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Monetary Valuation of Insurance against Climate Change Risk
W.J.W. Botzen
Institute for Environmental Studies
Vrije Universiteit
Amsterdam, The Netherlands
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
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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