A user’s guide to economic utility functions

Abstract

Economic modeling of behavior under uncertainty has almost exclusively used one of two approaches. First comes the mean–variance tradeoff, central to the financial economics literature. The alternative approach uses a specific function to assess expected utility. In this approach, almost all of the economics literature has used either the exponential utility (EU) function, with constant absolute risk aversion (CARA) or the power utility (PU) function with constant relative risk aversion (CRRA). Using a Taylor Series expansion, I show that higher-order terms (skewness and kurtosis) can significantly affect estimates of expected utility. I provide specific formulaic guidance allowing economists to assess when these terms become important. This guidance uses readily observable parameters such as mean, median and variance in a wide array of non-Gaussian statistical distributions. I next review two generalizations, one for CRRA utility, hyperbolic absolute risk aversion (HARA), and one for CARA utility, exponential power (EP). I then introduce the possibility of risk-seeking behavior, both in standard economic theory and in the “value” portion of prospect theory (PT), and provide a new Generalized Logistic Utility (GLU) that automatically incorporates such behavior in its functional form. Next, I introduce issues involved in modeling utility that includes a non-marketable component such as health, the environment, or altruism, and discuss how the choice of utility function alters these models. I then assess the choice between exact utility functions and Taylor Series approximations. I conclude by discussing methods to estimate utility function parameters and methods to choose among alternative estimates.

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