Risk aversion and the value of information

It is widely believed among economists and businessmen that increases in risk or in risk aversion should increase the value of information for decisionmakers. For instance, one suspects that risk-averse farmers should be willing to pay more for improved weather forecasts than risk-neutral ones. Similarly “defensive medicine’’ (i.e., the excess ordering of almost useless diagnostic tests) is often attributed to a risk-averse behavior by physicians. This widespread belief about a monotone relationship between the value of information and the degree of risk aversion has resisted accepting important theoretical contributions that have shown the possibility of a reverse relationship. Gould (1974) established the lack of unambiguous relationship between the degree of risk and information value. Freixas and Kihlstrom (1984) showed that information demand may decrease with the degree of risk aversion, and their result was reiterated in a different context by Willinger (1989). Unfortunately these important contributions did not have a wide impact because they were rather technical. The exception is a survey paper by Hilton (1981) who examined properties of information value. Among many other results, he showed, with the help of a very short numerical example, that an increase in risk aversion may indeed lead to a lower information value. However, he did not give the intuitive reason that justifies this surprising result. Our purpose is to explain precisely, in as simple terms as possible, why more risk aversion does not always induce a greater information value. We present the basic model, and we define the concept of (perfect) information value. A detailed numerical illustration is provided.