Behavioral Bias, Market Intermediaries and the Demand for Bicycle

Transcription

International Association for the
Study of Insurance Economics
Études et Dossiers
Extract from
Études et Dossiers No. 392
39th Seminar of the European Group of
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The Geneva Association__________________________Etudes et Dossiers no. 392
Behavioral Bias, Market Intermediaries and
the Demand for Bicycle and Flood Insurance
Mark J. Browne
Christian Knoller
Andreas Richter
Munich Risk and Insurance Center
Working Paper 10
June 8, 2012
An electronic version of the paper may be downloaded from the
MRIC website: www.mric.uni-muenchen.de/research/wp
Document free to download
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www.genevaassociation.org
Electronic copy available at: http://ssrn.com/abstract=1982483
Behavioral Bias, Market Intermediaries and the Demand for Bicycle and Flood Insurance
Mark J. Browne, Christian Knoller and Andreas Richter
MRIC Working Paper No. 10
June 2012
Abstract
It is widely accepted that the low demand for natural hazard insurance can to a large extent be explained
by behavioral biases, in particular the tendency to underestimate the likelihood of low probability events
and the preference for insurance against high probability, low consequence (HPLC) risks over insurance
against low probability, high consequence (LPHC) risks.
Our data that are from an insurer that provides coverage against both a LPHC risk (the flood peril) and a
HPLC risk (bicycle theft) represent a unique natural experiment and allow us to contribute to the literature on how these two behavioral biases influence the demand for flood insurance. Since we have information about the sales channel, we can analyze whether insurance agents can help policyholders to overcome these behavioral biases. We find that many more policyholders purchase insurance against the bicycle theft risk than against the natural hazard risk. We also find that policyholders’ insurance coverage
decisions are responsive to changes in their risk exposure. Our analysis indicates that individuals who
purchased their insurance via an insurance agent have a higher probability of insuring against the LPHC
natural hazard risk which is consistent with expected utility maximization.
Mark J. Browne
Department of Actuarial Science, Risk Management and Insurance
Gerald D. Stephens CPCU Chair in Risk Management and Insurance
Wisconsin School of Business
University of Wisconsin - Madison
975 University Avenue
Madison, WI 53706-3123
Phone: 608-263-3030
Email: [email protected]
Christian Knoller
Institute for Risk Management and Insurance
Ludwig-Maximilians-Universität Munich
Phone: +49 (0)89 2180 3764
Fax: +49 (0)89 2180 99 3764
Andreas Richter
Institute for Risk Management and Insurance
Ludwig-Maximilians-Universität Munich
Phone: +49 (0)89 2180 2171
Fax: +49 (0)89 2180 2092
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Electronic copy available at: http://ssrn.com/abstract=1982483
1 Introduction
Flood risk poses a significant threat to the property of a large number of individuals worldwide.
Many experts consider the amount of insurance coverage individuals buy for flood risk to be
inadequate. It is now widely accepted that the low demand for natural hazard insurance can to a
large extent be explained by behavioral biases, in particular the tendency of individuals to underestimate the likelihood of occurrence of catastrophic natural events, which are in most instances
low probability occurrences (see, for instance, Urbany et al., 1989; Kunreuther, 1996; Kunreuther and Pauly, 2004; Kunreuther and Pauly, 2005; Kunreuther and Michel-Kerjan, 2009; and
Schwarcz, 2009). Prior research has empirically investigated determinants of the demand for
flood insurance in the United States (Browne and Hoyt, 2000; Kriesel and Landry, 2004; MichelKerjan and Kousky, 2010; and Landry and Jahan-Parvar, 2011). The research to date suggests
that risk exposure and loss experience and thus the policyholder’s perception of flood risk is an
important driver of the insurance purchasing decision. Survey studies conducted in Switzerland
and the Netherlands also find a positive correlation between individuals’ risk perception and
their actual risk exposure. However, they also find that overall flood risk is perceived as rather
low and that risk perception strongly varies between individuals (see Siegrist and Gutscher,
2006; Botzen et al., 2009; and Botzen and van den Bergh, 2012).
Research by behavioral economists has found that the demand for insurance varies with the likelihood of loss. Laury et al. (2009) write that it is a “widely-reported puzzle that insurance rates
for low-probability, high-consequence losses are low relative to higher-probability, lowconsequence losses”. Individuals’ decisions when faced with risk and insurance have been studied extensively in laboratory experiments (see, for instance, Slovic et al., 1977; Schoemaker
and Kunreuther, 1979; McClelland et al., 1993; Ganderton et al., 2000; and Laury et al., 2009).
Experimental studies are convenient and have a high internal validity. However, the relevance of
their results for real world insurance decisions is not always without any doubt. According to
Sydnor (2010), “Experiments have revealed a range of choice anomalies that are difficult to exDocument free to download
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plain within the standard expected-utility-of-wealth model. …Yet, despite all this research, very
little has been done to explore the relevance of this work to real insurance markets.”
Our unique dataset containing information on insurance purchased to cover household contents
allows us to bridge the gap between the empirical finding that the demand for natural hazard insurance is low and the experimental finding that many individuals prefer insurance against high
probability, low consequence risks. We contribute to the literature on how this behavioral bias
and the biased perception of flood risk influence the demand for flood insurance. Our data are
from an insurer that provides coverage against both a low probability, high consequence (LPHC)
risk – the flood peril – and a high probability, low consequence (HPLC) risk – bicycle theft. Both
are optional insurance coverages that can be added to a policy that provides insurance for the
contents of an owned or rented residence. A broad range of perils are insured against in the base
policy. These include fire, burglary, and windstorm. The information about the additional coverage the policyholders have chosen gives us an interesting natural experiment about individuals’
preferences for insurance against LPHC and HPLC risks. As we have additional micro-level information about the policyholders in our dataset, e.g. several proxies for risk aversion and
wealth, we can analyze in more detail what drives the demand for both types of coverage.
Typically, the price for insurance increases with the policyholder’s risk exposure. Hence, the
problem of many empirical studies analyzing the effect of risk exposure and risk perception on
insurance demand is that they cannot disentangle price effects (the demand for insurance decreases with an increasing premium) from the effect of risk exposure. The dataset we use in our
study contains information on the household’s risk exposure including the ZÜRS classification,
which is an indicator of the risk posed by flood in an area. Although this variable is highly relevant for the policyholder’s flood risk exposure, it is not used in the premium calculation for the
natural hazard coverage we study. Hence, we do not have a price effect and can clearly analyze
whether policyholders react to an increase in the risk exposure.
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An important aspect of our data is that it indicates whether policyholders acquired their insurance contracts through an insurance agent or directly from the insurance company via either the
internet or a call center. In contrast to other studies that have considered the demand for insurance, we are able to test whether the probability of purchasing natural hazard insurance differs
by sales channel. According to Eckardt and Räthke-Döppner (2010), insurance agents “assist in
concluding insurance contracts by providing low-cost information to consumers regarding their
risk profiles, insurance needs, and suitable products”. It is reasonable to assume that insurance
agents play an important role in an individual’s decision whether to purchase insurance as they
can improve the policyholders’ risk perception. We are particularly interested in whether those
acquiring coverage through agents are more likely to insure against LPHC risks than those acquiring coverage through the internet or a call center, where insurance advice is relatively sparse.
Summing up, we address four research questions in this paper: (1) “Which coverage do policyholders prefer – flood insurance or bicycle theft insurance?”, (2) “Can we find systematic differences in the demand for these products with regard to socio-demographic variables?”, (3) “Does
risk perception influence the demand for both types of coverage?”, and (4) “What role do insurance agents play?”
We find that many more policyholders purchase insurance against the bicycle theft risk than
against the natural hazard risk. Hence, in line with findings from several experimental studies,
they prefer insurance against a HPLC risk over insurance against a LPHC risk. Our data indicate
that individuals who purchase coverage against bicycle theft have a slightly higher propensity to
purchase natural hazard coverage and vice versa. We do not find clear effects of sociodemographic factors like the policyholder’s wealth or profession on t he demand for the two
types of additional coverage. Although the demand for natural hazard coverage is relatively low,
we find that policyholders’ insurance coverage decisions are responsive to changes in their risk
exposure. They thus seem to have some idea about their risk exposure relative to other policyholders. Consistent with our expectation, we find that those who purchase insurance through an
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agent are more likely to purchase natural hazards coverage than other insureds. In contrast, we
find no evidence that they are less likely to purchase bicycle insurance. Thus, we report evidence
consistent with market intermediaries providing value by ameliorating the behavioral bias
against insuring low frequency events but do not find evidence consistent with their influencing
individuals not to insure HPLC risks.
The remainder of this paper is organized as follows. Section 2 provides an overview of the relevant literature on behavioral biases and the demand for (flood) insurance. Section 3 describes the
dataset and reports descriptive statistics. Our hypotheses are derived in Section 4. The empirical
model is described in Section 5. The results of our analysis are presented and discussed in Section 6. The paper concludes in Section 7.
2 Behavioral biases and the demand for (flood) insurance
Preference for insurance against HPLC risks
Consider a simple model. An individual with an initial wealth 𝑤𝑤 faces a risk 𝑅𝑅1 (𝑝𝑝1 , 𝐿𝐿1 ): a loss 𝐿𝐿1
occurs with probability 𝑝𝑝1 . The individual is risk averse (𝑢𝑢′ > 0, 𝑢𝑢′′ < 0). The expected utility
of the individual is given by the following equation:
𝐸𝐸𝐸𝐸 = 𝑝𝑝1 ∙ 𝑢𝑢(𝑤𝑤 − 𝐿𝐿1 ) + (1 − 𝑝𝑝1 ) ∙ 𝑢𝑢(𝑤𝑤).
Now assume that the individual faces a d ifferent risk 𝑅𝑅2 (𝑝𝑝2 , 𝐿𝐿2 ) with the same expected value
instead. However, 𝐿𝐿2 > 𝐿𝐿1 and 𝑝𝑝2 < 𝑝𝑝1 . Assuming equal loading factors, due to risk aversion the
individual will value insurance against 𝑅𝑅2 higher than against 𝑅𝑅1 .
In contrast to this theoretical finding, there is experimental evidence that many individuals prefer
insurance against HPLC risks over insurance against LPHC risks. In an early study, Slovic et al.
(1977) modeled the probability of a loss via the drawing of balls from an urn. Holding the expected value of losses constant, the researchers varied the probability and size of possible losses.
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They find that the propensity to buy insurance increased with the loss probability. Schoemaker
and Kunreuther (1979) report results consistent with these findings and discuss the adequacy of
expected utility theory and prospect theory for explaining these results. McClelland et al. (1993)
find an extreme bimodality in the willingness to pay (WTP) for coverage against low probability
risks. Individuals either had a very high WTP or a WTP of almost zero. This bimodality diminished when the loss probability increased. The participants in the experiments of Ganderton et
al. (2000) also preferred to buy insurance for losses that occurred with a higher probability.
Moreover, they find that individuals were more sensitive to changes in probabilities than to
changes in the size of the loss. Laury et al. (2009) discuss extensively the shortcomings in the
design of the experiments that had been conducted to date. In contrast to all other experiments,
they observe that participants bought more insurance for low probability events than for higher
probability events when the expected loss was held constant. In contrast, Shafran (2011) finds
that participants repeatedly making choices were more willing to take self-protection measures
against high probability risks. Addressing the same research questions, the results of the experiments reported in the literature vary widely, depending on t he design of the studies. However,
the experiments provide evidence that individuals have problems handling low probability
events.
Outside of the lab, there is a number of interesting insurance products like cellular phone insurance and extended warranties (for an interesting study thereon, see Huysentruyt and Read, 2010)
that indicate that many individuals tend to overinsure against HPLC risks. However, relatively
few empirical studies using real-world insurance data have addressed this issue. Sydnor (2010)
analyzes data on consumers’ choices of deductibles for home insurance. He finds evidence for an
extremely high level of risk aversion over modest stakes in the market. Analyzing the demand
for flood insurance in Florida, Michel-Kerjan and Kousky (2010) also find that more than 80%
of policyholders choose the lowest possible deductible. Moreover, people with a higher limit of
coverage are more likely to choose the lowest deductible. These results are in line with findings
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from Johnson et al. (1993) and Kunreuther and Pauly (2005), but contradict expectations based
on an expected utility model.
Underestimation of the flood risk exposure
According to Schwarcz (2009), the low demand for natural hazard insurance can to a large extent
be explained by the “mistake hypothesis”, that is, policyholders’ lack of information and limited
cognitive abilities. 1 The use of heuristics seems to bias individuals’ probability judgment. Kunreuther et al. (2009) state that besides mental accounting and planning myopia, the underestimation of the risk exposure is one of the main drivers of the low demand for natural hazard insurance. In particular, individuals tend to ignore events with a probability that is below a certain
threshold level.
There have been several studies that empirically analyze the determinants of the demand for
flood insurance using data from the NFIP. Browne and Hoyt (2000) use state level panel data
from 1983 through 1993 to examine determinants of flood insurance demand. Although theoretical analysis does not necessarily predict this result, they find that insurance demand increases
with income. While they find that high prices have a negative impact on insurance demand, they
also find that recent flood experience positively influences the demand. Specifically, they find
that the number of flood insurance purchases in a state is highly correlated with the number of
flood losses in that state during the prior year. Their empirical analysis suggests that the demand
for flood insurance coverage is relatively price inelastic. Although the Federal Housing Administration (FHA) requires flood insurance for FHA-backed mortgages, the number of FHA mortgages in a state is negatively correlated with insurance demand.
Kriesel and Landry (2004) use household-level survey data to investigate individuals’ propensity
to participate in the NFIP in the coastal zone of nine counties. In line with Browne and Hoyt
1
The mistake hypothesis reflects “the fact that time is scarce, cognitive resources are finite and information is limited” (Schwarcz, 2009).
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(2000), they find that individuals with higher incomes are more likely to purchase insurance, that
the price for flood insurance has a negative effect on pa rticipation in the NFIP, and that flood
insurance demand is rather price inelastic. In contrast, Grace et al. (2004) find a higher price
elasticity for catastrophe coverage than for non-catastrophe coverage. In contrast to Browne and
Hoyt (2000), Kriesel and Landry (2004) observe a positive correlation between FHA mortgages
and flood insurance. They also find that risk exposure drives the demand for insurance – households further away from the shoreline have a lower propensity to buy flood insurance and the
demand for flood insurance decreases with an increase in the hurricane return period.
Building on t his analysis, Landry and Jahan-Parvar (2011) also examine participation in the
NFIP. To a large extent they confirm the results of Kriesel and Landry (2004), but their results
for income and FHA mortgages are ambiguous. Moreover, they use a number of additional variables, including the Federal Emergency Management Agency (FEMA) risk classification. They
find that insurance coverage is higher in higher risk zones. This is another indication that risk
exposure drives the demand for insurance.
Using county-level and policyholder-level data (all NFIP flood insurance policies issued in Florida from 2000 t o 2005), the results from Michel-Kerjan and Kousky (2010) indicate that the
FEMA mapped flood zone is positively correlated with the demand for flood insurance. Summing up, the mentioned studies find evidence that in the NFIP factors enhancing the awareness
and perception of flood risk – especially loss experience and risk exposure (measured, for instance, by the distance to the shoreline, the hurricane return period and the FEMA classification)
– seem to be important drivers of flood insurance demand.
Besides those focused on the NFIP, there have been several studies that have analyzed the perception of flood risk and the demand for flood insurance. In Switzerland very detailed risk maps
for flood risk have been developed based on the risk assessment of experts. In a survey, Siegrist
and Gutscher (2006) find a positive correlation between participants’ risk perception and the
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experts’ risk assessment. However, they observe no differences in concrete prevention behavior
between people living in different flood risk areas. They find evidence that some people overestimate their flood risk while others highly underestimate their risk exposure. Own flood experiences are positively correlated with risk perception.
Botzen et al. (2009) analyze the role of geographical and socio-economic characteristics for risk
perception in the Netherlands based on a survey study of homeowners. They find that overall
participants assess the risk of flood as rather low. But the actual risk exposure is positively correlated with the perceived risk. Individuals living closer to a river or in low-lying areas have a
higher risk perception. However, individuals that are not protected by a dike tend to underestimate their risk. In a survey study, Botzen and van den Bergh (2012) analyze the demand for
flood insurance for homeowners in the Dutch river delta. Among other things, they find that the
perceived exposure to flood risk plays an important role for the participants’ WTP. But their results also indicate that many individuals almost completely neglect their flood risk exposure.
Viscusi and Zeckhauser (2006) asked individuals in the U.S. to rate their risk of being killed by a
hurricane, earthquake, flood, and tornado. Overall, 93.5% of the participants believed they faced
an average or below-average risk. This number was slightly lower for individuals that had experienced a natural hazard or that lived in a more risk prone area. Hence, both risk exposure and
loss experience had an effect on risk perception. However, this effect was lower than would be
expected based on rational calculation. The authors conclude that “risk belief results … are quite
sensible in direction, but insufficient in magnitude”. Summing up, t here is some evidence that
individuals tend to correctly estimate their flood risk exposure relative to others, but absolutely
underestimate their risk exposure. However, risk perception regarding natural hazards is still not
completely understood.
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Behavioral biases and information of policyholders
Given that the empirical evidence to date indicates that the low demand for natural hazard insurance is attributable at least in part to behavioral biases, it is important to think about remedies to
overcome these biases. Informing policyholders about their loss probabilities and loading factors
should help them to make better informed decisions (see Kunreuther and Pauly, 2004). In a survey conducted in Germany, Zhou-Richter et al. (2010) analyze the perception of long-term care
(LTC) risk and the propensity to purchase LTC insurance. When they first asked respondents to
estimate the probability that their parents would require LTC, the participants mostly underestimated the risk and had a rather low WTP for insurance covering this risk. However, after they
were provided information about their actual risk exposure, the percentage of participants willing
to purchase LTC insurance substantially increased. The process of purchasing flood insurance
might follow a similar process. Hence, informing people about their flood risk exposure might
increase their willingness to purchase flood insurance.
There is evidence that the abstract disclosure of probabilities will not strongly affect policyholders’ decision behavior (see, for instance, Agarwal et al., 2009 and Schwarcz, 2009). However,
most policyholders do not purchase their contracts directly from the insurance company but via
an intermediary, either an independent agent or an exclusive agent. While exclusive agents
usually sell the products of only one insurance company, independent agents sell products of
different insurers. 2 According to Cummins and Doherty (2006), the intermediary serves as a
“market maker” that helps individuals to identify their insurance needs and matches policyholders with appropriate products and, in the case of brokers, insurance companies. Eckardt and
Räthke-Döppner (2010) state that insurance agents “assist in concluding insurance contracts by
providing low-cost information to consumers regarding their risk profiles, insurance needs, and
2
Legally, agents are the representatives of sellers of insurers and brokers are the representatives of buyers of insurance. Since differences between exclusive and independent agents are not in the scope of this research project, only
a very global characterization of the different agents is given. More information on the specific characteristics in the
German market and a discussion about differences in service quality between different types of agents can be found
in Schiller (2011) and Eckardt and Räthke-Döppner (2010).
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suitable products”. Soane et al. (2010) write that the responsiveness of lay individuals to experts’
risk communication increases if there is an effective partnership between both parties and the
receiver trusts the expert. Additionally, many individuals prefer a direct contact to the expert. A
reasonable expectation is that policyholders will react to information provided by insurance
agents. Kunreuther et al. (2001) show that individuals have less of a problem in evaluating small
probabilities if they are given rich contextual information (for instance, a comparative scale or
scenarios) that provides them with the opportunity to consider the event in a familiar context that
evokes their own feelings of risk. Insurance agents might be able to provide this informational
context and thus be able to increase the willingness of policyholders to purchase flood insurance. 3
3 Dataset
Description of the observed variables
We use data from a portfolio of risks of a German insurer. 4 The insurer writes coverage on the
personal property (contents) of residential renters. We have cross-sectional information on a ll
policies that were in force in June 2010, no matter when the contract was originally signed. The
company writes most of its insurance in one German state. Although its market share in this area
3
Insurance agents are typically compensated with commissions based on the amount of insurance sold. The agent
thus has two objectives: to provide sound professional advice and to maximize compensation payments. The companies and products with the highest commissions are not necessarily the ones that best fit the needs of the policyholder. This might create an incentive for the agent not to recommend the optimal contract and insurance company
(see Schiller 2011). Inderst (2011) discusses the importance of advice in the market for retail financial services. He
states that advisors that are paid by commissions might not de-bias investors but rather “increase revenues through
churning when customers already have a bias towards excessive trading.” However, for two reasons this should not
be a problem in the case of flood insurance. Premiums for flood insurance, at least in Germany, are not very high
and thus premium based commissions will not be very high either. Consequently, agents might focus on enhancing
their relationship with their customers by providing advice to customers free from consideration of their potential
commission income, which in the case of hazard insurance would be negligible in any case. Secondly, commissions
only give the agent an additional incentive to inform policyholders about their flood risk exposure and the possibility to purchase flood insurance.
4
Since we are primarily interested in individuals’ decisions, in particular the role of intermediaries in addressing
behavioral bias, it is advantageous that our data are from a single insurer. Our analyses are free of confounding effects that would be introduced were our data from multiple insurers.
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is rather high, its book of business is not representative of the state as a whole. For instance, public sector employees are clearly overrepresented in the portfolio (see Table 3). The insurance
provides coverage for most of the contents in a policyholder’s living space, but not for the structure itself. Some items, such as jewelry and cash, are only insured up to specified limits of coverage. The insurance contracts provide protection against a number of risks including fire,
lightning, explosion, implosion, damages caused by broken water conduits, storm, hail, burglary
and robbery. Natural hazard risks, like flooding and earthquakes are explicitly excluded, but can
be insured through optional additional coverage. Since earthquakes hardly ever occur in the part
of Germany where the insurer writes coverage, flooding is the only relevant risk covered by the
natural hazard insurance. Additionally, policyholders can purchase coverage against the theft of
their bicycle. 5 These additional coverages cannot normally be purchased as stand-alone products
from another insurance company. Therefore, we can reasonably assume that if policyholders do
not purchase these coverages from the insurance company that provided our data, they do not
have coverage. Table 1 summarizes the variables that are contained in the dataset.
- Insert Table 1 here The “Zoning-System for Floods, Tailback and Heavy Rain” (ZÜRS) is an important aspect of the
risk exposure. ZÜRS was developed by the Association of German Insurance Companies (GDV)
to assign flood risk ratings to properties. Currently, ZÜRS ratings are only accessible to insurance companies. ZÜRS enables insurance companies to assign almost every building in Germany to one of four flood risk classes. It distinguishes these risk classes with regard to the return
period of major floods (see Table 2 and GDV, 2011).
- Insert Table 2 here The insurance company uses a territory rating system when pricing bicycle theft coverage to account for the differences in risk in different areas. Policies are sold via insurance agents (exclu5
In 2009, 80% of the households in Germany had at least one bicycle (see Federal Statistical Office, 2009).
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sive agents as well as independent agents) and directly (via internet and call center). Although
we do not have information on the income or wealth of policyholders, we do have the sum insured, the amount of living space and the county the policyholder lives in, which we use as proxies. Policyholders can pay their premium via direct debit or wire transfer 6. We also have information on the policyholder’s socio-demographic characteristics, including age and gender. For
families and couples, we only have the age and gender of the person who signed the insurance
contract.
Descriptive statistics
In our model estimation, we exclude outliers (sum insured > 200,000€ or living space > 300
square meters), and observations that contain missing values or errors. Since natural hazard coverage and bicycle theft insurance are not available in class 4 of the respective risk classification
systems, the data in our analyses does not include policyholders residing in buildings in this
class. The risk exposure of an apartment to flood risk heavily depends on whether the apartment
is on t he first floor or above. Flood insurance is not necessary for apartments on t he third or
fourth floor. Unfortunately, we do not have information about the floor in our dataset. Therefore,
we restrict our analyses to policyholders that live in houses because they would definitely be
exposed to the flood risk. 7
All of the policies in our data set were in force in June 2010. We restrict our analyses to those
policies that were initially written between 1997 and 2008. 8 For these contracts, the premium P
for the natural hazard coverage is calculated as a linear product of the sum insured. 9 Therefore,
6
Through direct debit, the policyholder allows the insurer to withdraw the premium from the policyholder’s bank
account every time it is due. Through a wire transfer, the policyholder transfers money from his or her bank account
to the insurer’s bank account.
7
We also ran our analysis including outliers and apartments. Results did not significantly change.
8
Policies are one-year in length and renewable.
9
P = a*(Sum Insured). The factor “a” in the equation is a fixed constant.
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the premium does not depend on any risk relevant characteristics of the insured. In particular, the
premium on these policies does not depend on the ZÜRS classification of the building in which
the policyholder resides.
While the base contract and the bicycle theft coverage do not contain a deductible, the natural
hazard coverage does. The amount of the deductible depends on t he ZÜRS-classification. In
class 1 it is 250€, in class 2 it is 10% of the loss, but at least 500€; in class 3 it increases to 20%
of the loss (at least 500€). 10 In contrast to the natural hazards coverage, the premium charged for
bicycle theft insurance is dependent on the insurer’s evaluation of the risk associated with bearing the risk. Descriptive statistics for the remaining 14,734 contracts in our data set are displayed
in Table 3:
- Insert Table 3 here About 13% of the policyholders in our sample have natural hazard coverage. 11 The demand for
bicycle theft coverage is significantly higher – more than one third of the policyholders in our
dataset insure their bicycle against theft (t = 47.0025, p < 0.001). Table 4 shows that policyholders holding insurance against bicycle theft do not necessarily also purchase additional coverage
against natural hazard risks (Pearson chi2(1) = 87.6846, p < 0.001).
- Insert Table 4 here There is a small correlation between the two risk classes (Pearson chi2(4) = 35.3732, p < 0.001).
- Insert Table 5 here –
10
Before 1997, policyholders could not purchase additional coverage for natural hazard risks. The insurance company completely changed the contract design for the base contracts in 2009. In doing so they also changed the pricing
scheme for the natural hazard coverage. For these policies, the ZÜRS classification and the building type are used
for risk classification. Hence, premium is higher for policyholders living in a house than for those living in an
apartment and higher for those living in ZÜRS class 3 than for those living in ZÜRS class 1. Customers holding an
old contract were offered the possibility to switch to the new conditions, but they did not have to. Only a few of
them did. We are aware that excluding these policyholders might induce a sample selection bias, but controlling for
this potential bias does not remarkably change our results.
11
According to the German Committee for Disaster Reduction (2004), this is about the same as the share of all content insurance contracts in Germany that had natural hazard coverage in 2004.
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4 Hypotheses
The data discussed above indicate that many policyholders prefer insurance against the HPLC
risk of bicycle theft over the LPHC risk posed by natural hazards. We now consider in more detail the factors which drive the demand for both products. In doing so we assume that an individual’s decision whether to purchase additional coverage against either natural hazards or bicycle
theft depends on t he premium, his or her wealth and income, risk aversion, and the perceived
risk. That is,
Pr(additional coverage = 1) = F(risk aversion, wealth, premium, perceived risk).
We are particularly interested in the effect of risk perception on insurance demand. Most of the
existing literature finds that the perception of flood risk depends on the actual exposure. As the
risk exposure differs between the three ZÜRS flood risk classes and premiums are the same for
all three classes, we would expect all else equal to observe higher demand by those in higher risk
classes. However, the deductible increases and thus the coverage decreases with increasing risk.
This will presumably weaken the expected effect. 12 Since risk classes are used in premium calculation for bicycle theft insurance, we do not expect to observe a similar effect with the bicycle
theft risk classes.
One of the main questions addressed by our study is whether insurance agents influence policyholders’ risk perception. We anticipate that agents increase policyholders’ awareness of flood
risk. Customers that purchase their contracts directly from the insurer via internet or a call center
without the services of an agent are less likely to be informed about the risks associated with
natural hazards. We hypothesize that the use of distribution channel is correlated with the demand for natural hazard coverage. Specifically, we hypothesize that individuals who purchase
insurance through an agent are more likely to purchase natural hazards coverage than those who
12
We do not have information on the claims for the different flood risk areas, so we cannot calculate whether premiums are adequate. But the insurance company affirmed that the premium per unit of coverage was lower for the
contracts in ZÜRS class 2 and 3 and they were losing money with these contracts. Hence, there seems to be some
cross-subsidization.
6-16
purchase their coverage over the internet or through a cal l center. Since it mig ht be easier for
individuals to imagine that their bicycle could be stolen than that a flood will destroy their house,
we do not necessarily expect the same result for the bicycle theft insurance. Of course, a positive
effect of the distribution channel on insurance demand could also be caused by a correlation with
one of the other three factors (premium, wealth, risk aversion). The premium policyholders have
to pay does not remarkably differ between distribution channels. Concerning wealth and risk
aversion, individuals purchasing insurance via an agent might significantly differ from those that
buy via the internet or a call center. However, the policyholders in our dataset do not remarkably
differ with regard to observable characteristics between the different distribution channels. We
are not aware of many studies analyzing the characteristics and behavior of policyholders between different distribution channels. Bauer et al. (2002) do not find a big impact of policyholders’ socio-demographic characteristics on their propensity to purchase insurance over the internet. One exception is that individuals purchasing insurance online tend to have slightly higher
incomes.
We consider living space and GDP per capita to be proxies for wealth in our model. The theoretical and empirical literature examining the effect of wealth on insurance demand has led to
mixed results. Palm and Hodgson (1992) find that earthquake insurance purchases are not correlated with policyholders’ wealth. In contrast, most of the empirical studies referenced earlier in
Section 2 report positive correlations between income and wealth and the demand for flood insurance. Our a priori prediction of the effect is therefore ambiguous.
With regard to sum insured, two potentially opposing effects are feasible – a wealth effect (the
sum insured should be positively correlated with the policyholder’s wealth) and a p rice effect
(the premium increases with the sum insured). While the effect of wealth cannot be clearly predicted, we expect the demand for insurance to decrease if the premium increases.
6-17
Pfeifer (2011) finds that in Germany more risk-averse individuals self-select into public sector
employment. As the demand for insurance should increase in risk aversion, public sector employment should be positively correlated with demand for both types of additional coverage. On
the other hand, anecdotal evidence suggests that public sector employees tend to be rather parsimonious and thus might be reluctant to purchase additional coverage. Hence, we do not expect a
clear effect for this variable.
5 Method
We estimate a bivariate probit regression to test our hypotheses. Individuals having purchased
the base contract have to decide if they also want to purchase natural hazard coverage and bicycle theft coverage. We observe two dichotomous dependent variables, 𝑦𝑦1 and 𝑦𝑦2 :
∗
𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (𝑦𝑦1 ): 𝑦𝑦1𝑖𝑖
= 𝛽𝛽 ′ 𝑥𝑥1𝑖𝑖 + 𝑢𝑢1𝑖𝑖
∗
𝑤𝑤𝑤𝑤𝑤𝑤ℎ 𝑦𝑦1𝑖𝑖 = 1 𝑖𝑖𝑖𝑖 𝑦𝑦1𝑖𝑖
> 0 𝑎𝑎𝑎𝑎𝑎𝑎 0 𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒,
∗
𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (𝑦𝑦2 ): 𝑦𝑦2𝑖𝑖
= 𝛽𝛽 ′ 𝑥𝑥2𝑖𝑖 + 𝑢𝑢2𝑖𝑖
∗
𝑤𝑤𝑤𝑤𝑤𝑤ℎ 𝑦𝑦2𝑖𝑖 = 1 𝑖𝑖𝑖𝑖 𝑦𝑦2𝑖𝑖
> 0 𝑎𝑎𝑎𝑎𝑎𝑎 0 𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒.
There might be unobserved characteristics of the policyholder that influence both the demand for
flood insurance and bicycle theft insurance. Hence, the two decisions might be interrelated and
the error terms in the two equations might be correlated:
𝑢𝑢1𝑖𝑖 = ∝𝑖𝑖 + 𝜀𝜀1𝑖𝑖 ,
𝑢𝑢2𝑖𝑖 = ∝𝑖𝑖 + 𝜀𝜀2𝑖𝑖 .
We assume a bivariate normal distribution:
(𝑢𝑢1 , 𝑢𝑢2 ) ~ 𝐵𝐵𝐵𝐵𝐵𝐵(0, 0, 1, 1, 𝜌𝜌) ,
6-18
with 𝜌𝜌 denoting the correlation parameter. 13
The policyholders in our dataset live in 44 different counties. We cluster our dataset on countylevel. Clustering is appropriate in this case as it is reasonable to expect that policyholders living
in the same county share characteristics we cannot observe that differentiate them from policyholders living in another county. Clustering standard errors on county-level takes this intracounty correlation into account (see, for instance, Nichols, 2007).
6 Results
Our results indicate that policyholders generally have a preference for bicycle theft coverage.
The greater propensity for individuals to insure against HPLC risks as opposed to LPHC risks is
consistent with prior literature. Hsee and Kunreuther (2000) find that people are more willing to
purchase insurance for an object, the more affection they have for the object. This provides
another explanation why many policyholders insure their bicycles. The results of the regression
analysis are presented in Table 6.
- Insert Table 6 here The two decisions, whether or not to purchase bicycle insurance and natural hazard insurance,
are weakly correlated (ρ = 0.13; chi2(1) = 29.9523, p < 0.001). The low but positive correlation
between the error terms of equations 1 and 2 indicates that individuals purchasing bicycle theft
coverage are also slightly more willing to purchase natural hazard coverage and vice versa.
The coefficients of the bivariate probit analysis show which factors are associated with the demand for natural hazard coverage and bicycle theft coverage. Policyholders in flood risk class 2
have a greater probability of purchasing natural hazard coverage than those living in flood risk
class 1. That their coverage decreases due to the higher deductible does not seem to matter too
13
For a more detailed description of the bivariate probit model see Greene (1996).
6-19
much. Interestingly, individuals living in ZÜRS class 3 do not purchase more natural hazard insurance than those in ZÜRS class 1 although their flood risk is clearly higher and the premium is
the same. Presumably, the high deductible makes these contracts unattractive. The bicycle theft
risk classes have no effect on the demand for bicycle theft coverage. As these risk classes are
used for premium calculation, this result is not surprising. Our results suggest that policyholders
have quite a good idea about their risk exposure regarding flood risk and bicycle theft, at least
relative to other policyholders in the same portfolio. However, the low demand for flood insurance provides evidence that overall they do not consider their flood exposure to be very high.
This result is in line with findings from several other studies that analyze individuals’ perception
of natural hazard risks.
One of the main interests of our study is testing whether purchasing insurance coverage through
an insurance agent, rather than remotely through the internet or a call center, is associated with
an increased likelihood of purchasing insurance against natural hazards. We find that policyholders that purchased their contract via an insurance agent have a higher probability of purchasing
natural hazard coverage than those that purchased their contracts directly from the company,
either through a call center or over the internet. However, the probability of purchasing bicycle
theft coverage is not associated with whether or not one acquired insurance through an agent.
Thus, policyholders that purchase from an agent do not seem to be more inclined to purchase
insurance in general. Taken together, these results are consistent with the hypothesis that agents
exercise influence in the insurance purchasing decision and that this results in insureds being
more likely to purchase coverage against LPHC risks (natural hazards) than they otherwise
would and not more or even less likely to purchase coverage against HPLC risks (bicycle theft)
than they otherwise would. In the expected utility paradigm, therefore, the influence of the agent
on the insurance purchasing decisions would increase the insured’s level of utility. Our findings
suggest that agents play an important role in improving their customers’ welfare by helping them
overcome a behavioral bias in their insurance purchasing.
6-20
The probability of purchasing natural hazard coverage increases with the sum insured. The
wealth effect (the sum insured should be positively correlated with the policyholder’s wealth)
seems to outweigh the price effect (the premium linearly increases with the sum insured). However, the probability of purchasing only bicycle theft coverage does not change with the sum
insured. Interestingly, the effect of the size of the house (living space) is opposite to the effect of
the sum insured. Controlling for sum insured, policyholders living in a larger house are less likely to purchase natural hazard coverage, but more likely to purchase only bicycle theft coverage
than those living in a smaller house. The GDP per capita does not influence the policyholders’
propensity to purchase both types of additional coverage. In summary, our results regarding
wealth are ambiguous – which is consistent with previous findings in the literature.
Research on mental accounting suggests that individuals use mental accounts to structure their
wealth and expenses (see Thaler, 1999). Compared to direct debit, wire transfer as payment method allows the policyholder to have better control or be more aware of the premium payment
and thus makes mental accounting easier. However, from a mental accounting perspective, insurance would rather be perceived as an investment and thus the bicycle theft coverage could
appear to be the more attractive choice because the chances to receive payouts from the contract
are much higher than for the natural hazard coverage. This might explain why individuals who
pay their premium via direct debit have a higher probability of purchasing bicycle theft insurance, but are not more likely to purchase natural hazard insurance than policyholders that pay
their premium via wire transfer.
Prior research has shown that individuals employed in the public sector tend to be more risk
averse than the population as a whole (see, for instance, Pfeifer, 2011). This would suggest a
greater demand for insurance coverage on their part. While this is supported in our data with the
bicycle theft coverage, it is not with the natural hazards coverage. We find that public sector employment is statistically significant and negatively associated with demand for natural hazards
coverage. One possible explanation for this result could be that individuals working in the public
6-21
sector tend to be rather parsimonious and thus might be more prone to do mental accounting. As
we have described for the payment method, the bicycle theft insurance might seem to be a better
“investment” than the natural hazard coverage from this perspective.
We find male policyholders have a slightly higher propensity to purchase both additional coverages, but are considerably more likely to purchase only bicycle theft coverage. The positive linear, but negative squared effect of age in our models on the demand for bicycle theft coverage
is consistent with other studies on the demand for insurance (see, for instance, Showers and Shotick, 1994).
7 Conclusion
The low demand for flood insurance worldwide has been an important research topic for many
years. The literature has identified behavioral biases as an important driver for this result, in particular individuals’ misperception of flood risk exposure and the bias of individuals against purchasing insurance against low probability risks. However, most of the findings are based on survey studies and laboratory experiments. We use a unique dataset from a German property insurance company as a natural experiment to investigate the role of these two behavioral biases on
the demand for flood insurance and to see if insurance agents can help individuals to overcome
these biases. The insurance company writes insurance on the personal possessions of homeowners and those renting their residence. Besides the base contract, policyholders can purchase additional coverage against natural hazards and the theft of their bicycle. The dataset contains information on the household’s risk exposure for these two risks and the distribution channel through
which insurance coverage was obtained.
We find that policyholders are much more willing to purchase bicycle theft coverage than natural
hazard coverage which indicates that they do not perceive flooding as a considerably important
risk and prefer to insure against HPLC risks. Individuals purchasing bicycle theft coverage are
6-22
also slightly more willing to purchase natural hazard coverage and vice versa. Our results empirically show that the preference for insurance against HPLC risks that had been found in several
experimental studies is a relevant factor for the (low) demand for natural hazard insurance.
Although we do not find clear effects of socio-demographic factors like the policyholder’s
wealth or profession on the demand for the two types of additional coverage, important differences in the policyholders’ behavior can be observed in the data. Although the demand for natural hazard insurance is low, policyholders react quite sensitively to their risk exposure. At least to
some extent they seem to understand whether the premium they have to pay is adequate for their
risk. Policyholders living in higher flood risk classes tend to be more likely to be insured than
those in the lowest risk class, even though this effect is weakened by a higher deductible for the
higher risk classes. Hence, although absolutely the flood risk perception may be low, relatively it
seems to coincide with the risk exposure quite well.
An important finding of this study is that individuals who purchased their insurance contract
with an insurance agent are more likely to purchase natural hazards coverage. We do not observe
a positive effect of the insurance agent on the demand for bicycle theft coverage. Our analysis is
consistent with insurance agents influencing the insurance purchasing decisions of their customers. Insureds who obtain coverage through agents are more likely than others to purchase coverage that is consistent with expected utility maximization.
6-23
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6-26
Appendix
Variable
Possible values
Natural hazard coverage
Yes or no
Bicycle theft coverage
Yes or no
Public sector employment
Yes or no
Building type
House or apartment
Flood risk classification (ZÜRS)
1 to 4
Risk classification for bicycle theft
1 to 4
Distribution channel
Insurance agent or direct business (internet, call
center)
Sum insured
In €
Payment method
Direct debit or wire transfer
Living space
In square meters
GDP per capita (in the county the policyholder lives in)
In 1,000 €
Age
In years
Gender
Male or female
County the policyholder lives in
1 to 44
Table 1: Variables
Flood risk
class
Return period
1
More than 200 years
2
Between 50 and 200 years
3
Between 10 and 50 years
4
Less than 10 years
Table 2: Return period of major floods
6-27
Variable
Mean
Std.Dev.
Min
Max
Natural hazard coverage
0.13
0.34
0
1
0.35
0.48
0
1
0.72
0.45
0
1
Distribution channel: insurance
agent
0.83
0.38
0
1
87,261.10
26,950.23
10500
198000
0.84
0.37
0
1
Living space
135.28
36.21
25
300
GDP per capita
30.40
6.89
21.82
59.91
Age
58.17
13.06
21
97
Gender: male
0.60
0.49
0
1
Sum insured
Payment method: direct debit
Table 3: Descriptive statistics
No
Yes
∑
No
Natural hazard coverage Yes
8,559
4,265
12,824
1,066
844
1,910
∑
9,625
5,109
14,734
Table 4: Additional coverage
Risk classes for bicycle theft coverage
Risk classes for
natural hazard
coverage
1
2
3
∑
1
8,899
1,258
62
10,224
2
3,294
418
13
3,731
3
640
146
4
790
∑
12,833
1,822
79
14,734
Table 5: Risk classes
6-28
(1)
Pr(Natural hazard
coverage = 1)
VARIABLES
Flood risk class 2 (ZÜRS)
Flood risk class 3 (ZÜRS)
Risk class 2 for bicycle theft
(2)
Pr(Bicycle theft
coverage = 1)
0.334***
(0.0730)
0.0952
(0.262)
0.0125
(0.120)
-0.258
(0.175)
-0.0425
(0.0423)
0.145**
(0.0596)
0.0107
(0.00780)
0.0604
(0.0458)
0.113***
(0.0405)
0.146***
(0.0192)
0.133***
(0.0185)
0.0905***
(0.00819)
-0.000871***
(7.11e-05)
-4.536***
(0.524)
Risk class 3 for bicycle theft
Insurance agent
Ln(living space)
GDP per capita
Ln(sum insured)
Direct debit
Gender: male
Age
Age²
Constant
Observations
0.159***
(0.0443)
-0.263***
(0.0953)
0.00815
(0.00513)
0.663***
(0.0783)
-0.0866**
(0.0374)
-0.00687
(0.0485)
0.0325
(0.0336)
-0.00649
(0.00895)
1.85e-05
(7.34e-05)
-7.451***
(0.565)
14,736
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
14,736
Table 6: Regression analysis
6-29

Behavioral Bias, Market Intermediaries and the Demand for Bicycle

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