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
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
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
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.
pi = probability of event i occurring (0 ≤pi ≤ 1)
Bi = benefit if event i occurs
Ci = cost if event i occurs
Example: rainfall and irrigation with three outcomes
prob(low) = ¼ NB(low) = 4.5
prob(normal) = ½ NB(normal) = 0.6
prob(high) = ¼ NB(high) = 0.0
E[NB] = 0.25*4.5 + 0.50*0.6 + 0.25*0.0 = 1.425
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.
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.).
Example: decision tree analysis for a vaccination program
Initial decision: trunk
Final outcomes: branches
Backward solution, with pruning.
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
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!
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.
Monte Carlo simulation
Goal: use as much information as available.
1. specify full probability distributions for key parameters 2. randomly draw from distributions and compute NB
3. repeat to generate a distribution of NB.
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.