Quasi-hyperbolic discounting

What is quasi-hyperbolic discounting?

Quasi-hyperbolic discounting is a model of time preference that gives an additional weight advantage to the present. Laibson (1997) used it to analyze dynamically inconsistent preferences and commitment.

The beta-delta model

The weights are 1 for the current period, then βδ, βδ², βδ³, and so on. Beta captures present bias: the extra discount applied to future utility when 0 < β < 1. Delta captures ordinary per-period discounting.

For a purely hypothetical example, set β = 0.7 and δ = 0.9. The current period has weight 1. Next period has weight 0.7 × 0.9 = 0.63, and two periods ahead has weight 0.7 × 0.9² = 0.567. These numbers weight utility in the model. They are neither estimates of typical human preferences nor automatically percentages of a cash payment; converting money to utility requires an additional assumption.

When next period arrives, its outcomes receive current-period weight 1, while outcomes still in the future retain the beta discount. That change in relative weighting makes a reversal possible. It does not mean every decision must reverse.

An illustration

Someone may plan to exercise later, then postpone when the effort becomes immediate. In this illustration, the immediate cost receives current-period weight; it is the delayed benefit that receives the additional beta discount.

Such preference reversals are possible under the model.

Why quasi-hyperbolic discounting matters

The model helps economists study saving, deadlines, and commitment devices: choices made today that limit what someone can do later. Its usefulness depends on how well its assumptions describe the decision at hand.