Exponential versus Hyperbolic Discounting : A Theoretical Analysis

This article casts doubt on the conclusion reached by experimentalists in behavioral economics (and other subjects such as social psychology and political science) that hyperbolic discounting explains their data better than exponential discounting. A dual expression to the exponential discounting equation is derived, the expression containing the full array of interest rates implied by every root solving the equation, including the negative and complex-valued interest rates, thereby employing and giving meaning to interest rates ignored by most economists for centuries. The dual expression has discount factors that are structurally similar to, and quantitatively identical with, those of the simple, hyperbolic discounting equation, making it difficult to distinguish which type of discounting was employed by subjects of past experiments, and implying that further, more detailed experiments are required to determine which type of discounting is most relevant