Social discounting. The Ramsey rule and climate change. Emma Heikensten

Transcription

1 Social discounting The Ramsey rule and climate change Emma Heikensten

2 How to derive the Ramsey rule? 2 periods, 0 and t Consumption now: co Consumption at t: ct=w-k Intertemporal utility: U(co, ct) Saving k yields f(k) for future consumption f(k) is increasing and concave, the marginal product is positive and decreasing.

3 tangent to this feasibility frontier. Because U is concave, indifference curves are convex. All plans represented by points above this curve yield an intertemporal welfare that is larger than How to maximize intertemporal consumption? U A. It clearly appears that the preferred consumption plan in the feasible set is plan A, which yields an intertemporal welfare U A. There is no feasible consumption plan that generates a level of intertemporal welfare larger than that. c t U(c 0,c t )=U A c t =f(k) A c 0 =w-k w c 0 Figure 1.1: The optimal consumption plan

4 The rate of return to capital and the welfare preserving rate of return to marginal savings should be equal ρk=ρu Market interest rate: ρm. A simple arbitrage argument ρk=ρu=ρm Investing in project where the costs are ϵ and the benefits ϵ*e^rt, where r is the internal rate of return to the project. To invest the minimum rate of return has to be r=ρk=ρu=ρm.

5 The intertemporal utility function Assuming additive time preferences: U(co, ct) = u(co) + v(ct) v(c)=e^-δt * u(c) δ is not the discount rate in the sense which future cash flows are discounted. It is the minimum interest rate that you would ask for give up money now for later. =u (co)/(u (ct) e^-δt )

6 Rate of return and the discount factor From previously we know that the internal rate of return to a project, r; And =u (co)/u (ct)*e^-δt

7 The Ramsey rule Taylor expansion of u (ct) around co r= δ + (1/t) ((ct-co)/co)*co*u (co)/u (co) Assuming: r =δ+ g*γ

8 So what does this imply? δ & γ can be either ethical policy choices or be determined by market rates. if determined by markets:δ will be chosen in relation to the market interest rate and γ withdrawn from inequality/risk aversion and by looking at choices of redistribution. The growth rate, g, is usually withdrawn from previous trends and beliefs about the future.

9 What numbers are used?

10 Does a couple of percentage points matter? The difference between different schemes increase as longer time periods are examined. Discount rate Value of 100 in 10 years Value of 100 in 100 years 3,5% ,003 4% ,0006 1,4% ,5 5% 61 0,7 0,00003 Value of 100 in 300 years

11 Should we apply a lower discount rate after 30 years? France and the UK use declining discount rate schedules All costs and benefits occurring in the same year are discounted at a rate that is declining over time. Two branches of literature on declining discount rates. Extended Ramsey model Expected Net Present value

12 Why should discount rates be declining over the years? Declining rates are justified by increasing uncertainty of future economic growth (can be seen as a type of insurance) When the uncertainty estimate is included in the Ramsey rule: Relative risk aversion: γ Relative prudence: (γ+1) Variance of the growth rate:

13 Choosing too low values or including uncertainty? The treatment of ethics on the one hand, and risk and uncertainty on the other, interact. Choosing an ethical standpoint would imply lower discount rates. Including uncertainty about growth rates the discount rate would decrease. Further in the future effects of climate change are more uncertain especially when looking at developing countries, agriculture, diseases and large flows of immigration to colder developed countries.

14 Which values do I consider reasonable? Market rates - More risk taking than what is appropriate Why would our generation have more right to the nature than coming generations? - Have no right to diminish their possibilities. Important uncertainties in growth Inequality aversion could be determined by market. δ γ (stern) γ Uncertainty measure Final discount rate 0,001 1,3 2 0,5*σ 2 (γ+1) γ 2-2,5

15 Some references Gollier C (2011). Pricing the future: The economics of discounting. Princeton Press. Chapters 1,2,3,4. Arrow et al (2012). How Should Benefits and Costs Be Discounted in an Intergenerational Context? RFF Discussion Paper October 2012 Caney, S. (2008). "Human rights, climate change, and discounting " Environmental Politics 17(4): Nordhaus, W. D. (2007). "A Review of The Stern Review on the Economics of Climate Change." Journal of Economic Literature 45(3): Weitzman, M. L. (2007). "A review of the Stern Review on the Economics of Climate Change." Journal of Economic Literature 45(3):