Does Opportunistic Fraud in Automobile theft Insurance Fluctuate with the Business Cycle?

Transcription

1 Caier de recerce/orking Paper Does Opporunisic Fraud in uomobile ef Insurance Flucuae wi e Business Cycle? Georges Dionne Kili C. ang oû/ugus 2011 Dionne: Canada Researc Cair in Risk Managemen, HEC Monréal and CIRPÉE ang: ssociae Professor, Deparmen of Insurance, Tamkang niversiy, Taipei, Taiwan

2 bsrac: e analyze e empirical relaionsip beween opporunisic fraud and business cycle. e find a residual opporunisic fraud exiss bo in e conrac wi replacemen cos endorsemen and e conrac wi no-deducible endorsemen in e Taiwan auomobile ef insurance marke. Tese resuls are consisen wi previous lieraure on e relaionsip beween fraud aciviy and insurance conracing. e also sow a e severiy of opporunisic fraud flucuaes in e opposie direcion o e business cycle. Opporunisic fraud is simulaed during periods of recession and miigaed during periods of expansion. Keywords: Opporunisic fraud, replacemen cos endorsemen, no-deducible endorsemen, auomobile ef insurance, business cycle JEL Classificaion: G22, G20, D80, D81

3 Does opporunisic fraud in auomobile ef insurance flucuae wi e business cycle? 1. Inroducion Insurance fraud as become an increasingly imporan issue rougou e world. Many researcers ave invesigaed is problem. Noneeless, few sudies ave examined e relaionsip beween fraud and e surrounding environmen. 1 Tis paper fills is gap and invesigaes e impac of e environmen on fraud from a macroeconomic sandpoin. I underlines e impac of e business cycle on insurance fraud. To our knowledge, insurance fraud as never been direcly linked o any macroeconomic facors in e lieraure. Dionne 2000 provides many reasons for insurance fraud, suc as canges in moraliy, povery, inermediaries beavior, insurers aiude, and naure of insurance conracs. loug i as been poined ou a moraliy or povery could affec insurance fraud, 2 no sudies ave provided relaed empirical evidence. However, fraud as been associaed wi moraliy, and moraliy as been linked o a counry s povery level. In addiion, e povery level of sociey is commonly linked o economic circumsances. Dionne and Gagné 2002 find a paricular paern of claim iming in Quebec s auomobile insurance conracs and conclude a opporunisic fraud is induced by e replacemen cos endorsemen. Dionne and Gagné 2001 also sow ow insurance fraud is affeced by e deducible level in insurance conracs. Similarly, our conribuion posis a opporunisic fraud 1 Boyer 2001 is one of e few researcers o discuss e impac of economic facors on insurance fraud, specifically a of e ax sceme of e insurance benefi. See also Baes e al. s 2010 sudy of eal producion efficiency. 2 Dionne and Gagné 2002 underline a povery is a possible reason for fraud. In e eoreical model of Dionne, Giuliano, and Picard 2009, e moral cos of fraud is one of e facors a affec individuals decision o defraud. 1

4 is induced by e naure of e insurance conrac, and furer explores e impac of e business cycle. I is unclear weer e business cycle as a posiive or negaive impac on insurance fraud. From e risk aversion sandpoin, people could become more risk-averse and esiae o play is ype of loery by commiing fraud wen an economic recession reduces eir weal level. Conversely, e moraliy sandard could decrease wen e economic siuaion worsens. Te marginal benefi from fraud could also increase wile e weal level decreases during a recession, and e incenive o defraud could increase. Hence, compeing predicions on e relaionsip beween e business cycle and insurance fraud are wor esing. Insurance fraud is an increasingly imporan problem in Taiwan. In auomobile ef insurance, a significan line in e propery-liabiliy insurance marke, 3 e amoun of fraud accouns for abou 5% of oal claims. I reaced 150 million NT dollars in i e loss raio of auo ef insurance a more an 35% eac year, fraud could be one of e reasons for suc a ig loss raio in is imporan business line. Furer, e loss raio flucuaes over ime and coincides wi e business cycle. 5 e ave colleced auomobile ef insurance daa from Taiwan s larges propery-liabiliy insurance company. 6 Our monly daa span a long policy period, comprising policies wrien in 2000 o 2007, i.e. a sudy period of 96 policy mons. 7 e can us es e relaionsip beween opporunisic fraud and e business cycle. 3 From 2000 o 2007, abou 26.37% of privae sedans were covered by ef insurance. Te premium is over 40 billion NT dollars abou 1.33 billion S dollars per year, and e grow rae is abou 10% per year. 4 Tis is rougly equivalen o 5 million S dollars. 5 If we rea GDP as a proxy variable for e flucuaion of business cycle, we find a e loss raio of auomobile ef insurance is significanly negaive correlaed wi e level of GDP. e lis e auomobile ef insurance loss raio of non-commercial veicles and e GDP of Taiwan in ppendix, from 1998 o Te opposie relaionsip beween e loss raio and GDP is apparen. Te significan correlaion coefficien is Tis insurance company conrols more an 20% of Taiwan s auomobile insurance marke. 7 For all e conracs wrien from 2000 o 2007, we collec eir complee claim records for e policy year. For example, e claim records of policies wrien in 2007 are exended o e daes in

5 e find a paricular paern of oal ef claim iming linked o e replacemen cos endorsemen. Te mon-by-mon es 8 indicaes a unlike parial ef claims, oal ef claims under replacemen cos endorsemen conracs increase over ime during e conrac year. Tis finding confirms a opporunisic fraud, raer an ex ane moral azard, arises from e replacemen cos endorsemen. Furer, esing by eac policy mon during e policy year poins o anoer paricular paern of claim iming for opporunisic fraud induced by no-deducible endorsemen. Te oal ef claims of no-deducible endorsemen are more common during e early mons of e conrac year. Tis opporunisic fraud evidence can also be separaed from ex ane moral azard. Furer, e empirical evidence affirms a opporunisic fraud flucuaes conversely wi e business cycle. Te claim iming paerns for e wo ypes of conracs menioned above are even more pronounced during a recession, wic implies a a recession amplifies e incenives for opporunisic fraud induced by conracs. Te paper is organized as follows. Te nex secion analyses e empirical ypoeses. Te ird secion describes e daa and e four secion discusses e empirical meodology used in is paper. Te fif secion presens e empirical resuls. Te final secion concludes e paper. 2. Hypoeses Opporunisic fraud incenive is induced by e naure of e insurance conrac. 9 Two imporan conrac ypes are replacemen cos endorsemen and no-deducible endorsemen. e 8 In is paper, e periods ave been reorganized according o policy periods. Hence, we es policy mons insead of calendar mons. 9 Picard 2000 infers a e severiy of insurance fraud ranges from build-up o planned criminal fraud. Te opporunisic fraud we invesigae in is paper is in e middle of e fraud specrum. Tere are also many oer conribuions discussing e opimal conrac design a could reduce e incenive o defraud. Crocker and Morgan 1998 eoreically invesigae e opimal insurance conrac under cosly sae falsificaion. Crocker and Tennyson 1999 empirically esed for e naure of e opimal insurance conrac under cosly falsificaion. Bond and Crocker 1997 and Boyer 2004 design e opimal insurance conrac under cosly sae verificaion see Derrig, 3

6 posi a e degree of incenive o defraud is also affeced by e business cycle. In is secion, four ypoeses are proposed for e empirical ess. Before we explore e impac of e business cycle, e claim iming paern of opporunisic fraud induced by eac conrac is idenified. 10 Tere are many facors explaining opporunisic fraud. 11 On e demand side, maximizing eir expeced uiliy, eac insured as a criical value of e probabiliy of a fraud being successful. Te lower is criical value, e greaer e insured s incenive o commi fraud. One can sow a is criical value decreases wen e difference beween e veicle s replacemen cos and e veicle s marke value increases near e expiraion of e insurance conrac. ccordingly, e insured would consider opporunisic fraud near e conrac s expiraion wi increasing probabiliy. On e supply side, e probabiliy of e insurer s conducing an audi also decreases near e conrac s expiraion because e marke value of e veicle decreases over ime. 12 Hence, as e eoreical model of Dionne and Gagné 2002 indicaes, opporunisic fraud probabiliy is iger near e expiraion of e replacemen cos endorsemen. e also infer e probabiliy of opporunisic fraud under suc an equilibrium model. On e demand side, e individual s expeced uiliy model is similar o a of Dionne and Gagné On e supply side, we modify eir insurer s audi probabiliy o become fla over ime , and Picard, 2000, for reviews of e lieraure. 10 Idenifying e exisence of fraud under asymmeric informaion is an imporan aim in e lieraure. For example, ris e al adop a new meodology o idenify fraud by allowing e misclassificaion error in e exising meod o separae fraudulen claims from ones claims. 11 Picard 1996 buil an equilibrium model beween e insurer and e insured o explain e successful fraud probabiliy in e marke. Dionne and Gagné 2002 exended is model. Te resul is a audiing is no sufficien o deer fraud. Hence, e success probabiliy of fraud does no correspond o e probabiliy of non-audi. 12 Te sringency of audi could affec e success probabiliy of fraud, bu i is no consan over ime. Dionne, Giuliano and Picard 2009 use red flags as e signals for conducing sringen audi in eir opimal audiing sraegy. Dionne and Gagné 2002 assume a e sringency of audi decreases near e expiraion of e replacemen cos endorsemen. 13 e make is assumpion because insurers in Taiwan do no, in pracice, implemen a paricularly sringen audi a e beginning of e conrac. Firs, e marke value of a veicle does no vary as muc as in Quebec from e beginning o e end of e overall policy period, because e conrac leng is only for one year, and e replacemen cos endorsemen conrac is no designed for new veicles exclusively in Taiwan. Second, insurance 4

7 Te eoreical model under replacemen cos endorsemen is presened in ppendix B. Te main resul is consisen wi Dionne and Gagné 2002 in a e equilibrium fraud probabiliy is iger near e end of e policy year. en we sudy opporunisic fraud induced by e replacemen cos endorsemen conrac in e empirical es, is conrac is compared wi e reference conrac wi bo depreciaion and deducible. e rea e conrac wi deducible and replacemen cos endorsemen as a ig-coverage conrac, and e reference conrac as a low-coverage conrac. conrac wi replacemen cos endorsemen reimburses e oal value of e car evaluaed a e beginning of e conrac period. Te former exibis e claim iming paern described above, wereas e laer does no. Hence, our firs ypoesis: Hypoesis 1: If e claims are induced by opporunisic fraud, individuals wo coose a replacemen cos endorsemen conrac ave a iger probabiliy of filing a claim, and is probabiliy is even iger near e end of e conrac period. In addiion, we examine incenives o defraud induced by e no-deducible endorsemen conrac. Dionne and Gagné 2001 propose a eoreical model and empirically verify a e design of e deducible would increase e incenive o build up a claim. However, is conclusion canno be applied direcly o our researc design because we invesigae opporunisic fraud raer an build-up. People puaively build up claims o exceed e deducible resold in e insurance conrac afer e even as occurred. Hence, e design of a deducible would encourage e incenive o build up. If e even as no acually occurred, people would ave a greaer incenive o inven fraudulen claims wen ere is no deducible designed in e conrac. Te incenive of opporunisic fraud is erefore iger under a no-deducible endorsemen. e companies in Taiwan rely eavily on e mecanism of deducible design in e replacemen cos endorsemen and a more sringen depreciaion rae in e no-deducible conrac. Tere is acually no difference in e audi approac beween e beginning and e end of e policy year as a wole. 5

8 derive is resul in ppendix C. e also discuss e claim iming paern for e conrac wi depreciaion in ppendix C. ile e veicle depreciaion from e insurer s indemniy is muc more sringen an a in e marke, and wen e incenive o cea is large enoug, e insured would ave a sronger incenive o organize opporunisic fraud a e beginning of e conrac period under a conrac wi depreciaion. Hence, under a fla audi mecanism, e equilibrium fraud probabiliy is iger a e beginning of e policy year. To idenify opporunisic fraud induced by e no-deducible endorsemen conrac in our empirical es, we compare is conrac wi e reference conrac, wic comprises bo a deducible and depreciaion. Te conrac wi depreciaion and no-deducible endorsemen is us a ig-coverage conrac, and e reference conrac is a low-coverage conrac. s sown in ppendix C, e relaive claim iming paern is focused on e beginning mons of e policy year. Our second ypoesis is erefore: Hypoesis 2: If e claims are induced by opporunisic fraud, individuals wo coose e non-deducible endorsemen conrac ave a iger probabiliy of filing claims. Tis relaive probabiliy is even iger a e beginning of e conrac period. loug e main researc problem is opporunisic fraud, we canno deny a e former pars of e above wo ypoeses could also be e resul of adverse selecion. nder adverse selecion, ig-risk individuals end o purcase e wo ypes of ig-coverage conracs and ave a iger probabiliy of making a claim. However, e claim would be equally disribued among e welve mons. In conras, only opporunisic fraud would creae a paricular paern in e iming of e claim during e mons of e policy year. Tis caracerisic enables us o clearly rule ou adverse selecion. Hence, wen e firs and second ypoeses are empirically susained, ey would provide evidence of opporunisic fraud raer an adverse selecion. 6

9 I is imporan o disinguis opporunisic fraud from ex ane moral azard. 14 Opporunisic fraud resuls from an individual s decision o inven a fraudulen claim or no. Ex ane moral azard arises from e decision o pay more or less aenion o self-proecion. nder e replacemen cos endorsemen, ex ane moral azard could be sronger near e end of e policy year. 15 Conversely, under e no-deducible endorsemen conrac, ex ane moral azard could be sronger a e beginning of e policy year. 16 Ex ane moral azard us as e same claim iming paern as opporunisic fraud. Dionne and Gagné 2002 sow a opporunisic fraud can be induced only wen e benefi from fraud is sufficienly large. Tey mainain a e benefi from fraud based on parial ef is minor. Te incenive o defraud roug oal ef is muc sronger an a relaed o parial ef. Tis difference in incenives provides an opporuniy o disinguis opporunisic fraud from ex ane moral azard. Self-proecion as an equal effec in erms of reducing e probabiliy of bo oal ef and parial ef, bu fraud solely leads o a sronger incenive o file a oal ef claim. ccordingly, opporunisic fraud could emerge mainly based on e probabiliy of a oal ef claim insead of a parial ef claim. Hence, our ird ypoesis is o disinguis opporunisic fraud from ex ane moral azard. Hypoesis 3: If e claim iming paerns in e firs and second ypoeses emerge only in relaion o e oal ef claim, opporunisic fraud exiss raer an ex ane moral azard. If e 14 In e lieraure, e consequences of ex ane moral azard and fraud are ofen mixed. For example, wen eiss e al discussed e disorion effec of regulaed insurance pricing, ey menion a regulaion could cause ex ane moral azard because e safey invesmens of drivers may be diminised. Tis regulaion could also cause fraudulen claims because e disincenive of filing fraudulen claims may also be reduced. 15 s described in Dionne and Gagné 2002, e benefis of prevenion decrease over ime under e replacemen cos endorsemen. Hence, e presence of replacemen cos endorsemen reduces self-proecion aciviies, increasing e probabiliy of ef. 16 Te depreciaion rae used for e insurer s indemniy is more sringen an a in e regular marke. Hence, e difference beween e loss indemniy and e veicle s marke value would be larger near e end of e year. Tis would give e insured more incenive o pay more aenion o self-proecion and o reduce e ex ane moral azard near e end of e year. ccordingly, under a no-deducible conrac, ere is greaer ex ane moral azard a e beginning of e policy year. 7

10 above paerns also emerge relaive o e parial ef claim, en ex ane moral azard may exis in e marke, and we canno conclusively deermine weer opporunisic fraud exiss. Invesigaing e impac of e business cycle on opporunisic fraud is e second obecive of is researc. eer opporunisic fraud will flucuae consisenly or inversely wi e business cycle is unclear. Regarding risk aversion, i as been acceped a mos people are risk-averse and exibi decreasing absolue risk aversion. In an economic recession, people s weal decreases and ey become more risk-averse. Tis will make em more esian o adop risky acions, including fraud. Hence, e probabiliy of opporunisic fraud could decrease during a recession. lernaively, because e individual s weal decreases during a recession, e incremen of uiliy from e benefi of fraud increases concomianly. Furermore, if recession reduces individuals o e povery level, ey may feel ey ave muc less o lose if ey ge caug commiing fraud. Tis may increase people s likeliood of defrauding during a recession. Fraud is igly relaed o an individual s moraliy. Moraliy may also vary wi weal level. Hused e al argue a socieal corrupion is igly relaed o GNP per capia. Tey provide empirical evidence a indirecly sows a individuals moraliy level is posiively relaed o eir weal. Dionne, Giuliano and Picard 2009 esablis in a eoreical model a moral cos is a facor a affecs individuals decision o defraud. Terefore, from e sandpoin of moraliy, recession reduces e average weal level. lower weal level could weaken moraliy and reduce e moral cos of fraud, wic raises e probabiliy of fraud. Because our four ypoesis encompasses wo conflicing effecs, we do no make a predicion on e sign of e effec. Hypoesis 4: Opporunisic fraud could be posiively or negaively affeced by e business cycle. 8

11 3. Daa Our daa se includes all e caracerisics of e insured and e insured veicles, suc as e gender, age, marial saus of e insured; e brand, age, size, regisered area, usage purpose of e insured veicle; e informaion on e conrac, suc as coverage; e selling cannel of e conrac; and e claim informaion for eac policy. Regarding e claim informaion, we collec no only e records on e claim amoun and reason, bu also e records on e dae of e claim. Tis could elp idenify e iming of e claim, specifically e policy mon during e policy period. Furer, we use e corresponding calendar dae o invesigae e impac of e business cycle. Our policy daa are reorganized by policy year, and e claim iming is described by policy mon, wereas e business cycle index is recorded by calendar year and calendar mon. ccordingly, because we invesigae e relaionsip beween business cycle and opporunisic fraud for eac policy mon, we mac e calendar dae of e claim o e corresponding calendar mon in e monly business cycle index. Te daa examined comprise e policies wrien from 2000 o 2007 and eir corresponding claims unil e end of Tis leng of daa allows us o mac e monly variaion in e macroeconomic business cycle index o es e relaionsip beween opporunisic fraud and business cycle. Hence we use e corresponding business cycle index of a poenial claim s calendar mon o measure e effec of e business cycle. Te business cycle index is e rend-adused monly index of e composie coinciden index from January 2000 o December Tis index, obained from e publised daa of e Council for Economic Planning and Developmen of Taiwan, reflecs e flucuaions of e business cycle. Te value of e index is iger wen e economy is ealier, and vice versa. 9

12 Te oal number of observaions in our daa se is 1,761,536. en we es weer opporunisic fraud exiss under e replacemen cos endorsemen, we use a sub-sample of replacemen cos endorsemen conracs ogeer wi conracs wi deducible and depreciaion. Te number of observaions in is sub-sample is 1,715,736. en we es weer opporunisic fraud exiss under no-deducible conracs, we use e sub-sample of no-deducible conracs plus conracs wi deducible and depreciaion. Te number of observaions in is sub-sample is 1,170,012. Because we canno observe e occurrence of parial ef for e conracs wiou e endorsemen of auo pars accessories, we can use only a smaller sub-sample of conracs wi e endorsemen of auo pars accessories wen we es e relaionsip beween coverage and claim iming for e parial ef case. Tis smaller sub-sample comprises 564,175 observaions. Observing e basic saisics of e variables in our empirical daa can elp us undersand e daa caracerisics and eir represenaiveness. Te variables are defined in Table 1. Te descripive saisics for ese variables are lised in Table 2. oal of 32.92% of ef insurance policies involve replacemen cos endorsemen, and only abou 2.48% of e policies ave zero deducible. bou 40% of e policies are sold roug dealer-owned agens. Regarding e srucure of e insured individuals, mos of e insured 91.23% are married, beween 30 and 60 years old 87.97%, and female 62.55%. s for e srucure of e insured veicles, 64.27% of e insured veicles ave engine capaciies equal o or less an 2000 c.c., and 39.29% of e insured veicles are concenraed in e mos popular brand in e marke. Concerning veicle disribuion across e regisered areas, 47.95% are regisered in e nor, 27.84% in e sou, and 2.29% in e eas of Taiwan % of e veicles are regisered in ciies. bou 20% of e veicles are brand new, and more an 70% are less an four years old. oal of 96.43% of e insured veicles are non-commercial or long-erm renal sedans. Tese 10

13 caracerisics indicae a people are more willing o purcase ef insurance for veicles for non-commercial use and for new veicles. 4. Empirical meodology Te firs empirical ask in is paper is o idenify weer opporunisic fraud exiss in e auomobile ef insurance marke in Taiwan. e es e evidence for fraud based on e iming paern of e condiional correlaion beween coverage and claims. Te conrac wi ig coverage is defined as eier e replacemen cos endorsemen or no-deducible conrac. Te claim is furer idenified as e oal ef claim and parial ef claim. To es e condiional correlaion beween coverage and claims, we use a wo-sage meod similar o e meodology for a condiional correlaion analysis in Dionne, Gouriéroux and Vanasse To idenify e ime paern of e condiional correlaion beween coverage and claim, we es eir condiional correlaion by policy mon. Hence, in eac model, 17 we conduc e following condiional correlaion es on welve pairs from e firs policy mon o e welf policy mon. Te wo-sage meod is as follows. In e firs sage, we esimae e claim probabiliy of e - policy mon for eac policy by means of e Probi regression Prob claim ki 1 X1 i X1 i1 k, 1,... 12, k, p, i 1,.. n, 2000, en we idenify e exisence of opporunisic fraud, we es e condiional correlaion beween claim and coverage under four models. In e firs model, we es e condiional correlaion beween oal ef claim and coverage of conrac wi replacemen cos endorsemen. In e second model, we es e condiional correlaion beween oal ef claim and coverage of conrac wi no-deducible endorsemen. In e ird model, we es e condiional correlaion beween parial ef claim and coverage of conrac wi replacemen cos endorsemen. In e four model, we es e condiional correlaion beween parial ef claim and coverage of conrac wi no-deducible endorsemen. en we idenify e relaionsip beween opporunisic fraud and business cycle, we es under wo addiional models. In e fif model, we es e effec of e business cycle on e condiional correlaion beween oal ef claim and e coverage of conrac wi replacemen cos endorsemen. In e six model, we es e effec of e business cycle on e condiional correlaion beween oal ef claim and e coverage of conrac wi no-deducible endorsemen. 11

14 were Prob denoes e probabiliy funcion, is e cumulaive sandard normal disribuion funcion, i 1,, n, denoes e observaions. Te observaions represen an unbalanced panel from policy year 2000 o policy year k = is for oal claim and k = p is for parial claim. X 1i is e vecor of explanaory variables a includes e caracerisics of e insured and e insured veicle, wic are lised in Table 1. Some of e explanaory variables, suc as sex, age of insured, and age of e insured veicle, are invarian during policy years. Oer explanaory variables could vary over policy years; ese include regisered area of veicle, marriage saus, and policy year variable. 1 k is e corresponding parameer vecor, and claim ki is e variable idenifying weer e insured claimed or no. claim ki is defined by policy mon, from firs policy mon o 12 policy mon of e wole policy year, for eac insured i. claim 1 wen insured i as filed a claim in - policy mon of policy year, ki oerwise claim 0. ki In e second sage, we run e oer Probi regression for e probabiliy of purcasing a ig-coverage conrac as: Probcoverage X 2i 2, l, li 1 X c, l, 2i claim, claim ki ki, Prob ˆ claim ec, l, ki Prob ˆ claim ki 2 Tis regression is also based on e sandard normal disribuion used o esimae e probabiliy of purcasing ig coverage. Te variable coverage li is a coice variable of e insured; namely weer e or se purcased a ig-coverage conrac or no in policy year. Tere are wo definiions of ig coverage l in is paper: l R, ND, wic denoes e replacemen cos endorsemen, and e no-deducible conrac, respecively. Te reference conracs are e conracs wi depreciaion and deducibles. Tey are defined as low-coverage. 12

15 X 2 i is e vecor of explanaory variables a conains e same variables as in X 1 i. claim ki as been defined above, and Prob ˆ claim ki is e esimaed probabiliy of claim ki. are e corresponding parameer vecors for e esimaion under eac policy 2, l,, c, l,, ec, l, mon, and wen we invesigae e ig-coverage conrac as l=r or l=nd. Te key esimaed coefficien used o es e problems of asymmeric informaion is c, l,. Tere is a significanly posiive correlaion beween e l coverage and claim in - policy mon if e esimaed c, l, is significanly posiive. To disenangle opporunisic fraud from ex ane moral azard, we es e condiional correlaion beween coverage and oal ef claim, and beween coverage and parial ef claim. Hence, e claim in e above wo regressions is furer defined according o oal claim k= or parial claim k=p. en we conduc e above es for e condiional correlaion beween coverage and oal ef claim, we can use e observaions from e full sample. en we conduc e above es for e condiional correlaion beween coverage and parial ef claim, we can use only a sub-sample of insured wo ave also purcased e auo pars accessories endorsemen. Because we are esimaing oal ef claims, we es only for e exising effecive conracs in eac policy mon. In oer words, e conracs for wic oal claims ave been filed are erminaed and eliminaed from our sample. ccording o e firs ypoesis, we es for e oal ef claim k= and replacemen endorsemen l=r. If e esimaed c, l,, l=r in equaion 2 is significanly posiive only for some - policy mons near e end of e policy year, i indicaes moral azard insead of pure adverse selecion. Opporunisic fraud could be induced by e replacemen cos endorsemen. ccording o e second ypoesis, we es for e oal ef claim k= and no-deducible 13

16 endorsemen l=nd. If e esimaed c, l,, l=nd in equaion 2 is significanly posiive only for some - policy mons occurring early in e policy year, is poins o moral azard insead of pure adverse selecion. Opporunisic fraud could us be induced by e no-deducible endorsemen. en e paricular ime paern emerges, we disinguis opporunisic fraud from ex ane moral azard. ccording o e ird ypoesis, we es e parial ef claim k=p for replacemen cos endorsemen l=r as well as for no-deducible endorsemen l=nd. If esimaed s in equaion 2 for all welve policy mons 1, in e policy year are c, l, insignifican, we can infer a e emerging claim iming paerns are evidence of opporunisic fraud insead of ex ane moral azard. e now ave o es e relaionsip beween opporunisic fraud and e business cycle. e can also es is relaionsip roug a wo-sage meod. e keep e regression in e firs sage uncanged. e en add e business cycle index o e explanaory variables in e regression of e second sage: Probcoverage X 2i 2, l, li 1 X C, l, 2i claim, claim ki ki, claim BC, l, ki claim Buscyc, Prob ˆ claim ki m Buscyc m ec, l, ki Prob ˆ claim ki 3 Buscyc m is e monly business cycle index, wic corresponds o eac calendar mon in eac year wi a poenial claim. In our paper, e claim records are ranged among 108 mons from January 2000 o December 2008, and are ranked from 0100 o e mac eac of e claim daes in our sample o is corresponding calendar dae, and find e corresponding mon for Buscyc m. Buscyc m is inroduced as an ineracion erm wi claim ki. Te key 18 Te firs wo codes of m represen e calendar mon, and e second wo codes of m represen e calendar year. For example, m=0100 is for e business cycle index of January

17 coefficiens used o measure e relaionsip beween opporunisic fraud and e business cycle for conrac l are BC, l, s during some - policy mons. ccording o our four ypoesis, e opporunisic fraud rae could rise or decline wi e recession according o eier of e wo conflicing effecs. If fraud is more severe in a recession, for ig coverage conrac represening conracs wi replacemen cos endorsemen, e BC, l, s l=r in equaion 3 sould be significanly negaive only for ose - policy mons near e end of e wole policy year; for ig coverage conracs represening e no-deducible conrac, e BC, l, s l=nd in equaion 3 sould be significanly negaive only for ose - policy mons a some beginning mons of e policy year. Tis indicaes a opporunisic fraud is more severe wile e economy is in a recession. Conversely, if e esimaed BC, l, s are significanly posiive in e above-menioned policy mons, is affirms a opporunisic fraud is more severe wile e economy is booming. Finally, if all e esimaed BC, l, s are insignifican, e business cycle as no impac on opporunisic fraud. 5. Empirical resuls Te firs empirical ask is o idenify weer opporunisic fraud exiss in e auomobile ef insurance marke in Taiwan. e ry o disenangle ex pos moral azard from adverse selecion and ex ane moral azard. Table 3 sows a for oal ef claims, e esimaed c, l, s l=r are significanly posiive only afer e six policy mon of e conrac in e subsample of replacemen cos endorsemen conracs versus e reference conracs; e esimaed c, l, s l=nd are significanly posiive only before e ird policy mon of e conrac in e subsample of 15

18 no-deducible endorsemen conracs versus e reference conracs. 19 Te condiional correlaions beween coverage and claims exibi significan ime paerns under bo conracs for oal ef claims. Te former finding is consisen wi a of Dionne and Gagné 2002, and suppors our firs ypoesis. Te second finding susains e paricular condiion in our second ypoesis and is inference. Hence, ese oucomes provide evidence only for e possible exisence of opporunisic fraud raer an adverse selecion. In e case of parial ef claims, all of e esimaed c, l, s are no significan in bo subsamples, meaning a e condiional correlaions beween coverage and parial ef claims are all insignifican. Tese oucomes preclude e exisence of ex ane moral azard and confirm e evidence of opporunisic fraud. Terefore, our ird ypoesis is suppored. ll e oucomes, wic suppor e firs o ird ypoeses, confirm a opporunisic fraud is induced by e wo conrac caracerisics: replacemen cos endorsemen and no-deducible endorsemen. Regarding e es associaed wi e business cycle, e empirical resuls of e esimaed coefficiens of C, l, and BC, l, in e second sage are lised in Table Because e es ere is o idenify e impac of e business cycle on opporunisic fraud, we need only es is relaionsip for oal ef claims. 19 Tere are 48 pairs of regressions wen we es e condiional correlaion beween wo dimensions of claim oal ef claim as well as parial ef claim and wo dimensions of coverage e coverage of conracs wi replacemen cos endorsemen as well as e coverage of conracs wi no-deducible endorsemen. I is redundan o repor complee resuls for all 48 pairs of regressions. Hence, we display only 48 key esimaed coefficiens from e second-sage regression in Table 3, and repor wo examples of ensuing regression resuls in ppendix D. 20 Tere are 24 pairs of regressions wen we es e relaionsip beween business cycle and opporunisic fraud. For similar reasons as before, i is redundan o repor complee resuls for all 24 pairs of regressions. Hence, we display only e key esimaed coefficiens C, l, and BC, l, from e second-sage regression in Table 4, and repor wo examples of ese coefficiens in ppendix E. 16 c, l,

19 Table 4 demonsraes a under replacemen cos endorsemen, all of e esimaed BC, l, s l=r are negaive and are significan only afer e 10 policy mon. Te esimaed reained eir ime paern: ey are significanly posiive only for policy mons near e end of C, l, s e firs policy year. nder a no-deducible conrac l=nd, all e esimaed BC, l, s are sill negaive; ey are significan only in e firs wo policy mons. Tese oucomes mean a e condiional correlaion beween coverage and claim is sronger wen economic condiions are deerioraing. Te claim iming paerns for ese ypes of conracs are reinforced by e business cycle. Suc empirical evidence is consisen wi e ypoesis a opporunisic fraud increases during a recession. Te business cycle accenuaes e iming paern of e wo conracs. 6. Conclusion Te main goal of is paper was o invesigae e impac of e business cycle on opporunisic fraud. Few sudies ave associaed e fraud problem wi e surroundings, and none ave discussed e impac of e business cycle on e severiy of fraud. e find a opporunisic fraud is more severe during a recession. e also es weer opporunisic fraud could be induced by differen kinds of insurance conracs. e confirm a ere are paricular ime paerns for oal ef claims induced by replacemen cos endorsemen and no-deducible endorsemen. e separae is evidence from adverse selecion. e also find a ese paricular claim iming paerns exis only in oal ef claims, as opposed o parial ef claims. Tis addiional evidence serves o differeniae opporunisic fraud from ex ane moral azard. Tese conclusions corroborae e finding of Dionne and Gagné

20 References ris, M., yuso, M., and Guillen, M., 2002, Deecion of auomobile insurance fraud wi discree coice models and misclassified claims, Journal of Risk and Insurance 69: Baes, L. J., Mukeree, K., and Sanerre, R. E., 2010, Medical insurance coverage and eal producion efficiency, Journal of Risk and Insurance 77: Bond, E.., and Crocker, K. J., 1997, Hardball and sof ouc: Te economics of opimal insurance conracs wi cosly sae verificaion and endogenous monioring coss, Journal of Public Economics 63: Boyer, M. M., 2001, Miigaing insurance fraud: lump-sum awards, premium subsidies, and indemniy axes, Journal of Risk and Insurance 68: Boyer, M. M., 2004, Overcompensaion as a parial soluion o commimen and renegoiaion problems: e cos of ex pos moral azard, Journal of Risk and Insurance 71: Crocker, K. J. and Morgan, J., 1998, Is onesy e bes policy? Curailing insurance fraud roug opimal incenive conracs, Journal of Poliical Economy 106: Crocker, K. J. and Tennyson, S., 1999, Cosly sae falsificaion or verificaion? Teory and evidence from bodily inury liabiliy claims, in: C. Laberge-Nadeau and G. Dionne, eds. uomobile Insurance: Road Safey, New Drivers, Risks, Insurance Fraud and Regulaion Boson, Mass.: Kluwer. Derrig, R., 2002, Insurance Fraud, Journal of Risk and Insurance 69: Dionne, G., 2000, Te empirical measure of informaion problems wi empasis on insurance fraud, in: Dionne, G., ed., Handbook of Insurance Boson, M: Kluwer cademic Publisers. Dionne, G., Giuliano, F., and Picard, P., 2009, Opimal audiing wi scoring: Teory and applicaion o insurance fraud, Managemen Science 22:

21 Dionne, G., Gouriéroux, C., and Vanasse, C. 2001, Tesing for evidence of adverse selecion in e auomobile insurance marke: commen. Journal of Poliical Economy 1092: Dionne, G.. and Gagné, R., 2001, Deducible conracs agains fraudulen claims: evidence from auomobile insurance, Te Review of Economics and Saisics 83: Dionne, G.. and Gagné, R., 2002, Replacemen cos endorsemen and opporunisic fraud in auomobile insurance, Journal of Risk and ncerainy 24: Hused, B.., 1999, eal, culure, and corrupion, Journal of Inernaional Business Sudies 30: Picard, P., 1996, udiing claims in e insurance marke wi fraud: Te credibiliy issue, Journal of Public Economics 63: Picard, 2000, Economic analysis of insurance fraud, in: Dionne, G., ed., Handbook of Insurance Boson, M: Kluwer cademic Publisers. eiss, M.., Tennyson, S. and Regan L., 2010, Te effec of regulaed premium subsidies on insurance coss: an empirical analysis of auomobile insurance, Journal of Risk and Insurance 77:

22 ppendices ppendix : Te relaionsip beween Taiwan s auo ef insurance loss raio of non-commercial veicles and GDP Year Loss raio GDP ,204, ,649, ,187, ,930, ,411, ,696, ,365, ,740, ,243, ,910, ,698, ,512,678 Noe: Te yearly loss raio daa come from e Taiwan Insurance Insiue. Te yearly GDP daa come from e Direcorae-General of Budge, ccouning and Saisics, Execuive Yuan, R.O.C. Te uni of GDP is million NT dollars. e esimaed e correlaion coefficien beween e loss raio and GDP for ese welve years. Te correlaion coefficien is , and is significanly differen from 0 a 1% of significance level. 20

23 ppendix B: Opporunisic fraud under replacemen cos endorsemen ssume a e consumer is risk-averse. Te expeced uiliy of an insured is equal o g D 1 g, were is e uiliy funcion for e risk averse individual, is e person s weal, no including e value of e veicle, is e marke value of e veicle a e beginning of e policy year, is e depreciaion rae for e marke value of e veicle, wic is an increasing funcion of ime, and denoes e mon of e policy year. is e discoun rae wen e fraudulen individual sells is veicle on e black marke, 0 1. D is e deducible specified in e conrac. g is e probabiliy of e fraud being successful. Te model assumes a e marke value of e veicle will be oally expropriaed if e fraudulen beavior of e individual is discovered by e insurance company. Tis causes e weal level of e fraudulen individual wo is caug o be limied o. Te individual will defraud if g D 1 g. Tere exiss a criical value of e probabiliy g ~ a wic ere is indifference beween being ones and disones: ~ ~ g D 1 g. Furermore, is criical value of e probabiliy of e fraud being successful is: ~ g. D Te expeced uiliy funcion of an individual wo as a probabiliy of engaging in fraudulen beavior can erefore be wrien as: 21

24 E [ ~ ~ g D 1 g ] 1. Te individual as a probabiliy equal o one of engaging in fraud wen e probabiliy of e fraud being successful is above g ~. On e conrary, e individual as a probabiliy equal o zero of engaging in fraud wen e probabiliy of e fraud being successful is below g ~. In addiion, ere is a probabiliy of fraud of beween 1 and 0 wen e probabiliy of e fraud being successful is equal o g ~. To summarize, e probabiliy of an individual engaging in fraud decreases wi g ~. s ime increases: ~ [ ] D[ 2 dg { d [ D ] 2 ] 2 }. [ D ] e resae e denominaor den of e above equaion as: den D, dg 2 2 {[ ] D d den [ D ] } '. Because e incenive for an individual o engage in fraud is iger wen D, e firs se of square brackes is smaller an e second se in e above equaion, and e firs derivaive of e uiliy under D is also smaller an e corresponding derivaive under. In addiion, is beween 0 and 1. ll of ese facors 22

25 make e value inside e brackes negaive. Moreover, 0, ence e sign of e above d g ~ equaion is negaive. d Te above analysis infers a g ~ will decrease wi, and a e probabiliy will increase wi. Hence, e probabiliy of individual engaging in fraud is iger near e end of e policy year. If e audi probabiliy of e insurance company is fla over e wole policy year, e equilibrium rae of fraud could also be iger near e end of e policy year. 23

26 24 ppendix C: Opporunisic fraud under e no-deducible conrac Firs, we examine weer e incenive of opporunisic fraud is iger under a no-deducible endorsemen. e sill assume e individual is risk-averse, 1 g D k g. Hence, e individual s insurance conrac is indemnified wi depreciaion. Te depreciaion rae k increases wi ime. Furermore, e depreciaion rae from e indemniy of e insurance company k is more sringen an a in e marke, i.e., k and k k. Te definiions of g,,, and are e same as ose in e model in ppendix B. Te oally expropriaed consrain is also e same as in ppendix B. Tere exiss a criical value of e probabiliy g ~ of e fraud being successful a wic ere is indifference beween being ones and disones: ~ 1 ~ g D k g. Furermore, is criical value of e probabiliy of e fraud being successful is: 2 1 ~ D g k. s e deducible increases: 0 ~ D dd dg k. Te above inequaliy means a e deducible increases, as does e criical value of e probabiliy of successful fraud, wile e incenive o defraud decreases. Hence, people wo purcase no-deducible conracs ave a sronger incenive o defraud.

27 25 e also discuss e claim iming paern for e conrac wi depreciaion bu wiou deducible. Te expeced uiliy of an individual o defraud under suc a conrac is as follows: 1 g k g. Tere exiss a criical value of e probabiliy of e fraud being successful g ~ a wic poin e individual is indifferen beween being ones and being disones: ~ 1 ~ g k g. Furermore, is criical value of e probabiliy of e fraud being successful is: ~ g k. Te expeced uiliy funcion of an individual wo as e probabiliy of engaging in fraud is erefore expressed as follows: 1 ] ~ 1 [ ~ g k g E. Te individual as a probabiliy of 1 of engaging in fraud wen e probabiliy of e fraud being successful is above g ~. On e conrary, e individual as a probabiliy of 0 of engaging in fraud wen e probabiliy of e fraud being successful is below g ~. Finally, e individual as a probabiliy of fraud of beween 1 and 0 wen e probabiliy of e fraud being successful equals g ~. To summarize, e probabiliy of e individual s engaging in fraud decreases wi g ~. s ime increases: 2 ] [ ] [ ] [ ~ 2 2 k d dg k k ] [ 2 k. e resae e denominaor of e above equaion as den k,

28 dg 1 2 {[ ] 2 2 k k k d den [ ] }. k 2 Here, e firs se of square brackes is smaller an e second se of square brackes and e firs derivaive of e uiliy funcion under k is smaller an e firs derivaive of e uiliy under. However, e erm 2 2 k could be iger an e erm, wic makes e value inside e brackes ambiguous. If e value of is 2 large enoug so a: k [ ] 2 k k k, [ ] e above condiion will make e sign of d g ~ d k 2 posiive. Tis condiion is especially rue wen e depreciaion for e indemniy provided by e insurance company is muc iger an e depreciaion in e marke, i.e., k and k. 2 k 2 Te above inference implies a wile e veicle depreciaion from e insurer s indemniy is muc more sringen an a in e marke, if e incenive o cea is large enoug e discoun on veicles sold on e black marke 1 is no oo ig, g ~ will increase wi, and will decrease wi. Hence, e probabiliy of individual engaging in fraud will be iger a e beginning of e conrac period. If e probabiliy of e insurance company conducing an audi remains fla over e wole of e policy year, e equilibrium rae of fraud may also be iger a e beginning of e policy year. Lasly, we discuss e relaive claim iming paern for e conrac wi depreciaion and no-deducible endorsemen in conras o e reference conrac. 26

29 e consider e impac of iming on e incenive induced by e no-deducible endorsemen. d g In oer words, we consider e impac of on ~ dd. Le H dg~ dd, dh d 1 R 2 R 2 2 k k 2 R R, were R 1 k D, R2. Te sign of is derivaive is ambiguous. Because e erm before e plus sign is negaive, e erm afer e plus sign is posiive, and e ne value of ese wo erms are uncerain. Hence, if e erm before e plus sign is larger an e laer, e above equaion is negaive. Tis means a e degree of criical value of fraud probabiliy decreases from mon o mon during a policy year. In oer words, e degree a no-deducible endorsemen conracs creae a relaively iger incenive o defraud decreases over ime. Tis corresponds o e second par of our second ypoesis, wic saes a e probabiliy of fraud for no-deducible endorsemen conracs is iger a e beginning of e policy year. 27

30 ppendix D: Complee empirical resuls of e 12 policy mon of Model 1, and e 1 s policy mon of Model 2 Variables 12 policy mon in model 1 1 s policy mon in model 2 1 s sage 2 nd sage 1 s sage 2 nd sage Esimae P-value Esimae P-value Esimae P-value Esimae P-value Inercep < <.0001 clm_a clm_ < sexf < < marria_ < age age <.0001 age <.0001 age <.0001 age <.0001 carage < < <.0001 carage < < carage < < carage < carage < ciy < nor < sou < eas < <.0001 ramak_n < ramak_f < ramak_ < < <.0001 ramak_ < ramak_c < capcd_ < capcd_ vecc_s cannel_d cannel_r cannel_t <

31 cannel_l cannel_f cannel_ y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 Hausman es Noe : In model 1, we esimae e condiional correlaion beween oal ef claim and e conrac coverage replacemen cos endorsemen. In model 2, we esimae e condiional correlaion beween oal ef claim and e conrac coverage no-deducible endorsemen. e applied e Hausman es and did no reec e random effec model. Te compued ci-square saisics are repored in e able. 29

32 ppendix E: Complee empirical resuls of e 12 policy mon of Model 1, and e 1 s policy mon of Model 2 Variables 12 policy mon in model 1 1 s policy mon in model 2 1 s sage 2 nd sage 1 s sage 2 nd sage Esimae P-value Esimae P-value Esimae P-value Esimae P-value Inercep < <.0001 clm_a clm_ clm*buscyc sexf < < marria_ < age age age age age carage < < carage < < carage < < carage < carage < ciy < nor < sou < eas < ramak_n < ramak_f < ramak_ < < ramak_ < ramak_c capcd_ < capcd_ < <.0001 vecc_s < <.0001 cannel_d

33 cannel_r cannel_t cannel_l cannel_f cannel_ y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 y_ < <.0001 Hausman es Noe : In model 1, we esimae e condiional correlaion beween oal ef claim and e conrac coverage replacemen cos endorsemen. In model 2, we esimae e condiional correlaion beween oal ef claim and e conrac coverage no-deducible endorsemen. e applied e Hausman es and did no reec e random effec model. Te compued ci-square saisics are repored in e able. 31