From data through discount rates to the area under the curve

The rate of discounting future goods is a crucial factor in intertemporal trade-offs, upon which depends not only individual well-being but also that of our planet: How much privation now for a temperate future for our grandchildren? What is the best way to measure how the value of future goods decreases with its delay? The most accurate discount functions involve several covarying parameters, making interpretation equivocal. A universal and robust measure is the area under the discount curve, the AuC. The AuC of a hyperbolic discount function is a logarithmic function of the discount rate, k. The same integral also approximates the area under a hyperboloid function. A simple technique converts each datum into estimates of the discount rate, eliminating rogue data points in the process. These trimmed estimates are converted into areas and tested against data, where they succeed at predicting the AuC and its relation to log(k).

Automated summary

The rate of discounting future goods has a significant impact on both individual well-being and the well-being of our planet. It is challenging to accurately measure how the value of future goods decreases with delayed consumption due to the complex parameters involved in discount functions. The area under the discount curve (AuC) serves as a universal and robust measure, which can be approximated using a hyperbolic discount function. By transforming each data point into estimates of the discount rate, converting them into areas, and testing against empirical data, the relationship between AuC and log(k) can be accurately predicted.