Immaterial damage valuation Immaterial damage valuation

in the context of flood riskin the context of flood risk

Marija BoMarija BoččkarjovakarjovaPiet RietveldPiet RietveldErik T. VerhoefErik T. Verhoef

International conference International conference ‘‘Deltas in Times of Climate ChangeDeltas in Times of Climate Change’’

Rotterdam, 29 September Rotterdam, 29 September –– 1 October 20101 October 2010

What is this study about?What is this study about?

The ProjectThe Project

•• KvR: adaptation options to KvR: adaptation options to climate changeclimate change–– yes or no? how much? when?yes or no? how much? when?

•• Small country, big delta:Small country, big delta:–– how much flood protection is how much flood protection is

““enoughenough””??

�� CostCost--Benefit AnalysisBenefit Analysis

Cost Benefit AnalysisCost Benefit Analysis

Costs (Costs (--))

–– InvestmentsInvestments

–– Maintenance Maintenance

BenefitsBenefits (+)(+)

–– Avoided damagesAvoided damages

•• Material (households, businesses, Material (households, businesses,

environment, LNC environment, LNC ……))

•• Immaterial (human victims, injuries, Immaterial (human victims, injuries,

evacuations, evacuations, ……))

??YES orYES or NONO

Avoided immaterial damagesAvoided immaterial damages

•• Do not have a priceDo not have a price

–– To be able to make various costs and benefits To be able to make various costs and benefits comparablecomparable, ,

they need to be expressed in the they need to be expressed in the same unitssame units

•• So, we have to attach some So, we have to attach some monetary valuemonetary value to to

immaterial damageimmaterial damage

–– Different methods to achieve thatDifferent methods to achieve that

–– We use: CHOICE EXPERIMENTS:We use: CHOICE EXPERIMENTS:

market price compatible, and thus can market price compatible, and thus can

directly be used in CBAdirectly be used in CBA

Focus of the studyFocus of the study

•• Valuation of immaterial damages Valuation of immaterial damages

in the context of flood risk:in the context of flood risk:

–– VOSLVOSL (value of statistical life saved) (value of statistical life saved)

–– VOSIVOSI (value of statistical injury)(value of statistical injury)

–– VOSE VOSE (value of statistical evacuation)(value of statistical evacuation)

Why a Why a ‘‘newnew’’ VOSL?VOSL?

•• Currently a VOSL of Currently a VOSL of 2.5 mln 2.5 mln €€ is used in flood safety is used in flood safety

(borrowed from transport safety valuation) (borrowed from transport safety valuation)

�� is that adequateis that adequate??

•• Benefit transfer issueBenefit transfer issue: VOSL appears to be different depending on: VOSL appears to be different depending on……

�� context of context of risk risk –– risk perceptionrisk perception

-- qualitativequalitative (dread, voluntariness, controllability)(dread, voluntariness, controllability)

-- quantitativequantitative (probabilities)(probabilities)

�� methodology usedmethodology used

�� welfarewelfare

What is a VOSL?What is a VOSL?

Basically,

VOSL is a trade-off between

some amount of money (to be paid)

and a change (reduction) in fatality risk

riskfatality in decrease

(euros)money ofamount VOSL =

What is a VOSL?What is a VOSL?

Value of statistical life (VOSL)

is a willingness to pay ( decrease in wealth)

for a small decrease in fatality risk

due to a particular negative event.

Changes in the fatality risk level imply

expected changes in human lives saved in a particular society.

Thus, willingness to pay for a decrease in risk exposure

can be translated into the money value per one statistical life saved.

∆P

Y∆VOSL =

Suppose, Suppose,

we want to decrease riskwe want to decrease risk

(so, we know )(so, we know )

But: But:

What about ???What about ???

∆P

Y∆

What is the problemWhat is the problem……

•• Paying for reducing flood risk Paying for reducing flood risk

–– No real markets with real, familiar goodsNo real markets with real, familiar goods

–– We cannot We cannot ‘‘observeobserve’’ datadata

What is the solutionWhat is the solution……

under controlled circumstancesunder controlled circumstances

ask people what they are willing to pay!ask people what they are willing to pay!

–– value value hypothetical goods hypothetical goods onon hypothetical marketshypothetical markets

–– collect data with the help of a collect data with the help of a surveysurvey

The surveyThe survey

The surveyThe survey

•• TNSTNS--NIPO internet panel (fall 2008)NIPO internet panel (fall 2008)�� a random representative samplea random representative sample

•• Survey structureSurvey structure

I I –– flood risk perceptionflood risk perception

II II –– explanation of flood and fatality probabilitiesexplanation of flood and fatality probabilities

III III –– flood risk valuationflood risk valuation

IV IV –– climate change climate change

V V –– demographicsdemographics

Data collected inData collected in4 dike4 dike--ring areasring areas

Riverside:Riverside:

�� Eiland of Dordrecht Eiland of Dordrecht 110110

�� Land van Heusden / Land van Heusden / de Maaskant de Maaskant 141141

Coast:Coast:

�� Zeeland Zeeland 151151

�� Central Holland Central Holland 135135

__________________________________________________

Total N respondents:Total N respondents: 537537

Our approachOur approach

We want:We want:

Informed choicesInformed choices

So, we provide extensive information on risk :So, we provide extensive information on risk :

Risk of floodingRisk of flooding

Fatality risk in floodingFatality risk in flooding

Yearly fatality riskYearly fatality risk

Fatality risk due to flooding in the coming 50 yearsFatality risk due to flooding in the coming 50 years

Visual aids: Visual aids: probability gridsprobability grids

–– YearlyYearly risk of flooding in Central Holland (1/10,000) risk of flooding in Central Holland (1/10,000)

Visual aids: Visual aids: probability gridsprobability grids

–– Risk of flooding in Central Holland (50 / 10,000) Risk of flooding in Central Holland (50 / 10,000)

in the coming 50 yearsin the coming 50 years

Visual aids:Visual aids:

Risk ladderRisk ladder

Yearly fatality risk due to Yearly fatality risk due to

flooding compared to other flooding compared to other

risks in the Netherlandsrisks in the Netherlands

And nowAnd now

ask about the moneyask about the money

�� Choice experimentChoice experiment

The situationThe situation: :

choice between moving two identical houses (choice between moving two identical houses (A A andand BB) in two polders) in two polders

with varying levels of flood safety and water board taxeswith varying levels of flood safety and water board taxes

Choice card CE3Choice card CE3

The method The method

We valueWe value::

Changes in the shown attributesChanges in the shown attributes

-- fatality riskfatality risk

-- risk of injuryrisk of injury

-- risk of evacuationrisk of evacuation

-- taxtax

Choice card CE3Choice card CE3

WE KNOW:WE KNOW:

Changes in the Changes in the

shown attributesshown attributes

With help of some With help of some

(advanced) statistics (advanced) statistics

we arrive at we arrive at

VOSLVOSL, , VOSIVOSI and and VOSEVOSE√√

Our main results Our main results

Estimate Estimate

Use of advanced statistical techniquesUse of advanced statistical techniques

(panel data structure, heterogeneity in preferences)(panel data structure, heterogeneity in preferences)

Sample mean values are in the rangeSample mean values are in the range::

VOSL VOSL (value of statistical life)(value of statistical life) 6.30 6.30 –– 6.90 mln 6.90 mln €€

VOIVOI (value of injury)(value of injury) 91,000 91,000 –– 99,000 99,000 €€

VOEVOE (value of evacuation)(value of evacuation) 2,300 2,300 –– 2,400 2,400 €€

��Statistically significant, robust estimatesStatistically significant, robust estimates

��Comparable to other estimates found in the literatureComparable to other estimates found in the literature

Composite valuation of Composite valuation of

immaterial damageimmaterial damage

Valued indicators of immaterial damage Valued indicators of immaterial damage

VOSL VOSL (value of statistical life)(value of statistical life) 6.30 6.30 –– 6.90 mln 6.90 mln €€

VOIVOI (value of injury)(value of injury) 91,000 91,000 –– 99,000 99,000 €€

VOEVOE (value of evacuation)(value of evacuation) 2,300 2,300 –– 2,400 2,400 €€

�� There should be a relationship between the threeThere should be a relationship between the three

Value of life and value of injuryValue of life and value of injury

Literature offers some longitudinal studies that looked at the Literature offers some longitudinal studies that looked at the

relationship between relationship between

the number of fatalities and the number of injuries* the number of fatalities and the number of injuries*

in flooding for various types of floods :in flooding for various types of floods :

Japan (Zhai, Fukuzono and Ikeda, 2006): Japan (Zhai, Fukuzono and Ikeda, 2006): 1 to 101 to 10

the US (Ashley and Ashley, 2008):the US (Ashley and Ashley, 2008): 1 to 61 to 6

* this ratio highly depends on many factors, such as the type of* this ratio highly depends on many factors, such as the type of flooding, flooding,

type of area flooded, etc.type of area flooded, etc.

Value of injury relative to VOSLValue of injury relative to VOSL

Assume:Assume:

N (injuries) to 1 fatalityN (injuries) to 1 fatality 55--10 to 110 to 1

VOSLVOSL 7.0 mln 7.0 mln €€

VOIVOI 100,000 100,000 €€

Value of injury relative to 1 VOSLValue of injury relative to 1 VOSL 7% 7% –– 14%14%

Value of life and value of evacuationValue of life and value of evacuation

This relation is more areaThis relation is more area--specific, specific,

and depends on a number of factors:and depends on a number of factors:

-- ratio of evacuations to floodsratio of evacuations to floods λλ

-- fraction of persons evacuated fraction of persons evacuated εε

-- fraction of persons affected fraction of persons affected αα

-- fraction of fatalitiesfraction of fatalities θθ

• The number of expected evacuated persons per year :

[7]

• The expected number of fatalities per year :

[8]

)(

yearlyevacuationtotal

yearperpersonsevacuated PNN ⋅⋅= ε

( ))(

1yearly

floodtotalyearper

fatalities PNN ⋅⋅−⋅⋅= θεα

• IF

and

• THEN

( ))(

)(

1

yearlyfloodtotal

yearlyevacuationtotal

fatalities

personsevacuated

PN

PN

N

N

⋅⋅−⋅⋅

⋅⋅

==θεα

ε

η

λ=)(

)(

yearlyflood

yearlyevacuation

P

P

( ) θαε

ελη

⋅⋅−

⋅==

1

fatalities

personsevacuated

N

N

We find:We find:

Value of injuryValue of injury per 1 fatality is 7per 1 fatality is 7--14% of VOSL14% of VOSL

Value of evacuationValue of evacuation per 1 fatality:per 1 fatality:

For the coastal area: For the coastal area: For a riverside area: For a riverside area:

1515--80% of VOSL 80% of VOSL 1 to 10 times VOSL1 to 10 times VOSL

ConclusionsConclusions

Conclusions (I): Conclusions (I): NOVELTYNOVELTY

•• Risk valuationRisk valuation in the context of flooding in the context of flooding

–– new in the Netherlandsnew in the Netherlands

–– new in hazard literaturenew in hazard literature

•• Simultaneous valuationSimultaneous valuation of risk of fatality, injury and evacuationof risk of fatality, injury and evacuation

((VOSLVOSL, , VOSIVOSI and and VOSEVOSE))

–– new in economic valuation literaturenew in economic valuation literature

•• Very low levels or riskVery low levels or risk valuedvalued

–– practically challenging practically challenging

Conclusions (II): Conclusions (II): RESULTSRESULTS

•• Elicited values:Elicited values:

–– VOSL VOSL (value of statistical life)(value of statistical life) 7 mln 7 mln €€

–– VOSIVOSI (value of statistical injury)(value of statistical injury) 100,000100,000 €€

–– VOSEVOSE (value of statistical evacuation)(value of statistical evacuation) 2,500 2,500 €€

Significant Significant

RobustRobust

Plausible Plausible

Conclusions (III): Conclusions (III): POLICY IMPLICATIONSPOLICY IMPLICATIONS

•• Composition of immaterial damage Composition of immaterial damage in the context of flooding in the context of flooding

–– is areais area--specific (coast vs riverside)specific (coast vs riverside)

–– taking only valuation of avoided fatalities (VOSL) in CBA may taking only valuation of avoided fatalities (VOSL) in CBA may

substantially underestimate substantially underestimate TOTAL immaterial damagesTOTAL immaterial damages

•• Higher obtained value of VOSLHigher obtained value of VOSL,, and new values for and new values for VOIVOI and and VOEVOE

mean that: mean that:

–– balances in CBA on the balances in CBA on the ““benefitsbenefits”” side are changing: side are changing:

immaterial damage is gaining more weight immaterial damage is gaining more weight

–– higher costs may be tolerated for flood protection measureshigher costs may be tolerated for flood protection measures

Thank you!Thank you!

The method The method

(a little bit of economics and statistics)(a little bit of economics and statistics)

So how do we do it?So how do we do it?

Respondents make choices between 2 shown alternatives depending Respondents make choices between 2 shown alternatives depending

on their level of on their level of U, utility U, utility (satisfaction)(satisfaction)..

However, However, we cannot control / observe all aspects of individual we cannot control / observe all aspects of individual ““utilityutility””,,

but only the attributes that we have shown in the choice cards.but only the attributes that we have shown in the choice cards.

Therefore, individual utility of each alternative can be thoughtTherefore, individual utility of each alternative can be thought of as of as

consisting of 2 parts: consisting of 2 parts: observed utility (V) observed utility (V) and and unobserved utility (unobserved utility (εε))::

ε+= VU

Choice card CE3Choice card CE3

√√

UtilityUtility……

As researchers, we hope As researchers, we hope –– and we can test that and we can test that –– that that choiceschoices offered offered

to the respondents were to the respondents were governed by the attributesgoverned by the attributes that were shown that were shown

on the cards (i.e. safety and payment).on the cards (i.e. safety and payment).

Therefore, we model Therefore, we model observed utilityobserved utility ((VV).).

We assume a We assume a linearlinear form of the observed part utility (form of the observed part utility (VV), so that utility ), so that utility

of safety and utility of money are additive:of safety and utility of money are additive:

TaxTaxinjPinjPfatalPfatalPevacno

TaxTaxevacPevacPevac

xxxV

xxASCV

***

**

.)(.)()()(.

.)(.)(.

βββ

ββ

++=

++=

And how do we get to VOSL?And how do we get to VOSL?

We can take We can take partial derivativespartial derivatives of the utility functionof the utility function with respect to risk with respect to risk

and money to obtain the and money to obtain the ““marginal utilitiesmarginal utilities””::

andand

Recall Recall VOSLVOSL is defined as:is defined as:

And therefore: And therefore:

TaxxV ∂∂ /)(/ fatalPxV ∂∂

∆P

WTP

∆P

∆YVOSL

_________

==

)(/

/

fatalP

Tax

xV

xVVOSL

∂∂

∂∂=

And finallyAnd finally……

valuation of immaterial damagevaluation of immaterial damage (VOSL)(VOSL)

If observed utility is:If observed utility is:

VOSLVOSL is a tradeis a trade--off between money and the level of risk, on the off between money and the level of risk, on the

margin.margin.

TaxTaxinjPinjPfatalPfatalP

TaxTaxevacPevacP

xxxV

xxASCV

***

**

.)(.)()()(2

.)(.)(1

βββ

ββ

++=

++=

Tax

fatalP

Tax

fatalP

fatalP

Tax

x

x

xV

xVVOSL

β

β )()(

)(/

/=

∂

∂=

∂∂

∂∂=

Valuation of immaterial damageValuation of immaterial damage((VOSE and VOSI)VOSE and VOSI)

Similarly to VOSL,Similarly to VOSL,

VOSI (VOSI (value of statistical injuryvalue of statistical injury)) is determined as: is determined as:

VOSE (VOSE (value of statistical evacuationvalue of statistical evacuation)) is determined as : is determined as :

Tax

evacP

evacP

Tax

xU

xUVOE

β

β .)(

.)(/

/=

∂∂

∂∂=

Tax

injP

injP

Tax

xU

xUVOI

β

β .)(

.)(/

/=

∂∂

∂∂=