Time declining social discount rate Alex Dubgaard

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1 Time declining social discount rate Alex Dubgaard Pearce, David, Ben Groom, Cameron Hepburn & Phoebe Koundouri (2003): Valuing the Future. Recent advances in social discounting, World Economics. Vol. 4, No. 2, April June 2003, pp

2 Tyranny of discounting When discounting over very long time horizons Costs and benefits will be valued extremely low compared to costs and benefits today Known as: Slavery of the future. Discounting is at odds with sustainable development.

3 Example: CLOSE DOWN DENMARK (I) Assume that cost-benefit calculations show that the global costs of stabilising greenhouse gases exceed the benefits by a wide margin. It is therefore decided to continue without major restrictions on global GHG emissions under the clause that those to gain will compensate those to lose in the future. Over a few hundred years Denmark will come below sea level future Danes will be compensated in full for their loss of property and be given an offer to settle down elsewhere in Europe.

4 Example: CLOSE DOWN DENMARK (II) Assumptions: The value of real estate in Denmark is estimated at a good USD 238 billion. We apply a social discount rate of 5 per cent. Compensation requirements if the Danes have to move after: 100 years: USD 1.8 billion in present value. 200 years: USD 13.8 million. 500 years: USD 6 ($six).

5 The Traditional Approach: Exponential Discounting with Constant Discount Rate

6 The (exponential) discounting principle Let the weight attached to a gain or loss in any future year, t, be w t Discounting implies that w t < 1 The discounting formula is: Where The weight w t is the discount factor and s is the discount rate. If s = 4 %, then the discount factor for 50 years hence would be:

7 The Power of Exponential Discounting

8 No discounting? Solution: don t discount? No discounting equivalent to discount rate= 0 With zero discounting everybody is equal now and in the future Do we care as much for someone a thousand years from now as we do for someone now? And should we? Bigger sacrifices of current generations Not equitable if future economic growth is positive Slavery of the present.

9 Time declining discount rates

10 Time declining discount rates Could be solution to tyranny of discounting Constant discount rate Seems not to be the way people discount Rather, individuals discount rates decline as times goes on. This implies that the discount rate s should be specified as s t s will decline as t increases.

11 Why time declining rates? I. People tend to have hyperbolic preferences II. Uncertainty speaks for declining discount rate: Weitzman: uncertainty about future interest rates Gollier: uncertainty about the state of the economy.

12 Weitzman s approach Interest rates provide relative valuations of the future relative to the present But these relative valuations are uncertain. The weights are the discount factors, Rather than averaging likely future discount rates what should be averaged are the probabilistic discount factors This process produces discount rates that decline with time A numerical example shows this (see Table).

13 Weitzman s argument As the period of discounting increases uncertainty about the future will have an impact on the effective discount rate Example: We are uncertain of what discount rate to use It can be 2% or 4% with equal likelihood (row 1 and 2) As t increases the effective discount rate (row 4) approaches the lowest discount rate of the two scenarios considered, i.e. 2%.

14 Possible specification of time declining discount rate Hyperbolic discounting Traditional approach: Exponential discounting (DF = discount factor): 1 DFC t ( 1 r) Time declining discount rate: Hyperbolic discounting (DF = discount factor): e.g. in terms of logarithmic discounting DF L 1 ( 1 t)

15 d(t) Example: Hyperbolic versus exponential discounting DF L 1 ( 1 t) 22 1 Logarithmic discounting 0,8 Exponential discounting 0,6 0,4 0,2 Short term costs have lower relative weight DF C 1 ( ) Long term costs have higher relative weight t t

16 Hyperbolic discounting and climate change Source: Pearce et al. (2003) 16

17 Problem of time-inconsistency Time-declining discount rates solve the tyranny of discounting issue but create a time inconsistency problem For hyperbolic discount functions Long term project implementation costs will be relatively overvalued Short term project implementation costs will be relatively undervalued Creates an incentive to postpone investment at any time period i.e., a time inconsistency problem.

18 Social choice approach The social choice approach says The discount rate should be determined by axioms that make tyranny of discounting impossible That is, current (future) generations must always take into account the well-being of future (current) generations; there must be no dictatorship of one generation over another. Chichilnisky approach Present-day decision-makers adopt a mixed goal: maximising the discounted value of net benefits and a sustainability requirement that effectively amounts to a requirement to consider future generations well-being.

19 British approach A relevant solution to the intergenerational discounting problem? Official British guidelines for social CBA have adopted a modified approach: