One of the issues with economic reality, as distinct from economic models, is that there are many types of income and cost risks that are not insurable, so you self-insure as best as you can. In the two-minute version of Modigliani's life-cycle model that Brian presented, we didn't get to one of those risks that may be hard to insure against, which is length of life (income needs are greater if you live that much longer). If your assets are entirely in the form of annuities that expire at end of life, such as social security, that provides such insurance. Most of us, however, will keep some substantial amount of our wealth in non-annuity form. Then you can undershoot or overshoot on how much to save for retirement. If you overshoot, presumably that adds to the estate and gets distributed to the heirs, not a terrible outcome in most cases. If you undershoot, the outcome can be much grimmer.
So the thought is that the adult children might provide such self-insurance and do so by saving for their parent's retirement. (Have some joint or trust account and give annual gifts into that account.) This might very well substantially increase the kid's motive to save. And with that let me bring in the title of this post and the notion that the dads in particular but probably both parents are tightwads. If that is so, then the typical moral hazard problem probably won't be manifest - the parents won't spend out of these funds unless they really need to do so. And if they don't need it, they bequest that saving back to you after they pass away (and if it is a concern, not to your siblings who perhaps didn't contribute likewise). In the meantime they've turned you into tightwad kids, which may be the best gift they could give you.
This would all happen naturally if the extended family lived under one roof. It may seem less natural when the family is scattered, but there is no reason it shouldn't happen even then.
And with that let me return to academic concerns and mention Samuelson's famous paper on An Exact Consumption-Loan Model.... which developed an analytic framework called an overlapping generations model and provided a theoretic rationale to pay-as-you systems like Social Security, where the younger generation makes a payment to the older generation that improves overall welfare, provided the next and each subsequent generation does likewise. (The model is deceptively simple. The math is quite hard because there are an infinite number of consumers and an infinite number of goods in the model .) There is no government in the model. The payment could happen because it becomes a social norm to do so. My suggestion above, meant seriously, makes sense if your kids (that most of you don't yet have) will do likewise for you when they come of age.
My tweak on Samuelson is that it's the income insurance that's needed, not the overall level of saving to be changed, but that if you did the one as I suggest you would create a nudge for the other and overall saving rates would rise. Something to ponder as we head into the holiday.
Have a good spring break.