Macroeconomic effects of the gender revolution

Be ghol , D ago; Fosso, Luca; Fu lane o, F ancesco
Wo king Pape
Mac oeconomic e ec s o he gende e olu ion
Wo king Pape , No. 19/2024
P o ided in Coope a ion wi h:
No ges Bank, Oslo
Sugges ed Ci a ion: Be ghol , D ago; Fosso, Luca; Fu lane o, F ancesco (2024) : Mac oeconomic
e ec s o he gende e olu ion, Wo king Pape , No. 19/2024, ISBN 978-82-8379-348-2, No ges
Bank, Oslo,
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Wo king Pape
Mac oeconomic E ec s o he Gende Re olu ion
No ges Bank Resea ch
Au ho s:
D ago Be ghol
Luca Fosso
F ancesco Fu lane o
Keywo ds:
Economic g ow h, gende
inequali y, labo ma ke ,
p oduc i i y, VAR wi h common
ends
19 | 2024
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ISSN 1502-8143 (online)
ISBN 978-82-8379-348-2 (online)
MACROECONOMIC EFFECTS OF THE GENDER REVOLUTION*
DRAGO BERGHOLT†, LUCA FOSSO‡AND FRANCESCO FURLANETTO§
Decembe 2024
Abs ac : U.S. labo ma ke da a exhibi a majo , secula decline in he employmen
and wage gaps be ween males and emales. In his pape , we iden i y he unde -
lying, s uc u al o ces and quan i y he spillo e om his gende con e gence o
he b oade mac oeconomy. A no el ime se ies model maps empi ical ends in
da a in o (agg ega e and gende -speci ic) s uc u al ends. Iden i ica ion is achie ed
wi h es ic ions de i ed om a neoclassical model wi h gende -speci ic labo . Em-
pi ically, we ind ha secula changes in emale-speci ic labo p oduc i i y accoun
o app oxima ely one- hi d o economic g ow h in he pos wa U.S. economy, in
addi ion o mos o he obse ed gende con e gence.
Keywo ds: Economic g ow h, gende inequali y, labo ma ke , p oduc i i y, VAR wi h common ends.
JEL Classi ica ion: C32, E10, E13, J2.
*This wo k should no be epo ed as ep esen ing he iews o he Eu opean Cen al Bank o No ges
Bank. The iews exp essed a e hose o he au ho s and do no necessa ily e lec hose o he Eu opean
Cen al Bank o No ges Bank. We hank o use ul commen s S e ania Albanesi, Jonas A ias, Philippe
And ade, Guido Asca i, Regis Ba nichon, Ma in Be aja, Paolo Bonomolo, Fabio Cano a, E em Cas el-
nuo o, And ea Ce a o, La y Ch is iano, Ma co Del Neg o, Ma in Eichenbaum, Domenico Giannone,
Luca Fo na o, Pe e Ka adi, Joseba Ma inez, Leona do Melosi, Ka el Me ens, Sil ia Mi anda Ag ippino,
E i Pappa, Gio gio P imice i, Lukasz Rachel, Giuseppe Ragusa, Gio anni Ricco, Juan Rubio-Rami ez,
Aysegul Sahin, S e an Schiman, semina pa icipan s a No hwes e n Uni e si y, Bos on Fed, Bos on Col-
lege, Chicago Fed, Dallas Fed, Fed Boa d, Uni e si y o Texas Aus in, Uni e si y o Cali o nia Da is,
Cle eland Fed, Washing on Uni e si y o Sain Louis, Eu opean Cen al Bank, No ges Bank, Uni e si y
o Aix-Ma seille, Uni e si y o Milano-Bicocca, 2021 Sailing he Mac o Con e ence in Ven o ene, 2021
con e ence in hono o Fabio Cano a in Hyd a, 2022 Pado a Mac o Talks, 2022 Ba celona Summe Fo-
um, 2022 Dolomi i Mac o Mee ings in Sel a Val Ga dena, 2022 Fo ske mø e in S a ange , 2023 SNDE
con e ence in O lando, 2023 IAAE con e ence in Oslo, 2023 CEF con e ence in Nice, 2023 Dyna e Con-
e ence in Mal a, 2023 Fall Midwes Mac o Mee ings in Lubbock, 2024 Wo kshop in Empi ical Mac oeco-
nomics King’s College London, 2024 RCEA In e na ional Con e ence in London, 2024 T2M Con e ence
in Ams e dam and 2024 SMN Con e ence in Mad id.
†No ges Bank. Email: d ago.be ghol @no ges-bank.no
‡Eu opean Cen al Bank. Email: luca. [email protected] opa.eu
§No ges Bank. Email: [email p o ec ed]. Co esponding au ho .
1 INTRODUCTION
Women’s inc eased labo ma ke pa icipa ion is a guably one o he undamen al changes
obse ed in mode n economies du ing he las cen u y. Conside , o example, he U.S.
labo ma ke da a in Figu e 1: in he 1960s, he employmen a e o emales was less
han hal o he employmen a e o males. Bu he emale- o-male employmen a io
inc eased s eadily h oughou he 1980s and 1990s, be o e con e ging o a ound 85 pe -
cen in ecen decades. Gende di e ences in wages display a simila pic u e. Al hough
women’s hou ly wages s ayed ela i ely la a 60 pe cen o men’s wages un il he mid
1970s (despi e a subs an ial employmen ca ch-up du ing ha pe iod), hey ha e since
ou g own male wages a abou he same pace as he addi ional g ow h in emale employ-
men , esul ing in a majo wage con e gence be ween he gende s. In o al, mo e han
60 pe cen o he emale- o-male employmen gap, and abou hal o he emale- o-male
wage gap, ha e disappea ed in he las 5-6 decades. I is ha dly a coincidence ha Goldin
(2006) e e s o a “quie e olu ion” when desc ibing hese ends.
The goal o ou pape is wo old: i s , we wan o quan i y he consequences o his
gende e olu ion o he U.S. mac oeconomy. In pa icula , we es ima e he spillo e
e ec s on economic g ow h in e ms o U.S. GDP, employmen , and p oduc i i y. An im-
po an pa o ou mo i a ion is he conce n ha alen may be signi ican ly misalloca ed
when only a mino i y o women pa icipa e in paid wo k, as ad oca ed by Hsieh, Hu s ,
Jones, and Klenow (2019). Second, we aim o shed ligh on he s uc u al d i e s behind
he gende con e gence in employmen and wages. A i s glance, he obse a ion ha
hese wo ends co-mo e may sugges ha labo demand ac o s ha e been dominan , as
s essed by Aguia and Hu s (2007) and Fukui, Nakamu a, and S einsson (2023). How-
e e , he agg ega e ime se ies shown in Figu e 1 a e silen abou any ealloca ion ac oss
di e en skill segmen s o he labo o ce, as well as ealloca ion ac oss sec o s. Ou aim
is o app op ia ely disen angle labo demand and labo supply ac o s once we con ol o
he ac ha he la ge inc ease in employmen o emale wo ke s was concen a ed in he
ma ke o high-skilled wo ke s and in he se ice sec o .
To iden i y he s uc u al ends o in e es in his pape , we de elop a neoclassical
model in ol ing gende -speci ic labo which builds on Albanesi (2024) and Fukui e al.
(2023).1The heo e ical amewo k allows us o de i e mu ually exclusi e iden i ica ion
es ic ions on h ee gende -neu al mac o ends and wo gende -speci ic labo ma ke
ends. In u n, we impose hese es ic ions on a S uc u al Vec o Au o eg essi e (SVAR)
model i ed o ele an mac o da a, as well as o da a on di e ences be ween emales and
males in wages and employmen . The esul ing econome ic amewo k allows us o
in e s uc u al gende ends empi ically, and o quan i y hei impo ance o he U.S.
mac oeconomy.
As ou key ocus is on slow-mo ing, s uc u al d i e s ha pe sis way beyond com-
mon business cycle ho izons, we use a SVAR model wi h common ends, as in Del Neg o,
Giannone, Giannoni, and Tambalo i (2017) and C ump, Eusepi, Giannoni, and Sahin
(2019).2The model can be seen as a mul i a ia e, unobse ed componen s model, in
1Albanesi (2024) es ima es a eal business cycle model wi h gende -speci ic labo o accoun o jobless
eco e ies. Fukui e al. (2023) ex end he model wi h home p oduc ion and open economy ea u es, show-
ing ha women’s ising pa icipa ion did no c owd ou males’ pa icipa ion, hus, being an expansiona y
ac o o he mac oeconomy.
2Mo e ecen ex ensions o he same model o explain in la ion dynamics include Asca i and Fosso (2024),
2

Figu e 1: Gende di e ences in employmen and wages
1965 1975 1985 1995 2005 2015
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
No es: The employmen (wage) gap is de ined as he emale- o-male a io in employmen (wage) a es.
Based on da a om The Cu en Popula ion Su ey, he Uni ed Census Bu eau, he Bu eau o Labo S a is-
ics, and au ho s’ calcula ions.
which he a iables en e in le els, and ansi o y and pe manen componen s in da a a e
disen angled om each o he . We seek o quan i y he la e . As an example, le us
conside GDP. Ou model decomposes obse ed GDP dynamics in o a cyclical and a pe -
manen componen . In u n, he pe manen componen —unde s ood as he empi ical o
educed- o m GDP end—is a unc ion o unde lying, s uc u al d i e s such as p oduc-
i i y and demog aphics (bo h o which can be gende -neu al o gende -speci ic). How-
e e , he mapping om hese s uc u al d i e s o he empi ical end in GDP is unknown
ex-an e. I is exac ly his iden i ica ion p oblem ha we add ess wi h es ic ions om eco-
nomic heo y. In pa icula , he heo e ical amewo k p esen ed he e implies a log-linea
mapping be ween end GDP and (gende -neu al) echnology shocks, (gende -neu al)
au oma ion shocks, (gende -neu al) labo supply shocks, as well as gende -speci ic labo
demand and labo supply shocks. We disen angle hese i e s uc u al o ces based on
hei long- un impac on economic a iables. This ep esen s a key dis inc ion om p e-
ious s udies es ima ing VARs wi h s ochas ic ends. Del Neg o e al. (2017) and C ump
e al. (2019), o example, es ima e selec ed common ends in da a, bu emain silen
abou he unde lying s uc u al sou ces. Ou amewo k, ins ead, allows us o es ima e
he mapping om s uc u al o empi ical ends, and o ins uc a Bayesian algo i hm we
deploy wi h p io in o ma ion de i ed om heo y.
We es ima e a baseline model whe e s anda d mac o da a o he U.S. economy a e
linked o da a on agg ega e gende di e ences in wages and employmen . The idea is o
Bianchi, Nicol`
o, and Song (2023), Hasenzagl, Pelleg ino, Reichlin, and Ricco (2022) and Ma ei-Faccioli
(2024).
3
in e he s uc u al d i e s o ends in wage and employmen di e ences be ween emales
and males, and o quan i y hei impo ance o he U.S. mac oeconomy. In a second s ep,
ollowing Dolado, Mo yo szki, and Pappa (2021) we use in o ma ion on indi iduals’ ed-
uca ion and sec o o employmen con ained in he Cu en Popula ion Su ey (CPS), and
es ima e ex ensions o he baseline model wi h da a on gende di e ences in skills and sec-
o s o employmen . The esul s om hese mo e g anula ex ensions a e hen compa ed
wi h hose om he baseline. The idea is o sepa a e “wi hin-skill” and “wi hin-sec o ”
ixed e ec s om “wi hin-gende ” ixed e ec s. Thus, we can disen angle undamen al
gende ends om ends in skills and sec o al composi ion, and gauge composi ional
e ec s ha may bias ou baseline esul s.
Ou main empi ical esul conce ns he mac oeconomic spillo e om gende -speci ic
labo ma ke ends in ou da a: hese ends, which cap u e he obse ed con e gence be-
ween emales and males, a e also essen ial o mac oeconomic g ow h in he pos wa
U.S. economy. Du ing he 70s, 80s and 90s o example, hey accoun o 30-50% o he
o e all end inc ease in GDP, and o 20-40% o he o e all end inc ease in p oduc-
i i y. Mo eo e , hey a e esponsible o a sizable sha e o he slowdown in end GDP
g ow h du ing he las 20 yea s, coinciding wi h a le eling-o o he gende con e gence
compa ed wi h ea lie decades. In o al, gende -speci ic ac o s explain almos one- hi d
o GDP g ow h in he pos wa U.S. economy, and hey p e en ed an o e all employmen
decline du ing his pe iod. Impo an ly, hese esul s a e ob ained when we con ol o
agg ega e mac o ends such as he e olu ion o o al ac o p oduc i i y.
In addi ion, s uc u al ac o s ha o igina e on he demand side o he labo ma ke
explain (i) mos o he long- e m gende con e gence in employmen and wages, (ii) he
end o he gende con e gence obse ed in he las 20-30 yea s, as well as (iii) almos
all ne spillo e s om gende -speci ic labo ma ke ends o he mac oeconomy. F om
an econome ic poin o iew, ou empi ical model sugges s ha he emale- o-male em-
ploymen a io ends o inc ease pe manen ly in pe iods when he e is a pe manen ise in
he wages o emales ela i e o he wages o males. This is consis en wi h a s o y abou
emale-speci ic p oduc i i y g ow h, which shi s labo demand owa ds emales. Supply-
side explana ions, by con as , should ha e implied s agnan wage g ow h o emales in
pe iods wi h s ong emale employmen g ow h. This is no wha we ypically see in ou
agg ega e da a.
Finally, while he ne spillo e om labo supply ac o s o he mac oeconomy is lim-
i ed, we documen an impo an ole o skill-biased ends in emales’ labo supply: when
gende gap da a by skill segmen s a e conside ed, a supply-d i en expansion o emale la-
bo in high-skill jobs eme ges, and a he same ime a con ac ion in he supply o emale
labo in low-skill jobs. In sum, hese wo o ces ha e led o subs an ial ealloca ion o
emales om low-skill o high-skill jobs. Mo eo e , he composi ional e ec s associa ed
wi h hese supply-d i en labo lows ac oss skill segmen s ha e likely con ibu ed o he
o e all con e gence in emale and male wages. A he same ime, hey ha e la gely coun-
e ac ed each o he in agg ega e da a on gende pay and employmen gaps. This is pa ly
why he ne spillo e e ec om gende -speci ic labo supply ac o s o he mac oecon-
omy a e so limi ed in ou baseline es ima ion. Bu ends in emales’ labo supply a e s ill
impo an o he mac oeconomy.
Ou pape speaks o a la ge li e a u e s udying he gende e olu ion. A use ul dis inc-
ion o ou pu poses is be ween pape s discussing labo demand ac o s and labo supply
4
ac o s. Among he o me , Galo and Weil (1996) emphasize echnological ac o s ha
a o ed he demand o women in combina ion wi h an inc ease in he e u ns o in ellec-
ual skills (Beaud y and Lewis (2014), Rendall (2024)) and he ise o he se ice sec o
(Ngai and Pe ongolo (2017), Bue a, Kaboski, and Zhao (2019)), while Jones, Manuelli,
and McG a an (2015) and Hsieh e al. (2019) poin o a educ ion in gende disc imi-
na ion and a educ ion in ba ie s o schooling as impo an d i e s o he con e gence
in wages. Among he la e , Albanesi and Oli e i (2016) and Goldin and Ka z (2002)
documen he impo ance o ad ances in ma e nal heal h and con acep ion, Fe n´
andez,
Fogli, and Oli e i (2004) emphasize cul u al ac o s de eloped du ing Wo ld Wa II, A -
anasio, Low, and S´
anchez-Ma cos (2008) poin o he c ucial ole o a ailabili y and
a o dabili y o child ca e, while G eenwood, Seshad i, and Yo ukoglu (2005) p opose a
model in which he eme gence o home appliances a o s emales’ ma ke p oduc ion a
he expense o home p oduc ion. We con ibu e o his li e a u e by p oposing a ho se ace
be ween labo supply and labo demand ac o s in he con ex o a mac oeconomic ime-
se ies model. While less de ailed in e ms o he unde lying ansmission mechanisms,
ou analysis p o ides a clea link be ween gende ends and mac oeconomic ou comes.
Wi hin he la ge li e a u e s udying he gende con e gence, ou pape is closely e-
la ed o wo seminal pape s quan i ying he ole o gende o mac oeconomic dynamics
in calib a ed quan i a i e se -ups. Bo h Hsieh e al. (2019) and Hea hco e, S o esle en,
and Violan e (2017) p opose a decomposi ion o US mac oeconomic g ow h in s uc u al
models wi h gende and ind a majo ole o gende o ces. Ou esul s a e in he same
ballpa k as hei s, bu ob ained using a simple ime se ies model which is subs an ially
less pa ame e ized and es ima ed ( a he han calib a ed) on US qua e ly da a. Albanesi
(2024) is also o pa icula in e es . Using an es ima ed eal business cycle model wi h
a gende dimension, she inds ha women’s ela i e labo supply and p oduc i i y ha e
been impo an o changes in he business cycle, and mo e gene ally, o he economic
pe o mance in he US.
The explici use o heo y o o m p io s o an es ima ed, empi ical ime se ies model
ela es ou wo k o he well-known DSGE-VAR me hodology p oposed by Del Neg o
and Scho heide (2004). As in hei case, we a e conce ned abou he po en ial mis-
speci ica ion induced by he igh c oss-equa ion es ic ions ea u ed by a ully speci ied
heo e ical model. The e o e, we use heo y only as a p io o in o m he VAR wi h
common ends. Di e en ly om Del Neg o and Scho heide (2004), we ocus on he
a iables’ pe manen componen s and no on he cycle. Mo eo e , we o m p io s abou
speci ic s uc u al elas ici ies, a he han he ull co a iance s uc u e implied by heo y.
The es o he pape is o ganized as ollows: sec ion 2 in oduces he empi ical end-
cycle model ha we i o U.S. labo ma ke da a (agg ega e and gende -speci ic). Sec-
ion 3 desc ibes he heo e ical amewo k ha disciplines ou empi ical assessmen o
ends, while sec ion 4 de i es he exac , heo y- obus iden i ica ion es ic ions. Sec-
ion 5 documen s he pape ’s main empi ical esul s. Sec ion 6 akes s ock and pu s ou
esul s in pe spec i e. Sec ion 7 ela es he gende con e gence in wages and employmen
o ends in he skills and he ise o se ices, while sec ion 8 conside s s uc u al changes
speci ic o male labo . Sec ion 9 concludes.
5
2 A TIME SERIES MODEL WITH COMMON TRENDS
The model ha we es ima e is a mul i a ia e ime se ies model wi h unobse ed compo-
nen s, see Wa son (1986), S ock and Wa son (1988,2007), and Villani (2009). I decom-
poses a ec o o obse able da a in o wo unobse able, s ochas ic componen s: he i s
componen is cha ac e ized by cyclical bu ansi o y luc ua ions. The second compo-
nen cap u es pe manen changes, o ends, in da a. One dis inc i e con ibu ion o ou
pape is o map hese ends in o a ec o o unde lying, s uc u al d i e s. Impo an ly,
he s uc u al d i e s may gi e ise o common ends in da a, e en i he s uc u al d i e s
hemsel es a e o hogonal o each o he . To ix ideas, conside an n×1 ec o o da a Y ,
which is he sum o wo unobse ed s a es:
Y =ˆ
Y +¯
Y ,(1)
ˆ
Y and ¯
Y ep esen he cycles and ends in ou da a, espec i ely. As such, equa ion (1)
is a pu ely s a is ical ( educed- o m) decomposi ion o he da a. The ocus o ou pape
will be on he empi ical ends in ¯
Y and, mo e p ecisely, on he unde lying causal d i e s
behind ¯
Y . We suppose ha ¯
Y can be decomposed in o q≤ns uc u al ends, collec ed
in he q×1 ec o X :¯
Y =VX (2)
He e, Vis a n×qma ix ha maps he educed- o m ends in o s uc u al, economic ac-
o s. Simila ly o Del Neg o e al. (2017) and C ump e al. (2019), we ea he s uc u al
ends as sepa a e andom walk p ocesses, po en ially wi h a d i :
X =c+X −1+u , u ∼ N(0q,Σu)(3)
Th oughou we assume ha he co a iance ma ix Σuis diagonal. This is s anda d gi en
ha u is a ec o o s uc u al end shocks. Ne e heless, he p esence o non-ze o,
o -diagonal elemen s in he ma ix Vs ill implies common, s ochas ic ends ac oss he
indi idual componen s o ¯
Y . A i al pa o ou analysis will be o iden i y V, gi en ha
we a e in e es ed in he causal d i e s o ends in da a. Mo eo e , since ou ocus is
on ends a he han on business cycle luc ua ions, only a minimal se o es ic ions is
imposed on ˆ
Y . In pa icula , we model ˆ
Y as a ec o au o eg essi e (VAR) p ocess in
educed- o m:
Φ(L)ˆ
Y =e , e ∼ N(0n,Σe)(4)
Φ(L) = I−Φ1L−... −ΦpLpis an n×nma ix o lag coe icien s. Σeis eely
es ima ed wi hou any es ic ions on he o -diagonal elemen s. Howe e , we assume ha
pe manen and ansi o y shocks a e mu ually unco ela ed, i.e. ha co (u , e ) = 0. In
he pa lance o Wa son (1986), he model is an ”independen end-cycle decomposi ion”
and ends do no a ec he cycle by cons uc ion.3
Equa ions (1)-(4) cons i u e he model ha we con on wi h da a. I is he combina-
ion o ele an (agg ega e and gende -speci ic) labo ma ke da a, oge he wi h a p ope
iden i ica ion o V, ha allows us o in e gende -speci ic ends and quan i y hei im-
po ance o he U.S. mac oeconomy. A i s me hodological con ibu ion o his pape
3I any hing, a iola ion o his assump ion may bias es ima es in he cyclical block gi en by (4). Howe e ,
we iew he assump ion as a he innocuous, gi en ha ou sole in e es is in secula ends and no in
cyclical luc ua ions.
6
4.2 REVISITING THE MAPPING TO EMPIRICAL TRENDS
We a e now in a posi ion o speci y a baseline, heo y-consis en mapping V om he
s uc u al ends X o ends in da a ¯
Y :






¯
GDP
¯
W
¯
L
¯w ,
¯
l ,






| {z }
¯
Y
=





1 1 1 ν14 ν15
1 0 0 ν24 ν25
0 1 ν33 ν34 ν35
0 0 0 1 −1
0 0 0 λ γ






| {z }
V






A
Ψ
α
a ,
ψ ,






| {z }
X
(23)
The i s column o Vimposes es ic ions on he s ochas ic echnology end. We no mal-
ize i o ha e a uni e ec on GDP and wages, and ze o long- un e ec s on he emaining
a iables. The second column o Vgo e ns he spillo e om he agg ega e labo supply
end, which is no malized o cause a uni inc ease in GDP and employmen , while he
hi d column in Vimposes ha au oma ion pe manen ly inc eases GDP and lowe s em-
ploymen . The la e es ic ion implies ha ν33 <0. Consis en wi h Figu e 2 we impose
ze o- es ic ions on he emaining elemen s in V o bo h labo supply and au oma ion.
No e ha mos ze o- es ic ions a e based on he assump ion ha mac o shocks do no pe -
manen ly a ec gende gaps in wages and employmen . This assump ion, which g ea ly
acili a es iden i ica ion o V, e ec i ely ules ou composi ional e ec s o gende -neu al
mac o shocks. Howe e , we inspec he possibili y o composi ional e ec s in sec ion 7.
The ou h and i h columns in Vgo e n he long- un implica ions o pe manen
changes in emale-speci ic labo p oduc i i y and labo supply, espec i ely. We no -
malize bo h o hese ends so ha hey ha e a uni a y e ec on he wage gap be ween
emales and males. Tha is, a he han es ima ing a , and ψ , , we iden i y ˜a , ≡a
γ−1
γ+λ
,
and ˜
ψ , ≡ψ
1+λ
γ+λ
, . This is pa icula ly con enien , as can be seen om he no malized,
log-linea e sions o (21)-(22):
ˆw , =cw, +ˆ
˜a , −ˆ
˜
ψ , (24)
ˆ
l , =cl, +λˆ
˜a , +γˆ
˜
ψ , (25)
A ha means ha he a iable is exp essed in loga i hms, wi h cw, and cl, being educed-
o m cons an s. Impo an ly, he gende subs i u ion elas ici ies λand γ, wo s uc u al
pa ame e s o pa icula in e es , en e di ec ly as coe icien s in (25). This means ha
λ=ν54 and γ=ν55 can be ead di ec ly om he es ima ed ma ix V.
The es ic ions imposed on each column in Va e mu ually exclusi e, which is wha
we need o sepa a ely iden i y he i e s ochas ic ends o in e es . The agg ega e ech-
nology end, o example, is he only agg ega e mac o end ha makes he eal wage
co-mo e wi h GDP in he long- un and, consis en wi h he balanced g ow h pa h as-
sump ion, is he only one ha has ze o long- un e ec on employmen . Agg ega e labo
supply and au oma ion can be disen angled in da a because he o me implies long- e m
co-mo emen GDP and employmen , while he la e c owds ou labo . Finally, emale-
speci ic labo demand and labo supply a e sepa able om agg ega e mac o ends be-
cause hey a e he only d i e s o long- un wage and employmen gaps be ween emales
13

Table 1: P io dis ibu ions and pos e io es ima es
P io Pos e io
Densi y Suppo Mean Mode 90% HPD
ν14 a →¯
GDP Uni o m [0,1] 0.91 0.98 (0.74, 0.99)
ν24 a →¯
WUni o m [0,1] 0.60 0.67 (0.33, 0.81)
ν34 a →¯
LUni o m [−0.5,0.5] 0.30 0.36 (0.09, 0.46)
ν15 ψ →¯
GDP Uni o m [0,2] 0.42 0.10 (0.02, 1.04)
ν25 ψ →¯
WUni o m [−2,0] -0.15 -0.02 (-0.48, -0.00)
ν35 ψ →¯
LUni o m [0,3] 0.54 0.29 (0.04, 1.23)
−ν33 α→¯
LΓ(0.3,0.15) (0,∞)0.39 0.40 (0.21, 0.60)
λ a →¯
l , Γ(1,0.5) (0,∞)1.53 1.63 (0.95, 2.18)
γ ψ →¯
l , Γ(3,1.5) (0,∞)3.26 3.17 (2.44, 4.20)
No es: The pos e io momen s a e gene a ed om he las 10,000 o 50,000 d aws gene a ed om he
RW Me opolis-Has ings algo i hm. Γ(µ, σ2) e e s o he Gamma dis ibu ion wi h mean µand a iance
σ2.
and males. Mo eo e , hey a e uniquely iden i ied because hey imply opposi e signs on
he co-mo emen be ween gende gaps in wages and employmen .5
4.3 PRIORS
The las s ep is o speci y p io shapes o he es ima ed pa ame e s. Table 1 summa izes
ou choice o p io s. We aim o an agnos ic app oach and use uni o m p io s o all elas-
ici ies go e ning he eedback om gende ends o he agg ega e mac oeconomy. The
suppo o each uni o m p io la gely e lec s he unce ain y bands compu ed du ing he
Mon e Ca lo exe cise, as shown in Figu e 2. Tha is, consis en wi h heo y, he emale-
speci ic p oduc i i y shock beha es quali a i ely as a echnology shock in he agg ega e
gi en ou p io s, while he emale-speci ic labo supply shock beha es as a gende -neu al
labo supply shock o agg ega e a iables. The p io o he agg ega e employmen e-
sponse o au oma ion has a Gamma dis ibu ion, e lec ing ha au oma ion (a decline in
α ) c owds ou employmen . No e ha we impose he p io on −ν33, since he Gamma
dis ibu ion has a posi i e suppo .
The inal wo pa ame e s ha we es ima e a e γand λ. The gende -speci ic labo
demand elas ici y γhas been quan i ied in a ew exis ing s udies. Weinbe g (2000), o
example, inds ha γis a ound 2.4 in he US, while Acemoglu, Au o , and Lyle (2004)
epo a sligh ly highe alue o 3. Albanesi (2024) and Fukui e al. (2023) ha e consid-
e ed alues be ween 4 and 5. Thus, we choose a Gamma-p io o γcen e ed a ound 3
wi h mos o he p obabili y mass loca ed be ween 1 and 5. The e idence on λ, which
cap u es complemen a i y be ween males’ and emales’ leisu e ime, is mo e scan . Ngai
5No e ha he ze o es ic ions on employmen in esponse o a echnology shock and on agg ega e wages
in esponse o au oma ion and labo supply shocks a e no c ucial o iden i ica ion. In Appendix D.2, we
show ha esul s change only ma ginally i we elax hese assump ions. In addi ion, a mo e conse a i e
se o p io s il ed agains mac o e ec s o gende shocks is e alua ed in Appendix D.1.
14
Figu e 3: Es ima ed empi ical end o eal GDP and agg ega e employmen
1965 1975 1985 1995 2005 2015
3.6
3.8
4
4.2
4.4
4.6
1965 1975 1985 1995 2005 2015
56
58
60
62
64
No es: obse ed da a ( ed solid line), median end es ima e (blue solid line), and 68% co e age bands
(blue shaded a eas). The g ey a eas ep esen NBER ecessions.
and Pe ongolo (2017) use a alue o 0.19 based on mic o-e idence om Goux, Mau in,
and Pe ongolo (2014).6Thus, we choose a Gamma p io o λwi h abou 60% o he
p obabili y mass below one, and whe e he es ima e om Goux e al. (2014) is co e ed by
he 90% c edible p io bands (e en hough much highe alues a e allowed as well du ing
es ima ion). A de ining ea u e o ou p io s is ha i ms can swi ch be ween emale and
male labo mo e easily han households (λ<γ) a he p io mode, a ea u e ha seems
highly easonable.
5 EMPIRICAL RESULTS
In his sec ion, we p esen he main empi ical esul s based on he es ima ed ime se ies
model desc ibed in sec ion 2. Gi en he heo e ical es ic ions de i ed in sec ion 3 and
sec ion 4, he ec o o obse able a iables Y includes: (i) eal GDP, (ii) eal agg ega e
wages, (iii) he agg ega e employmen - o-popula ion a io, (i ) he a io o emale- o-male
wages, and inally ( ) he a io o emale- o-male employmen . All a iables en e he
sys em in log-le els. The model is es ima ed o e he sample pe iod 1960:Q1-2019:Q4,
and we choose p= 4 lags in he sys em gi en ha da a a e obse ed a a qua e ly
equency. We use Bayesian me hods o es ima e he model. In pa icula , a Gibbs sample
is designed o gene a e 50,000 d aws, whe e he i s 80% o he d aws a e disca ded as
a bu n-in sample and he las 20% se e o gene a e pos e io momen s. The algo i hm
includes a Me opolis-Has ings s ep ha d aws om he pos e io o he elas ici ies in V.
De ails on he es ima ion s eps, da a sou ces and cons uc ion a e laid ou in Appendixes
A and B, espec i ely.7
6Goux e al. (2014) exploi a wo kweek educ ion policy in F ance o ob ain an es ima e ha e lec s pu e
c oss-hou e ec s ac oss pa ne s and no income e ec s.
7All ou da a a e published by he Bu eau o Economic Analysis and he Bu eau o Labo S a is ics, and
can be downloaded om he FRED websi e. In he baseline speci ica ion, da a on employmen and wages
include bo h single and ma ied indi iduals. In Appendix D.3, we es ic ou a en ion o ma ied couples
only. Olsson (2024) and Albanesi and P ados (2022) model explici ly he he e ogenei y in ma i al s a us.
15
Figu e 4: Pos e io dis ibu ions o coe icien s λand γ.
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
5.1 PERMANENT AND TRANSITORY COMPONENTS
The i s se o esul s is ela ed o he decomposi ion o obse able da a in o a iable-
speci ic, pe manen and ansi o y componen s. Figu e 3 epo s he es ima ed pe manen
componen s o agg ega e ou pu and employmen . Ou model-implied end es ima es
seem o be la gely consis en wi h popula na a i es o ends in US mac o da a: The
GDP end, o example, has displayed lowe a e age g ow h in he las 20 yea s o da a,
and i le eled o comple ely du ing (and jus a e ) he 2008 inancial c isis. Mo eo e ,
he model assigns a la ge sha e o he obse ed employmen decline in he las 15 yea s o
pe manen ac o s: i essen ially concludes ha he employmen a e was back o i s own
end by he end o ou sample, despi e being 3-4 pe cen age poin s lowe han be o e
he inancial c isis. A secula decline in end employmen s a ing in he la e 1990s is
impo an o his esul . In e es ingly, ou model-implied es ima e o he ou pu gap—
de ined as he di e ence be ween obse ed GDP and he in e ed pe manen coun e pa
(see Figu e C.2 in he appendix)—exhibi s a co ela ion coe icien o 0.88 wi h he ou pu
gap epo ed by he Cong essional Budge O ice (CBO). The la e cons i u es a classic
benchma k in he li e a u e. Such a high co ela ion is nei he ob ious no a ge ed, as ou
SVAR is no in o med by da a on he CBO es ima es. We conclude ha ou model o e s
a easonable desc ip ion o ends and cycles in GDP in he pos wa US economy, and
ha i can be used as a labo a o y o in es iga e he s uc u al d i e s o ends in da a.8
5.2 ESTIMATED PARAMETERS IN V
Pos e io s o he nine es ima ed pa ame e s in Va e summa ized in Table 1, while Figu e
4 plo s he ull pos e io dis ibu ions o λand γ. Despi e using a p io wi h subs an ial
mass below 1, we ob ain a pos e io densi y o λ ha is cen e ed a ound 1.5. This implies
ha a 1 pe cen inc ease in he wage o emales ela i e o ha o males, when caused
by pe manen p oduc i i y imp o emen s among emales, is associa ed wi h a 1.5 pe cen
inc ease in he employmen a e o emales ela i e o ha o males. Mo eo e , mos o he
pos e io p obabili y mass o λis loca ed be ween 1 and 2. The pos e io mean alue o
8An equi alen decomposi ion is p o ided in Appendix C o he emaining a iables.
16
γ, in con as , is 3.3. Thus, a pe manen ise in emales’ labo supply, scaled o educe he
ela i e wage o emales by 1 pe cen , inc eases he employmen a e o emales ela i e
o males by mo e han 3 pe cen a he pos e io mean. This numbe is close o, bu
somewha highe han hose ob ained by Acemoglu e al. (2004) and Weinbe g (2000)
( hey epo alues o 3 and 2.5, espec i ely). Howe e , he pos e io dis ibu ion o γ
in Figu e 4 co e s well bo h o hese es ima es.
When i comes o he emaining coe icien s in Table 1, he pos e io dis ibu ions
o ν14,ν24 and ν34 a e shi ed u he away om ze o compa ed wi h he p io s. These
elas ici ies go e n he sensi i i y o agg ega e ou pu , wages and employmen o a gi en
change in emales’ p oduc i i y. The shi is pa icula ly p onounced o ou pu , whe e
mos o he pos e io mass is loca ed close o he uppe bound o he uni o m p io . The
es ima ed eedback elas ici ies o emale-speci ic labo supply, ν15,ν25 and ν35, e eal
a di e en pa e n. He e, hey all mo e om he p io owa ds ze o in absolu e alues,
e lec ing ha a gi en change in emales’ labo supply has smalle e ec s on he mac oe-
conomy in da a han wha ou p io s would indica e. Howe e , o gauge he quan i a i e
ole o emales-speci ic labo supply shocks, we would ha e o ake in o accoun he
mo emen in ψ , as well. This is done below. Finally, he employmen sensi i i y o a
gi en change in au oma ion, ν33, has a pos e io cen e ed a ound -0.4. Taking he no mal-
iza ion o his end in o accoun , a back-o - he-en elope calcula ion sugges s ha mos o
he labo p oduc i i y imp o emen s a ising om au oma ion can be a ibu ed o highe
ou pu a he han o job des uc ion.9
5.3 TREND DECOMPOSITIONS
Es ima ed con ibu ions o he di e en s uc u al ac o s o each empi ical end in ou
da a a e documen ed in Figu e 5. Le us i s conside he ends in emale- o-male
employmen and wage a ios, which we decompose in o emale-speci ic labo demand
(g een) and emale-speci ic labo supply (ligh blue). Recall ha hese a e he only s uc-
u al ac o s ha a ec gende gaps in wages and employmen in ou amewo k. We ind
i ins uc i e o dis inguish be ween h ee sepa a e phases in ou sample: in he i s 15-20
yea s o da a, bo h emale-speci ic demand and emale-speci ic supply con ibu ed signi -
ican ly o a secula inc ease in he employmen a e o emales ela i e o ha o males.
Howe e , he p ominen ole o women’s labo supply also kep hei wage g ow h ela-
i ely modes , explaining why he wage gap be ween women and men emained somewha
s agnan du ing his pe iod. Then, s a ing a ound 1980, he ela i e labo supply inc ease
among emale wo ke s ceased o ake place, causing women’s wages o signi ican ly ou -
g ow he wage o males. The inal phase in ou da a s a ed in he la e 1990s. Since hen,
he wage and employmen g ow h among emales ha e been much mo e modes and mo e
in line wi h wha we obse e o men. While some con e gence has aken place, he gen-
de gaps ha e been much mo e s able in he las 20-25 yea s o ou da a. Impo an ly, ou
model la gely a ibu es his obse a ion o lowe , emale-speci ic p oduc i i y g ow h.
The second and hi d ows o Figu e 5 documen how gende -speci ic labo ma ke ac-
o s ha e a ec ed agg ega e ends in he pos -wa US mac oeconomy. Female-speci ic
9A uni inno a ion o ou no malized au oma ion shock aises ou pu by 1 pe cen and lowe s employmen
0.4 pe cen . Thus, labo p oduc i i y inc eases by 1.4 pe cen , and mo e han wo- hi ds o his is due o
highe ou pu .
17
Figu e 5: A s uc u al decomposi ion o he empi ical ends
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
1965 1975 1985 1995 2005 2015
0
0.1
0.2
0.3
0.4
0.5
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
1965 1975 1985 1995 2005 2015
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1965 1975 1985 1995 2005 2015
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
No es: Empi ical ends (black lines) s. he con ibu ions o indi idual s uc u al ends (colo ed ba s).
Ve ical axes ep esen log de ia ions om ini ial alues, ho izon al axes measu es ime in qua e s. Poin -
wise median es ima es a e epo ed.
p oduc i i y g ow h (g een), in pa icula , accoun s o a sizable sha e o he o e all in-
c ease in end GDP and eal wages. Mo eo e , emale-speci ic p oduc i i y g ow h ex-
plains mos o he pos wa ise in employmen a es, which would ha e allen on a e age
18

Table 2: G ow h ac o s in he US economy
A. Baseline accoun
(1) GDP (2) Labo p oduc i i y
To al AΨα a ψ To al A α a ψ
1960-1969 2.8 1.8 0.1 0.3 0.5 0.1 2.5 1.8 0.4 0.3 0.0
1970-1979 2.1 1.1 0.0 0.1 0.8 0.1 1.7 1.1 0.1 0.5 0.0
1980-1989 2.1 0.7 0.2 0.2 1.0 0.0 1.7 0.7 0.3 0.7 0.0
1990-1999 2.0 0.8 0.2 0.4 0.6 0.0 1.8 0.8 0.6 0.4 0.0
2000-2009 1.2 0.3 0.0 0.6 0.3 0.0 1.4 0.3 0.9 0.2 0.0
2010-2019 1.1 0.5 0.0 0.4 0.2 0.0 1.2 0.5 0.6 0.1 0.0
(3) Agg ega e employmen (4) Agg ega e wages
To al Ψα a ψ To al A a ψ
1960-1969 0.3 0.1 -0.1 0.2 0.1 2.1 1.8 0.3 0.0
1970-1979 0.4 0.0 0.0 0.3 0.1 1.6 1.1 0.5 0.0
1980-1989 0.5 0.2 -0.1 0.4 0.0 1.4 0.7 0.7 0.0
1990-1999 0.2 0.2 -0.2 0.2 0.0 1.2 0.8 0.4 0.0
2000-2009 -0.1 0.0 -0.2 0.1 0.0 0.5 0.3 0.2 0.0
2010-2019 -0.1 0.0 -0.2 0.1 0.0 0.6 0.5 0.1 0.0
B. Coun e ac ual: no gende ends
(1) GDP (2) Labo p oduc i i y
To al AΨα a ψ To al A α a ψ
1960-1969 2.7 2.1 0.3 0.3 – – 2.5 2.1 0.4 – –
1970-1979 2.1 1.7 0.3 0.1 – – 1.8 1.7 0.1 – –
1980-1989 2.1 1.4 0.4 0.3 – – 1.8 1.4 0.4 – –
1990-1999 2.0 1.2 0.3 0.5 – – 1.8 1.2 0.6 – –
2000-2009 1.0 0.4 0.0 0.6 – – 1.3 0.4 0.9 – –
2010-2019 1.1 0.6 0.1 0.4 – – 1.2 0.6 0.6 – –
(3) Agg ega e employmen (4) Agg ega e wages
To al Ψα a ψ To al A a ψ
1960-1969 0.2 0.3 -0.1 – – 2.1 2.1 – –
1970-1979 0.3 0.3 0.0 – – 1.6 1.6 – –
1980-1989 0.3 0.4 -0.1 – – 1.4 1.4 – –
1990-1999 0.1 0.3 -0.2 – – 1.2 1.2 – –
2000-2009 -0.2 0.0 -0.2 – – 0.5 0.5 – –
2010-2019 0.0 0.1 -0.1 – – 0.6 0.6 – –
No e: S uc u al decomposi ions o he a e age, annual end g ow h a es o (1) eal GDP, (2) labo p oduc i -
i y, (3) agg ega e employmen and (4) agg ega e wages (by decade), in o o al ac o p oduc i i y A, au oma ion
α, gende -neu al labo supply Ψ, emale-speci ic p oduc i i y a , and emale-speci ic labo supply ψ . Panel
A: baseline model wi h gende -speci ic end shocks. Panel B: es ic ed model wi h dogma ic ze o-p io s on he
elas ici ies go e ning eedback om gende -speci ic shocks o he mac oeconomy. All numbe s a e poin -wise
median es ima es.
since 1960 in he absence o his secula end. This sugges s a a he mu ed c owding
ou o men when women en e he labo ma ke , a poin which we e u n o in sec ion 8.
19
Female-speci ic p oduc i i y is also an impo an d i e o agg ega e labo p oduc i i y—
he e measu ed as ou pu pe wo ke —sugges ing ha women en e ing he labo ma ke
caused p oduc i i y gains beyond he me e scale e ec s o ha ing a g ea e labo o ce.
Finally, we no e ha while he end in emale-speci ic labo supply (ligh blue) has con-
ibu ed o agg ega e employmen , i has played only a minimal ole o GDP, eal wages,
and agg ega e labo p oduc i i y. This inding sugges s ha he pe iods wi h ex ao dina y
g ow h in emales’ labo supply did no coincide wi h ex ao dina y inc eases in end
GDP, causing he pos e io o ν15 o shi owa ds ze o (compa ed wi h hei espec i e
p io dis ibu ions).
When i comes o agg ega e, gende -neu al ac o s, o al ac o p oduc i i y (blue)
seems o be he quan i a i ely mos impo an d i e o end GDP, wages and labo p o-
duc i i y in ou da a. Agg ega e labo supply (pu ple) ne e plays an impo an ole o
GDP, bu has s imula ed o al employmen . Finally, labo -displacing au oma ion (yellow)
has no only con ibu ed signi ican ly o highe GDP and labo p oduc i i y o e ime, bu
also o lowe employmen . In pa icula , oge he wi h he slowdown o gende -speci ic
ends, au oma ion appea s o be he main cause o he secula decline in agg ega e em-
ploymen a es o e he ecen decades. Au oma ion also explains mo e o less he en i e
disconnec be ween eal wages and labo p oduc i i y in ou sample.10
Table 2 summa izes ou accoun o economic g ow h in he pos wa US economy. Fo
each decade, we decompose he a e age, annual g ow h a es in he end componen s o
GDP and labo p oduc i i y in o he es ima ed con ibu ions o he i e s uc u al d i e s.
Fo now, we es ic a en ion o Panel A, which documen s he g ow h accoun ing implied
by he baseline model. Impo an ly, bo h GDP g ow h and labo p oduc i i y g ow h ha e
declined subs an ially in ou da a, om abou 2.8and 2.5pe cen age poin s pe yea in
he 1960s, o 1.1-1.4pe cen age poin s in he las 20 yea s. The decline has mos ly aken
place in wo wa es, be ween he 1960s and 1970s, and a he beginning o he 2000s. Also
he g ow h a e o wages has allen consis en ly in ou sample, while employmen s a ed
o s agna e in he 1990s. The slow-down in economic g ow h (as well as he iming o
he wo wa es) is well-documen ed and has mo i a ed a la ge li e a u e on he possible
causes, see, e.g. Sy e son (2017) o a e iew.
Fo he sample as a whole, we ind ha mos o he slow-down is a ibu ed o o al
ac o p oduc i i y, which in annual g ow h e ms ell by mo e han 50% o e he i s
wo decades.11 Howe e , up un il he 1980s, lowe o al ac o p oduc i i y g ow h was
subs an ially coun e ac ed by a secula inc ease in emale-speci ic p oduc i i y: i s con-
ibu ion o end GDP g ow h wen om 0.5pe cen age poin s pe yea in he 1960s o
1pe cen age poin in he 1980s. Fo labo p oduc i i y, i s con ibu ion inc eased om
0.3 o 0.7pe cen age poin s pe yea . Thus, emale-speci ic labo p oduc i i y doubled i s
annual g ow h a e—and as a esul —i s con ibu ion o end g ow h, be ween he 1960s
and he end o he Cold Wa .
This pic u e has changed undamen ally in he las 30 yea s o da a: no only has
he o e all g ow h a e o gende -neu al mac o ends con inued o decline be ween he
10This esul implies ha he au oma ion end is he dominan d i e o he labo sha e decline, as in
Be ghol e al. (2022). This is isually con i med in Figu e C.3 in he appendix, whe e we compu e and
s uc u ally decompose he model-implied end in he US labo income sha e.
11The annual g ow h a e in o al ac o p oduc i i y ell om 1.8pe cen age poin s in he 1960s o 0.7
pe cen age poin s in he 1980s.
20
1990s and he 2010s, bu also wo- hi ds o emale-speci ic labo p oduc i i y g ow h has
disappea ed du ing his pe iod. The la e esul is impe a i e o g ow h accoun ing in
ecen decades acco ding o ou model: be ween he 1990s and 2010s, he slow-down in
emale-speci ic labo p oduc i i y is esponsible o abou hal o he o e all decline in
he g ow h a es o end GDP and labo p oduc i i y.
O e all, we a i e a h ee main akeaways om he es ima ion o ou empi ical model:
i s , gende -speci ic labo ma ke ends a e quan i a i ely impo an o he US mac oe-
conomy. Fo example, hey accoun o almos one- hi d o he o e all pos wa inc ease
in end GDP, and mo e han one- i h o he pos wa inc ease in labo p oduc i i y. Sec-
ond, abou i y pe cen o he slowdown in economic g ow h obse ed in he las 25 yea s
is a ibu ed o a slowdown in he employmen con e gence be ween emales and males.
Thi d, he ca ch-up o emales’ employmen obse ed in he las 60 yea s is mainly, i no
en i ely, a consequence o labo demand ac o s. No ably, all hese esul s a e con i med
also when using a p io speci ica ion il ed agains mac o e ec s o gende shocks, as
shown in Appendix D.1.
6 TAKING STOCK
The impo an impac o gende -speci ic labo ma ke ends o mac oeconomic g ow h
documen ed in his pape is consis en wi h he analyses by Hsieh e al. (2019) and Hea h-
co e e al. (2017) in he con ex o calib a ed models. Hsieh e al. (2019) de elop a Roy
model o occupa ional choice and conclude ha declining obs acles o human capi al ac-
cumula ion, as well as educed disc imina ion, may explain a ound hal o GDP pe -capi a
g ow h be ween 1960 and 2010. Hea hco e, S o esle en, and Violan e (2010) s udy a neo-
classical g ow h model wi h incomple e ma ke s and o e lapping gene a ions, and ind
ha emale-speci ic demand ac o s explain mos o he inc ease in emales’ labo supply,
which in u n d o e hal o he g ow h in ea nings pe capi a be ween 1967 and 2002
(Hea hco e e al.,2017). While he conclusions eached in hese pape s seem la gely con-
sis en wi h ou s, we ake a qui e di e en app oach by es ima ing an empi ical ime se ies
model wi h subs an ially ewe c oss-equa ion es ic ions.
6.1 WHY IS FEMALE-SPECIFIC PRODUCTIVITY IMPORTANT?
To be e unde s and why he da a p e e such an impo an ole o emale-speci ic p o-
duc i i y g ow h, we ind i in o ma i e o con on he implica ions o end shocks in
ou es ima ed model wi h empi ical pa e ns in da a.
The i s impo an piece o in o ma ion is he obse ed, common ise o women’s
wages and employmen ela i e o males. Recall ha , by cons uc ion, none o he gende -
neu al mac o shocks can accoun o his empi ical ea u e. Mo eo e , equa ions (24)-
(25) demons a e ha he co-mo emen be ween wage and employmen gaps na u ally
a ises om gende -speci ic labo p oduc i i y a , , as opposed o gende -speci ic labo
supply ψ , . No ably, he p e-1975 pe iod ep esen s an excep ion. Then he wage gap
was a he s agnan compa ed wi h he employmen gap, sugges ing ha emale-speci ic
labo supply mus ha e played an impo an ole as well. This is indeed cap u ed in ou
end es ima es, as illus a ed in Figu e 5.
21
To app ecia e why he es ima ion p ocedu e also chooses emale-speci ic p oduc i i y
as a d i e o mac oeconomic a iables such as GDP, i is impo an o unde s and how
his end depa s om he gende -neu al al e na i es. A i s na u al compa ison is wi h
o al ac o p oduc i i y, he la ges con ibu o o mac oeconomic g ow h acco ding o
ou model. This is he only mac oeconomic d i e ha can join ly cap u e he p ominen
upwa d ends o GDP, labo p oduc i i y, and agg ega e wages in da a. Au oma ion can-
no accoun o he end in wages, while nei he he wage end no he labo p oduc i i y
end can be accoun ed o by gende -neu al labo supply. Howe e , o al ac o p oduc-
i i y implies a balanced g ow h pa h in ou amewo k, whe e GDP, labo p oduc i i y
and wages all g ow a he same a e.12 In US mac o da a, ins ead, GDP and labo p oduc-
i i y ha e ended o ou g ow agg ega e wages. The only o he mac oeconomic d i e ha
can cap u e his phenomenon is au oma ion. Howe e , au oma ion by i sel has limi ed
explana o y powe because i implies (i) an ex eme wage disconnec whe e wages do no
g ow a all, and (ii) an o e all decline in agg ega e employmen . While au oma ion seems
likely o be impo an o GDP and labo p oduc i i y in pe iods wi h alling employmen
a es, bo h o hese implica ions a e on a e age a odds wi h he las 60 yea s o US labo
ma ke da a.
Female-speci ic p oduc i i y speaks o all o hese obse a ions. Quali a i ely, emale-
speci ic p oduc i i y beha es simila ly o o al ac o p oduc i i y in he sense ha bo h
GDP, labo p oduc i i y and wages ise in esponse o he shock. Bu quan i a i ely we
allow emale p oduc i i y o ha e di e en e ec s ac oss hese h ee a iables, in con as
o o al ac o p oduc i i y. The special case o balanced g ow h ollowing changes in
emales’ p oduc i i y, can be cap u ed in ou empi ical amewo k wi h he pa ame ic
es ic ions ν14 =ν24 and ν34 = 0. While hese es ic ions a e sa is ied a he p io
mean in ou baseline speci ica ion13 (see Table 1), he pos e io pa ame e s a e upda ed
o explain ends in da a. Table 1 summa izes how he model chooses o quan i a i ely
ma ch emale-speci ic p oduc i i y wi h ou mac oeconomic ime se ies: a he pos e-
io mean, a shock o women’s p oduc i i y—no malized o inc ease he ela i e wage
o women by 1pe cen —is associa ed wi h a 0.9pe cen inc ease in GDP, a 0.6pe cen
inc ease in he agg ega e eal wage, and a 0.3pe cen inc ease in he employmen a e.
Thus, highe emale-speci ic p oduc i i y does no only accoun o he join ise o hese
h ee a iables o e he ull sample, bu also o he slow-down in wage g ow h compa ed
wi h GDP, as well as he inc ease in end employmen . Impo an ly, hese e ec s a e
quan i a i ely ele an in ou es ima ion because la ge - han-no mal g ow h in he wage
o women ends o coincide wi h la ge - han-no mal g ow h in GDP, labo p oduc i i y,
and agg ega e wages, as well as a ise in agg ega e employmen . In he same ein, he
la ening o he wage gap end in he ea ly 2000s coincides wi h lowe income g ow h
and a e e sal o he agg ega e employmen a e.
Finally, we no e ha ν14 −ν34 ≈ν24 a he pos e io mean, implying ha emale-
speci ic p oduc i i y causes labo p oduc i i y and wages o espond simila ly. In u n,
his means ha emale-speci ic p oduc i i y has a negligible e ec on he o e all labo
12C i ically, we conside de ia ions om balanced g ow h in Appendix D.2. The ole o gende o ces is
e en la ge in ha speci ica ion.
13Thus, a he p io mean, emale-speci ic p oduc i i y shocks a e sepa a ely iden i ied om o al ac o
p oduc i i y solely because he la e comes wi h ze o- es ic ions on he esponses o gende gap a i-
ables.
22
Now we elax he abo e-men ioned assump ion and allow o he p esence o male-
speci ic end shocks Am, and Ψm, , in addi ion o he emale-speci ic shocks A , and
Ψ , . Con ac iona y, male-speci ic shocks may, o example, cap u e he impac o ideo
gaming and ec ea ional compu ing on he labo supply o young men, as discussed in
Aguia , Bils, Cha les, and Hu s (2021). The p esence o male-speci ic ends implies
ha he wage and employmen gaps w , and l , a e d i en by ou gende ends in
o al, and we need o impose addi ional iden i ica ion es ic ions on he sys em. To his
end, we augmen he baseline empi ical model wi h wo mo e obse ables— he male
employmen a e and male wages—bo h obse ed in log-le els. The join es ic ions
ha we impose on emale- o-male employmen and wage gaps, as well as on he le els
o males’ employmen and wages, allow us o iden i y all o he gende -speci ic ends
in he sys em. De ails abou he iden i ica ion s a egy and he heo y-consis en p io s
a e discussed in Appendix E whe e we p esen also impulse esponses o male-speci ic
shocks in he heo e ical model which is once again ou e e ence o se he p io s in he
empi ical model.
Resul s a e p esen ed in Figu e 7. The i s ow plo s he decomposi ion o end
employmen and wage gaps be ween emales and males. Bo h gaps a e d i en almos
exclusi ely by emale-speci ic shocks. Thus, igno ing male-speci ic shocks was la gely
inconsequen ial. The second ow in Figu e 7 e eals ha emale-speci ic shocks also
emains an impo an d i e o GDP and agg ega e employmen . The wo male ends, in
con as , a e ne e impo an a he agg ega e le el.
Finally, he hi d ow plo s he decomposi ion o ends in he le els o emale and
male employmen . A ew commen s a e in place: i s , he disappea ance o agg ega e
employmen g ow h obse ed in he las 20 yea s is en i ely d i en by emale labo which
s opped g owing a ound 2000. The employmen a e o males, ins ead, has declined e e y
decade since 1960 up un il he inancial c isis, and has since hen been ela i ely la . Sec-
ond, ou accoun o ends in he emale employmen a e is simila o ha o agg ega e
employmen , albei wi h a ela i ely la ge ole o emale-speci ic p oduc i i y and labo
supply (as opposed o he gende -neu al shocks). This is no su p ising, gi en ha hese
shocks ha e a smalle weigh in agg ega e employmen . Thi d, he speci ica ion wi h
males can shed ligh on whe he secula inc eases in emale employmen c owd ou male
labo . The c owding-ou elas ici y is a key s a is ic in Fukui e al. (2023). On a e age
o e he sample, an inc ease in emale employmen o 1 pe cen age poin , when d i en by
emale-speci ic demand, leads o a decline in male employmen o a ound 0.30 pe cen age
poin s acco ding o ou es ima es. Such a mu ed c owding ou elas ici y implies ela i ely
la ge e ec s on agg ega e employmen and economic ac i i y when women en e he labo
ma ke . The co esponding c owding ou elas ici y condi ional on emale-speci ic labo
supply is e en smalle , a ound 0.1. Pa o he di e ence could be ha he gende -speci ic
p oduc i i y shocks imply s onge income e ec s on spouses’ labo supply because hey
ha e a g ea e impac on he amily’s o al income. This would be in line wi h ou heo e -
ical model, as shown in Figu e E.1 in he Appendix. By compa ison, Fukui e al. (2023)
who do no make an explici dis inc ion be ween demand and supply-d i en o ces in hei
empi ical sec ion, epo a alue o 0.18. Howe e , hey e e o “ ela i e” c owding ou
elas ici ies ac oss egions wi h di e en exposu e o gende ends, making a compa ison
less s aigh o wa d.
O e all, we conclude ha i) male shocks play a mino ole, ii) ou model es ima es a
29

a he small deg ee o c owding ou , consis en ly wi h he la ge mac o e ec s o gende
shocks and iii) es ima es o he deg ee o c owding ou a e shock-speci ic, a poin ha o
he bes o ou knowledge is no el.
9 CONCLUSION
In his pape , we in es iga e and quan i y he implica ions o gende -speci ic labo ma -
ke ends o he U.S. mac oeconomy. Using a SVAR model wi h common ends, we
documen he impo ance o gende -speci ic s uc u al o ces no only o he educ ion o
gende inequali y (gende con e gence) in he labo ma ke , bu also o economic g ow h.
In pa icula , we show ha gende -speci ic labo ma ke ends accoun o up o 50% o
end g ow h in GDP o e he pe iod 1960-1990. Fu he mo e, he la ening o he gende
con e gence which s a ed in he 1990s is key o he ma ked slowdown in end g ow h
obse ed o e he las 25 yea s.
Impo an ly, we documen ha gende di e ences ma e o he mac oeconomy using
a pu e “mac o” app oach: an empi ical ime se ies model is disciplined by neoclassical
heo y and es ima ed on selec ed mac oeconomic a iables. In ha sense, ou “le he da a
speak” app oach is complemen a y ye e y di e en om he mo e hea ily pa ame ized
s uc u al models, such as hose pu o wa d by Hsieh e al. (2019), Hea hco e e al. (2010)
and Hea hco e e al. (2017). In e es ingly, and somewha unexpec edly, ou lexible se up
eaches e y simila conclusions on qui e g anula quan i a i e esul s, like he implica-
ions o gende con e gence o g ow h and p oduc i i y.
Rega ding u u e g ow h p ospec s, one possible conce n is ha he mu ed g ow h
since he 2000s ep esen s a new no mal unless he labo ma ke pa icipa ion among
women s a s accele a ing again. Is his likely o happen? On one side, gende di e -
ences in he US labo ma ke a e s ill sizable, and expe iences om o he coun ies (see
Albanesi, Oli e i, and Pe ongolo (2023) o an in e na ional compa ison) sugges ha
ample pocke s o g ow h may s ill be a ailable i he igh ins i u ional ea u es a e pu in
place.18 Howe e , u he g ow h could also p o e mo e di icul han in ea lie decades
gi en ha emales’ employmen a es a e much highe now, and gi en he much smalle
gap be ween emales and males compa ed wi h he pas . A e all, policies canno imp o e
economic pe o mance unboundedly, as he labo o ce pa icipa ion a e has a na u al up-
wa d bound o 100%. The ex en o which labo ma ke pa icipa ion among women could
s a o ise again ul ima ely depends on why i s opped in mid-2000s, and he ju y is s ill
ou on his ques ion.19
18In addi ion, one can imagine ha o he long-las ing sou ces o g ow h can be exploi ed by add essing
o he o ms o misalloca ion. Fo example, wage and employmen gaps be ween na i e and mig an s
a e s ill a om closed and he e is subs an ial e idence o skill downg ading o mig an s (Dus mann,
F a ini, and P es on (2013)).
19A slowdown in gende con e gence can be associa ed wi h cul u al ac o s (Fogli and Veldkamp,2011;
Fe n´
andez,2013), lack o amily- iendly policies (Blau and Kahn,2013), and inc eased income inequal-
i y inducing nega i e income e ec s on women ma ied o high-ea ning husbands (Albanesi and P ados,
2022). Goldin (2014) and Goldin (2021) a gue ha he gende wage gap would be educed u he i i ms
did no disp opo iona ely ewa d wo ke s o long hou s and du ies di icul o plan in ad ance. E osa,
Fus e , Kambou o , and Roge son (2022) alida e his iew in a Roy model wi h occupa ion-speci ic
non-con ex ea nings unc ions.
30
While we belie e ha he applica ion o he gende con e gence is pa icula ly in e -
es ing, ou me hodology can be applied o an a ay o ques ions conce ning o he secula
ends as well. Examples include demog aphics, clima e change, sec o al ends, immi-
g a ion, as well as linkages be ween g ow h and inequali y. In addi ion, ou amewo k
can be used o s udy gende di e ences a business cycle equencies (c . Albanesi (2024)
and Albanesi and S¸ahin (2018)). We plan o in es iga e some o hese opics in u u e
esea ch.
31
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35
APPENDIX
A A BVAR WITH COMMON TRENDS
This sec ion discusses he p io assump ions we o mula e on he ee pa ame e s o he
model p esen ed in sec ion 2 – including he assump ions on he p io ola ili ies o he
s uc u al ends’ shocks – and he ins uc ions o es ima e he model wi h a Gibbs sam-
pling algo i hm.
A.1 PRIOR ASSUMPTIONS
The ini ial condi ions o he s uc u al ends a e dis ibu ed acco ding o X0∼ N(X0, Iq).
In p inciple, we do no ha e in o ma ion abou X0. Howe e , we can use he in o ma ion
on ¯
Y0– he ini ial condi ions o he empi ical ends20 – as well as on he p io coe icien s
in V. Then, one can e ie e X0by sol ing he sys em in eq. (2), p o ided ha he num-
be o s uc u al ends q=n, as i is he case in ou model. The ini ial condi ions o he
cycles a e dis ibu ed acco ding o ˆ
Y0∼ N(0n, In). This assump ion implies ha cycles
luc ua e symme ically a ound a ze o mean. Finally, he p io s o he emainde model’s
coe icien s a e dis ibu ed acco ding o:
Σe∼ IW(κe,(κu+n+ 1)Σe)(A.1)
˜
Φ|Σe∼ N(˜
Φ,Σe⊗Ω)I(˜
Φ) (A.2)
Σu∼ IW(κu,(κu+n+ 1)Σu)(A.3)
whe e ˜
Φ = ec(Φ) and I(˜
Φ) is an indica o unc ion ha is equal o one, when he VAR o
he cycle block is s a iona y, ze o o he wise. The p io on he lag coe icien s is s anda d
Minneso a wi h mean ze o and o e all igh ness hype pa ame e equal o 0.2 (Giannone,
Lenza, and P imice i (2015)). IW is he In e se-Wisha dis ibu ion wi h κdeg ees o
eedom and mode Σ. The p io on he ansi o y inno a ions is a he loose, wi h deg ees
o eedom κe=n+ 2 o ensu e he exis ence o he mean and he p io mode Σe=I.
Nex , he p io on he ends’ shocks Σuis dis ibu ed acco ding o an In e se-Wisha ,
as well. The p io is a he igh , as we se he deg ees o eedom κu= 100. Finally,
he p io mode Σuis assumed o be diagonal. One non- i ial ask is o come up wi h
easonable p io s o he elemen s o σ2
u= [σ2
Aσ2
Ψσ2
ασ2
a σ2
ψ ]′, he ec o s acking he
shocks’ ola ili ies o he s uc u al ends in X . The eason is because he s uc u al
ends a e unobse able in he i s place. Howe e , i is s ill possible o o m ai ly non-
judgmen al p io s on hese s uc u al ola ili ies by combining wo pieces o in o ma ion
we al eady possess, namely: (i) he da a and (ii) he heo y-based p io belie s on he ee
pa ame e s in V(ν). To ix ideas, ecall ha empi ical and s uc u al ends a e linked by
he linea ela ionship ¯
Y =VX and ha X =c+X −1+u . Wi hou loss o gene ali y,
one can exp ess he empi ical ends in hei g ow h a es, as ollows:
∆¯
Y =V(c+u )
This equa ion implies ha he co a iance ma ix o he empi ical ends in g ow h a es is
deno ed by Σ∆¯
Y=V′ΣuV. Then, p o ided ha he co a iance ma ix Σuis diagonal, he
20Speci ically, we se ¯
Y0equal o he a e age o he HP- il e end g ow h a e om he p e-sample da a.
36
ollowing linea ela ions apply:
σ2¯
GDP =σ2
A+σ2
Ψ+σ2
α+ν2
14σ2
a +ν2
15σ2
ψ σ2
¯
W=σ2
A+ν2
24σ2
a +ν2
25σ2
ψ
σ2
¯
E=σ2
Ψ+ν2
33σ2
α+ν2
34σ2
a +ν2
35σ2
ψ σ2
¯
E −m=ν2
44σ2
a +ν2
45σ2
ψ
σ2
¯
W −m=σ2
a +σ2
ψ
On he le -hand side o each equa ion, he e a e he ola ili ies o he empi ical ends
in g ow h a es, while on he igh -hand side, he e a e he coe icien s o Vand ola il-
i ies o he s uc u al shocks. The empi ical ola ili ies a e a ailable in he da a and he
pa ame e s νij a e simply he alues a ound which he p io densi y o he long- un elas-
ici ies is cen e ed. The only unknowns a e he s uc u al ola ili ies. I u ns ou ha is
s aigh o wa d o e ie e he s uc u al ola ili ies in σ2
u, as hey a e he unknowns o a
linea sys em o 5 equa ions in 5 unknowns and, he e o e, he e always exis s a unique
solu ion o he sys em. Consis en ly, his is how we p oceed in p ac ice. Fi s , back ou
he empi ical ola ili ies om he HP- il e end g ow h a es o he endogenous a iables
using p e-sample aining. Second, plug he empi ical ola ili ies and he p io means o
he pa ame e s in V. Sol e he sys em o he unknown ola ili ies and use hem o cen e
he p io densi y o he s uc u al ola ili ies.
Finally, no ice ha he e y same easoning applies when o ming p io s o he ini ial
condi ions and he d i s o he s uc u al ends. Acco dingly, he ini ial condi ions X0
should be cen e ed a ound X0=V¯
Y0, wi h ¯
Y0being he las pe iod’s empi ical end
in le els (las pe iod in he aining sample). As o he d i s, he cons an s cshould be
cen e ed a ound c=VE(∆¯
Y ), wi h E(∆ ¯
Y )being he a e age o he empi ical ends in
g ow h a es (in he aining sample).
A.2 ESTIMATION OF THE STATE SPACE WITH GIBBS SAMPLING
Conside he unobse ed s a es o he model in sec ion 2 in he ollowing s acked o mu-
la ion: VX
ˆ
Y =Vc
0+I0
0AVX −1
ˆ
Y −1+I0
0IVu
e (A.4)
and he Co a iance ma ix o he model is gi en by Σ:
Σ = V′ΣuV0
0 Σe(A.5)
Then, he model samples 50000 d aws and e ains he las 10000 d aws om a Gibbs
algo i hm, acco ding o he ollowing s eps:
1. D aw om he join dis ibu ion X0:T,ˆ
Y−p+1:T, ν |c, A, Σu,Σe, Y1:T, which is gi en
by he p oduc o he ma ginal pos e io o ν- ec o o ee pa ame e s in V-
condi ional on he o he pa ame e s ν|c, A, Σu,Σe, Y1:Tand he dis ibu ion o
he unobse ed s a es condi ional on νand he o he pa ame e s X0:T,ˆ
Y−p+1:T|
ν, c, A, Σu,Σe, Y1:T.
37
(a) p(ν|c, A, Σu,Σe, Y1:T)∝ L(Y1:T|ν, c, A, Σu,Σe)p(ν),
whe e L(Y1:T|ν, c, A, Σu,Σe)is he likelihood o he da a ob ained om he
Kalman il e applied o he s a e space o he model. The pos e io o νis
es ima ed by in oducing a Me opolis-Has ings s ep.
(b) D aws om p(X0:T,ˆ
Y−p+1:T, c |ν, A, Σu,Σe, Y1:T)a e ob ained implemen -
ing Du bin and Koopman (2002) simula ion smoo hing algo i hm.
2. D aw om he join dis ibu ion A, Σu,Σe|X0:T,ˆ
Y−p+1:T, Y1:T. The es ima ion o
he emaining pa ame e s is ela i ely s aigh o wa d, p o ided ha he unobse ed
s a es ollow a he s anda d ec o au o eg essi e laws o mo ion.
(a) TREND BLOCK. he pos e io dis ibu ion o Σuis gi en by:
p(Σu|X0:T) = IW(Σu+
T
X
=1
(X −X −1)(X −X −1)′
| {z }
Su
, κu+T)
(b) CYCLE BLOCK. The pos e io dis ibu ions o he lag coe icien s in Aand he
co a iance ma ix Σeo he s a iona y VAR a e s anda d:
p(Σe|ˆ
Y0:T) = IW(Σe+Se, κe+T)
p(A|Σe,ˆ
Y0:T) = N ec(A),Σe⊗T
X
=1
ˆ
Z ˆ
Z′
+ Ω−1−1!
whe e ˆ
Z = (ˆ
Y′
−1,..., ˆ
Y′
−p),
A=PT
=1 ˆ
Z ˆ
Z′
+ Ω−1−1PT
=1 ˆ
Z ˆ
Y′
+ Ω−1A,
Se=PT
=1 e e′
+ (A − A)′Ω−1(A − A)
38
As documen ed in Table D.1, he elas ici ies go e ning eedback om emale-speci ic
p oduc i i y shi subs an ially away om ze o e en when we pu low p io weigh on
such an ou come. The pos e io s o ν14 and ν24, which go e n he eedback om emale-
speci ic p oduc i i y o GDP and agg ega e wages, a e cen e ed a ound 1.4and 0.75,
espec i ely. Gi en ha he es ima es o λand γa e ela i ely simila o hose in he
baseline, sugges ing ha also he in-sample es ima es o ealized p oduc i i y g ow h o
emale labo is a he simila ac oss speci ica ions, i ollows ha he high pos e io al-
ues o ν14 and ν24 do indeed e lec a majo ole o emale-speci ic p oduc i i y (in-
s ead o simply cap u ing lowe es ima es o emale-speci ic p oduc i i y g ow h). The
emaining pa ame e s ha go e n mac oeconomic eedback mo e less, especially hose
ha de e mine he eedback om emale-speci ic labo supply. Figu e D.1 demons a es
ha emale-speci ic p oduc i i y emains impo an o he US mac oeconomy e en in
a se ing wi h e y conse a i e p io s agains his ou come. No ably, he e ec on la-
bo p oduc i i y is e en s onge in his speci ica ion since employmen is sligh ly less
a ec ed by emales’ p oduc i i y compa ed wi h he baseline.
Figu e D.1: S uc u al decomposi ion wi h p io s s acked agains mac oeconomic eedback
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
1965 1975 1985 1995 2005 2015
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1965 1975 1985 1995 2005 2015
-0.05
0
0.05
0.1
0.15
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
No es: The colo ed ba s display he poin -wise median e olu ion o he empi ical ends a ibu able
o each s uc u al end.
D.2 REVISITING THE LONG-RUN RESTRICTIONS ON EMPLOYMENT
AND WAGES
In his exe cise, we elax he balanced-g ow h assump ion which implies ha employmen
is in a ian o changes in TFP. We se a p io on he employmen ha allows o nega i e
weal h e ec s on labo supply bu does no ule ou posi i e e ec s. We use a No mal
45

dis ibu ion cen e ed a ound -0.1, a alue b oadly based on Boppa and K usell (2020).
In addi ion, we also elax he ze o long- un e ec s o au oma ion and labo supply on
agg ega e wages. In pa icula , we es ic he e ec s o be nega i e wi h mos o he p io
densi y concen a ed a ound ze o. As shown in Figu e D.2, he da a a o a small bu
non negligible nega i e e ec o TFP shocks on employmen . This implies ha gende
shocks play an e en la ge ole in d i ing employmen up, especially in he i s pa o
ou sample. The key ole o gende shocks o GDP and p oduc i i y a e con i med also
in his speci ica ion. Finally, we do no ind e idence o a non-negligible e ec o ei he
au oma ion o labo supply on agg ega e wages.
Figu e D.2: S uc u al d i e s o empi ical ends – elaxing balanced g ow h pa h
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
1965 1975 1985 1995 2005 2015
0
0.1
0.2
0.3
0.4
0.5
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
1965 1975 1985 1995 2005 2015
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1965 1975 1985 1995 2005 2015
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
No es: The colo ed ba s display he poin -wise median e olu ion o he empi ical ends a ibu able o each
s uc u al end.
46
D.3 WHAT IF WE CONSIDER ONLY MARRIED INDIVIDUALS?
In his exe cise, we cons uc employmen and wage gende gaps based only on ma ied
indi iduals o be e e lec he coun e pa in he heo e ical model whe e decisions a e
aken a he household le el. As shown in Figu e D.3, all he main esul s a e con i med
al hough he ole o gende -speci ic labo supply shocks is u he educed in his exe cise.
Figu e D.3: S uc u al d i e s o empi ical ends – model wi h da a on ma ied indi iduals
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
1965 1975 1985 1995 2005 2015
0
0.1
0.2
0.3
0.4
0.5
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
1965 1975 1985 1995 2005 2015
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1965 1975 1985 1995 2005 2015
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1965 1975 1985 1995 2005 2015
0
0.2
0.4
0.6
0.8
1
No es: The colo ed ba s display he poin -wise median e olu ion o he empi ical ends a ibu able o each
s uc u al end.
47
E A MODEL WITH MALE-SPECIFIC SHOCKS
This sec ion ou lines he p io assump ions o he model speci ica ion ha join ly iden i ies
emale-speci ic and male-speci ic s uc u al ends, as p esen ed in sec ion 8. We augmen
he baseline speci ica ion wi h male-speci ic da a on employmen and wage a e le els.
This enables o iden i y a male-speci ic labo demand end and a male-speci ic labo
supply end in addi ion o emale-speci ic ends. Vis modi ied acco dingly:










¯
GDP
¯
W
¯
E
¯
W −m,
¯
E −m,
¯
Wm,
¯
Em,










| {z }
¯
Y
=










1 1 1 ν14 ν15 ν16 ν17
1 0 0 ν24 ν25 ν26 ν27
0 1 ν33 ν34 ν35 ν36 ν37
0 0 0 −1 1 1 −1
0 0 0 γ λ −γ−λ
1 0 0 ν64 ν65 ν66 ν67
0 1 ν73 ν74 ν75 ν76 ν77










| {z }
V










A
Ψ
α
ψ ,
a ,
ψm,
am,










| {z }
X
(E.1)
As in he baseline, he i s h ee columns de ine he long- un e ec s o agg ega e mac o
ends. Res ic ions on GDP, wages, employmen and he gende gaps a e iden ical o he
baseline. In addi ion, we assume ha he long- un e ec o echnology, au oma ion and
labo supply on he le el o males employmen and wages is iden ical o hei agg ega e
coun e pa s. This implies, o example, ha he long- un eedback o au oma ion o
agg ega e employmen and males employmen is iden ical – i.e., ν33 =ν73. Toge he wi h
he ze o long- un es ic ions on he gende di e en ials, such assump ion p ese es he
long- un gende neu ali y o mac o ends.
The emainde columns iden i y he ou gende -speci ic ends. A ew ema ks a e
in place. Fi s , simila ly o he baseline, emale(male)-speci ic labo demand is sep-
a able om emale(male)-speci ic labou supply because he o me implies he same
co-mo emen be ween gende gaps, while he la e implies a nega i e sign on he co-
mo emen be ween gende gaps. Consis en wi h he esul s om he heo e ical model
in Figu e E.1, emale-speci ic and male-speci ic shocks a e assumed o ha e non-nega i e
long- un e ec on GDP and a e mu ually exclusi e ia he opposi e sign e ec on he em-
ploymen gap. The uni o m p io s o he emainde gende -speci ic eedback o mac o
a e o mula ed using he impulse esponses in Figu e E.1 as a e e ence poin . Fu he -
mo e, bo h he emale-speci ic and he male-speci ic shocks a e no malized o ha e uni
long- un e ec s on he wage gap, so ha he eedbacks o he employmen gap can be
in e p e ed in e ms o γand λ, as in he baseline. Fu he mo e, we assume ha emale-
speci ic and male-speci ic shocks ha e symme ic e ec s on bo h he gende gaps and
mac o agg ega es. This implies ha he elas ici ies o mac o agg ega e wi h espec o
male-speci ic shocks span he same uni o m bounda ies o he mac o eedbacks o emale-
speci ic shocks. In his way, we emain agnos ic abou he ela i e s eng h o emale-
and male-speci ic shocks. Finally, we also es ima e he e ec s o emale-speci ic shocks
o males employmen and wages – i.e., ν64,ν65,ν74,ν75. As discussed in sec ion 8, his is
pa icula ly use ul because we can make in e ence on he c owding ou e ec , condi ional
on ei he a emale-speci ic shocks. These e ec s a e cap u ed by ν74 and ν75. The p io
on bo h hese elas ici ies is a he loose: i uni o mly spans he p obabili y se [-1,0]. This
allows he likelihood o isi bo h egions wi h la ge and small c owding ou e ec s. The
48
p io and pos e io es ima es a e summa ized in able E.1.
Table E.1: P io dis ibu ions and pos e io es ima es
P io Pos e io
Densi y Suppo Mean Mode 90% HPD
ν14 ψ →¯
GDP Uni o m [0,2] 1.61 1.39 (1.23, 1.92)
ν24 ψ →¯
WUni o m [−2,0] -0.24 -0.30 (-0.52, -0.03)
ν34 ψ →¯
EUni o m [0,3] 2.27 1.94 (1.89, 2.69)
ν64 ψ →¯
WmUni o m [0,1] 1.60 1.69 (1.07, 2.03)
ν74 ψ →¯
EmUni o m [−1,0] 2.73 2.07 (1.98, -3.53)
ν15 a →¯
GDP Uni o m [0,1] 0.94 0.99 (0.80, 0.99)
ν25 a →¯
WUni o m [0,1] 0.91 0.99 (0.77, 0.99)
ν35 a →¯
EUni o m [−0.5,0.5] 0.26 0.31 (-0.04, 0.46)
ν65 a →¯
WmUni o m [0,1] -0.01 0.00 (-0.21, 0.13)
ν75 a →¯
EmUni o m [−1,0] -0.33 0.41 (-0.63, -0.10)
ν16 ψm→¯
GDP Uni o m [0,2] 0.62 0.57 (0.13, 1.13)
ν26 ψm→¯
WUni o m [−2,0] -1.51 -1.52 (-1.97, -0.72)
ν36 ψm→¯
EUni o m [0,3] 0.81 0.91 (0.30, 1.25)
ν66 ψm→¯
WmUni o m [−1,0] -0.40 -0.20 (-0.89, -0.06)
ν76 ψm→¯
EmUni o m [0,10] 6.10 5.80 (5.30, 7.29)
ν17 am→¯
GDP Uni o m [0,1] 0.63 0.98 (0.09, 0.95)
ν27 am→¯
WUni o m [0,1] 0.72 0.82 (0.26, 0.94)
ν37 am→¯
EUni o m [−0.5,0.5] 0.15 0.20 (-0.29, 0.44)
ν67 am→¯
WmUni o m [0,2] 1.68 1.95 (1.18, 1.96)
ν67 am→¯
EmUni o m [0,1] 0.54 0.68 (0.07, 0.92)
−ν33 α→¯
EΓ(0.3, .15) (0,∞)0.39 0.41 (0.20, 0.54)
λ ai={ ,m}→¯
E −m, Γ(1, .5) (0,∞)1.31 1.57 (0.81, 1.61)
γ ψi={ ,m}→¯
E −m, Γ(3,1.5) (0,∞)6.28 6.7 (5.48, 6.81)
No es: The pos e io momen s a e gene a ed om he las 10,000 o 50,000 d aws gene a ed om he RW
Me opolis-Has ings algo i hm. Γ(µ, σ2) e e s o he Gamma p io densi y wi h mean µand a iance σ2.
49
Figu e E.1: Addi ional impulse esponses: male s emale shocks
No es: Impulse esponse unc ions om simula ions o he heo e ical model. Poin wise median, 90% and 68%
bands based on 1,000 independen d aws om he pa ame e dis ibu ions. The y-axes measu e esponses in
pe cen , he x-axes ep esen ime in qua e s.
50