On Time Discounting, Impatience, Precaution, and Risk Aversion

We study the association (under expected utility) between time discounting and risk aversion, in light of two different possible explanations for time discounting: impatience - defined as the discounting of sure outcomes even under non-changing circumstances, and precaution - defined as discounting due to uncertainty associated with the future. Regarding impatience, we show that even under weak stationarity assumptions and even for a finite number of time periods, impatient certainty preferences uniquely determine the lottery preferences, thus precluding an independent attitude towards risk. Regarding precautionary time discounting, we first show that this element of discounting can be disentangled from the risk-free inter-temporal marginal rate of substitution. We then analyze the determinants of precautionary discounting, establishing how it is determined, among other factors, by the different characteristics of the decision maker’s risk attitude, e.g. risk-aversion/risk-seeking, CARA, DARA. The implications to life cycle preferences are briefly discussed.

Yonatan Aumann's homepage: https://sites.google.com/site/aumannbiu