THE EVOLUTION OF TIME PREFERENCE WITH AGGREGATE UNCERTAINTY Running head: The Evolution of Time Preference

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. Department of Economics, Simon Fraser University, Burnaby, B. C., V5A 1S6 Canada, [email protected]; Department of Economics, Yale University, New Haven, CT, 06520-8281, [email protected]. Hillard Kaplan, Georg Nöldeke, Jeroen Swinkels, Claudia Valeggia, participants in numerous seminars, and three referees made helpful comments. We also thank the Canada Research Chair Program and the National Science Foundation (SES-0241506 and SES-0549946) for financial support. How much do people discount the future? How does their discounting change as they consider events further in the future? Perhaps more fundamentally, why do people discount at all? Irving Fisher’s (1930, pp. 84–85) pioneering study of intertemporal trade-offs called attention to one reason future rewards are discounted—an intervening death may prevent us from realizing such rewards. The possibility of death has played a recurring role in discussions of discounting (e.g., Menahem E. Yaari (1965)). Ingemar Hansson and Charles Stuart (1990) and Alan R. Rogers (1994) argue that evolution should select in favor of people whose discounting reflects the growth rate of the population with whom they are competing (see also Arthur J. Robson and Balazs Szentes (2007)). Putting these ideas together leads to models in which people discount at the sum of the population growth rate and the mortality rate. One difficulty with this argument is that the numbers don’t obviously match. Studies of contemporary rates of time preference have produced estimates as high as twelve to twenty percent per year (Emily C. Lawrance (1991)). Steffan Andersen, Glenn W. Harrison, Morton I. Lau and E. Elisabet Rutström (2008, Table III), arguing that estimated discount rates fall when correcting for the confounding effects of risk aversion, find (still surprisingly high) discount rates of about ten percent . In contrast, Michael Gurven and Hillard Kaplan (2007, pp. 330-331) use data from contemporary hunter-gatherers to estimate that annual mortality rates during our evolutionary history ranged from one percent for ten-year-olds to four percent for sixty-year-olds, while the average population growth rate over this two-million year period must have been approximately zero, suggesting discount rates of a few percent. A second issue is the growing evidence that intertemporal preferences exhibit a present bias not captured by the exponential discounting of standard models. This paper re-examines the foundations of intertemporal preferences. Like Hansson and Stuart (1990) and Rogers (1994), we view peoples’ preferences as having been Recent policy discussions, especially those regarding global warming, have focussed attention on the first question (e.g., William Nordhaus (2007)), while recent work in behavioral economics has directed attention to the latter (Shane Frederick, George Loewenstein and Ted O’Donoghue (2002)).