Context-Dependent Preferences and Distribution of Insurance Products: Theoretical Foundations and Experimental Results

ABSTRACT - Insurance decisions are hypothesized to be context-dependent, so that willingness to pay for a policy may differ when it is bundled with the product and/or with another insurance policy. The paper presents results of two questionnaire experiments dealing with bundling of commodities and insurance, i.e., distribution of insurance via the dealer of the commodities, bundling of different insurance policies, and risk aggregation. The hypotheses are derived on the basis of prospect theory and mental accounting. The findings support our hypotheses, but not for the entire group of respondents. They differ greatly between those with high and low personal involvement. The paper concludes with a discussion of the results, implications for marketing and public policy, and suggestions for future research.

Citation:

Christian Schade and Howard Kunreuther (1998) ,"Context-Dependent Preferences and Distribution of Insurance Products: Theoretical Foundations and Experimental Results", in E - European Advances in Consumer Research Volume 3, eds. Basil G. Englis and Anna Olofsson, Provo, UT : Association for Consumer Research, Pages: 278-285.

European Advances in Consumer Research Volume 3, 1998      Pages 278-285

CONTEXT-DEPENDENT PREFERENCES AND DISTRIBUTION OF INSURANCE PRODUCTS: THEORETICAL FOUNDATIONS AND EXPERIMENTAL RESULTS

Christian Schade, Goethe University Frankfurt a.M., Germany

Howard Kunreuther, Wharton School, University of Pennsylvania, U.S.A

[We would like to thank Hanne Boecken, Klaus Peter Kaas, Kerstin Kamlage, Tobias Schneider, Eli Snir, and Martina Steul for their helpful comments on the manuscript. Klaus Peter Kaas also revised early versions of the experiments. We acknowledge helpful discussions with Colin Camerer during the 1997 Bonn Workshop concerning further research on the bundling of insurance issue. Jan Pieter Krahnen, Christian Rieck, Eric Theissen and other participants in the Financial Markets Brown Bag Seminar, Spring 1997, Goethe University Frankfurt a.M., contributed to the paper. The comments of and discussions with Elizabeth Cowley, Andrea Groeppel, Tobias Langner, Volker Trommsdorf, Peter Weinberg, and other participants in the presentation of this paper at the ACR European Conference 1997 have been extremely valuable.]

ABSTRACT -

Insurance decisions are hypothesized to be context-dependent, so that willingness to pay for a policy may differ when it is bundled with the product and/or with another insurance policy. The paper presents results of two questionnaire experiments dealing with bundling of commodities and insurance, i.e., distribution of insurance via the dealer of the commodities, bundling of different insurance policies, and risk aggregation. The hypotheses are derived on the basis of prospect theory and mental accounting. The findings support our hypotheses, but not for the entire group of respondents. They differ greatly between those with high and low personal involvement. The paper concludes with a discussion of the results, implications for marketing and public policy, and suggestions for future research.

1. INTRODUCTION

Insurance decisions often seem to contradict expected utility theory since individuals do not make the implied tradeoffs between the cost of a policy and the expected benefits of a reduction in their loss potential. Furthermore, consumers exhibit framing effects and risk perception distortions. Insurance decisions are also context-dependent. Willingness to pay (WTP) may differ depending on whether the policy is presented alone or jointly with the insured objects or with other policies. The bundling of insurance with objects is only possible if both are distributed via the same channel. A better understanding of the impact of these factors on insurance decisions is relevant for improving insurers’ marketing activities. In order to improve these efforts, insurers may want to develop a detailed understanding of the factors influencing the insurance purchase decision. It may also help regulatory agencies decide on public policy actions, such as facilitating the distribution of subsidized flood insurance. For the same reasons it may be important to understand the effect of different risk presentations on consumer decisions.

In the next section we analyze deviations of actual insurance decisions from expected utility rule using the concepts from prospect theory and mental accounting principles. In section 3 the hypotheses are outlined. Section 4 deals with the design of the questionnaire experiments. The findings are presented in section 5 and discussed in section 6. In section 7 we provide implications for marketing and public policy. Finally, suggestions for further research are proposed in section 8.

2. THEORY

2.1 Standard utility theory and actual insurance decisions

From the perspective of standard utility theory and traditional microeconomics, insurance is purchased by risk-averse individuals from an insurer whose risk position is more diversified. A rational, risk neutral consumer would purchase coverage at a price that is equivalent to the expected loss. If he is risk averse, he would be willing to pay an additional risk premium. This is a precondition for risks to be insurable. Even an insurer who is able to diversify the risks perfectly and runs his business without profit must charge expected value plus administrative expenses. Consequently, in this context the existence of insurance markets could hardly be explained if a majority of individuals would be risk neutral or risk seeking (Schoemaker 1980, p. 67).

In sharp contrast, an overwhelming number of laboratory and field experiments (Kunreuther et al. 1978; Kahneman and Tversky 1979, Schoemaker 1980; Currim and Sarin 1989) show that the behavior of many individuals is consistent with risk seeking in the loss domain (i.e., they do not buy insurance voluntarily even if it is highly subsidized). Even allowing for risk seeking in the loss domain, many individuals’ behavior appears to be inconsistent with standard utility theory due to factors such as weighting of probabilities, framing, relying on recommendations of friends (see Kunreuther 1976, pp. 237-239; Kahneman and Tversky 1979).

2.2 Explaining insurance decisions via prospect theory

Prospect theory (PT) (Kahneman and Tversky 1979) has been one of the most influential approaches in the area of descriptive decision theory. This may partly be due to its similarity in structure with expected utility theory coupled with its ability to characterize actual behavior when choices are made under uncertainty. The evaluation of alternatives is explained by first determining the utilities of possible outcomes and then weighting these outcomes by a weighting function.

Unlike expected utility theory, two phases of decision making are hypothesized in PT: a coding phase (framing) and an evaluation phase. In the coding phase, the prospect may be simplified, common features of prospects may be segregated, and all outcomes from relevant alternatives are transformed into differences from a reference point. In the evaluation phase, the outcomes are processed on the basis of a value function, which is concave above and convex below the reference point, implying risk aversion with respect to gains and risk seeking in the domain of losses. Prospect theory also makes the assumption of loss aversion which means that the steepness of the value function is higher in the loss domain than in the gain domain (Figure 1).

In PT, probabilities are transformed into decision weights. The following characteristics of the PT weighting function are of central importance for our experiments: medium-sized probabilities are underweighted, small probabilities are overweighed, and the function is ill-defined for very small (near zero) and very large (near one) probabilities. Very small probabilities fall below a certain threshold value, probabilities near one are not distinguished from certainty.

In summary, PT provides an analytical framework which explains experimental results indicating that people are risk seeking in the loss domain, thus inhibiting demand for insurance. But, it also shows potential counterweights: framing effects and overweighing of small probabilities. These factors may therefore be relevant for marketing insurance policies.

Despite the fact that PT now exists for almost twenty years in a heavily researched area, it is the appropriate theoretical basis for many of the questions dealt with in this article, as will be shown in the following. First of all, it has been empirically substantiated through recent controlled experiments. Currim and Sarin (1989, p. 39) concluded that "the properties of the value functions and functions postulated in the prospect theory do hold in our data". PT also outperformed the standard expected utility model in direct comparisons of predictive power in all of their studies (Currim and Sarin 1989, pp. 32, 35 and 38).

2.3 Mental accounting

For the analysis of bundling issues, Thaler’s (1985) mental accounting approach, based on the PT value function, offers important insights. Thaler argues that customers’ joint versus separate valuation of compound outcomes can be predicted by a "pain reduction principle". If products are bundled rather than presented separately, two losses are presented simultaneously. Applying the "pain reduction principle", compound outcomes will in this case be valued jointly (integrated) (Thaler 1985, pp. 201-202). Figure 1 depicts the PT value function and shows that two separate losses (-A) and (-B) are less painful if they are valued jointly [V(-(A+B))] than individually [V(-A)+V(-B)].

2.4 Risk presentation, distribution channel, and bundling of insurance and commodities as marketing variables

Two aspects relevant for marketing insurance policies will be analyzed in the following: (1) how the exclusive offering of insurance compares to the joint offering of insurance with the insured commodity, an alternative only available if insurance is distributed via the dealer of the commodity, or jointly offered with another insurance policy, and (2) how the presentation of probabilities of multiple insured risks (aggregated or desegregated, for one period or for more than one period) affects willingness to pay for insurance. Relating the questions to the classical marketing mix factors, question (1) is closely related to distribution (place) and product policy, question (2) is related to communication policy (promotion).

3. HYPOTHESES

The following hypotheses underlying our experiments are stated and briefly related to the theoretical literature.

Hypothesis 1 (H1): Willingness to pay (WTP) for insurance will be higher if insurance is sold together with the insured commodity or with another (related) insurance product. WTP is higher, the more expensive the commodity/other insurance is.

The theoretical justification for H1 is the value function of PT together with Thaler¦s (1985) mental accounting explanation. Looking at Figure 1, the outcome (-A) is the price of the insured object, whereas (-B) is the premium for the insurance policy. Due to diminishing sensitivity for the payments, [V(-(A+B))] is much smaller than [V(-A)+V(-B)], thus a joint presentation of the insurance and insured object allows for a pain reduction with respect to the bundle’s price. If the price for the object is constant (ceteris paribus), WTP for the insurance policy will therefore be higher in the bundle than if it is presented alone. Or to put it differently, payments which will be evaluated far away from the reference point will be weighted less: the main reason why integration of losses reduces pain.

Hypothesis 2 (H2): If an insurance policy covers multiple (independent) risks, each of them having very small probabilities of loss, presenting risks in an aggregated form with respect to probabilities and time period of coverage leads to higher WTP than presenting them in a desegregated form.

H2 refers to the fact that very small probabilities may fall below a certain threshold value, whereas small probabilities tend to be overweighed. Aggregating very small probabilities to small ones may therefore lead to a higher weighting of potential losses and in turn to higher WTP for insurance.

Hypothesis 3 (H3): Willingness to pay for an insurance policy will be lower than its expected value.

This hypothesis refers to the gambling on losses property of PT value function and is a replication of other above-mentioned experiments. For this hypothesis to be confirmed it is necessary that the gambling on losses as suggested by the PT value function will not be (over-) compensated by over-weighting of probabilities in certain intervals of the PT weighting function.

4. EXPERIMENTAL DESIGN

4.1 Experiment 1: bicycle theft insurance

A hypothetical bicycle theft insurance policy is presented (a) alone, (b) in a bundle with the insured bicycle, or (c) in a bundle with household insurance (300 DM, approximately: $ 180) to three separate groups of respondents. This is a one-factorial design with three factor levels.

The bicycle is described as being brand new (2,000 DM). In cases (a) and (c) the insurance is offered the following day. In case (b) it is offered with the purchase. The probability that the bicycle will be stolen in one year is specified as being 10% for all three treatments. The insurance covers 80% of the damage (1,600 DM) leading to an expected value of the insurance of 160 DM. The insurance period is one year. All respondents were asked to state WTP for this insurance for one year.

4.2 Experiment 2: car repair insurance

A hypothetical car repair insurance policy covering all failures of engine, gears, and body is presented alone ((a) and (b)), together with the used car ((c) and (d)), or together with a full comprehensive liability, damage, and theft insurance (3,000 DM) ((e) and (f)) to six separate groups. The risk that repair will be necessary is presented either in aggregated form for all failures and for the full insurance period (two years) ((b), (d), (f)) or in desegregated form and for one year ((a), (c) and (e)). In (c) and (d) the insurance is called a warranty.

Experiment 2 is a two-factorial design with three and two factor levels for presentation of insurance and risks, respectively (3 x 2 design). The overall probability that one of the failures will happen during the full insurance period (2 years) is 8%. The probability that one of the failures will happen in one year is 2.5%, 1%, and 0.5% for engine, gears, and body failures, respectively. All damages would lead to repair costs of 5,000 DM. Insurance covers 100% of the repair price. Expected value of the insurance is therefore 400 DM (not discounted). All respondents were asked to state WTP for purchasing insurance for two years.

FIGURE 1

PROSPECT THEORY VALUE FUNCTION AND MENTAL ACCOUNTING IN A TWO LOSSES CASE

4.3 Subjects

The experiments were carried out with students from Goethe-University Frankfurt a.M., Germany, and from Humboldt-University Berlin, Germany, in January/February 1997. A vast majority of them are business or economics students. 100 students participated in experiment 1, 177 in experiment 2, the participants in each of the experiments almost equally divided into the three and six groups in experiments 1 and 2, respectively.

4.4 Procedure and instructions

Questionnaires were distributed in classrooms during several marketing courses. The respondents had approximately 15 minutes to respond to the questions and to fill out an additional form concerning age, gender, field of study, practical and theoretical knowledge about insurance, knowledge in decision theory, and involvement with insurance decisions. In insurance decisions, involvement may be strongly related to how concerned people facing risks are. Measurement of the last dimension was being obtained by a simple indicator: "I care/ I don’t care much about risks". This dimension turned out to be of central importance for explaining insurance decisions in our studies (see section 5). The concept and its measurement therefore should be explored in more detail in future studies. Finally, there was a debriefing form indicating the hypothetical nature of the described insurance products. Twenty and thirty-five students, respectively, were invited for a group discussion after completing the bicycle theft insurance and car repair insurance questionnaire, fifteen of them were, after completing the car repair insurance questionnaire, also asked for written comments on how they determined WTP.

TABLE 1

WTP FOR BICYCLE THEFT INSURANCE IN DIFFERENT CONTEXTS IN THE TOTAL GROUP AND IN THE SUBGROUPS OF CONCERNED AND NON-CONCERNED PERSONS

5. EXPERIMENTAL RESULTS

5.1 Data analysis and statistical methods

Data analysis utilized SPSS 7.0 for Windows 95. For H1 and H2 one-way and two-way analyses of variance implying a non-directional test over all treatments were calculated for both samples in their entirety as well as for the subgroups of non-concerned and concerned persons. The subgroup analyses lead to a much better understanding of the effects that certain factors have on WTP. Because H1 and H2 are directional, one-sided significances of differences between single treatments were also determined for the whole group as well as for the subgroups using joint Bonferroni parameter estimates, controlling for the effects of multiple pairwise comparisons. (Note: Only fixed significance levels (e.g. 5%) can be calculated for Bonferroni parameter estimates.)

For H3 confidence intervals were calculated for the comparison of actual WTP and expected values for the entire groups and over all treatments. In order to gain more detailed information on different reactions to risk, we also calculatd the percentage of people not willing to pay any amount for insurance. These individuals are called threshold-persons since they behave as if the probability of a loss is below some critical threshold level and hence they assume that the event "will not happen to me". The WTP also enables us to classify individuals as risk-loving, risk-neutral or risk-averse.

5.2 Results of experiment 1 (H2 not tested, here)

H1: Table 1 shows the means of WTP in the three different treatments for the total group (n=100) as well as for concerned (n=44) and non-concerned (n=55, one missing value) persons.

The results show the hypothesized effects for the total group and - more straightforward - for the subgroup of concerned persons. Consistent with the mental accounting explanation, WTP is highest when theft insurance is sold together with the bicycle (integration of two losses), WTP is lower if it is sold together with household insurance (integration of two losses, but the payment for the other insurance is smaller than that for the bicycle), and it is lowest if it is sold on a stand-alone basis. However, no statistically significant differences were found in one-factorial analyses of variance for the total group (sig. of F: 0.713) as well as for the subgroup of concerned people (sig. of F: 0.142). The difference between WTP in the basic condition (insurance alone) and WTP when insurance was bundled with the bicycle was significant at a 10% level, one-sided, for the subgroup of concerned subjects (joint Bonferroni parameter estimate).

H3: This hypothesis was strongly confirmed for the total group, even when all treatments are included in the analysis. This test is "harder" than a test that only includes the basic condition which leads to the lowest WTP. The tendency to reject this hypothesis is enlarged by including the two treatments where insurance is bundled that leads to higher WTP. WTP for theft insurance came out to be (over all treatments) much lower (n=100; mean=59.44 DM) than expected value (160 DM). The upper limit of the one-sided confidence interval for =0.01 was 72.45 DM, which is far below 160 DM.

Looking at the entire sample as well as the subgroups of concerned versus non-concerned people, the following percentages of threshold-persons (WTP=0), risk-lovers (WTP<160), risk neutral (WTP=160), and risk-averse (WTP>160) persons were found in the bicycle insurance experiment (Table 2).

Note the somewhat larger percentage of threshold persons in the non-concerned group than in the concerned group.

5.3 Results of experiment 2

In Table 3 WTP for insurance in the different experimental treatments: factor 1, bundling, and factor 2, risk-aggregation, are shown for (a) the total group, (b) the subgroup of concerned, and (c) the subgroup of non-concerned persons.

Overall, the results seem to support H1 and H2 but they have to be differentiated according to the subgroups. Looking at the data, bundling repair insurance with comprehensive insurance does not lead to higher WTP (in DM) than for insurance alone, for either the total group (see Table 3 (a): 203.10 DM compared to 210.10 DM) or for the subgroups (Table 3 (b): 220.60 DM compared to 213.40 DM in the concerned subgroup; Table 3 (c): 186.10 DM compared to 214.60 DM in the non-concerned group where WTP for the bundle is even much lower). Calling the insurance a warranty and bundling it with car sale leads to a higher WTP than selling insurance alone, for the total group (Table 3 (a): 264.50 DM compared to 210.10 DM in the total group) as well as for the subgroup of concerned subjects (Table 3 (b): 311.30 DM compared to 213.40 DM). Aggregation of probabilities yielded a higher WTP when compared with separate risks in the total group (Table 3 (a): 245.80 DM compared to 206.70 DM) as well as in the subgroup of non-concerned persons (Table 3 (c): 243.20 DM compared to 171.80 DM).

The statistcal significance tests provide additional confirming evidence of these points. Neither main effects (factor 1, sig. of F: 0.181; factor 2, sig. of F: 0.194) nor interactions (sig. of F: 0.933) were found to be significant in the two-factorial analysis of variance for the total group. Only the difference between the two levels of factor 2 (separate risks versus aggregation of probabilities) was significant at a 10% level, one-sided (joint Bonferroni parameter estimate). Much stronger significance levels were found in the two subgroups. The two-way analyses of variance led to significant results for factors 1 (sig. of F: 0.096) and 2 (sig. of F: 0.073) in the subgroups of concerned and non-concerned subjects, respectively.

TABLE 2

PERCENTAGES OF DIFFERENT REACTIONS TO RISK IN THE TOTAL GROUP AND IN THE SUBGROUPS OF CONCERNED (N=44) AND NON-CONCERNED (N=55) PERSONS

TABLE 3

WTP FOR DIFFERENT CONTEXTS, RISK PRESENTATIONS, AND SUBGROUPS

TABLE 4

PERCENTAGES OF DIFFERENT REACTIONS TO RISK IN THE TOTAL GROUP AND IN THE SUBGROUPS OF CONCERNED (N=99) AND NON-CONCERNED (N=74; FOUR MISSING VALUES) PERSONS

The difference between the repair insurance alone condition and the warranty with car condition was significant at a 5% level, one-sided, for the subgroup of concerned persons, the difference between the two separate versus aggregated risks conditions was significant at a 5% level, one-sided, in the group of non-concerned persons (joint Bonferroni parameter estimates). The surprisingly reverse results of the bundling treatment for non-concerned persons in the separate risks condition (Table 3 (c), column 1: 201.40 DM for insurance alone, 198.10 DM for car with warranty, 104.20 DM for bundle with comprehensive insurance) was found not to be significant (sig. of F: 0.256; joint Bonferroni: not significant on a 10% level).

H3 was also confirmed in experiment 2. WTP for repair insurance came out to be (over all treatments) much lower (n=177; mean=226.36 DM) than its expected value (400 DM). The upper limit of the one-sided confidence interval for =0.01 was 260.72 DM, which is far below 400 DM. The reasons why WTP is so low will be outlined in the discussion.

Looking again at the total group as well as the subgroups of concerned versus non-concerned people, the following percentages of threshold-persons (WTP=0), risk-loving (WTP<400), risk neutral (WTP=400), and risk-averse (WTP>400) persons could be found in the car repair insurance experiment (Table 4).

6. DISCUSSION

The bundling hypothesis H1 could be confirmed for the subgroups of high-involved/ concerned persons and for bundling of insurance with objects in both experiments 1 and 2 (in experiment 2 this effect may have been enlarged or lowered by labeling the insurance warranty). It had to be rejected for low-involved subjects and for the insurance-insurance bundles. A possible explanation for the last finding could be derived from some respondents’ statements for experiment 2: They argued that they did not want to buy repair insurance because purchasing expensive comprehensive insurance was presupposed: "I would not have bought the comprehensive insurance in reality." This effect - together with students’ budget constraints - might have overwhelmed the "integration of losses" effect.

The risk-aggregation hypothesis H2 was confirmed for the entire sample in experiment 2 and even more significantly for the subgroup of low-involved /non-concerned persons. The different impact of bundling and risk presentation on concerned versus non-concerned subjects needs further investigation. In the following we will only give tentative explanations: Low involvement with respect to insurance decisions may lead to high threshold probability levels for many of the individuals in the group. The probabilities stated in the separate risks condition in experiment 2 may have been already big enough for concerned subjects, but they may have been below the threshold value for non-concerned persons. For at least some subjects in that subgroup the aggregated probabilities may instead have passed the threshold leading to a significant effect of factor 2.

This explanation is consistent with the experimental finding of McClelland, Schulze and Coursey (1993) who indicated that threshold values may vary to a large extent between people, thus leading to a bimodal response mode. Evidence for the appropriateness of the threshold explanation can also be derived from answers of respondents confronted with the question how they determined their maximal WTP. Some of the respondents argued that the probability that repair will be necessary or expected value of repair expenditures was "too low" or even stated that is was "below their relevance threshold". Most of these subjects did not buy the insurance at all.

Evidence for the threshold explanation could furthermore be derived from statistical analyses. First, the number of people not willing to buy the insurance at all was higher for the group of non-concerned people (34.5%) compared to the group of concerned (15.9%) in the bicycle experiment indicating that thresholds may be more relevant for low-involved people (see also Table 2). We recoded the continuous WTP variable into two categories, WTP=0 and other values, and found the Pearson chi²-value to be significant (sig.: 0.092, two-sided) in the cross-tabulation of the involvement variable and the dichotomous WTP variable. Second, in the car repair experiment, the number of concerned versus non-concerned persons having a zero WTP differed significantly in the separate risks conditions (where thresholds are most relevant). Here, the non-concerned persons (43.2%) more frequently refused to pay anything for the insurance compared to the concerned (22.7%) persons (Pearson chi², sig.: 0.083, two-sided). Finally, at least in the car repair insurance experiment there is a definite gap between WTP=0 and the next higher value which is 100 DM, here. This also lends support to the threshold concept.

The involvement explanation may also account for the findings with respect to hypothesis H1. Non-concerned subjects may produce a large error term because they do not really care about the insurance decision and thus do not calculate values of objects, losses, and insurance premiums at all, perhaps relying on some kind of an affect referral heuristic (Wright 1975; see also Bettman 1979; for simplified heuristics in financial/insurance decisions see Kahn and Baron 1994; Hogarth and Kunreuther 1995). A rejection of the null hypothesis may therefore be difficult if these people are included in the analysis. Subjects belonging to the high involvement group may instead be calculating values and in turn integrating losses, therefore being more affected by bundling.

Hypothesis H3, based on the well-known fact that people tend to gamble on losses, could be clearly confirmed in experiments 1 and 2 for the total group. WTP in relation to expected value was lowest in experiment 1. The ratio of WTP/EV was 0.37 for the bicycle theft insurance experiment (59.44/160) compared to the ratio of 0.57 (226.36/400) in the car repair insurance experiment. This lower ratio for the bicycle theft insurance may be due to the aversion of deductibles by individuals because of loss segregation (see e.g. Johnson, Hershey, Meszaros and Kunreuther 1993). Note that for the bicycle theft insurance only 80% of the loss is covered by the insurance. WTP is considerably lower than expected value in experiments 1 and 2, the largest groups of subjects always being those either not willing to pay anything for insurance or those being risk-loving (see Tables 2 and 4). This leads to the question if there may be additional effects to the risk seeking property of the PT value function in the loss domain, which may lower WTP.

Other reasons leading to a lower WTP may be that students have budget constraints, that they perceive the probability to be lower than what is stated in the questionnaire, and that they perceive the amount of potential loss as being smaller. We found indirect evidence for all of these explanations. In the group discussion after experiment 1, some students stressed the point that they cannot afford a bicycle for 2,000 DM and therefore had difficulties in imagining this as a real decision situation. Some subjects also explicitly mentioned problems with the stated probabilities. Arguments such as: "I always carry my bicycle into the basement", "I am living in a safe neighborhood", and "I use two locks in order to prevent my bike from being stolen" indicate that these individuals do not accept the 10% probability for theft stated in the experiment.

In the written comments after experiment 2, one respondent stated that his budget urges him to live a bit riskier than he would like to. Others argued that they would only buy a used car if they had first tested it for technical defects. Some had a car mechanic among their friends thus arriving at the conviction that repair costs would be lower for them in reality. During the group discussion after experiment 2 some expressed their reluctance to deal with the somewhat artificial probabilities stated in the experiment. For example, they preferred to rely on the information that the car is only three years old instead of using the probability information. Most of them would have been more comfortable with more familiar indicators on the probability that repair will be necessary: total mileage of the car, brand, country of origin (e.g. Mercedes with a total mileage of 10,000 versus Italian car with 100,000). A recent paper by Gigerenzer and Goldstein (1996) shows that people are in fact able to make precise inferences if they are confronted with "natural" information: American respondents were able to give good estimates of the size of (unknown, medium-sized) German cities on the basis of indicators such as position of the soccer team, state capital, Intercity trainline, and exposition site.

7. MARKETING AND PUBLIC POLICY IMPLICATIONS

Some insurers seem to be aware of the fact that joint offering of insurance and insured commodities may offer advantages (H1). Household appliances and cars are often sold together with repair insurance - called warranty. Basically, the insurer offers to prolong the term of the regular warranty for a payment in addition to the price of the car or the appliance - similar to the hypothetical situations in experiments 1 and 2. Airplane and train tickets are often sold together with baggage and health insurance. Assuming that the effect is stable, further applications could be thought of: e.g. specialized accident or liability insurance could be offered together with dangerous sports equipment such as paragliders, ski, professional mountain bikes.

The aggregation versus desegregation issue with respect to multiple risks covered in an insurance contract has to be handled carefully by insurers. It is not easy to determine some kind of an optimal aggregation level, because threshold values may heavily differ between concerned and non-concerned persons and possibly between different types of risks. In one situation, aggregation may enlarge WTP, in other situations it may lower it. Because predictions are difficult, insurers may want to engage in market research activities in order to get detailed person- and situation-specific information. At the moment, many insurance representatives do not inform their customers about the probabilities of risks to be insured. But this does not change the importance of bundling decisions for insurers: aggregation or desegregation of risks may be important in the case of ambiguous probabilities as well (Hogarth and Kunreuther 1989). The issue of risk-presentation may also be of relevance for regulatory agencies deciding on the presentation of certain risks.

Because the integration of losses effect appears to be most reliable for concerned subjects leading to higher WTP for insurance bundled with commodities, insurers may be interested in strategies enlarging involvement for insurance decisions. They may also use involvement with risks and insurance as a relevant segmentation criterion leading to differentiated marketing strategies. Insurers may have a hard time selling insurance policies to risk-loving or even threshold-people (this group being bigger among non-concerned persons). However, insurers may want to develop a detailed understanding of how insurance decisions are made by different groups of persons leading to very different reactions because this may facilitate differentiated marketing strategies.

8. FURTHER RESEARCH

An important reason for considerably lower WTP and for quite low significance levels (10%) for some of the effects studied in our experiments may be that questionnaires are not the best instrument for revealing peoples’ preferences in terms of WTP: the situation is hypothetical and effects may be weakened by a large error term. The effects of bundling of insurance and insured commodities might be more effectively studied using preference revealing mechanisms such as the Becker, DeGroot and Marshak (1964) mechanism or double oral auction procedures. This may lead to a reduction in the error term, to more reliable results and stronger (significant) effects. The bundling issue may also be addressed using real objects in laboratory experiments or in controlled field experiments, thereby leading to higher involvement of the respondents, and hopefully to higher significance levels for the bundling effects in the whole group of respondents. It may also be necessary to control for different involvement levels more explicitly in future experiments, e.g. by pre-selecting concerned subjects, or inducing involvement. Therefore it is necessary to develop a scale for measuring that concept more precisely. Kapferer and Laurent (1985) as well as McQuarry and Munson (1987) introduce items for measuring personal involvement. But the concept has to be modified in order to capture the concepts of being "concerned" or "non-concerned" with respect to insurance decisions.

The issue of risk presentation suggests another set of laboratory experiments. These experiments may take into account that insurance representatives may not (be able or willing to) tell customers how probable are the losses for which they should insure against. People in turn may be ignorant or at least ambiguous concerning the risks they are facing. The effects of ambiguity and ignorance have been addressed by Hogarth and Kunreuther (1989, 1995). Addressing their findings, the results of McClelland, Schulze and Coursey (1993), and the issue of different involvement-levels of customers, may lead to better predictions regarding WTP for insurance in aggregated versus desegregated risks conditions.

Bundling of insurance with insurance (bundling of coverage), a central question for the product policy of insurers, needs to be further investigated. Bundling does not only affect the perception of probabilities (via the aggregation effect) but it may also lead to an integration of losses as was stated in H1 but not confirmed. It may, on the other hand, be affected by the subjects’ budget. Experiments controlling the budget effects therefore may offer important insights: different insurance bundles may be appropriate for different segments of customers. Whereas high-income customers should perhaps be confronted with highly bundled coverage, low-income customers may be offered insurance for specific risks.

The segmentation of customers may therefore prove to be an important research question regarding insurance marketing decisions. What are the relevant personal traits besides involvement? Also, is involvement, the extent to which the people are concerned, a stable determinant of insurance decisions? Another challenging question may be how thresholds in the perception of low probabilities are influenced by interactions between kinds of risks or consequences faced with (bicycle theft or nuclear accident), degree of perceived ambiguity or ignorance, and respondent’s traits.

LITERATURE

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Gigerenzer, Gerd and Daniel Goldstein (1996): Reasoning the Fast and Frugal Way: Models of Bounded Rationality, in: Psychological Review, Vol. 103, pp. 650-669.

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