Insurancefraud inTaiwan
Picard andWang
Motivation
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Data
Estimation
Insurance Fraud through Collusionbetween Policyholders and Car Dealers:
Theory and Empirical Evidence.
Pierre PicardDepartment of Economics, Ecole Polytechnique
Kili C. WangDepartment of Insurance, Tamkang University
Insurancefraud inTaiwan
Picard andWang
Motivation
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Estimation
Insurance fraud and collusion
• Claims fraud is an important source of inefficiency ininsurance markets.
• Collusion between policyholders and service providers(car repairers, health care providers...) make fraudeasier.
• Focus on the Taiwan automobile insurance market andon the role of car dealer-owned agents (DOAs).
Insurancefraud inTaiwan
Picard andWang
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On the role of DOAs
• In Taiwan, a large percentage of automobile insurancecontracts are sold through DOAs : 51.4% in our database.
• Most DOAs own a repair shop : they have aninformational advantage (difficult to establish that aclaim has been falsified).
• DOAs own the list of their clients : they have a largebargaining power.
• Repairing or maintaining vehicles, handling claims andrenewing insurance contracts enable DOAs to maintainconstant contact with their clients.
Insurancefraud inTaiwan
Picard andWang
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The curious timing ofautomobile claims in Taiwan
• Li et al. (2013) observe that a large proportion of claimsare filed during the last month of the policy year.
• This is confirmed by our own data base.
• They interpret this phenomenon as a recoupingpremium effect.
Insurancefraud inTaiwan
Picard andWang
Motivation
Model
Data
Estimation
Insurancefraud inTaiwan
Picard andWang
Motivation
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Estimation
Three types of damageinsurance contracts in Taiwan
• Type A contracts : widest scope of coverage (all kindsof collision and non-collision losses) + deductible.
• Type B contracts : the same area of coverage as type Acontracts with some exclusions in the case ofnon-collision losses + either deductible or nodeductible.
• Type C contracts : covers only collision losses withoutdeductible.
• Claims are per accident : one claim for each accident.
Insurancefraud inTaiwan
Picard andWang
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Bonus-malus system
• The insured who has not filed any claim during oneyear gets a discount on the next year premium.
• Symmetrically, there is an increase in premiumproportionally to the number of claims.
• The bonus-malus forgives the first claim within threeyears.
Insurancefraud inTaiwan
Picard andWang
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Manipulating claims
• Opportunist policyholders may take advantage ofmanipulating claims.
• Li et al. (2013) : the policyholders who didn’t file anyclaim before the policy going to an end may feellegitimate to recoup some money back from theinsurance company by filing small false claims near theend of the year.
• Policyholders may file one unique claim with thecumulated losses of two events in order to bear thedeductible burden only one time =⇒ postponing theclaim of an accident in case another accident follows.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Data
Estimation
• Type A and B contracts are particularly subject to thiskind of manipulation (they include coverage for otherlosses than collision between two cars).
• The Taiwanese bonus-malus system reinforce the gainof this manipulation for policyholders who plan torenew their contract : claims filed in the last month ofthe policy year t will be taken into account in thepremium paid in t+ 2 + first accident is forgiven.
• Thus, postponing claims and filing a unique claim fortwo events is at the same time a way to defraud thedeductible contractual mechanism and an abuse of theTaiwanese bonus-malus system
Insurancefraud inTaiwan
Picard andWang
Motivation
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Estimation
Interpreting the concentrationof claims during the last month
• Premium recouping interpretation =⇒ defrauders aremore likely to be policyholders who plan not to renewtheir contract with the same insurance company (theyhave lower moral cost of defrauding) : a "recoupgroup".
• Claims manipulation interpretation =⇒ defrauders aremore likely to be policyholders who have taken outdeductible contracts and who renew their contract : a"suspicious group".
• Type C contracts are difficult to manipulate =⇒may beused as a comparison base in the analysis of fraudulentbehaviors generated by the other contracts.
Insurancefraud inTaiwan
Picard andWang
Motivation
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• Let the First Claim Cost Ratio be
FCCR =average cost of first claimsaverage cost of all claims
.
• Postponing and cumulating claims =⇒ FCCR↗ in thelast policy month.
• That could also result from moral hazard (if a firstaccident makes drivers more cautious).
• Type C contracts may be used to isolate the moralhazard effect (the manipulation of claims is unlikely forsuch contracts).
Insurancefraud inTaiwan
Picard andWang
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• Figure 2 suggests that the claim postponing theory isgrounded in empirical evidence :
Insurancefraud inTaiwan
Picard andWang
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• Figure 3 confirms that DOAs may favor themanipulation of claims.
Insurancefraud inTaiwan
Picard andWang
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The Model• An economy with a competitive insurance market, in
which automobile insurance can be purchased eitherthrough car dealers who act as insurance agents(DOAS) and own car repair shops or through standardinsurance agents.
• Insurance policies : Premium P with loading factor σand deductible d for each accident.
• Each individual suffers 1 accident with probability π1and 2 accidents with probability π2, with0 < π1 + π2 < 1.
• Accidents are minor or serious, with repair cost ` and2` and probability qm and qs respectively (qm + qs = 1).
Insurancefraud inTaiwan
Picard andWang
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• There is a unit mass of risk averse individuals, withinitial wealth w and final wealth wf , and vN-M utilityfunction u(.), with u′ > 0, u′′ < 0. They may be more orless risk averse : types 1 have a smaller degree ofabsolute risk aversion that types 2 :
−u′′1 (wf )
u′1(wf )< −
u′′2 (wf )
u′2(wf ),
and they correspond to proportions λ1 and λ2 of thepopulation, with λ1 + λ2 = 1.
• Type 2 individuals purchase a larger coverage (lowerdeductible) than type 1 because they are more riskaverse.
• Car repairers are risk neutral.
Insurancefraud inTaiwan
Picard andWang
Motivation
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• Individuals have differentiated preferences betweenpurchasing insurance through a car dealer (DOA) orthrough a standard insurance agent.
• Hotelling model : both types of individuals areuniformly located on interval [0, 1] : a representativeDOA is at x = xD = 0 and a representative standardagent is at x = xA = 1. The expected utility is written as
uh(P, d)− t |x− xi| ,
where
uh(P, d) ≡ (1− π1 − π2)uh(w− P)+π1uh(w− P− d) + π2uh(w− P− 2d),
with h = 1 or 2 and i = D if the customer purchasesinsurance through the representative DOA and i = A ifhe goes through the standard agent.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Data
Estimation
The fraud mechanism
• Fraud = putting back claims to the suspicious periodand filing one large claim for two small losses, withthe complicity of a car repairer.
• Collusive gain : d+ v where v is is the gain frombonus-malus fraud.
• The policyholder makes a take-or-leave it offer G to thecar repairer:
gain of the policyholder: d+ v−G,gain of the car repairer: G.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Collusion and audit
• Collusion can be detected by audit, which costs ci,with i = D or A. If fraud is detected, no indemnity ispaid and the policyholder, and the repairer have to payfines, B and B′, respectively.
• Policyholder-repairer coalition bargaining power:defrauders are not punished with probability ξ i, withi = D or A.
• Assumption:
cD > cA and ξD ≥ ξA,or
cD ≥ cA and ξD > ξA.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Fraud and audit strategy
• Strategies: fraud rate αih ∈ [0, 1] and audit rateβih ∈ [0, 1].
• Individuals defraud if the audit rate is not too large.Insurers audit claims if the fraud rate is large enough.
• Nash equilibrium: the fraud rate αih and the audit rateβih should be mutually best-response.
• The equilibrium is in mixed strategies: βih is the auditrate that makes individuals indifferent betweendefrauding and not defrauding and αih is the audit ratethat makes insurers indifferent between auditing andnot auditing.
Insurancefraud inTaiwan
Picard andWang
Motivation
Model
Data
Estimation
Equilibrium contracts (case ofno bargaining power)
• The expected cost of an insurance contract is written as
Cih(dih, ci) = L− (π1 + 2π2)dih + FCih(dih, ci),
where L is the expected repair cost and FCih is the costof fraud (audit cost + cost of undetected fraud), with∂FCih/∂dih > 0 and ∂FCih/∂ci > 0.
• dih, Pih maximizes uh(P, d) w.r.t. P, d, s.t.
P = (1+ σ)× Cih(d, ci),
for h = 1, 2 and i = D, A.
Insurancefraud inTaiwan
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Motivation
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• Proposition 1: The equilibrium deductibles and fraud ratesare such that di1 > di2 ≥ 0, and αi1 > αi2 for i = A or D.
• Intuition: Type 2 individuals choose smallerdeductibles than type 1 because they are more riskaverse. This reduces the incentives to audit claims,hence a larger equilibrium fraud rate.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Estimation
• Proposition 2: The equilibrium fraud rates are such thatαD1 > αA1 and αD2 > αA2, that is, for both types ofindividuals the fraud rate is larger among insurance policiespurchased through D than through A.
• Intuition: insurers need additional incentives to auditclaims when insurance policies have been purchasedthrough D than through A, because audit is more costly(or because DOAs have a larger probability to escapethe penalties) for D than for A. This is reached whenthe fraud rate is larger. The proof shows that thisintuition remains valid if dDh 6= dAh for h = 1, 2.
Insurancefraud inTaiwan
Picard andWang
Motivation
Model
Data
Estimation
• There is a threshold x∗h such that type h individualspurchase insurance through D if x < x∗h and through Aif x < x∗h . The proportion of full coverage contracts θDand θA respectively for D and A is
θD =λ2x∗2
λ1x∗1 + λ2x∗2,
θA =λ2(1− x∗2)
λ1(1− x∗1) + λ2(1− x∗2).
• Proposition 3: θD > θA, i.e., the proportion of full coveragecontracts is larger among insurance policies purchasedthrough D than through A.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Data
Estimation
Data• Data source: a large insurance company in Taiwan. Its
market share in automobile insurance market is over20%.
• The policyholders : the owners of private usage smallsedans and small trucks.
• Data periods: from year 2003 to year 2006.
• Research period: from year 2003 to year 2005.
• 296,940 policyholders in the sample.• We isolate a subsample with the policyholders who
have filed at least one claim during the three years(33.26% of the full sample.)
Insurancefraud inTaiwan
Picard andWang
Motivation
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• Explained variables :• susp : dummy indicating that the insured belongs to the
suspicious group,• nodedt : dummy indicating a policy without deductible,• claimsusp : dummy indicating that the first claim of the
policy year has been filed during the suspicious period.
• Explanatory variables :• D : dummy indicating that the insurance policy has
been purchased through the DOA channel,• A, B : dummy variables indicating a type A or B
contract,• recoup : dummy indicating that the insured belongs to
the recoup group.
and observable variables about the insured (sex, maritalstatus, age, location in Taiwan, type of car...).
Insurancefraud inTaiwan
Picard andWang
Motivation
Model
Data
Estimation
Estimation
• Hypothesis 1: The fraud rate is higher in the suspiciousgroup than in the non-suspicious group.
• Methodology:Test the correlation between "belongingto the suspicious group" and "filing a claim in thesuspicious period". We use two stage probit regressionsto control for the endogeneity of the contract choiceand of the renewal decision:• Stage 1 :
Pr(suspit = 1|Xit) = Φ(αXit)
• Stage 2 :
Pr(claimsuspit = 1|suspit, suspit, recoupit, Xit)
= Φ(βessuspit + βssuspit + βrrecoupit + βXit).
• Prediction: βs should be positive and significantlydifferent from 0.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Remarks on adverse selectionand moral hazard
• Not mixing up with adverse selection :• adverse selection : the relationship between contract
coverage and the probability of filing a claim,• our fraud hypothesis: the relationship between the
nature of contract and the timing of the claims.
• Not mixing up with moral hazard :• moral hazard : larger coverage =⇒ less cautious driver,
particularly near the end of the contract period,• our fraud hypothesis: lower coverage (higher
deductible) =⇒ higher claim probability in the lastpolicy month,
• concern about the scope of coverage =⇒ robustness testby limiting our research sample to type-B contracts.
Insurancefraud inTaiwan
Picard andWang
Motivation
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• Hypothesis 2 : The fraud rate in the suspicious group iseven larger when insurance has been purchased through theDOA channel than through other distribution channels.
• Methodology:We further add Dit, and interactionvariables susp_Dit = suspit ×Dit and recoup_Dit =recoupit ×Dit in the second stage regression:
Pr(claimsuspit = 1|suspit, suspit, Dit, susp_Dit,recoupit, recoup_Dit, Xit)
= Φ(βessuspit + βssuspit + βDDit, βsDsusp_Dit,+βrrecoupit + βrDrecoup_Dit + βXit).
• Prediction : βsD should be positive and significantlydifferent from 0.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Data
Estimation
Table 4: Comparing thesuspicious and non-suspicious
groups
Insurancefraud inTaiwan
Picard andWang
Motivation
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Results for Hypothesis 1
• In Table 4 : βs is positive, and significantly differentfrom 0 at the 5% significance level
• There is a significantly positive conditional correlationbetween belonging to the suspicious group and filing aclaim in the suspicious period.
• The insured whose contract choice is in the suspicious groupare more likely than other policyholders to file their firstclaim during the suspicious period.
Insurancefraud inTaiwan
Picard andWang
Motivation
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Data
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Robustness test
• In Table 5 (restriction to B contracts) : βs is positive, andsignificantly different from 0 at the 1% significancelevel
• Within the sub-group of type-B contracts, theconditional correlation between the suspiciouscontracts and the claims in the last policy month issignificantly positive.
• This is not only the evidence of fraud which can bedistinguished from adverse selection, but it is also anevidence that can be distinguished from ex ante moralhazard.
Insurancefraud inTaiwan
Picard andWang
Motivation
Model
Data
Estimation
Table 5: Restriction to Bcontracts
Insurancefraud inTaiwan
Picard andWang
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Results for Hypothesis 2
• In Table 4 : βs is positive, but not significantly differentfrom 0 anymore. However, the βsDis positive andsignificantly different from 0 at 1% significant level.
• After we control for the interaction between the DOAchannel dummy variable and the suspicious groupdummy variable, the conditional correlation betweenchoosing the suspicious contract and filing claim insuspicious period disappears.
• This confirms the conjecture that the DOAs are themain channel of fraud.
Insurancefraud inTaiwan
Picard andWang
Motivation
Model
Data
Estimation
Robustness test
• In Table 5 (restriction to B contracts) :βs is positive, butnot significantly different from 0 anymore. However,the βsDis positive and significantly different from 0 at1% significant level.
• The policies of type-B contracts purchased through theDOA channel also provide significant evidence offraud.
• The whole fraud in the market comes from the DOA channel.
