Essays on Adverse Selection and Moral Hazard in Insurance Market

Transcription

1 Gorgia Stat Univrsity Gorgia Stat Univrsity Risk Managmnt and Insuranc Dissrtations Dpartmnt of Risk Managmnt and Insuranc Essays on Advrs Slction and Moral Hazard in Insuranc Markt Jian Wn Cntral Univrsity of Financ and Economics Follow this and additional works at: Rcommndd Citation Wn, Jian, "Essays on Advrs Slction and Moral Hazard in Insuranc Markt." Dissrtation, Gorgia Stat Univrsity, This Dissrtation is brought to you for fr and opn accss by th Dpartmnt of Risk Managmnt and Insuranc at Gorgia Stat Univrsity. It has bn accptd for inclusion in Risk Managmnt and Insuranc Dissrtations by an authorizd administrator of Gorgia Stat Univrsity. For mor information, plas contact scholarworks@gsu.du.

2 Prmission to Borrow In prsnting this dissrtation as a partial fulfillmnt of th rquirmnts for an advancd dgr from Gorgia Stat Univrsity, I agr that th Library of th Univrsity shall mak it availabl for inspction and circulation in accordanc with its rgulations govrning matrials of this typ. I agr that prmission to quot from, or to publish this dissrtation may b grantd by th author or, in his/hr absnc, th profssor undr whos dirction it was writtn or, in his absnc, by th Dan of th Robinson Collg of Businss. Such quoting, copying, or publishing must b solly for scholarly purposs and dos not involv potntial financial gain. It is undrstood that any copying from or publication of this dissrtation which involvs potntial gain will not b allowd without writtn prmission of th author. Studnt s Nam: Jian Wn

3 Notic to Borrowrs All dissrtations dpositd in th Gorgia Stat Univrsity Library must b usd only in accordanc with th stipulations prscribd by th author in th prcding statmnt. Th author of this dissrtation is: Nam: Jian Wn Addrss: 39 South Collg Rd, Haidian District Bijing, China, 0008 Th dirctor of this dissrtation is: His/Hr Nam: Martin F. Grac Dpartmnt: Risk Managmnt and Insuran Dpartmnt Addrss: PO Box 4036, Gorgia Stat Univrsity Atlanta, GA 3030

4 ESSAYS ON ADVERSE SELECTION AND MORAL HAZARD IN INSURANCE MARKET BY JIAN WEN A Dissrtation Submittd in Partial Fulfillmnt of th Rquirmnts for th Dgr of Doctor of Philosophy in th Robinson Collg of Businss of Gorgia Stat Univrsity GEORGIA STATE UNIVERSITY ROBINSON COLLEGE OF BUSINESS 00 3

5 Copyright by Jian Wn 00 4

6 ACCEPTANCE This dissrtation was prpard undr th dirction of th candidat s Dissrtation Committ. It has bn approvd and accptd by all mmbrs of that committ, and it has bn accptd in partial fulfillmnt of th rquirmnts for th dgr of Doctor in Philosophy in Businss Administration in th Robinson Collg of Businss of Gorgia Stat Univrsity. Dissrtation Committ: Dr. Martin F. Grac Chair Dr. Robrt W. Klin Dr. Mary Bth Walkr Dr. Zhiyong Liu H. Fnwick Huss Dan Robinson Collg of Businss 5

7 ABSTRACT ESSAYS ON ADVERSE SELECTION AND MORAL HAZARD IN INSURANCE MARKET By JIAN WEN July 30, 00 Committ Chair: Major Dpartmnt: Dr. Martin F. Grac Dpartmnt of Risk Managmnt and Insuranc Essay On xamins th asymmtric information problm btwn primary insurrs and rinsurrs in th rinsuranc industry and contributs uniquly to th sparation of advrs slction from moral hazard, if both ar prsnt. A two-priod principal-agnt modl is st up to idntify th signals of advrs slction and moral hazard gnratd by th actions of th primary insurr and to provid a basis for corrsponding hypothss for mpirical tsting. Using data from th National Association of Insuranc Commissionrs NAIC and A.M. Bst Company, th mpirical tsts show that th problm of advrs slction xists in th rinsuranc markt btwn th affiliatd insurrs and non-affiliatd rinsurrs, and vn btwn closly rlatd affiliatd insurrs and rinsurrs. Thr is no vidnc indicating th prsnc of moral hazard in th rinsuranc markt. To addrss th issu of soaring proprty insuranc prmiums and covrag availability in stats that ar subjct to hurrican risks, stat and fdral govrnmnts hav not only rgulatd th privat insuranc markt but hav also intrvnd dirctly into markts by stablishing govrnmnt-fundd insuranc programs. With coxisting public and privat insuranc 6

8 mchanisms and pric rgulation, th risk of cross subsidization and a subsqunt moral hazard problm may aris. By using data from th Florida Citizns Insuranc Corporation, th Florida Hurrican Catastroph Fund, th Flood Insuranc and th privat homownr insuranc markt in Florida from 998 to 007, th scond ssay xamins th moral hazard problms arising from govrnmnt rgulation and involvmnt in th privat insuranc sctor. In sum, th provision of national flood insuranc is found to b positivly rlatd to th population growth in th stat of Florida, which shows that stat immigrants can tak advantag of th lowr cost of flood insuranc whn rlocating in highr-risk aras. Furthr, w find that national flood insuranc and th catastroph fund complmnt th dvlopmnt of th privat insuranc sctor, whil th rsidual markt hindrs th dvlopmnt of privat proprty insuranc markt. 7

9 Essay On Distinguishing Diffrnt Effcts of Asymmtric Information: Evidnc from Proprty and Liability Rinsuranc Markt 8

10 Abstract This ssay xamins th asymmtric information problm btwn primary insurrs and rinsurrs in th rinsuranc industry and contributs uniquly to th sparation of advrs slction from moral hazard, if both ar prsnt. A two-priod principal-agnt modl is st up to idntify th signals of advrs slction and moral hazard gnratd by th actions of th primary insurr and to provid a basis for corrsponding hypothss for mpirical tsting. Using data from th National Association of Insuranc Commissionrs NAIC and A.M. Bst Company, th mpirical tsts show that th problm of advrs slction xists in th rinsuranc markt btwn th affiliatd insurrs and non-affiliatd rinsurrs, and vn btwn closly rlatd affiliatd insurrs and rinsurrs. Thr is no vidnc indicating th prsnc of moral hazard in th rinsuranc markt. 9

11 . Introduction Sinc th middl of th last cntury, th study of th problm of asymmtric information has bcom important in th fild of conomics and insuranc Akrlof, 970; Arrow 965; Rothschild & Stiglitz, 976. Much progrss has bn mad from both a thortical and an mpirical prspctiv. Bfor conomists took th qustion of information transparncy into considration, thy commonly assumd th prsnc of complt information. Th concpt of complt information implis that all th information is transparnt and qually known to both partis. Convrsly, th concpt of asymmtric information implis that th information known to on party may b unknown or only partially known or availabl to anothr. Of th two concpts, th lattr, asymmtric information, coms closst to dscribing or rflcting th ral conomic world. Prdictably, assuming th prsnc of asymmtric information could lad to outcoms that would diffr significantly from thos rsulting from an assumption of complt information. Insuranc pricing is a good xampl of this. Th insurr sts th prmium basd on actuarial data on th prvious loss xprinc within a normal population. In th long run, th company will brak vn, if th risk is at th avrag lvl as prsumd. Unfortunatly, popl who, in fact, rprsnt a highr-than-avrag risk lvl, may b abl to purchas insuranc covrag against thir mor frqunt or mor svr futur losss at a favorabl pric that was originally basd on th lowr, avrag, risk. This disconnct may occur bcaus insurrs lack sufficint information on th prcntag of th pool with highr risk and th xact risk lvls rprsntd, vn though th insurd is fully awar of th risk lvl. Thrfor, this asymmtric information situation may lad to highr losss for th insurr. 0

12 Th xistnc of asymmtric information normally ntails two complmntary problms: advrs slction and moral hazard. Th trm advrs slction rfrs to circumstancs which prmit an insurd with highr risk to buy insuranc at a prmium calculatd to srvic th avrag risk lvl. Th trm moral hazard rfrs to th tndncy of insurrs to xrcis lss prcaution than thy should, stablishing inadquat incntivs to control th risks rprsntd by thos to whom thy provid covrag. Advrs slction and moral hazard both contribut to th potntial for highr losss than th insurr may hav xpctd. Whn asymmtric information is known to xist, th optimal risk-sharing schm and pricing may wll nd to dviat from thos that would b institutd if complt information wr availabl Rothschild & Stiglitz, 976. In th prsnc of srious asymmtric information, th insurr may xprinc a much highr loss than xpctd; and in th worst cas, th insuranc markt itslf may totally fail Akrlof, 970. Thrfor, th dtction of possibl asymmtric information, including th discovry of prviously unknown risk, has th potntial to bnfit both th insurr and th insurd. For xampl, halth and lif insuranc undrwriting rquirs physical xamination and applis dductibls, coinsuranc and pricing tid to diffrnt risk lvls of th insurd. Common sns would conclud that such procdurs would hav th ffct of uncovring possibl risks, factoring ths risks into th covrag, and thrby rducing th dangr of asymmtric information. Whil th thortical analysis of asymmtric information in th insuranc markt was introducd almost half a cntury ago, mpirical tsting did not appar until th 980s. Now, from th xamination of lif, halth, annuity and automobil insuranc markts, w can s vidnc that, compard to othr insuranc markts, lif insuranc has lss of a problm of

13 asymmtric information du to strict rquirmnt of physical xamination to dtrmin th risk status of th insurd. As th insuranc for th insuranc companis, th rinsuranc industry furthr distributs th risks poold by th primary insurrs. It is not unusual for rinsuranc companis to b run nationally or intrnationally, which buffrs th advrs ffct of hug losss to th whol insuranc markt and ultimatly lowrs th prmium paid by individuals. With th catastrophic vnts in th past dcads, th proprty and liability rinsuranc markt hav xhibitd an incrasing ability to absorb big losss and stabiliz th whol insuranc markt in th U.S. Cummins, 007. Thrfor th proprty and liability rinsuranc markt is not only a critical part of th insuranc markt, but also an indispnsabl factor in stabilizing th conomy. Howvr, asymmtric information xisting btwn primary insurrs and th rinsurrs may still pos a srious thrat to th rinsuranc markt. Th ffct of asymmtric information on th rinsuranc markt can b analyzd from th prspctivs of advrs slction and moral hazard. For rinsuranc, advrs slction would b vidncd by high-risk firms gtting similar or vn bttr trms for thir rinsuranc purchas than low-risk firms. In contrast, moral hazard xists whn th primary insuranc companis loosn thir undrwriting critria, lading ultimatly to highr losss than xpctd. Both advrs slction and moral hazard would mak th actual loss highr than thos stimatd by th rinsuranc company, with ngativ consquncs for th insuranc markt. This xamination of asymmtric information shds light on challngs in th rinsuranc businss. Bttr knowldg of asymmtric information btwn th primary insurr and th rinsurr can hlp improv risk allocation and pricing in th rinsuranc markt. For th primary insuranc company, managing risk through purchasing rinsuranc is a much mor complx

14 mattr du to factors such as risk divrsification, progrssiv tax and financial nds than risk managmnt at th lvl of individual policy holdrs. This ssay xamins th asymmtric information problms btwn th rinsuranc and primary companis in th proprty and liability rinsuranc markt in th U.S. Rcntly, Jan- Baptist and Santomro 000 addrssd th asymmtric information problms which affct th fficincy of risk allocation btwn th primary insuranc companis and thir rinsurrs. Thy showd that long-trm contracts btwn th two will improv th allocation of risk by including and factoring in nw risk information ovr tim. Thy prdictd that th us of long-trm rinsuranc contracts will incras th dmand for rinsuranc, incras primary insurr s profits and lowr th probability of bankruptcy. Empirically, Dohrty and Smttrs 005 and Garvn and Grac 007 providd th vidnc of asymmtric information in th rinsuranc markt. Dohrty and Smtttrs 005 tstd th potntial moral hazard problm btwn th rinsurr and th primary company. Thy found that loss-snsitiv pricing was mainly usd to control moral hazard btwn th nonaffiliatd rinsurrs and insurrs, whil monitoring was widly usd to control moral hazard btwn th affiliatd rinsurrs and insurrs whr th monitoring cost was rlativly lowr. Garvn and Grac 007 xplord th advrs slction problm basd on th thortical prdictions by Jan-Baptist and Santomro 000. Thir findings ar consistnt with and supportiv of th thortical prdictions. Nvrthlss, ach of ths two works only focuss on on sid of th asymmtric information issu whil ignoring th xistnc and th ffcts of th othr on. 3

15 For xampl, Dohrty and Smttrs 005 assumd moral hazard as th only ffct of th asymmtric information; Garvn and Grac 007 only attributd th ffcts of th asymmtric information to advrs slction. Furthr, an intrsting rsarch qustion ariss: do advrs slction and moral hazard xist at th sam tim to b part of th asymmtric information problm? Th answr to this qustion is th contribution of this ssay, which distinguishs advrs slction from moral hazard, as thy xist btwn th primary insurr and th rinsurr. Th rason for sparating ths two factors of th asymmtric information is that thy lad to highr losss through diffrnt mchanisms. Accordingly diffrnt contract faturs ar rquird to corrct thm. Manwhil, affiliatd and non-affiliatd rinsurrs ar discussd sparatly, as th affiliatd rinsurrs blong to on financial group and non-affiliatd rinsurrs ar indpndnt companis with rspct to th primary insurr. Du to th varying rlationship btwn risnurrs and insurrs, asymmtric information is xpctd to prsnt diffrnt pattrns. Th ssay procds as follows: in th scond sction, rlatd litratur is rviwd. Thn, th two-priod principal-agnt modl is st up in th third sction. In th fourth sction, basd on th hypothsis drivd from th thortical modl, an mpirical tst is conductd on th panl data for th affiliatd and non-affiliatd proprty and liability rinsuranc markt from 99 to Litratur Rviw A sris of sminal paprs Akrlof, 970; Borch 96; Holmstrom, 979; Raviv, 979; Rothschild & Stiglitz, 976 built up th thortical foundation of asymmtric information studis in conomics. Akrlof 970 suggstd that markt quilibrium may not xist, du to th 4

16 xistnc of asymmtric information btwn th participants, in contrast to th quilibrium that would b xpctd if complt information wr availabl Mossin, 968. Furthrmor, Rothschild and Stiglitz 976 analyzd th comptitiv markt in which imprfct information, spcifically advrs slction, was considrd. Thy found out that low-risk individuals wr ngativly affctd by th prsnc of high-risk individuals, whil high-risk individuals bnfitd from th prsnc of low-risk individuals. Thy also found that singl pric quilibrium dos not xist and that th structur and xistnc of a possibl quilibrium dpnd upon particular assumptions. Holmstrom 979, on th othr hand, invstigatd th imprfct information problm in a principal-agnt modl with th considration of moral hazard. H concludd that th optimal contract is scond-bst du to th agnt s unobsrvd action, but additional information, lik monitoring or managrial accounting, will improv th fficincy of th contract. Thrfor, th dtction of asymmtric information and th corrsponding contract dsignd to addrss this issu ar critical to improving fficincy in th insuranc markt. In this cas, th principal-agnt modl provids a framwork for how to allviat th agncy problm, and, consquntly, dcrass th occurrnc of asymmtric information. Lambrt 983 charactrizd th optimal long-trm contract, dsignd to control th moral hazard of th agnt, as on in which th agnt s compnsation dpnds on not only th currnt priod but also th prvious priod. In addition, Laffont and Tirol 987 drivd th optimal dynamic incntiv mchanism undr th possibl monitoring of th agnt, and thy showd th xistnc of th possibl continuation quilibrium. Th mpirical tsts of asymmtric information on insuranc markts validat and supplmnt th thortical prdictions. Th mpirical hypothsis against th xistnc of 5

17 asymmtric information is statd as th positiv rlation btwn th risk lvls of thos who purchas insuranc covrag and th actual risk typ rvald aftr losss occur s Pulz & Snow, 994. Howvr, mixd rsults ar rportd in diffrnt businss lins of insuranc: th insignificanc of positiv rlation of insuranc quantity purchas and mortality risk of individuals in lif insuranc markt suggstd that information can b tratd as complt undr th currnt tst Cawly & Philipson, 997. For th annuity markt, Finklstin and Potrba 004 found a systmic rlationship btwn th x post mortality and th timing of annuity paymnts, consistnt with th prsnc of advrs slction. Pulz and Snow 994 and Chiaporri and Salani 000 rportd mixd rsults rgarding th prsnc of asymmtric information in th automobil insuranc markt. Th prvalnt xplanation attributs this mixd vidnc to th application of long-trm contract and risk classification in diffrnt insuranc businss lins. Bcaus insuranc prmiums ar contractd ovr multipl trms, and factors such as xprinc rating or risk slction ar usd to dtrmin th ral risk typ, th ffcts of asymmtric information can b modratd ovr tim. For instanc, th absnc of asymmtric information in lif insuranc can b attributd as th adoption of mdical xamination as part of undrwriting to rval th tru halth status of th insuranc applicants. Rinsuranc is also subjct to th asymmtric information problm btwn th insurrs and th rinsurrs. In comparison to th individual insurd, th incntiv for th insurr to purchas rinsuranc is mor complicatd. Th dcision to rinsur involvs issus such as risk managmnt, incrasing capability or th pursuit of tax bnfits. Basd on its own firm charactristics, th insurr has its own dgr of dmand for rinsuranc. As Mayr and Smith 990 pointd out, th ownrship structur, firm siz, gographic concntration and businss lins concntration hav significant ffcts on th dmand for rinsuranc. 6

18 Manwhil, th complicatd risk structur of th insurrs may rflct in multipl dimnsions in undrwriting, oprating and financing managmnt. As a rsult, it s costly for th rinsurr to collct complt information which would rval th tru risk of th insurr bfor th transaction is don. Consquntly, advrs slction occurs whn a high-risk firm concals information and rcivs bttr trms from th rinsurrs than thy would hav othrwis rcivd. Thrfor, long-trm contracts and th practic of rtrospctiv rating, which adjusts prmiums basd on th loss incurrd during th prvious policy priod, ar widly applid in th rinsuranc industry to solv th asymmtric information problm. Jan-Baptist and Santomro 000 showd that th nw information includd in pricing of both futur and past rinsuranc covrag for long-trm rinsuranc contracts can nhanc th ffctivnss of risk allocation btwn th primary insuranc companis and rinsuranc companis. Thy statd thr hypothss: Othr things bing qual, long-trm rinsuranc contracting rlationships will b associatd with highr lvls of rinsuranc covrag; Othr things bing qual, long-trm rinsuranc contracting rlationships will b associatd with highr insurr profits; 3 Othr things bing qual, long-trm rinsuranc contracting rlationships will b associatd with lowr lvls of bankruptcy. Garvn and Grac 007 did mpirical tsts of th abov hypothsis to s if thr is any advrs slction in th rinsuranc markt and, furthr, if th asymmtric information problm is solvd ovr tim. With panl data consisting of U.S proprty-liability insuranc firms, which rportd to th National Association of Insuranc Commissionrs NAIC during th priod 995 to 000 and A.M. Bst financial ratings for insuranc companis, thy found vidnc supporting th thortical prdictions by Jan-Baptist and Santomro. Ths findings imply that longr 7

19 rinsuranc rlationships lad to mor rinsuranc covrag, highr profitability, and lowr bankruptcy risk. Dohrty and Smttrs 005 tstd moral hazard in th rinsuranc markt with a multipriod principal-agnt modl of th rinsuranc transaction. Thy drivd prdictions on prmium dsign, monitoring, loss control and insurr risk rtntion. Thy found that a losssnsitiv prmium is usd to control moral hazard whn insurr and rinsurr ar not affiliats, whil monitoring is mphasizd whn th insurr and rinsurrs ar affiliats. Th problm of asymmtric information in rinsuranc markts has bn invstigatd in othr countris bsids th Unitd Stats. Adam and Diocon 006 tstd th asymmtric information problm in th UK proprty-liability rinsuranc markt. Two rlationships ar mainly tstd in thir papr. On is th rlationship btwn gross losss and th amount of rinsuranc purchasd by a primary insuranc company; th othr rlationship xamind is btwn th rinsuranc prmiums paid and th gross losss and rinsurd claims rcovrd by th primary insurr. Th lattr is a dmonstration of claim-contingnt pricing which charactrizs th rinsuranc transaction. Th Hausman ndognity tst undr th Hckman two-stag modl can sparat advrs slction from moral hazard; thy found that information asymmtry dos xist in th rinsuranc markt btwn th affiliatd insurrs and rinsurrs. Spcifically, advrs slction xists in th automobil and third party insuranc markts, and moral hazard appars in th miscllanous and pcuniary insuranc markts. In contrast, for th non-affiliatd insuranc companis, th claim-contingnt pricing rducs th problm of asymmtric information. 8

20 3. Thortical Modl Basd on th modl proposd by Dohrty and Smttrs 005, a two-yar principalagnt modl is st up to captur th asymmtric information btwn th insurrs and th rinsurrs in th rinsuranc markt. Dohrty and Smttrs 005 dvlop a two-priod principal-agnt modl from which to driv prdictions on prmium dsign, monitoring, loss control and insurr risk rtntion to idntify moral hazard in rinsuranc transactions. Th agnt, or primary insurr, pays a prmium Pt in priod of t to th rinsurr for a rinsuranc contract which is subjct to a dductibl or risk rtntion of S t. Undr this contract, th indmnity to th primary insurr in priod t is max[ 0, Lt St ], whr L t is incurrd dirct loss in priodt. Action a is takn by th primary insurr whn undrwriting businss, handling claims and controlling risks. Th action is not obsrvd by th principal, th rinsurr, whras it is assumd that action a gnrats a signal m that is imprfctly corrlatd with a, but still convys valuation information to th principal. Consquntly, th incurrd loss and signal dpnd on action by th primary insurr who writs insuranc businss to th insurd customr dirctly. On th othr hand, th principal, th rinsurr, rcivs prmium Pt in priod t and indmnifis th primary insurr with max[ 0, L S ] if th incurrd loss xhausts th stop loss. To rduc th moral hazard problm t t which may occur on th sid of th primary insurr, th rinsurr pays a cost of c to monitor th primary insurr. Th rinsurr picks prmiums for yar and yar to maximiz total profit subjct to th primary insurr s incntiv constraint and participation constraint. Th optimal prmium structur is thn drivd from th first-ordr conditions, and thn th modl prdicts th rlations btwn th rinsuranc prmium and dirct loss control, rtrospctiv rating, 9

21 xprincd rating and monitoring. Spcifically, th rinsuranc prmium P t is prdictd to b ngativly rlatd to th invrs of total dirct losss by th primary insurr in priod t, ngativly rlatd to th invrs of th amount of rinsurd losss in priod t, ngativly rlatd to th invrs of th amount of total dirct losss by th primary insurr in priod t, incrasing in th signal of m Dohrty & Smttrs,005, p 384. Th modl abov only focuss on th moral hazard of th asymmtric information problm. To captur th possibl advrs slction problm, on mor signal s, which signifis th opration quality of th primary insurr, is incorporatd into th modl abov in this ssay. Basically, th signal s is xpctd to rval th ral risk typ of th primary insurr to th rinsurr. Hnc, a masur of th loss volatility of th primary insurr, or a masur indicating thir ovrall financial capability, can provid th information rlativ to th risk typ of th insurr. Compard to signal s, anothr signal m in th modl convys th ffort xrtd by th primary insurr to th rinsurr, and signal m is imprfctly corrlatd to fforts undr th rinsuranc covrag. Anothr nw contract fatur considrd in this modl is th covrag cap, A, of th rinsuranc contract. This is dfind in th xcss of loss rinsuranc, whrby th primary insurr covrs th amount of ach claim up to th rtntion lvl and th rinsurr rpays th loss byond th rtntion lvl to th covrag cap to th insurr. Th diffrnc btwn rtntion lvl and th covrag cap is th actual rinsuranc covrag purchasd by th primary insurr. 3. Th Primary Insurr s Problm Assum th primary insurr is strictly risk-avrs, and its utility function is U w, ' '' whru w > 0, U w < 0, w is th surplus at th bginning of th contract. Th argumnts for this risk-avrs assumption ar th contxts of th progrssiv tax, th undrinvstmnt problm, 0

22 high bankruptcy costs and asymmtric information in th rinsuranc markt. Ths markt frictions mak th insurrs risk-avrs vn if th company is widly hld by public sharholdrs. At th bginning of on priod, th primary insurr pays prmium P to purchas on xcss-ofloss rinsuranc policy with th rtntion lvl of D, and covrag cap of A. Assum th incurrd loss ovr this priod is L. Th amount of rcovrd loss paymnt rcivd from th rinsurr dpnds on th amount of th incurrd losss. If th incurrd loss is lss than th rtntion lvl, L D th rinsurr dos not pay anything to th primary insurr. If th incurrd loss falls btwn th rtntion lvl and covrag cap, D L A th rinsurr pays th amount of L D to th primary insurr. If th actual loss is byond th covrag cap, A L th obligation of th rinsurr is th amount of A D. During th contract priod, th primary insurr xrts an ffort of to undrwrit businss from th insurd, control loss and assss th claims. W argu that this ffort is abl to gnrat signals to th rinsurr about ral oprational quality and incntivs of th primary insurr in th sns that th prformanc of th primary insurr nvrthlss rflcts th ffort it taks. W dnot signal s as th indication of th opration quality, which is th ral risk typ, of th primary insurr. W thn dnot signal m as th indication of th incntiv of th primary insurr. As a rsult, th conditional joint probability dnsity function of actual loss and signals ar rprsntd as f s, m, L. A two-yar framwork is considrd. In th first yar, th rinsuranc prmium is a function of actual loss, rtntion lvl, covrag cap and signals of th primary insurr s ffort: P = P L, D, A, s, m. For th scond-yar pricing, th actual loss of th first yar is also takn into account, as ar th scond yar losss, th rtntion lvl, th covrag cap and th signals in th scond-yar priod: P = P L, L, D, A, s,. m

23 For th simplicity of computation, a zro risk-fr rat is assumd in this rinsuranc modl. Dfin an insurr s nd-of-priod walth,π as a random variabl. Thn th insurr s walth as nd of th first yar isπ, and th walth as nd of th scond yar isπ. For i =, W i Pi Li if Li Di π i = W i Pi Di if Di < Li Ai W i Pi Li + Ai Di if Ai < Li Th xpctd utility of th insurr for two yars ar E U π and E U π, rspctivly. So th total xpctd utility of th primary insurr from taking th rinsuranc transaction is E U = E U π + E U. Th calculation of xpctd utility by intgration rfrs to th π appndix. Bcaus incurrd losss dpnd on ffort as f s, m, L, th primary insurr picks fforts and to maximiz its xpctd utility in two yars. 3. Th Rinsurr s Problm Th rinsurr incurs a monitoring cost of c and c to analyz tru risk typ of th insurr by obsrving th information dlivrd in th two priods, rspctivly. Th rinsurr maks th profit out of th prmium incom aftr dduction of loss rpaymnts and monitoring costs. Dfin th rinsurr s profit I i, i =, as a random variabl. Thn th rinsurr s profit in th first yar is I and its profit in th scond yar is I. Th profit Ii is dfind as follows. Pi if Li Di I i = Pi Li + Di if Di < Li Ai Pi Ai + Di if Ai < Li Rinsurrs will monitor th primary, among which long-trm contracts ar usually applid. Th application of monitoring ncourags th primary insurrs to tak appropriat masurs to control thir risks, thrfor rducs th potntial losss of risnurrs. Also s Dohrty 997.

24 Th rinsurr chooss th prmium P and P in two yars to maximiz th total profit I = E I + E. Th calculation of total profit by intgration rfrs to th appndix. I Th optimization problm is to maximiz th total profit of th principal, which is th rinsurr in this cas, subjct to th participation constraint and incntiv constraint by th agnt, th primary insurr. To solv this optimal problm, th optimal valus of P, P ;, } ar obtaind. Th optimization problm is statd as follows. Subjct to max P, P,, I E U U 3 E U = 0 4 E U = 0 5 { Equation 3 is th participation constraint of th primary insurr, whr U th rsrvation is th xpctd utility of th primary insurr that it would hav without rinsuranc. Equation 4 and 5 ar first-ordr conditions with rspct to th fforts in th two priods. Th incntiv constraints nsur that th primary insurrs mak fforts to maximiz thir xpctd utility. To simplify th joint probability dnsity function of actual loss f s, m, L, signal s and m ar assumd to b indpndnt of actual loss L as suggstd by Holmstrom 979. Furthr, signals s and m ar assumd to b indpndnt from ach othr, in that signal s is usd to addrss advrs slction, whil signal m is adoptd to captur moral hazard problm, rspctivly. Thrfor, th joint probability dnsity function of actual loss is writtn as f s, m, L = k s g m h L. 3

25 4 Lt,, γ γ λ dnot th Lagrangian multiplirs for constraints 3-5, th first-ordr conditions ar rducd as follows: ' ' ' ' D L if L h L h m g m g s k s k L P W U = γ λ 6 ' ' ' ' A L D if L h L h m g m g s k s k D P W U < = γ λ 7 ' ' ' ' L A if L h L h m g m g s k s k D A L P W U < = + γ λ 8 ' ' ' ' ' ' ' D L if L h L h L h m g m g m g s k s k s k L L h L h m g m g s k s k L P W U = γ γ λ 9 ' ' ' ' ' ' ' A L D if L h L h L h m g m g m g s k s k s k L L h L h m g m g s k s k D P W U < = γ γ λ 0 ' ' ' ' ' ' ' L A if L h L h L h m g m g m g s k s k s k L L h L h m g m g s k s k D A L P W U < = + γ γ λ whr ' s k, ' m g, and ' L h ar th drivativ functions of s k, m g, and L h with rspct to th ffort.

26 To mak Lagrangian multiplirs λ, γ, γ b positiv, w mak th following assumptions ' on th liklihood ratio by Lambrt 983: h L / h L is dcrasing in L ; ' h L /[ h L * h L ] is dcrasing in L. Equations 6- dfin th risk-sharing structur btwn th primary insurr and th rinsurr in th two-priod framwork. Th modl prdictions ar similar to th ons drivd by Dohrty and Smttrs 005. For xampl, both modls show that th rinsuranc prmium is not only rlatd to th concurrnt dirct loss by th primary insurr but also to th dirct incurrd loss in th last priod. Howvr, our modl uniquly incorporats th signals to rval th possibl advrs slction and moral hazard problm to th rinsurr ovr tim and gnrat sparat tstabl prdictions for mpirical studis. This modl allows us to distinguish advrs slction from moral hazard, if any, in th rinsuranc markt. Furthrmor, th modl taks into considration th covrag cap in th xcss-of-loss rinsuranc policy, a factor which Dohrty and Smttrs 005 dos not addrss. Th covrag cap and rtntion lvl togthr st th actual rinsuranc covrag purchasd by th primary insurr. Th modl prdictions and drivd hypothsis ar discussd as follows. 3.3 Modl Prdictions Concurrnt dirct loss: With th incras of th concurrnt loss, ' h L / h L dcrass basd on th modl assumption. According to th utility function of U th insurr in th first priod, P ' U =, U L ' U = ' ' U U so > 0. Th modl shows that L P th rinsuranc prmium is positivly rlatd to th concurrnt dirct loss. Th indpndnc of signals of advrs slction and moral hazard is assumd, and th distinctiv sparation of two ffcts is obtaind. Howvr, thy can b corrlatd which is discussd latr. In this cas, th two ffcts can still b distinguishd, but with diffrnt impacts on th rinsuranc dmand. 5

27 Signal for advrs slction: Th modl shows that th rinsuranc prmium incrass with th obsrvation of signal s. Ovr tim, signal s is xpctd to rval th tru typ of th primary insurr, such as its oprational quality, to th rinsurr, in ordr to mitigat a possibl advrs slction problm. Signal for moral hazard: Th modl suggsts that rinsuranc prmiums incras with th obsrvation of signal m. Signal m is xpctd to dtct th ffort incntiv drivn by th primary insurr with th rinsuranc covrag. With th prdictions drivd from th modl, w ar now abl to do th mpirical tst. 4. Th Empirical Analysis This sction prsnts an mpirical analysis basd on th thortical modl abov, along with th corrsponding rsults. First, th mpirical hypothss ar drivd from th thortical modl and th stimatd quations ar constructd. Scondly, th data st usd for th mpirical analysis and th construction of tstabl variabls ar introducd. Aftr considring th rlatd conomtric issus, th tst rsults for affiliatd, non-affiliatd proprty and liability insurrs and insurrs ar discussd and compard. 4. Hypothss From th thortical modl in sction thr, w drivd th mpirical hypothsis rgarding rinsuranc purchas and th signals of advrs slction and moral hazard. Th variabl corrsponding to advrs slction is xpctd to rval th tru risk typ of th primary insurr in trms of its ovrall opration quality and financial strngth. A.M. Bst ratings on primary insurrs, ar widly usd to rank and compar lvls of financial strngth among insuranc companis. Ths rankings appar as lttr ratings A++, A+, A-, B+, tc., and 6

28 th company with A++ has highst lvl of financial strngth. Bcaus A.M. Bst considrs th financial capability, loss xprinc, oprational and managrial risks into rating insuranc companis, th financial rating can b a good indicator of th tru risk typ of th companis. Th logic follows that highr rating of th insurr associats with lowr risk. In th contxt of advrs slction in rinsuranc markt, an insurr with lowr ratings is prdictd to dmand mor rinsuranc bcaus of thir insufficint financial capability or poor loss xprinc. Thrfor, th hypothsis with rspct to th advrs slction in th asymmtric information problm is statd as follows. Hypothsis : Othr things bing qual, a lowr A.M. Bst financial rating on primary insurrs is associatd with highr rinsuranc purchas. Th signal of moral hazard is dfind as th prcntag of rcovrd losss in th last priod. Th logic bhind this dfinition follows that th rcovrd losss from th rinsurr in th last priod has an impact on th insurr s incntiv to purchas rinsuranc nxt priod. Th mor th insurr rcovrs form th rinsuranc company, th highr incntiv to purchas rinsuranc. Manwhil, th insurr may not xrt mor ffort to control its risk than it would hav othrwis. Th hypothsis with rspct to moral hazard is statd as follows: Hypothsis : Othr things bing qual, a highr prcntag of rcovrd losss in th prvious priod will b associatd with highr rinsuranc purchas. To simplify calculation, w assum that advrs slction and moral hazard xist indpndnt of ach othr. Howvr, w hav also found that in most cass thy can b corrlatd. It is rasonabl to xpct that a primary insurr, who concals unfavorabl risk information and buys rinsuranc undr ths fals prtnss, may pos srious moral hazard to th rinsurr. In cass whr ths two factors do corrlat, any stimats mad undr th 7

29 assumption of indpndnc will b biasd. In cas of a positiv corrlation, th stimats for th ffcts of advrs slction and moral hazard would b highr than thy should hav bn othrwis, whil th stimats would b lowr than thy should hav bn othrwis in th cas of ngativ corrlation. 4. Estimatd Equations Following th hypothsis abov, th stimatd quation is statd as: REINS i, t L P α γ X + u R R K i, t i, t D = + βrati, t + βlvi, t + β3 + β LR D 4 + β 0 R 5 i, t + Li, t Li, t j= j i, j, t i, t Whr REINS i, t = Rinsuranc purchas for th primary insurr i in yart ; RAT i, t = A. M. Bst s rating for th primary insurr i in yart ; LV, = Loss volatility of th primary insurr i in yart ; i t L L R i, t D i, t = Prcntag of rcovrd loss out of th total dirct loss for primary insurr i in yar t ; P L R i, t R i, t =Proxy for th rinsuranc pric in which P R i, t is th cdd rinsuranc prmium and R Li t, is th rcovrd loss for th primary insurr i in yar t ; LR, =Loss ratio dfind as D i t L D i, t D i, t DPW in which L D i, t is th dirct loss and DPW, D i t is dirct writtn X i j, t prmium for th primary insurr i in yart ;, = Th jth control variabl for th primary insurr i in yar t. A st of control variabls includ log of total assts, liquidity, lvrag, rturn on quity, dummy variabl for a stock company, product Hrfindahl indx, gographic Hrfindahl indx, prcnt of 8

30 businss lins with long tail liabilitis 3, rinsuranc sustainability indx, ffctiv tax rat, prcntag of homownr writtn prmium in coastal stats 4, and masur of intrnal rinsuranc; u i, t = rror trm in quation for th primary insurr i in yart. Equation is th stimation of advrs slction with th incorporation of th ffct of moral hazard. Th indpndnt variabl RAT i, t rprsnts th financial strngth of th primary insurr, whrby th highr rating indicats strongr financial ability 5. Intuitivly, th mor vulnrabl primary insurr with lowr A.M. Bst rating is mor likly to purchas rinsuranc to protct against futur possibl advrs vnts. As a rsult, th stimatd cofficint sign of RAT i, t is xpctd to b ngativ with th prsnc of advrs slction aftr controlling for additional moral hazard. Anothr variabl for controlling advrs slction is LV, i t which capturs th loss volatility of th primary insurr. It is calculatd as th diffrnc of th losss incurrd ovr th two yars dividd by th dirct prmiums writtn. Compard to A. M. Bst ratings, this variabl mainly rvals th loss xprinc of th company and its risk typ in insuranc opration. Highr loss volatility mans this company is mor risky compard to th ovrall proprty and liability markt. Thrfor, th stimatd cofficint of b positiv in th prsnc of advrs slction. LV i, t is xpctd to 3 W follow th dfinition of long tail lins by Phillips, Cummins and Alln 998 and Garvn and Grac 007 and adopt th sam dfinition as wll. Long tail lins includ Farmownrs Multipl Pril, Homownrs Multipl Pril, Commrcial Multipl Pril, Ocan Marin, Mdical Malpractic, Intrnational, Rinsuranc, Workrs Compnsation, Othr Liability, Products Liability, Aircraft, Boilr and Machinry and Automobil Liability. 4 Th inclusion of prcntag of writtn prmiums in th coastal aras rflcts th significant impact of hurrican risks on th homownr insuranc markt. Furthr, rinsuranc plays an indispnsabl rol in th proprty insuranc markt in th coastal stats. 5 Th construction of variabl RAT i, t is xplaind in dtail latr in this sction. 9

31 Th prcntag of rcovrd losss from th last priod rflcts th impact of moral R Li, t hazard on th rinsuranc dmand. Th stimatd cofficint of D L with th prsnc of moral hazard. 4.3 Economtric Issus i, t is xpctd to b positiv Fixd Effct vrsus Random Effct: Th individual ffct can b controlld using fixd ffct or random ffct approachs. A fixd ffct modl assums that th individual ffct is corrlatd with th indpndnt variabls in th modl, whil a random ffct modl assums that thr is no corrlation btwn th individual ffct and th indpndnt variabls. Hausman 978 proposs a tst to chck a mor fficint modl against a lss fficint, but consistnt, modl. Undr th null hypothsis, both fixd ffct and random ffct stimats ar consistnt, but a random ffct stimat is mor fficint; whras, undr th altrnativ hypothsis, th fixd ffct stimat is consistnt, but th random ffct stimat is not consistnt. In this papr th Hausman tst shows that fixd ffct modl is appropriat for affiliatd, non-affiliatd and all companis togthr. Endognous Variabl: With th prsnc of moral hazard, th rinsuranc covrag may mak insurr tak lss prcaution controlling risks, which lads to highr incurrd losss. Hnc th right-hand sid xplanatory variabl of LR i, t is ndognous. It is corrlatd with th rror trm of th quation. To corrct th ndognity, th first stag stimation quation 3 is usd: LR D D i, t = α 0 + βreinsi, t + βreinsi, t + β3lri, t + β 4 ln DPW i, t + ε i, t 3 REINS =On lag of rinsuranc purchas for th primary insurr i in yar t ; i, t ε i,t =rror trm in quation 3 for th primary insurr i in yart. 30

32 From Wooldridg 00, th OLS stimators will b biasd if th ndognous variabls ar includd in th stimatd modl. To conduct an ndognity tst, a st of suitabl instrumnt variabls IV hraftr is ndd for this potntial ndognous variabl. Th rgrssion-basd approach introducd by Wooldridg 00 is applid. An appropriat IV nds to b corrlatd to th ndognous variabl and uncorrlatd with th rror trm in th modl. Intuitivly, th dirct loss is positivly rlatd to th dirct writtn prmium by th primary insurrs, and th dirct writtn prmium can srv as an IV pr s. Thrfor, log of dirct writtn prmium is usd as on IV for loss incurrd. In addition, on and two lags of rinsuranc purchas ar includd in th modl as on instrumntal variabl. This inclusion can b usd to tst its ffct on th concurrnt losss incurrd which may aris du to moral hazard with th rinsuranc covrag. Th rducd form of dirct incurrd loss is stimatd by using all th indpndnt variabls in th stimation and four IVs as th indpndnt variabls. Aftr th rsidual of this stimat is obtaind, th dpndnt variabl, th rinsuranc purchas in th quation, is rgrssd on all th indpndnt variabls and th obtaind rsidual, as wll. Th insignificant robust t-statistic of stimatd cofficint for th rror trm indicats that th dirct incurrd loss is not an ndognous variabl in th stimation and th corrsponding rsults ar unbiasd. Th corrsponding p-valu is 0.00 which implis that th variabl of concurrnt loss incurrd is ndognous in th stimation quations, and th OLS stimators ar biasd. W nd to apply IVs to fix th ndognity issu. In addition, quation 3 partly rflcts th potntial of moral hazard on th part of th primary insurr. With th prsnc of moral hazard, th highr lvl of rinsuranc purchas in th prvious priod will b associatd with th highr lvl of concurrnt dirct loss for a 3

33 primary insurr if othr firm charactristics ar controlld. Hnc, th stimatd cofficint of lag of rinsuranc purchas is xpctd to b positiv if moral hazard dos xist in th rinsuranc markt. Htroskdasticity: If th rror trms do not hav constant varianc with ach obsrvation, th htroskdasticity problm ariss. In this cas, th OLS stimators ar unbiasd and consistnt but infficint bcaus th assumption of th constant varianc for rror trms is violatd. In th prsnc of htoroskdasticity, th varianc of th cofficints obtaind from OLS tnds to b undrstimatd, so th OLS standard rror is not valid for constructing confidnc intrvals and t statistics. To solv this problm, Wightd Last Squar WLS stimators or robust standard rrors ar usually adoptd to improv fficincy. In th stimation, th Whit tst is mployd to dtct th possibl htroskdasticity problm. Th Whit tst statistics is 6.4 and corrsponding p-valu is This rsult rjcts th null hypothsis that th rsiduals in th modl ar homoskdasticity. Thrfor, th htroskdasticity issu occurs whn stimating th modl, and th stimators ar unbiasd and consistnt but infficint. In addition, th normal standard rrors ar invalid to construct th confidnc intrvals and th t -statistics. Thrfor, th robust standard rrors ar usd instad to improv th stimator fficincy in th prsnc of htroskdasticity. Individual Effct vrsus Poold OLS: Th rror trm u i, t in quation can b dcomposd as u i, t ai + ν i, t =, whr a i is calld individual ffct, ν i, t is idiosyncratic rror and u i, t is composit rror. Th individual ffct is usually unobsrvabl. If th unobsrvd individual ffct is corrlatd with othr indpndnt variabls in th modl, th poold OLS stimators ar biasd and inconsistnt. If th individual ffct is a random variabl and is uncorrlatd with othr indpndnt variabls, th poold OLS stimator is unbiasd and consistnt but infficint. 3

34 As a rsult, th prsnc of th individual ffct to choos th appropriat stimation mthod nds to b tstd. Brusch and Pagan 979 driv th Lagrang Multiplir LM tst to dtct th prsnc of individual ffct. Basd on th rsiduals from th quation, th LM tst statistics is 57.6, which rjct th null hypothsis of th absnc of individual ffct. In th prsnc of individual ffct, th poold OLS stimation is not appropriat for our modl. Ovridntifying Tst: To tst th modl idntification, Andrson Canon and Cragg- Donald tsts ar undrtakn by using STATA cod of xtivrg. Th small p-valu of ths tsts shows th modl proposd is idntifid. 4.4 Data Dscription and Variabls Construction A panl data st rprsnting th proprty and liability rinsuranc markt in th Unitd Stats from 99 to 006 is constructd to tst th hypothss. Th data includs th rinsuranc prmium, dirct loss, financial strngth ratings and othr firm charactristics of th primary insurrs. Th data ar collctd from NAIC annual statmnts and A.M. Bst Company for th corrsponding yars. Each insuranc company is rquird to rport its undrwriting businss, claims, profitability, rsrvs and othr rquird oprational and financial information to th stat commissionr vry yar, so th NAIC annual statmnts compris an xtnsiv and rliabl rsourc for th study of th insuranc and rinsuranc markt in th Unitd Stats. A.M. Bst Company is a privat rating agncy and, accordingly, th A.M. Bst rating is an indpndnt opinion on th company s ovrall financial strngth. Th ratings ar valuatd quantitativly and qualitativly basd on th company s balanc sht, oprating prformanc and othr businss information. In th contxt of insuranc industry, a company which is assignd a highr rating is blivd by invstors to hav nough financial rsourcs and xprtis to dal with th risks it is facing, including undrwriting risk, oprational risk and dfault risk. Thrfor, th ratings can 33

35 b indicators of risk status of primary insurrs. A.M. Bst ratings ar an indicator of financial strngth of companis, and th highr th rating, th strongr financial ability of th company 6. Insuranc companis can b catgorizd as affiliatd and non-affiliatd, which apply quit diffrnt risk managmnt stratgis du to thir financial structurs. For xampl, affiliatd insurrs can divrsify thir risks through th us of both xtrnal and intrnal rinsuranc within th group. Non-affiliatd insurrs only buy rinsuranc from othr outsid rinsurrs. Th data on affiliatd, non-affiliatd insurrs ar collctd sparatly. Tabl 3 and Tabl 5 list th dscriptiv statistics for th affiliatd, non-affiliatd and all proprty and liability insurrs from 990 to 006, rspctivly. Construction of Dpndnt Variabl Prvious studis apply diffrnt dfinitions for th rinsuranc variabl. For xampl, Mayrs and Smith 990, Garvn and Lanmm-Tnant 003 and Col and McCullough 006 us th following construction to masur th rinsuranc purchas: Intrnal & Extrnal cdd rinsuranc Rinsuranc = Dirct prmium writtn + int rnal + xtrnal assumd rinsuranc whr intrnal cdd rinsuranc rfrs to th intrcompany pooling or non-pool rinsuranc within affiliations. Garvn and Grac 007 us anothr ratio to dfin th rinsuranc purchas: Extrnal cdd rinsuranc xtrnal assumd rinsuranc Rinsuranc = Dirct prmium writtn + int rnal + xtrnal assumd rinsuranc Thy tstd advrs slction in th rinsuranc markt with th mphasis on unaffiliatd insuranc companis. Th numrator of th ratio is th nt cdd rinsuranc by th primary 6 For mor dtails on A.M. Bst rating, s 34

36 insurr. Thrfor, this crats a continuous variabl ranging from - to +. A ngativ rinsuranc purchas mans that this primary insurr actually acts as a rinsurr in th markt. Evn though Garvn and Grac 007 spcifically tstd advrs slction for th nonaffiliats in th rinsuranc markt and obtaind supporting vidnc in lin with th thortical prdictions, w ar still intrstd in how th rsults will chang if w considr th affiliation issu. To tst th simultanous ffcts of advrs slction and moral hazard in th rinsuranc markt, mpirical studis for affiliation and non-affiliats ar prformd, rspctivly. For affiliats, th rinsuranc purchas is dfind as: Intrnal cdd rinsuranc Pr mium REINS = Dirct prmium writtn + total assumd rinsuranc For non-affiliats, th rinsuranc purchas is dfind as: Extrnal cdd rinsuranc Pr mium REINS = Dirct prmium writtn + total assumd rinsuranc Construction of Indpndnt Variabls and Control Variabls A.M. Bst Rating: Th variabl of RAT, is constructd from th A.M. Bst financial i j strngth ratings as discussd bfor. Tabl lists A.M. Bst rating scals and associatd dscriptions. Mayr and Smith 990 transfr th lttr scals to numrical scals from 0 to 6, whil Dohrty and Phillips 00 convrt th various A.M. Bst financial strngth ratings to numrical scors ranging from 0 to 4. If th firm is ratd A++ or A+, it is assignd a scor of 4, 3 if th firm is ratd A, if it is ratd A-, if it is ratd B++ or B+, and 0 if it is ratd B and lowr. Bcaus this ssay attmpts to xamin th ffct of advrs slction on th rinsuranc purchas by diffrnt primary insurrs with diffrnt risk lvls, it is mor appropriat to brak ths ratings into dtaild subgroups to dscrib th risk typ of primary insurrs. Consquntly th sam approach by Mayr and Smith 990 is adoptd in this ssay. Accordingly, svn sub- 35

37 groups ar cratd from th lttr scals. If th firm is ratd A++ or A+, it is assignd 6; 5 if th firm is ratd A or A-; 4 if it is ratd B++ or B+; 3 if it is ratd B or B-; if it is ratd C++ or C+; if it is ratd C or C-, and 0 if it is ratd D and lowr. Tabl tabulats th transformd numrical scals and th associatd lttr scals. Loss Volatility: Two masurs of loss volatility ar applid: Loss volatility can b dfind as th diffrnc btwn th currnt losss incurrd and th prvious yar s losss incurrd, dividd by th currnt writtn prmiums, an approach proposd by Li and Schmit 008; To allow for volatility ovr a long tim priod, th scond masur of loss volatility is calculatd as th diffrnc btwn concurrnt losss incurrd and th avrag losss incurrd ovr th last thr yars, dividd by th currnt dirct writtn prmiums. Th ffcts of both loss volatility masurs on th dmand for rinsuranc ar tstd and compard. Th highr loss volatility indicats a mor risky opration of th insuranc company. Togthr with th A.M. Bst financial ratings, loss volatility is usd to rval th insurr s tru risk typ, furthr confirming th prsnc of advrs slction. Prcntag of Rcovrd Losss in th Prior Priod: As th signal of moral hazard, this variabl is constructd as th prcntag of rcovrd loss from th rinsuranc out of th total losss incurrd from th last yar. D Li, t Loss Ratio: Th variabl is calculatd as DPWi D, t. Th rinsuranc purchas is rlatd to th dirct gross loss, L D i, t by th primary insurr. Th sign of th cofficint of loss ratio is xpctd to b positiv, which mans that a gratr dirct gross loss will induc incrasd rinsuranc purchas. 36