Risk communication nudges and flood insurance demand ☆

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Introduction
Natural disaster losses have been rising globally in recent decades (Cutter and Emrich, 2005;Hoeppe, 2016).Socio-economic development in hazard prone areas coupled with projected climate change trends means that losses from natural disasters are expected to continue to rise in many regions in the future (Changnon et al., 2000;Jongman et al., 2012;Vousdoukas et al., 2018).Furthermore, individuals can take measures to protect against financial losses caused by natural disasters, such as purchasing insurance.
Despite the availability of cost-effective measures that limit damage costs from natural disasters, many individuals in areas prone to disaster fail to take them (Meyer et al., 2014;Petrolia et al., 2015;Poussin et al., 2015).For example, it has been observed that individuals do not purchase flood insurance at premiums that are close to actuarially fair levels or subsidized (Anderson, 1974;Kunreuther and Pauly, 2004;Kunreuther et al., 1978).Based on nationwide estimates in the United States (US), the proportion of single-family homes residing within Special Flood Hazard Areas (SFHAs) (1/100-year flood zones) that have flood insurance is around one-half, even though many of these homes are required to purchase insurance according to mortgage conditions (Dixon et al., 2006).The same study found that outside SFHAs, in lower risk flood zones where flood insurance is voluntary, the market penetration rate is around 1 percent.Furthermore, in the Netherlands a recent study found that only 2 percent of homeowners currently hold voluntary flood insurance (Robinson et al., 2021).
The tendency of individuals to underestimate low-probability events, like natural disasters, is one reason why preparedness for these events is often low (Viscusi and Zeckhauser, 2006;Kunreuther et al., 2001).A variety of explanations have been proposed related to theory and empirical research from the psychological and behavioural economic literature why individuals underestimate these risks and fail to prepare for them (Friedl et al., 2014;Browne et al., 2015;Fehr-Duda and Fehr, 2016).Low demand for insurance can be caused by search costs associated with gathering information about insurance premiums, coverage and underlying probabilities of loss (Kunreuther and Pauly, 2004).Lack of loss experience has also been shown to be consistently related to low insurance demand, which is perhaps driven by low perceptions of risk (Robinson and Botzen, 2019).
Given that individuals generally find it difficult to process low probabilities (Viscusi, 1998), they may rely on mental shortcuts to make preparedness decisions less complex (Kahneman, 2003).That is, individuals perhaps simplify their assessment of risk by selectively attending to only a few of the relevant facts when making disaster preparedness decisions (Meyer and Kunreuther, 2017).It follows that when facing a potential disaster, individuals may use a threshold model decision heuristic (Slovic et al., 1977;Kunreuther and Pauly, 2004;Robinson and Botzen, 2018) which predicts that they dismiss low probability risks if the probability is deemed as falling below a certain threshold level of concern.Many governments are already informing individuals about annual disaster probabilities.For example, they can find this information according to Federal Emergency Management Agency (FEMA) flood zone classification maps in the US and the flood hazard zoning system (ZÜRS) in Germany.Potential clients of a Dutch insurer that covers flood risk (Neerlandse) could also access their annual likelihood of flooding in the past.Despite these efforts, the aforementioned insufficient levels of disaster preparedness can lead one to doubt the effectiveness of these communication strategies, which is perhaps due to individuals regarding the low annual probability of disaster as below their threshold level of concern.
Appropriately designed choice architecture, i.e., altering the ways choices are framed and presented, can be used to nudge individuals towards certain decisions (Thaler and Sunstein, 2008).For instance, several forms of risk communication as a form of choice architecture have been tested that encourage individuals to pay attention to low probabilities by raising perceived risk above the threshold level of concern.The threshold model decision heuristic is especially applicable to our study that is concerned with a low yearly probability of flood risk, since neglect of risk is common in this setting (Robinson and Botzen, 2018;Botzen et al., 2015).Moreover, one risk communication intervention tested in our paper, namely the reframing of a low likelihood of flood risk occurrence (1 in 100 yearly flood probability) in terms of the cumulative likelihood across time (1 in 3 over forty years) has been shown to increase flood insurance demand in the US (Chaudhry et al., 2020;Bradt, 2019).This effect is perhaps driven by individuals perceiving the flood probability to be above their threshold level of concern once it has been reframed because the cumulative likelihood has also been shown to elevate flood risk perceptions (Keller et al., 2006).While Botzen et al. (2016) found an overall insignificant effect of such framing on investment in flood-proofing measures in the US, certain political subgroups were more likely to invest under the longer time horizon framing, perhaps due to their climate change beliefs.More specifically, it was conjectured that expressing the low probability risk over a longer time period may make the risk more salient to Democrat voters, who already have elevated concern about climate change and therefore higher perceptions of long-term flood risk compared to non-Democrat voters (Guber, 2013;de Bruin et al., 2014).It seems that individuals in this setting selectively appropriate information in ways that reinforce pre-existing attitudes, and thereby exhibit confirmation bias (Lord et al., 1979;Nickerson, 1998).
Other ways of communicating risk aim to facilitate individuals' comprehension of probabilities by accompanying numerical information with visual aids, e.g., risk ladders that communicate baseline probabilities on a scale alongside other risks commonly faced by individuals in practice (Corso et al., 2001;Smith et al., 1990;Sandman et al., 1994;Williams and Hammitt, 2001), and risk grids that display probabilities using an array of shaded and unshaded icons on a rectangular grid (Jones-Lee et al., 1985;Krupnick et al., 2002).It has been shown that these methods of communicating risk can have a positive effect on demand for risk reduction and can increase the sensitivity of demand to probability changes (Botzen and van den Bergh, 2012;Kaplan et al., 1985;Loomis and DuVair, 1993;Dekker et al., 2011).This implies that risk ladders and risk grids may assist comprehension of risk and raise preparedness intentions, compared to providing numerical probability information without a visual aid (for counter evidence see Weinstein et al. (1994) regarding risk grids).
Although there have been several studies that include single risk communication tools, and test for their effect on risk reduction choices, it has to the best of our knowledge not been examined yet whether combining reframed numerical probability information and visual aids can impact protection decisions against natural disaster events.We suspect that combining risk communication that aims to increase risk perceptions with communication that aids in probability comprehension may drive a stronger positive effect on insurance P.J. Robinson et al. demand than either communication method in isolation.Methods that aim to increase perceptions of risk may have little effect on individuals who do not understand risk in the first place.Additionally, there is ample research showing that certain individuals require visual stimuli in order to learn about and retain new information, although the effects of visual stimuli differ among population groups (Hamdani, 2015;Ormrod, 2006), e.g., older vs. younger individuals (Rabbitt, 2017;McPhee et al., 2004;Mahmood et al., 2009;Humphrey and Kramer, 1997).Moreover, in light of evidence that prior beliefs interact with the way that new information is incorporated into subsequent decisions (Botzen et al., 2016;Kappes et al., 2020;Talluri et al., 2018), we expect that pre-existing attitudes, e.g., climate change beliefs, also relate to the effectiveness of communication strategies that frame risk over a longer time horizon.
We test whether reframing flood probabilities as well as communicating of probabilities using risk comprehension aids, can be used to raise insurance demand, both together and in isolation.Acknowledging that the effectiveness of risk communication may differ among certain socio-economic subgroups and individuals with different pre-held beliefs, it is also relevant to examine under what conditions risk communication can be used effectively.We study these themes in an experiment on insurance demand against flood risk conducted with 1,800 Dutch homeowners.
The focus on flooding is driven by floods being the costliest of all natural disaster related events worldwide (Miller et al., 2008;Kousky, 2018).In this respect, the risk communication methods studied in this paper are relevant for policymakers who aim to raise flood preparedness of inhabitants in areas prone to flooding around the world.The Netherlands is an exemplary area for such a study because of the low flood risk awareness of residents (Filatova et al., 2011;Botzen et al., 2009), and high vulnerability to climate change due to the country's low-lying delta (Katsman et al., 2011;Klijn et al., 2012).The aim of our study is to draw generalizable lessons for other regions that also face natural disaster risks.
The remainder of this paper is structured as follows: Section 2 presents the experiment method and descriptive statistics.Section 3 details the main results related to the impact of risk communication on flood insurance demand.Section 4 discusses these results in relation to other studies and lessons which can be drawn from the findings.Section 5 concludes the paper.

Experiment method
In total 1,800 Dutch homeowners were recruited via invitation emails for the experiment through random draws of members of the survey panel of Panel Inzicht (https://panelinzicht.nl)during June and July 2020.The email did not state the nature of the experiment to prevent selection bias.Overall, the experiment follows a similar framing to that of Robinson et al. (2021), whereby homeowners had to decide whether or not to include flood coverage in an insurance policy that covers fire and burglary related losses, under a specified probability of flooding and expected flood damage amount.We chose to implement our study in the Netherlands, where perceptions of flood risk and individual preparedness against flooding is generally low (Botzen et al., 2009;Terpstra and Gutteling, 2008;Robinson et al., 2021;Bosschaart et al., 2016;Kerstholt et al., 2017).This may partly be a consequence of the lack of recent flood experiences here, apart from a few small localized events (Wind et al., 1999;van Stokkom et al., 2005;Aerts and Botzen, 2011).Note that flood insurance is not included in homeowners policies in the Netherlands but this coverage has been offered by a private insurer, Neerlandse, since 2016 on a voluntary basis.
Prior to implementing the experiment, a pre-test was conducted among 298 students of Vrije Universiteit Amsterdam.Both the pretest and the experiment among homeowners was conducted online which allowed for obtaining a large and diverse sample at a relatively low cost.Moreover, this method prevented communication between subjects and interviewer effects (Horton et al., 2011).We chose to implement the final experiment among homeowners rather than renters because they are more likely to be responsible for structural damage to their home if a flood occurs.The average age of these homeowners in our sample is close to 50 years and 51% are male.Furthermore, of those who were willing to reveal their education and income level, 81% hold either a Bachelor's degree, Master's degree or PhD, and the average household monthly after tax income level is between €3,000 and €3,999.In the actual Dutch population, the average age is 42 years as of 2020, 40% of Dutch adults (25-64 years) have higher education (2019), and average monthly disposable household income is €3,700 (2019).1 Our sample over-represents older and highly educated individuals compared to the Dutch population, which may be due to the fact that we targeted homeowners.
After some initial socio-economic questions, subjects were asked to: "Imagine that you have just moved in to a new home in the Netherlands which you purchased for €260,000.Your new home is at risk of flooding.The government will not reimburse you for any flood damage you suffer if you do not insure your home."Subjects were then randomly assigned to face one of six conditions: a condition in which the flood probability is described as a yearly 1 in 100 chance of flooding; a condition in which the yearly probability is described in terms of a 1 in 3 likelihood that at least one flood occurs over a forty-year time horizon; a condition in which the yearly flood probability is accompanied by a risk ladder that communicates to subjects the risk of flooding alongside other risks that individuals typically face in the Netherlands;2 a condition in which the flood probability over forty years is accompanied by the risk ladder; a condition in which the yearly flood probability is accompanied by a risk grid that communicates to subjects the risk of flooding according to an array of flooded and non-flooded houses; and a condition in which the flood probability over forty years is accompanied by the risk grid.3Appendix A displays the risk ladders and risk grids that were used to communicate the risk of flooding.Table 1 provides summary information regarding the numbers of subjects assigned to each experimental condition.
The following wording was used to describe the yearly flood probability: "Every year there is a 1 in 100 chance that your new home will be flooded."The conditions that included the flood probability framed over forty years used the alternative text: "Over the next forty years there is a 1 in 3 chance that your new home will be flooded at least once."Note that within conditions that included a risk ladder, additional text was included immediately following the description of the flood probability: "This means that every year [over the next forty years] 1 in 100 [1 in 3] homes in your neighborhood will flood (as you can see in the scale shown together with a number of other risks that a Dutch person faces on average)."4Within conditions that included a risk grid the following text was used instead: "This means that every year [over the next forty years] 3 out of 300 [100 out of 300] homes in your neighborhood will flood (as you can see in the picture where each blue-coloured home represents a flooded home)."The conditions asked subjects whether they would like to add flood coverage to a pre-purchased insurance policy which covers fire and burglary related losses.Fig. 1 presents the English translation of the way flood insurance demand was elicited.
The risk ladders use log-spacing, which results in an improvement in the communication of small probabilities over linearly-spaced risk ladders (Corso et al., 2001).Furthermore, flood risk is placed near the top of the ladder, behind the highest risk of bicycle theft.According to previous studies, perceived risk is greater for risks with such placing than for risk ladders that place the risk in question at the bottom of the ladder (Sandman et al., 1994;Logar and Brouwer, 2017).The risk grids employed an array of the same number of houses between the yearly flood probability and flood probability over forty years conditions.This counters the tendency for individuals to neglect denominators when making risky choices involving risk grids with different denominators (Garcia-Retamero and Cokely, 2017;Garcia-Retamero et al., 2010).
We chose one yearly probability (which is equivalent probabilistically to the probability of at least one flood occurring over forty years) and damage amount to compare the impact of risk communication over the various conditions.An annual flood probability of 1 in 100 was included in the experiment, since reframing of this probability in terms of the cumulative likelihood across time results in a relatively larger cumulative likelihood than if a lower annual probability had been adopted.For example, expressing a yearly probability of 1 in 1,000 in terms of at least one event occurring over a forty-year time horizon, results in a cumulative likelihood of around 1 in 25.This cumulative likelihood may not overcome individuals' threshold levels of concern.Moreover, it has been noted that on average the cumulative likelihood that we incorporate (1 in 3) is less likely to be subjectively distorted due to probability weighting, than any other likelihood in the probability space (Wakker and Deneffe, 1996).This entails that we compare behaviour under an annual probability that individuals may have a hard time processing (Tversky and Kahneman, 1992) to a cumulative likelihood that may be processed well.Moreover, including the 1 in 100 annual probability allows us to compare our findings to similar studies (Chaudhry et al., 2020;Bradt, 2019).The 1 in 100 probability is also commonly used in delineating flood inundation zones and for mapping and communicating flood risk.For example, the SFHAs used by FEMA in the US are defined as areas that will be inundated by a flood event with a 1 percent chance of being equaled or exceeded in any given year.Our decision to provide the flood risk in frequentist terms is driven by research that shows that individuals generally understand and process information better in frequency than e.g., percentage formats (Gigerenzer, 1996;Gigerenzer and Hoffrage, 1995).
Flood probabilities of 1 in 100 and higher in the Netherlands are found in areas where flood water depths as well as potential damage amounts are quite low on average (Ermolieva et al., 2017).We incorporated a damage amount of €6,400, which is less than the amounts used in similar studies, where lower probabilities were investigated (Botzen and van den Bergh, 2012;Robinson and Botzen, 2018).A damage of €6,400 would be more representative of a loss for a moderate to large pluvial flood event than catastrophic flooding that may result from dike failure (Spekkers et al., 2013;van Ootegem et al., 2015).The flood insurance premium was set at the actuarially fair (€64) level (equal to probability multiplied by damage).Notes: a The mean or proportion (M) is provided with the standard deviation (SD) in parentheses.
d Interior income categories are: between €1,000 and €1,499 = 2; between €1,500 and €1,999 = 3; between €2,000 and €2,999 = 4; between €3,000 and €3,999 = 5; between €4,000 and €4,999 = 6; between €5,000 and €6,999 = 7; between €7,000 and €9,999 = 8.P.J. Robinson et al.Following the flood insurance decision, subjects were asked a number of questions based on their risk preferences, current objective levels of flood risk and flooding experience, risk perceptions, as well as their socio-economic characteristics (Table 2). 5Risk preferences were elicited following Dohmen et al. (2011): "How do you see yourself: are you generally a person who is willing to take risks or do you try to avoid taking risks?Please use a scale from 0 to 10, where a 0 means you are 'completely unwilling to take risks', and a 10 means you are 'very willing to take risks'.You can also answer values in-between to indicate where you fall on the scale."Their surveybased measure is strongly correlated with the way that individuals make choices in paid lottery decisions.Moreover, the authors showed that the measure is a good predictor of a range of risky behaviours in practice.
Indicators of subjects' current flood risk and flooding experience were also derived.To determine whether subjects had experienced flooding at their home in the past (yes/no), we asked: "Has your home been flooded in the past when you were living in it?"Furthermore, to ascertain whether possible flood water levels may reach the current home of subjects (yes/no), they were asked: "Do you live on the ground floor?" To gain insights into subjects' perception of flood risk at the actual home they live in currently, we asked them to indicate the extent to which they agree with the following in line with Robinson and Botzen (2018) and Botzen et al. (2015): "I am worried about the danger of flood damage to my current house."Moreover, risk perceptions related to climate change were derived according to the extent subjects agreed with: "I am concerned about the consequences of climate change."This variable has been z-scored for the analysis in section 3. Appendix B displays the distribution of risk preferences, risk perceptions, age and income in our sample.
In the forthcoming results sections we adopt the Probit model to examine the relationship between flood insurance demand and variables of interest.Whereas, in general there are three statistical models used in applied microeconometrics where the dependent variable is a binary choice (such as ours): the Linear Probability model, the Logit model and the Probit model (Aldrich and Nelson, 1984).We prefer the Probit model to the Linear Probability model because the Probit model prevents predicted probabilities from falling outside the unit interval (Horowitz and Savin, 2001).The difference between the Logit and Probit model lies in the assumption Notes: ***Significant at 1%; **Significant at 5%; *Significant at 10%.Coefficient estimates are provided with standard errors in parentheses.The average marginal effects of risk preference, flooding experience, ground floor, worry, yearly ladder, yearly grid, forty-year, forty-year ladder and forty-year grid are italicized.
5 All correlation coefficients among explanatory variables are lower than 0.5, therefore multicollinearity should not pose a problem for our analysis (Hensher et al., 2005).
P.J. Robinson et al. about the distribution of the errors which are unobserved (Cameron and Trivedi, 2005).Nevertheless, predicted probabilities yielded from the Probit model and Logit model tend to be very similar (Wooldridge, 2010).In our experience, the Probit model is more widely accepted in the field of microeconomics, hence our decision to adopt the Probit model.However, applying either the Probit, Logit or Linear Probability model to our data provides almost identical qualitative results (see Appendix C).

Regression analysis
Table 3 provides a Probit model analysis of the likelihood of flood insurance purchase.Model I contains significant individual difference variables, risk preference, flooding experience, ground floor and worry.As expected, more risk seeking homeowners are significantly less likely to demand flood insurance.Whereas, those who have experienced a flood at their home in the past, as well as individuals who currently live on the ground floor, are significantly more likely to purchase insurance.Apparently, individuals' previous flooding experiences and objective levels of flood risk enter into their flood insurance choices for the hypothetical new home we ask them to consider in the experiment (see Kusev et al. (2009)).This result may follow from the availability heuristic (Tversky and Kahneman, 1974).Higher levels of worry about flooding at one's current home is also associated with significantly increased demand for flood insurance.
Model II includes the risk communication condition dummy variables yearly ladder, yearly grid, forty-year, forty-year ladder and forty-year grid.The baseline reference category is yearly.The Probit model coefficient estimates of model II show that on aggregate the impact of risk communication on flood insurance demand is not significant.
Model III adds to the regression analysis a variable that represents age decile categories (1 = data ≤ the 1st age decile; 2 = data > the 1st age decile and ≤ the 2nd age decile, etc.), i.e., age category, and interaction terms between age category and the risk communication conditions.For younger age categories there is a positive impact of variables yearly ladder and forty-year grid on demand for flood insurance.This positive impact is lower in magnitude for intermediate age categories.For higher categories of age the impact is negative, meaning that the yearly ladder and forty-year grid variables reduce demand for insurance among older homeowners.However, this latter effect is only significant (at the 10% level) with regards to the average marginal effect (ME) of forty-year grid for the oldest age category according to the fifth panel of Fig. 2.
There is also a negative effect (significant at the 10% level) of variable forty-year on flood insurance demand for older categories of age.Furthermore, there is a negative insignificant coefficient estimate on the interaction term between forty-year ladder and age category, although the graphical analysis in the proceeding section shows that the effect of this variable on flood insurance demand is Fig. 2. ME of yearly ladder, yearly grid, forty-year, forty-year ladder and forty-year grid risk communication on the likelihood of flood insurance purchase across the age category variable.
negative and significant at the 10% level among older age groups. 6It is interesting that the sum of coefficient estimates on interaction terms between yearly ladder and age category as well as forty-year and age category is less than the coefficient estimate on the interaction term between forty-year ladder and age category.This implies that the negative dependency of the impact of the risk ladder and fortyyear framing on flood insurance demand based on age, is stronger for the two components in isolation than when they are combined.Concerning the coefficient estimate on the interaction term between yearly grid and age category, the estimate and associated MEs are insignificant according to any standard significance level, as is the level-effect of yearly grid based on the coefficient estimate on this variable.
One may suspect that the correlation between age and risk communication effectiveness is partly related to concern about climate change.Because older individuals tend to be less concerned about the consequences of climate change (Andor et al., 2018; Shi et al.,  2016; Kellstedt et al., 2008; McCright, 2010; Tjernström and Tietenberg, 2008; Duijndam and van Beukering, 2021), 7 this might make them less sensitive to some forms of risk communication, specifically the framing of flood probabilities over longer time horizons.We can look at this by examining the significance of the coefficient estimates on interaction terms between age category and the risk communication conditions once the concern climate change variable, as well as interaction terms between concern climate change and the conditions of risk communication are added to the model (model IV).If the coefficient estimates on interaction terms between age category and the risk communication conditions fall in magnitude and significance, this would imply that (some of) the correlation between age and the impact of risk communication is related to climate change concern.That is, there would be confounding effects between the two interaction terms.Nevertheless, according to model IV the magnitude of the coefficient estimates on interaction terms between age category and the risk communication conditions remain fairly stable, as do the coefficient estimates on the level-effects of the risk communication.It seems that age may be related to the effectiveness of risk communication through other mechanisms than concern about climate change.
There are positive coefficients (significant at the 5% level) on the concern climate change and forty-year ladder interaction as well as the concern climate change and forty-year grid interaction.This implies that forty-year ladder and forty-year grid communication raises (lowers) demand for flood insurance among those who are more (less) concerned about the consequences of climate change.According to the analysis of MEs in the next section, the relation between climate change concern and the risk communication is mainly that individuals with the lowest levels of concern about climate change are less inclined to insure under the forty-year ladder and forty-year grid conditions, relative to the baseline.Only among those who display the highest level of concern about climate change is there a positive (significant at the 10% level) impact of forty-year grid on the likelihood of insurance purchase.We have chosen to omit other socio-economic variables, male, higher education and income, because of the reduction in sample size that would result from including these variables and since they are not predictive of insurance demand.That is, insignificant coefficient estimates were found on these socio-economic variables in an extension to model IV that includes these variables as covariates.Moreover, in other exploratory analyses we tested whether the impact of risk communication on flood insurance demand is sensitive to these other socio-economic variables.We found no significant coefficient estimates on interaction terms between risk communication and male, higher education as well as income (p-values > 0.1). 8

Graphical analysis
Figures 2 and 3 show the MEs of the risk communication on the likelihood of flood insurance purchase across age categories and concern about climate change, respectively.The figures are based on the most elaborate Probit model analysis of the likelihood of flood insurance purchase (model IV).There is overall a negative relationship between age and the effectiveness of the risk communication conditions (apart from yearly grid) in raising flood insurance purchase.Compared to the baseline, there is a positive significant effect of the yearly ladder variable on the insurance purchase likelihood among individuals aged ≤ the 4th age decile by 13 (standard error and p-value = 0.065 and 0.040), 11 (standard error and p-value = 0.057 and 0.044), 9 (standard error and p-value = 0.049 and 0.055) and 7 (standard error and p-value = 0.043 and 0.087) percentage points when age category = 1, 2, 3 and 4 respectively.There is also a positive significant impact of the variable forty-year grid for those aged ≤ the 2nd decile of age by 13 (standard error and p-value = 0.064 and 0.040) and 11 (standard error and p-value = 0.056 and 0.059) percentage points when age category = 1 and 2 respectively.
However, the effect of variables forty-year, forty-year ladder and forty-year grid is negative among individuals aged > the 8th age decile by − 10 (standard error and p-value = 0.061 and 0.098) and − 12 (standard error and p-value = 0.071 and 0.077) percentage points when age category = 9 and 10, the 6th age decile by − 8 (standard error and p-value = 0.043 and 0.071), − 9 (standard error and p-value = 0.051 and 0.065), − 11 (standard error and p-value = 0.060 and 0.070) and − 12 (standard error and p-value = 0.070 and 0.078) percentage points when age category = 7, 8, 9 and 10, and the 9th age decile by − 12 (standard error and p-value = 0.071 and 0.082) percentage points when age category = 10, respectively.Therefore, although in some conditions the risk communication leads to higher demand for flood insurance for younger individuals, in others it leads to lower levels of insurance demand among older individuals.
Among homeowners who have strong concern about the consequences of climate change, the variable forty-year grid raises the likelihood of flood insurance purchase by 11 (standard error and p-value = 0.061 and 0.061) percentage points compared to the baseline.Moreover, for individuals who strongly disagree, disagree, somewhat disagree and neither disagree nor agree with the concern about climate change statement, the forty-year ladder condition has a negative effect on flood insurance demand by − 24 (standard error and p-value = 0.092 and 0.010), − 20 (standard error and p-value = 0.077 and 0.011), − 15 (standard error and p-value = 0.060 and 0.013) and − 10 (standard error and p-value = 0.044 and 0.028) percentage points respectively.Among those who strongly disagree and disagree with the concern statement, the forty-year grid condition also has a negative effect on flood insurance demand by − 18 (standard error and p-value = 0.088 and 0.042) and − 13 (standard error and p-value = 0.073 and 0.066) percentage points respectively.

Discussion of results in relation to previous studies
Natural disaster losses are rising under climate change and socio-economic developments in disaster-prone regions.However, individuals tend to dismiss risks posed by natural disasters because they have a low occurrence probability.Risk communication has the potential to stimulate behavioural change by encouraging individuals to pay attention to low probabilities and facilitating their comprehension.We studied whether the communication of risk using probability visual aids, i.e., risk ladders and risk grids, as well as reframing of probabilities in terms of the cumulative likelihood across time, can be effective in nudging individuals towards higher demand for insurance against disaster risk.We conducted an online experiment of flood insurance choices made by 1,800 homeowners in the Netherlands, who were randomly assigned to face several conditions of risk communication.Possible moderators of the effects of risk communication were investigated, i.e., age and concern in relation to climate change consequences.
Insights into effective risk communication are useful for many regions around the world that face flood risk, and at the same time low public awareness of flood risk and flood preparedness (Burningham et al., 2008;Scolobig et al., 2012;Ludy and Kondolf, 2012;Viscusi and Zeckhauser, 2006;Lo, 2013).Furthermore, strong population heterogeneity in terms of climate change concern is observed 8 According to the suggestion of one reviewer, we examined whether for higher income individuals, older homeowners have different risk preferences, compared to younger homeowners.Since we find that among higher income homeowners, i.e., for those with income > median income category (5), age category and risk preference are negatively correlated (Spearman's rho = − 0.168, p-value < 0.05), older individuals with higher than median incomes are more risk averse.For these high income homeowners, we tested whether there is a change in the significance of coefficient estimates on interaction terms between risk communication and age after risk preference and its interaction effect with risk communication has been controlled for.There is no overall change in the significance of coefficient estimates on these interaction terms.Overall, this suggests that among high income homeowners, a difference in risk preferences is not driving a conditional effect of risk communication on flood insurance demand based on age.P.J. Robinson et al. worldwide (Duijndam and van Beukering, 2021;Capstick et al., 2015;Brechin, and Bhandari, 2011).The same naturally holds for population variations in age, which demonstrates that the importance of age and climate change concern regarding the influence of risk communication strategies as found in this study has potentially much wider implications than for the Netherlands alone.
The main finding of this paper is that reframing of probabilities over longer time horizons, especially in combination with visual aids, tends to raise (lower) flood insurance demand among younger (older) homeowners and those who are more (less) concerned about the consequences of climate change.Our analysis that accounts for individual-level heterogeneity based on age and climate change concern does not completely contradict the results of Chaudhry et al. (2020) and Bradt (2019).Both authors find that in the US extending the time horizon over which the flood probability is framed raises demand for insurance against flooding.Furthermore, there are several differences between our study and theirs.First, their samples are more familiar with flooding events.Chaudhry et al. (2020) sampled coastal counties including a large proportion of individuals living in SFHAs, where the annual likelihood of flooding is 1 in 100.For the Netherlands 1 in 100 yearly flood probabilities and higher are only found in a few less populated areas (Rijkswaterstaat, 2016).Moreover, almost one-half of the individuals recruited for Bradt's (2019) study had experienced a natural disaster in the past. 9Given the high risk of flooding within these two samples, individuals may be more likely to pay attention to flood risk in the first place than in our sample of Dutch homeowners who have very little experience with flooding.This would confirm the availability heuristic described earlier in this article, which predicts that individuals in the Netherlands are less likely to pay attention to the risk of flooding because they have less flood related experience.It has been shown empirically that flood experience positively impacts flood risk perceptions and flood preparedness (Osberghaus, 2017;Gallagher, 2014;Atreya et al., 2015;Robinson and Botzen, 2019).
In addition, we believe that perceptions of climate change which relate to perceptions of long-term flood risk are more salient to individuals who are more frequently exposed to natural disasters.In the sample of Bradt (2019) there is a high level of agreement that man-made climate change is occurring, and that sea-level rise is happening as a consequence of climate change.There is also a plethora of research showing that individuals selectively attend to information depending on whether the information reinforces their prior beliefs (Lord et al., 1979;Nickerson, 1998;Allahverdyan and Galstyan, 2014;Friedrich, 1993).This may also hold when individuals evaluate risk communication interventions, as it has been demonstrated that reframing flood probabilities over an extended time period effectively stimulates preparedness actions for individuals who likely already have high long-term flood risk perceptions Fig. A1.The yearly flood probability accompanied by a risk ladder that communicates the risk alongside other risks in the Netherlands. 9Around 30% had experienced flooding in particular.(Botzen et al., 2016).We find that framing of the flood probability over a longer time horizon in combination with visual aids reduces demand for flood insurance among homeowners with low concern about climate change, and raises demand among those with very high concern if a risk grid is used to communicate the flood probability.
Another difference between the Chaudhry et al. (2020) andBradt (2019) studies and our study, is that on average their samples are younger than our homeowner sample. 10Our analysis showed a moderating role of age on the impact of risk communication.It is important to mention that the younger and older homeowners in our sample may differ systematically regarding a range of characteristics and preferences, that may explain the interaction effect between the effectiveness of risk communication and age.For instance, Salthouse (2009) showed that some aspects of age-related cognitive decline begin in adults in their 20 s and 30 s.These cognitive declines and other perceptual limitations include: difficulty reading or perceiving pictures, reduced ability to search a visual   list for a target, lower capacity for filtering out other stimuli that is competing for the individual's attention and decreased working memory (McLaughlin and Mayhorn, 2014).Due to these limitations individuals tend to become more reliant on automatic processes, which can influence the way that risk communication messages are assessed and resulting behaviour (Finucane, 2008).Furthermore, it is uncertain to what extent the risk communication manipulations in our experiment created a demand effect to the socially desirable response.Age has been shown to be associated with social desirability (Hitchcott et al., 2020;Vigil-Colet et al., 2013), therefore it may also be the case that social desirability is driving the interaction effect.Another potential cause is related to differences in the expected      life remaining of older vs. younger homeowners.Older homeowners may not relate to framing of the flood probability over forty years because they do not expect to be living that long.Moreover, since the risk communication treatments altered the considered time horizon, time preferences may be influential as well, which can change over one's life cycle (Chao et al., 2009;Read and Read, 2004;Trostel and Taylor, 2001).One may examine in future research the precise cause of the conditional effect of risk communication on insurance demand based on age differences.
We tested whether the association between age and the impact of risk communication is partly related to concern about climate change.This does not appear to be the case, given that coefficient estimates on the risk communication variables as well as their interaction with age are rather robust to the inclusion of concern about climate change and its interaction with risk communication.Therefore, our findings reveal that the mechanisms through which age relates to risk communication effectiveness are likely different to climate change concern.
Before elaborating on several policy implications of our findings, it is important to mention that our study is not without limitations.The study did not utilize payments based on individuals' experimental insurance decisions.Incentive compatible rewards may more closely align choices with incentives faced in actual decisions and reduce the level of randomness involved in insurance decision making (Irwin et al., 1992;Robinson and Botzen, 2019).Whereas, we chose to adopt hypothetical incentives due to the practical difficulties associated with incentivizing losses in experiments (Etchart-Vincent, 2004;2009).Another limitation of our study is the inherently artificial nature of the experimental environment used to elicit respondents' insurance choices (Harrison and List, 2004).Nevertheless, data on the actual flood insurance purchases of homeowners is not publicly available in the Netherlands (Robinson et al., 2021) which prevents us from examining such data.However, there are also clear advantages to our experimental approach given that we test risk communication strategies that have not been applied in practice yet, and reduce the potential for confounding factors through randomized control.Moreover, our survey allows us to elicit and control for other important variables which is more difficult if one were to examine actual market data on flood insurance demand.

Lessons for risk communication
Of policy relevance is how visual aids and framing of risk to enhance flood awareness and preparedness can be effectively implemented in practice.Visual aids and framing can be implemented by governments in their risk communication strategies through information on websites, letters or brochures and through (required) information for individuals buying a new home in a flood-prone area.Nevertheless, it is important for top-down government campaigns to recognize heterogeneity in the population, as suggested in previous studies (Burningham et al., 2008;Haer et al., 2016;Maidl and Buchecker, 2015) and shown empirically in our study.
Our finding that risk communication strategies tend to work better for younger individuals can be seen as good news given that the literature has stressed the importance of triggering behavioural change among the youth (Cox et al., 2019;Haynes and Tanner, 2015).One way to reach younger individuals is through social media (Corner et al., 2015).Haer et al. (2016) using an agent-based modelling approach find that social networks can strongly influence individuals' behaviour, illustrating the potential of using social media to enhance social network effects.
Furthermore, political orientation has been shown to relate very strongly to climate change perceptions and concern in large datasets covering multiple countries (Marquart-Pyatt et al., 2014;Poortinga et al., 2019).We suggest that public policy should be careful implementing the types of risk communication tested in our study in politically conservative areas where climate change skepticism is likely to be higher than politically liberal areas (Dunlap and McCright, 2011).

Conclusion
Some studies have tested the influence of single risk communication tools, such as extending the time horizon over which the disaster probability is framed on insurance decisions.But, insofar as we are aware, no study has investigated whether combining reframed numerical probability information and visual aids, like risk ladders and risk grids, can nudge flood insurance demand.We examine potential moderators of the effectiveness of this type of risk communication, such as age and concern about the consequences of climate change.
Our results reveal that increasing the time period over which the flood probability is framed, combined with visual aids, tends to raise (lower) flood insurance demand among younger (older) homeowners and those who are more (less) concerned about the consequences of climate change.These findings indicate that the types of risk communication we tested are unlikely to facilitate preparedness on aggregate if they are applied uniformly across the entire population.On the contrary, flood risk communication should be carefully tailored towards subgroups that are responsive to such communication in terms of their preparedness choices, such as whether they decide to purchase flood insurance.Younger individuals may be reached through social media to utilize social network

Fig. 1 .
Fig. 1.Flood insurance demand elicitation over the yearly flood probability and the flood probability framed over forty years.
Flood insurance demand Dummy variable measure of flood insurance demand Insure = 1 and do not insure = 0 0.551 N = 1,800 Yearly Dummy variable measure of assignment to yearly 1 in 100 probability-no visualization condition Assigned to yearly 1 in 100 probability-no visualization condition = 1 and otherwise = 0 0.167 N = 1,800 Yearly ladder Dummy variable measure of assignment to yearly 1 in 100 probability-risk ladder condition Assigned to yearly 1 in 100 probability-risk ladder condition = 1 and otherwise = 0 0.167 N = 1,800 Yearly grid Dummy variable measure of assignment to yearly 1 in 100 probability-risk grid condition Assigned to yearly 1 in 100 probability-risk grid condition = 1 and otherwise = 0 0.167 N = 1,800 Forty-year Dummy variable measure of assignment to 1 in 3 probability over forty years-no visualization condition Assigned to 1 in 3 probability over forty years-no visualization condition = 1 and otherwise = 0 0.167 N = 1,800 Forty-year ladder Dummy variable measure of assignment to 1 in 3 probability over forty years-risk ladder condition Assigned to 1 in 3 probability over forty years-risk ladder condition = 1 and otherwise = 0 0.167 N = 1,800 Forty-year grid Dummy variable measure of assignment to 1 in 3 probability over forty years-risk grid condition Assigned to 1 in 3 probability over forty years-risk grid condition = 1 and otherwise = 0 0.167 N = 1,800 Risk preference General willingness to take risks Completely unwilling to take risks = 0 to very willing to take risks = 10 4.979 (2.062) N = 1,800 Flooding experience Dummy variable measure of previous flood experience Flooded in the past = 1 and not flooded in the past = 0 0.058 N = 1,800 Ground floor Dummy variable measure of ground floor home Ground floor home = 1 and non-ground floor home = 0 0.858 N = 1,800 Worry I am worried about the danger of flood damage to my current house Strongly disagree = 1 to strongly agree = 7 b 2.696 (1.570) N = 1,800 Concern climate change I am concerned about the consequences of climate change Z-scored Likert scale responses (strongly disagree = 1 to strongly agree = 7) 0.000 (1.000) N = 1,800 Age Continuous variable of age in years Age in years 49.854 (16.285)N = 1,800 Male Dummy variable measure of gender Male = 1 and female = 0 0.510 N = 1,800 Higher education c Dummy variable measure of higher education Higher education = 1 and non-higher education = 0 0.813 N = 1,585 Income d Ordinal variable measure of after tax household monthly income Less than €1,000 = 1 to €10,000 or more = 9 4.724 (1.495) N = 1,446

Fig. 3 .
Fig. 3. ME of yearly ladder, yearly grid, forty-year, forty-year ladder and forty-year grid risk communication on the likelihood of flood insurance purchase across the concern climate change variable.

Fig. A2 .
Fig. A2.The flood probability over forty years accompanied by a risk ladder that communicates the risk alongside other risks in the Netherlands.

Fig. A3 .
Fig. A3.The risk grid that communicates the yearly flood probability according to an array of flooded and non-flooded houses.
P.J.Robinson et al.

Fig. A4 .
Fig. A4.The risk grid that communicates the flood probability over forty years according to an array of flooded and non-flooded houses.

Table 1
Distribution of subjects over the experimental conditions.

Table 2
Summary of variables for homeowner sample.

Table 3
Probit model of the likelihood of flood insurance purchase.

Table C1
Logit model of the likelihood of flood insurance purchase.
Coefficient estimates are provided with standard errors in parentheses.The average marginal effects of risk preference, flooding experience, ground floor, worry, yearly ladder, yearly grid, forty-year, forty-year ladder and forty-year grid are italicized.P.J.Robinson et al.

Table C2
Linear Probability model of the likelihood of flood insurance purchase.