Alexander Adamou and Yonatan Berman and Diomides Mavroyiannis and Ole Peters (2019). Microfoundations of Discounting. RESEARCHERS.ONE, https://www.researchers.one/article/2019-10-7.

An important question in economics is how people choose between different payments in the future. The classical normative model predicts that a decision maker discounts a later payment relative to an earlier one by an exponential function of the time between them. Descriptive models use non-exponential functions to fit observed behavioral phenomena, such as preference reversal. Here we propose a model of discounting, consistent with standard axioms of choice, in which decision makers maximize the growth rate of their wealth. Four specifications of the model produce four forms of discounting - no discounting, exponential, hyperbolic, and a hybrid of exponential and hyperbolic - two of which predict preference reversal. Our model requires no assumption of behavioral bias or payment risk.

October 10, 2019 6:20 am

I think eq 3.7 and 3.8 have a minor typo in the denom. exp(r * (H + D)) instead of exp(r D) or something like that. 3.22 is correct.

October 11, 2019 8:05 am

You are right, many thanks! The article has been updated. Best wishes, Alex

Excellent article. Explains long-standing problems in a simple way, even making the solution seem obvious, trivial.

This analysis is effectively at an individual basis. Presumably, the reason for growth as a maximand is that it improves the likelihood of individual survival as well as the likelihood of progeny. However, we should keep in mind that growth can be maladaptive, like when a virulent infection or cancer eliminates its host population and itself as well.

If we examine societies, the question of the appropriate social discount rate comes up. While growth may be a reasonable maximand for an individual, it isn't clear whether this holds true for society as a whole. In many societies, and for humanity as a whole, endless growth is not feasible as there are effective resource boundaries of various kinds. Some may even argue that as the total resource base is obviously finite, growth is at the cost of another (competing human societies, other species). Indeed, there are arguments made that the objective of society today should be de-growth, i.e. negative growth. Certain species have adaptations for situations when resources are being depleted such as quorum sensing.

Two issue come to mind. First, if there is a positive social discount rate, it effectively implies that future generations are worth less than the present generation, something that seems ethically questionable to many. Put differently, would we agree that we are worth less than our ancestors?

Second, in practice a positive social discount rate incentivises the depletion of finite natural resources - e.g., the extraction of fossil fuels, and the dumping of waste (e.g. carbon, plastic, pesticides, fertilisers) at a rate that overloads the biosphere. This impoverishes future generations, and its consequences are readily apparent.

Some historical observations may be pertinent. First, many societies have had a prohibition on usury. Second, periodic jubilees where debts were cancelled were also practiced. Third, there have been societies that have argued that we cannot own nature, effectively implying a prohibition on depleting nature and by extension a zero or unspecified social discount rate. Some of these societies have lasted far longer than our current civilisation. Fourth, pillage is a war crime, presumably because natural resources are really something that future generations also have a right to, and if we deplete them, then sooner or later there will be nothing left. Fifth, while it is for an extremely short period, many countries are borrowing at negative interest rates for reasonable periods of time. Perhaps if growth is bounded, this should be expected.

It would be interesting to extend the analysis in this paper to consideration of social discount rates, and to see what specifications would imply positive, zero or even negative social discount rates. The importance of this analysis cannot be overstated - the survival of civilisation depends on getting this correct. Of course, dynamics are needed, but even redoing this analysis for society at large would be enormously valuable at this juncture.