Estimating Probability Risk Preferences: A Lorenz Curve Based Probability Weighting Function Approach

Abstract

The standard parameterizations of the probability weighting function confound the estimation of its fixed point and its shape as well as control its curvature with a single parameter. We derive a three-parameter probability weighting function based on Lorenz curves. This parameterization allows for independent estimation of the fixed point and for separate curvature estimates of the "bulge" and the "sag." We then test our probability weighting function in an experimental setting and analyze which factors influence individuals' probabilistic risk attitudes. The probability weighting function of our sample, in aggregate, follows the dominant empirical pattern of an inverse-S shape. As an individual's numeracy increases though, the curvature of her probability weighting function decreases. The fixed point differs with gender, with whether an individual is liquidity constrained, and with numeracy. Our sample of individuals does not appear to display more sensitivity to probability changes within the region of the bulge relative to probability changes within the region of the sag. Therefore, a single curvature parameter appears to be sufficient to characterize a heterogeneous probability weighting function in this choice context.