ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *

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1 ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, Perre-Andre Chappor, Davd Cutler, Jerry Hausman, Mchael Keane, Paul Mlgrom, Mchael Orszag, Rchard Zeckhauser, two anonymous referees, and many semnar partcpants for helpful comments and to Jason Abrevaya for provdng us wth GAUSS code. We are especally grateful to the employees of the U.K. nsurance company who generously provded us wth the data used n ths paper and answered many questons about t. The Natonal Scence Foundaton and the Natonal Insttute of Agng supported ths research.

2 ABSTRACT We use a unque data set of annutes n the U.K. to test for adverse selecton. We fnd systematc relatonshps between ex-post mortalty and annuty characterstcs, such as the tmng of payments and the possblty of payments to the annutants estate. These patterns are consstent wth the presence of asymmetrc nformaton. However, we fnd no evdence of substantve mortalty dfferences by annuty sze. These results suggest that the absence of selecton on one contract dmenson does not preclude ts presence on others. Ths hghlghts the mportance of consderng detaled features of nsurance contracts when testng theoretcal models of asymmetrc nformaton. 1

3 Theoretcal research on nsurance markets has long emphaszed the potental mportance of asymmetrc nformaton and documented the negatve welfare mplcatons of adverse selecton, whch can be a consequence of asymmetrc nformaton. Yet the emprcal evdence on the mportance of asymmetrc nformaton n nsurance markets s decdedly mxed. Several recent emprcal studes have not rejected the null hypothess of symmetrc nformaton n property-casualty, lfe, and health nsurance markets. These studes nclude Cawley and Phlpson (1999), who study the U.S. lfe nsurance market, Cardon and Hendel (2001), who study the U.S. health nsurance market, and Chappor and Salane (2000), who study the French automoble nsurance market. In contrast, Cutler (2002) revews a substantal lterature that suggests the mportance of asymmetrc nformaton n health nsurance markets, and Cohen (2001) offers some evdence for adverse selecton n U.S. automoble nsurance markets. These conflctng results rase the queston of whether asymmetrc nformaton s a practcally mportant feature of nsurance markets. Ths paper tests two smple predctons of asymmetrc nformaton models usng data from the annuty market n the Unted Kngdom. The frst s that hgher rsk ndvduals self-select nto nsurance contracts that offer features that, at a gven prce, are more valuable to them than to lower rsk ndvduals. The second s that the equlbrum prcng of nsurance polces reflects varaton n the rsk pool across dfferent polces. Most emprcal research on nsurance markets has tested smlar predctons usng only one feature of the nsurance contract: the amount of payment n the event that the nsured rsk occurs. Our detaled data on annuty contracts allow us to consder adverse selecton on many dfferent contract features. Our results, lke those n several other studes, suggest lttle evdence of adverse selecton on the amount of payment n the event that the nsured rsk occurs. However, we fnd strong evdence of adverse selecton along other dmensons of the nsurance contract. Ths underscores the mportance of consderng multple features of nsurance contracts when testng for adverse selecton, snce adverse selecton may affect not only the quantty of nsurance purchased but also the form of the nsurance contract. Our results also rase the nterestng queston of why selecton can be detected on some margns but not on others. 2

4 Annuty markets present an appealng settng for studyng asymmetrc nformaton ssues. Most tests for asymmetrc nformaton cannot dstngush between adverse selecton and moral hazard, even though the welfare and publc polcy mplcatons of the two are often qute dfferent. Moral hazard seems lkely to play a smaller role n annuty markets, however, than n many other nsurance markets. Whle recept of an annuty may lead some ndvduals to devote addtonal resources to lfe-extenson, we suspect that ths s lkely to be a quanttatvely small effect. If the behavoral effects of annutes are small and the assocated moral hazard problems are lmted, testng for asymmetrc nformaton n the annuty market provdes a drect test for adverse selecton. Annuty markets are also of substantal nterest n ther own rght. Mtchell, Poterba, Warshawsky, and Brown (1999) emphasze that annutes, whch provde nsurance aganst outlvng one s resources, play a potentally mportant welfare-mprovng role for retrees. But n spte of the potental nsurance value of annuty products for households that face uncertan mortalty rsks, voluntary annuty markets n both the Unted States and the Unted Kngdom are small. Adverse selecton has often been suggested as a potental explanaton for the lmted sze of these markets, for example by Brugavn (1993) and others. Ths paper s dvded nto fve sectons. The frst descrbes the general operaton of annuty markets, wth partcular reference to the Unted Kngdom, and summarzes how the theoretcal predctons of asymmetrc nformaton models can be tested n annuty markets. Secton two descrbes the data set that we have obtaned from a large U.K. nsurance company. The thrd secton reports our fndngs on the relatonshp between mortalty patterns and annuty product choce, usng hazard models to relate annutant mortalty patterns to annuty product characterstcs. Secton four nvestgates the prcng of dfferent annuty products, usng hedonc models to confrm that annuty prcng s consstent wth our estmates of mortalty dfferences across dfferent annuty polces. The fnal secton summarzes our fndngs and consders alternatve nterpretatons of the results. 1. Background on Annutes and Testng for Asymmetrc Informaton 1.1 Annuty Market Overvew 3

5 An annuty s a contract that pays ts benefcary, the annutant, a pre-specfed amount for as long as he s alve. It thus nsures the annutant aganst the rsk of outlvng hs accumulated resources. From the nsurer s standpont, a hgh-rsk annutant s one who s lkely to lve longer than hs observable attrbutes, such as age, would otherwse suggest. Yaar (1965) documented the welfare-mprovng role of annutes for ndvduals facng uncertan mortalty. In lght of ths, the small sze of the voluntary annuty markets n the Unted States and the Unted Kngdom has puzzled many researchers. Fredman and Warshawsky (1990) and Brown et al. (2001) offer several possble explanatons, ncludng bequest motves, the prevalence of annutzed publc sector socal securty programs and prvate defned beneft pensons, and the potental need for buffer stock savngs to pay for medcal and long-term care needs. Annuty demand may also be low f the expected annuty payments for a typcal ndvdual are low relatve to the annuty s premum. Hgh admnstratve costs or nsurance company profts may make annutes expensve n ths sense. Adverse selecton may also make annutes appear expensve for a typcal ndvdual n the populaton. If the typcal annutant s longer lved than the typcal ndvdual n the populaton, and annutes are prced to reflect the longevty of annutants, then annutes wll not be actuarally far from the standpont of typcal ndvduals. Several prevous studes have reported ndrect evdence of adverse selecton n annuty markets, n contrast to the drect evdence that we present. The prcng of voluntary annutes n both the U.S. and the U.K. mples that, for a typcal ndvdual, the expected present dscounted value of payouts s only 80 to 85 percent of the annuty's ntal premum. Part of the dvergence between the expected payout and the annuty's cost s due to admnstratve loads, but roughly half appears to be due to adverse selecton. Indeed, mortalty tables for voluntary annutants n both natons suggest that lfe expectancy for a typcal 65-yearold male voluntary annutant s twenty percent longer that for a typcal 65-year-old male. 1 Whle these mortalty patterns are consstent wth adverse selecton nto the annuty market, they do not provde evdence on the relatonshp between mortalty rates and the type of annuty purchased. Ths 4

6 relatonshp between product choce and ex-post rsk experence s the central predcton of theoretcal models of nsurance markets wth asymmetrc nformaton. Our data permt what s to our knowledge the frst drect nvestgaton of ths relatonshp. It s worth notng, however, that whle we nterpret our fndngs as supportve of the presence of adverse selecton n prvate annuty markets, t s unlkely that ths adverse selecton, and the assocated hgh effectve prces for annutes, can fully explan the lmted demand for voluntary annutes. Mtchell et al. (1999) show that for lfecycle consumers wth plausble rsk averson and mortalty uncertanty and no annuty ncome, that purchasng an annuty may rase lfetme expected utlty, even f the expected present dscounted value of payouts from the annuty s no more than 75 percent of the purchase prce. The Unted Kngdom provdes a partcularly rch settng for studyng adverse selecton, snce there are two separate annuty markets. One s a compulsory annuty market n whch ndvduals who have accumulated savngs n tax-deferred retrement savng accounts are requred to annutze a large porton of ther accumulated balance. There s also a voluntary annuty market n whch ndvduals wth accumulated savngs may purchase an annuty. Adverse selecton s expected to operate dfferently n these two markets. In the voluntary market, low rsk ndvduals, those wth hgh expected mortalty, have the opton of not buyng at all. As a result, selecton on the extensve margn, between annutants and non-annutants, should be larger n the voluntary market than n the compulsory market. Fnkelsten and Poterba (2002) present evdence that adverse selecton on ths extensve margn, as measured by the average prce of annuty contracts, s roughly half as great n the compulsory market as n the voluntary market. Because low-rsk ndvduals can opt out of the voluntary market, however, the voluntary annutant populaton wll be more homogenous than the populaton n the compulsory market. Ths could lead to more adverse selecton across product types wthn the compulsory than the voluntary annuty market Testng for Adverse Selecton n the Annuty Market 1 Fnkelsten and Poterba (2002) and Murth, Orszag, and Orszag (1999) present summary nformaton and mortalty comparsons for the U.K. annuty market. Brown, Mtchell, and Poterba (2002) present related nformaton for the U.S. market. 5

7 A central shared predcton of many models of asymmetrc nformaton, summarzed n Chappor (2000) and Chappor and Salane (2000), s that when observatonally dentcal ndvduals are offered a choce from the same menu of nsurance contracts, hgher rsk ndvduals wll buy more nsurance. The ntuton s straghtforward. Snce, at a gven prce, the margnal utlty of nsurance s ncreasng n rsk type, hgher rsk ndvduals wll choose to purchase more nsurance than lower rsk ndvduals who face the same set of optons. Of course, ths predcton, and any emprcal test based on t, apples condtonal on the characterstcs of the ndvdual observed by the nsurance company and used n settng nsurance prces. Chappor (2000) provdes a survey of exstng emprcal studes that have mplemented ths test for asymmetrc nformaton. Most theoretcal models of nsurance market equlbrum nvestgate nsurance contracts that vary only n terms of prce and the amount of payout n the event of a clam. Most prevous emprcal studes, such as Chappor and Salane (2000) and Cawley and Phlpson (1999), have smlarly lmted ther focus to whether ndvduals whose nsurance wll make a greater payment n the event of a clam exhbt hgher rsk ex post. In practce, however, most nsurance contracts are mult-dmensonal, wth several dfferent features that affect the effectve quantty of nsurance provded. Our data allow us to test for self-selecton on multple polcy dmensons. We examne selecton along three features of annuty polces that affect the effectve quantty of nsurance provded. One s the ntal annual annuty payment. Ths s the analog of the payment n the event of a clam, or quantty n most stylzed theoretcal models and n prevous emprcal studes. It s straghtforward to see that the amount of nsurance s ncreasng n the ntal amount of annuty payment. The second feature s the annuty's degree of backloadng. A more backloaded annuty s one wth a payment profle that provdes a greater share of payments n later years. Most annutes are nomnal annutes, whch pay out a constant nomnal amount each perod. Wth postve expected nflaton, the expected real payment stream from such an annuty s declnng over tme. An escalatng annuty, n contrast, provdes a payment stream that rses at a pre-specfed nomnal rate n each year. Annutes escalate at a nomnal rate of anywhere from three to 8.5 percent per year n our data. Whether they offer 6

8 rsng real payouts depends on the expected rate of nflaton. There are also real annutes, whch pay out a constant real amount n each year. Ther payouts are ndexed to the prce level. The payments from real annutes and from escalatng annutes are both backloaded relatve to those from nomnal annutes. A backloaded annuty has more of ts payments n later perods than an annuty wth a flat payment profle. An annutant wth a longer lfe expectancy s more lkely to be alve n later perods when the backloaded annuty pays out more than the flat annuty. Such an annutant therefore expects to gan more, at a gven prce, from a backloaded annuty than does an annutant wth a shorter lfe expectancy. The thrd feature of annutes that we focus on s whether the annuty may make payments to the annutant's estate. Some annutes offer guarantee perods. The nsurance company contnues to make payments to the annutant's estate for the duraton of the guarantee perod even f the annutant des before the guarantee perod expres. Annutes wth guarantee perods of one to ffteen years are present n our data sample, although n the compulsory market, regulatons forbd the sale of polces wth guarantee perods of more than ten years. "Captal protecton" s another form of payment to the annutant s estate. If at the date of the annutant's death the cumulatve sum of nomnal annuty payments s less than the premum pad for the annuty, a captal-protected annuty pays the dfference to the estate as a lump sum. Payments to the estate decrease the effectve amount of nsurance n a gven annuty contract. In the extreme, for example, a ffty year guaranteed annuty purchased, by a 65 year old male, offers effectvely no nsurance. Its payments wll almost surely be the same as those from a ffty year bond. Smlarly, an annuty that pays out more n the event of an early death, ether wth a guarantee perod or wth captal protecton, s more valuable to a short-lved than to a long-lved ndvdual. All three of these features thus satsfy the sngle crossng property: at a gven prce, the margnal value of each annuty product feature vares monotoncally wth rsk type. Theoretcal models of equlbrum wth adverse selecton therefore make clear predctons about the relatve mortalty patterns of ndvduals whose annutes dffer along these features. Those who buy backloaded annutes should be longer lved, condtonal on observables, than other annutants. Smlarly, those who buy annutes that make payments to the estate should be shorter-lved, and that those who buy annutes wth larger ntal 7

9 annual payments should be longer lved, condtonal on what the nsurance company observes about the nsured, than other annutants. These selecton patterns have mplcatons for equlbrum prcng that we explot n desgnng our second set of emprcal tests. In partcular, features of the annuty that are selected by hgh rsk types should be prced more hghly than those purchased by low rsk types. Of course, f contracts are not exclusve, so nothng prevents ndvduals from purchasng multple nsurance contracts, features selected by hgh rsk types can only be prced hgher f these features cannot be replcated by purchasng a combnaton of lower prced contracts. Wth exclusve contracts, ths prcng predcton holds even f the feature s replcable wth a combnaton of lower prced features. Both backloaded and non-guaranteed annutes satsfy the nonreplcablty condton. Buyers who want a backloaded annuty cannot replcate such an annuty by buyng several less expensve nomnal annutes, and someone who wants a non-guaranteed annuty cannot create one by purchasng multple (cheaper) guaranteed polces. Smlarly, wthn the class of guaranteed contracts, an ndvdual cannot replcate a short guarantee perod by buyng several (cheaper) contracts wth longer guarantee perods. Thus wth or wthout excludablty, under asymmetrc nformaton backloaded annutes should be prced hgher to reflect the fact that n equlbrum they are purchased by ndvduals who are longer-lved than the buyers of non-backloaded annutes. Smlarly, annutes that make payments to an estate should be prced lower than those that do not, to reflect the fact that n equlbrum they are purchased by shorter-lved ndvduals. 2 Our predctons wth respect to prcng and mortalty patterns n annuty markets wth adverse selecton would not emerge f nformaton were symmetrc. 3 Consder the case of polcy backloadng. Wth symmetrc nformaton, a longer-lved annutant has no ncentve to buy an annuty wth backloaded payments. Whatever annuty he buys, the nsurance company wll adjust the prce charged to reflect hs 2 If we also assume that annutes are exclusve contracts between the nsurers and the nsured, then models of nsurance market equlbrum wth asymmetrc nformaton also predct convex prcng: the margnal prce of nsurance rses wth the sze of the ntal payment. We test ths predcton below, even though we vew the exclusvty condton as unlkely to be satsfed n annuty markets. 8

10 ndvdual mortalty prospects. Snce the prce adjusts, any preference for an annuty of a gven tlt wll be nfluenced only by dscount rates, not by mortalty prospects. In the presence of asymmetrc nformaton, however, when the annutant has prvate nformaton that he s lkely to be long-lved and he chooses to buy a partcular annuty, the prce does not adjust to account for hs mortalty prospects. 2. Data and Descrptve Statstcs Our data set conssts of nformaton on the complete set of both compulsory and voluntary mmedate annutes sold by a large U.K. annuty company over a seventeen-year perod endng on December 31, The frst year n our sample, 1981, was the frst year when the company sold both voluntary and compulsory annutes. At the end of the sample perod, the frm was among the ten largest sellers of new compulsory annutes n the Unted Kngdom. 4 We restrct our attenton to annutes that nsure a sngle lfe, as opposed to jont lfe annutes that contnue to pay out as long as one of several annutants remans alve. The mortalty patterns of the sngle nsured lves on each polcy provde a straghtforward measure of ex-post rsk type. Our sample ncludes 42,054 annuty polces. Our data set ncludes almost everythng that the nsurance company knows about ts annutants. The only nformaton that was suppressed to protect confdentalty was the annutant's address and date of brth. We dd, however, obtan nformaton on the annutants' brth month and year. We have detaled nformaton on the type of polcy purchased by the annutant, and on the annutant's day of death, f the annutant ded before December 31, The nsurance company collects very lttle nformaton only age, gender and address about annutants. In partcular, t does not collect any nformaton on the wealth, ncome, educaton, occupaton, or other ndcators of socoeconomc status, even though such factors mght be related to mortalty rsk. The nformaton collecton practces at the frm we study are typcal for 3 Recent research by Chappor et al. (2002) suggests that n some models wth symmetrc nformaton n partcular when the prce of nsurance s marked up above expected clams t mght be possble to generate these same prcng and mortalty patterns. The dscusson here assumes that prces are not marked up above expected clams. 4 Informaton on the annuty market share of varous U.K. nsurance companes may be found at 5 Sample attrton s unlkely to be a problem n a data set of nsurance company records of annutants. Snce premums are pad up front and the company must pay each annutant regularly untl the he des, annutants are unlkely to leave the sample before they de. 9

11 nsurance companes sellng annutes n the U.K. Moreover, lke other frms n the market, t vares the annuty prce based only on age and gender, and not based on the ndvdual s geographc locaton. 6 A fundamental ssue n tryng to nfer market-wde phenomena such as adverse selecton from data for a sngle frm concerns whether the frm s representatve of the ndustry as a whole. Table 1 provdes an overvew of the characterstcs of the compulsory and voluntary annutes sold by our sample frm. Our frm appears typcal of the ndustry n terms of the relatve magntude of voluntary and compulsory sales, the dfferences n the average age and gender of compulsory compared to voluntary annutants, and the product mx of annutes sold. 7 In addton, n results not reported, we fnd that the age- and genderspecfc survval probabltes for voluntary and compulsory annutants n our frm match the ndustry-wde survval patterns for these two groups of annutants reported n Insttute of Actuares (1999a, 1999b). Usng 1998 ndustry-wde prcng data from Fnkelsten and Poterba (2002), we also found that average prces for our sample frm s compulsory products n 1998 closely match the ndustry-wde averages. Our sample sze s too small to permt such comparsons n the voluntary market, where the frm sold only ten annutes n Trends n annuty sales for our sample frm mrror ndustry-wde trends reported by the Assocaton of Brtsh Insurers (varous years) n the compulsory but not the voluntary market. In the former, our sample frm shows vrtually dentcal upward trends to the ndustry as a whole n terms of new premums ssued each year and amount of annuty payments made each year. For example, both the ndustry as a whole and our sample frm experenced about a 7.5-fold ncrease n annuty payments between 1983 and Ths trend n part reflects the expanson n the late 1980s of the set of retrement savngs plans that faced compulsory annutzaton requrements. In the voluntary market, the sample frm experences the 6 The use of only a very lmted set of characterstcs n prcng annutes s somewhat puzzlng gven the large varatons n mortalty by geographc area or soco-economc status, as well as the use of much rcher nformaton n the prcng of lfe nsurance contracts n the U.K. Ths s not due to any regulatory restrctons on characterstc-based prcng n annuty markets. Indeed, two years after the end of our sample perod, the largest UK annuty company Prudental began offerng compulsory annutes whose prces vary based on the annutant s health characterstcs. Analyzng the determnants and consequences of such rcher characterstc-based prcng n annuty markets may be a frutful area for further work. 7 For the relevant ndustry-wde data see, respectvely, Assocaton of Brtsh Insurers (varous years), Banks and Emerson (1999), and Murth, Orzsag and Orszag (1999). 10

12 same basc pattern as the ndustry of a general declne n new premums and annual payments n the 1990s, although the exact tmng s not the perfect match that t s n the compulsory market. Moreover, our frm experences an abnormally hgh number of voluntary sales n 1984 and n Fortunately, our emprcal fndngs on mortalty and prcng n the voluntary market are not affected f we exclude sales n these two years. However, because about one-quarter of the voluntary polces n our data were sold n those two years, we are reluctant to generalze our fndngs from the sample frm to the voluntary market as a whole. 8 The compulsory market represents the quanttatvely more mportant market, as t s roughly ten tmes the sze of the voluntary market both for our sample frm and for the ndustry. 3. Annutant Mortalty and Annuty Product Choce 3.1 A Hazard Model Framework for Studyng Annutant Mortalty We estmate mortalty dfferences among dfferent groups of annutants usng the dscrete-tme, sem-parametrc, proportonal hazard model used by Meyer (1990) and Han and Hausman (1990). Our duraton measure s the length of tme the annutant lves after purchasng an annuty. We let λ t, x, β, λ ) ( 0 denote the hazard functon, the probablty that an annutant wth characterstcs x des t perods after purchasng the annuty, condtonal on lvng untl t. The proportonal hazard model assumes that λ t, x, β, λ ) can be decomposed nto a baselne hazard λ ( ) and a shft factor φ( x, β ) as follows: 0 t (1) λ t, x, β, λ ) = φ( x, β ) λ ( ). ( 0 0 t ( 0 The baselne hazard, λ ( ), s the hazard when φ ( ) =1. φ ( ) represents the proportonal shft n the 0 t hazard caused by the vector of explanatory varables x wth unknown coeffcents β. We restrct the effects of the explanatory varables ( x ) to be duraton-ndependent. We adopt one of the common functonal forms for φ ( ), φ( x ; β ) = exp( x β ). The proportonal hazard model s then wrtten as: 8 An earler verson of the paper avalable on request provdes more detaled data comparng our sample frm wth the 11

13 (2) λ t, x, β, λ ) = exp( x β ) λ ( ). ( 0 0 t We model the baselne hazard λ ( ) non-parametrcally as a step functon. Ths allows us to avod 0 t mposng any restrctve functonal form assumptons. We have seventeen years of data and we allow for seventeen, annual, dscrete, tme perods. If we let δ = λ ( s ds denote the ntegrated baselne hazard, the proportonal hazard model n (2) becomes: t t 0 0 ) (3) λ t ; x, β, δ ) 1 exp{exp( x β )( δ δ )}. ( = t t + 1 Models n whch the hazard functon s gven by (3) can be estmated by maxmum lkelhood wth the log lkelhood functon gven by n (4) ln( L) = (1 c ) ln( λ ( t ; x, β, α)) λ( s ; x, β, α) ds = 1 0 where c s an ndcator varable that equals 1 f ndvdual survves untl the end of our sample perod and 0 otherwse. Eghty-four percent of the compulsory annutants and 47 percent of the voluntary annutants n our data set survved untl the end of our sample. We estmate hazard models for annutant deaths as a functon of all of the known characterstcs of the annutants and ther annuty polces. We estmate separate models for annutants n the voluntary and compulsory markets. In all of the hazard models we nclude ndcator varables for the age at purchase of the annuty (n fve-year ntervals), the year of purchase of the annuty, and the gender of the annutant. We also nclude ndcator varables for the frequency of annuty payments. Our man covarates of nterest are three annuty polcy characterstcs: the degree of backloadng, the presence of payments to the estate, and the ntal annual annuty payment. Under the null hypothess that there s symmetrc nformaton n the annuty market, the coeffcents on these varables wll be zero. Our key emprcal test focuses on whether these covarates have non-zero coeffcents, and whether ther sgn s that predcted by asymmetrc nformaton theory. t ndustry at large. 12

14 We nclude two ndcator varables to capture the degree of annuty backloadng. One s an ndcator for whether payments are ndexed to nflaton, and the other s an ndcator for whether payments are escalatng n nomnal terms. Nomnal annutes are the omtted category. The asymmetrc nformaton theory descrbed above suggests that ndvduals who buy ndex-lnked or escalatng annutes should be longer -lved than those who buy nomnal annutes. They should therefore have a lower hazard and so the predcted coeffcents on the ndcator varables for ndex-lnked and for escalatng n the hazard model are negatve. We cannot predct the relatve magntude of these two coeffcents, snce the relatve amount of backloadng n an escalatng and ndexed annuty depends on the degree of escalaton and the rate of expected nflaton. We also nclude two ndcator varables to capture payments to the estate. One s for whether the annuty s guaranteed, and the other s for whether the annuty s captal protected. An annuty cannot be both guaranteed and captal protected. The omtted category ncludes annutes that do not make any payments to the estate. The asymmetrc nformaton theory descrbed above predcts that ndvduals who buy annutes wth more payments to the estate wll be shorter-lved (.e. have a hgher hazard rate) than those who buy annutes that do not make any such payments. The predcted coeffcents on the ndcator varables for "guaranteed" and "captal protected" n the hazard model are therefore postve. The theoretcal models do not offer a predcton concernng the relatve longevty of guaranteed and captal protected annutants, as there s no clear measure of whch s relatvely more attractve to someone wth mortalty that dverges from the populaton average. Fnally, we nclude one other annuty product characterstc that satsfes the sngle crossng property and along whch we mght therefore observe self-selecton: the ntal annual annuty payment. Ths varable corresponds to the amount that would be pad out n lfe nsurance n the event of death or the amount that would be pad out from an automoble nsurance polcy n the event of an accdent. The asymmetrc nformaton theory descrbed above predcts that ndvduals who wll receve greater payments n the event of a clam wll be longer lved than those who face smaller payments. The predcted coeffcent on the payment varable n the hazard model s therefore negatve. 13

15 3.2 Basc Results on Annuty Choce and Mortalty Patterns Table 2 presents estmates of the hazard model n equaton (3). The frst two columns report our core hazard model estmates for the compulsory and voluntary markets, respectvely. The results closely match our theoretcal predctons of self-selecton under asymmetrc nformaton. To ascertan whether our mortalty estmates are senstve to the hazard model framework, we also estmated smple lnear probablty models of whether annutants who bought annutes at least fve years before the end of our sample perod ded wthn the frst fve years after ther purchase. The results, whch are reported n the thrd and fourth columns of Table 2, show the same mortalty patterns across products as the hazard models. Gven the smlarty of the fndngs, our dscusson of the fndngs focuses on the hazard model specfcatons n the frst two columns. Fnkelsten and Poterba (2000) descrbe the robustness of the fndngs n Table 2 to a number of other alternatve specfcatons. In both the compulsory and the voluntary market, there s strong evdence that ndvduals who buy more backloaded annutes are longer-lved. The coeffcents on ndcator varables for ndex-lnked and escalatng annutes are negatve and statstcally sgnfcant at the 1% level n both markets. These fndngs suggest that all else equal, ndvduals who buy these annutes have a lower mortalty hazard rate than ndvduals who buy level nomnal annutes. There s also evdence that voluntary annutants who buy annutes that make payments to the estate are shorter lved than annutants whose annutes do not make such payments. The coeffcent on the ndcator varable for guaranteed payouts s postve. Indvduals who buy guaranteed annutes have hgher hazards, and hence are shorter-lved, than observatonally smlar ndvduals who buy non-guaranteed, non-captal protected annutes. Ths coeffcent s statstcally sgnfcantly dfferent from zero. Addtonally, the coeffcent on the ndcator varable for a captal-protected annuty has the expected postve sgn, although t s not statstcally sgnfcantly dfferent from zero. The postve sgn ndcates that ndvduals who buy these annutes are shorter lved than observatonally smlar ndvduals who buy non-guaranteed, non-captal protected annutes. 14

16 In the compulsory market, although the results suggest that ndvduals who buy guaranteed annutes are shorter lved than ndvduals who buy non-guaranteed annutes, we are unable to reject the null hypothess of no dfference at standard statstcal confdence levels. However, n the compulsory market there s suffcent sample sze to allow us to look separately at hazard rates by length of guarantee perod. Of the 28,424 annutants n the compulsory market who purchased guaranteed annutes, 24,173 purchased fve year guaranteed annutes, and 4,150 purchased ten year guaranteed annutes. The remander, less than one half of one percent of the annutants, purchased guarantees of other lengths. In results not reported here, we fnd that although guaranteed annutants as a group are not sgnfcantly shorter lved than non-guaranteed annutants, annutants wth ten year guarantee perods, the longest n the compulsory market, are sgnfcantly shorter lved than annutants wth non-guaranteed annutes. We also fnd that the hazard ncreases monotoncally from no guarantee perod to fve years to ten years and that the mortalty dfferences between ndvduals wth fve- and ten-year guarantee perods are also statstcally sgnfcantly dfferent from each other. These results are consstent wth models of adverse selecton. 9 Table 2 also provdes evdence that n the compulsory market, but not n the voluntary market, annutants wth a hgher ntal annual payment are longer lved than annutants wth a lower ntal annual payment. The result n the compulsory market s consstent wth adverse selecton. These results are broadly consstent wth market-wde data on the relatonshp between the sze of the annuty and the mortalty of the annutant. For example, the Insttute of Actuares (1999a, 1999b) reports that those who buy larger compulsory annuty polces tend to lve longer than those who buy smaller polces, but that no such relatonshp s dscernable n the voluntary market. Ths may be because voluntary annutants are drawn to a substantal extent from the hghest wealth strata of the populaton, and that the varaton n mortalty rates by wealth wthn ths group s lmted. The fndngs of statstcally sgnfcant mortalty dfferences assocated wth backloaded and guaranteed annutes allow us to reject the null hypothess of symmetrc nformaton. In rejectng the null, 9 Small sample szes preclude us from testng smlar predctons for selecton by degree of backloadng or by amount of escalaton for escalatng annutes n the compulsory market, or for selecton by length of guarantee perod or 15

17 we reject the hypothess that these annuty polcy characterstcs are uncorrelated wth unobservable predctors of the ndvdual s mortalty. Indeed, our results suggest that there are unobserved aspects of the ndvdual s mortalty rsk that are correlated wth the ndvdual s choce of annuty contract. Snce ndcator varables for varous aspects of ths choce are the explanatory varables n our hazard models, the correlaton between these varables and the unobserved mortalty heterogenety makes t mpossble to gve a causal or structural nterpretaton to the coeffcents on these covarates. It may nevertheless be of nterest to comment on the relatve magntude of dfferent coeffcents. These relatve magntudes ndcate the degree of correlaton between partcular contract choces and the unobserved mortalty heterogenety, rather than the causal mpact of specfc contracts choces on subsequent mortalty experence. The coeffcents suggest substantal mortalty selecton based on annuty backloadng, some mortalty selecton based on payments to the estate, and very lttle f any selecton based on the ntal annual annuty payment. For example, n both the voluntary and the compulsory market, the coeffcent estmates ndcate that the mortalty dfferences between backloaded and nonbackloaded annutants are larger than the mortalty dfferences between male and female annutants. Mortalty dfferences between guaranteed and non-guaranteed annutants n the voluntary market are only slghtly smaller than mortalty dfferences between male and female annutants n the voluntary market. In contrast, t should be emphaszed that n both the voluntary and the compulsory annuty markets, the estmated mortalty dfferences across annutants wth dfferent amounts of ntal annual payment are small both n absolute terms and compared to the magntude of the effect of other annuty features on mortalty. For example, n the compulsory market, a standard devaton ncrease n the amount of the ntal annuty payment s assocated wth only a fve percent decrease n the mortalty hazard. The dfference between beng male or female, by comparson, s assocated wth a 64 percent shft n the mortalty hazard. In the compulsory market, our fndngs support selecton on the annuty payment n the drecton predcted by asymmetrc nformaton theory, but the coeffcent estmate suggests that the mortalty dfferences are amount of escalaton n the voluntary market. 16

18 not substantvely mportant. In the voluntary market, the selecton on the annuty payment has the opposte sgn than that predcted by asymmetrc nformaton theory, and agan s substantvely trval. These fndngs of lttle, f any, selecton on the ntal annuty payment are consstent wth results obtaned by Cawley and Phlpson (1999) for lfe nsurance and by Chappor and Salane (2000) for auto nsurance. Each of these papers examnes only one potental characterstc of the nsurance contract along whch selecton can occur. In the frst study t s the amount pad n the event of death, and n the second t s whether the ndvdual has more than the legally-requred mnmum level of nsurance. Both of these varables are smlar to the ntal annual payment n the annuty context. Whle our results, lke those n the other studes, suggest lttle selecton on ths varable, they suggest substantal screenng on other margns of nsurance polcy choce. The fndng of lttle selecton on the annuty payment s partcularly surprsng because f hgher wealth households are nclned to purchase larger annutes and f lfe expectancy s an ncreasng functon of wealth, ths alone should generate a negatve correlaton between the sze of the annuty payment and the mortalty hazard. 4. Prcng Dfferences across Annuty Products The foregong results suggest relatonshps between annuty product characterstcs and annutant mortalty. We now consder the relatonshp between these characterstcs and annuty prces. If annutants self-select among nsurance products on the bass of prvate mortalty nformaton, then equlbrum prces on dfferent annuty features should adjust to reflect feature-specfc average mortalty. 4.1 Calculatng Annuty Prces and the "Money's Worth" Concept The effectve prce of an annuty s the dfferental between the premum pad to purchase the annuty, and the expected present dscounted value of annuty payouts. The prce s therefore one mnus the annuty s money s worth, whch earler studes such as Mtchell, et al. (1999) have defned as the expected present dscounted value of annuty payouts dvded by the ntal premum. We compute the expected present dscounted value of future payouts usng the mortalty rates that apply to a typcal ndvdual n the populaton. The money s worth for an actuarally far annuty s unty, and t has an effectve prce of zero. Money s worth values may be less than one, and effectve prces may be postve, 17

19 when there are admnstratve costs assocated wth the annuty polcy, or f the nsurer prces the polcy to reflect lower mortalty rates among the ndvduals buyng the annuty than among the populaton at large. If the ndvduals who buy annuty product j are, on average, longer-lved than ndvduals who buy annuty product k, and f an nsurance company s costs and markup are the same across products, then a gven premum should n equlbrum purchase a lower payment stream for product j than for product k. From the standpont of an ndvdual facng a gven mortalty table, product j should have a lower expected present dscounted value of payments, and hence a hgher prce, than product k. The money s worth of a nomnal, non-guaranteed annuty can be computed as: (5) MW NOM T t t 1Π j = = = A *S t 1(1 + j). P In ths expresson, A denotes the per-perod payment from the nomnal annuty, P denotes the ntal premum payment, S t denotes the probablty that the annutant survves untl payment perod t, and j denotes the expected nomnal short-term nterest rate at tme perod j. The above formula s easly adjusted, as n Fnkelsten and Poterba (2002), for the case of ndex-lnked or escalatng annutes, and for annutes that make payments to the annutant's estate. In our calculatons for nflaton-ndexed annutes, we use data on the expected rate of nflaton, as reported by the Bank of England, on the day of annuty purchase. We calculate the money's worth value for each annuty n our data set usng a common mortalty table, the U.K. populaton cohort mortalty table provded by the Government Actuares' Department (GAD). Ths mortalty table provdes current and projected future mortalty rates by age and sex, and we use the relevant rates for each annutant n our data set. In each case, we use mortalty tables from the year n whch the annuty was purchased. For example, for a 65-year-old male who purchased an annuty n 1985, we use the GAD s 1985 mortalty table; ths table ncludes projectons for future mortalty rates for 65-year-olds n that year. In practce, these projectons have turned out to be reasonable. For example, a 65 year old man n 1985 was projected to have a 7.8 percent mortalty rate n 1998 (when he would be 78); n 18

20 practce, n 1998, the mortalty rate for 78 year old males was 7.5 percent. More generally, the rato of actual mortalty n 1998 to projected mortalty n 1985 for men and women who were 65 and 75 n 1985 ranged from 0.96 to Other studes, such as the Insttute of Actuares (1999a), more generally support the accuracy of hstorcal projectons of future mortalty rates. To dscount future annuty payouts, we would deally lke to use dscount rates that correspond to the assets n the nsurer s nvestment portfolo. At the end of our sample perod, roughly three quarters of our sample frm s annuty assets were held n nomnal government bonds, wth one quarter n corporate bonds. We therefore make two alternatve dscount rate assumptons. Frst, we use the zero-coupon yeld curve of nomnal U.K. Treasury securtes on the day of annuty purchase to measure the term structure of nomnal nterest rates. In addton to ths term structure for rskless nterest rates, we also construct an mputed term structure of nterest rates for more-rsky corporate bonds. Ths s dffcult n the frst part of our sample, because there was very lttle ssuance of new corporate bonds n the U.K. durng the 1980s. In 1993, however, Morgan Stanley Captal Internatonal began computng the yeld on a Eurosterlng Credt Index. Ths corresponds to a portfolo of corporate bonds, roughly sxty percent of whch are ssued by U.K. companes, all wth a ratng of at least BBB. Each month between 1993 and 1998, we compute the average dfference between the yeld on the MSCI bond ndex, and that on U.K. government bonds, for sx maturtes along the term structure. We then average the dfferences to construct an average maturty-specfc rsk premum for corporate bonds. We then add ths constant corporate rsk premum to our daly yelds for comparable-maturty U.K. government bonds for the whole perod. Ths provdes an estmate of the corporate bond yeld that we can use for dscountng. Mtchell et al. (1999) used a smlar approach n dscountng the payment streams for U.S. annutes. To explore how annuty prces are related to product characterstcs, we estmate regresson models that relate the effectve prce of the annuty to the characterstcs of the annuty and the annutant. The hedonc prcng equaton, whch we estmate by ordnary least squares, s: (6) PRICE = α + β INDEX + β + β 5 PAYMENT 1 + β 6 2 PAYMENT ESCALATING 2 + β 7 X + ε + β 3 GUARANTEED + β 4 CAPITAL 19

21 X ncludes the age of the annutant at tme of purchase (n fve year groupngs), the gender of the annutant, the year of purchase, and a seres of ndcator varables for the frequency of the annuty payments. Recall that we measure PRICE by 1 Money s Worth (MW). Equlbrum requres that the prces of varous annuty product features are affected by the selecton behavor of dfferent mortalty types. We therefore expect a postve coeffcent on an ndcator varable for whether the annuty s ndex-lnked and on an ndcator for whether the annuty s escalatng. Because we found the mortalty of the annutants who buy these products to be lower than that of nomnal annutants, we expect that the annual payments offered on these products wll be lower than those for nomnal annutes. As a result of the lower annual payments, the money s worth calculated usng a common mortalty table wll be lower, and the effectve prce of the annuty wll be hgher, for escalatng or ndexed products than for nomnal ones. Smlarly, we expect a negatve coeffcent on ndcator varables for whether the annuty s guaranteed or captal protected. The prcng predctons descrbed n the last paragraph hold whether or not nsurance companes can enforce exclusve contracts. If exclusve contracts can be enforced, however, then the models also predct a rsng margnal prce of the amount of ntal annuty payment (β 6 > 0). We can test the exclusvty of annuty contracts, ndrectly, by studyng the coeffcents on the varables measurng the amount of the ntal annuty payment. 4.2 Emprcal Fndngs Table 3 reports summary statstcs on the dstrbuton of the effectve annuty prce varable n both the voluntary and the compulsory markets, calculated usng the two dfferent term structures. As expected, effectve prces are always hgher when we use our estmate of the term structure for corporate nterest rates, rather than government nterest rates. As dscussed above, the average effectve prces that our sample frm charges n the compulsory market are close to those for the ndustry at large. The effectve prce s negatve for roughly one quarter of the transactons n the voluntary market; ths corresponds to money s worth values of greater than unty. These low and ostensbly unproftable prces may explan the abnormally hgh volume the sample frm experenced n the voluntary market n the 20

22 early years of the data, as well as ts subsequent dramatc declne. Ths agan ponts to cauton n usng the evdence from the frm s voluntary market to test for adverse selecton n the market as a whole. In the compulsory market, by contrast, only about fve percent of effectve prces are computed to be negatve. Negatve effectve prces may be generated by dscrete prce changes on the part of the frm. If nomnal nterest rates are fallng, and the frm adjusts prces nfrequently whle we value annuty products usng nterest rates that apply to the date of purchase, t s possble for the money s worth of the annuty to exceed unty, and for the effectve prce to correspondngly be negatve. Table 4 reports the hedonc regresson results, whch are generally supportve of the prcng patterns predcted under asymmetrc nformaton. We report separate results when prce s estmated usng the government and corporate borrowng rate term structures. The estmated coeffcents on the ndcator varables for guaranteed and captal protected annutes ndcate that annutes that make payments to the estate have sgnfcantly lower prces n both markets than do annutes that do not make such payments. Ths s consstent wth the hazard model results that suggest that annutants who purchase annutes that make payments to the estate are shorter lved than annutants who purchase annutes wthout such provsons. In results not reported here, we also found that ten-year guaranteed annutes n the compulsory market are prced sgnfcantly lower than fve-year guaranteed products, whch s consstent wth the selecton results n the compulsory market, by length of guarantee perod, reported above. The results for backloadng are smlarly supportve of asymmetrc nformaton models. Indexlnked annutes are prced sgnfcantly hgher than nomnal annutes n both the compulsory and voluntary market, reflectng the fact that the typcal annutant who purchases an ndex-lnked annuty s longer lved than the typcal annutant who purchases a nomnal annuty. In the compulsory market, there s also evdence that escalatng annutes have hgher prces than nomnal annutes. The general pattern of a hgher prce for backloaded annutes, and a lower prce for annutes that make payments to the estate, at our sample frm matches our theoretcal predctons as well as average prcng dfferences across products at all frms descrbed n Fnkelsten and Poterba (2002). The correspondence between our frm-specfc prcng patterns and the ndustry-wde prcng patterns provdes 21

23 further reassurance that our fndngs speak to an ndustry-wde adverse selecton phenomenon, and are not an dosyncratc feature of our frm. The hedonc prcng equatons also nclude the amount of the ntal annuty payment. The negatve coeffcents on ths varable n both markets are ndcatve of bulk dscounts smlar to those found by Cawley and Phlpson (1999) n the U.S. lfe nsurance market. The postve coeffcent on the square of the ntal annual payment s consstent wth Rothschld and Stgltz (1976) predcton of a hgher margnal prce for larger quanttes of nsurance. However, ths coeffcent s substantvely unmportant, so there s lttle evdence of convexty n prcng. Indeed, a graph of the estmated prce-payment schedule looks vrtually lnear n both the compulsory and the voluntary market. Chappor and Salane (2000) and Chappor (2000) note the dffculty of estmatng a frm s prcng polcy. Fxed costs and economes of scale and scope can ntroduce non-lneartes, and such nonlneartes can be dffcult to dstngush from the predctons of models of asymmetrc nformaton. Fortunately, n addton to the hedonc prcng relatonshp estmated above, we have drect nformaton on the sample frm's prcng polces. We were told that the frm prces annutes, wthn a gven class (such as guarantee perod, tlt, frequency of payment, gender and age) and n both markets, as follows. If a 10,000 purchase prce buys an annual payment of A, then a purchase prce of P buys an annual annuty payment of (P*A)/10,000+([P-10,000]*f)/10,000) where f s the fxed polcy fee. The fxed polcy fee (f) was 18 at the end of the sample perod. Ths formula ndcates the presence of bulk dscounts for polces of less than 10,000 and t ndcates a constant margnal prce. Our estmates from the hedonc regresson models suggest a very small bulk dscount and essentally lnear prcng wth respect to ncreases n annual payments. The consstency between these results, and the actual prcng polcy, provdes a check on the basc estmaton strategy that underles our hedonc regressons. The constant margnal prce also supports the assumpton, common n the annuty lterature, that such products are non-exclusve contracts. 5. Concluson and Dscusson We have used a unque data set consstng of annutants at a large U.K. nsurance company to nvestgate whether mortalty and prcng patterns across annuty products are consstent wth models of 22

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