Negligible senescence: An economic life cycle model for the future

Abstract

We propose a model of aging and health deficit accumulation model with an infinite time horizon and a steady state of constant health. The time of death is uncertain and endogenous to lifestyle and health behavior. This setup can be conceptualized as a strive for immortality that is never reached. We discuss adjustment dynamics and show that the new setup is particularly useful to understand aging of the oldest old, i.e. of individuals for which morbidity and mortality have reached a plateau. We then show how the existence of a steady state can be used to perform comparative dynamics exercises analytically. As an illustration we investigate the effects of more expensive health investment and of advances in medical technology on optimal short run and long run health behavior.

Fetal origins—A life cycle model of health and aging from conception to death

“…The equation of motion implies that individuals of better health (represented by greater H) experience a faster deterioration of their health (greater δH). This feature of self-depreciation (Dragone & Vanin, 2020) provides convergence: initial differences in health are depreciated away as individuals grow older such that differences in early-life development fade away and (asymptotically) do not matter in old age.…”

“…It captures the empirically observable process of health deficit accumulation as _ D ¼ μðD þ EÞ, in which D is health deficits, μ is the force of aging, and E measures influences on deficit accumulation that are not captured by the current state of health. The crucial feature is that the health deficit model is self-productive (Dragone & Vanin, 2020): the presence of many health deficits is conducive to the faster development of new deficits. This feature implies shock amplification: individuals with (small) initial health differences experience faster aging and develop more health deficits earlier in old age.…”

“…The exponential (or, more generally, convex) association of health deficits with age is a formal expression of the generality of biological aging understood as "intrinsic, cumulative, progressive, and deleterious loss of function that eventually culminates in death" (Arking, 2006). According to the terminology developed in Dragone and Vanin (2020), the accumulation of health deficits is a self-productive process: the presence of many health deficits is conducive to the faster development of new deficits. It is a natural outcome of theories of aging built on the redundancy and interdependence of health deficits such as reliability theory (Gavrilov & Gavrilova, 1991) and network theories of aging (Rutenberg, Mitnitski, Farrell, & Rockwood, 2018).…”

“…4 4 Prior life cycle models with endogenous longevity have been proposed by, among others, by Ehrlich and Chuma (1990), Forster (2001), Laporte and Ferguson (2007), Strulik (2015b), and Galama and Van Kippersluis (2019) within the health capital framework and by Strulik (2019), Strulik and Trimborn (2018), Dragone and Strulik (2020), and the studies referenced in footnote 1 within the health deficit framework. …”

The longevity society

“…This combination of increased time and age malleability implies changes in how individuals should behave over their lifetime. Having increased future time increases the value of investing in education, 26 health, 27 and financial savings. 28 Increased time also increases the value of enlarging one's options and delaying taking on commitments, which is consistent with marked changes in behaviour across the life course (table 2).…”