Boppa , Timo; Ha menbe g, Ka l; Hassle , John; K usell, Pe ; Olsson, Jonna
A icle
In eg a ed epi-econ assessmen : Quan i a i e heo 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: Boppa , Timo; Ha menbe g, Ka l; Hassle , John; K usell, Pe ; Olsson, Jonna
(2025) : In eg a ed epi-econ assessmen : Quan i a i e heo y, Quan i a i e Economics, ISSN
1759-7331, The Econome ic Socie y, New Ha en, CT, Vol. 16, Iss. 1, pp. 89-131,
h ps://doi.o g/10.3982/QE2430
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Quan i a i e Economics 16 (2025), 89–131 1759-7331/20250089
In eg a ed epi-econ assessmen : Quan i a i e heo y
Timo Boppa
Ins i u e o In e na ional Economic S udies, S ockholm Uni e si y and Depa men o Economics,
Uni e si y o Zu ich
Ka l Ha menbe g
Depa men o Economics, Uni e si y o Oslo
John Hassle
Ins i u e o In e na ional Economic S udies, S ockholm Uni e si y
Pe K usell
Ins i u e o In e na ional Economic S udies, S ockholm Uni e si y
Jonna Olsson
Depa men o Economics, NHH No wegian School o Economics
Aimed a pandemic p epa edness, we cons uc a amewo k o in eg a ed epi-
econ assessmen ha we belie e would be use ul o policymake s, especially a
he ea ly s ages o a pandemic ou b eak. We o e heo y, calib a ion o mic o-,
mac o-, and epi-da a, and nume ical me hods o quan i a i e policy e alua ion.
The model has an explici mic oeconomic, ma ke -based s uc u e. I highligh s
ade-o s, wi hin pe iod and o e ime, associa ed wi h ac i i ies ha in ol e bo h
aluable social in e ac ion and ha m ul disease ansmission. We compa e ma -
ke solu ions wi h socially op imal alloca ions. Ou calib a ion o Co id-19 im-
plies ha households shi hei leisu e and wo k ac i i ies away om social in-
e ac ions. This is especially ue o olde indi iduals, who a e mo e ulne able
o disease. The op imal alloca ion may o may no in ol e lockdown and changes
he ime alloca ions signi ican ly ac oss age g oups. In his ade-o , people’s so-
cial leisu e ime becomes an impo an ac o , aside om dea hs and GDP. We
inally compa e op imal esponses o di e en i uses (SARS, seasonal lu) and a -
gue ha , going o wa d, economic analysis ough o be an in eg al elemen behind
epidemiological policy.
Keywo ds. In eg a ed assessmen , epidemiology, Co id-19, ime-use da a.
JEL classi ica ion. C6, E6, I1.
Timo Boppa : [email p o ec ed]
Ka l Ha menbe g: [email p o ec ed]
John Hassle : [email p o ec ed]
Pe K usell: [email p o ec ed]
Jonna Olsson: [email p o ec ed]
Ha menbe g g a e ully acknowledges unding om he Resea ch Council o No way (P ojec 316301) and
Riksbankens Jubileums ond (P og am M23-0019).
©2025 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/QE2430
90 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
1. In oduc ion
May 2023, he Wo ld Heal h O ganiza ion announced he end o he eme gency phase o
Co id-19, wi h close o 7 million eco ded dea hs and wi h he ac ual dea h oll belie ed
o be e en highe . The pandemic as well as he policy esponses ac oss he wo ld a ec ed
i ually all ace s o li e o a la ge sha e o he wo ld’s popula ion. Policies p e iously
unimagined such as sus ained “lockdowns” we e quickly implemen ed. We e hese poli-
cies good? Mo e impo an ly, wha is an app op ia e policy esponse o he nex la ge
epidemic? And how should go e nmen s imp o e hei pandemic p epa edness? Echo-
ing Lucas (1988), “ he consequences o human wel a e in ol ed in ques ions like hese
a e simply s agge ing.”
A key pa o pandemic p epa edness is o ha e obus , o - he-shel models o he
in e ac ion be ween he economy and he epidemiological sp ead o a disease ha can
be used o compa ing di e en policy op ions: in eg a ed epi-econ assessmen models.
A he beginning o he pandemic, we clea ly did no ha e such models. Equally clea ly,
a la ge li e a u e wi h his aim quickly eme ged. The pu pose o he p esen pape is o
p opose a amewo k ha can quickly be deployed in he u u e when acing new pan-
demic h ea s. The amewo k was designed wi h Co id-19 in mind and sha es many
ea u es wi h pape s in he li e a u e ha eme ged. Howe e , i also o e s su icien gen-
e ali y ha compa isons can be made be ween di e en i uses; we make such compa -
isons in he pape . In pa icula , i makes clea how policy should a y, quali a i ely and
quan i a i ely, wi h he speci ic ea u es o he i us and i s consequences. Thus, he
goal is no o make a pos -mo em analysis o Co id-19 and possible policy e o s made;
such an e alua ion would equi e a weal h o mic oeconomic and mac oeconomic da a
ha may be a ailable now bu ce ainly was no a ailable a he onse o he pandemic.
Ra he , he use ulness o ou se ing is om he ex an e pe spec i e, as a policymake ’s
guide acing he nex pandemic, wi hou access o he da a equi ed o a ull e alua ion.
The ask o designing good epidemic policy is di icul o a leas wo easons, which
mo i a e he need o in eg a ed epi-econ assessmen models. Fi s , he unde s anding
o he e olu ion o he pandemic—i s oo s, i s dynamic e olu ion, and how di e en
in e en ions would a ec hese dynamics—may be qui e incomple e. F om ou pe -
spec i e, his incomple e knowledge only pa ly in ol es epidemiological and ela ed
na u al-science aspec s: since a i us sp eads h ough human in e ac ion, o a la ge ex-
en we also need knowledge o how people beha e and eac o he pandemic. He e,
economic analysis is a he hea o he ma e : he sp ead o a i us, and he p ecau-
ions aken o a oid i , a e undamen ally decisions made by people in ypical economic
con ex s: hey in ol e ade-o s in decisions abou how much and wha o consume
and abou how much and whe e o wo k; o i ms, a my iad o ela ed decisions appea
as well. We hus iew i as an impo an goal o economics o adap ou amewo ks o
inco po a e epidemics.
The second di icul y is (i) o iden i y ade-o s be ween, on he one hand, he mi -
iga ion o he public-heal h e ec s o he pandemic and, on he o he , economic al-
ues, such as ou pu and consump ion; and (ii), when a ade-o is una oidable, use
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 91
policy o s ike an app op ia e balance. He e again, quan i a i e economic analysis ap-
pea s cen al. Mo eo e , in ou iew i is no only help ul bu also necessa y o de-
elop cohe en quan i a i e heo e ical amewo ks o such e alua ions. In pa icula ,
by making clea —based on a solid unde s anding o he mechanisms in ol ed ( he i s
di icul y)—how he balance is s uck, policymake s can also hope o be mo e success-
ul in communica ing he easons behind hei in e en ions and ecommenda ions and
he eby be mo e e ec i e in achie ing he goals hey se ou .
To add ess hese challenges, we in oduce epidemiology in o a se ing wi h mic oe-
conomic ounda ions, hus bo h allowing posi i e and no ma i e analysis o be ca ied
ou explici ly. We o e an analysis o he Co id-19 pandemic, bu an e en mo e impo -
an goal o ou pape is he de elopmen o a co e se ing on which u he analysis—
o example, mo e complex o di e en i uses, a iche sociological se ing, mo e de-
mog aphic de ail—can be added seamlessly. Because o his mo e gene al pu pose, we
ha e imposed a numbe o equi emen s, which we now b ie ly lis and mo i a e.
Fi s , we build on explici mic o ounda ions: by clea ly desc ibing ac o s and hei
decision p oblems in an explici equilib ium con ex , we p oduce a se ing ha can p o-
ide ich answe s o coun e ac ual expe imen s. The se ing also allows compa ison o
he planne ’s op imum wi h ma ke alloca ions (whe e he ma ke alloca ion may in-
co po a e policy a iables). We say “ he” op imum since ou amewo k p esumes ull
insu ance and a dynas ic s uc u e wi h a ep esen a i e amily consis ing o membe s
o di e en age g oups. Ou amewo k can be ex ended o inco po a e lack o insu ance
as well bu we ega d he ep esen a i e-agen se ing as a use ul s a ing benchma k.
Second, we inco po a e elemen s o sociology. Ob iously, social in e ac ions a e key
o he sp ead o i uses, so speci ying he deg ee o such in e ac ions in di e en eco-
nomic ac i i ies—and disciplining he model pa ame e s wi h associa ed mic oeco-
nomic da a—is one o ou main goals. No less impo an , social in e ac ion is cen al
o any wel a e e alua ion in his a ea. An example is he changed na u e o leisu e ha
ma e ializes du ing imes o es ic ed social ac i i ies. In sho , he cos s o es ic ing
beha io —as, o example, in lock-downs—need o include e ec s on leisu e and i s na-
u e. In ou co e se ing, we ie all social in e ac ions o economic ac i i ies and g oup
hese ac i i ies by hei deg ee o social con ac .1
Thi d, ou pape aims o p o ide quan i a i e p edic ions: e en hough new, in e -
es ing mechanisms can su ace when we explo e and de elop his a ea u he , we see i
as seconda y o answe ing ques ions abou magni udes. To be clea , his a ea con ains
impo an quali a i e dimensions; o example, is i be e o lock down, o o a ge he d
immuni y while p o ec ing he heal hca e sys em? These a e, quali a i ely, adically di -
e en policies, and—as we show in his pape — hey can bo h be he op imal choice.
Howe e , he cen al issue is o ind ou which one applies in any gi en si ua ion and
his is a wholly quan i a i e ques ion ha can only be se led a e ca e ul calib a ion o
he model’s cen al pa ame e s.
1In ou app oach o ime use and sociological aspec s o consump ion, we combine and build u he
on he app oaches in Becke (1965,1974). Ou model o social in e ac ions abs ac s om, o example,
di e en no ions o al uism o ne wo k heo y. Clea ly, hese ea u es would be in e es ing o add o ou
se ing.
92 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
Fou h, his new a ea equi es nume ical me hods ha can p ope ly handle high-
dimensional nonlinea dynamic sys ems. We do no de elop adically new echniques
he e bu p o ide a solu ion me hod ha is designed o ex ensions. I has wo pa s. One
is s a ic: i sol es o wi hin-pe iod p ices and quan i ies gi en some bounda y condi-
ions and can accommoda e ich he e ogenei y and a complex ma ke economy. The
o he , a dynamic pa , connec s he bounda y condi ions and sol es o he e olu ion o
hese using backwa d and o wa d i e a ion oge he wi h dynamic-p og amming en e-
lope condi ions; he bounda y condi ions consis o s a e a iables and shadow alues
o addi ional in ec ions.
Equipped wi h hese elemen s, we use ou epi-econ in eg a ed assessmen model o
add ess Co id-19 and o he i uses: he seasonal lu and SARS.2
The epi-econ model
The gene al abs ac amewo k we p opose consis s o a mic oeconomic model o p o-
duc ion, consump ion, and ime alloca ion combined wi h a desc ip ion o he in ec ion
isks associa ed wi h he di e en ways o spend ime as well as a s a e-dependen law
o mo ion o he epidemic. In his amewo k, indi iduals a e he e ogeneous bu each
indi idual belongs o a la ge amily wi hin, which he e is ull insu ance agains any id-
iosync a ic shocks; a he same ime, he e a e many such amilies. Fo his amewo k,
which desc ibes a b oad class o models, we cha ac e ize equilib ium condi ions o he
compe i i e ma ke equilib ium bo h wi h “myopic” expec a ions, whe e people a e un-
awa e o he pandemic, and “pe ec o esigh ” (i.e., a ional expec a ions), whe e peo-
ple a e ully and co ec ly in o med o he pandemic. We also s udy he social planne ’s
p oblem and compa e i s key equa ions and implied alloca ion o he ma ke equa ions
and ou comes. In addi ion, we p o ide a obus solu ion algo i hm o all cases.
We pu a conc e e model s uc u e on his abs ac amewo k as ollows. U ili y is
a unc ion no only o consump ion o di e en goods and se ices, bu also he leisu e
ime indi iduals spend wi h he goods and se ices. In ou benchma k model, o sim-
plici y, we dicho omize: goods a e ei he consumed in public o in p i a e, whe e in-
p i a e consump ion does no in ol e social in e ac ion, and hus no isk o sp ead-
ing he disease. Simila ly, wo ke s can con ibu e o p oduc ion ei he om home o by
wo king “in he o ice,” wi h only he la e in ol ing any isk o ge ing in ec ed. We cal-
ib a e u ili y unc ions o e di e en goods and leisu e ac i i ies ha in ol e non i ial
subs i u ion, and simila ly, he e is non i ial subs i u ion be ween wo k a home and
wo king in he o ice, all cons ained o ma ch a ailable mic oeconomic da a.
Each amily has non i ial demog aphics among i s membe s. Again, we dicho omi-
ze in ou main model o “young” and “old” indi iduals; aside om di e ing in ypical
ways (li e expec ancy, p oduc i i y), hese wo ypes also di e in hei Co id-19 ulne -
abili y. Gi en he s ong age g adien in ulne abili y o he mos nega i e consequences
2Though playing ou on an en i ely di e en ime scale, in impo an ways he goal in his pape pa allels
ha in he a ea o clima e change, whe e No dhaus pionee ed a me ging o na u al-science models o he
clima e and he ca bon cycle wi h a s anda d neoclassical economic g ow h amewo k. See No dhaus and
Boye (2000), and o an explici ma ke -economy e sion, Goloso , Hassle , K usell, and Tsy inski (2014).
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 93
o Co id-19, his is he mos ob ious s a ing poin o e alua ion o he cu en epi-
demic, bu o he o addi ional he e ogenei y could be inco po a ed.
Key esul s and he na u e o op imal policy
Fo he baseline, dicho omous model, we ind a signi ican “ ea ac o ”: households
ealloca e hei ime subs an ially as a esponse o he epidemic—i hey a e ully in-
o med, also in absence o policy in e en ions. In ac , a ional expec a ions educes he
dea h oll in he Co id-19 case by 80%, ela i e o a myopic scena io wi hou beha io al
adjus men s.
S ill, a compa ison o he a ional-expec a ions compe i i e equilib ium and he so-
cial planne ’s op imal scena io u ns ou o be e y in e es ing. Speci ically, we ind ha
he quali y-o -li e componen is a i s -o de d i e o policy and ha GDP is a poo p oxy
o wel a e o li ing indi iduals since i neglec s he alue o quali y leisu e. Thus, as he
ea ac o al eady deals wi h he ade-o be ween he economy and li e qui e well, he
ac oss-g oup ex e nali ies come in o ocus. In pa icula , a social planne dis ibu es he
bu den o beha io al adjus men mo e e icien ly in he popula ion by making he young
and less ulne able adjus hei beha io beyond wha is in hei sel -in e es . In he
compe i i e equilib ium, he old a e olun a ily s aying home o p o ec hei li es, bu
his comes a a la ge u ili y cos since hei quali y o li e plumme s. As a esul , he plan-
ne educes ou pu subs an ially bu low u ili y du ing he pandemic’s peak inc eases as
he old and ulne able can enjoy mo e social leisu e.
The quali a i e ea u es o he op imal policy a e no a o egone conclusion—ou
amewo k is ich enough o a ionalize a ange o op imal policies, depending on he
calib a ion o he model. In ou baseline scena io, no cu e is expec ed o a i e. He e,
he social planne op imum is bes desc ibed as a “p o ec he heal hca e sys em” s a -
egy. The numbe o in ec ed is kep low enough so ha he heal h sys em is ne e o e -
bu dened, so ha “o e shoo ing” in e ms o he numbe o in ec ed be o e he d immu-
ni y is eached is minimized.
By con as , i a cu e o he disease (o a cheap, pe ec accine) is expec ed o a i e
soon enough, he social planne chooses a s a egy bes desc ibed as “supp ess”: keeping
he numbe o in ec ions low by lowe ing social ac i i y (and hus ou pu ) such ha he
epidemic ne e akes o (i.e., he ep oduc ion a e is kep , weakly, below one). Fu he ,
i he cos o o e bu dening he heal hca e sys em is low, a quali a i ely di e en op i-
mal alloca ion anspi es: he bes esponse now is o speed up he sp ead o he i us,
e en mo e so han unde he laissez- ai e equilib ium. This way, he wel a e cos s om
isola ing and p o ec ing he old all, as hey a e incu ed o e a sho e ime span. The
numbe o in ec ed a he peak o he epidemic is high, hough he numbe o dea hs
s ill emains a a a he low le el as hose a ec ed a e he young/less ulne able.
C oss-epidemic es ic ions on he alue o a s a is ical li e
A key inpu in o he calib a ion o he epi-econ model is he alue o a s a is ical li e.In
ou baseline model, we ollow Hall, Jones, and Klenow (2020) and calib a e he model
94 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
so ha he willingness o pay o an addi ional day o li e is six imes daily consump-
ion expendi u e. This is a easonable alue, bu he li e a u e ea u es a la ge ange o
alues (see, e.g., Viscusi and Aldy (2003)). We he e o e also conside a highe alue o
a s a is ical li e (a willingness o pay o 11.4 imes consump ion expendi u e, ollowing
Glo e , Hea hco e, and K uege (2022)). We show ha op imal policy can and o eason-
able scena ios does shi om a “p o ec he heal hca e sys em” s a egy o a “supp ess”
s a egy when using he highe alue o a s a is ical li e.
We conside he beha io al esponse o he seasonal lu a c oss-epidemic es ic ion
on ou calib a ed model. A alue o a s a is ical li e in he uppe end o he ange implies
coun e ac ually la ge esponses o he egula seasonal lu, which leads us o conclude
ha ou a ge o he alue o a s a is ical li e is in line wi h he obse ed willingness o
pay o a oiding he egula lu.
Rela ed li e a u e
Upon he onse o he Co id-19 epidemic, many economis s s a ed analyzing epidemi-
ology models.3As a esul , he e is a sizable such li e a u e and ou e iew o his e-
sea ch he e will be limi ed o he pape s ha a e he mos closely ela ed o ou wo k.
Epidemiological models had been used in economics p io o Co id-19 in analyses
o o he i uses.4Howe e , Eichenbaum, Rebelo, and T aband (2021)(hence o hERT)
is as a as we can ell he i s applica ion o epidemiology ha is also mac oeconomic in
he sense ha i desc ibes a whole economy o o wa d-looking agen s and ma ke de-
e mina ion o p ices. ERT does o e a wholly mic oeconomic s uc u e (including a io-
nal consume s and i ms wi h objec i es explici ly desc ibed) and he in e en ions hey
conside in ol e ully desc ibed policy ins umen s and compa isons be ween laissez-
ai e and ully op imal policy. I is also quan i a i e in ha he model’s economic pa-
ame e s a e selec ed o ma ch (s anda d) cha ac e is ics o mac oeconomic da a—and
he epidemiological pa ame e s a e chosen o ma ch known es ima es pe aining o he
speci ic ea u es o Co id-19. The ea u es o ERT jus desc ibed a e p e equisi es o us,
and we hus ollow ERT in many ways. Ou main concep ual addi ion, in e ms o ou
modeling and quan i a i e app oach, is o mo e owa d explici ly desc ibing ime use
and o inco po a e a sociological elemen in o i . In so doing, we a e aking s eps owa d
a de elopmen o a socioeconomic amewo k desc ibing how people in e ac and how
hey de i e u ili y om i ; we use hei obse ed ime-use choices, mo eo e , o con-
s uc u ili y unc ions ha desc ibe hese alua ions.
Simila pape s o ou s ha ollow ERT in conduc ing a ull, mic o ounded epi-
econ analysis include Be hune and Ko inek (2020), Chang and Velasco (2020), Fa boodi,
Ja osch, and Shime (2021), Ga ibaldi, Moen, and Pissa ides (2020), Glo e , Hea hco e,
K uege , and Ríos-Rull (2023), Jones, Philippon, and Venka eswa an (2021), Kapiˇ
cka and
3A keson (2020) desc ibes he co e model de eloped by epidemiologis s (Ke mack and McKend ick
(1927)) and we use i he e.
4See, o example, Geo a d and Philipson (1996), K eme (1996), Adda (2007), Chan, Hamil on, and Pa-
pageo ge (2016), and G eenwood, Ki che , San os, and Te il (2019).
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 95
Rupe (2022), K uege , Uhlig, and Xie (2022), and an Vlokho en (2020).5Compa ed o
his li e a u e, ou aim is en i ely quan i a i e and comp ehensi e: i is no o p o e he-
o ems o make quali a i e poin s bu o de elop a se ing o p ac ical, quan i a i e use.
In ha , we belie e we add signi ican ly o he epi-econ li e a u e. An impo an pa o
ou pape is he e o e ou app oach o sol ing he model nume ically; going o wa d,
compu a ional easibili y can p o e o be a hu dle. We do no ye o e a Dyna e-like
package bu ou Julia code, a ailable o he eade , is al eady as , use - iendly, and eas-
ily adap able. As a p oo o concep , we illus a e he powe o ou me hods in Sec ion 7
whe e we look a iche epidemics and demog aphics.
Finally, ou pape is no jus abou Co id-19 bu o e s a se ing ha can be used o
s udy di e en i uses, including hose expe ienced in he pas (we look a he seasonal
lu and SARS). We do belie e ha o wa d-looking heal h agencies and go e nmen s
need o s and eady when he nex epidemic su aces.
Roadmap
In he nex sec ion, we desc ibe he in eg a ed epi-econ assessmen amewo k com-
pac ly, o ocus on he gene al in e play be ween he economic and he epidemiological
sides o he model. The ea e , in Sec ion 3, we ou line he conc e e pa ame iza ion o
he model implemen ed o e alua e Co id-19. In Sec ion 4,wedesc ibehow hemodel
is calib a ed o ime-use da a and o he da a momen s. Sec ions 5and 6compa e he
esul s om he ma ke alloca ion o op imal policy, and show how op imal policy qual-
i a i ely as well as quan i a i ely depends on assump ions abou key pa ame e s. In Sec-
ion 7, we en ich he Co id-19 model along a numbe o dimensions, while in Sec ion 8
we es he model by calib a ing i o wo o he diseases: he common seasonal lu and
SARS. Finally, Sec ion 9concludes wi h a discussion o po en ial ex ensions ha could
easily be inco po a ed wi hin ou amewo k.
Addi ional analysis and u he de ails a e p o ided in he Supplemen al Appendix
(Boppa , Ha menbe g, Hassle , K usell, and Olsson (2024)).
5The e a e many pape s ha a e no ully mic o ounded o ha do no p o ide a comple e planne - s.-
ma ke s compa ison, bu ha a e e y in e es ing and aluable in o he ways and ha ha e ea u es com-
mon o hose en e ained he e. Al a ez, A gen e, and Lippi (2021) and Gianni sa ou, Kissle , and Tox ae d
(2021) se up and analyze ac able planning p oblems. Ou ocus on he e ogenei y, bo h among people and
sec o s, is sha ed, ei he ully o pa ially wi h Acemoglu, Che nozhuko , We ning, and Whins on (2021),
Acemoglu, Makhdoumi, Malekian, and Ozdagla (2024), Aum, Lee, and Shin (2021), Bodens ein, Co se i,
and Gue ie i (2022), B o he hood, Ki che , San os, and Te il (2021), and Giagheddu and Pape i (2023).
Kaplan, Moll, and Violan e (2020) ha e impo an insigh s as ega ds inequali y and he epidemic, which
ou ep esen a i e- amily amewo k abs ac s om. Eichenbaum, Rebelo, and T aband (2022b) and Pigu-
illem and Shi (2022) explo e he po en ial o es ing policies in epi-econ amewo ks. The sho pape (Bop-
pa , Ha menbe g, K usell, and Olsson (2022)) builds di ec ly and explici ly on he p esen se up in o de
o analyze he alue o accina ion; i does no conduc any model analysis ha o e laps wi h he p esen
wo k. Bognanni, Hanley, Kolline , and Mi man (2020) and Eichenbaum e al. (2024) compa e model ou -
comes wi h da a.
96 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
2. Gene al model amewo k
In his sec ion, we desc ibe he model amewo k compac ly and abs ac ly. We hen
cha ac e ize equilib ium/op imali y condi ions and compa e he compe i i e equilib-
ium wi h he social planne ’s solu ion. In he nex sec ion, we in oduce he mo e de-
ailed model s uc u e and calib a e he model.
2.1 Compe i i e equilib ium
We dis inguish be ween he ep esen a i e amily’s choices and s a es (e.g., x)andag-
g ega e choices and s a es, deno ed wi h ba s (e.g., x). In equilib ium, he ep esen a i e
amily’s choices and s a es coincide wi h he agg ega e choices and s a es (e.g., x=x).
We use he ollowing no a ion: o (x,y):Rm1×Rm2→Rn,D
x (x0,y0)deno es he
n×m1Jacobian o wi h espec o he ec o inpu x, e alua ed a (x0,y0),
Dx (x0,y0)=⎛
⎜
⎜
⎜
⎜
⎜
⎝
∂ 1
∂x1
(x0,y0)··· ∂ 1
∂xm1
(x0,y0)
.
.
.....
.
.
∂ n
∂x1
(x0,y0)··· ∂ n
∂xm1
(x0,y0)
⎞
⎟
⎟
⎟
⎟
⎟
⎠
.
2.1.1 The household p oblem Gi en he sho - un na u e o epidemics, we conside
an en i onmen wi hou economic s a e a iables (e.g., he capi al s ock is ixed). The
household p oblem o he ep esen a i e amily can hen be decomposed in o a dy-
namic p oblem o managing he epidemic s a e and a s a ic p oblem o op imizing pe-
iod wel a e gi en a pa h o he amily’s epidemic s a e.
Dynamic p oblem The dynamic p oblem ha he ep esen a i e amily aces is
V (S)=max
T,S (T,S)+βV +1Ss. . S=H(S,T,S ).
The ep esen a i e amily has an epidemic s a e ec o So dimension nS. The choices
o he ep esen a i e amily can be indi ec ly desc ibed as choosing he ec o o new in-
ec ions/ ansmissions To dimension nT. The choice yields an indi ec pe iod wel a e
(T,S)and a u u e epidemic s a e S=H(S,T,S), which depends no only on he
amily’s epidemic s a e and he ansmissions o he amily, bu also on he agg ega e
epidemic s a e a he ime, S .
S a ic p oblem The indi ec pe iod-wel a e unc ion is gi en by
(T,S)=max
x,c
u(x,c,S)s. . p c=w x+ ,μF
G(x,S,x ,S )=T,μG
0=Ceq(x,S),μeq
0≤Cineq(x).μineq
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 103
Figu e 1. Illus a ion o he model.
The e a e wo sec o s in he economy: he in-p iVa e (V) sec o and he in-puBlic (B)
sec o . When indi iduals spend leisu e in he in-p iVa e sec o (illus a ed by he igu es
in he bo om le in he igu e) hey a e a home (e.g., wa ching ele ision), and he e
is no isk o ge ing in ec ed. The goods and se ices used o he in-p iVa e leisu e a e
p oduced in he wo kplace o a home (illus a ed by he uppe hal o he le side o he
igu e, whe e people a e, o example, in he s udio p oducing a Ne lix show o in he
Amazon wa ehouse shipping a new TV se ). When people wo k in he wo kplace, hey
in e ac wi h hei colleagues, and he e is a isk o sp eading he i us.
The igh -hand side o he igu e illus a es he in-puBlic sec o . In his sec o , con-
sump ion and wo k ake place join ly, and he i us can sp ead be ween hose enjoying
leisu e (e.g., cus ome s in he es au an ) and hose wo king in he sec o (e.g., wai e s in
he es au an ). Howe e , e en in his sec o he e is a possibili y ( o a leas some em-
ployees, o example, he es au an ’s accoun an ) o wo k om home wi hou physically
in e ac ing wi h o he s. We now o malize his model.
Time alloca ions x Bo h he young and he old can spend ime on wo king in he B
sec o , ei he in he wo kplace (ni
Bw)o omhome(nBh), on wo king in he Vsec o ,
ei he in he wo kplace (ni
Vw)o omhome(ni
Vh
), and on leisu e, ei he Bleisu e (hi
B)
o Vleisu e (hi
V). The ime-alloca ion ec o o he ep esen a i e amily is
x=xy
xo=ny
Bw ny
Bh ny
Vw ny
Vh hy
Bhy
Vno
Bw no
Bh no
Vw no
Vhho
Bho
V
,
whe e he en ies deno e o al hou s spen on he ac i i ies by he young and he
old (i.e., no pe -capi a hou s spen on he ac i i ies). The dashed line sepa a es he
a iables o he young and he old. No e ha his o mula ion o he ime alloca ions
assumes homogenei y wi hin g oups: all young/old spend hei ime equally.
Time cons ain s Ceq and Cineq Each indi idual in he amily has one uni o ime a
hei disposal pe ime pe iod, and canno spend nega i e hou s on any ac i i y. These
104 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
cons ain s a e summa ized below, wi h he no a ion Popi=Si+Ii+Ri:
Ceq(x,S)=ny
Bw +ny
Bh +ny
Vw+ny
Vh+hy
B+hy
V−Popy
no
Bw +no
Bh +no
Vw+no
Vh+ho
B+ho
V−Popo,
Cineq(x)=x.
P oduc ion unc ion FP oduc ion o he wo consump ion goods is de e mined by he
unc ion
F(x)=yB(x)
yV(x),
whe e p oduc ion in bo h he Band he Vsec o is gi en by a Cobb–Douglas unc ion
o CES agg ega es,
yj(x)=kα
j˜
nν
jh ˜
n1−α−ν
jw ,
˜
njh =CESny
jh,no
jh;λn,εn,
˜
njw =CESny
jw,no
jw;λn,εn,
o j=B,V, and he cons an -elas ici y agg ega o CES(•)is de ined by
CES(x1,x2;λ,ε)=λx
ε−1
ε
1+(1−λ)x
ε−1
ε
2ε
ε−1.
The sec o -speci ic capi al s ocks kBand kVa e ixed (and cons an o e ime).
Family u ili y uThe amily’s pe iod u ili y unc ion is a weigh ed a e age o he u ili y
o he young and he old,
u(x,c,S)=max
cy,co
i=y,o
Popiuxi/Popi,ci/Popis. . cy+co=c,
whe e consump ion is op imally alloca ed be ween he wo g oups.
Le ha ed a iables deno e pe -capi a consump ion and ime alloca ions (e.g., ˆ
xi=
xi/Popi). The low u ili y o an indi idual membe o he amily is gi en by
uˆ
xi,ˆ
ci=logCES˜
ci
B,˜
ci
V;λ,ε+u,
˜
cB=CESˆ
ci
B,ˆ
hi
B;λB,εB,
˜
cV=CESˆ
ci
V,ˆ
hi
V;λV,εV,
whe e he cons an uis added o calib a e he alue o a s a is ical li e.
The nes ed CES s uc u e cap u es he idea ha he consume needs o spend leisu e
ime o de i e u ili y om a good o se ice. To de i e u ili y om nonsocial in-p iVa e
goods ( he ele ision se , he s eaming se ice subsc ip ion, he g oce ies) agen s need
o spend ime wi h i (wa ch TV, ha e dinne a home). Likewise, o de i e u ili y om
social in-puBlic goods (mo ie icke s o a es au an meal) agen s need o spend ime on
in-puBlic leisu e ( he ime spen in he mo ie hea e o es au an ).
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 105
In ec ion a e unc ion GThe in ec ion isks in he Band he Vwo kplaces a e gi en
by a cons an - e u ns- o-scale (i.e., linea ) andom mee ing echnology,
πB(x,S)=κB
i=y,oni
Bw +hi
BIi/Popi
i=y,oni
Bw +hi
B,
πV(x,S)=κV
i=y,o
ni
Vw
Ii/Popi
i=y,o
ni
Vw
.
The ec o o in ec ions is gi en by
G(x,S,x,S)
=Sy/Popy0
0So/Popo
P obabili y o being suscep ible
πB0πV0πB0000000
000000πB0πV0πB0
In ec ion isk pe ime uni , i suscep ible
x
Time alloc.
,
whe e he a gumen s o πBand πVa e supp essed. The dashed e ical line sep-
a a es he ime alloca ions o he young and he old while he dashed ho izon al line
sepa a es he in ec ion isks o he young and he old. The lowe -le and uppe - igh
blocks o ze os in he in ec ion- isk ma ix cap u e he ac ha he amily’s in ec ions
o he old do no depend on he ac i i ies o he amily’s young, and ice e sa.
3.3 The e minal condi ion
To compu e he equilib ium, we need a e minal condi ion o he g adien o he alue
unc ion a e he inal pe iod ,D
SV +1. We assume ha he epidemic is o e a = ,
and hus he alues o addi ional suscep ible, in ec ed, and eco e ed young indi iduals
a e all equal o = +1 (and likewise o he old). The alue o a single ime pe iod is
˜
uyand ˜
uo o a young and an old indi idual, espec i ely. The old li e o Tope iods and
he alue o an addi ional old pe son a e he inal pe iod is simply he discoun ed
sum o he pe iod u ili y ˜
uo o hei emaining li e expec ancy. The young li e o Ty
pe iods and a e assumed o i s ha e he pe iod u ili y o he young, and o he las To
pe iods o hei li e he pe iod u ili y o he old. In sum, he ma ginal alues o addi ional
indi iduals a e gi en by
DSV +1=UyUyUyUoUoUo
106 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
wi h
Uy=˜
uy1−βTy−To−
1−β+˜
uoβTy−To− 1−βTo
1−β,
Uo=˜
uo1−βTo−
1−β.
4. Calib a ion
In his sec ion, we desc ibe he calib a ion o he model. Table 3a he end o he sec ion
summa izes all pa ame e alues.
4.1 Calib a ion o he dynamic p oblem
Pe iod leng h and he discoun ac o βA pe iod in he model co esponds o a day. We
se he discoun ac o βsuch ha β365 =0.96.
Ini ial condi ion, S0We de ine young as indi iduals aged 15–60, while old e e s o in-
di iduals abo e 60. The ini ial popula ion size is no malized o one. Thus, calib a ing
o U.S. demog aphy, we se Popy
0, he young popula ion sha e a ime 0, o 0.73 and
Popo
0=1−Popy
0. The e is no popula ion g ow h. A ime 0, a sha e 0.001 o he pop-
ula ion, bo h young and old, is in ec ed,
S0=0.999 ·Popy
00.001 ·Popy
00 0.999 ·Popo
00.001 ·Popo
00
.
The law o mo ion o he epidemic HThe law o mo ion o he epidemic is desc ibed
by he eco e y a e π and he mo ali y a es πy
dand πo
d(which a e unc ions o he
numbe o cu en ly in ec ed).
In line wi h A keson (2020)andEichenbaum, Rebelo, and T aband (2021), we se
he a e age ime om in ec ion o eco e y o be 18 days. This ime also co esponds o
he ime om symp om o eco e y in Glo e e al. (2023). Since ou model is daily, π ,
he eco e y a e is se o 1/18.
We assume ha he dea h a e o he illness is an inc easing unc ion o he numbe
o in ec ed. The ma ginal dea h a e is gi en by a logis ic unc ion o which he midpoin
o he logis ic cu e occu s a he poin whe e he hospi als a e ge ing o e c owded,
which is assumed o occu when he ac ion o in ec ed in he popula ion eaches ˆ
I.8
The a e age dea h a e in any ime pe iod is hus gi en by
πi
d(I)=I
0
πi
d,low +πi
d,high −πi
d,low
1+e−k(z−ˆ
I)dz/I
wi h Ideno ing he sum o he young and he old in ec ed. Based on U.S. da a, he e we e
29.4 in ensi e ca e uni s (ICUs) pe 100,000 people a he onse o he Co id-19 c isis,
8Wi h ou calib a ion, his o mula ion is e ec i ely a s ep unc ion, bu con inuously di e en iable.
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 107
so we assume one ICU pe 3400 people.9Fu he , we assume ha 3% o he in ec ed
indi iduals equi e hospi aliza ion, and based on es ima es o Sweden, ha 29% o he
hospi alized a e in need o in ensi e ca e.10 Taken oge he , his gi es us an ˆ
I=1/(0.03×
0.29 ×3400)≈0.034. In o he wo ds, we assume ha he dea h a e will quickly inc ease
when he numbe o in ec ed eaches 3.4% o he popula ion.
The p obabili y o dying (on a gi en day) condi ional on being in ec ed, when he e
is no o e c owding in he hospi als, is se o 0.001 ×1/18 o he young and 0.025 ×
1/18 o he old, ollowing Glo e e al. (2023). The a e age in ec ion a ali y a e in he
popula ion, i he young and old we e in ec ed a he same a e, would hus be 0.7%.
When he heal hca e sys em is comple ely o e bu dened, he p obabili ies a e assumed
o eble, o 0.003 ×1/18 o he young and 0.075 ×1/18 o he old. The s eepness o he
logis ic cu e, k, is se o 1000.
4.2 Calib a ion o he s a ic p oblem
The calib a ion o he s a ic p oblem is mo e in ol ed. The calib a ion p oceeds in wo
s eps. Fi s , he economic pa ame e s ( he p oduc ion unc ion and p e e ences) a e
join ly calib a ed o ime-use da a and long- un g ow h ac s. Second, he epidemio-
logical pa ame e s a e calib a ed o e idence on he con agiousness o Co id-19.
4.2.1 Calib a ion a ge s
Calib a ion a ge s om he ATUS Fo he calib a ion a ge s o he alloca ion o ime,
we u n o he Ame ican Time Use Su ey (ATUS), which p o ides na ionally ep esen-
a i e es ima es o how and whe e Ame icans spend hei ime. Impo an ly, i includes
da a on he ull ange o nonma ke ac i i ies, om elaxing a home o es au an isi s
and a ending spo s e en s.
We di ide he 24 hou s a day in o h ee mu ually exclusi e and complemen a y ex-
haus i e b oad ca ego ies: sleep, wo k, and leisu e. Sleep is de ined as he ime spen
ei he sleeping o expe iencing sleeplessness. We de ine wo k as he sum o he ol-
lowing ac i i ies: ma ke wo k, co e housewo k (meal p epa a ion and cleanup, doing
laund y, i oning, dus ing, cleaning, e c.), o he home p oduc ion (home main enance,
ou doo cleaning, ehicle epai , e c.), necessi y shopping (g oce y shopping, going o
he bank, e c.), and ime spen in educa ion. We also add all a el ime associa ed wi h
any o hose ac i i ies. Leisu e, las ly, is de ined as he sum o he ollowing ac i i ies: en-
e ainmen /social ac i i ies/ elaxing, child ca e and ca ing o o he adul s, ga dening,
ime spen wi h pe , pe sonal ca e, ea ing and d inking, ec ea ional shopping, ci ic and
eligious ac i i ies, and own medical ca e. Again, all a el ime associa ed wi h any o
hose ac i i ies is added o he o al.11 Wi h hese de ini ions, we compu e he sha e o
9Based on in o ma ion om Socie y o C i ical Ca e Medicine, downloaded June 24, 2020 (link).
10Glo e e al. (2020) assume a hospi aliza ion a e o 2% o he young and 12.5% o he old, which wi h
ou popula ion sha es would gi e a weigh ed a e age o 4.9%.
11This de ini ion o leisu e is close o leisu e “Measu e 4” used by Aguia and Hu s (2007). Compa ed
o ha de ini ion, ou leisu e concep adds ec ea ional shopping, ga dening and ime spen wi h pe , bu
excludes sleeping and educa ion. In he ca ego y leisu e shopping, we include “Shopping, excep g oce ies,
ood, and gas,” “Compa ison shopping,” and “Resea ching pu chases, n.e.c.”.
108 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
Table 1. A e age minu es pe day spen in di e en ac i i ies.
Young Old
Ac i i y Minu es F ac ion o ime awake Minu es F ac ion o ime awake
Sleep 527 534
Time awake 913 1 906 1
Wo k 413 0.45 236 0.26
Leisu e 500 0.55 670 0.74
in-puBlic 163 0.18 150 0.17
in-p iVa e 337 0.37 520 0.57
No e: Sou ce: Ame ican Time Use Su ey (U.S. Bu eau o Labo S a is ics (2020)). Ac i i ies include associa ed a eling.
sleep, wo k, and leisu e o he young and he old, espec i ely. Fo he calib a ion, we
igno e sleep and ocus on he wo k–leisu e ade-o .
Wi h his classi ica ion, we also wan o know he sha e o leisu e ime spen on so-
cially in ensi e ac i i ies (hB s. hV) and he sha e o wo k ime a he wo kplace (nBw
and nVw s. nBh and nVh
). We de ine socially in ensi e ac i i ies as ac i i ies spen ou -
side he home and co espondingly ac i i ies as no socially in ense i hey ake place
in he esponden ’s home o ya d. We p e e his classi ica ion o he al e na i e “wi h
whom” c i e ion, since we conside , o example, he ac i i y o going o he mall o
ec ea ional shopping o be a socially in ense ac i i y, e en hough he indi idual may
go he e on his/he own. Table 1shows he ime spen in di e en ac i i ies by young
and old. As can be seen, despi e spending much mo e ime on leisu e in o al, he old
spend app oxima ely he same amoun o ime on socially in ense leisu e, ha is, leisu e
ou side hei home, as he young.12
Ou de ini ion o wo k includes ma ke wo k, household wo k, co e housewo k and
home p oduc ion, necessi y shopping, and ime spen in educa ion. In he same way as
o leisu e, we classi y all wo k ac i i ies acco ding o whe e hey we e pe o med: in he
home o ou side home. O he a e age wo king day, 31% o he ime wo king is spen a
home, and 69% ou side home, mainly a he wo kplace. Mo e in o ma ion can be ound
in Supplemen al Appendix A.1.
Calib a ion a ge o he size o he socially in ense sec o We use employmen s a is-
ics on he 4-digi NAICS le el om BLS o classi y sec o s in he US. The classi ica-
ion is based on i he sec o is assumed o p o ide goods/se ices o he socially in-
ense consump ion-leisu e bundle (and consequen ly i he wo k o ce in e ac wi h cus-
ome s). The ex en o which he sec o can be classi ied as socially in ense can be ully
(100%), o a high ex en (75%), o a somewha smalle ex en (50%), o no a all (0%). We
hen sum up he a ec ed wo k o ce, and ge ha ou o he o al wo k o ce (161,037,700
wo ke s), 20% wo k p oducing o he socially ac i e bundle. The lion’s sha e (43%) o he
wo k o ce wo king in he socially in ense sec o is wo king in he accommoda ion and
12Fo mo e de ails abou how people spend hei ime in in-puBlic and in-p iVa e leisu e, see he Sup-
plemen al Appendix A.2.
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 109
ood se ices p o ision, ollowed by “all o he e ail” (18%) and “nonag icul u al sel -
employed” (14%). An example o how he classi ica ion is done is gi en in Supplemen al
Appendix A.3.
4.2.2 Calib a ion o economic pa ame e s
P oduc ion unc ion, FThe p oduc ion unc ion has as pa ame e s he capi al s ocks
kBand kV, he Cobb–Douglas pa ame e s αand ν, and he CES agg ega ion pa ame e s
λnand εnde e mining he ela i e p oduc i i y o young/old and he subs i u abili y
be ween hem. We se α=1/3 and he subs i u abili y be ween young and old o εn=10,
hus mimicking close o pe ec subs i u ion while a oiding bang-bang solu ions.
In he da a, wo king hou s a e on a e age dis ibu ed be ween wo k om home (nh)
e sus in he wo kplace (nw)such ha nw/nh=2.3. In he absence o an epidemic, he
ma ginal p oduc s o nhand nwa e equal, deli e ing (1−α−ν)nh=νnw.Hencewe
ob ain ha ν≈0.202.
We can use hese alues o assess how much p oduc ion would be los i nw/nhwe e
o ced o all om 2.3 o, say, 1. The loss would be
3.30.4653.30.202
4.60.46520.202 ≈0.95,
ha is, ou pu would all by 5%. This is sizable, hough no eno mous. I nw/nh alls o
1/3 (2 hou s wo ked a he wo kplace plus 6 hou s wo ked om home ou o an 8 hou s
wo kday), he ou pu loss is 25%. We ind hese losses easonable in magni ude, sup-
po ing a choice o ν=0.202. No e also ha he choice o p oduc ion unc ion implies
ha p oduc ion canno ake place wi hou a leas some wo k in he wo kplace. Thus,
e en i he agen s o he planne would wan e e yone o wo k om home ( o supp ess
he sp ead o he i us) i is no easible, and consequen ly, he e will always be some
ansmissions in he wo kplace du ing he cou se o he epidemic.
The capi al s ocks kBand kVa e in e nally calib a ed so ha he e u n on capi al is
equalized ac oss sec o s in he p e-pandemic wo ld, and such ha he ma ginal p oduc
o capi al ne o dep ecia ion is equal o an annualized in e es a e o 4%. The ela i e
p oduc i i y o young and old, de e mined by λn, is in e nally calib a ed oge he wi h
he p e e ence pa ame e s.
Family u ili y uThe amily p e e ences a e pa ame ized by he CES pa ame e s λ,ε,
λB,εB,λV,εV, and he “ alue o being ali e” u.
Gi en p e e ence elas ici ies ε,εB,andεV, he o he p e e ence pa ame e s a e cal-
ib a ed as ollows. The ou e CES weigh λis se o ma ch he ou pu sha e o he in-
puBlic sec o o 0.2. The inne CES weigh s λBand λV oge he wi h he p oduc i i y
weigh λna e join ly calib a ed o ma ch he ime spen on leisu e o he young (0.55),
o he old (0.74), and he a io o in-puBlic leisu e and in-p iVa e leisu e o he young
(0.48).
The ou e elas ici y, ε, con ols he elas ici y be ween in-puBlic consump ion and in-
p iVa e consump ion, bu i also con ols he elas ici y be ween in-puBlic consump ion
and in-p iVa e leisu e as well as be ween in-puBlic leisu e and in-p iVa e consump ion.
110 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
How should he ma ginal u ili y o in-puBlic leisu e be a ec ed i I buy a new TV? We
hink a easonable benchma k is no a all, which mo i a es he benchma k ε=1, yield-
ing addi i e sepa abili y be ween he wo consump ion-leisu e bundles.13
To pick εBand εV, we pu addi ional es ic ions on he u ili y unc ion. Fi s , we
equi e ha he income e ec domina es he subs i u ion e ec in a ealis ic way: we
equi e ha i he economy g ows by 2%, hou s wo ked should all by app oxima ely
0.4% (Boppa and K usell (2020)). Second, we equi e ha he young should spend a
la ge ac ion o hei leisu e in he socially in ense Bac i i y han he old do, since
ha is wha he da a ells us. These wo es ic ions na ow down he se o pe missible
εB-εVcombina ions subs an ially. As ou benchma k calib a ion, we use εB=0.41 and
εV=0.80.14
As a sani y check o ou calib a ion o he u ili y unc ion, we examine he implied
F isch elas ici y o he young, which u ns ou o be 1.1. This migh a i s sound a he
high, bu gi en ha he model includes also he e y young (ou de ini ion o young
s a s al eady a he age o 15) and ha he F isch elas ici y should co espond o no only
he in ensi e ma gin elas ici y bu he agg ega e elas ici y including also he ex ensi e
ma gin, we hink a alue o 1.1 is easonable.
The “ alue o being ali e” uis calib a ed o ma ch es ima es o he alue o a s a-
is ical li e. The alue o a single ime pe iod, in ou case a day, VSTP,is o asimple
uni a ia e u ili y unc ion (c)gi en by he o mula
VSTP
c= (c)
c (c), (10)
whe e VSTP, he alue o a single ime pe iod, is exp essed in pe iod-0 uni s o consump-
ion; see, o example, Conley (1976)andShepa d and Zeckhause (1984).
The in ui ion o he equa ion is s aigh o wa d: he u ili y alue o an addi ional
pe iod o li e is (c), he pe -pe iod low u ili y. The u ili y alue o an addi ional uni
o consump ion is (c). The ma ginal alue o an addi ional pe iod o li e, in e ms o
consump ion, is hus (c)
(c).VSTP/c is he alue o an addi ional ime pe iod, exp essed
as a mul iple o pe -pe iod consump ion.
We use he young gene a ion’s equilib ium alloca ions o goods and ime and adjus
uso ha he abo e equa ion is sa is ied o a gi en es ima e o VSTP.15
A ange o di e en alues o a ime pe iod has been used in he li e a u e (see, e.g.,
Viscusi and Aldy (2003) o an o e iew). Fo ou baseline scena io, we assume ha a
pe iod o li e is wo h 6 imes pe iod consump ion, ollowing Hall, Jones, and Klenow
(2020) who base hei numbe on da a om The En i onmen al P o ec ion Agency
13We acknowledge ha his is no an ob ious conclusion and, he e o e, pe o m obus ness checks wi h
espec o he alue o ε, ound in Supplemen al Appendix A.4. E en hough he de ails o he ealloca ion
o ime in he e en o an epidemic change, he subs an i e conclusions emain. Mo eo e , we a gue ha
he ealloca ions wi h he benchma k ε=1 seem plausible.
14See Supplemen al Appendix A.5 o mo e de ails.
15Gi en ha he young and he old ha e di e en ime and goods alloca ions, in heo y i ma e s which
ype is selec ed. In p ac ice, howe e , he di e ence be ween ubased on he alloca ions o he young o he
alloca ions o he old is small.
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 111
Table 2. Calib a ion a ge s o he economic pa ame e s in he s a ic p oblem.
Ta ge Pa ame e
Ma ginal p oduc o capi al equal ac oss sec o s kV,kB
Ma ginal p oduc o capi al ne o dep ecia ion =in e es a e
Ou pu sha e o public sec o =0.2 λ
Leisu e young =0.55 λV,λB,λn
Leisu e old =0.74
in-puBlic leisu e/in-p iVa e leisu e o young =0.48
Hou s wo ked in he wo kplace s. om home (nw/nh=2.3) ν
Realis ic income s. subs i u ion e ec s εB,εV
hy
B/hy
V>h
o
B/ho
V
Chosen alue o VSTP u
Exogenously picked alues (see ex ) α,εn,ε
No e: The pa ame e s associa ed wi h each a ge a e he pa ame e s, which p ima ily de e mine he a ge .
(EPA). As a obus ness and o e alua e he impo ance o his assump ion, we will also
use a highe numbe ; o his, we will use 11.4, ollowing Glo e e al. (2023)whoalso
base hei numbe on da a om EPA and he U.S. Depa men o T anspo a ion.
A summa y o he a ge s used o he calib a ion o he s a ic economic p oblem is
gi en in Table 2.
4.2.3 Calib a ion o epidemiological pa ame e s We calib a e based on in o ma ion
a ailable a he ou se o he pandemic. In Sec ion 7, we conside a iche s uc u e.
In ec ion a e unc ion GThe in ec ion a e unc ion has as pa ame e s κBand κV.
We conside all in e ac ions equally con agious and se κB=κVand calib a e hem o
ma ch a chosen alue o R0. The es ima es o R0 o Co id-19 a e unce ain and ange
be ween a leas 1.4 and 3.9; we use 2.0 in ou benchma k simula ions.
We simula e he simples possible SIR model wi h a homogeneous popula ion gi en
his es ima e o R0. This gi es us a measu e o he inal numbe o eco e ed (which is
78%) i he epidemic we e o play ou unhinde ed. The ea e , we use he s eady-s a e
ime alloca ions in ou calib a ed model and ind he κB=κVyielding he same inal
numbe o eco e ed as in he economy wi hou endogenous beha io al esponses.16
4.3 Calib a ion o he e minal condi ion
Li e expec ancy, TiThe young and old li e up o pe iod Tyand To, espec i ely. We
calib a e Tyand To o ma ch he emaining li e expec ancies based on he g oup de i-
ni ion. No e ha a pe ec es ima e o his would ake in o accoun he mo ali y p o ile
by age wi hin each age g oup, and weigh he condi ional li e expec ancy by ha . Such
an es ima e would equi e u he es ima es, so ins ead we se he a e age age o a de-
ceased in he young g oup o 50 yea s, and he co esponding age in he old g oup o 80.
16The esul ing epidemiological sp ead is e y close bu no exac ly he same as he SIR model wi h ho-
mogeneous popula ion simula ed ini ially, since young and old ha e di e en ime alloca ions and di e en
dea h a es.
112 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
Table 3. Summa y o calib a ed pa ame e s.
Pa ame e Desc ip ion Value
P e e ence pa ame e s
βDiscoun ac o 0.961/365
λWeigh on ˜
cB0.26
λBWeigh on cB0.92
λVWeigh on cV0.71
εElas ici y be ween ˜
cBand ˜
cV1.0
εBElas ici y be ween cBand hB0.41
εVElas ici y be ween cVand hV0.80
VSTP Value o a s a is ical ime pe iod (as a mul iple o pe iod consump ion) 6.0
uIn insic alue o li e pe pe iod (in u ils) 2.5
Technology
αCapi al sha e 1/3
νHome wo k labo sha e 0.202
εnElas ici y o subs i u ion be ween young and old 10
λnP oduc ion weigh on young 0.62
kB/kVRela i e capi al s ock 0.25
Demog aphics
Popy
0F ac ion young 0.73
TyRemaining li e ime young 31.6 ·365
ToRemaining li e ime old 9.2 ·365
Epidemic a iables
R0Sp ead ac o s anda d SIR model 2.0
κB=κVSp ead ac o economic model 0.24
π Reco e y a e 1/18
πi
d,low Dea h a e (be o e o e c owding) [young, old] [0.001, 0.025]·1/18
πi
d,high Dea h a e (when o e c owded) [young, old] [0.003, 0.075]·1/18
Heal hca e sys em
ιhF ac ion o in ec ed in need o hospi aliza ion 0.03
ιiF ac ion o hospi alized in need o ICU 0.29
ιbInhabi an s pe ICU bed 3400
ˆ
IMidpoin logis ic unc ion ( ac ion in ec ed) 1/(ιh·ιi·ιb)
kS eepness pa ame e 1000
No e: See ex o desc ip ion o sou ces and me hodology.
This implies a emaining li e expec ancy o 31.6 yea s o he young, and 9.2 yea s o he
old (A ias and Xu (2019)).
Flow u ili y a e he e minal pe iod, ˜
uWe se he low u ili ies a e he e minal pe-
iod, ˜
uyand ˜
uo, equal o he low u ili ies o he young and he old absen he epidemic.
5. Resul s om he baseline model
In his sec ion, we con as how he epidemic plays ou in a planne alloca ion scena io
compa ed o in a compe i i e equilib ium. In he compe i i e equilib ium, he ep esen-
a i e amily ei he has ull in o ma ion abou he epidemic and ac s acco dingly (“ a io-
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 119
Figu e 7. The e olu ion o he epidemic in a ional-expec a ions compe i i e equilib ium and
unde he planne ’s alloca ion when a cu e a i es a e one yea .
a i al and dis ibu ion o a accine o (ii) a pe ec implemen a ion o es ing and ac-
ing.20 F om a modeling pe spec i e, bo h scena ios a e e y simila o he a i al o a
cu e, wi h he di e ence ha wi h he a i al o a accine o es ing and acing, hose
in ec ed a he poin o he a i al can s ill die om he disease. In p ac ice, his makes a
e y small di e ence in he model. We conside a scena io whe e i is known ha a cu e
a i es a e one yea .
The epidemic e olu ions o he a ional-expec a ions compe i i e equilib ium
and he planne ’s alloca ion unde his scena io a e shown in Figu e 7.The a ional-
expec a ions compe i i e equilib ium is la gely una ec ed by he a i al o he cu e,
since i a i es a e he epidemic is inalized and he agen s’ beha io is al eady con-
sis en wi h he absence o an epidemic a his poin . Howe e , he planne ’s alloca-
ion quali a i ely shi s owa d ull supp ession o he epidemic i he cu e a i es ea ly
enough. As Figu e 7b shows, i he cu e a i es wi hin a yea , he planne ’s s a egy shi s
quali a i ely: om a s a egy bes desc ibed as “p o ec he heal hca e sys em” o a “sup-
p ession” s a egy. An icipa ing ha he cu e is ins an aneously and pe ec ly dis ibu ed
a e exac ly a yea , he planne allows o an inc ease in he numbe o in ec ed nea he
day when he cu e is dis ibu ed. This an icipa ion would disappea i , o example, only
a haza d a i al a e is known.
6.2 A highe alue o a s a is ical li e: Lock-down again
We now highligh he impo ance o he choice o he alue o a s a is ical li e pe iod
o he op imal solu ion, as i oo can quali a i ely change he planne ’s solu ion. To il-
lus a e his, we conside a scena io whe e he cu e is known o a i e a e 15 mon hs.
Using he same alue o a s a is ical li e as be o e, he planne ’s s a egy is back o “p o-
ec he heal h ca e sys em.” Howe e , i we ins ead use a highe alue o a s a is ical
20When a planne is capable o pe ec ly iden i ying who is in ec ed, in ou model amewo k he planne
would le he in ec ed s ay a home un il hey a e eco e ed, and he epidemics would die ou quickly.
120 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
Figu e 8. The e olu ion o he epidemic unde he planne ’s alloca ion wi h wo di e en as-
sump ions abou he alue o a s a is ical li e, assuming a cu e a i es a e 15 mon hs.
li e pe iod (choosing 11.4 imes pe iod consump ion, ollowing Glo e e al. (2023)), he
op imal s a egy is o supp ess he in ec ion by ha she measu es. This is illus a ed in
Figu e 8, which shows he di e en app oaches aken by a planne , depending on which
alue is assigned o a s a is ical li e.
The “supp ess” s a egy, adop ed in he scena io wi h he highe alue o a s a is ical
li e, sa es li es: only 0.042% die in his scena io, while he inal dea h oll in he scena io
whe e he planne has a lowe alue o a s a is ical li e is 0.224%. Howe e , he supp ess
s a egy is o cou se cos ly in e ms o ou pu (and u ili y). Ou pu alls by 19.9% o e he
i s yea , while he ou pu all in he p o ec scena io is 10.1% du ing he i s yea .
6.3 Less cos ly hospi al o e c owding: Speed up in ec ions
We now u n o he impo ance o he o e c owding unc ion. Tha a planne wan s o
supp ess he epidemic o a oid o e c owded hospi als o cou se hinges on he assump-
ion ha o e c owding is a se e e p oblem, and di e en assump ions abou he se e i y
o o e c owding o hospi als can quali a i ely change he planne ’s solu ion.
To illus a e his, we conside a scena io whe e he dea h a e o hose in ec ed once
he hospi als a e o e c owded inc eases by only 20% (compa ed o 200% in he baseline).
The epidemic e olu ion o he a ional-expec a ions compe i i e equilib ium and he
planne ’s alloca ion is shown in Figu e 9.
In he a ional-expec a ions scena io, people a e sligh ly less a aid o ge ing in-
ec ed du ing he peak o he epidemic, and he epidemic e ol es somewha as e han
in he baseline scena io (compa e o Figu e 2b). Howe e , he planne alloca ion shi s
quali a i ely: he planne implemen s a s a egy simila o he a ional-expec a ions ou -
come: le he young ge in ec ed quickly, o each he d immuni y, while he old a e
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 121
shielding. By speeding up he p ocess, he planne sho ens he ime he old ha e o
shield a home and su e .21
No e ha he planne e en wan s he sp ead among he young o be as e han in he
myopic model (compa e Figu e 9b o he ligh e shaded a ea in Figu e 2a), which implies
ha he planne would need o delibe a ely inc ease social ac i i y o he young o e and
abo e he s eady-s a e “no-epidemic” le els. The implemen a ion o such a policy would
in ol e encou aging and acili a ing he sp ead in he popula ion. One way would be o
a ange sp ead e en s, simila o his o ical “measles pa ies” o “pox pa ies,” used by
pa en s be o e he e we e accines o inc ease he p obabili y o hei child en o ge
in ec ed and de elop immuni y a an ea ly age (since such in ec ions a e mo e dange -
ous la e in li e).
7. Ex ended model
In his sec ion, we en ich he model along h ee dimensions ele an o he Co id-19
epidemic. In pa , we use he iche model as a p oo o concep o ou me hods.
Fi s , we in oduce waning immuni y as in Gianni sa ou, Kissle , and Tox ae d
(2021): a e some ime, indi iduals who a e eco e ed om in ec ion lose hei immu-
ni y and become suscep ible again. In conc e e e ms, he law o mo ion o he epi-
demic now includes an exogenous ansi ion a e om eco e ed o suscep ible, which
we se o πs=1/730, ha is, on a e age immuni y las s o 2 yea s.
Second, we in oduce an exogenous seasonali y componen in he con agiousness
o he disease. I is by now well unde s ood ha Co id-19 sp eads as e du ing he win-
e season han du ing summe , e en hough he unde lying easons o his a e no
Figu e 9. The e olu ion o he epidemic, assuming dea h a es inc ease by only 20% once he
hospi al sys em is o e c owded.
21Tha he planne speeds up he sp ead o he disease compa ed o he a ional-expec a ions scena io
is a mani es a ion o wha Ga ibaldi, Moen, and Pissa ides (2020) call “immuni y ex e nali y”: ha agen s
shield oo much in he hope ha o he s ca ch he disease and each he d immuni y.
122 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
en i ely es ablished.22 In he model, we in oduce his by le ing he con agiousness pa-
ame e s κBand κVbe ime a ying. In he calib a ion, we had κB=κV=0.24. Now,
we le κB, =κV, =0.24 ·(1+0.5sin(2π /365)) so ha he exogenous con agiousness
a ies a an annual equency and he win e con agiousness is h ee imes he summe
con agiousness.
Thi d, we in oduce an addi ional ype, which we label “ e y old.” We spli he non-
young (popula ion ac ion 0.27) in o wo ypes o equal size: he old and he e y old.
In sho , he e y old a e e en mo e ulne able o he disease, ha e an e en lowe p o-
duc i i y, and e en ewe yea s le o li e absen any epidemic. The emaining li e ime
o he old is 1.5 ·9.2 ·365, ha is, 50% highe han he p e ious a ge , and he li e ime
o he e y old is 0.5 ·9.2 ·365, ha is, 50% lowe han he p e ious a ge . In he CES
agg ega o o labo , he p oduc ion weigh on he young was 0.62 and on he old 0.38.
We keep hese p oduc ion weigh s bu add he e y old inside he CES agg ega o , wi h
p oduc i i y weigh 0.5 ·0.38 =0.19. Finally, he dea h isk o he e y old is 50% highe
han he dea h isk o he old, which is kep a he p e ious a ge .
In he ollowing expe imen s, we assume ha an ins an aneous cu e a i es a e
h ee yea s. We summa ize he esul s o he expe imen s as ollows.
Resul 8(Newpolicy ade-offs). Waning immuni y, seasonali y, and addi ional he -
e ogenei y yield ich epidemiological dynamics and unco e new policy ade-o s.
7.1 Resul s om he ex ended model
Figu e 10 shows he epidemic e olu ion in he ex ended model o he a ional expec a-
ions compe i i e equilib ium and he planne ’s alloca ion.
As he igu e shows, wi h seasonali y he compe i i e equilib ium has a se e e i s
wa e. Howe e , since many people ge in ec ed in his i s wa e, and he immuni y is
assumed o las on a e age o 2 yea s, he e is no second wa e one yea la e . Howe e ,
in he hi d yea , he e is a new ou b eak, since enough people ha e los hei immuni y
by hen.
The planne , on he o he hand, inds i op imal o smoo h ou he in ec ions, and
hus he e is bo h a i s wa e and a second wa e a yea la e . Towa d he end o he
i s wa e, i is op imal o empo a ily exceed he heal h sys em capaci y when he con-
agiousness o he epidemic is declining as summe is app oaching. As a esul o he
declining con agiousness, he ex e nali y cos o ha ing young indi iduals in ec ed alls
and in ac becomes nega i e. The easoning behind his is s aigh o wa d: i we need
o ha e many indi iduals in ec ed a some poin , i is be e o ha e i when he con a-
giousness is low, since hen he isk o in ec ing o he s is diminished. O e all, he plan-
ne “p o ec s he heal hca e sys em” as be o e, bu he in ec ion cu e ollows seasonal-
i y. A e 600 days, he d immuni y has been eached, and he hi d wa e is jus a small
bump due o waning immuni y.
22The highe sp ead du ing he cold season could o ins ance be due o he ac ha people spend mo e
ime socializing indoo s, and/o ha d y ai d ies ou also he issues lining he ai ways, he eby inc easing
he isk o ge ing in ec ed. See A keson (2021) o a u he discussion and an epidemiological amewo k
wi h seasonali y.
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 123
In e ms o ime alloca ions, he main pic u e om he baseline model emains o
he young and old g oup: in he a ional-expec a ions scena io he young ha dly change
hei ime alloca ions, while he old all bu comple ely s op wo king in he o ice and
enjoying in-puBlic leisu e. The new g oup, he e y old, is so unp oduc i e ha hey
do no wo k a all e en in p e-pandemic imes, bu enjoy a mix o in-p iVa e and in-
puBlic leisu e. In he a ional-expec a ions compe i i e equilib ium, he e y old shi
o e o mo e in-p iVa e leisu e du ing he epidemic, bu unlike he old g oup, hey do
no en i ely cu down on in-puBlic leisu e.
In he planne ’s alloca ion, he young adjus hei beha io mo e han in he a ional-
expec a ions scena io; hey s a wo king om home and cu down on he in-puBlic
leisu e o a highe ex en when he planne can decide hei ac ions. Thus, bo h he old
and he e y old can enjoy mo e in-puBlic leisu e han in he a ional-expec a ions sce-
na io. A ull se o g aphs desc ibing he ime-alloca ions in he ex ended model can be
ound in Supplemen al Appendix B.1.
8. O he epidemics
The model can be applied o o he epidemics han Co id-19. S udying mul iple diseases
p o ides c oss-epidemic es ic ions: pa ame e alues ough o be consis en wi h ob-
se ed beha io o o he diseases, no only Co id-19. We choose a egula seasonal lu
in o de o es an epidemic ha we ac ually see e e y yea , and SARS o es one ha is
subs an ially mo e deadly han Co id-19. We es bo h epidemics unde he assump ion
ha he epidemic is o e a e one yea , ei he because he popula ion has eached he d
immuni y, o because a cu e/ accine/pe ec es and ace a i es and pu s an end o
he epidemic.
Figu e 10. The e olu ion o he epidemic in he ex ended model wi h waning immuni y, ex-
ogenous seasonali y, and h ee ypes. The dashed blue line ( igh -hand side axis) shows how he
con agiousness pa ame e a ies o e ime.
124 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
The seasonal lu
To simula e a seasonal lu, we se he e ec i e ep oduc ion numbe a he beginning
o he lu season, R , o 1.3, use a dea h a e o 0.045%, and se he a e age numbe o
days un il eco e y a 10. This co esponds o a egula lu season, no o a yea wi h a
pa icula ly se e e ins ance o he lu.23
Resul 9. The seasonal lu simula ions indica e ha a ela i ely low alue o a s a is ical
li e is mo e in line wi h obse ed policy ac ions.
When simula ing a seasonal lu wi h a high alue o a s a is ical li e pe iod (again
choosing 11.4 imes pe iod consump ion, ollowing Glo e e al. (2023)), a planne
would wan o lowe ou pu by 4.0% du ing he second qua e o he epidemic, and
he annual d op would be 2.8%. As a as we can ell, his is no how policymake s ha e
eac ed his o ically. Wi h he lowe alue o li e (ou baseline alue), he annual d op in
ou pu is subs an ially lowe : 1.1%.
SARS
Fo SARS, we use R0=2.4, dea h a es o 8% and 52% o he young and old, espec i ely,
and an a e age numbe o days un il eco e o 12, ollowing Pe e sen e al. (2020). Bo h
he ma ke and planne alloca ions o e in e es ing insigh s.
Resul 10. Fo SARS, he e ec i e ep oduc ion numbe ho e s a ound 1 in a ional-
expec a ions compe i i e equilib ium. This is in con as o Co id-19, which wi h age-
he e ogenei y, is no dange ous enough o he young o c ea e his ype o esponse.
SARS is pe cei ed as dange ous enough ha indi iduals endogenously choose o
lowe he amoun o in ec ious ac i i ies. The p ecau iona y beha io is inc easing in
he in ec ion isk, which is inc easing in he numbe o in ec ed. Howe e , he numbe o
in ec ed is dec easing in he s eng h o he p ecau iona y esponse. The in ec ion a e
he e o e s abilizes a ound a le el, which is consis en wi h he p ecau iona y beha -
io . The same ype o quali a i e e ec —an e ec i e ep oduc ion numbe ha ho e s
a ound 1 in a ma ke scena io—is also epo ed by Fa boodi, Ja osch, and Shime (2021)
and Bognanni e al. (2020). This esul is in con as wi h ou simula ions o he Co id-
19 epidemic, in which we do no ind ha he e ec i e ep oduc ion numbe s abilizes
a ound 1 in he a ional-expec a ions compe i i e equilib ium. Age he e ogenei y is key
o unde s anding his esul : o he young, he isk o an in ec ion does no p o ide a
s ong enough mo i e o a p ecau ion ha would s abilize he in ec ion a e.
Resul 11. Unde SARS, he planne ’s alloca ion bo h sa es li es and leads o a smalle
all in ou pu compa ed o he a ional-expec a ions compe i i e equilib ium.
23We e i y ha he chosen pa ame e s a e easonable by compa ing he dea h oll in ou model o he
ac ual numbe o dea hs due o he lu in he U.S. each yea ; o mo e de ails and sou ces o ou pa ame e s,
see Supplemen al Appendix B.2.
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 125
A planne would quickly lowe he amoun o in ec ious ac i i ies o ge he epidemic
unde con ol, and would he ea e no ha e o educe he ac i i ies as much. In he
a ional-expec a ions compe i i e equilib ium, people would ca y on wi h hei ac i -
i ies un il he numbe o in ec ed has inc eased subs an ially. A ha poin , indi iduals
would be so a aid o he epidemic ha hey endogenously es ic hei ac i i ies g ea ly.
The o al all in ou pu would he e o e be highe in he a ional-expec a ions scena io.
Quali a i ely, his is he same ype o mechanism as ound in Aum, Lee, and Shin (2021).
Again, in ou calib a ion o he Co id-19 epidemic, we do no ind his e ec since he
Co id epidemic is no pe cei ed as dange ous enough by he young. Fo mo e in o ma-
ion abou hese expe imen s, including de ails abou calib a ion and simula ion esul s;
see Supplemen al Appendix B.2 o he seasonal lu and Supplemen al Appendix B.3 o
SARS.
9. Conclusions
We ha e p esen ed a gene al amewo k o in eg a ed epi-econ assessmen —a oolbox
o policy e alua ion— ha we belie e is an app op ia e s a ing poin when con on ed
wi h pandemic challenges. The model is buil a ound Co id-19 and we also conduc
policy analysis o his case. We now emphasize some key ea u es and ou line a numbe
o ex ensions. Finally, we ou line how we ecommend using ou se ing in conc e e e ms
as a new pandemic h ea su aces.
In ou model cons uc ion, we ha e emphasized he impo ance o a sociology
componen . We hus connec economic and social-ac i i y decisions and show how
ime-use da a can be employed o discipline he pa ame e selec ion. One o ou key
indings—no a o egone conclusion, due o ou quan i a i e discipline—is ha he
alue o social li e can ma e signi ican ly when designing op imal policy. This is he
case in ou Co id-19 applica ion and e en mo e so when we s udy he seasonal o di-
na y lu; howe e , when we look a SARS, he di ec heal h consequences become mo e
impo an . Th oughou ou Co id-19 applica ion, we lis key insigh s compa ing ma -
ke and op imal-planning alloca ions, many o which a e non i ial and emphasize he
nonlinea i y o he p oblem unde s udy: ou comes can change quali a i ely as some
key pa ame e s a e changed.
In Sec ion 7, we en ich he baseline model—which by design is minimal (“dicho o-
mous”) along key dimensions—in a numbe o ways, o example, by including season-
ali y in he i us sp ead and mo e de ailed demog aphics. Fu he elabo a ions a e en-
i ely easible. Fo example, i is easy o in oduce wa es due o i us mu a ions, possibly
wi h highe and highe con agiousness bu lowe a ali y a e, hus gene a ing a se ing
whe e a pandemic g adually u ns in o a (seasonal) endemic disease. As desc ibed al-
eady in ou s udy o seasonal i us a ia ion, new ade-o s emphasizing he iming o
policy would hen su ace.
Rela edly, ano he s aigh o wa d ex ension is he in oduc ion o unce ain y; un-
ce ain y is, mo eo e , c i ical especially a he ea ly phases o a pandemic. The hallma k
o he a ional-expec a ions li e a u e in mac oeconomics is o endow agen s (and any
policymake ) wi h a co ec p obabilis ic assessmen o all ou comes. Howe e , o make
126 Boppa , Ha menbe g, Hassle , K usell, and Olsson Quan i a i e Economics 16 (2025)
hose assump ions he e does no appea easonable. Ins ead, we ecommend conduc -
ing sepa a e social planning e alua ions o a numbe o di e en assump ions on he
i us and i s consequences (and possible cu es), he eby spanning a la ge ange o ou -
comes. To look a ma ke ou comes, we would ecommend—as we do he e—sepa a ely
looking a bo h myopic and pe ec - o esigh pa hs, so as o b acke a ange o p i a e-
sec o eac ions o he i us.24 These analyses can be ca ied ou using o eseen and
un o eseen ansi ion pa hs (“MIT shocks”).
Ou model amewo k is a ic ionless neoclassical economic benchma k, allowing
a clea compa ison o he compe i i e equilib ium and he op imal ou come. Depa -
u es om his benchma k a e possible. Fo example, ollowing Eichenbaum, Rebelo,
and T aband (2022a), i is s aigh o wa d o include p ice and/o wage ic ions in ou
amewo k. This would amoun o in oducing p ice and wage se e s in he compe i-
i e equilib ium, wi h co esponding o wa d-looking Phillips cu es. Such ex ensions
open up o s udying op imal iscal and mone a y policy du ing an epidemic, which is
o pa icula impo ance o economic policymake s.
A concep ually di e en ex ension bu one ha is also possible—and easible— o
pu sue is o in oduce a u he elemen o sociology, one ha goes beyond ying in e ac-
ion o economic decisions: people in e ac in ne wo ks ( amily, iends, acquain ances,
e c.) wi h di e en mee ing in ensi ies and equencies.25 Wedidno addsucha ea u e
ye simply because we a e unsu e o how o connec i o indi idual da a (Azzimon i,
Fogli, Pe i, and Ponde (2020) o e a p omising a enue). Unlike in ou se ing, whe e
social in e ac ion is a byp oduc o economic decisions, such a amewo k would also
in ol e pu e ex e nali ies ha a e p esen e en in he absence o epidemiology.
A dimension whe e ou modeling is e y s ylized and ha de o ex end ega ds
household-le el, idiosync a ic in o ma ion: in eal li e, indi iduals upda e hei own
i us s a us— om ou pe spec i e, he subjec i e p obabili y o being in s a es S,I,and
R, espec i ely—based bo h on he deg ee and iming o in e ac ion chosen wi h o he s
( hese a e choice a iables) and on symp oms ( e e , head ache, e c.); a he same ime,
indi iduals a e much less in o med o he co esponding p obabili ies o o he s. A ull
ea men o his so (wi h a ional Bayesian upda ing), in ol ing a s a e a iable con-
sis ing o a ull dis ibu ion o endogenously e ol ing p obabili ies, is bo h concep ually
and nume ically ex emely challenging. The s a emen and assump ions unde lying an
associa ed planning p oblem a e e en mo e daun ing. Howe e , simple sho cu s a e
easible o pu sue. Fo example, one can assume a publicly obse able indi idual s a e
(like e e ) ha ollows a Poisson p ocess exogenous o he indi idual and ha en ails
highe in ec ion p obabili ies.26 One can also conside ad hoc lea ning, such as adap i e
expec a ions. As o medical ea men s, we show ha i is easy o inco po a e accina-
ion in Boppa e al. (2022).
Tu ning o he p ac ical use o he p esen se ing, we see ou amewo k as a skele-
on se ing o be illed wi h mo e de ail as new da a a i es. The skele on is ich enough
24A s aigh o wa d ex ension is o conside wo g oups o agen s wi hin he economy: one well-in o med
and one myopic.
25Spa ial ea u es could ob iously be in oduced he e, oo.
26This can be seen as an ex ension o he assump ion in B o he hood e al. (2021).
Quan i a i e Economics 16 (2025) In eg a ed epi-econ assessmen 127
al eady o conside a numbe o possible cases ha a e belie ed possible gi en any
ea ly in o ma ion abou he i us: based on di e en scena ios, we can compa e ma ke
ou comes, gi en di e en assump ions abou wha ma ke s expec , wi h op imal ou -
comes. As he new disease is e ealing i sel and i s implica ions o heal h ou comes,
along wi h upda ed expec a ions o possible cu es, hese new da a should con inuously
make us upda e he key model pa ame e s. The new in o ma ion should also make us
e ise he model by adding any he e ogenei y and new ea u es—such as he possibili-
ies men ioned ea lie in he p esen sec ion— ha seem o become ele an .27 Wi h he
model amewo k we ha e p oposed he e, we hus belie e ha policymake s can quickly
and obus ly ge a quan i a i e sense o he s eng h and weaknesses o di e en policy
ou es.
Clea ly, no only go e nmen agencies and policymake s mo e b oadly bu also he
gene al public dese e a ich appa a us wi h he use o which hey can compa e ou -
comes bo h on he indi idual le el and on he le el o designing use ul epidemiological
policy o ou popula ions. The access o o - he-shel amewo ks he eby also acili-
a es communica ion and helps build us in policymake s and hei ecommenda ions,
as hei decision-making e ol es along wi h he e olu ion o he pandemic.
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