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Long-term Social Discounting and Climate Finance

Climate change is profoundly altering our world in ways that pose major risks to human societies and natural systems. We have entered the "Climate Casino and are rolling the global-warming dice", warns the 2018 Nobel laureate for economics William Nordhaus. His early work recognized that while resource scarcity does not present a pressing threat to long-run economic growth, the human impact on the environment can lead to a sharp decline in wellbeing and consumption of next generations, which provides much greater cause for worry.

Clearly, large-scale investments are required to significantly reduce emissions, adapt to the adverse effects and reduce the impacts of a changing climate. To better understand the financial dimension of mitigation and adaptation actions that will address climate change, let’s consider the following use-case. You want to invest in your retirement and buy US Treasury Inflation-Protected Securities (TIPS), which provide protection against inflation and hold them till maturity in 30 years from now. How can we estimate the today’s value of, e.g., TIPS with a face value of $100 maturing in 30 years from now? Even if we put aside important details related to coupon payments, this is still a loaded question. First of all, we should realize that, even after adjustment for inflation, a dollar is worth more today than it would be worth tomorrow. In fact, the core principle of finance – time value of money - holds that the present value (cost) of the future cash flow (benefit) is worth less the longer investor should wait to receive it. Thus, we should discount the future value of $100 that we are expecting to receive in 30 years from now back to the present using a discount factor, which is a function of time to maturity and risk-free interest rates.

To be a little more quantitative, assume that the annualized rate of return on a risk-free investment r is constant in time. Then, in the unbounded economy, the today’s value of the future cash flow is determined by the simple discounting formula, d(T) = exp(-rT). The exponential discounting of future benefits is the direct consequence of the simple law that governs the cumulative growth of a risk-free investment: $1 invested today will yield exp(+rT) at time T. If, for simplicity, we assume zero coupon payments and use the average long-term real interest rate r =4.2%, the present value of $100 received in 30 years will be approximately $28 today. However, if you use the todays rate of 1.2%, this value is much higher ~$70!

Consider another example. Let say we are ready to use zero interest rates in our estimates of the present value of benefits differed for the distant future. However, in this extreme case, preventing a catastrophic collision with an asteroid in the next million years has the same present value as a planetary crash in the next hundred years. Clearly, this conclusion is wrong. Hence, even an ethical government policy, considering wealth of future generations as its own, should use non-zero interest rates in valuations of long-term social projects.

In financial project analysis with long-term horizons, such as those aimed at reducing greenhouse gas emissions, government-agencies are implementing a conceptually similar methodology of cost-benefit analysis. For instance, the U.S. Office of Management and Budget (OMB ) requires to use r = 7% in valuation of costs and benefits of intra-generational projects. In this case, the net present value of $100 received in 30 years is only $12. In fact, at really long time horizons that are typical for inter-generational environmental and infrastructure projects, exponential discounting can lead to a negligible present monetary value of future benefits. For example, the today’s value of $100 received in 200 years from now estimated with the constant rate of r = 3% is $0.3. In other words, to justify today’s investment of $100 the benefit received in 200 years should be worth at least $40,343 (in todays dollars)!

Thus, a conventional cost-benefit analysis with a constant social discount rate of long-term environmental projects requires astronomical numbers in expected benefits to justify today’s investment.

Despite the obvious importance of the rigorous discounting policy, currently there is neither a consensus about the valuation methodology nor even a clear definition of the time horizon that might be considered as the distant future. For instance, in evaluating public projects, France and the United Kingdom use discount rate schedules with declining over time interest rates. That is, the rate used today to discount benefits from year 200 to year 100 is lower than the rate used to discount benefits in year 100 to the present. In the United States, however, the OMB recommends that project costs and benefits be discounted at a constant rate, although a lower rate may be used for projects that affect future generations. These conflicting government approaches to discounting raise a difficult question: How should governments discount the costs and benefits of public projects that affect future generations?

In our R&D work we use the classic macroeconomic Ramsey framework, which leads to a risk-free social discount rate proportional to a rate of real per capita consumption growth. Yet, contrary to the conventional economic approach, we take into account that finite biophisical resources of our planet impose boundaries on consumption growth. We introduce the nonlinear (logistic) model of consumption, which allows for derivation of the simple expression forecasting declining long-term tail of a social discount curve. We have concluded that the discount rate of climate finance projects with time horizons > 300 years should be two times lower than the contemporary historical average. This estimate translates into 90 times higher present value of benefits differed to the distant future than valuations based on traditional methodology. We believe that our results can help to shape a more realistic climate finance discounting policy.

Those of you who are interested to learn more about this study could take a look at our paper: "Planetary boundaries of consumption growth: Declining social discount rates" which has been published in Physica A: Statistical Mechanics and its Applications, v.521 (2019) p.362.