Abstract
The Arrow–Pratt index, a gold standard in studies of risk attitudes, is not directly observable from choice data. Existing methods to measure it rely on parametric assumptions. We introduce a discrete Arrow–Pratt index, and its relative counterpart, that can be directly obtained from choices. Our approach is general: it is (i) non-parametric, (ii) applicable to both risk and uncertainty, (iii) and robust to probability transformation, non-additive beliefs and multiple priors. Our index can also be used to characterize various decision models through various simple consistency requirements. We analyze its properties and demonstrate how it can be measured.
Highlights
Arrow–Pratt index can be viewed as the gold standard for the study of risk attitudes (Machina 1982) under expected utility
This paper introduces a discrete approximation of the Arrow–Pratt index that is obtained from two indifferences
We have established that the discrete Arrow–Pratt index can be consistently defined for an interval under expected utility, and that the same holds for the robust version under biseparable utility
Summary
The (discrete) rate of substitution of good for good (represented by the cord) is r1 −r2 m−x on the first indifference curve. Baillon et al (2012) used such a setting, in which the change of good 2 is kept constant across indifference curves, and interpreted diminishing rates of substitution to mean m being closer to x than to y. A discrete Arrow–Pratt index of [x, y] if m is a preference midpoint of [x, y]. There may be many discrete Arrow–Pratt indexs of [x, y]. The definition is most useful if there is only one such, and this case is analyzed in the subsection
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