Contract design and insurance fraud: an experimental investigation *

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1 Conrac desgn and nsurance fraud: an expermenal nvesgaon * Frauke Lammers and Jörg Schller Absrac Ths paper nvesgaes he mpac of nsurance conrac desgn on he behavor of flng fraudulen clams n an expermenal seup. We es wheher or no peoples fraud behavor vares for nsurance conracs wh full coverage, a sragh deducble or varable premums (bonus-malus conracs). In our expermens flng fraudulen clams s mosly a domnan sraegy for selfsh parcpans. Whle some people never comm fraud, here s a subsanal share of people who only occasonally defraud. In addon, we fnd ha deducble conracs may be perceved as unfar and hus ncrease he exen of fraudulen clams compared o full coverage conracs. In conras, bonus-malus conracs sgnfcanly reduce nsurance fraud boh compared o full coverage and deducble conracs. Ths reducon canno solely be explaned by moneary ncenves. Our resuls ndcae ha bonus-malus conracs are herefore a good means o reduce nsurance fraud because hey reduce he ne-benef from fraud and are generally no perceved as unfar. Prelmnary verson Please do no ce whou auhors permsson Augus 2009 JEL Classfcaon: G22, C91, D03 Key words: nsurance fraud, expermen, farness, conrac desgn, deducble, bonus-malus * Fnancal suppor of he German Insurance Scence Foundaon (Deuscher Veren für Verscherungswssenschaf e.v.) s graefully acknowledged. WHU Oo Beshem School of Managemen, Burgplaz 2, Vallendar, Germany, frauke.lammers@whu.edu. Unversae Hohenhem, Char n Insurance and Socal Sysems, Fruwrhsr. 48, Sugar, Germany, j.schller@un-hohenhem.de.

2 Conrac desgn and nsurance fraud: an expermenal nvesgaon 2 1. Inroducon Fraudulen behavor of polcyholders s generally an mporan ssue n nsurance markes. Whn he las 15 years, here has been subsanal research on many dfferen aspecs of nsurance fraud. Frs of all, here exs many dfferen defnons. Raher src defnons may only encompass such suaons as fraud n whch polcyholders delberaely msrepresen he acual loss by flng fcous clams, nflang vald clams or delberaely causng damages. In hese suaons of hard fraud polcyholders know he rue sae of naure bu fle false clams n order o ge ndemny paymens from nsurance companes. Raher wde nsurance fraud defnons may also regard reduced carefulness of polcyholders 1 (ex ane moral hazard) or nsurance nduced ncreases n prces and or quany for ceran goods whch compensae consequences of unfavorable evens, such as an accden or an llness 2 (ex pos moral hazard) as sof nsurance fraud. In hs paper, we only consder hard nsurance fraud. Many emprcal papers, lke, e.g. Arís e al. (1999) or Caron and Donne (1997) ry o measure he acual amoun or fracon of fraudulen clams n dfferen nsurance markes. For example, Caron and Donne (1997) fnd ha abou 10% of all clams n he Quebec auomoble nsurance marke can be arbued o fraudulen behavor. These clams add up o abou mllon Canadan dollars per year. Relaed emprcal sudes, lke, e.g. Arís e al. (1999, 2002), Brocke e al. (1998, 2002), Donne and Gagné (2001), Derrg and Osaszewsk (1995) and Vaene e al. (2002) ry o denfy ceran observable characerscs of fraudulen clams n order o mprove he deecon of nsurance fraud. For example, n respec o mpac of pror clams Arís e al. (1999, 2002) fnd ha he number of prevous clams n he Spansh auo nsurance marke posvely affecs he fraud probably. Alhough hese sudes do no fnd a sgnfcan mpac of deducbles on fraudulen behavor, Donne and Gagné (2001) show ha n Canadan auo nsurance a hgher deducble s assocaed wh hgher repored losses. In respec o he heorecal research, wo dfferen models are used n order o derve effecve measures for fghng nsurance fraud. In he spr of Townsend (1979), Cosly Sae Verfcaon models, lke, e.g. Pcard (1996), Boyer (2000, 2001) and Schller (2006), 1 See, e.g., Ehrlch and Becker (1972) or Shavell (1979). 2 See, e.g., Pauly (1968), Gaynor e al. (2000) or Nell e al. (2009).

3 Conrac desgn and nsurance fraud: an expermenal nvesgaon 3 are manly concerned wh ncenve effecs of clams audng and he assocaed desgn of opmal nsurance conracs, when polcyholders have superor nformaon wh respec o he occurrence of nsured losses. In conras, Cosly Sae Falsfcaon models, lke, e.g. Crocker and Morgan (1998) and Lacker and Wenberg (1989), are manly concerned wh conracual ncenves when polcyholders can exaggerae her acual clam amoun by cosly and unobservable acves. In hs model framework nsurance companes can only reduce ncenves for fraudulen behavor by conracual means and specfcally he slope of he ndemny funcon. Small losses are generally overcompensaed whereas hgh losses are underpad. The above-menoned heorecal leraure usually employs sandard raonal choce models n he spr of Becker (1968), where selfsh and amoral ndvduals evaluae (poenal) gans and expeced sancons under uncerany. However, here s now a grea deal of evdence ha only some people behave srcly selfsh whle ohers care for socal norms or farness consderaons (see, e.g., Ichno and Magg, 2000, or Fehr and Schmd, 1999). The raonal choce approach mgh herefore no be he approprae model framework o derve effecve polces for fghng nsurance fraud. The leraure offers several explanaons as o why people mgh no be purely selfsh. For nsance, some people would never consder commng a crme, lke nsurance or ax fraud, due o socal norms. 3 Falk and Fschbacher (1999) repor ha sealng n he lab s also nf1uenced by phenomena such as peer pressure or neghbourhood effecs. Ther expermenal sudy fnds suppor for he mporance of socal neracon, snce subjecs n her expermen seal he more, he more ohers seal. 4 Fnally, oher work, lke Spcer and Becker (1980), provdes evdence ha people who beleve ha hey are reaed unfarly by he ax sysem are more lkely o evade axes n order o resore equy. Hence, n addon o socal norms and socal neracon, farness effecs wh respec o nsurance frms or he desgn of nsurance conracs mgh also sgnfcanly affec fraudulen behavor. The am of our expermenal sudy s o evaluae he mpac of socal norms and farness effecs on nsurance fraud whou consderng socal neracon or any monorng 3 In fac, some heorecal models, lke Pcard (1996) or Boyer (2000), do consder wo ypes of polcyholders: opporunss, who jus consder coss and benefs of her acons and hones people, who never comm any nsurance fraud. 4 Bosco and Mone (1997) fnd smlar resuls n a ax evason conex.

4 Conrac desgn and nsurance fraud: an expermenal nvesgaon 4 of clams. In respec o our man research queson, we wan o es wheher or no general fndngs from oher economc expermens, lke ax evason, publc good or cheap alk games, can be ransferred o he nsurance fraud conex. In parcular, no all people behave purely selfsh and amoral. Whle some people n our expermen never comm fraud, here s a subsanal share of people who only occasonally fle fraudulen clams. The laer group s especally neresng for polcy mplcaons. In a second sep, we herefore examne he queson wha rggers fraudulen behavor n hs group? Our focus s on nsurance-specfc effecs. In parcular, we wan o explore wheher and how pas losses and dfferen nsurance arrangemens, lke a sragh deducble or varable premums (bonus-malus conrac), affec he fraudulen behavor of parcpans when flng a fraudulen clam s a domnan sraegy for a selfsh ndvdual. We explcly consder hree dfferen reamens (nsurance arrangemens): a full coverage and a deducble nsurance conrac wh a fxed nsurance premum as well as a bonus-malus nsurance conrac wh full coverage and varable premum. In respec o nsurance-specfc effecs, we could no fnd any sgnfcan mpac of pas losses on he probably o comm nsurance fraud. However, people seem o perceve deducble conracs as unfar, as he exen of fraudulen clamng s sgnfcanly hgher as for full coverage conracs. Our resuls ndcae ha bonus-malus conracs wh a varable clam-dependen premum are generally no perceved as unfar. In fac, bonus-malus conracs sgnfcanly reduce fcous clams compared o a suaon wh a fxed premum even n hose perods n whch s he domnan sraegy o defraud. Mos noably, hs resul s surprsng as bonus-malus conracs wh full coverage are payoff-equvalen o deducble conracs. One can presume ha he reducon of fraud s due o wo effecs: a frs, lke deducble conracs, bonus-malus conracs reduce he ne-benef from nsurance fraud. However, hs conrac ype s no assocaed wh any negave consequences resulng from farness effecs. There are dfferen aspecs of nsurance conracs ha could be perceved as unfar by polcyholders. Frs, nsurance conracs ofen enal a deducble. Accordng o Arrow (1971) and Ravv (1979) a deducble conrac s opmal when nsurance premums enal lnear ransacon coss. In addon, as shown by Townsend (1979), a modfed deducble conrac s also opmal n a Cosly Sae Verfcaon model wh deermnsc audng,

5 Conrac desgn and nsurance fraud: an expermenal nvesgaon 5 where a fxed deducble s appled o all clams ha are above a ceran hreshold. Alhough deducbles may be opmal from a rsk sharng pon of vew and common n real nsurance markes, hey mgh be perceved as unfar by polcyholders. For example, by usng surveydaa Myazak (2009) fnds ha he deducble amoun nfluences percepons of ehcaly and farness regardng nsurance clam buld-up. In hs respec, deducble conracs may lead o (addonal) ncenves for nsurance fraud and farness effecs may explan why hgher deducbles are assocaed wh sgnfcanly hgher repored losses. Donne and Gagné (2001) show ha n Canadan auo nsurance a deducble rase from $250 o $500 ncreases he average clam by 14.6%-31.8% (or respecvely $628 o $812). Thus, her resuls ndcae ha hgher deducbles ncrease fraudulen acves. Moreno e al. (2006) argue ha bonus-malus conracs provde sgnfcan ncenves agans nsurance fraud n a mul-perod seng, when polcyholders are selfsh and raonal. Alhough heorecally appealng, hese conracual feaures may also nfluence he farness percepon of he nsured. As n Slwka (2007), movaon crowdng ou could occur, ha s, he agens could consder hese feaures as a sgnal from he nsurer ha nsurance fraud s consdered as he socal norm. Thus, experence rang (or specfcally bonus-malus conracs) may be consdered as unfar, because afer a clam s made subsequen nsurance premums are ncreased. Consequenly, even f polcyholders are n he frs place fully rembursed for a loss, hey face an mplc deducble as n a bonus-malus sysem: any ndemny s parly self-fnanced by hgher fuure premums. A bonus-malus conrac wh full coverage s herefore equvalen o a deducble conrac. In respec o he mplc deducble resulng from a bonus-malus scheme, s neresng o evaluae he perceved farness of hs conracual arrangemen and compare wh he percepon of equvalen deducble conracs. Only a few nsurance-relaed papers do explcly consder behavoral facors whch mgh affec fraudulen behavor of polcyholders. For example, Cummns and Tennyson (1996) relae her measured dfferences n clamng behavor n auomoble bodly njury lably nsurance o survey daa on consumer audes oward he accepably of specfc dshones pracces, lke ax evason or general fraudulen behavor, n auomoble nsurance. They fnd a srong posve relaonshp beween he aude of accepng dshones and fraudulen acves and raes of lably clamng. Ther sudy also shows ha clam raes

6 Conrac desgn and nsurance fraud: an expermenal nvesgaon 6 are sgnfcanly affeced by varables measurng he coss and benefs of clamng n each federal sae. By analyzng naonal survey daa for he Uned Saes, Tennyson (1997) fnds ha socal norms and ehcal facors sgnfcanly nfluence aude formaon n he nsurance fraud conex. In parcular, her resuls show ha he socal or ehcal envronmen for fraud s relaed o he respondens audes oward nsurance fraud. Boh he socal clmae for nsurance fraud (measured by he fracon of all oher respondens n he sae who fnd fraud accepable) and he responden s nernalzaon of socal norms of honesy more generally (measured by hs aude oward ax evason) are posvely and sgnfcanly relaed o he responden s audes owards nsurance fraud. Surprsngly, even hough he respondens aude o exaggerae clams s also posvely relaed o her negave percepon of nsurance nsuons, nsurance specfc farness effecs seem o be less mporan han socal norms wh respec o he aude owards nsurance fraud. The remander of hs arcle s organzed as follows: In secon 2 we descrbe he expermenal desgn. In secon 3 we derve our hypoheses. Secon 4 presens our resuls and gves a dscusson. Secon 5 concludes. 2. Expermenal Desgn In he expermen subjecs are randomly and anonymously allocaed no fxed groups of four. Each group plays fve perods ( 1,..., T 5) of he followng nsurance game: Parcpans ge a perod endowmen (W) and are nformed ha hey have o nsure agans a loss x j wh j 0, L, H and x0 0 x L xh. Losses are n each perod dencal and ndependenly dsrbued wh p , p 0. 2 L and p H Insurance s mandaory for each parcpan. Thus, each group member mus n every perod pay an nsurance premum (P) o a group-specfc nsurance accoun ha fnances all ndemnes (I) pad o he group members. Hence, n our expermen we apply a muual nsurance seup. All paymens from and o he group members are seled va he group-specfc nsurance accoun. Afer he las perod he nsurance accoun s auomacally balanced by he group members. If he nsurance accoun has a negave balance, all group members pay an addonal conrbuon.

7 Conrac desgn and nsurance fraud: an expermenal nvesgaon 7 A posve balance s shared by all group members. The nsrucons and herefore he whole expermen was framed n an nsurance-specfc wordng. 5 In respec o he clamng of ndemnes, we apply he sraegy mehod. 6 Before knowng he acual loss realzaon n perod, each player s asked whch ndemny j j I I x she would clam gven each possble loss. Hence, n each perod parcpans 0, L H. I s common knowledge ha sraeges drecly deermne he ndvduals perod payoffs. We do no consder monorng acves or punshmens for players who led. Indemnes are always pad as clamed, bu due o choose a clamng sraegy I I, I ransacon coss of 40% ( c 0. 4 ), he nsurance accoun s charged wh an amoun of 1.4I for each clam. Therefore, he nsurance accoun s a cosly means for reallocang premum and clam paymens of he four group members ha provdes coverage agans rsk. All perods are dencal and conss of four seps: Sep 1: Subjecs confrm he paymen of he nsurance premum o he nsurance accoun. Sep 2: Each player has o decde upon her clamng sraegy. Sep 3: Players are nformed abou he acual loss Sep 4: Acual ndemnes I I ~ x x~ n perod. ~ are pad accordng o. Afer he las perod he nsurance accoun s auomacally balanced by he group members. Overall, we conduc hree dfferen reamens ha are descrbed below. 5 For example, Abbnk and Henng-Schmd (2006) fnd ha a conex-free expermen framng does no have a sgnfcan mpac on a brbery game. Schoemaker and Kunreuher (1979) found a sgnfcan mpac of an nsurance framng on parcpans behavor n her survey. We also conduced a conex-free reamen and dd no fnd any sgnfcan dfferences wh respec o he nsurance-specfc wordng n our Base Treamen. 6 Ths approach goes back o Selen (1967). Parcpans have o sae conngen responses for each nformaon se. Bu only one response wll correspond o an effecve acon and wll deermne he responder s and oher players payoff. For example, Hoffmann e al. (1998), Brands and Charness (2000), Oxoby and MacLesh (2004), do no fnd any dfferences n behavor when usng he sraegy mehod n smple sequenal games. However, e.g. Bloun and Bazermann (1996), Güh e al. (2001) and Brosg e al. (2003) found sgnfcan dfferences beween he sraegy mehod and uncondonal decson-makng.

8 Conrac desgn and nsurance fraud: an expermenal nvesgaon 8 3. Hypoheses 3.1. Base Treamen In our Base Treamen he perod endowmen s W 25 and loss szes are x 10 and x 15. As parcpans are able o clam I 0,10,15 from he nsurance accoun, hs H j seup resembles a suaon wh a full-coverage nsurance conrac. The nsurance premum P 5 corresponds o expeced losses ncludng ransacon coss. I does no cover any fraudulen clams. In order o derve an opmal perod sraegy for compleely selfsh parcpans, we assume ha ndvduals possess a nondecreasng Bernoull uly funcon u 0 over fnal wealh. As behavor n perod 1 does no affec decson-makng n perod and parcpans are pad afer he las perod, s sraghforward o assume ha ndvduals do no dscoun her expeced perod uly where U, and hence maxmze In he Base Treamen expeced uly n perod s gven by p ju W P x j Ij P 1 c I j I j U. U U 3 (1) I denoes he expeced ndemny paymens clamed by each oher group member excep ndvdual. As all four group members pay he fla premum o he nsurance accoun and receve 1 4 of he accoun s balance, he nsurance premum cancels ou. Rearrangng (1) and consderng he ransacon cos parameer c 0. 4 gves p ju W x j 1.05I 0. Ij U 65. (2) As W, j x j and 1.05I are ndependen of he ndvdual s clamng behavor, here s no sraegc nerdependence beween group members. Thus, we can derve a domnansraegy equlbrum. One may presume ha opmal clamng sraeges may depend on he ndvdual s rsk averson. Obvously, hs s no he case, as he followng reasonng shows. Suppose a rsk-averse ndvdual wh 0 Ths sraegy leads o an expeced uly of u res o hedge her ncome rsk by choosng 0,10,15 L.

9 Conrac desgn and nsurance fraud: an expermenal nvesgaon 9 U,10,15 0.7u I 0.2u 21,5 1.05I 0.1u 19, I 0. (3) Sarng wh he resulng loery over fnal wealh mpled by 0,10,15 easy o show ha all ndvduals wh nondecreasng uly prefer ˆ 15,15, 15, s, as he resulng loery of fnal wealh frs-order sochascally domnaes all oher possble loeres resulng from ˆ. Proposon 1: If ndvduals are compleely selfsh and maxmze her fnal wealh n each perod accordng o a nondecreasng Bernoull uly funcon, here only exss an equlbrum n domnan sraeges where all ndvduals always clam hgh ndemnes rrespecve of he acual loss sze. Nowhsandng, he man purpose of our Base Treamen s o confrm ha fndngs wh respec o socal norms from publc good games wh sealng (Falk and Fschbacher, 1999) are also vald n an nsurance conex. Due o socal norms, some people may no engage n fraudulen behavor. In addon, for some people farness consderaons mgh be relevan. Thus, he seng s also nended o es wheher or no nsurance specfc facors, lke he loss hsory sgnfcanly affec ndvduals clamng behavour. In respec o pas loss experence, Proposon 1 mples ha pas losses do no have any mpac on clamng. In an expermenal nsurance marke Camerer and Kunreuher (1989) dd no fnd any sgnfcan mpac of loss experence on nsurance demand. However, e.g. Kunreuher (1996) repors ha n flood nsurance people end o cancel her polces afer several years whou loss experence. In lne wh fndngs from Slovc e al. (1977), Kunreuher presumes ha people appear o vew he purchase of nsurance as some knd of nvesmen raher han buyng a conngen clam. Thus, f people do no collec on her polces for a prolonged perod, hey end o le hem lapse. In our seup wh mandaory nsurance, parcpans may ac recprocally and defraud afer some perods whou any loss, as hey are unable o ex from he nsurance relaonshp. Alernavely, n respec o he percepon of nsurance as an nvesmen, pas loss experence may resul n fraudulen behavor n subsequen perods n order o ge some reurn ou of he nvesmen. In order o explan such knd of behavor, le us consder an ndvdual whch generally prefers o honesly repor losses, e.g. due o socal norms, bu wans o break even wh her nsurance conrac. In parcular, le us consder he followng consran

10 Conrac desgn and nsurance fraud: an expermenal nvesgaon 10 mn ~ 0,65I ~ x 1,05I (4) whch s a smplfed varan of he nequy averson preference funcon proposed, e.g. by Fehr and Schmd (1999). In our seng consran (4) has an neresng mplcaon wh respec o pas losses. For gven expecaons I, pas losses ceers parbus ncrease he endency o defraud n order o break-even n he nsurance relaonshp. An ndvdual ha always honesly clams her ncurred losses wh I x faces a defc n consran (4) as he ne benef of an ndemny of 1 pon s only 0.65 pons. Therefore, n he consdered expermen, fraud can be rggered by he consran o break even n he nsurance relaonshp. Hypohess 1: General fndngs from publc good games wh sealng are also vald n an nsurance fraud conex. In parcular, here are hree groups of people: hose wh selfsh preferences who always, hose wh socal norms who never, and hose ha consder for farness who only somemes comm fraud. Hypohess 2: Indvduals who have experenced a loss n he prevous perod are more lkely o comm fraud n he subsequen perod compared o ndvduals who have no experenced a loss Deducble Treamen In he Deducble Treamen (Deduc) he losses x L and x H are ncreased by 5 pons o x 15 and 20 L x, bu parcpans are sll only able o clam 0,10,15 H I as before. Hence, hs arrangemen s equvalen o an nsurance conrac wh a sragh deducble of 5 pons. The premum s unchanged bu he endowmen s ncreased o W 27. Proposon 1 s also vald for he Deducble Treamen. Ths s due o he fac ha he opmal sraegy ˆ 15,15, 15 n he Base Treamen s ndependen of losses. For hose ndvduals, who jus wan o break even on her nsurance relaonshp, ncenves o defraud ncrease as losses are hgher compared o he Base Treamen. However, he endency o defraud may also be ncreased by he fac ha some people generally seem o dslke deducbles. For example, Schoemaker and Kunreuher (1979) fnd j

11 Conrac desgn and nsurance fraud: an expermenal nvesgaon 11 ha people end o choose he lowes avalable deducble. A survey of Myazak (2009) reveals ha he deducble amoun nfluences percepons of ehcaly and farness regardng nsurance clam buld-up. In addon, Donne and Gagné (2001) show ha smple deducble conracs may creae addonal ncenves for flng fraudulen clams. As descrbed, n hs reamen only an nsurance conrac wh a deducble of 5 pons per clam s offered. Ths seup mees wo requremens: a frs, as only losses are ncreased bu ndemnes are unchanged, acual gans resulng from fraudulen behavor are he same for all reamens. Hence, f nsurance-specfc facors do no play a role, fraudulen behavor n hs reamen should no be sgnfcanly dfferen from he Base Treamen. However, he deducble may rgger addonal fraud f wll be consdered as unfar. Secondly, a player n he Deduc Treamen who suffers a low loss of 15 pons wll be fully rembursed f she clams a hgh ndemny of 15 pons. Gven he resuls from Myazak (2009) s sraghforward o expec ha fraud n suaons wh low losses s hgher n hs he Deduc han n he Base Treamen. Hypohess 3a: In he Deducble Treamen ndvduals are more lkely o fraudulenly clam a hgh ndemny for low losses compared o ndvduals n he Base Treamen. For he no loss suaon dfferen predcons are possble. On he one hand, f a subjec ncurs no loss, he deducble should play no mporan role snce ndemnes are he same compared o he oher reamen. On he oher hand, n he lgh of Slwka (2007) deducbles could work as a sgnal from he nsurer ha nsurance fraud s he socal norm. Thus, here could be spllover effecs from he low loss o he no loss suaon resulng n more fraud even n he no loss suaon. Such spllover effecs may also resul from he perceved (un)farness of he deducble conrac. Even f people dd no suffer a loss, hey may decde o ac recprocal n order o respond o he perceved unfarness of he deducble conrac. Hypohess 3b: Indvduals who ncur no loss n he Deducble Treamen are equally or more lkely o comm fraud compared o ndvduals n he Base Treamen.

12 Conrac desgn and nsurance fraud: an expermenal nvesgaon Bonus-Malus Treamen Fnally, n our Bonus-Malus Treamen (BoMa) losses and he endowmen are he same as n he Base Treamen ( x 10, x 15 and W 25) and arcpans can sll only clam L H I j 0,10,15. In hs reamen he nsurance premum s condoned upon pas clams. If ~ parcpans receved a posve paymen 1 I 0, her subsequen premum P s ncreased by 2 pons, oherwse he subsequen premum decreases by 1 pon. The nal premum s P 1 5. As premums depend on pror clamng, opmal sraeges can only be derved va backwards nducon. When decdng wheher or no o clam an ndemny, ndvduals now have o addonally consder he mpac on fuure premum adjusmens. Thus, he ndvdual s perod uly n perod s gven by p ju W P P x j Ij 1 4 P 3P 1.4 I j I U 3 where j. (5) P accouns for he sum of fuure premum adjusmens for all perods wh ( T ) f I 0 P. 2( T ) oherwse Rearrangng (5) gves p ju W 3 4 P P U P x 0.65I 0. 35I (6) j Here, premums do no cancel ou. However, premum paymens ( P, P ) and ndemnes clamed by oher group members ( I ) are ndependen of he ndvdual s clamng sraegy. As here are no fuure premum adjusmens n perod 5, clearly P 5 0 holds. Consequenly, opmal behavor for ndvduals wh Bernoull preferences n 5 s he same as n he Base Treamen. Bu for all oher perods, an ndvdual has o rade-off curren ndemny paymens and fuure premum adjusmens. The perod ne-benef of an ndemny paymen s sll j j 0.65I j. If a posve clam s made, he premum n each fuure perod wll be ncreased by 2 pons. Oherwse he premum n each fuure perod wll be decreased by 1 pon. Clearly, clamng I 15 j

13 Conrac desgn and nsurance fraud: an expermenal nvesgaon 13 srcly domnaes I 10. Gven our reasonng above, he objecve funcon for ndvduals j wh Bernoull preferences obvously smplfes o max 0.65I P (7) Ij j ~ 1 whch drecly mples he domnan sraeges 0,0, 0 and 15,15, 15 ~ 1. Proposon 2: If ndvduals are compleely selfsh and maxmze her fnal wealh accordng o a nondecreasng Bernoull uly funcon, here only exss an equlbrum n domnan sraeges where all ndvduals do no clam any srcly posve ndemnes n he frs perod and subsequenly clam hgh ndemnes rrespecve of he acual loss. Moreno e al. (2006) show ha bonus-malus conracs n a mul-perod model may provde sgnfcan ncenves agans nsurance fraud. One man queson n he BoMa Treamen s wheher or no moneary rewards and punshmens mgae nsurance fraud. In addon, we wan o es wheher hs nsurance arrangemen wh varable premums may be perceved as unfar and may herefore rgger fraudulen behavor. In hs respec, a comparson wh he Base and he Deduc Treamen may lead o furher nsghs. Frs of all, he decson problem for an average parcpans n perod 5 s equvalen o ha of he Base Treamen f P P holds. Consequenly, we do no expec any dfferences n clamng sraeges beween he BoMa and he Base Treamen n 5. Hypohess 4a): The behavor of ndvduals n perod 5 of he Bonus-Malus Treamen should no be sgnfcanly dfferen from he behavor n he Base Treamen. Our expermenal seup allows us o make anoher neresng comparson of perceved farness. As shown by Holan (2001), he effecve ndemny funcon of a fullcoverage bonus-malus conrac s equvalen o an ndemny funcon of an nsurance conrac wh a sragh deducble. He shows ha he (mplc) deducble n a bonus-malus conrac a a pon of me corresponds o he dscouned dfference of fuure premums n perods. In perod 5 he deducble s zero, as here are no fuure premums o pay. In perod 4 he deducble s 3 pons, because he fuure premum s for one perod ncreased by 2 pons f a clam s made or s decreased by 1 pon oherwse. Accordngly, deducbles for he oher perods are: 6 pons ( 3), 9 pons ( 2 ) and 12 pons ( 1).

14 Conrac desgn and nsurance fraud: an expermenal nvesgaon 14 For perods 2,..., 5 we can es wheher or no he poenal ne-benef from nsurance fraud or farness consderaons sgnfcanly affec clamng behavor. In perods 2-4 here s a srcly posve mplc deducble and n 5 here s full coverage. A selfsh Bernoull decson-maker would prefer o defraud n perods 2-5. However, f parcpans predomnanly care for farness, fraudulen behavor should sgnfcanly decrease over me as he mplc deducble decreases. Hypohess 4b): If ndvduals predomnanly care for farness, he exen of fraudulen clamng should decrease beween 2 and 5. As moneary ncenves n BoMa and Deduc Treamen wh a deducble of 6 and 5 pons are almos equvalen for 3, we are able o compare boh reamens wh respec o perceved farness. In he consdered perod he deducble n he BoMa s slghly hgher han n he Deduc Treamen. If a bonus-malus conrac s perceved as less unfar han a deducble conrac, ndvduals should comm less fraud alhough hey face a slghly hgher mplc deducble. More generally, we expec ha hs effec should also be vald n 2,3,4. Hypohess 4c): Indvduals n perods 3 and more generally n 2,3, 4 of he Bonus- Malus Treamen should comm sgnfcanly less fraud han ndvduals n he respecve perods of he Deducble Treamen Subjecs All compuerzed expermens were conduced n March (Base Treamen) and July 2009 (Deducble and Bonus-Malus Treamen) a he MELESSA laboraory of he Ludwg- Maxmlans-Unversy (LMU) Munch n Germany. Recrumen was done by he sysem of Grener (2004) and we used he expermenal sofware z-ree (Fschbacher, 2007). We conduced hree sessons wh 24 parcpans for each of our hree reamens. A sesson ook abou mnues. Subjecs were predomnanly sudens from he LMU wh a grea varey of majors. The fracon of sudens wh a busness or economcs major was abou 16%. All parcpans receved a fxed show-up fee of 4 Euros. Informaon on reamen earnngs excludng show-up fees are repored n Table 1.

15 Conrac desgn and nsurance fraud: an expermenal nvesgaon 15 Treamen Average earnngs Earnng range Base 8.85 (2.13) Deducble 9.33 (2.52) Bonus-Malus 9.50 (2.71) Table 1: Average reamen earnngs (n Euros, sandard devaon n parenheszes) 4. Resuls 4.1. General resuls In hs secon we presen some general resuls of he expermen. Fgure 1 shows he fraudulen behavor of subjecs over all perods per reamen. Fgure 1: Fraudulen behavor of subjecs per reamen In each perod, subjecs have wo possbles of commng fraud: They can clam a low/hgh ndemny when hey have ncurred no loss and/or hey can clam a hgh ndemny when hey have ncurred a low loss (due o he sraegy mehod boh choces are known). Over all reamens, 14% o 24% of subjecs never comm any knd of fraud whereas 7% o 36% always comm fraud. 50% o 69% of subjecs only somemes comm fraud. Ths confrms our Hypohess 1. Resul 1: Hypohess 1 s confrmed. Fgure 2 shows he clamng behavor per loss suaon for all reamens. As expeced, he hgher he ncurred loss, he more subjecs clam a hgh ndemny. However, neresngly, 9% of subjecs who have ncurred a hgh loss wll no clam any ndemny and

16 Conrac desgn and nsurance fraud: an expermenal nvesgaon 16 22% of subjecs n hs suaon wll only clam a low ndemny of 10 pons. Underreporng of losses s only raonal for selfsh parcpans n perod = 1 n he BoMa Treamen. In all oher suaons such behavor mgh be due o he hgh ransacon coss of 40%. 7 Fgure 2: Clamng behavor per loss suaon 4.2. Resuls for he Base Treamen Fgure 3 dsplays he clamng behavor n he case of no loss for each perod n he Base Treamen. Obvously, he number of fraudulen clams per perod ncreases. Fgure 3: Clamng behavor per perod (Base, no loss) 7 We also conduced a neural framng expermen wh and whou ransacon coss. We found ha whou ransacon coss 78% of subjecs clamed a 15 pons ndemny n a hgh loss suaon, whereas only 56% of subjecs clamed he hgh ndemny wh 40% ransacon coss.

17 Conrac desgn and nsurance fraud: an expermenal nvesgaon 17 In order o examne hese effecs n he Base Treamen we conduced a random effecs prob regresson for panel daa. As a dependen varable we consdered he probably of commng fraud n a gven perod n a suaon of no loss (fraud noloss) and low loss (fraud lowloss). Boh varables equal 1 f any knd of fraud s commed, 0 oherwse. The regresson esmaes are repored n Table 2. Dependen varable: Dependen varable: fraud noloss fraud lowloss (1) (2) (3) (4) Perod *** ** *** ** (0.068) (0.092) (0.087) (0.115) Female (0.476) (0.471) (0.951) (0.818) Loss_yn (0.254) (0.313) Consan ** ** (0.422) (0.496) (0.837) (0.807) Number of observaons Log-Lkelhood Wald Ch-squared *** 7.09 * *** 6.62 * Noes: Random effecs prob regresson. The dependen varable s fraud noloss for columns 1-2 and fraud lowloss for columns 3-4. Sandard errors are n parenheses. Sgnfcance a he 1%, 5%, and 10% level s denoed by ***, **, and *, respecvely. Table 2: Prob Esmaes for commng fraud n he Base Treamen In all models, we fnd a sgnfcan posve effec of he number of lapsed perods (Perod) on he probably of commng fraud. Ths fndng s n lne wh he vsual mpresson resulng from Fgure 3. Even hough here s no feedback n our Base Treamen, subjecs end o comm more fraud n laer perods. Ths ndcaes ha learnng was akng place alhough parcpans dd no ge any nformaon abou oher peoples behavor. In he frs model (Table 2, columns 1 and 3) he coeffcen for he perod effec n he no loss suaon s much hgher han n he low loss suaon. In a second model (see Table 2, columns 2 and 4), we examne Hypohess 2 and check for he mpac of prevous losses on he probably of commng fraud. We examne he mpac of he ndependen varable Loss_yn -1 ha equals 1 f he subjec suffered a loss n he prevous perod -1 and 0 oherwse. We fnd no sgnfcan effec of a loss n he

18 Conrac desgn and nsurance fraud: an expermenal nvesgaon 18 prevous perod on he decson o comm fraud. As hs varable s neher sgnfcan n any oher reamen, we have o rejec Hypohess 2 and do no furher consder model one. We canno confrm ha subjecs n our expermen a leas wan o break even as explaned n secon 3.1 or mgh have a arge earnng n her mnd and fear o fall shor of hs arge afer hey have experenced (hgh) losses. Resul 2: Hypohess 2 s rejeced. Fnally, we also conrol for gender, as here s subsanal evdence ha here are sgnfcan preference and behavor dfferences beween males and females n economc expermens. 8 However, n our Base Treamen he dummy varable Female (1 f female, 0 oherwse) s n neher model sgnfcan Resuls for he Deducble Treamen We would now lke o examne he mpac of deducbles on nsurance fraud. Fgure 4 shows he percenage of subjecs who comm fraud f hey have ncurred no loss or a low loss for all perods. Fgure 4: Percenage of subjecs who comm fraud In he Deduc Treamen more subjecs comm fraud n boh loss of suaons. The dfference beween boh reamens s 19% n he low loss suaon and hus hgher compared o he dfference of 12% n he no loss suaon. Overall, he amoun of fraud s hgher n he no loss suaon compared o he low loss suaon. Fgure 5 dsplays he clamng behavor 8 See, e.g., Croson and Gneezy (2008) for a recen leraure revew on gender dfferences.

19 Conrac desgn and nsurance fraud: an expermenal nvesgaon 19 of parcpans per perod n he Deduc Treamen for low losses. Agan, he probably of fraud seems o ncrease over me. Fgure 5: Clamng behavor per perod n he Deduc Treamen (low loss) Table 3 shows he resuls of a random effecs prob regresson for panel daa wh he dependen varables fraud noloss and fraud lowloss. For he Deduc Treamen we only fnd a sgnfcan posve effec of Perod n he low loss suaon. In he no loss and he low loss suaon Female s sgnfcan and consderably negave. Bu n he low loss hs dummy varable s only sgnfcan on a 10%-level. In addon, wh he posve and sgnfcan consan n he no loss suaon hs ndcaes ha females perceve a deducble as less unfar and herefore comm less fraud especally when no loss occurs.

20 Conrac desgn and nsurance fraud: an expermenal nvesgaon 20 Dep. varable: Dep. varable: fraud noloss fraud lowloss (1) (2) Perod *** (0.070) (0.085) Female *** * (0.586) (0.801) Consan *** (0.520) (0.648) Number of observaons Log-Lkelhood Wald Ch-squared *** *** Noes: Random effecs prob regresson. The dependen varable s fraud noloss for column 1 and fraud lowloss for column 2. Sandard errors are n parenheses. Sgnfcance a he 1%, 5%, and 10% level s denoed by ***, **, and *, respecvely. Table 3: Prob Esmaes for he Deduc Treamen In order o assess he sgnfcance of dfferences beween he Deduc and he Base Treamen, we addonally conduc a pooled random effecs prob regresson for panel daa. As dependen varables, we consder a frs he behavor n he no loss suaon (fraud noloss) and addonally he behavor n he low loss suaon (fraud lowloss). The resuls for he prob regresson are summarzed n Table A4 n he Appendx. As he dummy for he Deduc Treamen s sgnfcanly posve for he wo loss suaons, boh fraud probables are sgnfcanly hgher compared o he Base Treamen. However, when we regress fraud noloss, he reamen dummy s only sgnfcan on a 10%-level. The reamen dfference says sgnfcan when we conrol for loss_yn -1 n he prevous perod as well as for Female and Perod. Our daa s hus conssen wh Hypoheses 3a) and 3b): n he Deduc Treamen, he probably of commng fraud n a no loss and low loss suaon s hgher compared o he Base Treamen. Resul 3: Hypohess 3a) and 3b) are confrmed.

21 Conrac desgn and nsurance fraud: an expermenal nvesgaon 21 Apar from our economerc analyss wh respec o fraud probables, may also be neresng o compare average clamng per perod n he Deduc and he Base Treamen. Table 4 summarzes he average value of a clam for boh reamens n each perod for he dfferen possble losses. perod 1 perod 2 perod 3 perod 4 perod 5 Base no loss Deduc Dfference 47.95% 41.57% 12.04% 24.76% 3.28% Base low loss Deduc Dfference 21.80% 16.22% 9.68% 16.45% 11.11% Table 4: Average clam value n he Base and Deduc Treamen (n=72) Table 4 hghlghs ha he average ndemny n he Deduc Treamen s always srcly greaer han n he Base Treamen. In he no loss suaon boh reamens are equvalen. Parcpans can clam 0, 10 or 15 pons n each loss suaon. Obvously, n he no loss suaon people sgnfcanly defraud n boh reamens. Bu n hs suaon he average clam n he Deduc Treamen s consderably hgher, as boh fraud ypes (clamng 10 or 15 pons) are commed more ofen compared o he Base Treamen. In he low loss suaon he loss n he Deduc Treamen s ncreased by 5 pons. Hence, a low loss corresponds o 10 pons n he Base and o 15 pons n he Deduc Treamen. Surprsngly, for all perods he average clam n he Deduc Treamen s only slghly hgher compared o he Base Treamen bu consderably below he acual low loss of 15 pons. Fgure 6 dsplays he number of clams for he Base (sold lnes) and he Deduc Treamen (dashed lnes) n a low loss suaon.

22 Conrac desgn and nsurance fraud: an expermenal nvesgaon 22 Fgure 6: Clamng behavor n he Base and Deduc Treamen (low loss) Comparng he respecve clamng behavor n he Base and he Deducble Treamen (Fgure 5, Tables A1 and A2 n he Appendx) n he low loss suaon reveals ha wo effecs ncrease he average clam. Frs of all, people do more ofen clam a hgh ndemny n order o compensae he deducble, bu n addon, here s less underreporng. Therefore, people do no only end o defraud more, hey are also less wllng o bear nsured losses hemselves. However, hese resuls have o be aken wh care as underreporng dfferences are no sgnfcan. Bu, nsurance companes should consder boh effecs when hnkng abou deducble nsurance Resuls for he Bonus-Malus Treamen Frs of all, we wan o check wheher or no parcpans perceve he BoMa arrangemen as unfar. 9 Therefore, we compare clamng behavor n he Base and BoMa reamen for 5. The esmaes of he pooled random effecs prob regresson wh he dependen varable fraud noloss and fraud lowloss are dsplayed n Table A5 n he Appendx. As all varables (Treamen, Female and Consan) are nsgnfcan, our esmaes ndcae ha here are no any sgnfcan dfferences beween boh reamens. Ths resul s suppored by a Pearson's ch-square es whch leads o he values ( p , wo-sded) for he no loss and ( p ) for he low loss suaon. In our expermen subjecs do no 9 Clamng behavor for he BoMa Treamen s dsplayed n Table A3 n he Appendx.

23 Conrac desgn and nsurance fraud: an expermenal nvesgaon 23 consder he bonus-malus scheme as unfar, as hey do no ake advanage of he opporuny o defraud n he las perod. Hence, we can confrm Hypohess 4a). Resul 4: Hypohess 4a) s confrmed. As s a domnan sraegy o no repor any losses n = 1, we do no consder hs perod. The resuls from a random effecs prob regresson for panel daa wh dependen varables fraud noloss and fraud lowloss as descrbed above are dsplayed n Table 5. Dependen varable: fraud noloss Perod 2-5 Perod 2-4 (1) (2) Dependen varable: fraud lowloss Perod 2-5 Perod 2-4 (1) (1) Perod *** *** ** (0.079) (0.127) (0.098) (0.169) Female * ** * (0.293) (0.344) (0.526) (0.695) Consan ** ** (0.365) (0.469) (0.545) (0.743) Number of observaons Log-Lkelhood Wald Ch-squared *** 5.19 * *** 6.76 ** Noes: Random effecs prob regresson. The dependen varable s fraud noloss for columns 1-2 and fraud lowloss for columns 3-4. Sandard errors are n parenheses. Sgnfcance a he 1%, 5%, and 10% level s denoed by ***, **, and *, respecvely. Table 5: Prob regresson for he BoMa Treamen (no loss and low loss) We consder wo dfferen models for he BoMa Treamen. In model one, we nclude perods 2-5 for whch s a domnan sraegy o fraudulenly clam an ndemny. In conras, n order o evaluae he specfc effec of he bonus-malus arrangemen, model wo only ncludes perods 2-4, as he varable premum scheme s only effecve n hese perods. A comparson of boh models reveals ha he posve perod effec n model one s subsanally drven by perod 5. In model wo, he perod effec s only posve n he low loss suaon. In addon, n hs model women sgnfcanly comm less fraud when moneary ncenves are effecve. In respec o he perod effecs, he esmaes for he BoMa are very smlar o hose of he Deduc Treamen. Bu he perod effec s no

24 Conrac desgn and nsurance fraud: an expermenal nvesgaon 24 sgnfcanly negave. Thus, farness consderaons wh respec o he deducble sze do no sgnfcanly rgger nsurance fraud. Hence, Hypohess 4b) can be rejeced. Resul 5: Hypohess 4b) s rejeced. Whle here s a consan deducble of 5 pons n he Deduc Treamen, he mplc deducble decreases n he BoMa Treamen from 9 pons ( = 2) over 6 pons ( = 3) o 3 pons ( = 4). Alhough deducbles n = 3 are wh 5 pons (Deduc Treamen) and 6 pons (BoMa Treamen) almos he same, ndvduals do sgnfcanly comm less fraud n he BoMa Treamen. Table 6 dsplays he pooled random effecs prob regresson esmaes for he Deduc and BoMa Treamen n = 3. Dep. varable Dep. varable fraud noloss fraud lowloss (1) (2) 1 f BoMa Treamen *** * (0.218) (0.212) Female *** ** (0.228) (0.222) Consan *** ** (0.216) (0.205) Number of observaons Log-Lkelhood LR ch2(2) *** 9.1 ** Pseudo R Noes: Prob regresson. The dependen varable s fraud noloss for column 1 and fraud lowloss for column 2. Sandard errors are n parenheses. Sgnfcance a he 1%, 5%, and 10% level s denoed by ***, **, and *, respecvely. Table 6: Pooled prob esmaes for Deduc and BoMa Treamen (=3) Agan, a Pearson's ch-square es leads o he values ( p ) for he no loss and ( p ) for he low loss suaon. I s mporan o noe ha he reamen effec n he low loss suaon s less sgnfcan and he coeffcen s consderable lower compared o he no loss case. Our nerpreaon of hese resuls s ha he deerrence effec of he bonus-malus conrac s much sronger for he flng of fcous clams as for clam nflaon.

25 Conrac desgn and nsurance fraud: an expermenal nvesgaon 25 Furher dfferences n clamng behavor beween BoMa and Deduc Treamen for low losses n perods 2-4 are dsplayed n Fgure 7. Deduc clamng s depced n sold and BoMa clamng n dashed lnes. Fgure 7: Dfferences n clamng behavor beween BoMa and Deduc (low loss) Comparng boh reamens for he low loss suaon n perods 2-4 suggess ha here s sgnfcanly less fraud (clam nflaon) n he BoMa Treamen. Ths fndng s n lne wh resuls from he correspondng pooled random effecs prob regressons for panel daa ha only consders perods 2-4. Esmaes for hese regressons are dsplayed n Table A6 n he Appendx. In boh regressons he dummy varables for he BoMa Treamen n he wo loss suaons are negave and sgnfcan on a 1%-level. Hypohess 4d) s herefore confrmed. Resul 6: Hypohess 4d) s confrmed. Surprsngly, alhough here are no effecve ncenves n he BoMa Treamen no o comm nsurance fraud, he clamng-dependen premum reduces he probably o comm fraud n he no loss suaon compared o he Base Treamen. In Table 7 we repor he esmaes for a pooled prob regresson for Base an BoMa Treamen ha only consders perods = 2,3,4.

26 Conrac desgn and nsurance fraud: an expermenal nvesgaon 26 Dep. varable: Dep. varable: fraud noloss fraud lowloss Perods 2-4 Perods f BoMa Treamen ** (0.284) (0.529) Perod ** (0.095) (0.124) 1 f Female ** (0.293) (0.557) Consan ** (0.389) (0.644) Number of observaons Log-Lkelhood Wald Ch-squared *** 6.84 * Noes: Treamen dfference n random effecs prob regresson. The dependen varable s fraud noloss for column 1 and fraud lowloss for column 2. Sandard errors are n parenheses. Sgnfcance a he 1%, 5%, and 10% level s denoed by ***, **, and *, respecvely. Table 7: Pooled prob esmaes for Base and BoMa Treamen (=2,3,4) In hs regresson, Treamen s only sgnfcanly negave for he no loss suaon. Ths mples ha a bonus-malus conrac reduces he exen of fcous clams, bu does no have any mpac on clam nflaon compared o he Base Treamen. When comparng all hree reamens, we fnd ha bonus-malus conracs are no perceved as unfar as deducble conracs. Furhermore, when comparng hese conracs o full nsurance conracs we see ha conracs wh clam-dependen premums also lead o a lower fraud exen wh respec o fcous clams. Thus, bonus-malus conracs combne he advanage of a lower ne-benef of fraud of he deducble conrac and are no perceved as unfar as full coverage conracs. Ths conrac ype seems herefore o be preferable n order o reduce he exen of fraudulen clams.

27 Conrac desgn and nsurance fraud: an expermenal nvesgaon Conclusons The goal of our expermenal sudy was o evaluae he mpac of socal norms and farness effecs on nsurance fraud. Our resuls ndcae ha socal norms and farness consderably affec clamng behavor. Even f flng a fraudulen clam s a domnan sraegy for selfsh ndvduals, a sgnfcan share of people does no defraud. One mporan bu no so surprsng fndng s ha deducble nsurance conracs are seemngly perceved as unfar, because he exen of fraudulen clams s sgnfcanly hgher compared o a full nsurance conrac. Our resuls furher ndcae ha bonus-malus conracs wh a varable clamdependen premum are no perceved as unfar. In fac, hese conracs sgnfcanly reduce he exen of fcous clams compared o a suaon wh fxed premum even n hose perods n whch s he domnan sraegy o defraud. Ths effec s manly due o he decreased ne-benef of a fraudulen clam. Mos noably, hs resul s surprsng as bonusmalus conracs wh full coverage are payoff-equvalen o deducble conracs. Our analyss mples ha bonus-malus conracs are a good means o reduce nsurance fraud. One can presume ha bonus-malus conracs reduce he ne-benef of nsurance fraud, bu do no mply he same negave consequences from farness effecs as equvalen deducble conracs.

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