Precautionary effect and variations of the value of information

Consider an agent taking two successive decisions under uncertainty. After his first decision, a signal is revealed providing information about the state of nature and the second decision is taken accordingly. Suppose that the agent is an expected utility maximizer. The precautionary effect holds when, in the prospect of future information, his optimal initial decision is less than without (no signal). Indeed, the first decision is usually a scalar representing consumption, so that pre- caution is identified with less consumption. We introduce the second-period value of information as a function of the initial decision and show that, when this func- tion is decreasing, the precautionary effect holds true. More generally the condition enables the comparison of optimal decisions related to different signals, not necessarily comparable. It also ties together and clarifies many conditions for the precautionary effect that are scattered in the environmental economics literature. A practical illustration with Nordhaus’ DICE model is provided.