'My story is bunkier'

Wealthy French economist Thomas Piketty's latest cri du coeur also contains this;

Let me first say very clearly that r>g is certainly not a problem in itself.

Let us say, you could have fooled us, Tom. Say this, about 24 minutes into the conversation with Russ Roberts;

In any case, there are reasons to believe that we might again, have in the 21st century this inequality of developed countries and maybe also in emerging countries when they will have completed this catch-up process, we will have this inequality between r and g. Together with the final [?] that has increased inequality in r, this is one of the mechanisms that can contribute to explain relatively high and rising inequality of wealth.

Well, that's vieux chapeau. Today's news is;

In the real world, many shocks to the wealth trajectories of families can contribute to making the wealth distribution highly unequal.... There are demographic shocks: some families have many children and have to split inheritances in many pieces, some have few; some parents die late; some die soon, and so on. There are also shocks to rates of return: some families make good investments, others go bankrupt. There are shocks to labor market outcomes: some earn high wages, others do not. There are differences in taste parameters that affect the level of savings: some families consume more than a fraction 1-g/r of their capital income, and might even consume the full capital value; others might reinvest more than a fraction g/r and have a strong taste for leaving bequests and perpetuating large fortunes.

 Iow, just what Pikett's numerous critics have been saying all along (in this case Columbia's Xavier Sala y Martin);

Moreover, contrary to the claims of Piketty, the fact that r is greater than g implies neither the rich spend their savings on to their children, nor that wealth grows faster than GDP, or that rich dynasties are increasingly richer, or that social inequalities grow. 

Imagine, for example, a world in which individuals work when young and retire when old. Knowing that someday they will retire, so when young, save money and invest. When they are old they use their savings (and the rate of return on their savings) to survive. It's no longer a dollar inheritance to their children if they die with nothing. 

The children do the same as their parents and thus, generation after generation too. All economists know that in this world of "overlapping generations" the rate of return on capital, r, may be higher, exceeding the growth rate, g. If the economy is dynamically efficient, then it is true that "r> g" and yet, no one gets an inheritance! 

Unlike what Piketty says, logic does not dictate in any way, that "r> g" implies that inherited wealth grows faster than GDP, partly because inherited wealth can be exactly zero in worlds where "r> g"! 

In the real world, of course, the rich do not consume everything they have and leave part of their wealth in inheritance to their children. It is also true that for many of them an important part of that wealth is spent on lavish parties, boats, airplanes, luxury travel or philanthropic actions such as Bill Gates or Warren Buffet.