The Demand for Disaster Insurance An Experimental Study. Chinn Ping Fan*

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1 The Demand for Disaster Insurance An Experimental Study 本 文 發 表 於 25 兩 岸 經 濟 論 壇 : 產 業 經 濟 與 財 務 管 理 研 討 會, 25/4/18-19, 天 津, 南 開 大 學 Chinn Ping Fan* Many natural disasters have the characteristic of low probability and high losses. This paper investigates the demand for disaster insurance with the research tools of lottery experiment with monetary rewards and questionnaire survey. Many researchers claim that subjects tend to over-estimating low probability events. But for disaster insurance, it has also been found that there exists an under-demand phenomenon for disaster insurance, i.e., people are not willing to buy insurance at actuarially fair premium. I will use experimental data to test the validity of these statements. I also want to see if it is possible to enhance the demand for disaster insurance by supplying more information to the subjects or by providing bundled (covering fire, earthquake, flood and typhoon) disaster insurance. Subjects are required to participate in lottery experiment and also answering questionnaires. There responses in these two respects will be compared to check for any discrepancy.. *Department of Economics, Soochow University, Financial support from The National Science Foundation, Taiwan, ROC, under Grand No Z-31-1 is gratefully acknowledged

2 1.Introduction In the past fifty years financial losses from natural disasters have quadrupled. Facing this increased loss, government agencies and international organizations have been promoting insurance as an important tool for managing disasters and the insurance industry are also dealing with this difficult issues (Freeman and Kunreuther (24)). However, even with supply of well-design insurance policy, the insurance market will work properly only if there is also enough demand for disaster insurance. This paper studies the demand for disaster insurance with experimental approach. Huber et al (1997) and Chivers & Flores (22) both claimed that information is an important factor that influence demand for disaster insurance. Many research found that generally there is an under-demand for disaster insurance. Kunreuther and Pauly (24) claim that this is a natural result of rational decision making. The cost of information search may be too high for very low probability event, so people rationally decide to neglect very-low probability event, an earthquake, for example. They suggest that people may be more willing to purchase bundled catastrophe insurance. Baron et al. (22) analyzes factor determining how people take protective behaviors. They perceive that there are a large number of potential protective behaviors competing for limited resource, and hence, the probability of taking a particular protective behavior is quite small. This result supports Kunreuther and Pauly (24) suggestion that people may be more willing to purchase bundled insurance policy. Schade and Kunreuther (22) studied the willingness to pay for protective measures. One interesting finding is that some subjects have illusion of safety, i.e., an irrational belief that they themselves will not incur losses. This may be one factor explaining the under-demand for disaster insurance. Johnson et al.(1993)studied subjects perception of possible events and insurance decision with questionnaire survey. They found that the decision making process may be different in different frame, for example, for earthquakes, diseases, automobile accidents and terrorist attack. Freeman and Kunreuther (24) mentioned the successful experience of enterprises learning to purchase fire insurance in the nineteen-century England. Combining these results, I want to see if subjects are more willing to purchase disaster insurance when they presume the roll of a firm but not a household

3 Mcclelland et al. (1993) also studied the demand for insurance for very low probability disasters. They conducted auction experiment and found that the willingness to pay is bimodal. Some subjects are risk averse and willing to pay a lot, while others simply do not care. The paper focuses on the following issues. 1. A catastrophe is an extreme disaster, the probability of it happening is very low but the damages, if it happens, will be tremendous. Earthquake and terrorist attack maybe classified as such. While fire, flood, and typhoon are, comparatively speaking, with higher probabilities of happening but the damages are usually smaller. It is my speculation that subjects may have more difficulty in processing catastrophes, and hence, the demand for catastrophe insurance would be less stable. One possible solution is to bundle catastrophe events with more ordinary disasters. If subject could better handle information for bundled disasters, then there will be more demand for bundled insurance also. 2. Prospect theory claims that people often overestimate the importance of low probability event. If this is true, then there should be over-demand for disaster insurance. But this is not what we observe in the real world. I want to see if experimental evidence support the overestimation hypothesis. 3. Our subjects are also required to answer questionnaires. There responses in the lottery experiment and questionnaire survey will be compared to check for any discrepancy.. 2.Experiment Design and Procedure This research consisted of two parts; subjects participated in lottery experiment with monetary rewards and questionnaire survey, the latter will be reported in Section 4. Subjects were recruited from undergraduate students in Soochow University, Taipei, Taiwan. Two groups of prospects were presented to the subjects. The first group contains six possible disaster scenarios, and the second group includes four positive reward lotteries. The disaster - 3 -

4 scenarios describe various probability of summer typhoon (losses $1,), autumn typhoon (losses $4,) and earthquake (losses $1,) happening. Subjects were told to write down how much they would be willing to pay (WTP) to purchase a full-coverage insurance policy. The lotteries have positive rewards that are just the counterparts of the disasters; small prize ($1,), medium prize ($4,) and lotto ($1,). Subjects are also required to determine the WTP for these lotteries. There is a total of ten WTPs, and one of the ten uncertain prospects will be randomly chosen, this prospect will be played out and subjects monetary rewards are determined accordingly. The huge financial losses of the earthquake create difficulties for the experimental design. It is unethical for experimenter to collect money from subjects; hence, I need to provide subjects with initial endowment high enough to cover the possible financial losses of various disasters. I adopt the following design: each subject is entitled to a basic participation fee of NT$5. And the experiment dollars will be converted to New Taiwan dollar with a ratio of ten to one. So if a Autumn typhoon happens, NT$4 will be deducted for an uninsured subject, and this person will then receive a cash payment of NT$1 at the end of the experiment. And for the huge financial losses of an earthquake, an uninsured subject will receive zero cash payment and also need to provide five hours of his (or her) labor time to the experimenter. This rule is announced publicly and subject could refuse and leave the experiment site if they do not accept this ruld. The following are examples of disaster scenarios and cash reward lotteries

5 Scenario 6. In Taiwan, the probability of earthquake happening is much smaller than typhoon. But if happens, earthquake would cause gigantic financial losses. The insurance industry is now promoting a comprehensive home safety insurance that fully covers the losses from summer typhoon, autumn typhoon and earthquake. For the following disaster scenario, please write down the amount you are will to pay to purchase this insurance policy. Please note that since your basic cash reward is NT$5 only, so if earthquake happens and you are not insured, then your NT$5 cash reward will be completed deducted and also, you owe me five hours of your working time. Scenario 6. Summer Autumn Situation No disaster Earthquake Typhoon Typhoon Losses $ $-1 $-4 $-1 Probability Lottery 4. For the following lottery, please write down the acceptable selling price. Lottery 4 Situation No Prize Small Prize Medium Price Lotto Cash Reward $ $1 $4 $1 Probability It is obvious that Scenario 6 and Lottery 4 have exactly the same probability and outcome structures except that the Scenario 6 involves negative outcomes of the disasters. We adopt standard BDM procedure to elicit truthful valuation from the subjects 1, and the market prices are determined also by random drawings. The design of the experiment is illustrated in Table 1, in which S1 to S6 refers to the six disaster scenarios and L1 to L4 refers to the four lotteries. And the huge, medium, small and nothing refer to the different outcome values. 1 Literature discussions of BDM procedures

6 Table 1 Experimental Design Huge 1, Medium 4, Small 1, Nothing EV SD S1, L S2, L S3, L S S S6, L Experiment Result The basic descriptive statistics of the 188 subjects is reported in Table 2. Before analyzing the data, I want to distinguish the difference between the WTP of this research with other concepts. A certainty equivalent (CE) of a uncertain prospect is an amount of money that could generate the same utility level as the uncertain prospect. I do not claim that the WTP obtained in this research also represents the subjects CE for these uncertain prospects. One reason may lay in the incentive scheme of the experiment. As we mentioned earlier, the experiment dollar will be converted to New Taiwan dollars in the ration of $1=NT$1. Therefore, paying $25 to purchase an insurance policy will, in fact, only cost a subject NT$25. The connection between WTP and CE may be unclear, but as long as subject determine the WTP for these ten prospects in a consistent way, we can still analyze the reasoning behind these WTP to gain some understanding on the decision process of our subjects. Another relevant concept is the actuarially fair premium (AFP) for disaster insurance. Table 1 listed the EV of the ten uncertain prospect of this research. The AFP of a disaster needs to cover not only EV but also other factors: administration costs, long-tail risks, financial market considerations, etc. Therefore, the AFP of a disaster is definitely higher than it s EV. In Table, we first note that subjects mean WTP is very different from the EV of these prospects. For example, S1 has an EV of $12, and the mean WTP $24. The third row - 6 -

7 of Table 2 calculate the mean to EV (MTE) ratio of S1 is 24/12=1.7. Again, not claiming that EV is AFP, assuming subjects WTP is determined in a consistent way, how the MTE ratios change may still reveal meaningful information. Table 2. Basic descriptive statistics Statistics S1 S2 S3 S4 S5 S6 L1 L2 L3 L4 Mean MTE ratio St. Dev Skew Kurtosis Mode Median Maximum Minimum 5 Table 3 reports the percentage distribution of subjects WTP. For the six disaster prospects, a WTP of $ is risk-taking (no intention for purchasing insurance) and a WTP of $5 is risk-averse (paying the highest price for the insurance policy). And for the positive reward lottery, a WTP of $ means risk-averse (will accept any offer, eager to sell the lottery) while a WTP of $5 is risk-taking (refuse to sell the lottery except for the highest possible price). The distribution graphs are provided in Appendix I. Table 3. Percentage distribution of WTP S1 S2 S3 S4 S5 S6 L1 L2 L3 L4 $ $1-$ $1-$ $2-$ $3-$ $4-$ $

8 I propose the following hypothesis based on the information from the above two tables. And as a baseline for comparison, I assume there exist a B-group of subject who has a normally distributed WTP with a mean around the AFP of the uncertain prospect. Hypothesis 1. Subjects response patterns are closer to the B-group for bundled insurance policy. For the S4 (earthquake only) scenario, the distribution of subjects WTP is positively skewed with a kurtosis statistics smaller that 1. But as the insurance policy bundles more disaster coverage together (from S4 to S5 to S6), the distributions become negative skewed, and kurtosis moves closer to zero, so the WTP distributions become more centered. Table 3 show that subjects responses to S4 are very fat-tailed, 15% of the subjects simply refuse to purchase insurance and 18% is willing to pay over $4 for the insurance coverage, although the EV of S4 is only $5. Since many subjects are willing to pay a dramatically high price for the insurance coverage, so the MET ratio of S4 is But this ratio drops significantly for S5 (6.9) and S6 (1.71). So it seems that the average judgment for bundled insurance are more rational than single catastrophe insurance. The positive skewness of S4 means that more subjects in the low WTP range, these maybe the subject causing the under-demand phenomenon, but S5 and S6 have very small negative skewness statistics, so there are slightly more subject in the high WTP group. Hypothesis 2. Subjects do not consistently over-estimate low probability disasters. S2 and S3 both involves a 3% probability of disaster, the only difference is that S2 has a potential loss of $1, while S3 has a potential loss of 4,. But the distribution of WTP for S2 is positively skewed and leptokurtic; with a MTE ratio of 3.11, while the skewness of S3 is much smaller, and the mean WTP is also much closer to EV. Hypothesis 2 could also be supported by observing the WTP distributions of S1 and S3. With the same EV of $12, S1 involves a 12% chance of a $1, loss, while S3 involves a 3% chance of a $4, loss. However, the distribution of the WTP of S1 and S3 are quite similar. As for the lotteries, the WTP distribution of L2 and L3 are very similar, it appears that for L2, the 3% chance of winning $1, is greatly overstated, but this is not the case for the 3% chance of winning $4, for L3. In general, the experimental evidence do not support the prospect, we can not claim that low probability events are overstated in a systematic way

9 Hypothesis 3. With the same outcome and probability structure, subjects risk atitudes for disaster scenarios and lotteries are somewhat different. For small and medium outcomes, the WTP distributions for disasters are more fat-tailed than lotteries. The number of risk-averse and risk-taking subjects are both larger for disaster scenarios, so the WTP distributions are flatter. Table 4. t Test for paired sample (d.f.=187) Prospect pair Correlation Coefficient t statistics p value S1, L S2, L S3, L S6, L Table 5. F Test for variance (d.f.=187) F p S1, L S2, L S3, L S6, L The result of a simple t test for difference in paired sample mean is reported in Table 4, and Table 5 report the F test for difference in variance. It clearly shows that the sample mean WTP for the disasters and lotteries are different. Hypothesis 4: The response patterns of male and female are different. There are 72 male subjects and 116 female subjects in our experiment. Table 6 and 7 report the descriptive statistics for these two subject group

10 Table 6 Basic descriptive statistics for male subject Statistics S1 S2 S3 S4 S5 S6 L1 L2 L3 L4 Mean MTE ratio St. Dev Skew Kurtosis Mode Median Maximum Minimum 5 Table 7. Basic descriptive statistics for female subject Statistics S1 S2 S3 S4 S5 S6 L1 L2 L3 L4 Mean MTE ratio St. Dev Skew Kurtosis Mode Median Maximum Minimum It appears that male subjects are much less willing to purchase disaster insurance. This is especially striking when we observe that for the three disaster scenarios that involve earthquake (S4, S5, and S6), the mode of the male group is $. But this sex difference is much less evident for lotteries. It appears that female are more risk averse for negative rewards, but not for positive rewards

11 4.Questionnaire Analysis The questionnaire and subjects responses are reported in this section. Question 1. You are: Male (38%), Female (62%). Question 2. Have you ever purchased Lotto? Yes (77%), No (23%). Question 3. Suppose that you own a house, it s market price is ten milion NT dollars. Will you purchase fire insurance policy for this house? Definitely no (2%), Maybe, depending on insurance premium (54%) Definitely yes (42%), Don t know (2%). Question 4. Will you purchase earthquake insurance policy for this house? Definitely no (5%), Maybe, depending on insurance premium (59%) Definitely yes (24%), Don t know (12%). Question 5. Will you purchase typhoon-flood insurance for this house? Definitely no (16%), Maybe, depending on insurance premium (54%) Definitely yes (17%), Don t know (12%). Question 6. Suppose the insurance company is now promoting a Safe Home Comprehensive Insurance policy that covers fire, typhoon and flood and earthquake damages, will you purchase this insurance policy? Definitely no (1%), Maybe, depending on insurance premium (57%) Definitely yes (38%), Don t know (4%). Question 7. Suppose that bank always requires homeowner to purchasing fire insurance. Since 23, the insurance company is selling fire insurance with additional earthquake coverage. Except for the fire insurance required by banks, will you be will to pay more to purchase this additional earthquake coverage? Definitely no (8%), Maybe, depending on insurance premium (62%) Definitely yes (17%), Don t know (13%)

12 Question 8. The situation is the same as in Question 7, except that this house is not your residence, but your factory building. Except for the fire insurance required by banks, will you be will to pay more to purchase this additional earthquake coverage? Definitely no (4%), Maybe, depending on insurance premium (4%) Definitely yes (46%), Don t know (1%). Question 9. Again assume this house is your residence, and it is located in the She-Jir District that has a very high frequency of flooding. Suppose that the Central Bureau of Weather Forecasting estimated that the probability of flooding in She-Jir is 3 percent. The insurance company is now selling a flood insurance policy with a coverage of NT$1,, and the premium is NT$3,2. Will you purchase this flood insurance? Definitely no (16%), Definitely yes (53%), Don t know (31%). Question 1. Suppose that if your house is flooded, you will incur a financial loss of NT$3,,. Each unit of insurance will cover a loss of NT$1,, with a premium of NT$3,2. How many units of insurance will you purchase? unit (1%), 1 unit (13%) 2 units (37%), 3 units (4%). Question 11. Suppose again that this house is not your residence, but rather it is your factory building. If this factory is flooded, you will incur a financial loss of NT$6,,. Each unit of insurance will cover a loss of NT$1,, with a premium of NT$3,2. How many units of insurance will you purchase? unit (5%), 1 unit (3%) 2 units (5%), 3 units (16%) 4 units (18%), 5 units (1%) 6 units (43%). The results of the survey are not completely in line with what we found in the lottery experiment. Comparing Question 3 to Question 6, it appears that there are higher proportions of subjects willing to purchase fire and bundled disaster insurance. The demand for flood insurance is again fat-tailed (Question 4 and Question 9). Question 9 clearly states that the house is located in an easily flooded region of Taipei, but 16% of the subjects still refuse to purchase flood insurance. Question 8 and Question 11 show that when subjects are more willing to purchase disaster insurance for factory buildings

13 5.Conclusion With lottery experiment, I found that the WTP for catastrophe insurance is extremely fat-tailed. Hence, there may be insufficient demand. The fat-tailed phenomenon improved dramatically for bundled disaster insurance. The evidence from this research providence mixed support for prospect theory. Low probability events are not over-estimated in a systematic way, but subjects responses to negative and positive are indeed different. We also find that the WTP distribution of male and female subjects are different for negative rewards, but not for positive reward. The questionnaire survey provides are not completely consistent with experiment data. This may require further study. However, we do find that when the object in consideration is a factory building, but not a home residence, subjects are more willing to purchase disaster insurance

14 References 1. Baron, Jonathan, Gurmankin, A. D., Kunreuther, Howard (22): The Comparative Approach to Protective Behavior, University of Pennsylvania, The Wharton Risk Management and Decision Processes Center, Working Paper 2-12-HK. 2. Blanchard-Boehm, R. D., K. A. Berry and P. S. Showater (21) Should Flood Insurance Be Mandatory? Insights in the wake of the 1997 New Year s Day Flood in Reno-Sparks, Nevada, Applied Geography 21, pp Braun, Michael and Muermann, Alexander (23):The Impact of Regret on the Demand for Insurance, University of Pennsylvania, The Wharton Risk Management and Decision Processes Center, Working Paper 3-5-AM. 4. Browne, Mark J. and Robert E Hoyt, The Demand for Flood Insurance: Empirical Evidence, Journal of Risk and Uncertainty, 2:3; Chivers, James and Nicholas E. Flores, (22), Market Failure in Information: The National Flood Insurance Program, Land Economics, 78(4): Grace, Martin F., Robert W. Klein and Paul R. Kleinforfer, (22), The Demand for Homeowners Insurance with Bundle Catastrophe Coverage, University of Pennsylvania, The Wharton Risk Management and Decision Processes Center, Working Paper 2-15-PK. 7. Hogarth, Robin M. and Howard Kunreuther (1995), Decision Making under Ignorance; Arguing with Yourself, Journal of Risk and Uncertainty, 11(1): Hsee, Christopher K.and Howard C. Kunreuther, (2), The Affection Effect in Insurance Decisions, Journal of Risk and Uncertainty, 2:2; Huber, Osward, Roman Wider, and Odilo W. huber, (1997), Active information Search and Complete Information Presentation in Naturalistic Risky Decision Tasks. Acta psychological, 95: Johnson, Eric, J., John Nershey, Jacqueline Meszaros, and Howard Kunreuther, (1993), Framing, Probability Distortions, and Insurance Decsions, Journal of Risk and Uncertainty, 7(1): Kunreuther, Howard and Mark Pauly (24) Neglecting Disaster: Why Don t People Insure Against Large Losses? Journal of Risk and Uncertainty, 28(1):

15 12. Mcclelland, Gary H, William D Schulze and Don L. Coursey (1993), Insurance for Low-Probability Hazards: A Bimodal Response to Unlikely Events, 7(1): Schade, Christian and Howard Kunreuther (22), Worry and the illusion of Safety: Evidence from a Real-Objects Experiment, University of Pennsylvania, The Wharton Risk Management and Decision Processes Center, Working Paper 2-9-HK

16 Appendix S1 S S2 S S4 6 S5 S L1 L3 8 6 L2 L S1 L1 8 6 S2 L S3 L3 8 6 S6 L

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