Time-Horizon and Timescale Effects in the Quasi-Hyperbolic Discounting Model

Estimates of the parameters of the quasi-hyperbolic discounting model have been used for quantitative purposes in a range of contexts. I show these estimates are sensitive to time horizon (largest value of t in the data) and timescale (months, years, etc.), and argue that when the quantitative value of the parameters matters, estimates should be used only with great caution, if at all. Using online survey data, I show that β is decreasing in both time horizon and timescale, and vice versa for δ. The time-horizon effect is clearly at least partly the result of estimating a discontinuous discounting model using data that are generated by a continuous discounting process. The time-scale effect appears to be caused by a genuine difference across scales in how individuals discount. I discuss implications for positive and normative analysis as well as possible approaches to proceeding with quantitative analysis in the face of these challenges.