1. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 1 Dottorato Climate Change and Policy Modelling Assessment: Discounting in Modelling Francesco Bosello

2. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 2 Discounting It pertains to our perception of time or more specifically on the comparison (preference) between the present and the future. This weighting process that we are consciously or unconsciously always applying is highly relevant as it governs our (intertemporal) decisions. Incidentally note that even indifference between (equal weight to) present and future is indeed a weighting.

3. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 3 Discounting There are basically two approaches to the discounting issue Prescriptive approach: what is the right or fair weight we have to place to different times when we are planning (or we are evaluating a plan)? Descriptive or positive approach: what is the weight agents (people, firms, etc.) effectively use when they plan intertemporally? This can vary according to the aim and nature of the specific decision, but is intrinsically a decision maker (policy or other) choice This is subjective; it can vary among individuals, societies/cultures, history, but is not a decision by the planner Clearly the two are linked

4. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 4 Why people discount? Reasons to discount Uncertainty, egoism Pure time preference Distributional concerns (inter intra temporal) Typically the future worth less than the present this is represented by a (discount) factor that decrease today the importance of tomorrow In discrete time In continuous time In a perfect world Productivity of capital (efficiency)

5. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 5 Discounting in a Ramsey world Pure time preference discounts utility impatience Elasticity of marginal utility to consumption discounts consumption distribution

6. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 6 Solving and summarising: g θ ρ => dr and DF future decreases its importance This is the traditional exponential discount rate

7. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 7 Consequences: e.g. the almost (2006) Stern Review Assumptions: 2 time periods today and tomorrow (100 years) g = 2% CC damages = 5% of GDP in 2100 (from PAGE) Mitigation costs = 1% of GDP today Is it worth spending the money now? YES if DB/C>1 With Stern Assumptions: ρ = 0 (0.001) θ = 1 With usual Assumptions: ρ = 2 θ = 2 => dr ~ 6%

8. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 8 Worth noticing (1) According to the descriptive approach to discounting the path is: from δF/ δKn, g and θ (supposingly observable) to ρ According to the perscriptive approach to discounting the path should be: from ρ fixed and δF/ δKn, g (supposingly observable) to θ Under the modelling point of view: any model which produces an endogenous path for consumption growth, must assume an exogenous PRTP. In intertemporal dynamic optimisation models a too low PRTP (close to zero) implies explosions in the latest periods present consumption drops to zero and unrealistic capital accumulation.

9. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 9 Worth noticing (2) ρ has inherently a equity content: a high ρ places higher weight on the present generation => (assuming a richer future generation) it reflects a distributional concern moving the burden of lower climate change from the present to the future (from poor to rich) However climate change is already more severely affecting todays poor than todays rich. This would ask for more abatement today by todays rich In the vast majority of IA models different utilities are not weighted => only the first component is taken into account => there is an implicit bias in favor of postponing abatement

10. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 10 Why discount rate(s) should be low? 1) Uncertainty about consumption growth (Heal, 2002,2005) ~ => As long as σ increases, the Dr decreases (discount factor increases)

11. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 11 Why discount rates should be low? 2) Existence of different goods in the maximand (Sterner, Persson, 2007) As long as c and e are substitutes θ(c,e)>0, if they are complements θ(c,e) Dr, depending on the interactions with g(e) Assume a consumption good (c) and an environmental good (e)

12. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 12 Alternative to exponential dr: a time-varying dr Decreasing discount rate (Lowenstein and Prelec, 1992; Weizman, 1998, 1999, 2001) Decreasing the weight of near future periods – increase that of far future periods Change in social preferences/perception/values Normative reason (rather than set the level of dr, set its evolution). Uncertainty about the true discount rates WHY?

13. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 13 The Weitzman Approach Suppose you are uncertain about the right Dr to use Possible Drs are: Dr1 and Dr2 with Dr1 > Dr2 With associated probabilities P(Dr1) and P(Dr2) And P(Dr1) + P(Dr2) = 1 Now. you could average across Drs and use a typical exponential Discount Factor with a constant Dr = E[Dr]: E[Dr] = P(Dr1)*Dr1 + P(Dr2)*Dr2 => => DF(t)=(1/(1- E[Dr]))^t or exp(- E[Dr])t This is wrong: you should look at discount factors What is the right discount factor to use?

14. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 14 => The appropriate average discount factor is: That after rearranging becomes: And taking the limit as t goes to infinity gives:

15. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 15 Two major implications In the discounting process (inside discount factors) discount rates are declining over time (as time passes the distant future becomes more important) moving from high to low discount rates As time goes by the prevailing discount rate is the lowest With uncertainty on the discount rates

16. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 16 Example Suppose dr = 0.05, t = 10. Find h such that ExpDF = HypDF The traditional and hyperbolic DF are equal at one point in time (t = 10). h = 0.202 Exponential DF (one possible) Hyperbolic DF

17. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 17 Declining discount rate: the Hallegatte perscriptive approach t=0 t=K N K-N The intuition: 1 individual living N years. Calculate the NPV in t=0 of 1 at t=K and K>N Usual Hyp disc. Intergenerational disc.

18. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 18 Declining discount rate: the Hallegatte perscriptive approach t=0 t=K N Now: 1 individual living N years. Calculate the NPV in t=0 of 1 at t=K and K<N Usual Hyp disc. Intergenerational disc.

19. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 19 Declining discount rate: the Hallegatte perscriptive approach t=0 t=K N Introducing the complication of OLG, suppose N=3, K>N G1 disc. G2 disc. G3 disc. G1 G2 G3

20. CENTRO EURO-MEDITERRANEO PER I CAMBIAMENTI CLIMATICI 20 Example