Working Paper Contract design and insurance fraud: An experimental investigation

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1 econsor Der Open-Access-Publkaonsserver der ZBW Lebnz-Inforaonszenru Wrschaf The Open Access Publcaon Server of he ZBW Lebnz Inforaon Cenre for Econocs Laers, Frauke; Schller, Jörg Workng Paper Conrac desgn and nsurance fraud: An experenal nvesgaon FZID dscusson papers, No Provded n Cooperaon wh: Unversy of ohenhe, Cener for Research on Innovaon and Servces (FZID) Suggesed Caon: Laers, Frauke; Schller, Jörg (2010) : Conrac desgn and nsurance fraud: An experenal nvesgaon, FZID dscusson papers, No , hp://nbnresolvng.de/urn:nbn:de:bsz:100-opus-4879 Ths Verson s avalable a: hp://hdl.handle.ne/10419/37074 Nuzungsbedngungen: De ZBW räu Ihnen als Nuzern/Nuzer das unengellche, räulch unbeschränke und zelch auf de Dauer des Schuzrechs beschränke enfache Rech en, das ausgewähle Werk Rahen der uner hp:// nachzulesenden vollsändgen Nuzungsbedngungen zu vervelfälgen, denen de Nuzern/der Nuzer sch durch de erse Nuzung enversanden erklär. Ters of use: The ZBW grans you, he user, he non-exclusve rgh o use he seleced work free of charge, errorally unresrced and whn he e l of he er of he propery rghs accordng o he ers specfed a hp:// By he frs use of he seleced work he user agrees and declares o coply wh hese ers of use. zbw Lebnz-Inforaonszenru Wrschaf Lebnz Inforaon Cenre for Econocs

2 FZID Dscusson Papers CC ealh Care Manageen Dscusson Paper Conrac desgn and nsurance fraud: an experenal nvesgaon Frauke Laers and Jörg Schller Unversä ohenhe Forschungszenru Innovaon und Denslesung unversä ohenhe Forschungszenru Innovaon und Denslesung

3 Dscusson Paper CONTRACT DESIGN AND INSURANCE FRAUD: AN EXPERIMENTAL INVESTIGATION Frauke Laers and Jörg Schller Download hs Dscusson Paper fro our hoepage: hps://fzd.un-hohenhe.de/71978.hl ISSN X (Prnausgabe) ISSN (Inerneausgabe) De FZID Dscusson Papers denen der schnellen Verbreung von Forschungsarbeen des FZID. De Beräge legen n allenger Veranworung der Auoren und sellen nch nowendgerwese de Menung des FZID dar. FZID Dscusson Papers are nended o ake resuls of FZID research avalable o he publc n order o encourage scenfc dscusson and suggesons for revsons. The auhors are solely responsble for he conens whch do no necessarly represen he opnon of he FZID.

4 Conrac desgn and nsurance fraud: an experenal nvesgaon * Frauke Laers and Jörg Schller Absrac Ths paper nvesgaes he pac of nsurance conrac desgn on he behavor of flng fraudulen clas n an experenal seup. We es how fraud behavor vares for nsurance conracs wh full coverage, a sragh deducble or varable preus (bonus-alus conrac). In our experen, flng fraudulen clas s a donan sraegy for selfsh parcpans, wh no psychologcal coss of cong fraud. Whle soe people always co fraud, a subsanal share of people only occasonally or never defraud. In addon, we fnd ha deducble conracs ay be perceved as unfar and hus ncrease he exen of cla buld-up copared o full coverage conracs. In conras, bonus-alus conracs wh varable nsurance preus sgnfcanly reduce he flng of fcous clas copared o boh full coverage and deducble conracs. Ths reducon canno be explaned by oneary ncenves. Our resuls ndcae ha conrac desgn sgnfcanly affecs psychologcal coss and, consequenly, he exen of fraudulen behavor of polcyholders. July 2010 JEL Classfcaon: G22, C91, D03 Key words: nsurance fraud, experen, farness, conrac desgn, deducble, bonus-alus * Fnancal suppor fro he Geran Insurance Scence Foundaon (Deuscher Veren für Verscherungswssenschaf e.v.) s graefully acknowledged. WU Oo Beshe School of Manageen, Burgplaz 2, Vallendar, Gerany, frauke.laers@whu.edu. Unversae ohenhe, Char n Insurance and Socal Syses, Fruwrhsr. 48, Sugar, Gerany,.schller@un-hohenhe.de.

5 Conrac desgn and nsurance fraud: an experenal nvesgaon 2 1 Inroducon Praconers and heorss coonly agree ha fraudulen behavor by polcyholders s n addon o classcal adverse selecon and oral hazard probles one of he an hreas for nsurance copanes. Iporan fors of nsurance fraud are fcous clas and cla buld-up. People ay ake advanage of prvae nforaon and cla losses ha never occurred (fcous clas) or exaggerae he sze of an acual nsured loss (cla buld-up). Insurance frs ake hs hrea very serously as hey spend uch effor on fraud deecon syses and cla processng (Donne e al. 2009). 1 Because fraud s dffcul o unabguously verfy ex-pos, esaes of he oal aoun of fraud are no undspued (Derrg, 2002). owever, Caron and Donne (1997) esae ha abou 10% of all clas n he Quebec auooble nsurance arke can be arbued o soe for of fraudulen behavor. These clas would add up o abou llon Canadan dollars per year. Whle he exen of fraud s hard o easure, s even harder o exane facors ha nfluence fraudulen behavor. owever, hese facors are of grea porance for nsurance copanes n he fgh agans nsurance fraud. Up o now, os of he heorecal research ha exanes opal ways o abae nsurance fraud has been based on sandard econoc heory. Currenly, wo an odels are consdered: Cosly Sae Falsfcaon (Crocker and Morgan, 1998) and Cosly Sae Verfcaon (Townsend, 1979; Pcard, 1996). In boh odels, ndvduals are assued o be selfsh and aoral such ha hey only evaluae expeced oneary gans and sancons when decdng o defraud (Becker, 1968). In fac, Donne and Gagné (2002) provde real-world evdence ha he poenal gans of fraudulen acves ay nfluence behavor. They show ha, n he Canadan auo nsurance ndusry, he probably of hef for conracs wh generous wo-year replaceen coverage s sgnfcanly hgher near he end of he second year, when poenal fraud gans are hghes. owever, here s now a grea deal of evdence ha only soe people behave srcly selfshly, whle ohers consder nors or farness (Ichno and Magg, 2000; Fehr and Schd, 1999). For nsance, n lne wh fndngs fro Falk and Fschbacher (1999), soe people would never consder engagng n llegal behavor, lke nsurance or ax fraud, due o 1 Relaed eprcal 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), denfy observable characerscs of fraudulen clas, whch can prove he deecon of nsurance fraud and cla processng n general.

6 Conrac desgn and nsurance fraud: an experenal nvesgaon 3 nors. 2 Regardng he consequences of fraudulen behavor, he resuls of Gneezy (2005) ndcae ha people do no exclusvely care abou her own gan fro lyng; hey are also sensve o he har o ohers ha lyng causes. Oher work, lke Spcer and Becker (1980), provdes evdence ha people who beleve ha hey are reaed unfarly by he ax syse are ore lkely o evade axes o resore equy. ence, nors and farness effecs gh sgnfcanly affec fraudulen behavor. In he conex of nsurance fraud, he pacs of nors and farness are hard o easure n he feld. Consequenly, analyzng hese facors n he lab sees o be a prosng approach. To he bes of our knowledge, he presen sudy s he frs experenal work ha exanes facors nfluencng nsurance fraud. A closely relaed proble o he ssue of nsurance fraud s ax evason. 3 For exaple, Al e al. (1999) show ha nors play a crucal role n ax evason behavor and ha vong on fscal rules or councaon can affec hese nors. In addon, Gordon (1989) and Myles and Naylor (1996) argue ha an ndvdual can derve a psychc payoff fro adherng o he sandard paern of reporng behavor n hs reference group. Wh respec o farness consderaons, one can dsngush vercal and horzonal farness effecs. Vercal farness effecs resul fro ndvduals belefs ha hey are reaed unfarly by he ax syse (auhory). I has been shown ha people holdng such belefs are ore lkely o evade axes o resore equy (Spcer and Becker, 1980). Addonally, Forn e al. (2007) fnd evdence ha axpayers care abou horzonal farness when coparng her own ax burden wh ha of her peers. A reducon n he ean ax rae of an ndvdual s peer group leads he ndvdual o repor lower ncoe. ence, perceved unfar axaon ay ncrease ax evason. Our seup s closely relaed o publc good experens. We eploy a uual nsurance fraework n whch parcpans collecvely bear rsk n groups. Each group eber pays an nsurance preu o a group accoun and can hen cla ndeny payens fro he laer. As ndenes are assocaed wh ransacon coss and boh defcs and surpluses are shared equally beween group ebers, our seup resebles a publc good (bad) suaon. I has been shown ha socal and/or nernalzed nors can 2 In fac, soe heorecal odels, lke Pcard (1996) or Boyer (2000), consder wo ypes of polcyholders: opporunss, who consder only he coss and benefs of her acons, and hones people, who never co any nsurance fraud. 3 See, e.g., Andreon e al. (1998) for a revew of aor heorecal and eprcal fndngs on ax evason.

7 Conrac desgn and nsurance fraud: an experenal nvesgaon 4 enforce cooperaon n publc good suaons (Arrow, 1971a; Andreon, 1990). In addon, farness ssues play a pronen role as parcpans do no wan o be exploed by ohers (Falk and Fschbacher, 1999; Fehr and Gächer, 2000). Thus, non-cooperave behavor can be rggered by expecaons of derenal behavor by ohers. There s soe real-world evdence ha farness and nors also aer n nsurance arkes. As shown by Cuns and Tennyson (1996) and Tennyson (1997), cla frequences n he US auo nsurance ndusry are sgnfcanly relaed o saed audes owards dshones behavor n general (nors). The overall percepon of nsurance nsuons, whch can be seen as a proxy for vercal farness, s anoher nfluencng facor. As nors are dffcul o nfluence, nsurance-specfc facors ha affec vercal farness, lke conracual arrangeens, are crucal for fghng nsurance fraud. In real-world nsurance arkes, wo conracual arrangeens are very coon. Frs, deducble conracs specfy a fxed aoun of oney ha a polcyholder herself us bear n he case of a loss. I can be shown ha such a conrac for s opal fro a rsk allocaon perspecve n suaons wh syerc nforaon and ransacon coss (Arrow, 1971b; Ravv, 1979). owever, ore poranly, deducble conracs have been shown o be opal n suaons wh asyerc nforaon, lke adverse selecon and oral hazard (Rohschld and Sglz, 1976; Shavell, 1979). Second, bonus-alus conracs enal varable preus based on pas clang behavor. Such conracs ay allevae adverse selecon n a ul-perod seng, gve ncenves for loss prevenon and pede he flng of fcous clas (Cooper and ayes, 1987; Leare, 1985; Moreno e al, 2006). Wh respec o he pac of hese conracual arrangeens on vercal farness, o he bes of our knowledge, only led evdence wh respec o deducble conracs exss. Tennyson (2002) and Myazak (2009) fnd ha he deducble sze negavely nfluences percepons of he ehcaly and farness of he nsurance arrangeen and herefore ncreases he accepably of cla buld-up. In hs respec, Donne and Gagné (2001) esae ha, n he Canadan auo nsurance ndusry, a deducble ncrease fro $250 o $500 ncreases he average cla by 14.6%-31.8% (fro $628 o $812). Ther resuls ndcae ha hgher deducbles ncrease fraudulen acves and, n parcular, cla buldup. Bonus-alus conracs ay also nfluence nsured pares farness percepon. Inuvely, hese conracs could be perceved as unfar because subsequen nsurance

8 Conrac desgn and nsurance fraud: an experenal nvesgaon 5 preus are ncreased afer a cla s ade. Consequenly, even f polcyholders are n he frs place fully rebursed for a loss, hey face an plc deducble as any ndeny s parly self-fnanced by hgher fuure preus. Ths paper repors he resuls of a newly developed nsurance experen. Parcpans are allocaed no fxed groups of four. In each of fve perods, parcpans have o nsure agans poenal losses. Insurance s organzed n a uual seup where preus and ndeny payens are borne collecvely by all group ebers. In each perod, parcpans can freely decde o cla an ndeny rrespecve of acual losses. There are no sancons for fraudulen behavor, bu due o ransacon coss and he uual nsurance seup, clas negavely affec he group ebers payoffs. For a selfsh ndvdual, s raonal o cla he hghes possble ndeny n each perod. We perfored hree dfferen reaens. In he Base Treaen, preus only cover expeced acual losses and resulng ransacon coss. Avalable ndenes correspond o possble losses (full coverage). In he Deducble Treaen, ndenes are kep consan n coparson o he Base Treaen, bu all losses are ncreased by a fxed aoun. In he Bonus-Malus Treaen, here s full coverage, and preus depend on pror clang. If a cla s ade, preus are ncreased for all subsequen perods; oherwse, hey are decreased. In hs paper, we analyze he pacs of he wo an conracual nsurance arrangeens observed n pracce. We fnd ha deducble conracs sgnfcanly ncrease cla buld-up. In he case of a loss, subecs see o fnd accepable o recoup deducbles hrough cla nflaon. In addon o hs nuve resul, here s also a spll-over effec as deducble conracs also ncrease he flng of fcous clas. Taken ogeher, hese resuls confr ha deducbles are perceved as unfar and rgger fraudulen behavor. Our second an research focus s on conracs wh clang-dependen preus (bonus-alus schees). In lne wh heorecal predcons, bonus-alus conracs sgnfcanly reduce he flng of fcous clas n early perods. owever, our os poran resul s ha full coverage bonus-alus conracs whch enal an plc deducble are seengly no perceved as unfar: In he las perod, when subecs do no have o fear any fuure preu adusens, behavor s no sgnfcanly dfferen fro he Base Treaen.

9 Conrac desgn and nsurance fraud: an experenal nvesgaon 6 When addressng probles of adverse selecon and oral hazard, resuls fro oneperod odels sugges he use of deducbles o gve polcyholders opal ncenves. owever, hese conracs ay lead o serous sde effecs as hey can sgnfcanly ncrease fraudulen behavor. Our fndngs ndcae ha, due o behavoral aspecs, bonus-alus conracs are superor o deducble conracs n a ul-perod seng. These conracs can be desgned o gve he sae ncenves as deducbles whou causng he sae negave sde effecs. ence, nsurance copanes can use bonus-alus conracs as an effecve eans o address adverse selecon and oral hazard probles. In addon, as heorecal odels sugges, bonus-alus conracs reduce he flng of fcous clas n suaons where audng of clas s eher oo cosly or possble. The reander of hs arcle s organzed as follows: In secon 2, we descrbe he experenal desgn. In secon 3, we derve our predcons for he eprcal analyss. In secon 4, we provde nforaon abou he subecs of he experen. Secon 5 presens our resuls and dscusson, and secon 6 concludes. 2 Experenal Desgn In he experen, parcpans are randoly and anonyously allocaed no fxed groups of four. All payoffs durng he experen are calculaed n he experenal currency pons. Afer he experen, pons are convered no Euros a he rae of 1 pon o 10 cens. Each group plays fve perods ( = 1,..., T = 5 ) of he followng nsurance gae: Parcpans ge a perod endowen (W) and are nfored ha hey have o nsure agans possble losses x wh = 0, L, and x 0 = 0 < x L < x. Losses n each perod are dencal and ndependenly dsrbued, wh p = , p = 0. 2 L and p = Insurance s andaory for each parcpan. Thus, n every perod, each group eber us pay an nsurance preu (P) o a group-specfc nsurance accoun ha fnances all ndenes (I) pad o he group ebers. ence, n our experen, we apply a uual nsurance seup. All payens fro and o he group ebers are seled va he group-specfc nsurance accoun. Afer he las perod, he nsurance accoun s auoacally and equally balanced by all group ebers. If he nsurance accoun has a negave balance, all group ebers pay he sae addonal conrbuon. On he oher hand, a posve balance s equally shared by all group ebers.

10 Conrac desgn and nsurance fraud: an experenal nvesgaon 7 The nsrucons, and herefore he whole experen, were fraed usng nsurance-specfc wordng. 4 All nforaon was coon knowledge. The nsrucons can be found n he Appendx. Wh respec o ndeny clang, we apply he sraegy ehod. 5 Before knowng he acual loss realzaon n perod, each parcpan s asked whch ndeny she s gong o cla for each possble loss. In all reaens, parcpans can only cla one of hree possble ndenes, I = 0 0, I = 10 L, or I = 15, for each possble loss x. ence, n each perod, parcpans choose a clang sraegy s ( I( x ), I( x ), I( x )) ( x ) ( I I I ) I 0, L, =, where. I s coon knowledge ha sraeges drecly deerne ndvduals perod payoffs. We do no consder onorng acves or punshens for players who led. Indenes are always pad as claed, bu due o ransacon coss of 40% ( c = 0. 4 ), he nsurance accoun s charged wh an aoun of I for each cla. Therefore, he nsurance accoun provdes coverage agans rsk bu s a cosly eans of reallocang preu and cla payens of he four group ebers. All perods are dencal and conss of four seps: Sep 1: Subecs confr he payen of he nsurance preu o he nsurance accoun. Sep 2: Each player has o decde upon her clang sraegy Sep 3: Players are nfored abou her acual loss Sep 4: Acual ndenes I I( ~ x ) s. x~ n perod. ~ = are pad accordng o s. Afer he las perod, he nsurance accoun s auoacally balanced by he group ebers. Overall, we conduced hree dfferen reaens ha are descrbed below. L 4 For exaple, Abbnk and enng-schd (2006) fnd ha a conex-free experen frang does no have a sgnfcan pac on a brbery gae. Schoeaker and Kunreuher (1979) found a sgnfcan pac of an nsurance frang on parcpans behavor n her survey. We also conduced a conex-free reaen and dd no fnd any srucural dfferences wh respec o he nsurance-specfc wordng n our Base Treaen. The respecve resuls are avalable fro he auhors upon reques. 5 Ths approach goes back o Selen (1967). Parcpans have o sae conngen responses for each nforaon se, bu only one response wll resul n an effecve acon and deerne he responder s and oher players payoffs. For exaple, offann e al. (1998), Brands and Charness (2000), and Oxoby and MacLesh (2004) do no fnd any dfferences n behavor when usng he sraegy ehod n sple sequenal gaes. owever, e.g., Bloun and Bazerann (1996), Güh e al. (2001) and Brosg e al. (2003) found sgnfcan dfferences beween he sraegy ehod and uncondonal decson akng.

11 Conrac desgn and nsurance fraud: an experenal nvesgaon 8 and = 15 In our Base Treaen, he perod endowen s W = 25 and loss szes are x = 10 x. As parcpans are able o cla = { 0,10,15} I fro he nsurance accoun, hs seup resebles a suaon wh a full-coverage nsurance conrac. The nsurance preu P = 5 corresponds o expeced losses ncludng ransacon coss. I does no cover any fraudulen clas. In he Deducble Treaen (Deduc), boh losses, x L and x, are ncreased by 5 pons o x = 15 and x = 20. Parcpans are nfored ha here s a deducble of 5 L pons, and hus hey are only able o cla I = { 0,10,15}. The preu s unchanged, bu he endowen s ncreased o W = 27 o cover he hgher expeced losses of = 2.1. Tha s, when a loss occurs (30% of he e), hs loss s 5 pons hgher han n he Base Treaen, and ransacon coss of 40% have o be aken no accoun. Fnally, n he Bonus-Malus Treaen (), losses, he endowen, and ndenes are he sae as n he Base Treaen ( x = 10, x = 15, W = 25, = { 0,10,15}) I. In hs reaen, he nsurance preu s condoned upon pas clas. If ~ parcpans receved a posve payen > +1 I 0, her subsequen preu P s ncreased by 2 pons; oherwse, he subsequen preu decreases by 1 pon. The nal preu s P 1 = 5, and he preu n perod +1 s + 1 P 1 f I = 0 P =. (1) P + 2 oherwse L L 3 Theorecal predcons 3.1 Indvdual reaens In order o derve an opal perod sraegy, we assue ha ndvduals possess a nondecreasng Bernoull uly funcon u ( ) > 0. For he Base and Deduc Treaens, behavor n perod 1 does no affec decson akng n perod because preu payens are consan. Furherore, as parcpans are pad afer he las perod, s sraghforward o

12 Conrac desgn and nsurance fraud: an experenal nvesgaon 9 assue ha ndvduals do no dscoun her expeced perod uly U = E[ u ]. U and hence axze Relaed experenal research, lke Fschbacher and eus (2008), has shown ha people ay experence psychologcal coss of cong fraud. These coss ay vary beween ndvduals and ay depend on he aoun of oney defrauded or on oher facors, such as conracual arrangeens. For he sake of splcy, we assue ha coss correspond o θ K, where θ s connuously dsrbued n [ 0,1] accordng o ( θ ) F and K > I. These assupons ply ha coss vary by ndvdual accordng o he facor θ and are ndependen of he aoun defrauded bu ay depend on he conracual arrangeen n a reaen { Base, Deduc, } so we defne ( x ). These coss only occur f he ndvdual defrauds, θ K f I > x κ = (2) 0 oherwse In lne wh Palfrey and Prsbrey (1997), we assue ha for each subec s decsons n perod, here s an dencally and ndependenly dsrbued rando coponen, 2 ( 0, ) ε ~ N σ, ha s added o he psychologcal coss of cong fraud κ. Ths error er represens soe rando added propensy for he subec o eher co fraud or no, whch ay be correlaed wh unobservable ndvdual characerscs. In he Base and Deducble Treaens, expeced uly n perod s gven by ( W P x + I ( x ) ε + 1 4[ 4P ( 1+ c) ( I ( x ) + I )]) U = p u κ 3 (3) where I denoes he expeced ndeny payens claed by all oher group ebers excep for ndvdual. The ndvdual hus receves her endowen P, ay ncur a loss x wh probably p, receves he ndeny ( x ) W, pays he preu I and gh ncur psychologcal coss κ + ε for cong fraud. In addon, he effec on he nsurance accoun has o be consdered. Afer he las perod, he ndvdual wll receve one quarer of he balance of he nsurance accoun afer all preu payens are colleced and ndenes and ransacons coss are pad. As all four group ebers pay he fla preu

13 Conrac desgn and nsurance fraud: an experenal nvesgaon 10 o he nsurance accoun and receve one quarer of he accoun s balance, he nsurance preu cancels ou. Rearrangng (3) and consderng he ransacon cos paraeer c = 0.4 gves U ( W x.05i I ( x ) κ ε ) = p u 1. (4) In a hgh loss suaon, here s no possbly o defraud, and each ndvdual axzes her sae uly by clang I. For he no loss suaon, ndvduals can eher honesly cla I 0 = 0 or fle fcous losses by clang I = 10 or I = 15 L. Clearly, clang I srcly donaes I L because κ s ndependen of he cla sze for I > 0. As W, x and 1.05I are ndependen of he ndvdual s clang behavor, here s no sraegc nerdependence beween group ebers. ere, he opal acon of depends on he ndvdual coss κ. Consequenly, an ndvdual wll only ake a fcous cla f 0 < 0. 65I θ K ε. (5) As long as ε < 0. 65I θ K, ndvdual wll ake a fcous cla n perod. On average, because E[ ε ] = 0 possbles, wh, he argnal ndvdual wh θˆ s ndfferen beween boh ˆ 0.65I θ = > 0 wh Base, Deduc K =. (6) For he low loss suaon, ndvduals can eher honesly cla I L or engage n cla buld-up by deandng I. Slarly, he argnal ndvdual wh ~ θ ndfferen beween boh possbles. Fro (4) we ge ( I I ) s on average ~ 0.65 L θ = > 0 wh = Base, Deduc (7) K In he Base and he Deduc Treaens, he assupon K > I drecly ples ~ 0 < ˆ, θ θ < 1. ence, n he Base and he Deduc Treaens, an ndvdual whou any psychologcal coss θ = 0 axzes her expeced uly by choosng

14 Conrac desgn and nsurance fraud: an experenal nvesgaon 11 s ( = 0) = ( I, I, I ) θ. In conras, an ndvdual wh θ = 1 would never co any fraud and would herefore choose s ( ) ( I, I I ) As probably θ = =,. 1 0 θ s connuously dsrbued n [ 0,1] and E[ ε ] = 0 p for he populaon corresponds o F( θˆ ) and F( ~ θ ) ˆ ~ > θ, we have F( ˆ θ ) > ~ F( θ ) for Base, Deduc θ L, he expeced overall fraud, respecvely. Due o =. Consequenly, n he Base and Deduc Treaens, he fraud probably of fcous clas s hgher han ha for cla buld-up ( p ˆ > ~ p ). Furherore, when he psychologcal cos paraeer K ncreases, boh fraud probables decrease as ˆ ~ θ K < 0 and θ K < 0 hold. Proposon 1: In he Base and Deduc Treaens, ndvduals always cla hgh ndenes rrespecve of he acual loss sze f hey have no psychologcal coss of cong fraud ( θ = 0 ). If 2 ( 0, ) ε ~ N σ and θ s connuously dsrbued n [ 0,1] wh ( θ ) F, K > I, here wll be hree groups of ndvduals: hose who always, hose who never and hose who soees co fraud. For boh reaens, he fraud p ˆ > ~. When probables are consan for all perods and hgher for fcous clas ( ) he psychologcal cos paraeer K Base = K Deduc, we ge pbase pdeduc p K ncreases, he fraud probables decrease. For ˆ = ˆ and ~ p = ~ Base p. Deduc In he Treaen, preus depend on pror clang. ence, opal sraeges can only be derved va backwards nducon. When decdng wheher or no o cla an ndeny, ndvduals us now addonally consder he pac on fuure preu adusens. Thus, he ndvdual s uly n perod, ncludng he fuure pac of curren acons, s gven by where U = p u ( W x P ΔP + I ( x ) κ ε [ P + ΔP + 3( P + ΔP ) 1.4( I ( x ) 3I )]) + Δ P accouns for he su of fuure preu adusens, wh. (8)

15 Conrac desgn and nsurance fraud: an experenal nvesgaon 12 ( T ) f I = 0 ΔP =. 2( T ) oherwse Rearrangng (8) gves U = p u ( W I x 3 4( P P ) 3 4( ΔP ΔP ) ( x ) 1.05I κ ε ). (9) ere, preus do no cancel ou. owever, preu payens ( P, P, ΔP ) and ndenes claed by oher group ebers ( I ) are ndependen of he ndvdual s clang sraegy n perod. As here are no fuure preu adusens n perod = 5, clearly ΔP 5 = 0 holds. Consequenly, opal behavor n = 5 s he sae as n he Base and Deduc Treaens. For all oher perods, an ndvdual has o rade off curren ndeny payens and fuure preu adusens. The ne-benef ncludng he effec on he nsurance accoun of an ndeny payen n each perod s sll.65i ( x ) κ ε 0. If a posve cla s ade, he preu n each fuure perod wll be ncreased by 2 pons. Oherwse, he preu n each fuure perod wll be decreased by 1 pon. Gven our reasonng above, he obecve funcon for ndvduals n perod splfes o ( ( ) ) ax 0.65I Δ ( ) x 0.75 P κ ε. (10) I x Agan, for he no loss suaon, clang I srcly donaes I L. ere, he opal acon of depends on he ndvdual coss κ, ε, and he fuure preu adusens 0.75ΔP, whch decrease n. An ndvdual akes a fcous cla f ( T ) < 0.65I 1. 5( T ) θk ε 0.75 (11) wh The argnal ndvdual wh θˆ s ndfferen beween boh possbles n perod ( T ) ˆ 0.65I 2.25 θ = > 0. (12) K

16 Conrac desgn and nsurance fraud: an experenal nvesgaon 13 If han I As ˆ > 0 θ, he probably of a fcous cla p F( θˆ ) K Base = K holds, he probably of a fcous cla Base ˆ = ncreases n. pˆ, and n =5, boh probables are he sae ( p ˆ ) pˆ s, for 4, srcly lower ˆ =. Base p In he low loss suaon, an ndvdual ay only engage n cla buld-up by flng, bu she can also eher cla I L or I 0. In he laer wo cases, here are no psychologcal coss. I can be shown ha ndvduals ay prefer clang I 0 nsead of I L for 2. Therefore, underreporng ay be relevan for he frs wo perods. Such a socalled bonus hunger-sraegy n bonus-alus syses s well-known n nsurance arkes (Nn, 2009). ere, ndvduals do no repor (low) losses o save on fuure preu adusens and ge a preu bonus. For 2, he argnal ndvdual s ndfferen beween clang I 0 and I. Therefore, we ge ( I I ) 2.25( T ) ~ θ = > 0. (13) K In conras, underreporng s never opal for 3. The argnal ndvdual wh ~ θ s ndfferen beween clang I L and I, whch ples ( I I ) ~ 3 L = = K θ 0.65 ~ θ Base (14) Obvously, as ~ 1 ~ 2 ~ 3 < θ < θ θ holds, he fraud probably n he low loss suaon p~ ncreases n he frs hree perods and s subsequenly consan. An ndvdual whou any psychologcal coss ( = 0) clang I n he suaon of a low loss. θ wll always engage n cla buld-up by In a hgh loss suaon, underreporng s never opal because ( T ) < 0.65I 1. 5( T ) 0.75 holds for all. Thus, ndvduals always cla I. ( = 0) As before, n he Treaen, an ndvdual whou any psychologcal coss θ axzes her expeced uly by choosng s ( θ 0) ( I, I I ) = =,. In conras,

17 Conrac desgn and nsurance fraud: an experenal nvesgaon 14 an ndvdual wh θ = 1 would never co fraud and herefore chooses s ( = ) = ( I, I, I ) θ. 1 0 L Proposon 2: In he no loss suaon of he Treaen, he probably of fcous clas ( ) ( ) pˆ s ncreasng. In he low loss suaon, he probably of cla buld-up p~ ncreases n he frs hree perods and s subsequenly consan. For K Base = K, we ge 4 pˆ < pˆ = 5 Base, pˆ = pˆ Base, ~ 2 p ~ < pbase and ~ 3 p = ~ p Base. Gven Proposons 1 and 2, we derve he followng general predcons for our experen. Predcon 1: In all hree reaens, we expec o observe hree groups of ndvduals: hose who always, hose who never, and hose who soees co fraud. Predcon 2: In he Base Treaen, he probably of fcous clas s hgher han ha of cla buld-up. Predcon 3: In he Treaen, he probably of fcous clas s ncreasng. The probably of cla buld-up s only ncreasng for he frs hree perods and subsequenly consan. 3.2 Predcons for Treaen Effecs Deducble Treaen In hs reaen, an nsurance conrac wh a deducble of 5 pons per cla s offered. Ths seup ees wo requreens: Frs, as only losses are ncreased bu ndenes are unchanged, acual gans resulng fro fraudulen behavor are he sae as n he Base Treaen. ence, accordng o Proposon 1, f nsurance-specfc facors do no have any pac on he psychologcal coss of fraud, behavor n hs reaen should no be sgnfcanly dfferen fro he Base Treaen. owever, he deducble ay rgger addonal fraud f s consdered unfar. Second, a player n he Deduc Treaen who

18 Conrac desgn and nsurance fraud: an experenal nvesgaon 15 suffers a low loss of 15 pons wll be fully rebursed f she repors a hgh loss and hus clas a hgh ndeny of 15 pons. In he Deducble Treaen, he endency o defraud ay be ncreased by he fac ha soe people see o dslke deducbles. Donne and Gagné (2001) show ha sple deducble conracs ay creae addonal ncenves for flng fraudulen clas. In addon, a survey by Myazak (2009) reveals ha he deducble aoun nfluences percepons of ehcaly and farness regardng nsurance cla buld-up. A possble reason for hs fndng ay be ha people wan o be copleely rebursed for all losses n an nsurance relaonshp. Gven hese resuls, s sraghforward o assue he psychologcal cos paraeer of cong fraud o be generally lower n he Deducble Treaen ( K Deduc < K Base ). Due o ˆ ~ θ K < 0 and θ K < 0, he resulng fraud probables n he Deducble Treaen should be sgnfcanly hgher for he no loss and low loss suaons. The psychologcal effec of he Deducble Treaen ay be ore pronounced for he low loss suaon. ere especally, he deducble ay be perceved as unfar because ndvduals are no oally rebursed for an hones cla. Predcon 4: The probables boh for cla buld-up and fcous losses are sgnfcanly hgher n he Deducble Treaen han n he Base Treaen. Wh respec o Proposon 1 and Predcon 2, one could expec ha dfferences beween he wo fraud probables should also be sgnfcan n he Deducble Treaen. owever, due o farness effecs resulng fro he deducble, we expec he psychologcal coss for cla buld-up o be lower copared o fcous clas such ha he effec on he dfference s abguous Bonus-Malus Treaen Moreno e al. (2006) show ha bonus-alus conracs ay provde sgnfcan ncenves agans nsurance fraud n a ul-perod odel. One an queson n he Treaen s wheher or no oneary rewards and punshens reduce he probably of fcous clas, alhough he conracs are no ncenve copable n he sense ha raonal

19 Conrac desgn and nsurance fraud: an experenal nvesgaon 16 ndvduals wh no psychologcal coss prefer o defraud. In addon, we wan o es wheher hs nsurance arrangeen wh varable preus ay be perceved as unfar and ay herefore rgger fraudulen behavor. To he bes of our knowledge, no evdence exss abou farness aspecs of bonus-alus conracs. A coparson wh he Base Treaen ay lead o furher nsghs. Frs of all, he decson proble n perod = 5 s equvalen o ha of he Base Treaen f P = P holds. Consequenly, f K Base K =, here should be no dfferences n clang sraeges beween he and he Base Treaen n = 5. In addon, as ~ 3 p = ~ p Base, we would expec o fnd no dfference for cla buld-up n 3. owever, f K < K, ndvduals perceve he bonus-alus conrac as unfar, and he probably Base of cla buld-up n perod 5 should be sgnfcanly hgher because here are no fuure preu adusens. Furherore, n hs case we would have p > ~ p. ~ 3 In our vew, behavor n perods 3-5 ndcaes wheher or no bonus-alus conracs are perceved as unfar. Gven he lack of evdence for such farness effecs, we do no expec o fnd any dfferences. Predcon 5: In he Bonus-Malus Treaen, behavor n = 5 s no sgnfcanly dfferen copared o he Base Treaen. In addon, he probably of cla buld-up n 3 s also no sgnfcanly dfferen. All oher fraud probables (for fcous clas n 4, for buld-up n 2 ) are sgnfcanly lower n he Bonus-Malus Treaen, as descrbed n Proposon 2. Our experenal seup allows us o ake anoher neresng coparson of perceved farness. As shown by olan (2001), he effecve ndeny funcon of a fullcoverage bonus-alus conrac s equvalen o an ndeny funcon of an nsurance conrac wh a sragh deducble. e shows ha he (plc) deducble n a bonus-alus conrac a a pon n e corresponds o he dscouned dfference of fuure preus n perods τ >. In perod = 5, he deducble s zero as here are no fuure preus o pay. In perod = 4, he deducble s = pons because he fuure preu s ncreased by 2 pons for one perod f a cla s ade or decreased by 1 pon oherwse, and one fourh of each bonus-alus payen wll laer be rebursed hrough he group accoun. Base

20 Conrac desgn and nsurance fraud: an experenal nvesgaon 17 Accordngly, plc deducbles for he oher perods are: 4.5 pons ( = 3), 6.75 pons ( = 2 ) and 9 pons ( = 1). Durng perods 4, here s a srcly posve plc deducble, and n = 5, here s full coverage. As oneary ncenves n he and Deduc Treaens are slar n =2, we are able o copare boh reaens wh respec o perceved farness. The deducble s 5 pons n he Deduc Treaen, whereas he plc deducble n he Treaen s 6.75 pons n =2. Therefore, he plc deducble n he s slghly hgher han ha n he Deduc Treaen. If a bonus-alus conrac s perceved as less unfar han a deducble conrac ( K > K Deduc ), ndvduals should co less fraud, alhough hey face a slghly hgher plc deducble. More generally, we expec ha hs effec should be vald when 4. Predcon 6: In he Bonus-Malus Treaen, he probably of fcous clas s sgnfcanly lower n = 2, and ore generally when 4, han n he correspondng perods of he Deducble Treaen. 3.3 Conrol varables In a quesonnare afer he experen, several quesons concernng he parcpans gender, general rsk aude, nsurance experence (easured by he nuber of acual nsurance conracs hey have), and aor were asked. These varables are conrolled for n our eprcal analyss. Pror sudes offer soe evdence of he pac of hese varables on fraudulen behavor. Frs of all, n econoc experens, woen ofen behave sgnfcanly dfferenly han en (Croson and Gneezy, 2009). Tennyson (2002) repors ha woen are less lkely o accep fraudulen behavor. More specfcally, Dean (2004) fnds ha woen fnd cla buld-up less ehcal. Boh sudes ndcae ha woen should boh fle fewer fcous clas and engage less n cla buld-up. Addonally, Tennyson (2002) also fnds ha quesonnare respondens wh ore nsurance experence (ore polces and ore clas) are less accepng of nsurance fraud. As we only asked abou he nuber of nsurance polces held by each parcpan, we would expec ha people wh a hgher nuber of conracs co less fraud.

21 Conrac desgn and nsurance fraud: an experenal nvesgaon 18 In lne wh Dohen e al. (2009), we asked parcpans abou her general wllngness o ake rsk. As shown by hese auhors, hs ehod s a good predcor of rsky behavor and respondens' rsk audes. Croson and Gneezy (2009) repor ha woen are generally less wllng o ake rsks. owever, based on our heorecal odel above, we do no expec any sgnfcan pac of he wllngness o ake rsks on fraudulen behavor. owever, fndngs fro Gosh and Cran (1995) ndcae ha rsk audes and ehcal sandards are correlaed such ha less rsk-averse people have lower ehcal sandards. Consequenly, fraud probables ay ncrease n he wllngness o ake rsk. Fnally, sudens wh a busness or econocs aor have been shown o behave less pro-socally (Frey and Meer, 2004) and ore corruply n experenal sengs (Frank and Schulze, 2000) han sudens wh oher aors. Consequenly, we expec ha econocs and busness sudens are ore lkely o co nsurance fraud. 4 Subecs All copuerzed experens were conduced beween March and July 2009 a he MELESSA laboraory of he Ludwg-Maxlans-Unversy (LMU) n Munch, Gerany. Recruen was done usng he ORSEE syse (Grener, 2004), and we eployed he experenal sofware z-ree (Fschbacher, 2007). We conduced hree sessons wh 24 parcpans for each of our hree reaens. A sesson ook abou nues. Subecs were predonanly sudens fro LMU wh a grea varey of aors. The fracon of sudens wh a busness or econocs aor was abou 16%. All parcpans receved a fxed show-up fee of 4 Euros. Inforaon on reaen earnngs excludng show-up fees s repored n Table 1. Treaen Average earnngs Earnng range Base 8.85 (2.13) Deducble 9.33 (2.52) Bonus-Malus 9.50 (2.71) Table 1: Average reaen earnngs (n Euros, sandard devaons n parenheses)

22 Conrac desgn and nsurance fraud: an experenal nvesgaon 19 5 Resuls Frs, we presen soe general resuls of he experen. Fgures 1 and 2 show he probables of fcous clas and cla buld-up, respecvely, per perod and reaen. Fgure 1: Fcous clas per perod and reaen Fgure 2: Cla buld-up per perod and reaen

23 Conrac desgn and nsurance fraud: an experenal nvesgaon 20 Fgure 3 presens a suary of behavor per reaen over all perods. Fgure 3: Fraudulen behavor per reaen In each perod, subecs have wo possble ways of cong fraud: They can cla a low/hgh ndeny when hey have ncurred no loss, and/or hey can cla a hgh ndeny when hey have ncurred a low loss (due o he sraegy ehod, boh choces are known). Over all reaens, 14% o 24% of subecs never co any knd of fraud, whereas 7% o 36% always co fraud. The reanng 50% o 69% of subecs only soees co fraud. Ths fndng confrs Predcon 1. Resul 1: Predcon 1 s confred. In he Base Treaen, we expeced o fnd a hgher probably of fcous clas han of cla buld-up. Coparng he respecve fraud probables for all perods of 51% (fcous clas) and 39% (buld-up) gves soe evdence for a sgnfcan dfference beween he wo. A Pearson's ch-square es shows ha he dfference s sascally sgnfcan, χ 2 = ( p = , wo-sded). Resul 2: Predcon 2 s confred. Vsual nspecon of Fgures 1 and 2 reveals ha boh fraud probables are generally ncreasng over e. Even hough here s no feedback n our Base Treaen, subecs end o co ore fraud n laer perods. Ths behavor s n conras o Proposon 1. owever, s a coon fndng n experens. For exaple, Fschbacher and eus (2008) fnd ha parcpans who ook par n her experen a second e led ore ofen

24 Conrac desgn and nsurance fraud: an experenal nvesgaon 21 han hey dd he frs e. More generally, Sonneans e al. (1998) show n her publc bad experen ha cooperave behavor declnes over e. For he Treaen, we expec ha he probably of fcous clas s ncreasng. In addon, he probably of cla buld-up s expeced o ncrease only for he frs hree perods and hen subsequenly be consan. As Fgure 1 shows, he posve perod effec n he no loss suaon s anly drven by he las perod. A rando effecs log regresson (Table A1, colun 1) shows a hghly sgnfcan perod effec for perods 1-5. owever, when consderng only perods 4, can be shown ha hs effec s no longer sgnfcan. Ths resul ndcaes ha rrespecve of he poenal gan fro fraudulen behavor preu adusens have a sgnfcan deerren effec on he flng of fcous clas. In he no loss suaon, preu ncreases are soehow sunk when underreporng s no opon. ere, he resuls (Table A1, coluns 2 and 3) are osly n lne wh Predcon 3. For 3, here s a sgnfcanly posve perod effec (p < 0.008). Alhough he perod effec s weakly sgnfcan for 4 (p < 0.085), he overall regresson resuls are no longer sgnfcan. Resul 3: Predcon 3 s osly confred. In he Treaen, he probably of fcous clas s only ncreasng beween perods 4 and 5. The probably of cla buldup s, as predced, only sgnfcanly ncreasng for he frs hree perods. When coparng behavor n he Base and he Deduc Treaens, Fgure 2 shows ha, for all perods, people co less fraud n he Base Treaen. In order o assess he sgnfcance of hese dfferences, we conduced a pooled rando effecs log regresson for panel daa. Our regresson resuls (Table A2) show ha, n he buld-up regresson, he duy for he Deducble Treaen s sgnfcan (p < 0.042). For he flng of fcous clas, resuls are weaker. The reaen duy s only sgnfcan for 4 (p < 0.074). Resul 4: Predcon 4 s osly confred. In he Deducble Treaen, he probably of cla buld-up s sgnfcanly hgher han n he Base Treaen. The probably of fcous clas s only hgher when consderng he frs four perods. Subsequenly, we wan o check wheher or no parcpans gh perceve he arrangeen as unfar and choose o realae. Therefore, we copare clang behavor n he Base and Treaens for = 5, where fraudulen behavor has no fuure payoff consequences gven he bonus-alus schee. Subecs n he Treaen could hus

25 Conrac desgn and nsurance fraud: an experenal nvesgaon 22 wa unl he las perod before cong fraud. The esaes of he pooled rando effecs log regresson are dsplayed n Table A3, coluns 1 and 2, n he Appendx. We fnd no sgnfcan dfferences beween reaens. In addon, when coparng he buld-up behavor for perods 3 (Table A3, coluns 3), we also fnd no sgnfcan reaen effecs. Thus, n our experen, subecs see no o consder he bonus-alus schee as unfar as hey do no ake advanage of he opporuny o realae by cong fraud n he las perod(s). In a second sep, we exane he probables of flng fcous clas n perods 4 (Table A4). As expeced, subecs fle fewer fcous clas n he Treaen, and he reaen dfference s hghly sgnfcan (p < 0.014). Alhough Fgure 1 shows a dfference n he probables of cla buld-up for 2, hs dfference s no sascally sgnfcan. Resul 5: Predcon 5 s osly confred. Behavor n =5 s no sgnfcanly dfferen beween he Bonus-Malus and he Base Treaens. For 3, probables of cla buldup are also no sgnfcanly dfferen. For 4, probables for fcous clas are sgnfcanly lower n he Treaen. owever, for 2, probables for cla buld-up are lower n he Treaen, bu he dfference s no sascally sgnfcan. Fnally, we copare behavor n he Deduc and he Treaens. Whle here s a consan deducble of 5 pons n he Deduc Treaen, he plc deducble decreases n he Treaen fro 9 pons ( = 1) o 6.75 pons ( = 2), 4.5 pons ( = 3) and fnally 2.25 pons ( = 4). Alhough he deducbles n = 2 are a 5 pons (Deduc Treaen) and 6.75 pons ( Treaen), slar - and even hgher n he Treaen - ndvduals co sgnfcanly less fraud n he Treaen. Table A5 n he Appendx dsplays he pooled rando effecs log regresson esaes for he Deduc and Treaens n = 2. 6 Coparng boh reaens for 4 suggess ha here s sgnfcanly less cla buld-up n he Treaen. Esaes for hese regressons are dsplayed n Table A6 n he Appendx. In boh regressons, he duy varables for he Treaen are negave and sgnfcan (p < for fcous clas and p < for buld-up). 6 We fnd slar resuls for = 3, where he plc deducble n he Treaen s 4.5 pons and hus slghly lower han n he Deduc Treaen.

26 Conrac desgn and nsurance fraud: an experenal nvesgaon 23 Resul 6: Predcon 6 s confred. When coparng all hree reaens, we fnd ha bonus-alus conracs are seengly no perceved as beng as unfar as deducble conracs. Furherore, when coparng hese conracs o full nsurance conracs, we fnd ha conracs wh cladependen preus also lead o a lower fraud exen wh respec o fcous clas. Thus, bonus-alus conracs cobne he advanage of a lower ne benef copared o full coverage conracs wh fxed preus and are perceved as less unfar han deducble conracs. Ths conrac ype herefore sees o be preferable o reduce he exen of fraudulen clas. 6 Conclusons The goal of our experenal sudy was o evaluae he pac of conracual arrangeens on nsurance fraud. Our resuls ndcae ha conrac desgn ay affec clang behavor consderably. Even f flng a fraudulen cla s a donan sraegy for selfsh ndvduals, a sgnfcan share of people does no defraud. One poran fndng s ha deducble nsurance conracs are seengly perceved as unfar because he exen of fraudulen clas s sgnfcanly hgher copared o a full nsurance conrac. Our resuls furher ndcae ha bonus-alus conracs wh a varable cladependen preu are seengly no perceved as unfar. In fac, hese conracs sgnfcanly reduce he exen of fcous clas copared o a suaon wh fxed preus. Ths effec s anly due o he decreased ne benef of a fraudulen cla. Mos noably, he fraud-reducng effec of bonus-alus conracs wh full coverage s surprsng fro a heorecal pon of vew as hese conracs are payoff-equvalen o deducble conracs. Our analyss ples ha bonus-alus conracs are a good eans of reducng he flng of fcous clas. One can presue ha bonus-alus conracs reduce oneary fraud benefs bu do no ply he sae negave consequences fro farness effecs as equvalen deducble conracs.

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