Long-Term Care (LTC) Insurance Application I-Hsin Li

Transcription

1 Log-Tem Cae (LTC Isuae Aliaio I-Hsi Li Eoomis Deame Idiaa Uivesiy Wylie Hall 0 00 S. Woodlaw Bloomigo, IN 0 [email protected] Absa Due o a agig oulaio ad he aid gowh of log-em ae (LTC exeses, i is imoa o udesad he welfae effes of uhasig LTC isuae o he qualiy of life fo he eldely. We mus udesad how idividuals make deisios ad whih faos ae mos sogly osideed by hese idividuals whe makig hose deisios. This sudy ovides a alibaio exeise o deemie whehe aioal osumes should buy LTC isuae ad, also, o esimae he oimal imig of he LTC isuae aliaio. The uilized Rad Healh ad Reieme Suvey allow me o obai good measues of eah idividual s demogahi ifomaio by age. I show how idividuals would ea, based o he daa alulaed fom he meas, o LTC isuae aliaio deisio. Tha is, I have olleed geeal daa fom eah age gou, ahe ha seifi ifomaio o idividual ases. The esuls show ha idividuals do o ed o aly fo a LTC isuae oliy whe hey have a less ha % hae of eeig a usig home duig hei eieme yeas. The obabiliy of sayig i a usig home lays a majo ole i a idividual s hoie as o whehe o aly fo a LTC isuae oliy. Keywods: log-em ae isuae, usig home, life yle model, oio value model

2 Ioduio Due o he agig oulaio ad he aid gowh of log-em ae (LTC exediues i he Uied Saes, i is imoa o udesad wha welfae effes uhasig a LTC isuae oliy have o he qualiy of life fo he eldely. Aodig o he Admiisaio o Agig (000, fom 980 o 000, he eldely oulaio ove he age of ieased by %. Duig he same eiod, he umbe of eldely ove he age of 8 doubled. The Admiisaio o Agig s 00 ediio suggess ha by he yea 00, he oal eldely oulaio will eah 0 millio i he Uied Saes. Table I shows he oulaio gowh ae fo idividuals ove he age of. I addiio, he eldely oulaio i he Uied Saes is he lages demogahi gou o fae a high medial isk of beig disabled o havig hoi diseases ad, heefoe, eed LTC sevies. Fo examle, idividuals ove he age of may have a leas a 0% lifeime isk of beig admied o a usig home. Aoximaely 0% of hose who ee a usig home will say hee fo a leas five yeas (The Deame of Healh ad Huma Sevies, 00; Ameia s Healh Isuae Pla (AHIP, 999. Aoximaely % of idividuals fom ages 0 o have diffee yes of hoi diseases, wheeas aoximaely 8% of idividuals ove he age of 8 have hoi diseases, disabiliies ad aomayig fuioal limiaios (The MeLife Make Suvey o Nusig Home ad Home Cae Cos, 00; Ameia Assoiaio of Reied Pesos (AARP, 00. As LTC is fo hose idividuals who have hoi diseases o eed assisae oduig aiviies wihi hei daily lives, he aid iease i LTC exeses is udesadable. The A idividual whose age is ove he age of is alled he eldely i his sudy.

3 Cogessioal Budge Offie (CBO (00 idiaes ha he oal LTC exediue fo seios was $8 billio i 00 ad $. billio i 00. Also, he CBO saes ha his umbe is exeed o gow o $0 billio (.% of he GDP by he yea 00. The gowh of he oal usig home ad home ae oss fom 90 o 00 is dislayed i Table II. The aioal aveage ie of a semiivae oom i a usig home sevie was $9 a day i 00 (see Table III. Addiioally, based o a sudy odued by Alexih (00, he aveage legh of suh a say was. yeas ad he media legh of suh a say was. yeas i 00. Theefoe, i 00, a usig home say would os a eldely eso $8,0 ($9. o aveage, o $80,90.0 ($9. a he media level. Suh a exese would be a heavy bude fo a eldely idividual ad his family. Aodig o he CBO (00 ad he Healh, Uied Saes (00, he disibuio of he ayme soues fo LTC oliies has bee quie ueve. Table IV shows he disibuio of usig home exediues by fudig soue. I 00, % of LTC exeses wee aid fo by Mediaid las, % wee aid fo by family soues (idividual ou-of-oke aymes ad % wee aid fo by ivae LTC isuae omaies. This able imlies ha oly few idividuals have held LTC isuae oliies. Also, Bow ad Fikelsei (00 oi ou ha oly 0% of he eldely have held LTC isuae oliies. A ieesig quesio he aas eseahes aeio- If he LTC exediue is so exesive fo idividuals, why do hey o aly fo a LTC isuae oliy o elieve hei fiaial bude? Bow ad Fikelsei have seveal sudies ha exlai his limied size of he LTC isuae make. Thei 00 sudy imlies ha he suly-side make imefeios, iludig admiisaive oss, imefe omeiio, asymmei ifomaio ad aggegae The LTC exediue iludes usig home, home ae, ommuiy-based sevies, assised livig failiies, adul day-ae ees, ifomal ae ad hosie ae.

4 isk, ae o he majo auses of he limied size. Isead, he limied size is dive by he demad side faos. Fo examle, Bow ad Fikelsei sae ha Mediaid may be a subsiue fo ivae isuae. Suh a esul has lead eseahes o he olusio ha i ode o bee udesad he LTC make, hey mus fis udesad he demad aes ha affe he make. Bow ad Fikelsei (00b examie how Mediaid exlais he lak of ivae LTC isuae uhases. The heoeial esuls show ha eve a he aualiy fai emium, as log as Mediaid exiss i he make, idividuals would efe o o uhase a ivae LTC isuae oliy a all wealh levels. Theefoe, Mediaid has a majo owd-ou effe o he ivae LTC isuae make. This owd-ou effe is aibuable o he fa ha, omaed o he os of Mediaid, idividuals eed o sed a lage oio of hei wealh o oveage emiums if hey uhase ivae LTC isuae. A omleme ae wie by Bow, Coe ad Fikelsei (00 agee wih he above fidigs. Ree lieaue o he LTC isuae issue has also foused o fidig exlaaios o illusae he deemias fo he LTC isuae uhasig deisio ad hoosig LTC oveage. Fo examle, Cohe, Kuma ad Wallak 99 omile LTC isuae uhasig behavio ifomaio fom six LTC isuae omaies (see Table V fo deails by sudyig seleed uhases age 0 ad above, ad fid ha idividuals who do o wa o ely o hei hilde, believe he goveme will o ove he LTC fo hem, fae a highe medial isk, ae female o who have a highe eduaio level ae moe likely o buy LTC isuae. Cohe, Kuma ad Wallak 99 also eo ha i 990, he aveage age fo a idividual o uhase LTC isuae was 8.

5 Meie 999 suggess hee easos why youge idividuals wai o uhase LTC isuae uil hey eie. Fis, youge idividuals efe o o fae deadweigh losses i em of he fixed loadig oss. Seod, he oveage does o fi hei ue disabiliy os eeds. Thid, a idividual wih a lowe isk of beomig disabled may buy LTC isuae lae i life i ode o avoid he exeed iome loss. Meie he eommeds ha a oliy-make should eae a LTC isuae oliy ha youge idividuals will o be iluded as oibuos i he sysem. A sudy odued by Se 99 eos ha he haaeisis of hilde, eseially gede ad oximiy, ae imoa deemias i a ae s deisio egadig LTC isuae. Fo isae, daughes ae moe likely ha sos o ake ae of hei aes as ae hilde who live lose o hei aes. I addiio, if a hild las o akig ae of his aes, he he hild would ofe move lose o his aes o have his aes move lose o him. I suh ases, he aes may o eed o uhase LTC isuae oliies. Fuhemoe, Mello (00 examies whehe aes, i hei old age, us ifomal ae, suh as ha give by hei ow hilde, ad has diffee esuls fom he sudy of Se (00. He uses he 999 Asse ad Healh Dyamis suvey ad he Pael Sudy of Iome Dyamis i ode o exlai ifomal ae as a subsiue fo LTC isuae. Mello assumes ha he esee of a ifomal aegive edues a olde idividual s desie o uhase LTC isuae, o willigess o exed his LTC isuae oveage. Howeve, his fidigs show ha he esee of a ifomal aegive does o have a sigifia effe o he LTC isuae uhase deisio. Isead, eduaio, iome ad asses have sigifia osiive elaioshis i egad o he deisio.

6 A sudy odued by Fikelsei ad MGay (00 demosae he exisee of ivae ifomaio i he LTC isuae make. The auhos olude ha boh a idividual s esoal medial isk ad efeee fo isuae have a effe o he uhase of LTC oveage ad usig home use. MNamaa ad Lee (00 fid ha he omlex aual of LTC isuae oliies, ad, heefoe, he diffiuly i udesadig he oliies, as well as a lak of ifomaio abou medial isks of beig disabled o havig hoi diseases may be iial elemes i exlaiig why he isued idividuals do he LTC ovege few yeas afe hey have uhased i. Bau, Bui ad Pia (00 ad Bau ad Bui (00 aalyze he deemias of boh ubli ad ivae demad fo oveig LTC exediues. They sudy how a idividual makes a deisio of uhasig ubli o ivae LTC isuae, ad wha faos affe his willigess o ay fo LTC oveage. Do he faos ha ifluee ieess i buyig LTC isuae diffe fom hose ha deemie he quaiy of LTC oveage? The esuls he show ha, a io osiive exeiee wih LTC will deemie a idividual s willigess o buy LTC isuae, ad, o aveage, ubli isuae ogams ae efeed. O he ohe had, he soioeoomi vaiables, suh as iome, have a iflueial effe o he LTC oveage deisio. Ufouaely, o eseah exiss o he oimal imig of he LTC isuae aliaio o aswes he quesio: Should aioal osumes uhase LTC isuae? The imig of he LTC isuae deisio affes a idividual s welfae level. Fo examle, if a idividual uhases LTC isuae a a youg age, he will have a lowe ayme, bu fo a loge eiod of ime ha if he uhased he isuae lae i his life. Theefoe, he idividual may lose wealh o a sevie ha he is usue ha he will eed i he fuue. Howeve, whe a idividual uhases LTC isuae a olde age, eseially sholy afe eieme, he may o be able o

7 affod he osly emium. Theefoe, i is imoa o kow he bes ime o aly fo LTC isuae. I addiio, he obabiliy of beig laed i ad he legh of a say i a usig home ae iial faos ha affe he demad fo LTC isuae ad he imig of a idividual s aliaio. Fo examle, a idividual who believes ha he has a high isk of beig laed i o will sed a lo of ime i a usig home duig his eieme yeas may efe o aly fo a LTC isuae oliy befoe eieme i ode o edue his fiaial bude o LTC sevies. The eal iees ae is aohe fao ha has a subsaial effe o he LTC uhasig deisio. If a idividual exes o have a high eal iees ae i he fuue, whih meas ha he ue value will be moe exesive ha he fuue dolla, he he idividual may osoe his deisio due o he fa ha, wih a high eal iees ae, he ie of he LTC oliy will be heae i he fuue. Idividuals a save moe ow ad aly fo LTC isuae lae. Duig his sudy, usig he geeal ifomaio (suvival obabiliies, iome level, ou-of-oke medial exeses, usig home oss, LTC isuae emiums, LTC isuae oveage ad he obabiliy of eeig a usig home ha a idividual may fae i his lifeime, I will aswe wo quesios: Should aioal osumes uhase LTC isuae? ad ( Wha is he oimal imig of he LTC isuae aliaio? I addiio, I exlai how he hages i he obabiliy of usig home uilizaio, legh of a usig home say ad eal iees ae affe a idividual s deisio. Addiioally, wihi his sudy, I will use he oio value model o aalyze a vaiey of idividuals deisios i egad o hei LTC isuae uhases. I ode o odu his The oio value model omaes he maximum exeed values of he uiliy wihi he deisio se i ode o fid he highes exeed value of he uiliy. I was fis uilized by Sok ad Wise 990. They ague ha, usig his model o solve disee hoie oblems is less omliaed ad efoms bee i emiial ems ha he dyami ogammig model.

8 8 aalyzes, I have develoed a simle seve-eiod life yle model ad osued he daa a a aveage o media level i ode o solve eah idividual s maximum oblems ude he followig assumios: idividuals live a ime sa of seve eiods, ( idividuals fae ueai logeviy, ( idividuals fae he obabiliy of a usig home say i eah eiod exe fo eiod oe, ( idividuals a aly fo LTC isuae oly i he begiig of eah eiod, ( idividuals ao do o hage he LTC oliy oe i has bee uhased, ( he emium will be osa i omial dollas afe he idividual alies (i.e. he isuae omay ao hage he emium beause he idividual ages o his healh dimiishes, ( oly oe LTC isuae la ye exiss fo idividuals o hoose fom, (8 he isuae omay will oly ask he isued idividual o saisfy he waiig eiod (he eiod a idividual mus exeed befoe eeivig beefis oe i his lifeime, (9 he aoval ae of he LTC isuae aliaio is 00%; ad 0 isuae omaies will o dey ay feasible laims oe isued idividuals eed he LTC sevies. I aodae wih he geeal idividual ifomaio ha I omue fom he Rad Healh ad Reieme Suvey (HRS, I disove ha idividuals would efe o o uhase ay LTC isuae houghou hei whole life. This esul oiides wih he ue siuaio i he LTC isuae make whee oly 0% of he eldely ove yeas old have LTC oveage (Bow ad Fikelsei, 00. Howeve, whe a idividual believes ha he has a high hae of eeig a usig home duig his old age, he is moe likely o uhase a LTC isuae oliy duig his 0s. If a idividual has a high obabiliy of eeig a usig home, he he eal iees ae beomes a imoa eleme ha affes he LTC aliaio deisio. A low eal iees ae a ause a idividual o have a ealy aliaio. A idividual would efe o uhase See Seio s exlaaios of he LTC oliies fo moe ifomaio.

9 9 a LTC isuae oliy a a youge age, suh as 0s. I addiio, whe a idividual believes ha he has a high obabiliy of, afe a eai age (e.g. afe 0, eeig ad sayig i a usig home fo a log eiod of ime, he is moe likely o uhase he LTC oveage i his 0s. So ha, he has he fiaial suo o ay fo he LTC exeses a he ime he eeds he assisae. This sudy is osued as follows. I Seio, I desibe he LTC isuae ayme soues ad oliies. The model is desibed i Seio. Seio desibes he daa ad saisis. Seio oais he esuls ad Seio oais he olusio.. LTC.. LTC Payme Soues Family soues, Mediae, Mediaid ad LTC isuae ae he fou mai fudig soues fo LTC sevie exeses. Idividuals ad hei family membes may ay he oss of he LTC ou of hei ow savigs, ivesmes o asses. Howeve, sie he exese of LTC sevie is oe of he mos osly medial exeses, a idividual o his family s iome may o be eough fo he idividual o suo his exese. The eldely may also ay hei LTC exeses hough he Mediae ogam. I fa, he eldely who u he age of will auomaially eoll i he Mediae hosial isuae la. Howeve, he Mediae hosial la oly oves he full LTC os fo he fis 0 days. The, he idividual mus ay he o-ay fo he ex 80 days ad, fially, ay all of he exeses afe 00 days. The hid mehod o ay fo LTC sevies is o be eligible fo he Mediaid ogam. This ogam ays fo he os of he usig home ae, home healh ae ad ommuiy-based I 00, Mediae aid $ e day. The exeed ayme i 008 is $8.

10 0 sevies fo idividuals who qualify. Howeve, hee ae some equiemes fo a idividual o qualify fo his ogam (See Table VI fo he ifomaio abou iome ad asse limis. Mos of he eldely esos eed o sed dow hei iome fis i ode o be eligible fo he Mediaid ogam. Puhasig ivae LTC isuae is he fial way o ove a idividual s LTC exeses. Pivae LTC isuae oveage a ay u o 00% of a idividual s exeses deedig o wha ye of oliy o oveage he idividual hooses. The moe oliies a idividual holds, he moe exesive emium he eeds o ay fo... LTC Isuae (Poliies ad Pemiums Based o he 00 Fedeal LTC Isuae Pogam guidelie ifomaio, he mai oios fo LTC isuae ae he followig. Coveage: A failiy-oly o omehesive la. The failiy-oly la oves he exeses of he usig home ae, assised failiies, hosie ad esie ae. The omehesive la, o he ohe had, oves he usig home exeses, assised failiies, hosie sevies, esie ae ad home healh sevies. The omehesive oliy is moe exesive ha he failiy-oly la. ( Daily Beefi Amou. This amou is he daily amou of a idividual s beefis i dollas ha a isuae omay will ay o a isued idividual whe he says i a usig Ohe LTC isuae oliies ilude he followig. Waive of Pemium. This ye of oliy is sadad o may oliies; howeve, some omaies sill ilude his oliy as a addiioal oio. This waive allows a isued idividual o o ay he emium while he is eeivig he beefi. ( Resoaio of Beefi. As log as a isued idividual does o eed log-em ae duig eai eiods (i.e. suh as wihi six mohs afe hei oliy has aid fo he idividual s evious ae, his oio a kee he maximum beefi amou of isued eole as same as hey fis uhase. ( Pemium Refud a Deah. Wih his oliy, isuae omaies ay he isued idividual s family he emiums ha he idividual aid mius ay beefis ha he idividual eeived. I ode o uilize his oio, he isued idividual mus die a a eai age ad/o have aid his emiums fo a eai umbe of yeas. ( Dowgades. This oliy allows a isued idividual o ay less fo his emium whe he is o able o affod he oigial emium. Howeve, he idividual s oveage will be less omehesive duig he lowe emium eiods.

11 home o eeds home healh ae sevies. The moe daily beefi amou a idividual desies, he moe exesive emium he eeds o ay fo. ( Beefi Peiod. This eiod is he legh of ime ha a idividual a eeive his beefis. If he ayme does o exeed he isued idividual s daily beefi amou o if he idividual does o eed he LTC sevies evey day, he he beefi eiod will las loge. A loge beefi eiod will ause a iease i he idividual s emium, beause he loge beefi eiod a idividual hooses, he loge eiod he isuae omay eeds o ove he oss of he LTC sevies fo him. The omay he will equie he idividual o ay a highe emium. I addiio, a idividual s maximum lifeime beefi is he odu of he daily beefi amou ad he beefi eiod i days. This maximum lifeime beefi is he oal lifeime amou ha a isuae omay will ay o he isued idividual. Fo examle, if a idividual hooses $0 as his daily beefi amou ad has hose yeas as his beefi eiod, his maximum lifeime beefi will be $,0 ($0 yeas, ad also, his beefi is he oal lifeime amou ha he isuae omay will ove fo him. ( Waiig Peiod (o Elimiaio Peiod. This eiod is he umbe of days ha a idividual mus ay fo he LTC oss himself befoe he isuae omay begis o ay. If a idividual hooses a loge waiig eiod, he he will ay a lowe emium. I addiio, some omaies ask idividuals o saisfy his waiig eiod eah ime ha hey eed he LTC sevies, while ohes equie idividuals o oly saisfy he waiig eiod oe i hei lifeime. ( Iflaio Poeio (Auomai Iflaio Oio o Fuue Iflaio Oio. Ude a auomai iflaio oeio oio, he isued idividual s daily beefi amou ieases by % eah yea i ode o kee he emium osa. Covesely, wih he fuue iflaio oio,

12 he beefi ad emium ae adjused aodig o he medial Cosume Pie Idex (CPI evey wo yeas by he isuae omay. Obviously, he auomai iflaio oio is a bee hoie beause i esues ha he idividual s os will be osa, while a he same ime, he idividual will be eeivig a iease i beefis. Howeve, he emium fo his oio is moe exesive ha ha of he fuue iflaio oio. If a idividual hooses o fogo boh oios, he his daily beefi amou ad emium will o hage houghou he ouse of his oveage.. The Model Suose ha idividuals make hei ow deisios abou whe o aly fo LTC isuae afe hey eah he age of. Also, oside ha idividuals live fo a ime sa of seve eiods i whih eah eiod eeses a deade. Eah idividual will die wih eaiy a he ed of eiod seve, whih oesods o he age of 90. I he ieim, eah idividual faes he ueaiy of logeviy ad ius some obabiliy of eeig a usig home afe eiod oe. I have osued a simle life-yle model i ode o exlai a idividual s deisios ad evaluae he oimal imig of uhasig LTC isuae. I assume ha he ae of aeig he LTC aliaios is 00% ad suose isuae omaies will o dey ay isued idividual s easoable laims. Also, he emium is a fixed omial ayme oly deemied a he ime of uhase. I a be aid eiodially (weekly, mohly o aually. I his sudy, he emium will be aid i 0 aual aymes. A he sa of eah eiod, eah idividual hooses ue ad fuue osumio levels ad makes a deisio o whehe o aly fo he LTC isuae i eiod ( =,,,, i

13 ode o maximize his exeed disoued lifeime uiliy. Theefoe, he maximum oblem of a idividual is he followig: Max E { C } s.. a w o dm a 0 a a w o d mi(, q dm,,,, ( a w o d mi, q d m whee is he disoued fao ha aues he osume s ime efeee ad is he idividual s obabiliy of suvivig io eiod, whih is oige o havig suvived o eiod. The uiliy fuio fo eah eiod is oly a fuio of he osumio exediues. Usig a aihmi fom has he advaage of oduig a losed fom soluio. My uose hee is o aalyze how ueai usig home oss affe a idividual s deisio o whe o aly fo ad whehe o uhase he LTC isuae. I defie as he osa aual eal iees ae. I is he gowh ae of uhasig owe deived fom a idividual. Also, le a efe o he idividual s asses a he begiig of eah eiod. I assume ha o iiial asses exis ad ha o bequess a be give afe a idividual dies. Theefoe, eah idividual begis o aumulae his asses as savigs wihi he fis eiod ad will sed all of he moey ha he has duig he las eiod. I he ase ha a idividual dies befoe he las eiod, I esume ha hei iome ad asses would be ake by he goveme. The iome level, w, i eah eiod ous eihe fom labo eaig while

14 wokig o a esio o soial seuiy ayme while eied. o is defied as a idividual s ou-of-oke medial exeses wihou osideig he os of usig home ae a ime. I addiio, i ode o develo a deisio ule elaed o he LTC isuae aliaio, I deoe d as a idiao (dummy vaiable. This vaiable is equal o oe if he idividual uhases he LTC isuae i eiod ad zeo if he does o aly fo he LTC isuae a ime. Assumig ha oe a idividual has deided o uhase he LTC isuae a ime, he will be oveed by he LTC isuae oliy o he ed of his lifeime. Fo examle, if a idividual alies fo a LTC isuae oliy i eiod hee, he fo his seve-eiod budge osai, he idiao vaiable will beome d ( d d d d d d d (0 0. Le m be he emium i eiod. The emium will deed uo a eso s age. The olde a idividual is, he highe of a emium he fas whe uhasig he isuae. Moeove, aodig o he Fedeal LTC Isuae Pogam guidelie, isuae omaies ao iease a idividual s emium as he ges olde ad his healh dimiishes afe he has uhased he oliy. Tha is, he emium will be osa i omial dollas ove ime. LTC isuae is also guaaeed o be eewable, heefoe, I assume ha eah idividual would kee he same oliy a eah eewal eiod. This assumio allows me o kee he emium osa ove he ime eiods afe he oigial uhase. Fo isae, if a idividual uhases LTC isuae i eiod fou, m m m 0, ad m, m ad m would be he same ie as m i omial ems. The isuae omaies may be able o hage he emium fo a eie lass of oliy o idividuals. Theefoe, if a omay so desied, i ould aise he emium fo all idividuals ove he age of 0. Howeve, I do o ake his vaiable io osideaio duig his sudy.

15 Nex, begiig wih eiod wo, a idividual faes a os of usig home sevies,, wih some obabiliy. q eeses he LTC isuae oveage i my sudy. The LTC oliies used i his sudy ae he Failiy-oly, ( Daily beefi amou: $0, 8 ( Beefi eiod: yeas, ( Waiig eiod: 90 days ad ( Iflaio oeio: Auomai omoud iflaio, whih will maiai a emium osise i omial dollas, while he daily beefi amou ieases by a fixed eeage (% eah yea. Fially, he ems [ d mi, q ] i he budge osais desibe ha i eiod, a idividual will have hae o ee a usig home. If he ees a usig home, he he usig home oss will be whe he does o aly fo LTC isuae (d = 0. A idividual oly ays he diffeee bewee he usig home exeses ad he oveage amou, if he has LTC isuae. Howeve, whe he oveage is geae ha o equal o he usig home exeses, he he exeses will be fully oveed by he LTC oliy. Thus, he exese of he usig home ae i suh a siuaio would be zeo. I ode o solve his model, oe mus suose s deoes he aual eiod i whih a idividual uhases LTC isuae. The idividual mus eihe hoose o uhase LTC isuae a ime ( s o o o uhase LTC isuae i eiod ( s. He will make he deisio by omaig he exeed uiliy values ha migh be obaied if alyig fo he isuae i his aiula eiod ( s agais he exeed uiliy values ha ould be obaied by alyig fo a LTC isuae la i all ohe feasible eiods, s. Theefoe, I will solve his idividual s maximum oblem i ode o fid all of he oimal uiliy levels fo he followig eigh ases: eve aly, ( aly fo LTC isuae i eiod (0s, ( aly fo LTC isuae i eiod (0s, ( aly fo LTC isuae i eiod (0s, ( 8 The aioal aveage fo daily usig home oss e eso ove as e yeas has bee aoud $.88, so I se he DBA o $0.

16 aly fo LTC isuae i eiod (0s, ( aly fo LTC isuae i eiod (0s, ( aly fo LTC isuae i eiod (0s ad (8 aly fo LTC isuae i eiod (80s. Remembe ha a emium ayme elies uo he eiod i whih he idividual alied fo he LTC isuae. The lae i his life ha a idividual uhases he isuae, he highe he emium is fo ha idividual. Howeve, oe a idividual uhases he oliy, he emium will emai osa i omial ems houghou eah eiod of his lifeime. I ode o make my assumio leae, I defie m, o be he emium ha a idividual aually eeds j o ay i eiod whe he alies fo he LTC isuae i eiod j. Thus, m, m, m,. Fo examle, he emium i eah eiod fo a idividual who alies fo a LTC isuae oliy duig eiod would be m, m, m, m, m,. The fis se i solvig he maximum oblem is o wie ou he idividual s lifeime budge osai. I subsiue a, a, a, a, a ad a io he fial osai of Equaio ( i ode, ad divide boh he lef- ad igh-had sides by (. The, I le ilude he ems ha ae o elaed o he LTC isuae, ( w o, ad deoe e mi(, q i ode o save oaios. Thus, Equaio ( is asfomed io Equaio (: d m ( ( d e ( The seod se is o use Equaios ad ( o fid he Lagagia fuio(equaio ( ad, fom ha, deive he fis ode odiios wih ese o,,,,, ad, eseively. By deivig hese odiios, I am able o aai he idividual s oimal osumio levels fo he seve eiods.

17 L dm ( de ( The hid se is o lug hese oimal osumio levels io he uiliy fuio i ode o fid he oimal uiliy levels fo all of he ases. Theefoe, I am able o deemie whih uiliy level will give a idividual he lages exeed lifeime uiliy value. Fo examle, if alyig fo LTC isuae duig eiod gives a idividual he bigges value of he exeed lifeime uiliy, he his ase imlies ha eiod is he bes ime fo his idividual o aly fo LTC isuae. I ohe wods, alyig fo LTC isuae i his idividual s 0s will maximize his idividual s exeed lifeime uiliy. Moe deails o hese ses a be foud i he Aedix.. Daa The mai daa used fo his sudy ae olleed fom he he Rad HRS daa files, waves (yeas 99, 99, 998, 000, 00 ad 00; ( he 00 Fedeal LTC Isuae Pogam s deails ad aes, ( Naioal Vial Saisis Reos (NVSR fom he Naioal Cee fo Healh Saisis, ( MeLife Make Suvey o Nusig Home ad Home Cae Coss, yeas 00-00, ( he Healh, Uied Saes, yeas ad ( CPI fo all iems, medial ae sevies ad usig home ad adul day ae fom he Bueau of Labo Saisis i he U.S. Deame of Labo. The Rad HRS is a logiudial suvey, deived fom he iiial Healh Reieme Suvey (HRS, desiged o be used by eseahes o aalyze eieme ad healh issues amog he eldely i he Uied Saes. This suvey has bee olleed evey wo yeas sie 99, ad i iludes omehesive ifomaio o idividuals haaeisis, healh saus, healh

18 8 exeses ad eieme ifomaio. Howeve, beause he ifomaio of a idividual s legh of a usig home say is oe of he imoa vaiables i his sudy ad is available afe yea 99, I he olle daa fom yea 99 o 00. I oly gahe daa fo idividuals whose ages ae bewee wey-oe ad iey egadless of hei gede ad he esee of hei souse. I oal, I gahe,999 omlee obsevaios (see Table VII. The youges idividual i my samle is. Moeove, as meioed befoe, idividuals live fo seve eiods ad eah eiod idiaes e yeas. Fo ha easo, I have divided my samle io seve age gous ha ae equal o my seve eiods (e.g. age gou = - 0; age gou = - 0, e.. All he measues of idividuals demogahi ifomaio ae alulaed by age gous. Afe olleig he idividual s esoal ifomaio, he seod se is o omue he emium of he LTC isuae oliy fo his sudy. Thee ae may diffee LTC isuae la hoies available fom diffee isuae omaies. Diffee omaies also offe diffee ies fo diffee beefi levels. I ode o avoid diffiuly wih he above vaiables, I follow he ifomaio ovided by he 00 Fedeal LTC Isuae Pogam shoig guide i ode o alulae he emium ad oveage of LTC isuae. 9 Usig he ifomaio fom he Fedeal LTC Isuae Pogam has wo advaages: Ulike mos LTC isuae oliies, he Fedeal LTC Isuae Pogam ses is emium levels based o he Naioal Assoiaio of Isuae Commissioes (NAIC ae sabiliy guidelies i ode o assue he sabiliy of he emium fee, ( The Fedeal LTC Isuae Pogam offes less omliaed oliies ha ohe isuae las (see Table VIII. I he absa fom hoies of diffee hoies of he Fedeal LTC Isuae Pogam ad suose isead ha hee is oly oe ye of LTC isuae la. Is oes ae: Failiy-oly, ( Daily beefi 9 See he homeage of he Fedeal LTC Isuae Pogam (

19 9 amou: $0, ( Beefi eiod: yeas, ( Waiig eiod: 90 days ad ( Iflaio oeio: Auomai omoud iflaio. Nex, he Naioal Cee fo Healh Saisis is a ih soue of ifomaio abou he healh saus of Ameia. Fo his sudy, I uilized he life ables 0 i ode o osu a idividual s suvival obabiliy. I also olle ifomaio o usig home exeses fom he MeLife Make Suvey o Nusig Home ad Home Cae Coss ad he 00 Healh, Uied Saes. The MeLife Make Suvey o Nusig Home ad Home Cae Coss gives me he oss of usig home sevies fo he yeas 00 00, ad I obai he exeses of usig home sevies fo yeas fom he Healh, Uied Saes. Fom he Bueau of Labo Saisis, I fid he CPI fo all iems, medial ae sevies ad usig home ad adul day ae oss. I use his ifomaio o measue he gowh of iome, ou-of-oke medial exese ad usig home oss. The aveage aual CPI eeage hage fo all iems was aoud.8% fom 99 o 00. I addiio, he aveage aual CPI iease fo medial ae sevies ad usig home ad adul day ae oss was aoximaely.0% ad.%, eseively. Afe ombiig he above ifomaio, my omleed daa se iludes a ael of aggegaed idividuals ifomaio fom eiods o. I obai good measues of he idividuals demogahi ifomaio (iome, ou-of-oke medial exeses, usig home oss, isuae oveage, legh of a usig home say ad obabiliy of eeig a usig home by age gou. I olle geeal daa fo eah age gou, ahe ha seified ifomaio o idividual ases. Moe deails fo eah vaiable a be foud i he followig seios. 0 Life able is a able whih shows, wha he obabiliy is fo a idividual a eah age ha he dies befoe his ex bihday.

20 0.. Pemium ( m Assume ha a emium deeds oly uo a idividual s age. Based o his assumio, he idividual makes a deisio abou whehe o aly fo a LTC isuae oliy oly a he begiig of eah eiod. Tha is, eah idividual is able o uhase LTC isuae a age,,,,, o 8. The emiums omued fo his sudy is based o 00 ie ifomaio of he Fedeal LTC Isuae Pogam. Afe deidig o uhase he LTC isuae based o he above emium, he idividual s emium will be osa i omial dollas houghou his lifeime. While a idividual s emium ae will say he same, if he idividual had aemed o uhase he same isuae he ex yea a he same ie, he would have bee uable o do so due o iflaio. Theefoe, he eal ie of a oliy deeases ove ime. Thus, I alulae he eal ie of a isuae oliy by dividig i by he gowh of he CPI. The, I aslae he emium oss io ue dollas by dividig he emiums by he gowh of he eal iees ae ad sum u hese ese values of he emium fo eah age gou. All he ses desibed above ae show i Equaio (. PV ( emium, k emiumk s ( s,,,..., 0[ CPI ] Whee idiaes he eiod (,,...,, k is he ime a whih he idividual alies fo he LTC isuae ( k,,,,, ad 8 ad s deoes he yeas ha a idividual mus ay he emium. s ages fom o 0 deedig o whe he idividual uhased he LTC isuae. Fo isae, if a idividual uhases he LTC isuae i his 0s, he he will have o ay a emium fom age o he ed of his lifeime (age 90. Theefoe, he would ay his emium fo 0 yeas ( eiods.

21 Table shows all of he ossible lifeime emiums if a idividual whee o uhase LTC isuae a age,,,,, o 8. Fo examle, a idividual who uhases LTC isuae a age will ay $,0 i his 0s. He will he ay $,80 i his 0s ad fially, ay $9 whe he eahes his 80s i eal ems... Iome ( w The vaiable HwITOT i he Rad HRS eses he oal iome of idividuals a he household level ad has he sum of hee iome esoues: idividual eaigs, ( idividual iome fom a emloye esio o auiy, soial seuiy disabiliy (SDI, Sulemeal Seuiy iome (SSI, o soial seuiy eieme iome, ad ( ohe esoues suh as idividual iome fom goveme asfes ad idividual uemloyme o wokes omesaio. The iome fom a emloye esio o auiy, SDI o SSI o ohe soial seuiy eieme iome is zeo fo a wokig idividual, while idividual eaigs ae zeo fo he eied eldely. Ieviewees i he Rad HRS wee asked abou hei oal household iome fo he yea io o he ieview yea. I addiio, sie a household ould be eaed as eihe a oule household o a sigle household, I use he vaiable amed HwCPL o ideify how a household should be ideified. Whe he esode s maial saus was maied o aeed, he HwCPL was se o oe, whih mea ha he household was eaed as a oule household. If he esode was sigle, he he HwCPL was se o zeo ad he household was eaed as a sigle household.

22 Also, he oal household iome fo a oule s household was alulaed as he sum of he esode ad his souse s hee iome esoues. Theefoe, fo all oule households, I divide he oal household iome by wo i ode o esimae he idividual iome level. Fially, i ode o eae he iome vaiable fo he sudy, I aslae he iome values io eal 00 dollas by usig he ifleio ae beause he vaiable HwITOT is eoed i omial dollas. Fo examle, i ode o fid he iome values i yea 99 i eal ems, I mulily he values by. beause $ i 99 had he same uhasig owe as $. i 00. Also, i lae of he mea values, I aly he Rad HRS daase o obai he medias of iome values fo all eiods. The ouomes of his aliaio a be see i Table. These media values idiae geeal ifomaio abou a idividual s iome level duig eah eiod (age gou... Suvival Pobabiliy ( Isead of limiig he life ale ifomaio used wihi his sudy o oly oe yea, I o o uilize he ifomaio fom he NVSR of Naioal Cee fo Healh Saisis fom 99 o 00 i ode o osu suvival obabiliies. The wide age of yeas allows me o obai moe eliable aveage ifomaio fo his sudy. The NVSR s life ables oai ifomaio abou he obabiliy of dyig bewee ages x ad x. Howeve, his sudy eeds he obabiliy of suvivig fo a eso a eah age. I he fis alulae he obabiliy of beig alive bewee ages x ad x, x x obabiliy of dyig bewee ages x ad x. : oe mius he

23 Nex, as eah eiod i my model symbolizes a deade, I omue he suvival obabiliies via he Makov oess: ; ;.; ad Afe ha, I fid he aveage obabiliy of suvivig fo all seve eiods, fom he eigh yeas fo whih I have daa 99~00. All of he idividuals i he same eiod will fae he same suvival obabiliy (see Table. Fo examle, all of he idividuals whose ages ae bewee he age of ad 0 have a 89% hae o suvive o he ex eiod... Coss of Nusig Home Cae ( : Aveage Naioal Coss * Legh of Say is alulaed fom he odu of he aveage aioal usig home os e day ad he legh of a usig home say. Based o ifomaio fom he 00 o 00 MeLife Make Suvey o Nusig Home ad Home Cae Coss, ( usig home aveage mohly hage ables foud wihi he Healh, Uied Saes, 00 o 00 ad ( ieases i he CPI fo medial ae sevies fom 99 o 00 as ublished by he Bueau of Labo Saisis a he U.S. Deame of Labo, I obai 99, 99, 998, 000, 00 ad 00 s aveage aioal usig home os e day. The, I aslae hese amous io ese values (i 00 dollas. The daily usig home oss ae he same fo evey idividual i he sudy, egadless of he idividual s age. Nex, I use wo vaiables, he RwNHMDA ad RwNRSNIT, fom he Rad HRS daa file i ode o defie he aveage legh of a usig home say fo eah eiod. Boh vaiables eese he same ifomaio, ad mos of he values of hese wo vaiables ae he same. The vaiable RwNHMDA is available fom wave (yea 99 fowad ad eeses he umbe of days se i a usig home bewee he evious ieview eiod ad he ue ieview

24 eiod. RwNRSNIT eeses he umbe of ighs se i a usig home ad is available fom wave (yea 99. I is defied by he Rad HRS ha, if a esode was livig i a usig home duig he ieview oess, he boh vaiables wee se o he same umbe. If a idividual eoed ha he had se moe ha oe say i a usig home ad he oal umbe of days se i he usig home was less ha he duaio of ime bewee ieviews (i.e. bewee waves ad, he oly he umbe of days i a usig home (RwNHMDA was oued. Fo ha easo, i ode o uilize as muh as ifomaio as ossible abou usig home says, I ombie hese wo vaiables. I se he RwNHMDA o be equal o RwNRSNIT if he umbe of days se i a usig home was missig ad he umbe of ighs i a usig home was geae ha zeo. I addiio, beause RwNHMDA was o available i wave, I geeae he umbe of days se i a usig home fo his wave based o he eoded umbe of ighs se i a usig home. The usig home say was eoded bewee he evious ieview eiod ad he ue ieview eiod. Fo ew ieviewees, he eiod eomassed he las wo yeas. Tha is, if a idividual was ieviewed i 99, 998, 000, 00 ad 00, bu o i 99, he his usig home say i 998 may have exeeded 0 days (wo yeas o eah * yeas (i.e. say i a usig home fom 99 o 998. This is beause his idividual migh ee a usig home a some ime bewee 99 ad 99 ad emaied i he usig home duig he ieview eiod, yea 998. I his ase, he value of he idividual s usig home say would be a oulie fo yea 998, ad he aveage legh of say obaied fom he oigial values i he suvey will be oveesimaed. I ode o make all of he vaiables osise, i is eessay fo me o hek he aedae of he ieviewees fo all hese suvey yeas. I he divide eah ieviewee s usig home say legh by,,, 8, 0 ad deedig o he umbe of eiods ha he idividual

25 had missed bewee suvey ieviews. This muliliaio will allow me o obai a idividual s yealy usig home say legh. Fo examle, sie he suvey eiod is evey wo yeas, if a idividual aeded he ieview evey suvey yea (o fo a ew ieviewee, I divide his usig home duaios by wo i ode o obai his aveage yealy ifomaio o usig home say. Moeove, if a idividual missed oe ieview, ha meas his efeee eiod of he legh of say would be fou yeas isead of wo yeas, he I divide his say legh by fou. Nex, I odue he usig home oss vaiable by mulilyig he disibuio of he legh of a idividual s say by he ese value of he aveage aioal usig home oss. Table shows he aveage usig home oss ad he aveage legh of a usig home say by eiod. Aodig o my esuls, a idividual i his 0s may sed $,0 o aveage fo usig home sevies... Ou-of-Poke Medial Exeses ( o The vaiable RwOOPMD idiaes a idividual s oal ou-of-oke medial exeses i he Rad HRS. This vaiable is he sum of fou exeses: hosial ad usig home oss, ( doo, deis ad ouaie sugey oss, ( aveage mohly esiio dug oss ad ( home healh ae ad seial failiies o sevies oss. Howeve, i my model, I do o ou usig home oss as a a of ou-of-oke medial exeses; heefoe, I suba he usig home oss fom his vaiable. I addiio, by defiiio, if a idividual s isuae la aid fo all healh exeses, he he value of his ou-of-oke medial exeses will be zeo. Afe hekig eah idividual s isuae siuaio, I disove ha some idividuals had LTC exeses ha wee

26 oveed by Mediaid, aohe govemeal healh isuae o hei emloyes o souses isuae las. I hese ases, I do o seaae he os of usig home ae fom he idividual s oal ou-of-oke medial exeses beause he value of his usig home os is zeo. The Rad HRS iludes five ohos, he Iiial HRS, ( Asse ad Healh Dyamis Amog he Oldes Old Sudy (AHEAD, ( Childe of Deessio (CODA, ( Wa Baby (WB ad ( Ealy Baby Boome (EBB. I wave, he AHEAD ad Rad HRS uilized diffee defiiios fo he efeee eiod. I wave A, AHEAD esodes wee asked abou he evious yea s ou-of-oke medial exeses. Howeve, i wave H ad fom wave owad, HRS esodes wee asked abou he as wo yeas o he eiod sie he las ieview. Theefoe, fo he obsevaios fom wave A, I kee he iiial values beause he ou-of-oke medial exese i his ase was yealy exese. O he ohe had, fo wave H ad wave owad of he Rad HRS suvey, I mus hek he umbe of waves esodes had missed, ad use he eviously desibed alulaio mehod (divide he values by,,, 8, 0 o i ode o omue a idividual s yealy aveage of ou-of-oke medial exeses, beause i suh a ase, he efeee eiod of he vaiable beame wo-yea base o ove wo yeas if ieviewees did o aea a evey suvey ime. Fially, I omue he ese values of he meas of he ou-of-oke medial exeses fo eah idividual as based o he CPI fo medial ae ad he eal iees ae (see Table. The esuls of Table show ha as a idividual s age ieases, his ou-of-oke medial exeses iease. Theefoe, idividuals should aiiae ayig a aveage of $,0 fo hei ou-of-oke medial exeses duig eiod (80s.

27 .. Coveage of Nusig Home Sevies ( q The vaiable q is he odu of he usig home say legh a ime ad a idividual s daily beefi amou. Aodig o he 00 Fedeal LTC Isuae Pogam, he daily oveage of LTC sevies will ove u o 00% of a idividual s daily beefi amou fo a usig home failiy. Howeve, he LTC isuae la has a waiig eiod of 90 days, whih meas ha a idividual mus wai 90 days o be eligible fo beefis ad eeive oveage. If a idividual says i a usig home fo less ha 90 days, he he mus ay he usig home sevie exeses ou-of-oke. Addiioally, idividuals eed oly saisfy he waiig eiod oe i hei lifeime ad he umbe of days ha hey eeive sevie is oued umulaively. Fo isae, if a idividual sayed i a usig home fo wo days eah ime ha he uilized he sevie, he, o oly would he have o ay fo he usig home sevie exeses ou-of-oke, bu i would also ake him a loge ime o eah he 90 days eessay o eeive beefis, omaed o log usig home say aies. The obje of his ae is o exlai how idividuals make deisios abou whe ad if o uhase LTC isuae. Theefoe, I alulae eah isued idividual s oveage fo eah eiod via he followig alulaios: a isued idividual whose usig home say legh is less ha 90 days: q = 0, ( a isued idividual whose say legh is ove 90 days: q = e aveage days of say a ime 90 Daily Beefi Aou ad ( a isued idividual who has saisfied he waiig eiod a leas oe i his lifeime: q = e aveage days of say a ime Daily Beefi Aou. Afe followig he mehod desibed above ad omuig he ese values (00 dollas of he daily beefi aou fo eah eiod, I osu a able (Table oaiig he aveage oveage values of LTC i eal ems. Fo examle, if a idividual alies fo LTC isuae a he age of ad exes o

28 8 say i a usig home fo 0 days o aveage i his 0s, he he should exe ha he isuae omay would ay a aveage of $,0 fo his usig home sevies... Pobabiliy of Sayig i a Nusig Home ( Nusig home failiies ae isiuios ha ake ae of idividuals wih hoi diseases o idividuals uable o omlee he basi aiviies of daily life. Table shows he eeage of idividuals i he Rad HRS who have eve sayed i a usig home, by age gou, fom 99 o 00. This able shows ha.8% of he eldely bewee 8 ad 90 have sayed i a usig home. Ohe sudies have had simila esuls. Fo examle, Alexih (00 ad he eo fom he 00 ad 00 Healh, Uied Saes show ha oly.9% of he eldely ove 8 sayed i a usig home i 00 (Table IX ad X. I fa, he eeage of usig home uilizaio deeased fom 98 o 00 (Tables IX ad X. This eduio may esul fom seveal ossibiliies. Oe ossibiliy is ha a ieasig umbe of subsiues fo usig home ae, suh as home ae, exis ad ha a ieasig umbe of eldely idividuals hoose o eeive home ae o ommuiy sevies. The eldely would feel moe omfoable o have aes a home isead of eeig o a usig home. Aohe ossibiliy is ha he idividuals ieviewed ae wealhie ad, heefoe, bee able o maiai hei healh wih egula doo visis, healhy livig ad esiios. I addiio, a wealhie idividual will moe likely ha oo eso o have home healh ae beause he is able o affod he exesive oss. This siuaio will he edue he usig home use ae. Commuiy sevie is a sevie ha a eside a eeive he beefis fom his loal ommuiy. Fo examle, he ommuiy sevies a ovide seial eeds o eldely idividuals ad families. Also, i a ehae self-hel ad muual-hel abiliy o imove he qualiy of life of he eldely.

29 9 A hid ossibiliy is ha eole ae livig loge ad healhie ha hey wee i evious geeaios due o imovemes i medial ehoy. This iumsae may edue he usig home admissio ad osoe idividuals imig of eeig a usig home. A sudy odued by Lihebeg (00 examies he effe of ew dug usage o admissio of eldely Ameias o hosials ad usig homes, ad shows ha ew dug edue he gowh of he umbe of hosial dishages o usig homes. Moeove, he exediues of hosial ad usig home aes deease as he ieased dug exediues..8. Disoued fao β ad he eal iees ae As he fial oi fo Seio, I assume ha he disoued fao is equal o 0.99^0 = 0.9 beause he idividuals i my sudy live fo seve eiods ad eah eiod idiaes a deade. Fially, I follow he sudies odued by Diamod (00 ad Olsho (00 ad assume ha he aual eal iees ae is % aoss eah of he yeas i my model.. Resuls Afe solvig he seve eiod life yle model ad obaiig he oimal osumio levels ad uiliies fo eigh ases, I am ow able o show ha, give all of he geeal idividual ifomaio ad he % eal iees ae, a idividual would be bee off if hey do o aly fo a LTC isuae oliy (see Figues -. This esul is osise wih he ue siuaio i he small LTC isuae make as oly 0% of eldely esos uhased a LTC isuae oliy i 00 (Bow & Fikelsei, 00. Oe exlaaio fo his low eeage is ha idividuals ow live loge ad ae healhie due medial advaemes. As he esul, a aioal idividual would efe o o aly fo LTC isuae.

30 0 I addiio, wih he ue obabiliy of a usig home ey ha I omue fom he Rad HRS, eve hough a idividual may exe a low eal iees ae i he fuue (ex: % o % -- Figues - ad - o o beome a log-say eside a a usig home i his lae yeas (see Figues , he would sill efe o o uhase a LTC isuae oliy. This is beause idividuals believe hey ae ulikely o eed he usig home ae i hei eieme yeas. A idividual oly have a.8% hae of beig admied o he usig home afe he age of 8. Puhasig a LTC isuae oliy is he o a sma deisio fo a idividual o make i imovig his qualiy of life... Resuls ude he ieased obabiliy of usig home use ase I his subseio, I iease he obabiliy of eeig a usig home fo eah age gou o sae he imoae of he obabiliy of eeig a usig home. I isead assume he obabiliy of beig lae i a usig home is disibued as 0%, %, 0%, %, %, % ad 0% i eiod,,,,, ad eiod, eseively. I his ase, wih a % eal iees ae, he idividuals would be bee off if hey uhase LTC isuae ad aly fo he oliy i 0s (see Figue -. Addiioally, hagig he eal iees ae also has a effe o a idividual s deisio of whe o aly fo LTC isuae. The esuls show ha whe he eal iees ae is eihe % o %, idividuals would efe o uhase he LTC isuae ad aly fo he oliy ealy. Fo examle, i his ase uhasig LTC isuae i eiod (0s gives he idividual he highes value fo his lifeime disoued uiliy (Figues - ad -; ( whe he eal iees ae is %, he oimal imig fo alyig fo he LTC isuae is eiod (0s (Figue - ad ( if he eal iees ae is geae ha o equal o %, he he bes hoie fo he

31 idividual is o o aly fo he LTC isuae (Figues - o -9. These esuls ou beause a highe eal iees ae imlies ha he ese value is moe exesive ha he fuue value, whih meas ha idividuals may be able o affod he os of usig home sevies by hemselves i he fuue beause i will be heae. I addiio, if a idividual exes o have a log say i a usig home duig his lae yeas, he uhasig LTC isuae ad alyig fo he oliy i his 0s will give him he highes uiliy (see Figues -0 ~ -. Tha is, a idividual would efe o uhase LTC isuae igh a he ime he eeds he assisae... Resuls of emium ad/o usig home oss hages I examie how he deisio of whe o aly fo LTC isuae will be affeed if he LTC isuae emium deeases ad/o he usig home os ieases i his subseio. Figue - shows ha wih he oigial obabiliy of eeig a usig home ha used by he model, eihe a deeasig emium o ieasig usig home oss would hage he esuls of his sudy ad a aioal osume would o aly fo a LTC isuae oliy. Howeve, if a idividual believe ha he obabiliy of eeig a usig home is 0%, %, 0%, %, %, % ad 0% houghou he eiods i he model, he he idividual will make he bes fiaial deisio if he alies fo a LTC isuae oliy i his 0s (Figue - egadless of whehe he emium deeases o he usig home oss iease. Figue - illusaes, whe he usig home oss iease ad he isuae emiums deease a he same ime, idividuals will uhase LTC isuae if hey believe ha hey will fae a high obabiliy of eeig a usig home duig hei lae life. Agai, suh esuls

32 show ha a idividual s belief i whehe he will uilize a usig home is a imoa fao i ha idividual s deisio of whehe ad whe o aly fo LTC isuae. Fom he exeises i seio. ad., we a see ha he obabiliy of eeig a usig home ey is a majo fao i affeig a idividual s deisio of whe o aly fo LTC isuae. Howeve, idividuals ofe ao auaely esimae hei medial isk of eeig a usig home. I ode o avoid he iome loss o he exese of isuae emium, a idividual will efe o o uhase ay LTC isuae, uless he is eai abou his isk of beig admied o a usig home i he ea fuue.. Colusio I lae of alyig a omlex dyami ogammig model o he disee hoie oblem, his ae alies he oio value model o show whehe a aioal osume should uhase LTC isuae ad, if he osume should uhase he isuae, whe would be he oimal mome fo he LTC isuae aliaio usig a alibaio exeise. I ode o eae a esimaio of he mos fiaially soud imig fo a LTC isuae aliaio, I olle dae based o six soues: he Rad HRS, MeLife Make Suvey o Nusig Home ad Home Cae Coss, Fedeal LTC Isuae Pogam guidelies, NVSR fom he Bueau of Labo Saisis ad he Healh, Uied Saes. I obai eah idividual s iome level, ou-of-oke medial exeses, usig home oss ad isuae oveage ifomaio, ad, also, gahe he followig ifomaio by age gou: aveage legh of a usig home say, isuae emium, suvival obabiliy ad obabiliy of a usig home say. The esuls of he sudy show ha whe idividuals exe o have a osa % eal iees ae houghou hei lives ad fae a less ha % obabiliy of a usig home say

33 afe eied, he hey ae o ilied o aly fo LTC isuae as suh a deisio gives hem he highes exeed lifeime uiliy. Tha is, he fidigs sugges ha a aioal idividual should o aly fo a LTC isuae oliy due o a low obabiliy of usig home use. I addiio, his exeise allows me o ideify how oelaios, suh as he obabiliy of a usig home say, eal iees ae, legh of a usig home say, usig home oss ad isuae emium ifluee a idividual s deisio abou whehe ad whe o aly fo LTC isuae as well. A hage i a idividual s obabiliy of eeig a usig home ifluees a idividual s deisio o whe o aly fo a LTC isuae oliy. The highe he exeaio of eeig a usig home lae i life, he moe likely a idividual is o uhase a LTC isuae oliy. As he eal iees ae deeases, ouled wih a high obabiliy of eeig a usig home, idividuals ae moe likely o aly fo LTC isuae as wih a lowe iees ae, idividuals exe he LTC sevie will be moe exesive i he fuue. Theefoe, hey would aly fo a LTC isuae oliy ow ad have hei exeses of LTC oveed lae. Howeve, i he ase ha a idividual has a small hae o ee a usig home, loweig he eal iees ae does o eouage him o uhase ay LTC isuae oliy. I addiio, if a idividual has a highe isk of eeig a usig home afe eiod ad exes o say i a usig home fo a log ime, he he bes ime o uhase he isuae is duig eiod ; heefoe, he idividual a edue his fiaial bude o LTC sevies a he ime he eeds he ae. Fom all he exeises i his sudy, esuls sugges ha he belief of he isk of beig admied o a usig home is he mos imoa fao ha affes a idividual s deisio of he LTC isuae aliaio. Howeve, i is diffiul fo idividuals o esimae auaely

34 abou hei medial isk. Theefoe, a lak of ifomaio egadig he esimaio of a idividual s healh odiio may exlai he limied size of he LTC isuae make. This ae sugges ha eouagig eole o udesad he beefis of alyig fo LTC isuae a hel o elieve hem of medial exese budes i hei lae lives. Theefoe, he Uied Saes goveme should offe ogams o ofeees o middle-aged idividuals so ha hey a lea he deails abou he vaiey of LTC isuae oliies ha exis ad beome able o defie hei healh sauses auaely. A he same ime, he goveme eeds o oe he osume s ighs by makig sadad egulaios abou isuae laims i ode o ool ivae isuae omaies. As a esul, LTC isuae omaies should o be able o dey a isued laim jus simly beause he waied oo log o use he usig home ae. A LTC isuae oliy is suosed o hel he eldely beome eleased fom fiaial oblems a he ime a whih hey eed he LTC sevies ad, heefoe, imove he idividual s qualiy of life, o make i wose. Refeees Admiisaio o Agig (000a, The gowh of Ameia s olde oulaio. (h:// Admiisaio o Agig (00, A ofile of olde Ameias. Ameia s Healh Isuae Plas (AHIP, Guide o Log-Tem Cae Isuae, Washigo D.C., 999. Ameia s Healh Isuae Plas (AHIP, Reseah Fidigs: Log em ae Isuae i 00, Washigo D.C., 00.

35 Ameia Assoiaio of Reied Pesos (AARP, Beyod 0: A eo o he Naio o eds i healh seuiy, Washigo D.C., 00. Bau, R., Lii Bui, M., ad Pia, A.M. (00, Publi vs ivae demad fo oveig log em ae exediues. CRENoS wokig ae. Bau, R., ad Lii Bui, M. (00, Eliiig he demad fo lig-em ae oveage: a disee hoie modelig aalysis. FEEM Wokig Pae, Eoomi Theoy ad Aliaios Seies,..00, (seod oud a Healh Eoomis. Bow, J.R., ad Fikelsei, Amy (00, Why is he Make fo Log-Tem Cae Isuae So Small? Fohomig, Joual of Publi Eoomi. Bow, J.R., ad Fikelsei, Amy (00, The ieaio of ubli ad ivae isuae: Mediaid ad he log-em ae isuae make, Revised ad Resubmied, Ameia Eoomi Review Bow, J.R., Coe, Noma B., ad Fikelsei, Amy (00, Mediaid owd-ou of ivae logem ae isuae demad: evidee fom he Healh ad Reieme Suvey, Fohomig, Tax Poliy ad he Eoomy. Bukhause, V.R., Bule J.S. ad Gumus, Guli (00, Oio value ad dyami ogammig model esimaes of soial seuiy disabiliy isuae aliaio imig. Disussio ae o. 9. Bukhause, V.R., Bule J.S. ad Gumus, Guli (00, Dyami modelig of he SSDI aliaio imig deisio: he imoae of oliy vaiables, Disussio ae o. 9. Bukhause, V.R., Bule J.S. ad Gumus, Guli (00, Dyami Pogammig model esimaes of soial seuiy disabiliy isuae aliaio imig, Joual of Alied Eoomeis, Vol. 9: -8.

36 Cogessioal Buge Offie (CBO 00, Fiaig log-em ae fo he eldely, Washigo D.C. Cogessioal Budge Offie (CBO 00, A CBO sudy: The log em ae budge oulook, Washigo D.C. Cohe, Ma A., Kuma, Nada ad Wallak, Saley S. (Sig 99, Daa Wah: Who Buys Log-Tem Cae Isuae? Healh Affais. P 08-. Daula, Thomas, ad Moffi, Robe 99, Esimaig dyami models of qui behavio: he ase of miliay eelisme, Joual of Labo Eoomis, Vol., No., Duham-Taylo, ad Pizuk (00 Healh ae fiaial maageme fo use maages, hae : maagig log-em ae esoues Joes ad Bale Publishes, I. Fikelsei, Amy ad MGay, Kahlee (00, Mulile dimesios of ivae ifomaio: evidee fom he log-em ae isuae make. The Ameia Eoomi Review, Vol Healh, Uied Saes, 00 ad 00. Jeffey Bow, Thomas Davidoff, ad Pee Diamod (00, Auiies ad Idividual Welfae, The Ameia Eoomi Review, Vol 9, No, -89. Laue Olsho (00, Sed I While ou Ca Sill Ejoy I: Healh, Logeviy, Agig, ad Cosumio," Job Make Pae. Deame of Eoomis, Uivesiy of Wisosi- Madiso. MNamaa, Paul E., ad Lee, Nayoug (00, Log-em ae isuae oliy doig he U.S. fom 99 o 000: evidee ad imliaios fo log em ae fiaig, The Geeva Paes o Risk ad Isuae, Vol. 9, No.,. 0-.

37 Naioal Assoiaio of Isuae Commissioes (00: A shoe s guide o log-em ae isuae. Meie, Volke 999, Why he youg do o buy log-em ae isuae. Joual of Risk ad Ueaiy, 8, Mello, J. M. (00, Log-em ae ad usig home oveage: ae adul hilde subsiues fo isuae oliies? Joual of Healh Eoomis, 0 (: -. Se, Seve 99, Esimaig family log-em ae deisios i he esee of edogeous hild haaeisis, The Joual of Huma Resoues, Vol. 0, No., P -80. Sok, James H., ad Wise, David A. 990, Pesios, he oio value of wok, ad eieme, Eoomeia, Vol. 8, No.,.-80. Suki, B., ad Mulvey, J.,Mah (000, Ca Agig Baby Boomes Avoid he Nusig Home?, Ameia Couil of Life Isues. The U.S. Deame of Healh ad Huma Sevies, July 00. The MeLife Make Suvey of Nusig Home ad Home Cae Coss, The Fedeal Log Tem Cae Isuae Pogam (00: Pogam deails ad aes ( Uied Saes Goveme Aouabiliy Offie (GAO, 00: Reo o Cogessioal Commiees: Log-Tem Cae Isuae- Fedeal Pogam Comaed Favoably wih Ohe Podus, ad Aalysis of Claims Ted Could Ifom Fuue Deisios, Table : Beefi Oios i he Fedeal LTCI ogam ad i Idividual ad Gou Podus Sold fom July, 00 hough Mah, 00.

38 8 Aedix Hee shows he examle of ase oe (eve alyig LTC isuae. If a idividual eve alies fo LTC isuae, he equaios ( ad ( i he oe will u ou o be equaios (8 ad (9 hee: ( (8 L (9 So, he fis ode odiios wih ese o,,,,,, ad ae : ; : ; : ; : ; : ; : ; :

39 9 Theeuo I elae,,,,,, ad i ems of io equaio ( o fid he value of. Puig bak o equaio 0, I am aable of geig he oimal osumio levels fo seve eiods of ase oe.

40 0 Theefoe, he oimal uiliy i his ase is 0 u Afe ewiig he oimal uiliy level, I have 0 u

41 0 D k B u whee k B is a osa em, ad D. D D D D D D D k B

42 I use simila mehod o solve ase ( ~ ase (8, ad I ge he followig esuls: (, 0 e m D k B u (, 0 e m D k B u, 0 ( ( ( e m D k B u, 0 ( ( ( ( e m D k B u, 0 ( ( ( ( ( e m D k B u ( ( ( ( ( ( (, e e m D k B u ( ( ( ( ( (, e m D k B u

43 Tables Table I. Reside oulaio (Numbe i housads ea\age ,0,8 90 0,99, 99 90,,9, 980,8,9, ,0 0,0, ,9,,0 00 8,,,9 00 8,,89, 00 8,,9,80 Noe. Daa olleed fom Healh, Uied Saes, 00. Table II. Toal usig home ad home ae exediues (Amou i billio Nusig Home Home ae Noe. Daa olleed fom Healh, Uied Saes, 00.

44 Table III. The aioal aveage oss of a usig home ad home ae Nusig home ae (daily ae Home ae Semiivae oom Pivae oom (houly ae By 00*.9 90,00 (aual.0 8,000 (aual Noe. 00~00 MeLife Make Suvey o Nusig Home ad Home Cae Coss. * Ameia Couil of Life Isues, Ca Agig Baby Boomes Avoid he Nusig Home?, Suki, B., ad Mulvey, J.,Mah 000. Table IV. Healh, Uied Saes, 00: Nusig home exediues by soue of fuds (% Ou-ofoke aymes Pivae healh Isuae Ohe ivae fuds (LTCI Goveme Mediaid Mediae

45 Table V. Pimay easos fo uhasig LTC isuaes i ode:. Pesos who do o wa o ely o his/he hilde o ay fo LTC whe eeded. (Pesos who would like o avoid deedig o ohes fo ae ad o eseve hei ideedee.. Pesos who woy abou how o ay fo LTC whe eeded.. Pesos who believe hey may eed LTC sevies i he fuue. (Fom a family hisoy, eole have highe isk o be ill, so hey believe hey will eed LTC, o eole ae auio esos, hey hik hey may eed LTC i he fuue.. Pesos who hik isuae idusy offes adequae oveage fo LTC, whih goveme would o ove fo hem.. Pesos who would like o miimize hei fiaial exosue o oe hei asses ad would like o guaaee ha hey will be able o affod eeded LTC sevies.. Pesos who have fieds lose savigs by ayig fo usig home o home healh ae, so ha hey would like o avoid his siuaio.. Pesos who would like o avoid deedig o Mediaid. 8. Pesos who ae below age, female, maied esos, oal liquid asses ae geae ha ad equal o $00,000, o ollege-eduaed ae moe likely o buy a log-em ae isuae. Table VI. Iome ad Asse limis: Iome Asse Iome Asse Iome Asse Idividual $00 $,000 $ $,000 $ $,000 Coule $ $,000 $8 $,000 $9 $,000 Soue: Cees fo Mediae & Mediaid Sevies (CMS Table VII. Obsevaios i eah age gou ove six waves Age gous Obsevaios : -0 : -0 : -0, : -0, : -0, : -80, : 8-90,89

46 Table VIII. The Fedeal LTCI ogam V.S. ohe Pivae LTCI odus Beefi oios The Fedeal LTCI ogam Pivae LTCI odus Coveage Comehesive, Comehesive o Failiies-oly, o Failiies-oly Home-ae-oly Daily beefi amou (DBA $0 o $00 $8 o $00 Waiig eiods 0 days o 90 days 0 days o 0 days Beefi eiods yeas, yeas, o lifeime I yea o lifeime Iflaio oeio Auomai omoud o Fuue uhase oio Auomai omoud, Simle, Fuue uhase oio, Ohe, o Noe Noe. Uied Saes Goveme Aouabiliy Offie (GAO: Reo o Cogessioal Commiees: Log-Tem Cae Isuae- Fedeal Pogam Comaed Favoably wih Ohe Podus, ad Aalysis of Claims Ted Could Ifom Fuue Deisios, Table : Beefi Oios i he Fedeal LTCI ogam ad i Idividual ad Gou Podus Sold fom July, 00 hough Mah, 00 Mah, 00. Table IX. Nusig Home Use Rae Naioal Nusig Home Suvey Healh, Uied Saes (a (NNHS (b % 0.9 %.0 % 0.9 % -8.9 %.9 %. %. % 8+.8 % 0.0 %. %.9 % Noe. (a Bisho 999, Daa wah: Whee ae he missig eldes? The delie i usig home use, 98 ad 99, Exhibi : usig home esides age ad ode, e housad eldely, by age, 98 ad 99. Healh Affais, Vol 8, No..; ad (b Alexih (00, Nusig home use by oldes old Shaly delies, Exhibi : usig home use aes by age fo seleed yeas. The Lewi Gou, aioal ess lub.

47 Table X. The disibuio of he eldely oulaio i999 by sex % of eeig usig home All Male Female All Male Female ~.0%.0%.0% 0.9% 0.90% 0.98% ~8.%.0%.0%.%.0%.% 8+ 8.%.% 0.88%.8% 8.00%.% Daa esoue: Healh, Uied Saes, 00 ad 00--Table : Poulaio by age, sex, ad ae; ad Table 99 ad 0: Nusig home esides yeas of age ad ove by age, sex, ad ae. Daa Saisis ables Table Pemiums by age gous (ese values: 00 dolla Timig of Age gous Alyig LTCI : ~0 : ~0 : ~0 : ~0 : ~0 : ~80 : 8~90,0,80, ,8,89,0 - -,,, ,8 80,, ,,, ,9 0, , Table. Media iome by age gous (ese values: 00 dolla Age gous Media : -0,0 : -0,9 : -0,0 : -0,00 : -0,0 : -80, : 8-90,9

48 8 Table. Suvival obabiliies by age gous Age gous Aveage suvival obabiliies hough yea 99 o yea 00 : : : : : : : Table. Meas of Nusig home oss (00 dolla ad he legh of say by age gous Age gous Mea of NHC Mea of legh of say : : -0 0 : -0,0 : -0,0 0 : -0,98 0 : -80,0 08 : 8-90,0 Table. Mea of Ou-of-oke medial exeses by age gous (00 dolla Age gous Mea of OOPMD : -0 8 : : -0,98 : -0, : -0,9 : -80,9 : 8-90,0

49 9 Table. Meas of oveage by eiods (based o he mea legh of say i Daa Timig of Age gous Alyig LTCI : ~0 : ~0 : ~0 : ~0 : ~0 : ~80 : 8~ ,,9,0, 0 0 0,0,,, 0 0 0,08,8,90, ,0,80,0 8, ,0,0 8, , 9, ,8 Table. The obabiliy of a usig home say Age Gou % of eole eve sayed i usig home : -0 0 : % : -0 0.% : -0 0.% : -0.9% : -80.% : %

50 0 Figues Figue -. LTC isuae aliaio wih =0.0 Figue -. LTC isuae aliaio wih = Uiliy Values Uiliy Values Figue -. LTC isuae aliaio wih =0.0 Figue -. LTC isuae aliaio wih = Uiliy Values Uiliy Values

51 Figue -. LTC isuae aliaio wih =0.0 Figue -. LTC isuae aliaio wih = Uiliy Values Uiliy Values 0 0 Figue -. LTC isuae aliaio wih =0.0 Figue -8. LTC isuae aliaio wih = Uiliy Values Uiliy Values 0 0

52 Figue -9. LTC isuae aliaio = Uiliy Values Figue -0. LTC isuae aliaio wih legh of say 900 i 80s Uiliy Figue -. LTC isuae Aliaio wih legh of say 0 i0s ad 80s Uiliy Values Figue -. LTC isuae Aliaio wih legh of say 00 i 0s, 0s, ad 80s Uiliy Values

53 Figue -. LTCI Aliaio ude high obabiliy -- =0.0 Figue -. LTCI Aliaio ude high obabiliy -- = Uiliy Values Uiliy Values Figue -. LTCI Aliaio ude high obabiliy -- =0.0 Figue -. LTCI Aliaio ude high obabiliy -- = Uiliy Values Uiliy Values

54 Figue -. LTCI Aliaio ude high obabiliy -- =0.0 Figue -. LTCI Aliaio ude high obabiliy -- = Uiliy Values Uiliy Values Figue -. LTCI Aliaio ude high obabiliy -- =0.0 Figue -8. LTCI Aliaio ude high obabiliy -- = Uiliy Values Uiliy Values

55 Figue -9. LTCI Aliaio ude high obabiliy -- =0.0 Figue -0. LTCI Aliio ude high obabiliy--wih legh of say 900 i 80s Uiliy Values Uliy Values Figue -. LTCI Aliio ude high obabiliy--wih legh of say 0 i 0s ad 80s Uliy Values Figue -. LTCI Aliio ude high obabiliy--wih legh of say 00 i 0s, 0s, ad 80s Uliy Values.

56 Figue -. LTCI Aliaio whe deeasig emium / ieasig usig home oss Low emium High NHC.0 0 Alyig ime

57 Figue -. LTCI Aliaio whe deeasig emium/ieasig usig home oss wih high babiliy Low emium & high ob High NHC & high ob

58 Figue -. LTCI Aliio whe deasig emium ad ieasig usig home oss wih low/high obabiliy Low Pem. & High NHC Low Pem. & High NHC ude high ob