Estimating an Upper Bound on the Pratt Risk a Version Coefficient When the Utility Function Is Unknown*

Abstract

The use of stochastic efficiency techniques frequently requires knowledge of a risk aversion coefficient (RAC). For example, use of mean-variance programming models (for example. is the utility function at wealth level X . However, utility function estimates are not always available, can be expensive to obtain. are personalistic (thus, not necessarily applicable to groups of decision makers) and are sometimes of questionable reliability (for example, Whittaker and Winter 1980).In a situation where the resolution of risky choices is desirable and appropriate utility functions are unknown. incomplete rankings are often all that is possible without assumptions on R A G . Analysts facing rhis quandary have utilised RACs from other studies [for example, Holr and Brandt (1985) used the RACs from Kramer and Pope (I981)I. Such a procedure is questionable since individual characteristics influencing utility functions, the dispersion of the risky prospect, and wealth levels would change between studies. Furthermore, RACs have been used which have been too large (Grube 1986), and this can cause numerical difficulties [for example, in the programme implementing Meyer's (I 977) procedure, numerical overflows often occur because of large R A G , while expected value-variance models do not utilise all of their resources] or yield an excessiveiv large non-dominated set. Thus, needs arise for inferring the magnitude of the RAC when the appropriate utility function is not available. This paper provides formulae which satisfy these needs.RACs are needed either to aid in developing the 'best' risky prospects or to resolve choices among risky prospects. RACs aid in developing 'best' risky prospects when using techniques such as expected value-variance analysis where the RAC value is specified a priori. On the other hand, the RAC may be used expost after the risky prospects have been fully described to identify the dominant set. In the expost case, when dealing with known prospects, the RACs needed to rank these prospects can be developed utilising procedures such as those described by Grube ( I986), McCarl (1988) or Hammond (1974). Thus, in this paper attention is restricted to identifying bounds for a priori specification of the RAC.

Stochastic efficiency analysis of alternative basic grain marketing strategies

“…Thus, for any assumed level of α, r a (x) can be calculated. McCarl and Bessler (1989) state that  =2.5 are typically reported as the maximum value in applied MOTAD studies. Recently Conradie (2002) compared the observed crop mixes of 16 different farm types to those simulated with…”

“…Thus, for any assumed level of α, r a (x) can be calculated. McCarl and Bessler (1989) state that  =2.5 are typically reported as the maximum value in applied MOTAD studies. Recently Conradie (2002) compared the observed crop mixes of 16 different farm types to those simulated with (3) Equation (3) shows that the risk aversion parameter of the MOTAD model is equivalent to the r a (x) multiplied with the standard deviation of the risky prospect.…”

“…Thus, for any assumed level of α, r a (x) can be calculated. McCarl and Bessler (1989) Table 1 to describe the variability associated with the marketing strategies for each of the three crops. Mean price received: The mean price received from alternative grain marketing strategies is a primary indicator of their relative performance.…”

Risk management strategies using seasonal climate forecasting in irrigated cotton production: a tale of stochastic dominance

“…He proposed that in the absence of information on the risk aversion coefficient of the decision-maker(s) this method is suboptimal, as it does not identify points at which decision-makers change their preferences between options. McCarl and Bessler (1989) raised concerns about the size of the RAC bounds used to define efficient sets in the absence of knowledge about the utility function of the particular decision-makers under study. Under the assumptions of a constant absolute risk aversion utility function, finite number of mutually exclusive prospects, discrete distributions and data-free sampling error, McCarl (1988) developed a procedure to calculate ranges of the risk-aversion parameter where individuals prefer one risky outcome above others.…”

Using a Crop Simulation Model to Understand the Impact of Risk Aversion on Optimal Irrigation Management

“…Indeed, varied estimates of the risk aversion coefficient are not surprising because those studies most likely used different samples of farmers. McCarl and Bessler (1989) argued that the use of risk aversion coefficients estimated from other studies is not appropriate because every study uses different utility assumptions and net returns levels.…”