Commodity Bundling In Japanese Non-Life Insurance: Savings-Type Products As Self-Selection Mechanism. Abstract

Transcription

1 Commodty Bundlng In Japanese Non-Lfe Insurance: Savngs-Type Products As Self-Selecton Mechansm KLAUS WALLNER * Columba Unversty Economcs Department kw31@columba.edu (January 1997) Abstract Ths paper develops a self-selecton ratonale for the use of commodty bundlng n the case of savngs-type casualty nsurance n Japan. The savngs-cum-nsurance bundle s descrbed n detal. Two alternatve models to explan ts success are presented. The moral hazard model assumes that casualty nsurance clams depend on unobservable actons of the nsured (lack of care), whle the adverse selecton model centers around the assumpton that consumers have prvate nformaton about ther exogenous clam probablty. The lkelhood of a clam s nversely related to personal ncome, because preventve safety measures are normal goods. The evdence from casualty nsurance n Japan supports the adverse selecton theory, whle the moral hazard model s nconsstent wth some of the nsttutonal and emprcal facts. * I wsh to thank Mtsu Marne Research Insttute and Yasuda Fre and Marne Insurance Company for ther hosptalty durng research vsts n the summers of 1993 and 1994, and the Nambu-Foundaton for fnancng the latter stay. I have substantally benefted from the detaled comments on earler drafts of ths paper by Jay P. Cho, Prajt K. Dutta, Rchard E. Ercson, John E. McLaren and Hugh T. Patrck.

2 I. Savngs-Type Products 1. Overvew The sngle most mportant factor for understandng the current stuaton n the Japanese non-lfe nsurance ndustry s the extraordnary growth of the savngs-type products. Snce ther ncepton n the md-postwar perod, 1 these products have experenced rapd (f unstable) growth, whch only came to an end n 1990 wth the burstng of the nfamous asset prce bubble and the ensung recesson. Even though they account for only 5% of the nsurance prema, the savngs porton attached amounts now to half the labltes of the ndustry [19]. Savngs-type products bundle an ordnary nsurance polcy wth a tme depost. Upon expraton of the nsurance polcy, the customer receves the savngs porton augmented by a dvdend. The dvdend conssts of a guaranteed rate of return and a dscretonary amount related to the actual nvestment return whch the nsurance company acheved by managng these funds. The savngs porton s small compared to the nsurance coverage, and lke a deductble s not returned to the polcy holder n a total clam stuaton. The total (gross) premum, consstng of the savngs premum, the pure rsk premum, and a loadng to nclude commsson and general sales and acquston expenses, can be pad ether as lump-sum up front or n nstallments. Tradtonally savngs-type products offer medum term savngs-cum-nsurance bundles (3 to 10 years duraton), even though n October 1992 the frst annuty-type 30 years polcy was ntroduced. Savngs-type products now cover a varety of rsks, but the only two bg lnes are fre and personal accdent. The mpact of these polces on the balance sheets of non-lfe nsurance companes s enormous. Whle underwrtng results are not much affected, nvestment margns from managng savngs-type funds have n recent years provded up to 50 % of total shareholder nvestment ncome [4, p. 20]. In lght of such fgures, Japanese non-lfe 1 The frst savngs-type fre and personal accdent polces were sold n 1963 and 1974, respectvely. 2

3 nsurance companes have been descrbed as huge nvestment trusts, whch also wrte a lttle nsurance on the sde (though generally very proftably). 2 The paper s organzed as follows. The remander of secton I descrbes n more detal the nsttutonal characterstcs of savngs-type products. Exstng theores of commodty bundlng and ther relevance to savngs-type products are revewed n secton II. Sectons III and IV present the man alternatve models, moral hazard (MH) and adverse selecton (AS). The evdence examned n secton V supports AS, contradctng MH. Secton VI concludes. 2. Premum Settng Savngs-type polces can be dvded nto two categores. Frst, the so-called 'long term comprehensve ' nsurance polces, whch were orgnally devsed as savngs-type polcy. Second, the 'maturty refund endorsement type', whch s created by addng a maturty refund to an exstng conventonal type polcy. The rsk porton of the total premum of the latter type s dentcal to the correspondng normal product. 3 The two categores dffer manly n the approval procedure by the Mnstry of Fnance (MOF). For vrtually all savngs-type products, there exsts a comparable normal lne product, offerng smlar coverage. Formally, the premum rates on savngs-type products of the frst category are not fxed by ratng assocatons, unlke the rates on normal fre and personal accdent lnes. 2 Ths development has fundamentally altered the busness focus of the companes. Because of the rsng nfluence of nvestment sklls on company profts n a deregulated fnancal envronment, no longer can conventonal underwrtng clam prorty over ancllary actvtes such as nvestment management. The savngs-type polces exhbt the lack of sophstcated nvestment sklls n the past. Durng the eghtes, rsng nterest rates meant that the nsurance company could nvest the prema receved at ever hgher current market nterest rates, earnng large margns on these funds. Ths was made possble through very nfrequent (yearly) adjustment of the guaranteed rate of return, as well as the fact that almost 40% of the prema are receved n nstallments durng the polcy perod. Wth the end of the bubble economy and the resultng unexpected and prolonged declne n market nterest rates, the opposte and adverse effect occurred. The companes found themselves stuck wth hgh guaranteed rates of return, whle at the same tme not beng able to acheve an equally hgh rate on ther nvestments. Ths stuaton s a volaton of the golden rule of nvestment, whch prescrbes a precse match of the duraton of assets and labltes. Some of the savngs-type bundles were prced so that they result n an overall loss for the company. Ths experence has prompted the responses. Frst, rates of return on savngs-type products, whch are regulated and dentcal across all frms, are now adjusted more frequently. Second, the ndustry ncreasngly uses asset-labltes management systems. 3 The expense loadng may be adjusted, takng nto account that savng-type polces do not requre yearly renewal procedures, therefore save some expenses. However, ths dfference s hardly sgnfcant. 3

4 Belongng to the category of Lcensed Rates, savngs-type premum rates are determned by ndvdual calculaton by each nsurance company, ndependent flng wth and approval by MOF. 4 All of the maturty-refund type products are under the Lcensed Ratng system, and therefore, the Ratng Assocaton have had no drect nvolvement n these busnesses both n ther premum rates and polcy condtons. [17, p. 19] However, The Assocaton has also been collectng data and complng varous statstcal reports necessary as the bass for rate examnaton n those lnes of nsurance whch are not under the Assocaton ratng system.... The volume of nformaton data on these lnes of nsurance has been on the ncrease each year, takng up approxmately 30% of the total data processed by ths Assocaton at present [17, p. 25]. Therefore, the condtons are gven to make ndustry-wde collusve rate agreements possble, va MOF and the ratng assocaton. 5 As a matter of fact, savngs-type nsurance rates are dentcal across all frms n the ndustry. 3. Cross-Subsdzaton In savngs-type lnes, all expenses are charged aganst the nsurance porton of the premum. Ths accountng rule understates true underwrtng profts and exaggerates nvestment returns. To estmate the sze of ths bas, I calculate expenses for the two major savngs-type lnes Fre and PA at the same expense ratos as ther normal lne counterparts. Ths procedure corrects for the accountng bas by correctly attrbutng costs to the bundle components, and allows a clearer pcture of proftablty of nvestment and underwrtng n savngs-type lnes. 4 Insurance Busness Law, For a detaled descrpton of MOF regulaton of the non-lfe nsurance ndustry n Japan, and ts mpact on ant-compettve conduct by the frms, see [40]. 4

5 Expense Rato 6 (ER) PA Normal Savngs-type () Expenses (bny) at ER of normal lnes Overstated by Normal ER Fre Savngs-type () Expenses (bny) at ER of normal lnes Overstated by The last column n the above tables gves the amount by whch expenses n savngstype lnes are overstated because they nclude expenses whch belong to the nvestment part of the bundle. 7 Summng the entry n the last column n both tables yelds an estmate for the total amount of ths accountng asymmetry for each year. The followng 6 The expense-rato dvdes expenses (.e. corporate expenses for acquston of new customers, mantenance, agency commsson and money collecton) by the nsurance-porton of total prema. The clams-rato dvdes clams ncurred by the nsurance-porton of the total prema. The sum of clams-rato and expense-rato s called combned rato and provdes a drect measure of proftablty of the nsurance product. 7 Actual expenses are roughly smlar between savngs-type and normal lne nsurance, snce both use the same sales channels (hence smlar commsson rates) and marketng technques. 5

6 table presents ths sum, and compares t to the margn estmated to be earned on the nvestment of the savngs funds [4]. Savngs Prema (bn Y) Margn (%) Margn (bn Y) Cost-Overstatement (bny) , , , , , , , , , , , Investment proftablty on the savngs-type bundle s wdely overstated, and n realty these nsurance polces are very proftable. Ths hgher proftablty, a result of the better clam-rato, s masked by the cross-subsdzaton mplct n the accountng asymmetry Why Are Savngs-Type Products So Successful? Ths paper attempts to explan the success of the savngs-type products. Between 1977 and 1989, the percentage of fnancal assets n Japan nvested n savng deposts fell from 49% to 41.5% whle nsurance rose from 12.2% to 19%. 9 Part of ths shft n market share from banks to nsurance companes s attrbutable to the attractve rates offered on savng-type products n the non-lfe nsurance sector. It s surprsng that rates of return on savngs-type polces are superor to rates on competng products n the fnancal sector, 10 snce casualty nsurers do not possess superor nvestment sklls. In 8 Ths accountng rule per se has no real consequences, and the queston arses whether the reason s the convenence of not havng to dsentangle cost components, or whether the understated underwrtng profts offer any real beneft to the ndustry. Possbly, dsgusng the hgh proftablty from the eye of the publc facltates mantanng rates at ther hgh level. 9 Source: Fnancal Statstcs of Japan 1994, Insttute of Fscal and Monetary Polcy, MOF Japan. 10 The relevant competton comes from certfcates of depost (CD) offered by commercal banks and trust banks. A comparson of rates of return between the two products s complcated by the fact that CD-rates are adjusted much more frequently than dvdends on savng-type products, and also because CD-rates strongly depend on the amount nvested. Offcal MOF statstcs show CD-rates offered by commercal banks as averages across frms, and also across amounts. Ths dsguses that rates offered by banks to small savers are sgnfcantly less attractve than rates earned above certan threshold amounts such as 6

7 addton, regulaton n the nsurance ndustry hampers nvestment opportuntes more than those of banks. 11 In partcular the lqudty requrement s much hgher n the nsurance sector snce the ndustry needs to be prepared to cover clams resultng from large natural dsasters. 12 How are non-lfe nsurance companes able to offer hgher rates than banks? 13 The cross-subsdzaton dscussed above allows that the hgh underwrtng profts from these products are used to offer hgher rates than banks. The real beneft for the ndustry comes not from nvestng the savngs funds, but from the nsurance porton of the bundle. A further central queston concerns the use of the bundlng arrangement. If nvestment of the savngs funds s not attractve to the companes, why s the bundle offered? Why does mxed bundlng occur -.e., why are nsurance contracts offered to cover the same rsks, wth or wthout savngs contract ncluded? And why s the clamsrato of savngs-type products so much lower than that of pure nsurance polces? Ths paper argues that savngs-type bundlng s a self-selecton mechansm desgned to separate dfferent rsk groups. Rsk dfferences result from dfferences n ncome across consumers. Income and rsk are negatvely correlated because safety s a normal good, $10,000, $20,000, or $50,000. Even so, offcal MOF statstcs from the Insttute of Fscal and Monetary Polcy Fnancal Statstcs of Japan show that rates on tme deposts of at least two years untl maturty durng the calendar year 1992 were 5.5% untl January 20 of that year, then 5% untl Aprl 20, 4.4% untl June 22 and 4.07% from August 17. Ths compares to guaranteed rates of return on savng-type products of 5% for fve year polces and 4.5% for three year polces between December 1989 and January In addton, a dscretonary dvdend further boosts the return on savng-type products, but ths amount vares across frms and products and s adjusted almost weekly. These rates are pad even on small savngs polces. 11 The Insurance Busness Law authorzes MOF to supervse nvestment actvtes of the ndustry through the so-called Enforcement Regulatons. In the latter, permssble nvestment objects are specfed, as well as lmts on the percentage of assets of a company nvested n those categores. In addton, n order to obtan a lcense to wrte nsurance n Japan, each company has to provde a "Statement Showng the Methods of Utlzng Assets", also called "Investment Plan", whch s subject to approval by MOF. Ths plan can modfy the Enforcement Regulatons, and provdes a flexble tool for MOF to control actual nvestments. 12 Around 15-20% of ndustry assets are nvested n cash and postons of comparable lqudty. 13 Industry sources seem at a loss when asked for an explanaton of the successful development of the savngs-type products. The most frequently heard suggeston goes as far as nvokng customer rratonalty. It s clamed that the Japanese consumer consders an nsurance contract a waste of money f no clam results of t [the Insurance Councl Report, January 1963, states that "f buldng endowment nsurance and a fre mutual nsurance offer refunds to polcyholders upon accdent-free expraton of polcy perod, t would better sut sentments of a certan group of fre nsurance polcyholders"[36], and a consumer survey conducted by the Marne and Fre Insurance Assocaton of Japan n Aprl 1986 states that "the most prevalng reason why they (consumers) chose savngs-type nsurance s 'because buyng polces wth no refund upon expraton s a waste of money' (44.6 % of respondents)".] 7

8 and by spendng money on safer products and protectve equpment a consumer reduces the lkelhood of an accdent. Low rsk consumers are nduced to buy the bundle product through an mplctly lower nsurance premum. Savngs-type customers face mplctly lower nsurance premum rates, because they are recevng a cross-subsdy n form of hgh return on the savngs porton of the bundle. Hgher rsk consumers fnd t too expensve to buy the bundle because ther savngs are nsuffcent, and borrowng s costly. In effect the nsurance product s bundled wth a savngs contract, the reservaton prce of whch s negatvely correlated wth a consumer's clam lkelhood. Commodty bundlng allows nsurance companes to overcome the market falure resultng from asymmetrc nformaton, and to offer cheaper nsurance contracts to consumers wth a lower expected clam value. Ther lower reservaton prce for nsurance had prced those better rsk consumers out of the nsurance market as n the classcal lemons problem [2]. II Tyng/Bundlng Lterature Elsewhere I presented a concse overvew of the lterature on commodty bundlng [39]. Here I reexamne exstng theores n the lght of how well they are able to explan bundlng n the savngs-type nsurance case. Throughout the dscusson I wll refer to ten sales as the requrement of purchasng another good from the same seller as the tyng good. The rato n whch the two goods are consumed depends on the tastes of the buyer. Commodty bundlng s dfferent from te-n sales n that the quantty of the ted good s n fxed proporton to that of the tyng good. The consumer can decde how many of the bundles to purchase, but s not free to consume the goods n a rato dfferent from the rato n the bundle. Effcency explanatons have been put forward n cases of tyng rather than bundlng. Ths already suggests that the addtonal restrcton of fxng the proporton of the two goods n the bundle requres a dfferent explanaton. Effcency arguments are threefold. Frst, cost savngs can result from jont producton (economes of scope), dstrbuton, and lower search costs n consumpton. There are reasons to expect bundled sales of nsurance and savngs contracts to ental cost savngs n producton and dstrbuton. The start-up costs of approachng a potental new customer and gettng to talk to her, and developng trust through an ongong busness relatonshp, as well as head offce 8

9 functons such as mantanng the customer data bases are examples of cost components where such savngs should occur. Industry nsders agree, however, that the agency network and the commsson-based compensaton system used by nsurance frms s a much costler sales channel for savngs contracts than the network of branches used by banks. Moreover, t s clear that nsurance companes are more constraned than banks n ther nvestment actvtes, both by regulaton and through the need to mantan hgher levels of lqudty to provde for catastrophe losses, resultng n lower rates of return on ther nvestments. These dsadvantages tend to offset whatever cost savngs there are. Search costs for consumers are very lkely small for the knd of products bundled here, because both nsurance polces and depost savngs contracts are standardzed and rates are homogeneous. Hence, t seems that cost savngs can not explan the appeal of the savngs-type bundle. Second, tyng can sgnal nformaton to the buyer, such as n cases of experence goods where product qualty s unknown to consumers at the tme of purchase. Ths s not applcable here, snce the qualty of the purchase depends only on the company delverng on the promse to cover a clam and dsburse the savngs plus nterest. Even though there s no depost nsurance n Japan, the probablty of savers losng ther deposts due to nsolvency s vrtually zero because of an mplct MOF guarantee. Although there are large dfferences n the solvency margn rato among non-lfe nsurance companes, the balance sheets of all companes are so strong that default s certanly not an ssue. 14 Thrd, the transfer of rsk to a stage more effcent n bearng t can be a ratonale for tyng. In addton to dealng strctly wth tyng only, ths dea s lmted to vertcal relatonshps. There s no obvous reason why nsurance companes should be better bearers of depost rsks than commercal banks. On the contrary, the relatvely nfrequent adjustments n guaranteed rates of return on savngs-type products, causng varablty n 14 The solvency margn s a rsk-weghted assessment of captal and serves to evaluate the fnancal soundness of the nsurance company. For a descrpton of the detals of ths statstc, see Credt Susse, 1993, and for the solvency margns of ndvdual companes based on Fscal Year 1992 results, see Barclays de Zoete Wedd Research, The lowest rato of all companes s obtaned for Fuj, but ths result s stll descrbed as "more than adequate", and that for the second lowest, Da-Tokyo, as "more than satsfactory". 9

10 the nvestment margn, suggests that nsurance companes are not very effcent n dealng wth such rsks. Market power theores form another strand n the lterature on commodty bundlng. Telser [33] formalzes the long-standng ntuton that bundlng can act as a meterng devce dentfyng hgh ntensty users and chargng them more than low ntensty users. Ths theory does not explan savngs-type bundlng snce t requres complementarty n the use of the two bundled goods. Savngs and nsurance are f at all related, rather substtutes than complements. Furthermore meterng s a theory of tyng and has lttle applcablty to (mxed) bundlng. The leverage theory clams that a frm wth market power n the tyng good market can affect rvals' behavor n the ted market. Through bundlng a frm can nfluence the entry and ext decson of rvals n the ted good market (Whnston [41]), or the level of the strategc varable chosen by rvals (Carbajo et al [10]). Both models requre mperfect competton n the ted market. Insurance companes are very small players n the fercely compettve depost market, and the cross-subsdzaton dscussed above demonstrates that the nvestment margn s not the ncentve to bundle. Moreover, these theores cannot explan the dfference n clam rato between savngs-type and normal lnes of nsurance. Hence what happens n the market for savngs does not appear to be the drvng force behnd savngs-type bundlng. A better explanaton for savng-type bundlng s provded by an alternatve nterpretaton of the leverage theory, proposed by Bursten [8,9] and Kaplov [22]. These authors vew commodty bundlng as means to extract the proft potental nherent n the tyng market more fully, rather than the creaton of market power n the ted market. In the case of savngs-type bundlng frms are unable to extract fully the proft potental n the nsurance market because polces cannot be prced accordng to the exact wllngness to pay of each ndvdual consumer. Ths could be the result of asymmetrc nformaton, or a restrcton on the set of varables a polcy can be contngent on. Effcent prce dscrmnaton s acheved by offerng a bundle of products such that the reservaton prce for the bundle s correlated wth the varable affectng clam lkelhood. Recent contrbutons (Schmalensee [30], McAfee et al [26]) broaden the applcablty of ths theory by showng that the ncentve to bundle does not rest on negatvely correlated 10

11 reservaton prces for the bundle components n the populaton of consumers. Indeed t would be dffcult to argue that the reservaton prces for savngs and nsurance contracts are negatvely correlated, n partcular snce the bundle components can be purchased separately. However, these papers do not qute seem to explan savngs-type bundlng. Snce the reservaton prces for the bundle are always less dspersed than those for the ndvdual components alone, Schmalensee [30] argues that t s the lower dsperson whch allows frms to extract more surplus wth the bundle. In the savngs-type bundle case nsurance companes are legally barred from sellng savngs contracts separately, and the market level of returns on savngs s very compettve. Hence, the bundle prce has to be set low to nduce consumers to buy t. The frms are not able to make the alternatve opton of buyng the components of the bundle separately less attractve by lowerng CD rates. Ths constrant counteracts the effect of less dsperson of reservaton prces for the bundle. Key to understandng the proftablty of bundlng s the fact that clam ratos for savngs-type products are sgnfcantly lower than for normal lnes. Effectvely the companes are sellng the same product to a dfferent group of consumers (who selfselect nto savngs-type products) at a dfferent prce (the premum rate mplct n the bundle s lower than for normal lnes). Bundlng does not lower the dsperson of reservaton prces n the populaton of consumers, but offers a soluton to the problem of hdden nformaton wth respect to clam lkelhood. III. A Moral Hazard Model The strkng dfference n clam ratos between savng-type products and normal nsurance lnes can be theoretcally explaned by ether moral hazard (savng-type buyers are more careful) or adverse selecton (they belong to a better rsk class). Ths secton presents a moral hazard model, based on the assumpton that clam lkelhood s nversely related to the costly exercse of prudence by the polcy holder. Prudence s unobservable (or observable but not verfable), so that contracts contngent on the level of prudence are not feasble. The cost of prudence stems from the nconvenence of beng careful. 11

12 In ths model, the savng-type buyer s nduced to be prudent n the followng manner. Snce part or all of the savngs porton s lost n a total clam case, ths amount can be subtracted from the nsurance payment. Lke a deductble, ths amounts to ncomplete coverage, snce the net payment to the nsured s less than for normal lnes. Facng ncomplete coverage, savngs-type customers wll then fnd t optmal to lower the probablty of a loss by beng more careful. Let consumers have dentcal tastes U = U ( Y, S), where Y s monetary ncome and S ( sufferng ) represents the non-monetary dmenson of a loss, takng on the value one n the bad state of nature and zero n the good state. If consumers decde to purchase nsurance coverage avalable at premum π they wll receve K n the clam case to cover the monetary loss L. The probablty of an accdent s gven by p = ( 1 θ ) where θ [ 0, 1] s the (normalzed) level of self protecton of consumer. Dsutlty of selfprotecton s measured by C ( θ ) whch s ncreasng, convex and C ( 0) = C '( 0) = 0. Consumers can choose between normal and savng-type nsurance. 15 The savngs porton of the latter s only partally refunded n a clam case, and therefore the net nsurance payment to savng-type customers n a clam case s less than K, say K, where ( 0, K) s the part of savngs lost n a clam case. 16 Consumers frst decde whether to buy nsurance, and whch type. Once that decson s taken, the optmal level of self-protecton s chosen, and consumers face the revelaton of the state of nature under the so determned odds. The optmal level of self-protecton for each consumer, as a functon of the nsurance decson, s determned by 15 Wthout loss of generalty I am gnorng here those consumers who prefer to go wthout nsurance. 16 In a clam case, the nsurance contract automatcally lapses, and the savngs porton of the premum s not returned to the polcy holder. If the clam occurs after the tenth year of the nsurance contract, the nsured receves the dvdend and return therefrom related to the frst ten years back, but not the savngs porton tself. In case the whole savngs porton had been pad n a lump-sum up front, the part belongng to the perod after the clam occurred s returned to the polcy holder. Interestngly the savngs porton of those lapsed clam case polces s not used to cover part of those clams, but s allocated to the maturty refund of other polcy holders. Those who suffer a clam thus end up subsdzng the dvdends whch the lucker polcy holders receve on ther savngs. Ex ante, the expected return of an average polcy holder are therefore not lowered by the fact that the savngs porton s lost n a total clam case. 12

13 j { p U ( Y π L + K 1) + ( 1 p) U( Y π 0) C ( θ )} j {( 1 θ ) U ( Y π L K 1) θ U( Y π 0) C ( θ )} max,, θ = max +, +, θ where K j K f normal type = ( K ) f savng - type The frst order condton s j U ( Y π L K, ) U( Y π, ) C '( θ ) j ( π, 0) ( π +, 1) = '( θ ) = 0 U Y U Y L K C Lettng the superscrpts and denote savngs-type and normal lne customer, respectvely, θ > θ snce for savng-type customers monetary ncome s not equal n both states, and t s optmal for them to be more careful than normal type customers whose monetary loss s fully covered. Hence savngs-type customers have lower accdent probablty and the model mples lower clam-ratos n savng-type nsurance lnes. The fact that both normal and savngs-type nsurance polces are sold suggests consumer heterogenety. Ths heterogenety s ncorporated n the model by lettng consumers dffer n ther cost of prudence. It remans true that for each ndvdual consumer prudence s hgher under a savng-type nsurance polcy than under a normal type, but the choce between the two types s determned by a comparson of expected utlty (EU) levels. Consumer wll buy normal type nsurance f EU ( ) > EU ( ) or ( 1 θ ) U( Y π L + K, 1) + θ U( Y π, 0) C ( θ ) > ( 1 θ ) U( Y π L + K, 1) + θ U( Y π, 0) C ( θ ) where θ No, θ are the optmal levels of self-protecton of consumer under normal and savngs-type nsurance, respectvely. Let C ( ) C ( ) θ > l θ, > l. By mplcaton d No θ, < 0. Ths alone s not a d suffcent condton for effcent self-selecton of consumers nto the two types to be possble, snce hgher levels of self-protecton under the savng-type coverage tend to counteract the lower utlty from ncomplete coverage, and t s not clear that hgher cost consumers wll necessarly prefer normal type nsurance. For proper self-selecton of customers nto nsurance types accordng to ther dfferng costs of self-protecton, a C 13

14 s requred such that all consumers wth hgher costs are better off buyng normal type, and all consumers wth lower costs wll prefer savng-type products. A necessary condton for such a C to exst s gven by U ( ) = U ( ) U ( ) > U ( ),, l <. In words, f consumer s l l ndfferent, then any consumer wth lower costs of prudence must strctly prefer savngstype over normal nsurance. A suffcent condton for ths s (wrtten n the obvous shorthand notaton): ( ) < ( ) ) U U l ( θl θ ) [ U(, 1) U(, 0) ] > C ( θ ) Cl ( θ l ) ( ) > ( ) ) U U l ( θl θ ) [ U(, 1) U(, 0) ] < C ( θ ) Cl ( θ l ) Whether ) and ) hold depends on the cost of self-protecton (determnng the optmal level of prudence for each type, n each stuaton). Type l wll strctly prefer savngs-type nsurance f the cost of self-protecton s suffcently low. Ths condton s suffcent but not necessary for the separaton of consumers nto the nsurance types accordng to ther cost of prudence. Even f perfect separaton s not feasble, mperfect separaton (where some consumers wth hgher costs choose savngs-type whle lower costs choose normal type, over some range of costs) may be possble. Whle the drect proft ncentve of companes s not explctly characterzed n ths secton, t s clear that profts may be hgher f the companes can use ncentve schemes whch sort customers nto groups accordng to ther clam probablty. It s mportant to understand why some consumers choose not to buy the savngs-type polcy. The attractve condtons of the bundle are nsuffcent to compensate them for ther hgh dsutlty of exercsng care. Self-selecton wll work better f all consumers can afford both types, so that ther choce s only nfluenced by ther personal cost of prudence. Bndng ncome constrants force consumers to stck wth normal polces regardless of ther cost of prudence. On theoretcal grounds, ths model of moral hazard wth consumer heterogenety s plausble. Both elements are common n the nsurance lterature. Therefore the evdence examned n secton V must decde on the model s mert. and 14

15 IV. A Self-Selecton Model 1. The Demand For Insurance Consumers (ndexed =1...n, wth n large) lve for two perods (lfetme). In the frst perod, after the personal ncome Y s receved, the nsurance purchase and savngs decsons are made, and the state of nature s revealed. In the second perod all ndvduals receve the same fxed amount of ncome Y (n addton to the savngs from perod one), whch can be nterpreted as publc retrement payment. In the bad state, the ndvdual suffers a loss L, and the ndvsble nsurance pays out L to polcy-holders. There s no dscountng. Before nsurance, ncome n perod one s Y n the good state and (Y -L) n the bad state (known to consumers). Outsde opportuntes n the fnancal sector are represented by a compettve bankng ndustry, offerng the market rate of return for deposts. Consumers dffer only n ther normalzed ncome Y [ 0, 1 ]. The probablty θ of the bad state occurrng depends negatvely on Y : θ = ( 1 Y ), θ [ 0, 1] Y s dstrbuted n the populaton of consumers accordng to some contnuous dstrbuton functon whch s known to frms. Personal ncome affects θ because preventve safety measures are normal goods. 17 Wealthy ndvduals therefore nvest more n protectve equpment. 18 Dfferng levels of protecton by nsurance buyers are caused by the underlyng dfferences n ncome rather than by prudent behavor. 17 Could t be that safety s an nferor good, or that a customer substtutes nsurance for safety? The argument would be that hgher wealth allows for more self-nsurance. Ether self-nsurance, or holdng an nsurance polcy, could decrease spendng on safety, f nsurance and safety are substtutes. The nsured/rch would spend less on safety because ts beneft s less than wthout ether form of nsurance. I would lke to argue that the degree of substtutablty between nsurance and safety s small (at least n fre and personal accdent). Insurance can only promse to restore the materal level of wealth after the bad state of nature has occurred. However, even full nsurance rarely wholly ndemnfes. Deprecaton rates for durable goods are hgher, and damage assessment often less than the nsured's subjectve correspondng values are. Ths may reflect mperfectons n second hand markets, or could be the result of the nsurers' ncentve to keep damage payments small ex post. Furthermore there are sgnfcant non-monetary dmensons of loss, such as body njures. Therefore I assume that safety s a normal good. 18 For nstance, Mercedes Benz boasts that ts passenger cells reman undeformed at crashes aganst a concrete wall up to a speed of 60 km (around 38 mph), protectng passengers aganst njures. Other examples are safer sports equpment, modern and less fre-prone prvate homes, hgh-qualty and 15

16 The nstantaneous felcty functon U(Y,S) of all ndvduals s an ncreasng and concave functon of ncome, and a negatve functon of S whch measures the nonmonetary dmenson of a clam case. To llustrate the consumers' purchase decson for nsurance coverage I wll use the constant absolute rsk averson (CARA) utlty functon for ncome, U(Y,S) = -Se -λy whch has the vrtue of excludng ncome effects on rsk averson. S takes on the value S >1 n the loss case, S =1 otherwse. Consumer maxmzes von Neumann-Morgenstern expected utlty, and wll purchase nsurance avalable for premum π f the followng holds: ( π, ) (, ) + ( 1 ) (, ), ES = p + ( 1 ) U Y ES p U Y L S p U Y S where S p The reservaton premum π of consumer s obtaned from the followng equalty, expressng ndfference between buyng nsurance and not buyng: ( Y ) ( Y L) ( ) λ π λ λy ES e = 1 Y S e + Y S e λ( Y L) λy λ( π ) log[ ( 1 ) ] λ( Y L) λy { log[ ( 1 ) ] log } log ES Y = Y S e + Y e π 1 = Y S e + Y e ES + Y λ π s bounded above by L. Y affects the reservaton premum n two ways. As ncome rses the consumer purchases more safety and the reservaton premum for nsurance falls. Income also affects utlty through the non-monetary dmenson of a loss. Hgher ncome lowers the expected sufferng. Therefore the reservaton premum of consumer falls as ncome rses. The savngs behavor of consumers s modeled n the followng smple manner. If Y > Y n perod one the ndvdual saves a fxed proporton α ( 0, 1) of the dfference for consumpton n the next perod, otherwse savngs are zero: σ ( ) α Y Y f Y = > Y 0 otherwse mantenance of fre alarm systems, etc. And wealther people tend to lve n safer (suburban) resdental areas than poor people who lve n dangerous nner cty resdences close to busy streets. 16

17 A consumer can only chose a savngs-type product f her savngs are suffcent to afford the savngs premum,.e. f σ σ, snce loans are ether not avalable or too expensve to be used as savngs porton. Some consumers, whose savngs are just below the threshold needed for the savngs-type bundle wll fnd t optmal to save just a lttle more. Formally, the margnal beneft of rasng savngs above σ s * {[ ( π π )] π } mn,, where π s the nomnal nsurance premum on normal type polces andπ denotes the mplct lower nsurance premum rate on savngs-type polces. Margnal consumers wll then save ( Y Y) γ, γ > α and buy the savngstype product. Hence there s an ncome level ~ Y has suffcent savngs to buy the savngs-type product. > Y such that for all Y Y ~ consumer Consumers have the opton of buyng ether nsurance (Ins) or savngs contract (CD) alone, or the bundle (), or nether and spend all ncome on consumpton. The followng nequaltes determne a consumer's choce: ) π * Y > π < Y Ins * π > π ) ~ Ins, CD Y < Y < Y ) π * Y < π < Y nothng * π > π > π v) ~ Y < Y < Y CD * π > π v) ~ Y > Y, CD π < π v) CD Y > Y The resultng sortng of consumers nto the dfferent optons s llustrated n the followng dagrams, whch graph the ncome of consumers aganst ther reservaton premum. In a), some consumers who would have bought normal lne nsurance even at the hgher π swtch nto buyng the savngs-type product. These consumers le on the reservaton premum curve between ponts A and B. The pcture llustrates the relatve magntudes of the swtchng effect (between A and B) and the market expanson effect (between B and F). In dagram b), no swtches occur, and the only effect of offerng the 17

18 savngs-type bundle s to attract new consumers between the ponts C and D nto the nsurance market who would not have bought nsurance at the hgherπ. 2. The Supply Of Insurance a. Structure Insurance companes are offerng perfectly homogeneous products, are dentcal n the safety of ther operatons and undfferentated n ther dstrbuton systems. 19 MOF protects the olgopoly from entry, so that hgh underwrtng profts can persst. 20 Under these crcumstances, competton between frms s suffcently muted to analyze the ndustry as a monopoly. Insurance companes acheve a lower rate of return on ther nvestments (r INS ) than banks, because they are hampered by regulatory restrctons on nvestment possbltes. Polces contngent on the personal ncome of a customer are not feasble, ether because ncome s only partally observable (n partcular wealth), or because socety does not allow t for egaltaran reasons. By regulaton, companes have the exclusve rght to wrte nsurance polces, but can not ssue certfcates of deposts, unless bundled wth an nsurance polcy. The companes maxmze n two stages. In the frst stage, correspondng to the perod before the ntroducton of savngs-type products, the premum level for normal nsurance polces s myopcally set at the monopoly level. In the second stage the savngs-type product s desgned and premum rates for savngs-type nsurance as well as the dvdends pad on the savngs porton are determned (subject to approval by MOF). In the present smplfed settng, there s only one coverage, offerng full nsurance n the 19 A bref justfcaton of these categorcal assumptons s n order. Products are homogeneous because nsurance polces are standardzed and subject to lcensng by MOF. Insurance rates are fxed across the ndustry by the rate settng assocatons subject to MOF-approval. For the safety of operatons, see the extremely comfortable levels of solvency ratos calculated n [4]. Wth respect to dstrbuton systems, the homogenety assumpton s made for analytc convenence. 18

19 loss case, and therefore the only product desgn decson s the amount of savngs porton bundled wth the nsurance polcy. At the end of stage two, demand s realzed, and the state of nature s revealed and profts determned. b. Stage One The ndustry s unaware of the future ntroducton of savngs-type products, and sets the premum level collusvely so as to maxmze current profts: where φ 1 = expected proft at stage one, maxφ = ( π C ) Q (1) 1 π π = premum rate of the normal nsurance polcy, C = average expected cost per nsurance polcy, the sum of all expenses and the expected value of clams, and Q = quantty of polces sold. The frst order condton s the standard monopoly problem: dφ dπ dq = Q + π C dq Q dc = 0 dπ dπ dπ dq Q + π = C dq + Q dc dπ dπ dπ (2) Ths equaton mplctly defnes the proft-maxmzng premum level whch wll n the followng be referred to as π. In equaton (2) expected cost per nsurance polcy depends on the premum charged because average expected clams depend on the nsurance purchase decson of each ndvdual, and clam lkelhood vares across nsurance customers. c. Stage Two The nomnal rsk premum s dentcal for both types of products. Consumers are offered savngs contracts at the compettve CD-rate n the bankng sector, whch s lower than the rate of return on the savngs-type product. Ths leads to a dvergence of the 20 For a detaled analyss of collusve behavor n the nsurance ndustry n Japan, and the role MOF plays n mantanng the cartel, see Wallner [40]. 19

20 nomnal rsk premum π n the bundle (the same as for normal lnes, determned n stage one) and the mplct nsurance premum π n savngs-type nsurance (π <π due to the mplct cross-subsdy from the nvestment part of the bundle). Rsk prema cannot be nvested snce the nsurance company needs to hold lqud funds to dsburse the clams resultng from these prema as they occur. The ndustry problem then s to choose the savngs porton and the dvdend level so as to maxmze profts: where max ( ) ( ) ( ) σ, δ φ = π C Q + π C Q + r δ σ Q 2 φ 2 = proft at stage 2, π = the fxed net (nsurance) premum per polcy, INS (3) C = the total cost of a savngs-type polcy, the sum of all expenses and the expected value of clams, C = the total cost of a normal polcy, the sum of all expenses and the expected value of clams, Q, Q = number of savngs-type and normal polces sold, respectvely, r INS = the net rate of return whch nsurance companes acheve on ther nvestments, δ = the dvdend rate pad out to polcy holders on ther savngs portons, and σ = the savngs porton of the total premum per polcy, n Yen. Q, Q, C and C are functons of δ and σ. The frst order condtons are: d φ 2 dσ where dq dq dq dq = π + C C Q dc dc Q dσ dσ dσ dσ dσ dσ dq + ( rins δ ) Q + ( rins δ ) σ = 0 dσ (4) ( ) dq dq π + dσ dσ s the margnal premum revenue of alterng the savngs porton, 20

21 ( ) C dq dq C Q dc dc Q dσ dσ dσ dσ nsurance sde of dong so, s the margnal cost on the dq δ + δ σ dσ ( ) ( r ) Q ( r ) INS INS s the net margnal effect on the savngs sde, and dφ dq C Q dc 2 dq dc = ( π ) + ( π C ) Q dδ dδ dδ dδ dδ dq - σ Q + ( rins δ ) σ = 0 dδ (5) where dq dq (v) π + dδ dδ s the margnal nsurance premum revenue, (v) C dq Q dc dq dc + + C + Q dδ dδ dδ dδ s the margnal clam cost, and dq (v) σ Q + ( rins δ ) σ s the net margnal nvestment return. dδ d. Interpretaton Of The Frst-Order Condtons To nterpret these equatons, I refer agan to dagrams a) and b). Equaton (4) can gve rse to two dfferent cases. The frst case s shown n dagram b). The lne Y ~ ntersects the reservaton premum curve to the rght of the ncome level at whch the reservaton premum drops below π (pont E), so that there s a dscrete secton on the reservaton premum curve contanng consumers who do not purchase ether product. In ths stuaton, Q and C are not affected by changes n the sze of the savngs porton. Then term () s larger n absolute value than (), and a suffcent condton for dφ 2 0 dσ Y Y E ~ > < s that () s negatve. The latter happens f Q dq σ dq > σ,.e. 1 > = ε Q dσ Q dσ. In words, as long as the elastcty of Q wth, σ respect to σ, ε Q, σ, s less than unty or (by contnuty) not too elastc, profts wll rse f 21

22 the savngs porton n the bundle s lowered. The ncentve to decrease σ perssts as long as the lne Y ~ ntersects the reservaton premum curve to the rght of pont E. The other case s shown n dagram a). Y ~ ntersects the reservaton premum curve to the left of pont E and there are some consumers (between A and B) who would have bought normal type nsurance but swtch to the savngs-type. In ths case the margnal revenue and margnal cost terms ( and ) cancel each other (snce the nomnal nsurance premum and the expected clam value of the swtchng consumers s unaffected by the swtch), and the sgn of the effect of a change n σ on profts depends on the sgn of term ). If ε Q, σ =1 s to the left of pont E, then ~ Y wll be optmally set at the pont of untary elastcty. ε Q depends on the dstrbuton of ncome among the populaton of consumers and, σ there s nothng a pror we can say where the pont of untary elastcty falls relatve to E. However, n the followng I wll assume that everywhere to the rght of E, ε Q, σ <1. Ths assumpton, whle arbtrary, s very useful n the followng analyss. Dagram b) s then strctly excluded, and all the analyss wll relate to the case shown n a). The convenence of ths assumpton derves from the fact that t s a suffcent (but not necessary) condton for the use of equaton (2) n the analyss. Turnng next to equaton (5), n stuaton a) the margnal revenue term (v) can be rewrtten usng dq dπ dq dq = + dπ dδ dδ dδ (6) as dq dπ π = ε D Q β dπ dδ (7) where ε D = the elastcty of demand for nsurance, and β π = d dδ s a constant (at any gven level of π ) measurng how the mplct savngstype premum vares wth δ. Term (v) n equaton (5) s the margnal effect on nsurance costs as a change n δ attracts consumers wth dfferent clam probabltes to buy the product. Consder the maxmum possble bundle prce,.e. π plus the rate of return whch banks pay ther 22

23 customers on deposts, r CD (the bundle can obvously not be prced hgher, snce then consumers could purchase the components separately at a lower combned prce). The effect of margnally rasng δ above that level s to shft the lne π parallel down from π. Ths has the same effect on total expected clams as f π had been lowered n stage one. Therefore (v) can be rewrtten usng (2) as dq dπ Q + π = Q ( 1 + ε D ) β (8) dπ dδ and the sum of (v) and (v) becomes (9) ( 1 ) ε Q β Q + ε β = Q β D D The nterpretaton of ths term s as follows. In stage one π was determned by equaton (2), equatng margnal revenue wth margnal cost. In (9) margnal revenue s larger than n (2), because the nomnal premum s fxed, and the lower premum mplct n the bundle accrues only to the new savngs-type customers, n form of subsdzed return on ther savngs. The nfra-margnal buyers who change from normal type to savngs-type nsurance cause the swtchng effect, whch s contaned n (v). As long as there are some nfra-margnal buyers who are prevented from swtchng to the bundle, ntroducton of the savngs-type product may be n the nterest of the ndustry. The proftablty depends on the sgn of the dfference between (9) and (v), evaluated at Q =0: dφ2 dδ δ = rcd Q d π dq = ( rins δ ) σ dδ dδ (10) It s proftable on the margn to ntroduce the bundle by rasng δ above r CD f the followng condton holds: (11) - Q - ( r INS ) δ σ dq dπ dπ dδ > 0 23

24 dq or Q > ( rins δ ) σ dπ (12) Ceters parbus, bundlng s more lkely to be proftable on the margn the larger the sze of the market. Ths could explan why the savngs-type products were not ntroduced earler n the Japanese nsurance market. Bundlng s also more lkely to be proftable the smaller the loss margn caused by subsdzng the nvestment return, the smaller the savngs porton attached to the bundle (whch n turn s endogenously determned n equaton 4), and the smaller the swtchng effect. Equaton (12) may or may not be satsfed, and there s nothng we can say short of knowng the exact parameters of the problem and n partcular the dstrbuton of ncome n the populaton, as well as the consumers' utlty functon. If t s not proftable on the margn to ntroduce the savngs-type bundle, s t possble that t becomes proftable beyond a certan threshold level of δ? Consder what happens n equaton (5) f the frms rase δ further. dπ dδ 2 δ >> rins dq dq C Q dc dq = π σ Q + ( rins δ ) σ (13) dδ dδ dδ dδ The components on the rght-hand sde of (13) can be nterpreted as before as margnal revenue, expected clam cost, and nvestment margn. The latter ncludes σ Q, snce now Q >>0. Note that rsk averson mples π >E (L),.e. the expected clam for any consumer s strctly less than that consumer's reservaton premum. Ths n turn mples dq dq π C Q dc dq + ( rins δ ) σ > 0 (14) dδ dδ dδ dδ because the terms n (14) are nothng but π mnus the expected clam cost of the margnal customer ( ( ) π + r INS δ σ = π ). Snce for the margnal customer π = π, (14) s postve. Only f (14) s larger than σ Q, profts rse n δ and (13) s postve. σ Q s the effect of lowerngπ to all buyers of the savngs-type product, not only the margnal buyer. Ths condton hghlghts the role of the sze of the swtchng effect 24

25 (lowerng profts) relatve to the market expanson effect (rasng profts). If the swtchng effect s relatvely large, then t s never proftable to ntroduce the bundle. If the swtchng effect s only moderately large then t may be unproftable to ntroduce the bundle on the margn, but proftable beyond some threshold level of δ. If the swtchng effect s small enough t may be proftable to ntroduce the bundle at the margn. The nfra-margnal subsdes get larger as δ rses, and more people buy the savngs-type bundle. Hence even f (13) becomes postve beyond some threshold level of δ, eventually t wll turn negatve agan, settng a lower bound to the mplct nsurance premum n the savngs-type bundle. 21 e. Incentve To Oversubsdze So far, the dvdend rate pad on savngs portons s determned by the margnal cost and margnal beneft of subsdzng savngs-type products. The margnal beneft s the market expanson effect, and the underwrtng margn acheved on those new savngstype polces; the margnal costs are the subsdes to nfra-margnal savngs-type customers. There are addtonal effects of modfyng the dvdend rate. Frst, there are benefts from obtanng large amounts of savngs. 22 There are ncreasng returns to scale n nvestment management, and a company wth a larger portfolo can acheve hgher returns, by usng more sophstcated nvestment technques. One problem wth ths s that we need to come up wth an explanaton of why the frms manage ther funds themselves, nstead of contractng out (or equvalently, hrng outsde specalsts to work exclusvely for them). More plausbly, a larger volume of funds makes t possble for Japanese nsurance companes to fnd more attractve customers for ther loans, or to ncrease the cross-share holdngs n customer companes. Ths n turn, yelds a hgher 21 I have so far assumed a perfectly compettve bankng sector. For the nsurance ndustry, ths s the worst scenaro. The hgher the proft margn of banks n the depost busness, the more scope the nsurance ndustry has for lowerng the mplct nsurance premum on savngs-type products, wthout ncurrng a loss on ts nvestments. 22 To llustrate the magntude of the ncrease of total assets held by non-lfe nsurance companes n Japan, I present the followng fgures from [19] for the perod of fscal year 1975 untl 1992 (n bllon Yen): Fscal Year Assets 3,876 7,201 8,814 10,813 15,080 20,669 26,180 27,445 Savngs Type 621 1,439 2,420 3,605 6,878 10,581 13,825 14,324 25