Social Discount Rate

1. Social Discount Rate Guest Lecturer: Paulina Jaramillo 12-706 / 19-702 /73-359 Lecture 5

2. Admin Issues • Pipeline case study writeup - due Monday • Format expectations: • Framing of problem (see p. 7!), • Answer/justify with preliminary calculations • Don’t just estimate the answer! • Do not need to submit an excel printout, but feel free to paste a table into a document • Length: Less than 2 pages.

3. Real and Nominal Values • Nominal: ‘current’ or historical data • Real: ‘constant’ or adjusted data • Use deflator or price index for real • Generally “Real” has had inflation/price changes factored in and nominal has not • For investment problems: • If B&C in real dollars, use real disc rate • If B&C in nominal dollars, use nominal rate • Both methods will give the same answer

4. Nominal Discount Rates • Market interest rates are nominal • They ideally reflect inflation to ensure value • Buy $100 certificate of deposit (CD) paying 6% after 1 year (get $106 at the end). Thus the bond pays an interest rate of 6%. This is nominal. • Whenever people speak of the “interest rate” they're talking about the nominal interest rate, unless they state otherwise.

5. Real Discount Rates • Suppose inflation rate is 3% for that year • i.e., if we can buy a “basket of goods” today for $100, then we can buy that basket next year and it will cost $103. • If buy the $100 CD at 6% nominal interest rate.. • Sell it after a year and get $106, buy the basket of goods at then-current cost of $103, we will have $3 left over. • So after factoring in inflation, our $100 bond will earn us $3 in net income; a real interest rate of 3%.

6. Example • Real rate r, nominal i, inflation m • Real = nominal - inflation • Since inflation usually positive, real < nominal • So Simple method: r ~ i-m <-> r+m~i • More precise: • Example: If i=10%, m=4% • Simple: r=6%, Precise: r=5.77%

7. Garbage Truck Example • City: bigger trucks to reduce disposal $$ • They cost $500k now • Save $100k 1st year, equivalent for 4 yrs • Can get $200k for them after 4 yrs • MARR 10%, E[inflation] = 4% • All these are real values (why?) • See “RealNominal” spreadsheet for nominal values

8. Other Real and Nominal Values • Economic metrics like GDP, income, wages, etc. all come in real, nominal forms • Example: real vs. nominal GDP • If GDP is $990B in $2000.. (this is nominal) • and GDP is $1,730B in $2001 (also nominal) • Then nominal GDP growth = 75% • If 2000 2001 GDP equal to $1450B “in $2000”, then that is a real value and real growth = 46% • Then we call 2000 a “base year” • Use this “GDP deflator” to adjust nominal to real • GDP deflator = 100 * Nominal GDP / Real GDP • =100*(1730/1450) = 119.3 (changed by 19.3%)

9. Similar Idea : Exchange Rates / PPP • Big Mac handout • Common Definition of inputs • Should be able to compare cost across countries • Interesting results? Why? • What are limitations?

10. Is it worth to spend $1 million today to save a life 10 years from now? • How about spending $1 million today so that your grand children can have a lifestyle similar to yours?

11. Discounting Handout • How much do/should we care about people born after we die? • Ethically, no one’s interests should count more than another’s: “Equal Standing”

12. Social Discount Rate • Rate used to make investment decisions for society • Most people tend to prefer current, rather than future, consumption • Marginal rate of time preference (MRTP) • Face opportunity cost (of foregone interest) when we spend not save • Marginal rate of investment return

13. Intergenerational effects • We have tended to discuss only short term investment analyses (e.g. 5 yrs) • Economists agree that discounting should be done for public projects • Do not agree on positive discount rate

14. Climate Change • Discussions ongoing about how best to manage global CO2 emissions to limit effects of global change. • Should we sacrifice short-run economic growth to do something to improve environment and leave resources for the future?

15. Two Questions • What duty do we have to make sacrifices for future generations? • If we sacrifice, what is the optimal policy to maximize benefit? • So we should compare global change proposals with alternatives • Perhaps higher R&D spending on science or medicine would have higher benefits!

16. Government Discount Rates • US Government Office of Management and Budget (OMB) Circular A-94 • http://www.whitehouse.gov/omb/circulars/a094/a094.html • Discusses how to do BCA and related performance studies • Match real values with real discount rates, etc • How to do sensitivity analysis / which inputs to vary • What discount, inflation, etc. rates to use • Basically says “use this rate, but do sensitivity analysis with nearby rates”

17. OMB Circular A-94, Appendix C • Provides the current suggested values to use for federal government analyses • http://www.whitehouse.gov/omb/circulars/a094/a94_appx-c.html • Revised yearly, usually “good until January of the next year” • How would the government decide its discount rates? • What is the government’s MARR?

18. Historic Nominal Interest Rates (from OMB A-94)

19. Real Discount Rates (from A-94)

20. What do people think • Cropper et al surveyed 3000 homes • Asked about saving lives in the future • Found a 4% discount rate for lives 100 years from now

21. Hume’s Law • Discounting issues are normative vs. positive battles • Hume noted that facts alone cannot tell us what we should do • Any recommendation embodies ethics and judgment • E.g. focusing on ‘highest NPV’ implies net benefits is only goal for society

22. Some Issues Arise • Equal standing does not imply different generations have equal claims to present resources! • Harsanyi says only do so if their marginal gain is higher than our loss

23. If future generations will be better off than us anyway • Then we might have no reason to make additional sacrifices • There might be ‘special standing’ in addition to ‘equal standing’ • Immediate relatives vs. distant relatives • Different discount rates over time • Why do we care so much about future and ignore some present needs (poverty)

24. A Few More Questions • Current government discount rates are ‘effectively zero’ • What does this mean for projects and project selection decisions? • What does it say about intergenerational effects? • What are implications of zero or negative discount rates?

25. Comprehensive Everglades Restoration Project • Comprehensive project to restore natural water flow to the Florida Everglades. • Enhance water supply to South Florida region. • Provide continuous flood protection. See more info at http://www.evergladesplan.org/

26. Indian River Lagoon-South (IRLS) • Part of Everglades Restoration Project. • Total Cost of $1.21 billion. • Annual Benefits of $159 million after project is completed in 2015. • Find NPV of first 25 years of project.

27. $159 per year 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 $0.425 $2.043 $12.62 All values are in millions $447.3 $748.3 IRLS Cash Schedule

28. NPV of Project What would NPV be if we used a negative discount rate?

29. NPV of Project

30. Next Up: • Friday’s review: microeconomics • Supply, demand, pareto efficiency, etc. • Monday - Pipeline Case • Sensitivity Analysis (next wed) • Skim Clemen Chapter 5 Refers to decision/trees, etc that we have not done yet (ignore that part) • Next Friday: Using @RISK