Title: On the Euler Equations of Hyperbolic-Discounting Growth Models
Reference Number: 1032
Publication Date: August 2001
JEL Classifcation: E1

Paul Sau-Him Lau
The University of Hong Kong

Stimulated by recent studies on hyperbolic discounting, Barro (1999) examines the neoclassical model of capital accumulation using a continuous-time model and a general time preference function. However, the analysis seems rather complicated. This paper provides a complementary analysis to Barro (1999) by emphasizing the transparent derivation of the hyperbolic Euler equation and its intuition. To achieve these objectives, a discrete-time model and a specific time preference function first appearing in Phelps and Pollak (1968) are used. The analysis suggests that the derivation of the Euler equations in hyperbolic-discounting growth models shows similarity with the standard exponential-discounting case. Moreover, it shows that an interpretation of the hyperbolic Euler equation for the intertemporal consumption model in Harris and Laibson(2001) contains model-specific elements and therefore may not be valid for other dynamic models. This paper also extends some results in Phelps and Pollak (1968) and Long and Plosser (1983) by obtaining closed-form solutions for some hyperbolic-discounting growth models.

Key words: hyperbolic discounting, neoclassical and endogenous growth models

Last modified: 07/25/2002