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 Revsed May 2003 ABSTRACT In ths paper, we nvestgate the mportance of adverse selecton n nsurance markets. We use a unque data set, consstng of all annuty polces sold by a large U.K. nsurance company snce the early 1980s, to analyze mortalty dfferences among ndvduals who purchased dfferent types of polces. We fnd systematc relatonshps between ex-post mortalty and annuty polcy characterstcs, such as whether the annuty wll make payments to the estate n the event of an untmely death and whether the payments from the annuty rse over tme. These mortalty patterns are consstent wth the presence of asymmetrc nformaton n the annuty market. We fnd no evdence of substantve mortalty dfferences, however, across annutes of dfferent sze, even though models of nsurance market equlbrum wth asymmetrc nformaton would predct such dfferences. We also fnd that the prcng of varous features of annuty contracts s consstent wth the self-selecton patterns we fnd n mortalty rates. Our results therefore suggest that selecton may occur across many specfc features of nsurance contracts and that the absence of selecton on one contract dmenson does not preclude ts presence on others. Ths hghlghts the mportance of consderng the detaled features of nsurance contracts when testng theoretcal models of asymmetrc nformaton. We are grateful to Jeffrey Brown, Perre-Andre Chappor, Davd Cutler, Jerry Hausman, Paul Mlgrom, Mchael Orszag, Rchard Zeckhauser, an anonymous referee, and many semnar partcpants for helpful suggestons, 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 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 one of the consequences of asymmetrc nformaton. Yet the emprcal evdence of asymmetrc nformaton n nsurance markets s decdedly mxed. Several recent emprcal studes have faled to fnd evdence of asymmetrc 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 fnds evdence n support 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. Such self-selecton across polces by rsk type would not occur f the nsurer and the nsured had symmetrc nformaton. 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. Lke several recent studes, we do not fnd substantve evdence of adverse selecton on the amount of payment n the event that the nsured rsk occurs. However, we fnd strong evdence of substantal adverse selecton along other dmensons of the nsurance contract. Our fndngs therefore suggest 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 1

3 contract. Our results also rase the nterestng queston of why t seems possble to detect selecton on some margns but not on others. Annuty markets present a partcularly 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 lfeextenson, 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. 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. 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 annuty features. The fnal secton summarzes our fndngs and consders whether they can be explaned by factors other than adverse selecton. 1. Background on Annutes and Annuty Markets 1.1 Annuty Market Overvew 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 2

4 market 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. Whle we present drect evdence of adverse selecton n annuty markets, several prevous studes have provded ndrect evdence on ths ssue. 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 the U.S. and the U.K. suggest that lfe expectancy for a typcal 65-year-old 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. We are not aware of any publshed mortalty tables that dstngush annutants by the type of polcy that they purchase, even though ths relatonshp s the central predcton of models of nsurance markets wth asymmetrc nformaton. Our data permt a 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 3

5 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, even f the effectve prce of an annuty s 25 percent whch s hgher than the 15 to 20 percent prces estmated n voluntary annuty markets n the U.S. and U.K. purchasng an annuty may rase lfetme expected utlty. The Unted Kngdom's annuty market provdes a partcularly rch settng for studyng adverse selecton. There are effectvely two annuty markets n the U.K. One s a compulsory annuty market n whch ndvduals who have accumulated savngs n tax-preferred 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 use these assets to purchase an annuty. Adverse selecton s expected to operate dfferently n these two markets. In the voluntary market, low rsk people have the opton of not buyng at all. As a result, selecton on the extensve margn (.e. between annutants and nonannutants) should be larger n the voluntary market than n the compulsory market. 2 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. A wde varety of annuty products are sold n both the compulsory and voluntary annuty markets n the U.K., whch suggests scope for selecton among annuty products n both markets. We focus our analyss on annutes that offer a pre-determned payment stream. We also lmt our analyss 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. We pay partcular attenton to 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. A second s the annuty's degree of 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. 4

6 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. In a world 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 3% to 8.5% n our data. Whether they offer rsng real payouts depends on the expected rate of nflaton. There are also real (.e. nflaton-ndexed) annutes, whch pay out a constant real amount n each year. The payments from real annutes and from escalatng annutes are both backloaded relatve to those from nomnal annutes. We therefore refer to escalatng and ndex-lnked annutes as backloaded annutes. A 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. Annutes that make payments to the estate offer less nsurance than ones that do not. An extreme example makes ths clear: a 50 year guaranteed annuty purchased, by a 65 year old male, offers effectvely no nsurance. Its payments wll be the same as that of a 50 year bond, snce ths ndvdual s almost certan to be dead by age Testng for Asymmetrc Informaton n the Annuty Market Our emprcal work explores whether the annutants who choose dfferent annuty features dffer n ther mortalty experence and whether the prcng of these dfferent features reflects any selecton-based 2 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. 5

7 mortalty dfferences across annutes wth dfferent features. Models of asymmetrc nformaton n nsurance markets, such as those dscussed n Chappor (2000) and Chappor and Salane (2000), predct that annuty features that ncrease the effectve amount of nsurance provded should be selected by hgher rsk ndvduals. It s straghtforward to see that the amount of nsurance s ncreasng n the ntal amount of annuty payment. In addton, backloadng ncreases the effectve amount of nsurance and payments to the estate decrease the effectve amount of nsurance n a gven annuty contract. 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. Smlarly, an annuty that pays out more n the event of an early death, ether wth a guarantee perod or wth captal protecton, s of greater value to an ndvdual who s shorter lved than to one who s longer lved. These features thus satsfy the sngle crossng property: at a gven prce, the margnal value of the varous annuty product features vares monotoncally wth rsk type. Theoretcal models of equlbrum wth adverse selecton make several predctons about the relatve mortalty patterns of dfferent annutants. Those who buy more backloaded annutes should be longer lved, condtonal on observables, than those who buy less backloaded polces. Smlarly, those who buy annutes that make payments to the estate should be shorter-lved, and that those who buy annutes wth larger ntal annual payments should be longer lved, condtonal on what the nsurance company observes about the nsured, than other annutants. The theoretcal models also make predctons wth respect to the prcng of annuty contracts. Wth non-exclusve contracts, features of the annuty that are selected by hgh rsk types should be prced correspondngly hgher than those purchased by low rsk types. Ths presumes that 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 6

8 backloaded and non-guaranteed annutes satsfy the non-replcablty condton. Buyers who want a backloaded annuty cannot replcate such an annuty buy buyng several (cheaper) mmedate nomnal annutes, and someone who wants a guaranteed annuty cannot create one by purchasng multple nonguaranteed 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. Annutes wth longer guarantee perods should be prced even lower than those wth shorter guarantees. 3 Our predctons wth respect to prcng and mortalty patterns n annuty markets wth adverse selecton would not obtan n a settng wth symmetrc nformaton. Consder the case of the degree of backloadng of the annuty. 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 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 s not fully adjusted to take account of hs mortalty prospects. We test for asymmetrc nformaton n the annuty market by consderng both mortalty patterns and annuty prces. Whle n practce, unlke n the stylzed models, ndvduals dffer on dmensons other than smply ther rsk type, ths does not pose a problem for the nterpretaton of our emprcal analyss, provded our data set ncludes (as t does) all of the nformaton that the nsurance company uses n settng 3 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. 7

9 prces. If product choce s drven not by prvate nformaton about mortalty but rather by prvate nformaton on preference parameters such as dscount rates, rsk averson, or bequest motves whch are correlated wth mortalty, the ultmate effect s the same as that of prvate mortalty nformaton. Anythng that s correlated wth mortalty and s known by the ndvdual but not to the nsurance company, such as household wealth, even f the ndvdual does not recognze ts effect on hs mortalty, operates just lke asymmetrc mortalty nformaton. For example, hgher wealth annutants are lkely to face lower mortalty rsks, but nsurance companes cannot observe the total wealth of ther annuty buyers. Whle nsurers could n prncple try to obtan nformaton on the wealth of potental annutants, they do not, and wealth-related dfferences n mortalty are therefore lke other sources of mortalty dfference that are known to the buyer but not the nsurer. Smlarly, an annuty that makes payments to the estate may be partcularly valued by ndvduals wth strong bequest motves or a desre to make sure a survvng spouse receves adequate ncome. If these attrbutes are postvely related to mortalty rsk, they wll have the same effect on the market equlbrum as prvate nformaton about mortalty rsk. 2. Data and Descrptve Statstcs 2.1 Overvew of Data from the Sample Frm 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 U.K. sellers of new compulsory annutes. 4 Our data set ncludes almost everythng that the nsurance company knows about ts annutants. The only peces of nformaton that were suppressed to protect confdentalty were 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 4 Informaton on the annuty market share of varous U.K. nsurance companes may be found at 8

10 the annutant ded before December 31, The nsurance company collects very lttle nformaton only age, gender and address about the personal characterstcs of annutants. In partcular, t does not collect any nformaton on the annutants wealth, ncome, educaton, occupaton, or another other ndcators of socoeconomc status. The nformaton collecton practces at the frm we study are typcal for 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 We restrct our attenton to sngle lfe annutes, because the mortalty patterns of the sngle nsured lves on each polcy provde a straghtforward measure of ex-post rsk type. Our fnal sample sze s 42,054 annuty polces. Table 1 provdes an overvew of the characterstcs of the compulsory and voluntary annutes sold by our sample frm. The voluntary market accounts for about one tenth of the polces n our sample, and for a somewhat hgher fracton of premums. The relatve magntudes of the voluntary and compulsory market sales for our sample company are smlar to those reported by the Assocaton of Brtsh Insurers for the aggregate U.K. market. Dfferences between voluntary and compulsory annutants n our data sample also appear typcal of the U.K. market as a whole. Table 2 shows that voluntary annutants are substantally older, and more lkely to be female, than compulsory annutants. Ths s consstent wth Banks and Emmerson s (1999) tabulatons from the Famly Resources Survey. The product mx of annutes sold by our sample frm also matches the lmted aggregate data that exst on the product mx for the U.K. market as a whole. Index-lnked and escalatng products together make up less than 10 percent of the voluntary or the compulsory market, wth ndex-lnked polces less than 5 percent n each market. Murth, Orzsag, and Orszag (1999) report a smlar preponderance of nomnal annutes n a data set that ncludes all nsurance companes sellng annutes n the Unted Kngdom. 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. 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. 9

11 The modal polcy n the compulsory annuty market for 1997 and 1998, when compulsory annuty sales peaked for our sample frm, was a nomnal annuty wth a fve-year guarantee perod sold to a 65- year-old man. In the voluntary market, the modal polcy n 1984 and 1985, whch together account for more than one quarter of the voluntary annuty sales n the sample, was a nomnal annuty wth no guarantee, sold to a 74-year-old woman. 2.2 Is Our Sample Frm Representatve? The foregong dscusson suggests that our frm s typcal of the nsurance ndustry n terms of the nformaton about consumers that t uses n prcng annutes. In addton, the demographc characterstcs and product choces of voluntary and compulsory annutants n the frm appears representatve of ndustrywde patterns. We also examned whether average prces and mortalty for the frm s voluntary and compulsory products matched ndustry-wde aggregates. Our estmates of average mortalty patterns n the frm closely match ndustry-wde actuaral data. For example, we estmate, usng the survval rate of annutants at the frm, that a male aged 61 to 65 who purchased a compulsory annuty n 1992 would have a 92 percent chance of survvng at least fve years. Ths compares to a 90% fve-year survval probablty n the ndustry as a whole for a 65 year old male who purchased a compulsory annuty n In the voluntary market, our estmates for the frm suggest that a female aged 76 to 80 who purchased an annuty n 1992 would have a 75 percent chance of survvng at least fve more years; ndustry-wde data suggest a 74 percent survval probablty for an 80 year old female purchasng a voluntary annuty n Average prces for the sample frm s products n the compulsory market also closely match avalable data on ndustry-wde prces. As we explan below, we measure prce as the dfference between the expected present dscounted value of annuty payouts, and the purchase prce of the annuty, scaled as a percentage of the ntal purchase prce. Fnkelsten and Poterba (2002) report that the ndustry-wde Analyzng the determnants and consequences of such rcher characterstc-based prcng n annuty markets may be a frutful area for further work. 7 We chose genders and age ranges that represent the modal purchasers n each market. See Secton four for a descrpton of how we estmate mortalty for annutes n the sample frm; we estmate mortalty n fve-year age bns due to lmtatons to the degrees of freedom from estmatng age-specfc mortalty rates. Estmates of ndustry-wde 10

12 average prce for a nomnal, non-guaranteed polcy sold to a 65 year old male n the compulsory market n 1998 was ten percent of the purchase prce. Usng the same prcng formula and the same dscount rates, namely the nterest rates on government bonds, we fnd that that the average prce of the same polcy n our data set n 1998 was eleven percent of the purchase prce. Our sample sze s too small to permt such comparsons n the voluntary market; our sample frm sold only ten voluntary products n However, the average prce n our entre, 17-year, voluntary annuty sample seems low two percent compared to the 15 to 20 percent average prces that Fnkelsten and Poterba (2002) estmate for the entre voluntary annuty market n Substantal prce dsperson n the annutes offered by dfferent companes has been documented elsewhere, for example n Mtchell et al. (1999). However, the fact that the prces of voluntary annutes sold by our sample frm are lower than those of most other nsurers suggests cauton n nterpretng evdence of selecton n the voluntary market. Fnally, we nvestgated whether annuty sales trends for our sample frm mrrored ndustry-wde trends reported by the Assocaton of Brtsh Insurers (varous years). To the extent that the frm experenced dosyncratc growth or declnes n certan markets, t may be more dffcult to generalze the fndngs. Fgure 1 presents evdence for the compulsory market. On the rght-hand axs, we show trends n new premums collected each year for both the sample frm and the ndustry as a whole. Because ndustrywde data on new premums are only avalable n the compulsory market startng n 1991, we also present, on the left-hand axs, trends for our sample frm and the market as a whole n the amount of annuty payments made each year. Industry-wde data on payments are avalable startng n Ths measure combnes nformaton on new sales wth nformaton on polcy termnatons (.e. mortalty). For each measure, we denote frm sales wth sold lnes and ndustry-wde sales by dashed lnes. For ease of comparson, we set ndustry and frm new premums equal to 100 n 1991, and ndustry and frm payments n force equal to 100 n The scales for the ndustry and the frm are therefore dfferent, so that only mortalty for voluntary and compulsory annutants are based on Insttute of Actuares (1999a, 1999b); see Fnkelsten and Poterba (2002) for further detals on these data. 11

13 trends and not levels can be compared; ths s done n part to protect the anonymty of our company. Both seres show vrtually dentcal trends for the sample frm and the market as a whole. The upward trend n both measures n part reflects the expanson n the late 1980s of the set of retrement savngs plans that faced compulsory annutzaton requrements. Fgure 2 presents trends n the amount of new premums n the voluntary market for the sample frm and the ndustry as a whole. 8 The sample frm and the market experence the same basc pattern of a general declne n sales n the 1990s, although the exact tmng s not a perfect match. However, the abnormally hgh sales that the sample frm experenced n 1984 and 1985 appear to be an solated feature. The same s true when trends n payments n force are examned for the sample frm and the ndustry as a whole (not shown). Because 25 percent 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. To partally address ths concern, we examned the senstvty of our emprcal fndngs on mortalty and prcng n the voluntary market to excludng sales n these two years; our results were not affected. In sum, several strands of evdence suggest that our sample frm s compulsory market s typcal of the ndustry as a whole. The evdence on the smlarty to the rest of the voluntary market s consderably less compellng, gven both the frm s low prcng and the dosyncratc spke n sales n 1984 and Whle we present evdence from both markets n the emprcal work below, we therefore beleve the results from the voluntary market should be nterpreted wth cauton. The compulsory market represents the quanttatvely more mportant market, as t s roughly ten tmes the sze of the voluntary market. The compulsory market s also the market where, as dscussed above, we are more lkely to fnd evdence of selecton across annuty contract features. 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 12

14 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. The proportonal hazard model restrcts 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: (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 on the baselne hazard. 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: (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 t t t 0 0 ) 8 Numbers for ndustry-wde sales n the voluntary market n 1996 are omtted due to reportng problems n that year. 13

15 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. Our hazard models do not nclude any measure of "margnal prce" because all of the known characterstcs of the annuty product and the annutant, whch are n the models, should completely determne both the polcy premum and the margnal prce. 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 (monthly, termly, quarterly, sem-annually or annually). 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 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 choce that a long-lved ndvdual would make between an escalatng and an ndexed annuty wll depend on the rate of expected nflaton and on the ndvdual's dscount rate. 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 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" 14

16 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. Thus there s no predcton about the relatve sze of ther coeffcents. 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 theory descrbed above predcts that ndvduals who face 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. 3.2 Basc Results on Annuty Choce and Mortalty Patterns Under the null hypothess that ndvduals and nsurance companes have symmetrc nformaton, none of the annuty product characterstcs that we nclude on the rght hand sde of our hazard models should be correlated wth annutant mortalty. Under the alternatve hypothess, however, when ndvduals have nformaton that s correlated wth ther mortalty rsk, and use ths nformaton n selectng ther product type, the covarates wll be correlated wth ex post mortalty rsk. Our key emprcal test therefore focuses on whether the covarates have non-zero coeffcents, rather than the precse magntude of these coeffcents. We cannot assocate any causal nterpretaton wth our coeffcents, snce they wll be affected by the degree of correlaton between each covarate and the prvate nformaton of annuty buyers. 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 15

17 thrd and fourth columns of Table 2, show the same mortalty patterns across products as the hazard models. Indeed, mortalty dfferences across products that are statstcally nsgnfcant n the hazard model framework are statstcally sgnfcant n the lnear probablty model. Gven the smlarty of the fndngs, our dscusson of the fndngs focuses on the hazard model 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, ndcatng that ndvduals 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 at the 1% confdence level. 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, noncaptal protected annutes. 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 agan unable to reject the null hypothess of no dfference at standard statstcal confdence levels. However, n the compulsory market we can 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, 16

18 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 at the 5 percent level. These results are consstent wth models of adverse selecton n the nsurance market. We cannot test smlar predctons about selecton by degree of backloadng, or by length amount of escalaton for escalatng annutes n the compulsory market, or selecton by ether length of guarantee perod or amount of escalaton n the voluntary market, due to small sample szes. 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 the one predcted by models of nsurance market equlbrum 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. There s, however, no dscernable relatonshp between annuty sze and mortalty n the voluntary market, perhaps reflectng the fact that voluntary annutants are drawn to a substantal extent from the hghest wealth strata of the populaton. It s mportant to note that n both the voluntary and the compulsory annuty markets, the estmated effect of the amount of ntal payment on mortalty s small both n absolute terms and compared to the magntude of the effect of other annuty features on mortalty. The results n Table 2 suggest substantal mortalty selecton based on annuty back-loadng, some mortalty selecton based on payments to the estate, and very lttle f any selecton based on the ntal annual annuty payment. The lack of selecton on ths last dmenson supports 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 17

19 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. 3.3 Senstvty Analyss We developed a number of addtonal statstcal tests to explore the robustness of our fndngs. We examned whether the magntude of selecton effects among annuty products vared across groups of annutants. In partcular, when we ncluded a full set of nteractons between all of the covarates and the gender of the annutant n our basc hazard model, whle constranng men and women to exhbt the same baselne hazard, we were unable to reject the null hypothess that selecton effects among annuty products were the same for men and for women. We also estmated our hazard models allowng for unobserved heterogenety, assumng that ths heterogenety could be parameterzed by a gamma dstrbuton. The evdence for selecton was sometmes stronger, and never weaker, when we allowed for such unobserved dfferences across annutants. In addton to these tests, we estmated the hazard models separately for men and women to allow the baselne hazard to be dfferent for these two groups. We also estmated the models on several-year subsamples of our complete data set to check whether our results were contamnated by tme trends n the annuty market that could be correlated wth product characterstcs and mortalty. For example, n the voluntary market, where our sample frm had abnormally hgh sales, relatve to ndustry trends, n 1984 and 1985, we re-estmated the model excludng these years. We also re-estmated the hazard model usng length of lfe rather than length of lfe snce purchase of the annuty as our duraton measure. The results dscussed above were robust n sgn and sgnfcance to these varous checks. 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 18

20 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. An annuty that s actuarally far for such an ndvdual wll have a money s worth of one, and an effectve prce of zero. Money s worth values may be less than one, and effectve prces may be postve, 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, such as the populaton 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 1 Π 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 19

21 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. Note that n the absence of mortalty dfferences n the populaton purchasng dfferent types of products, or other dfferences n costs or profts across dfferent products, the money s worth should be the same for dfferent types of products. 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 ndvdual who buys an annuty n our data set. In each case, we use mortalty tables from the year n whch the annuty s sold. 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 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 the future payouts assocated wth an annuty product, we would deally lke to use a term structure of nterest rates that correspond to the assets n the nsurer s nvestment portfolo. At the end of our sample perod, we know that 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 assumptons about the nterest rate. 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. There was very lttle ssuance of new corporate bonds n the 20

22 U.K. durng the 1980s, so t s dffcult to estmate the yelds on newly-ssued corporate bonds durng ths tme perod. Ths makes t dffcult to construct a yeld ndex for ths tme perod, and we have not been able to fnd any data source that provdes a consstent nterest rate measure for U.K. corporate borrowers over the last two decades. 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 ssued by U.K. companes, all wth a ratng of at least BBB. 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 do ths every month between 1993 and 1998, and 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, and thereby construct an estmated 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. In practce, our estmates of the relatve prcng of dfferent features of the annuty contract are not senstve to our choce regardng the term structure. 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 + β 5 = α + β PAYMENT 1 INDEX + β 6 + β 2 PAYMENT ESCALATING 2 + β 7 X + ε + β 3 GUARANTEED + β 4 CAPITAL 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. 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, 21

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