OLG models with QH discounting to examine intergenerational investments and returns

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I came across this paper titled “Hyperbolic discounting in an intergenerational model with altruistic parents”. It is close to, but not exactly what I’m looking for, which is a quasihyperbolic discounting model that builds a general equilibrium around middle-aged generations funding a younger generation’s education and early-career opportunities (including entrepreneurial efforts and positive fertility decisions) that, in turn, create a sufficient tax base to better fund the pensions of longer-lived older generations.

One key idea to explore is the extent to which children, with their long expected lifespan, act as a high-gain return option when given sufficient early support, creating the kind of prosperity that can continue into old-age. While “classic” VFI will find the economic optima showing just how much present-minded agents should invest when to ensure their future-self satisfaction, the nature of human may be better modeled with QH discounting, leading to greater insight as to how much additional incentive is needed for medium to high earners to “do the right thing”.

And perhaps it can be shown that in some cases, the social cost of such incentives can themselves collapse the ultimate social gain, much like the gravity of a black hole prevents the escape of light. This sort of economic event horizon could explain “why we can’t have nice things” if we rely solely on pecuniary values rather than “enlightened self-interest” (and the “value” that such enlightenment offers to the members of its economy).

Any pointers?

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Just to comment that there is such a thing as “Dynastic OLG” models in which you have the ‘parent’ caring for the ‘child’ in the sense that they get some fraction of whatever the child’s utility is [but you make the model so that the child only ‘appears’ at the end of the parents’ life, so they are never both alive at the same time]. When you allow both the parent and child to be alive simultaneously and take this into account things get tricky because it becomes a dynamic game (so the equilibrium concept is much more complex).

PS. There have been a lot of improvements to Quasi-Hyperbolic discounting in the toolkit. It now works for almost any finite horizon value fn that you can write down.

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