Valen ini, Enzo
A icle
Pa e ns o in e gene a ional educa ional (im)mobili y
Economies
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Sugges ed Ci a ion: Valen ini, Enzo (2024) : Pa e ns o in e gene a ional educa ional (im)mobili y,
Economies, ISSN 2227-7099, MDPI, Basel, Vol. 12, Iss. 6, pp. 1-13,
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Ci a ion: Valen ini, Enzo. 2024.
Pa e ns o In e gene a ional
Educa ional (Im)Mobili y. Economies
12: 126. h ps://doi.o g/10.3390/
economies12060126
Academic Edi o : Gheo ghe
H. Popescu
Recei ed: 27 Ma ch 2024
Re ised: 13 May 2024
Accep ed: 17 May 2024
Published: 21 May 2024
Copy igh : © 2024 by he au ho .
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economies
A icle
Pa e ns o In e gene a ional Educa ional (Im)Mobili y
Enzo Valen ini
Depa men o Poli ical Science, Communica ion and In e na ional Rela ions, Uni e si y o Mace a a,
62100 Mace a a, I aly; [email p o ec ed]
Abs ac : In e gene a ional educa ion mobili y is a key dimension o social mobili y and explo es
he ex en o which educa ional a ainmen is ansmi ed ac oss gene a ions wi hin a socie y. The
implica ions o low educa ion mobili y conce n bo h equi y (e e yone should ha e he same op-
po uni ies) and e iciency (i would be good o he economy and socie y i he mos gi ed and
dese ing young people we e o s udy and no he child en o he al eady educa ed). The li e a u e
iden i ies se e al d i e s ha can in luence he le el o social mobili y in gene al and educa ion
mobili y speci ically, including cha ac e is ics o educa ional sys ems, public spending, deg ee o
u banisa ion, in o mal ic ions, and belie s. This pape seeks o iden i y ‘pa e ns o in e gene a ional
educa ion (im)mobili y’ h ough a clus e analysis ha akes in o accoun he le el o in e gene a-
ional mobili y in educa ion and a numbe o a iables conce ning i s possible d i e s, conside ing
da a on 82 coun ies (wi h di e en le els o de elopmen ). The ad an age o clus e analysis lies in
he possibili y o iden i ying egula i ies, bu a oiding easoning ‘on a e age’, i.e., sa egua ding he
possibili y ha di e en social pa e ns may exis . The esul s also allow us o specula e on possible
policies o inc ease school mobili y, highligh ing, among o he hings, he ‘equalising’ ole played by
public spending on educa ion.
Keywo ds: in e gene a ional educa ion mobili y; social mobili y; clus e analysis; public spending
in educa ion
1. In oduc ion
The s udy o he in e gene a ional ansmission o socio-economic s a uses is in e es -
ing and opical in se e al espec s.
On he one hand, i helps us del e in o he well-known heme o ‘equali y o wha ?’
(Sen 1980). In ac , i is qui e e iden ha a s ong co ela ion o socio-economic s a uses
be ween pa en s and child en is a sign o some lack o equali y o oppo uni y. F om his
poin o iew, inequali y o ou comes (e.g., income) can be mo e o less socially accep able i
i is accompanied, o no , by equali y o oppo uni y. None heless, high income inequali y
can i sel be an obs acle o a eal equali y o oppo uni y (Co ak 2013).
On he o he hand, mobili y ac oss gene a ions is no only an issue o equali y, bu
also o e iciency, especially when de ined in e ms o educa ional mobili y (D’Addio 2007).
I is impo an ha i is he mos able and willing people who s udy (and gain access o
he esul ing social oles) and no (only) people om ich amilies. O he wise, we would
end up wi h people wi h inadequa e abili ies in key oles (indeed, as o en seems o be
he case), and we would lose he oppo uni y o socially ake ad an age o he abili ies o
gi ed people jus because hey come om ‘disad an aged’ amilies o social backg ounds
(Glomm and Ra ikuma 1992;Lloyd-Ellis 2000;S a olani and Valen ini 2007).
The ocus o he esea ch p oposed in his pape is p ecisely on educa ional mobili y,
which among o he hings is conside ed o be a key elemen o o e all economic mobili y
ac oss gene a ions (Feins ein e al. 2006;D’Addio 2007;Je im and Macmillan 2015;Na ayan
e al. 2018;S uhle 2018).
The li e a u e iden i ies se e al ac o s ha may in luence he le el o educa ional
in e gene a ional mobili y (and, h ough i , in e gene a ional income mobili y).
Economies 2024,12, 126. h ps://doi.o g/10.3390/economies12060126 h ps://www.mdpi.com/jou nal/economies
Economies 2024,12, 126 2 o 13
Public spending in educa ion is a key elemen . I can no only imp o e he quali y
o educa ion in gene al, bu also bene i hose who would be a isk o s a ing o disad-
an aged. F om a heo e ical poin o iew, Solon (2004) p oposes a model acco ding o
which in e gene a ional income elas ici y inc eases as he e u n on in es men in human
capi al inc eases, bu which dec eases wi h he p og essi i y o public in es men in human
capi al. The model o Da ies e al. (2005) analyses in e gene a ional ea ning mobili y in a
amewo k whe e human capi al plays a c ucial ole and concludes ha mobili y is highe
wi h public han wi h p i a e educa ion. He ing on (2015) de eloped an o e lapping
gene a ions model and calib a ed i in o de o compa e he US and No way empi ically
and quan i a i ely, eaching he conclusion ha public educa ion spending plays a key
ole in in e gene a ional ea ning pe sis ence. Lee and Seshad i (2019) p esen a model
o human capi al in es men s ha explains he in e gene a ional pe sis ence o ea nings,
weal h, and college a ainmen and conclude ha educa ion subsidies can educe he in e -
gene a ional pe sis ence o economic s a us. Maye and Lopoo (2008) ocused on human
capi al in es men . They used da a om he Panel S udy o Income Dynamics and he US
Census o Go e nmen s and ound g ea e in e gene a ional mobili y in high-spending
s a es compa ed wi h low-spending s a es. Neidhö e e al. (2018) compu ed se e al in-
dexes o in e gene a ional educa ion mobili y o 18 La in Ame ican coun ies, inding
signi ican c oss-coun y di e ences also associa ed wi h public educa ional expendi u es.
Balcaza e al. (2015) used da a on 48 coun ies ha pa icipa ed in he P og amme o
In e na ional S uden Assessmen (PISA) in 2012, inding e idence o a co ela ion be ween
public spending on schooling and inequali y o oppo uni y in achie ing basic p o iciency
in eading, ma hema ics, and science. In Na ayan e al. (2018), eg essions in ol ing
da a on iche economies showed ha highe public spending on educa ion is associa ed
wi h highe ela i e in e gene a ional mobili y in educa ion, and he au ho s concluded
ha ‘[ ]his is consis en wi h he heo y ha public spending helps equalise oppo uni ies
h ough in es men s ha compensa e o he gap in p i a e in es men s be ween child en
o ich and poo pa en s’ (Na ayan e al. 2018, p. 19).
Mo eo e , i public spending on educa ion is speci ically di ec ed owa ds indi iduals
om disad an aged economic backg ounds and is inanced h ough axes ha pa icula ly
all on indi iduals om weal hy amilies (e.g., beques s axa ion), i can be pa icula ly
e ec i e in ebalancing oppo uni ies o access o educa ion i sel , os e ing equi y and
e iciency gains (S a olani and Valen ini 2007).
Public in e en ion in his ield can also conce n egula ion, and he p esence and
du a ion (in yea s) o compulso y educa ion can ce ainly in luence educa ional mobili y,
pa icula ly in he mos disad an aged con ex s. An uneduca ed (and he e o e mo e likely
o be ‘poo ’) pa en migh decide no o make hei child s udy (o hey may s udy less
han hey should). I a ce ain numbe o yea s o educa ion is compulso y, his choice is
limi ed. I is impo an o emphasise ha he yea s o compulso y educa ion in gene al a e
somewha ela ed o he le el o public spending on educa ion; howe e , hey ep esen a
sligh ly di e en aspec o public in e en ion di ec ly ela ed o egula ion a he han he
le el o spending.
Socio-economic seg ega ion is ano he ac o ha can s ongly in luence educa ional
mobili y. Van de Weide e al. (2021), using da a on 153 coun ies, ound ha p oxies
o seg ega ion a e nega i ely co ela ed wi h in e gene a ional educa ion mobili y. A
speci ic de ini ion o his concep conce ns spa ial/ esiden ial seg ega ion. Recen esea ch
sugges s ha mo e esiden ially seg ega ed a eas (i.e., whe e amilies wi h di e en socio-
economic backg ounds and aces li e in sepa a e neighbou hoods) end o ha e lowe
in e gene a ional mobili y. Che y e al. (2014) used adminis a i e eco ds o mo e han
40 million child en in he US and, wi h OLS (O dina y Leas Squa es) eg essions ac oss
700 a eas, ound ha high-mobili y a eas ha e less esiden ial seg ega ion. Connolly e al.
(2019) linked mic oda a om he US and Canada, and hei OLS es ima es sugges ha
‘inequali ies be ween whi es and blacks likely play an impo an ole in unde s anding
why he Uni ed S a es has lowe a es o in e gene a ional mobili y’ (Connolly e al. 2019,
Economies 2024,12, 126 3 o 13
p. 598). In ha case, ‘seg ega ion’ is o be unde s ood in e ms o ‘social seg ega ion’ (which
hen o en also becomes ‘spa ial’ seg ega ion). Co ak (2021) used da a om 266 Canadian
Census Di isions on a coho o men and women bo n be ween 1963 and 1970, inding ha
low-mobili y egions end o exis ou side o u ban a eas; eading his esul s, he unde lines
ha Du lau and Seshad i (2018) explici ly model he in luence ha inequali y has on
economic oppo uni y h ough i s impac on socio-economic seg ega ion. In he p esen
pape , esiden ial seg ega ion is mainly conside ed in e ms o he deg ee o u banisa ion,
which seems especially ele an o de eloping coun ies; ob iously, a lowe deg ee o
u banisa ion indica es g ea e spa ial seg ega ion and social isola ion.
As men ioned ea lie , income inequali y i sel can igge inequali y o oppo uni y in
access o educa ion in a dange ous icious ci cle. Co ak (2013) hypo hesises he exis ence
o his isk wi h a heo e ical app oach ha also e e s o empi ical esul s om he li e a-
u e. Rea don (2011) ca ied ou a desc ip i e s udy on he ela ionship be ween academic
achie emen and amily income in he US o e he las ew decades using da a om 12
na ionally ep esen a i e s udies ha included in o ma ion on amily income and s uden
pe o mance in ma h o eading. He ound ha socio-economic s a us is a p edic o o
s uden academic achie emen and educa ional ou comes. Campbell e al. (2005) used
mic oda a om he US census, and hei es ima es sugges ha an inc ease in amily income
and weal h inequali y leads o a g owing dispe sion o educa ional a ainmen s. Kea ney
and Le ine (2016) used US longi udinal mic oda a, and hei eg essions con i m ha
g ea e income inequali y migh lead o lowe le els o high school comple ion among
indi iduals om low-income amilies and, he e o e, o lowe a es o upwa d mobili y. A
s udy wi h US da a showed ha , wi h espec o income, abou 50 pe cen o in e gene a-
ional pe sis ence can be explained by pa en s’ in es men s in hei child en’s educa ion
(Res uccia and U u ia 2004). This mechanism ends o a ou access o educa ion o
indi iduals belonging o weal hy amilies. Duncan and Mu nane (2012) ound ha , in he
las ew decades, he amoun ha high-income amilies spen on hei child en’s educa ion
g ew by 150 pe cen , while he amoun spen by low-income amilies g ew by 57 pe cen .
The ele ance o cul u al con ex and ‘ amily cul u e’ in in luencing in e gene a ional
mobili y is o en conside ed in he li e a u e (Becke and Tomes 1979;Maye 1997;Pike y
2000; see McLanahan 2020 o a e y comp ehensi e e iew on he subjec ), bu less so in
he empi ical li e a u e. A ac o no s udied so a in he empi ical li e a u e lies in ‘cul u al
a i udes’ conce ning he impo ance o child en’s independence. I pa en s conside i
impo an o hei child en o be independen and sel -su icien , he link be ween pa en s’
economic s a us and child en’s oppo uni ies may be weakening. An ex eme case ha
can be used o exempli y his concep is as ollows: ‘i is impo an o me ha you a e
au onomous and independen , I do no pay o you s udies, you ha e o wo k o pay o
hem you sel ’.
The unde lying idea o he analysis in his pape is ha he ac o s lis ed so a (public
spending on educa ion, compulso y educa ion, income inequali y, seg ega ion/u banisa ion,
and impo ance o child en’s independence) may be mo e o less impo an in di e en
socio-economic con ex s. These di e ences may especially eme ge be ween ad anced
economies and de eloping coun ies ( ega ding he ends o in e gene a ional mobili y
o e ime in coun ies a di e en s ages o de elopmen , see also Leone 2019).
Some o he li e a u e sugges s ha mobili y will decline as incomes inc ease in he
absence o public in e en ions (Becke and Tomes 1979;Becke e al. 2018); he e o e, he
le el o public spending on educa ion could be mo e e ec i e in os e ing educa ional
in e gene a ional mobili y in ad anced economies. The e ec o income inequali y on
child en’s educa ional oppo uni ies may be g ea e in ich coun ies, since he link may
exis h ough he esou ces in es ed by pa en s in hei child en’s educa ion; he a ailabili y
o hese esou ces in addi ion o hose needed o sa is y basic needs is ce ainly g ea e in
ich economies. Compulso y educa ion may be mo e impo an o de eloping coun ies
because i has a g ea e in luence on low and middle le els o educa ion. The same applies
o he deg ee o u banisa ion because he di e ence be ween u al and u ban en i onmen s
Economies 2024,12, 126 4 o 13
is he g ea es cause o social seg ega ion in de eloping coun ies. Fo example, Reddy
and Singh (2021) ound ha , in India, he in e gene a ional pe sis ence in educa ional
a ainmen is much highe in u al a eas han in u ban a eas.
I is concei able ha he cul u al emphasis on child au onomy may ha e g ea e e ec s
in ad anced economies because he e a e ac ually mo e chances o be au onomous and
independen (less unemploymen , mo e educa ional ins i u ions, mo e public se ices,
mo e schola ships, e c.).
The a e age le el o educa ion (o en ela ed o pe capi a income) can also in luence
mobili y and can do so di e en ly in coun ies wi h di e en le els o de elopmen . ‘In he
wo ld’s poo es coun ies, a la ge majo i y o pa en s ha e no educa ion. When pa en s a e
equally dep i ed, i ma e s less wha household one is bo n in o, implying a high le el
o ela i e mobili y. As coun ies inc ease hei educa ion and income le els, he gaps be-
ween poo , middle-class and be e -o pa en s become mo e p onounced. Wi hou public
in e en ions, child en’s educa ion ajec o ies will e en ually s a o di e ge depending
on whe he hey a e bo n in o a poo , middle-class o uppe -class amily, which is when
ela i e in e gene a ional mobili y will decline’ (Van de Weide e al. 2021, p. 30).
On his basis, his pape p oposes a clus e analysis wi h da a om 82 coun ies
in an a emp o e i y he exis ence o di e en pa e ns in he ela ionships be ween
in e gene a ional mobili y in educa ion and he ac o s discussed abo e, wi h pa icula
e e ence o di e ences be ween economies a di e en s ages o de elopmen .
Mos o he empi ical analyses men ioned in his in oduc ion, on he con a y, use
indi idual da a and a mic o-econome ic app oach. The e o e, hey a e also able o deepen
he analysis in e ms o he causali y o he iden i ied ela ionships. This leads o he bigges
limi a ion o he analysis p oposed he e: om a echnical poin o iew, i does no allow us
o make conside a ions ega ding he causali y o he ela ionships. We shall e u n o his
ma e in he subsequen pa s o he a icle as well as in he closing ema ks. The app oach
ollowed in his a icle, as al eady men ioned, uses agg ega ed da a and ca ies ou a mo e
gene al, c oss-coun y analysis wi h a clus e me hodology.
Ne e heless, he app oach ollowed in he p esen a icle has inno a i e and use ul
aspec s ha can imp o e ou unde s anding o he analysed phenomenon. I allows us o
conside oge he se e al ac o s ha can in luence in e gene a ional mobili y in educa ion,
o also include among hese ac o s he cul u al aspec (independence o child en) ha
is gene ally no conside ed in he empi ical li e a u e, and o ca y ou an analysis on a
sample in ol ing a e y high numbe o na ions, e en a di e en le els o de elopmen ,
wi h a me hodology ha can highligh di e en ela ionships be ween hese ac o s and
mobili y depending p ecisely on he le el o de elopmen .
2. Me hodology and Da a
As highligh ed in he in oduc ion, he idea behind his pape is ha he a ious
ac o s possibly in luencing in e gene a ional mobili y in educa ion may ha e di e en
impac s in economies wi h di e en le els o de elopmen .
One way, hough no he only way, in which his concep can be de ined in an em-
pi ical analysis in which he uni s o analysis a e na ional economies is as ollows: is i
possible o iden i y pa e ns (i.e., g oup coun ies) acco ding o le el o income, mobili y in
educa ion, public spending on educa ion, compulso y educa ion, income inequali y, le el
o u banisa ion, and impo ance o child en’s independence?
Clus e analyses a e one o he bes ways o sea ch o g oups h ough da a (Kau mann
and Rousseeuw 1990). In ou case, i seems o be an app op ia e way o clus e na ions
acco ding o le el o income and le el o in e gene a ional mobili y in educa ion in he
i s ins ance and acco ding o he o he a iables in he second ins ance. The numbe
(82) o obse a ions a ailable in he da ase cons uc ed o his analysis also sugges s he
choice o his me hodology. I one hinks ha he ela ionships be ween he a iables may
be di e en o g oups o coun ies (e.g., high-, middle-, and low-income economies), he
Economies 2024,12, 126 5 o 13
numbe o a ailable obse a ions would no allow o eliable eg essions on subg oups o
he a ailable sample.
This pape seeks o iden i y ‘pa e ns o in e gene a ional educa ion (im)mobili y’
h ough a clus e analysis. The ad an age o clus e analyses lies in he possibili y o iden i-
ying egula i ies bu a oiding easoning ‘on a e age’, i.e., sa egua ding he possibili y ha
di e en social pa e ns may exis .
Be o e explo ing he de ails o he analysis echnique, i is use ul o desc ibe he
a iables and da a.
Table 1shows he a iables used in he analysis, he da abases o o igin, and, inally, he
mean and s anda d de ia ions ( o he 82 coun ies conside ed). All a iables a e a e aged
o e a ela i ely long pe iod o ime. This agg ega ion o e ime smoo hs ou he changes
in and de elopmen o a coun y o e 35 yea s. This may lead o an unde es ima ion o
any changes in ends du ing he pe iod unde analysis. On he o he hand, i seems o be
a good way o app oxima e he condi ions in which people bo n in he 1980s g ew up.
Table 1. Da ase desc ip ion and summa y s a is ics.
Va iable Sou ce Time Va iable
(Sho ened) Mean S anda d
De ia ion
GDP pe capi a
(Cons an 2017 In .
Dolla s)
Wo ld Bank
Wo ld De elopmen
Indica o s
(a e age alue
1980–2015) GDP USD 20197 15,392
Educa ional a ainmen (%
o he popula ion 25+ who
a leas comple ed uppe
seconda y school)
Wo ld Bank
Wo ld De elopmen
Indica o s
(a e age alue
1980–2015) EDU 53.8% 24.0
U ban popula ion
(% o o . popula ion)
Wo ld Bank
Wo ld De elopmen
Indica o s
(a e age alue
1980–2015) URB 61.9% 18.1
Gini Index
Wo ld Bank
Wo ld De elopmen
Indica o s
(a e age alue
1980–2015) GINI 0.369 0.083
Go e nmen expendi u e
on educa ion (% GDP)
Wo ld Bank
Wo ld De elopmen
Indica o s
(a e age alue
1980–2015) GOV_EDU 4.39% 1.36
Compulso y educa ion
(yea s)
Wo ld Bank
Wo ld De elopmen
Indica o s
(a e age alue
1980–2015) COMP_EDU 9.7 1.7
Sha e o pa en s indica ing
‘Child en’s Independence’
as an impo an quali y in
child en (%)
Eu opean Values
S udy—Wo ld Values S udy
In eg a ed su ey 1981–2021
(a e age alue
1981–2021) 1CHILD_IND 47.2% 14.3
Expec ed ank o a child
whose pa en s ank in he
bo om hal o he
educa ion dis ibu ion
Wo ld Bank
Global Da abase on
In e gene a ional Mobili y 2
1980s coho
(gene a ion bo n
be ween 1980 and
1989)
MOB_EDU 39.3 3.4
1
No all na ions a e in ol ed in all EVS and WVS wa es. A e ages we e calcula ed using he da a a ailable o e
he ime pe iod 1981–2021. Fo each a ailable wa e, he mic oda a we e p ocessed using he weigh s sugges ed
by he ele an guidelines. 2(GDIM 2023;Van de Weide e al. 2023).
All coun ies o which da a a e a ailable a e included in he analysis, wi h he sole
excep ion o hose classi ied by he Wo ld Bank (on 1 July 2020) as being in he ‘Low Income’
ca ego y in o de o a oid da a eliabili y p oblems (be ween 1980 and 2015, hese na ions
had ew alues o some a iables, so he alues o hose a iables would no be ue
Economies 2024,12, 126 6 o 13
‘pe iod a e ages’). These a e almos exclusi ely coun ies om Sub-Saha an A ica (a
egion ha is ne e heless ep esen ed in he da ase ).
Table A1 in Appendix Alis s he coun ies included in he analysis and he alues o
he a iable conce ning in e gene a ional mobili y in educa ion. Appendix Bde ails he
in o ma ion equi ed o e ie e da a om he da abases used o ensu e he ep oducibili y
o he analysis.
The a iable ela ed o in e gene a ional mobili y in educa ion is lis ed in he las ow
o Table 1and dese es a close look. I measu es ‘ he expec ed ank o an indi idual in
he educa ion dis ibu ion whose pa en s ank in he bo om hal o he pa en educa ion
dis ibu ion’ (Van de Weide e al. 2021, p. 8). The educa ion o pa en s is iden i ied by
e e ing o he pa en wi h he highes le el o educa ion, while, o he nex gene a ion,
he en i e popula ion is conside ed ( hus, bo h sons and daugh e s). This is a ank-based
measu e o ela i e mobili y. Rela i e mobili y ep esen s he ex en o which an indi idual’s
posi ion in he dis ibu ion o educa ional a ainmen s is independen o he posi ion o
his/he pa en s. I he educa ional a ainmen o each indi idual is independen o he
s a ing condi ions (i.e., pa en al s a us), he expec ed ank should be 50 o all indi iduals
(bo h o hose wi h pa en s who we e in he bo om hal o he anking o hei gene a ion
and o indi iduals wi h pa en s who we e be e placed in he same anking as he p e ious
gene a ion). Hence, he a iable ep esen s he deg ee o which an indi idual’s educa ional
le el is independen o he educa ional le el o pa en s. A highe alue o his a iable is
associa ed wi h g ea e in e gene a ional mobili y (o , in o he wo ds, g ea e equali y o
oppo uni ies).
No e ha he low s anda d de ia ion o he ‘compulso y educa ion’ a iable esul s
om 60 o he 82 coun ies ha ing alues be ween 9 and 12. This does no de ac om he
ac ha he e a e coun ies wi h high alues, such as The Ne he lands, which has a alue o
13 because ull- ime educa ion is compulso y om he ages o 5 o 16 and a leas pa - ime
educa ion is compulso y om he ages o 16 o 18. The e a e some e y low alues, such
as Bangladesh (5), Malaysia (6), and I aq (6). No e ha hese a e no he la es alues bu
he a e age o he alues o e he pe iod o ime conside ed calcula ed acco ding o he
a ailabili y o da a, which o en does no co e he en i e pe iod.
Clus e analyses a e a ec ed by he magni ude o he a iables. I was he e o e
necessa y o s anda dise (mean, 0; s anda d de ia ion, 1) he a iables o make hem
compa able.
The in en ion was o g oup na ions acco ding o he alues o hese (s anda dised)
a iables, and his was achie ed using a pa i ion clus e analysis me hod (k-means), in
which he obse a ions (coun ies) a e b oken up in o se e al nono e lapping g oups
(Has ie e al. 2009). Each g oup b ings oge he na ions ha sha e a common pa e n in
he mean alues o he a iables conside ed. The analysis used an i e a i e algo i hm ha ,
s a ing om k ini ial clus e cen es, minimises he Euclidean dis ance wi hin each clus e
be ween i s mean (k-clus e ing) and i s obse a ions while maximising he dis ance in e ms
o means among adjacen clus e s. Fo his, we used he command ‘clus e kmeans’ in S a a,
which implemen s an i e a i e p ocedu e. I begins wi h k ini ial g oup cen es, assigns
obse a ions o he g oup wi h he closes cen e , compu es he mean o he obse a ions
assigned o each o he g oups, and hen epea s he p ocess. These s eps con inue un il all
obse a ions emain in he same g oup om he p e ious i e a ion.
The eplicabili y o esul s dese es much a en ion in his ype o analysis. Two
impo an choices mus be made: he op imal numbe o g oups (k) mus be chosen and he
numbe o andom s a ing poin s ( ) mus be de e mined. Fo bo h issues, he p ocedu e
sugges ed by (Makles 2012) was ollowed.
Gi en a ce ain numbe o andom s a ing poin s, he op imal numbe o g oups can
be de e mined by compa ing he alues o he wi hin sum o squa es (WSS) o i s loga i hm
o each k. In his case, one can s op a he numbe o g oups k beyond which inc easing
he numbe o g oups does no con ibu e signi ican ly o he educ ion in he WSS (i.e.,
agmen ing in o u he g oups does no explain he da a any be e ). I is also possible
Economies 2024,12, 126 7 o 13
o compa e, o each k, he
η
2 coe icien , which is qui e simila o he R2. One should
s op a he numbe o g oups k beyond which inc easing he numbe o g oups does no
signi ican ly inc ease he
η
2 coe icien . Finally, he p opo ional educ ion in e o (PRE)
coe icien can be used. I illus a es ‘ he p opo ional educ ion o he WSS o clus e
solu ion k compa ed wi h he p e ious solu ion wi h k
−
1 clus e s’ (Makles 2012, p. 347).
Howe e , e en he numbe o andom s a ing poin s canno be chosen a bi a ily.
‘The bes way o e alua e he chosen solu ion is he e o e o epea he clus e ing se e al
imes wi h di e en s a ing poin s and hen compa e he di e en solu ions’ (Makles 2012,
p. 350).
Figu e 1 epo s he wi hin sum o squa es (WSS), i s loga i hm, he
η2
coe icien , and
he p opo ional educ ion in e o (PRE) as k inc eases. Each line ep esen s a di e en
epe i ion o he analysis as he numbe o andom s a ing poin s changes ( om 100 o 150).
Looking a he alues o WSS and
η2
, we see ha he g oups do no add much in o ma ion
when going beyond 4. Howe e , when looking a he PRE, we see ha , o up o k = 6,
in qui e a numbe o epe i ions (i.e., a ying he numbe o andom s a ing poin s) he
addi ion o ano he g oup con ibu es qui e signi ican ly o he educ ion in he WSS. So,
he mos p uden choice seems o be k = 6. Finally, among all he epe i ions wi h k = 6,
he epe i ion selec ed had he lowes WSS and he g ea es
η2
(in bo h cases, his occu ed
wi h 131 andom s a ing poin s).
Economies 2023, 11, x FOR PEER REVIEW 7 o 13
Gi en a ce ain numbe o andom s a ing poin s, he op imal numbe o g oups can
be de e mined by compa ing he alues o he wi hin sum o squa es (WSS) o i s loga-
i hm o each k. In his case, one can s op a he numbe o g oups k beyond which in-
c easing he numbe o g oups does no con ibu e signi ican ly o he educ ion in he
WSS (i.e., agmen ing in o u he g oups does no explain he da a any be e ). I is also
possible o compa e, o each k, he η
2
coe icien , which is qui e simila o he R
2
. One
should s op a he numbe o g oups k beyond which inc easing he numbe o g oups
does no signi ican ly inc ease he η
2
coe icien . Finally, he p opo ional educ ion in e -
o (PRE) coe icien can be used. I illus a es ‘ he p opo ional educ ion o he WSS o
clus e solu ion k compa ed wi h he p e ious solu ion wi h k − 1 clus e s’ (Makles 2012,
p. 347).
Howe e , e en he numbe o andom s a ing poin s canno be chosen a bi a ily.
‘The bes way o e alua e he chosen solu ion is he e o e o epea he clus e ing se e al
imes wi h di e en s a ing poin s and hen compa e he di e en solu ions’ (Makles
2012, p. 350).
Figu e 1 epo s he wi hin sum o squa es (WSS), i s loga i hm, he η
2
coe icien ,
and he p opo ional educ ion in e o (PRE) as k inc eases. Each line ep esen s a di e -
en epe i ion o he analysis as he numbe o andom s a ing poin s changes ( om 100
o 150). Looking a he alues o WSS and η
2
, we see ha he g oups do no add much
in o ma ion when going beyond 4. Howe e , when looking a he PRE, we see ha , o
up o k = 6, in qui e a numbe o epe i ions (i.e., a ying he numbe o andom s a ing
poin s) he addi ion o ano he g oup con ibu es qui e signi ican ly o he educ ion in
he WSS. So, he mos p uden choice seems o be k = 6. Finally, among all he epe i ions
wi h k = 6, he epe i ion selec ed had he lowes WSS and he g ea es η
2
(in bo h cases,
his occu ed wi h 131 andom s a ing poin s).
Figu e 1. K-means clus e analysis. Selec ion o he op imal numbe o g oups.
3. Resul s
The s eps illus a ed in he p e ious sec ion sugges g ouping he da a in o six g oups
wi h 131 andom s a ing poin s ia a k-means clus e algo i hm. Table 2 shows he esul s
o he esul ing clus e s/g oups in e ms o a e age alues o he (s anda dised) a iables.
Figu e 1. K-means clus e analysis. Selec ion o he op imal numbe o g oups.
3. Resul s
The s eps illus a ed in he p e ious sec ion sugges g ouping he da a in o six g oups
wi h 131 andom s a ing poin s ia a k-means clus e algo i hm. Table 2shows he esul s
o he esul ing clus e s/g oups in e ms o a e age alues o he (s anda dised) a iables.
To acili a e a possible eading o he ou comes, he clus e s we e o de ed acco ding o
he le el o GDP pe capi a. The idea is o in e p e he esul s by compa ing he a iables’
alues be ween clus e s wi h simila le els o de elopmen (High, Middle, and Low GDP).
Clus e A mus he e o e be compa ed wi h clus e B, clus e C mus be compa ed wi h
clus e D, and clus e E mus be compa ed wi h clus e F. The bold and unde lined numbe s
indica e ha he a e age alue o ha a iable o he clus e is meaning ully highe han
ha o he clus e i is compa ed o.
Economies 2024,12, 126 8 o 13
Table 2. Clus e cha ac e is ics (mean alues o s anda dised a iables).
Clus e
GDP MOB_EDU EDU URB GINI GOV_EDU
COMP_EDU
CHILD_IND
N
(Coun ies 1)
High
GDP
A 1.31 0.19 0.58 0.74 −0.50 0.49 0.86 0.11 14
B 1.23 1.11 0.69 0.77 −0.82 1.03 −0.05 1.33 11
Middle
GDP
C−0.37 −0.04 0.85 −0.07 −0.45 −0.05 −0.22 −0.17 22
D−0.54 −0.90 −0.76 0.42 1.77 −0.20 0.83 −0.80 12
Low GDP E−0.66 1.50 −1.13 −0.80 1.05 −1.05 −0.52 −1.13 5
F−0.77 −0.60 −1.10 −1.01 −0.04 −0.52 −0.77 −0.10 18
1
Appendix Clis s coun ies ha all unde he di e en clus e s. Bold and unde lined numbe s indica e ha he
a e age alue o ha a iable o he clus e is meaning ully highe han ha o he clus e in he same ca ego y
o GDP pe capi a (High, Middle, and Low).
Clus e analyses a e o en used in he li e a u e o gene a e hypo heses ha should
hen be es ed. In he p esen analysis, he p ocedu e could be: (a) o g oup coun ies in o
clus e s wi h di e en links be ween he a iables (e.g., public spending on educa ion is
associa ed wi h highe in e gene a ional mobili y in ich coun ies, whe eas he ela ionship
seems o be he e e se among poo coun ies); (b) o es he causali y o he ela ionships
(and i s di ec ion) in subg oups o coun ies based on he esul s o he clus e analysis
(e.g., a causali y analysis aking only na ions om clus e s A and B and ano he causali y
analysis aking only na ions om clus e s E and F). This would ce ainly be in e es ing,
bu i goes beyond he scope o his pape . Addi ionally, a pu ely echnical issue lies in
he numbe o na ions in each subg oup, which is oo small o ca y ou any analysis o
causali y (con inuing wi h he example gi en abo e, he e would be wo g oups: one wi h
25 coun ies and one wi h 23 coun ies). Indeed, his p esen s a limi a ion o his s udy and
implies a po en ial a ea o u u e inqui y, which will be discussed in he conclusions.
4. Discussion
Based on he in e p e a ion me hod desc ibed in he p e ious sec ion, he esul s can
be summa ised as ollows.
Among bo h high-GDP and middle-GDP coun ies, g ea e in e gene a ional mobili y
in educa ion is associa ed wi h highe le els o educa ion in gene al, lowe income inequal-
i y, highe public spending on educa ion, sho e pe iods o compulso y educa ion, and a
g ea e emphasis on child en’s independence.
The only di e ence be ween high-GDP and middle-GDP coun ies appea s o be he
deg ee o u banisa ion (i ele an among he o me and nega i ely associa ed wi h in e -
gene a ional mobili y among he la e ). This can be explained by conside ing ha clus e
D almos exclusi ely encompasses La in Ame ican and Ca ibbean coun ies (Appendix C)
ha a e highly u banised (on a e age, 70% o indi iduals li e in ci ies, a igu e second only
o No h Ame ica (78%)). This deg ee o u banisa ion, howe e , does no p o ec agains
signi ican socio-economic seg ega ion (‘ a elas’ in B azil and Colombia, ‘ illa mise ia’ in
A gen ina, ‘slums’ in Mexico, e c.).
Conce ning he impo ance o public spending on educa ion in high-GDP and middle-
GDP coun ies, u he e idence can also be ex ac ed om he esul s. I one o de s he
clus e s acco ding o he le el o mobili y ( hus, B, A, C, D), he same o de also applies o
he le el o public spending on educa ion.
Among low-GDP coun ies, g ea e in e gene a ional mobili y in educa ion is associ-
a ed wi h a highe deg ee o u banisa ion, highe income inequali y, lowe public spending
on educa ion, longe pe iods o compulso y educa ion, and a lowe emphasis on child en’s
independence.
I is no su p ising ha e en ela i ely poo coun ies ha e a high deg ee o in e gene -
a ional mobili y in educa ion (clus e E). As men ioned in he in oduc ion, he c ea o s o
he da abase hemsel es poin ou ha he ela ionship be ween in e gene a ional mobili y
and income u ns ou o be non-mono onic (Van de Weide e al. 2021). This may be due o
he ac ha mos pa en s a e no educa ed in poo na ions (in ac , he le el o educa ion
