Discounting, Explained

The climate policy landscape is shaped by the cost-benefit concept of discounting, where discount rates are an exogenous parameter in determining the rate at which governments achieve climate mitigation goals like decarbonization. Discounting refers to the present-value evaluation of a future event or a project with a long-run profile. That is, when a cost or benefit is in the future rather than in the present, those values are not directly comparable to present-day values and are discounted. To understand how discounting has led to insufficient climate action, an explanation of its technical operations is first necessary.

Here, we offer an explanation by example. 

Let’s suppose that Bobby decides to open a bank account and deposits $100. The account manager informs Bobby that they will be earning 1 percent interest. For the next three years, at the end of each year, Bobby checks their account balance. Let’s also assume Bobby made no other deposits or withdrawals during this time.

By the interest formula, the initial deposit of $100 will be scaled by (1 + r)^t, where r is the interest rate and t is the time elapsed. After the first year, Bobby will have $101; after the second year, Bobby will have $102.01; and after the third year, Bobby will have $103.03. The decision to not withdraw the $100 comes at an opportunity cost of the alternative investments of that initial deposit plus the accrued interests.

Let’s now suppose a different scenario. Someone now offers to give Bobby $100 either today, a year from today, two years from today, or three years from today. Since the choices are not occurring at the same point in time, Bobby cannot directly compare $100 today to $100 in three years. Instead, Bobby would use a discount rate to convert what $100 in t years is worth to them today.

Bobby’s individual calculus would follow: $100 * (1/(1+r)^t) = PV, where r is the discount rate, t is the time elapsed, and PV is the present value of $100 after t years. Let’s assume that Bobby decides to discount the value of $100 in the future by their bank’s interest rate. After the first year, the present-day value is $99; after the second year, the present-day value is $98.03; and after the third year, the present-day value is $97.06.

However, Bobby’s bank’s interest rate does not entirely capture their attitude towards the future. In fact, the degree to which Bobby prefers money today over money in the future lets them know that $100 two or three years from today is not worth $98.03 or $97.06 today, respectively. At this divergence, Bobby decides to discount the future at a greater rate; now, they discount the value of $100 in the future by 20 percent instead of 1 percent. After the first year, the present-day value is $83.33; after the second year, the present-day value is $69.44; and after the third year, the present-day value is $57.87. The discount rate of 20 percent satisfies Bobby’s revealed time preference. Bobby has now shown that discounting by a greater rate results in a lower present-day value of a future benefit or cost. 

In climate policy making and decision making, revealed time preference and opportunity costs are linked to keep the discount rate high. Revealed time preferences inform governments about how much future climate mitigation is worth to us privately today. The discount rate that is then constructed by this aggregated private factor involves long time spans when it comes to bringing the cost of future externalities like pollution and long-run natural resource degradation into the present. What’s more, the opportunity cost captures the benefit foregone of other government expenditures in favor of climate mitigation investments. This opportunity cost compares the benefit of a present public investment to the present benefit (the damage abated) of climate mitigation, which if discounted at higher rates does not justify spending much on climate action today.

Now, we offer another explanation by example. 

Let’s assume that climate change will cause $23 trillion in damages by 2050. At a discount rate of 3 percent (consistent with that of most high-income countries), the present-day value of such damage and suffering is around $9.76 trillion. However, at a discount rate of at least 5 percent (consistent with that of most low- and middle-income countries), the present-day value drops to around $5.59 trillion. The discounted values of these damage estimates do not raise sufficient urgency when compared against government spending in infrastructure and in the military.  

As such, in the aggregate, the policy challenge exists in how (by which discount rate) governments decide to pull damages out of the future and into the present. Economist Helen Scarborough from Deakin University in Australia suggests that governments should not assign a social discount rate based on revealed time preferences. Instead, Scarborough estimates the social discount rate by the social interest rate of consumption and intergenerational distributional preferences. This approach suggests an intergenerational equity-adjusted social discount rate as an alternative to a low social discount rate, such that policymakers can add positive intergenerational equity preferences towards future generations to their social discount rates.This intergenerational equity-adjustment is derived using a multinomial logit model as a function on the ages of the generations spanned and the time distance between the generation in the present and the generation in the future.

Scarborough offers their own explanation by example. 

Let’s assume a project with a present-day cost of $100 exists. If we discount the future benefit of $200 by 5 percent, the present-day benefit is $75. Since the present-day benefit is less than the present-day cost, the project is not feasible. However, if we added a distributional weight of 1.4 on the future benefit accrued by those in the future generation, the present-day value is $105 in the age range of newborn to 25 and the present-day value $120 in the age range of 25 to 50. Using an intergenerational equity-adjusted social discount rate, the present-day benefit is greater than the present-day cost and the project is now feasible.

The misspecification of the discount rate has likely delayed our global progress against climate change, but what’s more is that on its own, discounting at lower rates may no longer provide the equity and efficiency outcomes that are necessary for our intertemporal social welfare. Beyond the math, the fairness of delaying these damages onto our future generations calls for a more explicit reckoning than just a revealed preference.

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