### The x% puzzle

According to the Fed’s Survey of Consumer Finances (see table 1), the mean net worth of American families whose head is aged 65-74 has grown from 471.9 thousands of 2010 dollars in 1989 to 848.4 thousands in 2010 — a 2.8% annualized growth over 21 years. This is the fasted pace amongst all age groups in the survey and must be compared to a mere 0,65% for the average American family. Should we conclude from this that the group of elderlies has benefited from a higher return on capital that the rest of the population? Does that mean that the rate of return on capital is positively related to capital owners’ initial age? May we extrapolate that trend to infer that, in a few decade, these people or their heirs will hold all of America’s capital? Lastly, should we impose a punitive tax on elderlies’ wealth to avoid that?

Quite obviously, the answers to these questions are — by order of appearance: no, no, no and no.

Simply, the youngest of all these people aged 65-74 in 1989 — assuming he hasn’t passed away — was 86 in 2010. By 1999, all of these people were either dead of in the 75+ age group: we are comparing the net worth of two completely different groups of people. As a consequence, it doesn’t tell us anything about the rate of growth their capital has experienced, it doesn’t mean by any way that the elderlies benefits (or even have benefited) from higher returns than younger people and therefore any extrapolation (or political decision) based on these figures is plain bullshit.

Proof: it happens that most Americans aged 65-74 in 2010 were in the 45-54 age group in 1989. Using the same (elementary) logic we may build four vintages that presumably consist of the same people and measure how their mean wealth has evolved over time. Here are the results: the less-than-35 of 1989 (45-54 in 2010 [1]), have experienced a 9.9% annualized growth, the 35-44 (55-64) had 6.2%, the 45-64 (65-74) gained 2.9% and the net worth of the 55-64 in 1989 (75+ [2]) only grew by 1.3%. That is, the elderly we meant to tax today because they were making too much money from their capital basically experienced the lowest returns.

So this kind of reasoning is completely meaningless. It’s just like if you were compering the average size of NBA players in 1989 and 2010, finding that it grew more than the average size of the U.S. population and concluding the taller one is, the faster he grows. It’s stupid.

As a matter of fact, the mean wealth of the x% wealthiest as grown faster than the mean wealth of the whole population. That’s true. I don’t even need to find data and compute anything to confirm that for any small values of x (say below 10%), the x% today is richer than the x% one, two, three or four decades ago. This happens because the overwhelming majority of people living on that planet actually got richer over the past decades.

Now does that mean that the annualized growth between the mean wealth of the x% — say — twenty years ago and the mean wealth of the x% today equals the average growth rate of the wealth of the x% over the last two decades. Absolutely not. It’s a complete fraud unless you prove you’re talking about the same people (or their heirs [2]). It’s just like the elderlies: the more the group has changed, the less your conclusion holds. Maybe all of the members of the x% in 1987 lost all of their fortunes and where replaced by a brand new x% made of young entrepreneurs who made their through the ranking. Think about it: does that fit with Piketty’s data? Yes, absolutely. Does that fit with his conclusion? Absolutely not: it’s the exact opposite.

So where is the truth? Well we don’t really know. Forbes says that most billionaires (the two third) are self-made men and that the proportion of heirs in the ranking is declining — not rising — steadily and people like Lawrence Summers have pointed out similar patterns in the Forbes 400. To be sure, the size of these samples is way too small to draw any definitive conclusion but it’s still more significant than the “Forbes is biased” argument.

Anyway, wherever you sit in the “heirs vs. entrepreneurs” debate, you have to admit that entrepreneurs exist. Even if you think that they only represent a small and declining share of the x%, you can’t deny that some people built their current fortune during their lifetime. So there is turnover in the x% which means that some people get out that group and are replaced by other who get in. Well, believe it not, there is a direct relationship between the level of that turnover and the amount by which the mean wealth of the x% outperforms the mean wealth of the whole population. That is, the less we live in a Piketty world (e.g. the higher the turnover amongst the x%), the faster the x% should enrich themselves relative to the rest of us.

This happens because of a well-known statistical bias called the survivor bias. Let me explain: imagine that, over a given year, just one wealthy man leaves the x% and is replaced by another one. It might happen because he lost money or because the made less money than others. At the end of the year, his declining fortune will impact the mean of the whole population but, since he didn’t “survived” in the x% (hence, the name), it won’t have any effect on the mean wealth of the x%. That is, comparing the mean wealth of the x% through time is an implicit selection process where you only select the winners and forget the losers [4].

In other words, there are two ways to explain why the mean wealth of the x% has grown faster than the mean wealth of the whole population. According to Piketty, it means that the richer you are in the first place, the faster your capital grows over time (hence, the dynastic wealth world he foresees). But it might also be the opposite: this phenomenon is exactly what we should expect to see in a world of high wealth turnover, a world where fortune rewards skills, hard work and risk taking. Quite symptomatically, Piketty and its numerous followers have completely dismissed that possibility.

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[1] Remember these people are considered to be financially independent: most of the less-than-35 of 1989 were probably in the 25-34 range.
[2] Ok, some of the 75+ of 2010 were more than 85.
[3] By the way, Piketty thinks nothing may prevent inherited wealth to accumulate from one generation to another. There is at least one: people often have more than one kid.
[4] If not convinced, you may very easily simulate it using random wealth variations.

### ChallengeR #8 - Solutions

Votre mission consistait donc à trouver un moyen de faire en sorte que : > x == 0 [1] TRUE > x + 1 == 2 [1] TRUE > x / 2 == 1 [1...