Estimating Knightian Uncertainty from Survival Probability Questions on the HRS *

Since Frank Knight (1921) introduced the distinction, economists have recognized that risk is the special case of uncertainty in which probabilities are known. Based on subjective survival probability questions in the Health and Retirement Study we use an econometric model to estimate the determinants of individual-level uncertainty about personal longevity. This model is built around the Modal Response Hypothesis—a mathematical expression of the idea that survey responses of zero, one-half or one to probability questions indicate a high level of uncertainty about the relevant probability. Our results indicate that poor cognition and poor health are associated with increases in uncertainty about survival. To be Presented at Session on “Subjective Probability Distributions” American Economic Association Meetings, January 7-9, 2005Philadelphia Michael Hurd, Chair JEL Code C.4. Econometric and Statistical Methods: Special Topics _______________________ *A highly preliminary and incomplete versions of this paper was presented in a meeting organized by Daniel McFadden for the 6 Invitational Choice Symposium, Estes Park, Colorado, June 5-8, 2004 and at a workshop at the University of Washington, Seattle, on November 19, 2004. This version was presented at "Labor and Social Interaction in Economics" A Conference in Honor of Yoram Weiss' Sixty-Fifth Birthday The Eitan Berglas School of Economics, Tel-Aviv University, December 16 th -17 , 2004. We are grateful to grant U01-AG09740 from the Behavioral and Social Research Program of the National Institute on Aging for supporting the collection of the HRS data used in this paper and to grant R01-AG020638 for partial support of the research for this paper. Since Frank Knight (1921) introduced the distinction, economists have recognized that risk is the special case of uncertainty in which probabilities are known. Conventional economic theory, rooted in subjective expected utility (SEU) theory, is often interpreted as having erased this distinction so that evidence that individuals dislike uncertainty, such as the Ellsberg Paradox (Ellsberg 1961), is taken to be evidence against SEU theory itself and has provided a rationale for the development of non-expected utility theories. (See Starmer, 2000, for a survey.) However, recently Lillard and Willis (2001) and Kezdi and Willis (2003) have shown that Knightian uncertainty, as distinct from risk, may play an important role within conventional SEU theory whenever uncertainty pertains to an environment in which an individual will be subject to repeated risks. For example, in such environments, a mean-preserving spread in subjective uncertainty about the rate of return leads risk averse households to choose portfolios with smaller risk. More generally, increased uncertainty will influence choices whenever probabilities enter the objective function non-linearly. The goal of this paper is to use data on survival expectations elicited by questions in the Health and Retirement Study (HRS) to estimate the distribution of an individual’s beliefs about the probability of survival to a given age. For example, for persons younger than age 70, the survival question that we analyze in this paper is: “Using a number from 0 to 100, what do you think are the chances that you will live to be at least 80? ” In our analysis, we will develop and estimate an econometric model which allows us to use responses to these questions to study the determinants of subjective expected survival probabilities and the degree of subjective uncertainty about these probabilities. 1 See Manski (2004) for a survey of methods of eliciting subjective probabilities. 2 For persons older than 69, the target age is increased to 85, 90, 95 and 100 for individuals in successive five year age intervals so that the target is never closer than ten years in the future.