Healh Spending - Factors, Effects and Insurances

On The Rise of Healh Spending and Longeviy Raquel Fonseca 1 RAND Pierre-Carl Michaud RAND, IZA and NETSPAR Tius Galama RAND Arie Kapeyn RAND, IZA and NETSPAR December 2009 Absrac We use a calibraed sochasic life-cycle model of endogenous healh spending, asse accumulaion and reiremen o invesigae he causes behind he increase in healh spending and life expecancy over he period 1965-2005. We esimae ha echnological change along wih he increase in he generosiy of healh insurance may explain independenly 53% of he rise in healh spending (insurance 29% and echnology 24%) while income less han 10%. By simulaneously occurring over his period, hese changes may have lead o a synergy or ineracion effec which helps explain an addiional 37% increase in healh spending. We esimae ha echnological change, aking he form of increased produciviy a an annual rae of 1.8%, explains 59% of he rise in life expecancy a age 50 over his period while insurance and income explain less han 10%. Keywords: demand for healh, healh spending, insurance, echnological change, longeviy. JEL Codes: I10, I38, J26 1 Corresponding Auhor: Raquel Fonseca, 1776 Main Sree, CA 90401-2138: fonseca@rand.org. We would like o hank Michael Hurd, Arhur van Soes, Peer Kooreman, Rob Alessie, Dana Goldman, Darius Lakdawalla, Eric French, John Jones, Luigi Pisaferri and seminar paricipans a USC, Tilburg, NETSPAR, UCSB, and he Universiy of Michigan for heir helpful commens on previous drafs of his paper. Errors are our own. 1

1. Inroducion According o a recen repor from he Congressional Budge Office (CBO, 2008), per capia healh spending in 2005 was 6 imes wha i was in 1965. As a fracion of per capia income, healh spending in he U.S. has grown from 4% o 16%. Newhouse (1992) concludes ha more han half, perhaps even 65%, of he change is probably aribuable o echnological change, wih more generous healh insurance and he growh in income accouning for a mos one hird of he rise in healh spending. Over he same period, life expecancy has increased considerably, paricularly among he elderly. In 2005, a 50 year old men could expec o live 28.9 years compared o 22.95 in 1965. Culer, Deaon and Lleras-Muney (2006) argue ha echnological change is he leading explanaion for he increase in longeviy since evidence from he Healh Insurance Experimen (HIE, Manning e al., 1987) and oher recen sudies on he SES-healh gradien (Adams e al., 2003; Smih, 2007) sugges ha neiher growh in income nor he spread of healh insurance can explain changes in life expecancy of ha magniude. In a recen sudy, Hall and Jones (2007) show ha one can generae he growh in healh spending and he resuling change in life expecancy solely as a resul of growh in income using a model of endogenous healh spending (Grossman, 1972; Ehlrich and Chuma, 1990). Insead of modeling oher changes simulaneously, Hall and Jones show ha wih reasonable parameer esimaes and implied value of longeviy gains, one can generae he rise in healh spending and life expecancy, assuming i is an opimal response o he growh in income. 2

We follow a similar modeling approach, generaing healh spending growh as an opimal response o changing circumsances. We inroduce in our framework healh insurance and echnological change as explici possible compeing alernaives o income growh. We calibrae a sochasic life-cycle model of endogenous healh spending, asse accumulaion and reiremen wih deailed modeling of healh insurance, Social Securiy and axaion using micro-daa from 2000 o 2005. Our calibraion approach involves fiing life-cycle profiles of asses, medical expendiures, reiremen and moraliy. We also calibrae he parameers of he model such ha behavioral responses o changes in healh insurance and income are similar o hose repored in he lieraure. We hen perform counerfacual simulaions where we firs find he necessary produciviy gains such ha we reach 1965 healh spending levels. We find ha a 1.8% annual growh in produciviy is necessary o achieve he 1965 healh spending levels. Once we obain simulaed profiles for 1965, we inroduce sequenially each of he compeing explanaions for he rise in healh spending o undersand heir relaive imporance. We find ha far from compeing, hese are reinforcing forces: as much as 37% of he overall increase in healh spending is due o he fac ha hese occurred simulaneously. We ge a somewha differen sory when we sudy he facors joinly regarding he relaive imporance of each facor in independenly explaining he rise in healh spending. We find ha he increase in healh insurance copaymen has been as imporan as echnological change while growh in real income over his period explains a mos 10% of he rise in spending. Moreover, we find ha boh income and healh insurance copaymens can only explain up o 10% of he rise in longeviy while produciviy gains from echnology accoun for up o 60% of he gain in life expecancy. 3

The relaive imporance of income in our sudy differs from Hall and Jones (2006) for wo imporan reasons. Firs, Hall and Jones (2006) use real GNP per capia growh while we use real earnings growh, he firs one being much larger over his period. For workers in our sample, mos of he growh in real GNP was no refleced in earnings growh. The average worker saw a growh in earnings of roughly 25% over he period we cover compared o growh in GNP per capia nearing 200% beween 1965 and 2005. Second, we obain a lower income elasiciy of medical care. Hall and Jones need an income elasiciy of medical care close o 4 in order o explain, solely using income growh, ha medical expendiures rose by 800% while GNP per capia rose by roughly 200% beween 1950 and 2000. Our esimae of he income elasiciy (o a permanen change in income) is close o uniy which is in line wih he cross-naional esimaes from he lieraure and larger han hose from he micro-lieraure (beween 0.2 and 0.4) (see Newhouse, 1992). Hence, in our model income does no explain he rise in he share of healh spending. Insurance and echnology do, and income faciliaes he spillover effec. In secion 2 we presen he model. Secion 3 presens he daa and he calibraion. In secion 4 we perform he counerfacual simulaions. We conclude in secion 5. 2. Model We build a model where an agen makes decisions over he enire life-cycle regarding healh spending, consumpion and reiremen. The agen faces healh risk, job risk and insurance coverage risk (up o he age of Medicare eligibiliy). The framework is closes o he one considered by French and Jones (2007) wih hree imporan differences. Firs, we endogenize healh spending. Healh spending can affec healh which in urn affecs direcly fuure healh, uiliy and earnings. In ha sense, our modeling of healh 4

spending is closes o he human capial framework of Grossman (1972). 2 Second, an imporan difference is ha we do no allow for uncerainy in earnings and medical expendiures given healh, job and insurance saus. Once medical expendiures are endogenous, here is lile reason o hink of he realizaion of healh spending as sochasic condiional on a given healh insurance, job and healh saus. In fac, hey are assumed sochasic, ex ane, as he individual does no know ye his healh, job and healh insurance saus. Finally, anoher imporan difference is ha we assume labor supply is inelasic up before he agen chooses he age of reiremen and ha reiremen is an absorbing sae. We do his because labor supply plays a secondary role in our analysis. 2.1. Decisions and Preferences The agen makes decisions from age =,..., T and dies wih cerainy a age. In oher 0 words, he erminal age T is he limi on human life. A each age, we assume he agen makes hree decisions d = (c,m,r ). She chooses non-medical expendiures c, medical expendiures m and her reiremen saus r. If she reires, le r = 1 and r = 0 if no. For our purposes, we will assume reiremen is an absorbing sae and is possible afer age 54. A age 70, we assume everyone is reired (few in he daa work beyond ha age). A age, she has a healh sae h assumed o ake 6 values {0,1,2,3,4,5} where zero denoes deah and values 1 o 5 denoe he self-repored healh saus scale {poor, fair, good, very good, excellen}. We assume preferences are represened by he following uiliy funcion 2 Oher sudies invesigaing endogeneous healh invesmen include Blau and Gilleskie (2008), Galama e al. (2008), Khwaja (2009), Yogo (2009), Bajari, Hong and Khwaja (2009), Halliday, He and Zhang (2009), Juergen and Tran (2007), Suen (2009) 5

u(c,m,r ) = c 1!! 1!! + " h +e " +" 0 r h,>2. (1) The parameer! capures he degree of relaive risk aversion,! h measures he direc uiliy of good healh where h,>2 = I(h > 2). 3 Finally! 0,! conrol he direc uiliy of leisure in reiremen, which may vary wih age. We assume she has a beques moive. When she dies a age, she leaves a beques in erms of accumulaed asses, a, which give uiliy b( a ) =! log( a ). (2) b We assume ha he beques funcion is logarihmic and he parameer! measures he b srengh of he beques moive. 2.2. Asses A each age, he agen can decide o forgo consumpion and inves insead in a composie asse a wih annual reurn!. We specify a life-ime budge consrain following Hubbard, Skinner and Zeldes (1995). A each age, cash-on-hand, x, is he sum of las-period asses a and oal ne income y (including asse income) while oal expendiures is he sum of non-medical expendiures and ou-of-pocke medical expendiures oop (more deail is provided in secion 2.5). We assume asses mus be non-negaive a all ages (he agen canno borrow, paricularly agains pension wealh). End of period asses a + are defined 1 as a +1 = x + r!c!oop, a +1 " 0 for all. (3) 3 For simpliciy, we assume being in excellen, very good and good healh yields he same uiliy. 6

Governmen ransfers are given by r = max( c! x, 0) where c is a minimum min min consumpion level guaraneed by he exisence of subsance programs such as, emporary assisance for needy families (TANF), food samps, housing benefi and Supplemenal Securiy Income (SSI). 2.3. Income and Pensions An agen s oal ne income is given by e s o y = ax( y, y, y,! a ) (4) e where ax() is a ax funcion ha depends on annual earnings y, social securiy benefis s y, oher (spouse) income o y and asse income! a. Earnings - Earnings are assumed deerminisic, condiional on age, employmen and healh saus. If he individual is employed, we specify he log earnings equaion as logy e =! 0 +! 1 +! 2 2 5 +!! 3,s h,s (5) where h = I( h = s). Noe ha fuure earnings are uncerain due o uncerainy in healh, s and employmen. If unemployed or reired, earnings are zero. s=2 Reiremen Income - Prior o he age of 62, individuals do no receive reiremen income if hey decide o reire. They finance consumpion hrough heir accumulaed savings unil hey reach he age of 62. Afer he age of 62, hey are assumed o be eligible for Social Securiy a which poin hey can sar receiving benefis if hey reire. As for hose who elec no o reire prior o 62, hey can delay reiring/claiming Social Securiy 7

unil hey reach he age of 70 a which poin everyone is assumed o reire (and claim). Social Securiy benefis are a funcion of lifeime earnings and he age of reiremen. The measure of lifeime earnings used is he average indexed monhly earnings (AIME) denoedae, which represens he average of he 35 highes years of earnings. Before reiremen, we approximae he evoluion of AIME using he funcion ae = G( ae, y e, ) (7) + 1 where G () is an age-specific non-linear regression of nex period ae + 1 on curren earnings, e y. This funcion is esimaed on Social Securiy earnings records from he ae and Healh and Reiremen Sudy (secion 3.1.1). 4 To calculae Social Securiy benefis a he normal or full reiremen age (NRA), one simply ranslaes he AIME ino he Primary Insurance Amoun (PIA) by applying a concave funcion which is piece-wise linear. If he individual reires prior o he NRA, his benefi is reduced by an acuarial adjusmen facor (arf). The same holds if he individual reires beyond he NRA. We follow French (2005) and compue, a he ime where someone claims, a new AIME such ha pia ae * ( ) arf ( ) pia( ae ) = (6) holds. The new AIME is hen kep permanenly unil deah. Social Securiy benefis are hen given by y s = pia ae once an individual has claimed. * ( ) Oher Income Oher income is composed of he spouse s income. I is assumed o be a o e funcion of age and earnings, y = o(, y ). 4 The approximaion performs well in pracice. The main advanage is ha we avoid having o include he enire earnings hisory in he sae-space (French 2005). 8

2.4. Healh An individual s fuure healh saus is modeled as a dynamic ordered response process, which depends on curren healh saus, medical expendiure, hrough a healh invesmen funcion, and age. We firs discuss he healh invesmen funcion and hen discuss he dynamic healh process. Healh Invesmen There is lile guidance from he lieraure on he form of he healh invesmen funcion. As Elrich and Chuma (1990) argue, a funcion feauring diminishing reurns is probably realisic. We use he following producion funcion I( m, h, ) =! (, h ) 0 1!! 1 (1 + m )! 1 1!! 1. (8) The elasiciy of his funcion wih respec o medical expendiures is negaive and decreases wih m if! > 1. As Hall and Jones (2006) show, he rae a which he 1 elasiciy of he healh producion funcion o medical expendiures decreases is direcly relaed o he responsiveness of he opimal invesmen o income changes. Inuiively, wih consan life-cycle consumpion and moraliy rae, an addiional dollar spen on healh care is more valuable if he life exension i buys is valued more han he uiliy oday from spending ha dollar on consumpion. The more concave he uiliy funcion is relaive o he producion funcion, he more valuable is he dollar spen on healh. Hall and Jones (2006) consider a consan elasiciy producion funcion. We use a more flexible form in order o have addiional degrees of freedom when fiing o he daa.! +! h +! 00 0, 3 0 The produciviy erm is given by (, ) e h <! h =. We allow he 0 produciviy erm o increase in bad healh (fair and poor) and o increase wih age. We 9

inerpre he age coefficien in he produciviy erm as an ineracion beween depreciaion and produciviy. As he body depreciaes, here is more ha echnology can do o resore healh. A high levels of healh and younger ages, here is less knowledge in he medical field how o proec he body agains rapid depreciaion. Healh Process - Define nex period s healh index as * h +1 5 =! 0 () + I(m,h,) + "! h!1 I(h = h) + " (10) h=2 where! is a sandard normal healh shock and! ( ) is a a 0 4h order polynomial in age. The laen healh index is ransformed ino healh saus hrough he following rule, h = h " h < h =. * if!!, 0,...,5 h! 1 h where {! h } is a se of hresholds. Because of he normal error assumpion, his defines h= 1,...,5 a dynamic ordered probi process. 2.5. Employmen and Healh Insurance Employmen and healh insurance are sochasic and ou of he conrol of he agen. We assume ha four saes are possible: employed/unemployed wih or wihou healh insurance. The saes are defined as e = {0,1,2, 3} where zero is unemployed wihou insurance, 1 is unemployed wih healh insurance, 2 is employed wihou healh insurance and 3 is employed wih insurance. We assume he probabiliies of ransiing from one sae o he nex are firs-order Markov and depend only on age. Upon reiremen, he agens who had insurance coverage on heir job reain i while hose wihou have o wai unil hey become Medicare eligible. If he individual has healh insurance ( e = 1,3 ), we use a sandard healh insurance conrac wih a deducible and co-insurance rae o ransform oal ino ou-pocke expendiures. 10

Hence, we assume he availabiliy of reiree healh insurance for hose wih insurance on he job a he ime of reiremen. 5 Ou-of-pocke medical expendiures when he agen is no Medicare eligible are given by " oop (m,e ) = min(m,µ ) + µ max(m! µ,0) if e = 1,3 1 2 1 $ m if e = 0,2 (11) # where ( µ 1,, µ 2, ) are he corresponding deducible and co-insurance rae respecively if covered a age. If Medical eligible (age 65 and older), we use a similar insurance conrac as when e = 1,3. Because we follow annual medical expendiures and no docor visis and hospial says i is impossible o incorporae paymen rules under Medicare Par A oher han hrough an approximaion. 6 Bu Medicare Par B coverage which covers oupaien procedures is very similar o he median employer provided healh insurance conrac. We provide more deails in secion 3.2. 2.6. Soluion of he Dynamic Problem The agen maximizes he discouned sum of uiliy flows using a discoun facor!. A each age, he agen can choose d from a se of possible decisions D( s ) given he sae space s = (, e, h, r, a, ae ). The indirec uiliy of he agen a age is wrien as! 1 5 See French and Jones (2007) and Blau and Gilleskie (2008) for models where reiree healh insurance is also sochasic. Boh of hese sudies ake insurance as given and ou of he conrol of he individual (excep for he fac ha he individual can change/qui a job wih insurance). Marquis and Long (1995) analyze he price and income responsiveness of he demand for healh insurance in he non-group marke. They find a price (premium) elasiciy of -0.3 o -0.4 and an income elasiciy of 0.1. See Bajari, Hong and Khwaja (2009) for a sudy looking a healh insurance decisions in a life-cycle framework. 6 See Blau and Gilleskie (2008) for a model where docor visis raher han medical expendiures are modeled. 11

v(s ) = max u(d d!d(s ) ) +![" " p h (s,m )p e (s )v(s +1 s,d ) + p 0 (s,m )b(a +1 )] (12) h!=0 e where ph( s, m ) denoes he probabiliy of being in sae h + 1 = h a age + 1 and p ( s ) e denoes he probabiliy of employmen/healh insurance saus. Equaion (12) is subjec o preferences and consrains from (1) o (11). * * This problem can be solved for he opimal soluion: [ d ( s ), v ( s )] by =,..., T 0 backward recursion. We assume a erminal age of 105 and a saring age of 25. We assume everyone who is sill alive a age 105 dies. The currency used hroughou is housands of $USD 2004. We provide deails on he soluion mehod in he Technical appendix. 2.7. Simulaion We simulae he life-cycle rajecories of 1,500 hypoheical individuals saring a age = 25 by firs drawing iniial condiions from he join disribuion of AIME, asses and 0 healh in he daa (see secion 3.3). We hen apply he decision rules and updae he saespace a each age unil individuals reach age 105 (or die). We draw healh and employmen/healh insurance shocks from heir respecive disribuions. Since he sae a each age migh no fall on he grid, we use linear inerpolaion for consumpion, medical expendiure and reiremen decisions. 3. Daa and Calibraion We focus on describing he behavior of a relaively homogeneous group because he model allows for limied heerogeneiy. We chose o calibrae he model so ha i maches he behavior of non-hispanic whie men wihou a college educaion. We could no find 12

evidence ha growh in healh spending or life expecancy has been differen across sociodemographic groups. Many sudies documen preference heerogeneiy across groups and growh in income has been very differen for college graduaes relaive o he res of he populaion. We use hree main sources of daa. The firs is he Panel Sudy of Income Dynamics (PSID), which we use for labor force and insurance saus, healh saus, earnings and asses from age 25 ill deah. The PSID has informaion on medical expendiures a he household level. A second and more adequae source of daa on individual medical expendiures is he Medical Expendiure Panel Survey (MEPS) for he years 2000 o 2003. Finally, we use he HRS for wo purposes. Firs, we use Social Securiy earnings records of respondens o he Healh and Reiremen Sudy o esimae he relaionship beween AIME and earnings as described in equaion (7). Second, he PSID seriously underesimaes moraliy in old age and has sparse cell couns over age 80. Hence, we use healh saus (which includes moraliy) of respondens over age 50 from he HRS. Since cohor effecs may exis, we selec where possible daa from he cohor born beween 1936 o 1940 which is of reiremen age (age 60 o 64) in he year 2000. We use self-repored healh as our measure of healh. Alhough we are aware ha i is an imperfec measure of healh, here are no oher caegorical measure ha provide an all encompassing measure of healh over he life-cycle. We reverse he original scale so ha 1 equals poor healh and 5 excellen healh. Furhermore, we add he caegory 0 which is defined as deah. Deah is inferred from exi inerviews in he HRS and PSID as well as a maching procedure o he Naional Deah Records for HRS respondens. 13

We firs discuss he esimaion of auxiliary processes used in solving he model, such as he earnings, oher income, AIME, employmen/healh insurance and finally healh processes. We hen follow wih insiuional deails such as axes, compuaion of Social Securiy benefis and healh insurance premiums and co-insurance levels. We hen discuss how iniial condiions are drawn (he iniial disribuion of individuals a age 25). Finally, we discuss he esimaion of profiles from he daa used o calibrae parameers. This allows us o pin down a configuraion of srucural parameers maching he daa. 3.1. Auxiliary Processes 3.1.1. Earnings, AIME and Oher Income We esimae he earnings profile from he PSID using waves from 1980 o 2005. We use he sample of respondens aged 21 o 70 wih posiive earnings. Afer deleion of exreme cases, his leaves records on 3714 respondens wih on average 6.4 observaions per responden. 7 We use log earnings as he dependen variables and conrol a quadraic in age, indicaors for healh saes (2 o 5) and fixed effecs. Upon esimaion, we use he average of he fixed effecs for he 1940 cohor o race ou he earnings profile. Esimaes are repored below along wih sandard errors (in parenhesis). e 2 log( ) = 0.809+ 0.099! 0.001 + 0.098 (0.226) (0.009) (0.001) (0.035) y h + 0.14 h + 0.166 h + 0.158h,3,4,5 (0.036) (0.037) (0.037),2 (13) Our esimaes repor a subsanial penaly from being in poor healh ( h = 1 ) relaive o oher healh saes. Relaive o being in poor healh, being in fair healh is 7 We drop observaions wih earnings larger han $200 housand per year and less han $5 housands. 14

associaed wih a 9.8% increase in earnings, being in good healh 14% and being in excellen healh 15.8%. The esimaed earnings profile peaks a age 46 wih average earnings of jus over $32 housand dollars. The average indexed monhly earnings is he average of he highes 35 years of earnings where each year of earnings is indexed o age 60 wage levels using he Naional Wage Index. We use earnings hisories o esimae ha process. The process for AIME is esimaed from Healh and Reiremen Sudy Daa merged wih Social Securiy earnings hisories. We use daa from hose born beween 1936 and 1940. We posulae he following age-specific log-log regression: log ae =! +! I( y > 0) +! log y +! log ae + " (14) e e 0 1 2 3 # 1 where! is a predicion error. We consruc he AIME on he lef-hand side using he compued AIME from earnings hisories (35 highes years) and regress on curren earnings, wheher earnings are greaer han zero. The R-square from such regressions comes close o 0.99 for mos ages. The coefficiens a each age are displayed in he Technical appendix. We esimae he process for oher income using he 1980 o 2005 waves of he PSID. Oher income is defined as spousal income. We esimaed he following median regression Q 0.5 ( y o, y e ) =! 7.97+ 0.345 +!0.003 2 + 0.076 (0.319) (0.013) (0.0001) (0.0009) which yields an age profile peaking a age 44 wih a value of $11.51. y e + 5.55 I( y e (0.127) > 0) (15) 3.1.2. Employmen and Insurance Transiion Probabiliies We use he 1999 o 2005 waves of he PSID o esimae employmen and insurance probabiliies. We define a non-employmen as being unemployed and drop observaions 15

where respondens do no paricipae in he labor force.. We define someone as insured (prior o Medicare eligibiliy) if he is eiher covered by employer provided healh insurance (own or hrough spouse) or privae insurance. Figure 1a repors he fracion in each sae as a funcion of age. On average 17.9% of hose aged 25 o 64 do no have healh insurance. The fracion of uninsured workers seadily decreases wih age unil age 50 and hen increases slighly. A small fracion, 3.2%, are unemployed. The fracion of unemployed decreases slighly wih age. We esimae wo-year ransiion probabiliies as a funcion of age and he origin sae using a mulinomial logi model. The probabiliy of ransiion o each of he four saes is defined by 3 exp(! 0e +! e + "! ej I(e!1 = j)) j =1 p e (,e!1 ) = 3 3 1 + " exp(! 0k +! k + "! ek I(e!1 = k)). (16) k =1 e = 1,2,3 These are esimaed using he sample of respondens age 25-64. We compue annual ransiion probabiliies by aking he square roo of he biennial ransiion marix a each age. j =1 3.1.3. Healh Process To esimae he healh process, we ideally need panel daa on boh healh and individual level medical expendiures. MEPS is a shor panel (on average 2 years) ha does no allow o esimae annual ransiion probabiliies across healh saes reliably. On he oher hand, he PSID does no have individual level daa on medical expendiures (only a he household level). Finally, he PSID does no capure moraliy well, paricularly in old age. The HRS provides beer coverage in old age bu lacks daa on he populaion younger han 16

50 and has very noisy medical expendiure daa compared o he MEPS. Our sraegy is o combine all hree daa sources for he purpose of calibraing he healh process. Selfrepored healh is defined in he same way in all hree surveys. Hence, we resor o he following sraegy: Esimae he disribuion of medical expendiures as a funcion of self-repored healh saus and age in he MEPS. We assume he disribuion has wo-pars, firs wheher expendiures are posiive or no and hen log normally disribued when posiive. We keep boh he fracion of posiives, mean and variance of he log normal disribuion condiional on having posiive expendiures for each age and healh sae. Pool ogeher boh PSID daa for hose age <50 (waves 1999 o 2005) and HRS daa for hose age >50 (waves 1992 o 2006). The disribuion of self-repored healh is remarkably similar a he cuoff ages of 50 as can be seen from Figure 1b. Esimae parameers of he healh process (! ) oher han hose of he invesmen funcion (! ) by maximizing he following likelihood: L(! ",h i, i ) = # p h,psid (,h i,m i ;") f MEPS (m i h i,)dm i i,"psid! (17) $ # p h,hrs (,h i,m i ;") f MEPS (m i h i, i )dm i i,"hrs! where he probabiliies p (, h, m ;!) are ordered probi probabiliies for observing in h, x i i i daase x an individual a age + 1 in sae hi, + 1 = h given age, curren healh saus, medical expendiures and condiional on he produciviy parameers!. The inegrals are evaluaed using simulaion by drawing from he disribuion of medical expendiures in he 17

MEPS. We use 25 draws per responden/wave. The resuling maximum simulaed likelihood esimaor! ˆ( ") provides us wih a calibraion ha fis he healh process given a choice of produciviy parameers. We perform his condiional procedure because we calibrae! using oher momens from he daa. Based on various diagnosic ess, i became apparen ha he age-invarian assumpion on he hresholds of he dynamic ordered model was oo resricive, paricularly for moraliy ( h = 0 ). Hence, we allowed i he hreshold defining he upper bound for moraliy o depend on a fourh order polynomial in age. 3.2. Insiuional Deails There are hree imporan insiuions represened in he model. Firs, here is he income ax schedule. Second, he Social Securiy benefi calculaion formula and finally he Medicare and Non-Medicare healh insurance ou-of-pocke schedule. We use he 2001 Tax funcion aking ino accoun Federal axes and Social Securiy & Medicare axes. We allow for basic deducion in couples and he personal exempion. Prior o age 65, he deducion is $7.6 and afer 65 i is $9.65. We accoun for he parial ax reamen of Social Securiy benefis by axing only 50% of Social Securiy benefis. Social Securiy benefis are basically a funcion of hree facors: a measure of average earnings (AIME), birh year, and age a which benefis are firs drawn. For our purposes, he Social Securiy earnings es is irrelevan since we assume individuals wihdraw from he labor force a he ime where hey claim benefis. Furhermore, we model spouse benefis hrough oher income such ha he oher spouse's receip of Social Securiy does no play a disinc role. We assume individuals are born beween 1936 and 18

1940 and ha heir Normal Reiremen Age (NRA) is 65 years of age (in realiy i was 65 for hose born in 1936 and 65 and 6 monhs for hose born in 1940). To calculae he monhly benefi, he AIME is ransformed ino he Primary Insurance Amoun (PIA). The PIA is a piece-wise linear concave funcion of he AIME. The PIA is he benefi ha would be paid if claimed a he NRA. If he individual claims prior o he NRA, he PIA is reduced by 7.6%. Similarly, an individual can claim his benefi pas he NRA in which case a delayed reiremen credi (DRC) is graned. The credi is 6.5% for hose born in 1938 (6% for hose born in 1936 and 7% for hose born in 1940). Upon reaching 70, here is no DRC applied. For hose younger han 65 and insured, we use daa repored by Blau and Gilleskie (2008) from he Healh Insurance and Pension Provider Survey (HIPPS). The median deducible is found o be $0.2 and he median co-insurance rae is 20%. The median premium is $0.48. We do no impose a sop-loss on he insurance conrac (maximum ouof-pocke). Since here is no direc cos o invesing in healh, individuals in he model who desire o spend slighly more han he sop-loss would hen consume an infinie amoun of care. Esablishing an overall co-insurance rae and deducible for Medicare is more complicaed. Only Medicare Par B, which covers oupaien reamens, has a common deducible-coinsurance srucure (par D was no in place for hose respondens a he ime). There is no premium for par A and he cos-sharing schedule depends on hospial says, which we do no model. The premium for Medicare par B is $0.49 per year, he deducible $0.2 and he co-insurance rae 0.2 (20%). Hence, we choose o simply use he same price schedule for Medicare and Non-Medicare insurance. Therefore, wihin he 19

conex of our model, here is very lile difference in coverage prior and afer Medicare eligibiliy for hose insured. The main difference is he uncerainy in insurance coverage. We applied he insurance parameers o oal medical expendiures and compared wih acual ou-of-pocke expendiures repored in MEPS. A he mean, he compued ouof-pocke expendiures are very similar o hose from he daa, boh before and afer he age of Medicare eligibiliy. 3.3. Iniial Condiions We draw iniial condiions for asses, AIME, insurance coverage and healh saus from he empirical disribuion in he PSID daa a age 25 (we use age 24 o 28 o boos he sample and replicae observaions using frequency weighs). However AIME is no measured in he PSID. Since AIME is very close o earnings for hose respondens (hey have lile labor marke experience) we apply he following procedure. We firs compue someone s percenile in he earnings disribuion a age 25. We hen aribue he AIME of someone in he same percenile of he earnings disribuion from he HRS resriced SSA earnings records. This impuaion procedure preserves he correlaion beween earnings and oher oucomes (asses, insurance coverage and healh saus). 3.4. Momens To calibrae he model, we use four ses of momens. Firs, we use median asses by age from he PSID. Second, we use reiremen hazard raes by age from he Healh and Reiremen Sudy. Third, we use average medical expendiures by age from he MEPS. Fourh, we use moraliy raes from ages 50 o 100 compued from he Healh and 20

Reiremen Sudy. We discuss he consrucion of hose momens below. Figure 2 repors esimaes of hose momens by age. 3.4.1. Asses We esimae a median asse age-profile using he PSID following he mehodology of French (2005). Asses include all real and financial asses minus deb. We express all moneary amouns in $2004 and discard observaions wih asses larger han $1e+06. We esimae a median regression model of he form Q ( a, cohor, hhsize) =! +! + " + # hhsize 0.5 0 cohor where! are age fixed effecs. We also conrol for 5-year cohor fixed effecs (! cohor ) and household size ( hhsize ). Upon esimaion we predic for household size of 3 born beween 1936 and 1940. a 3.4.2. Reiremen Reiremen is a complex sae o measure. Firs, some workers reurn o work afer prolonged periods of inaciviy in old age while no considering hemselves reired. Second, some workers work while claiming Social Securiy benefis. Since our model considers a simplified definiion of reiremen, i is no clear which concep should be used. We eleced o use self-repors of respondens on wheher hey are reired in he HRS. We exclude as reired hose who repor being reired bu are sill a work. We use he reiremen ages from he cohor born beween 1931 and 1941 which has almos enirely 21

reired by 2004. We find peaks in he reiremen hazard a age 62 and 65 which are respecively he ages of early and normal reiremen age under Social Securiy. 3.4.3. Medical Expendiures We use median oal medical expendiures from he 2000 o 2003 waves of he MEPS. These expendiures include in-paien and ou-paien expendiures as well as drug expendiures. They do no however include nursing home expendiures. To be consisen wih oher moneary flows in he model, we express hose in $2004 dollars using he CPI. No surprisingly, medical expendiures increase seadily wih age. 3.4.4. Moraliy We use he moraliy profile from he Healh and Reiremen Sudy (older han 50) raher han from official life ables because we are looking a a specific sub-populaion (nonhispanic whie men wih high school or less educaion). We express biannual raes ino annual ones assuming a consan hazard wihin each age inerval. Even wih large samples, he moraliy raes a older ages are quie volaile as can be seen from Figure 3. Smoohing hese moraliy raes (using a quadraic in log moraliy raes) and compuing a life-able yields remaining life expecancy of 47.3 years a age 25 and 26.9 years a age 50. We also repor he moraliy raes for men in 2002. Whie males wihou college educaion have slighly lower life expecancy han average males. Life expecancy a age 25 according o he life able is 49.2 years and 27.6 a age 50. 22

3.5. Calibraion 3.5.1 Preferences and Producion Funcion In principle, we can esimae all srucural parameers of he model using a mehod of simulaed momens approach. For his paper, we have insead used a calibraion approach, which consis of choosing manually parameers such ha he fi of he momens is saisfacory for our purposes. However, we wish o emphasize ha here is no way for us o claim ha his is he unique and opimal se of parameer esimaes for his model. There migh well be oher parameers ha provide an equally (or even beer) fi of he model. In choosing hese parameers, we have borrowed parly from he lieraure on consumpion and labor supply. We should noe ha no esimaes of parameer values exis for a model ha simulaneously feaures endogenous healh spending, savings and reiremen. Table 1 provides he values of he parameers we have chosen. Esimaes of risk aversion vary subsanially across sudies. Sudies using linearized Euler equaions and consumpion daa end o esimae risk aversion parameers in he range 1.5 o 2.5 (Aanasio and Weber, 1995). Esimaes based on asse daa end o be much larger. Cagei (2003) esimaes on PSID daa risk aversion parameers ranging from 2.7 o 4.3. Recen esimaes by French (2005), French and Jones (2007) and De Nardi, French and Jones (2006) sugges a risk aversion coefficien in he range 3-7. Each of hese models are differen and he esimae of risk aversion can be very sensiive o he amoun of risk assumed, he sample used (elderly vs. young), he exen of liquidiy consrains and he presence of a consumpion floor. One of he reasons for he larger values in hese recen sudies is he role played by he consumpion floor in depressing savings (Hubbard, Skinner and Zeldes, 1995). Hence, a larger value of risk aversion is needed o raionalize savings when here is a consumpion floor. We chose a value of 2.6 for risk aversion. We 23

fix he consumpion floor a $3000 following he argumen ha few of he social programs in place apply o married men (accouning for 85% of he sample) and ha ake-up of hose problems is generally well below 50% (De Nardi, French and Jones, 2006). The real rae of reurn is se o 3%. There is considerable heerogeneiy in esimaes of he discoun rae. Some sudies find very low values, even negaive [-0.04, -0.02] (Hurd, 1989; French, 2005) while ohers find relaively larger values [0.04 o 0.07] (Gourinchas and Parker, 2002; Cagei, 2003; De Nardi, French and Jones, 2006). We use a value of 0.05. Hence, individuals can be characerized as relaively impaien and precauionary savings play an imporan role in consumpion decisions. We impose a relaively srong beques moive in order o raionalize he high level of asses in old age (relaive o annuiy income). The value of! b is se o 0.05. Nex, we pin down reiremen by choosing he marginal uiliy of leisure. We selec values such ha hey capure he disribuion of reiremen ages and a median reiremen age of 63.5 years. Finally, we calibrae he healh producion funcion and disuiliy/uiliy of poor healh saus. We use he average medical expendiure profile, which rises almos linearly wih age. This, along wih he life-cycle pah of healh and moraliy informs on he produciviy of medical care. 8 We find ha low values of produciviy are necessary o raionalize why individuals spend so lile on heir healh a earlier ages given he poenially imporan reurns in erms of wages and consumpion benefis. Wihou an age adjusmen, he medical expendiure profile is much flaer as we canno raionalize why 8 Trivially, a zero produciviy, here are no simulaed medical expendiures. Increasing he produciviy will lif he simulaed medical expendiure profile. Bu if he simulaed profile is below he rue profile, moraliy will be over-esimaed and vice versa if produciviy is oo high. Because he depreciaion adjusmen is wih respec o he acual medical expendiure profile, i is no unil he acual and simulaed profile are close ha moraliy will be mached. 24

agens delay healh invesmens unil old age. Given ha he healh producion funcion is concave, here is an incenive o smooh healh invesmen over he life-cycle. We calibrae he age-relaed increase in produciviy so ha we mach he medical expendiure profile. The increase in produciviy due o poor/fair healh is calibraed by making use of he differences in healh expendiures by healh saus. Toal medical expendiures are 8 imes larger for hose in poor healh han hose in excellen healh in he MEPS. Wihou he healh relaed produciviy parameer, we can only generae a facor of 5. We use a second piece of informaion o calibrae he healh producion funcion, in paricular is curvaure. We show in he echnical appendix, using a simplified version of he Hall and Jones (2007) model, ha boh price and income elasiciies depend on he curvaure of he healh producion funcion. The inuiion is ha in a healh producion model, he rae a which he marginal produc of medical expendiure relaive o he marginal uiliy of consumpion increases as income or price increases is direcly relaed o he value of life exension and herefore o he demand for healh. Hence, we calibrae he healh producion funcion parameer so ha i replicaes roughly, among hose of working age, he price (co-insurance) and income elasiciy found in he lieraure. The co-insurance elasiciy ends o fall beween -0.1 and -0.4 depending on he ype of services (prevenive vs. curaive and in-paien vs. ou-paien) (Ringel e al., 2000). Esimaes from he Healh Insurance Experimen (HIE) (Manning e al., 1987) yields an esimae around beween -0.17 and -0.22 which varies across co-insurance raes and is slighly larger for prevenive care (-0.17 o -0.43). For calibraion, we consider a change from a co-insurance rae of 0.2 o 0.5 and calculae he resuling change in medical expendiures. 25

As for he income elasiciy, cross-secional sudies end o obain esimaes in he range of 0.2 o 0.4 while sudies using cross-counry or ime-series variaion find an income elasiciy close o uniy. Cross-secional sudies face he problem of measuremen error and reverse causaliy. Income is in par deermined by healh and oher common facors, such ha regressing medical expendiures on income, even conrolling for imperfec measures of healh, leads o a negaive bias in he income elasiciy. Classical measuremen error in income migh add o his downward bias. One possible reason for he larger elasiciy a he cross-naional level is ha such analyses omi differences in echnology which are correlaed wih income (higher income counries have beer echnology). This leads o an upwards bias which is likely more severe in sudies looking a ime-series daa (as income and echnology are increasing simulaneously) (Newhouse, 1992). There is ye anoher imporan difference beween cross-secional and aggregae cross-naional sudies which resuls from he naure of income changes. If he naure of income shocks is ransiory, he response is likely o be smaller han if he shock is permanen. A permanen income shock raises he value of living longer if he value of life is a normal good. Viscusi and Aldy (2003) find ha he value of life increases wih income when performing a mea-analysis of value of life esimaes. Hence, he permanen responses should be larger han ransiory responses as he laer will no lead o a rise in he value of life. 9 Essenially, cross-secional sudies involve a mix of evoluionary, ransiory and permanen income differences while cross-naional differences involve o a large exen permanen differences in income across counries. Therefore, we will aemp 9 Dusmann and Windmeijer (2000) make a similar poin bu looking a ime allocaion joinly wih medical invesmen. In ha case he ransiory wage response can be negaive as workers spend less ime invesing in healh when heir wage rises emporarily while he posiive income effec dominaes for permanen wage changes. They find suppor for such effecs in German panel daa. 26

o replicae an income elasiciy o a permanen income change of 10% and a ransiory (anicipaed) change in income. We expec a permanen income elasiciy of roughly uniy while he ransiory response should be in line wih cross-secional sudies, perhaps larger due o absence of measuremen error in our simulaed daa. We se he curvaure of he healh producion funcion o! = 2.1. Hence he 1 producion funcion is assumed o be less concave han he uiliy funcion. We show in secion 3.5.3 he resuling elasiciies. 3.5.2 Fi of Momens In Figure 3, we compare momens of he daa wih hose calculaed on simulaed daa. Given he admiedly coarse calibraion, he fi is relaively good. Firs, moraliy is relaively close o he HRS daa. In paricular, we simulae a remaining life-expecancy of 27.1 years a age 50 while i is 26.6 in he HRS for his group. The progression of moraliy is very well approximaed before age 75 while we under-esimae moraliy in he ages 75 o 90 years old. The simulaed average medical expendiure profile racks he daa relaively well. We over-esimae expendiures in middle ages and under-esimae a older ages. The asse profile follows he hump-shape found in he daa and he slow decline afer reiremen. However, we end o over-esimae asses jus before reiremen. Finally, he simulaed reiremen paern capures well he spike a age 62 and he increasing hazard beyond age 65. However, i misses he peak a age 65. One reason is ha we have assumed everyone wih insurance a he ime of reiremen had access o reiree healh insurance. Hence, hose reiring a 62 and 63 do no have an incenive o delay unil age 65. 27

3.5.3 Co-Insurance and Income Elasiciies Table 2 presens various price (co-insurance rae) and income elasiciies from he simulaion. We repor hose for 3 differen age groups (25-35, 35-45 and 45-55). We focus on individuals younger han 55 (few sudies of price and income responses exis among he elderly). In he firs column, we compare oal medical expendiures for hose insured in he baseline scenario wih oal medical expendiures for he same people in a scenario where we increase he co-insurance rae over he enire life-cycle. This yields co-insurance elasicies ranging from -0.26 o -0.35 which falls in he range of esimaes repored in he lieraure. The elasiciy falls wih age primarily because medical expendiures become more of a necessiy wih age, hence less elasic. Individuals are generally in beer healh a age 25 such ha healh expendiures more ofen ake he form of prevenive or precauionary healh invesmen. These expendiures are more likely o be price sensiive since here is a subsiue (save unil healh deerioraes). Resuls from he HIE show ha elasiciies can be as high as -0.43 for prevenive care services. In he second column, we repor resuls for a permanen income change of 10%. The elasiciy esimae is large in he earlier age group (1.56) while jus below uniy in he older age groups (0.88 for 35-45 and 0.909 for hose 45-55). Overall, he elasiciy is 1.02 a he aggregae level. The las column shows ha a large componen of his response is no due o he curren change in income bu o he fac ha he change is permanen. The elasiciy for a ransiory change ranges beween 0.5 and 0.65. The permanen income change raises he value of life by a large amoun in he age group 25-35. We ake his as evidence ha our calibraion of he producion funcion is broadly consisen wih exising evidence on he sensiiviy of he demand for healh o co-insurance raes and income. 28

4. Simulaions We use he model o look a he relaive conribuion of various facors o he growh in healh spending and life expecancy in he las 50 years. According o a recen repor by he CBO (2008), per capia medical expendiures are roughly 500% larger oday han hey were in 1965 which represens an average growh rae of 3.6%. Figure 4 shows, using daa from Culer and Meara (1998), average medical expendiure by age in 2004 relaive o 1963 (adjused in 2004 dollars using CPI). The larges change is found for he elderly (65+). Over his period, here has been an increase in life-expecancy a age 50 of 6 years for men (from 22.9 o 28.9 years (6 years)). We invesigae wheher our model can replicae hese changes as a resul of growh in income, generosiy of insurance and echnological change. Newhouse (1992) reviews he reasons behind he increase in healh spending. The generosiy of healh insurance has increased over he las 50 years and he price elasiciy of he demand for healh is negaive. The average co-insurance rae has fallen from an average of 0.6 in he 1960s o 0.2 in 2005 (Newhouse, 1992). On he income side, real earnings have increased by 27.3%. Social Securiy has become more generous, which has also raised he income of reirees by an average of 20% for medium and low earners (Diamond and Gruber, 1997). 10 Given he posiive income elasiciy of demand, his should also explain a share of he rise in healh spending as argued by Hall and Jones (2006). Finally, echnological change has lead o large improvemens in he reamen of several condiions (Deaon, Culer and Lleras-Muney, 2006) and some have argued 10 Oher facors ha could explain he rise include populaion srucure (aging), physician induced demand and finally lagging facor produciviy in he healh secor. Newhouse (1992) reviews he evidence on each of hose and finds lile ground for he hypohesis ha hese explain a large share of wha acually happened over he period. 29

(Newhouse, 1992) ha he bulk of he increase is due o echnological change, which increases produciviy. There is lile evidence on he magniude of produciviy improvemens. Culer (2004) looks a cardio-vascular diseases, he leading cause of deah among men over his period, and concludes ha medical advancemens explain 2/3 of he improvemen in moraliy over he las half cenury, he oher hird likely explained by he decrease in smoking among men. Lichenberg (2003) provides evidence ha a large par of he gain in life expecancy in recen decades could be aribued o pharmaceuical innovaion. We firs implemen income and insurance changes a he same ime o obain a 1965 scenario. This means reducing average earnings by 27%, reducing he generosiy of social securiy benefis by 20% and increasing co-insurance raes o 0.6. This should no ge us o 1965 spending level unless echnological change plays a role. We model echnological change as a scalar ha varies he produciviy erm in equaion (8) as a funcion of calendar ime s : (,, )! +! h +! 00 0 h, < 3 0,! s z! z h = z e z = e 0 s s s where s = 0 refers o 2005 ( z 0 = 1). We calibrae he change in produciviy so ha maches he level of medical expendiures in 1965. We find an annual produciviy decline! =! 0.018 roughly fis he daa such ha z = 0.4. Table 3 repors a number of 50 z oucomes in he 1965 and 2005 scenario. The simulaed 1965 scenario yields spending levels close o hose ha would be prediced if we used he raio of 2005 o 1963 spending levels (spending is 6 imes higher in 2005) produced by CBO. The prediced average spending would by $0.697 while we obain $0.740. The simulaed average annual rae of increase in healh spending is 3% in real erms or 400% oal. We simulae ha he share of 30

ne income devoed o healh spending is 15% in 2003 while i is 3% in 1965. Given minor differences in he definiion of income (we use ne income raher han gross income or GNP), his rae of growh is consisen wih he daa complied by he CBO (4.5% in 1965 and 14.5% in 2005). Anoher imporan finding is ha he age paern of medical expendiures is much flaer in 1965 han in 2005, excep a very young ages. Culer and Meara (1998) repor daa on he age disribuions of oal medical expendiures from Naional Healh Surveys beween 1963 and 1987. Alhough we replicae he much more rapid growh in old age (relaive o he age 35-45), our simulaion also generaes high growh for hose aged 25-34. Culer and Meara (1998) repor very lile growh in ha age group. We ake his as suggesive evidence ha echnological change has been concenraed on he older populaion or on curaive raher han prevenive care. Neverheless, our calibraion of echnological change is probably a good firs-order approximaion o he scale of produciviy improvemens over his period. We simulae ha life expecancy a age 50 has grown by 16% beween 1965 and 2005. The relaive change from 2005 o 1965 was 25.8% (for all men). Hence, his explains roughly 60% of he improvemen in life expecancy beween 1965 and 2005. Noe ha we do no model oher changes in healh, such as he reducion in smoking over his period. Hence, i is no surprising ha we canno explain he enire gap. We also look a he average reiremen age. Ineresingly, he average reiremen age does no change much. However, as we will see nex, his is likely he resul of he fac ha he various changes (e.g. income, echnology, healh insurance copaymen) lead o cancel ou differen effecs on reiremen. 31

Nex we look a he relaive conribuion of each of hese changes (insurance, income and echnology) in explaining he rise in spending and life expecancy. We sequenially inroduce changes saring from he siuaion in 1965. Resuls are presened in Table 4. As can be seen from he second column of Table 4, increasing he generosiy of healh insurance increases subsanially medical expendiures. The average rises from $0.742 o $1.725 which represens a change of 132%. The effec is larger among younger individuals who we have found are more price sensiive (Table 2). Increasing he generosiy of healh insurance raises he income share of medical expendiures from 3.1% o 7.2%. There is no change in he average age of reiremen. An imporan finding is ha increasing he generosiy of healh insurance has a very small effec on life expecancy, less han 0.3 years. This implies ha he addiional producion of healh has lile healh benefi and would no be consumed if individuals had o pay for i. This is consisen wih he evidence from he HIE ha generous insurance had lile effec on healh oucomes wihin he ime frame of he sudy. Increasing real earnings and he generosiy of social securiy has surprisingly lile effec on healh spending. This is shown in column 3 of Table 4. Toal expendiures increase by 44% from $0.742 o $1.071. The average change in ne income is 16.6%. Par of he reason why expendiures do no rise sharply is due o he responsiveness of he reiremen age o he income change. We find ha i reduces he reiremen age by 2.4 years. This effec, along wih he progressiviy of income axes, miigaes he income effec. Furhermore, he raio of medical expendiures o income rises only by 1 percenage poin. Finally, here is a negligible gain in life expecancy of 0.19 years. 32

In column 4, we increase produciviy a 1.8% a year unil 2005. This implies an improvemen of 150% in produciviy over he period. This increases oal medical expendiures by abou as much as hey increase wih he change in insurance generosiy. The magniude of he change is similar across age groups which is mos likely he resul of our assumpion ha produciviy gains were disribued equally over he life-cycle and across healh saus. The average reiremen age increases by 1 year, in mos par due o he fac ha individuals can now expec o live 3 more years due o echnological improvemens. Of he hree changes (insurance, income and echnology), echnological change is he only one ha is capable of generaing appreciable gains in life expecancy. By iself, i explains roughly half of he increase in life expecancy from 1965 o 2005. None of he scenarios are able o generae healh expendiure levels of he magniude winessed in 2005, even if we sum heir relaive conribuion. For example, insurance leads o a 132%, income a 44% and echnology a 110% change in spending. This sums o 287%, i.e. well under he 464% ha we reach when we implemen all changes ogeher. Hence, we mus conclude ha here are imporan ineracion effecs. This exercise would imply hese ineracions are responsible for a rise of 176% in healh care spending over he las 50 years. In Figure 4, we show he sources of increase in healh spending. Increased generosiy of healh insurance accouns on is own for 29% of he insurance in expendiures while income only for 10%. Technological change accouns for 24% of he change. Bu he larges componen is he ineracion effec, which amouns o 37% of he oal change. 33

As for life expecancy, we repor in Figure 5 he sources of he increase as we esimae hem from he model. Technological change, aking he form of produciviy gains accouns for he bulk of he increase, 59%. Income and insurance explain a very small share of he oal increase (4% and 6% respecively). Ineracion effecs are smaller for life expecancy han hey are for healh spending, amouning o 6%. This leaves a residual caegory of 25% of he oal increase in life expecancy. Several candidaes are plausible o explain he remaining par, one is he reducion in smoking, he second is general improvemens in living condiions no capured by he model (air qualiy, working condiions, ec). 5. Conclusion We calibrae a sochasic life-cycle model of healh spending, asse accumulaion and reiremen which allows us o look a he deerminans of he rise in healh spending and longeviy over he las 50 years. We find ha wih reasonable parameer values, he model fis he daa relaively well and is able in paricular o replicae he income and price elasiciy of he demand for medical care. We hen perform a simulaion where we aemp o go back o 1965 by simulaneously decreasing he generosiy of healh insurance and income o 1965 levels. We back ou he rae of produciviy gains necessary o achieve 1965 spending levels and longeviy and find ha a rae of 1.8% fis he daa relaively well. We find ha boh insurance and echnological change independenly explain respecively 29% and 24% of he oal change in healh spending and ha income explains roughly 10%. The remainder, 37%, is due o wha we call synergy effecs or ineracions creaed by simulaneously increasing income, he generosiy of healh insurance and produciviy. As for life expecancy, we find ha he bulk of he gain is due o produciviy 34

growh while income growh and increased generosiy of healh insurance explain a relaively small fracion of he overall increase (less han 10%). 35

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Demand for Healh Insurance, Fuqua School of Business, Duke Universiy, forhcoming, Journal of Economerics. Licheenberg, F. (2003) Pharmaceuical Innovaion, Moraliy Reducion, and Economic Growh, in Measuring he Gains from Medical Research: An Economic Approach, ed. by Kevin M. Murphy and Rober H. Topel (Chicago: Universiy of Chicago Press 2003), pp. 74-109. Manning W.G., Newhouse, J. P., Duan, N., Keeler, E., Benjamin, B., Leibowiz, A., Marquis, M.S. and Zwanziger, J. (1987), Healh Insurance and he Demand for Medical Care: Evidence from a Randomized Experimen. The American Economic Review, 77:251-277. June 1987. Marquis, S.M., S.H. Long (1995): Worker demand for healh insurance in he non-group marke, Journal of Healh Economics, Volume 14, Issue 1, May, Pages 47-63, Newhouse, J. P., (1992), Medical Care Coss: How Much Welfare Loss? The Journal of Economic Perspecives, Vol. 6, No. 3, pages 3-21. Newhouse, J. P., and he Insurance Experimen Group (1993), Free For All? Lessons from he Healh Insurance Experimen, Harvard Universiy Press, Cambridge. Ringel, J., Hosek, S.D., Vollaard, B.A. and Mahnovski, S. (2000): The Elasiciy of Demand for Healh Care A Review of he Lieraure and Is Applicaion o he Miliary Healh Sysem, RAND Repor. Rus, J. and C. Phelan (1997). "How Social Securiy and Medicare Affec Reiremen Behavior in a World of Incomplee Markes." Economerica 65(4): 781-831. Smih, J. (2007): The Impac of Socioeconomic Saus on Healh over he Life-Course, Journal of Human Resources, 42(4):739-764, Fall. Suen, R. (2009): Technological Advance and he Growh in Healh Care Spending, Conference Healh and Macroeconomics in Sana Barbara.mimeo. Viscusi, W.K. and J. Aldy (2003). " The Value of a Saisical Life: A Criical Review of Marke Esimaes hroughou he World," Journal of Risk and Uncerainy, Springer, vol. 27(1), pages 5-76, Augus. Yogo, M. (2009): Porfolio Choice in Reiremen: Healh Risk and he Demand for Annuiies, Housing, and Risky Asses mimeo 37

Technical Appendix Soluion Mehod Because some of he sae variables are coninuous (asses and AIME), we define a bidimensional equally-spaced grid over ha space. We selec 35 poins for asses and 35 poins for AIME. The maximum for asses is se o 300 and he minimum 0. For AIME, he minimum is zero and he maximum 6. Since decision rules are likely more non-linear a low values of asses and AIME, we se he grid in erms of equally spaced poins using he square roo of asses and AIME ( 1/2 a and ae 1/2 ). We solve for value funcion a each poin on ha grid saring a erminal age T. We have wo coninuous decision variables. We define a grid for each of hese decisions (45 poins for consumpion and 45 for medical expendiures). We selec bounds of 0 and 25 for medical expendiures (25 is he 99 h percenile in he daa) and define he grid for consumpion in erms nex period's asses using he boundary condiions along wih cash on hand. For consumpion, we cener he grid around curren cash on hand and define an equally spaced grid away from ha poin. We use inerpolaion o calculae nex period's value funcion when he soluion for consumpion and medical expendiure does no fall on he grid given he curren sae and reiremen choice. Since we use an equallyspaced grid, we use he bi-dimensional cubic spline approximaion proposed by Habermann and Kindermann (2007). When reiremen is an opion, we compue he opimal soluion for each reiremen pah and compare value funcions o calculae r * ( s ). The decision rules are generally insensiive o he number of grid poins. We solve for decision rules using a program wrien in Ox from OxMerics (wih sub-programs wrien in C++) and he parallel message parsing inerface MPICH on a 16 processor core cluser wih 8 GB of RAM. A ypical soluion akes roughly 12 minues. 38

AIME Approximaion The following able provides age-specific coefficiens for he AIME regression. The average R-squared is 0.991. For ages above 60, he age 60 coefficiens are used. Table A.1 AIME Approximaion Coefficiens age earnings>0 log(earnings) log(aime(-1)) Consan 26 0.0848 0.1380 0.7425-0.6538 27 0.0706 0.0793 0.8654-0.2817 28 0.0713 0.0794 0.8360-0.3334 29 0.0221 0.0768 0.8792-0.2243 30 0.0511 0.0578 0.8719-0.2093 31 0.0072 0.0541 0.9255-0.1109 32 0.0075 0.0665 0.8884-0.1772 33 0.0605 0.0447 0.9012-0.1542 34 0.0104 0.0584 0.8906-0.1521 35 0.0014 0.0485 0.9140-0.1015 36 0.0588 0.0208 0.9410-0.0589 37 0.0513 0.0260 0.9312-0.0719 38 0.0269 0.0301 0.9430-0.0575 39 0.0269 0.0208 0.9636-0.0265 40 0.0166 0.0234 0.9645-0.0259 41 0.0033 0.0228 0.9777-0.0128 42 0.0259 0.0225 0.9610-0.0323 43 0.0158 0.0181 0.9818-0.0117 44 0.0048 0.0175 0.9871-0.0013 45 0.0058 0.0146 0.9916 0.0048 46 0.0060 0.0165 0.9874-0.0036 47 0.0033 0.0185 0.9807-0.0046 48 0.0047 0.0170 0.9870-0.0051 49 0.0059 0.0133 0.9912 0.0018 50 0.0056 0.0129 0.9931 0.0008 51 0.0040 0.0119 0.9956 0.0019 52 0.0000 0.0120 0.9964 0.0031 53 0.0163 0.0121 0.9757-0.0022 54 0.0135 0.0189 0.9567-0.0080 55 0.0060 0.0123 0.9840-0.0016 56 0.0056 0.0104 0.9880 0.0004 57 0.0158 0.0076 0.9853-0.0008 58 0.0134 0.0068 0.9875 0.0006 59-0.0019 0.0144 0.9674 0.0065 60-0.0056 0.0176 0.9578 0.0105 39

Price and Income Elasiciies We demonsrae how he price and income elasiciy of demand are relaed o he concaviy of he healh producion funcion. We add a co-insurance rae (price) o he model used by Hall and Jones (2006). Le 1 / h be he moraliy rae and h life expecancy (healh saus). Income y can be allocaed beween consumpion c and medical expendiures m. Ou-of-pocke medical expendiures are given by µ m where µ is he co-insurance rae. Healh is produced rough a producion funcion i( m ) which is increasing and concave. The problem is given by maxu(c,h) = " 0! s.. y = c + µm h = i(m) e 1 h u(c)d = hu(c) As in Hall and Jones, define! m = i '(m) i(m) m,! u = u '(c) u(c) c and condiion is! m " =! +! m u. The opimaliy s = m y = 1 µ!. The income elasiciy of opimal medical expendiures m * is given by 2 y! = 1 + " y y µ m where! is he derivaive of! wih respec o y. The uncompensaed price elasiciy is y y! =! 1 + ". µ µ m Boh! and! depend on he curvaure of he uiliy and producion funcions since hey µ y involved second derivaives of i( m ) and u( c ). If boh uiliy and producion funcions are of he consan elasiciy ype, he income and price elasiciies are 1 and -1. Alernaively as in Hall and Jones, if! > 0, for example if he producion funcion exhibis consan y elasiciy while he uiliy funcion exhibis decreasing elasiciy. In he case we consider boh uiliy and producion exhibi decreasing elasiciy such ha he curvaure of he producion funcion, aking he curvaure of he uiliy funcion as given, is idenified by calibraing he price and income elasiciies o exising evidence on heir magniude (for example, he HIE). 40

Figures Figure 1a Employmen and Insurance Saus Noes:.raw daa from 1999 o 2005 waves of PSID. Figure 1b Healh Saus Noes: raw daa from 1999 o 2005 waves of PSID for hose younger han 50 and HRS 1992-2004 for hose older han 50. 41

Figure 2 Momens for Calibraion Noes: The figures presen he momens from he daa used o calibrae parameers. See he discussion in secion 4.4. 42

Figure 3 Goodness-Fi of Model Simulaions Noes: Simulaed and daa profiles based on parameers presened in Table 1. 43

Figure 4 Increase in Healh Spending Share of Increase in Healh Spending 1965-2005 insurance 29% ineracion 37% income 10% produciviy 24% insurance income produciviy ineracion Noes: Based on simulaion oupu from Table 4. Insurance refers o he induced change brough by an increase in he generosiy of healh insurance keeping income and produciviy a he 1965 level. Income refers o he induced change brough by he increase in real earnings and he generosiy of Social Securiy keeping insurance and produciviy a he 1965 level. Produciviy refers o he induced change brough by improvemens in produciviy keeping income and insurance a he 1965 level. Finally, ineracion refers o he residual induced change brough by he ineracion of income, insurance and produciviy change when occurring simulaneously. 44

Figure 5 Increase in Life Expecancy Noes: Based on simulaion oupu from Table 4. Insurance refers o he induced change brough up by an increase in he generosiy of healh insurance keeping income and produciviy a he 1965 level. Income refers o he induced change brough by he increase in real earnings and he generosiy of Social Securiy keeping insurance and produciviy a he 1965 level. Produciviy refers o he induced change brough by improvemens in produciviy keeping income and insurance a he 1965 level. Finally, ineracion refers o he residual induced change brough by he ineracion of income, insurance and produciviy change when occurring simulaneously. Since he simulaed change in life expecancy is less han he observed relaive share. There is anoher residual caegory which capures he unexplained componen of he increase in life expecancy in he daa. 45

Tables Table 1 Srucural Parameers Chosen by Calibraion Parameer Definiion Value! Coefficien of relaive risk aversion 2.6! Uiliy benefi if healh saus >2 0.035 h! 0 Baseline log uiliy benefi of reiremen 4.65e-03! a Incremenal log uiliy benefi of reiremen by age 6.15e-04! b Srengh of beques moive 0.05! 00 Baseline log produciviy (age 25, good healh) -3.352! 0h % incremen in produciviy fair/poor healh 1! 0 % change in produciviy wih age 0.02! 1 Concaviy of producion funcion 2.1! Real ineres rae 0.03! Discoun facor 0.95 Noes: See discussion in secion 4.5 for he jusificaion. 46

Table 2 Price and Income Effecs on Medical Expendiures in 2005 Baseline Scenario Age Group Co-Pay (0.2 o 0.5) Permanen Income (+10%) Transiory Income (+10%) 25-35 -0.345 1.564 0.631 35-45 -0.281 0.888 0.576 45-55 -0.267 0.909 0.583 Noes: Simulaion based on calibraion in Table 1. The firs wo columns consider permanen changes. In he firs column, we increase he co-paymen from 0.2 o 0.5 across all ages for hose insured and look a he resuling change in oal medical expendiures. In he second column, we increase earnings by 10% over he enire working life. The repored elasiciy is he average elasiciy wihin he age group. In he las column, we increase earnings a he mid poin in he age inerval (30 for he firs, 40 for he second and 50 for he las age group). 47

Table 3 Simulaed Oucomes in 1965 and 2005 Scenarios Simulaion resuls Oucomes 1965 2005 Toal Medical Expendiures ($k) 25-35 0.131 1.376 35-45 0.563 3.210 45-55 1.020 4.535 55-65 1.172 5.363 65-75 1.039 6.149 75-85 0.740 6.052 85+ 0.945 7.585 Toal ($k) 0.742 4.183 ne income ($k) 24.030 28.221 share of ne income 0.031 0.148 Average reiremen age (years) 64.2 63.9 Life expecancy a age 50 (years) 23.88 27.65 Noes: simulaed resuls in 2005 and 1965 using he insurance, income and echnology changes. Amouns in housands of $US 2004. 48

Table 4 Simulaed Incremenal Changes Saring from 1965 Scenario Simulaion increase generosiy insurance increase real earnings and social securiy generosiy increase produciviy 2005 Oucomes 1965 Avg. Medical Expendiures($k) Age 25-35 0.131 0.397 0.235 0.398 1.376 35-45 0.563 1.355 0.816 1.201 3.210 45-55 1.020 2.265 1.418 1.941 4.535 55-65 1.172 2.538 1.614 2.233 5.363 65-75 1.039 2.494 1.530 2.198 6.149 75-85 0.740 1.925 1.197 1.887 6.052 85+ 0.945 2.378 1.620 2.302 7.585 Avg Medical Expendiures($k) 0.742 1.725 1.071 1.563 4.183 Ne income ($k) 24.030 23.991 27.985 23.760 28.221 Share of ne income 0.031 0.072 0.038 0.066 0.148 Average reiremen age (years) 64.2 64.3 61.9 65.1 63.9 Life expecancy a age 50 (years) 23.88 24.16 24.07 26.86 27.65 Noes: Simulaed oucomes. Firs column represens scenario in 1965. Column 2 o 4 inroduce changes one a a ime saring from 1965. Finally, he las column presens esimaes in 2005 (when all changes are inroduced a once). All amouns in housands $US 2004. 49