Models of the impact of socio-economic shocks on higher education development

Raye nye a, Olena e al.
A icle
Models o he impac o socio-economic shocks on highe
educa ion de elopmen
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Sugges ed Ci a ion: Raye nye a, Olena e al. (2024) : Models o he impac o socio-economic shocks
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Ci a ion: Raye nye a, Olena,
Volodymy Ponoma enko, Sil ia
Ma uso a, Kos yan yn
S yzhychenko, S anisla Filip, and
Olha B o ko. 2024. Models o he
Impac o Socio-Economic Shocks on
Highe Educa ion De elopmen .
Adminis a i e Sciences 14: 278.
h ps://doi.o g/10.3390/
admsci14110278
Recei ed: 2 Augus 2024
Re ised: 17 Oc obe 2024
Accep ed: 21 Oc obe 2024
Published: 26 Oc obe 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
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adminis a i e
sciences
A icle
Models o he Impac o Socio-Economic Shocks on Highe
Educa ion De elopmen
Olena Raye nye a 1,2,* , Volodymy Ponoma enko 2, Sil ia Ma uso a 1, Kos yan yn S yzhychenko 2,
S anisla Filip 1and Olha B o ko 2
1B a isla a Uni e si y o Economics and Managemen , Fu deko a 16, 85104 B a isla a, Slo akia;
[email p o ec ed] (S.M.); s anisla [email p o ec ed] (S.F.)
2Simon Kuzne s Kha ki Na ional Uni e si y o Economics, a . Nauki 9-a, 61166 Kha ki , Uk aine;
[email p o ec ed] (V.P.); [email p o ec ed] (K.S.); ol.i [email p o ec ed] (O.B.)
*Co espondence: [email p o ec ed]
Abs ac : This a icle is de o ed o he analysis o he impac o socio-economic shocks on he
dynamics o highe educa ion de elopmen . I is subs an ia ed ha , on he one hand, highe educa ion
in luences he de elopmen o socie y and he economy, on he o he hand, he de elopmen ends
o a coun y p o ide bo h oppo uni ies and limi a ions o i s de elopmen . An algo i hmic model
o s udying he impac o social and economic shocks on he de elopmen o he highe educa ion
sys em (HES) has been de eloped. To diagnose he ela ionship be ween highe educa ion and he
socio-economic de elopmen o Uk aine and Slo akia, he ollowing indica o s we e used: GDP pe
capi a, he Human De elopmen Index, school en ollmen , e ia y, and ne mig a ion. The p esence
o nonlinea ends in he change in indica o s has been shown and po ai s o he socio-economic
de elopmen o he coun ies ha e been cons uc ed. To assess he impac o socio-economic shocks
on he HES, he ime-se ies decomposi ion me hod and c oss-spec al analysis we e used. The ime-
se ies decomposi ion allowed us o iden i y cyclical componen s o indica o s, based on applying
c oss-spec al analysis, and he mos signi ican local ha monics and he lag o hei in luence on he
occu ence o shocks in he HES we e de e mined. The use o he de eloped models allows us o
p edic pe iods o shock poin s in he HES depending on shocks in he endencies o GDP pe capi a
and ne mig a ion.
Keywo ds: highe educa ion; shock poin s; c oss-spec al analysis; end; model; impac ; ha monic
1. In oduc ion
Educa ion is a key igge o he de elopmen o ci iliza ion, which is why signi -
ican ans o ma ions—caused by main ends in he de elopmen o he wo ld in he
21s cen u y—a e he ocus o esea ch by a ious in e na ional o ganiza ions, na ional
go e nmen s, and indi idual esea che s. As UNESCO expe s no e, educa ion is, on he
one hand, a igh ha expands human igh s, on he o he hand, i is a powe ul ool o
educing inequali y in socie y, allowing one o ully pa icipa e in he li e o socie y, b eak
ou o socially lowe s a a, and be ully ealized in li e.
To make his possible, a sys em o legal documen s and ins umen s has been de-
eloped in he in e na ional a ena. Thus, he human igh o educa ion is ensh ined in
he Decla a ion o Human Righ s (1948), Con en ion agains Disc imina ion in Educa ion
(UNESDOC 1960), he Global Con en ion on he Recogni ion o Quali ica ions conce ning
Highe Educa ion (UNESDOC 2019), egional con en ions (UNESDOC 2023). A signi ican
con ibu ion o he unde s anding o new asks, de elopmen goals, and mode niza ion o
educa ion in he 21s cen u y was made by he Wo ld Educa ion Fo um, “Educa ion 2030:
Incheon Decla a ion and F amewo k o Ac ion o he implemen a ion o Sus ainable De-
elopmen Goal 4: Ensu e inclusi e and equi able quali y educa ion and p omo e li elong
lea ning oppo uni ies o all” (UNESDOC 2015).
Adm. Sci. 2024,14, 278. h ps://doi.o g/10.3390/admsci14110278 h ps://www.mdpi.com/jou nal/admsci
Adm. Sci. 2024,14, 278 2 o 28
Tha is, highe educa ion aces ambi ious goals o u he ans o ma ion in he di ec-
ion o s eng hening equi y, inclusion, and gende equali y; enhancing quali y in educa ion
based on inno a i e app oaches; p omo ing li elong lea ning; and p o iding HE in eme -
gencies o na u al disas e s and mili a y con lic s. These di ec ions o es uc u ing he
highe educa ion sys em a e especially ele an o Uk aine, which is s i ing o ully
in eg a e in o he Eu opean scien i ic and educa ional communi y.
The main ask o mode n highe educa ion in Uk aine is o ensu e he app op ia e
quali y o aining o specialis s, which is based on mode n achie emen s o wo ld science
and e hical p inciples and educa es a de eloped pe sonali y. Howe e , any educa ion
should be aimed, i s o all, a ensu ing he social and economic needs o he s a e, i s
de elopmen , and i s in eg a ion in o Eu opean space. The Minis y o Educa ion and
Science o Uk aine is op imizing he ne wo k o highe educa ion ins i u ions in Uk aine.
In addi ion, indi idual educa ional ajec o ies a e being in oduced in o he ac i i ies
o uni e si ies; a ansi ion is being made o hyb id o ms o educa ion; a g an sys em
o admission o uni e si ies is being in oduced; and condi ions a e being c ea ed o
he digi aliza ion o educa ional p ocesses and he de elopmen o inno a i ely ac i e
en ep eneu ial uni e si ies.
The legal basis o hese ans o ma ions comp ises he laws o Uk aine “On Educa ion”
(2017); “On Highe Educa ion” (2014); “On Scien i ic and Scien i ic-Technical Ac i i ies”
(2016); “On Amendmen s o he Law o Uk aine “On Highe Educa ion” Rega ding En-
su ing he Righ o Ob ain Highe Educa ion o Pe sons Whose Place o Residence is he
Tempo a ily Occupied Te i o y o Uk aine” (2017); Resolu ions o Cabine O Minis e s
O Uk aine “On he app o al o he Na ional F amewo k o Quali ica ions” (2011); “On
he app o al o he Regula ion on educa ional and quali ica ion le els (deg ee educa ion)”
(2013); “On he app o al o he P ocedu e o implemen ing he igh o academic mobili y”
(2015); “On app o al o he lis o ields o knowledge and special ies o which highe
educa ion applican s a e ained” (2015); “Abou documen s on highe educa ion (deg ee)”
(2020) (O icial Websi e o he Pa liamen o Uk aine n.d.).
Al hough highe educa ion has a signi ican impac on he de elopmen o na ional
socio-economic sys ems, he economy and socie y also ha e a signi ican impac on he
de elopmen o he coun y’s highe educa ion sys em. The well-being o he popula ion,
ends in demog aphic p ocesses, he le el o economic de elopmen o he coun y, and
he in ensi y o mig a ion p ocesses a e he main ac o s ha de e mine he de elopmen o
highe educa ion. Al hough hese ac o s a e ep esen a i e o he global highe educa ion
sys em, each coun y has speci ic cha ac e is ics, which de e mine he ele ance o hese
s udies.
2. The Li e a u e Re iew
A la ge numbe o s udies, bo h a he le el o in e na ional o ganiza ions and in-
di idual scien is s and p ac i ione s, a e de o ed o he s udy o he ole and place o
highe educa ion and uni e si ies in he socio-economic de elopmen o ci iliza ion and
indi idual coun ies. The highe educa ion sys ems o coun ies and hei key componen s,
uni e si ies, a e in cons an de elopmen and in e ac ion bo h wi h each o he and wi h
he main s akeholde s— he s a e, ep esen a i es o he labo ma ke , public o ganiza ions,
po en ial applican s, and s uden s.
An analysis o how e ec i e educa ion policy is de eloped in each coun y allows
us o iden i y i s mos impo an componen s, namely: access and pa icipa ion, equi y,
socio-economic s a us, educa ion a ainmen , s uden and adul skills, economic and social
ou comes, social and heal h ou comes, ea nings, public e u ns, educa ion o inno a ion,
ca ee guidance, and s uden mobili y (OECD 2023,2022;Websi e OECD 2024).
The p og ess o coun ies in achie ing sus ainable de elopmen goals (SDG) h ough
he changing ole o highe educa ion, a new unde s anding o he phenomenon o highe
educa ion in he 21s cen u y, and i s de elopmen ends a e e lec ed in he ollowing:
he UN’s o icial annual epo “The Sus ainable De elopmen Goals Repo ” (Uni ed
Adm. Sci. 2024,14, 278 3 o 28
Na ions 2022,2023); he Eu opean Commission’s annual epo on EU educa ion and
aining sys ems “Educa ion and aining moni o ” (Eu opean Commission, Di ec o a e-
Gene al o Educa ion, You h, Spo and Cul u e 2022,2023); Educause’s annual epo on
ad ancing highe educa ion h ough he use o IT “EDUCAUSE Ho izon Repo ” (Pelle ie
e al. 2022,2024;Reini z e al. 2022). Thus, wi hin he amewo k o he 78 h session o
he UN Gene al Assembly (UNGA78, New Yo k 2023), he cen al e en was he SDG
Summi . Wo ld leade s and communi ies ook s ock o p og ess owa d achie ing he
Sus ainable De elopmen Goals by 2030 (SDG Summi 2023). Wi hin he amewo k o
Sus ainable De elopmen Goal 4—ensu e inclusi e and equi able quali y educa ion and
p omo e li elong lea ning oppo uni ies o all—i was emphasized ha he low le el o
digi al skills—skills in wo king wi h in o ma ion and communica ion echnologies—is
he main obs acle o he widesp ead use o he In e ne in educa ion, including highe
educa ion. In addi ion, he p oblem o eache s’ eadiness o signi ican changes in he
o ms, me hods, and ools o highe educa ion was add essed. The key ask, in his ega d,
is he de elopmen and adap a ion o eache s’ quali ica ion skills o he inno a ions o
scien i ic and echnological p og ess o he 21s cen u y (Uni ed Na ions 2022,2023;Websi e
In e na ional Associa ion o Uni e si ies n.d.).
Analysis o p og ess owa d sus ainable de elopmen o ci iliza ion equi es he
de elopmen o an e ec i e sys em o moni o ing ends in he ans o ma ion o highe
educa ion. Today, nume ous pla o ms ha e been c ea ed ha p o ide da abases and
epo s o highe educa ion indica o s (Depa men o Economic and Social A ai s o Uni ed
Na ions n.d.;Mig a ion Da a Po al n.d.;The UNESCO Ins i u e o S a is ics n.d.;OECD
Da a n.d.;Websi e o Eu os a n.d.;Websi e S a is a n.d.;Eu opean Commission, Eu opean
Educa ion and Cul u e Execu i e Agency 2022a,2022b,2024;Eu opean Commission’s
Di ec o a e-Gene al o Educa ion, You h, Spo and Cul u e 2023;Eu opean Educa ion and
Cul u e Execu i e Agency, Eu ydice 2023a,2023b,2024;Websi e Educa ion Coun s n.d.;
and o he s). Acco ding o he Incheon Decla a ion (Educa ion 2030: Incheon Decla a ion),
all indica o s a e di ided in o ou le els: global indica o s (compa able indica o s o all
coun ies o moni o p og ess in highe educa ion and ela ed asks); hema ic indica o s
( o a comp ehensi e assessmen o coun ies’ achie emen o educa ion asks); egional
indica o s ( o ake in o accoun he p og ess o educa ion wi hin he egional con ex ,
poli ical p io i ies, and concep s); and na ional indica o s ( o ake in o accoun he na ional
con ex , de e mining he ela ionship o highe educa ion wi h economic and social ends).
Highe educa ion is one o he key subsys ems o he socio-economic de elopmen
o any coun y. Tha is why a la ge numbe o s udies a e de o ed o he assessmen and
analysis o he impac o highe educa ion on socio-economic de elopmen . As in he case
o Uk aine, he analysis o he impac o highe educa ion on he p ocesses o pos -wa
es o a ion o a coun y’s socio-economic de elopmen is o pa icula in e es .
The de elopmen o highe educa ion is aimed a iden i ying ways o adap i o he
demands o he labo ma ke and c ea ing a quali a i ely new highe educa ion capable o
aking a wo hy place in he ma ke economy and sa is ying he needs o each indi idual
in ob aining knowledge and social expe ience. The au ho s (Volchik e al. 2018;Che ed-
nichenko and Gus china 2016;Mi go odskaya e al. 2023) p o e ha highe educa ion as
an open complex subsys em is de e mined by a se o subjec i e and objec i e ac o s and,
in u n, has a signi ican impac on he s a e o he social sys em as a whole. The au ho s
(Che y bock 2023;Ga ashchuk and Ku senko 2024;Fa ima e al. 2020) also emphasize ha
he e is a di ec dependence o he p ac ice-o ien ed issues o mode niza ion o highe
educa ion on many ac o s, including he cu en socio-economic s age o ans o ma ion o
socie y. Thus, highe educa ion plays a key ole, ha is, i con ibu es o he de elopmen
o a socie y based on knowledge. I is he highe educa ion sys em ha p o ides g adua es
wi h inno a i e skills ha help ans o m socie y in he u u e in acco dance wi h he ends
o scien i ic and echnological s uc u es h ough high-quali y educa ion, scien i ic and
echnical esea ch, g an s, and inno a ions.
Adm. Sci. 2024,14, 278 4 o 28
All his is happening agains he backd op o a global end o educing s a e unding
o highe educa ion. On he one hand, his is a isk ac o ha nega i ely a ec s he
inancial ac i i ies o uni e si ies and he s a e o hei ma e ial and echnical base; on
he o he , i is an oppo uni y o gi e uni e si ies mo e au onomy, o u n a adi ional
uni e si y in o an inno a i e and ac i e o ganiza ion o an en ep eneu ial ype. The la e
is a end in he ans o ma ion o he wo ld’s highe educa ion sys em.
The limi ed esou ces in a coun y do no always allow he s a e o p o ide adequa e
inancial suppo , which con ibu es o he de elopmen o he highe educa ion sys em.
Today, educa ion is inanced no only by budge unds, including he esou ces o he
ele an na ional p ojec , bu also by p i a e inancial esou ces. The s udies (Cha les and
Samon 2023;Ashi beko a and Nu mukhano a 2022;Panig ahi 2023) e lec on he easons
o he change in he und alloca ion policy in he educa ion sys em, conside he exis ing e -
ec i e uni e si y unding s a egies as well as he me hods o educa ion inancing and hei
consequences. The e a e se e al uni e si y unding s a egies, including public unding,
public–p i a e pa ne ships, cha i able dona ions, use ees, c owd unding, bond inancing,
and a ac ing exis ing asse s. Public unding (H abchuk e al. 2022;And onic 2023) is
a common s a egy in de eloped coun ies, which in ol es di ec unding o he digi al
in as uc u e and esou ces o uni e si ies. Public–p i a e pa ne ships (She i deen e al.
2024) can e ec i ely inance he digi al ans o ma ion o he highe educa ion sys em by
a ac ing he esou ces and expe ise o bo h he public and p i a e sec o s. Philan h opic
gi ing plays an impo an ole as indi iduals, ounda ions, and co po a ions a e in e es ed
in suppo ing educa ion and he de elopmen o digi al in as uc u e and esou ces.
An analysis o public unding o di e en le els o educa ion has led o he conclusion
ha highe educa ion equi es highe le els o unding. Thus, acco ding o OECD expe s,
he a e age expendi u e pe s uden is abou USD 10,700 a he p ima y le el, USD 11,900
a he seconda y le el, and USD 18,100 a he e ia y le el (Websi e OECD 2024). This
e lec s he ac ha highe educa ion equi es eache s o be mo e highly quali ied, o
cons an ly upda e hei skills and pedagogical skills, and o wo k wi h s uden s in di e en
ways. All his implies highe wages. Thus, he mode n de elopmen o highe educa ion
inancing is expe iencing changes due o new challenges ela ed o he s eng hening o
he digi aliza ion p ocess; he impac o o ce-ma gin ci cums ances on he de elopmen o
highe educa ion, such as pandemics and mili a y con lic s; changes in he emune a ion
sys em o scien is s and acul y; he use o g an unding; and he s eng hening o he ole
o uni e si ies in egional and na ional policies. Ano he challenge o he 21s cen u y ha
he highe educa ion sys em aces is globaliza ion p ocesses and he associa ed popula ion
mig a ion p ocesses. Much a en ion is paid oday o he s udy o he ela ionship and
mu ual in luence o he educa ional and socio-demog aphic sys ems o a coun y by bo h
go e nmen o ganiza ions and scien is s. This is due o he ac ha in ellec ual capi al is
one o he mos impo an de e minan s o long- e m economic de elopmen o a coun y.
The ela ionship be ween highe educa ion and mig a ion p ocesses in socie y was s udied
in (Raye nye a e al. 2023a,2023b); he esul s showed ha he Russian–Uk ainian mili a y
con lic caused a signi ican ou low o Uk ainians wi h hei amilies o Eu ope. This led o
a dec ease in he numbe o applican s o uni e si ies and a dec ease in he economically
ac i e popula ion o he coun y. In hese condi ions, uni e si ies aced he isk o dis up ing
hei inancial s abili y and educing he a ac i eness o highe educa ion in b oad sec ions
o he popula ion.
The wo k (Kalmukhanbe o a and Shna beko a 2022) examined mig a ion ends
a ound he wo ld as well as mig a ion ends in highe educa ion ins i u ions and also
de e mined ha educa ional mig a ion la gely de e mines he dynamics and na u e o a
coun y’s socio-economic de elopmen . The au ho s (Maha o e al. 2022;Chowdhu y 2019;
Cheng e al. 2023;S ojano ski e al. 2023), in hei wo k, examined he ela ionship be ween
mig a ion managemen and highe educa ion and also iden i ied nume ous and mul idi-
mensional ac o s in luencing mig a ion p ocesses in he de elopmen o educa ional and
socio-economic sys ems o a coun y in mode n condi ions. A all imes, he easons o

Adm. Sci. 2024,14, 278 5 o 28
mig a ion we e mili a y con lic s, poli ical ins abili y, lack o economic p ospec s, he desi e
o in eg a e in o he EU, and he oppo uni y o con inue educa ion om high school o
uni e si y le el. Thus, he inc ease in di e en ypes o mig a ion a e signs o globaliza ion,
and he sha e o mig an s in he pe manen popula ion o coun ies e lec s he deg ee o
in ol emen in globaliza ion p ocesses.
Unde s anding he new ole o highe educa ion in socie y necessi a es con inuous
moni o ing o educa ional p ocesses and modeling o key indica o s. Analysis and e alua-
ion o p ocesses and componen s o he educa ional sys em allow i s op imiza ion based
on he analysis o e ospec i e ends and he use o a wide ange o economic and ma he-
ma ical me hods and models o de e mining p omising oppo uni ies. Thus, in he pape s
(La chenko 2023;P us 2023), a gumen s a e p esen ed con i ming he need o use ma he-
ma ical modeling me hods as an in eg al pa o e ec i e sys em managemen . The au ho s
emphasize ha he p og ess o compu ing echnology has had and con inues o ha e a
huge impac on he de elopmen and applica ion o economic and ma hema ical me hods
in highe educa ion. Thanks o compu e echnology, he isk o e o s in sol ing p oblems
and he ime spen on hei solu ion a e signi ican ly educed. Ma hema ical me hods play
an impo an ole in he analysis o educa ional p ocesses since hey can p o ide accu a e
calcula ions and ull conside a ion o he in luence o ac o s using sho - e m o ecas ing
me hods and e ec i e managemen decisions.
Economic and ma hema ical modeling is widely used o app oxima e and o ecas
a ious aspec s o highe educa ion. Thus, he au ho s (B edyuk and Joshi 2017) modeled
he unc ioning o he highe educa ion sys em and he demand o i s se ices in Uk aine
based on a sys em o simul aneous equa ions and linea eg ession models. To analyze
he in luence o he popula ion segmen wi h highe educa ion on economic g ow h (GDP)
and he po e y line in 38 OECD coun ies, au ho s (Li e al. 2024) used an OLS eg ession
model and he panel quan ile model. As no ed by esea che s (Agasis i and Pe enko
2024), he mos common me hods used in indi idual publica ions o e he pas 20 yea s
a e desc ip i e s a is ics me hods and eg ession models in a ious o ms, such as pooled
eg ession, p i acy-p ese ing machine lea ning (PPML), and co a iance o mul i a ia e
p obi eg ession.
As he s udy showed, i is ad isable o use he appa a us o ec o au o eg essi e
models (Shapo 2021;Pe enuzzo and Timme mann 2017) o assess in e s a e in e depen-
dencies, assess he e ec i eness o any e o ms in he coun y, and highligh hei impac
on economic de elopmen . In mode n s udies (Ko obilis 2019;Cano a and Cicca elli 2013),
VAR models a e used o assess he impac o socio-economic ac o s on he highe educa ion
sys em. Combina ions o VAR models ensu e he achie emen o ad an ages in p edic i e
e iciency and ake in o accoun ime- a ying pa ame e s and he s ochas ic ola ili y o
educa ional p ocesses.
The conduc ed analysis o mode n ends in he de elopmen o highe educa ion and
he asks acing i allowed us o o mula e he goal and hypo heses o he s udy.
This a icle aims o analyze he impac o shocks in he social and economic de elop-
men o a coun y on he de elopmen end o highe educa ion based on he use o he
ime-se ies decomposi ion me hod and c oss-spec al analysis. To achie e he objec i e o
his s udy, he ollowing hypo heses we e o med.
Hypo hesis 1. The highe educa ion sys em is in cons an in e ac ion wi h he economic, social,
and demog aphic sys ems o he coun y, which de e mines hei mu ual in luence.
Hypo hesis 2. C isis changes in he economic, social, and demog aphic de elopmen o a coun y
cause isks in he unc ioning o i s highe educa ion sys em, which de e mines he need o moni o
changes and adap o hem.
Adm. Sci. 2024,14, 278 6 o 28
Hypo hesis 3. To assess and o ecas he impac o sho - e m/long- e m shock e ec s on he highe
educa ion sys em (HES), as well as hei lag delay, i is ad isable o use he me hods o ime-se ies
decomposi ion and c oss-spec al analysis.
This s udy’s s uc u e includes he ollowing Sec ions: In oduc ion, The Li e a u e
Re iew, Ma e ials and Me hods, Resul s, Discussion, Conclusions.
3. Ma e ials and Me hods
To de e mine he impac o social and economic shocks on he de elopmen o highe
educa ion, he algo i hmic model p esen ed in Figu e 1is p oposed.
Adm. Sci. 2024, 14, x FOR PEER REVIEW 6 o 28
Hypo hesis 2. C isis changes in he economic, social, and demog aphic de elopmen o a coun y
cause isks in he unc ioning o i s highe educa ion sys em, which de e mines he need o moni o
changes and adap o hem.
Hypo hesis 3. To assess and o ecas he impac o sho - e m/long- e m shock effec s on he highe
educa ion sys em (HES), as well as hei lag delay, i is ad isable o use he me hods o ime-se ies
decomposi ion and c oss-spec al analysis.
This s udy’s s uc u e includes he ollowing Sec ions: In oduc ion, The Li e a u e
Re iew, Ma e ials and Me hods, Resul s, Discussion, Conclusions.
3. Ma e ials and Me hods
To de e mine he impac o social and economic shocks on he de elopmen o highe
educa ion, he algo i hmic model p esen ed in Figu e 1 is p oposed.
Figu e 1. An algo i hmic model o s udying he impac o social and economic shocks on a coun-
y’s educa ional sys em.
This model e lec s he asks ha a e sol ed o achie e he esea ch goal.
To assess and analyze he s anda d o li ing o he popula ion, his wo k p oposes o
use he Human De elopmen Index (HDI). The HDI was de eloped in 1990 and is pub-
lished wi hin he amewo k o he UN De elopmen P og am in annual epo s on hu-
man de elopmen (Websi e UNDP n.d.).
The HDI is an in eg al indica o , and includes h ee g oups o indica o s, which ha e
he ollowing co ege o m:
HDI = {LE: ILR; ISL} (1)
whe e LE—li e expec ancy; ILR—li e acy a e o he coun y’s popula ion; ISL—s anda d
o li ing measu ed by GNI pe capi a a pu chasing powe pa i y (PPP) in US dolla s.
Figu e 1. An algo i hmic model o s udying he impac o social and economic shocks on a coun y’s
educa ional sys em.
This model e lec s he asks ha a e sol ed o achie e he esea ch goal.
To assess and analyze he s anda d o li ing o he popula ion, his wo k p oposes
o use he Human De elopmen Index (HDI). The HDI was de eloped in 1990 and is
published wi hin he amewo k o he UN De elopmen P og am in annual epo s on
human de elopmen (Websi e (UNDP) n.d.).
The HDI is an in eg al indica o , and includes h ee g oups o indica o s, which ha e
he ollowing co ege o m:
HDI = {LE: ILR; ISL} (1)
whe e LE—li e expec ancy; ILR—li e acy a e o he coun y’s popula ion; ISL—s anda d
o li ing measu ed by GNI pe capi a a pu chasing powe pa i y (PPP) in US dolla s.
The peculia i y o he HDI is ha he main place is occupied no by he abili y o
he popula ion o p oduc i e wo k, ha is, i s economic alue, bu by he social aspec
o de elopmen , which is achie ed on he basis o inc easing li e expec ancy, inc easing
income and aising he le el o educa ion.
Adm. Sci. 2024,14, 278 7 o 28
To de e mine sho - e m o long- e m shocks in he social and economic de elopmen
o a coun y and hei impac on he de elopmen o a highe educa ion sys em, he use o
ime-se ies decomposi ion me hods and c oss-spec al analysis a e p oposed.
The na u e o he sho - e m/long- e m shocks is he wa e na u e ha desc ibes he
cyclic componen in he ime se ies. The e o e, we a e making a ime-se ies decomposi ion
o he de ec ion o he cyclic componen s. The p elimina y s ep is o de e mine whe he
he e a e componen s in he ime se ies (Figu e 2). Fo his, Fishe ’s c i e ion and he
Fos e –S ewa me hod a e p oposed.
Adm. Sci. 2024, 14, x FOR PEER REVIEW 7 o 28
The peculia i y o he HDI is ha he main place is occupied no by he abili y o he
popula ion o p oduc i e wo k, ha is, i s economic alue, bu by he social aspec o de-
elopmen , which is achie ed on he basis o inc easing li e expec ancy, inc easing income
and aising he le el o educa ion.
To de e mine sho - e m o long- e m shocks in he social and economic de elop-
men o a coun y and hei impac on he de elopmen o a highe educa ion sys em, he
use o ime-se ies decomposi ion me hods and c oss-spec al analysis a e p oposed.
The na u e o he sho - e m/long- e m shocks is he wa e na u e ha desc ibes he
cyclic componen in he ime se ies. The e o e, we a e making a ime-se ies decomposi ion
o he de ec ion o he cyclic componen s. The p elimina y s ep is o de e mine whe he
he e a e componen s in he ime se ies (Figu e 2). Fo his, Fishe ’s c i e ion and he Fos-
e –S ewa me hod a e p oposed.
Fishe ’s F- es me hod is used o de e mine he p esence o a end in he a iance. Fo
his, he ini ial se ies mus be di ided in o wo agg ega es ha may in e sec .
Figu e 2. The de e mina ion o he componen s o he ime se ies.
A e ha , he a iances o he ob ained se ies (𝑆
 and 𝑆
) and he alue o Fishe ’s
F-c i e ion a e ound acco ding o he ollowing o mula:
𝐹=


 i
𝑆
>𝑆

 o 𝐹 = 


 i
𝑆
<𝑆

 (2)
I 𝐹<𝐹
∝(𝑚,𝑚), hen he hypo hesis abou he p esence o a end in he ime se ies
is no con i med and i can be assumed ha he e is no such end. In he o he case, when
he end in he a iance exis s, he e is also a end in he ime se ies. He e 𝑚,𝑚— he
numbe o elemen s in he i s and second ow.
Fos e –S ewa me hod. This me hod has g ea possibili ies and gi es mo e eliable e-
sul s han he p e ious one. In addi ion o es ablishing he p esence o a end in he se ies
i sel ( he end in he a e age), i makes i possible o es ablish he exis ence o a end in
he dispe sion o he ime se ies: i he e is no end in he dispe sion, hen he sp ead o
he le els o he se ies is cons an ; i he a iance inc eases, hen he se ies “shakes”.
Decomposi ion o he ime se ies helps us o de e mine he end and cyclic compo-
nen s. Cyclic componen s a e in es iga ed wi h he help o he Fou ie ans o ma ion
(spec al Fou ie analysis). In ou pape , we need o use he c oss-spec al (spec um) anal-
ysis o s udy o he impac a one- ime se ies (independen se ies ha has a shock in dy-
namics) on he o he ime se ies (an indica o o he de elopmen o he HES).
Figu e 2. The de e mina ion o he componen s o he ime se ies.
Fishe ’s F- es me hod is used o de e mine he p esence o a end in he a iance. Fo
his, he ini ial se ies mus be di ided in o wo agg ega es ha may in e sec .
A e ha , he a iances o he ob ained se ies (
S2
1
and
S2
2
) and he alue o Fishe ’s
F-c i e ion a e ound acco ding o he ollowing o mula:
F=S2
1
S2
2
i S2
1>S2
2o F=S2
2
S2
1
i S2
1<S2
2(2)
I
F<F∝(m1,m2)
, hen he hypo hesis abou he p esence o a end in he ime se ies
is no con i med and i can be assumed ha he e is no such end. In he o he case, when
he end in he a iance exis s, he e is also a end in he ime se ies. He e
m1
,
m2
— he
numbe o elemen s in he i s and second ow.
Fos e –S ewa me hod. This me hod has g ea possibili ies and gi es mo e eliable
esul s han he p e ious one. In addi ion o es ablishing he p esence o a end in he se ies
i sel ( he end in he a e age), i makes i possible o es ablish he exis ence o a end in
he dispe sion o he ime se ies: i he e is no end in he dispe sion, hen he sp ead o
he le els o he se ies is cons an ; i he a iance inc eases, hen he se ies “shakes”.
Decomposi ion o he ime se ies helps us o de e mine he end and cyclic compo-
nen s. Cyclic componen s a e in es iga ed wi h he help o he Fou ie ans o ma ion
(spec al Fou ie analysis). In ou pape , we need o use he c oss-spec al (spec um)
analysis o s udy o he impac a one- ime se ies (independen se ies ha has a shock in
dynamics) on he o he ime se ies (an indica o o he de elopmen o he HES).
Adm. Sci. 2024,14, 278 8 o 28
C oss-spec um analysis allows you o analyze wo ime se ies a he same ime. Sci-
en is s (Bloom ield 2000;Box and Jenkins 1976;B illinge 1975;B igham 1974;Ellio and
Rao 1982;P ies ley 1981;Shumway and S o e 2017;Wei 1989) conside c oss-spec um
analysis o be mo e ad anced han single-spec um (Fou ie ) analysis.
Wi h he help o c oss-spec um analysis, he ela ionship be ween wo ime se ies
is de e mined as a unc ion o equency. When conduc ing a c oss-spec al analysis, i is
assumed ha s a is ically signi ican peaks a he same equency will be p esen in he
s udied ime se ies as well as whe he hese pe iodici ies a e ela ed o each o he . I such
a si ua ion is obse ed, hen i is necessa y o de e mine he phase ela ionship be ween
hem. Conduc ing a c oss-spec al analysis is possible e en in he absence o peaks in he
powe spec um since cohe en modes a ce ain equencies may exis in his spec um o
ed noise. All his is checked using he cohe ence spec um. In c oss-spec um analysis, we
used wo se ies as ollows:
x=x+
n
2−1
∑
k=1Axk cos2πk
Tkx +Bxk sin2πk
Tkx +AxN/2 cosπN
Tkx  (3)
y=y+
n
2−1
∑
k=1 Ayk cos 2πk
Tky !+Byk sin 2πk
Tky !+AyN/2 cos πN
Tky !! (4)
whe e
Axk
,
Ayk
—cosine coe icien s in he Fou ie analysis;
Bxk
,
Byk
—sine coe icien s in
he Fou ie analysis; Txk,Tyk—pe iods o k-ha monics.
When a c oss-spec um s udy is conduc ed, i is a se o numbe s ha can be di ided
in o wo pa s: eal and imagina y. To ob ain an es ima e o he c oss densi y and quad a u e
densi y, he en i e complex o numbe s mus be smoo hed. In u n, he c oss-ampli ude
is he squa e oo o he sum o he squa es o he c oss-densi y and quad-densi y alues,
which can be in e p e ed as a measu e o he co a iance be ween he equency componen s
o he wo se ies (Shumway and S o e 2017).
When conduc ing a c oss-spec al analysis, he ollowing cha ac e is ics a e calcula ed:
Squa ed cohe ency. This is in e p e ed as he squa e o he co ela ion coe icien , i.e., he
cohe ence alue is he quad a ic co ela ion be ween he cyclic componen s in wo se ies
o he same equencies and a cons an phase di e ence in hei oscilla ions. Usually, his
indica o should be analyzed in combina ion wi h, o example, he spec al densi y.
Gain. The gain alue is calcula ed as he a io o he c oss-ampli ude alue o he spec-
al densi y es ima e o one o he wo se ies unde in es iga ion. Thus, when analyzing
wo se ies, wo gain alues will be calcula ed. Conclusions based on he ob ained alues
a e in e p e ed as s anda d eg ession coe icien s by he me hod o leas squa es o he
co esponding equencies.
Phase shi . To de e mine he delay in he impac o socio-economic shocks on he
highe educa ion sys em, a phase shi is used, which is calcula ed as he an
−1
a io o he
squa ed densi y es ima es o he c oss-densi y es ima e. Phase shi es ima es a e said o
be measu es o he deg ee o which each equency componen o one ime se ies leads
he o he .
4. Resul s
S ep 1. Building he in o ma ion space o he s udy. In o de o achie e he goal o
his s udy and con i m Hypo hesis 1, i is necessa y o o m a sys em o indica o s ha
would ha e a signi ican impac on he de elopmen o a coun y’s highe educa ion
sys em. Analysis o he speci ics o he ac i i ies o uni e si ies showed ha he success o
hei de elopmen depends on he gene al economic s a e o he coun y, demog aphics,
mig a ion p ocesses and, as a consequence, he income o he popula ion. To con i m
Hypo hesis 1, a monog aphic and compa a i e analysis o li e a y sou ces was ca ied ou ,
a ious app oaches o iden i ying indica o s ha a e in e ela ed wi h highe educa ion
indica o s we e analyzed.
Adm. Sci. 2024,14, 278 15 o 28
Adm. Sci. 2024, 14, x FOR PEER REVIEW 15 o 28
(a) (b)
(c) (d)
Figu e 8. The cyclic componen s o he ime se ies o Uk aine: (a) GDP pe capi a; (b) HDI; (c) ne
mig a ion; (d) School en ollmen , e ia y (% g oss).
The esul s o he decomposi ion o he cyclic componen s a e displayed in Table 3
o Slo akia.
Table 3. The de e mina ion o he local ha monics o he cyclic componen s o ime se ies o Slo-
akia.
Pe iods (Ha monics) Cos Coefficien Sin Coefficien Pe iodog am
GDP pe Capi a (54% *)
28 −2332.69 −736.889 83,782,463
14 2057.09 1773.415 103,272,582
9.33 −607.29 −62.699 5,218,262
4 −233.53 923.839 12,712,225
HDI **
28 −0.003369 −0.006847 0.000815
14 0.001833 0.006590 0.000655
9.33 −0.001735 0.001348 0.000068
2 0.001520 0.000783 0.000041
Ne Mig a ion (84.3%)
13579111315171921232527293133
-1500
-1000
-500
0
500
1000
1500
2000
C_GDP_U
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
C_HDI_U
1 3 5 7 9 111315171921232527293133
-2E5
-1E5
0
1E5
2E5
3E5
4E5
C_NM_U
1 3 5 7 9 111315171921232527293133
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
C_SE_U
Figu e 8. The cyclic componen s o he ime se ies o Uk aine: (a) GDP pe capi a; (b) HDI; (c) ne
mig a ion; (d) School en ollmen , e ia y (% g oss).
Table 3. The de e mina ion o he local ha monics o he cyclic componen s o ime se ies o Slo akia.
Pe iods (Ha monics) Cos Coe icien Sin Coe icien Pe iodog am
GDP pe Capi a (54% *)
28 −2332.69 −736.889 83,782,463
14 2057.09 1773.415 103,272,582
9.33 −607.29 −62.699 5,218,262
4−233.53 923.839 12,712,225
HDI **
28 −0.003369 −0.006847 0.000815
14 0.001833 0.006590 0.000655
9.33 −0.001735 0.001348 0.000068
2 0.001520 0.000783 0.000041
Ne Mig a ion (84.3%)
28 1597.036 237.974 36,500,181
14 344.582 −660.473 7,769,452
9.33 −505.006 −76.564 3,652,498
4 16.039 −458.319 2,944,384

Adm. Sci. 2024,14, 278 16 o 28
Table 3. Con .
Pe iods (Ha monics) Cos Coe icien Sin Coe icien Pe iodog am
School En ollmen , Te ia y (% G oss) (98.6%)
28 −8.47473 −2.85324 1119.469
14 0.23808 3.86553 209.986
7 0.62066 0.98384 18.944
2.33 0.35496 0.25007 2.639
*— he pe cen age o he cyclic componen desc ibed by he gi en ha monics. **— he HDI o Slo akia is no
signi ican s a is ically.
The analysis o he da a om Table 3shows he ollowing esul s o Slo akia:
(1)
Fou ha monics desc ibe he cyclic componen s wi h high-le el adequacy, especially
o he ne mig a ion and school en ollmen , e ia y (% g oss) ime se ies;
(2)
The decomposi ion o he cyclic componen in o ha monics o he HDI is s a is ically
insigni ican . The e o e, we canno use he HDI ime se ies o Slo akia in c oss-
spec al analysis;
(3)
Pe iods 28, 14, and 9.33 yea s a e he mos powe ul in he cyclic componen s o he
in es iga ed se ies.
The models o he cyclic componen a e he combina ion o he ha monics wi h di e -
en ampli ude and equency. The o mula o he cyclic componen wi h ou ha monics is
ou lined below:
C( )=
4
∑
k=1Akcos2π
Tk
[ −1]+Bksin2π
Tk
[ −1] (5)
In Figu e 9we can see eal and modeling cyclic componen s wi h he coe icien s om
Table 3.
Analysis o Figu e 9shows ha he simula ion da es a e e y close o he eal da es. In
his case, we can use ou Fou ie decomposi ion o he o ecas ed ime se ies. The cyclic
componen s o he Uk ainian ime se ies a e p esen ed in Table 4.
Table 4. De e mina ion o he local ha monics o he cyclic componen s o ime se ies o Uk aine.
Pe iods (Ha monics) Cos Coe icien Sin Coe icien Pe iodog am
GDP pe capi a (83% *)
32 83.924 −360.916 2,196,861
16 447.443 670.988 10,406,881
10.67 297.391 −89.240 1,542,480
5.33 26.015 270.493 1,181,490
HDI **
32 −0.000377 −0.012717 0.002590
16 0.010010 0.004827 0.001976
10.67 0.003043 0.006889 0.000907
8 0.001366 0.005041 0.000436
Ne Mig a ion (60.1%)
32 6328.9 −40,376.5 26,725,010,000
16 62,227.2 16,349.8 66,232,610,000
10.7 43,244.2 23,296.1 38,604,270,000
6.4 −10,247.0 37,205.5 23,828,040,000
Adm. Sci. 2024,14, 278 17 o 28
Table 4. Con .
Pe iods (Ha monics) Cos Coe icien Sin Coe icien Pe iodog am
School En ollmen , Te ia y (% G oss) (82%)
32 −4.67935 −4.25002 639.3433
16 2.60886 4.21360 392.9697
10.7 1.63436 0.41103 45.4413
5.33 0.11185 1.96365 61.8948
*— he pe cen age o he cyclic componen desc ibed by he gi en ha monics. **— he HDI o Uk aine is no
signi ican s a is ically.
Adm. Sci. 2024, 14, x FOR PEER REVIEW 17 o 28
10.7 1.63436 0.41103 45.4413
5.33 0.11185 1.96365 61.8948
*— he pe cen age o he cyclic componen desc ibed by he gi en ha monics. **— he HDI o
Uk aine is no signi ican s a is ically.
(a) (b)
(c)
Figu e 9. Real and model cyclical componen s o ime se ies o Slo akia: (a) GDP pe capi a; (b) ne
mig a ion; (c) school en ollmen , e ia y (% g oss).
Analysis o he da a om Table 4 shows he ollowing esul s o Uk aine:
(1) Fou ha monics desc ibe he cyclic componen s wi h high-le el adequacy, especially
o he GDP pe capi a and school en ollmen , e ia y (% g oss) ime se ies;
(2) The decomposi ion o he cyclic componen in o ha monics o he HDI is s a is ically
insigni ican . The e o e, we canno use he HDI ime se ies o Uk aine in c oss-spec-
al analysis;
(3) Pe iods 32, 16, and 10.7 yea s a e he mos powe ul in he cyclic componen s o he
s udied se ies.
Combina ions o ou ha monics in he cyclic componen s acco ding o Fo mula (1)
a e shown in Figu e 10.
C_GDP_S
M_GDP_S
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
M_NM_S
C_NM_S
13579111315171921232527293133
-3000
-2000
-1000
0
1000
2000
3000
4000
M_SE_S
C_SE_S
1 3 5 7 9 111315171921232527293133
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
16
Figu e 9. Real and model cyclical componen s o ime se ies o Slo akia: (a) GDP pe capi a; (b) ne
mig a ion; (c) school en ollmen , e ia y (% g oss).
Analysis o he da a om Table 4shows he ollowing esul s o Uk aine:
(1)
Fou ha monics desc ibe he cyclic componen s wi h high-le el adequacy, especially
o he GDP pe capi a and school en ollmen , e ia y (% g oss) ime se ies;
(2)
The decomposi ion o he cyclic componen in o ha monics o he HDI is s a is ically
insigni ican . The e o e, we canno use he HDI ime se ies o Uk aine in c oss-
spec al analysis;
(3)
Pe iods 32, 16, and 10.7 yea s a e he mos powe ul in he cyclic componen s o he
s udied se ies.
Adm. Sci. 2024,14, 278 18 o 28
Combina ions o ou ha monics in he cyclic componen s acco ding o Fo mula (1)
a e shown in Figu e 10.
Adm. Sci. 2024, 14, x FOR PEER REVIEW 18 o 28
(a) (b)
(c)
Figu e 10. Real and modeling cyclic componen s o he ime se ies o Uk aine: (a) GDP pe capi a;
(b) ne mig a ion; (c) school en ollmen , e ia y (% g oss).
Figu e 10 shows a high-le el adequacy o he model o he cyclic componen s. The e-
o e, we can use he cons uc ing models in he o ecas ing o he shocks.
S age 3. C oss-spec al analysis. A his s age, we in es iga ed he impac o social and
economic shocks on he de elopmen o highe educa ion. We calcula ed he ollowing
cha ac e is ics: c oss-ampli ude, c oss-cohe ency, and phase spec um shi . These cha -
ac e is ics a e p esen ed in Table 5 o Slo akia.
Table 5. C oss-spec um analysis o he school en ollmen , e ia y (% g oss) ime se ies in Slo akia.
Pe iods (Ha monics) C oss Ampli ude Squa ed Cohe ency Phase Spec um
GDP pe Capi a
28 174,618.0 0.786324 0.16
14 128,963.8 0.674899 0.38
9 43,427.2 0.648288 0.64
2.15 478.2 0.586338 1.45
Ne Mig a ion
28 103,077.3 0.956477 −3.10
14 64,334.9 0.858773 3.06
9 17,182.4 0.637566 2.90
2.112 785.7 0.435656 1.08
M_GDP_U
C_GDP_U
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
-1500
-1000
-500
0
500
1000
1500
2000
M_NM_U
C_NM_U
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
-2E5
-1E5
0
1E5
2E5
3E5
4E5
M_SE_U
C_SE_U
1 3 5 7 9 111315171921232527293133
-20
-15
-10
-5
0
5
10
15
Figu e 10. Real and modeling cyclic componen s o he ime se ies o Uk aine: (a) GDP pe capi a;
(b) ne mig a ion; (c) school en ollmen , e ia y (% g oss).
Figu e 10 shows a high-le el adequacy o he model o he cyclic componen s. The e-
o e, we can use he cons uc ing models in he o ecas ing o he shocks.
S age 3. C oss-spec al analysis. A his s age, we in es iga ed he impac o social
and economic shocks on he de elopmen o highe educa ion. We calcula ed he ollow-
ing cha ac e is ics: c oss-ampli ude, c oss-cohe ency, and phase spec um shi . These
cha ac e is ics a e p esen ed in Table 5 o Slo akia.
Table 5. C oss-spec um analysis o he school en ollmen , e ia y (% g oss) ime se ies in Slo akia.
Pe iods (Ha monics) C oss Ampli ude Squa ed Cohe ency Phase Spec um
GDP pe Capi a
28 174,618.0 0.786324 0.16
14 128,963.8 0.674899 0.38
9 43,427.2 0.648288 0.64
2.15 478.2 0.586338 1.45
Adm. Sci. 2024,14, 278 19 o 28
Table 5. Con .
Pe iods (Ha monics) C oss Ampli ude Squa ed Cohe ency Phase Spec um
Ne Mig a ion
28 103,077.3 0.956477 −3.10
14 64,334.9 0.858773 3.06
9 17,182.4 0.637566 2.90
2.112 785.7 0.435656 1.08
Sou ce: Au ho s’ calcula ions.
The cha ac e is ics a e calcula ed o wo exogenous ac o s: GDP pe capi a and
ne mig a ion. The HDI ac o was excluded om he shock analysis because i s spec al
densi y and spec al pe iodog am we e insigni ican .
Resul s o he c oss-spec al cha ac e is ics analysis o Slo akia include he ollowing:
(1)
GDP pe capi a and ne mig a ion ha e simila cohe ence pe iods wi h school en oll-
men . Mos o he cohe ence pe iods a e 28, 14, and 9 yea s. In hese pe iods, he
cohe ences a e mo e han 60%. In he sho - e m ha monics (2.15 yea s o GDP pe
capi a and 2.112 yea s o ne mig a ion), he cohe ences ha e a e age alues o 58%
and 43%, espec i ely;
(2)
The phase shi analysis o GDP pe capi a shows ha all he s onges phase shi
alues a e posi i e. This means ha school en ollmen has always delayed i s esponse
o changes in he na ional economy— his delay is less han one yea ;
(3)
The e is a lag in he esponse o GDP pe capi a and school en ollmen o he change
in ne mig a ion o he ou s onges pe iods o mo e han 1 yea . This means ha
he impac o ne mig a ion has g ea e ine ia han he impac o school en olmen in
Slo akia.
The dependencies o he phase spec um om he equencies a e displayed in Figu e 11.
Adm. Sci. 2024, 14, x FOR PEER REVIEW 19 o 28
Sou ce: Au ho s’ calcula ions.
The cha ac e is ics a e calcula ed o wo exogenous ac o s: GDP pe capi a and ne
mig a ion. The HDI ac o was excluded om he shock analysis because i s spec al den-
si y and spec al pe iodog am we e insigni ican .
Resul s o he c oss-spec al cha ac e is ics analysis o Slo akia include he ollow-
ing:
(1) GDP pe capi a and ne mig a ion ha e simila cohe ence pe iods wi h school en oll-
men . Mos o he cohe ence pe iods a e 28, 14, and 9 yea s. In hese pe iods, he
cohe ences a e mo e han 60%. In he sho - e m ha monics (2.15 yea s o GDP pe
capi a and 2.112 yea s o ne mig a ion), he cohe ences ha e a e age alues o 58%
and 43%, espec i ely;
(2) The phase shi analysis o GDP pe capi a shows ha all he s onges phase shi
alues a e posi i e. This means ha school en ollmen has always delayed i s e-
sponse o changes in he na ional economy— his delay is less han one yea ;
(3) The e is a lag in he esponse o GDP pe capi a and school en ollmen o he change
in ne mig a ion o he ou s onges pe iods o mo e han 1 yea . This means ha
he impac o ne mig a ion has g ea e ine ia han he impac o school en olmen
in Slo akia.
The dependencies o he phase spec um om he equencies a e displayed in Figu e
11.
(a) (b)
Figu e 11. The phase shi o he in luence o GDP pe capi a and ne mig a ion on school en ollmen ,
e ia y (% g oss) in Slo akia: (a) GDP pe capi a; (b) ne mig a ion. No e ha he poin s o he phase
shi co esponding o he ha monics wi h he g ea es cohe ence a e highligh ed in ed. Sou ce:
Au ho s’ calcula ions.
Figu e 11 shows ha he phase shi s ( ed poin s) o he mos signi ican ha monics
(Table 5) o he GDP pe capi a indica o ha e posi i e alues. This means ha i a shock
occu s in he dynamics o his indica o , a shock in he dynamics o he school en ollmen ,
e ia y (% g oss) in Slo akia will occu wi h a lag o 0.16, 0.38, 0.64, and 1.45 yea s. A he
same ime, he ne mig a ion indica o (Figu e 11) has a highe ola ili y o he phase shi
om −3 o 3 yea s. Fo h ee signi ican ha monics, he phase shi is posi i e (Table 5).
This means ha shock effec s in ne mig a ion will p o oke shock poin s in he dynamics
o he school en ollmen , e ia y (% g oss) wi h a lag o 3.06, 2.9, and 1.08 yea s. Fo a
local ha monic wi h a pe iod o 28 yea s and a phase shi o −3 yea s, he shock o he
dynamics o school en ollmen , e ia y (% g oss) will occu ea lie by 3 yea s.
In Table 6 we can see he cha ac e is ics o he c oss-spec al analysis o Uk aine.
Figu e 11. The phase shi o he in luence o GDP pe capi a and ne mig a ion on school en ollmen ,
e ia y (% g oss) in Slo akia: (a) GDP pe capi a; (b) ne mig a ion. No e ha he poin s o he phase
shi co esponding o he ha monics wi h he g ea es cohe ence a e highligh ed in ed. Sou ce:
Au ho s’ calcula ions.
Figu e 11 shows ha he phase shi s ( ed poin s) o he mos signi ican ha monics
(Table 5) o he GDP pe capi a indica o ha e posi i e alues. This means ha i a shock
occu s in he dynamics o his indica o , a shock in he dynamics o he school en ollmen ,
e ia y (% g oss) in Slo akia will occu wi h a lag o 0.16, 0.38, 0.64, and 1.45 yea s. A he
Adm. Sci. 2024,14, 278 20 o 28
same ime, he ne mig a ion indica o (Figu e 11) has a highe ola ili y o he phase shi
om
−
3 o 3 yea s. Fo h ee signi ican ha monics, he phase shi is posi i e (Table 5).
This means ha shock e ec s in ne mig a ion will p o oke shock poin s in he dynamics
o he school en ollmen , e ia y (% g oss) wi h a lag o 3.06, 2.9, and 1.08 yea s. Fo a
local ha monic wi h a pe iod o 28 yea s and a phase shi o
−
3 yea s, he shock o he
dynamics o school en ollmen , e ia y (% g oss) will occu ea lie by 3 yea s.
In Table 6we can see he cha ac e is ics o he c oss-spec al analysis o Uk aine.
Table 6. C oss-spec um analysis o he school en ollmen , e ia y (% g oss) ime se ies o Uk aine.
Pe iods (Ha monics) C oss Ampli ude Squa ed Cohe ency Phase Spec um
GDP pe Capi a
32.00000 28,755.68 0.564066 −0.55312
16.00000 35,110.07 0.646984 −0.16393
10.66667 19,121.25 0.717169 0.11739
2.00000 517.85 0.676645 0.00000
Ne Mig a ion
10.66667 1,828,773 0.583530 0.32880
8.00000 957,896 0.774502 0.00588
6.40000 815,322 0.843280 −0.28994
5.33333 677,208 0.583016 −0.57788
I we look a he da a om Table 6 o Uk aine, we can see a di e en pic u e han
o Slo akia. Mos powe ul cohe encies a e in he a e age- e m pe iods (10.67 yea s o
GDP and 8 and 6/4 yea s o ne mig a ion) and sho - e m pe iods (2 yea s o GDP pe
capi a and 5.33 yea s o ne mig a ion). I is he same si ua ion wi h he signs o he phase
shi s— he signs a e comple ely di e en in Uk aine compa ed o Slo akia. The lags in he
esponse o school en olmen s o changes in GDP pe capi a and ne mig a ion a e e y
small (less han a yea and up o six mon hs).
The dependencies o he phase spec um om he equencies o Uk aine a e shown
in Figu e 12.
Adm. Sci. 2024, 14, x FOR PEER REVIEW 20 o 28
Table 6. C oss-spec um analysis o he school en ollmen , e ia y (% g oss) ime se ies o Uk aine.
Pe iods (Ha monics) C oss Ampli ude Squa ed Cohe ency Phase Spec um
GDP pe Capi a
32.00000 28
,
755.68 0.564066 −0.55312
16.00000 35,110.07 0.646984 −0.16393
10.66667 19,121.25 0.717169 0.11739
2.00000 517.85 0.676645 0.00000
Ne Mig a ion
10.66667 1,828,773 0.583530 0.32880
8.00000 957,896 0.774502 0.00588
6.40000 815,322 0.843280 −0.28994
5.33333 677,208 0.583016 −0.57788
I we look a he da a om Table 6 o Uk aine, we can see a diffe en pic u e han o
Slo akia. Mos powe ul cohe encies a e in he a e age- e m pe iods (10.67 yea s o GDP
and 8 and 6/4 yea s o ne mig a ion) and sho - e m pe iods (2 yea s o GDP pe capi a
and 5.33 yea s o ne mig a ion). I is he same si ua ion wi h he signs o he phase
shi s— he signs a e comple ely diffe en in Uk aine compa ed o Slo akia. The lags in he
esponse o school en olmen s o changes in GDP pe capi a and ne mig a ion a e e y
small (less han a yea and up o six mon hs).
The dependencies o he phase spec um om he equencies o Uk aine a e shown
in Figu e 12.
(a) (b)
Figu e 12. The phase shi o he in luence o GDP pe capi a and ne mig a ion on school en ollmen ,
e ia y (% g oss) o Uk aine: (a) GDP pe capi a; (b) ne mig a ion (sou ce: Au ho s’ calcula ions).
The models o cyclical componen s, phase shi s, and consis ency alues gi e us an
idea o he impac o economic and social shocks on he de elopmen o highe educa ion
in Uk aine. Figu e 12 shows ha bo h indica o s ha e a high ola ili y o phase shi al-
ues. Thus, o GDP pe capi a, he phase shi changes om −3 yea s o 2.7 yea s; o he
ne mig a ion indica o , his is om −2.3 yea s o 3 yea s. Howe e , unlike Slo akia, in
Uk aine, he mos signi ican ha monics o he indica o s (Figu e 12, ed poin s) ha e
small lags.
Analysis o he shock effec o GDP pe capi a on he numbe o applican s shows
ha he mos signi ican ha monics ha e a pe iod o 32, 16, 10.6, and 2 yea s. Fo 2 yea s,
he shock in highe educa ion occu s simul aneously wi h he shock in he dynamics o
GDP pe capi a. Fo long- e m ha monics, he ollowing esul s we e ob ained: o 10.6
Figu e 12. The phase shi o he in luence o GDP pe capi a and ne mig a ion on school en ollmen ,
e ia y (% g oss) o Uk aine: (a) GDP pe capi a; (b) ne mig a ion (sou ce: Au ho s’ calcula ions).
The models o cyclical componen s, phase shi s, and consis ency alues gi e us an
idea o he impac o economic and social shocks on he de elopmen o highe educa ion

Adm. Sci. 2024,14, 278 21 o 28
in Uk aine. Figu e 12 shows ha bo h indica o s ha e a high ola ili y o phase shi
alues. Thus, o GDP pe capi a, he phase shi changes om
−
3 yea s o 2.7 yea s; o
he ne mig a ion indica o , his is om
−
2.3 yea s o 3 yea s. Howe e , unlike Slo akia,
in Uk aine, he mos signi ican ha monics o he indica o s (Figu e 12, ed poin s) ha e
small lags.
Analysis o he shock e ec o GDP pe capi a on he numbe o applican s shows ha
he mos signi ican ha monics ha e a pe iod o 32, 16, 10.6, and 2 yea s. Fo 2 yea s, he
shock in highe educa ion occu s simul aneously wi h he shock in he dynamics o GDP
pe capi a. Fo long- e m ha monics, he ollowing esul s we e ob ained: o 10.6 yea s,
he shock in highe educa ion will occu 0.12 yea s a e he shock in GDP; o ha monics
wi h pe iods o 16 and 32 yea s, he shock in school en ollmen , e ia y (% g oss) will occu
wi h an ad ance o 0.16 and 0.55 yea s, espec i ely.
The mos signi ican ha monics o he ne mig a ion indica o a e 10.7, 8, 6.4, and
5.3 yea s (Table 6). Shocks in ne mig a ion o 8 yea s will p o oke shock phenomena in
school en ollmen , e ia y (% g oss) almos simul aneously; o 10.7 yea s, shocks in highe
educa ion a e ypical wi h a lag o 0.32 yea s; shocks in he ne mig a ion indica o wi h a
pe iod o 6.4 and 5.3 yea s p o oke shocks in highe educa ion wi h an ad ance o 0.28 and
0.58 yea s. Thus, iden i ying he momen s o occu ence o shocks in he unc ioning o he
HES allows o he p e en i e de elopmen o a se o s a e decisions ha will adjus he
s a egy o he de elopmen o highe educa ion as well as he de elopmen o a se o
measu es o suppo o s imula e he ac i i ies o uni e si ies.
Ano he ad an age o using he c oss-spec al analysis me hod is he abili y o p e-
dic he eac ion o he highe educa ion sys em o shocks in he de elopmen o he
socio-economic en i onmen . Using c oss-spec al analysis, he cohe ence be ween local
ha monics in he school en ollmen , e ia y, GDP pe capi a, and ne mig a ion indica o s
and hei phase shi we e de e mined. This allows us o p edic shocks o he socio-
economic en i onmen o each ha monic and build scena ios o eac ions o he highe
educa ion sys em in Slo akia and Uk aine. To p edic shocks, we in oduce he ollowing
de ini ions:
Posi i e shock is a local minimum poin , cha ac e izing a change in he end om
alling o g owing. In o ecas ing his shock, he Minis y o Educa ion mus de elop ac ions
o c ea e oppo uni ies o apid g ow h o he HES o educe he pe iod o o e coming
pas nega i e ends;
Nega i e shock is a local maximum poin , e lec ing a change in he end om
ascending o descending. In his case, he Minis y mus de elop a se o measu es aimed
a p o ec ing he na ional HES om he nega i e in luences o he ex e nal wo ld and
na ional en i onmen based on changes in public unding, c ea ing condi ions o a ac ing
na ional and in e na ional applican s o he coun y’s HES and inc easing i s a ac i eness
o localize nega i e ends.
The p ojec ed alues o he shocks o GDP pe capi a and ne mig a ion and he
de e mina ion o he HES esponse o hese shocks o Uk aine and Slo akia a e p esen ed
in Table 7.
Table 7. Shocks in GDP pe capi a and ne mig a ion and eac ion o shocks in school en ollmen ,
e ia y (% g oss) in Slo akia and Uk aine.
Shocks GDP pe Capi a Ne Mig a ion School En ollmen
Slo akia
Posi i e 2038–2041 yea s 2041–2042 yea s 2039–2041 yea s
Nega i e 2031–2032 yea s
2047–2048 yea s
2032–2033 yea s
2048–2049 yea s
Adm. Sci. 2024,14, 278 22 o 28
Table 7. Con .
Shocks GDP pe Capi a Ne Mig a ion School En ollmen
Uk aine
Posi i e 2033–2034 yea s
2049–2050 yea s
2030–2031 yea s
2050 yea
2032–2033 yea
2049–2050 yea s
Nega i e 2025–2026 yea s
2042–2043 yea s
2025–2026 yea s
2039 yea
2045 yea
2025–2026 yea s
2041–2046 yea s
Sou ce: Au ho s’ calcula ions.
The da a in Table 7indica e he ollowing:
(1)
Fo Slo akia, one posi i e shock is p edic ed in he dynamics o GDP pe capi a and
ne mig a ion, which will o m a posi i e end in he de elopmen o he HES wi h
a lag o 1 yea . The eme gence o wo nega i e shocks is also expec ed, which will
p o oke he eme gence o c isis phenomena in he HES wi h a lag o 1 yea ;
(2)
Fo Uk aine, wo posi i e and wo nega i e shocks a e p edic ed o he GDP pe
capi a indica o and wo posi i e and h ee nega i e shocks o he ne mig a ion
indica o . They will lead o (1) an inc ease in he a ac i eness o highe educa ion
in 2032–2033 and 2049–2050. In his case, i is ad isable o implemen he scena io o
in ensi e de elopmen and he c ea ion o p e equisi es o he ac i a ion o Uk aine’s
HES in he na ional and in e na ional educa ional ma ke s; (2) he eme gence o c isis
phenomena in 2025–2026 and 2041–2046. In such condi ions, a scena io and a ious
measu es o suppo he de elopmen o he coun y’s HES should be o med.
Tha is, as calcula ions ha e shown, he delay in he eac ion o he HES o Slo akia is 1
yea , while he Uk ainian HES eac s o shocks in he socio-economic en i onmen wi hou
a lag delay. This conclusion is con i med by he g aphical ep esen a ion o he models o
cyclical componen s o he analyzed indica o s (Figu e 13), which also e lec s he o ecas
alues o he indica o o school en ollmen , e ia y (% g oss) o Uk aine and Slo akia,
conside ing ce ain lags in he delay o eac ions o shocks in he ex e nal en i onmen .
Adm. Sci. 2024, 14, x FOR PEER REVIEW 22 o 28
a lag o 1 yea . The eme gence o wo nega i e shocks is also expec ed, which will
p o oke he eme gence o c isis phenomena in he HES wi h a lag o 1 yea ;
(2) Fo Uk aine, wo posi i e and wo nega i e shocks a e p edic ed o he GDP pe
capi a indica o and wo posi i e and h ee nega i e shocks o he ne mig a ion in-
dica o . They will lead o (1) an inc ease in he a ac i eness o highe educa ion in
2032–2033 and 2049–2050. In his case, i is ad isable o implemen he scena io o
in ensi e de elopmen and he c ea ion o p e equisi es o he ac i a ion o
Uk aine’s HES in he na ional and in e na ional educa ional ma ke s; (2) he eme -
gence o c isis phenomena in 2025–2026 and 2041–2046. In such condi ions, a scena io
and a ious measu es o suppo he de elopmen o he coun y’s HES should be
o med.
Tha is, as calcula ions ha e shown, he delay in he eac ion o he HES o Slo akia
is 1 yea , while he Uk ainian HES eac s o shocks in he socio-economic en i onmen
wi hou a lag delay. This conclusion is con i med by he g aphical ep esen a ion o he
models o cyclical componen s o he analyzed indica o s (Figu e 13), which also e lec s
he o ecas alues o he indica o o school en ollmen , e ia y (% g oss) o Uk aine and
Slo akia, conside ing ce ain lags in he delay o eac ions o shocks in he ex e nal en i-
onmen .
Thus, Hypo hesis 3 has been con i med using he selec ed ma hema ical ools— he
ime-se ies decomposi ion me hod, single Fou ie analysis, and c oss-spec al analysis.
(a) (b)
Figu e 13. Es ima ed alues o he cyclical componen o indica o s o GDP pe capi a, ne mig a-
ion, and o ecas esponses o numbe o en an s: (a) Slo akia; (b) Uk aine (sou ce: Au ho s’ calcula-
ions).
5. Discussion
In he amewo k o his s udy, he use o agg ega ed indica o s o socio-economic
de elopmen and he sys em o highe educa ion is impo an . Acco ding o he Sus ain-
able De elopmen Goals, one o he aims o sus ainable de elopmen is o ensu e inclusi e
and equi able quali y educa ion and li elong lea ning oppo uni ies o all (Uni ed Na-
ions 2022, 2023). The e o e, in ou opinion, as an agg ega e indica o , i is app op ia e o
use he school en ollmen indica o , which e lec s he a ac i eness o highe educa ion
due o he numbe o s uden s en e ing uni e si ies. These indings co ela e wi h s udies
(Cao e al. 2024; Ku ylo and Ka aman 2023; K emen e al. 2023; Le chuk 2024; Algi das
and Tomas 2023; Ba ool and Liu 2021 e al.), which also s a e ha one o he indica o s o
he effec i eness o he highe educa ion sys em is he numbe en olled/g adua ed s u-
den s.
In his s udy, GDP pe capi a and ne mig a ion we e selec ed as indica o s o he
socio-economic en i onmen o he highe educa ion sys em, and al hough he e a e many
indica o s o socio-economic de elopmen , examining he impac s on he highe educa-
ion sys em is a s eng h o his s udy. Howe e , an impo an aspec is inding a balance
-1.5
-1
-0.5
0
0.5
1
1.5
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
GDP Ne Mig a ion School En ollmen
-1.5
-1
-0.5
0
0.5
1
1.5
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
GDP Ne Mig a ion School En ollmen
Figu e 13. Es ima ed alues o he cyclical componen o indica o s o GDP pe capi a, ne mig a ion,
and o ecas esponses o numbe o en an s: (a) Slo akia; (b) Uk aine (sou ce: Au ho s’ calcula ions).
Thus, Hypo hesis 3 has been con i med using he selec ed ma hema ical ools— he
ime-se ies decomposi ion me hod, single Fou ie analysis, and c oss-spec al analysis.
Adm. Sci. 2024,14, 278 23 o 28
5. Discussion
In he amewo k o his s udy, he use o agg ega ed indica o s o socio-economic
de elopmen and he sys em o highe educa ion is impo an . Acco ding o he Sus ainable
De elopmen Goals, one o he aims o sus ainable de elopmen is o ensu e inclusi e and
equi able quali y educa ion and li elong lea ning oppo uni ies o all (Uni ed Na ions
2022,2023). The e o e, in ou opinion, as an agg ega e indica o , i is app op ia e o use he
school en ollmen indica o , which e lec s he a ac i eness o highe educa ion due o he
numbe o s uden s en e ing uni e si ies. These indings co ela e wi h s udies (Cao e al.
2024;Ku ylo and Ka aman 2023;K emen e al. 2023;Le chuk 2024;Algi das and Tomas
2023;Ba ool and Liu 2021), which also s a e ha one o he indica o s o he e ec i eness o
he highe educa ion sys em is he numbe en olled/g adua ed s uden s.
In his s udy, GDP pe capi a and ne mig a ion we e selec ed as indica o s o he
socio-economic en i onmen o he highe educa ion sys em, and al hough he e a e many
indica o s o socio-economic de elopmen , examining he impac s on he highe educa ion
sys em is a s eng h o his s udy. Howe e , an impo an aspec is inding a balance
be ween he mic o-desc ip ion o he esea ch objec and agg ega ion. The e o e, based on
he con en analysis and esea ch o a numbe o s udies de o ed o mig a ion p ocesses, he
choice was based on he use o hese wo indica o s. In addi ion, he au ho s (Maha o e al.
2022;Chowdhu y 2019;Cheng e al. 2023;S ojano ski e al. 2023) de e mined ha mig a ion
p ocesses in luence he de elopmen o he educa ional sys em and (Kalmukhanbe o a and
Shna beko a 2022) de e mined ha educa ional mig a ion la gely in luences he dynamics
and cha ac e o he coun y’s socio-economic de elopmen .
F om he poin o iew o s udying he in e ac ion o he highe educa ion sys em
wi h he socio-economic en i onmen , i is impo an o highligh long- e m and sho -
e m ends. To achie e he goal o his esea ch, emphasis was placed on he s udy o
sho - e m ends, which a e ep esen ed by a cyclical componen . The e o e, he me hod
o c oss-spec al analysis was used, which made i possible o de e mine shocks in he
de elopmen o he socio-economic en i onmen o he highe educa ion sys em and
hei impac on i . F om he poin o iew o long- e m co-in eg a ion be ween he socio-
economic en i onmen and he sys em o highe educa ion, i is app op ia e o use VAR
models, which, in u n, allows o conduc ing impulse analysis and iden i ying shocks in
long- e m ends.
O cou se, in hese s udies, he choice o ma hema ical me hods and models o
app oxima ing p ocesses has a s ong in luence. Wi hou educing he opinion on he
e ec i eness o spec al analysis, i is necessa y o no e he ollowing. The Fou ie ans o m
has one d awback, namely, i s a s again a e he las obse a ion, which limi s o ecas ing
in he long- e m managemen ho izon. To elimina e his disad an age, i is in e es ing o
use wa ele analysis.
In addi ion, in ou s udy, we ook h ee exogenous ac o s ha signi ican ly change he
beha io o highe educa ion. Howe e , i would be in e es ing o expand he lis o hese
indica o s, which would allow o using long- e m models wi h memo y and ape iodic
me hods o s udy cyclical componen s.
6. Conclusions
To achie e he objec i e o his s udy, he ollowing esul s we e ob ained:
An algo i hmic model has been de eloped ha allows diagnosing shock poin s in he
coun y’s socio-economic de elopmen and hei impac on he de elopmen ends o he
highe educa ion sys em. The concep ual basis o he model is a se o esea ch hypo heses
ha de e mine i s objec i e.
P ac ical implemen a ion o he algo i hmic model allows us o de elop a se o ecom-
menda ions and solu ions aimed a inc easing he sus ainabili y and a ac i eness o he
highe educa ion sys em h ough imely moni o ing o he eac ions o he highe educa ion
sys em o socio-economic shocks. Also, he p oposed model has p ac ical signi icance o
managemen a he s a e- and uni e si y-le els when o ming he s a egy and ac ics o
Adm. Sci. 2024,14, 278 24 o 28
unc ioning, conside ing esou ce capabili ies and dis u bances o he ex e nal en i onmen .
This c ea es he p e equisi es o making e ec i e decisions o inc ease he compe i i eness
o he na ional highe educa ion sys em in he global educa ional space and ensu e all i s
i al unc ions.
To p o e he i s wo hypo heses, an in o ma ion space o he s udy was o med,
including ou indica o s ha e lec economic, social, and demog aphic de elopmen and
he de elopmen o he highe educa ion sys em o 1990–2023. The cons uc ed po ai s o
he socio-economic de elopmen o Uk aine and Slo akia showed he p esence o consis en
ends in he change in he indica o s o GDP pe capi a, he Human De elopmen Index,
co e age o e ia y school educa ion, and ne mig a ion. The nonlinea na u e o he
change in hese indica o s and he de ini ion o local minimum poin s in hei ends made
i possible o con i m he hypo hesis abou he in luence o social and economic ac o s on
he highe educa ion sys em o hese coun ies.
The complex in e ac ions be ween he highe educa ion sys em and socio-economic
ac o s made i possible o jus i y he easibili y o using a special model basis, namely,
he ime-se ies decomposi ion me hods and c oss-spec al analysis ( hi d hypo hesis). A
de ailed analysis o he ou indica o s o he p esence o a end in dispe sion and a e age
showed ha all indica o s ha e cyclical componen s. Howe e , he cyclical componen
o he HDI is no signi ican , he e o e, we excluded his indica o om ou s udy. Thus,
o de e mine he impac o shocks in he ex e nal en i onmen on highe educa ion, he
indica o s o GDP pe capi a and ne mig a ion we e used.
To achie e he objec i e o his s udy, we conside ed he shock om wo sides. On he
one hand, we made one Fou ie ans o m, which helped us ind he s onges ha monics
and de e mine he modeling pe iod o he cyclical componen . Fo his pu pose, we
analyzed each ime se ies sepa a ely wi hou hei mu ual in luence. On he o he hand,
we used c oss-spec al analysis, which shows us he cohe ence be ween ha monics om
di e en ime se ies wi h di e en ampli udes, pe iods, and equencies. Calcula ion o he
h ee main cha ac e is ics o c oss-spec al analysis (c oss-ampli ude, cohe ence, and phase
shi ) allowed us o iden i y he closes ha monics in he analyzed ime se ies. S udying he
phase shi allowed us o de e mine he delay in he eac ion o highe educa ion (school
en ollmen , e ia y, %) o shocks in economic (GDP pe capi a) and social (ne mig a ion)
de elopmen . The esul s showed ha he HES in Slo akia eac s o socio-economic shocks
wi h a one-yea lag; he Uk ainian HES is sensi i e o hem and eac s wi hou delay.
Wi h he help o he cons uc ed models, posi i e and nega i e shocks in he socio-
economic en i onmen o he highe educa ion sys em we e de e mined, which allowed o
p oposing scena ios o he beha io o he coun y’s highe educa ion managemen . The
i s is implemen ed when nega i e shocks appea and is aimed a suppo ing he HES o
main ain i s a ac i eness o na ional and o eign applican s, and he second is used wi h
posi i e shocks and is aimed a s imula ing he ac i i ies o uni e si ies h ough inno a i e
and ac i e, en ep eneu ial beha io in he educa ional se ices ma ke . Shock pe iods in
he indica o s o GDP pe capi a and ne mig a ion we e p edic ed. Using a phase shi ,
poin s o posi i e and nega i e shocks o he highe educa ion sys em o Uk aine and
Slo akia we e de e mined.
The ob ained esul s and ques ions o discussion de e mine u he di ec ions o
esea ch. O pa icula in e es is he expansion o he lis o indica o s o he socio-economic
en i onmen ha in luence he unc ioning o a coun y’s HES. Fo example, i is ad isable
o conside he in luence o indica o s such as he income o he popula ion, he quali y o
li e o he popula ion, he cos o educa ion, he quali y o educa ional se ices, he le el
o secu i y, e c. In addi ion, i would be in e es ing o s udy he use o VAR models and
wa ele analysis o assess he long- e m co-in eg a ion o ha monics o cyclical componen s
and o o ecas he sho - e m eme gence o shock phenomena.