How do we compare the costs of greenhouse gas mitigation measures taken today with the benefits produced by these actions in the future? How do we calculate the value of an investment when benefits will continue to accrue over centuries? These are important questions, because the way we value the benefits of mitigation measures will guide us in developing cost-effective solutions to the threat of climate change. This report highlights one important variable in this determination that is often left unexamined in current climate change models-uncertainty in future interest rates.
Underlying existing climate change models is a specific set of assumptions regarding emissions levels, economic growth and flexibility, technological innovation, climate change policies, and the magnitude of climate change damages. Though this set of assumptions varies from model to model, each includes a discount rate, which is used to compare costs and benefits over time. The discount rate tells us how high future benefits need to be to justify spending a dollar today. While there is considerable debate regarding the appropriate discount rate to apply to any cost-benefit analysis conducted across generations, most climate models choose one rate (2-7 percent is a common range) and hold it constant over the time horizon of the model.
This study questions that conventional approach. Rather than assuming that interest rates remain fixed over hundreds of years, authors William Pizer and Richard Newell argue that future rates are uncertain. Using an integrated assessment model of climate change, they demonstrate that acknowledging uncertainty about future rates will lead to a higher valuation of future benefits-regardless of the initial rate one chooses. This is a significant finding, because it reveals that including the effect of interest rate uncertainty could raise valuations by as much as 95 percent relative to conventional discounting at a constant rate. In other words, changing the approach to discounting in this manner results in significantly higher projected benefits of addressing climate change.
This report is the first to be published as a technical report in the Pew Center’s economics series. The results of this and other ongoing Pew Center analyses will be incorporated into a dynamic general equilibrium model in order to produce a set of model estimates that better capture the full complexity of the climate change issue.
The Pew Center and authors would like to thank William Cline, Ev Ehrlich, and Randy Lyon for commenting on previous drafts of this report. The authors would also like to recognize Michael Batz for research assistance and Andrew Metrick and participants in seminars at the 2000 NBER Summer Institute and 2000 American Economic Association meetings for helpful comments on previous versions of this paper. Greater technical detail on the approach and results described in this paper are given in Newell and Pizer (2000).
Most environmental policies involve a trade-off between short-term costs and longer-term benefits. Investments in cleaner technologies and abatement equipment, for example, require up front expenditures that produce environmental improvements over time. In cases where a pollutant decays within a few years, the time horizon for analyzing costs and benefits depends on the lifespan of the investment-perhaps as long as 50 or 100 years. By contrast, the benefits of climate change mitigation measures are linked not only to the lifespan of physical capital but also to the lifespan of greenhouse gases (GHGs), which may remain in the atmosphere for centuries. For this reason, climate change presents specific challenges for determining the proper balance between future benefits and present-day costs.
This paper explores some of the analytic difficulties of applying conventional discounting techniques to long-term problems such as global climate change. In particular, the paper focuses on the influence of uncertainty in the discount rate on the valuation of future climate damages, finding that this uncertainty has a large effect on valuations at horizons of 100 years or more in the future. Relative to the standard approach that ignores this uncertainty, the paper finds that the valuation today of benefits 300 years or more in the future rises by a factor of many thousand solely due to this uncertainty in discount rates. The paper also finds that the debate over which is the “right” rate to use is rendered less important once uncertainty in that rate is taken into account.
How do we compare costs and benefits that are separated by many decades or even centuries, thereby involving intergenerational comparisons? Individual experience typically involves trade-offs of at most 20-30 years, as one invests in a new house or saves for retirement. Businesses face decisions with similar horizons as they choose to invest in research and new equipment. In each of these cases, the market interest rate plays a central role: it allows us to convert costs and benefits at different points in time into comparable costs and benefits at a single point in time. This procedure is known as discounting.
Discounting is used as a tool for modeling optimal solutions for many long-term problems, including climate change. For example, an integrated assessment model of climate change can be used to estimate the time-profile of benefits associated with the reduction of one ton of carbon emissions in the year 2000. In order to use this information to conduct a policy analysis, the standard approach would be to choose a single interest rate, convert this path of values into equivalent discounted values in 2000 based on the chosen interest rate, and add them up.
Several practical issues complicate the application of this straightforward concept. Current tax policy creates a distinction between the rate of return to corporate investments (10 percent) and the rate of return that is available to individual investors after corporate taxes (7 percent). Focusing on the rate available to individuals, there is also a difference between the rate of return to equity (7 percent), the return to bonds (4 percent), and the return to each of these remaining after personal income taxes. While no consensus exists on the appropriate rate to use for discounting, there is a tendency to focus on the return to bonds (4 percent) for evaluating longer-term policies.
There is concern, however, among economists and non-economists about using conventional discounting techniques to value public benefits over hundreds of years, where trade-offs are evaluated across multiple generations. On the basis of equity, some argue that lower discount rates should be used to compare the value of costs and benefits between generations. Such an argument is common regarding the use of discount rates in the context of climate change modeling, which involves complex projections centuries into the future.
Here we focus on uncertainty in market interest rates, and evaluate the potential consequences for long-term discounting. Few markets exist for assets with maturities exceeding 30 years, making the interest rate beyond that horizon even more uncertain than the ambiguity among pre- and post-tax returns to bonds and equity. By focusing on the impact of this uncertainty, this study shows, perhaps surprisingly, that uncertainty about future changes in interest rates can have important consequences for the valuation of benefits over distant horizons.
To best understand how future interest rates are likely to change, we examine the behavior of long-term government bond rates in the United States. These rates reveal persistent changes, including a secular decline from near 6 percent in 1800 to 3 percent at the end of the 20th century along with five noticeable shifts of at least 1 percent lasting ten years or more. This leads us to believe that it should not be surprising if persistent changes in interest rates occur in the future, i.e., future rates are uncertain.
We use these data on long-term government bond rates to estimate the uncertainty surrounding interest rates in the past, to simulate uncertain rates in the future, and to compute the appropriate discount factors for various time horizons and alternative base rates. Starting with the assumption that the initial rate should equal the average rate of return to government bonds (4 percent), but that future rates follow an uncertain random trajectory (estimated based on historical data), we find that the discount factor after 400 years is over 40,000 times higher than if we instead assume that the rate remains fixed at 4 percent forever.
When we construct similar measures of the uncertainty effect for alternative initial rates of 2 percent and 7 percent, we find that the effect of uncertainty is larger for higher interest rates-this makes sense because higher rates have a larger opportunity to decline with uncertainty and thereby raise valuations. Comparing the discount factors directly, we find that the valuation of benefits occurring in the future is less sensitive to the choice of the initial discount rate when the effect of uncertainty is taken into account. That is, not only do valuations rise when one considers uncertainty, but they become less sensitive to whether the analysis is based on the after-tax return on bonds or the pre-tax return on equities.
Applied to one estimate of the consequences of climate change, the effect of uncertainty is large. Using the government bond rate of 4 percent, the expected present value of consequences from current carbon dioxide (CO2) emissions increases by over 80 percent when we incorporate the effect of future interest rate uncertainty. An initial rate of 7 percent yields a 95 percent increase in the value of carbon mitigation, while an initial rate of 2 percent yields an increase of about 55 percent.
The results of this study show that the conventional application of constant discount rates undervalues the benefits of GHG abatement measures. Moreover, they suggest that the concern expressed by those who argue for low discount rates is at least partially addressed-without abandoning conventional economic theory-by viewing future interest rates as uncertain. While this will not yield the same dramatic effects as the decision to arbitrarily apply a lower discount rate, uncertainty does have a large effect on valuations at horizons of 100 years or more in the future.