Fol yn, Richa d; Olsson, Jonna
A icle
Subjec i e li e expec ancies, ime p e e ence
he e ogenei y, and weal h inequali y
Quan i a i e Economics
P o ided in Coope a ion wi h:
The Econome ic Socie y
Sugges ed Ci a ion: Fol yn, Richa d; Olsson, Jonna (2024) : Subjec i e li e expec ancies, ime
p e e ence he e ogenei y, and weal h inequali y, Quan i a i e Economics, ISSN 1759-7331, The
Econome ic Socie y, New Ha en, CT, Vol. 15, Iss. 3, pp. 699-736,
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Quan i a i e Economics 15 (2024), 699–736 1759-7331/20240699
Subjec i e li e expec ancies, ime p e e ence he e ogenei y,
and weal h inequali y
Richa d Fol yn
Depa men o Economics, No wegian School o Economics and Adam Smi h Business School,
Uni e si y o Glasgow
Jonna Olsson
Depa men o Economics, No wegian School o Economics
This pape examines how objec i e and subjec i e he e ogenei y in li e ex-
pec ancy a ec s sa ings beha io o heal hy and unheal hy people. Using da a
om he Heal h and Re i emen S udy, we i s documen sys ema ic biases in
su i al belie s ac oss sel - epo ed heal h: hose in poo heal h no only ha e a
sho e ac ual li espan bu also unde es ima e hei emaining li e ime. To gauge
he e ec on sa ings beha io and weal h accumula ion, we use an o e lapping-
gene a ions model whe e su i al p obabili ies and belie s e ol e acco ding o a
heal h and su i al p ocess es ima ed om da a. We conclude ha di e ences in
li e expec ancy a e impo an o unde s and sa ings beha io , and ha he belie
biases, especially among he unheal hy, can explain up o a i h o he obse ed
heal h-weal h gap.
Keywo ds. Li e expec ancy, p e e ence he e ogenei y, subjec i e belie s, li e cy-
cle.
JEL classi ica ion. D15, E21, G41, I14.
1. In oduc ion
The de e minan s o he weal h dis ibu ion a e o undamen al in e es o economis s.
S anda d consump ion/sa ings heo y p edic s ha people who place a la ge weigh on
u u e s a es will be weal hie han people who a e mo e impa ien , all else equal. This
pape explo es one eason o pu a highe weigh on he u u e: he highe p obabili y o
su i e o old age.
Howe e , an indi idual’s consump ion/sa ings decision is no necessa ily guided by
he objec i e (s a is ical) su i al p obabili y bu a he he indi idual’s belie s abou
su i al. The i s con ibu ion o his pape is o documen new ac s abou a wi hin-
Richa d Fol yn: [email p o ec ed]
Jonna Olsson: [email p o ec ed]
We a e g a e ul o James Banks, Timo Boppa , Pe K usell, Alexande Ludwig, Hannes Malmbe g, Ay¸segül
¸Sahin, Paolo Sodini, Ch is ian S ol enbe g, Magnus Åhl, E ik Öbe g, and pa icipan s in nume ous con e -
ences and semina s o help ul discussions and commen s. The collec ion o da a used in his s udy was
pa ly suppo ed by he Na ional Ins i u es o Heal h unde g an s R01 HD069609 and R01 AG040213, and
he Na ional Science Founda ion unde awa ds SES 1157698 and 1623684.
©2024 The Au ho s. Licensed unde he C ea i e Commons A ibu ion-NonComme cial License 4.0.
A ailable a h p://qeconomics.o g.h ps://doi.o g/10.3982/QE2016
700 Fol yn and Olsson Quan i a i e Economics 15 (2024)
coho s eepness bias in su i al belie s: people o e es ima e he heal h g adien o su -
i al.
I has p e iously been shown (e.g., Hame mesh (1985), Elde (2013), Ludwig and
Zimpe (2013), Heime ,My se h,andSchoenle(2019)) ha he e is a sys ema ic la ness
bias o e age: younge people end o unde es ima e hei su i al p obabili ies, while
olde people o e es ima e hei chances o a long li e. We show ha wi hin a coho , in-
di iduals in bad heal h no only ha e a sho e expec ed li e span bu a e also ela i ely
mo e downwa d biased abou hei su i al chances, while indi iduals in good heal h,
and hus wi h highe su i al p obabili y display an upwa d bias. These sys ema ic bi-
ases exace ba e he li e expec ancy he e ogenei y in he popula ion.
The di e ences in belie s abou su i al ansla e in o ime p e e ence he e ogenei y
in he popula ion. Ou second con ibu ion is o quan i y his he e ogenei y and i s im-
plica ions o sa ings and weal h accumula ion in an o e lapping-gene a ions model.
Wi h a s ochas ic heal h and su i al p ocess, he e ec i e discoun a e a ies depend-
ing on age, heal h, and he o ecas ho izon. O e a 1-yea ho izon, he e ec i e dis-
coun a e o 50-yea -olds anges om 2% o an indi idual in bes heal h o a ound
20% o an indi idual in wo s heal h. A a 10-yea ho izon, his gap sh inks somewha
bu s ill amoun s o 8 pe cen age poin s be ween bes and wo s heal h. Fo 70-yea -
olds in wo s e sus bes heal h s a e, he di e ence a he 10-yea ho izon is close o 10
pe cen age poin s. This esul ing ime p e e ence he e ogenei y is in line wi h he dis-
pe sion (Cal e , Campbell, Gomes, and Sodini (2021)) and he age g adien (Ku eishi,
Paule-Paludkiewicz, Tsujiyama, and Wakabayashi (2021)) o he ime p e e ence dis i-
bu ion ound in o he empi ical s udies.
To gauge he quan i a i e e ec o su i al he e ogenei y on sa ings beha io and
weal h accumula ion, we use an o e lapping-gene a ions gene al-equilib ium model
wi h uninsu able idiosync a ic shocks. Agen s ace he e ogeneous su i al isk ha de-
pends on hei age and cu en heal h s a e, and a e subjec o heal h shocks ha ol-
low a p ocess es ima ed om da a. The cu en heal h s a e also a ec s labo ea nings
and medical expendi u e isk. Besides his unce ain y, we addi ionally include s anda d
pe sis en and ansi o y shocks o labo p oduc i i y du ing wo king age. A e agen s
each a ixed e i emen age, hey a e en i led o e i emen bene i s mimicking he US
social secu i y sys em. Finally, ou model includes p obabilis ic beques s ha ea u e in-
e gene a ional pe sis ence o income and weal h. We pu posely use an o he wise s an-
da d model o consump ion/sa ings o es ablish a benchma k and ocus on he su i al
he e ogenei y sa ings channel.
We compa e h ee scena ios. The i s scena io is a s anda d model in which he e is
no heal h isk: all agen s ace he same labo ea nings isk, he same medical expendi u e
isk, and he same su i al isk, and hus ha e he same e ec i e discoun ac o , condi-
ional on age. In he second scena io, we in oduce heal h isk ha a ec s labo ea nings
and medical expendi u es. In e ms o su i al isk, indi iduals a e pe ec ly in o med
abou hei ue su i al p obabili y condi ional on heal h and age. In he hi d scena io,
agen s belie e and ac acco ding o hei subjec i e su i al belie s. Thus, ou analysis is
designed o answe he ques ion: wha i we u ned o he discoun ac o he e ogene-
i y implied by he biases in su i al belie s we unco e ed in he empi ical pa ? Would
sa ings pa e ns look quan i a i ely di e en ?
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 701
The simula ions show ha he su i al expec a ion channel is impo an o unde -
s anding weal h accumula ion. No su p isingly, agen s in bad heal h, and hus wi h a
sho e expec ed li e span sa e less han hei heal hy coun e pa s, and he di e ences
in sa ings a es a e la ge. Fo example, o 60-yea -olds in he middle o he weal h dis-
ibu ion, he o al sa ings a es o an agen in he bes , and an agen in he wo s heal h
s a e di e by 5 pe cen age poin s when hey a e endowed wi h co ec objec i e be-
lie s abou su i al. When we le hem ac acco ding o he es ima ed subjec i e belie s
ins ead, he di e ence doubles o 10 pe cen age poin s.
These di e ences in sa ings beha io ansla e in o la ge di e ences in accumula ed
weal h: in he model wi h subjec i e su i al belie s, median weal h di e s by 193% be-
ween hose in he wo s and bes heal h s a es a ages 55–59. This heal h-weal h g a-
dien is e y close o he magni ude we obse e in he da a. A i h o his di e ence is
d i en by he e oneous su i al belie s, especially by indi iduals in poo heal h unde -
es ima ing hei emaining li e span. Thus, he biases in su i al belie s a e impo an o
unde s and he heal h-weal h g adien in olde ages.
This pape speaks o h ee b oad s ands o li e a u e. The i s is conce ned wi h
subjec i e su i al expec a ions (Hame mesh (1985), Smi h, Taylo , and Sloan (2001),
Hu d and McGa y (2002), Ludwig and Zimpe (2013), Elde (2013), Gan, Gong, Hu d,
and McFadden (2015), G oneck, Ludwig, and Zimpe (2016), Heime , My se h, and
Schoenle (2019), de B esse (2023)). Many s udies ha e documen ed he exis ence o an
age bias in subjec i e li e expec ancies, and a ew o he pape s wi hin his g oup a e con-
ce ned wi h he implica ions o he consump ion/sa ings beha io . Some p edic indi-
idual su i al p obabili ies and con as hem wi h elici ed belie s (Gan, Hu d, and Mc-
Fadden (2005), Bissonne e, Hu d, and Michaud (2017), G e enb ock, G oneck, Ludwig,
and Zimpe (2021)), bu none o hese look a he implica ions o wi hin-coho sa ings
beha io in a s uc u al model whe e belie s change in he e en o heal h shocks, o
analyze he implica ions o weal h inequali y.
The second s and a e mac oeconomic s udies poin ing ou he impo ance o he -
e ogenei y in ime p e e ences o explain weal h inequali y (e.g., K usell and Smi h
(1998), Hend icks (2007), Quad ini and Ríos-Rull (2015), K uege , Mi man, and Pe i
(2016)) and s udies documen ing ime p e e ence he e ogenei y in he popula ion
(Eppe e al. (2020), Cal e e al. (2021)). Compa ed o hese pape s, we p o ide a
mic o- ounda ion o one sou ce o ime p e e ence he e ogenei y—di e ences in li e
expec ancy—and e alua e i s impo ance.
The hi d is he li e a u e abou he gene al impac o heal h (including li e ex-
pec ancy) on weal h (Smi h (1999), Lee and Kim (2008), Coile and Milligan (2009), De
Na di, F ench, and Jones (2009), Kopecky and Ko eshko a (2014), Capa ina (2015), De
Na di, Pashchenko, and Po apakka m (2017), Po e ba, Ven i, and Wise (2017), Ma ga is
and Wallenius (2023), o name a ew). In con as o hese pape s, we include he e o-
genei y in subjec i e li e expec ancy and examine i s impac on sa ings and consump-
ion beha io .
In he nex sec ion, we desc ibe how we es ima e he heal h and su i al p ocess
and gi e de ails abou he sys ema ic bias in su i al expec a ions. Sec ion 3desc ibes
702 Fol yn and Olsson Quan i a i e Economics 15 (2024)
he model we use o quan i y he impo ance o he he e ogenei y in su i al expec a-
ions. A e ha , we discuss he pa ame iza ion and hen we p esen ou esul s. The
las sec ion concludes. The Supplemen al Appendix o he wo king pape (Fol yn and
Olsson (2024)) con ains addi ional esul s and de i a ions.
2. Empi ical e idence
2.1 Da a
We use he Heal h and Re i emen S udy (HRS), a ep esen a i e panel o elde ly US
households, o in es iga e he e olu ion o heal h and longe i y in he la e s ages o
li e. The su ey includes ques ions abou sel - epo ed heal h and expec a ions abou
su i al, and eco ds he da e o dea h, i applicable.
Ou analysis is based on he su ey yea s 1992–2014 aken om he HRS da a com-
piled by RAND, e sion 2018 (V2) (Heal h and Re i emen S udy (2023)).1The i s co-
ho included in he su ey was be ween 51 and 61 yea s old in 1992, and he ea e new
(olde and younge ) coho s we e added. Many o he esponden s died o e he sample
pe iod, making i an ideal da a se o s udying su i al.
In his sec ion, we i s documen he ela ionship be ween heal h and weal h, and
be ween belie s abou su i al and weal h. We hen b ie ly desc ibe how we es ima e
he objec i e su i al p obabili ies. In Sec ion 2.4, we show how a e age elici ed belie s
abou su i al a e biased, and in Sec ion 2.5, we es ima e a subjec i e li e expec ancy
p ocess ha eplica es his bias.
2.2 The heal h-weal h g adien and he li e expec ancy/sa ings channel
The HRS asks pa icipan s o assess hei heal h using one o he i e ca ego ies excel-
len , e y good,good, ai ,o poo . Figu e 1shows ne o al weal h o e he li e cycle by
sel - epo ed heal h s a e compu ed o he pooled sample o all esponden s.2,3The
heal h-weal h g adien is well documen ed, bu he unde lying causal ela ionship is
deba ed (A anasio and Hoynes (2000), Dea on (2002), Duncan, Daly, McDonough, and
Williams (2002), A anasio and Emme son (2003), Haja , Kau man, Rose, Siddiqi, and
Thomas (2010)). One line o a gumen is ha low economic s a us leads o poo heal h.
The e could be many easons: poo people ha e access o less o lowe -quali y medical
ca e, do no in es enough in p e en i e heal h measu es, and/o ha e mo e heal h-
de e io a ing habi s. Howe e , he e a e also many a gumen s o he e e sed causali y:
poo heal h has economic consequences in i sel . Fi s , poo heal h may es ic he in-
di idual’s ea nings po en ial by making i mo e cos ly o wo k and/o by lowe ing he
1The HRS (Heal h and Re i emen S udy) is sponso ed by he Na ional Ins i u e on Aging (g an NIA
U01AG009740) and is conduc ed by he Uni e si y o Michigan.
2Ne o al weal h is de ined as sum o housing, o he eal es a e, ehicles, businesses, IRA and Keogh
accoun s, s ocks, checkings, and all o he sa ings, ne o mo gages and o he deb s.
3In he Appendix o he wo king pape (Fol yn and Olsson (2024)) (hence o h e e ed o as he Supple-
men al Appendix), we disagg ega e hese weal h p o iles by ace, sex, household size, and educa ion (see
Sec ion A.4). The o e all pic u e emains unchanged.
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 703
Figu e 1. Median ne o al household weal h by sel - epo ed heal h s a e. Pooled sample om
HRS 1992–2014. Asse s a e adjus ed o ou lie s, ime, and coho ixed e ec s. Colo s indica e he
heal h s a e: da k g een is excellen while ed is poo heal h. E o ba s indica e 95% con idence
in e als.
wage. Second, poo heal h may lead o la ge medical expendi u es. Thi d, poo heal h
may lowe he sa ings incen i es due o a lowe su i al expec ancy. This las channel is
he ocus o his pape .
I indi iduals adjus hei sa ings beha io based on hei su i al p ospec s, his
could be ei he on he basis o objec i e (s a is ical) su i al p obabili ies o subjec i e
su i al belie s, which a e also su eyed by he HRS. To assess how weal h co ela es
wi h su i al belie s, we eg ess ne o al weal h on an indica o o whe he an indi id-
ual belie es o ha e abo e-median su i al chances compa ed o o he esponden s o
he same age, ace, and sex. Table 1shows a posi i e co ela ion be ween ha ing abo e-
median belie s and being weal hie .4The posi i e ela ionship also holds when addi-
ionally con olling o educa ion and couple s a us.5O he empi ical s udies co obo-
a e he exis ence o he li e expec ancy/sa ings channel and sugges a causal link. Fo
ins ance, Heime ,My se h,andSchoenle(2019) adminis e a no el su ey and es ima e
ha g ea e su i al op imism co ela es wi h highe sa ings a es, no only a e con-
olling o s anda d demog aphic cha ac e is ics such as educa ion, ma i al s a us, and
income, bu also inancial li e acy and isk ole ance.
Ano he p edic ion o he li e expec ancy/sa ings channel is ha indi iduals who
ecei e a bad heal h shock, ha is, a plausible dec ease in li e expec ancy, should ex-
hibi lowe asse g ow h.Table2 epo s he esul s om eg essing he 2-yea change in
ne o al weal h (again using an in e se hype bolic sine ans o ma ion) on a nega i e
4All empi ical esul s in his pape a e epo ed wi h s anda d e o s and con idence in e als ha ake
in o accoun he s a i ica ion and clus e ing o he HRS; see he Supplemen al Appendix, Sec ion A.3.
5We apply an in e se hype bolic sine ans o ma ion since asse s a e hea ily skewed and con ain ze os
and nega i e alues. All coe icien s o in e es a e posi i e and signi ican a he 1% le el when al e na-
i ely using asse s in le els. The Supplemen al Appendix, Sec ion A.5.1 con ains u he in o ma ion and
obus ness checks.
704 Fol yn and Olsson Quan i a i e Economics 15 (2024)
Table 1. Ne o al weal h and abo e-median subjec i e su i al belie s.
Dep. Va iable: Ne To al Weal h (In e se Hype bolic Sine T ans o ma ion)
Men Women
(1) (2) (3) (4) (5) (6)
Abo e median SSB 0.418 0.230 0.221 0.575 0.374 0.353
(0.045) (0.040) (0.039) (0.032) (0.029) (0.029)
Age FE Yes Yes Yes Yes Yes Yes
Educa ion FE Yes Yes Yes Yes
Couple FE Yes Yes
Obse a ions 54,212 54,212 54,212 70,537 70,537 70,537
No e: The able shows he esul s o eg essing ne o al weal h (a e an in e se hype bolic sign ans o ma ion) on an
indica o o abo e-median su i al belie s compa ed o indi iduals o he same age, ace, and sex. The eg ession includes ully
in e ac ed ixed e ec s as indica ed. Nonblack popula ion. Clus e ed s anda d e o s in pa en heses.
heal h shock de ined as an indica o o a de e io a ion in sel - epo ed heal h be ween
su ey wa es. As column 1 shows, men who expe ience a nega i e heal h shock decu-
mula e hei asse s mo e compa ed o men o he same ace, age, and ini ial heal h who
do no . Column 2 addi ionally con ols o educa ion, while columns 3–4 show he co -
esponding esul s o women. A nega i e heal h shock is associa ed wi h a as e decu-
mula ion (o slowe accumula ion) o asse s in all speci ica ions. Mo e de ails a e gi en
in he Supplemen al Appendix o he wo king pape (Fol yn and Olsson (2024)) (hence-
o h e e ed o as he Supplemen al Appendix); see Sec ion A.5.2.6
While hese esul s a e indica i e, a ecen s udy by K ae ne (2022) using he plausi-
bly exogenous iming o cance diagnoses shows ha news abou a bad heal h shock in-
Table 2. Heal h shocks and changes in weal h.
Dep. Va iable: Rela i e Change in Ne To al Weal h
Men Women
(1) (2) (3) (4)
Nega i e heal h shock −0.149 −0.130 −0.134 −0.115
(0.023) (0.023) (0.018) (0.018)
Age FE Yes Yes Yes Yes
Heal h FE Yes Yes Yes Yes
Educa ion FE Yes Yes
Obse a ions 61,528 61,528 80,615 80,615
No e: The able shows he esul s o eg essing changes in ne o al weal h (a e an in e se hype bolic sign ans o ma ion)
on an indica o o a de e io a ion in sel - epo ed heal h be ween wo consecu i e su ey wa es. The eg ession includes ully
in e ac ed ixed e ec s as indica ed. Nonblack popula ion. Clus e ed s anda d e o s in pa en heses.
6I is possible ha he decumula ion o asse s associa ed wi h a heal h de e io a ion is d i en by lowe
labo income o la ge medical expendi u es. In he Supplemen al Appendix, Sec ion A.5.2, we show ha
he esul s also hold in he subsample aged 65 and olde (who a e likely o be e i ed and on Medica e) e en
a e accoun ing o ou -o -pocke medical expendi u es.
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 705
c eases he p obabili y o an immedia e in e i os ans e , sugges ing a causal link be-
ween su i al p ospec s and weal h decumula ion. Thus, i a dec ease in li e expec ancy
inc eases own consump ion and/o inc eases he p obabili y o in e i os ans e s is
an open ques ion, and one in e p e a ion o in e i os ans e s om he gi e ’s pe -
spec i e is o iew hem as “consump ion o gi -gi ing.” While bo h in e i os ans-
e s and own consump ion show up as a decumula ion o asse s and he eby a ec he
heal h-weal h g adien in olde ages in he same way, hey ha e di e en implica ions
o weal h among he younge ecei ing gene a ion, and hus o he weal h dis ibu-
ion. Ou s uc u al model does no allow o in e i os ans e s, and consequen ly,
lea es his ques ion open o u u e esea ch.
2.3 Objec i e heal h and su i al p obabili ies
In his pape , we examine he e ec o he e ogenei y in su i al expec ancy on sa -
ings beha io and i s implica ions o weal h inequali y h ough he lens o a s uc u al
model. The e o e, we need o o mula e he e ogenei y in su i al expec a ions, bo h ob-
jec i e and subjec i e, in a way ha can be used in such a model.
Fo ou quan i a i e model, we use a Ma ko p ocess o heal h ansi ions and su -
i al a an annual equency. We es ima e his Ma ko p ocess as desc ibed in Fol yn
and Olsson (2021). Concep ually, he me hod is a s aigh o wa d maximum likelihood
es ima o whe e he p obabili y o obse ing he ansi ions in he da a is maximized.
We b ie ly summa ize he me hod and es ima ion sample in he nex ew pa ag aphs.
To pu s uc u e on he Ma ko p ocess, we ollow Pijoan-Mas and Ríos-Rull (2014)
and use a logi model, whe e su i al and heal h ansi ions condi ional on su i al a e
modeled as unc ions o he cu en heal h s a e and age. The p obabili y o su i al ol-
lows he usual bina y logi model while, condi ional on su i al, heal h ansi ions a e
modeled using mul inomial logi . Fo example, he one-pe iod-ahead su i al p obabil-
i y is gi en by
ps
+1=1
1+e−g(x |γ),(1)
whe e g(•)is a unc ion o he co a ia e ec o x which con ains ace, sex, age, heal h,
and po en ially o he obse ables such as educa ion. Su i al p obabili ies a e go e ned
by he pa ame e ec o γ o be es ima ed. T ansi ion p obabili ies o heal h condi-
ional on su i al a e de ined in an analogous manne .7
Es ima ion sample We exclude all obse a ions wi h missing age, ace, sex, o sel -
epo ed heal h, as well as indi iduals wi h only a single obse a ion (since hen we do
no ha e any ansi ion p obabili y o es ima e). We only conside indi iduals aged 50
o olde .8Fu he mo e, we es ic he sample o maximum age o 99 yea s a ansi-
ion s a (e en hough indi iduals can be olde when we obse e hem in he end o
7In Fol yn and Olsson (2021), we p o ide de ails abou he es ima ion and also pe o m an ex ensi e
e alua ion o he esul s. The es ima ed Ma ko p ocess is shown o p edic ac ual mo ali y e y well, bo h
sho and long e m. See he Supplemen al Appendix, Sec ion B o a b ie o e iew.
8Each incoming HRS coho is aged 51 o abo e, bu he su ey con ains younge indi iduals who a e
spouses o age-eligible esponden s.
706 Fol yn and Olsson Quan i a i e Economics 15 (2024)
a ansi ion). This lea es us wi h 34,196 indi iduals and 219,539 obse a ions in o al.
We es ima e he heal h and objec i e (s a is ical) su i al p ocess sepa a ely o he sub-
samples o men/women and he black/nonblack popula ion, since i is well known ha
he li e expec ancies o hese g oups ollow e y di e en ajec o ies.9Table B.1 in he
Supplemen al Appendix shows desc ip i e s a is ics and he numbe o indi iduals and
obse a ions by subg oup.
Resul s F om hese es ima es, we cons uc a i s -o de Ma ko p ocess de ined on
i e heal h s a es and he abso bing s a e o dea h, which go e ns he objec i e heal h
and su i al p obabili ies. This p ocess can be used o calcula e objec i e li e expec an-
cies condi ional on age, heal h, ace, and sex. No su p isingly, he e is a subs an ial
heal h g adien in li e expec ancy. Fo example, o a 70-yea -old nonblack man in ex-
cellen heal h, he p edic ed p obabili y o su i ing an addi ional 10 yea s is app ox-
ima ely 75%, while he p obabili y is jus a ound 35% i ins ead s a ing ou in poo
heal h. Fo a b ie o e iew o he esul s, see he Supplemen al Appendix, Sec ion B.2.
I is impo an o no e ha e en hough he heal h and su i al p ocess is based
on sel - epo ed heal h—a subjec i e measu e o how esponden s pe cei e hei heal h
s a e— he esul om he es ima ion is an objec i e s a is ical li e expec ancy o each
combina ion o ace, sex, age, and heal h. Sel - epo ed heal h can be hough o as
le ing he esponden s hemsel es agg ega e he mul idimensional in o ma ion abou
hei heal h ( ha is po en ially unobse able o he econome ician) in o a single ca e-
go ical a iable, and he a iable can also cap u e subjec i e pe cep ions o he espon-
den . The es ima ed Ma ko p ocess maximizes he p obabili y o obse ing he heal h
ansi ions and su i al in he da a condi ional on sel - epo ed heal h, i espec i e o
why a pa icula heal h s a e was epo ed.
2.4 Expec a ione o sinsu i alp obabili ies
In he expec a ions su ey module o he HRS, esponden s a e asked abou he p ob-
abili y hey assign o ce ain e en s. One o hese ques ions is abou he p obabili y o
su i ing o a ce ain age, o example: “Using a numbe om 0 o 100, wha do you hink
a e he chances ha you will li e o be a leas 100 yea s?”10
The exac a ge age depends on he esponden ’s age and su ey wa e. Fo ins ance,
in 1995, esponden s below he age o 70 we e asked abou he p obabili y o li ing un il
he age o 80, while esponden s abo e he age o 85 we e asked abou he a ge age o
100. In la e su eys, indi iduals we e asked abou su i al belie s o up o wo a ge
ages.
9Fo he emainde o he pape , he “black” sample consis s o esponden s who iden i y as black o
A ican-Ame ican, while “nonblack” is he complemen a y g oup, which also includes Hispanics. The HRS
is no la ge enough o disagg ega e he nonblack g oup u he , since he (unweigh ed) sample o pe son-
yea obse a ions is app oxima ely 72.7% whi e, 15.7% black/A ican-Ame ican, 9.4% Hispanic, wi h o he
e hnici ies oge he con ibu ing he emaining 2.3%.
10Be o e he esponden answe s he ques ions abou expec a ions, he in e iewe discusses p obabili-
ies and e i ies ha he esponden unde s ands he concep .
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 713
In wha ollows, we pa i ion he sample in o g oups indexed by k, such ha each
unique combina ion o (x,T) o ms a sepa a e g oup. Deno e by kall indi idual/ a ge
age/yea obse a ions ha sa is y
k=(i,j, )|xi =xk,Tij =Tk,
ha is, all obse a ions whe e he indi iduals a e asked abou hei su i al belie s o e
he same ho izon, a e o he same age, epo he same heal h s a e, and sha e any o he
co a ia es in xi .Deno ebyps
k he (weigh ed) sample a e age o epo ed su i al belie s
condi ional on (xk,Tk), ha is,
ps
k=
(i,j, )∈k
wi ·φTk(xk,zi )
(i,k, )∈k
wi
,(5)
whe e wi a e he esponden -le el sampling weigh s.
Now conside he logi coun e pa o (5), which we deno e by
ps
k=P (ali e a agek+Tk|xk,ν)
ha is, he p edic ed p obabili y o being ali e o g oup k, aking in o accoun all pos-
sible heal h ansi ions o Tk. We assume exac ly he same unc ional o m as o he
objec i e heal h and su i al p ocess, bu allow he pa ame e ec o νgo e ning su -
i al o di e .
The obse ed sample momen o each g oup can hen be w i en as
ps
k=
ps
k+uk,
whe e ukis he de ia ion om he g oup mean no explained by ou model. Ou aim is
o minimize hese g oup-speci ic esiduals using he leas -squa es objec i e unc ion
J(ν)=1
W
k
Wkps
k−
ps(xk,Tk|ν)2,(6)
whe e Wk=(i,j, )∈kwi is he sum o weigh s in g oup k. The es ima ed ec o νis
hence he a g min o J(ν).
Es ima ion sample We use all a ge ages om Table 3 o he es ima ion o he subjec-
i e li e expec ancy p ocess. In he main pape , we p esen he esul s o nonblack men,
as hese a e la e inco po a ed in o ou quan i a i e model.
Resul s The es ima ed subjec i e su i al belie s o nonblack men a e shown in pink
in Figu e 6, jux aposing he objec i e su i al p obabili ies es ima ed in Fol yn and Ols-
son (2021) in blue. As can be seen, he subjec i e belie abou su i al in heal h s a e
excellen o e y good is almos 100% o all ages. This does no mean ha indi iduals
in hose heal h s a es belie e ha hey will li e o e e . Ra he hey belie e ha dea h is
necessa ily p eceded by a de e io a ion in heal h.
714 Fol yn and Olsson Quan i a i e Economics 15 (2024)
Figu e 6. One-yea objec i e and subjec i e su i al p obabili ies by heal h s a e o nonblack
men (model es ima es). Shaded a eas indica e 95% con idence in e als. Fo each boo s apped
sample, we ees ima e he objec i e heal h p ocess.
Figu e 7summa izes he esul s, showing he li e expec ancy by age and heal h s a e
using he objec i e and he subjec i e su i al p ocess. A all ages, he di e ence in li e
expec ancy be ween he bes and he wo s heal h s a e is la ge when using subjec-
i e li e expec ancies. The di e gence be ween objec i e and subjec i e li e expec ancies
is pa icula ly la ge o men in bad heal h, who subs an ially unde es ima e su i al a
Figu e 7. Li e expec ancy by age and heal h o nonblack men. Colo s indica e he heal h s a e:
da k g een is excellen while ed is poo heal h. In panel 7a, he black line depic s he weigh ed
popula ion a e age. Shaded a eas indica e 95% con idence in e als.
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 715
younge ages. Con e sely, indi iduals in all heal h s a es o e es ima e hei chances o
su i al la e in li e. Figu e C.8 in he Supplemen al Appendix plo s he objec i e and sub-
jec i e li e expec ancy o he emaining demog aphic g oups, which exhibi e y simila
pa e ns.
Figu e C.9 in he Supplemen al Appendix plo s he model-p edic ed subjec i e su -
i al p obabili ies agains hei da a coun e pa s, showing ha bo h se s o momen s
a e well aligned.
3. Economic model
In his sec ion, we desc ibe he o e lapping-gene a ions model used o quan i y he im-
plica ions o su i al he e ogenei y. Time is disc e e and each pe iod co esponds o
one yea . Agen s de i e u ili y om consump ion and ace idiosync a ic isk in he o m
o shocks o hei labo income, medical expendi u es, heal h and su i al, as well as
s ochas ic beques s om hei pa en s. Ma ke s a e incomple e as agen s can only sa e
in a iskless asse while bo owing is no pe mi ed.
3.1 The agen ’s p oblem
The e is a uni mass o indi iduals dis ibu ed ac oss N coho s acco ding o he e godic
dis ibu ion implied by he ansi ion ma ix o su i al p obabili ies. An indi idual o
age ∈{1, ,N }and heal h h∈{1, ,5
}has a one-pe iod su i al p obabili y o age
+1gi enbyπs
h ,wi hπs
h =0 in he e minal pe iod.13
Indi iduals a e assumed o be wo king o he i s T −1 yea s o hei li e and ex-
ogenously e i e in he pe iod in which hey a ain age T . While wo king, hey a e hi
by pe sis en and ansi o y labo p oduc i i y shocks. Du ing e i emen , indi iduals
ecei e social secu i y e i emen bene i s, which depend on hei las pe sis en labo
p oduc i i y in wo king age.
Beques s a e modeled ia p obabilis ic in e gene a ional links along he lines o
S aub (2019) so ha child en wi h highe li e ime income a e mo e likely o ha e
income- ich pa en s, and hus expec o ecei e highe beques s.
Re i emen Le x=(a,p,h,η,1b, )be a e i ed indi idual’s s a e ec o , whe e ais
cash-a -hand, p ep esen s p e- e i emen labo p oduc i i y, his he cu en heal h
s a e, ηis he pe sis en componen o medical expendi u es, 1bis a beques indica o ,
and is age. In each pe iod, an indi idual chooses consump ion cand sa ings k o be in-
es ed in isk- ee p oduc i e capi al. Indi iduals ea n a g oss e u n Ron hei sa ings
and ecei e g oss e i emen income w·y , which is p opo ional o he economywide
wage a e w,andwhe e
y =ω ·Rss(p)
is a unc ion o he a e age ea nings p o ile a he ime o e i emen , ω ,andRss(•),
which mimics he eg essi e eplacemen a e o he US social secu i y sys em applied
13Since he model does no use calenda ime, we om now on use o deno e age.
716 Fol yn and Olsson Quan i a i e Economics 15 (2024)
o he las p e- e i emen labo p oduc i i y p. Re i emen income is axed using he
nonlinea ax schedule Ty(•)so ha a e - ax e i emen income amoun s o
ι=wy
−Ty(wy
).(7)
Agen s ecei e an inhe i ance b∗≥0 a mos once in hei li e, which we ack using
he indica o 1b.Theya ebo nins a e1b=1 and ansi ion o 1b=0 when hei pa en s
die. As long as 1b=1, he uple (b∗,1b)e ol es acco ding o
b
∗,1
b∼⎧
⎪
⎪
⎨
⎪
⎪
⎩
b∗(p,h, ),0
wi h p ob. 1−πs
∗πb
ph ,
(0, 0)wi h p ob. 1−πs
∗1−πb
ph ,
(0, 1)wi h p ob. πs
∗.
(8)
Once 1b=0, no addi ional beques s a e expec ed and (b
∗,1
b)=(0, 0)ob ains wi h ce -
ain y. I is no possible o di ec ly model in e gene a ional links be ween a pa en and
a child as his would double he numbe o s a e a iables. We he e o e assume ha
pa en s a e exac ly 30 yea s olde (wi h age ∗= +30) and su i e wi h he age-speci ic
popula ion-a e age p obabili y πs
∗ o he nex pe iod. Condi ional on pa en al dea h,
child en ecei e beques s wi h p obabili y πb
ph ∈(0, 1) o e lec ha many pa en s do
no lea e sizeable es a es. To cap u e he in e gene a ional pe sis ence o income and
weal h, we map agen s in o income quin iles and use he in e gene a ional income
quin ile ansi ion ma ix om Che y, Hend en, Kline, and Saez (2014) o s ochas i-
cally connec child en o po en ial pa en s. This c ea es a posi i e so ing be ween chil-
d en’s and pa en s’ income and weal h so ha iche child en a e mo e likely o ecei e
highe beques s. Since ou mapping o income quin iles elies on he s a es (p,h, ),
bo h he p obabili y o ecei e a beques πb
ph and he amoun ecei ed b∗a e unc ions
o (p,h, ). We desc ibe he echnical de ails o hese linkages in Sec ion D.1 in he Sup-
plemen al Appendix.
The nex pe iod cash-a -hand is gi en by
a=Rk +b
∗+ι−mh,η,ν, +1+ξ,(9)
whe e ma e ou -o -pocke medical expendi u es ha acc ue be ween ages and +1,
which a e allowed o depend on heal h h, a pe sis en componen η, and a ansi o y
shock ν, simila o he app oach aken in De Na di, F ench, and Jones (2010).
Because hese expendi u e shocks can be qui e la ge, we assume ha he go e n-
men gua an ees a minimum consump ion le el cby making a ans e ξwhene e
agen s do no ha e he esou ces o co e he medical expendi u es hemsel es. The
equi ed ans e is he e o e de ined as
ξ=max0, c+mh,η,ν, +1−Rk −b
∗−ι. (10)
In he p ocess, whene e agen s ecei e a posi i e ans e ξ>0, hey a e no pe mi ed
o sa e o he nex pe iod and, he e o e, choose k=0andc=c.
Nonsu i o s lea e hei asse holdings as beques s o hei o sp ing. Any ou -o -
pocke medical bills m(η,ν, +1)incu ed in he las pe iod o li e a e deduc ed, and
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 717
beques s a e addi ionally subjec o he es a e ax Tb(•). Thus, a e - ax beques s a e
gi en by
b=max0, Rk +b
∗−mη,ν, +1
−Tbmax0, Rk +b
∗−mη,ν, +1, (11)
whe e we assume ha descendan s a e no liable o any medical bills exceeding a de-
ceased indi idual’s asse s.14
Finally, we impose a wa m-glow beques mo i e as in De Na di (2004),
Vb(b)=φ1(b+φ2)1−σ−1
1−σ,
whe e φ1go e ns he weigh indi iduals assign o lea ing beques and φ2is a pa ame e
con olling o wha ex en beques s a e a luxu y good.
To summa ize, a e i ed indi idual’s maximiza ion p oblem is de ined by he alue
unc ion
V (a,p,h,η,1b, )=max
c≥0,k≥0c1−σ−1
1−σ+βπs
h EV x|p,h,η,1b,
+β1−πs
h EVbb|h,η,1b,
subjec o c+k≤aand he laws o mo ion (9)and(11), whe e x=(a,p,h,η,1
b, +
1)is he con inua ion s a e condi ional on su i al. Heal h he ol es acco ding o he
ansi ions es ima ed om he HRS, while he su i al p obabili ies πs
h ollow ei he
he objec i e o subjec i e su i al belie s discussed in he p e ious sec ion. Las ly, he
pe sis en componen ηo medical expendi u es ollows an AR(1) p ocess.
Wo king age Indi iduals o wo king age sol e a p oblem almos iden ical o ha o e-
i ees, excep ha hey addi ionally ace bo h pe sis en and ansi o y labo ea nings
isk. The pe sis en isk componen is cap u ed by he s a e a iable pand is assumed
o ollow a i s -o de Ma ko p ocess, while he ansi o y shock is i.i.d. o e ime.
Toge he wi h he age-heal h ea nings p o ile ωh , hey pin down an indi idual’s labo
p oduc i i y y, which is allowed o depend on heal h h,
y=ωh p. (12)
Mo eo e , wo ke s a e subjec o pay oll axes Tss(•), which we model as a unc ion o
p oduc i i y, so ha hei a e - ax labo income is
ι=y−Tss(y)w−Tyy−Tss(y)w. (13)
The emaining p oblem is he same as o e i ees, including he medical expendi u e
shocks, he consump ion loo , go e nmen ans e s, and he in e gene a ional linkages
and beques s.
14As (11) sugges s, i is possible ha child en die in he same pe iod as hei pa en s so ha an inhe i ance
immedia ely becomes pa o a child’s es a e.
718 Fol yn and Olsson Quan i a i e Economics 15 (2024)
3.2 Technology
The p oduc ion side o he model is s anda d. Compe i i e i ms employ labo and cap-
i al hi ed om households o p oduce a homogeneous inal good, which is used o
bo h consump ion and in es men . The agg ega e p oduc ion unc ion is assumed o
be Cobb–Douglas, F(A,K,L)=AKαkL1−αk. Capi al dep ecia es a he a e δk.
3.3 Go e nmen
We assume ha he go e nmen uns a PAYGO social secu i y sys em ha has o balance
in each pe iod, and ha ans e s as well as any emaining (was e ul) go e nmen expen-
di u es ha e o be ully inanced by income and inhe i ance axes. We i s desc ibe he
social secu i y sys em and he ea e he gene al go e nmen budge .
Social secu i y sys em We use a s ylized e sion o he ac ual e i emen income o -
mula used in he US social secu i y sys em. I cap u es he main ea u es, such as a
eg essi e eplacemen a e based on p e- e i emen income and a cap o maximum
bene i s. In he model, we de ine e i emen bene i s o be a p oduc o he economy-
wide wage w, he a e age li e-cycle p o ile componen om he las yea be o e e i ing
ω , and a unc ion ha mimics he eg essi e eplacemen a e
ι(p)=w·y (p)=w·ω ·Rss(p).
The eplacemen unc ion Rss(•)is gi en by
Rss(p)=⎧
⎪
⎪
⎨
⎪
⎪
⎩
ρ1pi p≤p∗
1,
ρ1p∗
1+ρ2p−p∗
1i p∗
1<p≤p∗
2,
ρ1p∗
1+ρ2p∗
2−p∗
1+ρ3minp∗
max,p−p∗
2else,
whe e p∗
1and p∗
2a e bend poin s and p∗
max is he con ibu ion and bene i base (CBB)
in he social secu i y income o mula, exp essed in e ms o he indi idual’s las p e-
e i emen pe sis en labo s a e p, which becomes pe manen once e i ed. The Sup-
plemen al Appendix, Sec ion D.2.1 desc ibes in de ail how we map he dolla quan i ies
aken om social secu i y egula ions o hei model coun e pa s.
The go e nmen expendi u es on e i emen a e inanced by a pay oll ax. The pay-
oll ax unc ion is de ined as
Tss(y)=τss ·min{ymax,y},
whe e ymax ep esen s maximum axable ea nings. The de i a ion o o al pay oll axes
aised in each pe iod can be ound in he Supplemen al Appendix, Sec ion D.2.2. To
balance he social secu i y sys em, we ind τss such ha o al expendi u es on social
secu i y bene i s equal o al pay oll axes.
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 719
Go e nmen budge The go e nmen needs o inance lump-sum ans e s ξ o house-
holds de ined in (10). We deno e he agg ega e ans e s by and p o ide de ails on how
hese a e compu ed in he Supplemen al Appendix, Sec ion D.3.1. Addi ionally, he go -
e nmen inances nondisc e iona y expendi u es ha amoun o a cons an ac ion g
o ou pu , G=gY.
We adop he same income ax unc ion as in Hea hco e, S o esle en, and Violan e
(2017), which is de ined as
Ty(ι)=ι−λι1−τ, (14)
whe e ιis ei he ea nings (ne o pay oll axes) o e i emen income, and we deno e o al
income ax e enue by Tinc. Addi ionally, he go e nmen collec s Tes a e in es a e axes.
We p o ide de ails on how o compu e Tes a e and Tinc in he Supplemen al Appendix,
Sec ions D.3.2 and D.3.3.
We assume ha he p og essi i y pa ame e τin (14) is ixed, and we pin down λsuch
ha he go e nmen budge is balanced in each pe iod, ha is, +G=Tes a e +Tinc(λ).
3.4 Equilib ium
The equilib ium de ini ion is mos ly s anda d and can be ound in he Supplemen al Ap-
pendix, Sec ion D.4. The one no ewo hy addi ion is ha we equi e ha o each coho ,
a e - ax es a es le by pa en s a e consis en wi h he beques s expec ed and ecei ed
by child en gi en he s ochas ic in e gene a ional links. This in oduces compu a ional
complica ions, which we discuss in he Supplemen al Appendix, Sec ion H.
4. Calib a ion
4.1 P e e ences
We assume log p e e ences, ha is, σ=1, and hus u(c)=logc. The common discoun
ac o β=0.979 is se o ob ain a capi al- o-ou pu a io o 3.0 in he scena io wi h sub-
jec i e su i al belie s. In ou benchma k calib a ion, we shu down he wa m-glow be-
ques mo i e by se ing φ1=0, and hence all beques s a e acciden al. We discuss al e -
na i e scena ios in Sec ion 5.4.
4.2 Ex e nally calib a ed pa ame e s
Demog aphics Agen s a e assumed o en e he economy a age 20, which co esponds
o model age 1, and e i e a he age o 65, implying ha T =46. The maximum a ain-
able age is 109, and hence we le N =90.15
15The eason o imposing such a high maximum age is ha o he wise he scope o upwa d bias in
belie s abou su i al in old age is limi ed: i agen s know o su e ha hey a e going o die a he age o
100, say, any gap be ween objec i e and subjec i e belie s sh inks by cons uc ion, e en a younge ages.
Howe e , se ing a high maximum age has no e ec on he age dis ibu ion: as shown in Figu e E.2, he
mass o indi iduals aged 100+in he economy is only 0.06%.
720 Fol yn and Olsson Quan i a i e Economics 15 (2024)
Ea nings We assume ha he loga i hm o labo ea nings ollows a p ocess wi h an-
si o y and pe sis en shocks,
logyh =logωh +log p +log , ∈{1, ,T −1},
whe e ωh is he age-heal h p o ile, p is he pe sis en componen , and is he ansi-
o y componen o ea nings. The pe sis en componen is assumed o ollow an AR(1)
p ocess,
logp =ρplogp −1+υ ,
wi h au oco ela ion ρpand inno a ion υ
iid
∼N(0, σ2
υ). The ansi o y shock is log-
no mally dis ibu ed wi h log
iid
∼N(0, σ2
). The s ochas ic pa o he wage p ocess is
he e o e cha ac e ized by he pa ame e s (ρp,σ2
υ,σ2
),whichwese o(0.9695, 0.0384,
0.0522), ollowing K uege , Mi man, and Pe i (2016). We use he Rouwenho s p oce-
du e o disc e ize he pe sis en pa o he p ocess in o an i e-s a e Ma ko chain, and
we disc e ize he ansi o y shock in o h ee s a es.
The age-heal h p o ile o labo ea nings is es ima ed o nonblack men aged 20 o
65 using PSID da a (PSID (2023)). No su p isingly, he e is a s ong heal h g adien . This
is pa ly d i en by lowe wages condi ional on wo king, and pa ly by a la ge ac ion
o indi iduals in bad heal h no wo king a all. Since we abs ac om he labo supply
decision, ou es ima es o he age-heal h ea nings p o ile cap u es bo h ma gins. Mo e
de ails can be ound in he Supplemen al Appendix, Sec ion E.3.
Medical expendi u es Following F ench and Jones (2004), De Na di, F ench, and Jones
(2010), we es ima e he medical expendi u e shocks om he ou -o -pocke medical ex-
penses epo ed a biennial equency in he HRS o he sample o nonblack men aged
50 and abo e. Since he HRS includes ha dly any indi iduals below he age o 50, we
assume ha agen s do no ace any ou -o -pocke medical cos s a hese ages.
We impose ha bo h he mean and a iance o log medical expendi u es a e s a e-
dependen and gi en by he ollowing p ocess:
logmi =αi+x
i β+z
i γ+σ(xi )(ηi +νi ),
ηi =ρmηi −1+ζi , (15)
ζi
iid
∼N0, σ2
ζ,
νi
iid
∼N0, σ2
ν. (16)
The ec o xi con ains a hi d-o de polynomial in age, heal h, as well as heal h in e -
ac ed wi h age. Addi ionally, zi includes con ols no p esen in he economic model
such as ma i al s a us, educa ion le el, 5-yea coho dummies, and ime ixed e ec s,
as well as in e ac ions o hese e ms. We un a ixed e ec s es ima o on he le el o
log medical expendi u es and eco e he pa ame e s go e ning he a iances and co-
a iances om he esiduals using GMM. Once we ha e iden i ied he pa ame e s o
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 721
Table 4. Calib a ed pa ame e s.
Pa ame e Desc ip ion Value Sou ce
P oduc ion echnology pa ame e s
αkCapi al sha e 36% K uege , Mi man, and Pe i (2016)
δkDep ecia ion a e 9.6% K uege , Mi man, and Pe i (2016)
ATo al ac o p oduc i i y 0.896 Fixes equilib ium wages a uni y
Social secu i y
ρ1Replacemen a e b acke 1 90% 2000 SS ules
ρ2Replacemen a e b acke 2 32% 2000 SS ules
ρ3Replacemen a e b acke 3 15% 2000 SS ules
b$
1Bendpoin 1 $6384 2000 SS ules
b$
2Bendpoin 2 $38,424 2000 SS ules
e$
max Con ibu ion and bene i base (CBB) $76,200 2000 SS ules
cConsump ion loo $2325 5% o a e age annual ea nings
Go e nmen budge
gGo . spending (sha e o GDP) 6% B inca Hol e , K usell, and Mala y (2016)
τTax p og essi i y 0.137 B inca e al. (2016)
τbMa ginal ax on es a es 30% Au ho s’ app oxima ion
medical expendi u es o e a 2-yea pe iod, we use a simula ed me hod o momen s p o-
cedu e o eco e he implied pa ame e s a annual equency, which yields ρm=0.920,
σ2
ζ=0.084, and σ2
ν=0.457. Mo e de ails can be ound in he Supplemen al Appendix,
Sec ion E.4.
Fo he pu pose o including medical expendi u e shocks in he OLG model, we
disc e ize he pe sis en componen (15) using he Rouwenho s p ocedu e wi h se en
s a es, and we disc e ize he ansi o y componen (16) in o i e possible ealiza ions.
Beques s We assume ha es a es a e ax exemp up o he amoun χband subjec o
a p opo ional ax τb he ea e . We se χb=19.75 so ha in equilib ium 2% o es a es
a e subjec o es a e axes, while τbis se o 30%.16 The in e gene a ional income quin-
ile ansi ion ma ix used o link pa en s o child en is aken om Che y e al. (2014,
Table II) and ep oduced in Table D.1 in he Supplemen al Appendix. Las ly, we allow
he p obabili y o ecei e a beques condi ional on pa en al dea h o di e by income
quin ile. To his end, we use he Su ey o Consume Finances (SCF) wa es 1998–2007
and compu e he ac ion o esponden s aged 60–70 who epo ha ing e e ecei ed an
inhe i ance by each income quin ile, which gi es he p obabili ies 20.5%, 25.2%, 27.4%,
33.3%, and 40.4% o he lowes o highes quin ile.
Remaining ex e nally calib a ed pa ame e s The emaining pa ame e s a e lis ed in Ta-
ble 4. The bend poin s and he con ibu ion and bene i base a e epo ed in US dolla s
o acili a e he in e p e a ion. The alue o he consump ion loo is simila o he le -
els used by De Na di, F ench, and Jones (2010)o Palumbo (1999).
16The op ma ginal ax a e in 2023 was 40% (see h ps://www.i s.go /pub/i s-pd /i706.pd ); howe e ,
no all axable es a es all in o he op ca ego y. We choose 30% as an app oxima ion.
722 Fol yn and Olsson Quan i a i e Economics 15 (2024)
4.3 Heal h and su i al p ocess
We use he p ocesses o heal h ansi ions and su i al p obabili ies desc ibed in Sec-
ion 2.3 (heal h ansi ions and objec i e su i al p obabili ies) and Sec ion 2.5 (subjec-
i e su i al p obabili ies) o nonblack men. Agen s en e he model a he age o 20, bu
he heal h and su i al p ocesses we es ima e based on he HRS da a s a s a he age o
50. We he e o e es ima e a heal h p ocess o he ages 20 o 50 using PSID da a. We use
da a om he yea s 1984 o 2019 and he subsample o nonblack male household heads,
and assume ha su i al is ce ain du ing his age span ( u he de ails can be ound
in he Supplemen al Appendix, Sec ion E.1). F om he age o 50, we use ou es ima ed
p ocess based on he HRS da a, and agen s s a acing a posi i e p obabili y o dea h.
The esul ing coho sizes and dis ibu ion o heal h s a es a e shown in Figu e E.2 in he
Supplemen al Appendix.
While he model is sol ed wi h i e heal h s a es, in wha ollows we epo esul s
only o he bes , middle, and wo s heal h s a es o educe isual clu e .
5. Resul s
We sol e he model unde h ee dis inc assump ions abou heal h he e ogenei y and
su i al expec a ions:
(i) No heal h he e ogenei y (NHH): In his scena io, all agen s o he same age ace
he same ea nings p o ile, he same medical expendi u e isk, and he same su -
i al isk. We elimina e heal h he e ogenei y and use he a e age su i al a es
(depic ed by he black line in Figu e 7a), an a e age ea nings p o ile, and he a -
e age medical expendi u e p ocess. The p obabili y o ecei ing an inhe i ance
and he amoun ecei ed a e also a e aged ac oss heal h.17
(ii) Objec i e su i al he e ogenei y (OSH): In he second scena io, we use he ob-
jec i e p ocess o heal h ansi ions and su i al p obabili ies desc ibed in Sec-
ion 2.3. In his case, indi iduals a e pe ec ly in o med abou hei ue su i al
p obabili y condi ional on heal h and age. Medical expendi u es and labo ea n-
ings a e allowed o di e by age and heal h.
(iii) Subjec i e su i al he e ogenei y (SSH): In he hi d scena io, agen s con e sely
o m belie s and ac acco ding o he subjec i e su i al p ocess es ima ed in Sec-
ion 2.5. Howe e , his subjec i e p ocess does no co espond o he ue su i al
p ocess, which we use when simula ing he model.
In he emainde o his sec ion, we i s con as he e ec i e discoun a es ha
a ise in he objec i e e sus subjec i e su i al belie scena ios. These a e impo an
d i e s o sa ings beha io , which we discuss nex . We hen u n o he implica ions o
weal h accumula ion ac oss heal h and also b ie ly discuss gene al equilib ium e ec s,
which a e mos ly unchanged ac oss all h ee scena ios. In ou benchma k calib a ion,
17These a e ages a e compu ed using he age-speci ic heal h dis ibu ion implied by ou es ima ed
heal h ansi ion p obabili ies and he ini ial dis ibu ion o e heal h a age 20 obse ed in he PSID.
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 729
The las ow in Table 5shows he gene al equilib ium esul s om he model wi h
no heal h he e ogenei y. The Gini coe icien o weal h is sligh ly highe han in any
o he models wi h heal h he e ogenei y. The d i e o his is an inc eased numbe o
la ge acciden al beques s. The la ges amoun s beque hed s em om dea hs in ela i ely
young ages (be ween ages 50 and 65). In a model wi h no heal h he e ogenei y, hese
dea hs a e equally likely o happen o agen s in he op o he asse dis ibu ion as o
agen s in he bo om. Wi h heal h-dependen su i al on he o he hand, i is mo e likely
ha dea hs in ela i ely young ages happen o agen s in poo heal h, who a e on a e age
poo e . Thus, he lack o heal h he e ogenei y gi es ise o la ge beques s, which in u n
gi es ise o sligh ly la ge weal h inequali y.
5.4 A model wi h an ac i e beques mo i e
The e a e many d i e s o sa ings ha could a y ac oss heal h bu a e no included
in ou model: he exis ence o (employe - ied) heal h o li e insu ance, human capi al
in es men , endogenous e i emen decisions, po olio composi ion, p i a e pensions,
and pe manen cha ac e is ics such as pa ience, o name a ew (see, o ins ance, De
Na di, F ench, and Jones (2010), Capa ina (2015), o De Na di, Pashchenko, and Po a-
pakka m (2017) o s udies aking a b oade pe spec i e including se e al channels).
These mechanisms could all add ealism o he model and make he li e-cycle p o iles
mo e in line wi h he da a. One mechanism o en in oduced o cap u e he slow de-
cumula ion o asse in olde ages is a wa m-glow beques mo i e. In his sec ion, we
he e o e use a model calib a ion wi h an ac i e beques mo i e (φ1>0) o show how i
in e ac s wi h (subjec i e) su i al he e ogenei y.
5.4.1 Calib a ion Whe e applicable, we use he same calib a ion as in he main ex .
We de e mine he discoun ac o β, he p e e ence pa ame e s go e ning he beques
mo i e (φ1and φ2) and he es a e ax exemp ion h eshold χbusing he me hod o sim-
ula ed momen s, ha is, we minimize he weigh ed sum o squa ed dis ances be ween
a ge ed and simula ed momen s om he model wi h subjec i e belie s abou su i al.
We again a ge a capi al- o-ou pu a io o 3 and ha 2% o es a es should be subjec
o es a e axes. Addi ionally, we y o ma ch he old-age, li e-cycle p o ile o asse s. To
his end, we use he median weal h le els a ages 60, 65, 70, 75, 80, and 85 obse ed in he
HRS, ela i e o median weal h a age 55. We choose his app oach as i is quan i a i ely
no possible o ma ch weal h in le els and a he same ime impose a capi al-ou pu -
a io o 3 in a model wi h p oduc i e capi al as he only asse (a e all, mos o he weal h
in he da a is held in esiden ial eal es a e). The capi al- o-ou pu a io and he ac ion
o es a es subjec o es a e ax a e pe ec ly ma ched, while he asse holdings by age
and hei da a coun e pa s a e shown in Table G.1 in he Supplemen al Appendix. Some
aspec s o ou model a e oo simplis ic o ma ch he da a momen s exac ly. Fo example,
because we impose an exogenous e i emen age o 65, he li e-cycle p o ile o asse s
peaks exac ly a his age, whe eas his is no he case in he da a.
The es ima ed pa ame e s a e lis ed in Table 6. As he able shows, he beques luxu y
shi e is small. The eason is ha we y o ma ch he median asse holdings la e in li e.
I beques s we e a luxu y good, he median asse le el would all quickly owa d ze o.
730 Fol yn and Olsson Quan i a i e Economics 15 (2024)
Table 6. Pa ame e s o he model wi h a beques mo i e.
Pa ame e Desc ip ion Value
Model wi h beques
βDiscoun ac o 0.942
φ1Beques weigh 11.157
φ2Beques shi e 0.001
χbEs a e ax exemp ion 18.333
5.4.2 Resul s
C oss-sec ion and li e cycle Figu e 11 shows he li e-cycle p o iles o he scena ios
wi h objec i e su i al he e ogenei y (OSH) and subjec i e su i al he e ogenei y (SSH).
O e all, due o he beques mo i e, olde agen s do no decumula e hei weal h, and he
esul ing median asse p o ile is mo e in line wi h he da a in bo h scena ios. Be o e e-
i emen , agen s in excellen heal h ha e mo e weal h han agen s in wo se heal h. The
main eason o his is he highe labo income o he o me g oup.
Howe e , he heal h-weal h g adien is subs an ially smalle p io o e i emen han
in he baseline calib a ion wi hou a beques mo i e (compa e o Figu e 10), and is e en
e e sed a e he age o 75, wi h agen s in poo heal h being iche . This shows ha he
e ec o combining su i al he e ogenei y wi h a beques mo i e o his ype is no en-
i ely s aigh o wa d. The expec ed u ili y om lea ing a beques is no only a unc ion
o heamoun expec ed obehandedo e o hedescendan s,bu alsoo hesu i al
p obabili y: agen s wi h low (objec i e o subjec i e) su i al p ospec s pu mo e weigh
on he beques mo i e. Hence, he e a e wo e ec s om lowe li e expec ancy ha wo k
in opposi e di ec ions: a sho e expec ed li e span makes agen s wan o sa e less o
hei own consump ion in old age, bu a s onge beques mo i e induces hem o sa e
mo e. The ne e ec a ies depending on he calib a ion o beques pa ame e s, bu he
Figu e 11. Median li e-cycle p o iles o weal h, model wi h an ac i e beques mo i e.
Quan i a i e Economics 15 (2024) Subjec i e li e expec ancies 731
second mechanism is always p esen wi h a wa m-glow beques mo i e o his ype: a
sho e li e span makes agen s wan o sa e mo e o lea e beques s.22
Thus, in bo h he OSH and he SSH scena io, he model misses he c oss-sec ional
co ela ion be ween weal h and heal h in olde ages ha is p esen in he da a. The
sligh ly s onge e e sal o he heal h-weal h g adien in he SSH model ollows di ec ly
om he biases ha ampli y he heal h-su i al belie g adien .
No e also ha in e y high ages, agen s keep less asse s in he SSH model han in
he OHS model. Agen s in he subjec i e belie model o e es ima e he p obabili y o a
long li e and, he e o e, pu a lowe weigh on wa m-glow beques s, esul ing in lowe
sa ings.
Dynamic esponses o heal h shocks Nex , we compa e changes in weal h ollowing
nega i e heal h shocks in he da a o hei model coun e pa s. To his end, we eg ess
he change in ne o al weal h (using an in e se hype bolic sine ans o ma ion) on a
nega i e heal h shock de ined as an indica o o a de e io a ion in sel - epo ed heal h
be ween su ey wa es. We es ic he sample o ages 65 and abo e in o de o ocus on
he pa o he li e cycle whe e li e expec ancy and beques conside a ions a e impo -
an d i e s o sa ings. We simula e a panel o 100,000 agen s and collapse he da a o
wo-yea equency o eplica e he biennial HRS.23 The changes in asse s and heal h a e
de ined analogously o he da a, aking di e ences o e 2-yea pe iods.
The esul s in Table 7show ha he model wi h a beques mo i e p oduces dynamic
sa ings esponses ha a e di icul o squa e wi h he da a. The es ima ed sa ings e-
sponse o a nega i e heal h shock in he model wi h an ac i e beques mo i e is e ec-
i ely ze o, whe eas he model wi hou an ac i e beques mo i e p oduces sa ings e-
sponses ha a e well in line wi h he da a.
Table 7. Heal h shocks and changes in weal h.
Dep. Va iable: Rela i e Change in Ne To al Weal h
Da a Model
(1) (2) No beques Beques
Nega i e heal h shock −0.116 −0.105 −0.1081 0.0001
(0.026) (0.026) (0.001) (0.000)
Age FE Yes Yes Yes Yes
Heal h FE Yes Yes Yes Yes
Educa ion FE Yes
Obse a ions 35,821 35,821 1,297,804 1,297,804
No e: The able shows he esul s o eg essing changes in ne o al weal h (a e an in e se hype bolic sign ans o ma ion)
on an indica o o a de e io a ion in sel - epo ed heal h be ween wo consecu i e su ey wa es. The eg ession includes ully
in e ac ed ixed e ec s as indica ed. Columns 1 and 2 a e he same as he i s wo columns in Table A.5 in he Supplemen al
Appendix. Fo he model columns, we use he SSH scena io whe e agen s ac acco ding o hei subjec i e belie s. Sample
es ic ed o nonblack males age 65 and abo e. Clus e ed s anda d e o s in pa en heses.
22To aid in ui ion, in Sec ion G.1 in he Supplemen al Appendix we show he mechanisms a play in a
simple wo-pe iod model example.
23We s a he simula ion wi h 100,000 agen s a he age o 20, o which 86,809 a e s ill ali e a he age
o 65.
732 Fol yn and Olsson Quan i a i e Economics 15 (2024)
In sum, in a model wi h heal h he e ogenei y, bo h he c oss-sec ional implica ions
and he dynamic esponses o heal h shocks make he model wi h a beques mo i e cali-
b a ed o ma ch median asse holdings in old age di icul o align wi h da a. The ela i e
s eng h o he di e en e ec s we poin o in his sec ion o cou se a ies depending on
calib a ion, bu should be kep in mind when combining a wa m-glow beques mo i e
wi h dynamically e ol ing expec ed longe i y.
6. Conclusions
This pape explo es how a ia ion in objec i e and subjec i ely pe cei ed li e expec ancy
a ec s sa ings beha io o heal hy and unheal hy people. Using HRS da a, we show ha
he e exis s a wi hin-coho s eepness bias in su i al belie s: indi iduals in bad heal h
no only ha e a sho e expec ed li e span, bu a e also ela i ely mo e downwa d biased
abou hei su i al chances, while indi iduals in good heal h, and hus wi h highe su -
i al p obabili y display a mo e upwa d bias. These sys ema ic biases exace ba e he
su i al expec ancy he e ogenei y in he popula ion.
The di e ences in belie s abou su i al ansla e in o ime p e e ence he e ogene-
i y, and consequen ly, sa ings beha io . We show ha biases in belie s abou su i al
can explain app oxima ely one- i h o he di e ences in accumula ed weal h be ween
hose in excellen e sus poo heal h, mos ly because he la e g oup unde es ima es
hei li e expec ancy.
This pape ies in o a s ando cu en esea chin es iga ing p e e ence he e ogene-
i y and i s impo ance o indi idual choices and agg ega e ou comes. We p o ide an
in ui i ely plausible and mic o- ounded sou ce o he e ogenei y: he pe cei ed p oba-
bili y o su i ing o u u e s a es o he wo ld. Ou quan i ica ion o his channel shows
ha li e expec ancy he e ogenei y is impo an and should be included in he lis o po-
en ial sou ces o he e ogenei y ha we need o conside in ou analyses. In es iga ing
he impo ance o he s eepness bias o wi hin-coho di e ences in e ms o po o-
lio alloca ions, demand o inancial p oduc s, o e i emen beha io is le o u u e
esea ch.
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736 Fol yn and Olsson Quan i a i e Economics 15 (2024)
Co-edi o Mo en Ra n handled his manusc ip .
Manusc ip ecei ed 31 Oc obe , 2021; inal e sion accep ed 1 May, 2024; a ailable online 24
May, 2024.
The eplica ion package o his pape is a ailable a h ps://doi.o g/10.5281/zenodo.11092578.
The Jou nal checked he da a and codes included in he package o hei abili y o ep oduce
he esul s in he pape and app o ed online appendices.
