# Insurance Decisions (Or the Lack Thereof) For Low Probability Events

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Joel E. Urbany, Joan T. Schmit, and Daniel D. Butler (1989) ,"Insurance Decisions (Or the Lack Thereof) For Low Probability Events", in NA - Advances in Consumer Research Volume 16, eds. Thomas K. Srull, Provo, UT : Association for Consumer Research, Pages: 535-541.

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http://acrwebsite.org/volumes/6959/volumes/v16/NA-16

Marketing researchers have given little attention to the study of consumer insurance purchase decisions, in spite of the fact that such decisions reflect high uncertainty and potentially "irrational" behavior. The objective of this paper is twofold. First, we present several interesting problems regarding consumer insurance decision-making derived from the psychology, insurance, and finance literatures. Second, we examine one of those problems (consumers' perceptions of low probability events) in some depth, reviewing the available literature and presenting some initial insight obtained from exploratory interviews with a small group of consumers.

Decisions about insurance are one of the unavoidable necessities of adult life. Insurance purchase decisions are economically very important, with total premiums written by insurance companies in the United States exceeding $350 billion in 1986 (Insurance Information Institute 1987). In spite of the economic significance of insurance purchases, the high level of uncertainty associated with consumers' insurance decisions which makes the problem interesting (Formisano, Olshavsky, and Tapp 1982), and the extensive work already conducted in other fields, consumer researchers have given little attention to research problems associated with insurance decision-making. The purpose of this paper is to introduce some of the interesting issues and empirical paradoxes which have been identified in the study of consumer insurance decision-making. We consider briefly below some of the "biases" in insurance decisions which have been examined in other fields. We then discuss one issue, insuring against low-probability events, in greater detail, examining the empirical evidence available and determining the perceptions of such events among a small convenience sample of consumers.

ANOMALIES IN INSURANCE DECISION-MAKING

In the fascinating literature of consumer insurance decision-making, a number of biases have been identified which may have major implications for the insurance industry from both managerial and public policy perspectives. A review of the literature provides a "laundry list" of issues which are in need of greater study. Researchers have found, for example, that consumers are willing to pay more than would be anticipated according to expected utility theory for zero deductible insurance policies (i.e., in which a loss is totally covered) (Schoemaker and Kunreuther 1980; Pashigian, Schkade, and Menefee 1966). Researchers have also identified experimentally a low willingness to pay for comprehensive insurance at its expected value (Schoemaker and Kunreuther 1980) as well as a clear effect of "framing" (i.e., describing the insurance problem in different ways) on choice (e.g., Hershey and Schoemaker 19803. More recently, Hogarth and Kunreuther {1985) have found that ambiguity surrounding an estimate of an event probability has a clear effect on consumers' willingness to pay for insurance against that event and that the effect of ambiguity reverses sign when going from relatively low to relatively high probabilities. Researchers have only scratched the surface on these issues.

In this paper, we focus on an issue of theoretical interest in the decision-making literature (e.g., Slovic et al. 1977) which also has critical implications for the insurance industry: consumers' perceptions of low probability events and how those perceptions affect insurance decisions.

LOW PROBABILITY EVENTS

Research in the insurance literature has identified a strong aversion among consumers to insure against some events (floods and earthquakes) which appear to have a low probability of occurring (Kunreuther 1976; Anderson 1974). On the other hand, others have observed an "overwillingness" among consumers to purchase airline insurance to protect against the extremely unlikely possibility of a fatal airline accident (Eisner and Strotz 1961). In both cases, consumers appear to behave in a manner inconsistent with expected utility theory (see Kunreuther 1976). To confuse matters even more, researchers have experimentally studied consumer insurance choices for low probability events to provide a more careful explanation of the phenomenon, but have produced results which are diametrically opposed (Slovic et al. 1977; Hershey and Schoemaker 1980). A description of the field and experimental research addressing consumers' insurance purchase behavior for low probability events is presented below. We then discuss the rationale and method for the exploratory interviews which were undertaken in the current study.

Field Research

Several insurance studies conducted in the early 1970s have led to the common conclusion that, contrary to expected value theory, consumers are not well-protected against low probability events like natural disasters. In studying the impact of natural hazards on mortgage default, Anderson and Weinrobe (1986) found not a single loan file (from a sample of 332) for which earthquake insurance existed to cover property in San Fernando during the 1971 earthquake. In fact, only $32 million of the $553 million of property damage from the San Fernando quake was covered by insurance. Similarly, Anderson (1974) found that few flood victims of Hurricane Agnes in 1972 (four years after passage of the National Flood Insurance Program) had coverage. Of the $3 billion of damage caused by Agnes, only $5 million was covered through the federal program.

Like Anderson and Weinrobe, Kunreuther et al. (1973) identified perceptions and behavior among consumers living in "disaster-prone" areas of the country which clearly differed from that predicted by expected utility theory. The award-winning study (also described in Kunreuther 1976) involved interviews of 2,055 consumers in 43 areas subject to flooding and 1,006 consumers in 18 earthquake susceptible areas of California. In each group, approximately half of the consumers interviewed held insurance against the disaster. The following results were obtained in the study:

1. Over 30 percent of the two samples was unaware that insurance was available for these natural disasters;

2. As would be expected, the vast majority of the uninsured samples was unable to provide any estimate of insurance premiums. A surprisingly high percentage of the insured samples was uninformed about insurance costs as well;

3. For consumers who could estimate costs, event probabilities, and loss sizes, actual purchase behavior was not well predicted by expected utility theory.

Kunreuther explains the failure to purchase disaster insurance to be a function of limited knowledge, concluding that

...half of the uninsured individuals in flood-susceptible communities and two-thirds of the uninsured homeowners in earthquake susceptible areas are unable to estimate the insurance cost, damage, or probability of a future disaster. (p. 237)

As such, the problem appears to be one of information. In addition to (or perhaps as a result of) poor information about insurance, consumers may fail to consider (or may be unable to understand) the notion of event probabilities. Consumers' perception and handling of probabilities becomes a more important issue in light of other research which has found that insurance against airline accidents (another low probability event) is purchased by consumers more readily than would be predicted by consideration of the probability of the event (Eisner and Strotz 1961). We point out later the possibility that greater information availability might explain the "overpurchase" of flight insurance as well as the "underpurchase" of earthquake insurance (Tversky and Kahneman 1973).

Experimental Research

The basic inconsistencies between insurance decisions observed in the field and those predicted by expected utility theory led researchers into the laboratory to examine consumers' perceptions of insuring against low probability events in a more controlled fashion. In the two studies reviewed below, subjects made "simulated" insurance decisions, typically (although not always) using paper and pencil instruments. Slovic et al. (1977), in two very different contexts (the "urn" problem [The urn problem presented subjects with sets of insurance decisions in which the probability of a loss was represented by the number of blue balls in an urn full of red and blue balls. For example, one choice required the subject to envision an urn with 999 red balls and 1 blue ball. The random selection of a blue ball would lead to a loss of 1000 points in the game but such a loss could be avoided by purchasing insurance for a premium of 1 point.] and the "farm" game [The farm game was a creative computer simulation in which subjects played the role of a farmer who had to make various insurance decisions for his/her farm. Subjects simulated a number of years' performance, making decisions about crops, fertilizer, and insurance.]), found results very similar to Kunruether's field study: subjects demonstrated an aversion to insuring against low probability events, even with "fair" insurance premiums (i.e., equal to expected value). Slovic et al. offer two explanations for their results, one based on the way consumers value losses (a convex utility function) and another focusing on the way consumers perceive probabilities. The latter (which is most relevant here) suggests that consumers may have intuitive probability "thresholds." That is, a consumer may evaluate the likelihood of an event to be essentially zero because it is below a threshold probability which would signify when the consumer should become worried or concerned about that event. The authors present substantial evidence to support this point.

In direct contrast to Slovic et al.'s work, however, Hershey ag Schoemaker (1980)(HS) found the majority of their subjects deciding to purchase insurance for low probability events and far fewer choosing to insure against high probability events. HS presented their subjects with choice problems in the following form:

A. you stand a p chance of losing L dollars

B. you can buy insurance for S dollars to protect you from this loss

(CHOOSE BETWEEN A AND B),

where p is presented as a probability (e.g. .001) and S and L are stated in dollar amounts (S is the expected value of the loss, which is an actuarily fair insurance premium). The contrast to the Slovic et al. results is striking, particularly because HS used Slovic et al.'s questionnaire to replicate their (Slovic et al.'s) results with subjects who had already been through their own study. While HS argue that Slovic et al.'s results are suspect because of a less realistic methodology, that assessment does not reflect a true evaluation of differences in methodology which might have caused the different results. HS may have observed greater risk aversion (i.e., greater incidence of insuring against low probability, high loss events) than Slovic et al. because the losses presented in HS's problems were stated in dollar terms, which were likely more vivid to subjects. On the other hand, Slovic et al.'s "urn" studies presented subjects with probabilities in a very vivid, intuitive fashion (e.g., chance of pulling 1 blue ball out of an urn with 1000 balls, only two of which are blue). As such, subjects may have more clearly understood what the probabilities represented in the Slovic et al. study, classifying the lower probabilities below some threshold level of worry or concern. The true explanation of the opposing results of the two studies, however, is not readily apparent.

The "Probability Bias"

Central to the explanation of these divergent results is what HS refer to as a phenomenon of "probability bias." Little is known about the way consumers actually conceive of and utilize information about probabilities in decision-making. As noted earlier, Slovic et al. discuss a "worry" threshold. If small probabilities are categorized below such a threshold, they are believed to represent little or no concern or worry. In contrast, HS explain their finding that subjects were more likely to insure against low probability events than high probability events as an "overweighting" of low probabilities relative to high probabilities, which was reported to be consistent with prospect theory (Kahneman and Tversky 1979). However, Kahneman and Tversky's empirical illustration of "low probability overweighting" [Kahneman and Tversky (1979) used the following problem to demonstrate the overweighting of low probabilities: Choose between: A. A .001 percent chance of $6000 and B. A .002 percent chance of $3000. Subjects' overwhelming tendency to choose option A indicates an overweighting of the .001 probability relative to its objective probability (the choice implies that $6000(.001) is greater than $3000(.002).] implies that low probabilities may be weighted more than they objectively should be-not that they will be weighted more than high probabilities in a decision. Further, Kahneman and Tversky's data indicate that a probability of .001 may have more than "half as much" weight as a probability of .002 because the two probabilities are seen as being essentially the same (i.e., both are categorized as "very low"). As such, Kahneman and Tversky's work seems less relevant to the interpretation of HS's results and is actually more consistent with Slovic et al.'s conclusion that consumers may place probabilities into certain cognitive categories.

Other Issues

There are two other general issues which are relevant in considering the implications of the research described above. In the experimental studies, objective data about losses and probabilities of losses were presented to subjects in different manners. Since consumers rarely have explicit probabilities to work with in making insurance decisions, an important (and more basic) research issue relates to how consumers naturally think of and estimate probabilities. Secondly, an issue not addressed extensively in this literature is the "vividness" or memory availability of the event which is being insured. In other words, the failure to purchase insurance might be explained as a function of the apparent triviality of an event which has not been personally experienced or with which the consumer has not had at least second hand experience (which might lead to a "no chance" categorization of the event). Such an explanation would be consistent with Tversky and Kahneman's (1973) and Kunreuther's (1976) work.

In short, there appears to be a great deal of controversy surrounding the issue of how consumers conceive of and use information about low probability events in making insurance decisions. Below we describe some initial exploratory interviews which were undertaken to examine how consumers naturally describe events which have low objective probabilities.

METHOD

Several exploratory interviews were undertaken to address the following issues:

1. How do consumers naturally describe the chances of certain low probability (but potentially insurable) events?

2. How does the "vividness" of an event affect consumers' estimates of its likelihood?

3. How do consumers "categorize" probabilities on a "chance" scale (ranging from "no chance at all" to ''almost certain" chance)? How does that categorization change when the probabilities represent the chance of a monetary loss and the scale used is a "worry" scale (ranging from "no worry" to "a great deal of worry")?

The method and results for each of the three research questions will be described in brief. The respondents in the study were eleven administrative employees in the university library system who have been involved in insurance decisions in the past. The respondents ranged in age from their mid twenties to their mid fifties and participated in a personal interview which lasted approximately 30 minutes.

Issue One: Natural Description of Event Probabilities

Two events were used in the study to provide a reference point for respondents. The respondents were asked (in a totally open-ended manner) at different times in the interview to describe the probability in the next year of (1) a person who flies 1000 hours/year between New York and Los Angeles being involved in a fatal airline accident and (2) a property-damaging earthquake occurring in a specified (nearby) city. The two events differ on two key dimensions. First, the true probability of the airline accident is far smaller (1 in approximately 6 million, based upon data provided by the Insurance Information Institute 1987) than the probability of the earthquake [The city is situated near a major fault line and an expert in the field reported that the state is three years past due for a major earthquake. He noted that actuaries have estimated the probability of an earthquake between 1988 and 1994 to be near certainty.]. Second, our own speculation and discussion with others indicated that, since a noticeable earthquake had not occurred in the region in a number of years and two fatal commercial airline accidents (which had received a great deal of press) had occurred nationally in the previous year, that the airline accident "event" would be more available in memory.

RESPONDENTS' DESCRIPTIONS OF PROBABILITY

Table 1 presents the general comments made by respondents regarding the probability of a fatal airline accident. Nearly all respondents had flown in the past two years and none had purchased flight insurance. The comments presented in Table 1 indicate that (1) many of our respondents did attempt to use numbers to describe the probabilities and (2) the vast majority thought that the chance of an airline accident was very small. One respondent differed from the rest, describing the airline accident as having "more of a likelihood now than in past years." This respondent had recently been in a near-accident on a flight that had to be met by fire-trucks upon landing. Later in the interview, respondents were asked (after a brief definition of "odds") to choose which of six stated chances (1 in 10 million, 1 in 5 million, 1 in 1 million, 1 in 500,000, 1 in 32,000, and 1 in 1,000) best described the true probability of each event. These numeric estimates are presented in Table 1 for both events, although we will focus here on the airline accident for the moment to make one major point.

While nearly all respondents said that the chance of the airline accident was essentially nil, they gave a wide variety of objective odds on the event. In effect, this suggests that consumers may lump a wide variety of probabilities into a category which represents "remote" or "essentially zero chance" events. Note also that, in the objective question, none of the respondents used the two lowest odds categories, which actually came closest the true probability.

Issue Two: Event n Vividness" or Availability

As noted earlier, we speculated that the airline accident event would be more available in memory than the earthquake event for most subjects. While we have no true manipulation check for our exploratory -sample, the results do show different objective probabilities being estimated for the two events. Focusing on the objective probability estimates in Table 1, six of the eleven respondents gave the airline accident a higher probability than they gave the earthquake in spite of the fact that the earthquake has a substantially higher probability. The four respondents who gave the earthquake a higher probability (one of whom felt that an earthquake was imminent) appear to be familiar with the history of the city in question and the frequency with which mild tremors occur in the state. (i.e., Three of the four mentioned the state's earthquake fault without any prompting.)

Issue Three: The "Categorization" of Probabilities

An important issue in the controversy discussed above appears to be the degree to which consumers distinguish among low probabilities. To examine this, we presented respondents with an "own categories" classification task (Sherif 1963). Using the logic of the "urn" game (Slovic et al. 1977), we showed respondents a picture of a basket containing 10,000 jelly beans. We then gave them a stack of cards which described 19 "baskets" containing varying numbers of black jelly beans among 10,000 (the numbers of black jelly beans ranged from 1 to 6,000). For each basket, respondents were asked to think about the likelihood of picking a black jelly bean on a random draw of one. The interviewer spread two cards (one reading "no chance at all" and the other reading "almost certain chance") out on a table and explained that these were the extremes on a continuum which represented the probability of picking a black jelly bean. Respondents were asked to sort the cards into piles (as many or as few as they wanted) along that continuum according to the chance reflected in the cards in picking a black jelly bean. It was emphasized that the piles could be adjusted and readjusted and that the end cards could be moved to suit the respondent's classification scheme.

Once the respondents had completed the first classification task, they were asked to repeat the task, with two minor adjustments to the process. First, they were told to think of each "basket" as representing the probability that a certain event would occur which would cause $20,000 damage to their personal property. Secondly, the ends of the continuum were anchored by "no worry at all" and "a great deal of worry." The purpose of this second classification task was to explore whether respondents would create fewer categories when prompted to think of probabilities associated with a real world (although unspecified) event.

The exploratory results reported in Table 2 indicate that respondents did use fewer categories with which to classify the probabilities on the "worry" scale than on the "probability" scale. The lowest category in each task (either "no chance at all" or "no worry") contained on average the four lowest probabilities, while the highest category contained two more probabilities when subjects were asked to think of a specific loss situation. The results suggest that there may be very small probabilities which consumers lump into a single "unlikely" or "not worrisome" category. The same may be true for higher probabilities. We find, however, that our respondents (on average) grouped a relatively larger number of probabilities into the category labeled "a great deal of worry" indicating (as one would expect ) a concern for higher probabilities when considering the likelihood of an event in which a major loss would occur.

DISCUSSION

Our empirical evidence is clearly limited by the small size and convenience nature of the sample. Since our respondents all work in university library administration, they may be better informed about the events than the average consumer. Given this, the fact that they all overestimated the probability of the airline accident and nearly all underestimated the probability of the earthquake is even more interesting. The sample did provide exploratory insight into the issues raised here, leading to some tentative conclusions:

1. Consumers may classify a wide range of event probabilities into a category which represents an essentially zero chance of occurrence. This is reflected both in our respondents' tendencies to group probabilities less than .01 in the same "no chance" and/or "no worry" category and the fact that respondents provided a wide variety of objective probability estimates for the airplane accident, even though nearly all of them thought the accident was highly unlikely. This is consistent with Slovic et al.'s (1977) "worry threshold" hypothesis.

2. Consumers may give more "available" or "vivid" events a higher probability of occurring. This is speculative but is based on the finding that several respondents gave the airline accident a higher probability than the earthquake even though the earthquake had a substantially higher true probability. The "availability" explanation is further reflected in the fact that the respondents who did give the earthquake a high probability of occurring were very familiar with the area and its earthquake history.

CATEGORIZING CHANCES: THE "PROBABILITY" CONTINUUM VERSUS THE "WORRY" CONTINUUM

Research on more generalizable samples may provide further insight into why consumers fail to protect themselves against certain low probability events but purchase excessive coverage against others. Research is needed on the effects of event availability/vividness and size of loss on perception of probability and willingness to pay for insurance. Research which examines consumer perceptions and choice behavior in making insurance decisions has the potential to contribute importantly to the interests of public policy, consumer education, and insurance management.

REFERENCES

Anderson, Dan R. (1974), 'The National Flood Insurance Program - Problems and Potential," Journal of Risk and Insurance, Vol.41., No.4 pp. 579-599.

Anderson, Dan R. and Maurice Weinrobe (1986), "Insurance Issues Related To Mortgage Default Risks Associated With Natural Disasters, " Journal of Risk and Insurance, Vol. 53, No. 3 pp. 501-513.

Eisner, Robert and Robert H. Strotz (1961), Flight Insurance and the Theory of Choice," Journal of Political Economy, 56, 355-68.

Formisano, Roger A., Richard W. Olshavsky, and Shelley Tapp (1982), "Choice in a Difficult Task Environment," Journal of Consumer Research, 8 (March), 474-9.

Hershey, John C. and Paul J. H. Schoemaker (1980), "Risk Taking and Problem Context in the Domain of Losses: An Expected Utility Analysis," Journal of Risk and Insurance, Vol. 47, No. 1 pp. 111-133.

Hogarth, Robin M. and Howard Kunruether (1985), "Ambiguity and Insurance Decisions," American Economic Review, 75, 386-90.

Insurance Information Institute (1987), 1987-88 Property/Casualty Fact Book New York: III.

Kahneman, Daniel and Amos Tversky (1979), "Prospect Theory: An Analysis of Risk Under Uncertainty," Econometrica, Vol. 47, No. 2 pp. 263-291.

Kunreuther, Howard C. (1976), "Limited Knowledge and Insurance Protection," Public Policy Vol. 24, No.2, 227-261.

Kunreuther, Howard C., R. Ginsberg, L. Miller, P. Sagi, Paul Slovic, B. Borkan, and N. Katz (1978), Disaster Insurance Protection: Public Policy Lessons, New York: Wiley.

Pashigian, B.P., L. L. Schkade, and G. H. Memefee (1969), "The Selection of an Optimal Deductible for a Given Insurance Policy," Journal of Business, 39, 35-44.

Shoemaker, Paul J. H. and Howard C. Kunreuther (1979), "An Experimental Study of Insurance Decisions," Journal of Risk and Insurance, Vol. 46, pp. 603-618.

Sherif, Carolyn (1963), "Social Categorization as a Function of Latitude of Acceptance and Series Range," Journal of Abnormal and Social Psychology, 67, 148-56.

Slovic, Paul Baruch Fischoff, Sarah Lichtenstein, Bernard Corrigan, and Barbara Combs (1977), "Preference for Insuring Against Probable Small Losses: Insurance Implications," Journal of Risk and Insurance, Vol. 44, No. 2 pp. 237-259.

Tversky, Amos and Daniel Kahneman (1973), "Availability: A Heuristic for Judging Frequency and Probability," Cognitive Psychology, 5, 207-32.

Von Neumann, J. and O. Morgenstern (1947), Theory of Games and Economic Behavior, 2nd ed., Princeton, New Jersey: Princeton University Press.

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