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Cost-Benefit Analysis 2

Cost-Benefit Analysis 2 . How much pollution is too much?. Case Study: lead in drinking water. Standards required under the Safe Drinking Water Act. Lead leaches from solder (copper pipe) in water systems. EPA considered three options:. Case Study: lead in drinking water.

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Cost-Benefit Analysis 2

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  1. Cost-Benefit Analysis 2 How much pollution is too much?

  2. Case Study: lead in drinking water • Standards required under the Safe Drinking Water Act. • Lead leaches from solder (copper pipe) in water systems. • EPA considered three options:

  3. Case Study: lead in drinking water • Determining costs of compliance: • Which systems nationally would require remedial action and at what level? • Cost estimates of mitigating actions: • Water monitoring • Corrosion control studies • Control of pH • Public education efforts.

  4. Case Study: lead in drinking water • Impacts of lead contamination • Adults • Hypertension • Heart disease • Cancer • Infant mortality • Children • Growth inhibition • Reduced intelligence • Impaired hearing • Cancer

  5. Case Study: lead in drinking water • Which option should the EPA choose?

  6. Case Study: lead in drinking water • EPA chose Option B due to large uncertainties with Option A.

  7. Benefit-Cost Analysis (CBA) Summary • CBA used extensively by Federal agencies. • Advantages: • offers structured decision making. • Offers a method for evaluating the most efficient alternative. • Disadvantages • Does not cope well with uncertainty. • Tendency to leave out impacts that cannot be valued.

  8. Benefit-Cost Analysis (CBA) Summary • Guidelines for using CBA: • 1) Agencies should not be bound by outcomes of CBA, since other criteria may be more important; • 2) Benefits and costs should be quantified, but uncertainties should be explicitly noted; • 3) CBA studies should be subject to external review; • 4) Standard set of methods should be established; • 5) Assumptions should be clearly stated; • 6) Distributional impacts should be addressed: who wins, who loses?

  9. CBA, Climate Change, and Uncertain Discounting • Benefits from reducing climate change are long-term (> 100 years). • Few markets exist for investments with maturities exceeding 30 years. • What is the correct discount rate in 100 years? 200 years?

  10. CBA, Climate Change, and Uncertain Discounting • Interest rate on U.S. long-term government bonds. • Over the past 100 years, rates ranged between 2% and 7% (after inflation).

  11. CBA, Climate Change, and Uncertain Discounting • Present value of $100 in 100 years: • 7% discount rate => PV = $100/(1.07)100 = $0.12. • 2% discount rate => PV = $100/(1.02)100 = $13.80. • Let’s assume 7% and 2% are equally likely. • The expected (or mean) value of $100 is = 0.5*$0.12 + 0.5*$13.80 = $6.96. • Is $6.96 closer to $13.80 or $0.12? • That is, which discount rate (2% or 7%) dominates?

  12. CBA, Climate Change, and Uncertain Discounting • Add one more year: present value of $100 in 101 years: • 7% discount rate => PV = $100/(1.07)101 = $0.11. • 2% discount rate => PV = $100/(1.02)101 = $13.53. • Expected value = 0.5*$.11 + 0.5*$13.53 = $6.82.

  13. CBA, Climate Change, and Uncertain Discounting • PV fell from $6.96 after 100 years to $6.82 after 101 years, a decline of 2%. • Conclusion: at a 100 year time horizon, the higher discount rate (7%) has no effect at all and the lower rate (2%) dominates • 2% is the effective discount rate.

  14. CBA, Climate Change, and Uncertain Discounting • High rates discount future benefits so much that they add little to expected present value. • Suppose discount rate uncertainty ranges from a low of 2% to a high of 10%: • Expected PV of $100 in 100 years = $6.77. • Expected PV of $100 in 101 years = $6.91. • Expected PV drops by 2% (($6.77/ $6.91)-1). • Effective discount rate is still 2%.

  15. CBA, Climate Change, and Uncertain Discounting • Why can’t we simply average 2% and 7% for the discount rate 100 years from now? • Answer: because the discount factor matters, not the discount rate; discount factor: 1/(1+i)t • Discount factor for 7% = 1/(1.07)100 = 0.0011. • Discount factor for 2% = 1/(1.02)100 = 0.1380.

  16. CBA, Climate Change, and Uncertain Discounting • Over the long run we might expect an average interest rate of 4%. • An unexpectedly low discount rate raises valuations by a large amount. • An unexpectedly high discount rates reduces valuations by a small amount. • Conclusion: Uncertain discount rates raise estimates of future valuations relative to constant discount rates.

  17. CBA, Climate Change, and Uncertain Discounting • Simulation experiment: • Assume the 30 year bond interest rate follows a random walk over time: • it = it-1 + et, where et is random fluctuation (+/-). • This means that the interest rate for the current year is equal to the previous year interest rate plus a random factor that can be positive or negative.

  18. CBA, Climate Change, and Uncertain Discounting • I set a minimum of 2% and a maximum of 7%. • Each of these ten path is equally likely. • I generated 10,000 possible interest rate paths. • I figured the discount factor for each path, and averaged for the year.

  19. CBA, Climate Change, and Uncertain Discounting • A constant discount rate will underestimate the present value of future dollars. • After 80 years, discounting at a constant rate (4%) undervalues by 1.7 times. • After 100 years, discounting at a constant rate (4%) undervalues by a factor of 2.3. • After 200 years, constant discounting is off by a factor of 14.

  20. CBA and Uncertain Discounting • At a constant discount rate of 4%, the PV of $100 for 100 years is $2,450. • If the discount rate falls to 2% in just 20 random years, PV rises to $2,958 (+21%). • On the other hand, If the discount rate rise to 6% for 20 random years, the PV falls to $2,276 (-7%). • Below average discount rates have much more impact than do above average discount rates.

  21. CBA, Climate Change, and Uncertain Discounting • Uncertain discount rates increase our estimates of future valuations in comparison with constant discount rates. • Unexpectedly low discount rates raise valuations by a large amount. • Unexpectedly high discount rates reduce valuations by a small amount.

  22. CBA and Uncertain Discounting • Consequence: this means that over long time horizons, assuming that the discount rate is constant will produce a smaller NPV of benefits than will the more realistic case of variable discount rates.

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