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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.