# 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