1. AGEC 608 Lecture 10, p. 1 AGEC 608: Lecture 10 Objective: Examine arguments regarding the social discount rate and the “appropriate” discount rate Readings: –Boardman, Chapter 10 Homework #3: Chapter 4, problem 2 Chapter 5, problem 1 Chapter 6, problem 4 due: today Homework #4: Chapter 7, problem 3 Chapter 10, problems 1 + 2 Chapter 13, problem 3 due: April 11

2. AGEC 608 Lecture 10, p. 2 Discounting for time Choosing a social discount rate is equivalent to choosing a set of weights for the above problem. It is generally assumed that the weights decline over time (due to impatience and the productive role of investment). The value of weights is not a matter of agreement.

3. AGEC 608 Lecture 10, p. 3 Conceptual foundation See Fig. 10.1

4. AGEC 608 Lecture 10, p. 4 Five possibilities for w t 1. Marginal rate of return on private investment (r z ) 2. Marginal social rate of time preference (p z ) 3. Social opportunity cost of capital 4. Shadow price of capital 5. Hyperbolic discounting Plus, any of the above can be adjusted for: Risk or Real economic growth

5. AGEC 608 Lecture 10, p. 5 w t = marginal rate of return on private investment Argument (due to Harberger): Government removes resources from the private sector, so return on government project should exceed return on private investment s = ar z + (1-a)p z where a = ΔI/(ΔI + ΔC) (a ≈ 1 “crowding out”): Main Criticism: If project if financed by taxes rather than loans, then consumption will be crowded out.

6. AGEC 608 Lecture 10, p. 6 w t = marginal social rate of time preference Argument: Social discount rate should equal rate at which individuals are willing to postpone consumption s = p z (low value 0 – 2%) Main Criticism: Aggregation across individuals is difficult. Future ignored.

7. AGEC 608 Lecture 10, p. 7 w t = weighted social opportunity cost of capital Argument: Projects are financed by domestic borrowing (a), foreign borrowing (b) and domestic consumption (1-a-b): WSOC = ar z + bi + (1-a-b)p z (range 5%-7%) Main Criticism: Each project is financed differently, so each project must be assessed using a different rate.

8. AGEC 608 Lecture 10, p. 8 w t = shadow price of capital Argument : Projects generate flows of investment ( ≈ 15%) and consumption (≈85%). These should be weighted differently: Range 1.5%-2.5% Main criticism: complicated, w/high information requirement δ =capital depreciation f = fraction of return reinvested

9. AGEC 608 Lecture 10, p. 9 w t = hyperbolic discounting Argument: Empirical evidence suggests people use lower discount rates for event far in the future and constant discount rates assign very low weight to future events. Rate should decline over time, but this raises both theoretical and practical concerns.

10. AGEC 608 Lecture 10, p. 10 w t in practice US Office of Management and Budget real interest rates:1.6%-7.9% (1979-2003) www.whitehouse.gov/omb/circulars/a094/DISCHIST-2003.pdf 7% (2003) www.whitehouse.gov/omb/circulars/a094/a094.html

11. AGEC 608 Lecture 10, p. 11 Discounting for time and uncertainty r = rate of return on investments (risk free (f) and risky portfolio (m)). beta = measure of systematic risk for investment i. no risk w/risk

12. AGEC 608 Lecture 10, p. 12 Examples