Non-parametric Test of Time Consistency: Present Bias and Future Bias, by Kan Takeuchi, Games and Economic Behavior, 71(2), pp.456-478, 2011.
In this paper, I present the very novel theory to characterize any time inconsistency.
Definition (Equivalent Delay Function): For X<Y, the equivalent delay, T(X,Y), makes the following two options equally valuable, (1) Receive X now, and (2) Receive Y with the delay of T(X,Y).
Theorem: A decision-maker exhibits present bias, if and only if, T is sub-modular.
Remark: Note that this characterization of time inconsistency is completely non-parametric and independent of the form of the utility function.