Final Flashcards
Get a 78 or higher (93 cards)
1
Q
Benefits and costs are the product of:
A
dX: The real impact of the policy
How much does the quantity of goods (or “bads”) change as the result of the policy?
P: The valuation (price) of the impacted goods
For each good, how much value do we place on each unit gained/lost?
2
Q
A market price may provide the marginal social benefit and marginal social cost of a good
A
Simplest case: the policy changes the quantity of a good that is currently consumed in an undistorted (i.e., efficient) market
MSB = P = MSC
3
Q
Are there distortions in the market?
A
Taxes or subsidies result in two prices (one paid by consumers, one received by producers); which to use?
Prices in (unregulated) monopolized markets overstate the true costs (monopolists charge P > MC)
Negative externality: e.g., the “price” of pollution (in the absence of regulation) is equal to 0, but the marginal social cost is not
Positive externality: price captures marginal private benefit but understates marginal social benefit
Are “accounting” and “economic” measures the same?
E.g., data gathered from a non-profit could understate the true (opportunity) cost of volunteer’s time
4
Q
If distortions exist, you need a measure of the “shadow price” (different from the market price)
A
Shadow price: what the market price would be if the good was traded in a market in which
demand = marginal social benefit, and
supply = marginal social cost
5
Q
Two general methods for obtaining shadow prices
A
- Indirect market methods (BGVW Ch. 14)
- Contingent valuation methods (BGVW Ch. 15)
6
Q
Indirect market methods
A
E.g., trade-off method, hedonic pricing, travel cost methods
Rely on “revealed” (as opposed to stated) preferences
7
Q
Contingent valuation methods
A
Obtain values from surveys (stated preferences)
Recommend to avoid if possible
8
Q
Meta-analysis
A
Meta-analysis is every bit as useful for determining the proper valuation of policy impacts as it is for determining the likely impacts themselves
9
Q
Value of life
A
We previously addressed policies that affect life/death/health in cost-effectiveness section ($ per life saved)
10
Q
When is CEA useful?
A
Fixed budget.
Fixed goal.
Ranking of alternatives.
11
Q
But CEA doesn’t tell you whether the life-saving is a “good idea” per say.
A
Better to implement a policy that costs $1 million per life saved vs. $10 million per life saved.
But is $1 million option worth doing?
12
Q
Value of (statistical) life
A
In general, policies subject to CBA or other analysis of this nature do not change the probability of a particular person’s death from 1 (certain death) to 0 (no chance of death) or vice-versa; they deal with small changes in the risk of death
13
Q
Discussion of the “value of life” actually concerns the Value of a Statistical Life (VSL), which is a probabilistic measure
A
If we say that a policy will save 1 statistical life, this means that the risk of death for some group of people is reduced so that, on average, one person’s life will be saved
A policy that decreases the probability of death by 100% for 1 person saves one life
A policy that decreases the probability of death by 0.0001% for 1 million people saves one statistical life
14
Q
How would you expect willingness to pay (or accept) to differ between saving a life vs. saving a statistical life?
A
A lot of anti-CBA rhetoric revolves around the immorality of monetizing life.
That word “statistical” is often missing and critics don’t know better.
What if we called it “value of a risk reduction” instead?
15
Q
Rationale for estimating VSL
A
Estimating the “value of life” (VSL) does not make a philosophical statement about how much we feel a life is worth: we are simply evaluating what people’s behavior says about their willingness to pay (accept) for small decreases (increases) in the risk of death
-Private behavior indicates that people place finite value on changes to the risk of death, as they make decisions that increase the probability of death (e.g., drive cars, play contact sports, take risky jobs).
-It would be inconsistent to value risk changes infinitely in a public policy context
-If lives had infinite social value, then we should undertake any policy that has any chance of saving any number of lives, regardless of the cost (e.g., ban non-emergency use of cars?)
-By implication, we should not undertake any non-life-saving policies (e.g., public funding for education?) until we have exhausted all potentially life-saving policies (In practice, we’d run out of resources first
)
-If we want to be able to make decisions between policies that save lives and policies that do not, we need to assign value to expected lives saved
-Remember two of the basic foundations of economics: scarcity of resources and opportunity cost
16
Q
Life-saving policies are funded by taxes or reduced expenditures on other policies, which may indirectly impact the probability of death
A
E.g., higher taxes ->less $ for healthy food, medical care, newer/safer cars, etc. -> increased risk of death
17
Q
Suppose someone is willing to pay $5 to reduce the risk of a fatal accident from 2 in a million to 1 in a million
A
The decrease in risk is: ∆p = 0.000002 – 0.000001 = 0.000001 In this case the implied value of a statistical life is: VSL = WTP / ∆p = $5 / 0.000001 VSL = $5,000,000
18
Q
Trade-off method:
A
determine the trade-off people are willing to make between the probability of death (or any other impact we’d like to value) and something else that is more easily monetized
19
Q
Estimating VSL: wage premiums
A
This approach makes use of the additional wages that people require in order to accept jobs with a higher probability of death (“wage premium” or “compensating differential”)
If you require a wage premium of $400/year to accept a job with an additional 1 in 10,000 annual risk of death (otherwise identical to the best alternative job), then your implied VSL is $4,000,000
∆p * VSL = ∆wages
VSL = ∆wages / ∆p = $400 / 0.0001
20
Q
Estimating VSL: consumption choices
A
How much will consumers pay for goods or services that reduce the probability of death?
E.g., smoke detectors, car airbags, medication
Studies of medical goods/services complicated by insurance
Related method: how does consumer behavior change in response to new information about risks?
E.g., new information comes out about how calcium supplements affect heart attack risk; how does behavior change?
21
Q
What about discounting lives saved in the future?
A
Should be discounted; money spent to save lives today could be invested so that there would be more money available to save lives in the future (opportunity cost!)
22
Q
Differences in economic status?
A
E.g., income effects yield different WTP for a given reduction in risk
Most analyses use an average WTP across population
23
Q
Adjustments for age / life expectancy?
A
E.g., should we differentiate the benefit of a heart transplant for a 20 year old vs. a 85 year old?
Could, for example, determine the value of saving an additional year of statistical life, multiply by (discounted) number of expected life years saved
No conclusive theoretical basis for requiring constant (age-independent) value of a year of statistical life
Some empirical evidence that age is a factor in people’s preferences (e.g., would rather save a 30 year old than a 60 year old); valuation of prevented death by age commonly found to have inverted U shape
24
Q
Voluntary vs. involuntary risks
A
Studies have found that involuntary risks should be valued at 1.2–1.6 times the value of voluntary risks
25
What do studies tell us about VSL?
Wide range of estimates
BGVW Table 16-1: best estimate $5.5 million, suggest sensitivity analysis from $2.4 million – $7.2 million
Ashenfelter and Greenstone (2004) literature review: typical average VSL range $1 million – $5 million
Robinson et al. (2010) meta-analysis: best estimate $6.5 million, 95% confidence interval from $5.1 million to $8.2 million
Office of Management and Budget (OMB): research indicates rough range of $1 million to $10 million
26
Asset valuation method
If a property is located in/near a known environmental hazard (trash dump, high smog area, etc.) or environmental amenity (beach, park, etc.), then we can estimate the feature’s value by comparing against the prices of otherwise similar properties not near these features
The values of these amenities (or, more generally, of government policies or projects that impact the well-being of the property owners) are said to be “capitalized” into the market value of the properties
Example: If a new park is built in a neighborhood, and the value of the park to local residents is $5,000 per household, then home prices should increase by $5,000 to reflect this added value(true even if this $5,000 is the NPV of a stream of future benefits rather than a benefit that is enjoyed instantaneously)
27
Problem: in practice, you can’t always find properties that differ only in this particular respect, so you need to control for any differences in other relevant characteristics
Solution: regress price on the set of all relevant characteristics, including the variable of interest
-Resulting estimate for the variable of interest describes the relationship between this variable and price, with all other relevant attributes held constant
-Referred to as hedonic pricing or hedonic regression
Note: We won’t be running regressions in this course; focus on conceptual understanding (we can’t find an “otherwise identical” comparison group, but we can use statistical techniques to allow “all else equal” comparisons)
28
Hedonic pricing
Health context: hedonic pricing could be used to estimate a premium for fatality risk in wage rates
Health context: hedonic pricing could be used to estimate a premium for fatality risk in wage rates
29
Some problems with hedonic pricing
- Assumes that decision-makers are fully informed about the relevant attributes (level of job fatality risk, pollution exposure levels in house’s location, etc.)
- Assumes a sufficient variety of options for individuals to be able to choose an optimal combination of attributes
- Assumes that all relevant variables are included in the regression (or uncorrelated with the variable of interest)
30
Travel cost method
-The travel cost method is typically used to estimate the value of recreational sites (e.g., national parks)
-Even if everyone pays the same price for admission (potentially zero), people visiting from different geographic areas face different opportunity costs
Example: total cost of traveling to Yosemite National Park is lower for someone living in Los Angeles than for someone living in New York
-We can explore people’s willingness to pay for a visit to a recreational site by estimating the relationship between the total cost of a visit (including opportunity cost of travel time, cost of lodging, admission fees, etc.) and the quantity of visits
31
Travel cost method
In practice, it is typically most feasible to collect data from actual visitors to a particular site (rather than surveying the general population of potential visitors)
In this case, the level of analysis is visitors’ geographic zone of origin (“zonal travel cost method”) rather than the individual or household
32
Person-visit
one person, visiting once (if you go 3 times, that’s 3 person-visits; if a family of 3 goes once, that’s also 3 person-visits)
Zone creation is subjective, but households within a zone should have similar travel costs and similar values of other relevant variables
33
visit rate
The visit rate (average visits per person) can then be regressed on total cost per person-visit and other explanatory variables to estimate the demand curve for a “representative” individual
This gives the willingness-to-pay curve for a representative visitor; net benefits by zone are then given by consumer surplus for someone with that zone’s particular total cost per visit
34
Some obstacles for travel cost method
-Provides estimates of willingness to pay for an entire site, but the issue under consideration often involves changes to specific features of the site
-ifficult to measure cost of visiting a site
Opportunity cost (value) of time may differ across zones
Opportunity cost of time spent at site is also relevant, but can be complicated
If constant across zones, can be ignored without biasing consumer surplus estimates (affects WTP and total cost equally), but this is not necessarily the case
-People may derive benefits from the time spent traveling, or have multi-purpose trips (do other things on the way) – what portion of the cost should be allocated to visiting recreational site?
-Travel cost may be a result of preferences regarding recreational sites (proximity to various rec. sites may play a role in deciding where to live)
-Sample only includes those who actually visit the site
Can be dealt with econometrically, just shouldn’t use simple OLS regression
35
Contingent valuation methods
In general, it is preferable to estimate individuals’ valuations of goods and services on the basis of their observed behavior, as such behavior credibly reveals their preferences
In some cases, however, there are no good behavioral data available
In these cases, the only viable method may be the use of surveys designed to elicit information about individuals’ preferences
Such surveys are known as contingent valuation surveys (or hypothetical valuation surveys) because respondents do not actually face the decisions under consideration and are not actually required to pay their reported valuations
36
General outline of contingent valuation methods:
Identify the population (those who are affected and have standing) and construct a sample
Recall from week 1: those who have standing are those whose costs or benefits “count” (should be included)
Survey respondents about their valuations of the good
Estimate respondents’ valuations (willingness to pay) from survey responses
Make inferences about the population’s valuation based on the results from the sample
37
CVM: specific methods
- Open-ended willingness-to-pay method
- Closed-ended iterative bidding method
- Contingent ranking method
38
Open-ended willingness-to-pay method
Ask respondents to state their maximum WTP
Has become less popular over time; respondents may need some initial guidance, may report zero value if valuation is low, etc.
39
Closed-ended iterative bidding method
Ask respondents whether willing to pay a specified amount; increase or decrease amount until answer changes
Used to be very common, but rarely used now because results have been shown to be highly sensitive to starting value
40
Contingent ranking method
Ask respondents to rank specific combinations of monetary payments and quantities of the good
May be easier for respondents to answer accurately because only ordinal information is required; results sensitive to order in which alternatives are presented
41
Dichotomous choice (referendum) method
Most commonly used contingent valuation method
Ask respondents whether or not willing to pay a particular price; each receives a randomly chosen price
The fraction of respondents willing to pay each price is used to estimate the probability that a random member of the population would be willing to pay any particular price; this can then be used to estimate willingness to pay for the average individual
Easy for respondents to answer, but requires large samples for reasonable levels of precision
Related method: “double dichotomous choice” (follow-up question; e.g., double price if willing to pay, halve price if not)
Gives more information, but several concerns about how initial price (and being offered a new price) affects responses to second price
42
payment vehicle
Contingent valuation surveys should specify a payment vehicle, which identifies how the costs of providing the good will be paid
E.g., higher sales taxes, higher utility bills
Specifying a payment vehicle makes survey questions seem more real to respondents, and the particular payment vehicle may affect willingness to pay
E.g., are the taxes raised to fund a project guaranteed not to be used for other purposes?
Survey results will thus be the most reliable when the payment vehicle specified is as close as possible to the one that will actually be used if the project is implemented
43
Some problems with CVM
BGVW spends 13 pages (382-396) summarizing the major problems with contingent valuation methods
A few of the big ones:
Respondents may have trouble clearly understanding the issue they are being asked about and placing it in the proper context
Survey responses tend to be systematically biased in a number of different ways
E.g., hypothetical willingness to pay for benefits tends to be much higher than observed WTP when presented with the same situation in reality
Respondents may have incentives to behave strategically (misrepresent true preferences in an attempt to influence the outcome)
Susceptible to framing problems (responses are affected by how the questions are asked)
44
Some problems with CVM
Contingent valuation methods are generally viewed as a last resort, to be used when there are no viable behavior-based alternatives (direct or indirect market methods)
45
Use vs. non-use values
Everything discussed so far has related to the idea of “use value”
People who consume a resource attribute some value to its use, but what about non-users?
Is there a value to knowing that you could use something?
In most cases, no; regular markets have “non-users” also, but we do not care about their potential value
However, some environmental goods may have additional properties that make them valuable to non-users
Krutilla (1967) establishes three conditions for the validity of including non-use values in CBA: uniqueness, irreversibility, and non-augmentation
“unique phenomena of nature … irreversibility of some consequence … supply is not readily subject to enlargement by man”
46
Option value
is the amount a potential user is willing to pay to avoid risk of losing option to visit the park (relevant when future use, prices, qualities, etc., are uncertain)
47
Existence value
is the value an individual derives from the park’s existence independent of any plans to use it (i.e., even when their probability of use is 0)
48
Existance Value sub categories
```
Pure existence value (park has intrinsic value)
Altruistic existence value (desire for others to have access to park)
Bequest value (desire for park to be available to future generations)
```
49
For potential users, you can get the option price:
𝑂𝑝𝑡𝑖𝑜𝑛 𝑃𝑟𝑖𝑐𝑒=𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑆𝑢𝑟𝑝𝑙𝑢𝑠+𝑂𝑝𝑡𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒
50
Option value
is the risk premium associated with someone’s willingness to pay to preserve the right to use something; a risk-neutral person would have an option value of zero
In practice, can be extremely difficult to measure (and even its sign is often ambiguous); analysts frequently resort to using expected surplus alone to approximate option price (i.e., treat option value as 0)
51
Existence value
In order to estimate existence value separately, you might survey people who do not intend to visit Yosemite, as their entire willingness to pay would reflect its existence value
But be careful, these people may not have the same existence value as the general population
A number of other methods have been suggested (e.g., based on membership and fees for preservation societies), but all face serious limitations
A common practice is to attempt to estimate existence values, and to conduct cost-benefit analysis with and without them
Existence value is conceptually important, but the difficulty of reliable measurement makes its inclusion difficult
52
Sensitivity analysis
is used to explore how results change if different estimates and assumptions are used
53
Why do sensitivity analysis?
Basic analysis generally uses the best estimates for our parameters, predicted impacts, valuations, etc.
However, there is almost always some amount of uncertainty; this set of estimates is just the base case, and we need to address the uncertainty inherent to the analysis
54
What are the sources of uncertainty?
Unpredictability of future events
Limitations on precision of data/estimates
Large confidence intervals on estimates and/or wide range of estimates from various sources
Extreme case: missing data
55
Sensitivity analysis: two key questions
Where is the uncertainty greatest?
When does it potentially matter the most?
56
Where is the uncertainty greatest?
Unless you have a very small number of variables and a very small number of possible values for each, it’s not feasible to simply look at each possible combination
3 variables, 2 possible values each: 8 possible combinations
5 variables, 3 possible values each: 243 possible combinations
10 variables, 4 possible values each: 1,048,576 possible combinations
Not to mention that the notion of a finite number of possible values is doubtful
57
When does it potentially matter the most?
If my conclusion is that a policy should be undertaken, is this result robust to the use of more conservative estimates?
If my conclusion is that a policy should not be undertaken, is this result robust to the use of less conservative estimates?
58
How do the two key questions interact?
- There might be a lot of uncertainty about a variable, but varying it doesn’t change the result.
- The might be little uncertainty about a variable, but even minor variations change the result.
59
Sensitivity analysis: basic categories
-Variable-by-variable analysis
+Threshold analysis
-Scenario analysis
-Monte Carlo analysis (simulation)
60
Variable-by-variable analysis (partial sensitivity analysis)
Holding everything else constant, what happens to the results when one variable is changed? (An impact, a valuation, time horizon, discount rate, etc.)
It’s an art (as opposed to a science) to decide how many sensitivity analyses to provide (I can’t give you a step-by step algorithm)
61
Two key questions to guide Variable-by-variable analysis
Which variables are you most uncertain about?
Which variables have the greatest impact on results?
Caution: variables may be correlated (then not very informative to hold one constant while changing the other)
62
breakeven value
In addition to showing the results for particular values (each plausible value if there are few, endpoints of confidence interval, etc.), a common approach is to find the breakeven value: that at which, given other baseline assumptions, NPV=0 (sign changes +/–)
63
threshold analysis
Determining variables’ breakeven values is called threshold analysis
Remember the internal rate of return (IRR)? It is the breakeven value of the discount rate (so common that it has a name!)
Another threshold analysis we’ve encountered: cost-effectiveness analysis (the breakeven value of the benefit per unit of effectiveness)
Yet another: internal weights when dealing with policy that has conflicting efficiency and equity effects
64
Variable-by-variable is often best shown graphically
X-axis: range of values for chosen variables
Y-axis: show result (e.g., NPV) for range of values of chosen variable
Can indicate in the graph the threshold that needs to be passed (e.g. NPV=0)
Good example: BGVW (4th) Figure 6-6 (how NPV varies with discount rate)
This informs policymakers about the importance of each variable and how extreme their values must be to reverse the results
65
Threshold analysis is particularly useful with missing or unreliable data
If you don’t have a good estimate of a variable, you might omit it and then find the value at which its inclusion would reverse your results
E.g., existence value of an environmental feature
Caution: you must hold everything else constant when performing threshold analysis for any given variable; if you change anything else, the threshold value for your variable may change
66
Scenario analysis
-Start with the baseline scenario
+Most plausible values (usually “best guess” point estimate) for all unknowns
-Then create other possible scenarios that link variables together, and see what results are produced by each.
67
Common examples:
| for baseline sceneario
Good economy / bad economy
Not necessarily the same as best/worst case; different variables have different relationships with the state of the economy
68
Monte Carlo analysis provides a solution for each of these limitations
Specify probability distribution for each variable subject to important uncertainty
May have theory/evidence to justify a particular distribution (e.g., OLS regression estimation gives mean and standard error for normal/t distribution)
Common (though not necessarily correct) fallback: uniform distribution over plausible range
Create a random draw for each of these variables
Calculate outcome (e.g., NPV) for this set of values
Repeat steps 2 and 3 a large number of times (e.g., 10,000)
69
Monte Carlo analysis (simulation) Can use output to estimate many useful things, including
```
-Mean and median of NPV
Sample mean and median NPV values
-Standard deviation of NPV
Sample SD of simulated NPV values
-Probability that NPV will be positive
% of simulated NPVs > 0
-Distribution of NPVs (histogram)
-NPV used as example, but applies to any outcome measure (e.g., cost-effectiveness ratio)
```
70
Monte Carlo analysis (simulation) The more replications you use, the better (at the cost of computational time, though trivial in many cases)
Law of large numbers: as number of replications goes to infinity, sample distribution approaches true underlying distribution (given specified distributions for each variable)
71
Value of Monte Carlo analysis
Monte Carlo analysis adds value to the more simplistic types of sensitivity analysis by providing a more complete picture of the possible outcomes
E.g., how likely is the base case? How big is the spread of outcomes? Normally distributed, bi-modal, skewed, etc.?
This is especially important for CEA/CUA since ratios are involved (costs and benefits do not enter linearly as in NPV)
Variable-by-variable and scenario analysis can still be very useful – no particular reason you can only use one type of sensitivity analysis!
Don’t underestimate the value of the ability to display results graphically!
72
Decision-making under uncertainty
Decision-making is relatively straightforward when all relevant variables are known with certainty
What are the options? Which of these is the best?
In reality, many decisions must be made in the presence of uncertainty about important variables such as future income and prices
Is it better to choose an alternative that could turn out extremely well but is very risky, or to pick a safer option that has less upside?
73
Uncertainty
refers very generally to lack of complete knowledge (about an underlying parameter, relationship between variables, individual or social preferences, etc.)
Example: There’s some true value for the elasticity of demand for health insurance, but we’re not completely sure what it is
74
Risk
may have knowledge of probabilities, but not of realizations (results of random draw); generally deals specifically with uncertain outcomes [Measured by variance, standard deviation]
Example: Costs of Affordable Care Act depend on usage rates of health care in future, and we don’t know what these will actually be
75
Expected value
The expected value of an uncertain situation is the probability-weighted average of the possible payoffs
Conceptually: if the uncertain situation occurred an infinite number of times, what would be the average payoff?
Consider a situation of uncertainty in which there are n possible outcomes (1, 2, …, n) that have a positive probability of occurring
E.g., in coin toss game, n = 2
For each possible outcome, p is the probability and X is the payoff if the outcome occurs (e.g., profit for a firm)
EV = p1X1 + p2X2 + … + pnXn
76
risk-neutral
individual does not care about risk (prefers the option with the highest expected value, regardless of risk)
77
risk-averse
individual dislikes risk (would rather have a given amount of money with certainty than face a risky situation with the same EV)
-Equivalently: may prefer a lower-EV option if it is less risky
78
risk-loving
individual likes risk (would rather face a risky situation than get the same EV with certainty)
Equivalently: may prefer a lower-EV option if it is riskier (willing to take less on average to get higher upside)
79
Example: attitudes toward risk
Suppose that you are presented with two one-year job offers when you finish your degree:
Job 1: guaranteed salary of $60,000
Job 2: guaranteed salary of $40,000 and a 50% chance of an additional $60,000 bonus
In terms of final outcomes: 50% chance of $40,000 and 50% chance of $100,000
Which job would you choose?
Which job would a risk-neutral person choose? Risk-loving? Risk-averse?
First, calculate EVs
EVJob1 = $60,000 (trivial; $60,000 with probability 1)
EVJob2 = 0.5($40,000) + 0.5($100,000) = $70,000
Second, can we rank the risks?
Job 1 is riskless
Job 2 has risk (could be quantified with something like standard deviation)
Risk-neutral: Job 2 (only cares about higher EV)
Risk-loving: Job 2 (likes higher EV and higher risk)
Risk-averse: We need more information (likes higher EV, dislikes higher risk)
Choice depends on degree of risk aversion; is the extra $10,000 in expected income offered by Job 2 worth the risk?
80
Expected value criterion
In CBA, uncertainty about the payoffs (e.g., NPV) from different alternatives is often addressed with the expected value criterion: the alternative with the best expected value is regarded as the best choice
+Essentially treats expected values as if they were certain amounts; equivalent to assuming decision-maker is risk-neutral (ranks outcomes based on expected values, regardless of amount of risk)
81
Expected value criterion continued
In cases of uncertainty, expected value criterion says you implement a policy if its expected NPV > 0
Or in the case of choosing among exclusive policies, choose the one with the largest expected NPV
Caveat: What you consider a baseline NPV is not necessarily the same as the expected NPV
E.g., if 𝑁 is the number of people who will benefit from a program and 𝑏 is the per-person benefit, then 𝐸[𝑁∗𝑏] only equal to 𝐸[𝑁]∗𝐸[𝑏] if 𝑁 and 𝑏 are uncorrelated
E.g. if uncertain about the discount rate, then discounting at the expected rate (wrong) doesn’t give the same answer as discounting at each possible rate and then taking the expected value (right)
Importance of Monte Carlo analysis!
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What to do when EV isn’t enough
In circumstances in which the EV criterion is not appropriate, there are two primary options
Replace uncertain outcomes with certainty equivalents
83
certainty equivalents
Certainty equivalent: the amount the decision-maker would accept (with certainty) in lieu of facing a situation of uncertainty
Solves the problem without requiring any other methodological changes, but requires strong assumptions about the decision-maker’s attitude toward risk
Finding CE requires us to know the utility function in general, or detailed information about preferences for a particular situation
Can view all costs and benefits used throughout the course as having been certainty equivalents
84
What to do when EV isn’t enough: Use risk-adjusted discount rates:
if higher risk makes a project less attractive, we can deal with this by discounting expected future net benefits at a higher rate [Instead of using certainty equivalents; don’t do both!]
Conceptually, the appropriate discount rate reflects the decision-maker’s risk aversion, the riskiness of the project, the riskiness of the existing portfolio of projects, and the correlation between these two risks
The math involved in deriving the appropriate discount rate is relatively complicated (it involves the risk-free rate, the cost of borrowing, and variance/covariance terms)
For details, you can look into the Capital Asset Pricing Model
85
What to do when EV isn’t enough: Rules of thumb for discount rate approach:
-If the project is riskless, use the risk-free rate
-If the project does not change the risk of the decision-maker’s portfolio, use the cost of funds (e.g., real interest rate on bonds with appropriate maturity date)
Represents social rate of time preference, adjusted for portfolio risk [Most common approach in practice]
If the project does not change the risk of the decision-maker’s portfolio, and that riskiness is given by the market’s riskiness, use the market rate of return
Note: If the project displaces enough private investment to change the cost of private investment, you still need to adjust for this (e.g., by using the shadow price of capital method)
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Key principles for addressing risk
-While the certainty equivalent and risk-adjusted discount rate approaches seem quite different, they serve the same function, and incorporate common principles
-Never analyze risk in a vacuum; look at it in the context of the set of activities that are already being undertaken
-Diversification is key: the biggest determinant of the overall risk of a portfolio is the covariance between the components, not their individual variances
Personal finance example: don’t invest all your money in one stock, or in a group of stocks whose performances are very closely related (e.g., stocks of companies from a single industry)
Public policy example: diversify your local economy’s activities/industries (e.g., how did “single-industry” Rust Belt cities respond to the modernizing economy? Detroit vs. Pittsburgh)
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Decision trees
-A decision tree “maps” a risky decision: it displays the outcomes, probabilities, and payoffs that follow a choice
-The first event in time is at the left – the decision tree “branches” to the right
-The elements of decision tree include:
+Decision nodes (squares)
+Chance nodes (circles)
+Probabilities (of uncertain events)
+Outcomes/payoffs (at the end of branches)
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Simple Events
.g., P(Large), P(Approved)
What is the probability that a randomly selected project was large?
What is the probability that a randomly selected project was approved?
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Conditional Events
e.g., P(Approved|Large)
| Probability that project was approved, given that it was large
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backward induction
According to expected value criterion, best alternative is an initial proposal of 100 units, followed by revision if rejected
This procedure of starting at the end and working back to the beginning is called backward induction
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Quasi-option value:
the expected value of information gained by waiting to make an irreversible decision
With imperfect information, you have to make decisions that you may end up regretting; gathering better information increases the likelihood that you’ll make the best decision
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Quasi-option value example
The expected values of the three alternatives are:
EV(100, revision prepared) = $14.125m
EV(100, no revision prepared) = $6.75m
EV(50) = $9.25m
The best alternative is submitting a 100-unit proposal and preparing a revised proposal in case it is rejected, resulting in an EV of $14.125m
If the developer had the option to wait and see if the initial 100-unit proposal was rejected before preparing a revision (original situation), its best alternative would have an EV of $14.3875m
The quasi-option value of this information (whether or not the initial proposal will be rejected) is thus $262,500
EVwaiting – EVnot waiting = $14.3875m – $14.125m = $0.2625m
What might you regret without the option to wait? Paying $750,000 for a revised proposal after it turns out the first one got approved.
What’s the probability you’ll experience this regret? 0.35
What’s the expected value? (0.35)($750,000) = $262,500
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Calculating expected value for developer
Now consider initial decision (50 or 100 units)
For 100 units, another decision node could follow (might be rejected): assign payoff of $9.75m to “rejected” branch (EV of best choice if that situation arises)
Can now calculate EV for each branch:
EV(100 units) = 0.35($23m) + 0.65($9.75m) = $14.3875m
EV(50 units) = 0.90($10.5m) + 0.10(–$2) = $9.25m
