This paper studies the effect of the space (distance) between lotteries' outcomes on risk-taking behavior and the shape of estimated utility and probability weighting functions. Previously investigated experimental data shows a significant space effect in the gain domain. As compared to low spaced lotteries, high spaced lotteries are associated with higher risk aversion for high probabilities of gain and higher risk-seeking for low probabilities of gain. Hence, the investigation is carried under cumulative prospect theory that respects framing effect and characterizes risk attitudes with respect to probabilities and outcomes. The observed certainty equivalents of lotteries are assumed to be driven by cumulative prospect theory. To estimate the parameters of cumulative prospect theory with maximum likelihood, the usual error term is added. The cumulative prospect theory is incapable of explaining the space effect as its parameters cannot explain the average behavior. Taking account of heterogeneity, a two-component mixture model shows that behavioral parameters of around 25% of the sample can explain the observed differences in relative risk aversions. The results confirm the previous findings of aggregation bias associated with representative-agent models. Furthermore, the results have implications for experimental designs as high space between lotteries' outcomes is required to guarantee the curvature of utility functions.
