Comparative impatience under random discounting

The random discounting model has been used as a tractable model which is consistent with preference for flexibility. By taking Goldman (J. Econ. Theory 9:203–222, 1974) as an example, we illustrate that under random discounting, the average time preference and preference for flexibility may be conflicting to each other and their mixed effect contributes to revealed impatience. To obtain sharp results in comparative statics, we ask under what kind of probability shifts on discount factors, it is possible to say that one agent always exhibits a more impatient choice than the other even when both agents have flexibility concern. We provide a behavioral definition of impatience comparisons and identify that the relative degree of impatience is measured as a probability shift of a random discount factor in the monotone likelihood ratioorder.