Fu no, Ma ilena; Ca acciolo, F ancesco
A icle
P opensi y sco e in he ails and e u ns o educa ion in
I aly
Economies
P o ided in Coope a ion wi h:
MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Fu no, Ma ilena; Ca acciolo, F ancesco (2025) : P opensi y sco e in he ails and
e u ns o educa ion in I aly, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 2, pp. 1-28,
h ps://doi.o g/10.3390/economies13020050
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Published: 13 Feb ua y 2025
Ci a ion: Fu no, M., & Ca acciolo, F.
(2025). P opensi y Sco e in he Tails
and Re u ns o Educa ion in I aly.
Economies,13(2), 50. h ps://doi.o g/
10.3390/economies13020050
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A icle
P opensi y Sco e in he Tails and Re u ns o Educa ion in I aly
Ma ilena Fu no * and F ancesco Ca acciolo
Depa men o Ag icul u al Sciences, Uni e si àdegli S udi di Napoli Fede ico II, 80055 Napoli, I aly;
[email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac : The p opensi y sco e de ining he p obabili y o comple ing a gi en deg ee o
educa ion— o balance co a ia es—and he Mince equa ion is he e es ima ed a a ious de-
g ees o highe educa ion. The no el y is in implemen ing p opensi y sco e and eg ession
es ima o s oge he in a double- obus app oach in o de o ensu e agains misspeci ica ion.
The model is analyzed no only a he a e age bu also in he ails o bo h componen s
o gain a de ailed analysis o he ail beha io and obus ness. Analyzing su ey da a
om he 2010 and 2020 wa es, we ind a nega i e impac o sou he n egions and gende
on educa ion. This impac becomes milde a he mean and is no signi ican in he igh
ail. The mixing o p opensi y sco e and quan ile eg ession shows he i ele ance o
educa ion a low wages and, in a ew cases, dec easing p emia as school yea s inc ease.
The p i a e sec o ewa ds lowe p emiums o young wo ke s, and hese dis ibu ions a e
mo e dispe sed, i.e., show highe inequali y. In he women’s subse , he e is a ma ked pay
gap, e en wide o hose wo king in he p i a e sec o .
Keywo ds: double– obus ; p opensi y sco e; quan ile eg ession
JEL Classi ica ion: C20; E24
1. In oduc ion
In his pape , we ocus on e u ns on educa ion in I aly in he las decade, analyzing
he mos ecen wa e o he Banca d’I alia Su ey o Household Income and Weal h, SHIW.
Re u ns may di e due o educa ional a ainmen bu also due o gende and o egional
economic di ide—wi h no he n egions ha ing be e oppo uni ies and d aining skilled
wo ke s om he o he egions.
Many me hods ha e been implemen ed o measu e e u ns on educa ion, and his
analysis p oposes ano he app oach. He e, he p opensi y sco e and he eg ession model
a e coupled in a double- obus (DR) app oach, and we implemen i no only a he
cen e /a e age bu also in he ails o bo h componen s. The DR es ima o (Robins e al.,
1994;Lunce o d & Da idian,2004) is gene ally implemen ed o compu e a e age ea men
e ec s. I combines p opensi y sco e (Rosenbaum & Rubin,1983) and OLS- i ed alues
o gua an ee agains misspeci ica ion. In his s udy, we implemen DR o e alua e e u ns
on educa ion bo h on a e age and in he ails o gain a mo e de ailed analysis o he ail
beha io oge he wi h mo e obus esul s.
In DR, he p opensi y sco e es ima o (PS) compu es he p obabili y o each obse a ion
being ea ed condi ionally on he obse ed co a ia es. Weigh ing he obse a ions in each
g oup by he in e se p obabili y o being in ha g oup de ines he po en ial ou come.
The es ima ed ea men e ec is gi en by he compa ison o he po en ial ou comes o
ea men and con ol, and i is gene ally implemen ed on a e age. I aims o con ol o
Economies 2025,13, 50 h ps://doi.o g/10.3390/economies13020050
Economies 2025,13, 50 2 o 28
he po en ial bias occu ing when ea ed indi iduals sys ema ically di e om hose ha
a e un ea ed by balancing he co a ia es o he wo g oups.
1
The o he componen o
he DR app oach is OLS eg ession, which ela es indi iduals’ ea nings o hei deg ee o
educa ion, con olling o se e al o he ac o s such as age, gende , egion o esidence, and
ield o educa ion, and which p o ides he i ed alues o he ou come in each g oup as
compu ed a he condi ional mean. The combina ion o hese wo es ima o s is e y help ul
since pooling PS and OLS oge he yields a consis en es ima o i a leas one o he wo is
co ec ly speci ied (Neugebaue & an de Laan,2005).
The compa ison o po en ial ou come and OLS- i ed alues o ea ed and un ea ed
indi iduals compu es he a e age ea men e ec . Howe e , he impac o ea men on he
ou come dis ibu ion is no necessa ily cons an , as in he case o he e ogenei y. The e o e,
we ocus on he ea ed/un ea ed di e ence, no only a he mean bu also in he ails, a
a ious loca ions.
Ca acciolo and Fu no (2017) p oposed o analyze a bina y ea men e ec a he
quan iles by in oducing a quan ile eg ession es ima o in place o he OLS esul s. The
impac on he ails may di e om he ea men es ima ed on he a e age: addi ional
schooling may g an highe ea nings in he uppe ail, o mo e quali ied jobs, compa ed o
i s impac a a e age o lowe incomes. I may e en be he case ha he e ec o ea men
is opposi e in he ails, nega i e a he lowe and posi i e a he uppe quan iles, hus
balancing on a e age. Replacing he OLS-es ima ed ou comes in each g oup wi h quan ile
eg ession es ima es allows o compu ing he ea men e ec in he ails o he ou come
dis ibu ion while also g an ing g ea e obus ness. Indeed, quan ile eg essions a e less
a ec ed by anomalous alues han OLS. Nex , Fu no and Ca acciolo (2020) ex ended his
app oach o he mul i a ia e se ing, in case o mo e han one ea men op ion, such as
di e ing leng hs in aining p og ams/schooling, di e en policy in e en ions, o di e se
d ugs/doses in clinical ials.
In hese wo wo ks, he ocus is on mo ing he es ima ed eg ession away om
he mean, p o iding i ed alues o he ou come a he quan iles, while keeping he
PS es ima es cons an a he condi ional mean. This app oach excludes by assump ion
he e ogenei y in he p obabili y o ea men . Howe e , he p obabili y may change as well.
Fo ins ance, he p obabili y o highly educa ed wo ke s being employed is lowe in he le
ail o less-quali ied jobs and highe in he igh ail. The sys ema ic disc epancy be ween
ea ed and un ea ed indi iduals is no necessa ily cons an , and a non-cons an balancing
p obabili y is called o .
In wha ollows, we examine he odds o being ea ed in he ails and compu e
he p obabili y o being in one g oup o ano he in he ails, mo ing bo h p opensi y
sco e and eg ession es ima es away om he mean. We couple p opensi y sco es in he
ails and quan ile eg ession es ima es. This p o ides a ail es ima o o he ea men
e ec wi h espec o bo h componen s o he double- obus , he p opensi y sco e, and he
eg ession model.
The i s example conside s only he p opensi y sco e and shows he p esence o
changing coe icien s ac oss di e en loca ions. We compu e a logi model o de ine he
p obabili y o being employed using SHIW da a om he 2010 and 2020 wa es o he Banca
d’I alia. The impac o he explana o y a iables on he p obabili y o employmen does
change ac oss he selec ed loca ions. In ou indings, educa ion is posi i e a and abo e he
median, he nega i e impac o sou he n egions does no disappea in he igh ail, and
gende is posi i e a he median and becomes non-signi ican a he uppe qua ile.
In a second analysis, he double- obus app oach is implemen ed o compu e e u ns
o educa ion a he mean and in he ails, using SHIW da a om he yea s 2010 and 2020.
The 2024 OECD (OECD,2024) coun y no e s a es ha educa ion le els in I aly ha e g own
Economies 2025,13, 50 3 o 28
slowe han he OECD a e age. I aly emains one o he 12 OECD membe s whe e uni e -
si y deg ees a e no he mos common educa ion quali ica ion o he
25–34 age
b acke .
This delay has long been known despi e e ia y educa ion wa an ing be e employmen ,
bu in I aly, i s ewa d is lowe han elsewhe e. Ou es ima es show he ollowing:
1. The e is li le o no ele ance o educa ion a low wages.
2.
Rewa ds in he p i a e sec o we e highe han in he public sec o o pos -uni e si y
educa ion in 2020, wi h a mo e dispe sed dis ibu ion— he p i a e sec o is cha ac e -
ized by g ea e wage inequali y.
3.
The educa ional p emiums o younge gene a ions a e limi ed in bo h wa es, excep
o he pos -uni e si y p emiums in 2020. This can be in e p e ed as an excess supply
o educa ed wo ke s o else as senio i y, wi h olde coho s like baby boome s shi ing
unce ain y on o he younge gene a ions; bo h in e p e a ions ag ee wi h he OECD
s a emen o low ewa ds o e ia y educa ion in I aly.
4.
The women’s subse esul s a e cha ac e ized by a gende pay gap, which is wide in
he p i a e sec o .
2. P e ious Resul s in Analyzing SHIW Da a
In his sec ion, while ecognizing he exis ence and ele ance o a ious da a se s
p o ided by he I alian S a is ical Agency (ISTAT), he I alian Resea ch Ins i u e on Labo
(ISFOL), he Eu opean Union, and he I alian Social Secu i y Ins i u e (INPS), we ocus on
wo ks analyzing SHIW da a o he sake o compa abili y.
Se e al empi ical s udies analyze SHIW da a o es ima e he e u ns o schooling
and he gende wage gap in I aly. Thei esul s do no p o ide unequi ocal measu es
o he e u ns o educa ion and he gende wage gap. Canna i and D’Alessio (1998) use
ins umen al a iables o he 1993 wa e and, by choosing amily backg ound a iables
as ins umen s, ob ain an es ima e o he e u ns o educa ion close o 7%. Colussi (1997)
uses he same sample and simila ins umen al a iables and p o ides an es ima e o 6.6%,
which is no signi ican ly di e en . Flabbi (1999) analyzes he 1991 SHIW wa e o compu e
he e u ns o schooling o women and men sepa a ely. He inds ha he es ima ed
coe icien s ob ained using ins umen al a iables a e highe o men, 0.62 compa ed o
0.56 o women, while he OLS e u ns a e 0.22 o women and 0.17 o men. B unello and
Miniaci (1999) use he 1993 and 1995 wa es and selec amily backg ound as ins umen al
a iables. Thei OLS es ima e o male educa ion e u ns is 4.8%, while he ins umen al
a iable esul is 5.7%. Con e sely, B unello e al. (2001), analyzing he 1984, 1989, and
1995 wa es, ind highe e u ns o women wi h bo h OLS and ins umen al a iable
es ima o s, hus e e sing he sign o he wage gap. Gius inelli (2004), using SHIW da a
om 1990 o 2000 also inds highe e u ns o women. Howe e , hese esul s a e a odds
wi h he gene al indings on he gende wage gap in he li e a u e. In 2019, he Eu opean
Commission anked I aly among he Eu opean coun ies wi h he lowes gende pay gap,
a less han 8%, a small bu no negligible igu e. Ciccone e al. (2006) analyzing he 1987,
1995, 1998, and 2000 wa es ind inc easing e u ns a highe educa ional le els, wi h u he
imp o emen s in he sou he n egions. Zizza (2013), analyzing da a om 1995 o 2008,
es ima es a aw gende wage gap o a ound 6%, which inc eases o 11–12% in an ex ended
e sion o he model.
Unlike p e ious s udies, ou app oach uses a double- obus me hod o compu e
e u ns o educa ion, no only a he mean bu also in he ails. This me hod unco e s
sub le insigh s, such as he ading ele ance o educa ion a lowe wage le els and he
di e en ewa ds o pos -uni e si y educa ion be ween he p i a e and public sec o s in
2020, highligh ing a p onounced gende pay gap, pa icula ly in he p i a e sec o .
Economies 2025,13, 50 4 o 28
3. The Double Robus App oach
In wha ollows, we desc ibe he DR app oach selec ed o measu e e u ns o educa ion
in I aly. I me ges p opensi y sco e and quan ile eg ession. Cen al o his me hod is
weigh ing obse a ions by hei p obabili y o being educa ed/ ea ed, calcula ed h ough a
logis ic model. The p opensi y sco e app oach is u he e ined by implemen ing expec iles,
which mo e he logis ic eg ession away om he condi ional mean, adding de ails on
he ail beha io o he p obabili y dis ibu ion. Meanwhile, in he eg ession model, we
compu e he uncondi ional dis ibu ions o mo e and less-educa ed indi iduals. Thei
di e ence, compu ed a a ious quan iles, p o ides a iche unde s anding o he e u ns
o educa ion a se e al poin s o he wage dis ibu ion.
Conside he ou come a iable Y
i
, which assumes he alue Y
i0
in he con ol g oup, i
he ea men a iable Z
i
is 0, and Y
i1
when he ea men a iable akes a uni alue (
Zi= 1
o ea men ). To measu e he ea men e ec , he s anda d double- obus app oach
combines he p opensi y sco e and eg ession app oaches and is de ined as ollows:
n−1∑n
i=1(ZiYi
P(Zi=1|X)−Zi−P(Zi=1|X)
P(Zi=1|X)ˆ
Yi1)−∑n
i=1((1−Zi)Yi
1−P(Zi=1|X)+Zi−P(Zi=1|X)
1−P(Zi=1|X)ˆ
Yi0)(1)
The e ms
ˆ
Yi1
and
ˆ
Yi0
ep esen he i ed alues o he OLS eg ession compu ed
in he ea ed and he con ol g oups, espec i ely. The p opensi y sco e weigh s each
obse a ion by he p obabili y o being ea ed. The p obabili y weigh s, P(Z
i
= 1|X),
wi h
0 < P(Zi= 1|X)<1
, a e a unc ion o he unobse able la en a iable Z
i
, which is
app oxima ed by a se o obse ed co a ia es X. Consequen ly, he p obabili y o ea -
men is es ima ed by assuming ha P(Z
i
= 1|X) ollows a pa ame ic model, namely
logis ic eg ession:
P(Zi=1|X) = exp(Xβ)
{1+exp(Xβ)}(2)
Equa ion (2) compu es he p obabili y o being highly educa ed as a unc ion o X,
which, in ou model includes coho , egion o esidence, gende , and ield o s udy.2This
p obabili y p o ides he weigh s used o compu e he po en ial ou come. The ou come
Y
i
is weigh ed by he in e se o his p obabili y, yielding he po en ial ou come o he
ea ed,
ZiYi
P(Zi=1|X)=Yi
P(Zi=1|X)
, when Z
i
= 1, and he po en ial ou come o he un ea ed
(1−Zi)Yi
1−P(Zi=1|X)=Yi
1−P(Zi=1|X)when Zi= 0.
Equa ion (1) calcula es he a e age di e ence be ween he ea ed and con ol g oups.
In he ea men g oup, when Z
i
= 1, i compa es weigh ed obse ed and i ed alues
o he eg ession, espec i ely, Y
i
and
ˆ
Yi1
wi h weigh s equal o
1
P(Zi=1|X)
and
P(Zi=0|X)
P(Zi=1|X)
,
espec i ely:
n−1∑(Yi
P(Zi=1|X)−1−P(Zi=1|X)
P(Zi=1|X)ˆ
Yi1)−∑ˆ
Yi0 o Zi=1 (3)
In he con ol g oup, when Z
i
= 0, Y
i
is weigh ed by
1
P(Zi=0|X)
and
ˆ
Yi0
is by
P(Zi=1|X)
P(Zi=0|X)
,
yielding he ollowing:
n−1∑ˆ
Yi1 −∑(Yi
1−P(Zi=1|X)−P(Zi=1|X)
1−P(Zi=1|X)ˆ
Yi0) o Zi=0 (4)
The nex s ep is o mo e beyond he a e age di e ence be ween he ea ed and
con ol g oups. To achie e his, we analyze he p opensi y sco e es ima o and he eg es-
sion a a ious loca ions, de ia ing om he condi ional mean. We conside expec iles
(
Newey & Powell,1987)
o in oduce a shi ing weigh ha adjus s he es ima ed logis ic
Economies 2025,13, 50 5 o 28
eg ession beyond he condi ional mean. Equa ion (2) is modi ied o include an asymme ic
weigh ing sys em, which shi s he equa ion up o down owa d he ails:
P(wiZi=1|X) = wi
exp(Xβ)
{1+exp(Xβ)}(5)
whe e he asymme ic weigh is de ined as
wi=(θi u >0
1−θelsewhe e
and u ep esen s he
e o e m. Fo ins ance, o compu e he
θ
= 25 h expec ile,
wi
assigns weigh s 0.75 o
obse a ions below he eg ession, pulling he es ima ed equa ion owa d he lowe ail,
while assigning a weigh o 0.25 o obse a ions abo e i .
Rega ding he eg ession componen , he e ms
ˆ
Yi1
and
ˆ
Yi0
in Equa ions (3) and (4)
ep esen he i ed alues o he eg ession model Y
ij
=X
α
+ e
ij
compu ed sepa a ely o
each g oup, wi h j= 0.1. In ou analysis, Y ep esen s ea nings and Xdeno es he ma ix o
explana o y a iables. The i ed alues
ˆ
Yi0
and
ˆ
Yi1
a e eplaced wi h he uncondi ional
dis ibu ions o he i ed alues wi hin each g oup, now deno ed as
ˆ
∼
Yi1
and
ˆ
∼
Yi0
. While in
he OLS amewo k, condi ional and uncondi ional e ec s coincide, hei in e p e a ion
di e s when analyzing he ails, i.e., in he quan ile amewo k (F olich & Melly,2010).3
To es ima e he uncondi ional dis ibu ions, we implemen he app oach p oposed by
Melly (2006). Fi s , he condi ional dis ibu ions o he dependen a iables a e es ima ed
h ough quan ile eg ession (Koenke ,2005) a mul iple quan iles (e.g., k= 100), sepa a ely
o he ea ed and con ol g oups, using he ollowing objec i e unc ion:
∑Y>Xα
θ|Y−Xα|+∑Y<Xα(1−θ)|Y−Xα|(6)
whe e θ ep esen s he selec ed quan ile.
The analysis wi hin each g oup yields wo se s o es ima ed coe icien s,
ˆα1(θ)
o
he ea ed g oup and
ˆα0(θ)
o he con ol. The co esponding i ed alues,
ˆ
Yi0(θ)|X0=
X0ˆα0(θ)and ˆ
Yi1(θ)|X1=X1ˆα1(θ)
, ep esen he ou come dis ibu ion a a gi en quan-
ile, which is condi ional on he co a ia es Xwi hin each g oup. Es ima ing kquan ile
eg essions wi hin each g oup esul s in k alues o
ˆ
∼
α0(θ)and o ˆ
∼
α1(θ)
. Addi ionally, he
co a ia es a e boo s apped wi hin each g oup as well, yielding ksamples o
∼
X0and ∼
X1
.
By boo s apping bo h he co a ia e coe icien s, i is possible o es ima e he uncondi-
ional dis ibu ions o he dependen a iable o ea ed and un ea ed g oups as ollows:
ˆ
∼
Yi0 =∼
X0ˆ
∼
α0(θ)
and
ˆ
∼
Yi1 =∼
X1ˆ
∼
α1(θ)
. These e ms eplace he OLS- i ed alues
ˆ
Yi0
and
ˆ
Yi1
in
Equa ion (1), esul ing in he ollowing:
Q∑n
i=1(ZiYi
P(wiZi=1|X)−Zi−P(wiZi=1|X)
P(wiZi=1|X)
ˆ
∼
Yi1)−
∑n
i=1((1−wiZi)Yi
1−P(wiZi=1|X)+Zi−P(wiZi=1|X)
1−P(wiZi=1|X)
ˆ
∼
Yi0)
(7)
Equa ion (7) enables he compu a ion o he double- obus di e ence be ween he
ea ed and con ol g oups a any quan ile o in e es Q. This o mula ion allows o
quan ile-le el compa ison and ensu es obus ness agains bo h model misspeci ica ion and
ex eme alues.4
4. The Da a and he Model
The SHIW da a a e analyzed o e he pas decade, ocusing on he 2010 and 2020
wa es.
5
The sample consis s o employees aged 20 o 65. Educa ion is measu ed by he
numbe o yea s equi ed o comple e a deg ee.
Economies 2025,13, 50 6 o 28
Table 1 epo s he summa y s a is ics o he model a iables. The educa ion sec ion
shows a subs an ial inc ease in he numbe o wo ke s wi h uni e si y and pos -uni e si y
deg ees o e ime. This g ow h may aise conce ns abou job misma ch and o e educa ion,
whe e highly educa ed wo ke s a e employed in lowe -skilled jobs due o an o e supply
o highly educa ed labo exceeding ma ke demand. The o he sec ions analyze gende ,
whe e he pe cen age o wo king women sligh ly dec eases in he las wa e; age, whe e
he a e age age o young wo ke s sligh ly inc eases o e ime—i.e., i akes a li le longe
o secu e he i s job; egion o esidence, whe e he pe cen age o sou he n wo ke s
dec eases in he 2020 wa e, possibly due o mig a ion owa d he weal hie no he n
egions; eal annual wages, wi h a e age alues inc easing o e ime while he doubled
s anda d de ia ions in 2020 signals highe inequali y; and numbe o hou s wo ked, wi h
an almos s able mean bu inc eased dispe sion o e ime, possibly due o g ea e lexibili y
in job con ac s.6
Table 1. Desc ip i e s a is ics.
2010, n = 13,733 2020, n = 10,876
Educa ion Women Men Women Men
A mos junio high 4004 4324 2000 2278
High school 1727 2013 1469 1886
Uni e si y 802 738 1443 1448
Pos -uni e si y 46 79 146 206
Gende 2010 2020
Women 6579 47.9% 5058 47%
Men 7154 52.1% 5818 53%
100% 100%
Young wo ke s 2010 2020
A e age age 25.7 (s d = 3.01) 25.9 (s d = 3.06)
Region o esidence
Sou h 2010 2020
0 9039 65.8% 7213 66.4%
1 4694 34.2% 3663 33.7%
100% 100%
Real annual wages ne o axes
Sample mean 2010 2020
6828.80 (s d = 9997.2) 8599.50 (s d = 18475.2)
Numbe o wo ked hou s
Sample mean 2010 2020
36.947 (s d = 9.45) 36.345 (s d = 10.53)
No e: s anda d de ia ions in pa en hesis.
4.1. Employmen
As an example o changing p obabili y, Table 2conside s he p obabili y o being
employed in he 2010 and 2020 wa es as a unc ion o age and age squa e— e lec ing a
non-linea impac o wo k expe ience, educa ion, gende (a dummy a iable equal o one
o men), and egion o esidence. This able p esen s he esul s o he logis ic model,
compu ed a he median and in he ails. The expec ile weigh s allow he logis ic eg ession
Economies 2025,13, 50 7 o 28
o mo e away om he condi ional mean, as desc ibed in Equa ion (5), while a he mean,
he weigh s a e se o one.
Table 2. P obabili y o unemploymen , expec ile logis ic eg essions.
0.25 0.50 0.75
Yea 2010, n = 5599
Coe . S d. E . z Coe . S d. E . z Coe . S d. E . z
Age −0.0196 0.005 −3.46 0.1129 0.011 9.61 0.0229 0.008 2.92
Age squa e 0.0005 0.0001 5.98 −0.0006 0.0001 −3.86 0.0003 0.0001 2.81
Educa ion −0.0679 0.008 −8.74 0.0944 0.010 9.28 0.0202 0.009 2.23
Sou h −1.149 0.056 −20.4 −1.284 0.068 −18.9 −1.133 0.067 −16.8
Men −0.1381 0.057 −2.40 0.3156 0.068 4.60 0.0978 0.066 1.48
Yea 2020, n = 3957
Coe . S d. E . z Coe . S d. E . z Coe . S d. E . z
Age −0.0645 0.007 −8.63 0.1390 0.018 7.68 0.0076 0.009 0.79
Age squa e 0.0011 0.0001 10.6 −0.0009 0.0002 −4.08 0.0004 0.0001 2.96
Educa ion −0.0259 0.096 −2.71 0.1798 0.012 14.8 0.0829 0.011 7.57
Sou h −1.194 0.068 −17.4 −1.249 0.082 −15.1 −1.048 0.081 −12.8
Men −0.0936 0.068 −1.37 0.3115 0.084 3.71 −0.0907 0.083 −1.09
No e: he non-signi ican es ima ed coe icien s a e in i alics.
The impac o he explana o y a iables on he p obabili y o being employed changes,
demons a ing he impo ance o accoun ing o he e ogeneous p obabili ies. In homoge-
nous se ings, linea eg essions a di e en loca ions would p oduce pa allel lines ha
shi up o down acco ding o he weigh s de ining he speci ic loca ion, wi h only he
in e cep changing om one loca ion o ano he . Howe e , di e ing es ima ed slopes and
non-pa allel eg ession lines indica e he e ogenei y, as he eg ession line shi s and il s o
main ain he p opo ion o posi i e and nega i e esiduals de ined by he weigh s.
In his example, age and educa ion inc ease he p obabili y o being employed a and
abo e
θ
= 0.50, while a
θ
= 0.25, hey ha e a nega i e impac in bo h wa es. The impac o
educa ion a ies signi ican ly ac oss
θ
, ollowing an in e se u-shaped pa e n—nega i e a
θ
= 0.25, posi i e and signi ican a
θ
= 0.50, and s ill posi i e bu smalle a
θ
= 0.75. This
sugges s a declining p obabili y o employmen o highly educa ed wo ke s, possibly due
o an excess supply. The nega i e impac o esiding in sou he n egions emains almos
s able ac oss θ.
Gende is no s a is ically signi ican in he uppe ail bu i is posi i e and signi ican
a
θ
= 0.50, and nega i e— hough no signi ican in 2020—a
θ
= 0.25. Figu e 1p esen s he
box plo s o p obabili ies a
θ
= 0.25, 0.50, and 0.75. These dis ibu ions di e subs an ially
in e ms o dispe sion, pa icula ly as measu ed by he in e qua ile ange: IR(0.25) = 0.075,
IR(0.50) = 0.148, and IR(0.75) = 0.231. Smalle p obabili ies, and hus la ge po en ial ou pu
alues, a e equi ed o balance employed/unemployed co a ia es in he uppe ail.
Economies 2025,13, 50 8 o 28
Economies 2025, 13, x FOR PEER REVIEW 7 o 27
slopes and non-pa allel eg ession lines indica e he e ogenei y, as he eg ession line
shi s and il s o main ain he p opo ion o posi i e and nega i e esiduals de ined by
he weigh s.
In his example, age and educa ion inc ease he p obabili y o being employed a and
abo e = 0.50, while a = 0.25, hey ha e a nega i e impac in bo h wa es. The impac
o educa ion a ies signi ican ly ac oss , ollowing an in e se u-shaped pa e n—nega-
i e a θ = 0.25, posi i e and signi ican a = 0.50, and s ill posi i e bu smalle a =
0.75. This sugges s a declining p obabili y o employmen o highly educa ed wo ke s,
possibly due o an excess supply. The nega i e impac o esiding in sou he n egions
emains almos s able ac oss
Gende is no s a is ically signi ican in he uppe ail bu i is posi i e and signi ican
a = 0.50, and nega i e— hough no signi ican in 2020—a = 0.25. Figu e 1 p esen s
he box plo s o p obabili ies a = 0.25, 0.50, and 0.75. These dis ibu ions di e subs an-
ially in e ms o dispe sion, pa icula ly as measu ed by he in e qua ile ange: IR(0.25)
= 0.075, IR(0.50) = 0.148, and IR(0.75) = 0.231. Smalle p obabili ies, and hus la ge po en-
ial ou pu alues, a e equi ed o balance employed/unemployed co a ia es in he uppe
ail.
Figu e 1. Box plo showing he p obabili y o being employed a = 0.25, 0.50, 0.75, in 2020.
4.2. Re u ns o Educa ion
Nex , we conside e u ns o educa ion as compu ed by he double- obus me hod a
= 0.25, 0.50, and 0.75. In he PS componen , he p obabili y o comple ing a highe le el
o educa ion—namely high school, uni e si y, and pos -uni e si y deg ees—is es ima ed
h ough logi and weigh ed logi models, wi h weigh s shi ing he model owa ds he
ails.
This p obabili y is a unc ion o he coho , de ined as he yea o he wa e minus age,
which is in oduced o accoun o changes in he educa ional sys em o e ime ha may
ha e a ec ed wo ke s in di e en coho s di e en ly,7 gende , and egion o esidence, o
measu e he nega i e impac o he lagging sou he n economy—as documen ed in he
li e a u e and h oughou Table 3.
Fields o educa ion also play a signi ican ole, as he p obabili y o achie ing a de-
g ee depends on he ield o he p e iously comple ed deg ee (Balla ino & B a i, 2009).
Figu e 1. Box plo showing he p obabili y o being employed a θ= 0.25, 0.50, 0.75, in 2020.
4.2. Re u ns o Educa ion
Nex , we conside e u ns o educa ion as compu ed by he double- obus me hod a
θ
= 0.25, 0.50, and 0.75. In he PS componen , he p obabili y o comple ing a highe le el
o educa ion—namely high school, uni e si y, and pos -uni e si y deg ees—is es ima ed
h ough logi and weigh ed logi models, wi h weigh s shi ing he model owa ds he ails.
This p obabili y is a unc ion o he coho , de ined as he yea o he wa e minus
age, which is in oduced o accoun o changes in he educa ional sys em o e ime ha
may ha e a ec ed wo ke s in di e en coho s di e en ly,
7
gende , and egion o esidence,
o measu e he nega i e impac o he lagging sou he n economy—as documen ed in he
li e a u e and h oughou Table 3.
Table 3. P obabili y o comple ing a deg ee, expec ile logis ic eg ession.
High school
Yea 2010, n = 13480
θ= 0.25 θ= 0.50 θ= 0.75
Coe . z Coe . z Coe . z
Coho −0.0007 −32.4 −0.018 −20.8 0.0008 37.6
Sou h −0.151 −4.08 −0.177 −4.62 −0.106 −3.26
Men 0.013 0.37 −0.048 −1.28 −0.070 −2.21
Yea 2020, n = 8086
Coe . z Coe . z Coe . z
Coho −0.0009 −0.87 −0.026 −25.8 0.0008 27.6
Sou h −0.083 1.69 −0.220 −4.52 −0.216 −4.39
Men −0.626 −13.5 0.058 1.24 0.022 0.47
Economies 2025,13, 50 15 o 28
Table 6. Con .
Yea 2020
Coe . S d. E . Coe . S d. E . Coe . S d. E .
High school −0.545 0.079 −6.84 −0.027 0.039 −0.70 0.396 0.097 4.07
Uni e si y −0.230 0.043 −5.28 0.221 0.040 5.47 0.754 0.061 12.29
Pos -uni e si y −0.260 0.071 −3.64 0.326 0.037 8.66 0.740 0.040 18.25
No e: he non-signi ican es ima ed coe icien s a e in i alics.
Economies 2025, 13, x FOR PEER REVIEW 14 o 27
Figu e 3. Uncondi ional wage dis ibu ions a y ac oss di e en educa ion le els, wi h dispe sion
inc easing as educa ion le el ises, especially o hose wi h pos -uni e si y deg ees. In 2010, he
uppe quan ile o pos -uni e si y deg ee holde s was signi ican ly lowe compa ed o hose wi h
uni e si y deg ees. By 2020, wage p emiums o pos -uni e si y deg ee holde s imp o ed.
Figu e 3. Uncondi ional wage dis ibu ions a y ac oss di e en educa ion le els, wi h dispe sion
inc easing as educa ion le el ises, especially o hose wi h pos -uni e si y deg ees. In 2010, he
uppe quan ile o pos -uni e si y deg ee holde s was signi ican ly lowe compa ed o hose wi h
uni e si y deg ees. By 2020, wage p emiums o pos -uni e si y deg ee holde s imp o ed.
In he 2020 wa e, howe e , he uni e si y and pos -uni e si y educa ional p emiums
inc ease in he p i a e sec o . The pos -uni e si y wage dis ibu ion ises signi ican ly
abo e he uni e si y plo and su passes i s coun e pa in he g aph depic ing he en i e
sample. The g ea e dispe sion o wage dis ibu ions in he p i a e sec o leads o inc eased
inequali y, bu i also o e s g ea e oppo uni ies o highly educa ed wo ke s in 2020.
The pos -uni e si y plo s con i m he comp essed wage dis ibu ions o highe edu-
ca ion in he public sec o in 2020, hough his pa e n was no obse ed in 2010. Figu e 4
illus a es he public sec o , showing highe p emiums and lowe dispe sion compa ed o
he p i a e sec o .
Economies 2025,13, 50 16 o 28
Economies 2025, 13, x FOR PEER REVIEW 14 o 27
Figu e 3. Uncondi ional wage dis ibu ions a y ac oss di e en educa ion le els, wi h dispe sion
inc easing as educa ion le el ises, especially o hose wi h pos -uni e si y deg ees. In 2010, he
uppe quan ile o pos -uni e si y deg ee holde s was signi ican ly lowe compa ed o hose wi h
uni e si y deg ees. By 2020, wage p emiums o pos -uni e si y deg ee holde s imp o ed.
Economies 2025, 13, x FOR PEER REVIEW 15 o 27
Figu e 4. Uncondi ional wage dis ibu ions in he public sec o ac oss di e en educa ion le els
inc eased in 2020 compa ed o 2010. In con as o he p i a e sec o , as shown in Figu e 3, hese
dis ibu ions a e less dispe sed and a e cen e ed a ound highe medians.
4.2.2. Young Wo ke s
The nex sec ion o Table 6 ocuses on young wo ke s aged 20−30, a g oup cha ac e -
ized by a ela i ely high unemploymen a e. 13 P e ious s udies ound educed educa-
ional p emiums o highe educa ion wi hin his subse . A possible explana ion sugges s
an excess supply o highly educa ed wo ke s, esul ing in o e quali ica ion o a ailable
jobs (Balla ino & Sche e , 2013). The educed p emiums may be a ibu ed o skill-biased
echnical change (Na icchioni e al., 2010), whe e o e educa ed wo ke s accep lowe -
quali ied jobs due o an o e supply o skills, displacing wo ke s wi h high school o lowe
deg ees. This phenomenon, e e ed o as “unskilled bias”, sugges s ha he demand o
high-skilled wo ke s has inc eased less han hei supply, he eby educing he educa-
ional p emiums. As s a ed by (Na icchioni e al., 2010), “ he inc ease in ela i e supply o
educa ion has exe ed a nega i e impac on ela i e wages, while echnical change−p oxy o he
demand o wo ke s−is no s a is ically di e en om ze o”.
This could explain he low p emiums a = 0.25. An al e na i e explana ion consid-
e s gene a ional shi s, whe e baby boome s ans e unce ain y o younge gene a ions,
who, in u n, ace diminishing oppo uni ies o ca ee ad ancemen and wage g ow h
(Ba bie i, 2011).14 Compa ed o o he OECD coun ies, Biage i and Scicchi ano (2011) ind
ha e u ns o educa ion in I aly a e lowe . Ou esul s show ha , a he lowe end o he
wage dis ibu ion, he impac o educa ion is gene ally nega i e, whe eas i becomes pos-
i i e and inc eases a and abo e he median. Thus, young highly educa ed wo ke s ecei e
minimal educa ional p emiums in lowe -quali ied jobs.
In Table 1, he pe cen age o uni e si y and pos -uni e si y deg ees in 2020 mo e han
doubles he alues o 2010, suppo ing he excess supply/unskilled bias hypo hesis as an
explana ion o lowe p emiums among young wo ke s. Howe e , when hey secu e be -
e jobs, hei educa ional p emiums imp o e, pa icula ly a he 75 h pe cen ile o uni-
e si y and pos -uni e si y deg ees. Figu e 5 displays he uncondi ional wage dis ibu-
ions o his subse , wi h pos -uni e si y deg ee holde s exhibi ing he highes dispe sion
in bo h wa es. The dis ibu ions a e highly skewed, wi h a longe le ail in 2010 and a
longe igh ail in 2020.
The bo om sec ion o Table 6 epo s he esul s o young wo ke s in he p i a e
sec o . In gene al, educa ional p emiums a e lowe o young wo ke s compa ed o p e-
ious esul s, wi h he pos -uni e si y deg ee in 2010 p o iding no signi ican p emium.
The g aphs in Figu e 6 compa e uncondi ional wage dis ibu ions o he ull da a se
(le ), he p i a e sec o (middle), and young wo ke s ( igh ). The subs an ial dispe sion
in pos -uni e si y deg ee dis ibu ions is e iden , wi h inc eased dispe sion/inequali y
among young wo ke s. The g aphs also show ha young wo ke s’ wage dis ibu ions a e
gene ally posi ioned lowe han hei coun e pa s in he ull sample.
Figu e 4. Uncondi ional wage dis ibu ions in he public sec o ac oss di e en educa ion le els
inc eased in 2020 compa ed o 2010. In con as o he p i a e sec o , as shown in Figu e 3, hese
dis ibu ions a e less dispe sed and a e cen e ed a ound highe medians.
4.2.2. Young Wo ke s
The nex sec ion o Table 6 ocuses on young wo ke s aged 20
−
30, a g oup cha ac e -
ized by a ela i ely high unemploymen a e.
13
P e ious s udies ound educed educa ional
p emiums o highe educa ion wi hin his subse . A possible explana ion sugges s an
excess supply o highly educa ed wo ke s, esul ing in o e quali ica ion o a ailable jobs
(Balla ino & Sche e ,2013). The educed p emiums may be a ibu ed o skill-biased echni-
cal change (Na icchioni e al.,2010), whe e o e educa ed wo ke s accep lowe -quali ied
jobs due o an o e supply o skills, displacing wo ke s wi h high school o lowe deg ees.
This phenomenon, e e ed o as “unskilled bias”, sugges s ha he demand o high-skilled
wo ke s has inc eased less han hei supply, he eby educing he educa ional p emiums.
As s a ed by (Na icchioni e al.,2010), “ he inc ease in ela i e supply o educa ion has exe ed a
nega i e impac on ela i e wages,while echnical change
−
p oxy o he demand o wo ke s
−
is
no s a is ically di e en om ze o”.
This could explain he low p emiums a
θ
= 0.25. An al e na i e explana ion conside s
gene a ional shi s, whe e baby boome s ans e unce ain y o younge gene a ions, who,
in u n, ace diminishing oppo uni ies o ca ee ad ancemen and wage g ow h (Ba bie i,
2011).
14
Compa ed o o he OECD coun ies, Biage i and Scicchi ano (2011) ind ha
e u ns o educa ion in I aly a e lowe . Ou esul s show ha , a he lowe end o he wage
dis ibu ion, he impac o educa ion is gene ally nega i e, whe eas i becomes posi i e and
Economies 2025,13, 50 17 o 28
inc eases a and abo e he median. Thus, young highly educa ed wo ke s ecei e minimal
educa ional p emiums in lowe -quali ied jobs.
In Table 1, he pe cen age o uni e si y and pos -uni e si y deg ees in 2020 mo e han
doubles he alues o 2010, suppo ing he excess supply/unskilled bias hypo hesis as an
explana ion o lowe p emiums among young wo ke s. Howe e , when hey secu e be e
jobs, hei educa ional p emiums imp o e, pa icula ly a he 75 h pe cen ile o uni e si y
and pos -uni e si y deg ees. Figu e 5displays he uncondi ional wage dis ibu ions o
his subse , wi h pos -uni e si y deg ee holde s exhibi ing he highes dispe sion in bo h
wa es. The dis ibu ions a e highly skewed, wi h a longe le ail in 2010 and a longe
igh ail in 2020.
Economies 2025, 13, x FOR PEER REVIEW 16 o 27
Young wo ke s in he p i a e sec o ecei e smalle educa ional p emiums, as high-
ligh ed by he compa ison o he hi d and ou h sec ions o he able and illus a ed in
Figu e 7 o he 2020 wa e. In he p i a e sec o , he dispe sion o pos -uni e si y deg ee
p emiums signi ican ly dec eases, sugges ing ha he g ea e ewa ds o e ed by he p i-
a e sec o do no necessa ily bene i younge gene a ions.
Figu e 5. Uncondi ional wage dis ibu ions a di e en deg ees o educa ion o young wo ke s. The
pos -uni e si y dis ibu ion is qui e dispe sed and shows a longe le ail in 2010, while in 2020,
he e is a longe igh ail. The e a e a ew ou lie s a he uppe end o he, a mos , junio high plo .
Figu e 5. Uncondi ional wage dis ibu ions a di e en deg ees o educa ion o young wo ke s. The
pos -uni e si y dis ibu ion is qui e dispe sed and shows a longe le ail in 2010, while in 2020, he e
is a longe igh ail. The e a e a ew ou lie s a he uppe end o he, a mos , junio high plo .
The bo om sec ion o Table 6 epo s he esul s o young wo ke s in he p i a e sec o .
In gene al, educa ional p emiums a e lowe o young wo ke s compa ed o p e ious
esul s, wi h he pos -uni e si y deg ee in 2010 p o iding no signi ican p emium. The
g aphs in Figu e 6compa e uncondi ional wage dis ibu ions o he ull da a se (le ),
he p i a e sec o (middle), and young wo ke s ( igh ). The subs an ial dispe sion in pos -
uni e si y deg ee dis ibu ions is e iden , wi h inc eased dispe sion/inequali y among
young wo ke s. The g aphs also show ha young wo ke s’ wage dis ibu ions a e gene ally
posi ioned lowe han hei coun e pa s in he ull sample.
Economies 2025,13, 50 18 o 28
Young wo ke s in he p i a e sec o ecei e smalle educa ional p emiums, as high-
ligh ed by he compa ison o he hi d and ou h sec ions o he able and illus a ed in
Figu e 7 o he 2020 wa e. In he p i a e sec o , he dispe sion o pos -uni e si y deg ee
p emiums signi ican ly dec eases, sugges ing ha he g ea e ewa ds o e ed by he p i a e
sec o do no necessa ily bene i younge gene a ions.
4.2.3. Gende Gap
Finally, we examine he subse o women o e alua e he p esence o a gende pay gap.
The gende gap is no only associa ed wi h equal pay o women, bu also wi h di e ences
in he p ocess o selec ion o employmen . Women’s pa icipa ion a es a e lowe and a e
concen a ed in high-wage posi ions (Picchio & Mussida,2011), acing ba ie s such as he
glass ceiling. Depalo and Gio dano (2010) ound e idence o a gende pay gap in I aly.
The esul s in Table 7indica e ha , in 2010, women’s educa ional p emiums we e
gene ally lowe compa ed o he ull sample esul s, showing he exis ence o a gende
gap in educa ional p emiums. The bo om sec ion o Table 7compa es, a he median,
he ull sample esul s om Table 4(middle column) wi h hose o he women’s subse
and he women in he p i a e sec o . The able highligh s in bold he subse es ima es
ha signi ican ly di e om he ull sample esul s. Examining he women’s subse and
conside ing a con idence in e al o
±
2
ˆ
σ
, i is e iden ha almos all esul s signi ican ly
di e om he ull sample esul s in bo h wa es. The only excep ion is he ield o he
humani ies, which o e s he same ewa ds o bo h men and women.
Economies 2025, 13, x FOR PEER REVIEW 17 o 27
Figu e 6. Con .
Economies 2025,13, 50 19 o 28
Economies 2025, 13, x FOR PEER REVIEW 18 o 27
Figu e 6. Uncondi ional wage dis ibu ions a e p esen ed ac oss di e en ca ego ies. The op le
g aphs show dis ibu ions o he en i e da a se , he op igh g aphs ep esen he p i a e sec o ,
and he bo om g aphs ocus on young wo ke s aged 20–30. In 2010, he pos -uni e si y wage dis-
ibu ion in he p i a e sec o was mo e dispe sed compa ed o he en i e da a se , wi h e en
g ea e dispe sion obse ed in he pos -uni e si y p emiums o young wo ke s. By 2020, he p i-
a e sec o exhibi ed g ea e dispe sion in uni e si y wage p emiums ela i e o he en i e da a
se . Pos -uni e si y p emiums o young wo ke s showed an e en wide dispe sion, while o he
educa ion le els we e less dispe sed and had lowe p emiums.
Figu e 6. Uncondi ional wage dis ibu ions a e p esen ed ac oss di e en ca ego ies. The op le
g aphs show dis ibu ions o he en i e da a se , he op igh g aphs ep esen he p i a e sec o , and
he bo om g aphs ocus on young wo ke s aged 20–30. In 2010, he pos -uni e si y wage dis ibu ion
in he p i a e sec o was mo e dispe sed compa ed o he en i e da a se , wi h e en g ea e dispe sion
obse ed in he pos -uni e si y p emiums o young wo ke s. By 2020, he p i a e sec o exhibi ed
g ea e dispe sion in uni e si y wage p emiums ela i e o he en i e da a se . Pos -uni e si y
p emiums o young wo ke s showed an e en wide dispe sion, while o he educa ion le els we e
less dispe sed and had lowe p emiums.
In bo h wa es, all es ima es o he women’s subse a e in bold, excep o hose
ela ed o g adua es in he humani ies in 2010 and pos g adua es in he same ield in 2020.
Women ac oss all deg ees and ields—aside om he humani ies— ecei e lowe ewa ds.
In he p i a e sec o subse , he s a is ically signi ican di e ences indica e educed e u ns
compa ed o bo h he ull sample and he women’s subse , wi h he sole excep ion o he
pos -uni e si y deg ees in social sciences in 2020.
Figu e 8p esen s he box plo o he uncondi ional dis ibu ions o educa ional p emi-
ums. In 2020, he p emiums exhibi g ea e dispe sion a lowe educa ional le els, and he
pos -uni e si y p emium a he 75 h pe cen ile is lowe han in 2010. This e ec is e en
mo e p onounced in he p i a e sec o , as shown in he middle sec ion o he able.
Economies 2025,13, 50 20 o 28
Economies 2025, 13, x FOR PEER REVIEW 19 o 27
Figu e 7. Uncondi ional wage dis ibu ions a e shown ac oss di e en educa ion le els: he op le
g aph ep esen s he ull sample, he op igh g aph shows young wo ke s, and he bo om g aph
ocuses on young wo ke s in he p i a e sec o . In he p i a e sec o , he dispe sion o pos -uni e -
si y wage p emiums signi ican ly dec eases, and he highe ewa ds seen in he p i a e sec o in
Figu e 2 do no bene i he younge gene a ion as much.
4.2.3. Gende Gap
Finally, we examine he subse o women o e alua e he p esence o a gende pay
gap. The gende gap is no only associa ed wi h equal pay o women, bu also wi h di -
e ences in he p ocess o selec ion o employmen . Women’s pa icipa ion a es a e lowe
and a e concen a ed in high-wage posi ions (Picchio & Mussida, 2011), acing ba ie s
such as he glass ceiling. Depalo and Gio dano (2010) ound e idence o a gende pay gap
in I aly.
The esul s in Table 7 indica e ha , in 2010, women’s educa ional p emiums we e
gene ally lowe compa ed o he ull sample esul s, showing he exis ence o a gende
gap in educa ional p emiums. The bo om sec ion o Table 7 compa es, a he median, he
ull sample esul s om Table 4 (middle column) wi h hose o he women’s subse and
he women in he p i a e sec o . The able highligh s in bold he subse es ima es ha
signi ican ly di e om he ull sample esul s. Examining he women’s subse and con-
side ing a con idence in e al o ±2𝛔, i is e iden ha almos all esul s signi ican ly di -
e om he ull sample esul s in bo h wa es. The only excep ion is he ield o he hu-
mani ies, which o e s he same ewa ds o bo h men and women.
Figu e 7. Uncondi ional wage dis ibu ions a e shown ac oss di e en educa ion le els: he op le
g aph ep esen s he ull sample, he op igh g aph shows young wo ke s, and he bo om g aph
ocuses on young wo ke s in he p i a e sec o . In he p i a e sec o , he dispe sion o pos -uni e si y
wage p emiums signi ican ly dec eases, and he highe ewa ds seen in he p i a e sec o in Figu e 2
do no bene i he younge gene a ion as much.
Table 7. (a) Women’s subse . (b) Women in he p i a e sec o . (c) Compa ison o double- obus
esul s: ull sample e sus women’s subse s a he median.
(a)
0.25 0.50 0.75
Yea 2010
Coe . S d. E . Coe . S d. E . Coe . S d. E .
High school −0.317 0.028 −
11.30
0.226 0.019 11.87 11.87 0.023 30.68
Uni e si y 0.141 0.024 5.74 0.550 0.012 42.99 42.99 0.016 55.77
Pos -uni e si y 0.480 0.012 37.15 0.780 0.011 67.18 67.18 0.015 73.95
Economies 2025,13, 50 21 o 28
Table 7. Con .
(a)
0.25 0.50 0.75
Yea 2020
Coe . S d. E . Coe . S d. E . Coe . S d. E .
High school −0.371 0.035 −
10.60
0.101 0.027 3.65 0.640 0.039 16.05
Uni e si y −0.259 0.051 −5.02 0.538 0.027 19.85 1.08 0.024 44.12
Pos -uni e si y −0.177 0.152 −1.16 0.628 0.042 14.94 1.01 0.034 29.38
(b)
0.25 0.50 0.75
Yea 2010
Coe . S d. E . Coe . S d. E . Coe . S d. E .
High school −0.302 0.042 −7.21 0.244 0.023 10.32 0.704 0.028 24.67
Uni e si y 0.160 0.016 9.57 0.467 0.016 28.18 0.870 0.020 42.50
Pos -uni e si y −0.142 0.024 5.95 0.286 0.019 14.56 0.598 0.013 43.02
Yea 2020
Coe . S d. E . Coe . S d. E . Coe . S d. E .
High school −0.460 0.055 −8.33 0.100 0.033 2.98 0.657 0.058 11.21
Uni e si y −0.055 0.056 −0.98 0.593 0.027 21.91 1.04 0.033 31.46
Pos -uni e si y 0.262 0.021 12.19 0.605 0.019 30.81 0.928 0.020 45.79
(c)
Yea 2010 Full sample Women subse Women in p i a e sec o
Coe . S d. E . Coe . S d. E . Coe . S d. E .
Uni e si y humani ies 0.543 0.008 68.74 0.529 0.012 42.49 0.305 0.016 18.59
Uni e si y science 0.560 0.008 71.01 0.524 0.012 43.43 0.389 0.016 24.23
Uni e si y social sc. 0.589 0.008 73.85 0.544 0.012 44.31 0.387 0.016 23.88
Pos -uni e si y
humani ies 0.701 0.007 92.07 0.662 0.011 57.49 0.929 0.132 7.00
Pos -uni e si y science 0.764 0.008 90.39 0.672 0.039 17.20 0.286 0.019 14.81
Pos -uni e si y social sc. 0.692 0.008 85.92 0.743 0.011 65.32 0.867 0.132 6.55
Yea 2020 Full sample Women subse Women in p i a e sec o
Coe . S d. E . Coe . S d. E . Coe . S d. E .
Uni e si y humani ies 0.558 0.012 45.49 0.461 0.020 22.50 0.574 0.047 12.03
Uni e si y science 0.625 0.013 47.87 0.495 0.022 22.28 0.581 0.025 22.88
Uni e si y social sc. 0.596 0.013 46.14 0.499 0.021 23.35 0.501 0.024 20.47
Pos -uni e si y
humani ies 0.501 0.009 50.23 0.507 0.013 36.56 0.100 0.018 5.49
Pos -uni e si y science 0.711 0.011 61.69 0.659 0.015 43.12 0.496 0.020 24.47
Pos -uni e si y social sc. 0.769 0.011 70.65 0.714 0.013 52.69 0.817 0.023 34.12
No e: The non-signi ican es ima ed coe icien s a e in i alics. In bold a e he es ima ed coe icien s in each
women’s subse ha signi ican ly di e om he analogous es ima es compu ed in he en i e sample.
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Economies 2025, 13, x FOR PEER REVIEW 21 o 27
Uni e si y science
0.625
0.013
47.87
0.495
0.022
22.28
0.581
0.025
22.88
Uni e si y social sc.
0.596
0.013
46.14
0.499
0.021
23.35
0.501
0.024
20.47
Pos -uni e si y hu-
mani ies
0.501
0.009
50.23
0.507
0.013
36.56
0.100
0.018
5.49
Pos -uni e si y sci-
ence
0.711
0.011
61.69
0.659
0.015
43.12
0.496
0.020
24.47
Pos -uni e si y social
sc.
0.769
0.011
70.65
0.714
0.013
52.69
0.817
0.023
34.12
No e: The non-signi ican es ima ed coe icien s a e in i alics. In bold a e he es ima ed coe icien s
in each women’s subse ha signi ican ly di e om he analogous es ima es compu ed in he en i e
sample.
Figu e 8 p esen s he box plo o he uncondi ional dis ibu ions o educa ional p e-
miums. In 2020, he p emiums exhibi g ea e dispe sion a lowe educa ional le els, and
he pos -uni e si y p emium a he 75 h pe cen ile is lowe han in 2010. This e ec is e en
mo e p onounced in he p i a e sec o , as shown in he middle sec ion o he able.
Figu e 9 compa es he uncondi ional dis ibu ions ac oss he ull sample (le ), he
women’s subse (middle), and women in he p i a e sec o ( igh ). The g aphs illus a e
ha , in bo h wa es, pos -uni e si y p emiums o women in he p i a e sec o a e lowe
han uni e si y-le el p emiums.
Figu e 8. Uncondi ional wage dis ibu ions o women ac oss di e en educa ion le els show no able
changes. In 2020, wage p emiums o lowe educa ion le els a e mo e dispe sed, while he op
p emiums o pos -uni e si y deg ees a e lowe compa ed o 2010. Addi ionally, he e a e a ew
ou lie s a he lowe end o he 2020 pos -uni e si y dis ibu ion.
Figu e 9compa es he uncondi ional dis ibu ions ac oss he ull sample (le ), he
women’s subse (middle), and women in he p i a e sec o ( igh ). The g aphs illus a e
ha , in bo h wa es, pos -uni e si y p emiums o women in he p i a e sec o a e lowe
han uni e si y-le el p emiums.
In summa y, educa ion p o ides wage p emiums in each wa e. While highe deg ees
yield g ea e p emiums in he p i a e sec o , young wo ke s and women employed in he
p i a e sec o gene ally ecei e lowe educa ional p emiums.
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Economies 2025, 13, x FOR PEER REVIEW 22 o 27
Figu e 8. Uncondi ional wage dis ibu ions o women ac oss di e en educa ion le els show no a-
ble changes. In 2020, wage p emiums o lowe educa ion le els a e mo e dispe sed, while he op
p emiums o pos -uni e si y deg ees a e lowe compa ed o 2010. Addi ionally, he e a e a ew
ou lie s a he lowe end o he 2020 pos -uni e si y dis ibu ion.
Figu e 9. Con .
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Economies 2025, 13, x FOR PEER REVIEW 23 o 27
Figu e 9. A compa ison o uncondi ional wage dis ibu ions is p esen ed: o he op le , o he
en i e sample; o he op igh , o he women’s subse ; and o he bo om, o women wo king in
he p i a e sec o .
In summa y, educa ion p o ides wage p emiums in each wa e. While highe deg ees
yield g ea e p emiums in he p i a e sec o , young wo ke s and women employed in he
p i a e sec o gene ally ecei e lowe educa ional p emiums.
5. Conclusions
The ea ning p o iles ac oss di e en le els o educa ion a e analyzed using he dou-
ble- obus app oach a he mean and in he ails. The p opensi y sco e is implemen ed o
compu e changing p obabili ies a di e en loca ions. These esul s a e combined wi h
quan ile eg ession-based uncondi ional dis ibu ions o analyze e u ns o educa ion, o-
cusing on he 2010 and 2020 wa es o Banca d’I alia SHIW da a.
The double- obus app oach is applied no only a he cen e bu also in he ails o
bo h componen s, he p opensi y sco e and he eg ession model, p o iding a deepe un-
de s anding o he beha io and enhancing obus ness.
In he p opensi y sco e, coho , gende , ield o s udies, and egion o esidence sig-
ni ican ly in luence he likelihood o a aining highe educa ional deg ees. The nega i e
Figu e 9. A compa ison o uncondi ional wage dis ibu ions is p esen ed: o he op le , o he
en i e sample; o he op igh , o he women’s subse ; and o he bo om, o women wo king in he
p i a e sec o .
5. Conclusions
The ea ning p o iles ac oss di e en le els o educa ion a e analyzed using he double-
obus app oach a he mean and in he ails. The p opensi y sco e is implemen ed o
compu e changing p obabili ies a di e en loca ions. These esul s a e combined wi h
quan ile eg ession-based uncondi ional dis ibu ions o analyze e u ns o educa ion,
ocusing on he 2010 and 2020 wa es o Banca d’I alia SHIW da a.
The double- obus app oach is applied no only a he cen e bu also in he ails
o bo h componen s, he p opensi y sco e and he eg ession model, p o iding a deepe
unde s anding o he beha io and enhancing obus ness.
In he p opensi y sco e, coho , gende , ield o s udies, and egion o esidence signi i-
can ly in luence he likelihood o a aining highe educa ional deg ees. The nega i e impac
o sou he n egions diminishes a he mean and becomes non-signi ican a he op qua ile.
The double- obus esul s e eal sec o al di e ences in educa ional p emiums, wi h he
