Economic Questions (Calculation Based)
flyingpig
Class9.pdf
TECON 480 – Class 9
August 16, 2019
Part 2 - Formulating the cost-benefit model
• Instructions available on Canvas for the following:
• Assignment #2 (due Sat, Aug 17 at midnight)
• Assignment #3 (due Mon, Aug 19 at midnight)
• Assignment #4 (due Wed, Aug 21 at midnight)
• Final report (due Sat, Aug 24 at midnight) • Includes template to use as starting point
• Final Exam due Sun, Aug 25 at midnight
• No class on Fri, Aug 23
2
Announcements / Reminders
Last Class
• Discussed the timing of costs and benefits and the concept of discounting
3
Today’s Class
• Work through an example of calculating NPV using a spreadsheet
• See an example of a CBA presentation of results
• Discuss the various components of presenting CBA results:
• Annotated model
• Written report
• Presentation slides
• Verbal presentation
4
Sensitivity Analysis in Discounting
• Determining the appropriate discounting method and the value of the social discount rate is often difficult, and this
creates a risk of bias (why?)
• Consequently, sensitivity analysis should usually be conducted on the discount rate
• We will discuss this concept more generally later in the course
• Useful to plot the NPV of a project for several possible values of the discount rate
5
Sensitivity Analysis in Discounting
Example:
• Suppose that implementing a carbon tax in WA would cost $20 billion in 2017 and $10 billion in 2020
• Benefits of $3 billion per year would be received annually from 2021 until 2050
• Calculate the NPV of the carbon tax using the following values for the social discount rate:
6 { }1%,2%,...,10%i =
Hint: use Excel to automate the calculations
(see ‘NPV example’ in the “Miscellaneous Files” folder on Canvas)
Undertaking & Presenting the Analysis
• In Part III, we turn to carrying out the analysis
• See ‘Example CBA Report’ in the ‘Miscellaneous Files’ folder in Canvas
• This (far from perfect!) report provides an example of how CBA is carried out in practice
• Also provides some insight into:
• The importance of uncertainty (our next topic)
• How to present (or not present) results to stakeholders
• Do you notice anything good or bad about each slide?
7
8
• “The estimated annual cost of congestion in the Greater Toronto-Hamilton area in 2006 was $6 billion. The figure is
part of a seminal study on the subject conducted by HDR
Corp. and released by Metrolinx in 2008.”
https://www.thestar.com/business/2013/11/29/gridlock_the_6
_billion_at_least_problem.html
9
Annotated Model Example
10
• See the Excel spreadsheet that I developed for the Metrolinx cost of congestion study:
• In the Miscellaneous Files folder:
TECON 480 - Class 9 (Annotated Model)
Written Report Example
11
• See the summary version of the report that we submitted to Metrolinx:
• In the Miscellaneous Files folder:
TECON 480 - Class 9 (Written Report)
Presentation Slides Example
12
• See the slides that we presented to Metrolinx:
• In the Miscellaneous Files folder:
TECON 480 - Class 9 (Presentation Slides)
Presentation Example
13
SR-710 North Study
• Details available at:
https://www.metro.net/projects/sr-710-conversations/
• “Caltrans and Metro are working together on the State Route 710 North Study to evaluate mobility and find traffic
congestion solutions between the western San Gabriel Valley
and the east/northeast area of Los Angeles.”
14
15
Presentation Example
16
• See consultant’s presentation of CBA results from 8:30 – 27:15 of the video linked below:
https://www.youtube.com/watch?v=IThg7XUiejw
Questions:
• What are the strengths of this presentation?
• What do you think could be improved?
Final Exam
• “Take-home” exam, “open book”
• Available on Canvas early next week
• Due by midnight on Sun, Aug 25
• Cumulative: anything discussed in class and/or in posted class notes
• No questions specifically related to the Pacific Avenue BRT project
• 8 short-answer questions, each worth 10 points
• 25% of overall course grade
17
Final Report
• Due by midnight on Aug 24
• 25% of course grade
• Objective: use your work from Assignments #1-4 and feedback provided to prepare a cost-benefit analysis report that you would
submit to project stakeholders
• Explain how the work was conducted, what assumptions were made (and why) and what the results of the analysis were
• Should be accessible to non-economists and those that have no knowledge of the CBA process
• Format up to you: it is important that reports are professional in appearance and that information is conveyed as clearly as possible
• No minimum or maximum number of pages, though 10-20 pages (including tables/graphs/figures) would be a rough guideline
• See “Final Report Template” for a starting point regarding the structure of the report and some more detailed instructions
18
Introduction
• When we conduct a CBA, we have to predict/forecast the future
• The decision/recommendation resulting from the CBA will be based on predictions that are uncertain by nature
• The purpose of this material is to understand how analysts can take uncertainty into account
19
Expected Value Analysis
• Expected value analysis: modeling uncertainty as contingencies with specific probabilities of occurrence
• Contingencies: possible events, outcomes, or states of the world
• One - and only one - of the relevant set of possibilities will occur
• Have to define different “scenarios” and assign probabilities to each of them
20
Expected Value Analysis
• Begin with the specification of a set of contingencies that are exhaustive and mutually exclusive
• In practice, this means the contingencies capture the full range of likely variation in net benefits and accurately represent possible
outcomes between the extremes
• Next step is to assign probabilities to each of them
• Probabilities must be non-negative and sum to one
• Probabilities can be based on historically observed frequencies, subjective assessments, or expert opinion
� They can be based on information, theory, or both 21
Example: assign probabilities to the effects of sea level rise in Tacoma
Example
• Assume there is a water storage system that irrigates agricultural land when there is not enough rainfall
• First, assume two extreme contingencies (equally likely)
• Extreme
• 22 inches of rainfall
• $0 in net benefits from the storage system
• Deficient
• 0 inches of rainfall
• $4.4 million in net benefits from the storage system
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Example
• If we assume a linear relationship between rainfall and net benefits, a straight line between both extreme contingencies
represents the different set of alternatives
� Label A
• If we assume a non-linear relationship for which each additional inch of rainfall decreases the net benefits slightly
more than the preceding inch, we would have a convex curve
below the straight line
� Label B
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Example
• We can represent this situation graphically
• Horizontal axis: number of inches of summer rainfall in an agricultural region
• Vertical axis: net benefits of a water storage system which increases as the amount of rainfall decreases
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Example
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Example
• We can then define a “normal” contingency
• 11 inches of rainfall
• The average of the “extremes”
• The expected net benefits of the “normal” contingency are:
• $2.2 million in the linear case A
• Around $0.6 million in the non-linear case B 26
Example
• Next, have to assign a set of probabilities:
• �� : probability of the normal contingency
• �� : probability of the deficient contingency
• �� : probability of the excessive contingency
• The sum of these probabilities has to equal 1:
�� + �� + �� = 1
• In this case, could base these probabilities on historically observed frequencies (what is the implicit assumption here?)
27
Calculating Expected Values
• To compute the value of the project, we have to:
• Calculate the net benefits of each contingency and then multiply by that contingency's probability of occurrence, and
• Sum all of these “weighted” benefits:
• For � contingencies
• In more general terms:
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[ ] ( ) ( ) ( )1 1 1 2 2 2 ... n n nE NB p B C p B C p B C= − + − + + −
[ ] ( ) 1
n
i i i
i
E NB p B C =
= −∑
Calculating Expected Values
Example:
• Suppose that you study for 15 hours for an upcoming economics exam. Your professor could prepare the exam with
three varying levels of difficulty: easy, fair, unfair. In talking
with past students, you assign the probabilities as 10%, 40%,
and 50%, respectively. Based on the three different levels of
difficulty, you forecast your grade being 95, 80, and 60,
respectively.
• What is your expected grade for this exam?
29
Sensitivity Analysis
Several key ideas to sensitivity analysis:
• We face uncertainty about the predicted impacts and the values assigned to them
• “Base case” contains most plausible estimates
• Purpose of sensitivity analysis is to show how sensitive predicted net benefits are to changes in assumptions
• If the sign of net benefits doesn't change after considering the range of assumptions, then the analysis is robust and we can have greater confidence in it
• Looking at all combinations of assumptions is infeasible
30
Sensitivity Analysis
• Three common approaches:
1. Partial sensitivity analysis: how do net benefits change as
one assumption varies, holding other assumptions constant?
• Should be used for the most important or uncertain assumptions
2. Best/worst case analysis: Can be used to find worst and best
case scenarios
3. Monte Carlo sensitivity analysis: Creates a distribution of net
benefits by drawing key assumptions from a probability
distribution, with variance and mean drawn from information
on the risk of the project
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Partial Sensitivity Analysis
• The value of a parameter where the net benefits switch sign is called the breakeven value
• A thorough investigation of sensitivity ideally considers the impact of changes in each of the important assumptions
• This is the approach we are taking in Assignment #4
32
Example of Partial Sensitivity Analysis
• My Mom’s gym: uncertainty regarding membership levels
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Fore caste d Profitability at V arious Me m be rship Le v e ls
-
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
500 600 700 800 900 1000 1100 1200 1300
# of Me m be rs
Monthly Revenues
and Expenses
-10,000
-5,000
-
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
50,000
55,000
Monthly
Net Incom e
Net Income
Revenue
Expense
Best & Worst Case Analysis
• Here we differentiate 3 scenarios:
1. Base Case: Assign the most plausible numerical values to
unknown parameters to produce an estimate of net benefits
that is thought to be most representative
• The NPV that you have calculated without sensitivity analysis
2. Worst Case: Assign the least favorable of the plausible range
of values to the parameters
3. Best Case: Assign the most favorable of the plausible range
of values to the parameters 34
Best & Worst Case Analysis
• Worst case analysis is useful as a check against optimistic forecasts and for decision-makers who are risk averse
• In worst case scenarios, care must be taken when determining which are the most conservative assumptions
35
Limitations of these Methods
• Partial and best/worst case sensitivity analyses have two limitations:
1. May not utilize all available information about the assumed values of parameters
• Worst and best cases are highly unlikely
2. Do not directly provide information about the variance of the statistical distribution of the realized net benefits
• One would feel more confident about an expected value with a smaller variance because it has a higher probability of producing net benefits near the expected value
36
Monte Carlo Sensitivity Analysis
• Monte Carlo Analysis addresses these limitations
• Idea is to simulate the model a large number of times to learn more precisely about the distribution of the net benefits
• Can be performed with statistical software (can also be conducted via Microsoft Excel, which has a specialized tool
called @RISK):
https://www.youtube.com/watch?v=q7mxT3OuWUk 37
Monte Carlo Sensitivity Analysis
Steps of Monte Carlo Analysis:
1. Specify probability distributions for all of the important uncertain quantitative assumptions
• When no theoretical or empirical evidence suggests a particular distribution: • Use a uniform distribution, if all values are equally likely
• Use a normal distribution, if a value near the expected value is more plausible
2. Execute a trial by taking a random draw from the distribution for each parameter to compute net benefits
3. Repeat the trial many times
• Average of the trials provides an estimate of the expected value of net benefits
• An approximation of the probability distribution of net benefits can be obtained by creating a histogram
• As the number of trials approaches infinity, the frequency will converge to the true underlying probability
38
Monte Carlo Sensitivity Analysis
• Example: Monte Carlo sensitivity analysis of a vaccination program
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Monte Carlo Sensitivity Analysis
• Trials can be used to directly calculate the sample variance, standard error, and other summary statistics describing net
benefits
• Parameters such as the value of time and life that are uncertain can be examined
• Parameters could be treated as random variables, or the Monte Carlo analysis could be repeated for a number of
combinations of fixed values of time and life
• Result is a collection of histograms that provides a basis for assessing how sensitive our assessment of net benefits is to
changes in these critical values
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Monte Carlo Sensitivity Analysis
• Figure 10: The Optimal Level of Capital Spending
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Frequency Distribution for K*
Mean = $30.7 billion
10 15 20 25 30 35 40 45 50 55 60
Optimal Capital Spending, $ billion
Current Capital
Spending =
$13.2 billion
90% Confidence Interval =
($20.3 billion, $43.7 billion)
Monte Carlo Sensitivity Analysis
• Figure 15: The Optimal Level of Operating Subsidy
42
Frequency Distribution for Optimal Subsidy Level
Mean = $33.4 billion
0 20 40 60 80 100 120 140 160
Optimal Operating Subisdy, $ billion
90% Confidence Interval =
($12.8 billion, $62.8 billion)
Current Operating Subsidy
= $15.0 billion
Monte Carlo Sensitivity Analysis
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Value of Time ($/hr)
10th Percentile Median 90th Percentile
15 20 25
� 0
0.03
0.06
0.09
0.12
0.15
5 10 15 20 25 30 35
Value of Time ($/hr) dist 80% conf mean±std mode
80% confidence interval
Monte Carlo Sensitivity Analysis
• Example: benefit of reducing waiting time duration & variability
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Assignment #2
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• Any remaining questions?
