This paper deals with derivation and estimation of the risk preference function in the presence of output price uncertainty. The derivation depends neither on a specific parametric form of the utility function nor on any distribution of output price. The risk preference function is flexible enough to test different types of risk behavior (e.g., increasing, constant, and decreasing absolute risk aversion). We also test for asymmetry in the distribution of output price, which appears in the risk preference function. Moreover, we allow heterogeneity in production technology. Parameters of production technology and risk preference function are jointly estimated using the system of equations derived from the first-order conditions of expected utility of profit maximization and the production function. The estimated parameters of the risk preference function are used to calculate absolute, relative, and downside risks for each producer. A panel data on salmon farming from Norway is used as an application.
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Subal C. Kumbhakar (2002) studied this question.