By Winfried Koeniger and Carlo Zanella
http://d.repec.org/n?u=RePEc:iza:izadps:dp15073&r=dge
We analyze how intergenerational mobility and inequality would change relative to the status quo if dynasties had access to optimal insurance against low ability of future generations. Based on a dynamic, dynastic Mirrleesian model, we find that insurance against intergenerational ability risk increases in the social optimum relative to the status quo. This implies less intergenerational mobility in terms of welfare but no quantitatively significant change in earnings mobility. Earnings mobility is thus similar across economies with different incentives and welfare, illustrating that changes in earnings mobility cannot be interpreted readily in welfare terms without further analysis.
I must confess that I have a hard time buying that it can be socially optimal to insure successful people against the failures of their offspring. It is natural that talent and entrepreneurship regress to the mean over generations, and successful dynasties insure themselves against that risk by building wealth and buying education and entrance into the right circles. Why would society subsidize that if it leads to lower aggregate outcomes? I think the issue is that when we think about an untalented rich kid going to a top school, it is taking away the spot of a talented poor kid, thus hurting the social outcome. There is not such trade-off in the model. Or maybe I am just confused, there are a lot of margins in play here.
NEP-DGE Blog 
Thanks for the comments.
Here are some thoughts on your remarks.
It is true that dynasties self insure themselves via wealth accumulation and education investment for their offspring.
In fact, that is exactly what we model.
The point is whether these actions are socially optimal in the current status quo.
They are not if one accounts for plausible frictions such as uninsurable risk and borrowing constraints, which is what we do in our analysis.
Moreover, current generations may not put the same weight on the welfare of future generations as society.
So, in these circumstances the subsidies we characterize come into play and they improve the aggregate outcome (given that they implement the social optimum).
he trade-off you mention (“when we think about an untalented rich kid going to a top school, it is taking away the spot of a talented poor kid”) is in fact captured in our analysis, at least to some extent, because we account for borrowing constraints when modeling the status quo.
So, some families without sufficient resources may indeed not be able to choose the socially optimal investment for their able offspring.
The subsidies, which implement the social optimum, relax such financial constraints.
In our analysis we also answer the question whether asset accumulation rather than education investment should be subsidized, depending on the ability of the parents and their offspring.
I hope this clarifies.