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

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

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

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

9. 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. 10 Table 2 Coverage Choices in 2003 Conditional on Coverage Choices in 2002 No. of Policies (Claims in 2002) Policy Choices in 2003 Comprehensive (H) Collision (L) Comprehensive in 2002 (H) HH: 32970 (11169) 33.87% HL: 5044 (2455) 48.67% Collision in 2002 (L) LH: 759 ( 70) 9.22% LL: 36607 ( 3202) 8.74%

11. 11 Table 3 Deductible Choices in 2003 Conditional on Deductible Choices in 2002 No. of Policies (Claims in 2002) Policy Choices in 2003 Low DeductibleHigh Deductible Low Deductible in 2002 HH: 33141 (11232) 33.89% HL: 797 (301) 37.76% High Deductible in 2002 LH: 1591 ( 539) 33.87% LL: 12080 ( 4091) 33.86%

12. 12 Table 4 Summary Statistics (Choices of Coverage in 2003, Conditional on 2002 Choices) High Coverage in 2002 N=38014 Low Coverage in 2002 N=37366 VariableMeanStd DevMeanStd Dev Low_Coverage_030.13270.33920.97970.1411 No_Claim_020.64160.47950.91240.2827 Age42.0246 9.167840.94269.4475 Male0.25780.43740.35990.4800 Married0.92290.26680.90660.2910 Car_age1.66551.73122.55322.0279 Exhaust1.8942 0.68651.88270.4850 Clmcoefp03-0.17130.2240-0.13140.2047

13. 13 Table 5 Summary Statistics (Deductible Choices in 2003, Conditional on 2002 Choices) Low Deductible in 2002 N=33938 High Deductible in 2002 N=13671 VariableMeanStd DevMeanStd Dev High_Deductible_030.02350.15140.88360.3207 No_Claim_020.66020.47370.66130.4733 Age42.2216 9.084142.16749.2838 Male0.25630.43660.33510.4720 Married0.92520.26310.90340.2954 Car_age1.73701.74562.24002.0509 Exhaust1.9028 0.71381.98080.5878 Clmcoef_03-0.19060.2268-0.24480.2474

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

15. 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 W 2 = (-4847.02) 2 / 3032.19 = 7748 (rejected) (2) Claims in 2002 and choosing high deductible in 2003 are not correlated; W 1 = (-376.25) 2 / 1961.88 = 72.16 (rejected) Spurious results?

16. 16 Table 6 Staying with Low Coverage in 2003 (Logistic Regressions, Conditional on Choosing Low Coverage in 2002) VariableModel 1Model 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

17. 17 Table 7 Switching to Low Coverage in 2003 (Logistic Regressions, Conditional on Choosing High Coverage in 2002) VariableModel 1Model 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

18. 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. 19 High Coverage Claim (P) No Claim (1-P) (H)(H) H H(P)H 11,169 (29.4%) Type 1: adverse selection, rigid L H(P)L 2,455 (6.5%) Type 2: price effect H H(1-P)H 21,801 (57.4%) Type 3: advantageous selection, rigid L H(1-P)L 2,589 (6.8%) Type 4: adverse selection, learning Insurance Buying Decision (1) t = 1 t = 2 38,014 13,624 (35.8%) 24,390 (64.2%)

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

21. 21 Table 8 Staying with High Deductible in 2003 (Logistic Regressions, Conditional on Choosing High Deductible in 2002) VariableModel 1Model 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

22. 22 Table 9 Switching to High Deductible in 2003 (Logistic Regressions, Conditional on Choosing Low Deductible in 2002) VariableModel 1Model 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

23. 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. 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. 25 Extension --Testing Risk Aversion Due to New Car Staying with Low Coverage Contract in 2003 Conditional on Choosing Low Coverage in 2002. VariableModel 1Model 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

26. 26 Extension --Testing Risk Aversion Due to New Car Switching to Low Coverage Contract in 2003 Conditional on Choosing High Coverage in 2002. VariableModel 1Model 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

27. 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.