Moral Hazard in Natural Disaster Insurance Markets: Empirical Evidence from Germany and the United States

Theory

The work of Ehrlich and Becker (1972) provides the theoretical foundation for our investigation. They developed a model of the interaction between market insurance, self-protection (defined as actions that reduce the probability of a claimable event), and self-insurance (defined as actions that reduce the impact of an event). The model shows that market insurance and self-insurance are substitutes for one another. Ehrlich and Becker (1972) found that there is only a small incentive for self-insuring against large losses, as it is preferable to insure these large losses. This assumes that premiums are independent of risk reduction activities, as is likely to hold. The link between risk reduction and premiums is weak in Europe (Surminski et al. 2015) and the United States, where in general, flood insurance premiums are not linked to household risk reduction other than increasing a household’s elevation. Taken together this may produce a moral hazard effect whereby individuals with natural disaster insurance coverage invest less in risk reduction measures.

Dionne and Eeckhoudt (1985) extended the research of Ehrlich and Becker (1972) by investigating the role of risk aversion in household risk reduction investments. They found that risk aversion is an important factor for self-insurance, which means that highly risk-averse agents are likely to invest more in damage prevention. This is supported by the theoretical work of de Meza and Webb (2001) showing that advantageous selection may occur in insurance markets when very risk-averse individuals purchase both insurance coverage and take other measures to reduce their risk.

Moreover, the assumed rationality of individuals in standard models of adverse risk selection and moral hazard may not hold in practice. The literature suggests that individuals most often base decisions on subjective risk, which is generally an underestimation of low-probability/high-impact objective risk (Pahl et al. 2005). Individuals tend to misperceive risk, for example, due to bounded rationality (Kunreuther and Pauly 2004). Decision processes may also deviate from expected utility theory as, for example, prospect theory predicts (Kahneman and Tversky 1979).

Moreover, social psychological theories can explain common risk misperceptions. For instance, optimism bias can occur, implying that individuals overestimate the probabilities of pleasant outcomes (Sheppard et al. 2002; Smits and Hoorens 2005), while valence effects imply underestimation of bad outcome probabilities (Rosenhan and Messick 1966). These effects suggest that individuals do not purchase insurance or take measures to limit damage from natural disasters because such disasters are viewed as unpleasant outcomes.

Additional evidence also suggests that individuals have difficulties assessing low-probability risks or negative risk in general (e.g., Rosenhan and Messick 1966; Sheppard et al. 2002; Kunreuther, Novemsky, and Kahneman 2001; Botzen, Aerts, and van den Bergh 2009). Moreover, individuals tend to use favorable and unfavorable information in a manner that results in positively biased views, or comparative optimism (Sharot and Garrett 2016).

Khalil (2010) argues that an individual’s key convictions form the basis for behavior and are very resistant to updating when more information becomes available. Hence, these convictions may not change when employing risk reduction measures or buying insurance. This argument is supported by Windschitl et al. (2013), who showed that people select information that supports their beliefs and behavior. Additionally, Tyler and Rosier (2009) showed that the degree to which people feel that they are accountable is an important driver of decisions to protect against a hazard. The more autonomy individuals have over natural hazard risk, the more likely that these individuals will invest in risk reducing measures.

The aforementioned features of the way people process low-probability hazards may translate into poor decision-making with respect to natural disaster insurance purchases (Botzen and van den Bergh 2012a, 2012b; Kunreuther, Pauly, and McMorrow 2013). As a result, individuals may not buy natural disaster insurance based on objective risk, but rather based on risk preferences (Lindell and Hwang 2008) or how risk information is processed (Sheppard et al. 2015), both of which are intrinsic characteristics of the individual. This could contradict the standard theoretical economics literature, which predicts that in the absence of linkages between policyholder risk reduction and the premiums charged we should observe that risk reducing measures and insurance are substitutes for one another and that moral hazard occurs. These predictions assume that policyholders are following a traditional economically rational decision-making process. However, if the purchase of insurance is driven by risk aversion or other intrinsic motivations, the above substitution effect may not occur in practice when the underlying intrinsic motivations are unaffected by the purchase of insurance (Pahl et al. 2005; Sharot and Garrett 2016).

Overall, it is ambiguous whether characteristics of natural disaster insurance markets in both countries indicate the presence of moral hazard (Section III). The theoretical literature indicates that in the absence of linkages between policyholder-level risk reduction and the premiums charged, we should observe that risk reducing measures and insurance are substitutes. Similarly, the theoretical models predicting the presence of moral hazard assume that policyholders are following an economically rational decision process. However, if the purchase of insurance is driven by risk aversion, the above substitution effect may not occur in practice, as the underlying risk convictions or feelings of accountability are unaffected by the purchase of insurance (Pahl et al. 2005; Sharot and Garrett 2016). For instance, the empirical work of Carson, McCullough, and Pooser (2013) provides evidence in favor of the risk-aversion hypothesis of Dionne and Eeckhoudt (1985) but none in favor of the substitution effects proposed by Ehrlich and Becker (1972).

Insurance penetration rates vary significantly across locations, both in Germany and the United States, signaling varying risk preferences and levels of risk aversion (Section III). Furthermore, low-deductible choices could be due to risk aversion (Carson, McCullough, and Pooser 2013), also muting moral hazard incentives (Dionne and Eeckhoudt 1985). Alternatively, deductible levels may be high enough that moral hazard behavior is muted when the deductible level is known, regardless of the policyholder’s level of risk aversion.

Our statistical and methodological approach was guided by the approaches taken in previous studies investigating moral hazard in insurance markets. However, here multiple statistical methods were applied across varied market constructs to investigate different aspects of moral hazard and to act as a robustness check. As noted earlier, the presence of moral hazard is theoretically ambiguous and hard to predict; therefore, it is sensible to apply several models to different regions in order to draw a more general conclusion about moral hazard in natural disaster insurance markets, as we aim to do in our study. Several consistent model results over different datasets would indicate that the findings regarding moral hazard in natural disaster insurance is a generalizable feature of voluntary natural disaster insurance markets.

Statistical Method 1: Probit Models

For the first set of statistical models, we applied an approach similar to that of Cutler, Finkelstein, and McGarry (2008), who investigated the presence of moral hazard and adverse risk selection in health insurance by estimating probit models of simple relations between risk reducing activities (as a proxy for risk preferences) and insurance. In this study, we estimated probit models that investigate the relation between risk reducing behavior and natural disaster insurance purchases. Probit models were estimated for both the German and the U.S. datasets. The objective of this analysis was not to arrive at a “causal” interpretation of the parameters, such as estimating the direct influence of risk reduction behavior on insurance coverage, but instead to establish a general relation between insurance and risk reduction activities.

The overall presence of moral hazard can be investigated by estimating the combined correlation between risk reduction measures and insurance. This correlation aggregates the various relevant observable and unobservable factors that determine the joint decision process, and allows for detecting the overall moral hazard signal. In particular, an insurance disincentive (moral hazard) that systematically outweighs the risk-aversion effects across the sample population should result in a negative overall combined correlation. Moreover, the theoretical model developed by Ehrlich and Becker (1972) that we tested here implies a simple negative relation between insurance and risk reduction activities since these are substitutes.

Statistical Method 2: Bivariate Probit Models

The second set of statistical models was drawn from Chiappori and Salanié (2000) who modeled the joint decision process of risk reduction and insurance uptake. Chiappori and Salanié (2000) applied a bivariate probit model approach to investigate the presence of moral hazard. The bivariate approach jointly estimates two probit models of risk reduction measures and insurance uptake, which allows for estimation of the cross correlation (ρ) between the error terms of the two probit models. A statistically significant value for ρ indicates the two equations are dependent in the sense that the error terms of the equations are correlated. Therefore, the estimated ρ is an estimate of the unobserved relationship between having insurance and carrying out risk reducing measures and the key indicator of moral hazard.¹

The use of bivariate probit models also allows for circumventing the potential problem of endogeneity, as the dependent variables are excluded from the opposing regression, resulting in each decision being treated as “seemingly unrelated” to the other (Petrolia et al. 2015). A statistically significant negative value for ρ implies moral hazard, which is consistent with the theoretical prediction that insurance and self-insurance (or self-protection) are substitutes, while a statistically significant positive value for ρ indicates advantageous selection based on an unobserved relationship. Our application of the Chiappori and Salanié approach jointly estimates a probit model of insurance uptake and a probit model of employing a risk reduction measure.

Statistical Method 3: Propensity Score Matching

The third approach applies propensity score matching (PSM) to the German data (for more details see Appendix A or Rosenbaum and Rubin [1983]). Our PSM approach is in line with other studies that use matching methods to investigate moral hazard in insurance markets (e.g., Barros, Machado, and Sanz-de-Galdeano 2008). It is also similar to the studies reported by Cohen and Siegelman (2010) that exploit natural experiments in order to detect moral hazard and adverse risk selection in damage outcomes. The PSM results provide evidence of effects on damage of possible adverse risk selection and risk reducing behavior by insured households, which can lead to moral hazard and adverse risk selection. The presence of aspects of adverse risk selection should mean that those with insurance should suffer a greater degree of damage than those without insurance, while moral hazard could be the result of behavioral change resulting in a greater degree of vulnerability and greater damage suffered during an event.

Statistical Method 4: Sample Selection Models and the Influence of Deductibles

In the fourth and final approach we used the U.S. data to investigate the effect of known deductible levels on the likelihood of undertaking any short- or long-term preparation activities. We undertook three separate statistical estimations. First, a Heckman sample selection model (Carson, McCullough, and Pooser 2013) was used to control for endogeneity in a similar manner to that employed by Petrolia et al. (2015). Moreover, this model builds upon the work of Carson, McCullough, and Pooser (2013) by examining the potential for a nonlinear relationship between the deductible and the number of behavioral risk reducing measures employed. Second, a probit model of the likelihood of having window protection in place was applied. Third, another probit model estimated the likelihood of having done any other risk reduction. The purpose of these last two models is to investigate whether there is a nonlinear relationship between the deductible and the specific preparation actions of a household.

Flood Insurance Market in Germany

The German flood insurance market is based on free-market provision and voluntary purchase (Keskitalo, Vulturius, and Scholten 2014). The German government can also provide ad hoc compensation after a major flood event. Flood insurance is often provided as bundled coverage with other natural hazard risks as a supplement to regular building or contents insurance (Keskitalo, Vulturius, and Scholten 2014; Seifert et al. 2013).

Flood insurance premiums are to a certain extent differentiated on the basis of flood probability. The Zürs flood zoning system uses four zones of flood probabilities ranging from 1 (less than 1/200 chance of flooding) to 4 (greater than 1/10 chance of flooding) (GDV 2008). Moving from zone 1 to zone 4 entails an increase in premiums (Seifert et al. 2013). The majority of households are located in zone 1, 10% to 12% are in zone 2, and just 3% of households live in zones 3 and 4 (GDV 2008). Deductibles are set as either a percentage of the damage suffered or as a percentage of the value of the insured property (Schwarze et al. 2011).

The market penetration rate of flood insurance in Germany has increased strongly in recent years. The penetration rate has grown over approximately 10 years to 19% and 33% for contents and residential buildings, respectively, (GDV 2013) from between 3% and 10%, respectively (GDV 2003). The national average hides large regional differences in penetration rates (Seifert et al. 2013). For instance, 95% of households are estimated to have flood insurance in Baden-Württemberg, but only 11% in Bremen (Keskitalo, Vulturius, and Scholten 2014). Overall, the former East Germany is estimated to have higher penetration rates than the former West Germany, due to a history of compulsory flood insurance in the East. It has been argued that adverse risk selection is one of the reasons for the observed low market penetration of flood insurance in some areas, which has resulted in calls for introducing mandatory flood insurance coverage (Schwarze and Wagner 2007; Seifert et al. 2013).

Thieken et al. (2006) conducted surveys of German insurance companies and households in flood-prone areas in 2002, in order to examine characteristics of flood insurance policy conditions in Germany, and whether flood insurance provides incentives for risk reduction. This survey revealed that deductibles were not dependent on the Zürs zoning system. Thieken et al. (2006) found that flood insurance deductibles in Germany ranged between €500 and €5,000. These deductibles provide a small incentive for taking risk reducing measures; namely, an expected loss of between €2.50 and €25 in areas with a flood probability of 1/200. Deductibles and premiums were also found not to be dependent on flood risk reduction measures implemented by policyholders (Thieken et al. 2006).²

Windstorm and Flood Insurance in the United States

In the United States, a standard multiperil homeowners insurance policy is normally required as a condition for a mortgage. These policies cover damage from fire, wind, hail, lightning, and winter storms, among other common noncatastrophe perils (Czajkowski, Kunreuther, and Michel-Kerjan 2012). Although catastrophe perils are covered in the standard homeowners insurance policy, in highly hazard-prone areas of the United States some of these perils are subjected to separate deductibles that are generally a percentage of the insured value of the home. For example, both hurricane deductibles and more general windstorm deductibles are applied in hurricane and wind-prone areas of the United States. Percentage deductibles generally vary from 1% to 15% of a home’s insured value, depending on the risk faced (Insurance Information Institute 2014).

Nineteen states in the United States have hurricane deductibles, including the states of Alabama, Delaware, Louisiana, Maryland, Mississippi, New Jersey, New York, North Carolina, and Virginia, where our U.S. survey respondents were situated (Insurance Information Institute 2014). The deductibles help, potentially, to avoid moral hazard but may substantially lower the attractiveness of the insurance for consumers (Carson, McCullough, and Pooser 2013).

Whether these deductibles can be applied in the case of recent major events, such as Hurricanes Irene and Sandy, has been a contestable legal issue (Pomerantz and Suglia 2013). It is, therefore, of interest to examine whether moral hazard is a major issue in the U.S. natural disaster insurance market, and whether deductibles are effective overall in stimulating policyholders to mitigate risks, as is being studied here.

While standard U.S. homeowners insurance covers a number of catastrophe perils, coverage for flood damage resulting from rising water is explicitly excluded in homeowners insurance policies (Michel-Kerjan, Czajkowski, and Kunreuther 2015). Since 1968 the National Flood Insurance Program (NFIP), administered by the U.S. Federal Emergency Management Agency (FEMA), has been the primary source of residential flood insurance in the United States (Michel-Kerjan 2010; Michel-Kerjan and Kunreuther 2011). The NFIP was developed in 1968 because ever since the severe Mississippi floods of 1927 the private insurance industry believed flood risk was uninsurable. This was due to adverse risk selection, the possibility of massive losses, and the inability to correctly price the product, stemming from the level of sophistication in hazard assessment in the 1960s (Michel-Kerjan, Czajkowski, and Kunreuther 2015). As of January 1, 2014, there were 5.47 million NFIP policies in force nationwide, which generated $3.53 billion in premiums for a total of $1.28 trillion under coverage. Less than 5%, approximately, of total flood insurance coverage is provided by private insurers (Michel-Kerjan, Czajkowski, and Kunreuther 2015).

To set premiums and support local governments, the NFIP maps participating communities by designating flood risks through different flood zones on the flood insurance rate maps (FIRMs) (Michel-Kerjan, Czajkowski, and Kunreuther 2015). A building that was in place before the mapping of flood risk was completed in that area is often given subsidized rates, while homes built after the risk mapping are charged premiums reflecting FEMA’s flood maps. Around a quarter of properties are still subsidized today (Michel-Kerjan, Czajkowski, and Kunreuther 2015). Premiums are determined using the actuarial rate formula, which is focused on the high-risk A and V 100-year flood zones³ (Michel-Kerjan, Czajkowski, and Kunreuther 2015).

Federal law requires property owners in these 100-year floodplains with a mortgage from a federally backed or regulated lender to purchase flood insurance. Despite the mandatory purchase requirement, due to weak enforcement take-up rates are typically low (50% or less), especially in noncoastal areas (Dixon et al 2006; Czajkowski, Kunreuther, and Michel-Kerjan 2012). Take-up rates can vary substantially depending upon location (Dixon et al. 2006). FEMA rates also vary depending on the elevation of the first floor of the dwelling in relation to the 100-year return flood event. However, FEMA does not collect elevation information for many of the insured houses (Michel-Kerjan, 2015). Michel-Kerjan, Czajkowski, and Kunreuther (2015) show that the NFIP’s overall pricing strategy leads to important divergences from the true risk for a number of residents covered by the program. Rates are not risk based at the individual level (probabilistically defined), so prices might be too high in some areas and too low in others.

The NFIP offers deductibles ranging between $500 and $5,000. Michel-Kerjan and Kousky (2010) find that 97% of NFIP policyholders choose deductible levels of $1,000 or less. Finally, to encourage risk reduction, the NFIP operates the Community Rating System (CRS), a voluntary program that rewards communities that undertake mitigating activities with premium discounts, depending on the level of actions taken. However, the risk reduction emphasis of the CRS program is at the community level, not the individual policyholder level.

There have been recent calls for reform of the NFIP, including more private market involvement (Michel-Kerjan and Kunreuther 2011). One example is the 2016 committee-approved House of Representatives legislation aimed at promoting private insurers to enter the flood insurance market (the Flood Insurance Market Parity and Modernization Act of 2016). Adverse risk selection would be a deterrent in this regard. Moreover, the movement toward risk-based premiums as a part of the recent flood insurance reform acts⁴ is aimed at providing incentives for risk reduction, for which it is relevant to know to what extent insurance acts as a risk reduction disincentive (moral hazard).

Survey Data

Statistical Method 1: Probit Models

For both the U.S. and German samples the likelihood of a household having an insurance policy (ℙ(Insured_i = 1) was estimated as a probit model, ϕ(⋅), which is a function of three sets of variable vectors: behavioral measures that reduce risk, measures of subjective risk perceptions, and measures of objective risk as described below; α_n are the estimated coefficients for variable vectors.

[1]

Considering the German sample first, the behavioral measures were the employment of self-protection or self-insurance measures. German subjective risk preferences were modeled through a dummy variable for the catchment area, and whether the individual felt she would not be flooded again. Objective risk measures were if the respondent had been flooded before and was located within a 100-year floodplain.¹⁰ Following the approach developed by Cutler, Finkelstein, and McGarry (2008) for health insurance, a negative correlation between the risk reducing behaviors and insurance would indicate that moral hazard occurs, while advantageous selection is present if there is a positive correlation.

A similar approach was taken for the U.S. data sample, whereby the behavioral measures include short-term preparation or longterm risk reduction activities that were undertaken prior to the arrival of an impending hurricane. Undertaking these measures are hurricane risk reducing in that they could reduce damage to one’s property (putting up storm shutters, taking in furniture, permanent modifications to one’s home, etc.) or oneself (purchase of food and water supplies, making reservations in case evacuation is needed, plan to evacuate, etc.). A subjective risk perception proxy is how safe one feels in staying in the home throughout the hurricane event; objective risk is measured as a household’s location in or out of a 100-year floodplain, how far the home is located from the coast, and previous experience of hurricane damage.

Table 1 provides the results of the estimated German probit model. These results do not provide evidence for the overall presence of moral hazard, since the undertaking of two of the three risk reducing measures is not significantly related with the likelihood of having a flood insurance policy, while those households who employed water barriers are 6.4% more likely to have flood insurance (the marginal effect). This indicates that the average risk preferences were such to overcome the theoretical disincentive emanating from insurance. Overall, there is no evidence of insured households being more vulnerable to floods. The significant marginal effects of the three information variables further complement this finding. These variables show that individuals who were more proactive in understanding and coping with the flood risk that they face are also more likely to have flood insurance. This finding would be in line with the findings of Cutler, Finkelstein, and McGarry (2008), indicating that these households are more risk-averse, which translates into taking a more proactive attitude toward educating themselves about the risk.¹¹

We expected risk perception to be related to the purchase of insurance, but mixed results were found for the subjective risk variables. This is because the variable for the perceived future likelihood of being flooded was statistically insignificant, while the catchment area proxy for risk cultures and regional risk differences was the single most powerful influence. Two of the risk variables included in this probit model, being located in the 100-year floodplain and being flooded before, are insignificant. These variables are commonly viewed as being important determinants of flood insurance purchases. Their insignificance in this context can be explained by the importance of the risk reducing and informational variables that capture individual risk preferences, which outweigh the importance of subjective and objective risk factors. Overall, these probit results provide evidence that suggests moral hazard is not present in the German flood insurance market, since the proactive actions of a policyholder in mitigating risks are mostly uncorrelated with flood insurance purchases, which is not the relation that theory would suggest.

Table 2 presents the relationship between undertaking any risk reducing behavior for hurricanes (self-insurance) and having homeowners (Model 1) and flood insurance coverage (Model 2) in the United States. The data were pooled across the three hurricanes and controls for unobserved hurricane-specific fixed effects through hurricane dummy variables (Irene, Isaac, Sandy), with Sandy being the omitted category.¹² The coefficient signs across both pooled Models 1 and 2 indicate that those survey respondents that engage in short- or long-term ex-ante property risk reducing behavior (preparation, window protection, and risk reduction) were more likely to have homeowners or flood insurance, compared to those who did not engage in these activities. These effects were statistically significant in both models at the 1% and 5% levels. That is, those without homeowners or flood insurance were more vulnerable due to a lack of risk reducing measures, and thus those that had insurance did not exhibit evidence of an overall moral hazard effect.

For example, for two otherwise average U.S. respondents, the probability of having homeowners or flood insurance among those that engaged in preparation activities was 23 and 12 percentage points higher, respectively, than for those that did not engage in any preparation activities. We see similar statistically significant percentages for those that engaged in window protection, who were 4% and 11% more likely to have homeowners and flood insurance, respectively. Moreover, those that engaged in long-term risk reduction were 12% more likely to have flood insurance as compared to those that did not engage in either risk reducing activity.

For both Models 1 and 2, those who had experienced previous hurricane damage were more likely to have homeowners and flood insurance than those respondents who had not experienced hurricane damage, which is statistically significant at the 1% level. While those farther from the coast were more likely to have homeowners insurance, respondents located in the 100-year floodplain were more likely to have flood insurance. This effect decreases with distance from the coast, as indicated by the negative coefficient sign. Hurricane Isaac respondents were also more likely to have flood insurance than those from Sandy. This finding is likely a remnant from Hurricane Katrina striking the same geographic area as Isaac in 2005, causing massive flooding damage. Lastly, those respondents who engaged in ex-ante personal risk reducing behavior or had plans to evacuate were less likely to have homeowner’s insurance. These results suggest a trade-off in risk aversion to property losses versus risk aversion to personal harm among our respondents. The results in Table 2 do not indicate the presence of moral hazard in regard to U.S. natural disaster coverage.¹³

The probit models applied to both the United States and Germany were estimated with two different datasets with different relevant explanatory variables. Neither set of probit models indicated the presence of moral hazard in either market. This suggests that the absence of moral hazard is a robust finding independent of the market features and may be the result of behavioral characteristics of those who voluntarily buy natural disaster flood insurance.

Statistical Method 2: Bivariate Probit Models

The probit models discussed in the previous subsection were further confirmed by estimating bivariate probit models, based on work by Chiappori and Salanié (2000). Bivariate probit models were estimated for both the German and the U.S. samples. The likelihood of a household having both an insurance policy and conducting behavioral risk reducing measures as shown in equation [2], ℙ(Insured_i,1 = 1,Behavioral measures_i,2 = 1), was estimated as a joint probit model, Φ(⋅). This is a function of two sets of variable vectors (as behavioral measures are now a dependent variable): (1) measures of subjective risk perceptions and (2) measures of objective risk as described in the previous section. β_n,j are the estimated coefficients for variable vectors where j = 1 if the individual probit model is estimating the probability of holding insurance, and j = 2 if the model is estimating the probability of employing a risk reduction measure. ρ is the correlation between the error terms of the individual probit models.

[2]

The variables included in the bivariate models for both the German and U.S. samples follow the same principles as for the probit models described above, for the same reasons. The most striking difference between these two sets of models is that the two probit models are jointly estimated. Therefore, there is one model predicting insurance use and another predicting the use of a risk reduction measure. The use of a risk reduction measure in these models is defined in both Germany and the United States as employing one of the household self-protection or self-insurance measures. The new variable of interest is ρ, which is the cross-correlation of probit error terms and can be directly estimated.

The German bivariate probit model was estimated twice: once with the informational variables included and once without. The results are presented in Table 3. It can be argued that the results of the two estimated models support the absence of moral hazard because they show the importance of proactive information gathering. When these information variables are excluded, there is a strong positive relation (ρ) between the models of flood insurance purchases and carrying out risk reduction measures. The proactive information-gathering activities of the insured households implies a higher degree of risk aversion, which outweighs the moral hazard disincentive for protection activities that originate from insurance. Once proactive information-gathering activities have been controlled for, there is no longer a statistically significant unobserved relationship driving the joint decision process.

The bivariate probit models for the U.S. sample are similar to the bivariate probit models presented for Germany, in that they estimate the relation between having either homeowners or flood insurance and employing risk reducing measures. Table 4 shows the estimate of ρ for these bivariate probit models, which is statistically significant. This implies a dependency between the two equations and also that the joint decision process is positively related due to an unobservable relationship. This indicates advantageous selection rather than moral hazard.

In parallel with the previous subsection, the bivariate probit models do not present evidence for moral hazard, due to the lack of a statistically significant negative ρ estimate (which would indicate a negative relationship between insurance and risk reduction measures). The results of the bivariate probit models further confirm the absence of moral hazard in voluntary natural disaster insurance markets.

Moreover, we find some evidence for advantageous selection, since the U.S. results show a positive joint dependency between insurance purchases and risk reduction, which suggests that similar behavioral characteristics influence both decisions to insure and decisions to reduce risk. A similar relationship was found for Germany, where households aware of their flood risk or that develop social coping networks were more likely to have both flood insurance coverage and at least one risk reduction measure in place. These results indicate that households with flood insurance have a different mind-set or intrinsic behavior than those without insurance. The bivariate model results confirm that the absence of moral hazard is due to the intrinsic behavior of the households with insurance.

Statistical Method 3: PSM

Our application of PSM is a novel approach to estimating a causal relationship between insurance purchase and damage outcomes. The method follows two steps: The first step refines the control group (the noninsured group) and treatment group (the insured group) to a subsample that is strongly comparable with each with respect to risk defined as vulnerability (susceptibility to damage), exposure (the value of what can be damaged), and hazard (the probability and intensity of an event) (Kron 2005). The second step compares the damage outcomes of the control and the treatment groups in order to estimate the effects of the treatment, which is in this case having an insurance policy.

The key PSM equation is shown in equation [3]. It shows that the presence of a behavioral change due to insurance would be detected though an average treatment effect on the treated (ATT) estimate that is significantly different from zero. The ATT is the difference in expected flood damage, E(⋅), if a household suffers damage while insured (Flood damage₁ | Insured = 1), compared to the damage suffered when not insured (Flood damage₀ | Insured =0). However, as Flood damage₀ cannot be directly observed, we must use the flood damage suffered by the noninsured population. This potentially introduces a confounding bias (SB) due to risk selection into insurance, which has been filtered out from this ATT. This provides an indication of the importance of risk traits in determining both damage outcomes and insurance purchasing. [3]

We report results of five different matching methods in order to provide an informal robustness check. See Appendix A for more details on PSM.

The PSM analysis was applied to Germany and focused on the link between insurance and flood damage outcomes. The matching analysis of flood damage outcomes provides further support for the absence of an overall moral hazard effect. The presence of adverse risk selection or moral hazard would cause systematic differences in these variables between the insured and the noninsured samples. A mean comparison of experienced flood damage between groups of individuals with and without flood insurance reveals that insured individuals in Germany suffered significantly higher flood damage to contents and buildings (Table 5). It can be argued that because a mean comparison contains the ATT and a selection bias (for more details see Hudson et al. 2014), it estimates the combined effect of the risk selection and the element of moral hazard. Adverse risk selection would be expected to increase damages. The behavioral effect of having insurance coverage is more ambiguous, as insurance could cause individuals to become more lax, or insured individuals may take more risk reducing measures because they are generally very careful (risk-averse). It is thus an empirical issue to estimate whether individuals with flood insurance experience a systematically different level of flood damage than uninsured individuals.

Panel A of Table 6 presents summary statistics of the hazard experience. It shows that an element of adverse risk selection may be present because the treatment group scored higher on various hazard indicators than the control group. In other words, respondents with flood insurance suffered from a worse flood event, as the difference in water levels shows. This suggests that households with flood insurance face a higher flood risk, as the overall shape of the water-level distribution can be argued to be the same across different flood magnitudes, although it is centered at different locations. Furthermore, water level can be considered to be the most important variable of influence on flood damage (DEFRA 2006; Merz et al. 2010). In conclusion, adverse risk selection may be present in the German flood insurance market, since the insured households faced higher risk than noninsured households, which indicates that higher-risk households have a greater incentive to purchase flood insurance coverage. Problems with adverse risk selection can, in practice, be limited by reflecting in insurance premiums the higher flood risks of individuals in floodplains who demand flood insurance.

The PSM estimates can be regarded as providing an indication of the presence of a moral hazard effect, because the method removes risk selection effects on flood damage. The results presented in Table 5 show that the expected difference in flood damage between the groups with and without flood insurance is lower once adverse risk selection has been controlled for using PSM. The latter removed effects on flood damage resulting from risk-related factors that determined whether people purchased flood insurance. The ATT estimates suggest that any behavioral change by insured people does not increase flood risk, because the difference in damage between the insured and noninsured was statistically insignificant. For moral hazard to be present the insured group would have to undertake fewer protective measures, resulting in higher overall damage once adverse risk selection has been controlled for. The results presented in Tables 1 and 3, however, indicate this is not the case.

The summary statistics displayed in Panel B of Table 6 indicate that the insured group was more informed about the risk they faced as well as being more likely to be a part of a flood support network. It is also arguable that the insured group is more risk-averse than the noninsured group, as every member of the insured group employed at least one of the flood-coping measures indicated in Table 6, while only 56% of the noninsured group did so.¹⁴ Therefore, it is possible that the higher level of risk aversion has reduced any negative moral hazard effect.

The previous results are based on data from both the Elbe River and Danube River catchment areas; however, there may be differences between these two catchments. For historical reasons, the flood insurance cultures in the two catchment areas have developed differently. The Elbe catchment is mainly located in the former German Democratic Republic (East Germany), where flood insurance was a part of the compulsory insurance policies a household was required to have. Even now, after the reunification of Germany, a large number of households in that area still have an equivalent set of contracts, while insurance penetration in the former West Germany (including the German part of the Danube catchment) is much lower (Thieken et al. 2006). In order to investigate if the PSM results are being driven by regional effects, the model was estimated first using only the sample of households located in the Elbe catchment area, and then restricted to the Danube catchment. The results of these spilt sample models are presented in Table B1 in Appendix B. These results are broadly similar to the pooled model results and do not provide evidence of a moral hazard effect after controlling for risk selection into insurance. Moreover, a split sample analysis of the relation between flood risk reduction activities and flood insurance coverage (Table B2) reveals that the positive relation between insurance and risk reduction is stronger in the area where the decision to buy flood insurance is more consciously made (the Danube catchment).¹⁵

The analysis of relations between flood insurance and flood damage outcomes provides an additional confirmation of the absence of moral hazard. The novel finding of the PSM analysis is that the results confirm that German households with flood insurance suffer greater losses during a flood, not because insured households prepare less well for floods, but because these households face, on average, higher levels of flood risk.

Statistical Method 4: Sample Selection Models and Deductibles

Sample selection models and a focused analysis of the role of insurance deductibles was applied to the U.S. data. The purpose was to investigate the deductible’s role in the likelihood of undertaking any short- and longterm preparation activities, while controlling for having flood insurance in place, previous hurricane damage experience, the perceived level of safety, and objective measures of risk.¹⁶ These models were applied only for those respondents who had homeowners insurance.

We undertook three separate statistical estimations pooled across hurricanes, as shown in equation [4]. The first element of equation [4] is a Heckman sample selection model (Carson, McCullough, and Pooser 2013), where the selection stage is a probit model of the likelihood of undertaking any short-term preparation and the outcome component of the model estimates the effects of the explanatory variables on the actual number of preparation activities undertaken. In the first element of equation [4], E(Event prep_i|x, Short term =1) is the expected number of preevent preparation activities that take place, given that the household has employed at least one short-term preparation measure; ψ is a vector of estimated coefficients for the independent variables; λ(xy/σ₂) is the inverse Mills ratio; is the correlation between the error terms of the two stages; and σ₁ is the standard deviation of the outcome component.

The second element of equation [4] is a probit model of the likelihood of having window protection in place, ℙ(Window protection_i = 1). The third element of equation [4] is a probit model of the likelihood of employing preparation measures other than window protection, ℙ(Other measure_i = 1). Across all three models, four dummy variables for deductibles of various sizes are included (Deductibles_i). [4]

Table 7 presents the pooled hurricane results from the Heckman sample selection (Model 1) and probit (Models 2 and 3) estimations.

Similar to the results presented in Table 4, we see little evidence of moral hazard for the insured. In contrast, the likelihood of undertaking any short- or long-term preparation activities, as well as the number of preparation activities undertaken, has a positive and statistically significant relationship with having flood insurance in place. As would be expected, coefficient signs indicate that having experienced hurricane damage in the past, feeling less safe, and living in the 100-year flood plain are generally positively related to undertaking more preparation activities. However, having experienced damage is the only statistically significant variable.

In terms of the deductible coverage, the Model 1 selection-stage coefficient value of having a known deductible does not suggest this increases the likelihood of undertaking any preparation activities. From the Model 1 second-stage results compared to those having an unknown deductible amount (the omitted category), coefficient signs generally indicate that knowing one’s deductible increases the number of preparation activities undertaken, but knowing only that one has a deductible greater than $2,500 was statistically significant. Similarly, from Models 2 and 3, while most coefficient signs on the various deductible levels are positive, only knowing the deductible is $2,500 or greater had a statistically significant impact on the likelihood of undertaking window protection or long-term risk reduction. The lack of statistical significance for any of the deductible variables in the three models, other than for the highest deductible levels (> $2,500) is notable (Carson, McCullough, and Pooser 2013), especially since only 12% of respondents believed their deductible to be greater than $1,000, if they knew it at all. These results indicate the deductible’s relative lack of importance in incentivizing short-term preparation or longer-term risk reduction ahead of the hurricane for our insured respondent sample.

A second group of bivariate probit models estimated the joint relationship between a policyholder knowing his deductible and employing a risk reducing measure (see Appendix B, Table B3). The estimated values for ρ are, for the most part, statistically insignificant, which implies that knowledge of the deductible has not influenced household risk reduction action. These findings suggest that the reasons for engaging in risk reducing behavior emanate from the individual, and not from an external financial incentive like the deductible.

Summary of Overall Results

The results of each of the four sets of models across both countries indicate that moral hazard is not present in the investigated markets. Each set of model results individually (with the exception of the PSM set) produced findings that are both internally and externally consistent with the wider literature regarding natural disaster insurance. Each of these findings was reproduced across two countries, several different natural disaster insurance markets, and several statistical methods. Therefore, it does not appear insured individuals are less likely to employ risk reducing measures, and due to our extensive testing, it can be concluded that the absence of moral hazard is a generalizable feature of natural disaster insurance markets. In fact, there is slight evidence for a higher tendency toward self-protection across insured individuals, while there was no systematic difference in the levels of self-insurance. Moreover, we also observed that individuals with flood insurance were more proactively informing themselves about the risk, which suggests that they are more risk-averse, as these households tended to score more highly on the subjective risk preference variables.

These findings taken together are not consistent with the theoretical predictions of Ehrlich and Becker (1972). Overall, there is no evidence for moral hazard. The higher degree of risk aversion may be what is preventing the predicted insurance disincentives from occurring. Moreover, our results confirm that the higher damage suffered during a flood by those with insurance (compared to those without) is a result of higher risk traits rather than changes resulting in a greater susceptibility to flood damage.

These findings suggest that the reasons for engaging in risk reduction emanate from the individual and not from residual risk incentives, such as the deductible that insurers often employ to prevent moral hazard. This supports the conclusions drawn from the models in the previous subsections.