Risk Classification, Rating Innovation, & Self Selection in Automobile Insurance Market

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Risk Classification,

Rating Innovation, & Self Selection

in Automobile Insurance Market

Chu-Shiu LiAsia University, Taiwan

Chwen-Chi Liu

Sheng-Chang Peng Feng Chia University, Taiwan

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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.

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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).

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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.

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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.

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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.

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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.

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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)

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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.

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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.

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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).

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Rating System in Taiwan

premium =

basic . manufactured . insured premium coefficient coefficient

insured = gender-age + claim coefficient coefficient coefficient

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Table 1 Gender-Age Coefficients

Gender

Pricing Coefficient

Age

Male Female

Age under 20 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

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Covered Drivers (LDP vs. ULDP)

Policy Type

PolicyholderCovered Drivers

Policyholder Spouse Children Others

ULDPMarried ○ ○ ○ ○

Single ○ ○

LDPMarried ○ ○

Single ○

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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)

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Testing hypotheses-1

Hypothesis 1: For claim policies, the relationships between drivers and policyholders in LDP show single or husband-wife pattern; while in ULDP, the pattern is single, husband-wife, or parents-children.

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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.

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Testing hypotheses-2

Hypothesis 2: Policyholders with high price sensitivity will purchase LDP while those with low price sensitivity will buy ULDP.

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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.

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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

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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)

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Summary Statistics

ULDP LDP

Continuous variable

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

Binary variable

With liability coverage 0.0996 0.0609

High replacement price (≧NT$ 1 million) 0.0830 0.1092

Number of policies 2,529 1,346

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Testing Results: Hypothesis 1

Distribution of Age Gap between Policyholder and Driver for LDP

0

20

40

60

80

100

-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

Number of Claims

Age Gap

LDP

0

20

40

60

80

100

-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

Number of Claims

Age Gap

ULDP Distribution of Age Gap between Policyholder and Driver for ULDP

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Testing Results: Hypothesis 1

0

10000

20000

30000

40000

50000

60000

70000

80000

-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/child

Husband-Wife Mother-First Child

Distribution of Age Gap

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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.

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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”)

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Testing Results: Hypothesis 2 (2/2)

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 ***

Liability coverage -0.0536 **

With liability coverage -0.2672 *** -0.2663 *** -0.2691 ***

Replacement price -0.0093 -0.0903 *

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

Probit regression on the determinants of purchasing LDP for policyholders

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Testing Results: Hypothesis 3(1/3)

ULDP LDPt test(p value)

Claim frequency 0.6967 0.4086 -13.26

(0.7005) (0.6117) (<.0001)

Claim payment (NT$ 1,000) 18.1556 8.2830 -6.70

(68.9228) (19.9163) (<.0001)

Loss ratio (= total claim payment/total premium)

0.5299 0.2732 -7.49

(1.4481) (0.6805) (<.0001)

Testing Results: Hypothesis 3(2/3)

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Variable Loss ratio Intercept -0.5428 **

(0.2297)LDP -0.9258 ***

(0.0806)Policyholder age -0.0029

(0.0039)Female policyholder 0.0961

(0.0903)Married policyholder 0.2945 **

(0.1199)Domestic car 0.1006

(0.1456)Dummies Exhaust, Car brand, Regions, Policy yearLog Likelihood -5127 Observations used 3,875

Tobit regression on the determinants of loss ratio

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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.

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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.

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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.

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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.

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Thank you