Land Allocation under Uncertainty for Alternative Specifications of Return Distributions: Reply

Abstract

The relevance and usefulness of mean-variance portfolio analysis is not a point we wish to question. For roughly thirty years, this analysis has been a cornerstone of financial and production analysis under risk. Our goal is to delimit circumstances in which it can be straightforwardly applied and those where some modification may be necessary. Before addressing Tew and Reid (TR) regarding the empirical illustration in Collender and Zilberman (CZ), we review the CZ contribution. CZ is concerned with resource allocation under uncertainty in the context of nonnormal returns. Much empirical evidence is available to suggest that agricultural decision makers frequently make decisions under such circumstances.' Literature supporting this view is cited in CZ. Since CZ was published, Buccola has concluded that the chance of encountering approximately Gaussian returns in reasonable agricultural situations is small. Having established the relevance of the problem, our contributions a~e twofold. First, we develop a decision-making technique that does not impose counterfactual assumptions. Second, we develop a test for the statistical significance of losses in expected utility resulting from the counterfactual imposition of the mean-variance framework. The first contribution is accomplished through the development of the EUMGF approach. The approach facilitates decision making consistent with expected utility maximization without imposing normality of returns. The relaxation of this assumption is consistent with empirical evidence. The second contribution is accomplished by developing a test statistic for differences in expected utility. CZ and the subsequent article by Collender and Chalfant illustrate that one can use the EUMGF approach to determine if departures from normality are relevant in the decision-making process, given the risk preferences of the decision maker. CZ do not contend that departures from normality are always important, just that they may be. This is more likely true as partial risk aversion increases and/or distributions depart further from normality.