A NEW ARGUMENT IN FAVOR OF HYPERBOLIC DISCOUNTING IN VERY LONG TERM PROJECT APPRAISAL

Abstract

This paper characterizes the long term social discount rate (SDR) in terms of indices of variation and identifies a class of discount functions that assign weight to the distant future in terms of the asymptotes of their hazard rates. Let A(t) be a discount function supported on [0, +∞[, whose instantaneous discount rate is δ(t) = -( ln A(t))′. In this paper, we study the limiting behavior of δ(t) and a criterion to relate this limit to so-called long and heavy-tailed discount functions. Moreover, we study the discount functions of regular variation and, more specifically, the rapidly and the slowly-varying (singular) discount functions. In this way, the hyperbolic discounting exhibits long (and then heavy) tailedness, and it is intermediate between rapidly and the slowly-varying discount functions, which makes it a suitable function for long term discounting processes.