| Period of Evaluation for the Hyperbolic Form | Mean | Reservoir User | Pivot User | Low Efficient Peer | High Efficient Peer |
|---|---|---|---|---|---|
| t = 0 | 0.02 | 0.03 | 0.01 | 0.02 | 0.01 |
| t = 5 | 0.04 | 0.08 | 0.08 | 0.05 | 0.03 |
| t = 10 | 0.01 | 0.01 | 0.00 | 0.05 | 0.01 |
| t = 15 | 0.00 | 0.00 | 0.00 | 0.05 | 0.02 |
| t = 20 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| t = 25 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| t = 30 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
Note: An instantaneous discount rate for a discounting form ψt is
The instantaneous discount rate for the exponential discounting form is constant and equal to ln(1 + ρ). For the hyperbolic discounting form, the instantaneous discount rate equals μ / (1 + t), which declines over time. The p-values give results from the method of convolutions approach (Poe, Giraud, and Loomis 2005) with the FTPw model. We round p-values < 0.001–0.00. All tests are one-sided and use 1,000 normal random draws of the mean and standard error estimates. The subgroups (reservoir user, pivot user, low efficient peer, and high efficient peer) come from the four clusters we identify from a kmeans cluster analysis with a Euclidean similarity matrix. We name each cluster by looking at the mean values of the explanatory variables in each cluster and consider how the mean values within the cluster deviate from the mean values for the whole sample.
