Tolerance Limits and Expected Utility Analysis

Abstract

Virtually all applied work in the economics of uncertainty has used the expected utility framework (Machina). In agricultural economics, expected utility analysis has been applied in many studies involving agricultural production (Anderson), pest management strategies (Musser, Tew, and Epperson), rural bank portfolio behavior (Robison and Barry), and farm policy (Kramer and Pope). These empirical analyses follow one of two general approaches. The first is comparison of expected value and variance of net returns from alternative risky prospects and is usually referred to as meanvariance or EV analysis. The second, stochastic dominance (or efficiency) analysis, involves comparing probability distributions of net returns (or other monetary outcomes) from risky decision alternatives. In both, the underlying probability distribution for net returns is estimated either directly (stochastic efficiency) or implicitly (EV analysis). Risky alternatives are then compared on the basis of the expected utility they generate. In this paper, we determine the degree of confidence, in a probabilistic sense, that can be placed in estimated distribution functions used to estimate expected utility and order risky prospects. Tolerance limits are defined and used to show how an investigator can determine the probability that a specified proportion of the underlying probability density is within a particular range of the sample data. Tolerance limits for the entire distribution are presented for specific sample sizes. These values can be used to measure the statistical confidence one can have in estimated distribution functions for expected utility analysis. In some circumstances, we can be reasonably confident that results based on estimated distribution functions will actually hold for the unknown, underlying population distributions.