Social Discount Rate

The social discount rate is an economic concept that has its origins in macroeconomics and growth theory (especially the Ramsey model ) and is particularly important in environmental economics . It is used for compounding or discounting in cost-benefit analyzes of social projects and should be distinguished from the private or individual discount rate ( time preference ). The social discount rate is often viewed from the perspective of intergenerational equity.

Reason

While impatience is the main (empirical) rationale for individual discount rates, making the concept descriptive, the social discount rate is usually interpreted as a normative concept - it is the discount rate that maximizes intertemporal social welfare. In contrast to the individual discount rate, it does not necessarily have to be positive. At least three different reasons for a positive discount rate can be found in the literature:

• the welfare of future generations has less value than that of those living today - this argument has been considered ethically unjustifiable since Frank Ramsey and is rejected by most economists;
• the likelihood that humanity will die out as a result of a random cataclysm (e.g. meteorite ) before the cash flow to be discounted occurs;
• the assumption that future generations will be wealthier than the present generation.

Ramsey rule

The social discount rate is an intertemporal shadow price that makes it possible to compare payment flows occurring at different points in time. It is usually derived from Frank Plumpton Ramsey's dynamic growth model . A utilitarian social welfare function is assumed (which is maximized by a social planner ):

${\displaystyle \int _{0}^{\infty }U(C(t))e^{-\delta t}\mathrm {d} \,t}$

Here stands for the social welfare (the total social benefit) at the point in time that is dependent on consumption . It is the social rate of time preference, ie a part of the social discount rate. The welfare function formulated in this way is nominated in (non-measurable) utility units. In order to work with measurable values, a concrete welfare function with a numéraire (usually: money) must be assumed. In the theory of optimal growth, the utility function called power utility is usually assumed (for all ): ${\displaystyle U(C(t))}$ ${\displaystyle t}$ ${\displaystyle C}$ ${\displaystyle \delta }$ ${\displaystyle t}$

${\displaystyle U(C)={\frac {C^{1-\gamma }}{1-\gamma }}}$

where the aversion to intertemporal inequality or the elasticity of consumption is the welfare function. The social discount rate can be derived from the welfare function specified in this way (so-called Ramsey rule or Ramsey formula ): ${\displaystyle \gamma }$

${\displaystyle r_{t}=\delta +\gamma g_{t}}$

where (sometimes also ) is the social discount rate, the (social) time preference rate (or the social rate of pure time preference), the growth rate of consumption and a weighting factor for this, the relative aversion to intertemporal inequality. ${\displaystyle r_{t}}$ ${\displaystyle \rho _{t}}$ ${\displaystyle \delta }$ ${\displaystyle g_{t}}$ ${\displaystyle \gamma }$

The social time preference rate is usually assumed for ethical reasons , because it is interpreted as a fundamental weighting of the welfare of future generations. The relative aversion to intertemporal inequality can be approximated empirically and is usually assumed to be a realistic approximation. The growth rate of consumption usually corresponds to long-term projections of the growth rate of the gross domestic product or is assumed to be uncertain. ${\displaystyle \delta =0}$ ${\displaystyle \gamma =2}$

If the growth rate is uncertain, this can be expressed in a modified Ramsey formula. Assuming that the uncertain future growth rates are independent of each other and normally distributed with the expected value and variance , the formula looks like this: ${\displaystyle g_{t}}$ ${\displaystyle \mu _{g}}$ ${\displaystyle \sigma _{g}^{2}}$

${\displaystyle r_{t}=\delta +\gamma \mu _{g}-0{,}5\gamma ^{2}\sigma _{g}^{2}}$

If the uncertainty is great enough, the social discount rate can also become negative.

Hyperbolic Discounting

Under certain conditions, the assumption of an uncertain growth rate in consumption leads to a decreasing discount rate: for points in the near future, cash flows are discounted at a higher discount rate, while future cash flows are discounted at lower discount rates. Because of the usual shape of the discount rate-time curve, this approach is known as hyperbolic discounting .

A special form of hyperbolic discounting is the gamma discounting proposed by Martin L. Weitzman . To deal with the uncertainty about the “correct” social discount rate, Weitzman asked a large sample of economists what they believed to be the “best estimate for an appropriate real discount rate that should be used to evaluate environmental projects over a long time horizon ”. He received a total of 2160 values; If one ignores 49 non-positive values ​​(three negative, 46 times zero), they give approximately a gamma distribution . The approach was criticized by Partha Dasgupta as lacking a theoretical basis and too sweeping.

A much discussed problem of hyperbolic discounting is the so-called time inconsistency - decisions that are made in advance at the time for the time no longer appear desirable or attractive at the time. Starting from point in time is the discount rate between points in time and the low long-term discount rate; at the moment , however, it is the high short-term discount rate. Against this objection it was pointed out that the time inconsistency only occurs when the pure time preference varies over time; if the hyperbolic structure of the discount rate is a result of uncertainty about objective conditions in the world (e.g. growth rate of consumption), time inconsistencies do not arise. ${\displaystyle 0}$ ${\displaystyle t}$ ${\displaystyle t}$ ${\displaystyle 0}$ ${\displaystyle t}$ ${\displaystyle t+1}$ ${\displaystyle t}$

Social Discount Rates in Climate Economics

The theoretical discussion of social discount rates was particularly stimulated by the economics of climate change . In 2006 the influential Stern Report appeared , in which a comparatively low social discount rate was chosen. Furthermore, Stern chose a positive (very small) value for the time preference on the grounds that this represents the probability that humanity will perish at any point in time due to a random (stochastic) event. This led to an intense debate about the appropriate choice of social discount rates for their use in climate economics and especially in so-called integrated assessment models ( IAM ). It was not only about the selection of the “correct” parameters for the Ramsey function, but also generally about the type of definition of the social discount rate. While most economists view this as a normative approach, some economists (notably William D. Nordhaus and Richard Tol ) argue that the social discount rate should be the market rate. The choice of the social discount rate is important because it is one of the most influential factors in economic climate models (IAM). The present value of $ 1 million in damage in 100 years is $ 369,000 at a discount rate of 1%, $ 52,000 at 3%, and $ 1,152 at 7%. ${\displaystyle \delta }$ ${\displaystyle t}$

Values ​​for intertemporal inequality aversion in climate economic models are usually in the range . ${\displaystyle 1\leq \gamma \leq 3}$

Recommendations for social discount rates

In some countries there are government recommendations for social discount rates for the evaluation of environmental projects. In the UK , the 2018 Green Book recommends a decreasing social discount rate: 3.5% for the first 30 years, 3% for years 31–75, 2.5% for years 76–125. Lower discount rates are recommended in a health context. In France , as a result of the so-called Legégue report , a decreasing social discount rate was recommended for the first time (4% for the first 30 years, 2% beyond); In 2013 the values ​​were updated and are now 2.5% by 2070 and 1.5% after 2070 (“risk-free social discount rate”).

literature

• Christian Gollier: Pricing the Planet's Future: The Economics of Discounting in an Uncertain World . Princeton University Press, Princeton, Oxford 2013, ISBN 978-0-691-14876-2 .
• John Gowdy, Richard B. Howarth, Clem Tisdell: Discounting, Ethics and Options for Maintaining Biodiversity and Ecosystem Integrity . In: Pushpam Kumar (Ed.): The Economics of Ecosystems and Biodiversity: Ecological and Economic Foundations . Routledge, Abingdon, New York 2010, ISBN 978-0-415-50108-8 , pp. 257-283 .
• Kenneth Arrow et al .: Should Governments Use a Declining Discount Rate in Project Analysis? In: Review of Environmental Economics and Policy . tape 8 , no. 2 , 2014, p. 145-163 , doi : 10.1093 / reep / reu008 .
• Nicholas Stern: Economics of Climate Change: The Stern Review . Cambridge University Press, Cambridge 2007, ISBN 978-0-521-70080-1 .

Individual evidence

1. ↑ Gollier (2013) also cites Ramsey Henry Sidgwick , Roy F. Harrod , Tjalling C. Koopmans and Robert M. Solow (p. 31) in this context .
2. ↑ This interpretation was first discussed by Nicholas Stern in his Stern report on climate economics.
3. ^ Martin L. Weitzman: Gamma Discounting . In: American Economic Review . tape 91 , 2001, p. 260-271 .
4. ↑ “best estimate of the appropriate real discount rate to be used for evaluating environmental projects over a long time horizon” in Weitzman (2001), p. 271.
5. ↑ Partha Dasgupta: Human Well-Being and the Natural Environment . Oxford University Press, Oxford 2001, ISBN 0-19-924788-9 , pp. 187-190 .
6. ^ Arrow (2014); Gollier (2013), pp. 64–66.
7. ↑ See Arrow et al. (2014).
8. ↑ Charles Kolstad, Kevin Urama et al. a .: Social, Economic, and Ethical Concepts and Methods . In: Ottmar Edenhofer u. a. (Ed.): Climate Change 2014: Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change . S. 230 .
9. ^ HM Treasury: The Green Book: Central Government Guidance on Appraisal and Evaluation . ISBN 978-1-912225-57-6 ( PDF ).
10. ↑ Jincheng Ni (2017): Discount rate in project analysis . France Stratégie; PDF .
11. ↑ Émile Quinet et al .: L'Évaluation socioéconomique des investissement publics . Comissariat général à la stratégie et à la prospective, 2013 ( PDF ).