**Hyperbolic Discounting**

**Definition of Hyperbolic Discounting:**
Hyperbolic discounting is a way of accounting in a model for the difference in the preferences an agent
has over consumption now versus consumption in the future.

For a and g scalar real parameters greater than zero, under hyperbolic
discounting events t periods in the future are discounted by the factor
(1+at)^{(-g/a)}.

The expression hyperbolic discounting describes the "class of generalized hyperbolas". This formulation comes from a 1999 working paper of C. Harris and D. Laibson, which cites Ainslie (1992) and Loewenstein and Prelec (1992).

In dynamic models it is common to use the more convenient assumption that agents have a common discount rate applying for any t-period forecast, starting now or starting in the future. Hyperbolic discounting is less convenient but fits the psychological evidence better, and when contrasted to the constant-discount-rate assumption can get models to fit the noticeable fall in consumption that U.S. workers are observed to experience when they retire. In a constant-discount-rate model the worker would usually have forecast the fall in income and their consumption expenses would be smooth.

One reason hyperbolic preferences are less convenient in a model is not only that there are more parameters but that the agent's decisions are not time-consistent as they are with a constant discount rate. That is, when planning for time two (two periods ahead) the agent might prepare for what looks like the optimal consumption path as seen from time zero; but at time two his preferences would be different.

Contrast quasi-hyperbolic discounting. (Econterms)

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