# 2.4.2.1 Discount rates

Climate change impacts and mitigation policies have long-term characters, and cost analysis of climate change policies therefore involve a comparison of economic flows that occur at different points in time. The choice of discount rate has a very big influence on the result of any climate change cost analysis.

The debate on discount rates is a long-standing one. As the SAR (Second Assessment Report) notes (IPCC, 1996, Chapter 4), there are two approaches to discounting: a prescriptive approach based on what rates of discount should be applied, and a descriptive approach based on what rates of discount people (savers as well as investors) actually apply in their day-to-day decisions. Investing in a project where the return is less than the standard interest rate makes the investor poorer. This descriptive approach based on a simple arbitrage argument justifies using the after-tax interest rate as the discount rate. The SAR notes that the former leads to relatively low rates of discount (around 2-3% in real terms) and the latter to relatively higher rates (at least 4% after tax and, in some cases, very much higher rates). The importance of choosing different levels of discount rates can be seen, for example when considering the value of US$ 1 million in 100 years from now. The present value of this amount is around US$ 52,000 if a 3% discount rate is used, but only around US$ 3,000 if a discount rate of 6% is used.

The prescriptive approach applies to the so-called social discount rate, which is the sum of the rate of pure time-preference and the rate of increased welfare derived from higher per-capita incomes in the future. The social discount rate can thus be described by two parameters: a rate of pure preference for the present (or rate of impatience, see Loewenstein and Prelec (1992)) δ, and a factor γ that reflects the elasticity of marginal utility to changes in consumption. The socially efficient discount rate r is linked to the rate of growth of GDP per capita, g in the following formula:

##### r = δ + γ g

Intuitively, as suggested by this formula, a larger growth in the economy should induce us to make less effort for the future. This is achieved by raising the discount rate. In an inter-generational framework, the parameter δ characterizes our ethical attitude towards future generations. Using this formula, the SAR recommended using a discount rate of 2-4%. It is fair to consider δ =0 and a growth rate of GDP per capita of 1-2% per year for developed countries and a higher rate for developing countries that anticipate larger growth rates.

Portney and Weyant (1999) provide a good overview of the literature on the issue of inter-generational equity and discounting.

The descriptive approach takes into consideration the market rate of return to safe investments, whereby funds can be conceptually invested in risk-free projects that earn such returns, with the proceeds being used to increase the consumption for future generations. A simple arbitrage argument to recommend the use of a real risk-free rate, such as the discount rate, is proposed.

The descriptive approach relies on the assumption that credit markets are efficient, so that the equilibrium interest rate reflects both the rate of return of capital and the householders’ willingness to improve their future. The international literature includes several studies that recommend different discount rates in accordance with this principle. One of them is Dimson et al., 2000, that assesses the average real risk-free rate in developed countries to have been below 2% per year over the 20th century, and on this basis, suggests the use of a low discount rate. This rate is not incompatible with the much larger rates of return requested by shareholders on financial markets (which can be as high as 10–15%), because these rates include a premium to compensate for risk. However, the descriptive approach has several drawbacks. First, it relies on the assumption of efficient financial markets, which is not a credible assumption, both as a result of market frictions and the inability of future generations to participate in financial markets over these time horizons. Second, financial markets do not offer liquid riskless assets for time horizons exceeding 30 years, which implies that the interest rates for most maturities relevant for the climate change problem cannot be observed.

Lowering the discount rate, as in the precriptive approach, increases the weight of future generations in cost-benefit analyses. However, it is not clear that it is necessarily more ethical to use a low (or lower) discount rate on the notion that it protects future generations, because that could also deprive current generations from fixing urgent problems in order to benefit future generations who are more likely to have more resources available.

For discounting over very long time horizons (e.g. periods beyond 30 years), an emerging literature suggests that the discount rate should decrease over time. Different theoretical positions advocate for such an approach based on arguments concerning the uncertainty of future discount rates and economic growth, future fairness and intra-generational distribution, and on observed individual choices of discount rates (Oxera, 2002). The different theoretical arguments lead to different recommendations about the level of discount rates.

Weitzman (2001) showed that if there is some uncertainty on the future return to capital, and if society is risk-neutral, the year-to-year discount rate should fall progressively to its smallest possible value. Newell and Pizer (2004) arrived at a similar conclusion. It is important to observe that this declining rate comes on top of the variable short-term discount rate, which should be frequently adapted to the conditions of the market interest rate.

It is also important to link the long-term macro-economic uncertainty with the uncertainty concerning the future benefits of our current preventive investments. Obviously, it is efficient to bias our efforts towards investments that perform particularly well in the worse states (i.e., states in which the economy collapses). The standard approach to tackle this is to add a risk premium to the benefits of these investments rather than to modify the discount rate, which should remain a universal exchange rate between current and future sure consumption, for the sake of comparability and transparency of the cost-benefit analysis. Using standard financial price modelling, this risk premium is proportional to the covariance between the future benefit and the future GDP.

Whereas it seems reasonable in the above formula to use a rate of growth of GDP per capita of g=1-2% for the next decade, there is much more uncertainty about which growth rate to use for longer time horizons. It is intuitive that, in the long run, the existence of an uncertain growth should reduce the discount rates for these distant time horizons. Calibrating a normative model on this idea, Gollier (2002a, 2002b, 2004) recommended using a decreasing term structure of discount rate, from 5% in the short term to 2% in the long term. In an equivalent model, but with different assumptions on the growth process, Weitzman (1998, 2004) proposed using a zero discount rate for time horizons around 50 years, with the discount rate being negative for longer time horizons. These models are in line with the important literature on the term structure of interest rates, as initiated by Vasicek (1977) and Cox, Ingersoll and Ross (1985). The main difference is the time horizon under scrutiny, with a longer horizon allowing considerable more general specifications for the stochastic process that drives the shape of the yield curve.

Despite theoretical disputes about the use of time-declining discount rates, the UK government has officially recommended such rates for official approval of projects with long-term impacts. The recommendation here is to use a 3.5% rate for 1-30 years, a 3% rate for 31-75 years, a 2.5% rate for 76-125 years, a 2% rate for 125-200 years, 1.5% for 201-300 years, and 1% for longer periods (Oxera, 2002). Similarly, France decided in 2004 to replace its constant discount rate of 8% with a 4% discount rate for maturities below 30 years, and a discount rate that decreases to 2% for longer maturities. Finally, the US government’s Office of Management and Budget recognizes the possibility of declining rates (see appendix D of US, 2003).

It is important to remember that these rates discount certainty-equivalent cash flows. This discussion does not solve the question of how to compute certainty equivalents when the project’s cash flows are uncertain. For climate change impacts, the assumed long-term nature of the problem is the key issue here. The benefits of reduced GHG emissions vary according to the time of emissions reduction, with the atmospheric GHG concentration at the reduction time, and with the total GHG concentrations more than 100 years after the emissions reduction. Because these benefits are only probabilistic, the standard cost-benefit analysis can be adjusted with a transformation of the random benefit into its certainty equivalent for each maturity. In a second step, the flow of certainty-equivalent cash flows is discounted at the rates recommended above.

For mitigation effects with a shorter time horizon, a country must base its decisions (at least partly) on discount rates that reflect the opportunity cost of capital. In developed countries, rates of around 4–6% are probably justified. Rates of this level are in fact used for the appraisal of public sector projects in the European Union (EU) (Watts, 1999). In developing countries, the rate could be as high as 10–12%. The international banks use these rates, for example, in appraising investment projects in developing countries. It is more of a challenge, therefore, to argue that climate change mitigation projects should face different rates, unless the mitigation project is of very long duration. These rates do not reflect private rates of return and the discount rates that are used by many private companies, which typically need to be considerably higher to justify investments, and are potentially between 10% and 25%.