Wunde , Ch is oph
A icle
In a amilial Ups eam T ans e s and Household
P oduc ion
Schmolle s Jah buch – Jou nal o Applied Social Science S udies. Zei sch i ü Wi scha s- und
Sozialwissenscha en
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Wunde , Ch is oph (2007) : In a amilial Ups eam T ans e s and Household
P oduc ion, Schmolle s Jah buch – Jou nal o Applied Social Science S udies. Zei sch i ü
Wi scha s- und Sozialwissenscha en, ISSN 1865-5742, Duncke & Humblo , Be lin, Vol. 127, Iss. 1,
pp. 33-45,
h ps://doi.o g/10.3790/schm.127.1.33
This Ve sion is a ailable a :
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Schmolle s Jah buch 127 (2007), 33-45
Duncke & Humblo , Be lin
In a amilial Ups eam T ans e s
and Household P oduc ion
By Ch is oph Wunde *
Abs ac
The a icle in es iga es in e gene a ional ans e s om child en o pa en s and p o
ides e idence o an exchange mo i e. The ans e s a e, he e o e, in e p e ed as ex
pendi u es o in a a nilial se ices. The applica ion o he household p oduc ion ap
p oach o he ans e -se ice ela ionship p o ides a new pe spec i e in o he ollowing
discussion: as cul u al backg ound de e mines he echnology o he household p oduc
ion o a g ea ex en , i is supposed ha eligion as one o he main cul u al ac o s has
an e ec on he incidence o ans e s.
JEL Classi ica ion: DJ3, Z12
1. ln oduc ion
The social and demog aphic changes o he pas decades ha e subs an ial
consequences o he ela ionship be ween he young and he old gene a ions.
The pe sis en high unemploymen a es and inc eases in li e expec ancy ha e
pu eno mous p essu e on he social secu i y sys em. In Ge many, o example,
Ronald Po alla, he gene al sec e a y o he Ch is ian Democ a s in he lowe
house o pa liamen , sugges ed ecen ly ha adul child en should pay main
enance o hei unemployed pa en s ( c . F ank u e Allgemeine Zei ung,
2006). The aim o he policy p oposed is o subs i u e a p i a e, in a amilial
ans e o he s a e educed- a e unemploymen bene i , he A bei slosengeld
II. Ano he example is he e o m o he public pension scheme in Ge many.
The in oduc ion o a sus ainabili y ac o aimed a educing he g ow h o
pensions and, simul aneously, he con ibu ions paid by younge , wo king peo
ple. Making a p ognosis abou how he consequences o such policies a ec
* Acknowledgemen s: I would like o hank he pa icipan s o he 5 h Eu opean Doc
o al Semina in Budapes , 2005, and o he 7 h In e na ional Ge man Socio-Economic
Panel Use Con e ence in Be lin, 2006, o hei help ul discussion and Johannes
Schwa ze o his c i ical commen s and con inuous suppo . I also hank Ul ich Meye
o he s imula ing discussion.
Schmolle s Jah buch 127 (2007) 1
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34 Ch is oph Wunde
he in e gene a ional edis ibu ion o income among he membe s o he a
mily equi es in o ma ion on he mo i es o p i a e ans e s, as well as on
he mode o ac ion o he ans e wi hin he amilial con ex . This a icle o
cuses on in a amilial ups eam ans e s om adul child en o hei elde ly
pa en s.
In he nex sec ion, we p o ide a sho e iew o he s anda d mic oeco
nomic model o p i a e ans e s ha dis inguishes be ween al uism and
exchange as he mo i e o he ans e . Fu he , he household p oduc ion
app oach is applied o he analysis o in a amilial ans e s. Sec ion 3 gi es
an o e iew o he da a and he mul ile el econome ic amewo k o he
analysis o social ela ions wi hin he amily. The es ima ion esul s a e dis
cussed in sec ion 4. Sec ion 5 concludes he pape .
2. P e e ences o Technology -
Wha De e mines In a amilial T ans e s?
Economis s analyzing in a amilial ela ionships cus oma ily dis inguish be
ween wo main mo i es o in e gene a ional inancial ans e s: al uism and
exchange. The undamen al cha ac e is ic o al uism wi hin he amily is ha
a pe son's well-being depends posi i ely on he well-being o he membe s o
his o he amily. Becke (1974) wo ked ou ha a edis ibu ion o income
(wi h o al amily income emaining cons an ) has no e ec on he consump
ion o he membe s o he amily as lang as he al uis ic bene ac o con inues
he ans e s. This esul , he edis ibu i e neu ali y p ope y, ollows om
he ac ha a educ ion in he al uis 's income induces an equal sized de
c ease in he in a amilial ans e s and ice e sa. l also has impo an impli
ca ions o social policymaking. Ba o (1974) showed, o example, ha
changes in he public pension scheme can lead o an adjus men in he pa em
o p i a e ans e s ha could ully o se he in e gene a ional edis ibu ion.
In con as o an uncondi ional al uis ic ans e , he gi e may also expec a
se ice in e um. Va ious a ian s o his exchange mo i e we e es ablished in
he li e a u e. Fo example, Pa k (2003) in e p e ed child- o-pa en s ans e s
as a e-paymen o an implici loan o human capi al in es men , S a k (1995)
pos ula ed a demons a ion e ec ,1 and Ko liko and Spi ak (1981) saw he
in a amilial ans e s as an exp ession o a isk-sha ing beha io among he
membe s o he amily.
The heo e ical app oaches ega ding al uis ic and exchange- ela ed mo
i es ha e in common he ac ha hey model he ans e decision as a u ili y
1 The idea behind he demons a ion e ec is ha he sandwich-gene a ion p o ides
ups eam ans e s o se an example o he own o sp ing ha is expec ed o adop his
beha io in he u u e.
Schmolle s Jah buch 127 (2007) 1
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ln a amilial Ups eam T ans e s and Household P oduc ion 35
maximiza ion p oblem. In his con ex , Cox (1987) se up a gene al amewo k
o he analysis o mo i es o p i a e income ans e s. The model allows
he iden i ica ion o he dominan mo i e o he ans e : i hypo hesizes ha ,
in he case o al uism, he ans e T inc eases when he al uis 's income
inc eases, and i dec eases when he bene icia y's income inc eases, i.e.,
äT
/
ÖyA > 0 and äT
/
Öyn < 0, whe e he index A deno es he al uis o , mo e
gene ally, he gi e and B is he bene icia y o ecipien . In he case o up
s eam ans e s, Ais he child and Bis he pa en . In addi- ion, he edis ibu
i e neu ali y p ope y mus be sa is ied (i.e., äT
/
Öyn -äT
/ ÖyA = -1 ). This
condi ion ega ding he de i a i es can be used o an empi ical es o
whe he he child is an e ec i e al uis .
In he case o an exchange mo i e, he model in e p e s ans e s as expen
di u es o in a amilial se ices. Hence, he o al ans e amoun is he p o
duc o he quan i y o se ice supplied and i s implici p ice. Two hypo heses
ega ding YA and YB can be de i ed. Fi s , an inc ease in he gi e 's income
leads o an inc ease in ans e s ( äT
/
ÖyA > 0). This esul is iden ical o he
one ob ained om assuming al uism. Second, he e ec o a change in he
ecipien 's income on he ans e amoun is no de e mined ( äT
/
Öyn � 0). This
ambiguous deduc ion is he essen ial di e ence o al uis ic beha io . The e
o e, he dis inguishing ea u e be ween al uism and exchange is ha an in
c ease in he ans e amoun due o an inc ease in he ecipien 's income, i.e.,
äT
/
Öyn > 0, is only compa ible wi h an exchange mo i e.
Finally, i has o be poin ed ou ha he implica ions o he analysis o he
ans e amoun a e no alid o he ans e decision. Cox (1987) showed ha
he p obabili y o a ans e occu ence inc eases wi h an inc ease in A's in
come and dec eases wi h an inc ease in B's income independen ly, whe he
he ans e decision is based on al uism o exchange. The e o e, an analysis
o he in e gene a ional ans e s will no each unambiguous conclusions i i
ocuses on he ans e decision only.
As he economic esea ch in he a ea o in a amilial ans e s la gely con
cen a es on he iden i ica ion o one domina ing mo i e, he combina ion o
di e en mo i es ega ding he ans e beha io has ha dly been conside ed
ye . Kohli and Kuenemund (2003) igh ly emphasized ha he ans e beha
io wi hin amilies is a mul idimensional, complex conglome a ion. Thus,
one has o be awa e ha he esul s ob ained om esea ch limi ed o he al u
ism-exchange con as can only p o ide limi ed conclusions.
This a icle applies he household p oduc ion app oach o he analysis o
in a amilial ans e s. This no el iewpoin enables esea ch o go beyond he
dual-mo i e amewo k o al uism and exchange and, he e o e, yields new
insigh s in o he mechanism by which ans e s ope a e. Hence, he cen al
poin o he analysis is no longe he mo i e o ans e s alone, bu includes
he household's echnology and he join consump ion o household commod-
Schmolle s Jah buch 127 (2007) 1
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36 Ch is oph Wunde
i ies.
2 The hea o he ma e o he household p oduc ion app oach is he no
ion ha households "combine ime and ma ke goods o p oduce mo e basic
commodi ies ha di ec ly en e hei u ili y unc ion" (Becke , 1965 p. 495).
Commodi ies a e "child en, p es ige and sel es eem, heal h, al uism, en y
and pleasu es o he senses" (Becke , 1998, p. 8).3 Becke (1965) de i ed ha ,
in he simple case o cons an e ums in p oducing he commodi y and gi en
p ices (including he wage a e), he household's esou ce cons ain can be
w i en as
(1) L(p;b; +w ;)Z; = +wH,
whe e p; and w a e p ice ec o s gi ing he uni p ices o he ma ke goods
and ime used in he p oduc ion o he household commodi y Z;, espec i ely.
b; and ; deno e ec o s gi ing he inpu o ma ke goods and ime pe uni o
Z;, espec i ely. Cons an e ums o scale imply ha b; and ; a e ixed alues.
Thus, he exp ession wi hin b acke s can be in e p e ed as he ull p ice o one
uni o Z;. The uni p ice mul iplied by he amoun o he commodi y yields
he o al cos o Z;. The igh -hand side o equa ion 1 deno es he maximum
money income: V is nonwo king income and wH ep esen s he eamings i all
he ime we e composed o wo king ime.
The household p oduc ion app oach allows he analysis o in a a nilial
ans e s om he iewpoin o ei he he ecipien o he gi e . Fo he ecipi
en , he in a amilial ans e p o ides addi ional mone a y income and, conse
quen ly, elaxes his o he budge cons ain . Two aspec s a e no ewo hy:
Fi s , i he ans e is uncondi ional, i will be in e p e ed as ano he sou ce o
money income and, hence, en e s he igh -hand side o equa ion 1. Al uis ic
ans e s a e an example. Second, he ans e may also be gi en on he condi
ion ha i mus be used o a speci ied pu pose. This issue can be illus a ed
in he con ex o ups eam ans e s as ollows: elde ly pa en s may ecei e
inancial suppo om hei child en ha mus be used in he p oduc ion o ,
say, unc ionali y, e.g., he ans e could be in e p e ed as a p ice sub en ion
o a speci ic heal h good o se ice. In his case, he ans e has o be consid-
2 The issue o join consump ion is no add essed in his pape .
3 Se ing up an explici p oduc ion unc ion o al uism, Becke (1998) d ew an im
p ecise pic u e o al uism. On he one hand, al uism is -as indica ed by he quo a ion
abo e -in e p e ed as a commodi y. On he o he hand, Becke a gued ha al uism is a
ype o mo i a ion ha changes beha io . In he la e con ex , al uism is a p ope y o
he u ili y unc ion because om his poin o iew al uis ic "means ha [a pe son's]
u ili y unc ion depends posi i ely on he well-being o [ano he pe son]" (p. 173).
Combining bo h a gumen s -al uism as a commodi y ha can be p oduced acco ding
o he household p oduc ion unc ion and as a p ope y o he u ili y unc ion -leads o
he conclusion ha p e e ences a e no cons an , bu can be al e ed by he household
p oduc ion. Howe e , Becke ea ed al uis ic beha io as a cons an in emal ype o
mo i a ion when analyzing al uism in he amily.
Schmolle s Jah buch 127 (2007) 1
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ln a amilial Ups eam T ans e s and Household P oduc ion 37
e ed on he le -hand side o equa ion 1. The p ice o he ma ke good used in
he household p oduc ion is educed by he ans e pe uni o he subsidized
ac o inpu .
The household p oduc ion app oach is also applicable o he analysis o he
gi e 's si ua ion. The ollowing example explains his issue. When b inging
up child en, he sandwich-gene a ion pa en s ha e o decide whe he o in es
hei own ime o o subs i u e an in a a nilial se ice ("babysi ing"), e.g.,
p o ided by g andpa en s. In his case, he in a a nilial ans e s nigh be e
ga ded as expendi u es o he se ice. The e o e, he c ucial ques ion in his
example is: unde wha ci cums ances do he pa en s ou sou ce he o sp ing's
upb inging? The answe can be deduced om s anda d cos nini niza ion: he
ans e -se ice egime occu s (o is ex ended) when he a io o he ma ginal
p oduc i i y o he se ice and he ma ginal p oduc i i y o he sandwich-gen
e a ion's ime is g ea e han he a io o he p ice o he se ice and he wage
a e. The e o e, a low ma ginal p oduc i i y o ime is accompanied by a en
dency o make use o he se ice, whe eas households wi h a high ma ginal
p oduc i i y end owa ds he use o hei own ime.
l becomes clea ha he undamen al poin o he decision whe he and o
wha ex en o use in a a nilial se ices o own ime, i.e., he decision on he
use o ac o inpu s, is he echnology o he household p oduc ion. Di e 
ences in he p oduc i i y be ween wo households e lec he di e en echnol
ogies. We hypo hesize ha no ms a e one o he main de e minan s o echnol
ogy in he amilial con ex . In his con ex , he cul u al backg ound o he
membe s o he a nily ep esen s a e y in luen ial sou ce o he household's
echnology. Fo example, eligious no ms play a decisi e ole: he Ca holic
Chu ch ega ds ma imony as a equi emen o he upb inging o child en.
The educa ion o he o sp ing should be o ien ed owa ds eligious alues as
well. Addi ionally, eligious sec s o en p oclaim a adi ional ole beha io .
The e o e, a amily in luenced by eligious no ms may es ima e he p oduc i 
i y o one uni o own ime spe on b inging up child en a a ela i ely la ge
alue han he p oduc i i y o one uni o in a amilial se ice.4 As a conse
quence, we conclude ha eligious a nilies may ha e a highe p opensi y o
b ing up child en on hei own, a he han making use o in a a nilial se 
ices, and, hence, ans e paymen s a e less likely.
The pape p oceeds wi h empi ical es s o he hypo heses de i ed om he
u ili y maxi niza ion amewo k ega ding he mo i es o he ans e . The
es ima ion esul s a e in e p e ed aking he e lec ions on he household p o
duc ion in o accoun .
4 A u he aspec is ha social cos s may e ol e and al e he ac o p ices. Fo
example, aking up a p o essional ca ee , a Ca holic mo he has o bea social cos s
because o he disapp o al o he membe s o he pa ish o a nily. This issue can be
conside ed on he le -hand side o equa ion 1.
Schmolle s Jah buch 127 (2007) 1
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38 Ch is oph Wunde
3. Da a and Es ima ion S a egies
This pape uses da a om he Ge man Socio-Economic Panel S udy (SOEP)
o he yea s 1996 o 2004. The SOEP is a longi udinal da ase ha con ains
in o ma ion on all household membe s (c . Haisken-DeNew and F ick, 2005).
The da a co e a wide ange o opics ha a e o in e es o he analysis o
ups eam in e gene a ional ans e s, e.g., in o ma ion abou child en's and
pa en s' socioeconomic cha ac e is ics and household composi ion. A majo
ad an age o he SOEP is ha people a e included in he panel e en when hey
ha e mo ed ou o he o iginal household. The e o e, i is possible o c ea e a
da ase wi h ma ched child-pa en s pai s when he child has g own up and
o med a household o his o he own.
Despi e he ad an ages o he SOEP, he e is also a se ious sho coming ha
makes an in es iga ion o in a amilial ans e s a challenging ask. The di i
cul y a ises om he impossibili y o di ec ly linking he ans e s gi en o he
ans e s ecei ed. The eason i is no possible o build a di ec linkage be
ween he dono and he ecipien is ha he wo ques ions in he ques ionnai e
ega ding incoming and ou going in a amilial paymen s ha e di e en o mu
la ions. The ans e s ecei ed om people li ing ou side he household a e
eco ded as pa o he income ques ion "[ ... ] please s a e wha sou ces o
income you ecei ed in he pas calenda yea " whe e one answe ca ego y is
"[o] he ypes o inancial assis ance om pe sons who do no li e in he
household". In con as , he ques ion ega ding mone a y ans e s gi en o
pa en s in he ques ionnai e is: "Ha e you pe sonally gi en paymen s o sup
po du ing he las yea [ ... ] o ela i es o o he pe sons ou side o you
household" (In a es Sozial o schung, 2004 ). The answe ca ego ies include
he o al amoun pe yea ha is ans e ed "[ ]o pa en s/s ep pa en s".
5 The
analysis o in a amilial ans e s and u iliza ion o he SOEP would be im
p o ed conside ably i he ques ionnai e bad a consis en design ega ding he
incoming and ou going ans e s.
E en a e pooling nine panel wa es, he o al numbe o ans e s epo ed
is ela i ely small. The p opo ion o child en p o iding inancial suppo o
hei pa en s is abou 2 % pe yea . The a e age ans e amoun gi en is o
hose who gi e be ween 1600 and 2100 eu os pe yea (in cons an 2000
p ices).
An impo an indi idual cha ac e is ic o he in es iga ion is he child en's
eligious a ilia ions. Un o una ely, his in o ma ion is only a ailable o
s l mus be poin ed ou ha he e is a ansla ion e o in he ques ionnai e. The
English e sion indi idual ques ionnai e asks o paymen s o suppo gi en o "s ep
pa en s" bu he Ge man e sion asks o ans e s gi en o "Schwiege el e n", which
means pa en s-in-law. As he esponden s a e usually con on ed wi h he Ge man e 
sion o he ques ionnai e, his ansla ion e o has no consequences o his s udy.
Schmolle s Jah buch 127 (2007) 1
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ln a amilial Ups eam T ans e s and Household P oduc ion 39
1997 and 2003. The e o e, he missing alues o he emaining yea s ha e
been eplaced, i.e., he eligious a ilia ion om 1997 was assigned o he yea
1996 and he in o ma ion on 2003 was subs i u ed o he missing alues om
1998 o 2004. Such a p ocedu e is s aigh o wa d, because a pe son's eli
gious a ilia ion is one o he mo e cons an cha ac e is ics and i does no
change o mos people du ing hei whole li e.
The da a ega ding he in a amilial child- o-pa en s ans e s ha e a hie 
a chical s uc u e. The longi udinal da a p o ide epea ed ans e obse a ions
on indi iduals, i.e., hese obse a ions o e ime a e nes ed wi hin child en. In
addi ion, child en a e nes ed in highe le el clus e s when se e al siblings be
long o he same o iginal household. The s a is ical analysis o hie a chically
s uc u ed da a equi es an econome ic model speci ica ion ha allows o
clus e ing a di e en le els. The necessi y o a special es ima ion app oach
a ises om he ac ha he dis inguishing ea u es o he clus e s a e only
obse able o a ce ain ex en and, as a consequence, he e is clus e -speci ic
unobse ed he e ogenei y, which esul s in dependence be ween uni s in he
same dus e . Consequen ly, he e is co ela ion be ween he epea ed ans e
obse a ions pe child and be ween di e en child en wi hin he same amily.
The wi hin- amily co ela ion a ises because siblings who ha e g own up in
he same o iginal household sha e he same a nily backg ound and hey may
show simila beha io and ha e analogous a i udes conside ing in a a nilial
mone a y ans e s. Winkelmann (2005) ga e a u he example when he ap
plied an o de ed p obi model wi h in a a nily co ela ion o an analysis o he
subjec i e well-being o he membe s o he amily. I he clus e ing is ig
no ed, he a iance o he es ima ed pa ame e s may be biased and one may
d aw mis aken conclusions ega ding he s a is ical signi icance le el. In addi
ion, Rod iguez and Goldman (2001) demons a ed ha igno ing he unob
se ed e ec s can lead o a subs an ial bias in he es ima ed coe icien s when
he ela ionship be ween he obse ed esponse and he unde lying la en a i
able is nonlinea , which is he case in he analysis o he ans e decision
whe e only a bina y ou come is obse ed.
An econome ic model wi h andom e ec s a he household and indi idual
le el is applied o an analysis o he ans e decision by ex ending he s an
da d logis ic eg ession amewo k o a mul ile el model. Gibbons and He
deke (1997) and Sk ondal and Rabe-Heske h (2004) p o ided o e iews o
he applica ion o models wi h a nes ed e o componen s uc u e. Combining
he longi udinal da a and he a nily clus e s, he esul ing h ee-le el model
can be w i en o he i- h child in a nily h a ime as
(2)
whe e x�i and z' h a e he child's and he pa en s' obse ed cha ac e is ics,
espec i ely, ß and y ep esen he co esponding coe icien ec o s o in e -
Schmolle s Jah buch 127 (2007) 1
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40 Ch is oph Wunde
es , and ßo is an o e all cons an e m. The andmn e ec s a he household
and child le el a e deno ed µh and h;, espec i ely. The o me cap u es he
ime-in a ian household speci ic e ec , and he la e con ols o a ime-in
a ian indi idual-speci ic e ec . Bo h a e assumed o be andom and no 
mally dis ibu ed wi h mean ze o and cons an a iances, a! and a;. :hi is he
idiosync a ic e o e m on he hi d le el. The le -hand side a iable i,;1 e
p esen s an unobse able la en a iable, which is ela ed o he obse ed bin
a y esponse hi h ough a h eshold concep . The obse ed esponse hi indi
ca es whe he he i- h child in amily h makes a ans e a ime . Unde he
assump ions s a ed abo e, he ma ginal likelihood depends only on he ixed
e ec s, ß and y, and he a iances o he andom in e cep s, a; and a!.
One can calcula e he ma ginal p obabili y by in eg a ing ou he andom
in e cep s, which is easible by making use o he assump ion o he condi
ional independence among he ans e occu ences gi en he amily- and he
child-speci ic unobse ed e ec s. The pa ame e s a e es ima ed by i s -o de
ma ginal quasi-likelihood and es ic ed i e a i e gene alized leas squa es
using he so wa e package MLwiN. The econome ic model o he ans e
amoun is es ima ed using x mixed, which is pa o he s a is ical so wa e
S a a ( e sion nine). The s a ing poin o he econome ic model is equi alen
o he app oach in equa ion 2 apa om he ac ha he ans e amoun is
subs i u ed o he la en ans e p opensi y.
4. Es ima ion Resul s
The es ima es o he coe icien s o he child's and he pa en s' income in
he ans e decision eg ession exhibi a posi i e and nega i e sign, espec
i ely. Al hough he mo i e unde lying he ans e canno be iden i ied, he
heo e ical hypo heses a e clea ly con i med by hese highly s a is ically sig
ni ican es ima ion esul s. Fo bo h al uism and exchange, he heo e ical
model p edic s a posi i e co ela ion be ween he ans e p obabili y and he
child's income, on he one hand, and a nega i e co ela ion be ween he ans
e p obabili y and he pa en s' income, on he o he hand.
The coe icien es ima ed o he child's income in he ans e amoun e
g ession is s a is ically signi ican and posi i e. Also, his inding is in line
wi h he heo e ical amewo k, bu i does no p o ide in o ma ion abou he
unde lying ans e mo i e. The heo y p edic s an inc ease in he ans e
amoun o bo h al uism and exchange when he child's income ises. The
mos in o ma i e esul is, howe e , ha he pa en s' income has a posi i e
e ec on he ans e amoun , i.e., an inc ease in he pa en s' income leads o
an inc ease in he ans e amoun . As men ioned abo e, he e ec o a change
in he pa en s' income on he ans e amoun is he essen ial indica o o dis
inguish be ween an al uis ic and an exchange mo i e. Al uism unambigu-
Schmolle s Jah buch 127 (2007) 1
OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/
DOI h ps://doi.o g/10.3790/schm.127.1.33 | Gene a ed on 2023-04-04 12:37:50