1. CHAPTER 6 THE SOCIAL DISCOUNT RATE

2. DOES THE CHOICE OF DISCOUNT RATE MATTER? Yes – choice of rate can affect policy choices. Generally, low discount rates favor projects with the highest total benefits. High SDRs rates favor projects where the benefits are front-end loaded. Yes – choice of rate can affect policy choices. Generally, low discount rates favor projects with the highest total benefits. High SDRs rates favor projects where the benefits are front-end loaded.

3. APPROPRIATE SOCIAL DISCOUNT RATES WITH EFFICIENT CAPITAL MARKETS

4. Two considerations of importance to individual decisions provide a basis for discounting future costs and benefits the marginal rate of time preference the marginal rate of return on private investment Two considerations of importance to individual decisions provide a basis for discounting future costs and benefits the marginal rate of time preference the marginal rate of return on private investment

5. An Individual’s Marginal Rate of Time Preference (MTRP) An individual’s MRTP is the proportion of additional consumption that an individual requires in order to postpone (a small amount of) consumption for one year.

6. Equality of Discount Rates Given efficient capital markets, an individual’s MRTP equals the market interest rate. In a two-period model, an individual may consume everything (T) in the first period, she may invest it all in the first period and consume T(1 + i) in the second period, or she may consume at any intermediate point, which is represented by the budget constraint in Figure 10.1.

7. MRTP in a Two-Period World Consumption is maximised at the point where the indifference curve is tangent to the budget constraint, -(1 + i), i.e. at point A. At point A, the slope of the indifference curve is - (1+p), the marginal rate of substitution (MRS) is 1+p, and MRTP is p. Consequently, i = p ≠ r. Note that as current consumption increases, MRS and MRTP decrease.

8. Rate of Return on Private Investment Equals the Market Rate Equals MRTP Given a more general, multi-individual, two-period model, the marginal social rate of time preference will equal the marginal rate of return on investment, where the slope of the social indifference curve equals the slope of the consumption possibility frontier. These rates would also equal the economy-wide market interest rate, i (= r), This implies that all individuals will have the same MRTP because if their MRTP > i they would borrow at i and consume more in the current period until their MRTP = i; if MRTP < i they would invest until their MRTP = i. Since everyone’s MRTP equals i, it should be the unanimous choice for the social discount rate. Given a more general, multi-individual, two-period model, the marginal social rate of time preference will equal the marginal rate of return on investment, where the slope of the social indifference curve equals the slope of the consumption possibility frontier. These rates would also equal the economy-wide market interest rate, i (= r), This implies that all individuals will have the same MRTP because if their MRTP > i they would borrow at i and consume more in the current period until their MRTP = i; if MRTP < i they would invest until their MRTP = i. Since everyone’s MRTP equals i, it should be the unanimous choice for the social discount rate.

9. Consumption and Investment in a Two Period Model An actual economy (with taxes, risk and transaction costs) would not operate at the optimal point X, but at a point such as Z. Here, society would underinvest and r x > p x. Furthermore, because different people face different tax rates, risk preferences and transaction costs, numerous values exist for both MRTPs and the marginal rate of return on investment.

10. ALTERNATIVE SDRs

11. ALTERNATIVE SDR METHODS 1 Methods that assume that the social discount weights are constant over time SDR(1) = the marginal rate of return on private- sector investments, r z ; SDR(2) = the marginal social rate of time preference, p z ; SDR(3) = a weighted average of p z, r z, and i, where i is the government's real, long-term borrowing rate, where the weights reflect the amount of the project's resources that are financed by consumption, investment, and foreign borrowing, respectively. Methods that assume that the social discount weights are constant over time SDR(1) = the marginal rate of return on private- sector investments, r z ; SDR(2) = the marginal social rate of time preference, p z ; SDR(3) = a weighted average of p z, r z, and i, where i is the government's real, long-term borrowing rate, where the weights reflect the amount of the project's resources that are financed by consumption, investment, and foreign borrowing, respectively.

12. ALTERNATIVE SDR METHODS 2 Methods that assume that the social discount rates vary over time SDR(4) = The shadow price of capital method, distinguishes between a project’s effect on investment and on consumption. SDR(5) = Future generations model A, discount rate declines with the time horizon of the project. SDR(6) Future generations model B, discounts benefits and costs using s G, a rate based on the growth in real per capita consumption. Methods that assume that the social discount rates vary over time SDR(4) = The shadow price of capital method, distinguishes between a project’s effect on investment and on consumption. SDR(5) = Future generations model A, discount rate declines with the time horizon of the project. SDR(6) Future generations model B, discounts benefits and costs using s G, a rate based on the growth in real per capita consumption.

13. Logic of Each Alternative

14. SDR(1) Using the Marginal Rate of Return on Private Investment (r z ) The argument for using the marginal rate of return on private investment as the social discount rate is that society should receive an equal rate of return in the public sector to what it would have received had the resources remained in the private sector. The assumption is that almost all of the resources for public-sector investment are obtained by crowding out private-sector investment The argument for using the marginal rate of return on private investment as the social discount rate is that society should receive an equal rate of return in the public sector to what it would have received had the resources remained in the private sector. The assumption is that almost all of the resources for public-sector investment are obtained by crowding out private-sector investment

15. Finding r z using CAP-M (it’s expected market return, adjusted for inflation, but not taxes) The capital asset pricing model (CAP-M) provides guidance about how to value a benefit stream in the presence of systematic risk. It states that the expected rate of return on equals the risk-free rate plus an amount thatcompensates for systematic risk: E(r z ) = r f +  m  [E(r m ) - r f ] where E(r z ) is the expected rate of return on investment, E(r m ) is the expected rate of return to the market portfolio, r f is the risk-free rate of return, E(r m ) - r f is the market risk premium, and  i is a measure of systematic risk. The capital asset pricing model (CAP-M) provides guidance about how to value a benefit stream in the presence of systematic risk. It states that the expected rate of return on equals the risk-free rate plus an amount thatcompensates for systematic risk: E(r z ) = r f +  m  [E(r m ) - r f ] where E(r z ) is the expected rate of return on investment, E(r m ) is the expected rate of return to the market portfolio, r f is the risk-free rate of return, E(r m ) - r f is the market risk premium, and  i is a measure of systematic risk.

16. ADJUSTING for SYSTEMATIC RISK 2 Investments whose payoffs vary more than the business cycle have beta > 1. Investments whose payoffs vary directly with the business cycle have beta = 1. Investments whose payoffs vary weakly with the business cycle have 0 < beta < 1. Investments whose payoffs are independent of the business cycle have beta = 0. Investments whose payoffs vary inversely with the business cycle have a negative beta. Since  m = 1, E(r z ) = E(r m ) =.08 - 2 = 6% ±2% Investments whose payoffs vary more than the business cycle have beta > 1. Investments whose payoffs vary directly with the business cycle have beta = 1. Investments whose payoffs vary weakly with the business cycle have 0 < beta < 1. Investments whose payoffs are independent of the business cycle have beta = 0. Investments whose payoffs vary inversely with the business cycle have a negative beta. Since  m = 1, E(r z ) = E(r m ) =.08 - 2 = 6% ±2%

17. CAP-M

18. The Certainty of Debt and Taxes

19. SDR(2) Using the Marginal Social Rate of Time Preference Method (p z ) In practice, the best return that most people can earn in exchange for postponing consumption is the real after-tax return on savings. Starting with the nominal, pre-tax interest rate on government bonds and adjusting for taxes on savings and inflation yields estimates of p z between 0.00 and 0.04. Thus, this method suggests using a real SDR = 2% with sensitivity analysis at 0% and 4%. In practice, the best return that most people can earn in exchange for postponing consumption is the real after-tax return on savings. Starting with the nominal, pre-tax interest rate on government bonds and adjusting for taxes on savings and inflation yields estimates of p z between 0.00 and 0.04. Thus, this method suggests using a real SDR = 2% with sensitivity analysis at 0% and 4%.

20. SDR(3)Discounting Using the Weighted Social Opportunity Cost of Capital (WSOC) If a is the proportion of t a project's resources that displaces private domestic investment, b is the proportion financed by borrowing from foreigners, and 1-a-b is the proportion that displaces domestic consumption, SDC = the weighted average of these rates: WSOC = ar z + bi + (1 - a - b)p z where i is the government’s real, long term borrowing rate. Obviously, the previous methods are special cases of this more general approach, since As p z < i < r z, and p z < WSOC < r z If a is the proportion of t a project's resources that displaces private domestic investment, b is the proportion financed by borrowing from foreigners, and 1-a-b is the proportion that displaces domestic consumption, SDC = the weighted average of these rates: WSOC = ar z + bi + (1 - a - b)p z where i is the government’s real, long term borrowing rate. Obviously, the previous methods are special cases of this more general approach, since As p z < i < r z, and p z < WSOC < r z

21. SDR(4) The Shadow Price of Capital (SPC) Method The shadow price of capital method requires that discounting be done in four steps: -Costs and benefits in each period are divided into those that affect consumption and those that affect investment. (When in doubt use 15% investment, 85% consumption.) -Flows into and out of investment are multiplied by the SPC to convert them into consumption equivalents. -Changes in consumption are added to changes in consumption equivalents. -Resulting amounts are discounted at p z. The shadow price of capital method requires that discounting be done in four steps: -Costs and benefits in each period are divided into those that affect consumption and those that affect investment. (When in doubt use 15% investment, 85% consumption.) -Flows into and out of investment are multiplied by the SPC to convert them into consumption equivalents. -Changes in consumption are added to changes in consumption equivalents. -Resulting amounts are discounted at p z.

22. SDR(5) Time Declining Discount Rates There are three justifications for using a time- declining SDR: -Some evidence suggests that people use lower discount rates for events that occur farther into the future. -Long-term environmental and health consequences have small PV when discounted using a constant rate. -Constant rates do not appropriately take into account the preferences of future generations. There are three justifications for using a time- declining SDR: -Some evidence suggests that people use lower discount rates for events that occur farther into the future. -Long-term environmental and health consequences have small PV when discounted using a constant rate. -Constant rates do not appropriately take into account the preferences of future generations.

23. SDR(6) BASED ON THE REAL GROWTH RATE Society should treat all generations' welfare equally but should consider that future generations will likely have higher per capita consumption than the current generation due to ongoing economic growth.

24. Based on Solow/Swan modelSolow/Swan model Based on Solow/Swan modelSolow/Swan model y = f(k) = income n =  (employment) d = depreciation s = savings y = f(k) = income n =  (employment) d = depreciation s = savings