Delay Functions as the Foundation of Time Preference: Testing for Separable Discounted Utility

Delay functions, which vary timing of rewards but fix the money dimension, can elicit the form of discount functions with minimal assumptions. We present a general theorem that characterizes the set of discount functions and utility indices compatible with any 'regular' preference. We provide conditions to test for separable discounted utility (SDU). We elicit individual delay functions for a range of amounts and time horizons. When we impose SDU assumptions, we classify more than half our analysis sample as exponential discounters. However, we reject SDU assumptions for 68% of the sample in favor of magnitude-dependent discounting with time distortion.