Immediacy Premium: A Linear Estimator of Hyperbolic Delay Discounting Rate (k).

The estimation of delay discounting rates (k) typically assume that the relative subjective value of a reinforcer declines as a reciprocal function of its delay. Despite the prevalence, estimates of k based on least-squares fits of relative subjective value to the hyperbolic discount function appear to have serious limitations. This curve-fitting method provides curves, which when averaged, may not accurately reflect the individual subjects’ data. The present study used the hyperbolic discounting function to derive a new dependent measure, termed immediacy premium, which is a linear function of delay. By averaging linear rather than reciprocal functions, the averaged data are more representative of individual data, and comparisons between mean data across treatments or samples is more meaningful. Based on data published, the assumptions of least-square based estimates were evaluated for estimation methods based on relative subjective value and immediacy premiums. This analysis yielded mixed support for each method, thus advising for the implementation of both methods when drawing inferences on treatment effects and population differences.