Table 1. Discounting functions D(⋅) for three popular discounting models, with implications for impatience.

Model	Discounting function	Implication for impatience
Constant discounting [5]	D(t) = 1/(1 + r)t, where r reflects the discount rate.	Constant
Quasi-hyperbolic discounting [17]	D(t) = β/(1 + r)t, with 0 < β ≤ 1 for t > 0 and D(t) = 1 otherwise, and r reflects the per-period discount rate.	Decreasing when t = 0 is involved, constant otherwise
Generalized hyperbolic discounting [27]	D(t) = 1/(1 + γt)a/γ, with a, γ > 0, where γ captures differences from constant discounting.	Decreasing throughout