Impatience and Sex

What does a biological perspective imply about impatience? The rate of mortality will contribute to impatience, as is thunderingly obvious, and well-known in economics, certainly since Irving Fisher. A specifically biological contribution is the rate of population growth. If population is growing, then a reproductive strategy that entails the earlier production of offspring would be smiled upon by evolution. Consider a population in which all individuals produce 4 offspring at age 2. The population quadruples in two periods or, equivalently, doubles every period. A type that produced these 4 offspring at age one instead would do much better, quadrupling every period.

However, back-of-the-envelope calculations suggest that the sum of the mortality rate and the population growth rate may be inadequate to produce a plausible pure rate of time preference. That is, even for hunter-gatherers, mortality may be  only 1-2% for most ages, for those who are not on the walls-of-death at the beginning of life or at the end. And the rate of population growth over the 1.8 million years of our evolutionary history must be close to zero, as an arithmetical necessity. However, the pure rate of time preference seems likely to be more than 1-2%.

One approach to closing the apparent gap is to suppose the average population growth rate of near zero cloaks a more dramatic detailed scenario. Perhaps, for example, there are long runs of peace and plenty generating substantial population growth. Occasionally, however, there are random demographic disasters of biblical proportions. Suppose these disasters are equal opportunity grim reapers, wreaking the same proportionate damage on all ages. Larry Samuelson and I (AER, 2009) show that the relevant rate of population growth is the rate that obtained during the sunny eras of peace and plenty, thus potentially closing the gap.

Another mechanism to close the gap is sex, finally validating the title of this post. (Thanks for your patience ;). Sorry if you were expecting something more lubricious.) This idea was formulated by an anthropologist, Alan Rogers (AER, 1994). Although there are mathematical difficulties with Alan’s model, and not all plausible models deliver the desired result, the intuition can be resuscitated. (This paragraph relies on work with Balazs Szentes.) This intuition is as follows. A prime motivation for saving for the future is to favor offspring. However, sexual reproduction means that each offspring has a value that is only 1/2 of each parent’s value. This is an instance of “Hamilton’s rule” from biology, but is also, more familiarly, the free-rider problem. That is, offspring are a public good to each couple, and there is a temptation for each parent in the couple to undercontribute.