Decomposing Insurance Buying Behavior --- Evidence of Adverse Selection

1. Decomposing Insurance Buying Behavior --- Evidence of Adverse Selection Chu-Shiu Li, and Chwen-Chi Liu, Feng Chia University, Taiwan Jia-Hsing Yeh, Chinese University of Hong Kong

2. Background • Positive correlation between risk and coverage(Rothschild and Stiglitz, 1976) • Empirical testing in auto insurance market Failed: Richaudeau (1999), Chiappori and Salanié (2000), Dionne et al. (2001), Saito (2006) Successful: Cohen (2005) --- learning effect

3. Background • Possible reasons for the nonexistence of adverse selection: -- Risk aversion (Advantageous selection) -- Habit persistence -- “strong and empirically implausible assumptions”Chiappori et al. (2006)

4. Motivation • Alternative view of this paper: -- Adverse selection might not characterize the entire insurance market. -- To allow all the possible behaviors to exist.

5. Objective • Decompose observations into groups with different patterns of insurance policy buying behavior • Testing patterns of (Incurred claimst | policy choicet)  policy choicet+1 ?

6. Presumptions • Two important presumptions in Rothschild and Stiglitz (1976): -- The agents are identical or “observational identical” -- Decision makers know their risk class.

7. Insurance Buying Decision (1) H H(P)H Type 1: adverse selection, rigid Claim (P) L H(P)L Type 2: price effect High Coverage H H(1-P)H Type 3: advantageous selection rigid (H) No Claim (1-P) L H(1-P)L Type 4: adverse selection, learning t = 1 t = 2

8. Insurance Buying Decision (2) H L(P)H Type 5: adverse selection, learning Claim (P) L L(P)L Type 6: price effect, rigid Low Coverage H L(1-P)H Type 7: demand for more coverage, learning (L) No Claim (1-P) L L(1-P)L Type 8: adverse selection, rigid t = 1 t = 2

9. Data • Private auto damage insurance policies in 2002 (509,216) and 2003 (435,378). • Two subsets: 1. Zero deductible comprehensive vs. moving collision (high coverage) (low coverage) (75380) 2. Comprehensive form B without deductible vs. with deductible (high coverage) (low coverage) (47609)

10. Table 2 Coverage Choices in 2003 Conditional on Coverage Choices in 2002

11. Table 3 Deductible Choices in 2003 Conditional on Deductible Choices in 2002

12. Table 4 Summary Statistics (Choices of Coverage in 2003, Conditional on 2002 Choices)

13. Table 5 Summary Statistics (Deductible Choices in 2003, Conditional on 2002 Choices)

14. Empirical Analyses • Hypothesis testing: Is there a positive correlation between coverage and risk? risk: incurred claim (Ct -1) in the previous year coverage: the choice of coverage or deductible (Dt) this year • Logit Regression: Dt = f (Ct -1, B, X) • Nonlinear effects

15. Initial Analyses • Testing independency: risk vs. coverage (Chiappori and Salanié, 2000) • (1) Claims in 2002 and choosing high coverage in 2003 are not correlated W2 = (-4847.02)2 / 3032.19 = 7748 (rejected) • (2) Claims in 2002 and choosing high deductible in 2003 are not correlated; W1 = (-376.25)2 / 1961.88 = 72.16 (rejected) • Spurious results?

16. Variable Model 1 Model 2 Model 3 Intercept + + + NoClaim_02 +*** +*** +*** E[NoClaim_02] – *** – E[Low_Cov_02] –*** Age – – ** – *** Male + +*** +*** Married – + – Car_age +*** +*** +*** Exhaust – – – ** Clmcoef_03 +*** +*** +*** Log Likelihood – 3228.37 – 3202.33 – 3026.17 Table 6 Staying with Low Coverage in 2003 (Logistic Regressions, Conditional on Choosing Low Coverage in 2002)

17. Variable Model 1 Model 2 Model 3 Intercept – – – NoClaim_02 –*** –*** –*** E[NoClaim_02] – *** – *** E[High_Cov_02] –*** Age – *** – *** – *** Male +*** +*** +*** Married – *** – ** – *** Car_age –*** + +*** Exhaust – *** – *** – *** Clmcoef_03 +*** +*** +*** Log Likelihood – 13,035.45 – 13,023.65 – 12,940.73 Table 7 Switching to Low Coverage in 2003 (Logistic Regressions, Conditional on Choosing High Coverage in 2002)

18. Findings (1) • Strong positive relationship between no claims in 2002 and low coverage selection in 2003. • An insured with a high claim coefficient chooses low coverage. (price effect) • Some of the insured keep choosing high coverage in 2003 even no claims in 2002. -- habit persistence -- risk aversion

19. Insurance Buying Decision (1) H H(P)H 11,169 (29.4%) Type 1: adverse selection, rigid 13,624 (35.8%) Claim (P) L H(P)L 2,455 (6.5%) Type 2: price effect 38,014 High Coverage H H(1-P)H 21,801 (57.4%) Type 3: advantageous selection, rigid (H) No Claim (1-P) L H(1-P)L 2,589 (6.8%) Type 4: adverse selection, learning 24,390 (64.2%) t = 1 t = 2

20. Insurance Buying Decision (2) H L(P)H 70 (0.2%) 3,272 (8.8%) Type 5: adverse selection, learning Claim (P) L L(P)L 3,202 (8.6%) 37,366 Type 6: price effect, rigid Low Coverage (L) H L(1-P)H 689 (1.8%) Type 7: demand for more coverage, learning No Claim (1-P) 34,094 (91.2%) L L(1-P)L 33,405 (89.4%) Type 8: adverse selection, rigid t = 1 t = 2

21. Variable Model 1 Model 2 Model 3 Intercept + + + NoClaim_02 +** +** +** E[NoClaim_02] + + E[High_D_02] + Age + + + Male + + + Married – – – Car_age +*** +*** +** Exhaust +*** +*** +*** Clmcoef_03 + + + Log Likelihood – 4484.67 – 4484.49 – 4484.28 Table 8 Staying with High Deductible in 2003 (Logistic Regressions, Conditional on Choosing High Deductible in 2002)

22. Variable Model 1 Model 2 Model 3 Intercept – – – NoClaim_02 – – – E[NoClaim_02] +*** +*** E[Low_D_02] + Age – – – Male + + + Married – * – * – * Car_age + – – Exhaust +*** +* + Clmcoef_03 +*** +*** +*** Log Likelihood – 3,465.59 – 3,457.47 – 3,457.35 Table 9 Switching to High Deductible in 2003 (Logistic Regressions, Conditional on Choosing Low Deductible in 2002)

23. Findings (2) • Strong positive relationship between no claims in 2002 and staying with a high deductible in 2003. • Having no claims in 2002 did not provide a strong incentive to switch from a low to a high deductible. • There is no evidence that the deductible choice in 2002 affect the choice in 2003. Habit persistence effect is weak.

24. Conclusion • A positive relationship between risk and coverage might exist for some policyholders but not necessarily for all. • The coexistence of adverse selection, advantageous selection, habit persistence, and a price effect as important factors determining insurance buying behavior

25. Variable Model 1 Model 2 Model 3 Intercept +*** +*** +*** NoClaim_02 +*** +*** +*** E[NoClaim_02] + *** + *** E[Collision_02] –*** Age + + – Male +* + +*** Married – – – New_Car –*** –*** –*** Exhaust – – – Clmcoef_03 +*** +*** +*** Log Likelihood – 3245.80 – 3238.75 – 3185.15 Extension --Testing Risk Aversion Due to New CarStaying with Low Coverage Contract in 2003 Conditional on Choosing Low Coverage in 2002.

26. Variable Model 1 Model 2 Model 3 Intercept –*** –*** –*** NoClaim_02 –*** –*** –*** E[NoClaim_02] – *** + E[Collision_02] –*** Age –*** –*** –*** Male +*** +*** +*** Married – ** –** –*** New_Car +*** – – Exhaust –*** –*** –*** Clmcoef_03 +*** +*** +*** Log Likelihood – 13,054.89 – 13,022.68 – 12,947.93 Extension --Testing Risk Aversion Due to New CarSwitching to Low Coverage Contract in 2003 Conditional on Choosing High Coverage in 2002.

27. Extension • For those who choose low coverage in 2002, new car induces the insured not to stay with low coverage in 2003. • For those who choose high coverage in 2002, new car does not have significant effect on switching (or staying) behavior. • Keep choosing high coverage in two years has nothing to do with New Car. Habit persistence would be the major conjecture.