درباره اولویت برای سیاست های پوشش کامل بیمه: چرا مردم بیش از حد بیمه خریداری می کنند؟

One of the most intriguing questions in insurance is the preference of consumers for low or zero deductible insurance policies. This stands in sharp contrast to a theorem proved by Mossin [Mossin, J. (1968). Aspects of rational insurance purchasing. Journal of Political Economy, 76, 553–568], that under quite common assumptions when the price of insurance is higher than its actuarial value, then full coverage is not optimal. We show in a series of experiments that amateur subjects tend to underestimate the value of a policy with a deductible and that the degree of underestimation increases with the size of the deductible. We hypothesize that this tendency is caused by the anchoring heuristic. In particular, in pricing a policy with a deductible subjects first consider the price of a full-coverage policy. Then they anchor on the size of the deductible and subtract it from the price of the full-coverage policy. However, they do not adjust the price enough upward to take into account the fact that there is only a small chance that the deductible will be applied toward their payments. We also show that professionals in the field of insurance are less prone to such a bias. This implies that a policy with a deductible priced according to the true expected payments may seem “overpriced” to the insured and therefore may not be purchased. Since the values of full-coverage policies are not underestimated the insured may find them as relatively better “deals”.

In a seminal paper, Mossin (1968) showed that under quite common assumptions, full-coverage insurance is not optimal. More precisely, he demonstrated that if the price of insurance is proportional to but higher than the expected payments made by the insurer and if the insured is risk averse, then full coverage is sub-optimal for the insured. He also showed that there exists a policy with a strictly positive deductible, which dominates the full-coverage policy. Mossin’s normative logic stands in contrast to the high demand for full-coverage policies and policies with very low deductibles. For example, almost all liability insurance policies provide full coverage or a zero deductible. Consider also collision damage insurance for rental cars. While specific rates vary by location, a typical collision damage waiver (CDW) for a rental car costs on average $25 per day, which is equal to $7200 on an annual basis. In stark contrast, comprehensive automobile insurance for one’s own car does not cost more than $1000 per year in most locations in the US. The difference in price is clearly non-trivial. Why are people willing to pay such high rates for CDW when renting a car? Another example arises from deductibles on automobile insurance policies. The deductible on automobile insurance is often as low as $100 and almost always below $500, which means that consumers are insured against losses of $500 or less. Cummins and Weisbart (1978) report that when Herbert Denenberg, Pennsylvania’s Insurance Commissioner during the 1970s, tried to raise the minimum auto insurance deductible from $50 to $100, he was forced to withdraw this idea by massive consumer outcry. Merchants who sell various electrical products such as cell phones costing $200 or less also offer insurance against loss, for a non-trivial additional cost. Consumer purchases of such insurance do not seem to be rational even when those policies include a service component. Companies offering such warranty in their service policies stand to make a high profit due to such consumer preferences. According to a Harvard Business School case (see Burns, 2004), to a first approximation Circuit City sold electronics at cost and made its profits on extended warranties. The situation is even more salient in medical insurance. For example, the US Bureau of Labor Statistics reports that during the years 1994–1997, 34% of full time employees in the private sector enrolled in non-HMO medical care organizations had no deductibles in their medical plans. This percentage rose to 42% for “Preferred provider organizations” (US Department of Labor, 1999). Note also that HMOs typically have zero deductibles. An attempt to explain the preference for full coverage was offered by Pashigian, Schkade, and Menefee (1966), who used US aggregate data as well as detailed data of automobile insurance purchases in Missouri. They found that the levels of deductibles chosen by clients are too low to be explained by expected utility theory. According to Pashigian et al. these deductibles can be reconciled with expected utility only if the insureds anticipate two or more accidents per year. This figure is considerably higher than the number of accidents actually expected by the average driver. Pashigian et al. conclude that: “the observed selection of deductibles can be explained [only] if there is a systematic tendency to overestimate the objective probabilities of an accident greater than the deductible.” (p. 40). In light of the difficulty of standard utility theory to explain the demand for low deductibles, Ben-Arab, Briys, and Schlesinger (1996) try to explain “excessive” insurance purchasing by assuming a multi-period habit-formation utility function. This type of utility function introduces a greater desire to smooth consumption over time than a “usual” one-period utility. It therefore gives rise to a higher incentive for insurance purchasing, and tolerance of lower deductibles. Wakker, Thaler, and Tversky (1997) argue that people buy too much insurance since they are averse to probabilistic insurance. Such behavior is not consistent with expected utility maximization. Other researchers such as Braun and Muermann (2004), explain it by aversion to regret.2Schoemaker (1976) demonstrates that when faced with decisions described as insurance against hypothetical losses, subjects chose full coverage alternatives over those with deductibles. Nonetheless, when the same choices were framed as lotteries, their choice pattern was reversed.3 Schoemaker’s findings imply that framing affects the way people evaluate insurance alternatives. Likewise, in an elaborate experimental design, Johnson, Hershey, Meszaros, and Kunreuther (1993) find that students preferred insurance alternatives framed as “rebates” rather than as policies with a deductible. Framing clearly affects the way people make choices among insurance alternatives, but there may be other factors at play when people evaluate the monetary value of alternative insurance policies. In this paper, we provide a new explanation based on the anchoring heuristic for the preference for full coverage and test it experimentally.4 We argue that the price of a full-coverage policy is a natural starting point for evaluating a policy with a deductible. Insureds continue from this starting point and calculate the price of policies with partial coverage by anchoring on the value of the deductible. In anchoring on the amount itself they neglect to take into account the probabilities associated with actual damages. Since they do not adjust for the probability that damage will actually occur, they end up underestimating the price of such policies. Insurance companies are unlikely to make such errors and hence the prices they set for policies with a deductible may seem unjustifiably high to customers. On the other hand insureds are less likely to underestimate the values of full-coverage policies, and hence they may deem such policies as more adequately priced then the partial coverage policies offered by the insurance companies, and hence prefer them to policies with a deductible. We used insurance sellers as subjects in the experiments reported in this paper. We assumed that insurance sellers would pay more attention to pricing decisions than buyers would pay to their purchasing decisions. The reason is that sellers need to think of both their potential customers as well as their competitors in making their decisions. However, we have no reason to expect sellers to be less prone to biases such as the anchoring heuristic, unless they have had some real experience in selling insurance policies in the past. Research on the insurance behavior of both buyers and sellers indicate that biases in terms of probability assessment that were found in studies of insurance in the context of natural disasters as early as 1977 (see Kunreuther et al., 1978) still persist today.5 We conducted three experiments to test our hypothesis. In all these experiments, we asked subjects to play the role of insurance sellers and to price policies with and without a deductible. They competed with other sellers and their objective was to set prices so as to maximize their profits. We compare the prices the subjects set relative to the true expected damages under each policy. We argue that if individuals underestimate the value of a policy with a deductible, the prices they set for policies with a deductible would be low relative to the expected damages covered under full-coverage policies. In the first two sets of experiments, subjects were amateur insurance consumers, and in the third the subjects were professionals in the field of insurance. In all contexts, subjects were requested to price a policy of full coverage and a policy with a specific deductible (D = 100 in the first and third experiment, D = 60 or D = 120 in the second experiment). The paper is structured as follows. In Section 2, we review some of the literature on anchoring. In Sections 3, 4 and 5 we present the experiments. The first experiment, presented in Section 3, used Israeli MBA students as subjects. In Section 4 we present the results of the second experiment, which is similar to the first experiment with two variations. First, we added an American sample of MBA students as a test of the generalizability of the results across countries. Second, instead of a single policy with a deductible, we split the sample and presented each group with a different deductible to allow a stronger test of our hypothesis about the effect of anchoring. Section 5 presents the results of the third experiment, in which professionals in the field of insurance were the subjects. Section 6 concludes.

Our results show that amateurs tend to underestimate the value of policies with a deductible. This bias occurs because subjects are inclined to estimate the value of such policies by calculating the value of an equivalent full-coverage policy, and then subtracting the deductible. In this case, the higher the deductible, the higher the undervaluation of the policy. This bias emanates from subjects’ tendency to anchor on size of the deductible without adjusting enough. The findings suggest that in purchasing insurance policies subjects’ behavior is affected by the anchoring heuristic (Chapman and Johnson, 2002 and Kahneman, 1992), which leads consumers to purchase insurance with low or no deductibles. According to Epley and Gilovich (2006) the anchoring literature deals either with a “phenomenon” (namely, estimates gravitate toward an anchor) or with a “process” where people adjust their final estimates from an initial anchor. They further argue that true insufficient adjustments occur when people adjust insufficiently from values they “generate themselves as starting points from values known to be incorrect but close to the target value.” (p. 312). The authors claim that such self-generated anchors help simplify the complex cognitive process involved in making judgments. Along these lines, it appears that our subjects might have gone through a similar process. They were not provided with an anchor but the amount of deductible was construed by them as a good enough estimate for the price of a policy with a deductible even though they did not verify that it was the correct value. It definitely helped them come up with a plausible value without engaging in an effortful evaluation and they figured out that the error, if existed, could not be substantial. We also find that in comparison with amateurs, professionals are less likely to exhibit the above bias. Professionals are likely to value and price deductible policies correctly (i.e., according to the true expected payments), whereas the general public (amateurs) may find the prices the professionals set for policies with a deductible to be too high compared with their own underestimated expected payments. Note that the professionals in our studies had a similar academic background to that of the amateurs. Yet, the professionals’ experience helped them perform better than the amateurs in the present quantitative experimental setting. Possibly, the professionals’ experience in the field minimizes the tendency to anchor on the deductible when evaluating policies with deductibles. The preference of subjects for low deductibles is often interpreted as an indication of high-risk aversion. Our results suggest that such behavior can also result from cognitive biases. One may argue that such a bias may not have significant effects on market behavior since the more sophisticated insurance sellers may eventually lead the market to a more rational equilibrium. The truth may actually be the opposite. Even if professional insurance sellers are (relatively) immune from this bias, the fact that amateur consumers are affected by it has direct implications since two sides are needed for market transactions. A real life example can illustrate this argument. During the time we ran one of the experiments, the Direct Insurance Corporation, one of the largest insurance companies in Israel advertised insurance rates for car owners. The advertised rates for policies with different levels of deductible for a $30,000 2004 Toyota Corolla, for drivers whose age was 25 or higher, are displayed in Table 4.We used those publicly advertised rates and circulated a survey among MBA students enrolled in a graduate course on “Risk management and insurance” at the Hebrew University. We asked the students to indicate what level of coverage they would choose if they had a car of a similar value and were offered those rates. Forty three students responded to the survey. Twenty-two of them (51%) chose the lower three levels of deductible. Note that in raising the deductible from $137 to $180, an increase of $43, the insured saves $35. Practically, unless the insured is certain that he or she will have an accident, or is extremely risk averse; the lower deductible is not a highly valued alternative. By increasing the deductible from $180 to $245, an increase of $65, the insured saves $42; again unless there is a very high probability of an accident (71%), the higher deductible is more reasonable. We do not have data on the percentage of insureds that buy policies at each level of deductible from the Direct Insurance Company, but it is reasonable to assume that if the insurer advertised this price list, there was demand for all those deductibles. The fact that the insureds in our sample failed to comprehend the implications of the alternatives presented to them has direct market implications. It also complements other studies where investors made costly mistakes, such as in the study of Benartzi and Thaler (2002). Our findings have some ramifications both from the point of view of consumer groups and from the perspectives of regulators in the insurance industry. In the Benartzi and Thaler (2002) study investors appear not to have well defined preferences as their choices depend on irrelevant alternatives, and hence intervention in this market may be desirable. Whereas in their study the bias is due to framing, in our experiments as in Choi, Laibson, Madrian, and Metrick (2004), the bias stemmed from anchoring. A similar argument has been proposed by Gneezy, List, and Wu (2006) who showed that in certain situations subjects preferred the worst outcome of a lottery over the lottery itself. They attribute their finding to the uncertainty effect and claim that in some situations of uncertainty people tend to discount lotteries for uncertainty in a manner similar to the one we discussed above. Finally, the current findings may also be useful in analyzing behavior in other areas where high risk aversion is invoked as an explanation, such as the issue of the risk premium puzzle (Mehra and Prescott, 1985 and Mehra and Prescott, 2003). Future research should examine whether bounded rationality and computational limitations can further our understanding of behavior in other financial puzzles.