Constraining the social discount rate by consideration of uncertainties

An article that just appeared in the journal Global and Planetary Change, authored by me and Mark Freeman and Michael Mann, reported a simulation experiment that sought to put constraints on the social discount rate for climate economics. The article is entitled Harnessing the uncertainty monster: Putting quantitative constraints on the intergenerational social discount rate, and it does just that: In a nutshell, it shows how a single, policy-relevant certainty-equivalent declining social discount rate can be computed from consideration of a large number of sources of uncertainty and ambiguity.

In the previous three posts

Those three posts provided us with the background needed to understand the simulation experiment that formed the core of our paper.

Basic Procedure

The goal of our simulation experiment was to explore different sources of uncertainty that are relevant to decision making in climate economics. In particular, we wanted to constrain the social discount rate, ρ, within a prescriptive framework embodied by the Ramsay rule:

ρ = δ + η × g.

As explained earlier, the parameters d and h represent ethical considerations relating to pure time preference and inequality aversion, respectively. The anticipated future economic growth is represented by g.

To derive candidate discount rates from this framework we therefore need estimates of future economic growth. We obtained these estimates of g in our experiment by projecting global warming till the end of the century using a climate model (a simple emulator), and converting that warming into a marginal effect on baseline economic growth through an empirical model of the temperature-growth relationship reported by Marshall Burke, Solomon Hsiang and Edward Miguel in 2015.

Their model is shown in the figure below:

It can be seen that, controlling for all other variables, economic productivity is maximal at an annual average temperature of around 13°C, with temperatures below or above that leading to a reduction in economic output. This descriptive model has been shown to be quite robust and we relied on it to convert warming forecasts to economic growth rates.

Experimental Design

We projected economic growth as a function of three variables that are the source of considerable uncertainty: the sensitivity of the climate to carbon emissions, the emissions trajectory that results from our policy choices, and the socio-economic development pathway that the world is following. We formed all possible combinations of those three variables to examine their effect on projected global growth.

The figure below shows our experimental design.

  • We fixed climate sensitivity at a constant mean but varied the uncertainty of that sensitivity, expressed as its standard deviation in 6 steps from 0.26°C to 1.66°C
  • We employed the climate forcings (i.e., the imbalance of incoming and outgoing energy that results from atmospheric greenhouse gases) provided by several of the IPCC’s Representative Concentration Pathways (RCPs). Specifically, we used RCP 2.6, RCP 4.5, RCP 6.0, and RCP 8.5 for the period 2000 through 2100. These RCPs span the range from aggressive mitigation and limiting global temperature rises to approximately 2°C (RCP 2.6), to continued business as usual and extensive warming (RCP 8.5).
  • We compared two Shared Socio-Economic Pathways (SSPs). SSPs form the basis of the IPCC’s projections of future global development in Working Group 3. We employed two scenarios, SSP3 and SSP5. SSP3 assumes low baseline growth and slow global income convergence between rich and poor countries; SSP5 assumes high baseline growth and fast global income convergence.

Our experiment thus consisted of 48 cells, obtained by fully crossing 6 levels of uncertainty about climate sensitivity with 4 RCPs and 2 SSPs. For each cell, 1,000 simulation replications were performed by sampling a realization of climate sensitivity from the appropriate distribution. For each realization, global temperatures were projected to the end of the century and the economic effects of climate change were derived by considering the relevant SSP in conjunction with the empirical model relating temperature to economic production. Cumulative average growth rates for the remainder of the century were then computed across the 1,000 replications in each cell of the design.

These 48 projected global economic trajectories to the end of the century, each of which represented the expectation under one set of experimental conditions, were then converted into candidate social discount rates.

At this stage the ethical considerations (top left of the above figure; see my previous post here for a discussion) were applied to each trajectory, by combining each of the 48 projected global economic growth rates (g) with four combinations of η and δ. Specifically, we used values for η and δ obtained by a recent expert survey, such that δ was either 0% or 3.15% with probability 65% and 35%, respectively, and η was 0.5 or 2.2 with equal probability.

This yielded a final set of 192 candidate discount rates across all combinations of experimental variables which were then integrated via gamma discounting into a single certainty-equivalent declining discount rate. I explained gamma discounting in a previous post, and you may wish to re-read that if the process is not clear to you.


Although the experiment was quite complex—after all, we explored 3 sources of scientific, socio-economic, and policy uncertainty plus 2 sources of ethical ambiguity!—the crucial results are quite straightforward and consist of a single declining discount rate that is integrated across all those sources of ambiguity and uncertainty.

The figure below shows the main result (the article itself contains lots more but we skip over those data here).

The solid black line represents the (spot) certainty-equivalent declining discount rate that applies at any given point in time. For example, if we are concerned with a damage cost that falls due in 2050, then we would discount that cost at 3%. If we are worried about damages at the end of the century, then we would discount that cost by less than 2%.

The figure also shows various previous estimates of declining discount rates that were derived by different means but all based on the underlying principle of gamma discounting.

Our approach differs from those precedents in two important ways: First, we explicitly consider the major (if not most) sources of uncertainty and ambiguity, and we encompass their effects via gamma discounting. Second, our approach explicitly models the impact of future climate change on economic production.

When the likely impact of climate change on the global economy is considered, a more rapid decline of the discount rate is observed than in previous work. By 2070, our estimates of the spot rate dips below the other past benchmark estimates in the above figure. It should be noted that our results mesh well with the median long-run social discount rate elicited from experts.

We consider this article to provide a proof of concept, with much further exploration remaining to be performed. We take up some of those open issues and the limitations of our work in the article itself.

There is one clear message from our work: uncertainty is no reason to delay climate mitigation. Quite on the contrary, our extensive exploration of uncertainty yielded a lower discount rate (form around 2070 onward) than existing proposals. This lower discount rate translates into a considerable increase in the social cost of carbon emissions, and hence even greater impetus to mitigate climate change.

One caveat to our conclusion is that our discounting model assumes that things can be done only now or never. This makes sense in many situations when individuals or firms are confronted with a choice about a potential project. However, there are limitations to this approach. To take an extreme example, suppose we knew that the precise value of climate sensitivity would be revealed to us by some miraculous process in exactly a year’s time. In that it case, it would not be impossible that we might decide to wait that year to learn the precise climate sensitivity before acting. 

A possible alternative approach that stretches the decision path over time involves so-called real options models. Real options analyses account for the sequential nature and path dependence of choice processes. We flag this alternative briefly, but it remains for future work to apply it to climate economics in a more systematic fashion.