INTERPRETATIONS AND TRANSFORMATIONS OF SCALE FOR THE PRATT-ARROW ABSOLUTE RISK AVERSION COEFFICIENT: IMPLICATIONS FOR GENERALIZED STOCHASTIC DOMINANCE: REPLY

The Pratt-Arrow measure of absolute risk aversion, as defined by r(x) = -u"(x)/u'(x), is well known to be invariant to linear transformations. However, this invariance property applies with respect to transformations of u and not with respect to arbitrary rescalings of the outcome variables, x. The effects of this misunderstanding has led to ambiguity in classifying attitudes by risk aversion coefficients. It is shown that inappropriate rescalings of the outcome variable can lead to inaccurate rankings produced by generalized stochastic dominance. The Pratt-Arrow absolute risk aversion coefficient (Pratt), defined as r(x) -u"(x)/u'(x), has been used in many analyses which order alternative action choices under conditions of uncertainty (Cochran, Robison, and Lodwick; Cochran et al.; Danok, McCarl, and White; Holt and Brandt; King and Lybecker; King and Oamek; Kramer and Pope; Lemieux, Richardson, and Nixon; Meyer 1977b; Rister, Skees, and Black; Tauer 1985; Wilson and Eidman 1985; Zacharias and Grube). Problems arise, particularly in applications of generalized stochastic dominance (or stochastic dominance with respect to a function-SDWRF) (Meyer 1977a) when Pratt-Arrow coefficients elicited in one study are used as secondary data in other studies with different outcome ranges. It is well known that the Pratt-Arrow measure is invariant to linear transformations (King and Robison, p. 512). However, this invariance property applies only to transformations of u

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