Hyperbolic Discounting and the Time-Consistent Solution of Three Canonical Environmental Problems

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in August 2017Abstract. In this paper I propose a time-consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, (iii) economic growth and pollution. I then compare results with those for conventional exponential discounting using the normalization that both methods provide the same present value of an infinite constant flow. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the Modified Green Golden Rule.

Renewable resource use with imperfect self-control

“…These undesirable outcomes, however, need to be attributed to time inconsistency and the continuous reversal of resource management plans and not to the feature of hyperbolically declining discount rates. Together with the results from Strulik (2020), this suggests that hyperbolic discount rates are perhaps not the best way to study cases of resource mismanagement that are caused by present-biased preferences.…”

“…In fact, hyperbolic discounting abolishes the threat of extinction and leads in the long-run to the social optimum, i.e. it establishes the Green Golden Rule (Strulik, 2020). The intuition for this non-obvious result can be understood after inspection of the transitional dynamics of resource stock and discount rate.…”

“…When the discount rate declines hyperbolically, however, there exists always a finite point in time at which the discount rate falls short of any positive growth rate of the resource, a condition that eliminates asymptotic extinction and ensures sustainability. With further declining discount rate, the harvesting behavior converges towards the long-run social optimum (Strulik, 2020). Duncan et al (2011) show that time-inconsistent hyperbolic discounting can lead to overexploitation and asymptotic extinction of renewable resources.…”