EFFICIENCY CRITERIA AND RISK AVERSION: AN EMPIRICAL EVALUATION

analysis. Variation in risk preference assumpA conceptual link among mean-variance tions are incorporated into a risk function by (EV), stochastic dominance (SD), mean-risk changing r, the Pratt-Arrow risk aversion co(ET), and Gini mean difference (EG) is estab- efficient in SD analysis, and oc, the exponent lished for determining risk efficient decision conditioning the degree to which segments of sets. The theoretical relations among the the associated density functions are to be emvarious efficiency criteria are then empirically phasized in ET and EG analyses. demonstrated with a soybean and wheat The objective of this paper is first to present double-crop simulation model. Empirical a collection of general results which provide a results associated with extended Gini mean conceptual link among the efficiency criteria, difference (EEG) and extended mean-absolute and to demonstrate empirically the varying Gini (EE) for risk analysis are encouraging. degrees of similarity among the criteria. Recommendations on the appropriate efficidifference. provided in a concluding section. EFFICIENCY CRITERIA In situations with unknown preferences, a Expected Value (EV) and Stochastic risk efficient set of decisions is determined Dominance (SD) based on an assumed preference relation and various approximations of decision probability Markowitz's EV analysis which employs the distributions. Numerous efficiency criteria first two moments of a density function as the specifying restrictions on preferences and criterion for ranking decisions is extensively probability distributions are prevalent in the employed in the agricultural economics literaliterature. Efficiency criteria popular in agri- ture. The efficiency criteria determining EV cultural economics literature include mean- for any two distributions F and G is that F variance (EV) and stochastic dominance (SD) dominates G if /F > yG and F < a2G hold with analyses, whereas mean-risk (ET) and Gini at least one strict inequality, where 0 and a2 mean difference (EG) analyses are generally denote a distribution's mean and variance, reless popular (Yitzhaki, 1982). spectively. Unfortunately, EV analysis may A necessary condition for one distribution to lead to unwarranted conclusions when the asdominate another, common to all of these cri- sumptions of normality or a quadratic utility teria under risk aversion, is expected value function are violated. EV analysis penalizes analysis where a comparison of the first decisions equally for deviations above and moment of the decision density functions is per- below the expected value which can be a shortformed. Necessary and sufficient conditions coming given an asymmetric distribution for various efficiency criteria differ based on (Selley). their representation of a risk function-a Baumol amends Markowitz's analysis by exmeasure of dispersion unique to each cri- plicitly considering confidence limits. The risk terion. Specifically, variance of a density func- involved in a given action choice is repretion is employed in EV, modified semivariance sented by k standard deviations, a, from the in ET, and Gini mean difference in EG mean, t, with k indicating the degree of risk