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
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
2
Background

Possible reasons for the nonexistence of
adverse selection:
-- Risk aversion (Advantageous selection)
-- Habit persistence
-- “strong and empirically implausible
assumptions” Chiappori et al. (2006)
3
Motivation

Alternative view of this paper:
-- Adverse selection might not
characterize the entire insurance
market.
-- To allow all the possible behaviors to
exist.
4
Objective


Decompose observations into groups
with different patterns of insurance
policy buying behavior
Testing patterns of
(Incurred claimst | policy choicet)
 policy choicet+1 ?
5
Presumptions

Two important presumptions in
Rothschild and Stiglitz (1976):
-- The agents are identical or
“observational identical”
-- Decision makers know their risk class.
6
Insurance Buying Decision (1)
H
H(P)H
Type 1:
adverse selection, rigid
L
H(P)L
H
H(1-P)H
Type 3:
advantageous selection
rigid
L
H(1-P)L
Type 4:
adverse selection, learning
Claim
(P)
High Coverage
(H)
No Claim
(1-P)
t=1
t=2
Type 2:
price effect
7
Insurance Buying Decision (2)
H
Claim
(P)
L(P)H
Type 5:
adverse selection, learning
L
L(P)L
Type 6:
price effect, rigid
Low Coverage
H
(L)
No Claim
(1-P)
t=1
L(1-P)H
Type 7:
demand for more coverage,
learning
L L(1-P)L
Type 8:
adverse selection, rigid
t=2
8
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)
9
Table 2 Coverage Choices in 2003
Conditional on Coverage Choices in 2002
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%
10
Table 3 Deductible Choices in 2003
Conditional on Deductible Choices in 2002
Policy Choices in 2003
No. of Policies
(Claims in 2002)
Low 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%
High Deductible
11
Table 4 Summary Statistics (Choices of Coverage
in 2003, Conditional on 2002 Choices)
High Coverage in 2002
N=38014
Variable
Mean
Std Dev
Low Coverage in 2002
N=37366
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
-0.1713
0.2240
-0.1314
0.2047
Clmcoefp03
12
Table 5 Summary Statistics (Deductible Choices
in 2003, Conditional on 2002 Choices)
Low Deductible in 2002
N=33938
Variable
Mean
Std Dev
High Deductible in 2002
N=13671
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
-0.1906
0.2268
-0.2448
0.2474
Clmcoef_03
13
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
14
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?
15
Table 6 Staying with Low Coverage in 2003
(Logistic Regressions, Conditional on
Choosing Low Coverage in 2002)
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
+***
+***
+***
– 3228.37
– 3202.33
– 3026.17
Log Likelihood
16
Table 7 Switching to Low Coverage in 2003
(Logistic Regressions, Conditional on
Choosing High Coverage in 2002)
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
+***
+***
+***
– 13,035.45
– 13,023.65
– 12,940.73
Log Likelihood
17
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
18
Insurance Buying Decision (1)
13,624
(35.8%)
H
H(P)H
11,169 (29.4%)
Type 1: adverse selection, rigid
Claim
(P)
L
38,014
High Coverage
(H)
H(P)L
2,455 (6.5%)
Type 2: price effect
H
No Claim
(1-P)
24,390
(64.2%)
t=1
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
t=2
19
Insurance Buying Decision (2)
3,272
(8.8%)
Claim (P)
37,366
Low Coverage
(L)
No Claim (1-P)
34,094
(91.2%)
t=1
H
L(P)H 70 (0.2%)
Type 5: adverse selection,
learning
L
L(P)L 3,202 (8.6%)
Type 6: price effect, rigid
H
L(1-P)H 689 (1.8%)
Type 7: demand for more
coverage, learning
L L(1-P)L 33,405 (89.4%)
Type 8: adverse selection, rigid
t=2
20
Table 8 Staying with High Deductible in 2003
(Logistic Regressions, Conditional on
Choosing High Deductible in 2002)
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
+
+
+
– 4484.49
– 4484.28
Log Likelihood
– 4484.67
21
Table 9 Switching to High Deductible in 2003
(Logistic Regressions, Conditional on
Choosing Low Deductible in 2002)
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
22
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.
23
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
24
Extension --Testing Risk Aversion Due to New Car
Staying with Low Coverage Contract in 2003 Conditional on
Choosing Low Coverage in 2002.
Variable
Model 1
Model 2
Model 3
Intercept
+***
+***
+***
NoClaim_02
+***
+***
+***
+ ***
+ ***
E[NoClaim_02]
–***
E[Collision_02]
Age
+
+
–
Male
+*
+
+***
Married
–
–
–
New_Car
–***
–***
–***
Exhaust
–
–
–
Clmcoef_03
+***
+***
+***
– 3245.80
– 3238.75
– 3185.15
Log Likelihood
25
Extension --Testing Risk Aversion Due to New Car
Switching to Low Coverage Contract in 2003 Conditional on
Choosing High Coverage in 2002.
Variable
Model 1
Model 2
Model 3
Intercept
–***
–***
–***
NoClaim_02
–***
–***
–***
– ***
+
E[NoClaim_02]
–***
E[Collision_02]
Age
–***
–***
–***
Male
+***
+***
+***
Married
– **
–**
– ***
New_Car
+***
–
–
Exhaust
–***
–***
–***
Clmcoef_03
+***
+***
+***
– 13,054.89
– 13,022.68
– 12,947.93
Log Likelihood
26
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.
27