Precautionary saving in the presence of labor income and interest rate risks

This paper deals with the classic issue of precautionary saving in a standard two-period setting. The literature has identified conditions on the individual’s utility function under which either labor income uncertainty or interest-rate uncertainty can lead to positive precautionary saving. We allow for both sources of uncertainty simultaneously. We extend the Jensen inequality from one risk to two positively quadrant dependent risks. The main result of the paper is that “positive quadrant dependent” uncertainty raises saving if and only if “partial relative prudence” is larger than 2. We characterize the condition that “partial relative prudence” exceeds 2 via preferences over simple binary lotteries, in the style of Eeckhoudt and Schlesinger (Am Econ Rev 96:280–289, 2006).