We consider discounted-utility models with a reference stream of outcomes. We provide a common framework for the main empirically supported discount functions in terms of three underlying functions: The delay, speedup and generating functions. Each of the delay and speedup functions can be uniquely elicited from behavior and, hence, can be fitted to the data. These two functions determine whether the discount function is subadditive, additive or superadditive; and whether the discount function exhibits declining, constant or increasing impatience. The third function, the generating function, links the speedup function to the discount function. Our framework nests several important attribute-based models that are typically considered to be in a separate class. We also show that apparent intransitivities of time preferences can be accounted for by framing effects.
time discounting framing effects impatience additivity common difference effect intransitive preferences