Hyperbolic or exponential time discounting function?. Empirical evidence using a conditional Consumption Capital Asset Pricing Model

The main objective in this article is to shed light on the term structure of subjective time preference rates using a conditional Consumption Capital Asset Pricing Model. More precisely, we challenge the relevance of the exponential time discounting function assumption, which leads to a constant subjective time preference rate. We alternatively consider the hypothesis of a set of different time preference rates depending on the investment time horizons referred to in the literature as the hyperbolic time discounting setting. This hypothesis is empirically tested using a bivariate two-factor model of inflation and real consumption to condition the term premiums of bonds as in La Bruslerie and Fouilloux (2014). We have considered US bond market monthly data from 1970:4 to 2013:1. Our results clearly cast doubt on the assumption of a flat term structure, as implied by the standard exponential discounting function. A decreasing term structure of time preference rates is reported. It is particularly clear for the 1991-2013 period. Our results give strong support for the hyperbolic time discounting function hypothesis.