1. AGEC 608 Lecture 07, p. 1 AGEC 608: Lecture 7 Objective: Discuss methods for dealing with uncertainty in the context of a benefit-cost analysis Readings: –Boardman, Chapter 7 Homework #2: Chapter 3, problem 1 Chapter 3, problem 2 Chapter 4, problem 3 due: next class Homework #3: Chapter 4, problem 2 Chapter 5, problem 1 Chapter 6, problem 4 due: March 27

2. AGEC 608 Lecture 07, p. 2 Homework #2 Hint for Chapter 4, question 3b Net benefits = Change in consumer surplus + after tax change in producer surplus + net gain to taxpayers (lower tax) + net gain to taxpayers x METB (less DWL) Tax payers enjoy a reduction in tax payments and the reduction in tax payments also leads to a reduction in deadweight loss

3. AGEC 608 Lecture 07, p. 3 Three methods for dealing with uncertainty 1. Expected value analysis assign probability weights to contingencies 2. Sensitivity analysis vary assumptions and examine outcomes 3. Value new information find the value of information as it applies to the uncertainty under consideration

4. AGEC 608 Lecture 07, p. 4 1. Expected value analysis Goal: imagine a set of exhaustive and mutually exclusive outcomes, determine their relative likelihoods, and compute the probability- weighted value of benefits and costs. Contingencies (scenarios) should represent all possible outcomes between extremes.

5. AGEC 608 Lecture 07, p. 5 1. Expected value analysis p i = probability of event i occurring (0 ≤ p i ≤ 1) B i = benefit if event i occurs C i = cost if event i occurs

6. AGEC 608 Lecture 07, p. 6 1. Expected value analysis Example: rainfall and irrigation with three outcomes prob(low) = ¼ NB(low) = 4.5 prob(normal) = ½NB(normal)= 0.6 prob(high) = ¼NB(high)= 0.0 E[NB] = 0.25*4.5 + 0.50*0.6 + 0.25*0.0 = 1.425

7. AGEC 608 Lecture 07, p. 7 1. Expected value analysis If the relationship between outcomes and the underlying uncertainty is linear, and if outcomes are equally likely, then only two events are required to obtain an accurate estimate. But in general, the less uniform the probabilities, and the more variant the net benefits, the more important sensitivity analysis will be to obtaining an accurate picture of expected outcomes.

8. AGEC 608 Lecture 07, p. 8 1. Expected value analysis What if the project is long-lived? If risks are independent, then the E[NB] approach can be applied directly. If risks are not independent, then some advanced form of decision analysis is required (Bayesian inference, dynamic programming, etc.).

9. AGEC 608 Lecture 07, p. 9 1. Expected value analysis Example: decision tree analysis for a vaccination program Initial decision: trunk Final outcomes: branches Backward solution, with pruning.

10. AGEC 608 Lecture 07, p. 10 2. Sensitivity analysis Goal: study how outcomes change when we change underlying assumptions. “Complete” sensitivity analysis is typically impossible. Three main approaches: partial sensitivity analysis worst-case and best-case analysis Monte Carlo simulation

11. AGEC 608 Lecture 07, p. 11 2. Sensitivity analysis Partial sensitivity analysis choose an important assumption in the model and find the “break even” value for the parameter of interest. At what value of “x” would the project be worthwhile? Practical problem: how can you determine what is important (and therefore crucial for sensitivity analysis) before doing the sensitivity analysis!

12. AGEC 608 Lecture 07, p. 12 2. Sensitivity analysis Worst-case and best-case analysis Study outcomes associated with extreme assumptions. If net benefits are a non-linear function of a parameter, then care may be required. It often may be necessary to examine combinations of parameters.

13. AGEC 608 Lecture 07, p. 13 2. Sensitivity analysis Monte Carlo simulation Goal: use as much information as available. Three steps: 1. specify full probability distributions for key parameters 2. randomly draw from distributions and compute NB 3. repeat to generate a distribution of NB.

14. AGEC 608 Lecture 07, p. 14 3. Value new information Goal: find out if it is beneficial to delay a decision in order to use information that may become available in the future. Especially important if decisions are irreversible (quasi-option value) Example: irreversible development of a wilderness area.