Monetary Valuation of Insurance against Climate Change Risk

W.J.W. Botzen

Institute for Environmental Studies

Vrije Universiteit

Amsterdam, The Netherlands

wouter.botzen@ivm.vu.nl

and

J.C.J.M. van den Bergh1

ICREA

and

Institute of Environmental Science and Technology

& Department of Economics and Economic History

Autonomous University of Barcelona

Spain

jeroen.bergh@uab.es

May 2009

1 Also affiliated with Faculty of Economics and Business Administration & Institute for Environmental

Studies, Vrije Universiteit, Amsterdam. Fellow of NAKE and Tinbergen Institute.

1

Abstract

Climate change is expected to increase the frequency and severity of certain natural

catastrophes, such as flooding. This is likely to increase the willingness to pay (WTP) for

natural catastrophe insurances, even though it is uncertain how large this effect will be. In

various countries the public sector offers partial compensation of damage caused by

natural catastrophes, which may reduce the need for private insurance coverage and

hamper the development of insurance markets. We present a stated preference survey

using choice modeling with mixed logit estimation methods to examine the effects of

climate change and availability of government compensation on the demand for flood

insurance by Dutch homeowners. Currently, insurance against flood damage is not

offered in the Netherlands. We estimate the dependence of WTP on prior risk

perceptions, actual measures of risk, risk aversion, and socio-economic characteristics.

Results indicate that opportunities for a (partly) private flood insurance market exist.

Keywords: Choice modeling, Flood insurance, Mixed logit, Public compensation

scheme, Risk and uncertainty, The Netherlands.

2

1. Introduction

Climate change is projected to increase the frequency and severity of weather extremes,

which is likely to have considerable consequences for the insurance sector (IPCC, 2007).

Several studies have examined the impact of climate change on insurance claims (e.g.,

Mills, 2005; Kunreuther and Michel-Kerjan, 2007; Dlugolecki, 2008; Botzen et al.,

2009a). Few empirical studies have estimated the effect of climate change on the demand

for natural catastrophe insurances. The willingness to pay (WTP) for insurance is

expected to increase due to a rise in the probability of suffering weather-related damage,

but it is uncertain how large this rise will be. Indeed, insight into the influence of climate

change on WTP for disaster insurances is required so that insurers can assess the future

profitability of offering coverage against damage caused by natural disasters. This is very

relevant given that climate change is likely to continue in the coming decades due to

committed radiative forcing by past emissions and rapid projected growth of emissions,

notably in industrializing Asian economies (Pielke et al., 2007; Botzen et al., 2008a).

Climate change projections for the Netherlands indicate an increase in flood risk

due to more extreme precipitation and sea level rise (Middelkoop et al., 2001; Aerts et al.,

2008a). Botzen and van den Bergh (2009) estimate risk premiums for flood insurance

demand in the Netherlands under different climate change scenarios using prospect and

rank dependent utility theories and parameters obtained from existing experimental

studies. Their results indicate that rising flood probabilities from 1 in 1250 up to 1 in 550

cause WTP to increase more than the expected value of the loss. The representative agent

assumption underling that study, which results in average WTP values, is relaxed here by

estimating individual heterogeneity in WTP using a stated preference survey among

homeowners with choice modelling and mixed logit estimation methods. A stated

preference study is in order here since flood insurance is not available in the Netherlands,

which implies that insurance demand cannot be analysed using data on revealed

preferences. This study estimates demand for flood insurance under climate change

scenarios with increasing flood probabilities. Apart from climate change, socio-economic

developments, such as settlement in vulnerable areas as well as population and economic

growth, are likely to increase damage of natural disasters (Bouwer et al., 2007), while

investments in damage mitigation may limit rising trends in disaster losses (Botzen et al.,

3

2009b). Therefore, the influence of socio-economic developments on WTP for disaster

insurance needs to be analyzed in addition to potential effects of climate change to arrive

at reliable estimates of future demand.

Botzen and van den Bergh (2008) examined the pros and cons of introducing

flood insurance in the Netherlands. Advantages may be that insurance can be useful in

efficiently spreading of risks, enhance households’ financial security, and provide

incentives to policyholders to limit flood damage. For example, stimulating ‘flood

proofing’ of buildings in addition to investing in dikes may limit the occurrence of

extremely large flood damages (Aerts et al., 2008b). The undertaking of these mitigation

investments could for example be stimulated by providing premium discounts (Botzen et

al., 2009b). It was proposed to employ a public-private partnership for insuring flood

risks, with a role for the government in covering extreme damages to overcome problems

with correlated risks. A similar scheme has been suggested to insure weather-related risk

in the USA (Kunreuther and Pauly, 2006).

The absence of flood insurance in the Netherlands at this moment may be due to

supply side problems, such as correlated risks, uncertainty of risks, adverse selection and

moral hazard, or because of a lack of demand for insurance coverage (Freeman and

Kunreuther, 2003). It will be examined here whether demand is the main impediment of

the establishment of a partly private flood insurance market by estimating the level of

WTP relative to the expected value of loss per policy. It has sometimes been suggested

by Dutch insurers that problems with adverse selection may be severe in the case of

offering flood insurance, because only individuals who live in unprotected areas with

high flood risks would demand insurance (de Vries, 1998). Examining how WTP relates

to actual risk derived from geographical characteristics will provide insight into potential

problems with adverse selection.

In addition, this study analyzes the effect of the current institutional setting,

characterized by availability of government compensation of flood damage, on insurance

demand. The Dutch government can grant partly compensation of damage caused by

large-scale floods via the Calamities and Compensation Act (WTS), as is also the

situation in several other countries (Crichton, 2008). Decisions about granting relief and

its extent are a political decision. Experiences with flood damage in 1993 and 1995

4

resulted in considerable relief payments via the WTS. As a consequence, households may

expect that the government will compensate future flood damage unconditional on the

risk they take. This may reduce the desirability of private insurance, which is often

referred to as crowding out (Harrington, 2000).

The main objectives of this valuation study are fourfold. First, it will estimate

WTP for flood insurance in the Netherlands under the current institutional setting and

climate conditions. This is of practical interest for insurers and the government in

evaluating whether demand for flood insurance will be sufficiently high to make a private

market viable. Second, the role of expectations about government compensation of

disaster damage will be analyzed by comparing WTP with and without relief of flood

damage by the government. This can aid the government in assessing what conditions

need to be created to stimulate, or at least not hamper, the emergence of a market for

flood insurance. Third, the effects of climate change and socio-economic developments

on the demand for flood insurance will be assessed. This is accomplished by eliciting

insurance demand under different scenarios of increased flood probabilities due to

climate change and varying levels of expected flood damage. This provides insights into

the risk characteristics of individuals faced with climate change risk, which allows for

accurately prediction of behavioral responses to risk related to climate change and

flooding.2 Fourth, bid functions will be estimated to identify factors behind WTP using as

explanatory variables perceptions of flood risk, actual measures of flood risk based on

geographical characteristics, estimates of individual risk aversion, actual insurance

purchase behavior, and socio-economic characteristics.

The remainder of this paper is organized as follows. Section 2 explains the setup

of the survey and its implementation. Section 3 explains the design of the choice

experiment and the estimation methods. Section 4 provides the estimation results of logit

and mixed logit models of the choice experiment. Section 5 concludes.

2. Explanation of the questionnaires

2.1. The commodity valued

2 Care must be taken in transferring the results to other contexts than insurance since it has been shown that

in eliciting risk attitudes the insurance context may induce extra risk aversion (e.g., Hershey et al., 1982).

5

WTP for flood insurance is elicited by means of a choice experiment. The choice

experiment values insurance with different levels of coverage in situations with varying

flood probabilities and damages caused by river flooding on both homes and contents.

Careful consideration is given to communicate these small flood probabilities in between

the current safety standard of 1 in 1250 and increases in probabilities up to 1 in 100 due

to climate change, as will be elaborated upon below.

2.2. Communicating small probabilities

In general, individuals have difficulties to understand the likelihood of low-probability

events and differences in probabilities (Viscusi, 1998). A large literature exists on

valuation of small risk using surveys (Hammitt and Graham, 1999), especially on

estimating the value of a statistical life by eliciting WTP for reductions in small health or

accident risks (Vassanadumrongdee and Matsuoka, 2005; Alberini et al., 2004, 2006,

2007; Bhattacharya et al., 2007; Van Houtven, 2008). Risk ladders and square grids are

commonly used as visual aids to improve respondents’ understanding of small

probabilities and changes in probabilities. A risk ladder shows the current or baseline risk

on a probability scale together with other risks that the respondent commonly faces (e.g.,

Hammitt, 1990; Vassanadumrongdee and Matsuoka, 2005). Changes in risk can be

communicated by depicting both the baseline and the new probability on the risk ladder,

and using an arrow to indicate the change in the probability. Such a risk ladder illustrates

the size of the change and also how the new probability compares with the other risks.

Square grids are often in the order of 10,000 or 100,000 squares on which risks are

represented using colored squares (e.g., Jones-Lee et al., 1985; Krupnick et al., 2001;

Alberini et al., 2004; Bhattacharya et al., 2007). Changes in probabilities can be presented

on such a grid by increasing or decreasing the number of randomly filled squares. Risk

ladders and square grids are likely to be suitable risk communication devices for this

study. During the pilots of the survey we tested which device respondents perceive as the

clearest and most useful.

2.3. Pre-tests

6

During the design of the survey, subsequent versions of the questionnaire were reviewed

by experienced stated choice practitioners, economists, natural scientists, water

management experts, and psychologists. After incorporating their comments, three pre-

tests of the questionnaire were conducted between August and October 2007, using face-

to-face interviews. Four trained and carefully instructed and supervised interviewers (2

male and 2 female) interviewed 88 households. Particular attention was paid to the

comprehension of flood probabilities and the choice experiment.

Different risk communication devices were tested, such as risk ladders, 10,000

square grids on which baseline risk and changes in risk are represented using colored

squares, and a variety of textual explanations. The results indicated that the square grids

were generally regarded as difficult and too abstract so that they are omitted from the

final survey. The risk ladders were perceived as providing very clear and useful

information. Textual comparisons of flood risks for different kinds of households with

other risks, such as fire risk, have been tested, since they may increase comprehension as

shown by Kunreuther et al. (2001). However, as these comparisons were not regarded to

add much extra information to the risk ladders, they are excluded.

We have tested a labeled experiment (one label per insurance type with label-

specific attributes) consisting of insurance options that cover flood damage on home

contents, housing, both, and no insurance. The resulting choice experiment turned out to

be overly complex. Instead, an experiment with generic (unlabeled) alternatives that

values an insurance covering both damage on home contents and buildings was used in

the final pre-tests and survey. This turned out to be easier for respondents. Both yearly

and monthly premiums were provided in the choice experiment and their levels were

derived from answers to open-ended WTP questions. A fourth and final pre-test was

conducted to test the on-line implementation of the questionnaire, which resulted in

minor adjustments in layout.

2.4. The structure of the questionnaires

A description of the survey and an overview of the questions is given in Botzen et al.

(2008b). The questionnaire opens with questions about the experience of the respondent

with flooding, flood damage and evacuation because of flood threats and knowledge

7

about the causes of flooding. In addition, several questions address the perception of

flood risks using both qualitative and quantitative answer categories. The answers to

these risk perception questions are discussed in detail in Botzen et al. (2008c). These

questions familiarize the respondents with flood probabilities. The assessed perceptions

may be important in decision making under risk as several studies suggest (Viscusi,

1989) and serve as explanatory variables. Moreover, questions are included about risk

aversion and actual insurance purchases.

Whereas the previous questions were identical in all versions of the questionnaire,

some subsequent explanations differ, giving rise to two versions. In version 1 the current

regulation for compensating flood damage by the government is explained. In short, this

states that the government may partly compensate damage caused by major floods, while

this compensation is not granted for small flooding events. The uncertainty about

receiving relief is mentioned and several recent examples of floods where damage has

been partly compensated are given. The other version describes a scenario explaining that

relief of flood damage by the government will no longer be granted, but that it is possible

to purchase insurance coverage instead.

Next, a short text is included about flood probabilities in all versions. It is

explained why flood probabilities differ across regions, providing a comparison of risks

in a textual context (see Hsee et al., 1999) and the idea of expressing probabilities in

terms of return periods or frequencies is mentioned. In addition, estimated flood

probabilities of an area not protected by dikes (1 in 100) are compared with flood

probabilities of urban areas that are protected by dikes (1 in 1250). This explanation

precedes our main risk communication device, which is a risk ladder on which flood risks

are compared with other insurable risks commonly faced by Dutch citizens (see appendix

A). All adverse events are expressed as yearly probabilities. Furthermore, risk ladders are

shown that illustrate an increase in the flood probability from the current safety standard

of 1 in 1250 to 1 in 600 and 1 in 400 as a result of climate change. Three contingent

valuation questions with payment cards that elicit WTP for flood insurance under flood

probabilities of 1 in 1250, 1 in 600 and 1 in 400 are included before the choice

experiment. These changes in risk are communicated by stating the probability and

frequency of the new risk, as well as the proportional changes relative to the baseline

8

probability (“doubled” or “tripled”) in order to facilitate comprehension (e.g., McDaniels,

1992). The results of these questions are not discussed in detail in this paper, which

focuses on the valuation of flood insurance with a choice experiment.

The choice experiment values flood insurance with varying coverage levels in

situations with different flood probabilities and expected damages (see appendix B for an

attribute and level overview). An unlabelled experiment is used where respondents

choose between insurance “Situation A”, “Situation B” or an “opt out” (see appendix B).

It is explained that flood probabilities differ due to the uncertain effect of climate change

on flood risk and flood damage relates to the severity of the flood. Individuals are

instructed to choose the “opt out” in case they do not want insurance or find the insurance

in both situations unattractive. The experiment starts with an example ‘practice choice

card’ that is carefully explained in the text. Subsequently, respondents are asked their

preferences at three random choice cards. Finally, a fixed card with a dominant option is

shown to identify respondents who have trouble to understand the experiment. Follow-up

questions ask for the main reasoning behind the choices made and the perceived

difficulty of the experiment. In the valuation questions respondents are asked to consider

their budget constraint to avoid hypothetical bias. The questionnaire concludes with the

usual socio-demographic questions.

2.5. Administration of the survey and sample characteristics

The survey was administered over the Internet using Sawtooth CBC software.3 This

computer based method has the advantage that follow-up questions can be automated,

high quality graphics can be included, a large underlying design for the choice model can

be applied, interviewer effects can be avoided, and a geographically spread sample can be

obtained at relatively low costs. Respondents were selected from the consumer panel of

Multiscope and contacted by e-mail.4 The sample consists of random draws of panel

members that live in the river delta in the Netherlands with a common flood probability

standard of 1 in 1250. The survey starts with a selection question and only respondents

who own a house are allowed to continue. Renters are not included in the sample because

3 See www.sawtoothsoftware.com.

4 For more information see www.multiscope.nl.

9

the insurance valued covers damage on both home contents and buildings. For this

reason, the levels of the damage and premium attributes in the choice experiment are

representative for homeowners only. A total of 1140 respondents filled out the

questionnaire while 982 observations remain after excluding respondents who live in flats

higher than the first floor and who live outside the sample area.

Our sample has slightly more male (58%) than female respondents. On average

respondents are 46 years old. The proportion of respondents who are older than 60 years

is about 11%, which is smaller than is the case in the actual Dutch population. Fewer

older individuals are represented in the Internet sample, because they are generally less

active on the Internet than younger people. We do not regard this as troublesome in this

application since the increased flood risk posed by climate change is less applicable to

older respondents since it will take several decades for the altered risk to become

relevant. The median and average after-tax household income is the answer category

“between € 2501 and € 3000 per month”, which is close to the average after-tax income

of a household that owns a house in the Netherlands, namely € 3025 per month (Statistics

Netherlands, 2008).

3. Experimental design and estimation method

3.1. The experimental design

The choice experiment entails a choice between two situations in which flood insurance

is available with as attributes the flood probability, expected damage, the percentage of

coverage, and the premium. An “opt out” option is included for respondents who do not

want the insurance. Appendix B shows an example choice card and an overview of the

levels of the attributes included in the experiment. We chose 75% as the lowest coverage

level in our choice experiment since this equals the maximum allowed deductible in

catastrophe insurance markets in several states of the USA (Kunreuther et al., 2008). The

risk (probability and damage) is presented as scenarios that are exogenous to the

individual. The expected flood damage of € 70,000 is an estimate of the current average

flood damage per household as has been computed as in Botzen and van den Bergh

(2009), while the other two levels of the experiment (€ 40,000 and € 120,000) can be

regarded as minimum and maximum estimates. The respondents indicate whether they

10

prefer to buy insurance and if yes which insurance policy they favour. Other studies have

valued insurance in situations with varying risk using choice experiments. For example,

Schneider and Zweifel (2004) examine demand for nuclear risk insurance in Switzerland

using damage, coverage, and price as insurance attributes.

The experiment used in this study tries to assess the factors of influence on the

insurance decision. In particular, individuals decide whether to buy a certain degree of

insurance coverage against a risk -probability and damage- for a certain price (premium).

An advantage of the choice experiment over the contingent valuation method is that it

provides more information about the factors that influence demand for flood insurance.

The choice experiment allows for simultaneously examining effects of varying flood

probabilities, expected damages, coverage levels, and premiums on choices for insurance.

Furthermore, the experiment is closer to reality where respondents can choose between

different insurance options without a need to state a maximum WTP amount, which may

result in smaller biases.

A statistically efficient design was used as it contributes to maximum accuracy of

coefficient estimates (i.e. low standard errors) of the attributes (Ferrini and Scarpa, 2007).

In total, 250 versions of the design have been generated to which respondents were

randomly assigned.5 This means that many combinations of the levels of the attributes

appear in the experiment. The generated design has been checked for strictly dominant

choices, which were then excluded from the final design. Each respondent answered three

random choice cards. After removing protest responses, this resulted in a total of 2751

completed choices.6

3.2. Estimation methods

Choice models are based on the random utility model. In this model, the probability pni of

an individual n choosing alternative i is set equal to the probability that the utility of

5 The design has been generated by means of the software Sawtooth CBC using the efficient design module

(“Balanced Overlap”). 6 In total 65 protesters were excluded. Such responses are motivated by individuals saying that they do not

believe that flood damage is not already covered, do not believe or accept the stated flood probability, do

not believe or accept the change in the flood probability, or do not believe that offering flood insurance is

possible. In version 2 a protest response may result from individuals not accepting the abolishment of

government compensation.

11

alternative i is greater than or equal to the utility associated with an alternative j for every

alternative in the choice set (j = 1…J). This can be formalized as

];,...,1)()[( jiJjjVVprobp njnjninini ≠=∈∀+≥+= εε (1)

where Vni and εni are the observed and unobserved components of individual n´s utility

associated with alternative i, respectively. Different assumptions about the distribution of

εni result in different choice models.

The logit model

The logit model is the most commonly used choice model. It is derived under the

assumption that εni is iid extreme value distributed for all i. This means that the

unobserved components of utility are independently and identically distributed across

alternatives. Therefore, the unobserved factors are uncorrelated over alternatives and

have the same variance for all alternatives. This independence assumption also applies to

sequential choices made over time. The logit probability is given by the formula

(McFadden, 1974)

∑=

j

nj

ni

ni xe

xe

pβ

β (2)

The mixed logit model

The independence assumption within the logit model is restrictive, because unobserved

characteristics associated with alternatives in a choice situation may be similar.

Moreover, unobserved factors that affect the choice in one choice situation (or choice

card) may affect the choice in a subsequent choice situation, which induces dependence

among choices over time. The more general mixed logit model is very flexible and can

overcome these problems by allowing for random taste variation, unrestricted substitution

patterns and correlation in unobserved characteristics over different choice situations

(McFadden and Train, 2000). Therefore, the mixed logit model may be better in

describing choice behavior than logit (Rieskamp et al., 2006). The mixed logit probability

is (Train, 2003)

12

∫∏∑=

= βββ

βdf

xe

xe

pT

t

j

njt

nit

ni )(1

(3)

Formula (3) shows that the mixed logit probability is a weighted average of the logit

representation (4) evaluated at different values of β with weights given by the density

f(β). The panel data structure is presented by the time subscript t and is explicitly

modeled since respondents were asked to answer three sequential choice cards (so that

T=3). Coefficients can be specified as random in the mixed logit model, meaning that

they vary over decision makers. In this case, the model estimates the mean coefficients

and standard deviations of the random parameters, which represent unobserved

heterogeneity in preferences. The parameters are estimated using maximum simulated

likelihood with Monte Carlo integration using 200 Halton draws, which are generally

found to produce more precise results than random draws (e.g., Bhat, 2001).

Coding of the explanatory variables

A detailed explanation of the explanatory variables and their descriptive statistics are

given in appendix C. Different methods of coding categorical variables have been

applied. Dummy variables are used for several categorical variables. Continuous

variables are created from categorical variables that represent monetary classes, such as

the value of the house as well as home contents (e.g., Blumenschein et al., 2008). A

variable representing the total value of property is created by adding the home contents

and house values. Ordinal qualitative variables7, which are partitioned into J intervals,

can be included using J-1 dummies or can be transformed into values on the real axis

using an approach proposed by Terza (1986). An advantage of the dummy approach is

that the interpretation of the coefficients is straightforward, but many variables are

needed in case J is large. In this case, the transformation of Terza (1986) can result in

gains in efficiency and bias. For this reason the latter approach has been applied in

several studies (e.g., van Praag et al., 2003. The transformation (see appendix D) is used

7 These variables are characterized by a continuous unobservable ordinal latent index and each interval is

ranked (1 through J) in increasing order according to its supremum (Terza, 1986).

13

here for variables with a large number of categories, which are the perceived risk of

suffering flood damage and the risk seeking index.

4. Estimation results of the choice models for flood insurance demand

The choice experiment is unlabelled, which implies that there is no reason to expect a

general preference for one of the two situations with flood insurance shown to

respondents. This is supported by the data, since both situations with insurance (A and B)

were chosen about 19% of the time each, while the “opt out” or no insurance was chosen

62% of the time. The choice experiment was followed by a question that asks how

difficult it was for respondents to make a choice, with the answer options very easy, easy,

neutral, difficult, and very difficult. Only 2.7% of the respondents indicated that the

choice experiment was very difficult and 14% indicated that it was difficult. The last

choice card included a dominant option to check understanding of the experiment by

respondents. The dominated option was chosen by only 2% of the respondents. Based on

these answers and the pilot of the survey we are confident that the experiment was not too

difficult for the large majority of respondents, despite the inclusion of the probability

attribute and the unfamiliarity of Dutch homeowners with buying flood insurance in

practice.

4.1. Results of a model for insurance demand without heterogeneity

It is common practice in studies that value insurance coverage or health risk to use a

general utility function in the retained attributes and not anchor the utility function in

expected utility theory (e.g., Schneider and Zweifel, 2004; Goldberg and Roosen, 2007).

A reason for this is that often expected utility theory provides a poor description of

individual choices under risk (Camerer, 1998). Common violations of expected utility

theory relevant to the insurance application at hand are that individuals may ignore low

probabilities or weigh them in a non-linear fashion (Slovic et al., 1977; Schmeidler, 1989;

Tversky and Kahneman, 1992; Mason et al., 2005). In addition, it is often found in

insurance markets that individuals place a larger value on the level of coverage than

predicted by expected utility theory (Doherty and Eeckhoudt, 1995). The following utility

specification is used for the model that includes only the attributes of the experiment:

14

pricecoveragedamage

highyprobabilitmiddleyprobabilitlowy probabilitU Insurance

***

* **

764

321

βββ

βββ

+++

++=

constant U ceNo insuran *8β= (4)

The utility of having insurance is dependent on the expected flood damage, the

probability of flooding, insurance coverage, and price.8 The parameters of the attributes

are the same for both scenarios because the experiment is unlabelled, i.e. there is no a

priori reason to expect that the attributes have a different effect on the utility in the

generic scenarios A or B. The utility of the option without insurance is modeled with a

constant term. The three probability variables are dummy variables representing the low

(1/600), middle (1/400) and high (1/100) flood probability. The current flood probability

(1/1250) is excluded so that the coefficients β1, β2, and β3 measure the effect relative to

having insurance under the current flood probability. Using dummies for the probability

variable allows us to examine non-linear effects without restricting the functional form of

this non-linearity. Subsequently, an adequate functional form for a continuous probability

variable can be derived from the coefficient estimates of the dummy variables.

The two left columns of Table 1 show the estimation results (equation 4). The

pseudo R2 is 0.27, which indicates a good fit for this type of models. The coefficients of

all attributes are statistically significant at the 1% level and of the expected sign. In

particular, the utility of flood insurance increases with flood risk (probability and

damage) and coverage level, while it decreases with price. The dummy variables of the

flood probability indicate a monotonic and non-linear increase of utility when the

probability rises. This relation is concave, which means that utility and WTP increase less

than proportional with a decreasing slope in response to a probability increase.

The specification with the probability variables coded as dummy variables

provided useful insights about the non-linear shape of the relation between utility of

insurance and flood probability. A disadvantage of the dummy specification is that it is

8 Individuals may value the insurance according to the monetary payoff (damage*coverage), as appeared to

be the case in a choice experiment of nuclear risk insurance by Schneider and Zweifel (2004). This is

examined by including an interaction between the coverage and damage attribute in equation 4. The

coefficient of this interaction term is insignificant (at the 10% level). Furthermore, non-linearity in the

reaction to damage has been estimated by including damage2 as explanatory variable in equation 4. The

non-linear reaction is insignificant (at the 10% level). It should be noted that coverage cannot be modeled

in a non-linear fashion, since the choice experiment included no more than two levels of this attribute (75%

and 100%) in order to reduce complexity of the choice decision for respondents.

15

only possible to evaluate insurance demand for the flood probability levels captured by

the dummies, that is 1/600, 1/400, and 1/100, and not for the whole range of probabilities

in between 1/1250 and 1/100. The flood probability is a continuous variable (between 0

and 1) and this property can be exploited by including it as a single variable in the utility

specification. The non-linear relation between probability and utility of flood insurance

observed in equation 4 can be approximated by specifying the utility function dependent

on the square root of the probability.9 This model can be written as:

pricecoveragedamageyprobabilitSQRTU Insurance ***))((* 4321 ββββ +++=

constant U ceNo insuran *5β= (5)

The results of this more parsimonious model (5) are shown in the two right columns of

Table 1. Overall, results are very similar to the model (4), apart from the relation with the

flood probability that is now captured by a single variable instead of the three dummies.

Table 1. Results of logit models without heterogeneity

Logit model (equation 4) Logit model (equation 5)

Variable Coefficient Wald-statistic Coefficient Wald-statistic

Flood probability low 0.2835*** 2.63 n.a. n.a.

Flood probability middle 0.4270*** 3.97 n.a. n.a.

Flood probability high 0.7750*** 7.43 n.a. n.a.

SQRT flood probability n.a. n.a. 9.5121*** 7.50

Flood damage 0.0036*** 3.31 0.0036*** 3.33

Insurance coverage 0.0100*** 3.56 0.0102*** 3.62

Insurance premium -0.0407*** -20.84 -0.0407*** -20.85

Constant 1.4028*** 5.10 1.5638*** 5.67

Number of observations 2751 2751

Log likelihood -2217 -2219

Pseudo R2 0.27 0.27

Notes. One, two and three stars (*) indicate respectively significance at the 10%, 5%, and 1% level and n.a. stands for not applicable.

Estimations are performed with Limdeb software.

9 Non-linearity of continuous variables in choice experiments is often modeled by including a squared term

of the variable in addition to its level. Main results are rather similar if the squared of the flood probability

and the flood probability level are included instead of the square root of the probability (equation 5) or the

dummies (equation 4). The coefficient of the level is significant and positive and the coefficient of the

squared term is negative and significant. An unrealistic characteristic of such a specification in this

application is that the utility of insurance declines if the probability rises for very large probabilities. We

further experimented with modeling the probability variable with the logarithm of the probability. Overall

results are rather similar again. Specification 5 is preferred as it stays close to the results of specification 4.

16

4.2. Results of a model for insurance demand with observed and unobserved

heterogeneity

Insights into individual heterogeneity in flood insurance demand are of interest to

insurers for two main reasons. First, this provides information about what groups of

costumers insurers could target. Second, it is very useful to know how demand for flood

insurance relates to risk characteristics of individuals to determine pricing strategies, i.e.

premium differentiation, and to assess potential problems with adverse selection. Adverse

selection could hamper the development of flood insurance markets if mainly high risk

individuals who live in unprotected areas are interested in purchasing insurance and

insurers are unable to adequately distinguish low from high risk customers and charge the

latter a higher (risk based) premium. Examining heterogeneity further provides relevant

insights into risk characteristics of individuals faced with low-probability, high-impact

climate risk.

Observed heterogeneity in demand for flood insurance is examined by including

explanatory variables in the logit model (5) about individual risk perceptions, experiences

with flooding, individual risk aversion, and geographic as well as socio-economic

characteristics. In addition, a variable is included about the availability of compensation

of flood damage via the government to estimate differences in insurance demand between

the two questionnaire versions. Unobserved heterogeneity is examined by specifying the

coefficient of the probability variable as random using a mixed logit model, because the

behavioral economics literature indicates that individuals can react in very different ways

to probabilistic information.

Explanatory variables representing personal characteristics that are constant

across the choice alternatives can be included in two ways in our model. Such variables

are either interacted with the attributes that vary in the alternatives with flood insurance

or they are interacted with the constant of the no insurance alternative in equation 5.

These variables can only be included in this manner since random utility models measure

differences in utility between alternatives (equation 1). In this application, it is estimated

whether the utility of insurance coverage is related to actual risk faced by the respondent

by including an interaction with the coverage attribute and a variable representing

individuals who live close to a main river and are more likely to suffer large flood

17

damage. Moreover, an interaction variable between price and a variable representing the

high-income category is included to test for diminishing marginal utility in income. Other

explanatory variables are included in the utility specification of the alternative without

insurance so that they capture the utility difference between the insurance alternatives

versus no insurance. This results in the following model:

)*(**) *(cov*

**)(*

654

321

income highpricepriceriver main tocloseerage

coveragedamageyprobabilitSQRTU Insurance

βββ

βββ

+++

++=

nkceNo insuran xconstant U **7 ββ += (6)

where xn represents variables for availability of government relief, individual perceptions

about the flood probability and damage, experience with floods, insurance purchases, risk

aversion, (other) geographical characteristics, and socio-economic characteristics.

The mixed logit model includes a random parameter for the square root of the

flood probability to capture unobserved individual heterogeneity in the response to

probability. A triangular distribution is specified for the coefficient of probability with

the standard deviation set equal to the mean value of the coefficient. This distribution is

particularly useful for two reasons. First, it is behaviorally plausible since coefficients are

positive for all individuals, meaning that WTP for insurance increases for all individuals

if the probability of suffering damage rises. Second, it prevents problems with the long

tail of the lognormal distribution, which has been applied in some studies and may cause

unrealistically large WTP estimates (Hensher and Greene, 2003). We note that similar

results are obtained with specifications with normal and triangular distributions with

various constraints on the variance, which indicates robustness of our findings.

Table 2 below provides the estimation results of the logit and a mixed logit model

of equation (6). The fit of the model improves considerably compared with model (5)

without heterogeneity as reflected by the increase in log likelihood and pseudo R2. The

standard deviation of the random coefficient is statistically significant. This indicates that

individual preference heterogeneity exists in the coefficient of the probability attribute

around the mean coefficient and that the mixed logit specification is preferred to logit.

The log likelihood increases from –2061 for the logit model to –2027 for the mixed logit,

which confirms that the logit specification can be rejected based on the likelihood ratio

test with 342 =χ and 1 degree of freedom (McFadden and Train, 2000). The overall fit

18

of the mixed logit model is very good as the pseudo R2 statistic of 0.33 indicates (see

appendix D), which is similar to a linear R2 of approximately 0.7 (Domencich and

McFadden, 1975; Louviere et al., 2000).

The attributes of the choice experiment determine the utility of having insurance

(UInsurance in equation 6) so that a positive coefficient indicates a positive relation between

the attribute and the value placed on flood insurance. The coefficients of the attributes are

statistically significant and have the expected sign: the utility of insurance increases with

flood probability and damage as well as coverage level, while it decreases with the

insurance premium. The coefficient of the probability variable is about 80% larger in the

mixed logit specification than in the logit specification. This indicates that the mean

relation between the utility of insurance and the flood probability is considerably

underestimated if the coefficient is mistakenly specified as fixed instead of random.

Coefficients of other variables are very similar between the logit and mixed models. The

interaction variable of insurance coverage and individuals living close to a main river has

a positive and significant coefficient, which implies that high-risk individuals place a

larger value on flood insurance coverage than individuals who face a lower flood risk.

The interaction variable between the insurance premium and the high-income category is

significant and positive. High-income individuals worry less about the price and have a

higher WTP for flood insurance as can be expected from consumer theory.

It is noted that the other explanatory variables determine the utility of having no

insurance (U No insurance in equation 6) so that a positive coefficient indicates a negative

relation between the variable and the value placed on flood insurance. Table 2 shows that

the probability of choosing for insurance is lower if compensation of flood damage by the

government is available, implying that government relief crowds out demand for private

insurance. Perceptions of the risk of flooding are important determinants in the choice for

flood insurance. In particular, the probability of choosing for flood insurance is positively

related to a respondent’s perceptions that climate change increases flood risk, the

expected probability of flooding and the expected flood damage. The probability of

choosing for flood insurance is lower if individuals expect that their flood risk is lower

than an average resident and if it is expected that the return period of flooding equals

zero. A variable that represents the expected return period of flooding of individuals who

19

stated a non-zero return period is of the expected sign but not significant. Respondents

who indicate causes of flooding that are beyond their or water managers’ direct control,

such as extreme weather events or climate change, are less likely to buy insurance. This

is consistent with studies showing that individuals have lower flood risk perceptions if

they regard floods as natural phenomena (e.g., Brilly and Polic, 2005). Individuals who

have experienced a flood and have been evacuated for a threat of flooding are more likely

to demand flood insurance. This is consistent with findings that individuals with a

personal experience of a risk have a higher risk perception and are more likely to

purchase insurance (e.g., Michel-Kerjan and Kousky, 2008).

Actual insurance purchases of the individual may be a good indicator of risk

aversion since they represent revealed preferences for financial protection. An insurance

index has been derived from eleven potential insurance purchases of the respondent (see

Table C1 in appendix C).10

Results indicate that individuals with many actual insurance

purchases are also more likely to purchase flood insurance. A risk seeking index has been

derived by asking individuals how well they correspond to a risk averse individual who

prefers to be well insured. The probability of buying insurance relates to this risk seeking

index in the expected way, i.e. more risk seeking individuals are less likely to insure.

Actual flood risks in the Netherlands are strongly related to geographic

characteristics and the presence of dike infrastructure (Aerts et al., 2008a). Such

geographical characteristics are included as explanatory variables in our insurance

demand model. These data are obtained with the use of Geographical Information

Systems (GIS) maps, which are related to the respondent’s zip codes.11

A variable has

been constructed that represents the difference between the elevation of the zip code area

of the individual and the height of the potential water level of a flood.12

This variable is

an indicator of the height of the water level at the individual’s home once a flood occurs.

10

It is not possible to include separate variables for these actual insurance purchases in the model because

they are highly correlated. These correlations arise because risk averse individuals are more likely to

purchase many insurance policies. Another advantage of including insurance purchases as a single variable

is that this saves on degrees of freedom. 11

This data is based on zip code numbers and letters for 950 respondents, which is highly accurate because

the GIS data can be obtained on street level. The data for 32 respondents are based on zip code numbers

only because letters are incomplete. 12

Adjustments have been made for respondents who live in flats on the first floor by adding 2.5 meter to

the height of the area.

20

The positive coefficient indicates that the higher the house is situated above potential

water level, the less likely will the individual purchase flood insurance. Moreover,

respondents in rural areas are more likely to demand flood insurance. It is also examined

whether respondents who live in areas unprotected by dikes have a larger demand for

flood insurance. A variable that represents respondents living in unprotected areas is

statistically insignificant, which suggests that demand for flood insurance is not higher in

these high-risk areas. Statistical analyses of the variables indicating individual risk

perceptions show that individuals in unprotected areas do not have higher perceptions of

flood risk than individuals who live in protected areas (Botzen et al., 2008c). This

suggests minor problems with adverse selection if flood insurance markets were to

emerge.

The socio-economic variables indicate that the probability of choosing for flood

insurance relates negatively to being female and age of the respondent. It has often been

observed that older individuals have a lower risk perception and purchase less insurance.

However, the opposite effect is usually found for females, which is contrary to our results

(Slovic, 2000). A possible explanation is that females have less monetary resources to

spend on insurance since being female correlates negatively to reported values of income

and value of home contents and homes in our data. It may further be that females have a

lower perception of flood risk and therefore demand less flood insurance.13

Individuals

with a higher value of property are more likely to self-insure and demand less flood

insurance. Households with more children and individuals with a high education value

flood insurance more than smaller families and individuals with a low education.

13

We find that relations between gender and perceptions of the probability of flooding are insignificant,

while a negative and significant relation exists between being female and the expected flood damage

variable (Botzen et al., 2008c).

21

Table 2. Estimation results of the choice experiment

Logit model Mixed logit

Variable Coefficient Wald-statistic Coefficient Wald-statistic

Attributes and interactions (U Insurance):

Flood probability 10.0541*** 7.67 18.7052*** 11.99

Flood damage 0.0041*** 3.70 0.0044*** 3.72

Insurance coverage 0.0072** 2.33 0.0077** 2.36

Insurance coverage * Close to main river 0.0032*** 2.58 0.0035*** 2.59

Insurance premium -0.0447*** -20.48 -0.0486*** -20.12

Insurance premium * High income 0.0117*** 3.44 0.0131*** 3.60

Government compensation (U No insurance):

Government relief of damage is available 0.3837*** 4.33 0.4143*** 4.27

Risk perception and experience (U No insurance):

Climate change causes higher flood risk -0.3650*** -3.80 -0.3970*** -3.77

Risk of suffering flood damage -0.2414*** -4.84 -0.2700*** -4.93

Lower flood risk than average resident 0.3906*** 4.06 0.4041*** 3.83

Expected flood damage -0.0009*** -3.53 -0.0010*** -3.68

Zero expected return period flood 1.2239*** 4.11 1.3310*** 4.12

Return period flood 0.0011 1.34 0.0011 1.27

Flooding is exogenous to human control 0.3906*** 4.06 0.3650*** 3.70

Experience with flooding and evacuation -0.7845*** -2.95 -0.8688*** -3.00

Individual risk aversion (U No insurance):

Insurance purchase index -0.3281** -2.42 -0.3649** -2.47

Risk seeking index 0.2019*** 4.25 0.2272*** 4.35

Geographical characteristics (U No insurance):

Elevation of house relative to water level 0.0002** 2.08 0.0002** 1.93

Area is not protected by dikes -0.0827 -0.57 -0.1049 -0.66

Rural area -0.7143*** -3.57 -0.7247*** -3.31

Socio economic characteristics (U No insurance):

Age 0.0085** 2.07 0.0088** 1.95

Female 0.3000*** 3.15 0.3366*** 3.23

Value of property 0.0012*** 3.87 0.0013*** 3.91

Children -0.2453*** -2.59 -0.2885*** -2.77

University degree -0.3163*** -2.83 -0.331*** -2.70

Standard deviation flood probability n.a. n.a. 18.7052*** 12.00

Constant 0.6173* 1.68 1.0616*** 2.70

Number of observations 2751 2751

Log likelihood -2061 -2027

Pseudo R2 0.32 0.33

Notes. One, two and three stars (*) indicate respectively significance at the 10%, 5%, and 1% level and n.a. stands for not applicable.

Estimations are performed with Limdeb software.

22

Individual specific parameters conditional on choice are estimated for the flood

probability attribute that was specified to follow a random distribution (e.g., Hensher et

al., 2003). Individual specific conditional parameters are estimated with simulation of the

formula (Train, 2003):

n

n

T

t

nnt

n

n

T

t

nntn

n

dgxchoiceP

dgxchoiceP

ββ

θββ

ββ

θβββ

β

∫ ∏

∫ ∏

=

=

=

1

1

)|(), |j (

)|(), |j (

(7)

where )|( θβg is the distribution of β in the population and θ are the parameters of this

distribution, such as the mean and variance. Appendix E shows the kernel density of the

parameter estimates of the flood probability. Figure E1a indicates that indeed all

respondents have a positive coefficient of the flood probability, which means that the

utility of insurance is higher in the face of an increased likelihood of flooding. As a

comparison, we have estimated individual coefficients unconditional on choice using

only the moments (mean β and standard deviation σ) of the coefficient estimates of the

flood probability based on 10,000 simulations with the formula ti *σββ += with t the

triangular distribution. The resulting distribution (Figure E1b) approximates the

conditional parameter distribution, but has slightly fatter tails. The individual parameters

conditional on choice (7) will be used in subsequent predictions and WTP estimations

since they are derived using all available information and the conditional method

prevents arbitrary assignment of respondents to the unconditional simulated coefficients.

Elasticities and marginal effects of the mixed logit model

The coefficient values shown in Table 2 can be interpreted as an estimate of the weight of

a variable in the utility expression of an alternative, but their sizes have no immediate

behavioral interpretation. For this reason elasticities and marginal effects are estimated

for the explanatory variables using the mixed logit model. Elasticities indicate the

percentage change in the probability of choosing a particular alternative with respect to

the percentage change in the level of an attribute of that alternative or explanatory

variable, ceteris paribus. The marginal effect is the change in choice probability for an

23

alternative given a unit change in an explanatory variable, ceteris paribus. Both

elasticities and marginal effects are computed for continuous variables using probability

weighted sample enumeration, as shown in appendix D (Loeviere et al., 2000). Only

marginal effects are computed for categorical variables since elasticities are not defined.

The marginal effects of dummy variables indicate the change in the average probability

that an individual chooses flood insurance while changing the value of the dummy from

zero to one (Hensher et al., 2005).

Table 3 below shows the elasticities in between brackets and marginal effects

without brackets. The damage elasticity is 0.21, so that an increase in flood damage of

1% leads to a 0.21% increase in the probability that an individual will choose to buy

flood insurance. The elasticity of insurance coverage is 0.77, which indicates that

coverage is more important in the choice for flood insurance than the damage attribute.

The price elasticity is -0.8 and, therefore, relatively inelastic. This implies that increasing

the price by 1% decreases demand by slightly less than 1%. It is useful to compare the

price elasticity of our hypothetical choice model with price elasticities observed in actual

flood insurance markets. For example, the price elasticity estimated with our choice

model is similar to the price elasticity of –0.89 estimated for the quantity of catastrophe

insurance demanded in Florida (Kunreuther et al., 2008). This close similarity of

elasticities obtained with stated and revealed preferences gives confidence in the validity

of our findings.

The elasticities and marginal effects of the explanatory variables that model the

utility difference between the choice alternatives without and with flood insurance

provide several relevant insights into the relative importance of these variables in the

choice decision. Of special interest in this study is the influence of the availability of

damage relief by the government. The choice probability for no flood insurance is 0.07

lower if compensation of flood damage is available via the government. Thus, on average

demand for flood insurance in the current institutional setting is approximately 7% less

because of the government compensation scheme, which is non-negligible. The marginal

effect on the risk perception variable that represents individuals who expect a zero flood

return period is large (0.21), indicating that such individuals are unlikely to purchase

flood insurance. Another important factor in the choice for flood insurance is the

24

experience with flooding and evacuation. Individuals with previous experiences of flood

threats place a much larger value on flood insurance coverage as the large marginal effect

of -0.16 shows. The elasticity and marginal effect on the value of property indicate that

individuals with a larger wealth are considerably less likely to purchase private insurance

because of their larger ability to self-insure.

Table 3. Elasticities (in between brackets) and marginal effects of variables

Variable Elasticity (…) or Marginal effect

Attributes (U Insurance):

Flood damage (0.21); 0.06

Insurance coverage (0.77); 0.01

Insurance premium (-0.80); -0.03

Other variables (U No Insurance):

Government relief of damage is available 0.07

Climate change causes higher flood risk -0.07

Risk of suffering flood damage a

-0.03

Lower flood risk than average resident 0.07

Expected flood damage (-0.02); -0.01

Zero expected return period flood 0.21

Return period flood not significant

Flooding is exogenous to human control 0.06

Experience with flooding and evacuation -0.16

Insurance purchase index -0.07

Risk seeking index b

0.04

Elevation of house relative to water level (0.01); 0.004

Area is not protected by dikes not significant

Rural area -0.14

Age (0.12); 0.07

Female 0.06

Value of property (0.15); 0.09

Children -0.05

University degree -0.06 Notes. a The marginal effect (ME) of this ordered categorical variable (range 1-11) in the table is calculated as the change in the

proportion of choices for the no insurance alternative while changing the value from the mode answer (2) to the subsequent

higher category (3). The ME of a change from category 1 to 2 is -0.04 and the ME’s of an increase in categories 3 to 10 are

respectively -0.02, -0.01, -0.02, -0.02, -0.02, -0.02, -0.02, -0.02. b The ME of this ordered categorical variable (range 1-6) in the table is calculated as the change in the proportion of

choices for the no insurance alternative while changing the value from the mode answer (4) to the subsequent higher

category (5). The ME’s of an increase in categories 1 to 4 of one category are respectively -0.04, -0.03, and -0.03 and the

ME of a change from category 5 to 6 is -0.04.

It is more intuitive to estimate the effect of the flood probability on choices for flood

insurance for a range of flood probabilities than to estimate a single elasticity or marginal

25

effect since the relation is non-linear. The frequency of choices for a situation with flood

insurance have been calculated for flood probabilities between 1 in 1,000 and 1 in 100,

which is within the range of climate change scenarios used in the choice experiment. The

results are shown in Figure 1. The proportion of homeowners who choose to buy flood

insurance rises in response to increases in risk with a decreasing slope.

25

30

35

40

45

50

55

1/1000 2/1000 3/1000 4/1000 5/1000 6/1000 7/1000 8/1000 9/1000 10/1000

Flood probability

% f

loo

d in

su

ran

ce

Figure 1. Effects of climate change on % of choices for flood insurance

4.2. Simulations of market shares for flood insurance under varying premiums and a

range of climate and socio-economic scenarios using mixed logit

Demand curves for flood insurance

Potential markets shares of flood insurance are approximated by estimating the

percentage of choices for flood insurance in our sample under varying monthly premiums

in between € 10 and € 80, which comprises the range of premium levels in the choice

experiment.14

Figure 2 shows the estimated demand curves for flood insurance that

reflect potential market penetration under current climate conditions characterized by the

dike design standard of a once in 1250 year flood event and average flood damage of €

70,000. The actuarially fair premium, that is, the expected value of damage, is about € 5

per month under these conditions.15

It can be expected that actual premiums will be

higher to cover other costs, such as transaction or bureaucratic costs, and to allow for an

14

Total predicted choices for flood insurance are computed under these scenarios where the individual is

assumed to choose the alternative with the highest prediction probability. Prediction probabilities are

computed using coefficient estimates of the mixed logit model (Table 2) and specific premium and

coverage levels and values of the dummy that represent availability of government compensation. Flood

damage and probability are fixed at € 70,000 and 1/1250, respectively, and the other explanatory variables

take on their sample values. 15

Computed as 70,000/1250/12 = 4.67.

26

economic return, i.e. a profit margin for insurers. Demand curves are depicted for

insurance policies with 75% and 100% coverage under the current institutional setting

characterized by availability of partly compensation of damage via the government (with

WTS) and a scenario where this compensation is not available (without WTS).

0

10

20

30

40

50

60

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Premium (€ per month)

% M

ark

et

pe

ne

tra

tio

n

100% coverage without WTS

100% coverage with WTS

75% coverage without WTS

75% coverage with WTS

Figure 2. Demand curves of insurance products with 75% or 100% coverage with

government compensation of damage (with WTS) and without government compensation

(without WTS)

The potential market share is approximately 45% for flood insurance with 100%

coverage that costs € 10 per month in the current situation and it is about 5% lower for

flood insurance with 75% coverage. These potential market shares could be 10% higher if

the government does not provide compensation of flood damage. This difference between

the market shares in situations “with WTS” and “without WTS” decreases slightly for

higher premiums. Markets shares decline to almost zero if premiums are as high as € 80

per month, indicating that the highest premium level included in the choice experiment is

an adequate cut of point to stimulate respondents to choose for the alternative without

flood insurance. Overall, results suggest that the potential market penetration can be

sufficiently high for a partly private insurance market even if premiums would be

considerably above the actuarially fair level.

The curves in figure 2 show total demand for flood insurance, but estimation

results (equation 6) indicate that coverage is valued more by individuals who live close to

a main river and the influence of price on demand is less for high-income individuals. To

27

examine the size of these effects we estimated separate demand curves for these different

consumer segments and discuss the main findings here. The demand curve for individuals

living close to a river is about 7% points higher for a premium of € 10 than the curve for

individuals living far from a river and this difference declines if premiums are higher.

Demand curves for high-income individuals are considerably less steep than demand

curves for low and middle-income individuals. In particular, the demand curve for high-

income individuals is about 3% points higher if the premium is € 10 and this difference

increases by about 10% points for the middle range of premiums. This means that mostly

low and middle-income individuals will choose not to insure if premiums are much

higher than the actuarially fair level of € 5.

Market shares under a range of climate change and socio-economic scenarios

Next, market shares are estimated under a range of climate change and socio-economic

scenarios about availability of government relief and expected flood damage. The

specific levels of the flood damage and probability attributes in the experiment are used

for estimating the percentage of choices for flood insurance. It is likely that insurers will

adjust their premiums in response to changes in flood risk. As a result, our model

includes two opposing effects of climate change on demand for flood insurance, namely

demand rises due to increased risk and demand reduces because of higher prices. The

final effect on demand is estimated by simulating the effects of the socio-economic and

climate change scenarios on choices for flood insurance and additionally allowing

premiums to adjust so as to reflect the change in risk. In these estimations it is assumed

that premiums are set according to risk, i.e. probability multiplied by damage, plus a

surcharge for operational expenses (e.g., transaction costs) of 35% of the total premium.

This surcharge is derived from an estimate of operational costs relative to premium

revenues of the National Flood Insurance Program (NFIP) in the USA that operates like a

public-private partnership (Kunreuther et al., 2008). Coverage is set equal to 100% in our

estimations. The results could be interpreted as indicators of the potential market

penetration of flood insurance in these hypothetical future situations.

The results shown in Table 4 provide three main insights. First, expected market

penetration is about 50% under current conditions and moderate increases in flood risk,

28

while it may rise up to 60% if government relief is not available. Second, the effects of

higher risk and prices balance out for changes in flood probabilities up to 1 in 400 in case

flood damage can be mitigated to € 40,000, while the effect of higher premiums

dominates if flood probabilities rise and expected flood damage remains € 70,000 or

increases to € 120,000. Third, the market collapses in case climate change results in an

extreme rise in flood risk (1 in 100) due to the large expected rise in insurance premiums

in the scenarios of middle and high flood damage. Implementing measures that reduce

flood damage may be an effective means to prevent such a collapse of insurance demand

due to its ameliorating effect on premiums.

Table 4. Potential market penetration for flood insurance under climate change and

socio-economic scenarios with premiums adjusted to reflect changes in risk

Socio-economic scenarios Climate change scenarios

Government relief Expected Current climate Small change Middle large change Extreme change

available: Flood damage: 1 in 1250 1 in 600 1 in 400 1 in 100

No € 40,000 58% 59% 59% 46%

No € 70,000 58% 56% 53% 21%

No € 120,000 58% 52% 44% 4%

Yes € 40,000 49% 50% 47% 38%

Yes € 70,000 49% 47% 45% 16%

Yes € 120,000 49% 43% 36% 3%

Comparing the market share predictions of our choice model in Table 4 with revealed

preferences, i.e. actual insurance purchases in existing markets for flood insurance, may

be a useful test for the validity of our results. The market penetration of the flood

insurance program in the USA can be a good comparison case. This is a relevant test for

the risk aversion implied by our model even though flood risks are not the same in the

USA and the Netherlands, since these differences are reflected in the risk-based

premiums with similar surcharges for operational expenses. Homeowners in the USA

may purchase private flood insurance coverage and can also receive ex-post relief of

flood damage via the federal government, so that the relevant comparison is the socio-

economic scenario with availability of government relief in the Netherlands. Kriesel and

Landry (2004) show that about 49% of the eligible properties have purchased flood

insurance with varying levels of partial coverage in a sample of coastal areas in the USA.

This is very close to our model predictions of between 45% and 49% of Dutch

29

homeowners demanding flood insurance under current climate and socio-economic

conditions, for respectively low (75%) and high (100%) coverage.

4.3. Willingness to pay estimates for flood insurance using mixed logit

WTP measures for changes in the attribute values are commonly computed as the ratio of

the coefficient value of the attribute of interest to the coefficient of the cost attribute.

Table 5 shows the monthly WTP estimates for the coverage and damage attributes of the

choice experiment. A distinction is made between WTP for low and middle-income

categories and the high-income category, as well as coverage for individuals who live

close to or far away from a main river. The ratios 52 / ββ− , 53 / ββ− , and

543 /)( βββ +− give the low and middle-income category estimates for damage and

coverage for individuals far away and close to a river, respectively (equation 6). The

estimates for the high-income group are calculated by adding 6β to the denominator.

Mean WTP per € 1000 flood damage is in between € 0.09 and € 0.12 per month or € 1.08

up to € 1.44 yearly. This implies that a rise in expected flood damage would increase

WTP close to the expected value of the loss with the current safety standard of 1 in 1250

years. The WTP estimate for coverage indicates that increasing coverage by about 10%

points increases WTP by about € 2.3 up to € 3.2 per month for individuals living close to

a river and in between € 1.6 and € 2.2 otherwise.

Table 5. WTP estimates for insurance related to damage and coverage (in € per month)

Attribute choice experiment WTP low and middle income WTP high income

Flood damage per € 1000 0.09 0.12

Insurance coverage per percent for:

- Individual living close to river 0.23 0.32

- Individual living far from river 0.16 0.22

Next, the non-linear effect of the flood probability on WTP for flood insurance will be

examined using a range of probability values. The estimation results of the choice model

can be used to assess changes in an individual’s utility of having flood insurance

characterized by specific levels of the attributes or explanatory variables compared with

30

having no insurance. These changes in utility can be translated to changes in consumer

surplus (CS) according to

−

=∆ ∑∑

==

0

1

01

1

1

lnln1

)(J

j

njJ

j

nj

n

n

Ve

VeCSE

α (8)

where αn is the marginal utility of income, which equals the negative of the coefficient of

the insurance premium, and 1

njV and 0

njV represent utility after and before the change.

Calculating the average improvement in consumer surplus in a specific situation with

flood insurance compared with the situation without flood insurance gives an estimate of

average WTP for flood insurance.

The effects of changes in the flood probability due to climate change on mean

WTP for flood insurance under situations with and without availability of compensation

of damage via the government (WTS) are depicted in Figure 3, ceteris paribus. The

insurance has 100% coverage and the expected damage equals € 70,000. WTP for flood

insurance rises from about € 150 (€ 200) to € 340 (€ 410) with a slightly declining slope

if flood probabilities increase from 1/1000 to 10/1000 with (without) availability of

government relief.

50

100

150

200

250

300

350

400

450

1/1000 2/1000 3/1000 4/1000 5/1000 6/1000 7/1000 8/1000 9/1000 10/1000Flood probability

Yearl

y W

TP

in

eu

ro

Without WTS

With WTS

Figure 3. Effects of climate change on WTP for flood insurance with government

compensation of damage (with WTS) and without government compensation (without

WTS)

Table 6 shows WTP for flood insurance with high (100%) or low (75%) coverage in

situations with varying flood probabilities, damage and availability of government relief.

The mean WTP of the entire sample is computed, which is relevant as a social welfare

measure of introducing flood insurance. In addition, mean conditional willingness to pay

(CWTP) is estimated as the average WTP for individuals who are interested in buying

31

flood insurance, which is an indicator of potential revenue per policy for insurance

companies.16

The risk premium is given in between brackets below the WTP and CWTP

estimates, which is the difference between the willingness to pay measure and the

expected value of the flood damage per insurance policy (probability*damage*fraction

covered). The risk premium of CWTP can be interpreted as an indicator of average

potential profit on an insurance policy. The risk premium of WTP can be interpreted as

the average net benefit of introducing flood insurance for the population, since it

represents the difference between the average improvement in welfare of introducing

insurance and the average expected value of the payouts.

The WTP measures in Table 6 indicate that possibilities may exist for a profitable

flood insurance market in the current situation, which is consistent with findings of

Botzen and van den Bergh (2009). In particular, risk premiums of CWTP are positive

with the current safety standard of flooding under all scenarios of expected flood damage,

insurance coverage and availability of government relief. Furthermore, average welfare

improves for the entire population in the river delta in the current situation by more than

the expected value of the flood damage covered. This is the case because average

consumer surplus or mean WTP is larger than the expected payouts of damage, as is

reflected by positive risk premiums. WTP and CWTP values are about 20% less if

coverage is small (75%) in most scenarios compared with complete coverage. This is

consistent with practical experience with flood insurance demand in the USA, which

indicates a strong preference of homeowners for low deductibles (Michel-Kerjan and

Kousky, 2008). Demand for flood insurance is also considerably lower if damage relief

from the government is available.

Finally, the results in Table 6 suggest that offering flood insurance may remain

profitable if flood probabilities rise moderately. Risk premiums of CWTP are still

positive if climate change increases flood probabilities to 1 in 600 and 1 in 400 under

most scenarios. However, most risk premiums are negative if climate change would result

in an extreme rise of flood probabilities to 1 in 100, since WTP increases less than the

expected value of damage.

16

We compute CWTP as WTP for individuals who choose flood insurance at least once in the choice

experiment, which is the case for 52% of the sample.

32

Table 6. Mean willingness to pay (WTP), conditional willingness to pay (CWTP), and

risk premiums for flood insurance with high or low coverage levels in situations with

varying flood risk and availability of government relief (in € per year)

Insurance coverage and Flood probabilities under climate change scenarios

socio-economic scenarios

Current climate Small change Middle large change Extreme change

Insurance Government Expected 1 in 1250 1 in 600 1 in 400 1 in 100

coverage relief flood damage: WTP CWTP WTP CWTP WTP CWTP WTP CWTP

100% No € 40,000 180 220 209 259 233 290 388 491

{148} {188} {142} {192} {133} {190} {-12} {91}

100% No € 70,000 196 240 227 280 252 312 414 520

{140} {184} {111} {164} {77} {137} {-286} {-180}

100% No € 120,000 225 274 260 317 286 352 458 569

{129} {178} {60} {117} {-14} {52} {-742} {-631}

75% No € 40,000 150 185 176 220 197 248 340 436

{126} {161} {126} {170} {122} {173} {40} {136}

75% No € 70,000 164 202 192 239 214 268 364 463

{122} {160} {104} {151} {83} {137} {-161} {-62}

75% No € 120,000 190 233 221 273 246 305 405 510

{118} {161} {71} {123} {21} {80} {-495} {-390}

100% Yes € 40,000 134 167 159 199 178 226 314 405

{102} {135} {92} {133} {78} {126} {-86} {5}

100% Yes € 70,000 148 183 174 217 195 245 337 432

{92} {127} {57} {101} {20} {70} {-363} {-268}

100% Yes € 120,000 172 212 201 250 224 280 377 478

{76} {116} {1} {50} {-76} {-20} {-823} {-722}

75% Yes € 40,000 110 138 131 166 149 190 271 355

{86} {114} {81} {116} {74} {115} {-29} {55}

75% Yes € 70,000 122 152 144 182 163 207 292 380

{80} {110} {57} {95} {32} {76} {-233} {-145}

75% Yes € 120,000 143 177 168 211 189 238 329 423

{71} {105} {18} {61} {-36} {13} {-571} {-477} Notes. Mean and conditional WTP are shown without brackets and corresponding risk premiums are given below these values in

between brackets.

5. Policy implications and conclusions

This paper has examined the demand for low-probability, high-impact flood insurance

using choice modeling. In particular, this study has estimated the effects of climate

change and socio-economic developments, the availability of government compensation,

risk perception and actual risk, and household characteristics on the willingness to pay for

flood insurance. The survey has been conducted among homeowners in the river delta of

the Netherlands, which is vulnerable to flooding and climate change.

At present, flood insurance is not generally available in the Netherlands and the

government may compensate damage. The government and insurers investigate the

33

possibilities of introducing flood insurance, because the current scheme may be evaluated

as undesirable. The results of our survey provide four main insights for the feasibility of

introducing flood insurance in the Netherlands. First, estimation results suggest that

offering flood insurance may be profitable in the current situation. Second, the effect of

crowding out of demand by the availability of government compensation is shown to be

considerable. Third, the effect of climate change is to increase the proportion of

homeowners that take insurance and the WTP for flood insurance in a non-linear way.

Fourth, results suggest that problems with adverse selection may be minor.

With respect to the first insight, it should be noted that a considerable proportion

of homeowners are willing to pay for flood insurance, namely about 45% according to

the choice model in case premiums are twice as high as actuarially fair levels. Demand is

expected to rise if the government abolishes the current regulation of damage relief and

credibly refrains from compensating flood damage, according to the second insight of

this study. Nevertheless, there remains a large proportion that is unwilling to insure even

if the government scheme will be abolished, which may be undesirable for equity

reasons. This could be overcome by making insurance coverage compulsory for all

homeowners. Compulsory insurance may be justified from the welfare measures obtained

with this study, since the average improvement in welfare due to introducing flood

insurance (WTP) in the current situation is larger than the expected value of the loss per

insurance policy. With respect to the third finding, offering insurance remains profitable

if climate change results in a moderate increase in flood probabilities, but not if flood

probabilities rise extremely. The relation between WTP and flood probability is less than

proportional. The choice model shows that the percentage of homeowners choosing to

buy flood insurance decreases considerably if climate change results in large increases in

flood probabilities and insurers adjust premium in accordance with risk.

Relating to the fourth finding, the role of perceptions of flood risks in demand for

flood insurance seems to be more important than actual measures of risk based on

geographical characteristics. An important measure of flood risk is whether areas are

protected by dikes. Results indicate that this variable that represents individuals who live

in unprotected areas is insignificant, which suggests that worries about adverse selection

may be unfounded. The importance of risk perceptions in insurance demand suggests that

34

individuals may follow an updating process of prior beliefs of the flood probability, since

prior risk perceptions are a significant determinant of WTP in addition to the flood

probabilities stated in the survey. Therefore, the coefficients of the probability as stated in

the questionnaire may not fully reflect the potential effects of climate change on

insurance demand in case climate change results in a gradual updating of risk

perceptions, which influence WTP positively. Indeed, our estimates of the effect of

climate change on WTP for insurance based on the flood probabilities stated in the survey

may be seen as conservative estimates.

This study can be seen as exemplary of the possible effects that climate change

could have on the demand for natural catastrophe insurances. The use of choice modeling

with current state-of-the-art mixed logit estimation provides relevant insights into effects

of socio-economic and climate developments on market penetration and willingness to

pay for catastrophe insurances. Indeed, the insights are of interest for the insurance

industry in assessing the future profitability of offering insurances against extreme

weather events in a changing climate. An important lesson for policymakers is that they

can play a significant role in stimulating or at least not preventing the emergence of

private insurance markets by refraining from ex-post damage compensations.

35

Appendix A. The risk ladder used to communicate probabilities

The linear17

risk ladders depict the risk of car-theft, fire in a residential building,

flooding, car-fire and the risk of a fatal traffic accident. A derivation of the probabilities

depicted on the risk ladder and risk ladders depicting probability changes are given in

Botzen et al. (2008b).

Figure A1. Risk ladder that compares the current flood probability with other risks

17

The risk ladder has a scale that increases with 2/4000 per step, which is usually defined as a linear scale

(e.g., Vassanadumromgdee and Matsuoka, 2005).

1 in 2000

1 in 400

1 in 650

1 in 350

1 in 4000

Low Risk

1 in 500

1 in 1000

High Risk

Car theft

1/450

Fire in house

1/950

Flood

1/1250

Fire in car

1/1650

Traffic casualty

1/4000

The probability of theft of your car is 1 in 450.

This means that per year 1 out of 450 cars gets

stolen.

The probability of fire in your house is 1 in 950.

This means that per year 1 out of 950 houses

catch fire.

The probability of flooding is 1 in 1250.

This means that a flood event happens 1

time per 1250 years.

The probability of fire in your car is

1 in 1650. This means that per year 1

out of 1650 cars catch fire.

The probability that you die as a result of a

traffic accident is 1 in 4000. This means that

per year 1 out of 4000 traffic participants die.

36

Appendix B. Overview of attributes and levels of the choice experiment

Figure B1. Attributes and levels used in the choice experiment

Attributes Levels

Flood probability Once per 1250 years

Once per 600 years

Once per 400 years

Once per 100 years

Damage on home contents and house € 40,000

€ 70,000

€ 120,000

Insurance coverage High (100%)

Low (75%)

Insurance premium € 10 per month

€ 20 per month

€ 35 per month

€ 55 per month

€ 80 per month

Figure B2. Example of a choice card

Situation A Situation B

Flood probability

Once per 600 year (1/600)

Once per 100 year

(1/100)

Damage on home and contents

€ 70.000 € 40.000

Insurance

coverage

High

Low

Insurance

premium

€ 55 per month (€ 660 per year)

€ 35 per month (€ 420 per year)

None of

these

situations

37

Appendix C. Description explanatory variables and descriptive statistics

Table C1. Summary overview of the variables used in the statistical analysis

Flood probability Attribute choice experiment, probability of flooding

Flood damage Attribute choice experiment, total flood damage in 1000 €

Insurance coverage Attribute choice experiment, coverage flood insurance in % of total damage

Close to main river Dummy variable, 1=distance of the respondent’s zip code area is within 10 kilometers

from the nearest main river

Insurance premium Attribute choice experiment, monthly insurance premium in €

High income Dummy variable, 1=monthly household after tax income is within the highest category

> € 4,000

Government relief of damage is available Dummy variable, 1=questionnaire version stating that respondents may receive partly

relief of flood damage by the government

Climate change causes higher flood risk Dummy variable, 1=respondent expects that climate change causes higher flood risks

Risk of suffering flood damage Categorical variable, (range 1-11), 1=no risk and 11=extremely high risk

Lower flood risk than average resident Dummy variable, 1=respondent expects that his/her flood risk is lower than that of an

average resident in the Netherlands

Expected flood damage Continuous variable, total damage a respondent expects if a flood occurs in 1000 €

Zero expected return period flood Dummy variable, 1=respondent expects return period to be zero

Return period flood Continuous variable, flood return period that the respondent expects in 1000 years

Flooding is exogenous to human control Dummy variable, 1=respondent mentions only climate or natural conditions and not

human or water management as causes for flooding

Experience with floods and evacuation Dummy variable, 1=respondent has experienced a flood and has been evacuated in the

past

Insurance purchase index Dummy variable, 1=respondent has purchased more than 8 of the following

insurances: health insurance with no deductible, home, home contents, dentist,

continuous travel, all-risk car, life, bike, legal assistance, and disability insurance

Risk seeking index Categorical variable (range 1-5), 1=very risk averse, 5=not risk averse at all

Elevation of house relative to water level Continuous variable, elevation of the living area relative to the potential water level of

a flood in centimetre

Area is unprotected by dikes Dummy variable, 1=the area is not protected by dikes

Rural area Dummy variable, 1=the area is a rural area

Age Continuous variable, age in years

Female Dummy variable, 1=respondent is female

Value of property a Continuous variable, total market value of the house and home contents of the

respondent in 1000 €

Children Dummy variable, 1=respondent has at least 2 children

University degree Dummy variable, 1=highest degree is university education

Notes. a For housing value the respondent could mark one of the following categories: < € 100,000, € 100,000 - € 150,000, € 150,000 -

€ 200,000, € 200,000 - € 250,000, € 250,000 - € 300,000, € 300,000 - € 350,000, € 350,000 - € 400,000, € 400,000 - €

500,000, € 500,000 - € 600,000, > € 600,000. For home contents values the respondent could mark one of the following

categories: < € 25,000, € 25,000 - € 50,000, € 50,000 - € 75,000, € 75,000 - € 100,000, € 100,000 - € 125,000, € 125,000 - €

150,000, € 150,000 - € 175,000, € 175,000 - € 200,000, € 200,000 - € 300,000, > € 300,000. Continuous value of housing and

home contents variables were constructed by setting the housing and home contents value of each respondent to the midpoint

of the interval (€ 650,000 and €350,000 were used for respectively the highest housing and home contents value categories).

38

Table C2. Descriptive statistics of the explanatory variables

N. Obs. Mean Std. Dev.

Close to main river 982 0.78 0.41

High income 982 0.15 0.36

Climate change causes higher flood risk 982 0.66 0.47

Risk of suffering flood damage a

982 4.19 2.20

Lower flood risk than average resident 982 0.48 0.50

Expected flood damage 981 69.9 186.56

Zero expected return period flood 982 0.04 0.19

Return period flood 982 229.58 4665.53

Flooding is exogenous to human control 982 0.40 0.49

Experience with floods and evacuation 982 0.03 0.17

Insurance purchase index 982 0.12 0.33

Risk seeking index a

982 3.24 1.16

Elevation of house relative to water level 982 -133.93 625.27

Area is unprotected by dikes 982 0.11 0.32

Rural area 982 0.05 0.22

Age 982 45.50 12.02

Female 982 0.42 0.49

Value of assets 982 410.29 168.94

Children 982 0.33 0.47

University degree 982 0.21 0.40 Notes. a The statistics of this variable are in accordance with the coding in Table C1. This original coding has been transformed for

the analysis according to Terza (1986) as is described in appendix D

39

Appendix D. Statistical appendix

Coding of ordinal qualitative variables

Terza (1986) proposes to transform ordinal qualitative variables with J classes as follows:

))()(/())()(( 11 −− −−=Φ jjjj

j NNnn θθθθ (D1)

where n and N are the pdf and cdf of the standard normal distribution, respectively, and

)(

)(

21

1

2

1

1

1

ppN

pN

+=

=−

−

θ

θ

:

)...( 121

1

1 −−

− ++= JJ pppNθ

and pj is the percentage of the sample observed in category J.

For the lowest category equation (D1) reduces to

)(/)( jj

j Nn θθ−=Φ (D2)

For the highest category the equation (D1) is

))(1/()( 11 −− −=Φ jj

j Nn θθ (D3)

The pseudo R2 statistic

model Base

model stimated2 1 LL

LLRpseudo

E−= (D4)

where LLBase model is the log-likelihood of a model with coefficients constrained equal to

zero.

Calculating elasticities and marginal effects with probability weighting sample

enumeration

The direct point elasticity is computed as follows:

∑

∑

=

=

−

=N

n

in

N

n

iniknjkin

i

iknp

pxpp

xE

1

^

1

^^

))1((β

(D5)

The marginal effect is computed as follows:

∑

∑

=

=

−

=N

n

in

N

n

injkin

i

iknp

ppp

xM

1

^

1

^^

))1((β

(D6)

Here i

p is the aggregate probability of choice alternative i, in

p^

is an estimated

probability for alternative i and individual n and k refers to the kth explanatory variable.

40

Appendix E. Kernel plots of random parameters

BPROB

.025

.050

.076

.101

.126

.000

10 15 20 25 305

Kernel density estimate for BPROB

Den

sit

y

BPROB

.0099

.0199

.0298

.0398

.0497

.0000

0 5 10 15 20 25 30 35 40-5

Kernel density estimate for BPROB

Den

sit

y

Figure E1. Kernel density plots of a) individual specific parameters of the probability

attribute conditional on choice (left) and b) unconditional on choice (right)

Acknowledgements

We thank Joop de Boer, Marija Bockarjova, Laurens Bouwer, Roy Brouwer, Sebastiaan

Hess, Vincent Linderhoff, George Loewenstein, Marije Schaafsma, and colleagues at the

Insitute for Environmental Studies (IVM) for suggestions and comments on the

questionnaires. Alfred Wagtendonk helped in preparing the GIS data. We thank Ada

Ferrer-i-Carbonell, Anna Alberini and William Greene for helpful discussions and

suggestions regarding the econometric analysis. Peter Wakker provided useful comments

on the paper. This research was carried out in the context of the Dutch National Research

Programme “Climate Changes Spatial Planning” (www.klimaatvoorruimte.nl). The usual

disclaimer applies.

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