Deductible or Co-Insurance: Which is the Better Insurance Contract under Adverse Selection?

Transcription

1 Sooeonom Insttute Sozaökonomses Insttut Workng aper No. 4 edutbe or Co-Insurane: W s te Better Insurane Contrat under Adverse Seeton? Mae Breuer pdate: Otober 4

2 Sooeonom Insttute nversty o Zur Workng aper No. 4 edutbe or Co-Insurane: W s te Better Insurane Contrat under Adverse Seeton? January 4 Autor s addresses Mae Breuer E-ma: [email protected]. ubser Sozaökonomses Insttut Bbotek Workng aper Rämstrasse 7 CH-86 Zür one: Fa: RL:.so.unz. E-ma: [email protected].

3 edutbe or Co-Insurane: W s te Better Insurane Contrat under Adverse Seeton? Mae Breuer* nversty o Zur ABSTRACT Te standard souton to adverse seeton s te separatng equbrum ntrodued by Rotsd and Stgtz. suay te Rotsd-Stgtz argument s deveoped n a mode tat aos or to states o te ord ony. In ts paper adverse seeton s dsussed or ontnuous oss dstrbutons. Ts gves rse to te ne probem o ndng te proper orm o an nsurane ontrat to mpose parta nsurane o te o rsks. Ts paper ontrbutes to te dsusson on optma nsurane. It anayzes to bas orms o nsurane ontrats: A ontrat t a dedutbe and a ontrat mposng a postve o-nsurane rate. Sne g rsks an aays se-revea temseves as g rsks and buy te optma nsurane ontrat at g rsks premums te areto-superor nsurane ontrat s te one tat eaves te o rsks t ger epeted utty e deterrng g rsks rom jonng te ontrat tat s desgned or o rsks. Te dedutbe ontrat turns out to be superor premums ontan a suenty g oadng. Keyords: Insurane Adverse Seeton edutbe Co-Insurane JEL-Cassaton: * Address or orrespondene: Sooeonom Insttute nversty o Zur Hottngerstr. 83 Zur Stzerand. E-ma: [email protected].. one: Te autor ses to tank atrk Eugster B Jordan Bors Krey ane Smuk Hong Wu and eter Zee or ter epu omments on earer drats.

4 . Introduton Insurane eonomsts ave pad a ot o attenton to adverse seeton. Startng t te semna ontrbuton by Rotsd and Stgtz 976 adverse seeton s no seen as one o te most severe probems o nsurane markets under asymmetr normaton ausng eare osses or even a ompete breakdon o nsurane markets. Te noton o a separatng equbrum n ompettve nsurane markets under asymmetr normaton provdng u nsurane to te g rsks e restrtng te o rsks to parta nsurane s e understood. Rotsd and Stgtz empoy te Nas equbrum onept to get ter resuts. Oter equbrum onepts su as Wson 977 or Rey 979 ave ome to derent resuts but ave aso ontrbuted to our understandng o nsurers beavor and o nsurers are restrted n desgnng poes n prvate nsurane markets under adverse seeton. Hoever tere s peret ompetton on te nsurane market te anayss by Rotsd and Stgtz s st reevant. Te Rotsd-Stgtz argument s deveoped n a mode tat aos or to states o te ord ony namey one state o oss ourrene and one state t no oss. remums n te Rotsd-Stgtz do not ontan a oadng but are atuaray ar. Hoever n te gt o te vast terature about optma nsurane tars or ontnuous oss dstrbutons t s someat surprsng tat te terature remans sent about te adequate orm o nsurane ontrat to enore ts separatng equbrum oss dstrbutons are ontnuous. Tereore ts paper anayzes adverse seeton oss dstrbutons are ontnuous and premums ontan a near oadng. We te generazatons o te mode s partpaton onstrants and nentve-ompatbty onstrants to ontnuous dstrbutons o osses are stragtorard te agents are no onronted t a ne deson parameter namey te orm o ontrat to mpose parta nsurane. Ts s not a trva probem. In at nsurers ave to ook or te orm o ontrat tat eaves te o rsks t a eve o epeted utty as g as possbe e dsouragng g rsks rom optng or te ontrat taored or te o rsks.

5 Te oong anayss onentrates on to bas types o ontrats: Fu overage o osses above a nonzero dedutbe on te one and and o-nsurane ontrats on te oter and. Ts aos to ontrast te desgn o an nsurane ontrat s knon to be optma en premums ontan a near oadng te dedutbe ontrat t anoter standard desgn o nsurane ontrats. Sne g rsks an aays opt or u overage n te Rotsd-Stgtz mode te nsurane ontrat tat eaves te o rsks t ger epeted utty e deterrng g rsks rom jonng te ontrat tat s desgned or o rsks s n at aretosuperor.. Te mode Let te nsured popuaton onsst o to types o rsks g rsks and o rsks. Bot rsk types may suer a oss o L. Te mamum oss s L. Te dstrbuton o s desrbed by te densty untons and. Epeted osses are tereore L d or. Lo rsks are assumed to be better rsks n te sense o rst order stoast domnane FOS tat s ~ F ~ d d F ~ ~ > or at east one t F representng te umuatve densty untons. As usua n modes o te Rotsd-Stgtz type utty untons > < and nta eat are te same or bot rsks. Wtout any nsurane g and o rsk ndvduas obtan epeted utty E and E respetvey dened as Berger and Cummns 99 are an eepton n ts respet. In te seond part o ter paper tey ao or ontnuous oss dstrbutons and araterze g and o rsks by mean preservng spreads. Hoever n su a mode adverse seeton probems ony arse nsurers are not rsk neutra. Te mamum amount o te oss may e be as g as te ndvdua s eat. Assumng a mamum oss tereore s not a very restrtve assumpton. Hoever t turn out to be etremey epu or omparsons o te to types o ontrats.

6 E L d or. 3 Indvduas are uy aare o ter on rsk type. Insurers on te oter and annot denty an ndvdua s rsk type. Atng n a ompettve envronment and prots restrted to be non-postve tey rater ave to rey on se-seeton o nsured to estabs a sustanabe separatng equbrum tere s one. 4 An nsurane ontrat s dened by a premum and an ndemnty sedue I. Te premums are assumed to meet te non-protonstrant. We Rotsd and Stgtz 976 assume te premums to be atuaray ar tat s tey meet te epeted vaue o te ndemnty premums n ts paper may ontan a onstant oadng. Rotsd and Stgtz 976 ave son tat under peret ompetton te ony possbe equbrum s a separatng one provdng at most parta overage or te o rsks. Let te to ontrats * * * * I and I or g and o rsks be a separatng equbrum. Wrtten ormay n te most genera orm nsurers ave to nd a par o nsurane ontrats tat mamze te o rsks epeted utty under te oong restrtons: * * 3 E L I L d E or * * L I L 4. * * L I L d d Condton 3 s te partpaton onstrant statng tat or bot types o rsk te epeted utty obtaned rom te nsurane poy taored or ea o tem must not be oer tan te epeted utty rom remanng unnsured. Te ony bndng nentve ompatbty onstrant on te oter and s gven by 4: Hg rsks must ave an nentve to revea temseves as g rsks and opt or te 3 4 Te stuaton o no nsurane overage s abeed by te nde or reasons o ompatbty to te ater seton: It s equvaent to a o-nsurane rate or a dedutbe o. As n te orgna mode by Rotsd and Stgtz tere mgt be no stabe separatng equbrum te raton o g rsks n te entre nsurane popuaton s o. 3

7 ontrat taored or tem nstead o enjoyng te oer premums o te o rsks ontrat. Hoever unt no notng as been sad about te ndemnty sedue tat s approprate to redue o rsks nsurane overage. In at oos e onentrate on to bas orms o nsurane tars namey ontrats song a dedutbe and ontrats t a onstant o-nsurane rate. Hg rsks an aays rey on gettng ter reservaton eve o epeted utty E mn rom optma nsurane at g rsks premums by oosng ter optma o-nsurane rate or dedutbe. Lo rsks epeted utty n equbrum on te oter and s ger one an nd te orm o nsurane ontrat tat mnmzes te o rsks oss n epeted utty aused by te reduton o overage tat s neessary to pus te g rsks epeted utty rom buyng te o rsks ontrat don to E mn. In at te better ontrat n ts sense oud be areto-superor. In at oos t turn out tat te optma orm o an nsurane ontrat gy depends on te amount o te oadng ator. Hoever t s useu to begn te anayss or te ase o atuaray ar premums tat do not ontan a oadng. 3. Atuaray ar premums 3. Insurane ontrats t a onstant o-nsurane rate Let te nsurane ontrat demand a o-nsurane rate overage redues to o every oss. 5 Indemnty ten s smpy o every oss so tat te 5 I L and te atuaray ar premum s gven by 6 L d or. erentatng 6.r.t yeds: 5 In te terature t s more ommon to abe te repaement rate and te o-nsurane rate -. Te termnoogy used ere make t easer to ompare te resuts o ts seton t ndngs on ontrats o te dedutbe type anayzed n seton 3.. 4

8 7 L d or. Aordng to 7 te reduton o te premum due to a ger o-nsurane rate s near. I bot rsk types buy te ontrat taored or tem tey obtan epeted utty o 8 E L d or. erentatng 8.r.t. and usng 7 yeds: E 9 L L d L d or. erentatng 9 agan.r.t. yeds E < L L d L d proves tat E s onave n. At 9 an be rertten as E L L d d ; onsequenty E as a mamum see Mossn 968. Furtermore te unton derease more rapdy as se-nsurane rates get ger. Hoever g rsks opt or te o rsks ontrat payng premum tey obtan epeted utty o: EL L d. Observe tat at g rsks an enjoy te same epeted utty as o rsks by buyng te same nsurane ontrat. Sne nsurers are not abe to observe an ndvdua s rsk tey annot prevent any g rsk rom dong so. Consequenty a u nsurane ontrat oud resut n a poong o te rsks and g rsks oud obtan epeted utty tat s ger tan te epeted utty tey oud enjoy 5

9 t u nsurane or atuaray ar premums E as to be g enoug to pus EL don to E at. nortunatey a. Sne nsurers do not reeve premums rom te g rsks tat over ter epeted osses ts orm o poong rsks s o ourse not sustanabe. Hoever t s te g rsks treat to jon te o rsks ontrat tat urges te nsurer to oer ony parta overage or o rsks. Te obvous souton to ts knd o asymmetr normaton probem s to oer ontrats tat ombne o rsks premums t a postve o-nsurane rate to dsourage g rsks rom optng or te o rsks ontrat and to et tem buy u overage n eange to g rsks premums. In a separatng equbrum EL E. Consequenty or atuaray ar premums te o-nsurane rate ger o-nsurane rate redues te o rsks epeted utty too. Te margna eet o a ger o-nsurane rate on o rsks epeted utty E an be obtaned by appyng 9 or. erentatng EL.r.t. on te oter and yeds: EL 3 d < L L L d. At 3 reads as EL 4 d L < L d so tat te sope o te EL -urve at s negatve. Comparng 3 t 9 or urtermore reveas tat EL as more egt on g osses and orrespondngy on ger margna uttes tan E. Tereore te margna negatve eet o a derease o on epeted utty s unambguousy stronger or g rsks odng te o rsks poy tan or o rsks rrespetve o te eve o. Sne bot rsk types enjoy te same epeted utty at g rsks epeted utty must aays be oer tan o rsks epeted utty > and te derene beteen bot epeted uttes must nrease monotonay t. Epeted utty as a unton o te o-nsurane rate or bot rsks tereore ook as ustrated n gure. 6

10 Te derene n te eet on bot rsk types s stronger te more rsk averse ndvduas are and te more egt g rsks densty unton as on ger osses ompared to o rsks densty unton. Fgure : Epeted utty as a unton o o-nsurane rate E E E E E 3. Insurane ontrats t a dedutbe No et te nsurane ontrat presrbe a dedutbe t. Te varabe represents te dedutbe as a raton o te mamum oss L. Ts aos onvenent omparsons beteen dedutbe and o-nsurane ontrats. By mutpaton t te mamum oss L an easy be transated nto a number gvng te absoute dedutbe ed n an nsurane poy. Consequenty ndemnty payments are or 5 I. L L or > Te orrespondng atuaray ar premums or g and o rsks are gven by d 6 L or. erentatng 6.r.t. yeds: 7

11 7 L d L F or. Te premum reduton due to redung te eve o nsurane tereore s not near any more as t as n te ase o a o-nsurane ontrat but s gest at o dedutbes and dmnsng t ger. I bot rsk types opt or te ontrat taored or tem ter epeted uttes read as: 8 E L d L d or. In anaogy to te prevous seton derentatng 8.r.t. and usng 7 proves tat under atuaray ar premums bot rsk types oud preer a dedutbe o zero tat s or u nsurane overage: 9 E L d L L d L L d d d or. Condton 9 s zero at and ony. To see e an epet a mamum at one o tese to etreme ponts t s neessary to derentate 9 one more.r.t..ts yeds at E L d d L d and at : E L d L L > Consequenty tere s a mnmum at. Sne tere are no oter etreme ponts e ave a orner souton or te mamum o E at.. I oever g rsks opt or te o rsks ontrat tey obtan epeted utty o 8

12 . d L d L EL Agan at te g rsks an enjoy te same epeted utty as te o rsks smpy by buyng te same nsurane ontrat. Te margna eet o an nreasng dedutbe on an be obtaned by appyng 5 and 9 or. Rertng yeds: E 3 L F L d I L F L d L L d d L I L E. Te eet o a ger dedutbe on g rsks optng or te o rsks ontrat on te oter and an be obtaned by derentatng.r.t. and appyng te same transormatons: 4 L F L d I L F L d L L d d L I L EL. Note tat bot 3 and 4 ave etreme ponts at and ony. Furtermore derentatng 4 agan.r.t gves 5 > L L L d L EL beause te o rsks oss dstrbuton oud not domnate te g rsks oss dstrbuton n te sense o FOS. Tereore as a mnmum at so tat e ave a orner mamum at > EL. 9

13 Sne bot rsk types epeted uttes ave a mamum at tey must derease at a < <. Tereore or > E < and EL < t a mnmum someere beteen zero and one. Epeted utty as a unton o te dedutbe and ten onve as nreases. or bot rsks tereore s rst onave Conentratng on te ast transormatons o equatons 3 and 4 t s ear tat ter seond terms must domnate te rst terms restran te negatve margna eet o an nreasng on epeted utty. By assumpton n 3 as ess egt on ger osses and tereore on ger margna uttes tan n 4 so tat te ntegra n 4 eeeds ts ounterpart n 3 or rsk averse ndvduas. Te eet on te ntegra s te stronger te more egt te g rsks densty unton as on g osses ompared to te o rsks densty unton. Furtermore derenes beteen bot ntegras are greater te more rsk adverse ndvduas are. Havng a oser ook at te seond terms one nds tat te margna negatve eet o a ger dedutbe or a ertan < < s te stronger or g rsks reatve to o rsks te more te vaues o te dstrbuton untons and F F F der at ts. Lo and g rsks epeted uttes as untons o te dedutbe tereore gy depend on te oss dstrbuton untons. Tey der more dstntve or sma osses and sma dedutbes o rsks oss dstrbuton unton as not too mu egt on o osses. F To ustrate gure sketes g and o rsks epeted utty as unton o.

14 Fgure : Epeted utty as a unton o dedutbe E E E E E 3.3 W type o nsurane poy s te better one under adverse seeton premums are atuaray ar? Te anayss n setons. and. as son tat epeted utty as a unton o te o-nsurane rate s strty onave or bot rsks. Epeted utty as a unton o a dedutbe ten onve as or bot rsks on te oter and s rst onave and nreases. From ts oos tat te approprate o-nsurane rate to pus g rsks epeted utty rom buyng te o rsks ontrat don to E mn mama oss ustrated n gure 3. s aays ger tan te dedutbe dened as proporton o te L tat eaves te g rsks at te same eve o epeted utty as

15 Fgure 3: Comparng dedutbe and o-nsurane E E o E o E E mn E E E Hoever to nd te areto-superor nsurane ontrat one as to ompare te eves o epeted utty o rsks an rea n bot nsurane sedues en pusng g rsks epeted utty don to te eve o epeted utty g rsks get rom buyng u nsurane at g rsks premums. Note tat E mn E mn tse depends on te derenes beteen g and o rsks oss dstrbutons: Te more ake bot dstrbutons are te ess g and o rsks premums der and te ger s. E mn nortunatey t turns out tat neter orm o sedue s te best n a stuatons. Weter o rsks preer a dedutbe to a o-nsurane rate gy depends on te dstrbuton untons F and F and te eve o epeted utty g rsks an obtan rom u nsurane at g rsks premums. E.g. derenes beteen bot rsks oss dstrbuton untons are not very arge and tereore s reatvey g and as not too mu egt on sma E mn osses a dedutbe may be te o rsks rst oe o nsurane ontrat. I on te oter and o rsks oss dstrbuton unton as amost a egt on sma osses a o-nsurane rate s more key to be optma. F E mn

16 4. remums ontanng a oadng Te someat negatve resut obtaned n seton 3 anges e ao premums to ontan a oadng. More speay assume premums to be atuaray ar tmes a onstant oadng o κ t κ representng te oadng ator. nder symmetr normaton te optma nsurane ontrat oud no be a ontrat t a dedutbe as as been son by Arro 97 and oters. 6 Hoever as be son beo ts resut ods unambguousy under adverse seeton ony te oadng ator eeeds a mnmum amount up to a ertan pont. 4. Insurane ontrats t a onstant o-nsurane rate As n seton 3. premums depend on te o-nsurane rate but no addtonay ontan te oadng κ : 6 κ L d or. From derentatng 6.r.t. near ay: t s ear tat premums st depend on n a 7 κ L d or. Sne ndvduas utty unton does not ange t s easy to obtan te nsured s epeted utty by nsertng 7 nto 8. erentatng ts ne unton.r.t. yeds E 8 L L d L d κ or s greater tan zero at. Consequenty under symmetr normaton every nsured gets a ger epeted utty by dedng or a postve onsurane rate rater tan a u nsurane ontrat. It s nterestng to observe tat 8 an even be postve at κ s suenty g ndatng a orner so- 6 See e.g. Ravv 979 or Goer and Sesnger

17 uton at sne E s onave n as an be son by derentatng 8 agan.r.t. : E 9 L κ L d L d or. For te ase o asymmetr normaton ts aso mpes tat te g rsks reservaton eve o epeted utty by reveang temseves as g rsks and aeptng te ger premums s not te one tey obtan at but te eve tey obtan at ter optma postve eve o. nortunatey tout urter assumptons on te utty unton and te oss dstrbutons no urter statements about te optma eve o or g and o rsks an be made. nder symmetr normaton te optma amount o or g rsks an e be ger or oer tan te optma amount o or o rsks. Te optma eve o o-nsurane does not even ave to nrease monotonay t a ger oadng ator κ. 7 Hoever as noted beore tere s a eve o κ tat ndues ndvduas to buy no nsurane overage. Furtermore sne an nrease o redues te transers g rsks reeve rom te o rsks n orm o subsdzed premums o rsks an aays pus te g rsks don to ter reservaton eve o epeted utty by oosng an adequate eve o mgt be. Let κ be te mnmum vaue o κ tat eads te o rsks to oose te orner souton at means no nsurane proteton at a. Hg rsks o buy te nsurane ontrat taored or te o rsks on te oter and oud st opt or parta nsurane < < at a oadng o κ n partuar as ong as ter premums are subsdzed by te o rsks. Consequenty κ s te rta vaue or a separatng equbrum n a o-nsurane ontrat tat aos te o rsks to obtan at east parta nsurane proteton. I κ κ o rsks opt out and do not 7 On te one and an nrease o te oadng ator makes nsurane overage more epensve. On te oter and t redues te nsured s eat and tereby nreases ter rsk averson utty untons so dereasng absoute rate o rsk averson ARA. See Eekoudt and Goer 995 apter or ts argument. 4

18 buy any nsurane rrespetve o te estene o g rsks and normatona asymmetres. Insurers on te oter and ten an be sure tat ter nsured are g rsks and adjust ter premum and te o-nsurane rate appropratey. 4. Insurane ontrats t a dedutbe By ntrodung a onstant oadng te premum unton 6 anges to 3 or d L κ. Insertng te ne premum unton nto te epeted utty unton 7 and derentatng.r.t. gves 3 d d L d L d L E κ κ or. Note tat te oadng anges one o te etreme ponts o 9: We 9 and 3 bot ave etreme ponts at t s true tat > E at or any postve κ. As epeted u nsurane overage s not optma any more en premums are not atuaray ar. Hoever rom te FOC 3 t s not ear tere are any oter etreme pont beteen and and tese etreme ponts are mama. To take tese questons 3 s derentated one more.r.t. : 3 d L d L L d d L L L d L d L E κ κ κ κ 5

19 or. As as aready been noted by Mossn s negatve te rst dervatve 3 s postve or zero. 8 Consequenty dependng on te amount o te oadng ator κ E as a mamum at some beteen and or nreases monotonay tn ts range n ase t s mamzed at te orner souton. Ca te oadng ator at te o rsks do not buy a dedutbe ontrat any more κ. Agan g rsks reservaton eve o epeted utty tey an get rom aeptng te ger premums s not te one tey obtan at but te one tey obtan at ter optma postve eve o. Moreover te optma eve o does not neessary nrease t κ. 9 Hoever t remans true tat o rsks an aays pus te g rsks don to ter reservaton eve o epeted utty by nreasng and tereby redung ter transers to te g rsks. Hg rsks oud st s to buy te o rsks dedutbe ontrat at a oadng ator o κ n ase nsurers an be sure about ter nsured s type and adjust te premums and te dedutbe appropratey. κ 4.3 W type o nsurane poy s te better one under adverse seeton premums nude a oadng? Te resuts derved n seton 4 so ar do not ook enouragng: For any oadng ator κ beo κ or κ te amounts o oadng tat ndue o rsks to buy no nsurane te nsurane ontrat s o te o-nsurane o dedutbe type respetvey no genera onusons about te superorty or nerorty o eter type o ontrat an be derved. Loadng ators above κ or κ on te oter and ead te o rsks to abstan rom buyng a postve amount o nsurane n at east on o te to ontrats. Hoever one standard resut rom te terature on optma nsurane poes s tat an nsurane ontrat presrbng a dedutbe s superor to oter desgns o 8 9 Te rst dervatve s zero or postve te terms n parenteses o 3 or 3 are zero or postve. In 3 tese terms are mutped by a negatve term e te oter terms n 3 are aays negatve. Footnote 7 appes. 6

20 nsurane ontrats en te oadng s near. Ts nudes tat κ κ beause oterse tere oud be an amount o oadng eadng to parta nsurane n a o-nsurane ontrat and to no nsurane n a dedutbe ontrat. ue to rsk averseness o te ndvduas ts oud ontradt te am tat te dedutbe ontrat s te optma desgn o an nsurane ontrat. Consequenty e ave to dstngus beteen tree eves o te oadng: I te oadng ator s κ κ te resuts o seton 3 appy and t s not possbe to derve any genera onusons about te superorty or nerorty o eter type o ontrat tout addtona normaton about te oss dstrbutons. I κ κ κ te dedutbe ontrat eaky domnates te o-nsurane ontrat sne te ormer mgt ao te o rsks to get at east a parta nsurane n a separatng equbrum e te atter eaves te o rsks t no nsurane proteton at a. I nay κ κ o rsks not buy any postve amount o nsurane. In ts stuaton any ndvdua tat buys nsurane proteton an be assumed to be o te g-rsk type; te probem o asymmetr normaton eases and te market equbrum s eent. O ourse te oadng an be so g tat even g rsks abstan rom buyng nsurane proteton n ase te nsurane market eenty breaks don ompetey. 5. Conuson Generazng te Rotsd-Stgtz mode by aong or ontnuous dstrbutons o osses does not ange ts prnpa resut: Te ony possbe sustanabe equbrum s a separatng ontrat. Hg rsks get u nsurane e o rsks are restrted to parta overage to dsourage g rsks rom buyng te o rsks ontrat. Hoever te ne queston arsng s knd o nsurane ontrat s desrabe to mpose parta overage: a ontrat song a dedutbe or a ontrat t a onstant o-nsurane rate. Te anayss as son tat bot orms o ontrat may be avourabe under ertan rumstanes gy dependng on te premums oadng ator. I te oadng ator s zero or suenty sma no genera statement about te areto-superorty o eter o te to orms o nsurane ontrats an be made tout urter normaton about bot rsks oss dstrbutons. A o-nsurane ontrat s neror under symmetr n- 7

21 ormaton and a near oadng mgt domnate a dedutbe ontrat. For ger but not too g oadng ators oever te dedutbe ontrat s unambguousy areto-superor sne o rsks oud gve up nsurane proteton ompetey provded by a o-nsurane ontrat. Fnay or etremey g onsurane rates bot rsk types do not buy nsurane proteton any more and te nsurane market breaks don ompetey. 8

22 Reerenes Arro Kennet J. 97: Essays n te Teory o Rsk Bearng Cago: Markam. Berger Larene A. and Cummns J. avd 99: Adverse Seeton and Equbrum n Labty Insurane Markets Journa o Rsk and nertanty 5: Eekoudt Lous and Goer Crstan 995: Rsk. Evauaton Management and Sarng Ne York et.: Harvester Weatsea. Goer Crstan and Sesnger Harrs 996: Arro s Teorem on te Optmaty o edutbes: A Stoast omnane Approa Eonom Teory 7: Mossn Jan 968: Aspets o Ratona Insurane urasng Journa o ota Eonomy 76: Ravv Artur 979: Te esgn o an Optma Insurane oy Ameran Eonom Reve 69: Rey Jon G. 979: Inormatona Equbrum Eonometra 47: Rotsd Mae and Stgtz Josep E. 976: Equbrum n Compettve Insurane Markets: An Essay on te Eonoms o Imperet Inormaton Quartery Journa o Eonoms 9: Wson C.A. 977: A Mode o Insurane Markets t Inompete Inormaton Journa o Eonom Teory 6:

23 Workng apers o te Sooeonom Insttute at te nversty o Zur Te Workng apers o te Sooeonom Insttute an be donoaded rom ttp://.so.unz./resear/p/nde.tm 4 edutbe or Co-Insurane: W s te Better Insurane Contrat under Adverse Seeton? Mae Breuer February 4 8 p. 34 Ho d te German Heat Care Reorm o 997 Cange te strbuton o te emand or Heat Serves? Raner Wnkemann eember 3 p. 33 Vadty o srete-coe Eperments Evdene or Heat Rsk Reduton Harry Teser and eter Zee Otober 3 8 p. 3 arenta Separaton and We-Beng o Youts Raner Wnkemann Otober 3 p. 3 Re-evauatng an Evauaton Study: Te Case o te German Heat Care Reorm o 997 Raner Wnkemann Otober 3 3 p. 3 onstream Investment n Ogopoy Stean Bueer and Armn Smutzer September 3 33 p. 39 Earnng erentas beteen German and Fren Speakers n Stzerand Aejandra Cattaneo and Raner Wnkemann September 3 7 p. 38 Tranng Intensty and Frst Labor Market Outomes o Apprentesp Graduates Rob Euas and Raner Wnkemann September 3 5 p. 37 Co-payments or presrpton drugs and te demand or dotor vsts Evdene rom a natura eperment Raner Wnkemann September 3 p. 36 Wo Integrates? Stean Bueer and Armn Smutzer August 3 3 p. 35 Strateg Outsourng Revsted Stean Bueer and Justus Hauap Juy 3 p. 34 Wat does t take to se Envronmenta oy? An Empra Anayss or Stzerand ane Habeer Sara Ngg and Armn Smutzer 3 3 p. 33 Mobe Number ortabty Stean Bueer and Justus Hauap 3 p. 3 Mutpe Losses E-Ante Mora Hazard and te Non-Optmaty o te Standard Insurane Contrat Mae Breuer 3 8 p. 3 Lobbyng aganst Envronmenta Reguaton vs. Lobbyng or Loopoes Andreas ok and Armn Smutzer 3 37 p. 4 A rodut Market Teory o Worker Tranng Hans Gersba and Armn Smutzer 34 p. 3 Weddngs t nertan rospets Mergers under Asymmetr Inormaton Tomas Borek Stean Bueer and Armn Smutzer 37 p. Estmatng Verta Foreosure n.s. Gasone Suppy Zava Aydemr and Stean Bueer 4 p. Ho mu Internazaton o Nuear RskTroug Labty Insurane? Yves Sneder and eter Zee 8 p.

24 Heat Care Reorm and te Number o otor Vsts? An Eonometr Anayss Raner Wnkemann 3p. 9 Inrastruture Quaty n ereguated Industres: Is tere an ndernvestment robem? Stean Bueer Armn Smutzer and Men-Andr Benz 4 p. 8 Aqustons versus Entry: Te Evouton o Conentraton Zava Aydemr and Armn Smutzer 35 p. 7 Subjektve aten n der emprsen Wrtsatsorsung: robeme und erspektven. Raner Wnkemann 5 p. 6 Ho Spea Interests Sape oy - A Survey Andreas ok 63 p. 5 Lobbyng Atvtes o Mutnatona Frms Andreas ok 3 p. 4 Subjetve We-beng and te Famy Raner Wnkemann 8 p. 3 Work and eat n Stzerand: Immgrants and Natves Raner Wnkemann 7 p. Wy do rms rerut nternatonay? Resuts rom te IZA Internatona Empoyer Survey Raner Wnkemann 5 p. Mutatera Agreement On Investments MAI - A Crta Assessment From An Industra Eonoms ont O Ve Andreas ok 5 p.