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 choicet1 ?

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
No. of Policies (Claims in 2002) Policy Choices in 2003 Policy Choices in 2003
No. of Policies (Claims in 2002) 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
Table 3 Deductible Choices in 2003
Conditional on Deductible Choices in 2002
No. of Policies (Claims in 2002) Policy Choices in 2003 Policy Choices in 2003
No. of Policies (Claims in 2002) Low Deductible High 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
Table 4 Summary Statistics (Choices of Coverage
in 2003, Conditional on 2002
Choices)
High Coverage in 2002 N38014 High Coverage in 2002 N38014 Low Coverage in 2002 N37366 Low Coverage in 2002 N37366
Variable Mean Std Dev Mean Std Dev
Low_Coverage_03 0.1327 0.3392 0.9797 0.1411
No_Claim_02 0.6416 0.4795 0.9124 0.2827
Age 42.0246 9.1678 40.9426 9.4475
Male 0.2578 0.4374 0.3599 0.4800
Married 0.9229 0.2668 0.9066 0.2910
Car_age 1.6655 1.7312 2.5532 2.0279
Exhaust 1.8942 0.6865 1.8827 0.4850
Clmcoefp03 -0.1713 0.2240 -0.1314 0.2047
13
Table 5 Summary Statistics (Deductible Choices
in 2003, Conditional on 2002
Choices)
Low Deductible in 2002 N33938 Low Deductible in 2002 N33938 High Deductible in 2002 N13671 High Deductible in 2002 N13671
Variable Mean Std Dev Mean Std Dev
High_Deductible_03 0.0235 0.1514 0.8836 0.3207
No_Claim_02 0.6602 0.4737 0.6613 0.4733
Age 42.2216 9.0841 42.1674 9.2838
Male 0.2563 0.4366 0.3351 0.4720
Married 0.9252 0.2631 0.9034 0.2954
Car_age 1.7370 1.7456 2.2400 2.0509
Exhaust 1.9028 0.7138 1.9808 0.5878
Clmcoef_03 -0.1906 0.2268 -0.2448 0.2474
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
Table 6 Staying with Low Coverage in 2003
(Logistic Regressions, Conditional
on Choosing Low Coverage in
2002)
 
17
Table 7 Switching to Low Coverage in 2003
(Logistic Regressions, Conditional
on Choosing High Coverage in
2002)
 
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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)
Type 6 price effect, rigid
37,366
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
Table 8 Staying with High Deductible in 2003
(Logistic Regressions, Conditional
on Choosing High Deductible in
2002)
 
22
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
Extension --Testing Risk Aversion Due to New Car
Staying with Low Coverage Contract in 2003
Conditional on Choosing Low Coverage in 2002.
 
26
Extension --Testing Risk Aversion Due to New Car
Switching 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.