Hyperbolic discounting and the time‐consistent solution of three canonical environmental problems

Holger Strulik

doi:10.1111/jpet.12497

Abstract

AbstractIn 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, and (iii) economic growth and pollution. 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.

Highlights

Economic scholars agree that the appropriate choice of the discount rate is of preeminent importance in the evaluation of policies that matter for the distant future
I compared the solutions to those obtained under conventional exponential discounting, applying the normalization that both methods provide the same present value of a constant flow
I showed that hyperbolic discounting leads to a more conservative use of resources and the environment than exponential discounting and that it establishes the social optimum at the steady state

Summary

Introduction

Economic scholars agree that the appropriate choice of the discount rate is of preeminent importance in the evaluation of policies that matter for the distant future. It has been suggested that sophisticated social planners, who are aware of the time-inconsistency problem, could achieve consistent decisions by using Markovian strategies in a dynamic game with (not yet existent) future planners (Karp, 2005, Gerlagh and Liski, 2017). This solution, is not entirely satisfying either. It is reassuring that the implementation of a hyperbolic discounting rule, given its multiplicative separability, will lead to time-consistent decisions This means that it will not cause future policy reversals and that there is no need for commitment or sophistication of strategies by the current policymakers.

Welfare and Discounting

Optimal Harvesting of a Renewable Resource

Hyperbolic Discounting and the Tragedy of the Commons

Findings

Conclusion