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Hyperbolic Discounting

A major component of Eckstein-Keane-Wolpin models is the intertemporal decision problem that forward-looking agents face when making their choices. In this modeling framework, agents maximize their expected present value of utility over the remaining lifetime. respy controls discounting of future payoffs through one or multiple parameters in the params. This guide gives a brief overview of the currently available time preferences and how to incorporate them in your model.

We load an example model for illustrative purposes.

import respy as rp
params, options = rp.get_example_model("robinson_crusoe_basic", with_data=False)

Standard discounting (delta)

The standard discount factor in respy is called delta (\(\delta\)) and specified in the params object. respy expects this parameter to be specified and will raise an error otherwise.

The standard discount factor represents time-consistent preferences for \(\delta \in (0,1]\). However, it can also be set to 0 for a static specification, rendering agents completely myopic.

params.head(1)

		value
category	name
delta	delta	0.95

Hyperbolic discounting (beta)

Aside from standard discounting, respy also supports time-inconsistent preferences to be modeled. These types of time preferences follow O’Donoghue and Rabin (1999) and are known as (quasi-)hyperbolic discounting or \(\beta\)-\(\delta\) preferences. In this case, in addition to \(\delta\), we also specify a parameter \(\beta \in (0, 1]\). This parameter implements a present-bias (or impatience) in agents.

To implement hyperbolic discounting, add a parameter of category beta and name beta to the params DataFrame.

params.loc[("beta", "beta"), "value"] = 0.7
params

		value
category	name
delta	delta	0.95
wage_fishing	exp_fishing	0.30
nonpec_fishing	constant	-0.20
nonpec_hammock	constant	2.00
shocks_sdcorr	sd_fishing	0.50
	sd_hammock	0.50
	corr_hammock_fishing	0.00
beta	beta	0.70

For an extended example of implementing hyperbolic discounting in one of respy’s example models, check out the tutorial linked below.

Tutorials Find out how to implement hyperbolic discounting in Impatient Robinson.

References

• O’Donoghue, T. and and Rabin, M. (1999). Doing It Now or Later. American Economic Review, 89(1): 103-124.