Reexamining the Accident Externality from Driving. Using Individual Data

Transcription

1 Reexamining the Accident Externality from Driving Using Individual Data Rachel J. Huang * Associate Professor, Graduate Institute of Finance, National Taiwan University of Science and Technology, Taiwan Larry Y. Tzeng Professor, Department of Finance, National Taiwan University, Taiwan Kili C. Wang Associate Professor, Department of Insurance, Tamkang University, Taiwan * Corresponding Author. address: rachel@mail.ntust.edu.tw

2 Reexamining the Accident Externality from Driving Using Individual Data Abstract This paper examines the accident externality from driving by using a unique individual level data set with 155,581 observations from Taiwan. If the average number of kilometers driven per vehicle per year increases by one thousand kilometers, we find that the impact of the accident externality per year on the loss probability is about 1.06%, while the impact of the accident externality per year on the loss severity is about $130. In addition, we find that the externality and the kilometers driven are heterogeneous in terms of the individual s age, the vehicle s age and the registration area. Policy implications on insurance premium tax are also provided. Keywords: accident externality, automobile insurance, loss probability, loss severity. JEL classification: H23, D62, G22 1

3 1. Introduction Each driver can affect the risk of accidents to others. The more kilometers each driver covers, the higher the potential for other drivers to risk an accident. This is referred to as the accident externality from driving. Such an externality could be very costly to a society and has received much attention in the literature. For example, by using aggregate panel data for the United States, Edlin and Karaca-Mandic (2006) provided intriguing evidence to support the existence of an accident externality from driving. They found that the statewide insurance costs caused by accident externalities could range from $1,725-$3,299 per driver per year. According to their estimates, a Pigouvian tax could raise over $220 billion per year nationally to correct for accident externalities. By adopting Edlin and Karaca-Mandic s (2006) methodology, Saito, Kato and Shimane (2007) also found evidence of a positive and significant externality in Japan. Although the literature has provided several insightful findings related to accident externalities, most of the papers in the literature employ aggregate data and cannot analyze the issues in detail which can only be done through individual data. Analysis using individual data could provide complementary information and help social planners delicately cope with the externality. In this paper, we intend to fill this gap. The purpose of this paper is to decompose the accident externality from three angles. First, we will examine how other people s driving influences an individual s loss frequency and loss severity. It is well known in the literature that the social optimum may not be the same as the private optimum in the presence of a negative externality. We elaborate on the difference between the social and private optima in regard to driving in the Appendix and show that, if drivers are risk averse, the difference between the social 2

4 and private optima in regard to driving requires information on the accident externality both in terms of frequency and severity. Second, we will investigate whether the impacts of the accident externality could be heterogeneous. After collecting tax from the producer of the negative externality, a social-welfare maximizing government might wish to compensate the victims. Therefore, it is important to recognize who will suffer more due to other people s driving, i.e., the heterogeneity of the accident externality from driving. Third, we will examine who is the person causing accident externality. We identify what types of individuals would like to drive more. If the number of kilometers driven is unobservable to the government, the government could design a tax system which depends on the individual s characteristics that reflect the incentive to drive. To the best of our knowledge, our paper is the first to elaborate on the accident externality from these three angles. In order to accomplish the above purpose, we hand collected our individual level data in Taiwan by integrating the data from a vehicle manufacturer and that from an insurance company. Our insurance data include both the occurrence and the amount involved in the accident. 1 Thus, we can investigate the impact of the accident externality on the frequency and severity separately. Our insurance data also contain individuals demographic variables which can be used to analyze the heterogeneity of the accident externality. Furthermore, our data from the vehicle manufacturer contain some information which can be used to calculate the number of kilometers each policyholder was assumed to drive. This information not only assists us to examine who drives more but also provides us a direct measurement for the source of accident externality. By taking the average, we obtain the average number of kilometers driven per vehicle. This variable could directly represent other people s driving. 1 We use insurance claim data as the proxy for accidents. 3

5 The major findings are as follows. First, we confirm the existence of the accident externality arising from driving in Taiwan. Moreover, we find that the accident externality exists both in terms of the accident probability and accident severity. On average, an individual will increase her accident probability by 1.06% per year when the average number of kilometers driven per vehicle per year increases by one thousand kilometers. 2 Being conditional upon an accident, the externality in terms of the loss severity is about $130 per vehicle per year when the average number of kilometers driven per vehicle per year increases by one thousand kilometers. Taking into consideration the average numbers of cars in Taiwan during our sample period, the total externality of the society is about $ million dollars per year, which is about 7.46% of the total income tax in Taiwan. Second, our findings support the view that the accident externality arising from driving could be heterogeneous. We find that the impacts of the accident externalities on the probability of an accident are larger to young policyholders and old cars. They are larger in cities and the northern part of Taiwan where population densities are higher. We also find that the impact of accident externalities on the severity give rise to more costs in relation to males than females, and old cars than new cars. However, the cost is smaller in cities and the northern part of Taiwan. Third, the heterogeneity effect of driving is found. Policyholders over the age of 20, males, married people, new cars and people living in the suburbs or southern Taiwan tend to drive more kilometers than the corresponding groups. The remainder of this paper is organized as follows. The data are described in 2 Note that the average accident probability in our sample is about 11.32%. A 1.06% increase is quite significant. 4

6 Section 2, the empirical methodology is introduced in Section 3, and the empirical results are reported in Section 4. Section 5 concludes the paper. 2. Data Our data are obtained from two sources. One is a large vehicle manufacturer whose market share is about 38% in Taiwan for the year The service and maintenance centers of the manufacturer record the kilometers assumed for each customer who visits the centers for vehicle repairs or maintenance. Thus, the data allow us to calculate the kilometers driven by the individual and the average kilometers driven per vehicle. The other source is an insurance company whose written premium was about 20% of the automobile insurance market in The insurance data contain claim records, including the claim number and claim amount, so that we can use the claim data as a proxy for accident information. In addition, this part of the data contains the insurance policy and the variables used for underwriting, such as the individual s age, gender, marital status and the insured vehicle s age, brand, and registered area. With the help of those characteristics, we can control the heterogeneity of observations and further investigate the heterogeneity of the accident externality impacts. On the other hand, using kilometers driven by the individual as our dependent variable and demographic variables as independent variables, we further investigate who tends to drive more. We incorporate two data sources together and obtain our final sample. The individuals we investigate are those who purchase insurance in our sample insurance company, and also have their vehicles maintained or repaired by our sample manufacturer from the year 2000 to the year We delete some observations for those who are not insured within a whole calendar year on year 2000 and year We also delete those 5

7 observations from the sample that do not have at least two maintenance or repair records during our sample period as well as the vehicles for commercial purposes. To compute the claim number and claim size, we further consolidate the claim data from different insurance policies for each vehicle where the claims might be caused by the same car accident. For example, if a car hit another car and nobody was injured, the policyholder might file claims for the first-party car damage insurance and the third-party property liability when she is at fault. These damages are actually caused by one accident. Thus, we merge the claims which are filed on the same date among different insurance policies for the same vehicle as one claim, and sum up the claim amount as the accident size. We only care about the insurance polices which cover the damage from a car accident. They include compulsory automobile liability insurance, voluntary third-party bodily injury liability insurance, voluntary third-party property liability insurance, and the first-party comprehensive coverage insurance. Since this study focuses on the externality caused by driving, in the first-party comprehensive coverage insurance, our sample only includes the vehicle-to-vehicle collision losses. After the above sample extraction, we obtain 155,581 observations in our final data. Table 1 shows the definitions for all variables used in this study. The basic statistics for each variable are provided in Table 2. Note that the frequency of claims is about 11.32%. It is much higher than the data from the United States or other developed countries. The high accident probability is mainly contributed by the first-party comprehensive coverage insurance, which accounts for 44.79% of the insurance per year during our sample period. The high probability might be due to the fact that Taiwan is a country with a limited territory but a high population density and large numbers of 6

8 vehicles. The total area in Taiwan is about 35,980 km 2, which is a slightly smaller than the Netherlands and slightly larger than Belgium. Most of the population (about 23 million) are located in the plains, which cover about 27% of the territory. In addition, the total number of vehicles excluding motorcycles was about 6.77 million in Taiwan in the year 2009 with an average annual growth rate of 2.4% over the period from 1999 to The average amount of each claim was 26,647.3 NT dollars, 3 with the maximum amount for one claim reaching 3,533,860 NT dollars. The key variables in this paper are the number of kilometers driven per year for each vehicle, km, and the average number of kilometers driven per year per vehicle, km. Since policyholders may not come back to the car dealer for maintenance regularly, we need to estimate the kilometers driven per year for each vehicle. For example, let us assume that one vehicle has three maintenance records as shown in Figure 1. Thus, we record the kilometers driven for this vehicle in the year 2001 as: b a c b The average number of kilometers driven per year for each vehicle in our sample is about thousand, whereas the average number of kilometers driven per year per vehicle is about thousand. The reason why these two numbers are different is that we calculate km before we delete the data with incomplete insurance information, so that the average number of kilometers driven per year per vehicle will be closer to that of the population. The insured are mostly between 30 and 60 years old. Most of the policyholders are female and married. The percentage of female policyholders is over 70%, and the percentage of married policyholders is over 90%. The major reason why most of the 3 The average exchange rate was about NT$ for one US dollar during our sample period. 7

9 policyholders are married middle-aged females is that there are insurance premium discounts for them in Taiwan, and the insurance policies cover all the drivers of the insured vehicle. Thus, most families will register their vehicles and insure the vehicles under the name of a married middle-aged female member of the family. It should be noted that our final sample is limited to a specific car brand since the vehicle manufacturer only looks after its own brand of vehicles. Another drawback is that our observations are insured by a specific insurance company. Thus, our data might have certain bias. We compare our data with the data from our sample insurance company which contains different car brands and find that our final data has significant higher percentage of age group 30 to 60 years old, females, new cars, small cars (with capacity smaller than 2,000 c.c.) and sedan. 3. Methodology First of all, we first adopt the following Probit regression to test the effect of the accident externality on the loss probability: Prob( claim 1) F( km + km X ), (1) it 1 km it t km it x where claim it is a dummy variable that equals 1 when the insured i has filed at least one claim in year t, otherwise it equals 0. F is the cumulative standard normal distribution function. km it is the estimated number of kilometers driven per year for individual i in year t. km t denotes the average number of kilometers driven per year per vehicle in year t. X it is the vector of control variables for the insured s information, and includes the characteristics of the insured and the characteristics of the insured s car which are used for underwriting. The s are the corresponding coefficients. We are 8

10 interested in the coefficient of km t, km. In the literature, most papers such as Vickrey (1968) assume that should be positive. km To examine the effect of the externality on the loss severity, we adopt ordinary least squares (OLS) regression with the following form: claim amount km km X. (2) it 2 km it + t km it x it The dependent variable is the amount of the claim for individual i in year t, and it denotes the error term. In the OLS regression, only the observations which have a claim are included. In other words, we estimate the accident externality that is conditional upon the loss events. The size of the accident externality is calculated according to the coefficient of km t,. Note that km km could be positive if an increase in km t increases the chance of an accident involving more cars, and then increases the claim size. On the other hand, km could be negative if an increase in km t increases traffic density, decreases driving speed, and further reduce the claim size. We learn this problem to our empirical findings. To examine whether the accident externality has a heterogeneous effect on individuals with different characteristics, we use the cross terms of the average number of kilometers driven per year per vehicle and the control variables, which include km it, the policyholder s age, gender and marriage status, and the vehicle s age and registration location. In other words, Equations (1) and (2) are modified as Prob( claim 1) F( km + km X + km km km X ), (3) it 3 km it t km it x 1 it it 2 and claim amount km km X km km km X. (4) it 4 km it + t it x 1 t it t km it2 it 9

11 In the above Equations, we will focus on the coefficients 1, 2, 1 and 2. To examine the factors affecting the individual s driving behavior, we also run the following OLS: km X. (5) it 5 it 3 it Since the individuals driving decisions might be affected by the economic conditions, we adopt year dummies in Equation (5) in addition to the individual characteristics to control the effect. Note that in Equations (1) to (4) we do not consider year dummies because the average kilometers driven for all individuals are the same within a year. 4. Empirical Results 4.1 The Accident Externality s Impact on Loss Frequency and Loss Severity Table 3 confirms the negative accident externality from driving with respect to loss frequency and loss severity in Taiwan. Our findings in Table 3 are consistent with those in Edlin and Karaca-Mendic (2006) as well as Saito, Kato and Shimane (2007). They found that accident externality exists in terms of total insurance costs. We make a step forward to show that accident externality exists both on loss frequency and loss severity. The first two columns in Table 3 present the results of estimating Equation (1). The average number of kilometers driven per year per vehicle has a significant positive effect. When the average number of kilometers driven per year per vehicle increases by one thousand kilometers, it will increase the total accident probability by 1.06% on basis of the coefficient of km, Compared to the average accident probability of 11.32%, the impact of the externality can not be neglected. Note that one thousand kilometers per year is not a huge distance in driving. If one decides to drive around the island of Taiwan, or have a round trip between Paris and Amsterdam or between Boston and Philadelphia, 10

12 then the total kilometers for that trip will be over one thousand kilometers. In addition, the number of kilometers driven by the individual is also significantly positively correlated with the loss probability. If the policyholder increases the number of kilometers driven by one thousand kilometers per year, then she will increase her own accident probability by 0.15% on basis of the coefficient of km, This probability increase is much lower than that due to an increase in km. It is because km represents the average kilometers among all vehicles. A one-kilometer increase in km could be viewed as everyone in the society consuming one more kilometer. The traffic density will have a significant increase compared to the case where the policyholder alone decides to drive one more kilometer. Our empirical results on control variables are generally consistent tot the findings in the literature. Specifically, we find that the single female has a higher probability of facing a car accident. New cars have a higher accident probability than old cars. These findings are generally consistent with the findings in Wang, Chung and Tzeng (2008). If the vehicle is registered in cities or northern Taiwan, which represents a high population density area, then the probability of an accident is also higher. This result is consistent with Belmont (1953) and Lundy (1965) who found that accident rates increased with traffic volume. The last two columns of Table 3 report the effects of the OLS regression on the loss severity that is conditional on a loss being obtained. They show that an increase in the average number of kilometers driven per vehicle per year will significantly increase the accident severity. The coefficient of km indicates that a one-thousand kilometer increase in km will increase the policyholder s accident amount by NT$4,150, which is about $130. Taking into account the total number of vehicles (excluding motorcycles) in 11

13 Taiwan, the conditional estimated externality per vehicle per year is about $ million dollars per year for a one-thousand kilometer increase in km. Similar to the effect on loss probability, we find that the policyholder s own number of kilometers driven also has a significantly positive effect on loss severity. The impact of km on accident severity is also lower than the impact of km on it. However, contrary to the findings in relation to loss probability, we find that if an accident occurs, single females or the vehicles registered in high population density areas will have lower accident costs. These phenomena might be correlated with driving speed. On average, the driving speed of female drivers might be lower than that of male drivers. People could also drive slowly in high population density areas. Thus, the lower accident severity might be caused by the lower driving speed. 4.2 The Heterogeneity Effect of the Accident Externality The heterogeneity effect of the accident externality is presented in Table 4. The first two columns of Table 4 show that, in terms of probability, people under the age of 20 will suffer more than people aged more than 20 when other people drive more. In addition, when other people drive more, the loss probability is higher in cities and in the north of Taiwan than in the suburban areas and in other parts of Taiwan. In short, young people, old cars and people living in high population density areas face a more severe accident externality from driving in terms of probability. To see whether the above differences are not only statistically but also economically significant, we use the information in Table 4 to compare the marginal probabilities of the externality for the individuals with different characteristics and show the results in Table 5. Table 5 indicates that the marginal probability of the externality for people under the age of 20 is %, which is 0.687% higher than that for people over the age of 20. Vehicles more than 4 years old face an 12

14 additional 1.259% accident probability when the average number of kilometers driven increases by a thousand kilometers compared to the vehicles less than 4 years old. The last two columns of Table 4 report the heterogeneity for the severity of the accident externality conditional on the occurrence of an accident. When the average number of kilometers driven per vehicle increases, the conditional loss severity for female policyholders, new cars, and the cars registered in northern Taiwan will be significantly decreased. Specifically, male policyholders will face an additional NT$3,900 ($122) in accident costs compared to female policyholders when km increases by one thousand kilometers. Compared to one-year-old cars, the vehicles that are more than 4 years old will face an additional NT$24,430 ($763) in accident costs when km increases by one thousand kilometers. 4.3 The Heterogeneity Effect of Driving Table 6 reports the heterogeneity effect of driving. It shows that both the individual s and the vehicle s characteristics have significant explanatory powers on kilometer driven. We find that people over the age of 20 significantly drive more than people younger than 20 years old. However, the average kilometer driven decreases by age for the people over the age of 20. People with age between 20 to 25 drives about 4,000 kilometers more per year than people older than 60. Female significantly drives less than male. The difference is about 1,340 kilometers per year. Married people significantly drive more than single policyholders. Table 6 also shows that the kilometer driven decreases in vehicle age. In average, people with new cars drive about 1,200 kilometers more than people with cars over the age of 4 per year. Although vehicles with capacity over 3,000 c.c. usually consume more gas per kilometer, we find that people having cars with capacity over 3,000 c.c. tend to 13

15 drive more than 1,500 kilometers per year than people having cars with capacity less than 2,000 c.c.. We also find that people living in cities or northern Taiwan tend to drive less. It might due to the fact that in cities and northern Taiwan, the public transportation system is more available and convenient. The above evidences suggest that, to reduce the incentive to drive, the government could design a system to increase the driving cost of the individuals who are over the age of 20, males, married, having new cars, with larger size vehicle, and living in the suburbs or southern Taiwan. Comparing the heterogeneity effect of driving and the heterogeneity effect of the accident externality, we find that the people suffering the accident externality more tend to coincide with the people driving less. For example, people with age younger than 20 years old, old cars, small cars or living in cities tend to face higher accident externality in terms of accident probability. These policyholders also tend to drive less than the corresponding groups. Thus, it is possible to design a public system which benefits policyholders who suffer accident externality more and drive less at the same time. 5. Conclusions The literature has indicated that the accident externality from driving is significant in different countries. However, most papers estimate the cost of the externality by using aggregate data, and the details regarding the externality are not clear. Our paper examines the accident externality from driving by using data at the individual level in Taiwan. We find that the impact of the accident externality in each year on the loss probability is about 1.06% when the average number of kilometers driven per year per vehicle increases by one thousand kilometers. Being conditional upon an accident, the impact of the externality on the loss severity is about $130 when the average number of 14

16 kilometers driven per year per vehicle increases by one thousand kilometers. In addition, we find that the externality is heterogeneous in terms of the individual s characteristics, such as gender, age and the vehicle s age and registration area. We also find that people who are more than 20 years old, males, married people, those who have new cars and those who are living in lower population density areas, such as the suburbs or southern Taiwan, drive larger numbers of kilometers. Our findings may generate further policy implications. The literature has proposed that a Pigouvian tax on gasoline, automobile insurance based on miles driven, and pay-as-you-drive insurance could reduce the accident externality from driving. Indeed, the above policies could reduce the number of kilometers driven and further decrease the externality. In addition to these policies, our findings suggest an alternative mechanism to correct the accident externality from driving. To handle the heterogeneous effect, a government could launch an insurance premium tax due to the accident externality. Rather than apply a constant tax rate as with most premium taxes, the proposed tax rate could be designed to be positively correlated with the individual s characteristics which indicate whether the insured is driving more, and negatively correlated with the characteristics which disclose whether the insured is suffering more as a result of the accident externality. To avoid a significant increase in the number of uninsured after the insurance premium tax, we suggest that this type of tax be levied on compulsory insurance rather than voluntary insurance. Another possible way to correct the accident externality from driving is that the government can design a bonus-malus system on compulsory insurance basing who cause more the accident externality and/or who is suffered from the accident externality. 15

17 Appendix As mentioned in the Introduction, understanding the accident externality from driving in terms of its probability and severity can help the government correct the externality more accurately. Let us use a simple model, which is modified on the basis of Dupor and Liu s (2003) paper, to illustrate how governments could use the information from our paper to correct the externality. Assume that the individuals are homogeneous and endowed with wealth w. The representative individual might face an accident loss l, which is a function of the number of kilometers driven, km, and the average kilometers driven by the society, km. The loss probability,, is also a function of km and km. Assume that driving could bring the individual some benefit, e.g., saving time for the individual or having fun with driving. Let Bkm denote the corresponding monetary reward from driving with Bkm 0. Thus, the individual will take km as given and choose the optimal number of kilometers driven to maximize her expected utility: Eu ( km, km ) u ( w L ( km, km ) B ( km )) 1 ( km, km ) u ( w B ( km )), (6) where u denotes the individual s utility function with u 0 and u 0. The corresponding first-order condition is ( km, km) M u( wl( km, km) B( km)) km Lkmkm (, ) ( km, km) u( w L( km, km) B( km)) B( km) km 0. ( km, km) uw ( Bkm ( )) km 1 ( km, km) u( w B( km)) B( km) (7) 16

18 On the other hand, the government knows that everyone s decision regarding km will also affect the average kilometers driven, km. Thus, a benevolent social planner will take the externality into consideration. Thus, the first-order condition of the government will be ( km, km) N M u( wl( km, km) B( km)) km L( km, km) ( km, km) u( w L( km, km) B( km)) km ( km, km) uw ( Bkm ( )) km 0. (8) The private optimum will reach the social optimum if and only if N M 0, i.e., ( km, km) uw ( Lkmkm (, ) Bkm ( )) km L( km, km) ( km, km) u( w L( km, km) B( km)) (9) km ( km, km) uw ( Bkm ( )) 0. km As argued by Dupor and Liu (2003), to correct the externality, the government should design a system such that Equation (9) will hold. In other words, understanding ( km, km) km and L( km, km), which is respectively about 1.06% and $ in km Taiwan when km increases by one thousand, can help the government to design a system to reach the social optima. If the representative individual is assumed to be risk neutral, then the expected cost of the accident externality is sufficient to determine the difference between the social and private optima. Specifically, let u 1. Equation (9) may then be written as 17

19 ( km, km) L( km, km) ( wl( km, km) B( km)) ( km, km) km km ( km, km) ( w B( km)) km ( km, km) L( km, km) ( Lkmkm (, )) ( kmkm, ) km km ( km, km) L( km, km). km In other words, estimating the expected costs associated with the accident externality, ( km, km) L( km, km), would help the government to correct the externality. km 18

20 References Belmont, D. M Effect of Average Speed and Volume on Motor-Vehicle Accidents on Two-Lane Tangents. Proc. Highway Res. Board 32: Dupor, B. and W. Liu, 2003, Jealousy and Equilibrium Overconsumption. American Economic Review 93(1): Edlin, Aaron S. and Pinar Karaca-Mandic The Accident Externality from Driving. Journal of Political Economy 114(5): Lundy, Richard A Effect of Traffic Volumes and Number of Lanes on Freeway Accident Rates. Highway Res. Record 99: Parry, Ian W.H Is Pay-as-You-Drive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? American Economic Review 95(2): Parry, Ian, W.H., Margaret Walls, and Winston Harrington Automobile Externalities and Policies. Journal of Economic Literature 45(2): Saito, Kuniyoshi, Takaaki Kato, and Tetsuya Shimane Traffic Congestion and Accident Externality: A Japan-U.S. Comparison. Third Annual Asia-Pacific Economic Association (APEA) Conference, July 25-26, Hong Kong, China, 34 pages. Turner, D. J. and R. Thomas Motorway Accidents: An Examination of Accident Totals, Rates and Severity and Their Relationship with Traffic Flow. Traffic Engineering and Control 27 (July/August): Vickrey, William Automobile Accidents, Tort Law, Externalities, and Insurance: An Economist s Critique. Law and Contemporary Problems 33 (Summer): Wang, J.L, C. Chung and L.Y. Tzeng An Empirical Analysis of the Effects of Increasing Deductible on Moral Hazard. Journal of Risk and Insurance 75(3):

21 182 days 289 days Date: 10/01/ /01/ /01/ /15/ /15/ days 274 days Kilometers: a b c Figure 1 An example of the estimation of kilometers driven. 20

22 Table 1 Definitions of Variables Variables Definition Dependent Variables claim A dummy variable that equals 1 when the insured has filed at least one claim in the current year, otherwise it equals 0. claim amount The claim amount (in thousands of New Taiwanese dollars) for the insured who has filed the claim. Independent Variables Kilometers km The estimated thousands of kilometers driven for each vehicle. km The average thousands of kilometers driven per year per vehicle which are driven in the whole area of Taiwan. Individual s characteristics age2025 A dummy variable that equals 1 if the insured is between the ages of 20 and 25, otherwise it equals 0. Age2530 A dummy variable that equals 1 if the insured is between the ages of 25 and 30, otherwise it equals 0. Age3060 A dummy variable that equals 1 if the insured is between the ages of 30 and 60, otherwise it equals 0. Age60up A dummy variable that equals 1 if the insured is over the age of 60, otherwise it equals 0. Female A dummy variable that equals 1 if the insured is female, otherwise it equals 0. Married A dummy variable that equals 1 if the insured is married, otherwise it equals 0. Vehicle s characteristics carage1 A dummy variable that equals 1 when the car is one year old, otherwise it equals 0. carage2 A dummy variable that equals 1 when the car is two years old, otherwise it equals 0. carage3 A dummy variable that equals 1 when the car is three years old, otherwise it equals 0. carage4 A dummy variable that equals 1 when the car is four years old, otherwise it equals 0. capacity2 A dummy variable that equals 1 when the insured car equals or is over 2000 c.c. and is under 3000 c.c., otherwise it equals 0. capacity3 A dummy variable that equals 1 when the insured car equals or is over 3000 c.c., otherwise it equals 0. sedan A dummy variable that equals 1 when the car is a sedan and is for non-commercial or for long-term rental purposes, otherwise it equals 0 truck A dummy variable that equals 1 when the car is a small freight-truck and is for non-commercial purposes or for business use, otherwise it equals 0 city A dummy variable that equals 1 when the owner of the car lives in a city, otherwise it equals 0. north A dummy variable that equals 1 when the car is registered in the north of Taiwan, otherwise it equals 0. south A dummy variable that equals 1 when the car is registered in the south of Taiwan, otherwise it equals 0. east A dummy variable that equals 1 when the car is registered in the east of Taiwan, otherwise it equals 0 21

23 Table 2 The Basic Statistics of the Variables Variables Mean STD Min Max Dependent Variables claim claim amount Independent Variables Kilometers km km Individual s characteristics age age age age60up female married Vehicle s characteristics carage carage carage carage capacity capacity sedan truck city north south east Number of obs

24 Table 3 The Effect of Average Driving on Loss Probability and Severity Probit Model OLS Model Variables Estimate coefficient P-value Estimate coefficient P-value Intercept < Kilometers km < km < <.0001 Individual s characteristics age age age age60up female < married Vehicle s characteristics carage < carage < carage < carage capacity capacity sedan truck <.0001 city < north south east Likelihood ratio Adj. R-sq Number of Obs

25 Table 4 The Heterogeneity Effect of Average Driving on Loss Probability and Severity Probit Model OLS Model Variables Estimate coefficient P-value Estimate coefficient P-value Intercept Kilometers km km Individual s characteristics age age age age60up female married Vehicle s characteristics carage < carage < carage < carage < capacity < capacity sedan truck <.0001 city < north south east Heterogeneity Effect km * km km *age km *age km *age km *age60up km *female

26 km *married km *carage < km *carage < km *carage < km *carage < km * capacity km * capacity km * sedan km * truck <.0001 km *city < km *north km *south km *east Likelihood ratio Adj. R-sq Number of Obs

27 Table 5 The Marginal Probability of the Externality for Individuals with Different Characteristics Characteristics Yes (1) No (2) Difference (1)-(2) p-value Younger than 20 years old policyholders More than 4 years old vehicles < Living in cities < Living in northern Taiwan < Note: Yes means the group has the characteristics described. For example, in the first row, Yes means the group of younger than 20 years old policyholders. No means the group does not have the characteristics described. 26

28 Table 6 The OLS Regression on Individual s Driving Variables Estimate P-value coefficient Intercept <.0001 Individual s characteristics age <.0001 age <.0001 age <.0001 age60up <.0001 female <.0001 married Vehicle s characteristics carage <.0001 carage <.0001 carage <.0001 carage capacity <.0001 capacity <.0001 sedan <.0001 truck <.0001 city <.0001 north south <.0001 east <.0001 year dummy yes Adj. R-sq Number of Obs