Valuation of Ambiguity Effect on Earthquake Retrofit on Willingness to Pay

Transcription

1 Valuation of Ambiguity Effect on Earthquake Retrofit on Willingness to Pay Toshio Fujimi, Graduate School of Science and Technology, Kumamoto University Hirokazu Tatano, Disaster Prevention Research Institute, Kyoto University Abstract Earthquake retrofit is one of the most important measures for mitigating economic loss and saving residents lives from earthquakes. The Japanese government initiated the policy that 90% of houses must become earthquake-resistant and has provided various supports for earthquake retrofit such as financial aid to homeowners and free checking for earthquake resistance. However, earthquake retrofits are not as widespread as expected. Home owners hesitate to carry out earthquake retrofit for several reasons, including budget or time constraints, confidence in the house s strength, low perceived earthquake risk, and ambiguity of earthquake retrofit effectiveness. This study focuses on the last reason. In our survey, 23% of respondents state ambiguity as the reason for not implementing earthquake retrofit. Many homeowners experience ambiguity about earthquake retrofit effectiveness because they do not understand it well. Ambiguity causes many people to become pessimistic. Ambiguity aversion was originally identified by Ellsberg (1961) and has been confirmed through many empirical analyses. In this study, we evaluate how ambiguity about earthquake retrofit effectiveness decreases homeowners willingness to pay. For this purpose, we conducted a web-based questionnaire survey with 1200 homeowners in late March The questionnaires asked their perceived risk of earthquake and subjective probability of destruction of their houses in an earthquake. Then, two types of earthquake retrofit plans were presented to them; a standard earthquake retrofit plan and an earthquake retrofit plan with warranty that their houses would be repaired for free of charge if destroyed after earthquake retrofit was performed. The latter plan eliminates any ambiguity of effectiveness. Six hundred respondents were asked their willingness to pay for the former plan, and the remaining 600 were asked their willingness to pay for the latter plan. The survey revealed that willingness to pay for the earthquake retrofit plan with warranty was much greater than for the standard plan, suggesting that ambiguity about earthquake retrofit effectiveness reduces its value. Keywords: Earthquake retrofit, Ambiguity, Warranty, Economic Value

2 1. Introduction Earthquake retrofit is one of the most important measures for mitigating economic loss and saving residents lives from earthquakes. Approximately 90% of deaths in the Kobe earthquake were caused by house collapse. In Japan, approximately 11.5 million houses (25% of all housing) do not satisfy the earthquake resistant codes. Earthquake retrofit reduces secondary losses caused by earthquakes. Collapsed building debris block the passage of emergency vehicles and become fuel for fires. The government is promoting earthquake retrofit with the goal that 90% houses will satisfy the earthquake resistant codes by However, earthquake retrofits are not as widespread as expected. Homeowners hesitate to perform earthquake retrofit for five reasons, identified by the Japan Building Disaster Prevention Association: budget constraints, underestimation of earthquake risk, acceptance of house destruction risk, doubt of earthquake retrofit effectiveness, and distrust of earthquake retrofit companies. This study focuses on the last two reasons. Many homeowners face ambiguity about earthquake retrofit effectiveness because they have little understanding of it. Ambiguity is defined as being uncertain about probability, created by missing information that is relevant and could be known (Frisch and Baron, 1988). Many people facing ambiguity become pessimistic. Ambiguity aversion was originally identified by Ellsberg (1961) and has been confirmed through many empirical analyses in fields such as medical services, the insurance market, warranty of consumer electronics, and nuclear-waste transport (Curley and Yates, 1986; Kunreuther et al., 1995; Hogarth and Kunreuther, 1995; Riddel and Shaw, 2006). Our research hypothesis assumes that homeowners hesitate to implement earthquake retrofit due to ambiguity aversion about its effectiveness. They overestimate the possibility of the house s destruction by earthquake even after earthquake retrofit because they understand little about it and distrust earthquake retrofit companies. In this study, we evaluate how ambiguity about earthquake retrofit effectiveness decreases homeowners willingness to pay. Our research objective is to estimate how ambiguity about the earthquake retrofit effectiveness reduces its value. We also propose a plan of earthquake retrofit with warranty and examine its effectiveness. Meguro and Takahashi (2001) proposed a plan with a warranty that an earthquake retrofitted house would be repaired free of charge if it is damaged by an earthquake. The warranty eliminates ambiguity about the effectiveness of earthquake retrofit. We compare the warranty with ex-ante subsidies in terms of economic efficiency.

3 2. Data 2.1 data To explore our hypothesis, we conducted a web-based questionnaire survey in late March 2009, with a sample of 1200 homeowners proportional to the population of each prefecture in Japan. In the questionnaires, we first asked for information related to respondent attributes such as income, age, gender, number of family members, and address. We then inquired about house attributes such as value, structure, age, and construction method. Finally, we investigated the subjective probability of an earthquake with Japanese seismic intensity of 6 weak, 6 strong, and 7. In order to reduce respondents difficulties in expressing their subjective probabilities of earthquake, objective earthquake risk and risk ladder images were presented to the respondents (Figure 1). This figure is the National Seismic Hazard Maps for Japan (2005). The table of the risk ladder shows the probabilities of various events in 30 years. We used a web-based interactive tool by which respondents indicated their subjective probability by the yellow marker (Figure 2). The window over the gauge automatically shows the probability that corresponds to the yellow marker. Probabilities in 30 years Injury by car accident 24.0% Death by cancer 6.8% Sneak thief 3.4% Loss from fire 1.9% Snatch 1.2% Loss from heavy rain 0.5% Loss from typhoon 0.5% Death by car accident 0.2% Death by fire 0.2% Death by airplane accident 0.002% Figure 1: National Seismic Hazard Maps and Risk Ladder in Japan (The Headquarters for Earthquake Research Promotion, 2005) Then, we asked respondents subjective probability of house destruction due to an earthquake, by explaining the classifications of damage to them. There are three categories: partial destruction, half destruction, and complete destruction. A similar classification is used by the government and insurance companies in Japan. In partial destruction, residents can live in their house without repair, and repairs cost up to 5% of the house s value. In half destruction, residents cannot live in their house without repair, and repairs cost up to 50% of the house s value. In complete destruction, residents have to reconstruct their house, and repairs cost 100% of the house s value. The respondents were asked their subjective probability of partial,

4 half, and complete house destructions contingent on an earthquake with each seismic intensity. At this stage, we also presented the risk ladder to respondents and used the gauge shown in Figure 2. After reading a simple explanation of seismic diagnosis and reinforcement methods, respondents were asked to imagine a hypothetical earthquake retrofit in which their houses are strengthened to over 1.5 IS (Seismic Index of Structure) that is officially categorized as no possibility of collapse. Then they were asked their subjective probability of house destruction after that earthquake retrofit contingent on an earthquake with each intensity scale. Figure 2: National Seismic Hazard Maps and Risk Ladder in Japan (The Headquarters for Earthquake Research Promotion, 2005) Finally, two types of earthquake retrofit plans were presented to them. One was a standard earthquake retrofit plan. The other was an earthquake retrofit plan with a warranty that their houses would be repaired free of charge if destroyed after the earthquake retrofit. In this phase, respondents were evenly and randomly divided into two groups (A and B), with each group presenting a different plan. The 600 respondents in Group A were asked their willingness to

5 pay for the former plan, which permits ambiguity about the retrofit effectiveness. The other 600 respondents in Group B were asked their willingness to pay for the latter plan, which prevents ambiguity about retrofit effectiveness. Their willingness to pay was determined by the doublebounded dichotomous choice method (Hanemann et al., 1991). First, we asked, Will you implement the earthquake retrofit at a cost of 50,000 yen per year for 30 years? If the answer was yes, we asked the follow-up question, How about 100,000 yen? If the answer was no, we asked, How about 20,000yen? Figure 3 shows the distribution of the sample average of willingness to pay (WTP). It appears that WTP for the plan with the warranty is higher than for plan without the warranty. However, we cannot reach that conclusion from this finding alone because each respondent s house had a different value and each respondent faces a different risk. An econometric method is required to analyze this problem Sample A Sample B Over 100 Figure 3: Distribution of sample average of WTP 3. Method 3.1 model To examine the impact of ambiguity about earthquake retrofit effectiveness on WTP, we analyzed the data according to the econometric model based on the expected utility (EU) model. Before earthquake retrofit, a homeowner faces the risk represented by the following condition. 1,0;,0.05y;,0.5y;, ), (1) ( y

6 where 1, 2, and 3 are the subjective probability of partial, half, and complete destruction of the house, respectively. y denotes the house s value. After completing earthquake retrofit, the homeowner faces the risk represented by the following condition. Q 1 q q q,0; q,0.05y; q,0.5y; q, ) (2) ( y where q 1, q 2, and q3 are the subjective probability of partial, half, and complete destruction of the house after earthquake retrofit, respectively. In the EU model, WTP for the earthquake retrofit is determined by the following equation. E [ u( w, Y, Z)] EQ[ u( w WTP, Y, Z)] (3) where u ( ) is the utility function, w is the homeowner s wealth, and Y is a random variable of the house s value. Z is a random variable of household s health condition such that z if the house is completely destroyed, and 0 otherwise. E [ ] and E Q[ ] represent expected values with probability and Q, respectively. We specified the expected utility function by the Mean-Variance model. The left and right hands of equation (3) are respectively written by E Q E [ u( w, Y, Z)] E [ w Y] V [ w Y] 3u( z) and (4) [ u( w WTP, Y, Z)] E [ w Y WTP] V [ w Y WTP] q3u( z), (5) Q where is a parameter representing risk attitude. V [ ] and V Q [ ] are variances with the probability and Q, respectively. The parameter represents the risk attitude that may differ by respondents income. Therefore, is formulated as follows. 0 inc Income, (6) where Income denotes the respondent s income. When a homeowner chooses the earthquake retrofit plan with the warranty, she faces no monetary risk. WTP is determined by the following equation. E [ u( w, Y, Z)] w Y WTPw q3u( z), (7) where WTP w is willingness to pay for earthquake retrofit policy with warranty. Arranging the equations, WTP and WTP w are written as follows. Q WTP EQ [ Y ] E [ Y ] ( VQ [ Y ] V [ Y ]) ( q3 3) and (8) WTP w y E Y ] V [ Y ] ( q ), (9) [ 3 3

7 where u( z) is a parameter to be estimated. 3.2 Estimation method The willingness to pay is determined by the double-bounded dichotomous choice method (Hanemann et al., 1991), where the first bid B is presented to a respondent. The larger bid u d B is presented if he accepts. The smaller bid B is presented if he rejects. The probability yy that respondent i will accept both bids is denoted by P i. yy Pi u u Pr[ WTP B ] 1 F( B WTP), (10) where is the error term whose distribution function is F ( ). The probability that respondent i will accept the first and reject the second, the probability that he will reject the first and accept the second, and the probability that he will reject both are respectively denoted as follows. yn Pi u u Pr[ B WTP B] F( B WTP) F( B WTP) ny Pi d d Pr[ B WTP B ] F( B WTP) F( B WTP) (11) nn i P d Pr[ B WTP ] F( B d WTP) The log likelihood is expressed as follows. N yy yn yn yn ny ny nn nn ln L ln ( di ln Pi di ln Pi di ln Pi di ln Pi ), (12) i 1 yy yn ny nn where d i is a dummy variable if respondent i accepts both bids. d i, d i, and d i are similar dummy variables. This is maximized to estimate parameters. In this study, we 2 assume ~ Normal (0, ). 4. Results The estimation results are shown in Table 1. For Group A, estimates are not statistically significant except sigma. The EU model does not explain respondents decision about the standard earthquake retrofit plan clearly. For group B, all estimates are statistically significant at the 5% level. Negative estimates of 0 implies that the average respondent is risk averse. Positive estimates of inc signify that respondents are less risk averse as income increases. Negative gamma indicates that the house condition gets worse in complete house destruction. Thus, the signs of all estimates are reasonable. The EU model fits the data well for the earthquake retrofit plan with warranty.

8 Table 1: Estimation results Group A Group B σ (22.56)** (21.16)** β (0.12) (-2.04)** β_income (-0.99) (2.19)** γ (-1.03) (-3.05)** n lnl By using estimated models, we calculated the mean WTP. The mean WTP for standard earthquake retrofit and that with warranty are 57,339 yen and 71,881 yen per year, respectively. The warranty value is 14,152 yen per year. According to the EU model, it can be divided into two factors as shown in the following equation. WTP ˆ WTP ˆ ( y E [ Y]) ˆ V [ Y] residual (13) w Q Q The first parenthetic term on the right side represents the difference of expected values between earthquake retrofit policies with and without warranty. The second term indicates the difference of risk premiums between earthquake retrofit policies with and without warranty. These can be directly calculated with sample data. The former is 1,268 yen per year. The latter is 1,450 yen per year. The residual of equation (13) is 11,434 yen per year, representing ignored factors including ambiguity premiums. This suggests that a large part of the warranty value is the ambiguity premium. 5. Policy Implications In Japan, ex-ante policies are popular for promoting earthquake retrofit. For example, local governments provide a homeowner with a subsidy for performing earthquake retrofit. We compared the ex-ante subsidy with the ex-post warranty from the economic point of view. First, we roughly estimated the expected warranty cost. We used the objective probability of earthquake with over 6 on the seismic intensity scale for 30 years from the National Seismic Hazard Maps for Japan (2005). The upper limits of each category of probability were used. We used 50% in the category over 26%. From the Japan Meteorological Agency database, we know the ratios of earthquakes with 6 weak, 6 strong, and 7 seismic intensity are 72.4%, 24.1%, and 3.4%, respectively, from 1990 to We used these ratios. There are no reliable data of

9 objective probability of complete destruction with 1.5 IS. Idota et al. (2007) shows that the partial destruction ratios of houses with 1.3 IS in earthquakes with 6 weak, 6 strong, and 7 seismic intensity are 46%, 17%, and 0%, respectively. The half destruction ratios of houses with 1.3 IS in earthquakes with 6 weak, 6 strong, and 7 seismic intensity are 30%, 73%, and 17%, respectively. The complete destruction ratios of houses with 1.3 IS in earthquakes with 6 weak, 6 strong, 7 seismic intensity are 2%, 10%, and 83%, respectively. We overestimate the destruction ratio because houses with 1.5 IS are stronger than those with 1.3 IS. This implies that expected warranty costs tend to be overestimated. The sample average expected warranty cost for 30 years was 78,043 yen. From Section 4, the sample average estimated warranty value for 30 years was 424,560 (14,152 30). These findings suggest that warranty of earthquake retrofit can be more efficient than an ex-ante subsidy even when the warranty cost is overestimated. This is because the expected warranty cost is calculated with objective probability whereas the destruction risk of a reinforced house is overvalued due to the homeowner s ambiguity aversion. In this case, the warranty is equivalent to a subsidy of 424,560 yen at an expected cost of 78,043 yen. 6. Summary In this study, we evaluated how the ambiguity about earthquake retrofit effectiveness decreases homeowners willingness to pay. For this purpose, we estimated values of earthquake retrofit plans with and without warranty by conducting a web-based questionnaire survey. The warranty eliminates ambiguity about effectiveness of earthquake retrofit. We compare warranty with ex-ante subsidies in terms of economic efficiency. Ambiguity about effectiveness of earthquake retrofit reduces its value to a great extent. Warranty can be more efficient than exante subsides for promoting earthquake retrofit. Future studies should focus on the following issues. First, we should consider effectiveness of attributes of house and respondent. Second, behavior of ambiguity aversion should be modeled explicitly. Third, government intervention is justified if both house-owners and construction companies face ambiguity. Designing mechanism is necessary to prevent moral hazard of construction companies (e.g., slipshod work). References Curley SP and Yates FJ (1986) An Empirical Evaluation of Descriptive Models of Ambiguity Reactions in Choice Situations. Journal of Mathematical Psychology 33: Ellsberg D (1961) Risk, Ambiguity, and the Savage Axioms. Quarterly Journal of Economics 75:

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