To endorse or not to endorse (fe)males?
The differences in actuarially fair prices between genders
Actuarially fair prices from insurer’s point of view are equal to the expected cost of insurance claims plus administrative costs. Therefore, if administrative expenses are the same for all insurees, the insurance prices of two policyholders should only differ if the expected value of claims is not the same. If one believes the ‘women-are-terrible-drivers’ jokes, the actuarially fair insurance prices for women should be higher than for men. In peer-to-peer insurance, this would imply that you should avoid endorsing females. However, does data support this ‘folk wisdom’?
Figure 1: Number of accidents for car drivers by age, gender, and responsibility
CRASH AND BURN
Looking at reported car crashes, it does not seem so. Figure 1 presents the number of accidents of passenger vehicle drivers by age and responsibility for the car crash, separately for males and females. The picture shows that men are more frequently involved in accidents
irrespective of their responsibility for the collision. The difference between males and females in the number of accidents they did not cause can be attributed to the differences in the share of male and female drivers and the distances they travel. Of course, if there are more male than female drivers, the number of accidents caused by men will be higher even if their driving skills are the same. Assuming that the number of accidents for which the driver is not responsible does not depend on the driving style or skills, but rather on the miles traveled, we can calculate the ratio between the probabilities of accident caused by men and women. Figure 2 shows the differences between the two probabilities in percentages. We can observe that the men below the age of 65 are more likely to cause an accident than women. More specifically, male drivers aged between 18–25 have a 26% higher probability of being responsible for the collision then females in the same age group. The difference is the highest for 36–40-year-old persons (45%).
Figure 2: Difference in probability of an accident caused by men and women (in %), year 2017
As one would expect, the differences in the likelihood of causing an accident between genders are not specific to the year 2017. Figure 3 and Figure 4 reveal similar patterns for years 2007 and 2012.
Figure 3: Difference in probability of an accident caused by men and a women (in %), year 2012
Figure 4: Difference in probability of an accident caused by men and women (in %), year 2007
Figure 5: Fatal passenger vehicle crash involvements per 100 million miles traveled by driver age and gender
Figure 5 below reinforces this evidence by showing driver fatal car crash involvements per 100 million miles driven in the U.S. Again we can observe that young men (ages 20-29) were on average involved in 3 more collisions with the fatal result per 100 million miles traveled than women of the same age.
However, the expected costs of insurance claims do not depend only on the probability of collision, but also on the values of damages. As such data are not available, the severity of a car accident is used as an approximation. The academic research presents mixed results regarding gender differences in vehicle crash injury severity (see for example Kim et al., 2013; Fountas et al., 2018; Morgan et al., 2011), most likely due to lack of data on miles traveled and other characteristics. Fortunately, the data set used above allows to present differences in probability of an accident caused by a man and probability of an accident caused by a woman for different car crash injury severity (see Figure 6). The figure shows that men appear to be more likely to cause accidents with severe and no injury while women have on average slightly higher likelihood of causing a minor car crash injury.
Figure 6: Difference in probability of an accident with different injury severity caused by men and women (in %), year 2007
So what can we infer from this evidence? It appears that young and middle-aged men are more prone to cause and be involved in car accidents. They are also more likely to cause severe car crash injuries and are known for driving more expensive cars. Therefore, the expected value of men’s future claims is likely to be higher than for women of the same age. This implies that the actuarially fair prices for young and middle-aged women should, in fact, be lower than that of their male peers. However, the current prices of insurance policies do not (or cannot, due to the legal reasons) capture such heterogeneity of expected values of claims, even though the data on car accidents presented earlier indicate that the differences in prices could be as high as 30 to 50 percent. Peer-to-peer insurance based on social proof presents a possible path towards such actuarially fair prices.
To sum up, females should have an easier job in obtaining their endorsers in the peer-to-peer insurance. However, at the same time, the social proof enables the diligent male drivers to differentiate themselves from their more aggressively driving buddies.
Written by: Dr. Tjaša Bartolj
Sources:
Kim, J. K., Ulfarsson, G. F., Kim, S., & Shankar, V. N. (2013). Driver-injury severity in single-vehicle crashes in California: a mixed logit analysis of heterogeneity due to age and gender. Accident Analysis & Prevention, 50, 1073–1081.
Fountas, G., Anastasopoulos, P. C., & Abdel-Aty, M. (2018). Analysis of accident injury-severities using a correlated random parameters ordered probit approach with time variant covariates. Analytic Methods in Accident Research, 18, 57–68.
Morgan, A., & Mannering, F. L. (2011). The effects of road-surface conditions, age, and gender on driver-injury severities. Accident Analysis & Prevention, 43(5), 1852–1863.
