Jean Lemaire, Sojung Park,Kili Wang
IAJ, 7 June 2013 1. Mileage Rating in one US company
 2. Statistical Studies

 3. Pros and Cons of Mileage Rating 4. Data from Taiwan

 5. Regression results

 6. Impact on Taiwanese Bonus-Malus System
 7. Conclusions

 Age, sex, marital status of main driver Make and model of car
 Use of car
 Territory

 Claims and traffic violations history

 Annual mileage (7,500 miles only cut-off)Optional program introduced in PA last May
 Uses On-Star Telematics
◦ Factory-installed, all new GM cars
◦ Professionally installed for $100

Annual monitoring costs: $200
 Benefits: automatic crash response, emergency
services, roadside assistance, stolen vehicle
assistance. GPS + Hands-off calling for $100.
 Monthly e-mail of mileage to the Insurance company
and policyholder
 Discounts at renewal: 32% (3,500 miles); 13% (11,000miles); 5% (15,000 miles)
 Premium increase if policyholder found to exceed
7,500 miles Breaking habits, driving between midnightand 4 am
 Speeds of 80 miles per hour Type of road travelled Ptolemus (2012) estimates that 2 million carsin Europe and the US use telematics-based
ratingTraditionally, insurers have been reluctant to use
mileage rating, as odometer tampering was notdifficult Insurers use proxy variables instead Butler (2006) argues that 12 commonly used rating
variables are proxies for mileage: sex, car age,previous accidents at-fault and not-at-faults
accidents, credit score, zip code, income, militaryrank, existence of previous insurer, premiums byinstallments, years with employer, collision
deductible, tort rightsSituation may change rapidly, due to telematics, GPS,tampering-resistant odometers, and the decreasing
cost of these new technologiesLemaire (1985). 4,000 Belgian drivers, average annual
km 15,344. Claim frequencies rise from 5.84%(< 5,000 km) to 10.44% (> 30,000 km)
 Ferreira and Minikel (2010). 2.87 million car years, MA.
Increasing mileage from 10,000 to 30,000 raises claim
frequency from 5% to 8%
 Litman (2011). 500,000 vehicles years, Vancouver.
Claim frequencies increase from 4% (< 5,000 km) to10% (> 35,000 km)
 →Accident rates increase with mileage, butless than proportionately.

 PAYD: Pay-As-You-Drive Large literature, but not peer-reviewed.
 Mostly lobbying groups

 In favor of PAYD: environmental groups,

associations representing females, seniors, lowincome groups
 NOW: Females drive less than males (10,143 v.
16,553) but not rating difference after age 30
 Opposing PAYD: Oil industry, insurance industry(insurers would carry most of the costs, whilemost benefits are externalities).
 Bordoff(2008) estimates social benefits at $257
per vehicle, but only $34 insurer benefits At renewal, drivers provide mileage +sometimes photo of odometer. Random
checks by insurer, or audits, for instance withannual inspection
 Clear conflict of interest for policyholder
 Some odometers can be tampered Mileage disregards other dangerous behavior
 No additional revenue through the sale ofancillary services

More accurate Based on own behavior, not on a group Does not rely on age, gender, territory, variables that
could become unlawful
 Individuals have more control over their price Subsidies across groups are reduced
 Uninsured driving may reduce Less fraud Incentive to improve driving skills, and to reduce mileage
 Reduced traffic, pollution, time wasted in jams
 Accident externalities: costs are reduced for everyone
 Shorter delay between improved driving and pricedecrease Numerous side benefits available Installation and monitoring costs
 Less predictable premiums

 Only used for discounts → decreased income
 Adverse selection possible, since optional
 System can be gamed
 Invasion of privacy Practical problems

 Regulatory hurdles 32,260 sq. km (the size of Belgium) $37,000 GDP per capita (equals Germany) Very high population and traffic density
 →only 4,675,000 cars.

Few couples own two Data covers compulsory bodily injury liability,
voluntary bodily injury + property damage
 Rating variables: use of car, gender, age
 Bonus-malus: 10 classes; premium levels 70,80, 90, 100, 110, 120, 130, 140, 150, 160
 One-class discount if no claim, 3-classpenalty per claim 0.25 million policy-years, from leading car

manufacturer, insurer, and repair shops
 Policy years 2001 to 2007
 Dependent variable: number of claims
 Explanatory variables◦ Gender◦ Age◦ Vehicle type and use◦ Mileage (km per day)◦ Marital status◦ Car age
◦ City / rural◦ Territory (north, south, central, east)◦ Engine cubic capacity

Age group

Males

FemalesAll< 300.0674

0.0652

0.066130-60

0.04730.0562

0.0537> 60

0.04770.05230.0500All0.0493

0.05670.0545

 Probit or Ordered Probit model

Probit(Cit)=α+β1Xit+β2Yit +β3BMSit+β4Milesit +β5Dit + εit
Number ofclaims

Frequency

O247,989

18,223

22,690

3136

42552

Variable

Parameter
estimate

Wald Chi-square

Pr > ChiSq

Age 30-60-0.0735

21.61< 0.0001

Age 60+-0.08228.94

0.0028

Female+0.057734.90< 0.0001

Bonus-malus+0.6183

311.39< 0.0001

Variable

Parameter
estimate

Wald Chi-square

Pr > ChiSq

Age 30-60-0.053911.50

0.0007

Age 60+-0.0295

1.130.2875

Female+0.0739

56.48<0.0001

Bonus-malus+0.5928

283.41<0.0001

Mileage+0.0424

756.34<0.0001

Variable

Parameter
estimate

Wald Chi-square

Pr > ChiSq

Age 30-60-0.0586

12.57

0.0004

Age 60+-0.0614

4.77

0.0289Female+0.0459

21.47< 0.0001

Bonus-malus+0.054110.93

0.0009Married-0.0298

3.31

0.0689Car age 0-1+0.1856

69.69< 0.0001

Car age 1-2+0.0724

13.86

0.0002Car age 2-3+0.0198

0.990.3198

Car age 3-4+0.0272

1.650.1986

Car age 4+-0.0033

0.020.8883

Variable

Parameterestimate

Wald Chi-square

Pr > ChiSq

Engine capacity 2-0.0564

31.41<0.0001

Engine capacity 3-0.0606

8.610.0033

City-0.0073

0.64

0.4222

North-0.0720

12.61

0.0004South-0.0323

2.52

0.1127

Middle-0.01830.70

0.4018

Variable

Parameter
estimate

Wald Chi-square

Pr > ChiSq

Age 30-60-0.0366

4.85

0.0276

Age 60+-0.00480.03

0.8641

Female+0.062138.82< 0.0001

Bonus-malus+0.15468.16

0.0043

Mileage+0.0436

783.32<0.0001

Married-0.0320

3.76

0.0524Car age 0-1+0.1852

68.86< 0.0001

Car age 1-2+0.0650

11.060.0009

Car age 2-3+0.0150

0.560.4526

Car age 3-4+0.0232

1.190.2751

Car age 4+-0.0046

0.040.8444

VariableParameter
estimate

Wald Chi-square

Pr > ChiSq

Engine capacity 2-0.0758

55.99<0.0001

Engine capacity 3-0.0752

13.090.0003

City+0.0214

5.370.0204

North-0.0713

12.26

0.0005South-0.0347

2.890.0890

Middle-0.01460.440.5053

 A huge literature deals with bonus-malus

design … independently of other variables
 which creates a potential double-counting
problem Authors seems to be aware of the problem“The use of more a priori classification variables is expectedin free market countries, which decreases the need for a
sophisticated BMS”
 Adverse selection and insurer’s lack of knowledge of driving
behavior is often cited as main reasons to introduce BMS, withannual mileage frequently as main example But did not model it, until Taylor (1997) Complicated Bayesian model, but simple

simulation
 Unfortunately, Taylor has no access to realdata, so made-up example
 Nine-class BMS
 Due to unspecified a priori variables, portfolio
subdivided in ten rating classes

Risk Group

Mean cell claim
frequency

Within-cell coefficientof variation

1

6.5%

0.75

2

8.9%

0.65

3

11.4%

0.60

4

13.7%

0.55

5

16.1%

0.50

620.1%

0.45

7

24.9%

0.40

829.7%

0.40

936.0%

0.40

1050.5%

0.40

Average

15.7%

BMS Class

Stationary %Raw claim
frequency

Expectedclaim
frequency

Ratio “raw /expected”

166

121485291717102

3101817103

4421

19111

542320116

6330

22139

7232

22145

8138

24

156

9146

26175

BMS Class

Premium ignoringcovariates

Premium recognizing
covariates

140

61

257

73

359

74

471

80

577

83

6100

100

7107

104

8125

112

9152126

Mileage class (km/day)

Mean cell claim
frequency

Within-cell coefficientof variation0 – 19.02

0.03516.353219.02 – 25.24

0.03466.328025.24 – 30.44

0.04345.687330.44 – 35.27

0.04705.404435.27 – 40.32

0.0511

5.234940.32 – 46.130.05545.0129

46.13 – 54.73

0.05934.848754.73 – 62.22

0.06324.704662.22 – 76.42

0.0721

4.398076.42+

0.08384.1553

Average: 44.29

0.05455.0813

Miles

BMS
1BMS
2BMS
3BMS
4BMS
5BMS
6BMS
7BMS
8BMS
9BMS
10

1.932

.009 .010

.012

.005

.006

.006

.006

.010

.015

2.919

.008 .011

.012

.004

.005

.006

.005

.008

.013

3.908

.008 .012

.014

.007

.008

.008

.007

.012

.019

4.886

.011 .015.019.006

.007

.009

.009.013

.019

5.893

.013 .016

.017

.007

.009

.007

.011

.013

.022

6.870

.012 .016

.016

.010

.010

.010

.009

.015

.026

7.878

.013 .016

.017

.008

.009

.012

.010

.014

.024

8.857

.014 .017

.021

.008

.011

.011

.013

.017

.028

9.851

.016 .018

.025

.008

.011

.011

.012

.020

.032

10.824.019 .214

.023

.011

.013

.012

.014

.020

.035

All

.882

.012 .015

.018

.007

.009

.009

.010

.014

.023

BMS Class

Stationary %Raw claim
frequencyExpectedclaim
frequency

Ratio “raw /expected”

188.19%

1.43%

5.40%

26.40%

2

1.25%

12.36%

5.82%

212.36%3

1.52%

11.47%

5.76%

199.13%4

1.77%

16.54%

5.77%

286.73%5

0.75%

20.78%

5.80%

358.23%6

0.90%

27.60%

5.83%

473.38%7

0.92%

35.01%

5.79%

604.58%8

0.97%

41.13%

5.84%

704.35%9

1.42%

51.58%

5.83%

884.79%10

2.33%

72.77%

5.88%

1237.59%

BMS Class

Current BMS
level

Premium
ignoring
covariates

Premium
recognizing
covariates

170

8.62%

9.21%

280

74.71%

74.06%

390

69.33%

69.45%

4100

100.00%100.00%5110

125.59%124.94%6120

166.81%165.09%7130

211.59%210.85%8140

248.63%245.65%9150

311.79%308.58%10160

439.85%431.62%

 Annual mileage appears to be, by far, themost important rating variable Bonus-malus remains a very importantcomponent in auto insurance pricing
 Making the bonus-malus system tougher
would improve its rating accuracy Mileage and bonus-malus should be thebuilding blocks of rating Other variables (age, car age, engine cubic
capacity, and some territories) could beadded, at the price of a complicated system