We examine the evolutionary foundations of intertemporal preferences. When all the risk affecting survival and reproduction is idiosyncratic, evolution selects for agents who maximize the discounted sum of expected utility, discounting at the sum of the population growth rate and the mortality rate. Aggregate uncertainty concerning survival rates leads to discount rates that exceed the sum of population growth rate and death rate, and can push agents away from exponential discounting. (JEL D11, D81, D91)
We reexamine Alan R. Rogers' (1994) analysis of the biological basis of the rate of time preference. Although his basic insight concerning the derivation of the utility function holds up, the functional form he uses does not generate equilibrium evolutionary behavior. Moreover, Rogers relies upon an interior solution for a particular kind of intergenerational transfer. We show such interior solutions need not generally arise. Hence Rogers most striking prediction, namely that the real interest rate should be about 2 percent per annum, does not follow. (JEL D11, D91)
Where do preferences come from? What determines their properties? Though traditionally reluctant to ask such questions, economists have recently turned to evolutionary models for answers. We focus on intertemporal preferences here, arising out of the evolutionary implications of different reproductive strategies or life histories. An agent’s life history specifies the agent’s number and timing (and in a richer model, quality) of offspring. Evolution will select the life history that maximizes the growth rate of the associated group of individuals. We begin with the simplest possible biological life history, that of a semelparous agent that, if it survives a fixed number of years, reproduces and then dies. We show the evolutionary criterion for success in this case entails hyperbolic time discounting of the log of the number of offspring produced. The rate of time preference is a function of age, however, not of time relative to the present, and there are no preference reversals in the sense of behavioral economics. At the same time, the optimal strategy maximizes the exponentially discounted number of offspring, provided we discount at the sum of the death rate and the maximal growth rate. Conventional discounting thus suffices to induce optimal choices from the agent. More generally, if the animal is iteroparous, that is, has a nondegenerate profile of offspring, we show the evolutionary indifference curves over offspring of various ages are hyperplanes that are not parallel, but tilt to reflect greater impatience as the growth rate increases. There is no additively separable function of the age profile of expected offspring that is globally equivalent to this basic biological growth-rate The Evolution of Intertemporal Preferences
The economics of hunting and gathering must have driven the biological evolution of human characteristics, since hunter-gatherer societies prevailed for the two million years of human history. These societies feature huge intergenerational resource flows, suggesting that these resource flows should replace fertility as the key demographic consideration. It is then theoretically expected that life expectancy and brain size would increase simultaneously, as apparently occurred during our evolutionary history. The brain here is considered as a direct form of bodily investment, but also crucially as facilitating further indirect investment by means of learning-by-doing.