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

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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

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Background Possible reasons for the nonexistence of adverse selection:

-- Risk aversion (Advantageous selection)-- Habit persistence -- “strong and empirically implausible assumptions” Chiappori et al. (2006)

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Motivation Alternative view of this paper:

-- Adverse selection might not characterize the entire

insurance market.-- To allow all the possible behaviors to exist.

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Objective Decompose observations into groups with different patterns of insurance policy buying behavior Testing patterns of

(Incurred claimst | policy choicet) policy choicet+1 ?

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Presumptions Two important presumptions in Rothschild and Stiglitz (1976):

-- The agents are identical or “observational identical”-- Decision makers know their risk class.

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High Coverage

Claim (P)

No Claim (1-P)

(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

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Low Coverage

Claim (P)

No Claim (1-P)

(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

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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)

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

No. of Policies(Claims in 2002)

Policy Choices in 2003Comprehensive

(H)Collision

(L)

Comprehensive in 2002 (H)

HH: 32970 (11169) 33.87%

HL: 5044 (2455) 48.67%

Collisionin 2002 (L)

LH: 759 ( 70) 9.22%

LL: 36607 ( 3202) 8.74%

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

No. of Policies(Claims in 2002)

Policy Choices in 2003Low Deductible High Deductible

Low Deductible in 2002

HH: 33141 (11232) 33.89%

HL: 797 (301) 37.76%

High Deductiblein 2002

LH: 1591 ( 539) 33.87%

LL: 12080 ( 4091) 33.86%

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

High Coverage in 2002N=38014

Low Coverage in 2002N=37366

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

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

Low Deductible in 2002N=33938

High Deductible in 2002

N=13671Variable 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

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Empirical Analyses Hypothesis testing: Is there a positive correlation between coverage and risk?

risk: incurred claim (Ct -1) in the previous yearcoverage: the choice of coverage or deductible (Dt) this year Logit Regression:Dt = f (Ct -1, B, X) Nonlinear effects

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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?

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Table 6 Staying with Low Coverage in 2003 (Logistic Regressions, Conditional on Choosing Low Coverage in 2002)

Variable Model 1 Model 2 Model 3Intercept + + +

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

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Table 7 Switching to Low Coverage in 2003 (Logistic Regressions, Conditional on Choosing High Coverage in 2002)

Variable Model 1 Model 2 Model 3Intercept – – –

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

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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

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High Coverage

Claim (P)

No Claim (1-P)

(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%)

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Low Coverage

Claim (P)

No Claim (1-P)

(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%)

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Table 8 Staying with High Deductible in 2003 (Logistic Regressions, Conditional on Choosing High Deductible in 2002)

Variable Model 1 Model 2 Model 3Intercept + + +

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

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Table 9 Switching to High Deductible in 2003 (Logistic Regressions, Conditional on Choosing Low Deductible in 2002)Variable Model 1 Model 2 Model 3Intercept – – –

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

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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.

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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

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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 3Intercept +*** +*** +***

NoClaim_02 +*** +*** +***

E[NoClaim_02] + ***

+ *** E[Collision_02] –***

Age + + –

Male +* + +***

Married – – –

New_Car –*** –*** –***

Exhaust – – –

Clmcoef_03 +*** +*** +***Log Likelihood – 3245.80 – 3238.75 – 3185.15

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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 3Intercept –*** –*** –***

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

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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.