Mortality and the business cycle: evidence from an estimated DSGE model for Germany

Shams akh , Fa zaneh
A icle — Published Ve sion
Mo ali y and he business cycle: e idence om an
es ima ed DSGE model o Ge many
In e na ional Economics and Economic Policy
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Sugges ed Ci a ion: Shams akh , Fa zaneh (2024) : Mo ali y and he business cycle: e idence om an
es ima ed DSGE model o Ge many, In e na ional Economics and Economic Policy, ISSN 1612-4812,
Sp inge , Be lin, Heidelbe g, Vol. 22, Iss. 1,
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ORIGINAL PAPER
Mo ali y and he business cycle: e idence
om an es ima ed DSGE model o Ge many
Fa zaneh Shams akh 1
Accep ed: 8 Augus 2024
© The Au ho (s) 2024
Abs ac
This s udy add esses he ela ionship be ween ansi o y mac oeconomic condi ions
and heal h by analyzing he dynamics o dea h o e business cycle luc ua ions
in Ge many du ing 1998:Q4–2014:Q4. A dynamic s ochas ic gene al equilib ium
(DSGE) model wi h popula ion g ow h is de eloped o inco po a e demog aphic
shocks including mo ali y. The es ima ion esul s indica e ha mo ali y in Ge many
is coun e -cyclical, sugges ing ha heal h in Ge many de e io a es du ing ecessions
whe eas i imp o es o e economic expansions. Mo eo e , he s uc u e o mo ali y is
ound o a y wi h espec o he business cycles. While o mos o he sample pe iod
non-wo king popula ion seems o be mo e exposed o dea h du ing ecessiona y imes,
he e a e e idences o highe a ali y o wo king people in Ge many du ing he ecen
inancial and economic c isis. In he ligh o he demog aphic change ha Ge many is
cu en ly expe iencing, indings o his s udy ha e impo an implica ions o heal h
policies conce ning aging as well as wo king-age popula ion.
1 In oduc ion
While he e is no much doub on he a o able heal h ou come o long-las ing eco-
nomic g ow h, he consequences o sho - e m economic up u ns on indi iduals’
well-being ha e become qui e a con o e sy. The a gumen was p ima ily igge ed by
Ruhm (2000), who ound a p o-cyclical pa e n in mo ali y in he US du ing 1972–
1995. The coun e -in ui i e na u e o Ruhm’s inding inspi ed u he analysis on he
ela ionship be ween mo ali y, as one o he main indica o s o he o e all heal h s a-
us, and ansi o y economic condi ions. Simila ly, using he same me hod as Ruhm,
Ge d ham and Ruhm (2006) cap u e p o-cyclical a ia ions in mo ali y o OECD
coun ies du ing 1960–1997, which is ound o hold o di e en sou ces o dea h
in hese coun ies. Besides, addi ional in es iga ions ha e been h ough o un eil he
BFa zaneh Shams akh
[email p o ec ed]
1Depa men o Economics, Uni e si y o Duisbu g-Essen, Uni e si ss ae 2, D-45117 Essen,
Ge many
0123456789().: V,- ol 123
10 Page 2 o 28 In Econ Econ Policy (2025) 22:10
di e en aspec s o his phenomenon and he mechanisms a wo k, which can also be
speci ic o economic and social se ings o a coun y (Lee 1997). Al oge he , changes
in li es yle, quali y o sleep, nu i ion, and leisu e ime; an inc ease in wo k- ela ed
s ain, wo king pace, and ime; and wo k- ela ed acciden s ollowing s eng hening
he economy and in ense use o labo in esponse o high demand a e iden i ied as he
main causes o p o-cyclicali y o a ali y obse ed in indus ialized coun ies.1
Al hough based on exis ing li e a u e one can ha dly d aw a clea conclusion on he
channels h ough which empo a y economic a ia ions can lead o dea h, mo ali y
is shown o be cyclical and ime a ying ela ed o business cycles. The cu en pape
aims o examine hese ea u es h ough a unique app oach, which has been ba ely
applied by p e ious s udies. I de elop and es ima e a non-linea DSGE model o
in es iga e he dynamics o mo ali y o e business cycle luc ua ions in Ge many.
This s udy makes a mul i- old con ibu ion o he exis ing empi ical s udies. Fi s ly,
he non-linea es ima ion allows o cap u e he possible ime a iabili y o mo ali y
a ia ions wi h espec o economic oscilla ions. Second, con a y o all he p eceding
wo ks, no speci ic es ic i e p e-assump ion abou links be ween mo ali y, o o he
measu es o heal h, and economic a iables is imposed in he model; ins ead, he da a
is le o alk. Fu he mo e, obse ing bo h a iables o GDP and employmen in he
model allows o ack he changes in dea h wi h espec o di e en measu es o he
business cycle, which in u n econciles wi h he p io a gumen s. Also, he p esence
o popula ion g ow h in he model makes i possible o in e he heal h ou come o
bo h wo king people and hose ou o he labo ma ke . In addi ion, including he
componen s o demog aphic change in he model enables he s udy o he beha io
o e ili y and mig a ion along wi h mo ali y. Las ly, since economic enhancemen
is usually an icipa ed o be a d i e o bo h ou pu and employmen , by in ol ing
di e en shocks in he model, I am able o disen angle, a he same ime, he possible
e ec s o echnological ad ances, om changes in hou s wo ked conce ning mo ali y,
he ask ha could no be exe cised by adi ional empi ical analysis.
The es o his pape is o ganized as ollows: he nex chap e has a b ie bu
comp ehensi e e iew o he s ands o a gumen s on he heal h ou come o business
cycles. Sec ion 3ou lines he model used o he es ima ion. The elemen s inco po a ed
in he model in o de o analyze he dynamics o mo ali y a e explained in his chap e .
Sec ion 3desc ibes he da a and he es ima ion s a egy. Es ima ion esul s desc ibed in
ables and igu es a e discussed in de ails in Sec ion 4. Finally, Sec ion 5summa izes
he indings o he s udy and concludes.
1Some s udies s ill do no suppo hese no ions. A mic oda a analysis in Finland by Böcke man e al.
(2007) shows ha obesi y dec eases du ing economic up u ns measu ed by employmen a e. Howe e ,
hey do no cap u e any signi ican e ec o economic expansions on physical ac i i y. Likewise, Colman
and Da e (2014) ind empi ical e idence o a d op in as ood in ake and expendi u e on physical ac i i y
du ing ecessions in he US, due o he ollowing income e ec on households’ esou ces. None heless,
he ul ima e ou come on heal h is shown o be mode a e and unce ain. Also, Johansson (2004)’s analysis
o a e age hou s wo ked pe employee o e economic successions and i s ansi o y e ec on heal h in
23 OECD coun ies du ing 1960–1997 indica es ha , con olling o income, highe wo king hou s du ing
phases o economic up u ns is associa ed wi h less mo ali y.
123
In Econ Econ Policy (2025) 22:10 Page 3 o 28 10
2 Li e a u e e iew
Ruhm (2000) shows ha in he US du ing 1972–1995 unemploymen a e is nega i ely
ela ed o o al mo ali y, as one pe cen age poin inc ease in s a e’s joblessness declines
he a ali y a e by 0.5 o 0.6%. He also obse es a educ ion in physical ac i i y
and an inc ease in smoking, obesi y, and unheal hy in ake o e empo a y economic
g ow h in he US. Th ough a close examina ion o mic oda a, Ruhm (2003) inds ha
de e io a ion o physical heal h du ing economic up u ns is mo e p onounced among
employed Ame icans.
Neumaye (2004) and G anados (2005) eplica e (Ruhm 2000)’s analysis o Ge -
man and Spanish da a, espec i ely, and ind a p o-cyclical pa e n o agg ega e
mo ali y, and o he majo i y o dea h causes in hese coun ies. G anados (2005)
a ibu es he dea h pa e n in Spain mainly o a ic- ela ed inju ies, which is ampli-
ied ollowing economic eco e ies. Simila ly, Lin (2009) inds e idences o heal h
imp o emen o e economic down u ns in Asia-Paci ic coun ies o e he pe iod 1976
o 2003.
On he con a y, some o he esea ch cap u es coun e -cyclical pa e ns o mo ali y
o e economic luc ua ions. This shape o a ia ions is usually a ibu ed o he p es-
su es o job losses and economic dis esses du ing ecessions, which lead o highe
s ess, and unheal hy beha io s such as g ea e endency o smoke and alcohol con-
sump ion ha impai he heal h condi ions and consequen ly inc ease mo ali y a es.2
In his ega d, i is discussed ha he p esence o some so o insu ance schemes
migh alle ia e he ecessions’ ha dships ha consequen ly changes he magni ude
o di ec ion o e ec s. Howe e , he c oss-coun y analysis o Ge d ham and Ruhm
(2006) sugges s he s onge p o-cyclical e ec s in coun ies wi h ela i ely in e io
social secu i y sys em.
Following hese con adic o y indings, some li e a u e c i icizes he use o unem-
ploymen a e as he measu e o business cycle due o possible ime lags be ween
business cycles and employmen a ia ions.3Acco dingly, based on P obi models,
Ge d ham and Johannesson (2005) apply o he business cycle indica o s a he han
unemploymen a e including GDP a ian s and ind a coun e -cyclical mo ali y isk
ha is only signi ican o men and is mo e no iceable o wo king-age ones in Sweden
du ing 1981–1996.
Fu he mo e, some o he s ha e a o ed s udying age-speci ic mo ali y ins ead o
o e all dea h luc ua ions. Mille e al. (2009) closely sea ches he mechanisms behind
p o-cyclical beha io o mo ali y in he US cap u ed by Ruhm (2000), by epea ing
his analysis wi h leng hy da a un il 2004 and unning he eg ession o a wide ange
2Almos all he empi ical li e a u e a e unanimous ha he a e o suicides inc eases o e economic
ecessions (Ruhm 2000; G anados 2005; Edwa ds 2008;Lin2009). The only excep ion, p esumably, is
Neumaye (2004) who shows ha suicide is p o-cyclical in Ge many.
3Cla k and Summe s (1982) also sugges ha unemploymen a e is a misleading measu e o labo ma ke
condi ion since i does no e lec he a ia ions in pa icipa ion in esponse o changes in agg ega e demand.
Ins ead, employmen a e is a be e indica o o he labo ma ke dynamics.
123
10 Page 4 o 28 In Econ Econ Policy (2025) 22:10
o age g oups. Thei esul s demons a e he mos (p o-) cyclical mo ali y a es o
hose age g oups wi h p obably he lowes labo o ce pa icipa ion, including he
young adul s be ween 18 and 24. Howe e , he age g oup o e 80 con ibu es he mos
(abou 70%) o o e all mo ali y luc ua ions. Based on hese indings, Mille e al.
sugges ha mechanisms behind p o-cyclical beha io o mo ali y should be sough
ou o labo ma ke and beyond he indi iduals’ own heal h and wo k beha io , ac o s
ha Mille e al. a ibu e o business cycle ex e nali ies. They also go a he u he
by analyzing he age-speci ic pa e n o di e en causes o dea h o e business cycles,
and hey ind no e idence o wo k-s ess- ela ed dea hs among wo king popula ion.
The e is mo e empi ical e idence o p o-cyclical a ia ions in he heal h s a us o he
age g oups wi h small labo ma ke a achmen s in de eloped coun ies (S e ens e al.
2015; Rolden e al. 2013). These indings a e sugges i e o o he con ibu ing ac o s
a he han job- ela ed s ess, such as ai pollu ion, social suppo , o ca egi ing, in he
mo ali y o elde ly people du ing economic expansions. Compa a i ely, employing
he same app oach as Ruhm (2000) o Canadian da a, A iizumi and Schi le (2012)
obse e ha he p o-cyclical pa e n ound o he US does no hold o aged popula ion
in Canada who a he enjoy speci ic elde ly heal h ca e acili ies p o ided by he
Canadian go e nmen . Ne e heless, he wo king-age popula ion in Canada s ill shows
a p o-cyclical mo ali y o e economic luc ua ions.
In addi ion, i is discussed ha he ela ionship be ween mac oeconomic condi ions
and mo ali y may al e o e ime. Consequen ly, some ecen s udies ha e examined
his link wi h mo e ecen da a. Ruhm (2015) ex ends his analysis o 2009 o he US
and concludes ha o e he las h ee decades, o al mo ali y changed om being
s ongly p o-cyclical o being mos ly un ela ed o business cycles. Simila ly, Tekin
e al. (2013) do no cap u e any e idence o he e ec s o he ecen inancial c isis on
heal h beha io in he US. Also, based on agg ega e da a o he US o e 1961–2010 and
using a ime- a ying pa ame e (TVP) model, Lam and Pié a d (2017) conclude ha
in ecen yea s, he des uc i e in luence o inc eased wo king hou s on indi iduals’
heal h s a us du ing upwa d economic luc ua ions is domina ed by he posi i e e ec
o medical de elopmen s o mos o he age g oups. Ne e heless, hey s ill obse e
a p o-cyclical mo emen in mo ali y caused by mo o ehicle acciden s al hough his
pa e n has weakened o e ime.
Finally, some p io esea ch looks a mo ali y beha io among di e en socio-
economic g oups. Edwa ds (2008) inds ha he p o-cyclical mo ali y in he US
is limi ed o wo king-age males wi h high school o highe educa ional a ainmen .
In addi ion, Xu (2013) ind e idence o wo sening he men al heal h o educa ed
employed indi iduals du ing he economic boos .
These s udies, al hough wi h opposing esul s, add ess di e en aspec s o indi idu-
als’ heal h beha io o e economic luc ua ion. Acco dingly, he possible dissimila i y
in heal h ou come o wo king and non-wo king popula ions poin ed ou by he li e -
a u e is wo hy o a en ion. None heless, as hese s udies mainly ely on eg ession
analysis, hey can be highly subjec o omi ed a iables biases. The DSGE app oach
employed by his s udy esol es his quanda y also and, a he same ime, ul ills some
o he gaps in he li e a u e.
123

In Econ Econ Policy (2025) 22:10 Page 5 o 28 10
3Themodel
The benchma k new Keynesian DSGE model wi h nominal p ice and wage igidi-
ies and ic ions in consump ion and in es men in oduced by Fe nández-Villa e de
and Rubio-Ramí ez (2006) is employed as he baseline model o his s udy. In a
closed-economy amewo k, ollowing Bu iel e al. (2010), I adjus he model o be
exp essed in pe -capi a e ms and ex ended along a balanced s eady-s a e g ow h pa h
de e mined by echnology and popula ion g ow h. As desc ibed la e , he p esence o
popula ion g ow h in he model allows o explo e he beha io o mo ali y, as one o
he componen pa s o popula ion change, o e business cycle luc ua ions. A de ailed
desc ip ion o he model is p esen ed below.
3.1 Households
I is assumed ha he economy is inhabi ed by a con inuum o homogeneous house-
holds indexed by jwi h he ollowing li e ime u ili y unc ion:
E0
∞

0
β L d {log (cj −hcj −1)+υlog mj
p
−ϕ ψ
(ls
j )1+γ
1+γ}(1)
whe e cj is pe -capi a consump ion, mj /p pe -capi a eal money balances, and ls
j
pe -capi a hou s wo ked. L deno es he size o in ini y-li ed households ha changes
by popula ion g ow h. βindica es he discoun ac o , h he habi pe sis ence, and γ he
in e se o F isch labo supply elas ici y. Va iables d and ϕ ep esen an in e empo al
p e e ence shock and a labo supply shock, espec i ely, and a e o mula ed as a i s -
o de au o eg essi e p ocess AR(1):
d =ρdd −1+σdεd, whe e εd, ∼N(0,1)(2)
ϕ =ρϕϕ −1+σϕεϕ, whe e εϕ, ∼N(0,1)(3)
3.1.1 Popula ion dynamics
The size o he household L is supposed o ollow a andom walk wi h d i :
L =L −1exp (L+zL, )whe e zL, =σLεL, and εL, ∼N(0,1). (4)
Acco dingly, he popula ion g ow h is de ined as ollows:
γL
=L
L −1
=exp(L+zL, )(5)
whe e Lco esponds o s eady-s a e g ow h o popula ion.
In demog aphic e ms, he na u al change in popula ion is igge ed by h ee com-
ponen s o dea h, bi h, and mig a ion. I use his no ion and inco po a e hese h ee
123
10 Page 6 o 28 In Econ Econ Policy (2025) 22:10
ea u es in popula ion g ow h. This adjus men simply allows he s udy o he dynam-
ics o mo ali y wi hin his se -up. By de ini ion, I design he popula ion g ow h as
ollows4:
γL
=(γ B
)αB(γ D
)−αD(γ M
)αM(6)
whe e γB
,γD
, and γM
espec i ely ep esen he g ow h o bi h, dea h, and ne
mig a ion. Pa ame e s o αB,αD, and αMindica e he a e o co esponding e en s.
The i al e en s o bi hs and dea hs, also ne mig a ion, a e supposed o be exposed
o h ee shocks ha , in u n, s imula e he changes in popula ion h ough changes
in mo ali y, e ili y, and mig a ion. These p ocesses a e acco dingly o mula ed as
ollows, wi h pe sis ence a ound hei co esponding mean:
γB
=exp(B+zB, )(7)
γD
=exp(D+zD, )(8)
γM
=exp(M+zM, )(9)
Households can ade an amoun o A ow-Deb eu secu i ies aj +1, ha pay one
uni o consump ion in e en ωj, +1, pu chased by household ja ime a eal
p ice qj +1, . Households also hold an amoun bj o go e nmen bonds ha pay a
nominal g oss in e es a e o R .I isassumed ha a[1]=0, aand a>0. In addi ion,
households own he capi al k ha ea ns a ma ke eal en al a e and is o med
based on ollowing law o mo ion:
γL
+1kj =(1−δ)kj −1+1−κ[γL
xj
xj −1
]xj (10)
whe e δis he dep ecia ion a e o capi al and κ[.]is an adjus men cos unc ion
such ha κ[x]=0, κ[x]=0, and κ[x]>0. xspeci ies he g ow h a e
o in es men . Gi en hese assump ions, he household’s pe -capi a budge cons ain
eads as ollows:
cj +xj +mj
p
+bj +1
p
+qj +1, aj +1dωj +1,
=wj ls
j +( uj −[uj ])kj −1+1
γL
mj −1
p
+R −1
1
γL
bj
p
+1
γL
aj +T +F (11)
whe e wj indica es he eal wage, and uj >0 shows he in ensi y o capi al u iliza-
ion. Mo eo e , [uj ]is he physical cos o use o capi al in esou ce e ms. I is
assumed ha [1]=0, and  >0. Also, T is he lump-sum ans e , and F is
he p o i o he i m.
4Popula ion aged 15 yea s and o e a e conside ed in his s udy; hus, he bi h a iable is en e ed in o he
model wi h a lag o 56 pe iods, since li ebo ns no mally ake 14 yea s o join he sample popula ion.
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In Econ Econ Policy (2025) 22:10 Page 7 o 28 10
The e o e, he i s -o de condi ions o he ep esen a i e household wi h espec
o cj ,bj ,uj ,kj , and xj ake he ollowing o ms:
d (cj −hcj −1)−1−hE βγ L
+1d +1(cj +1−hcj )−1=λj (12)
λj =E βλj +1
R
 +1(13)
=[uj ](14)
qj E γL
+1=βE γL
+1λj +1
λj (1−δ)qj +1+ +1uj +1−a[uj +1] (15)
1=qj 1−κγL
xj
xj −1−κγL
xj
xj −1γL
xj
xj −1
+E βγ L
+1qj +1
λj +1
λj
κγL
+1
xj +1
xj γL
+1xj +1
xj 2
(16)
wi h (ma ginal) Tobin’s q , de ined as Q
λ he a io o wo Lag angian mul iplie s in
he Lag angian unc ion ela ed o household’s maximiza ion p oblem.
The di e en ia ed labo supplied by each household in each pe iod ls
j is accumu-
la ed by in e media e good p oduce s h ough he ollowing p oduc ion unc ion:
Ld
=L 1
0
(ls
j )
η−1
ηdjη
η−1=L ld
(17)
whe e 0 ≤η≤is he elas ici y o subs i u ion among di e en ypes o labo , and ld
and Ld
ep esen pe -capi a and agg ega e labo demand, espec i ely. Subjec o his
p oduc ion unc ion, in e media e good p oduce s maximize hei p o i :
maxlj
w L ld
−1
0
wj L ls
j dj (18)
wi h wj showing he di e en ia ed labo wages and w he agg ega e wage.
This deli e s he pe -capi a labo demand unc ion and agg ega e wage as ollows:
ls
j =wj
w −η
ld
(19)
w =1
0
w1−η
j dj1
1−η(20)
Households ollow Cal o p ice se ing o se hei wages. In his sense, i is assumed
ha in each pe iod, only a ac ion o households (1−θw)upda e hei wage wand
123
10 Page 8 o 28 In Econ Econ Policy (2025) 22:10
he es θwindex hei wage o in la ion in he p e ious pe iod. Indexa ion is adjus ed
by χw∈[0,1]pa ame e . This yields he eal wage as ollows:
w1−η
=θwχw
−1
 1−η
w1−η
−1+(1−θw)w∗1−η
3.2 Final good p oduce
Pe ec ly compe i i e inal good p oduce agg ega es in e media e goods yi using he
ollowing design:
y =1
0
(yi )−1
di
−1(21)
whe e is he subs i u ion elas ici y among in e media e goods. Maximizing i s p o i
subjec o he p oduc ion unc ion, he inal good p oduce a i es a he ollowing
inpu demand unc ion:
yi =pi
p −
yd
(22)
p =1
0
p1−
i di1
1−(23)
wi h yd
indica ing inal good p oduce ’s agg ega e pe -capi a demand and p indica ing
agg ega e p ice.
3.3 In e media e good p oduce s
The echnology used by in e media e good p oduce iis Cobb-Douglas and exp essed
(in pe -capi a e ms) as ollows:
yi =A kα
i −1ld
i 1−α−φ(24)
whe e φis he ixed cos o p oduc ion and A is he le el o echnology wi h he
ollowing low o mo ion:
A =A −1exp (A+zA, )whe e zA, =σAεA, and εA, ∼N(0,1). (25)
μz
de e mines he long- un g ow h o ou pu and is gi en as:
μz
=exp (A+zA, )(26)
In a pe ec ly compe i i e ac o ma ke , in e media e good p oduce s en inpu s
so as o: ki −1
ld
i
=α
1−α
w
(27)
123
In Econ Econ Policy (2025) 22:10 Page 15 o 28 10
p io assump ion o labo supply elas ici y as well as dea h and bi h a e pa ame e s
is shown o pe ec ly mi o he in o ma ion in he da a. In gene al, he pa ame e s a e
ound o be s ongly iden i ied, and he da a seems o be qui e in o ma i e.
In addi ion, he s abili y o he es ima ion is e alua ed wi h B ooks and Gelman
(1998) diagnos ic ool o MCMC Con e gence. Quali a i ely speaking, h ough his
me hod, one can in e i he sample deli e ed by he MCMC simula ion makes a good
ep esen a ion o he pos e io dis ibu ion. The co esponding esul s o indi idual
pa ame e s (uni a ia e) and he whole se o pa ame e s simul aneously (mul i a ia e)
in he o m o g aphs a e p esen ed in Appendix (Figs. 11,12,13 and 14).
4.4 E ec o shocks
The impo ance o he shocks in explaining mac oeconomic luc ua ions can be
assessed h ough analyzing he Bayesian a iance decomposi ion, impulse- esponse
unc ions (IRFs), and his o ical decomposi ion ob ained om he es ima ion. These
p ope ies a e discussed in his sec ion, mainly wi h he ocus on he e ec o mo ali y
shock.
4.4.1 Va iance decomposi ion
The esul o uncondi ional a iance decomposi ion is summa ized in Table 3.The
igu es demons a e he pe cen age sha e o he a ia ions in he key obse ed a iables
ha a e explained by h ee shocks desc ibing he popula ion dynamics o e an in ini e
ho izon.
As expec ed, he majo pa o he luc ua ions in he Ge man economy is de e -
mined by o he shocks in he model including labo supply, echnology, and p e e ence
shocks, al oge he measu e up o mo e han 98%. The es is explained by he com-
ponen s o popula ion g ow h con ibu ing he mos o he changes in consump ion.
Among hese h ee demog aphic shocks, mig a ion has he mos and e ili y has he
leas impac on he Ge man economy. As isible, 0.002 and 0.001% o ola ili y in
espec i ely GDP and employmen g ow h in Ge many is d i en by mo ali y shock.
4.4.2 Impulse- esponse unc ions
The eac ion o he key a iables o he model o s ochas ic shocks can be iden i ied
h ough IRFs. Figu es1,2,3,4,5, and 6depic he ajec o y o esponse o he
model o one s anda d de ia ion shock o e 40 pe iods (10 yea s) ho izon, d awn as
Table 3 Va iance decomposi ion Va iable Shocks
G ow h a e Mo ali y Fe ili y Mig a ion
GDP 0.002 0.001 0.13
Hou s 0.001 0.00 0.04
Consump ion 0.02 0.006 1.20
123

10 Page 16 o 28 In Econ Econ Policy (2025) 22:10
010203040
-5
0
5
el. de . . s eady-s a e
10-4 P oduc ion (g ow h)
0 10203040
-2
0
2
el. de . . s eady-s a e
10-4 Employmen (g ow h)
010203040
-5
0
5
el. de . . s eady-s a e
10-4 Consump ion (g ow h)
0 10203040
0
0.05
el. de . . s eady-s a e
Dea h (g ow h)
Fig. 1 Mo ali y shock
solid black lines su ounded by 90% con idence in e als. Acco dingly, he na ow
con idence in e al seen a ound he es ima ed pa hs indica es a high ce ain y o e he
ob ained es ima es.
As i is seen, he s ochas ic mo ali y shock o a size o one pe cen di ec ly inc eases
he numbe o dea hs by abou 0.4%. This leads o a decline in o al ou pu g ow h
by abou 0.002% and consump ion g ow h by abou 0.004%. Following an inc ease
in mo ali y, he g ow h o hou s wo ked pe head goes up by oughly 0.001% as he
i s eac ion o a all in he size o he labo o ce. Ne e heless, wi hin one pe iod,
when he impac o he shock seems o disappea , we obse e a decline in he supplied
labo ollowing he mo ali y shock. Al hough he size o he e ec on employmen is
small, i akes abou 10 pe iods o ebound.
Compa a i ely, he mig a ion shock has a la ge impac on he Ge man economy,
as 1 s anda d de ia ion shock expands he ne mig a ion g ow h by abou 3%. This, in
u n, adds abou 0.01% and 0.02% o GDP and consump ion g ow h, espec i ely. The
e ec o he shock on employmen is a he small, limi ing he g ow h o hou s wo ked
by abou 0.007% in he i s qua e . Ne e heless, a e he i s pe iod, he e seems
o be some small mo emen in employmen s imula ed by p obably added mig an
wo ke s o he ma ke (Fig.2).
0 5 10 15 20 25 30 35 40
-2
0
2
el. de . . s eady-s a e
10-3 P oduc ion
0 5 10 15 20 25 30 35 40
-2
0
2
el. de . . s eady-s a e
10-3 Employmen
0 5 10 15 20 25 30 35 40
-5
0
5
el. de . . s eady-s a e
10-3 Consump ion
0 5 10 15 20 25 30 35 40
0
2
4
el. de . . s eady-s a e
Mig a ion
Fig. 2 Mig a ion shock
123
In Econ Econ Policy (2025) 22:10 Page 17 o 28 10
0 10203040
-0.01
0
0.01
el. de . . s eady-s a e
P oduc ion (g ow h)
010203040
-0.02
0
0.02
el. de . . s eady-s a e
Employmen (g ow h)
0 10203040
-0.01
0
0.01
el. de . . s eady-s a e
Consump ion (g ow h)
Fig. 3 P oduc i i y shock
Clea ly, a posi i e shock o echnology inc eases he ou pu and consump ion g ow h
in he i s pe iod. In esponse o a 1% shock, ou pu g ow h goes up by 0.02% and
g ow h a e o consump ion by 0.04%. Howe e , in line wi h Gali (1999), we obse e
ha hou s wo ked espond nega i ely o he posi i e echnology shock in he i s
qua e by d opping by abou 0.1%. This can be a ibu ed o he p ice and wage
igidi ies in he ma ke ha lead o a lagged eac ion o i ms in upg ading he demanded
labo se ices. As can be seen, he g ow h o hou s wo ked eco e s and picks up in he
second pe iod ha , in u n, ein o ces he g ow h o ou pu . The impac o echnology
shock o he model ades a e almos 20 pe iods (Fig.3).
A posi i e shock o household ime p e e ences encou ages hei cu en consump-
ion and inc eases i s g ow h by 0.1% in he i s qua e ha consequen ly boos s
he ou pu g ow h. The ollowing highe demand and p oduc ion equi e highe hou s
o wo k. As a esul , in esponse o he shock, he g ow h a e o hou s de elops by
0.07%. The enhanced g ow h g adually slows down a e he i s pe iod, bu i akes
abou 15 pe iods o ebound (Fig. 4).
In esponse o a 1% nega i e labo supply shock, he g ow h a e o hou s wo ked
pe uni sho ly d ops by 0.2%. This ansla es o a cu back in consump ion g ow h
by abou 0.08% and a dec ease o oughly 0.2% in GDP g ow h in he i s pe iod.
0 10203040
-0.01
0
0.01
el. de . . s eady-s a e
P oduc ion (g ow h)
010203040
-0.01
0
0.01
el. de . . s eady-s a e
Employmen (g ow h)
0 10203040
-0.02
0
0.02
el. de . . s eady-s a e
Consump ion (g ow h)
Fig. 4 P e e ence shock
123
10 Page 18 o 28 In Econ Econ Policy (2025) 22:10
0 10203040
-0.05
0
0.05
el. de . . s eady-s a e
P oduc ion (g ow h)
010203040
-0.05
0
0.05
el. de . . s eady-s a e
Employmen (g ow h)
0 10203040
-0.01
0
0.01
el. de . . s eady-s a e
Consump ion (g ow h)
Fig. 5 Labo supply shock
Following he dec ease in employmen , he eal wages a e expec ed o ise ha , in
u n, encou age wo k and subsequen ly consump ion. As a esul , as i is e iden , in
line wi h employmen and consump ion, he ou pu g ow h u ns a ound in he 10 h
qua e and mo es upwa ds. The ola ili y caused by he labo supply shock needs
abou 30 qua e s o ade ou (Fig.5).
Finally, a 1% shock o e ili y aises he numbe o li e bi hs by oughly 0.2%;
howe e , as expec ed, his does no ha e any isible impac on he economy o e he
i s 40 pe iods a e he shock onse (Fig.6).
4.4.3 His o ical decomposi ion
The con ibu ion o shocks o he his o ical pa h o he g ow h a iables can be in es-
iga ed h ough his o ical decomposi ion igu es. As expec ed, he p oduc i i y shock,
he p e e ence shock, and he labo supply shock a e he main de e minan s o he
change in GDP g ow h, g ow h a es o consump ion, and hou s wo ked in Ge many
o e he sample ime ho izon. Acco dingly, as he dynamics o mo ali y is o he
main in e es in his pape , I ocus he e only on elemen s o popula ion change and
010203040
-1
0
1
el. de . . s eady-s a e
10-4 P oduc ion (g ow h)
0 10203040
-1
0
1
el. de . . s eady-s a e
10-4 Employmen (g ow h)
010203040
-2
0
2
el. de . . s eady-s a e
10-5 Consump ion (g ow h)
0 10203040
0
0.02
0.04
el. de . . s eady-s a e
Bi h (g ow h)
Fig. 6 Fe ili y shock
123
In Econ Econ Policy (2025) 22:10 Page 19 o 28 10
analyze he capaci y o a mo ali y shock, as well as e ili y and mig a ion shocks o
in luence he mo emen o a ge a iables. Figu es7,8, and 9display he his o ical
decomposi ion o espec i ely GDP g ow h a e, consump ion g ow h a e, and g ow h
a e o employmen in e ms o hou s wo ked. The de ia ion o he g ow h a iables
om hei co esponding s eady s a es is plo ed in dappled ba s. The pa s ela ed o
he cumula i e con ibu ion o shocks o he de ia ions a e illed in solid colo s wi h
ed, g een, and blue ep esen ing mo ali y shock, mig a ion shock, and e ili y shock,
espec i ely.
The o e all impac o popula ion unde lying o ces, howe e small, is ob ious, wi h
ne mig a ion ha ing ela i ely he la ges and bi h e en ha ing he leas con ibu ion
o g ow h. EU enla gemen s o 2004 and 2007 and he ollowing labo mobili y
a e clea ly cap u ed by he mig a ion shock, indica ing a posi i e con ibu ion o
subsequen mig a ion lows o he Ge man p oduc ion and consump ion g ow h. The
posi i e e ec o mig a ion on he Ge man labo ma ke appea s o lag. In gene al, as
Fig.7sugges s, he phases o downwa d ou pu g ow h in Ge many a e co ela ed wi h
a descending mig a ion g ow h and con a iwise, displaying a p o-cyclical design o
mig a ion in Ge many.
Mo ali y in Ge many howe e shows a di e en pa e n. As Fig.7shows, du ing he
sample pe iod, he sequences o upwa d economic g ow h a e associa ed wi h declining
dea h g ow h while du ing he episodes o dep essed economic g ow h a ali y is seen
o de elop. Likewise, he nega i e con ibu ion o he mo ali y shock o GDP g ow h
du ing he ea ly 2000s ecession as well as he ecen inancial c isis is wo h no ing.
The nega i e impac o mo ali y on GDP g ow h is especially p ominen in he second
qua e o 2002 and also in he i s qua e o 2009. These e idences demons a e ha
mo ali y in Ge many is an i-cyclical. This is in con as wi h Neumaye (2004)who
inds a nega i e ela ionship be ween he s a e unemploymen a e and agg ega e mo -
ali y a e o Ge many du ing he yea s 1980–2000 based on a ixed-e ec es ima ion.
Fig. 7 His o ical decomposi ion o GDP g ow h
123
10 Page 20 o 28 In Econ Econ Policy (2025) 22:10
Fig. 8 His o ical decomposi ion o employmen g ow h
Howe e , he does no cap u e a p o-cyclical beha io o mo ali y o males and o
age g oup 45–65 wi hin a dynamic model.
T acking he mo emen o employmen o e he sample pe iod p o ides u he
de ails on he beha io also s uc u e o mo ali y in Ge many. As an in e es ing ac , i
is seen ha excep o he pe iods in ol ed wi h he ecen economic and inancial c isis,
mo ali y mo es p o-cyclically wi h espec o employmen as he lowe g ow h a e o
dea hs is shown o p opo iona ely sh ink he g ow h o hou s wo ked (pe pe son) and
ice e sa (Fig.8). Since mo ali y da a also includes he popula ion who is ou o labo
o ce, his end, as one could in e , implici ly shows ha a ali y in Ge many mos ly
in ol es he non-wo king popula ion speci ically he elde ly. Howe e , ema kably, a
Fig. 9 His o ical decomposi ion o consump ion g ow h
123

In Econ Econ Policy (2025) 22:10 Page 21 o 28 10
e e se pa e n is obse ed du ing he G ea Recession o 2008. I is seen ha in his
in e al, highe g ow h o mo ali y is associa ed wi h lowe hou s wo ked pe pe son
s a ing in 2008:Q3 when mo ali y shock is shown o educe he g ow h o hou s
wo ked. Simila ly, ollowing he s eep all in GDP speci ically in he i s qua e o
2009, we see ha de eloping mo ali y among people a wo k mi iga es he downwa d
push o employmen by a posi i e con ibu ion o g ow h o hou s wo ked. In he second
qua e o 2009, when he Ge man economy expe iences a subs an ial eco e y, he
labo ma ke is s ill slow-mo ing. A his ime, he e ec o he dea h shock on he labo
o ce is ela i ely s ong. I isibly na ows he unemploymen and, in u n, abso bs
pa o he dep ecia o y impac o sluggish employmen g ow h on GDP. I is plain o
see ha he mo ali y shock posi i ely con ibu es o GDP g ow h in 2009:Q2.
Las ly, he e ec o he e ili y shock is obse ed only a he end o he sample
pe iod. I is seen ha his shock accommoda es a mino pa o GDP g ow h a ia-
ions om he las qua e o 2014. Likewise, a he same ime, his shock ma ginally
con ibu es o he change in consump ion g ow h. The e ili y e ec obse ed he e
can be mainly a ibu ed o a ela i ely signi ican swing in he pa e n o p egnancy
beha io in Ge many du ing 2002, which, in u n, has deli e ed a delayed impac on
he economy. As he da a sugges s, he e was a ela i ely s ong all in he numbe o
li e bi hs in Ge many in he i s qua e o 2002 p obably esul ing om he eco-
nomic ecession in ol ing Ge many in he ea ly 2000s. Ne e heless, succeeding he
end o ecession he coun y wi nessed a la ge inc ease in he numbe o li e bi hs in
he las qua e o 2002.
4.5 Model e alua ion
As he s anda d p ac ice in he DSGE li e a u e, o assess he i o he es ima ed model
o he ac ual da a, I compu e and compa e some s a is ics gene a ed by he model based
on he es ima ed pos e io mean wi h hose o he sample. Mo i a ed by he ques ion
o in e es , he s anda d de ia ion o he g ow h a iable o mo ali y, in addi ion o
bi h and mig a ion g ow h, and hei c oss-co ela ions wi h con empo aneous ou pu
and hou s g ow h a e p o ided and displayed in Table 4.
As is e iden , he es ima ed model is qui e e ec i e in eplica ing he second
momen s o he ac ual demog aphic da a in Ge many. The ola ili y in e ed by he
es ima ion is almos iden ical o ha o he da a. Ne e heless, he model deli e s
smalle co ela ions, al hough wi h equal signs, wi h GDP and employmen g ow h
compa ed o wha is obse ed in he da a.
Table 4 Second momen s
Va iable s de . co . GDP g ow h co . HOURS g ow h
Da a Model Da a Model Da a Model
Dea h 0.037 0.037 −0.227 −0.072 −0.303 −0.067
Bi h 0.015 0.018 0.008 0.005 0.086 0.007
Ne mig a ion 3.370 3.326 −0.412 −0.036 −0.060 −0.030
123
10 Page 22 o 28 In Econ Econ Policy (2025) 22:10
5 Conclusion
The impac o ansi o y mac oeconomic shocks on indi iduals’ heal h s a us has been
ques ioned by se e al esea ch. This pape has add essed his issue by analyzing he
dynamics o dea h o e business cycle luc ua ions in Ge many h ough de eloping
and es ima ing a non-linea DSGE model ha coun s o ime asymme ies in he
da a. The esul s p o ide e idence o he an i-cyclicali y o mo ali y in Ge many,
sugges ing ha heal h in Ge many de e io a es du ing ecessions whe eas i imp o es
o e economic expansions.
Mo eo e , i is ound ha he s uc u e o mo ali y can a y wi h espec o eco-
nomic cycles. While o mos o he sample pe iod non-wo king popula ion seems
o be mo e exposed o dea h, he e appea s o be a highe a ali y o wo king peo-
ple du ing he ecen inancial and economic c isis. In Ge many, wo king popula ion
enjoys a o able insu ance schemes and job secu i y p o isions ha can mi iga e he
ad e se e ec s o economic ha dships; howe e , his migh no be e icien enough
unde a se e e economic down u n. Besides, some o he ac o s ou side he labo ma -
ke can play a de e minan ole. Pe haps by a deep ecession, he oppo uni y cos s
o de eloping unheal hy habi s such as alcohol use and smoking among employed
people dec ease, ha consequen ly impai s hei heal h.
In addi ion, he coun e -cyclical dea h obse ed o non-wo king indi iduals who
a e supposedly mos ly he elde ly10 shows he ulne abili y o olde popula ion o
economic luc ua ion in Ge many, al hough his g oup has he leas a achmen o he
labo ma ke . Despi e he heal h ca e insu ance co e age o elde ly popula ion in
Ge many, he access o his g oup o some medical ca e se ices migh be changing
o e business cycles.
O e all, he indings o his s udy highligh he ad e se heal h ou comes o se e e
economic down u ns, unde sco ing he need o policies ha sa egua d he heal h and
well-being o he popula ion du ing economic c ises. The ecen COVID-19 pandemic
was a se e e combined heal h and economic c isis, whe e go e nmen policies could
alle ia e a pa o he economic bu den. No ably, du ing he pandemic, unemploymen
in Ge many inc eased only mode a ely, hanks o suppo measu es such as sho - ime
wo k schemes. These measu es likely mi iga ed he de imen al economic impac o
he c isis and hei associa ed e ec s on public heal h. Howe e , by o cing an eme -
gency public heal h esponse, he pandemic ine i ably a ec ed he dis ibu ion o
public heal h se ices. In pa icula , he public heal h esponse p io i ized sho - e m
eme gency ea men o e po en ial longe - e m physical and men al heal h impai -
men s. Recen s udies ha e highligh ed some o he longe - e m nega i e e ec s o
he COVID-19 pandemic on men al heal h among he adul popula ion (Pa zina e al.
2024). Simila ly, long COVID, de ined as a pos -COVID synd ome (Kozłowski e al.
2024), is shown o ha e had a nega i e impac on labo supply and labo p oduc i i y
in he EU (Ramos e al. 2024). This e idence b ings o ligh he need o mo e a ge ed
in e en ions ha add ess he longe - e m heal h implica ions o a c isis and suppo
he mos ulne able g oups o hese e ec s.
10 Acco ding o o icial Ge man s a is ics, in a e age, mo e han 80% o yea ly dea hs in Ge many is ela ed
o people aged o e 65 (S a is isches Bundesam (Des a is), 2017).
123
In Econ Econ Policy (2025) 22:10 Page 23 o 28 10
Appendix
0.1 0.2 0.3 0.4 0.5
0
100
200
300
S de . Technology shock
0.1 0.2 0.3 0.4 0.5
0
10
20
30
S de . P e e ence shock
00.511.522.5
0
5
10 S de . Labo supply shock
0.1 0.2 0.3 0.4 0.5
0
50
100
S de . Mo ali y shock
0.1 0.2 0.3 0.4 0.5
0
100
200
S de . Fe ili y shock
12345
0
2
4
6
8S de . Mig a ion shock
0.66 0.68 0.7 0.72 0.74 0.76
0
10
20
30
40
Habi pe sis ence
0510
0
0.1
0.2
0.3
0.4
Labo disu ili y
1.4 1.6 1.8 2 2.2 2.4
0
1
2
3
4
In . F isch elas ici y
0.4 0.6 0.8 1
0
10
20
30
Coe . P e e ence shock
0.4 0.6 0.8 1
0
5
10
15
Coe . Labo supply shock
-202468
10-3
0
200
400
Technology g ow h
-0.02 0 0.02
0
50
100
Dea h g ow h
-0.02 0 0.02
0
100
200
Bi h g ow h
-5 0 5
0
0.5
1
Mig a ion g ow h
8.5 9 9.5
10-3
0
2000
4000
Bi h a e
9.5 10 10.5
10-3
0
2000
4000
Dea h a e
012
10-3
0
1000
2000
Mig a ion a e
Fig. 10 P io and pos e io dis ibu ions
123
10 Page 24 o 28 In Econ Econ Policy (2025) 22:10
246810
104
1
2
3
410-3
S de . Technology shock (In e al)
246810
104
0.5
1
1.5
210-6
S de . Technology shock (m2)
24681
0
104
0
2
410-9
S de . Technology shock (m3)
246810
104
0.03
0.04
0.05
0.06
S de . P e e ence shock (In e al)
246810
104
1
2
3
410-4
S de . P e e ence shock (m2)
24681
0
104
0
0.5
1
1.5 10-5
S de . P e e ence shock (m3)
246810
104
0.3
0.4
0.5
0.6
S de . Labo supply shock (In e al)
246810
104
0.02
0.03
0.04
0.05S de . Labo supply shock (m2)
24681
0
104
0.005
0.01
0.015
0.02S de . Labo supply shock (m3)
246810
104
7
8
9
10 10-3
S de . Mo ali y shock (In e al)
246810
104
0.8
1
1.2
1.4 10-5
S de . Mo ali y shock (m2)
24681
0
104
2
4
6
810-8
S de . Mo ali y shock (m3)
246810
104
3
3.5
4
4.5 10-3
S de . Fe ili y shock (In e al)
246810
104
1.5
2
2.5
310-6
S de . Fe ili y shock (m2)
24681
0
104
4
6
810-9
S de . Fe ili y shock (m3)
246810
104
0.5
0.6
0.7
0.8S de . Mig a ion shock (In e al)
246810
104
0.04
0.06
0.08
0.1 S de . Mig a ion shock (m2)
24681
0
104
0.02
0.04
0.06 S de . Mig a ion shock (m3)
Fig. 11 Ma ko chain Mon e Ca lo uni a ia e con e gence diagnos ics
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