The Use of Telematics Devices to Improve Automobile Insurance Rates

Men on average drive significantly longer distances than women.

“As found by other authors, the influence of Gender is masked by the fact that men on average drive significantly longer distances than women.”

• cites Ayuso, Guillen, & Pérez-Marín, 2016 sourceSupported
• cites Verbelen, Antonio, & Claeskens, 2018 sourceSupported
• cites Wüthrich, 2017 sourceCould not verify

  Section 2.1 compares trip distances for individual drivers A, B and C, but does not compare men with women. A search for gender, male/female drivers, and distance driven found no passage reporting a sex-based difference or its statistical significance; the Introduction also says the dataset lacks other driver information. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

The overall effect of the driving distance variable is positive.

“The overall effect of the driving distance variable is positive”

Speed limit violations increase the expected number of accident claims.

“We confirm that speed limit violations and driving in urban areas increase the expected number of accident claims.”

There is a positive relationship between distance driven and the number of excess zeros observed in the number of claims.

“We discover a positive relationship between the distance driven and the number of excess zeros observed in the number of claims.”

Driving in urban areas increases the expected number of accident claims.

“We confirm that speed limit violations and driving in urban areas increase the expected number of accident claims.”

In the all-claims ZIP model, the expected number of claims is higher for inexperienced drivers than for experienced drivers.

“Thus, we find an increasing expectation in the number of claims for women drivers as opposed to men, inexperienced drivers as opposed to experienced, and owners of old and powerful vehicles as opposed to owners of newer and less powerful cars.”

The relationship between distance driven and zero-inflation is not linearly dependent.

“Here, we have shown that this relationship is not linearly dependent, as we report that the zero-inflation part plays a significant role.”

The coefficient for the logarithm of the number of kilometres driven per year in the logit model is positive.

“The coefficient for the logarithm of the number of kilometres driven per year in the logit model (which predicts zero inflation) is positive, i.e. the probability of observing false zeros increases with increasing distance.”

The sample consists of drivers aged less than 37 years.

“The sample consists of drivers aged less than 37 years, so Age may not have enough range to show a significantly different effect by Gender .”

The ZIP model gives better goodness of fit than the classical Poisson model (non-zero-inflated Poisson model).

“Moreover, we have shown that the ZIP model gives better results in terms of goodness of fit than those obtained with the classical Poisson model (non-zeroinflated Poisson model).”

• Also stated in: § 4. RESULTS · boosted

  “The goodness of fit results are always better in the zero-inflated models because they take into account differences between false zeros (non-risk exposure) and true zeros (risk exposure and zero claims).”

The percentage of cars parked overnight in a garage is higher among those who made at least one claim than among those who made no claim.

“Unexpectedly, in the case of cars parked overnight in a garage, the percentage value is higher among those who made at least one claim than it is among those who made no claim.”

In the all-claims ZIP model, the expected number of claims is higher for owners of powerful vehicles than for owners of less powerful vehicles.

“Thus, we find an increasing expectation in the number of claims for women drivers as opposed to men, inexperienced drivers as opposed to experienced, and owners of old and powerful vehicles as opposed to owners of newer and less powerful cars.”

In the all-claims ZIP model, the expected number of claims is higher for owners of old vehicles than for owners of newer vehicles.

“Thus, we find an increasing expectation in the number of claims for women drivers as opposed to men, inexperienced drivers as opposed to experienced, and owners of old and powerful vehicles as opposed to owners of newer and less powerful cars.”

Driving at night presents larger mean values in the claims group than in the no claims group.

“As for the new driving behaviour indicators derived from telematics, driving at night and driving in urban areas present larger mean values in the claims group than in the no claims group.”

In the at-fault claims model, the percentage of kilometres driven at night has an impact on the expected number of at-fault claims.

“In common with the result in Table IV, the percentage of kilometres per year driven over the speed limit, and additionally here the percentage of kilometres driven at night, have an impact on the expected number of claims in which the driver is at fault.”

In the all-claims ZIP model, the expected number of claims increases as the percentage of urban kilometres driven per year increases.

“Thus, the number of claims increases as these two regressors increase.”

Driving in urban areas presents larger mean values in the claims group than in the no claims group.

“As for the new driving behaviour indicators derived from telematics, driving at night and driving in urban areas present larger mean values in the claims group than in the no claims group.”

In the at-fault claims model using only telematics variables, the percentage of kilometres driven at night is significant at the 10% level.

“The percentage of kilometres driven at night is significant at the 10% level when we only consider the telematic variables but the AIC value for this model is lower than that obtained for the first model.”

The probability of excess zeros increases with distance driven.

“The probability of excess zeros increases with distance.”

• Also stated in: § 5. CONCLUSIONS · plain

  “The coefficient for the logarithm of the number of kilometres driven per year in the logit model (which predicts zero inflation) is positive, i.e. the probability of observing false zeros increases with increasing distance.”

In the at-fault claims model, the age squared parameter is significant, indicating a non-linear relationship between age and the expected number of claims.

“However, the significance of the age squared parameter indicates a non-linear relationship between the two variables.”

The zero-inflation part plays a significant role.

“Here, we have shown that this relationship is not linearly dependent, as we report that the zero-inflation part plays a significant role.”

Drivers that made a claim have held their driving licence for fewer years than those that made no claim.

“drivers that made a claim for at least one accident are, on average, younger than those that made no claim and have held their driving licence for fewer years.”

The hold-out analysis indicates very similar Chi squared values: 1,041.3 with 6 degrees of freedom in the training sample and 1,005.9 with 6 degrees of freedom in the test sample for the model of all claims and all variables.

“The hold out analysis indicates very similar values (1,041.3 with 6 degrees of freedom in the training sample and 1,005.9 with 6 degrees of freedom in the test sample for the model of all claims and all variables).”

For at-fault claims, the model including all variables has the lowest AIC value among the compared specifications.

“Here, again, a better goodness of fit is obtained for the specification that includes all variables (both telematic and non-telematic) and the model that includes only the telematics variables (the lowest AIC value being obtained for served column 1).”

In the at-fault claims model, inexperienced drivers show a higher expected number of claims than more experienced drivers.

“Inexperienced drivers (measured in terms of the number of years in which they have been in possession of a driving licence) and drivers of old vehicles show a higher expected number of claims than that recorded by their more experienced counterparts and drivers of newer vehicles.”

The Chi squared test of differences between observed and fitted frequencies was 946.7 for the whole sample.

“The Chi squared test of differences between observed and fitted frequencies was equal to 946.7 for the whole sample.”

In the all-claims ZIP model, night driving is not statistically significant in explaining the expected number of claims.

“No significance is observed in the case of night driving.”

In the all-claims ZIP model, the percentage of urban kilometres driven per year is statistically significant in explaining the expected number of claims.

“As for the new telematic regressors, twothe percentage of kilometres per year driven over the speed limit and the percentage of urban kilometres driven per yearare significant in explaining the expected number of claims.”

In the all-claims ZIP model, the expected number of claims increases as the percentage of kilometres per year driven over the speed limit increases.

“Thus, the number of claims increases as these two regressors increase.”

The differences in the mean for the exposure risk regressor and other classical and telematic regressors between drivers with no claims and drivers with claims are statistically significant, except for vehicle age and the percentage of kilometres driven over the speed limit squared.

“The Mann-Whitney test shows that the differences in the mean for the exposure risk regressor (Table II), as well as for the other classical and telematic regressors (Table III) are statistically significant in the cases of drivers with no claims and drivers with claims, with the exception of vehicle age (p-value=0.331) and the percentage of kilometres driven over the speed limit squared (p-value=0”

In the all-claims ZIP model, the percentage of kilometres per year driven over the speed limit is statistically significant in explaining the expected number of claims.

“As for the new telematic regressors, twothe percentage of kilometres per year driven over the speed limit and the percentage of urban kilometres driven per yearare significant in explaining the expected number of claims.”

In the all-claims ZIP model, the expected number of claims is higher for women drivers than for men.

“Thus, we find an increasing expectation in the number of claims for women drivers as opposed to men, inexperienced drivers as opposed to experienced, and owners of old and powerful vehicles as opposed to owners of newer and less powerful cars.”

Drivers that made a claim for at least one accident are, on average, younger than those that made no claim.

“From a univariate point of view, drivers that made a claim for at least one accident are, on average, younger than those that made no claim”

Insureds making at least one claim have a higher value for ownership of a powerful vehicle than those making no claims.

“A similar conclusion can be drawn in the case of ownership of a powerful vehicle, where those insureds making at least one claim present a higher value than those making no claims.”

In the models, the interaction between Age and Gender is not significant.

“The results for all the models, which are available from the authors, show that this interaction is not significant.”

• Also stated in: § 4. RESULTS · plain

  “Our conclusion for this sample is that there is no interaction between Age and Gender.”

The model predicts the highest number of expected claims for younger women with little driving experience, driving old and powerful vehicles, driving in urban zones, and exceeding the speed limit.

“Our model predicts the highest number of expected claims for younger women, with little driving experience, driving old and powerful vehicles, driving in urban zones, and exceeding the speed limit.”

In the at-fault claims model, drivers of old vehicles show a higher expected number of claims than drivers of newer vehicles.

“Inexperienced drivers (measured in terms of the number of years in which they have been in possession of a driving licence) and drivers of old vehicles show a higher expected number of claims than that recorded by their more experienced counterparts and drivers of newer vehicles.”

The part of the zero accident frequency not explained by traditional insurance risk factors increases with the distance driven by the policyholder.

“We have shown that the part of the zero accident frequency not explained by traditional insurance risk factors increases with the distance driven by the policyholder.”

For at-fault claims, the model using only telematics variables has a lower AIC value than the model using only classical variables.

“As in Table IV, a lower AIC is obtained for the specification using only telematic variables as opposed to that using only classical variables (columns 2 and 3, respectively).”

In the all-claims ZIP model, the parameters for gender, driving experience, vehicle age, and vehicle power are statistically significant.

“In the case of the classical variables, all the parameters for gender, driving experience, vehicle age and the power of the vehicle are statistically significant.”

In the at-fault claims model, the percentage of kilometres per year driven over the speed limit has an impact on the expected number of at-fault claims.

“In common with the result in Table IV, the percentage of kilometres per year driven over the speed limit, and additionally here the percentage of kilometres driven at night, have an impact on the expected number of claims in which the driver is at fault.”

Longer driving should result in a higher premium.

“longer driving should result in higher premium”

Including standard telematics variables significantly improves risk assessment of insureds.

“Recently, it has been proven that including standard telematics variables significantly improves risk assessment of insureds”

• cites Baecke & Bocca, 2017 sourceNot checked — no full text of the source

The positive relationship between distance driven and excess zeros is due to a learning effect, where good drivers are more frequent than expected among those that drive long distances.

“We argue that this is due to a learning effect, where good drivers are more frequent than expected among those that drive long distances.”

There is a learning effect for large values of distance travelled.

“We show the existence of a learning effect for large values of distance travelled”

• AssumptionRests on an assumption: The high frequency of zeros may be due to insureds not wishing to claim for small accidents to avoid a premium increase or to low vehicle use.

Under the Poisson model with exposure, the probability of zero claims declines naturally as distance driven increases.

“Under this model, the probability of zero using the Poisson distribution is calculated as follows, P(𝑌 𝑖 = 0) = exp(-𝐷 𝑖 𝜆 𝑖 ), so it depends on the distance and, since 𝜆 𝑖 is always positive by definition, then the probability of zero claims declines naturally as distance driven increases.”

• AssumptionThe authors state this as an assumption: In the ZIP model, with probability p the only possible observation is 0, and with probability 1-p a Poisson(λ) random variable is observed.
• AssumptionThe authors state this as an assumption: The new Y* variable follows a Poisson distribution with parameter exp(β0 + β1 x_i1 + ... + βk x_ik).

None of the cited ZIP model contributions has analysed the role of exposure to risk in terms of distance driven.

“none of these contributions has analysed the role of exposure to risk in terms of distance driven.”

• cites Cameron & Trivedi, 2013 sourceNot checked — no full text of the source
• cites Winkelmann, 2003 sourceNot checked — no full text of the source
• cites Lambert, 1992 sourceNot checked — no full text of the source

If α1 is significantly different from zero, the relationship between expected claims and distance driven is not linear.

“the derivative of ( 5) with respect to 𝐷 𝑖 shows how much the expected claims would change as a function of 𝐷 𝑖 and indicates that if 𝛼 1 is significantly different from zero, then the relationship is not linear.”

• AssumptionThe authors state this as an assumption: In the ZIP model, with probability p the only possible observation is 0, and with probability 1-p a Poisson(λ) random variable is observed.
• AssumptionThe authors state this as an assumption: The new Y* variable follows a Poisson distribution with parameter exp(β0 + β1 x_i1 + ... + βk x_ik).

Vehicle telemetry and GPS-based information such as percentages of kilometres driven at night, over the speed limit, and in urban zones can be included in the ratemaking process, improving results obtained when just using classical driver variables such as age and gender.

“We have shown that indeed vehicle telemetry, and the collection of information using GPS-based technology such as percentages of kilometres driven at night, over the speed limit, and in urban zones, among others can be included in the ratemaking process thus improving the results obtained when just using classical driver variables, such as age and gender.”

The results validate conclusions drawn in previous studies that new indicators related to distance travelled and driving habits are relevant, used in conjunction with classical regressors.

“These results seem to validate the conclusions drawn in previous studies (Ayuso, Guillen, & Nielsen, 2018, Lemaire, Park, & Wang, 2016and Ferreira & Minikel, 2013), in which the relevance of the new indicators related to distance travelled and driving habits is highlighted, but where they are used in conjunction with the classical regressors.”

• cites Ayuso, Guillen, & Nielsen, 2018Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Lemaire, Park, & Wang, 2016 sourceNot checked — no full text of the source
• cites Ferreira & Minikel, 2013Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Insurance prices should not necessarily be linearly proportional to distance driven.

“Since insurance premiums are based on expected number of claims, this is an important result as it potentially shows that insurance prices should not necessarily be linearly proportional to distance driven.”

• AssumptionRests on an assumption: Insurance premiums are based on the expected number of claims.

The positive relationship between distance driven and excess zeros can be understood as an indication of a learning effect.

“This can be understood as an indication of a learning effect, or in terms of distance driven, that even if exposure to risk increases with distance driven, the probability of not making a claim also increases compared to that of drivers in the group that drive a shorter distance.”

The positive sign of the log-distance parameter in the logit part means that greater distance driven is associated with a greater proportion of excess zero claims, not a greater probability of the insured having zero claims.

“This value (0.404) in the first column does not mean that the greater the distance driven, the greater the probability of the insured having zero claims.Rather it means that the greater the distance driven, the greater the proportion of excess zero claims, indicating a deviation from the Poisson distribution that can be captured by the ZIP model.”

The goodness of fit results are always better in zero-inflated models because they take into account differences between false zeros (non-risk exposure) and true zeros (risk exposure and zero claims).

“The goodness of fit results are always better in the zero-inflated models because they take into account differences between false zeros (non-risk exposure) and true zeros (risk exposure and zero claims).”

Good drivers, identified as those reporting no claims, are more frequent than expected among drivers that drive long distances than among those that drive shorter distances, all other things being equal.

“This finding is evidence of the fact that good driversif we identify them with those reporting no claimsare more frequent than expected among the group of drivers that drive long distances than among those that drive shorter distances, all other things being equal.”

• AssumptionThe authors state this as an assumption: Good drivers can be identified with those reporting no claims.

Among policyholders with the same characteristics but different exposure to risk in terms of distance driven per year, those with greater exposure present a larger proportion of excess zero claims than those with less exposure.

“This means that when considering policyholders with the same characteristics but with different exposures to risk in terms of distance driven per year, we can conclude that those with a greater exposure present a larger proportion of excess zero claims than those with less exposure.”