The Use of Annual Mileage as a Rating Variable
Jean Lemaire, Sojung Park, Kili Wang
Jean Lemaire (contact person) is the Harry J. Loman Professor of Insurance and Actuarial Science at the Wharton School of the University of Pennsylvania.
Address: 458 JMHH, 3730 Walnut Street, Philadelphia, PA 19104-6302.
E-mail: .
Tel: (215) 898-7765.
Fax: (215) 898-1280
Sojung Park is Assistant Professor at the College of Business Administration, Seoul National University.
Address: Kwanak-gu, Seoul 151-742, Republic of Korea
E-Mail:
Phone: +82-2-880-6907
Fax: +82-2-884-0408
Kili Wang is Associate Professor, Department of Insurance, Tamkang University, Taipei.
Address: 151 Ying-Chuan Rd., Tamsui, Taipei County 251, Taiwan
E-mail:
Tel: +886-2-26215656-3333
Fax: +886-2-2620-9505
None of the authors is a graduate student.
The Use of Annual Mileage as a Rating Variable
Abstract
Auto insurance carriers may be at a crossroads concerning the classification variables they use. Regulators are questioning the use of some traditional variables like gender and territory, and request more precise criteria. Insurers are being pressured to find new variables that predict accidents more accurately and are socially acceptable. They have been reluctant to use annual mileage, despite its obvious correlation with claims, due to their inability to verify policyholders’ statements, and the relative easiness to tamper with odometers. This had led to the use proxy variables like distance between home and work. This situation may change, due to the development of telematics, on-board computers, GPS transmitters, tampering-resistant odometers, and the fast decrease in cost of these new technologies. Insurance carriers need to explore ways to introduce PAYD, Pay-As-You-Drive insurance.
The advantages of PAYD pricing are substantial: (i) Mileage pricing is directly based on exposure to risk, and not on the behavior of groups such as single males sharing a zip code. Drivers have more control over their premium. Pricing does not rely on variables such as gender and territory, that can become unlawful; (ii) Mileage-pricing would make insurance for low-mileage cars more affordable, which can reduce uninsured driving; (iii) Fraud opportunities are reduced; (iv) Consumers have an incentive to drive less, leading to lower accident risks: (v) PAYD will have reduce total national mileage driven, with a positive effect on the environment (CO2 emissions, noise, traffic congestion); (vi) Telematics devices can provide side benefits such as roadside assistance and stolen car recovery.
Disadvantages of PAYD include: (i) Installation and monitoring costs can be substantial for some categories of drivers; (ii) Premiums, depending on variable mileage, become less predictable for drivers and insurers; (iii) Mileage monitoring is currently used to provide discounts, resulting in an overall reduction of premium income for insurers; (iv) Distance-based pricing, currently offered as an option, could create adverse selection, for instance with motorists in multi-vehicle households shifting driving from mileage-priced cars to cars with fixed premiums; (v) Customer tracking can be perceived as intrusive and as an invasion of privacy.
A major US carrier uses a large number of variables in rating in Pennsylvania: age, sex, and marital status of principal driver, make and model of car, zip code, claims and traffic violations history, use of car, annual mileage with a single cut-off point, at 7,500 miles per year. In 2012, the company introduced a voluntary program to monitor mileage, using a telematics device. Using the catchy slogan “Just have your car send us your driving habits”, the rating plan involves the use of a transmitter. Odometer readings are e-mailed monthly to the subscriber and the insurer. A premium discount is then offered at each renewal, for instance 32% for 3,500 annual miles, 13% for 11,000 miles, 5% for 15,000 miles. If the policyholder had his premium based on self-reported annual mileage under 7,500, and if the actual mileage exceeds that threshold, the next premium is increased.
In this research we investigate the impact of the use of mileage as a rating variable, using unique data originating from Taiwan. As in that state the leading brand of cars also owns an extended network of repair shops that customers visit for routine maintenance and oil changes, data that include driver classification variables (age, gender, and marital status of main driver, territory, use of car, engine cubic capacity, bonus-malus class), claim records, and annual mileage extrapolated from odometer readings collected during oil changes, were available for over a quarter million vehicle-years.
The conclusions of Logit and Probit regression models are very strong. Annual mileage is an extremely powerful predictor of the number of claims at-fault. Its significance, as measured by Wald’s chi-square and its associated p-value, by far exceeds that of all other variables, including bonus-malus (BMS). This conclusion applies independently of all other variables possibly included in rating. Mileage is the most accurate variable that insurers could introduce. The inclusion of mileage as a new variable should, however, not take place at the expense of BMS; rather the information contained in the bonus-malus premium level complements the value of annual mileage, as the significance of BMS is not decreased by the inclusion of mileage. The Taiwanese BMS is fairly mild: penalties are not severe, when compared to BMS in force in other countries. Should Taiwanese companies decide to make transition rules and premium levels more severe, the significance of BMS would most probably increase. An accurate rating system should include annual mileage and BMS as its two main building blocks, possibly supplemented by the use of other variables like age, territory, and engine cubic capacity.
In addition, our data provide us with a unique opportunity to implement path-breaking work by Taylor with real-life data. Indeed, in 1997 Taylor was the first author to model the relation between BMS and other rating factors. He noted that failing to consider jointly a priori classification variables and BMS could lead to double-counting similar effects. For instance, young drivers are likely to be penalized by a high a priori surcharge, while gravitating to the malus zone of the BMS, thereby cumulating an explicit a priori penalty with an implicit BMS surcharge. Taylor developed a sophisticated Bayesian model to calculate two sets of BMS premium levels: one that ignores correlations with a priori variables, and one that incorporates them. Through an example, Taylor showed that the range of BMS premium levels should be reduced significantly when covariates are taken into account. Unfortunately, Taylor could not access real-life data, and had to use an artificially-created example.
We applied Taylor’s model to our data to check whether the inclusion of annual mileage as an a priori rating variable would require a modification of the existing BMS. As expected, a selection effect according to mileage takes place, with more low-mileage users ending up in the best BMS class, and high-mileage users more likely to occupy to top BMS class, creating a potential double-counting effect if annual mileage is introduced as a rating variable without modifying the BMS. However, the interaction between mileage and BMS is small, so that the introduction of mileage in rating would not justify a significant weakening of the BMS. The double-counting effect is minimal. Mileage cannot “replace” BMS rating. Consequently, BMS should continue to play a major role in auto insurance rating in Taiwan.
Admittedly, several characteristics of Taiwan and its insurance market are quite unique: extreme traffic density, low number of cars given the high average wealth level, compulsory insurance that only requires bodily injury coverage with fairly low policy limits. However, our results are so strong that we can confidently extend them to all affluent countries: annual mileage is a strong predictor of the number of claims; BMS should remain an important component of auto insurance rating.