I am re-reading Fisher’s The Genetical Theory of Natural Selection and was reminded of this passage that predates modern economic arguments about the evolution of the rate of time preference by over 50 years. For those who want to follow the maths, *m* is the Malthusian parameter (the relative rate of increase or decrease of a population), *l*_{x} is the number living to age *x*, and *b*_{x} is the rate of reproduction at age *x*:

In view of the close analogy between the growth of a population supposed to follow the law of geometric increase, and the growth of capital invested at compound interest, it is worth noting that if we regard the birth of a child as the loaning to him of a life, and the birth of his offspring as a subsequent repayment of the debt, the method by which *m* is calculated shows that it is equivalent to answering the question—At what rate of interest are the repayments the just equivalent of the loan? For the unit investment has an expectation of a return *l*_{x}b_{x}dx in the time interval *dx*, and the present value of this repayment, if *m* is the rate of interest, is *e*^{-mx}l_{x}b_{x}dx; consequently the Malthusian parameter of population increase is the rate of interest at which the present value of the births of offspring to be expected is equal to unity at the date of birth of their parent. The actual values of the parameter of population increase, even in sparsely populated dominions, do not, however, seem to approach in magnitude the rates of interest earned by money, and negative rates of interest are, I suppose, unknown to commerce.

Fisher’s result that time preference should reflect the population growth rate matches that of Hansson and Stuart, about which I have posted before. Fisher also notes that this outcome is not what we see. This is where we need to call on other ideas, such as aggregate risk.

## Author: Jason Collins

Economics. Behavioural and data science. PhD economics and evolutionary biology. Blog at jasoncollins.blog
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Have you seen Alan Rogers’ old paper on the evolution of time preference? Can be had at

http://harbaugh.uoregon.edu/Readings/Time/Rogers%201994%20AER,%20Evolution%20of%20time%20preference.pdf

I’ve been meaning to write a post on that paper for a while (it is on my reading list page) but there is another paper that argues that the math does not add up. I want to get across the two arguments before I give my two cents. Still, even with a mathematical problem, it’s an important paper.