Risk Classification,
Rating Innovation,
& Self Selection
in Automobile Insurance Market
Chu-Shiu Li
Asia University, Taiwan
Chwen-Chi Liu
Sheng-Chang Peng
Feng Chia University, Taiwan
1
Background(1/4)

Risk classification
-- a fundamental task for insurers to maintain
solvency, profitability, and fairness.
-- entails information costs.
-- insurers may perform ratemaking through
categorization based on easily available
(costless) characteristics.
2
Background(2/4)

A typical automobile insurance contract usually
involves a premium based on the characteristics of
the policyholder and car factors.

The implicit agreement between the insured and
insurer is that the policyholder should be the driver
covered by the insurance contract.

In some countries, other drivers can be added in
insurance contract with an additional fee (or no fee).
3
Background(3/4)

Automobile insurance In Taiwan
--- a regulated rating system where all insurers use
entirely the same (restricted) risk classification
factors and sell the same coverage types of
automobile insurance.
--- it appears as a monopoly (or Cartel) market with
different branch firms and costs.
--- an insured car covered by physical damage
insurance receives claim payment regardless of
the driver.
4
Background(4/4)

The legal environment to allow the inconsistency
between policyholder and driver creates at least two
major problems:
1. premium arbitrage in that female family
member (e.g., mother), having lower premium
rate, usually is policyholder, while other family
members (e.g., children) are car users;
2. there is cross-subsidization between
policyholders with single and multiple car users
as the latter involves higher risk than the former.
5
Motivation(1/2)

Regulation: Rating innovation is permitted in Taiwan.

A real case:
One insurer chose to provide vehicle damage insurance
policies with driver restriction while introducing a 35%
premium discount compared with the regulated standard
contract in 2006.
This forms two risk policies:
--1. “unlimited driver policy” (ULDP) with the regulated
premium, covering all drivers;
--2. “limited driver policy” (LDP) with the discounted
premium, covering policyholder and spouse while
policyholder’s children are excluded.
6
Motivation(2/2)

LDP (limited driver policy)
--- claim payments will be made only after
validation of the driver.
--- consumers self select according to contract type
based on the set of individuals who will drive the
car.
--- policyholders without children are expected to
prefer LDP in order to distinguish themselves
from high-risk groups with younger drivers.
7
Objective
Is it profitable for insurer
--- to adopt the additional rating factors allowed?
--- to sell multiple contracts?
“unlimited driver policy” (ULDP) and
“limited driver policy” (LDP)
8
Literature (number of risk classes)

Early debate
Tryfo (1980): in a captive market where the number
of insureds remains the same, the profitability of an
insurer will not be affected by the number of risk
classes used.
Doherty (1981): additional risk classification is able
to create economic rent in the short run. But the
competitive pressure in the long run, which depends
on reaction function of competitors, may drive the
excess profit away.
9
Literature (categorization)

Hoy (1982): there is the possibility of welfare
improvement by using imperfect information to
categorize risk classes.

Crocker and Snow (1986): any market equilibrium
with costless categorization Pareto dominates the
equilibrium in which categorization is not allowed.
However, when the acquisition of information is
costly, the market can be an efficient mechanism
without categorization.
10
The Role of LDP in Literature
LDP
--- similar to the case reflecting additional risk
classification is able to create economic rent in the
short run as in Doherty (1981)
--- a perfect example of “costless categorization”
mentioned in Crocker and Snow (1986).
11
Rating System in Taiwan
premium =
basic . manufactured .
premium
coefficient
insured
coefficient
insured = gender-age +
claim
coefficient
coefficient
coefficient
12
Table 1 Gender-Age Coefficients
Gender
Pricing Coefficient
Age
Age under 20
Male
Female
1.89
1.70
Age 20 above but under 25
1.74
1.57
Age 25 above but under 30
1.15
1.04
Age 30 above but under 60
1.00
0.90
Age 60 above but under 70
1.07
0.96
Age 70 above
1.07
0.96
13
Covered Drivers (LDP vs. ULDP)
Policy
Type
ULDP
LDP
Policyholder
Covered Drivers
Policyholder
Spouse
Children
Others
Married
○
○
○
○
Single
○
Married
○
Single
○
○
○
14
Testing hypotheses-1

Since ULDP covers all drivers, insurers have no
idea who will drive the car.

The term of “policyholder” merely reflects the
imperfect information as discussed in Hoy
(1982).
The possible compositions of potential drivers
fall into two categories:
--- the single person or husband-wife pattern
(as the restricted condition in LDP).
--- all kinds of drivers, such as singles, couples,
and, in particular, children. (ULDP)

15
Testing hypotheses-1

Hypothesis 1: For claim policies, the
relationships between drivers and
policyholders in LDP show single or husbandwife pattern; while in ULDP, the pattern is
single, husband-wife, or parents-children.
16
Testing hypotheses-2

Those policyholders who meet the requirement of LDP
and switch to LDP might be more price sensitive as 35%
discount of the premium is a good deal in terms of
financial benefit.

Policyholder, qualified for LDP but without switching to
buy it, might have other reasons such as preferring a
wider range of drivers to be covered just for in case or
not aware of the availability of LDP.

However, there is another important reason: they are
price insensitive and prefer to renew the current policy
without bothering on switching or not. This leads to the
second hypothesis.
17
Testing hypotheses-2

Hypothesis 2: Policyholders with high price
sensitivity will purchase LDP while those with
low price sensitivity will buy ULDP.
18
Testing hypotheses-3

Based on the attributes of covered drivers,
the variations of possible losses in terms of
adjusted gender-age coefficients can be
obtained.

Hypothesis 3: In terms of claims, LDP has
lower loss ratio than ULDP, implying higher
profit.
19
Methodology

To test the first hypothesis about the purchase
patterns between policyholders and drivers, we use
diagram analyses.

A t-test is applied to examine the second hypothesis
on the comparison of profitability between LDP and
ULDP.

The determinants of policy choice:
Probit Model

The analyses of loss ratio by comparing with two
policies:
Tobit Regression
20
Data

A unique dataset with ULDP and LDP from insurer A
for policy years 2006 to 2008.

The data include complete car insurance information,
features of policyholders, vehicles, claim records,
accident drivers, and contract details

Policy types: comprehensive coverage without
covering unknown perils for private vehicle damage
insurance, with deductible (Coverage B_D) or with
no deductible (Coverage B_ND)
21
Summary Statistics
ULDP
LDP
Policyholder age
43.1803
45.4814
Female policyholder
0.7730
0.8083
Married policyholder
0.8055
0.9279
Premium (NT$ 1,000)
30.0802
24.9431
Liability coverage (NT$ million)
0.3009
0.2047
Premium liability (NT$ 1,000)
0.1232
0.0671
Replacement price (NT$ million)
0.7854
0.7912
With liability coverage
0.0996
0.0609
High replacement price (≧NT$ 1 million)
0.0830
0.1092
Number of policies
2,529
1,346
Continuous variable
Binary variable
22
Testing Results: Hypothesis 1
LDP
Number of Claims
100
80
60
40
20
0
-25 -23 -20 -13 -11 -9
-7
-5
-3
-1
1
3
5
7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
Age Gap
ULDP
Number of Claims
100
80
60
40
20
0
-25 -23 -20 -13 -11 -9
-7
-5
-3
-1
1
3
5
Distribution of
Age Gap
between
Policyholder
and Driver for
LDP
Distribution of
Age Gap
between
Policyholder
and Driver for
ULDP
7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
Age Gap
23
Testing Results: Hypothesis 1
Distribution of Age Gap
husband/wife
mother/child
80000
70000
60000
50000
40000
30000
20000
10000
0
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44
Age Gap
Husband-Wife
Mother-First Child
24
Testing Results: Hypothesis 1

The one-peak distribution is formed by an age gap
at about 0 years, reflecting a husband/wife pattern.
This result matches the actual state of the LDP.

For ULDP data  double peaks (with age gaps 0
and 23 years). We conjecture that the left peak is
the distribution of age gaps for married couples and
the right peak is the distribution of the age gaps for
parents-children.
25
Testing Results: Hypothesis 2(1/2)

Two proxies of price sensitivity: “Liability
Coverage” and “With Liability Coverage”.

Those policyholders with higher liability
coverage are less likely to purchase LDP.

Policyholders have more incentive to select LDP
to save on premium expenditure for more
expensive cars. ( “high replacement price”)
26
Testing Results: Hypothesis 2 (2/2)
Probit regression on the determinants of purchasing LDP for policyholders
Variable`
Model 1
Model 2
Model 3
Model 4
Policyholder age
0.0023
0.0021
0.0021
0.0021
Female policyholder
0.0283
0.0247
0.0227
0.0279
Married policyholder
0.6240 ***
0.6249 ***
0.6260 ***
0.6221 ***
-0.2672 ***
-0.2663 ***
-0.2691 ***
-0.0093
-0.0903 *
Liability coverage
-0.0536 **
With liability coverage
Replacement price
High replacement price
0.2641 ***
Dummies
Regions, Policy year
Log Likelihood
-2395.1
-2392.3
-2392.3
-2388.4
Observations used
3,875
3,875
3,875
3,875
27
Testing Results: Hypothesis 3(1/3)
Claim frequency
Claim payment (NT$ 1,000)
Loss ratio (= total claim
payment/total premium)
t test
(p value)
ULDP
LDP
0.6967
0.4086
-13.26
(0.7005)
(0.6117)
(<.0001)
18.1556
8.2830
-6.70
(68.9228)
(19.9163)
(<.0001)
0.5299
0.2732
-7.49
(1.4481)
(0.6805)
(<.0001)
28
Testing Results: Hypothesis 3(2/3)
Tobit regression on the determinants of loss ratio
Variable
Intercept
LDP
Policyholder age
Female policyholder
Married policyholder
Domestic car
Dummies
Log Likelihood
Observations used
Loss ratio
-0.5428 **
(0.2297)
-0.9258 ***
(0.0806)
-0.0029
(0.0039)
0.0961
(0.0903)
0.2945 **
(0.1199)
0.1006
(0.1456)
Exhaust, Car brand, Regions, Policy year
-5127
3,875
29
Testing Results: Hypothesis 3 (3/3)

The group that purchases LDP has significantly
lower average loss frequency and lower average
severity than ULDP group regardless of the
deductible.

The loss ratio of LDP is also significantly lower than
that of ULDP, implying better profit which supports
our hypothesis.
30
Discussion (1/3)




This paper highlights the unique market in Taiwan in
which vehicle damage insurance does not concern
who drives the car.
Those who choose to buy LDP tend to be low risks
choose a contract with more detailed risk
classification.
From the insurers’ view, LDP outperforms ULDP in
terms of all profit indicators.
It is interesting to consider whether, over time, LDP
will dominate the vehicle damage insurance market.
31
Discussion (2/3)

Based on the existing data of Insurer A, the propensity
of the insured to buy LDP is not as high as expected.
Possible reasons:
-- The majority of the demand for automobile insurance
comes from families rather than single persons.
-- Married policyholders account for 84% to 89% of the
various types of policies.
-- A contract bought by parents that can also cover
children may be a superior choice for a family.
-- For a young driver dependent on parents, LDP is
not necessarily cheaper than ULDP.
32
Discussion (3/3)

We still have the problem of imperfect information
discussed in Hoy (1982) as not all policyholders of
ULDP are high risks with younger drivers.

Since ULDP is a model policy mandated by authority
and LDP is only available from one specific insurer
before 2006, those who purchase ULDP may do so
simply because they do not know the existence of
LDP or their agents never recommend it.
33
Thank you
34