Monetary Valuation of Insurance against Climate Change Risk

Transcription

1 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 Bergh 1 ICREA and Institute of Environmental Science and Technology & Department of Economics and Economic History Autonomous University of Barcelona Spain jeroen.bergh@uab.es December Also affiliated with Faculty of Economics and Business Administration & Institute for Environmental Studies, Vrije Universiteit, Amsterdam. Fellow of NAKE and Tinbergen Institute.

2 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. 1

3 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). 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., 2

4 2009). 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., 2009). 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

5 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). 4

6 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 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 Pre-tests 5

7 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 pretests of the questionnaire were conducted between August and October 2007, using faceto-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 labelspecific 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 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 6

8 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 7

9 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 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 . 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 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 4 For more information see 8

10 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 9

11 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 Estimation methods Choice models are based on the random utility model. In this model, the probability p ni 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. 10

12 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 p ni = prob[( V + ε ) ( V + ε ) j j = 1,..., J; i j] (1) ni ni nj nj where V ni and ε ni are the observed and unobserved components of individual n s utility associated with alternative i, respectively. Different assumptions about the distribution of ε ni 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 ε ni 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) p ni = βxni e βx e j nj (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 rime. 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) 11

13 p T βxnit e = = f ( β dβ βx t 1 njt e j ni ) 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). (3) 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 variables 7, 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., 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). 12

14 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 dominant 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 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: 13

15 U Insurance = β1 * probability low + β 2 * probability middle + β 3 * probability high + β * damage + β * coverage + β * price U 4 No insuran ce β 8 * 6 7 = constant (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 β 2, β 3, and β 4 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 R 2 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. Furthermore, non-linearity in the reaction to damage has been estimated by including damage 2 as explanatory variable in equation 4. The non-linear reaction is insignificant. 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. 14

16 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: = β 1 * ( SQRT ( probability)) + β 2 * damage + β3 * coverage + β 4 * price = constant (5) U Insurance U No insuran ce β 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 *** 2.63 n.a. n.a. Flood probability middle *** 3.97 n.a. n.a. Flood probability high *** 7.43 n.a. n.a. SQRT flood probability n.a. n.a *** 7.50 Flood damage *** *** 3.33 Insurance coverage *** *** 3.62 Insurance premium *** *** Constant *** *** 5.67 Number of observations Log likelihood Pseudo R 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. 15

17 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 16

18 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: U Insurance = β * SQRT( probability) + β * damage + β * coverage + β * (coverage* close to main river) + β * price + β *( price* high income) U No insurance = β 7 * constant + β k * xn (6) where x n 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 R 2. 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 χ 2 = 34 and 1 degree of freedom (McFadden and Train, 2000). The overall fit

19 of the mixed logit model is very good as the pseudo R 2 statistic of 0.33 indicates (see appendix D), which is similar to a linear R 2 of approximately 0.7 (Domencich and McFadden, 1975; Louviere et al., 2000). The attributes of the choice experiment determine the utility of having insurance (U Insurance 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 18

20 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. 19

21 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 averse 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). 20

22 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 *** *** Flood damage *** *** 3.72 Insurance coverage ** ** 2.36 Insurance coverage * Close to main river *** *** 2.59 Insurance premium *** *** Insurance premium * High income *** *** 3.60 Government compensation (U No insurance): Government relief of damage is available *** *** 4.27 Risk perception and experience (U No insurance): Climate change causes higher flood risk *** *** Risk of suffering flood damage *** *** Lower flood risk than average resident *** *** 3.83 Expected flood damage *** *** Zero expected return period flood *** *** 4.12 Return period flood Flooding is exogenous to human control *** *** 3.70 Experience with flooding and evacuation *** *** Individual risk aversion (U No insurance): Insurance purchase index ** ** Risk seeking index *** *** 4.35 Geographical characteristics (U No insurance): Elevation of house relative to water level ** ** 1.93 Area is not protected by dikes Rural area *** *** Socio economic characteristics (U No insurance): Age ** ** 1.95 Female *** *** 3.23 Value of property *** *** 3.91 Children *** *** University degree *** *** Standard deviation flood probability n.a. n.a *** Constant * *** 2.70 Number of observations Log likelihood Pseudo R 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. 21