Highlights Chapter 10

1. Highlights Chapter 10

2. Overview • This chapter addresses the basic question about whether public projects should have a difference interest rate than private projects. • The issue is selection of a real social discount rate (SDR) with different weights in each of the future years. • Given these weights, denoted by wt, and estimates of the real annual net social benefits, NBt, the estimated net present value (NPV) of a project is given by: • The social discount rate (SDR) is equivalent to deciding on the appropriate set of weights to use in above. Sometimes the weights are referred to as social discount factors.

3. Discounting - given amount of real resources in the future is worth less today than the same amount is worth now, because: • using investment, one can transform resources that are currently available into a greater amount in the future. • People have a preference for consuming resources now, rather than in the future. • Social discount weights decline over time; • specifically, 0 <wn<wn-1< ... < w1<w0 = 1. • Key issue in this chapter concerns determining the weights.

4. Three issues • Whether market interest rates can be used to determine the weights. • Whether to include unborn future generations in determining the weights. • Whether society values a unit of investment the same as a unit of consumption. • Why worry about SDR: High SDRs favour project that are front loaded (benefits close to the present) and low SDRs favour projects with highest total benefits

5. Present and Future consumption – time preference and interest • The slope of the indifference curve reflects time preference • i is the market rate. • The marginal rate of time preference and market rate of interest determines the optimum ratio of present (CT)to future consumption (CT+1)

6. Perfect competition implies that social discount = private interest At x, social discount rate px - = rx the marginal rate of return on investment = market interest i • At X, the slope of the social indifference curve, -(1 + px), equals the slope of the consumption possibility frontier, -(1 + rx). • Consequently, the marginal social rate of time preference, px equals rx, the marginal rate of return on investment. • Furthermore, at point X these rates would also equal the economy-wide market interest rate, i. • Finally, at X, all individuals 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 and, if MRTP < I, they would postpone consumption by saving until their MRTP = i. Since everyone’s MRTP equals i, it would be the obvious choice for the SDR. Externalities, imperfect information At Z society would under invest and rz > pz

7. Non market approach to SDRS • Ramsey presented the “optimal growth rate method,” • Society discounts future consumption for two reasons: • society is impatient and prefers to consume more now than in the future; • there is economic growth. • Thus, px = d + ge, where px is the SDR based on the optimal growth rate method, • d is the pure rate of time preference, • g is the growth in per capita consumption, and • e is a constant (elasticity), that measures how fast the social marginal utility of consumption falls as per capita consumption rises. If e = 1, a 10 percent reduction in consumption today from (say) $40,000 to $36,000 would be viewed as an acceptable trade-off for a 10 percent increase in consumption (say) from $80,000 to $88,000 at some future point.

8. Marginal Rate of Return on Private Investment (rz) • Some favour a adjusted private rate as the basis for the SDR • Marginal Rate of Return on Private Investment (rz) government should be able to demonstrate that society will receive a greater rate of return than it would have received had the resources remained in the private sector. • This is easy when the investment is a pure public good – less so when the private sector could have provided some or all of the good.

9. SDR > private interest rate • In the absence of taxes and government borrowing, the demand curve for investment funds by private-sector borrowers is represented by Do and the supply curve of funds from lenders (or savers) is represented by So. • With corporate taxes and personal income taxes, the demand and supply curves would shift to DI and DS, respectively, resulting in a market clearing rate of i and a divergence between rz and pz, as discussed previously.

10. Harberger approach • Social discount rate should be obtained by weighting rz and pz by the respective size of the relative contributions that investment and consumption would make toward funding the project. SDR = arz + bpz where a = ΔI/(ΔI + ΔC) and b = (1 - a) = ΔC/(ΔI + ΔC). • Numerical Values of rz - the best proxy for rz is the real before-tax rate of return on corporate bonds (currently 4.5%),

11. Criticisms of the Calculation and use of rz. • Private sector rates of return incorporate a risk premium. Therefore, if benefits and costs are measured in “certainty equivalents,” as recommended by the text, then using private sector rates would result in “double counting,” i.e. it would account for risk in two ways. • A project might be financed by taxes, rather than by loans – hence, consumption would also be crowded out. • A project may be partially financed by foreigners at a lower rate than the corporate bond rate. • Private sector returns may be pushed upward by distortions caused by negative externalities and market prices that exceed marginal costs. Then rz needs to be adjusted down. • There is no fixed pool of investment where government investment replaces private investment dollar for dollar. If the government is not fully employing all its resources, then complete crowding out of private investment is unlikely. In this case rz is adjusted down.

12. Marginal Social Rate of Time Preference Method (pz) • SDR should be thought of as the rate at which individuals in society are willing to postpone a small amount of current consumption in exchange for additional future consumption (and vice versa). In principle, pz represents this rate. • The best return that many people can earn in exchange for postponing consumption is the real after-tax return on savings (i-CPI)

13. Criticisms of the Calculation and Use of pz: • Individuals differ in preferences and opportunities – some save and some borrow and some save by reducing debt. Since reducing some debt isn’t taxed, people who do this earn a much higher after-tax return than other people. • Because many individuals simultaneously pay mortgages, buy government bonds and stocks and borrow on credit cards at high interest rates, it is unclear whether individuals have a single MRTP. • As pz < rz, use of pz as the SDR may justify very long-term investments that provide low returns at the expense of higher-returns in the private sector, thereby harming efficiency, unless the public projects provide significant social benefit.

14. Government’s Borrowing Rate (i) • Reflects the government’s actual cost of financing a project. • Starting with the average monthly yield on 10-year Treasury bills for a 5 year period will yield about 3.5%

15. Criticisms of the Calculation and Use of i • Justified if only project beneficiaries pay the taxes needed to retire the government’s loan, which is unlikely. • Government cannot borrow at an unchanging real interest rate. • Government borrowing will raise real interest rates and also crowd out some private sector investment. • Use of i as the SDR assumes that the government’s borrowed funds were foreign, but this is unlikely.

16. Using the Weighted Average Approach (WSOC) • If a is the proportion of a project's resources that displace private domestic investment, • b is the proportion of the resources that displace domestic consumption, and • 1-a-b is the proportion of the resources that are financed by borrowing from foreigners, then…. • the weighted social opportunity cost of capital (WSOC), computes the social discount rate as the weighted average of rz, pz, and I and is given by. WSOC = arz + bpz + (1 - a - b)i As pz < i < rz, it follows that pz < WSOC < rz.

17. Criticisms of the Calculation and Use of WSOC • All the criticisms of using pz, rz, and i. • The value of the WSOC depends on the source of a project’s funding and thus would vary among projects. Governments usually prefer a single discount rate.

18. THE SHADOW PRICE OF CAPITAL (SPC 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. • 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 pz.

19. SPC (continued) A general expression for the shadow price of capital is: where rz is the net return on capital after depreciation, δ is the depreciation rate of the capital invested, f is the fraction of the gross return on capital that is reinvested, and pz is the marginal social rate of time preference.

20. Estimates of rz and pz (4.5 percent and 1.5 percent, respectively) are provided above, and with estimates for depreciation on capital being over 10%, the SPC can be quite high (> 15%) • SPC is not used when • a project is strictly tax financed; • the supply of foreign funds is extremely responsive to the interest rate; • the project is small; • the percentage of costs and benefits that comes from investment is the same in every period

21. Criticisms of the Calculation and Use of the SPC • difficult to explain to policymakers how and why NPV calculations are made • heavy information requirements relative to other discounting approaches • allocation of costs and benefits to investment and consumption is fairly subjective and open to manipulation • value of the SPC depends on the values of pz and rz and there can be subject to the above criticisms that apply to determining these parameters

22. Intergenerational Discounting (Time-declining SDR) • People use lower discount rates for events that occur farther into the future. • Long-term environmental and health consequences have very small present values when discounted using a constant rate, often implying that spending a relatively small amount today to avert a costly disaster several centuries in the future is not cost-beneficial. • Constant rates do not appropriately take into account the preferences of future, as yet unborn, generations. • Constant rates do not appropriately allow for uncertainty as to market discount rates in the future.