Discussions on “Decomposing Automobile Insurance Policy Buying Behavior – Evidence of Adverse Selection” by

Chu-Shiu Li, Chwen-Chi Liu and Jia-Hsing Yeh

Tong YuUniversity of Rhode Island

tongyu@uri.edu

ARIA, August 6, 2007

Summary

• Issue– To present evidence on the presence of adverse selection

– More specifically, to see if there is an positive relation between risk and insurance purchase

• Data– Coverage and claim information of Taiwan auto insurance in years

2002 and 2003, facilitating two sets of analyses:• High-coverage policy (comprehensive policy) versus low-coverage policy

(collision only) – both without deductible

• Policy without deductible versus policy having deductible

Summary

• Testable Conditions– A positive link between insurance claims and subsequent coverage

– A negative link between insurance claims and subsequent deductible choice

• Specific Cases favoring Adverse Selection– 1. L in year t, no loss, L in year t+1

– 2. H in year t, no loss, L in year t+1

– 3. L in year t, loss, H in year t+1

– 4. H in year t, loss, H in year t+1

Summary

• Results– T 6 – Prob(LC in 03|LC in 02) is positively related to the No_Claim

dummy of 2002 (NoClaim_02)– T 7 – Prob(LC in 03|HC in 02) is negatively related to NoClaim_02 – T 8 – Prob(HD in 03|HD in 02) is positively related to NoClaim_02– T 9 – Prob(HD in 03|LD in 02) is negatively related to NoClaim_02

– Results are obtained after controlling for some characteristics of insured and auto, e.g., age, gender, car age, expected losses of a policyholder, etc

• Carefully describe the procedure to compute expected loss, e.g., E[NoClaim_02]

Minor Suggestions

• Also look at the group having high coverage in 2003

• Perform an unconditional test examining coverage choice and prior-year claim experience– Need discuss the benefit of decomposing year t insured

type

– Compare the results across various groups

Major Issue

Risk ≠ Loss Experience

Major Issue

Risk ≠ Loss Experience• Loss experience is not private information to policyholder. It

is available to insurers as well

• Hard to conclude the finding is supportive to adverse selection

• Test against alternative hypotheses: learning and habit persistence

Direct Test on Adverse Selection

• Develop a model to compute the price of each insurance contract in year t+1

• Look at insurance purchase in the over- and under-price groups respectively

• Underlying assumption: Risk is quantifiable

• Feasible??

Solution 1 – Estimate Risk

• Get claim information for more years. Say 5 years, L1, L2 , L3 , L4 , and L5.

• Test Prob(C2|C1) as a function of insured’s subsequent loss experience Li

• Underlying assumption: Insurers have better information on their own future losses than insurers

Solution II – Get around Risk

• Identify insured factors potentially correlated with insured’s AS incentive but uncorrelated with insurance price, e.g., income, education

• Test if the loss and coverage relationship differs across insured groups with different values of insured characteristics

• Specifically, interact loss experience with some of the control variables used in the regressions

Conclusions

• Smart idea, neat data, good potential

• The authors need to differentiate adverse selection from competing hypotheses

• Risk ≠ Loss Experience