A Model of Delay Discounting that Generalizes Standard Models

The paper presents an unusually comprehensive empirical comparison of delay discounting/intertemporal choice models. A three-component model is developed, with power laws modeling subjective time, subjective money, and magnitude sensitivity. It nests several other models in the literature, among others: exponential, hyperbolic, arithmetic, hyperboloid, and Killeen's additive utility model. The model not only leads to mathematical parsimony, but also allows all derivative models to be succinctly tested against each other using four datasets collected from three online studies. Two of the most used and discussed models in the literature, exponential and hyperbolic (also the quasi-hyperbolic model), are among the worst-fitting of those considered here, and are manifestly inferior to a new model with optimal parameter settings. Results across all studies and datasets are highly concordant, and robust to alternative re-analyses, for instance: using individual-level versus aggregate data; using nonparametric versus parametric tests; and across variants of the basic model