An experimental test for stability of the transformation function in rank-dependent expected utility theory and order-dependent present value theory

We propose and analyze a generalization of present value maximization, 'time-order dependent present value (TODPV),' for intertemporal income choice. The model is analagous to the rank dependent expected utility model (RDEU) for choice under risk. The main feature of interest in the model is the 'payment transformation function,' which operates on proportions of a fixed total of payments just as the probability weighting function in RDEU operates on probabilities. These models can accomodate many choice patterns, for both risky and intertemporal choice, so we conduct experiments in an attempt to (i) measure the structure of preferences over lotteries and intertemporal income streams and (ii) test for stability of the probability and payment transformation functions over different choice sets. The design is based on manipulations of the 'probability triangle' and the 'intertemporal choice triangle.' If, as in many previous studies of the RDEU model, a representative agent approach is taken, then the average preference structure in both the domain of risky choice and the domain of intertermporal choice can be characterized as 'homothetic' in the respective choice triangles. This implies a strictly concave transformation function, and is at odds witht the finding of an 'inverted S' shaped function that many researchers have suggested for the RDEU model. Individual analysis reveals considerable heterogeneity of preferences. A disaggregated analysis in which we classify subjects according to which transformation function is most consistent with their revealed choice behavior shows that a linear and a strictly concave transformation function are the most common for both risky choice and for intertemporal choice. Direct estimation of the transformation function is consistent with this classification. In particular, there is no evidence of an inverted S-shaped transformation function for choice under risk, contrary to several previous studies. The difference between our results and those of previous studies can be mainly attributed to the choice of functional forms used in estimating the transformation function, or to the limited space of lotteries upon which estimates have been based.