1 extreme events scott matthews courses: 12-706 / 19-702
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Extreme Events
Scott MatthewsCourses: 12-706 / 19-702
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Admin
HW 5 Due Now
Group Project 2 Out today. Due Monday Nov 24
Next week: 2 case study writeups due
2 PAGES MAX !! DO NOT SUBMIT MORE!
Recap of Decision Trees
When thinking about strategies for decisions we could make 2-way sensitivity graphs.
Purpose: if parameters changed, did that affect our intended strategy? i.e., what would have to happen to change
our mind about our strategy?
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2-way Simple DA sensitivity
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Extreme Events
Low probability, high consequence (cost) events Natural disasters (e.g., hurricanes) Catastrophic infrastructure failure
Considered hard to assess..But can assess with sensitivity analysis:
On risk tolerance / utility“how risk averse do you need to be for it to matter?”
On probability - “how likely is it to happen?” On expected losses (consequences)
“how much would you have to lose for it to matter?”
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Relevant Thoughts
As you (the decision maker) become more risk averse, you tend to worry ONLY about the worst case
As you accept more risk, converge to risk neutralExample: using exponential utility (similar to
Deal or No Deal) Recall definition of R parameter in function Equally willing to risk winning R or losing R/2 For individuals, generally R ~ $1000s Recall goal is to maximize CE
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Exponential Utility Function u(x)=1-exp(-x/R)
-
0.20
0.40
0.60
0.80
1.00
1.20
$- $3,000,000 $6,000,000 $9,000,000 $12,000,000
$ amount
Utility
R=1,000,000 R=2,000,000 R=3,000,000
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Exponential Utility Function u(x)=1-exp(-x/R)
(2.00)
(1.50)
(1.00)
(0.50)
-
0.50
1.00
$(4) $(1) $2 $5 $8 $11 $14 $17 $20Millions
$ amount
Utility
R=1,000,000 R=2,000,000 R=3,000,000
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Example: Infrastructure Failure
Probability (P) of happening: About 0.5%
Damage (D) if occurs - $100 millionTypical EMV = P*D = ~$500k
Can pay to remove large potential cost by buying insurance (cost $20 million)
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A risk neutral decision maker would ride out the risk all the wayto p(fail) of about 0.2. What about a risk averse DM?
Extreme Events Spreadsheet
Lets look at the same example, and effects from changing R, Loss, p(fail), ..
What is our base case decision strategy? Does the strategy change as the parameters
change?
If it does not, then even though the event is “Extreme” we should be comfortable with our decision.
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In-Class Case Study:Clean Air Regulation
Scott MatthewsLecture 2412-706 / 19-702
New Type of Problem
Handout of Tables includedWhat happens when we cannot/will
not monetize all aspects of a BCA? Example: what if we are evaluating
policies where a benefit is lives or injuries saved?
How do we place a value on these benefits?
Are there philosophical problems?
In-Class Case Study
Consider this ‘my example’ of how to do a project for this class (if relevant)
Topical issue, using course techniquesAs we discuss, think about whether you
would do it differently, be interested in other things, etc.
Metrics for this case are ugly (literally): morbidity and mortality for human health
Effectively I ‘redo’ a published government report with different data
Background of CAA
Enacted in 1970 to protect and improve air quality in the US EPA was just being born Had many sources - mobile and stationary CAA goal : reducing source emissions Cars have always been a primary target Acid rain and ozone depletion
Amended in 1977 and 1990 1990 CAAA added need for CBA (retro/pro)
History of Lead Emissions
Originally, there was lead in gasolineStudies found negative health effectsTailpipe emissions (burning gas) were seen
as a primary source of leadRegulations called for phaseout of lead
We have also attempted to reduce lead/increase awareness in paints, etc.
Today, new cars must run on ‘unleaded’ gasoline (anyone remember both?)
Construction of Analyses
Estimate emissions reduced since 1970 For major criteria pollutants (SO2, NOX,…) Estimated ‘no control’ scenario since 1970 Estimated expected emissions without CAA Compared to ‘actual emissions’ (measured) Found ‘net estimated reduced emissions’
Assumed no changes in population distribution, economic structure (hard)
Modeled 1975/80/85/90, interpolated
Analyses (cont.)
Estimated costs of CAA compliance Done partially with PACE data over time Also run through a macroeconomic model
With reduced emissions, est. health effects Large sample of health studies linking ‘reduced
emissions of x’ with asthma, stroke, death, .. Used ‘value of effects reduced’ as benefits 26 ‘value of life studies’ for reduced deaths Does a marginal amount of pollution by itself kill?
Value of Life Studies Used
Actually should be calling these ‘studies of consumer WTP to avoid premature death’ Five were ‘contingent valuation’ studies Others estimated wage/risk premiums
Mean of studies = $4.8 million (1990$) Different than “Miller” from earlier Standard dev = $3.2 million ($1990) Min $600k, Max $13.5 million ($1990)
Putting everything together
Had Benefits in terms of ‘Value from reducing deaths and disease’ in dollars
Had costs seen from pollution controlUse min/median/max rangesConvert everything into $1990, get NBMedian estimated at $22 trillion ($1990)!
$2 trillion from reducing lead 75% from particulates
Is this the best/only way to show results?
‘Wish List’ - added analysis
Disaggregate benefits and costs by pollutant (e.g. SO2) and find NB Could then compare to existing cost-
effectiveness studies that find ‘$/ton’Disaggregate by source- mobile/stationary
Could show more detailed effects of regulating point vs. non-point sources
Has vehicle regulation been cost-effective?Why did they perhaps NOT do these?
My Own Work
I replicated analysis by using only median values, assumed they were exp. Value
Is this a fair/safe assumption?See Table 3
Implied Results
Source Abated EPA(million
tons)MortalityBenefits
OtherBenefits
TotalBenefits
Implied$/ton
(billions $1990)TSP 214 $19,945 $205 $20,150 $94,126Lead 2.517 $1,339 $536 $1,875 $744,934CO 763.1 0 $3 $3 $3NOx 72 0 $2 $2 $28SO2 189.5 0 0 $0 $0
Source Abated Distributed across all non-lead sources(million
tons)MortalityBenefits
OtherBenefits
TotalBenefits
Implied$/ton
(billions $1990)PM 214 $3,445 $264 $3,709 $17,325Lead 2.517 $1,288 $587 $1,876 $745,153CO 763.1 $12,281 $2 $12,283 $16,097NOx 72 $1,158 $2 $1,160 $16,119SO2 189.5 $3,050 $0 $3,050 $16,094
Recall Externality Lecture
External / social costs A measure of the costs borne by society
but not reflected in the prices of goodsCan determine externality costs by
other methods - how are they found? Similar to health effects above, but then
explicitly done on a $/ton basis
Compare to other studiesExternal Costs
(1992$ / metric ton of air emissions)
Species Min Median Mean Max
Carbon Monoxide (CO) $1 $520 $520 $1,050
Nitrogen Oxides (NOx) $220 $1,060 $2,800 $9,500
Sulfur Dioxide (SO2) $770 $1,800 $2,000 $4,700
Particulate Matter (PM) $950 $2,800 $4,300 $16,200
Volatile Organic Compounds (VOC) $160 $1,400 $1,600 $4,400
Global Warming Potential (in CO2 equivalents) $2 $14 $13 $23
Large discrepancies between literature and EPA results!Using numbers above, median NB = $1 T
Source Category Analysis
Using ‘our numbers’, mobile and stationary source benefits (not NB) nearly equal ($550B each in $92)
See Tables 12 and 13 for costs and NB
Up to 1982, stationary NB > mobileAfter 1982, mobile >> stationary
Final Thoughts
EPA was required to do an analysis of effectiveness of the CAA
Their results seem to raise more questions than they answer
The additional measures we showed are interesting and deserve attention
Questions intent of EPA’s analysis
Other Uses - Externality “Adders”
Drop in as $$ in the cash flow of a project
Determine whether amended project cash flows / NPV still positive
Mutiple Effectiveness Measures
So far, we have considered externality problems in one of 2 ways: 1) By monetizing externality and
including it explicitly as part of BCA 2) Finding cost, dividing by measured
effectiveness (in non-monetary terms)While Option 2 is preferred, it is only
relevant with a single effectiveness
MAIS Table - Used for QALY Conversions
Comprehensive Fatality / Injury Values
Injury Severity 1994 Relative Value
MAIS1 .0038
MAIS2 .0468
MAIS3 .1655
MAIS4 .4182
MAIS5 .8791
Fatality 1.0
Single vs. Multiple Effectiveness
Recall earlier examples: Cost per life saved Cost per ton of pollution
When discussing “500 Interventions” paper, talked about environmental regs Had mortality and morbidity benefits Very common to have multiple benefits/effectiveness Under option 1 above, we would just multiply by $/life
and $/injury values.. But recall that we prefer NOT to monetize and instead
find CE/EC values to compare to others
Multiple Effectiveness
In Option 2, its not relevant to simply divide total costs (TC) by # deaths, # injuries, e.g. CE1 = TC/death, CE2 = TC/injury
Why? Misrepresents costs of each effectiveness
Instead, we need a method to allocate the costs (or to separate the benefits) so that we have CE ratios relevant to each effectiveness measure
Options for Better Method
Use “primary target” as effectiveness Allocate all costs to it (basically what
we’ve been doing)Add effectiveness measures together
E.g., tons of pollution Is as ridiculous as it sounds (tons not
equal, lives not equal to injuries)
Improved Method
In absence of more information or knowing better, allocate costs evenly E.g., if 2 pollutants each gets 1/2 the cost Easy to make slight variations if new information or
insight is available
Could use our monetization values to inform this (e.g., external cost values, $/life values, etc.)
Recall from previous lectureExternal Costs
(1992$ / metric ton of air emissions)
Species Min Median Mean Max
Carbon Monoxide (CO) $1 $520 $520 $1,050
Nitrogen Oxides (NOx) $220 $1,060 $2,800 $9,500
Sulfur Dioxide (SO2) $770 $1,800 $2,000 $4,700
Particulate Matter (PM) $950 $2,800 $4,300 $16,200
Volatile Organic Compounds (VOC) $160 $1,400 $1,600 $4,400
Global Warming Potential (in CO2 equivalents) $2 $14 $13 $23
Another Option
For each effectiveness, subtract marginal cost/benefit values of all other measures from total cost so that only remaining costs exist for CE ratios Again could use median $ values on
previous slide to do this Examples..
Wrap Up
There is no “accepted theory” on how to do this.
However when we have multiple effectiveness measures, we need to do something so we end up with meaningful results.
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