Empirical Utility Functions and Insurance Consumption Decisions

In order to investigate the usefulness of the von Neumann-Morgenstern utility concept in an actual decision making context, 30 subjects were interviewed. Their responses to questions were used to acquire a utility function which was then incorporated in a deductible selection model. The utility function was found to have little external validity either when used to predict choices between two lotteries or in hypothetical insurance consumption decisions. Used in this model it did, however, appear to be slightly more useful in describing actual deductible selections when compared with an expected monetary value model. An effort was made to determine the influence of personal variables on the deductible selection decisions. Using chi-square tests it was determined that the level of deductible is related to the individual's subjective probability-of-loss estimate and his income tax bracket. Utilization of the variables in stepwise regression and discriminant analyses yielded insignificant results for all variables. The question of whether utility functions are amenable to use in actual decision-making contexts has been the subject of considerable debate. Reflecting those who disparage its value, Houston states:1 Modem decision theory represents an important breakthrough or contradiction of the traditional interpretation of utility. However, it is only fair to note that many regard the theory as non-operational in all but the most trivial cases. Representing a more optimistic viewpoint are Friedman and Savage who note:2 Michael L. Murray, D.B.A., is Assistant Professor in the College of Business Administration of The University of Iowa. This paper, funded by a research grant from A.R.I.A., was presented at the 1971 Annual Meeting of A.R.I.A. 1 Houston, David B., "Risk, Insurance and Sampling," Journal of Risk and Insurance, December, 1964, pp. 522. 2 Friedman, M. and L. J. Savage, "The Utility Analysis of Choices Involving Risk," The Journal of Political Economy, August 1948, reprinted in Whether a numerical utility function will in fact serve to rationalize any particular class of reactions to risk is an empirical question to be tested; there is no obvious contradiction as was once thought to exist. This paper reports the result of a continuing effort to determine empirically the usefulness of utility3 functions in an actual decision context. The decision which is being analyzed is the selection of an automobile collision insurance deductible. This decision is viewed in both a descriptive and a normative manner. In the descriptive vein, a number of personal variables of the respondents to the study are analyzed for their ability to predict the Hammond, J. D. (ed.), Essays in the Theory of Risk and Insurance, Scott, Foresman and Co., Glenview, Illinois, 1968, pp. 97. 3The utility concept which is used in this paper and which is referred to in the two previous quotations is that which is referred to as "4von Neumann-Morgenstern utility" as developed in their landmark work: von Neumann, John and Morgenstem, Oskar, The Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944, pp. 1-31.