Philadelphia Reflections

Making Money With Math

Two themes run through the following modification of the Health Savings Account idea. The first is, we should seek ways to extend the period of time, during which compounding has a chance to work. The definition of forbidden perpetuity was created in the Seventeenth Century: one lifetime, plus 21 years. There is no reason why an American judge could not declare some other period of time to be a perpetuity, but this one has served for several centuries and therefore probably is at least as useful as any other. It seems to be an adequate compromise between fairness of inheritance, and Puritan encouragement of self-advancement through merit and industry. Longer than that would discourage the work ethic for descendants, and shorter than that would discourage the work ethic of elderly parents who might not live to be rewarded for late-life efforts. Perhaps other considerations were at work, but I personally feel no pressure to change the traditional definition. Therefore, the average longevity plus 21 years is here accepted as the limit of tax-exempt inheritance. It, therefore, sets a time limit we should accept when we are looking for the maximum return on a Health Savings Account; from birth to 105 years later, and a little longer if average longevity increases.

That's the first goal. The second is to create uniformity in the name of fairness and to use the uniformity to calculate the future. Obviously, people die at different ages, but the last year of life is the point beyond which everyone has less interest in accumulating money for himself, and the first year of life is the time when birth costs occur to everyone. So everyone gets his full life expectancy to calculate returns, and the average longevity is a surrogate for that. That leaves an extra 21 years, which we utilize, to include the grandparents in the family circle, permitting the idea that grandparents are funding grandchildren. Because American demographics reveal 2.1 children per mother, they result in one grandparent funding, one child. Thus, the stipulation that each person who dies must contribute one average grandchild's cost to the inheritance pool, in one way or another.

If you estimate the average rate of compounding accurately, you should be able to calculate the maximum income achievable by Health Savings Accounts. Somewhat less accurately, it is possible to calculate and make mid-course adjustments to, future reductions of health care cost for individual persons. If the maximum is known and adjusted for failure to contribute to the fund, it should be possible to calculate the incentive for continuing to fund or to borrow to fun, in the face of some household disruption. A sense of security is created. More than anything else, an incentive to save is created in the young. Furthermore, each subscriber can calculate the very large consequences of seemingly minor middle-man costs, and therefore resist them.

Finally, a consequence of this design is to maximize the lifetime income of the designated escrow fund. Not only is the duration of compounding stretched to its maximum, but it is aimed at stretching from childhood to the time of maximum health expense, usually the last year of life, and thereby getting the most out of the investment. Exceptions will of course occur. By using national averages, the bookkeeping cost is reduced. By using Medicare cost data, accuracy is enhanced. And by switching the cost-shifting to the reinsurance level from the (at present) largely hospital level, subscribers should barely notice it is happening.

Originally published: Thursday, November 12, 2015; most-recently modified: Thursday, May 23, 2019