The Hyperbolic Factor: a Measure of Time-Inconsistency

Many studies have found that discounting is hyperbolic rather than constant. Hyperbolic discounting induces time-inconsistent behavior and is becoming increasingly popular in economic applications. Most studies that provide evidence in favor of hyperbolic discounting either are merely qualitative or they depend on assumptions about, or parametric fittings of, utility functions. This paper provides a quantitative measure for the degree of deviation from stationarity and the induced time-inconsistency that can overcome the problems mentioned. This measure, the hyperbolic factor, also provides simple preference foundations of the most popular discount functions. Moreover, it can easily be calculated from data and does not require knowledge of utility. Thus, the hyperbolic factor provides an easy tool for theoretical preference foundations, critical empirical tests, and quantitative measurements of hyperbolic discounting.