Discount Functions for Fitting Individual Data

The commonly used hyperbolic and quasi-hyperbolic discount functions imply decreasing impatience, which is the prevailing empirical phenomenon in intertemporal choice, in particular for aggregate behavior. At the individual level there is much variation, however, and there will always be some individuals who exhibit increasing impatience. Hence, to fit data at the individual level, new discount functions are needed. This paper introduces such functions, with constant absolute (CADI) or constant relative (CRDI) decreasing impatience. These functions can accommodate any degree of decreasing or increasing impatience, which makes them sufficiently flexible for analyses at the individual level. The CADI and CRDI discount functions are the analogs of the well known CARA and CRRA utility functions for decision under risk.