Evidence of Adverse Selection in Automobile Insurance Policy Buying Behavior

1. Discussions on “Decomposing Automobile Insurance Policy Buying Behavior – Evidence of Adverse Selection” byChu-Shiu Li, Chwen-Chi Liu and Jia-Hsing YehTong YuUniversity of Rhode Islandtongyu@uri.eduARIA, August 6, 2007

2. 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

3. 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

4. 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]

5. 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

6. Major Issue Risk ≠ Loss Experience

7. 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

8. 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??

9. Solution 1 – Estimate Risk • Get claim information for more years. Say 5 years, L1, L2 ,L3 ,L4 , andL5. • 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

10. 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

11. Conclusions • Smart idea, neat data, good potential • The authors need to differentiate adverse selection from competing hypotheses • Risk ≠ Loss Experience