/(g+n+\delta)$$ (capital/output ratio=savings rate/(growth rate+population growth rate + capital depreciation rate)). The later formula being that of the Solow growth model (and the one I just used directly in my summary). Their objection is that if $$g$$ goes to zero then Piketty’s formula would predict that the capital/income ratio goes to infinity — clearly unrealistic. It seems clear from the surrounding text that Piketty is aware of the Solow growth model and capital depreciation but leaves it out for simplicity, and because Piketty’s main use for the formula is to argue that as population growth rates slow, possibly accompanied by a slowing per-capita growth rate, we would expect the capital/income ratios to rise; and thus Frances historically lower population growth rate and higher capital/income ratios provide a better guide to what we should expect capital/income ratios to be in the future, than the historical experience of the US with its higher population growth rate. At least by my reading the book does not claim that $$K/Y$$ is about to go off to infinity. I call this a lesser criticism not because the point is unimportant, but because it feels like they are taking down a Strawman.
• BBCW (the four French) Economists: Object to Piketty’s use of house prices as way to measure wealth. Suggest using rental prices of housing instead. Doing this for French data makes the increase in the French Capital/Income ratio since World War II smaller, but still in same direction, as Piketty’s findings. Their objection seems somewhat misguided as Piketty is using the price of assets as a measure of their value which is very much following the standard approach and it is not clear why using rental prices might be better (other than being less affected by booms and busts). In any case, they find much the same trends as Piketty; a rising ratio in France since WWII, only less pronounced. They also suggest that this is important for Piketty’s ideas on wealth inequality being self-reinforcing, but since the wealth of the rich is in stocks & bonds, not houses, it does not seem so important.
• Rognlie: Loosely, makes same point as the Four French Economists only for the US economy, and focusing on capital share of income rather than wealth-to-income ratio. Namely that it is substantially about housing prices.
• Financial Times: Points out some (¿)minor(?) spreadsheet errors relating to Chapter 11 (Wealth Inequality). Important, but do not appear to change any of the main conclusions. In his response Piketty mentions that the World Top Incomes Database, the definitive data source, will shortly be expanded to include Wealth data.

# Summary of Piketty, Part 3: Inheritance of Capital

[This is the fourth of five posts on Capital in the 21st Century. The first is here.]

The third part of Piketty’s Capital in the 21st Century is about the Inheritance of Wealth; there is also some discussion of global wealth and of taxation but I shall skip those here. Piketty investigates inheritance of wealth looking at just France as that is the only country where the data is good enough to do so.

Piketty considers two key aspects of inheritance: the value of inheritance relative to incomes, and how concentrated inheritances are in the hands of a few.

The value of inheritance relative to the economy as a whole is shown to have been high in the 19th century, fallen massively as a result of the two World Wars, and is currently rising, although not yet back to 19th century levels. The concentration of inheritances however reduced substantially during the 20th century and remains much lower; this does not mean that inheritance is no longer important, just that inheritance matters in a different way than it used to.

So how important are inheritances relative to earnings from working? Piketty shows that in the 19th century Inherited Wealth offered riches simply unattainable by working and saving; a ratio of three-to-one as measured by lifetime resources. This ratio fell below one just after the world wars, and while trending upward is now only just above one. Thus in the 19th century the richest French inherited their wealth, while nowadays the richest French are much more mixed between earning and inheriting. Piketty predicts that inheritances will become more concentrated in the future, perhaps leading to a return to a situation in which the richest people are those who inherited their wealth. It is in this increasing concentration of wealth by inheritance that Piketty sees the main role for $$r>g$$. $$r>g$$ further allows for greater accumulation of assets over the lifetime, leading to higher ratios of assets at age of death to assets at age of receipt of inheritance, meaning a larger role for inheritance. This combination of an increasing role for inheritance, together with it’s increased concentration, are the channels by which $$r-g$$ is proposed to drive increased inequality.

The following facts are all for France, except F11.12. This reflects that France is the only country where we have good inheritance data over a long time period. This is especially true of gifts, inheritance transferred between living parents and children (such as helping to buy a house) rather than transferred upon the death of the parents.

### Inheritance of Capital:

Wealth inequality a century ago was much higher than now. Then most capital was land, and the wealthiest 10 percent owned nine-tenths of it. Now most capital is housing, industrial and financial, and the wealthiest 10 percent own around two-thirds of it, rest is owned by next 40-or-so percent, with poorest half owning none. Whether we will return to the wealthiest 10 percent owning nine-tenths depends on how concentration of wealth evolves, and the inheritance and accumulation of wealth are key to understanding this.

There are two main ways to accumulate capital, savings (whether from earnings or from capital income) and inheritance: this is where Piketty argues for key role or $$r>g$$, namely that when $$r-g$$ is large, inheritance will become more important relative to savings. And within savings large $$r-g$$ is likely to increase the importance of capital income relative to earnings.

So how important is the role of Inheritance in Wealth? There are two questions here, first how much of Wealth is inherited on average, and second how concentrated is this Inheritance.

How much of Wealth is inherited on average? In France inheritance accounts for 18% of the lifetime resources (sum of all the income and assets you will have over a lifetime) of the average individual; calculated for those presently 50 years old which is the average age at which people inherit. In the late 19th century it was 25%. Following the World Wars it fell to 10%, since rising to 18%, and Piketty forecasts that it will continue to rise back to 25% (F11.9)

How concentrated is Inheritance? Measuring the concentration of inheritance as the ‘Faction of each cohort receiving in inheritance at least the equivalent of the lifetime labor income received by bottom 50% labor earners’, we see that in 19th France this was around 10% of the population, for those inheriting in mid-20th century this fell to 1% and has since returned to 10%. Piketty forecasts that it will continue to rise to 15%. (F11.11)

Combining these findings on how much of Lifetime resources are inherited, and on the concentration of inheritance, we see that while the importance of inheritance in the economy on average has returned to the levels of the late 19th century, Piketty’s forecasts suggest that it is more widely spread. This argues for both a substantially increased role of inheritance relative to recent decades, but not one with the same levels of concentration as seem in the late 19th century. Piketty forecasts inheritance to play a much larger role in the incomes of the Top 1%, but not to the complete exclusion of labour earnings as in the 19th century.

Other points on Inheritance of Wealth:

• Inheritance flows as a percentage of total private wealth, also called the annual rate of transmission of wealth by inheritance, has been rising. By accounting identity, these flows can be expressed as $$m \mu$$, where $$m$$ is the mortality rate and $$\mu$$ is the ratio of average wealth at time of death to average wealth of living individuals. $$m$$ has fallen due to people living longer than before (F11.2), but this has been more than countered by the increase in $$\mu$$ (F11.5), with the result that $$m \mu$$ has increased (F11.4).
• A technical modification of $$\mu$$ is needed to include ‘gifts given’ in the wealth at time of death. $$\mu$$ will reflect savings decisions and depreciation. For example if retirees draw down assets and die with none left than $$\mu$$=0. Piketty argues that changes in the pattern of assets across age groups among Parisians over time (T11.1) can be explained by changes in $$r-g$$; Parisians are chosen simply as they are the only group for which Piketty has the required data.
• The importance of gifts (a.k.a. intervivos transfers) has increased substantially in the past few decades and now account for around half the value of inheritances (F11.5). This is likely a response to ageing, with the average age of recipients of gifts being 35-40. The average age at which one received inheritance used to be 30 and has now increased to 50. This directly reflects parents living longer, with the difference between average age at death and average age of heirs (aka. generational duration) remaining roughly constant at 30 years (F11.3).
• In 19th France the annual flow of inheritance accounted for around 20% of GDP, around 1920 this fell to about 5%, and in last decade or two has increased again to 10-15% of GDP (recall that capital income averages around one-third of GDP). (F11.1; shows Fiscal flows measure, based on declaration of gifts and inheritance to tax authorities, and Economic flows, explained below. Both measures in theory should give same number.) (F11.12 shows similar findings for UK & Germany.)
• Economic Flow of Inheritance: the annual flow of inheritance as a percentage of GDP can be calculated as $$m \mu \frac{K}{Y}$$; ie. as inheritance flows as a percentage of total private wealth times the capital-output ratio.
• How big are Top 1% of Inheritances compared to the Top 1% of Earnings? Measured as the Lifetime Resources that each contributes Piketty finds that Top 1% inheritances in the 19th century were some three times the Lifetime resources from Top 1% earnings; meaning that inheritance offered the possibility of earnings unachievable by working. Nowadays this ratio is around 1, meaning that it is possible to enter into the Top 1% of lifetime resources by earnings alone (F11.10). This finding is reflected in the earlier findings on the Share of Capital Income amongst top incomes (US & France: F8.3, F8.4, F8.9, F8.10).

Part 4: Some Criticisms of Piketty

# Summary of Piketty, Part 2: Income Inequality and Wealth Inequality

[This is the third of five posts on Capital in the 21st Century. The first is here.]

The second part of Piketty’s Capital in the 21st Century looks at inequality within developed countries. Two main types of inequality are considered: income inequality (inequality in how much people earn each year) and wealth inequality (inequality in how much people own).

For income inequality two main trends are evident, the rise of the top 10 percent (top decile), and the rise of the top one percent (top centile) or even 0.1 percent. The increasing share of the top decile is likely a reflection of changes in education, technology (computers and the internet), and globalisation; it is ‘bigger’ in the sense of accounting for a larger share of national income. The increasing share of the top centile is often described as the rise of the supermanagers (high-aid CEOs), but this is not enough, as the top 0.1 percent have risen even further and their income comes mostly from capital income. It is this rise of the top centile (and 0.1 percent) that Piketty considers most alarming.

Wealth Inequality fell substantially during the first half of the 20th century, stayed largely flat for a few decades, and has been increasing for the past few decades. The fall is explained by the two world wars, together with the period of high inflation that many countries experienced inbetween. Piketty argues that the flatlining of the next few decades occoured because the (after-tax) return on capital was lower than the economic growth rate, thus capital did not simply tend to accumulate when ‘left to itself’. This period of the (after-tax) return on capital being lower than the economic growth rate appears to be a historical anomaly, and has ceased to be the case in recent decades. As a result wealth inequality has begun to increase back towards its historical levels. There is one other major difference between post-war wealth inequality and historical wealth inequality, the part of the population not in the top decile actually holds a non-trivial fraction of the wealth (ie. many households own their houses).

### Income and Wealth Inequality:

• The income rich and the wealth rich are not the same people. There is some overlap, but generally the people who make the top incomes and the people with the top wealth are not the same people. Retired people, with lots of wealth but little income, are one example of this.
• Wealth is always and everywhere much more unequally distributed than income.
• For most people income consists of wages, capital income is the most important form of income only for the very rich. Around 1930 capital income was the main source of income for the top 1% incomes, nowadays capital income is the main source of income for the top 0.1% incomes (US & France: F8.3, F8.4, F8.9, F8.10).
• What does ‘low’ or ‘high’ inequality mean when talking about countries? Piketty gives some examples of countries that show us what such concepts might mean, for example Scandinavia in the 1970s provides a benchmark of low inequality, the US in 2010 a benchmark for high inequality. The following tables show what the shares of various groups are for labour income, capital ownership, and total income are for these cases, respectively: T7.1, T7.2, T7.3.

### Income Inequality

• There are two main trends currently occurring. One is that the top quintile (20%) or decile (10%) are leaving the average and poor behind. The second is that the top 1% or even 0.1% are leaving everyone else even further behind.
• Income share of top decile in US and Europe: F9.7F9.8.
• Income share of the top 1% in various countries: F9.2F9.3, F9.4.
• Income share of the top 0.1% in various countries: F9.5F9.6.
• That the top quintile or decile are leaving behind the median and poor seems mostly due to a combination of factors such as an increase demand for high-skill workers (due to technology such as telecommunications and computers that allow them to be more productive and reach larger audiences), a slowing supply of high-skill workers (since education levels appear to be levelling out; almost everyone already has high-school education, many people now have university education), and globalisation (which massively increased the supply of workers, and hence the competition in the non-university educated jobs).
• The reasons why the top 1% of incomes have seen such a large increase in their share of earnings is not so clear. Is this a return to a more normal state of affairs?, as suggested by the observation that pre-WW2 they were much higher than now. Or is it due to their being more productive (thanks to technological improvements) like for the top decile, only even more so. Or is it due to their capturing the political process and manipulating the rules in their favour? Or is it because CEO pay is set by friends of CEOs and so they simply scratch each others backs? While there is some evidence for each of these arguments we do not yet know their relative importance. What we do know is just that the top 1% and 0.1% have been making an increasingly large share of income over the last decades, that this is true in all developed counties, and that it seems likely to continue. Interestingly their share is much higher in the US than in the other Anglo-Saxon countries (F9.2, F9.5).
• Who are the top 1% of incomes in US? By vast majority CEOs, Managers, Finance, plus some Doctors and Lawyers. Who are not the top 1% of incomes in US? Film stars, Sports stars, and Small-Business Owners. Piketty mentions this point. The numbers can be found in Bakija, Cole, and Heim (2012WP).
• Historically income inequality fell substantially around the period of the two world wars, and has been increasing since. A substantial part of this is due to the simultaneous fall and then rise in the importance of capital (F8.1, F8.2, F8.7, F8.8), and fall and rise is much greater within the top 1% than in the rest of the top decile (F8.6). One interpretation of this is that the post-war period was the exception, and presently rising inequality represent a return to the norm, this is the argument made by Piketty.

### Wealth Inequality

• The top decile and top 1% wealthiest hold very large shares of total wealth (F10.1, F10.3, F10.4, F10.5).
• The bottom third (approximately) of the population holds around zero wealth.
• The shares of wealthiest used to be much higher before the world wars, and have been increasing during the last few decades. Piketty argues this present increase likely represents a return to normal.
• Part of his reason for arguing that increasing wealth inequality is likely to continue is that capital income is much larger than savings (F10.8) and so most wealth accumulation likely occurs from the reinvestment of capital income, tending to lead to higher concentrations of capital. This is made in combination with the observation that the return on capital ($$r$$) is higher than the growth rate of the economy ($$g$$), a so simply by saving a fraction of the ‘extra $$r-g$$’ part of capital income there will be a tendency to increased concentration of capital ownership (F10.10, Piketty provides a few other graphs arguing that $$r>g$$ is very much the historical norm, and that the only exception has been the couple of decades post-WW2) .
• This argument of Piketty’s, that $$r>g$$ will lead to increasing wealth inequality, has been one of the most strongly criticised parts of the book. Disagreement is not so much that $$r>g$$ is the normal state of affairs — which seems to have been widely accepted — but his conclusion that this naturally leads wealth inequality to increase involves some strong assumptions about how people decide how much to save. However Piketty’s assertion does not appear strongly at odds with the evidence, that generally suggests that the rich have higher savings rates. That Piketty does not present any evidence on what determines savings is though a major weak point in his arguments.
• The shares of the wealthiest are higher in Europe than in US, this is likely explained by the higher population growth in the US which makes wealth accumulated in the past become more dispersed (this logic is reasonable and related to the case of capital/income ratios, but not watertight). (F10.6)
• Superentrepreneurs, eg. Bill Gates, are very few in number and as such play no quantitative role in the increases in inequality of recent decades.

For more numbers on income and wealth inequality for a wider selection of countries, see the Chartbook of Economic Inequality.

Part 3: Inheritance of Capital Wealth

# Summary of Piketty, Part 1: Capital/Income Ratio and the Capital Share of Income

[This is the second of five posts on Capital in the 21st Century. The first is here.]

The first part of Piketty’s Capital in the 21st Century is about the Capital/Income ratio and the split of Income between Capital Income and Labour Income. Piketty finds that Capital/Income ratios are increasing, and predicts they will continue to do say. Alongside this increase in Capital/Income ratios, and as a result of it, the share of income going to Capital appears to be increasing, and is also predicted to continue to do so.

Increasing Capital/Income ratios are the result of two forces. The first is a recovery to higher historical levels after the destruction of large amounts of capital in the first-half of the 20th century, mainly as a result of the World Wars. The second is decreasing income growth rates — due to both slowing technological progress and slower population growth — which mechanically means that the same rates of savings will result in higher Capital/Income ratios.

Increasing Capital/Income ratios automatically result in an increasing share of income going to Capital, unless they are fully offset by falling interest rates. The evidence suggests that interest rates do fall as Capital/Income ratios increase, but that they do not fall enough to fully offset the increasing importance of capital.

### Capital/Income Ratios:

Main point: Capital/Income ratios are rising, and will continue to do so. There are two main reasons. The first is a return to historical norms after a massive fall in Capital/Incomes due to the destruction of capital in the World Wars. The second is a slowing growth rate of income (partly due to falling population growth), so that the same rate of savings leads to substantially higher Capital/Income ratios.

Return to historical norms after a massive fall in Capital/Incomes due to the destruction of capital in the World Wars: The focus here will be on France & Britain, simply because the data for these two countries goes back much further. The observations follow directly from

Capital in Britain , 1700-2010

Capital in France, 1700-2010

Here we see that the Capital/Income Ratio was high, until the two World Wars (and high inflation between them) substantially reduced the ratios. Since World War II they have been on an upward tendency. The first of the main points here is that Capital is currently becoming more important; and that this represents a return to historical norms after the destruction of the early 20th Century.1

The growth rate of national income is an important determinant of the levels at which the Capital/Income Ratio will settle: If a country saves a fraction $$s$$ of income each year, and has per-capita income growth of $$g$$, population growth of $$n$$, and capital deprecates (wears-out) at rate $$\delta$$ then the Capital/Income Ratio ($$K/Y$$) of that country will eventually stabilize at

$$\frac{K}{Y}=\frac{s}{g+n+\delta}$$

(think of the Solow growth model; Piketty calls this relationship $$\beta=s/g$$). Population growth rates have fallen over recent decades, it is possible that per-capital income growth may be slowing as well. Thus we expect that the Capital/Income ratio will rise. As a rough guide, we might expect it to rise from levels historically experienced in countries such as the US that have had higher population growth (2.5 million people in 1776 to 300 million in 2006), to the levels historically experienced in countries such as France that have not seen so much population growth (25 million people in 1789 to 61 million in 2006). The US Capital/Income ratio has historically been about 4, while that for France has historically been around 7.

Capital in France, 1700-2010 (again)

Capital in the United States, 1770-2010

Some further points on the Capital/Income ratio:

• Most capital is privately held: public (Government) holdings of wealth are small compared to private holdings, especially net public capital (assets-debt), and in many countries has been further decreasing in importance over recent decades (think privatization). (See F3.3, F3.4, F3.5, F3.6, F4.4, F5.1)
• Some of the fall in the Capital/Income Ratio during the mid-20th reflects physical destruction of capital, some reflects falling prices. Piketty addresses this decomposition and finds that both play important roles. Thus, some of the rise since World War II simply reflects ‘price recovery’. (See Chapter 5)
• Most capital is domestic: the difference between domestic wealth and national wealth, that is the importance of how much one country owns in foreign countries, is small. The only notable exceptions are from when countries, such as Britain and France, had large overseas Empires. While net foreign wealth remains small, gross holdings have increased over recent decades. (See F5.2, F5.7)
• The only issue not covered in-depth is what determines the savings rate, $$s$$. Since we expect that in the long-run the Capital/Income ratio will converge to $$K/Y=s/(g+n+\delta)$$ the savings rate is important in determining where the Capital/Income ratio is going to. Piketty does discuss it briefly and provides some Tables (T5.1, T5.2, T5.3, T5.4) showing that it varies across countries. The question is why it varies across countries, and over time, and will it change in the future? This is a weakness in Piketty’s predictions for increasing Capital/Incomes, but given the history and current trends of Capital/Income ratios it is unlikely to be a major one (F3.1, F3.2, F4.6, F5.3).
• Capital/Income ratios for some other rich countries, F5.3.
• Interesting aside: Slaves were an important part of the ‘wealth’ of the US in the late eighteenth century, F4.10.

### The Share of Income going to Capital

Main point: Increasing Capital/Income ratios automatically result in an increasing share of income going to Capital, unless they are fully offset by falling interest rates. The evidence suggests that interest rates do fall as Capital/Income ratios increase, but that they do not fall enough to fully offset the increasing importance of capital.

The income of capital is just the amount of capital times the income per unit of capital; the latter is called the return on capital or the interest rate. Thus the share of income going to capital, $$\alpha$$ — the Capital Share of Income — is simply the Capital/Income ratio times the interest rate $$r$$, that is

$$\alpha=r \frac{K}{Y}$$

There is little to say here other than simply to give the graphs of the Capital Share of Income for Britain and France and simply observe that the capital share of income is not constant, and that it is higher when the Capital/Income ratio is higher.

The capital-labor split in Britain, 1770-2010

The capital-labor split in France, 1820-2010

Over the last decades the Capital/Income ratio has been rising, and the Capital Share of Income has risen along with it. The conclusion that the Capital/Income ratio will continue to rise leads us to conclude that the Capital Share of Income will continue to rise.

Some further points on the Capital Share of Income:

• The return on capital (interest rate) does vary, but is comparatively stable. This fits with our earlier observation that, by accounting identity, the only way an increase in the Capital/Income ratio will not lead directly to an increase in the Capital Share of Income is if the return on capital falls enough to offset it. (F6.3, F6.4)
• An increasing share of capital is seen in many countries, F6.5.2
• Technical note I: The point about whether $$r$$ falls enough when $$K/Y$$ rises to keep $$\alpha$$ constant is, in the language of Economics, a question of whether the elasticity of substitution between capital and labour is equal to one. The empirical evidence presented suggests that $$r$$ falls a little, but not enough to keep $$\alpha$$ constant; that the elasticity of substitution between capital and labour is greater than one.
• Technical note II: Economists often use a ‘Cobb-Douglas production function’. This function assumes that the capital share of income is constant; that the elasticity of substitution between capital and labour is equal to one. One can easily fix this by using a ‘Constant Elasticity of Substitution (CES) production function’ which allows for an elasticity of substitution between capital and labour greater than one.

Part 2: Income Inequality and Wealth Inequality

1. The observation about falling Capital/Income Ratios, and a return to ‘normal’ ratios since, is much more relevant to countries such as Britain and France that were devastated by the wars, than to countries such as US that were largely (physically) unaffected. This is evident comparing the graphs of Capital/Income Ratios for these countries. []
2. For more, see Karabarbounis and Nieman (2014) – The Global Decline of the Labor Share. []

# Summary of Piketty

I here provide a summary of Capital in the 21st Century by Thomas Piketty. The summary is broken into three parts by theme. The first part of the summary covers the Capital/Income ratio and the Capital Share of Income. The second part of the summary covers Income inequality and Wealth inequality. The third part of the summary is about Inherited Wealth. I also provided a “fourth” part discussing some of the main objections and criticisms that have been raised.

By my reading the book is largely a description of past trends, present trends, and probable future trends in income, capital, and inequality. This summary therefore concentrates on summarizing and describing those trends. I deliberately omit treatment of Piketty’s policy suggestions (largely Chapters 14 & 15).

I omit some other parts of Piketty’s book. Those describing historical and present trends in population growth rates (and ageing demographics), on the grounds they are well covered elsewhere. Those on global inequality as it is somewhat of a side-issue from his main topic; inequality in the developed countries in particular inequality in income and wealth of the top percentiles. Those on the differing size of governments (measured as a percentage of GDP) between countries and over the past century; as well as historical changes in top tax rates. Those on what tax rates on income and capital should be (Piketty’s policy prescriptions).

Much of Piketty’s book is about explaining how the data is put together: what are the sources?, what assumptions and definitions are made?, what is the uncertainty in the measurements?, if we used different measures would things change much? I ignore these important aspects here (go read the book!) and concentrate solely on describing some of the main findings. At this point massive kudos are due to Piketty for putting all of the graphs and data from his book online, without which this summary would not be possible in its existing form.

Some criticism of the book has been based on the grounds that the book contains a theory of inequality. The theory, such as it is, consists mostly of simple accounting equations. One has the feeling Piketty received the same advice Stephan Hawking got when writing A Brief History of Time: “Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein’s famous equation, $$E=mc^2$$. I hope that this will not scare off half of my potential readers.” For those who do think the book is about theory, allow Debraj Ray to clear things up. Those interested in Piketty’s theory will have to look at the technical appendixes of his book, or at his published papers.

Enough chat, here are the various parts of the summary.

Oddly enough almost all of the reviews seem to ignore Chapter 11 on the relative importance of inheritance in capital wealth. Odd since this seems to address one of the most contentious aspects of the book, I can only offer two possible reasons, either most reviewers didn’t reach chapter 11 before their deadlines, or the reviewers simply don’t like France (for reasons of data availability it is mostly about France, Britain and Germany get a mention, but the US and other countries are ignored simply as the needed historical data is non-existent).

For those who prefer to read a review instead of a summary, here are a few of the better ones.
Solow in New Republic
Shenk in The Nation (starts mid page 6))
Debraj Ray
Podcast interview on EconTalk

If your interest is in inequality at a global level, which has been falling, as well as a discussion of population and heath, a good book is Angus Deaton The Great Escape: Health, Wealth and the Origins of Inequality.