The housing channel of intergenerational wealth persistence

Wold, Ella Ge z; Aas ei , Knu A e; B andsaas, Ei ik Eylands; Juels ud, Ragna
Enge ; Na ik, Gisle James
Wo king Pape
The housing channel o in e gene a ional weal h
pe sis ence
Wo king Pape , No. 16/2023
P o ided in Coope a ion wi h:
No ges Bank, Oslo
Sugges ed Ci a ion: Wold, Ella Ge z; Aas ei , Knu A e; B andsaas, Ei ik Eylands; Juels ud, Ragna
Enge ; Na ik, Gisle James (2024) : The housing channel o in e gene a ional weal h pe sis ence,
Wo king Pape , No. 16/2023, ISBN 978-82-8379-306-2, No ges Bank, Oslo,
h ps://hdl.handle.ne /11250/3166797
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Wo king Pape
The housing channel o in e gene a ional weal h pe sis ence
No ges Bank Resea ch
Au ho s:
Ella Ge z Wold
Knu A e Aas ei
Ei ik Eylands B andsaas
Ragna Enge Juels ud
Gisle James Na ik
Keywo ds:
Housing ma ke , in e gene a ional
weal h, weal h inequali y
16 | 2023
No ges Bank Wo king Pape 1
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ISSN 1502-8143 (online)
ISBN 978-82-8379-306-2 (online)
The housing channel o in e gene a ional weal h pe sis ence∗
Ella Ge z Wold†Knu A e Aas ei ‡Ei ik Eylands B andsaas§
Ragna Enge Juels ud¶Gisle James Na ik‖
Decembe 2023
Abs ac
We use No wegian ax da a and a li e-cycle model wi h housing o s udy how weal h
ansmi s ac oss gene a ions h ough he housing ma ke . A e con olling o a ich
se o a ibu es, households wi h iche pa en s a e nea ly 15% mo e likely o be
homeowne s a age 30. Mo eo e , when en e ing, hey ha e highe le e age and buy
homes wo h 15% mo e. Es ima es using in e na ional s ock ma ke e u ns as a shi -
sha e ins umen suppo a causal in e p e a ion. We u he documen ha housing
ou comes when young a e impo an de e minan s o midli e weal h. This holds also
when using plausibly exogenous a ia ion in homeowne ship caused by he iming o
in a- amily dea hs. As a esul , housing gaps caused pu ely by pa en al weal h ex-
plain 12% o in e gene a ional weal h pe sis ence, making housing equally impo an
as he combined impac o a wide ange o household cha ac e is ics including income
and educa ion. We explo e new mechanisms o pa en al suppo , such as in a- amily
housing ansac ions below ma ke alue. Th ough he lens o ou model, house p ice
expec a ions s and ou as a key d i e o he magni ude o he housing channel o in-
e gene a ional weal h pe sis ence.
Keywo ds: Housing ma ke , in e gene a ional weal h, weal h inequali y
JEL Codes: D31, E24, G51, R21
∗This pape should no be epo ed as ep esen ing he iews o No ges Bank o he Fede al Rese e
Sys em. The iews exp essed a e hose o he au ho s and do no necessa ily e lec hose o No ges Bank
o he Fede al Rese e Sys em. We g a e ully hank Ma eo Benne on, Alessand a Fogli, La s Lochs oe ,
E ling Røed La sen, Ni zan Tzul-Ilan and an anonymous e e ee o he No ges Bank Wo king Pape Se ies o
insigh ul commen s, as well as pa icipan s a he BI No wegian Business School, he 2023 CEBRA Annual
Mee ing a Columbia Uni e si y, he 14 h No dic Con e ence on Regis e Da a and Economic Modelling,
No ges Bank, he No wegian School o Economics, he No wegian Uni e si y o Science and Technology,
S a is ics No way, he UCLA/SF Fed Con e ence on Housing, Financial Ma ke s and Mone a y Policy, he
Uni e si y o S . Gallen wo kshop on Mac oeconomic implica ions o housing, household inances, and weal h
dynamics, he 3D-In-Mac o Wo kshop, he 12 h Eu opean and 17 h No h Ame ican Mee ings o he U ban
Economics Associa ion.
†BI No wegian Business School. Email: ella.g.w[email p o ec ed]
‡No ges Bank and BI No wegian Business School. Email: kn[email p o ec ed]
§Boa d o Go e no s o he Fede al Rese e Sys em. Email: [email p o ec ed]
¶No ges Bank. Email: [email p o ec ed]
‖No ges Bank and BI No wegian Business School. Email: [email p o ec ed]
1 In oduc ion
Many pa en s con inue o inancially suppo hei child en as hey en e adul hood – ei he
indi ec ly o di ec ly. The housing ma ke s ands ou as especially a ac i e o pa en al
suppo as i) ba ie s o en y make pa en al suppo key o ea ly homeowne ship, and
ii) high le e age in housing in es men s ampli ies e u ns o equi y. Mo e han 40% o
homeowne s in he Uni ed S a es epo ecei ing inancial suppo om pa en s in o de
o buy a home. The same holds in No way, he se ing o ou s udy.1In his pape we
i s s udy how pa en al weal h a ec s child housing ou comes, and second, o wha ex en
hese housing ou comes inc ease la e -in-li e weal h. Toge he , hese wo e ec s pin down
he housing channel o in e gene a ional weal h pe sis ence.
To illus a e how impo an housing can be o weal h accumula ion, conside a nume ical
example using he ac ual e olu ion o asse p ices. Imagine in es ing $100 in s ocks o he
No wegian housing ma ke in he ea ly 1990s. C ucially, and in line wi h he da a, he hous-
ing in es men is ini ially le e ed a 0.9, whe eas he s ock pu chase is no . Twen y- i e yea s
la e , he $100 has g own o $6,000 in he housing ma ke , compa ed o $4,600 in he s ock
ma ke (wi h he equi alen o mo gage paymen s e-in es ed each yea ).2In his simple
example, he owne s ays in he home h oughou and pays down he mo gage uni o mly,
yielding an a e age le e age o only 0.26 o e he 25 yea s o ou hough expe imen . I he
household ins ead e-in es s in mo e expensi e housing o e ime, as young people ypically
do, he housing e u n will be subs an ially highe .
The high e u n on equi y in he housing ma ke applies o e e yone – i espec i e o
pa en weal h. S ill, subs an ial ba ie s o en y means ha housing can be impo an o
in e gene a ional weal h pe sis ence. Fi s , housing is gene ally indi isible. Second, buying
o selling a home en ails sizable ansac ion cos s. Thi d, and pe haps mos impo an ly,
lende s apply bo owing cons ain s, such as loan- o- alue and deb - o-income caps. F ic-
ions hus p e en many young households om accessing he ela i ely high e u ns ha
he housing ma ke p o ides. This c ea es a na u al ole o a luen pa en s o suppo
hei o sp ing in he housing ma ke , by accele a ing en y and acili a ing highe home
in es men s ela i e o income. As ou nume ical example illus a es, he consequences o
la e -in-li e weal h can be la ge.
In his pape , we use No wegian ax da a me ged wi h housing ansac ions da a om
1These numbe s a e based on an online su ey we pe o med on homeowne s below he age o 50 using
he pla o m Su ey Monkey, see Appendix Figu e A.1. The sha e is simila o ha in o he su eys.
2Speci ically, we assume an addi ional amoun equal o he deb se icing cos s o he mo gage is
e-in es ed each yea when calcula ing he e u n on he s ock in es men . Fo de ailed calcula ions, see
Appendix B.
1

he Land Regis y o s udy he impo ance o pa en al weal h o housing ma ke ou comes
and he eby midli e weal h. To complemen he adminis a i e da a we also pe o m su eys
in No way and he US on inancial suppo om pa en s o child. To be e unde s and
why pa en al weal h ma e s, we documen se e al mechanism and assess hei quan i a i e
impo ance. The ea e , we build a li e-cycle model wi h housing ha i s he empi ical
pa e ns and use i o assess he impo ance o house p ice g ow h and mo gage egula ion
o he magni ude o he housing channel o in e gene a ional weal h pe sis ence.
We i s documen la ge gaps in housing ou comes by pa en al weal h. Ou baseline
weal h measu e is simply an indica o o whe he wi hin-coho pa en al weal h is in he
uppe hal o he weal h dis ibu ion, al hough we also conside pe cen ile weal h anks o
obus ness. We show ha households wi h iche pa en s a e 15 pe cen age poin s (≈30%)
mo e likely o be homeowne s a age 30. Condi ional on en e ing he housing ma ke , hey
buy homes ha a e wo h $60 000 (≈30%) mo e and a e eigh pe cen age poin s (≈10%) mo e
le e aged. We e e o hese di e ences as “housing gaps”. The documen ed housing gaps
se e as ou s a ing poin o making ou dis inc con ibu ions o he exis ing li e a u e.
Ou i s con ibu ion is o documen he impac o pa en weal h on housing ou -
comes, using a s uc u al media ion analysis (a s a is ical decomposi ion) and a shi -sha e
ins umen o pa en al weal h. We decompose he housing gaps in o h ee componen s o
media o s: pu e pa en al weal h,o he pa en al a ibu es and household a ibu es. This is
use ul, as i allows us o de e mine no only he ela i e impo ance o di e en a ibu es
and how i has e ol ed o e ime, bu also de e mine why ce ain a ibu es a e impo an .
Speci ically, an a ibu e can be impo an i he e is a la ge gap in his a ibu e o because
i has a la ge impac on housing ou comes.
Ou media ion analysis a ibu es nea ly hal o he obse ed gaps in homeowne ship
and pu chase p ice o pa en al weal h, and he o he hal o household a ibu es. Fo
le e age howe e , pa en al weal h alone explains he en i e gap. O he pa en al a ibu es
ha e modes impo ance. This means ha e en a e accoun ing o a wide se o pa en al
and household cha ac e is ics, we s ill ind ha households wi h iche pa en s a e nea ly
15% mo e likely o be homeowne s a age 30. Mo eo e , condi ional on en e ing, hey buy
homes ha a e wo h 15% mo e and a e nea ly 10% mo e le e ed.
I unobse able a iables co ela ed wi h pa en al weal h ha e di ec impac s on housing
ou comes, his could bias ou esul s. We he e o e exploi plausibly exogenous a ia ion in
pa en weal h esul ing om in e na ional s ock ma ke e u ns in e ac ed wi h lagged s ock
ma ke exposu e in a shi -sha e analysis. The es ima ed impac o pa en al weal h on en y
p obabili ies aligns quan i a i ely wi h he pu e pa en al weal h componen iden i ied in he
media ion analysis, suppo ing a causal in e p e a ion o ou indings.
2
Ou second con ibu ion is o documen he impac o housing ou comes on in e gen-
e a ional weal h pe sis ence, again using a s uc u al media ion analysis and an ins umen al
a iable app oach based on he iming o in a- amily dea hs. We decompose he weal h pe -
sis ence in o a pu e pa en al weal h channel, an o he pa en al a ibu es channel, a household
a ibu es channel, and a housing channel.
Fo he housing channel o be impo an , wo condi ions mus be sa is ied. Fi s , housing
ou comes mus be highly co ela ed wi h pa en al weal h (ou i s con ibu ion). Second,
housing ou comes mus ha e a subs an ial impac on weal h accumula ion. We ind ha
households wi h iche pa en s a e 15 pe cen age poin s (=35%) mo e likely o hemsel es be
weal hy a midli e. Mo e han 1/4 o his in e gene a ional weal h pe sis ence is accoun ed
o by ea lie homeowne ship o households wi h iche pa en s. O he homeowne ship
e ec , oughly hal is due solely o he impac o pa en al weal h on housing. This impac is
la ge, equal in size o he combined e ec o pa en al weal h on household income, educa ion,
loca ion and numbe o household membe s.
I unobse able a iables co ela ed wi h housing ou comes ha e di ec impac s on midli e
weal h, his could bias ou esul s. We he e o e exploi plausibly exogenous a ia ion in he
iming o housing ma ke en y caused by he iming o in a- amily dea hs. The es ima ed
impac o en y age aligns quan i a i ely wi h he media ion analysis, suppo ing a causal
in e p e a ion o ou indings.
Ou hi d con ibu ion is o unco e h ough which mechanisms pa en al weal h a -
ec s housing ou comes. We conside a no el channel e e ed o as in a- amily sales. Riche
pa en s a e 60% mo e likely o co-pu chase a house wi h a child, and nea ly 10% mo e likely
o sell a house di ec ly o a child. Homes sold by pa en s o hei o sp ing ha e an es ima ed
p ice discoun o 25%. Mo eo e , as p e iously es ablished o o he coun ies, e.g. Guiso
and Jappelli (2002), we ind e idence suppo i e o di ec weal h ans e s. Finally, ollowing
Bene on e al. (2022), we show ha pa en al equi y ex ac ion is posi i ely co ela ed wi h
en y in he housing ma ke . We ex end hei esul s and documen ha he impo ance o
his channel a ies wi h pa en al weal h – also when condi ioning on homeowne ship. To
quan i y he impo ance o he mechanisms conside ed, we pe o m back-o - he-en elope cal-
cula ions based on i) he sha e o pa en s who engage in each mechanism, and ii) he impac
on child en’s en y p obabili ies. We ind ha he mechanisms discussed can explain mo e
han hal o he impac o pa en al weal h on o sp ings’ housing ou comes.
Ou ou h con ibu ion is o use a s anda d li e-cycle model wi h housing and ex-
ogenous pa en al weal h o i) show ha ou empi ical indings can be eco e ed unde a
s anda d calib a ion and ii) assess coun e ac ual scena ios. We model pa en al suppo as
a inancial ans e in ea ly adul hood, and pick he ans e size in he model o ma ch
3
he empi ical magni ude o he housing channel o in e gene a ional weal h pe sis ence (con-
ibu ion 2), which esul s in plausible ans e magni udes. Ha ing shown ha a s anda d
model augmen ed o include exogenous pa en al weal h can eplica e he empi ical es ima es,
we mo e on o a coun e ac ual analysis in which we change (expec ed) house p ices and
mo gage ma ke egula ion. This is in e es ing o a leas wo easons. Fi s , policy mak-
e s ha e a numbe o ools hey can use o in luence hese ac o s. Second, hese ac o s
a y subs an ially ac oss bo h ime and space, making hem impo an o hinking abou
ex e nal alidi y and wha we can expec o he housing channel o in e gene a ional weal h
pe sis ence mo ing o wa d.
Ou model indings sugges ha while ealized house p ice g ow h has a modes impac
on he housing channel, expec ed house p ice g ow h has a subs an ial impac . Lowe ing
house p ice expec a ions and allowing households o adjus hei po olios and le e age in
esponse o hese expec a ions subs an ially educes he housing channel o in e gene a ional
weal h pe sis ence. This is d i en by a la ge educ ion in he impac o pa en suppo on
homeowne ship, as homeowne ship – especially a ea ly ages – becomes less a ac i e. As
a second coun e ac ual scena io, we use he model o e alua e how he housing channel o
in e gene a ional weal h pe sis ence depends on mo gage egula ion. Tigh e mo gage eg-
ula ion, especially s ic e loan- o- alue limi s, inc eases he impo ance o pa en al suppo ,
he eby s eng hening he housing channel o in e gene a ional weal h pe sis ence.
Rela ed li e a u e
Ou pape lies a he in e sec ion o h ee dis inc li e a u es, which s udy i) he pe sis ence o
weal h ac oss gene a ions, ii) he impo ance o pa en s o child housing ma ke ou comes,
and iii) he ele ance o housing ou comes o la e -in-li e weal h. In his pape , we lean
on he combined insigh s o hese h ee li e a u es, and o e he i s decomposi ion and
quan i ica ion o he housing channel o in e gene a ional weal h pe sis ence.
Fi s , se e al s udies ha e documen ed ha weal hy pa en s end o ha e weal hy chil-
d en. See o ins ance Chi eji and S a o d (1999), Cha les and Hu s (2003), Bose up e al.
(2016), Black e al. (2017), Ade mon e al. (2018) and Fage eng e al. (2021). We con ibu e
by ocusing on he housing ma ke as a key d i e o weal h pe sis ence ac oss gene a ions.
Because he housing ma ke is hea ily egula ed, policy make s ha e ample oom o a ec
in e gene a ional weal h pe sis ence wo king hough housing.
Second, a numbe o pape s ha e shown ha pa en s ma e o child en’s housing ma -
ke ou comes. Mos o hese s udies – including Engelha d and Maye (1998), Guiso and
Jappelli (2002), Luea (2008), Kolodziejczyk and Le h-Pe e sen (2013), Blickle and B own
4
(2019), B andsaas (2021) and Boileau and S u ock (2023) – ocus on he impac o pa en al
ans e s on housing ma ke en y. Rela edly, Bene on e al. (2022) s udy he impo ance
o pa en al home equi y ex ac ion. Hal o sen and Lindquis (2017), Lee e al. (2020) and
Bond and E iksen (2021) documen a posi i e co ela ion be ween pa en al weal h and en y
in o he housing ma ke , while Daysal e al. (2023) show ha inc eases o pa en al housing
weal h passes h ough o child housing weal h. We con ibu e by aking a b oade app oach,
ocusing no only on pa en al ans e s o one single mechanism, bu on he causal in luence
o pa en al weal h in gene al. This is c ucial, as i allows us o quan i y how impo an
housing is o in e gene a ional weal h pe sis ence. We also documen no el mechanisms,
and assess he quan i a i e impo ance o each mechanism.
Finally, he e exis s a somewha smalle li e a u e es ablishing he impo ance o hous-
ing and mo gage decisions o weal h accumula ion o e he li e cycle. Using No wegian
da a, Eggum and La sen (2023) show ha capi al gains on housing a e impo an o weal h
inequali y. Di e al. (2007) and Tu ne and Luea (2009) show ha homeowne ship s a us is
impo an o weal h accumula ion using PSID da a, while Bach e al. (2020) use Swedish
ax da a and ind ha housing and mo gage choices aken while young a e key de e mi-
nan s o households’ posi ion in he weal h dis ibu ion a e i emen . Rela edly, Be ns ein
and Koudijs (2020) documen he “c i ical impo ance” o mo gage decisions o household
weal h building. We con ibu e by using plausibly exogenous a ia ion in age o en y caused
by he iming o in a- amily dea hs o quan i y he impac o en y age on midli e weal h,
and by isola ing he impac which is wo king h ough pa en weal h.
2 Da a
In his sec ion we p esen he egis e da a which is he basis o ou empi ical analysis and
wo online su eys we conduc ed o complemen he egis e da a.
2.1 Regis e da a
We use No wegian adminis a i e da a om S a is ics No way, me ged wi h housing ansac-
ion da a om he Land Regis y. The o me p o ides household balance shee in o ma ion
and allows us o link pa en s and child en. The la e gi es us accu a e in o ma ion on
housing ansac ions and allows us o ollow he owne ship o speci ic houses o e ime. In
his sec ion we discuss sample selec ion and he measu emen o key a iables, and p o ide
some summa y s a is ics o special in e es .
5
The homeowne ship gap a age 30 is decomposed acco ding o equa ion (2). The house-
hold a ibu e componen is ma ked in ed in Figu e 1a, and accoun s o oughly hal o
he homeowne ship gap on a e age. Tha is, he ac ha households wi h iche pa en s
ha e o he obse able cha ac e is ics han hose wi h poo e pa en s can accoun o hal o
hei ex a owne ship a es. Among hese a ibu es, household income is by a he mos
impo an cha ac e is ic, ollowed by he numbe o household membe s and educa ion, as
shown in Appendix Figu e A.5. The o al impo ance o household a ibu es has inc eased
o e ime.
O he pa en al a ibu es – educa ion, income, loca ion and numbe o child en – a e
less impo an in explaining owne ship gaps, as cap u ed by he g ay a ea. The sha e o
his componen has emained small and s able h oughou he sample pe iod. Finally, he
pu e pa en al weal h componen is cap u ed by he blue a ea in Figu e 1a and accoun s o
oughly hal he owne ship gap on a e age. This implies ha , e en a e con olling o a
la ge se o household and pa en cha ac e is ics, households wi h iche pa en s a e nea ly
15% mo e likely o be homeowne s a age 30. The size o he pu e pa en al weal h componen
has emained qui e s able o e ime.
.45 .5 .55 .6 .65 .7
Homeowne ship 30
2005 2007 2009 2011 2013 2015 2017
Low PW (PW20=0) High PW (PW20=1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(a) Homeowne ship a age 30
100000 150000 200000 250000 300000
House p ice upon en y (USD)
2005 2007 2009 2011 2013 2015 2017
Low PW (PW20=0) High PW (PW20=1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(b) Pu chase p ice upon en y ($)
75 80 85 90 95
Le e age upon en y (%)
2005 2007 2009 2011 2013 2015 2017
Low PW (PW20=0) High PW (PW20=1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(c) Le e age upon en y (%)
Figu e 1: Housing ou comes by pa en al weal h
No es: The housing ou come gaps a e decomposed in o h ee obse able componen s, pu e pa en al weal h,
pa en al a ibu es and households a ibu es, in acco dance wi h equa ion (2). hiis (a) homeowne ship
a e a 30, (b) he pu chase p ice upon en y, o (c) he compu ed le e age upon en y. pw20
i= 1 i a e age
pa en al inancial weal h when he household is aged 19-21 is abo e he yea -speci ic median, po
iis pa en
income, educa ion, loca ion and numbe o child en, xiis hh income, inancial weal h, educa ion, loca ion
and numbe o adul household membe s.
As a obus ness exe cise, we add wo-yea u u e income g ow h and he isky asse sha e
o pa en s and o sp ing as addi ional con ol a iables in Appendix Figu e A.6a. This
sho ens he sample by wo yea s and inc eases he impo ance o o he pa en al a ibu es
12

sligh ly. O he wise he esul s a e la gely unchanged. We also epo esul s when pa en
weal h is cap u ed by con empo aneous pa en weal h in Appendix Figu e A.7a. Bo h he
o al homeowne ship gap and he pu e pa en al weal h componen become sligh ly la ge ,
bu he main imp ession emains unchanged.
Housing ou come II: House pu chase p ice We nex conside he associa ion be ween
pa en al weal h and he house pu chase p ice upon en y, which is obse ed only o hose
households who en e he housing ma ke . Figu e 1b depic s he pu chase p ice upon en y
in eal USD by pa en al weal h.8By he end o ou sample pe iod, households wi h iche
pa en s buy homes wo h app oxima ely $60,000 (≈30%) mo e when en e ing he housing
ma ke . The pu chase p ice gap has oughly doubled in absolu e e ms o e he ime pe iod,
and has inc eased also in pe cen age e ms. By he end o ou sample, he household a -
ibu es componen can explain abou 40% o he pu chase p ice gap. The mos impo an
household cha ac e is ic is he numbe o household membe s, which is highe o hose wi h
pa en s in he uppe hal o he weal h dis ibu ion. As be o e, also income and educa ion
a e impo an household a ibu es.
O he pa en al a ibu es a e somewha mo e impo an in explaining di e ences in pu -
chase p ices han di e ences in homeowne ship a es. S ill, he o he pa en al a ibu es
componen is modes in size. This lea es a subs an ial ole o he pu e pa en al weal h
componen , which accoun s o 50% o he obse ed di e ence in pu chase p ices be ween
households wi h abo e e sus below median weal hy pa en s. Tha is, e en a e con olling
o a ich se o obse ables, households wi h iche pa en s buy homes wo h an addi ional
15% when en e ing he housing ma ke . No e ha he pu e pa en al weal h componen has
inc eased o e he sample pe iod. Appendix Figu es A.6b and A.7b con i m ha , once again,
he esul s a e obus o also con olling o u u e income g ow h and isky asse sha es, as
well as using con empo aneous pa en al weal h.
Housing ou come III: Le e age upon en y Le e age is ano he ma gin o adjus men
ha is likely o a y wi h pa en al weal h, and which again condi ions on en y. Indeed,
Figu e 1c shows ha households wi h iche pa en s a e oughly eigh pe cen age poin s
(≈10%) mo e le e ed. The le e age gap has inc eased o e ime, and households wi h iche
pa en s ha e le e age a es abo e 90% owa ds he end o he sample. This is high conside ing
he LTV-cap o 85%, and can be explained by i) banks being allowed o de ia e om he
cap o 10% o new mo gages, ii) measu emen e o in ou LTV-measu e and iii) addi ional
8P ices in NOK a e i s de la ed o ob ain cons an 2015-p ices, and a e hen con e ed o USD using
a cons an exchange a e o USDNOK=8.5.
13
unobse ed colla e al o mo gage gua an ees.
In e es ingly, and in con as o he o he housing ou comes, household a ibu es a e
no impo an in explaining he le e age gap. In ac , he le e age gap is en i ely a ibu ed
o he pu e pa en al weal h channel o mos o he sample. We in e p e his o e lec ha
mos i s ime buye s a e cons ained by he egula o y LTV-cap a 85%, and ha especially
households wi h iche pa en s a e likely o ecei e addi ional colla e al o gua an ees om
hei pa en s ha enable hem o exceed his limi .9Appendix Figu es A.6c and A.7c con i m
ha , also o le e age, he esul s a e obus o con olling o u u e income g ow h and
isky asse sha es, as well as using con empo aneous pa en al weal h.
3.2 The causal impac o pa en al weal h
The p e ious sec ion showed ha , e en a e con olling o a ich se o pa en al and house-
hold cha ac e is ics, pa en al weal h is an impo an media o o housing ou comes. How-
e e , he e could be omi ed a iables which in luence his ela ionship, challenging a causal
in e p e a ion. Fo ins ance, p e e ences a e likely o in luence housing ou comes di ec ly,
bu a e unobse ed o us as econome icians.10 I hese p e e ences a e co ela ed wi h
weal h and ansmi ed om one gene a ion o he nex , hey will impac ou β-es ima es in
equa ion (1). In his sec ion we use plausibly exogenous a ia ion in pa en al weal h caused
by a shi -sha e (Ba ik) ype ins umen , in o de o gauge he ex en o which ou abo e
es ima es imply a causal impac o pa en al weal h on housing ou comes.
Ou ins umen is based on in e na ional s ock ma ke e u ns and ini ial s ock ma ke
exposu e. We measu e in e na ional s ock ma ke e u ns by he e u n on he S&P 500
index, .11 The annual e u n a ies om -24% o 18% du ing ou sample pe iod, c ea ing
non- i ial a ia ion in inancial weal h. Pa en s ha e di e en exposu e o s ock ma ke
e u ns based on hei balance shee s, and we use his o ob ain c oss-sec ional a ia ion. Ou
ins umen is he in e ac ion be ween s ock sha es and in e na ional s ock ma ke e u ns.
The i s -s age equa ion is
pw
i, =α+β1s ock-sha ei, −1× +β2po
i, +β3xi, +ϵi, (3)
9This is also consis en wi h indings in Aas ei e al. (2022) who s udy he household balance shee
e ec s o in oducing LTV-caps in No way.
10As discussed in he p e ious sec ion howe e , including he isky asse sha es o pa en s and o sp ing
as a p oxy o isk a e sion has e y limi ed impac on ou esul s.
11In p inciple, we could also use No wegian s ock ma ke e u ns. Howe e , he exogenei y h ea s migh
be la ge in his case. Also, he inancial asse holdings o No wegian households con ain a subs an ial sha e
o in e na ional s ock ma ke exposu e, ensu ing a s ong i s s age. Acco ding o S a is ics No way, 55%
o s ock owne ship is h ough mu ual unds, in which 80% o in es men s a e in e na ional – implying an
in e na ional exposu e o a leas 40%.
14
We measu e pa en al weal h con empo aneously in o de o ob ain a s ong ins umen .
The exclusion es ic ion is ha s ock-ma ke weal h changes o pa en s only a ec house-
holds’ en y p obabili ies h ough hei e ec on pa en al weal h. To add ess he conce n
ha he e migh be di ec e ec s on he households own s ock ma ke weal h, we can con ol
o he (child) household’s s ock ma ke weal h changes. The second-s age is
hi, =αIV +βIV
1ˆpi, w+βIV
2po
i, +βIV
3xi, +ϵIV
i, (4)
(1) (2) (3) (4) (5)
P(en y) P(en y) pw
i, P(en y) P(en y)
pw
i, 0.0131*** 0.0189*** 0.0204***
(0.00156) (0.00180) (0.00167)
s ock-sha ei, −1× 0.0166*** 0.875***
(0.00187) (0.0838)
Model OLS OLS OLS IV IV
N 3,955,433 3,955,433 3,955,433 3,955,433 3,955,433
Clus e s 1,043,389 1,043,389 1,043,389 1,043,389 1,043,389
Mean 0.0438 0.0438 0.457 0.0438 0.0438
S anda d con ols Yes Yes Yes Yes Yes
HH s ock sha e in e ac ion No No No No Yes
Table 2: IV-analysis: s ock ma ke e u n.
No es: en yi, = 1 i household ipu chases a house in yea and did no own housing in yea −1,
en yi, = 0 i household idid no pu chase a house in yea and did no own housing in yea −1.pw
i, = 1
i a e age pa en al inancial weal h is abo e he yea -speci ic h eshold, and ze o o he wise. S ock-sha e is
he sha e o non-deposi inancial weal h, is he annual e u n on he S&P 500.
The eg ession esul s a e epo ed in Table 2. Column 1 epo s he OLS esul s. The
poin es ima e indica es ha ha ing pa en s in he uppe hal o he weal h dis ibu ion
inc eases he en y p obabili y by 1.3 pe cen age poin s in a gi en pe iod. The educed
o m esul s a e epo ed in he second column, while he i s -s age esul s a e epo ed in
he hi d column. The F-s a is ic on he i s s age is well abo e 100, sugges ing a s ong
ins umen . Scaling he educed o m esul s by he i s s age esul s gi es he same es ima e
as he IV-es ima e epo ed in Column 4. I says ha ha ing pa en s in he uppe hal o he
weal h dis ibu ion inc eases en y p obabili ies by 1.9 pe cen age poin s. The IV-es ima e
exceeds he OLS-es ima e, bu he 95% con idence in e als o e lap – consis en wi h a causal
in e p e a ion o he OLS-es ima es.
15
In Column 5 we explici ly con ol o he in e ac ion o (child) household s ock ma -
ke sha es and in e na ional s ock ma ke e u ns. This inc eases he es ima ed impac o
pa en al weal h sligh ly, bu he ake-away emains unchanged. In sum, ou e idence indi-
ca es a causal e ec o pa en al weal h on o sp ing’s en y a es in o he housing ma ke .12
4 The housing channel o in e gene a ional weal h pe -
sis ence
So a we ha e documen ed la ge housing gaps caused by pa en al weal h. This is impo an
in i sel , as homeowne ship is gene ally hough o p o ide bo h p i a e and social bene i s
(Coulson and Li (2013), Sodini e al. (2023)). In his sec ion we quan i y he ole o he
housing ma ke in d i ing in e gene a ional weal h pe sis ence. As in Sec ion 3, we p oceed
in wo s eps. Fi s , we use a media ion analysis o s a is ically decompose in e gene a ional
weal h pe sis ence in o di e en componen s and isola e he housing ma ke channel. Second,
we use plausibly exogenous a ia ion in housing ou comes caused by he iming o in a-
amily dea hs o es ima e he causal impac o housing ou comes on midli e weal h.
4.1 Media ion analysis
In his sec ion we conside he co ela ion be ween household weal h and pa en al weal h
and decompose his co ela ion in o ou obse able channels: pu e pa en al weal h,o he
pa en al a ibu es,household a ibu es, and housing.
F amewo k Le midli e weal h ¯widepend on pa en al weal h when he household is aged
19-21 (deno ed pw20
i), o he pa en al a ibu es a midli e (¯po
i), household a ibu es a midli e
(¯xi) and housing ou comes (hi) – as in equa ion (5). Any o he a iables which a ec
household weal h a e g ouped oge he in he e o e m ϵi. We i s lay ou he s uc u al
amewo k, and he ea e we desc ibe he measu emen o a iables.
¯wi=α0+α1pw20
i+α2¯po
i+α3¯xi+α4hi+ϵi(5)
12Wi h some assump ions, he impac on en y a es can be ansla ed in o an es ima ed impac on
homeowne ship a es a age 30. Assume ha adul s en e he economy a age 18, and ha he baseline
en y a e equals he sample mean o 4.4%. I he en y a e inc eases by 1.9 pe cen age poin s each yea
(column 4), he homeowne ship a e a 30 inc eases by 13 pe cen age poin s. I he en y a e inc eases by
1.3 pe cen age poin s each yea (column 1), he homeowne ship a e a 30 inc eases by 9 pe cen age poin s.
The la e is oughly equal o he size o he pu e pa en al weal h channel in Figu e 1a.
16
Using equa ion (5) o exp ess he co a iance be ween ¯wiand pw20
i, and di iding by he
a iance o pw20
i, we a i e a
co ( ¯wi, pw20
i)
a (pw20
i)=
i)pa en al weal h
z}|{
α1+
ii)pa en al a ibu es
z }| {
α2
co (¯po
i, pw20
i)
a (pw20
i)+
iii)hh a ibu es
z }| {
α3
co (¯xi, pw20
i)
a (pw20
i)+
+α4
co (hi, pw20
i)
a (pw20
i)
| {z }
i )g oss housing
+co (ϵi, pw20
i)
a (pw20
i)
| {z }
)unobse ables
(6)
The le -hand side in equa ion (6) is he co ela ion be ween pa en al weal h and household
weal h, and cap u es ou measu e o in e gene a ional weal h pe sis ence. As be o e, his
e m is simply he eg ession coefficien om eg essing household weal h on pa en al weal h
wi hou con ols.
The decomposi ion in (6) ea u es ou dis inc obse able channels. Fi s , he e is a pu e
pa en al weal h channel, cap u ed by he α1coefficien om equa ion (5). The emaining
channels a e he p oduc s o wo e ms. The o he pa en al a ibu es channel is he impac
o o he pa en al a ibu es on household weal h, α2, imes he co ela ion be ween hese
o he pa en al a ibu es and pa en al weal h. The household a ibu es channel is he
impac o household a ibu es on household weal h, α3, imes he co ela ion be ween hese
household a ibu es and pa en al weal h. Finally, he g oss housing channel is he impac
o housing ou comes on midli e weal h, α4, imes he co ela ion be ween housing ou comes
and pa en al weal h, co (hi, pw20
i)/ a (pw20
i). No e ha he la e a io is he le -hand side
o equa ion (2) in he p e ious sec ion, i.e. i is he eg ession coefficien om eg essing
housing ou comes on pa en al weal h. Subs i u ing his e m om equa ion (2), we can
ew i e equa ion (6) as
co ( ¯wi, pw20
i)
a (pw20
i)=
i)pa en al weal h
z}|{
α1+
ii) (ne ) housing
z}|{
α4β1+
iii)pa en al a ibu es’
z }| {
(α2+α4β2)co (¯po
i, pw20
i)
a (pw20
i)
+ (α3+α4β3)co (¯xi, pw20
i)
a (pw20
i)
| {z }
i )hh a ibu es’
+co (ϵi, pw20
i)
a (pw20
i)+α4
co (ηi, pw20
i)
a (pw20
i)
| {z }
)unobse ables’
(7)
He e, he g oss housing channel has been eplaced by he (ne ) housing channel, which is
wha we e e o as he housing channel o in e gene a ional weal h pe sis ence. This channel
is gi en by α4×β1, and cap u es he impac o pa en weal h on child midli e weal h h ough
17

housing. Speci ically, β1is he impac o pa en weal h on housing ou comes om equa ion
(1), and α4is he impac o housing ou comes on child midli e weal h om equa ion (5).
The di e ence be ween he g oss and he ne housing channel is a ibu ed o o he pa en al
a ibu es o household a ibu es.
In he upcoming analysis we i s es ima e he α-coefficien s om equa ion (5) and he
co a iance- a iance e ms. We use hese coefficien s o compu e he componen s o in e gen-
e a ional weal h pe sis ence as speci ied in equa ion (6). Using ˆα4and ˆ
β1we also sepa a ely
epo he (ne ) housing channel om equa ion (7).
Measu emen Ne household weal h a midli e is measu ed when he household is in i s
ea ly 40s. Pa en al weal h is, as be o e, measu ed based on a e age inancial weal h when
he household is aged 19-21. Howe e , again, we also conside con empo aneous measu es.
In ou baseline analysis, bo h household weal h and pa en al weal h a e dummy a iables
which cap u e whe he weal h holdings a e abo e o below he yea -speci ic median. Findings
om he ecen li e a u e on in e gene a ional weal h pe sis ence sugges ha he co ela ion
be ween pa en and child weal h anks ( om 1 o 100) is qui e well app oxima ed by a linea
ela ionship, see o ins ance Ade mon e al. (2018) and Fage eng e al. (2021). This is also
he case in ou sample, as shown in Appendix Figu e A.8. This sugges s ha he simple
di ision o abo e/below he median cap u es he main ea u es o he da a. S ill, we also
epo esul s using weal h anks o obus ness.
C ucially, we include housing ou comes hias media o s. As ou baseline, we ocus on
he ex ensi e ma gin, i.e. homeowne ship. To allow o some dynamic e ec s, we include
homeowne ship indica o s a di e en ages, speci ically ages 27, 30, 33 and 36. We do no
include ages below 27, as he numbe o households we obse e bo h in hei ea ly 20s and
in hei ea ly 40s is limi ed. These housing ou comes cap u e only he ex ensi e ma gin,
ha is, he decision o become a homeowne o no a di e en poin s o e he li e cycle.
As an ex ension, we also use ou comes condi ional on en y o cap u e he in ensi e ma gin.
These es ima es a e necessa ily based solely on he oughly 70% o households who become
homeowne s by middle age.
Es ima ion We es ima e all he componen s o in e gene a ional weal h dependence sep-
a a ely, epo ing de ailed eg ession esul s in he appendix, and summa izing he main
esul s he e. We i s es ima e equa ion (5) o ob ain ˆα1,ˆα2,ˆα3and ˆα4. The esul s a e
epo ed in he i s column o Appendix Table A.1. A e ob aining he α-es ima es, we
eg ess po
i,xiand hion pw20
i, one-by-one, o ge he co a iance- e ms in equa ion (6). The
esul s a e epo ed in Columns 2-11 o Appendix Table A.1. Gi en he β1-es ima e om
18
he p e ious sec ion, we hen ha e wha we need o calcula e he dis inc componen s o
in e gene a ional weal h pe sis ence as speci ied in equa ions (6)-(7).
The componen s a e summa ized in Table 3. Fi s , o al in e gene a ional weal h pe -
sis ence is 15 pe cen age poin s. This means ha households wi h pa en s in he uppe hal
o he weal h dis ibu ion a e 15 pe cen age poin s (=35%) mo e likely o hemsel es be in
he uppe hal o he weal h dis ibu ion a midli e. This numbe is simply he es ima ed
coefficien om eg essing midli e household weal h on pa en al weal h, i.e. he le -hand
side o equa ions (6) and (7).
In e gene a ional weal h pe sis ence 0.15 (100%)
Pa en al weal h channel 0.08 (55%)
Pa en al a ibu es channel 0.01 (5%)
Household a ibu es channel 0.02 (13%)
G oss housing channel 0.04 (27%)
Ne housing channel 0.02 (12%)
Table 3: Decomposing in e gene a ional weal h pe sis ence
No es: The able shows esul s om decomposing in e gene a ional weal h pe sis ence in acco dance wi h
equa ion (6). The g oss housing channel is u he decomposed in o a ne housing channel as in equa ion
(7). Pa en al weal h is pw20. Pa en al a ibu es a e educa ion, income, loca ion and numbe o child en.
Household a ibu es a e educa ion, income, loca ion and numbe o adul household membe s. Housing
ma ke measu es a e homeowne ship indica o s a ages 27, 30, 33 and 36.
As seen om he second ow o Table 3, he pu e pa en al weal h componen accoun s
o 55% o in e gene a ional weal h pe sis ence. O he pa en al a ibu es – such as pa en al
income, educa ion, loca ion and numbe o child en – do no accoun o a la ge sha e
o he obse ed in e gene a ional pe sis ence. Household a ibu es, on he o he hand, a e
mo e impo an , explaining 13% o he co ela ion be ween pa en al weal h and child weal h.
S ikingly, housing ou comes a e subs an ially mo e impo an han bo h pa en al a ibu es
and o he household a ibu es in explaining in e gene a ional weal h pe sis ence – see he
ou h ow o Table 3. In ac , mo e han 1/4 o he co ela ion be ween pa en al weal h
and household weal h is explained by households wi h iche pa en s ha ing be e housing
ou comes, i.e. he g oss housing channel.
Finally, he ne housing channel accoun s o 12% o in e gene a ional weal h pe sis ence
and implies ha households wi h iche pa en s a e wo pe cen age poin s mo e likely o
be in he uppe hal o he weal h dis ibu ion a midli e due o he impac o pa en al
weal h on housing. This key numbe will se e as an impo an momen o ma ch in he
19
heo e ical model in Sec ion 6. No e ha he ne housing channel is abou he same size as
he household a ibu es channel. A use ul in e p e a ion o he magni ude is hus ha he
di ec impac o pa en al weal h on homeowne ship is equally impo an o in e gene a ional
weal h pe sis ence as he di ec impac o pa en al weal h on household income, educa ion,
loca ion and numbe o household membe s.
The esul s so a ha e been based on whe he weal h is abo e o below he median. In
Appendix Table A.2 we ins ead use he ank om 1 o 100 o cap u e household weal h and
pa en al weal h. In o al, inc easing he pa en al weal h ank by one inc eases he household
weal h ank a midli e by 0.3, which is simila in magni ude o p e ious indings.13 Compa ed
o he esul s in Table 3, he ne housing channel becomes sligh ly smalle , and d ops om
jus abo e 10% o jus below 10%. Quali a i ely, he esul s a e unchanged.
The in ensi e ma gin o homeowne ship A bene i o using homeowne ship indica o s
a di e en ages is ha no household is excluded om he sample, as long as i is in he da a
o ha pa icula age. Howe e , we do no cap u e he impac wo king hough a iables
such as pu chase p ice and le e age, which a e de ined only o households who en e he
housing ma ke . To e alua e he impo ance o he in ensi e ma gin, we edo ou analysis
on a sample o (e en ual) homeowne s. The esul s a e epo ed in Appendix Table A.3.
Measu ing housing ou comes by only pu chase p ice and le e age upon en y yields a ne
housing channel o 11%. I we also include age o en y, he ne housing channel inc eases
o 16%. These esul s sugges ha he ex ensi e ma gin esul discussed abo e should be
iewed as a lowe bound o he o al e ec .
4.2 The causal impac o housing on weal h accumula ion
P ecisely es ima ing he housing channel o in e gene a ional weal h pe sis ence equi es
an unbiased es ima e o he impac o housing on midli e weal h, i.e. coefficien α4 om
equa ion (5). In his sec ion we use plausibly exogenous a ia ion in housing esul ing om
a ia ion in he iming o g andpa en dea h o es ima e he causal impac o age o en y
in he housing ma ke on midli e weal h. We es ic ou sample o households o whom we
obse e exac ly one g andpa en dea h in ou sample pe iod.14 This means ha we ely on
a ia ion in iming only o iden i ica ion.
13Fo ins ance Fage eng e al. (2021) ind a ank- ank coefficien o 0.24 ( o non-adop ees) using No we-
gian da a, Ade mon e al. (2018) ind a ank- ank coefficien o 0.3-0.4 using Swedish da a and P e e and
Killewald (2015) ind a ank- ank coefficien o 0.39 ( o ages 35-44) using US PSID da a
14No e ha a g andpa en is de ined as an indi idual, no a household. In he analysis, we conside he
dea h o any one g andpa en . The esul s a e simila i we only conside he dea h o a ” inal” g andpa en
on one side, i.e i we condi ion on he deceased g andpa en no ha ing a su i ing spouse.
20
The s eng h o he ins umen elies on g andpa en dea h ha ing a non- i ial impac
on housing ou comes. To documen ha his is he case, we es ima e en e en s udy a ound
g andpa en dea h, based on he ollowing equa ion
yi, =α+δ +
k=3
X
k=−2
βkIk
i, +ϵi, (8)
The ou come a iable yi, is he p obabili y o en e ing he housing ma ke , de ined o
households who a e no in he housing ma ke (yi, = 0) o a e en e ing he housing ma ke
in yea (yi, = 1). We de ine a ec o o ime dummies o he yea s p io o and ollowing
he dea h o a g andpa en , Ik
i, , wi h kdeno ing he numbe o yea s since he g andpa en
dea h ook place. All βk-coefficien s a e ela i e o k=−3, which we se as ou baseline. δ
cap u es ime ixed e ec s.
.044 .046 .048 .05 .052
-3 -2 -1 0 1 2 3
Time ela i e o g andpa en dea h
En y p obabili y
Figu e 2: E en s udy a ound g andpa en dea h
No es: Reg ession esul s om es ima ing equa ion (8) wi h yi, =en y p obabili yi, . Sample: households
who expe ience exac ly one g andpa en dea h in he sample pe iod.
Figu e 2 e eals a subs an ial spike in he p obabili y o en e ing he housing ma ke
exac ly in he yea o g andpa en dea h. The en y p obabili y inc eases by mo e han en
pe cen , om a ound 4.6% o 5.1%. This esponse con i ms ha he iming o g andpa en
dea h causes a ia ion in age o en y in he housing ma ke . No e ha he e is a small
decline in en y p obabili ies in he yea p io o g andpa en dea h. This could mean ha
some households an icipa e he upcoming dea h o a g andpa en , and choose o delay en y.
This an icipa ion e ec migh be especially ele an o households who expec o inhe i
hei g andpa en s’ house. I we exclude such households om he sample, he e a e no
signi ican an icipa ion e ec s - see Appendix Figu e A.9.15 All ou esul s a e obus o
15Speci ically, we exclude households who en e he housing ma ke in he same municipali y in which
21
To e alua e whe he pa en s sell homes o hei child en a discoun ed p ices, we p edic
house pu chase p ices based on squa e me e s, numbe o ooms, numbe o ba h ooms,
municipali y and yea o pu chase – as in equa ion (11). Da a o hese a iables a e o en
missing, lea ing a sample o nea ly 99,000 en ies o he housing ma ke o which we ha e all
he housing cha ac e is ics. O hese ansac ions, 3,300 a e sales om pa en o child and
a e excluded in he es ima ion. Reg ession esul s a e epo ed in Table A.8 in he appendix.
hp icei, =α+β1sqmi, +β2 ooms +β3ba h ooms +δkmunicipali yk+δ yea +ϵi, .(11)
0 .00002 .00004 .00006 .00008
Densi y
-80000 -60000 -40000 -20000 0 20000
Residual house p ice (USD)
Figu e 4: Es ima ed house sale discoun s (USD).
No es: The esidual house p ice is he di e ence be ween he lis ed pu chase p ice and he es ima ed ma ke
alue (11). The dashed line ep esen s he a e age esidual house p ice when pa en s sell o hei child en.
The dis ibu ion ep esen s he a e age esidual house p ice om 1,000 andomly d awn samples.
Using he es ima ed coefficien s om equa ion (11), we calcula e he di e ence be ween
ac ual pu chase p ices and p edic ed pu chase p ices o all ansac ions in ou sample. Fo
he in a- amily sales, he a e age pu chase p ice is $87,000 less han p edic ed, which implies
a discoun in excess o 25%. To make su e ha he la ge es ima ed discoun o pa en al
sales is no a s a is ical luke, we do a simple exe cise in which we edo he calcula ions o
andomly d awn samples o ac ual ansac ions, uncondi ional on whe he hey a e wi hin
amily o no . Speci ically, om ou ansac ions da a we d aw 1,000 andom samples o 3,300
ansac ions, which is he size o ou in a- amily sales sample. Lea ing ou each sample one-
by-one, we e-es ima e equa ion (11) and use he esul s o p edic pu chase p ices o all
ansac ions. We hen calcula e he a e age esidual house p ice o each sample, esul ing
in he smoo h dis ibu ion in Figu e 4. On a e age, esidual house p ices a e close o ze o,
28

and i ually all mass lies be ween -$20,000 and $20,000. This is in s a k con as o he
a e age esidual o in a- amily sales, which is cap u ed by he dashed, ed line o he le
in Figu e 4. We hus conclude ha pa en s a e indeed selling houses o hei child en a
sizable discoun s.
5.3 How impo an a e he mechanisms conside ed?
We end his sec ion by pe o ming back-o - he-en elope calcula ions o assess how impo an
he di e en mechanisms a e in explaining he en y gap be ween households wi h iche and
poo e pa en s. No e ha he mechanisms conside ed seek o explain only he pa o he
en y gap which is accoun ed o by pa en al weal h. To assess each mechanism’s magni ude,
we i s mul iply he sha e o pa en s who engage in mechanism i={equi y wi hd awal,
ans e , co-pu chase, di ec sale}by he impac o mechanism ion he en y p obabili y.
Bo h e ms a e allowed o di e by pa en al weal h. This gi es us he implied en y a e
explained by each mechanism o households wi h iche and poo e pa en s. Then, we ake
he di e ence in implied en y a es be ween households wi h iche and poo e pa en s, and
di ide by he o al en y gap accoun ed o by pa en al weal h. This gi es us he sha e o
he en y gap which is a ibu ed o each mechanism.
(1) (2) (3) (4) (5) (6) (7)
Sha e o pa en s Impac on en y En y accoun ed o Sha e o gap
pw20=1 pw20=0 pw20=1 pw20=0 pw20=1 pw20=0 accoun ed o
Equi y ex ac ion 24% 19% 1.40 pp 0.94 pp 0.34 pp 0.18 pp 29%
T ans e 8.5% 3.9% 1.55 pp 1.55 pp 0.13 pp 0.06 pp 13%
Co-pu chase 0.012×0.052 0.007×0.037 100 pp 100 pp 0.062 pp 0.026 pp 7%
=0.062% =0.026%
Di ec sale 0.022×0.052 0.020×0.037 100 pp 100 pp 0.114 pp 0.074 pp 7%
=0.114% =0.074%
Sum 33% 23% 0.65 pp 0.34 pp 56%
Table 7: Mechanisms: assessing he magni udes
No es: The numbe s in columns 5-6 a e ound by mul iplying he numbe s in columns 1-2 and columns 3-4
based on pa en al weal h. The numbe s in column 7 a e ound by aking he di e ence be ween he numbe s
in columns 5 and 6, and di iding by he o al en y gap explained by pa en al weal h o 0.55 pp.
Pa en al equi y ex ac ion The esul s o he back-o - he-en elope calcula ion o pa en al
equi y ex ac ion a e epo ed in he i s ow o Table 7. Conside ing only (po en ial) i s
ime buye s, 24% o high-weal h pa en s and 19% o low-weal h pa en s ex ac equi y in a
gi en pe iod. Fo households wi h iche pa en s, pa en al equi y ex ac ion inc eases he
29
en y p obabili y by 1.40 pe cen age poin s (see Column 6 o Table 5, ow 1 + ow 3). Fo
households wi h poo e pa en s, pa en al equi y ex ac ion inc eases he en y p obabili y
by 0.94 pe cen age poin s (see Column 6 o Table 5, ow 1). Combining hese wo se s o
numbe s, we ha e ha – o households wi h iche pa en s – pa en al equi y ex ac ion in-
c eases hei en y p obabili y by 0.24×1.40 = 0.34 pe cen age poin s. Fo households wi h
poo e pa en s, pa en al equi y ex ac ion inc eases hei en y p obabili y by 0.19×0.94
= 0.18 pe cen age poin s. The en y p obabili y gap be ween households wi h iche and
poo e pa en s accoun ed o by pa en al equi y ex ac ion is hus (0.34-0.18)/0.55=29%.23
Pa en al ans e s The esul s o he back o he en elope calcula ion o pa en al ans-
e s a e epo ed in he second ow o Table 7. Conside ing only (po en ial) i s ime buye s
as be o e, 8.5% o iche pa en s and 3.9% o poo e pa en s p o ide ans e s in a gi en
pe iod. Recei ing a ans e inc eases he en y p obabili y by 1.55 pe cen age poin s, wi h
no signi ican di e ence ac oss pa en al weal h g oups (see Column 6 o Table 6). Combin-
ing hese wo se s o numbe s, we ha e ha – o households wi h iche pa en s – ans e s
inc ease hei en y p obabili y by 0.085×1.55 = 0.13 pe cen age poin s. Fo households
wi h poo e pa en s, ans e s inc ease hei en y p obabili y by 0.039×1.55 = 0.06 pe cen -
age poin s. The en y p obabili y gap be ween households wi h iche and poo e pa en s
accoun ed o by pa en al ans e s is hus (0.13-0.06)/0.55 =13%.
Co-pu chasing The esul s o he back o he en elope calcula ion o pa en al co-pu chasing
a e epo ed in he hi d ow o Table 7. 1.2% o households wi h iche pa en s en e ing
he housing ma ke co-pu chase oge he wi h hei pa en , see Figu e 3a. Gi en an en-
y a e o 5.2%, his implies ha 0.062% o high-weal h pa en s o (po en ial) en an s
co-pu chase a home oge he wi h a child in a gi en pe iod. Fo households wi h poo e
pa en s, 0.7% o en an s co-pu chase oge he wi h a pa en . Gi en an en y a e o 3.7%,
i ollows ha 0.026% o low-weal h pa en s o (po en ial) en an s co-pu chase a home o-
ge he wi h a child in a gi en pe iod. Because co-pu chasing only akes place condi ional
on he child household en e ing he housing ma ke , he impac on en y is se o one. This
implies ha co-pu chasing inc eases en y a es by 0.062 pe cen age poin s o households
wi h iche pa en s, and 0.025 pe cen age poin s o households wi h poo e pa en s. As a
esul , co-pu chasing can explain 7% o he o al en y gap accoun ed o by pa en al weal h.
Di ec sales The esul s o he back o he en elope calcula ion o di ec housing sales
om pa en o child a e epo ed in he ou h ow o Table 7. 2.2% o households wi h
23On a e age o e he sample pe iod, he gap in en y a es is 1.5 pp, see Appendix Figu e A.3. Roughly
1/3 o 0.55 pp is due o pa en al weal h.
30
iche pa en s en e ing he housing ma ke buy di ec ly om a pa en , see Figu e 3b. Gi en
an en y a e o 5.2%, his implies ha 0.114% o high-weal h pa en s o (po en ial) en an s
sell a house o a child in a gi en pe iod. Fo households wi h poo e pa en s, 2.0% o en an s
buy di ec ly om a pa en . Gi en an en y a e o 3.7%, his implies ha 0.074% o low-
weal h pa en s o (po en ial) en an s sell a house o a child in a gi en pe iod. Because a
di ec sale om pa en o child only akes place condi ional on he (child) household en e ing
he housing ma ke , he impac on en y is again se o one. This implies ha di ec sales
inc eases en y a es by 0.114 pe cen age poin s o households wi h iche pa en s, and
0.074 pe cen age poin s o households wi h poo e pa en s. As a esul , di ec sales can also
explain 7% o he o al en y gap accoun ed o by pa en al weal h.
To al Adding up he mechanisms conside ed, we ha e explained 56% o he di e ence in
en y p obabili ies caused by pa en al weal h.24 Which mechanisms a e we missing? One
mechanism gene ally conside ed o be impo an based on su eys and anecdo al e idence –
and consis en wi h he impo ance o pa en al weal h o LTVs in Figu e 1c – is mo gage
gua an ees. Tha is, a pa en ag ees o be liable o he mo gage in case he child should
ail o mee he paymen obliga ions. In gene al, he e a e likely a numbe o di e en ways
pa en s can assis hei child en inancially in he housing ma ke . Ou back-o -en elope
calcula ions sugges ha pa en al equi y ex ac ion, o he ans e s and in a- amily ans-
ac ions can accoun o mo e han hal o he impac o pa en al weal h on housing ma ke
en y a es.
Be o e mo ing on o he model, we b ie ly summa ize ou esul s. Fi s , we ha e doc-
umen ed subs an ial housing gaps be ween hose wi h iche s. poo e pa en s, and de-
composed hese gaps in o a pu e pa en al weal h componen , an o he pa en al a ibu es
componen and a household a ibu es componen . Ins umen ing pa en al weal h wi h
a shi -sha e IV based on in e na ional s ock ma ke e u ns suppo a causal impac o
pa en al weal h on housing ma ke ou comes. Second, we ha e seen ha he g oss housing
channel can accoun o oughly one qua e o o al in e gene a ional weal h pe sis ence,
and ha hal o his is d i en pu ely by pa en al weal h. An ins umen al a iable app oach
based on he iming o in a- amily dea hs suppo s a causal in e p e a ion o he impac
o housing on midli e weal h. Finally, in e ms o how pa en al weal h is ansmi ed, we
ind e idence o pa en al housing equi y wi hd awal, inancial ans e s, co-pu chasing, and
24An implici assump ion when adding up he impo ance o each mechanism is ha he e is limi ed
o e lap. This migh no be he case. Fo ins ance, pa en s who ex ac equi y migh also gi e inancial
ans e s. Howe e , only ou pe cen o pa en s ex ac ing equi y o gi ing ans e s engage in bo h suppo
o ms simul aneously. We hus conside he assump ion o no o e lap o be accep able o ou back-o - he-
en elope calcula ion.
31
di ec sales om pa en o child a subs an ially discoun ed p ices.
6 Model and coun e ac ual exe cises
In his sec ion, we build a li e-cycle model wi h housing and exogenous pa en al suppo
o i) explo e i a calib a ed s aple model, augmen ed wi h inancial suppo om pa en s,
can ep oduce ou empi ical es ima es o he housing channel o in e gene a ional weal h
pe sis ence and ii) conduc coun e ac ual analyses o unde s and he oles o house p ice
g ow h and mo gage ma ke egula ion. These coun e ac uals a e chosen o add ess ex e -
nal alidi y and he mos immedia e policy ques ion s emming om ou empi ical analysis.
6.1 Model se -up
Pa en al suppo is ixed in acco dance wi h a “wa m glow” beques mo i e and akes he
o m o an ini ial cash ans e o an annual cash ans e . Modeling pa en al suppo as a
ans e is in line wi h he su ey e idence p esen ed in Appendix Figu e A.11, as well as
he esul s om Sec ion 5. We i s desc ibe he baseline model wi hou pa en al suppo in
Sec ions 6.1.1-6.1.2. In Sec ion 6.1.3, we add pa en al suppo o he model. We discuss he
implica ions o endogenizing pa en al suppo gi en al e na i e beques mo i es in Appendix
D.1. Compu a ional de ails a e epo ed in Appendix D.5.
6.1.1 En i onmen
We ex end a wo kho se li e-cycle model wi h housing, modi ied o ma ch ou No wegian
se ing, o isola e he e ec o pa en al suppo . Fo a ho ough discussion o hese models
we e e o Yang (2009); A anasio e al. (2012); Da is and Van Nieuwe bu gh (2015).
Demog aphics A household is bo n a age Ts, e i es a age T , and dies a age Td. Each
pe iod is one yea , and we do no conside mo ali y isk o beques mo i es o he (child)
household.
P e e ences The expec ed li e ime u ili y o a household is gi en by
E

Td
X
a=Ts
Bau(ca, ha, sa)
(12)
32
whe e B>0is he discoun ac o , c > 0is non-housing consump ion, h∈ H(s)⊂R2
is housing consump ion, and s∈ {0,1}is he owne ship s a us which equals 0 o en e s
and 1 o owne s. The easible se o housing depends on whe he he house is en e - o
owne -occupied. The expec a ion Eis aken o e sequences o idiosync a ic shocks ha we
speci y below. In wha ollows, we omi he dependence o a iables on age a, excep whe e
i is misleading. Households ha e CRRA p e e ences wi h a Cobb-Douglas agg ega o o e
housing and consump ion
u(c, h, s) = (c1−ηhηχ(s))1−γ
1−γ,(13)
whe e 0< η < 1is he weigh on housing, γmeasu es isk a e sion, and χ(s)is he
homeowne ship p emium. The owne ship p emium is 1 o en e s and 1 + χ o owne s.
Endowmen s Households a e endowed wi h an unce ain labo income s eam du ing
wo king age
log yi,a = (a) + νi,a +εi,a, a =Ts, . . . , T .(14)
We le (a)deno e he de e minis ic componen , νis a pe sis en income shock, and ε∼
N(0, σ2
ε)is a ansi o y shock. The pe sis en shock ollows an AR(1) p ocess
νi,a =ρνi,a−1+ui,a,(15)
whe e ρis he pe sis ence pa ame e and u∼ N (0, σ2
ν). In e i emen , income is cons an
and equal o a ixed p opo ion (ϕ e )o he household’s income in he las pe iod o wo king
li e (a=T )
log(yi,a) = log(ϕ e ) + (a=T ) + νi,T , a =T + 1, . . . , Td(16)
Social wel a e sys ems p o ide a consump ion loo ca e en o he cheapes uni . House-
holds a e endowed wi h an ini ial le el o ne wo h xTs.
Housing ma ke The ma ke alue o a house is linea in house size h. The house p ice
ollows a s ochas ic p ocess wi h d i µhand ola ili y σh
log(pa+1) = log(pa) + ϵh
a+1, ϵ ∼ N (µh, σ2
h).(17)
The en al p ice is assumed o be a cons an ac ion κo he ma ke alue ph. Households
ha e he op ion o en , deno ed s= 0, o own, s= 1, in o de o consume housing se ices.
Houses a e cha ac e ized by hei sizes, which belong o disc e e ini e se s H(s) ha depend
33

on owne ship s a us. Buying and selling owne -occupied housing en ails adjus men and
ansac ion cos s ha a e p opo ional o he ma ke alue o he house and we deno e
hese p opo ional cos s by mband ms, espec i ely. We le c(p, s, h, s′, h′)deno e he o al
ansac ion cos o a household who swi ches housing enu e om s o s′and house size om
h o h′. Fo example, a cu en en e (s= 0) li ing in a en al uni o size hwho buys (s′= 1)
a house o size h′when he p ice is p, pays a ansac ion cos o c(p, 0, h, 1, h′) = (1+mb)ph′.
Mo eo e , homeowne s expe ience dep ecia ion δ, which includes main enance and axes.
Financial ma ke Households can sa e in a one-pe iod isk- ee bond wi h e u n .
Bo owing agains colla e al (owne -occupied housing) is allowed, bu households mus sa -
is y a loan- o- alue (LTV) and a loan- o-income (LTI) cons ain . We model bo owing as
a one-pe iod mo gage ha is olled o e each pe iod. The mo gage has an in e es a e o
+ m, whe e m≥0is he mo gage p emium. Households will ne e simul aneously hold
bo h a mo gage and sa e in he isk- ee bond since he mo gage p emium is posi i e. We
le bdeno e he ne posi ion in bonds. The e ec i e in e es a e is o ne sa e s and
+ m o bo owe s
6.1.2 Household op imiza ion
We now ou line he decision p oblem o households wi h non-weal hy pa en s. Fo ead-
abili y, we deno e all one-pe iod-ahead a iables wi h p imes (′).
Budge equa ion All households choose consump ion cand a ne bond posi ion b. Ren e s
pay en while homeowne s ha e he alue o hei house on hei balance shee . Changing
housing s a us in ol es ansac ion cos s. Fo a household wi h weal h xand income y, he
budge equa ion is
x+y=c+b+ c(p, s, h, s′, h′) + (1 −s′)κph′+s′ph′(18)
E olu ion o weal h Nex -pe iod weal h is gi en by he ne posi ion in bonds and he
s ochas ic ma ke alue o owne -occupied housing ne o dep ecia ion
x′=b(1 + (b)) + s′p′h′(1 −δ)(19)
Decision p oblems The e a e i e disc e e choices. Cu en en e s choose o en o own
and cu en owne s choose o sell and en , sell and buy, o emain in he cu en house.
34
A household sol es
V(x, h, s, ν, p, a) = max
c,h′,b′,s′{u(c, h′) + BE[V(x′, h′, s′, ν;, p′, a + 1)]}(20)
subjec o
c > 0(21)
h′∈ H(s′)(22)
s′∈ {0,1}(23)
b′≥ −LTV ph′s′(24)
b′
y≥ −LTIs′(25)
and he budge cons ain and he law o mo ion (equa ions (18) and (19)). I he household
chooses o en (s′= 0), he las wo cons ain s collapse o a single no-bo owing cons ain .
6.1.3 Modelling pa en al suppo
To be consis en wi h he empi ical s a egy, exac ly hal o he households in ou model
a e assumed o ha e weal hy pa en s. Pa en al suppo is exogenous and akes he o m o
a inancial ans e , in line wi h ou empi ical indings. We model wo di e en o ms o
ans e s, an ini ial ans e o an annual ans e , o allow o di e en ans e iming.
Ini ial ans e We i s conside an ini ial one- ime ans e , modelled as an addi ional
cash endowmen ha households hold a he beginning o adul hood, τP W
Ts. Fo households
wi h non-weal hy pa en s, τP W
Ts= 0. Modelling in e gene a ional ans e s as a once-and-
done ans e occu ing when households en e wo king li e is a s anda d way o model
in e gene a ional pe sis ence, see e.g., Lee and Seshad i (2019).
Annual ans e The second o m o pa en al suppo we conside is ins ead an annual
ans e , τP W , e e y yea om =Ts o wen y yea s. Fo households wi h non-weal hy
pa en s, τP W = 0. F equen ans e s is no mally a p edic ion o models wi h al uis ic
pa en s and child en (e.g., Al onji e al. (1997); Ba czyk e al. (2022)), and is consis en
wi h empi ical ans e pa e ns (McGa y,2016).
35
6.2 Pa ame e iza ion
Ou pa ame e iza ion s a egy consis s o h ee s eps. Fi s , we ix he ex e nal pa ame e s,
i.e., pa ame e s we can se wi hou elying on model dynamics and ha a e common ac oss
all ypes o households. Second, we in e nally calib a e wo p e e ence pa ame e s, he dis-
coun ac o Band he owne ship u ili y p emium χ, o ma ch homeowne ship and inancial
weal h a di e en ages. He e we ma ch momen s o households wi h below-median weal hy
pa en s. Thi d, we pick he pa en al suppo pa ame e s o ma ch he ne housing channel
o in e gene a ional weal h pe sis ence as speci ied in equa ion (7) in Sec ion 4.1. Model pa-
ame e s a e epo ed in Appendix Table D.1, and we elega e he discussion o he s anda d
i s s ep o Appendix D.2.
6.2.1 In e nal calib a ion
In he second s ep we choose he emaining p e e ence pa ame e s o ma ch li e-cycle mo-
men s o weal h and homeowne ship o households wi h non-weal hy pa en s. Speci ically,
we se he discoun ac o Band he u ili y shi e o homeowne ship χby a ge ing he
homeowne ship a e and inancial weal h a each age be ween 25 and 45. The momen s a e
calcula ed as he a e age ac oss ou sample o households wi h non-weal hy pa en s. Ap-
pendix Figu e D.1 shows he empi ical momen s along wi h he co esponding model-implied
momen s o weal h and homeowne ship. The calib a ed model ma ches he empi ical mo-
men s qui e well, bu i somewha o e -p edic s bo h inancial weal h and homeowne ship
a es as households become middle-aged.
6.2.2 Calib a ing pa en al pa ame e s
We choose ou pa en al ans e pa ame e s, τP W
Tsand τP W o ma ch he es ima ed hous-
ing channel o in e gene a ional weal h pe sis ence as de ined in equa ion (7) in Sec ion 4.
Speci ically we a ge a ne housing channel o β1α4= 0.02, which means ha households
wi h iche pa en s a e wo pe cen age poin s mo e likely o be ich hemsel es a midli e,
due o be e housing ou comes as a esul o highe pa en al weal h. We he e pe o m he
same eg essions on model da a as we did on he ac ual da a, de ails in Appendix D.3. The
ans e pa ame e s a e well iden i ied since highe ans e s inc ease he e ec o pa en al
weal h on housing β1, while lea ing he posi i e ela ionship be ween housing ou comes and
midli e weal h α4almos unchanged. The esul s a e epo ed in Table 8.
36
Model
Da a Ini ial T ans e Annual T ans e
Ne housing channel 0.02 0.02 0.02
sum(α) 0.45 0.75 0.74
sum(β) 0.20 0.12 0.11
Table 8: Media ion analysis in he da a and in he model
No es: The ne housing channel is Pj=27,30,33,36 α4,j β1,j , whe e α4,j is he e ec o homeowne ship on weal h
and β1,j is he impac o pa en al weal h on homeowne ship, a age j.
We se he ini ial ans e τP W
Ts= 39.3and he annual ans e s τP W = 1.14 o eplica e a
ne housing channel o in e gene a ional weal h pe sis ence o wo pe cen age poin s, as seen
om he i s ow o Table 8. These ans e pa ame e s imply li e- ime alues o oughly
$40,000 and $17,000 espec i ely, using he discoun ac o Bo e 20 yea s o he annual
ans e s. The li e- ime alue o he ini ial ans e is la ge because young households o a
g ea e ex en a e cons ained om smoo hing consump ion in e empo ally. Hence, when
households ecei e hei en i e ans e a a e y young age, hey spend less on housing and
mo e on consump ion han i pa o he ans e is paid ou la e . Also no e ha housing
is mo e impo an o weal h accumula ion in he model han in he da a (la ge α’s), while
pa en al weal h is somewha less impo an o housing. The la e e lec s ha in hese
models, all households become owne s when hey a e sufficien ly weal hy, which diminishes
he link be ween pa en al weal h and housing ou comes.
A e he implied ans e sizes easonable? B andsaas (2021) inds he mean ans e size
o housing pu poses in PSID da a o be oughly $4,000. Howe e , he e a e wo easons
why ou calib a ed ans e s should be la ge . Fi s , house p ices a e conside ably highe
in No way han in he US – abou h ee imes highe pe squa e oo .25 Second, we a ge
he o al impac o pa en al suppo , while di ec ans e s in p ac ice a e only one o many
suppo o ms.
6.3 Coun e ac ual exe cises
In his sec ion we un wo expe imen s o be e unde s and how he housing channel o
in e gene a ional weal h pe sis ence depends on ea u es o he housing ma ke . Fi s , we
25Fo example, in 2017 he median lis ing p ice pe squa e ee in he US was $132 while he a e age
sale p ice pe squa e ee in No way was abou $400. Sou ces: Na ional Associa ion o Real o s (FRED
mnemonic medlisp ipe squ eeus) and S a is ics No way (Table 06035)
37
Hal o sen, E. and Lindquis , K.-G. (2017). Ge ing a oo on he housing ladde : The ole o
pa en s in gi ing a leg-up. No ges Bank Wo king Pape 19/2017.
Kaplan, G., Mi man, K., and Violan e, G. L. (2020). The housing boom and bus : Model mee s
e idence. Jou nal o Poli ical Economy, 128(9):3285–3345.
Kolodziejczyk, C. and Le h-Pe e sen, S. (2013). Do i s - ime house buye s ecei e inancial ans e s
om hei pa en s? The Scandina ian Jou nal o Economics, 115(4):1020–1045.
Lee, H., Mye s, D., Pain e , G., Thunell, J., and Zissimopoulos, J. (2020). The ole o pa en al
inancial assis ance in he ansi ion o homeowne ship by young adul s. Jou nal o Housing
Economics, 47:101597.
Lee, S. Y. and Seshad i, A. (2019). On he in e gene a ional ansmission o economic s a us.
Jou nal o Poli ical Economy, 127(2):855–921.
Luea, H. M. (2008). The impac o inancial help and gi s on housing demand and cos bu dens.
Con empo a y Economic Policy, 26(3):420–432.
McGa y, K. (2016). Dynamic aspec s o amily ans e s. Jou nal o Public Economics, 137:1–13.
P e e , F. T. and Killewald, A. (2015). How igid is he weal h s uc u e? in e gene a ional
co ela ions o amily weal h. Popula ion S udies Cen e , Uni e si y o Michigan.
Rouwenho s , K. G. (1995). Asse p icing implica ions o equilib ium business cycle models. In
Cooley, T. F., edi o , F on ie s o business cycle esea ch, pages 294–330. P ince on Uni e si y
P ess.
Sodini, P., Van Nieuwe bu gh, S., Ves man, R., and on Lilien eld-Toal, U. (2023). Iden i ying he
bene i s om homeowne ship: A swedish expe imen . Ame ican Economic Re iew. o hcoming.
Tu ne , T. M. and Luea, H. (2009). Homeowne ship, weal h accumula ion and income s a us.
Jou nal o Housing Economics, 18(2):104–114.
Yang, F. (2009). Consump ion o e he li e cycle: How di e en is housing? Re iew o Economic
Dynamics, 12(3):423–443.
Yao, J., Fage eng, A., and Na ik, G. (2015). Housing, deb and he ma ginal p opensi y o
consume. Wo king Pape .
44

A Addi ional igu es and ables
42% 44%
0
10
20
30
40
50
No way USA
Online su ey, No wegian and US homeowne s below age 50, n=677.
Sha e who ecei ed inancial suppo in o de o buy a home (%)
Figu e A.1: Sha e o homeowne s who epo ecei ing inancial suppo om pa en s o
g andpa en s when buying a home (%). Online su ey.
No es: The igu e shows esul s om an online su ey conduc ed on he su ey pla o m Su ey Monkey.
The sample consis s o 300 esponden s in No way and 377 esponden s in he US. All esponden s a e
homeowne s below age 50. The igu e shows he sha e (%) o esponden s ecei ing inancial suppo om
pa en s o g andpa en s when buying a home.
0
20
40
60
80
Sha e esponses (%)
Low weal h Medium low Medium high High weal h
Online su ey, No wegian pa en s, n=240.
Fo wha pu pose would you p e e
suppo ing you child inancially?
Housing
Consump ion
S ocks
O he asse s
(a) P e e ed inancial suppo o m
0
20
40
60
80
Sha e esponses (%)
Low weal h Medium low Medium high High weal h
Online su ey, No wegian pa en s, n=240.
Ha e you inancially suppo ed a child in he housing ma ke ,
o is his some hing you would conside in he u u e?
Yes
No
Don' know
(b) A i udes owa ds housing suppo
Figu e A.2: Su ey esponses by (sel - epo ed) weal h
No es: The igu e shows esul s om an online su ey conduc ed on he su ey pla o m Su ey Monkey.
The sample consis s o 240 indi iduals esiding in No way, aged 40+, wi h child en. Panel (a) shows esul s
o he p e e ed way o p o iding inancial suppo o a child. Panel (b) shows esul s o whe he he
pa en s ha e o plan o suppo hei child in he housing ma ke .
45
.03 .04 .05 .06 .07
En y p obabili y
2005 2007 2009 2011 2013 2015 2017
Low PW (PW20=0) High PW (PW20=1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
Figu e A.3: En y p obabili y by pa en al weal h: decomposed in o channels i)-iii) as in
equa ion (2).
No es: The igu e shows he en y p obabili y o households wi h pa en al weal h below and abo e he
median. The en y p obabili y gap is hen decomposed in o h ee obse able componen s, pu e pa en al
weal h, pa en al a ibu es and households a ibu es, in acco dance wi h equa ion (2). hiis he p obabili y
o en e ing he housing ma ke . pw20
i= 1 i a e age pa en al inancial weal h when household is aged 19-21
is abo e he yea -speci ic h eshold, po
iis pa en income, educa ion, loca ion and numbe o child en, xiis
hh income, inancial weal h, educa ion, loca ion and numbe o hh membe s. Sample consis s o households
no in he housing ma ke o en e ing he housing ma ke .
.3 .4 .5 .6 .7
Homeowne ship a 30
0 20 40 60 80 100
Pa en al inancial weal h ank a 20
(a) Homeowne ship a age 30
150000 200000 250000 300000 350000
House p ice upon en y (USD)
0 20 40 60 80 100
Pa en al inancial weal h ank a 20
(b) Pu chase p ice upon en y (USD)
Figu e A.4: Housing ou comes by pa en al weal h ank (1-100)
No es: Pa en al weal h ank om 1 o 100 is calcula ed based on he yea -speci ic dis ibu ion o pa en al
inancial weal h when he child is aged 19-21.
46
0 .02 .04 .06 .08
Homeowne ship 30
2005 2007 2009 2011 2013 2015 2017
Income Financial weal h
Loca ion Educa ion
Adul membe s
Decomposing he houshold a ibu es channel
Figu e A.5: Homeowne ship a 30 by pa en al weal h a 20: he household a ibu es com-
ponen in equa ion (2)
No es: The igu e decomposes he household a ibu e componen in equa ion (2). Household a ibu es a e
decomposed in o household income, loca ion, membe o adul s in he household, he household educa ion
le el and household inancial weal h. hiis a homeowne ship indica o a age 30. Sample consis s o 30-yea
old’s.
.5 .55 .6 .65 .7
Homeowne ship 30
2005 2007 2009 2011 2013 2015
Low PW (PW20=0) High PW (PW20=1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(a) Homeowne ship a age 30
100000 150000 200000 250000 300000
House p ice upon en y (USD)
2005 2007 2009 2011 2013 2015
Low PW (PW20=0) High PW (PW20=1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(b) Pu chase p ice upon en y ($)
75 80 85 90
Le e age upon en y (%)
2005 2007 2009 2011 2013 2015
Low PW (PW20=0) High PW (PW20=1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(c) Le e age upon en y (%)
Figu e A.6: Housing ou comes by pa en al weal h a age 20: decomposed in o channels i)-iii)
as in equa ion (2). Fu u e household income g ow h and isky asse sha es o pa en s and
o sp ing as addi ional con ol a iables.
No es: The igu e shows housing ou come gaps, decomposed in o h ee obse able componen s, pu e pa en al
weal h, pa en al a ibu es and households a ibu es, in acco dance wi h equa ion (2). pw20
i= 1 i a e age
pa en al inancial weal h when he household is aged 19-21 is abo e he yea -speci ic median, po
iis pa en
income, educa ion, loca ion, numbe o child en and isky asse sha e, xiis hh income, inancial weal h,
educa ion, loca ion, numbe o adul household membe s, isky asse sha e and wo-yea u u e income
g ow h. The sample behind (a) consis s o 30-yea old households. The sample behind (b) and (c) consis s
o only households en e ing he housing ma ke .
47
.5 .55 .6 .65 .7
Homeowne ship 30
2005 2007 2009 2011 2013 2015 2017
Low PW (PW_ =0) High PW (PW_ =1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(a) Homeowne ship a age 30
100000 150000 200000 250000 300000
House p ice upon en y (USD)
2005 2007 2009 2011 2013 2015 2017
Low PW (PW_ =0) High PW (PW_ =1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(b) Pu chase p ice upon en y ($)
75 80 85 90 95
Le e age upon en y (%)
2005 2007 2009 2011 2013 2015 2017
Low PW (PW_ =0) High PW (PW_ =1)
i) pu e pa en al weal h ii) pa en a ibu es
iii) household a ibu es
(c) Le e age upon en y (%)
Figu e A.7: Housing ou comes by pa en al weal h a −1: decomposed in o channels i)-iii)
as in equa ion (2)
No es: The igu e shows housing gaps decomposed in o h ee obse able componen s, pu e pa en al weal h,
pa en al a ibu es and households a ibu es, in acco dance wi h equa ion (2). pw
i, −1= 1 i a e age pa en al
inancial weal h in yea −1is abo e he yea -speci ic median, po
iis pa en income, educa ion, loca ion and
numbe o child en, xiis hh income, inancial weal h, educa ion, loca ion and numbe o adul household
membe s. The sample behind (a) consis s o 30-yea old households. The sample behind (b) and (c) consis s
o only households en e ing he housing ma ke .
20 40 60 80
Household ne weal h ank a midli e
0 20 40 60 80 100
Pa en al inancial weal h ank a 20
(a) Household ne weal h
0 20 40 60 80
Household inancial weal h ank a midli e
0 20 40 60 80 100
Pa en al inancial weal h ank a 20
(b) Household inancial weal h
Figu e A.8: Household weal h anking (1-100) in ea ly 40s by pa en al inancial weal h
anking (1-100) when child is 19-21.
No es: The igu e shows household ne weal h anking (panel (a)) and household inancial weal h anking
(panel (b)) by pa en al inancial weal h anking when child is 19-21. Household weal h in ea ly 40s is anked
om 1-100 based on he yea -speci ic dis ibu ion a e emo ing age e ec s. Pa en al inancial weal h when
he (child) household is 20 yea s is anked om 1-100 based on he yea -speci ic dis ibu ion.
48
.048 .05 .052 .054 .056 .058
-3 -2 -1 0 1 2 3
Time ela i e o g andpa en dea h
En y p obabili y
Figu e A.9: E en s udy a ound g andpa en dea h - only households no inhe i ing hei
g andpa en s house
No es: Reg ession esul s om es ima ing equa ion (8) wi h yi, =en y p obabili yi, . Sample: households
who expe ience exac ly one g andpa en dea h in he sample pe iod - households en e ing he housing ma ke
in he same municipali y as hei deceased g andpa en esided a e excluded om he sample.
150000 160000 170000 180000 190000 200000
-3 -2 -1 0 1 2 3
Time ela i e o g andpa en dea h
G oss pa en inancial weal h (USD)
Figu e A.10: E en s udy a ound g andpa en dea h
No es: Reg ession esul s om es ima ing equa ion (8) wi h yi, equal o g oss pa en inancial weal h.
Sample: households who expe ience exac ly one g andpa en dea h in he sample pe iod.
49

0
10
20
30
No way USA
Online su ey, No wegian and US homeowne s below age 50, n=677.
Fo m o pa en al suppo by coun y (%)
T ans e
Mo gage gua an ee
Co-owne /co-signe
Housing gi
Housing pu chase
Figu e A.11: The sha e o esponden s ecei ing di e en o ms o pa en al o g andpa en al
housing suppo (%).
No es: The igu e shows esul s om an online su ey conduc ed on he su ey pla o m Su ey Monkey.
The sample consis s o 300 esponden s in No way and 377 esponden s in he US. All esponden s a e
homeowne s below age 50. The igu e shows he sha e (%) o esponden s ecei ing a ious o m o pa en al
o g andpa en al housing suppo .
-5000 0 5000 10000 15000
-3 -2 -1 0 1 2 3
Time ela i e o (child) en y in housing ma ke
Low FW High FW
Bank deposi s (USD)
Figu e A.12: Bank deposi s (USD). E en s udy a ound housing ma ke en y ( =0)
No es: This igu e shows he e olu ion o bank deposi s a ound ime o en y in o he housing ma ke .
en yi, = 1 i household ipu chases a house in yea and did no own housing in yea −1, while
en yi, = 0 i household idid no pu chase a house in yea and did no own housing in yea −1. ”Low
FW” (”High FW”) means a e age pa en inancial weal h when he household is aged 19-21 is below (abo e)
he yea -speci ic median.
50
-10000 -5000 0 5000
-3 -2 -1 0 1 2 3
Time ela i e o (child) en y in housing ma ke
Low FW High FW
Pa en s seconda y housing weal h (USD)
Figu e A.13: E en s udy: pa en al seconda y housing weal h (USD).
No es: The igu e shows an e en s udy on pa en al seconda y housing weal h a ound (child) housing ma ke
en y. En y: en yi, = 1 i household ipu chases a house in yea and did no own housing in yea −1,
en yi, = 0 i household ihousehold idid no pu chase a house in yea and did no own housing in yea
−1. ”Low FW” (”High FW”) means a e age pa en inancial weal h when he household is aged 19-21 is
below (abo e) he yea -speci ic median.
51
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
¯w ci ypincomepeducpchild enpen y-age hp ice income educ ci y hh membe s
pw20 0.0846∗∗∗ 0.0280∗∗∗ 43627.9∗∗∗ 0.115∗∗∗ -0.0433∗∗∗ -0.268∗∗∗ 93206.2∗∗∗ 20926.9∗∗∗ 0.150∗∗∗ 0.0714∗∗∗ 0.145∗∗∗
(0.0103) (0.0044) (1645.9) (0.00696) (0.0135) (0.0590) (3664.8) (918.4) (0.00724) (0.00618) (0.00490)
owne -27 0.0269∗∗
(0.0115)
owne -30 0.0400∗∗∗
(0.0127)
owne -33 0.1081∗∗∗
(0.0157)
owne -36 0.2780∗∗∗
(0.0157)
ci yp0.0680∗∗∗
(0.0240)
incomep8.90e-08∗
(4.91e-08)
educp0.0125
(0.0113)
income 1.80e-08
(8.49e-08)
educ 0.0644∗∗∗
(0.0105)
ci y 0.123∗∗∗
(0.0127)
hh membe s 0.0362∗∗
(0.0158)
child enp-0.0203∗∗∗
(0.0053)
N 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909
Table A.1: Reg ession esul s om es ima ing equa ion (5) (Col.1) and he co a iance- e ms in equa ion (6) (Col.2-11).
52
In e gene a ional weal h pe sis ence 0.33 (100%)
Pa en al weal h channel 0.20 (61%)
Pa en al a ibu es channel 0.02 (6%)
Household a ibu es channel 0.05 (15%)
G oss housing channel 0.06 (18%)
Ne housing channel 0.03 (9%)
Table A.2: The impo ance o a ious channels o in e gene a ional weal h pe sis ence. Rank-
ank analysis.
No es: The able shows esul s o decomposing in e gene a ional weal h pe sis ence in o a pa en al weal h
channel, pa en al a ibu e channel, household a ibu e channel and g oss housing channel as de ined in
equa ion (6). The g oss housing channel can u he be decomposed in o a ne housing channel as in
equa ion (7). Pa en al weal h is he ank om 1-100 based on a e age inancial wage when he household
is 19-21. Household weal h is he ank om 1-100 based on midli e ne weal h. Pa en al a ibu es a e
educa ion, income, loca ion and numbe o child en. Household a ibu es a e educa ion, income, loca ion
and numbe o adul household membe s. Housing ma ke measu es a e homeowne ship indica o s a ages
27, 30, 33 and 36.
h = P ice & LTV h = P ice, LTV & Age
In e gene a ional weal h pe sis ence 0.19 (100%) 0.19 (100%)
Pa en al weal h channel 0.10 (53%) 0.10 (53%)
Pa en al a ibu es channel 0.01 (5%) 0.01 (5%)
Household a ibu es channel 0.06 (32%) 0.04 (21%)
G oss housing channel 0.02 (11%) 0.04 (21%)
Ne housing channel 0.02 (11%) 0.03 (16%)
Table A.3: The impo ance o a ious channels o in e gene a ional weal h pe sis ence. In-
ensi e ma gin o homeowne hsip.
No es: The able shows esul s o decomposing in e gene a ional weal h pe sis ence in o a pa en al weal h
channel, pa en al a ibu e channel, household a ibu e channel and g oss housing channel as de ined in
equa ion (6). The g oss housing channel can u he be decomposed in o a ne housing channel as in
equa ion (7). Pa en al weal h is pw20. Pa en al a ibu es a e educa ion, income, loca ion and numbe o
child en. Household a ibu es a e educa ion, income, loca ion and numbe o adul household membe s.
Housing ma ke ou comes a e pu chase p ice and le e age upon en y (Column 2) o pu chase p ice upon
en y, le e age upon en y and age o en y (Column 3).
53
D Model Appendix
Pa ame e Value Sou ce
Ex e nally Calib a ed
σ2
νVa . pe s. inc. shock 0.012 Fage eng e al. (2017)
σ2
νVa . ans. inc. shock 0.023 Fage eng e al. (2017)
ρShock pe sis ence 0.95 S anda d
ϕ e Replacemen Ra io 0.842 Fage eng e al. (2017)
(a)Li e-cycle income Fig. D.2d Fage eng e al. (2017)
cConsump ion Floo NOK100,000 Wel a e sys em
n/a Ini ial Weal h Fig. D.2c Fage eng e al. (2017)
pini Ini ial house p ice 89.78 Own calcula ion
TsS a ing age 22
T Re i emen age 67 Fage eng e al. (2017)
TdFinal age 100
mbPu chase cos 0.025 Yao e al. (2015)
msSales cos 0.025 Yao e al. (2015)
κRen - o-p ice a io 0.044 Own calcula ion
Risk- ee a e 0.016 Yao e al. (2015)
mMo gage p emium 0.039 Own calcula ion
LTV Maximum loan- o- alue 0.9 Regula ion
LTI Maximum loan- o-income 5.0 Regula ion
δDep ecia ion 0.02 Yao e al. (2015)
µhP ice g ow h 0.0288 Own calcula ion
σhP ice s d de 0.0468 Own calcula ion
H(0) Ren al sizes [1.0,1.75] Own calcula ion
H(1) Owne -occupied sizes [1.75,2.27,3.25] Own calcula ion
ηWeigh on housing 0.35 S anda d
γRisk A e sion 2.0 S anda d
In e nally Calib a ed
BDiscoun ac o 0.9689 In e nal es ima ion (6.2.1)
χOwne ship u ili y shi 0.0103 In e nal es ima ion (6.2.1)
Pa en al Pa ame e s
τP W
TsIni ial ans e 39.3 In e nal es ima ion (6.2.2)
τP W Annual ans e 1.14 In e nal es ima ion (6.2.2)
Table D.1: Calib a ed Pa ame e Values
60

Figu e D.1: Model Fi
No es: The da a plo s homeowne ship a e and a e age inancial weal h o households wi h non-weal hy
pa en s in ou sample. The model line is he equi alen o he model sample, whe e inancial weal h is 0
o bo owe s (b < 0) and he amoun sa ed in bonds o sa e s (b > 0).
D.1 The implica ions o endogenizing pa en al suppo
In he model, pa en al suppo was ea ed as ixed. In his appendix we b ie ly discuss he
implica ions o elaxing his assump ion.
We assume ha pa en s suppo hei adul o sp ing in he housing ma ke due o a
beques mo i e.27 We conside a s ylized example in which pa en s can choose o gi e
”housing beques s” bhand ”o he beques s” bo, in which we can hink o o he beques s
as s ocks. Due o ba ie s o en y in he housing ma ke , we assume ha dh
dbh>do
dbo, i.e.
ha pa en al suppo is mo e impo an o becoming a homeowne han becoming a s ock
owne . Fu he , we assume ha he e u n on housing exceeds ha on s ocks – in line wi h
Appendix B– so ha d¯w
dh >d¯w
do . We conside h ee al e na i e beques mo i es:
1. ”Wa m glow” mo i e: pa en s ecei e u ili y om gi ing beques s, i.e. u(bh+bo)
2. ”Al uism” mo i e: pa en s ecei e u ili y om child’s midli e weal h, i.e. u( ¯w)
3. ”Homeowne ship” mo i e: pa en s ecei e u ili y om child’s homeowne ship, i.e. u(h)
27An al e na i e explana ion is ha pa en s suppo child en o minimize dynas y ax paymen s. Speci i-
cally, due o ax alua ion ules, pa en al owne ship o seconda y housing en ails subs an ially la ge weal h
and p ope y axes han i a child owns he same house as a p ima y house. We ind i unlikely ha his is
an impo an mo i a ion o wo easons. Fi s , his incen i e only applies o pa en s who own seconda y
housing and chooses o ans e he home o a child which is no ye in he housing ma ke . This g oup
accoun s o only 2% o en an s in o he housing ma ke . Second, om 2010 o 2017 (i.e. he yea s o
which we sepa a ely obse e seconda y housing), he sha e o pa en s which own seconda y housing while
hei adul child is no in he housing ma ke has inc eased om less han se en pe cen o nea ly ele en
pe cen . This is he opposi e o wha he ax mo i e would p edic , as he ax alue o seconda y housing in
his pe iod has inc eased om 40% o 90% (while he ax alue o p ima y housing has emained unchanged).
61
We ask - wha happens o pa en al suppo i he op ion o be a homeowne is comple ely
emo ed? While his is no a policy ele an coun e ac ual, i nes s mo e ealis ic exe cises
in which homeowne ship is made less a ac i e.
Fi s , gi en he wa m glow beques mo i e, pa en s only ca e abou gi ing, and so o al
beques s a e he same. Second, gi en he al uism mo i e, o al beques will go down, as
hey a e now less efficien in inc easing child midli e weal h. This happens bo h because
dh
dbh>do
dboand because d¯w
dh >d¯w
do . Thi d, gi en he homeowne ship mo i e, pa en s no longe
ha e any eason o gi ing beques s, and so pa en al suppo alls o ze o.
Wha a e he implica ions o o al in e gene a ional weal h pe sis ence? Fi s , keeping
pa en al suppo ixed, emo ing homeowne ship om he able educes in e gene a ional
weal h pe sis ence, as pa en al housing beques s had an especially la ge e ec on child midli e
weal h (i.e. la ge han s ocks). Second, i any hing, pa en al suppo will decline, meaning
ha he e migh be an addi ional educ ion in in e gene a ional weal h pe sis ence. As such,
he educ ions in in e gene a ional weal h pe sis ence iden i ied in he model exe cises should
be iewed as lowe bounds.
D.2 Ex e nal Calib a ion
T ansac ion cos s In No way, home buye s pay a ansac ion ax (‘documen ee’) o
2.5% o he pu chase p ice. We he e o e se mb= 0.025. The main di ec cos o selling is
he eal es a e agen commission, which a e ages 2% (Yao e al.,2015). We se he cos o
be sligh ly highe , ms= 0.025, since selle s addi ionally usually pay o ad e isemen and
o he cos s associa ed wi h home sales.
Income P ocess Fo he s ochas ic componen we use he pa ame e alues om Fage eng
e al. (2017) on No wegian da a. They es ima e σ2
ν= 0.012,σ2
ε= 0.023, and ϕ e = 0.842.
We se ρ= 0.95, a s anda d alue in he li e a u e. We epo hei es ima ed income p o ile
(a)in Figu e D.2d. Thei es ima es do no accoun o any co ela ions be ween pa en al
weal h and income, howe e . We he e o e adjus he income p o ile (a)by he income gap
be ween households wi h poo pa en s and he a e age income o all households in ou da a.
Figu e D.2d plo s he esul s. Fo simplici y, we assume ha income isk does no depend
on pa en al weal h.28
Finally, we se he consump ion loo c=NOK100,000 (≈$12,000), oughly ma ching
wha is le a e sub ac ing en al paymen s om a e - ax minimum disabili y paymen s.
28Fage eng e al. (2017) ind ha income isk is almos independen o educa ion. Since educa ion is
s ongly co ela ed wi h pa en al weal h, his sugges s ha any di e ence based on pa en al weal h is o
limi ed size.
62
Housing Pa ame e s To ind he g ow h a e and ola ili y o house p ices we use exis ing
home p ice indices. We de la e he nominal index by median household income, a e ax,
since income is s a iona y in he model. We hen use he obse ed mean g ow h and s anda d
de ia ion o se µh= 0.0288 and σh= 0.0468. Figu e D.2b plo s he ime ends o nominal
and eal- and income-de la ed house p ices in No way, as well as he mean g ow h a es and
s anda d de ia ions.
We calib a e house sizes o ma ch he 5 h, 25 h, 50 h, and 75 h pe cen iles o squa e
me e s o esiden ial uni s, which co espond o 44, 77, 100, and 143 squa e me e s, espec-
i ely. We no malize he smalles uni o ha e a size o 1. We assume ha he wo smalles
uni s can be en ed, so ha H(0) = [1.0,1.75]. We hen assume ha only he 3 la ges uni s
can be owned, such ha H(1) = [1.75,2.27,3.25].
We es ima e en - o-p ice a ios κin No way in wo s eps. Fi s , we use s a is ics on
yea ly en pe squa e me e , by ooms in he uni and p ice pe squa e me e , by ype
(single- amily, small mul i amily, and mul i amily). We hen di ide he en pe squa e
me e o uni s wi h 5 ooms by he single- amily squa e me e p ice, he 4 oom en al p ice
by he small mul i- amily p ice, and he 3 and 2 ooms p ices by he mul i amily p ice. In
he yea s we ha e da a, 2012-2022, he a ios a e ela i ely s able. We se κequal o 0.044,
he a e age en - o-p ice a ios o hese ou uni s’ se ies o e all yea s, see Figu e D.2e.29
P e e ence Pa ame e s We se he p e e ence weigh on housing η o 0.35, oughly
equal o he a e age o households aged 27-45 in Yao e al. (2015). We se he isk a e sion
pa ame e γ o 2.0, a s anda d alue in li e-cycle models.
Ini ial Condi ions To ind a household’s ini ial inancial weal h, we d aw om he empi -
ical dis ibu ion o households wi h non-weal hy pa en s, es ima ed non-pa ame ically (see
Figu e D.2c). We so he ne wo h o households aged 20-23 wi h non-weal hy pa en s and
di ide hem in o 10 equally sized bins by g oss inancial weal h. Households a e andomly
alloca ed o bins and ecei e an ini ial endowmen equal o he a e age o hei bin.
We d aw he households’ ini ial p oduc i i y shock om he s a iona y dis ibu ion im-
plied by equa ion (15). All households s a as en e s, bu a e allowed o choose o become
homeowne s in he i s pe iod.
Households d aw he ini ial house p ice ps om a uni o m dis ibu ion. We calib a e he
mean o he ini ial p ice in he ollowing way. In he ea ly 1990s, he a e age ma ke alue
o a ‘s a e home’, was abou 3.5 imes he a e age household income. Using ou calib a ed
29Fo simila models calib a ed o he Uni ed S a es, a s anda d alue is 0.05, based on Da is e al. (2008).
Ou somewha lowe es ima e could be d i en by di e ence in ax egula ion – en al income in duplexes a e
ax exemp i he owne li es in one uni – and o he ins i u ional di e ences.
63
income p ocess, he a e age income o households aged 20-80 is NOK 449,000 (≈$53,000)
and so we se he a e age ini ial p ice equal o 89.78 o one uni o housing, so ha he
p ice o he smalles owne -occupied uni is 3.5 imes he a e age income. The edges o he
dis ibu ion a e se a ±20%, so ha ps∼ U[0.8×89.78,1,2×89.78].
Remaining Ex e nal Pa ame e s The isk- ee a e is 0.016, he maximum le e age
dis 0.9, he maximum deb - o-income le el is 5.0, and housing dep ecia ion δis 0.02. We se
he mo gage p emium m o 0.039, he a e age sp ead since 1990, simila o wha is ound
in E a d (2014).
D.3 Mimicking Empi ical Reg essions in he Model
To e-c ea e he in e media ion analysis in he simula ed panel om he model, we pe o m
he ollowing analysis. We i s simula e households wi hou weal hy pa en s ( he pa en al
weal h dummy pw= 0). We hen simula e he same households, gi ing hem he same
shocks, bu his ime wi h weal hy pa en s (pw= 1). We de ine ¯w o be one i households
ha e abo e median weal h a age 43. We hen e alua e whe he a gi en household owned a
home a ages 27, 30, 33, and 36 o ge he homeowne ship indica o s.
To calcula e he housing channel, we un wo se s o eg essions - exac ly as in he
empi ical analysis. Fi s , we eg ess homeowne ship indica o s ha age jon a pa en al
weal h dummy and household cha ac e is ics:
hj
i=βj
0+βj
1piw+βj
3xi+ηi o j= 27,30,33,36
This mi o s equa ion (1) in Sec ion 3, bu wi hou o he pa en al cha ac e is ics powhich
a e no ele an in ou model se ing. Household cha ac e is ics xiis a ec o con aining
he house p ice when he household en e s he economy ( ela ed o he yea and egional
con ol a iables in he empi ical eg ession) as well as income (y) and dummies o bo h
income shocks (νand ϵ). All o he indi idual le el con ols a e measu ed a age j. The β1
pa ame e s cap u e he e ec o pa en al weal h on he p obabili y o being a homeowne a
age j.
Nex , we eg ess midli e weal h ¯won pa en al weal h, household cha ac e is ics and
homeowne ship indica o s:
¯wi=α0+α1pw
i+α3xi+X
j=27,30,33,36
αj
4hj
i+ϵi
64
This mi o s equa ion (5) in Sec ion 4, again lea ing ou he o he pa en al a ibu es.
The α4’s cap u e he e ec o homeowne ship on he p obabili y o being abo e median
weal hy a age 43. He e, he indi idual cha ac e is ics xia e measu ed a age 43.
We hen ha e wha we need o calcula e he (ne ) housing channel o in e gene a ional
weal h pe sis ence, as de ined in equa ion (7), which is Pjαj
4βj
1. The esul s a e epo ed in
Table 8.
D.4 Modeling Pa en al Suppo
To model he ini ial and he annual ans e s wi hou in oducing addi ional s a e a iables
we modi y he income p ocess. We add an age-dependen ans e o he le el o income
yi,a = exp( (a) + νi,a +εi,a) + τ(a).(26)
Fo he ini ial ans e we de ine
τ(a) = 


τP W
Tsi a=Ts,
0else.
(27)
And simila ly o he annual ans e
τ(a) = 


τP W i Ts≤a < Ts+ 20,
0else.
(28)
D.5 Nume ical De ails
The p oblem is sol ed backwa ds, by i s sol ing he alue unc ion o a e i ee a age T,
when dea h is ce ain. Fo each disc e e choice, we sol e o op imal consump ion choice
using B en ’s oo - inding algo i hm. The op imal policy is hen gi en by he disc e e choice,
and i ’s associa ed consump ion choice, ha maximizes u ili y. This p ocess is epea ed
backwa ds, un il age a=Ts.
The pe sis en income shock is disc e ized ollowing Rouwenho s (1995), while o he
shocks a e disc e ized on an equal p obabili y basis. Tha is, o ng id poin s, he p obably
o each ou come is 1/n and he alues o he shock a each g id poin is equal o he midpoin s
o he n−1quan iles o he unde lying dis ibu ion.
The pe sis en income shock ν ollows a 4-s a e Ma ko chain p ocess, and he ansi o y
income shock is disc e ized o 2 s a es, while he house p ice shock has disc e ized o 5
s a es. The ne wo h xand p ice pg ids a e bo h une enly spaced, wi h highe densi y
65

o lowe alues wi h 63 and 7 g id poin s, espec i ely. Fo alues no in he g ids we use
linea in e pola ion.
The model is sol ed in Julia 1.8.5, and in addi ion o s anda d packages we use
In e pola ions.jl 0.14.7 and Op im 1.7.4 o in e pola ion and op imiza ion ou-
ines.
66
D.6 Supplemen a y Model Figu es
(a) Mo gage P emium m(b) House P ices
(c) Ini ial Weal h (d) Calib a ed Income P ocess
(e) Ren - o-P ice Ra ios, Selec Sizes and Uni s ( ) Ren - o-P ice Ra ios, All Sizes and Uni s
Figu e D.2: Calib a ion Figu es
67
Figu e D.3: The Pa en al Weal h Housing Channel and P ice G ow h - Coefficien s
No es: This igu es plo s he coefficien s om he media ion analysis, see Sec ion 6.3.1 o mo e.
68
(a) LTV
(b) LTI
Figu e D.4: Coefficien s om he Media ion Analysis
No es: This igu es plo s he coefficien s om he media ion analysis, see Sec ion 6.3.2 o mo e.
69