sus ainabili y
A icle
Is he Value Added Tax Sys em Sus ainable? The Case
o he Czech and Slo ak Republics
Ka eˇ ina K zikallo á1,* and Filip Tošeno ský2
1Depa men o Accoun ing and Taxes, Facul y o Economics, VSB—Technical Uni e si y o Os a a,
17. lis opadu 15/2172, 708 00 Os a a, Czech Republic
2Depa men o Quali y Managemen , Facul y o Ma e ials Science and Technology,
VSB—Technical Uni e si y o Os a a, 17. lis opadu 15/2172, 708 00 Os a a, Czech Republic;
[email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +420-5973-22222
Recei ed: 7 May 2020; Accep ed: 16 June 2020; Published: 17 June 2020


Abs ac :
The alue added ax is an impo an pa o e enues o he Eu opean Union and i s
Membe S a es. The aim o he pape is o s a is ically analyse he ex en o posi i e impac o
selec ed legisla i e measu es in oduced in he igh agains ax e asion and discuss subsequen ly
he sus ainabili y o he cu en alue added ax sys em in he Eu opean con ex . The analysis was
conduc ed o he Czech and Slo ak Republics, wo adi ionally s ong ading pa ne s, and o
an impo an commodi y, coppe . In he analysis, eg ession me hods applied o o icial ime se ies
da a on coppe expo om he Czech Republic o Slo akia we e employed oge he wi h app op ia e
s a is ical es s o de ec po en ial signi icance o he new legisla i e ools, he alue added ax con ol
s a emen and e e se cha ge mechanism. Mo eo e , he s udy conside s undamen al economic
ac o s ha a ec o eign ade in pa allel. Based on he analysis, he e is sound e idence ha
he majo his o ical u na ound expe ienced by he ime se ies ook place due o he hen o hcoming
legisla i e measu es ha we e o es ain he possibili y o ca ousel auds. The esul s con i m
he posi i e impac o he measu es and also sugges he necessi y o mo e sys ema ic changes in
he ax sys em.
Keywo ds:
alueadded ax; axe asion; e e secha gemechanism; in e na ional ade; sus ainabili y;
Eu opean Union
1. In oduc ion
The main ole o axes in economy is o secu e income o public budge s [
1
]. Sch a zens alle [
2
]
emphasizes ha an economically sus ainable ax sys em should gene a e su icien e enues o inance
go e nmen ac i i ies. The p ocess o gaining su icien esou ces in ol es he use o ools o ackle ax
e asion and a oidance. A dec ease in ax e asion boos s ax collec ion, he eby helping o inc ease
he quali y o public se ices p o ided o ci izens by go e nmen s and municipali ies [
3
]. Taxes also
a ec he beha iou o households and companies. The alue added ax (VAT), in compa ison o
income ax, is no he p ima y ool o in luencing he dis ibu ion o ax bu den o s imula ing
indus ies h ough in es men incen i es [
4
]. VAT educes ma ginal cos s o public unds and inc eases
he ax a io. This way i becomes a e y e ec i e ool o mos o he coun ies ha adop ed
i [
5
]. Resea ch esul s p oduced by Zimme manno
á
, Skaliˇcko
á
, and Ši ok
ý
[
6
], which a e i o
he condi ions p e ailing in he Czech Republic, also show ha he e is a s a is ically signi ican
and posi i e ela ionship be ween he egional VAT e enues and he egional GDP. This inding can
help policy make s imp o e hei economic planning and managemen on egional and na ional le els.
The sus ainabili y o a ax sys em is an essen ial pa o he sus ainabili y o he en i e economy. Jano
á
,
Sus ainabili y 2020,12, 4925; doi:10.3390/su12124925 www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2020,12, 4925 2 o 25
Hampel, and Ne udo
á
[
7
] e en sugges ed a new concep in his ega d, he so-called ax sus ainabili y
index, a ool ha can be used in o mula ing ax policies on na ional and EU le els. Tax e asion
clea ly h ea ens economic sus ainabili y. Mo eo e , VAT is he ax ha is associa ed wi h ax e asion
he mos , which u he highligh s i s impo ance. Acco ding o Hybka [
8
], he main eason o VAT
e asion migh be he complica ed ules ha p e en i s p ope applica ion. The isk o ax e asion also
a ises a a ime when he socie y’s a en ion is ocused on o he ma e s, now speci ically on he igh
agains COVID-19. Fo ob ious easons, he inancial adminis a ion has limi ed access o ou ine
con ol p ocedu es now, which auds e s a e well awa e o . This ac also unde lines he imeliness o
his opic.
VAT, like o he consump ion axes, is one o he mos ha monized axes in he Eu opean Union. In
he Czech Republic speci ically, i is egula ed by he Ac No. 235/2004 Coll., on AT, as amended, which
came in o e ec when he coun y joined he EU. The p o isions i in oduced we e based on he ele an
Eu opean Communi y Di ec i e, namely he Six h Council Di ec i e 77/388/EEC o 17 May 1977, on
he ha moniza ion o he laws o he Membe S a es ela ing o u no e axes—Common sys em o
alue added ax: uni o m basis o assessmen . The Six h Di ec i e has been amended many imes
and, on 1 Janua y 2007, was eplaced by he Council Di ec i e 2006/112/EC o 28 No embe 2006 on
he common sys em o alue added ax (“VAT Di ec i e”) [
9
]. Ne e heless, he VAT Di ec i e has also
been unde going changes and amendmen s since i s in oduc ion. The EU Membe S a es a e obliged
o implemen mos o hese changes in o hei na ional legisla ion. Howe e , hey ha e a choice in
some a eas, such as he e e se cha ge mechanism (RCM) o domes ic supplies o goods and se ices.
This egime is olun a y o Membe S a es and is limi ed only by he scope o commodi ies in
acco dance wi h he Di ec i e. This sys em was es ablished as one o he ools o igh ax e asion,
pa icula ly auds in he chain and missing ade auds o ca ousel auds. The mechanism,
unlike he common scheme, wi hin which VAT is decla ed on ou pu by he supplie and subsequen ly
claimed by he pu chase , is cha ac e ized by he ule ha he obliga ion o decla e he ou pu ax
is shi ed o he pu chase . A he same ime, he pu chase is en i led o he inpu ax deduc ion in
acco dance wi h he gene al ules o applica ion o VAT ( he use o pu chased goods and se ices o
he pu pose o ca ying ou an economic ac i i y). This scheme he e o e ies o a oid he si ua ions
when he supplie issues an in oice wi h he ou pu ax, bu does no pay he ax, while he pu chase
claims he inpu ax deduc ion. The applica ion o he common VAT sys em o domes ic supplies wi h
he subsequen supply o goods o ano he Membe S a e ha is VAT exemp ed a ou s ax e asion,
especially in he o m o he al eady men ioned ca ousel auds [
10
]. Gi en he impo ance o ax
e asion elimina ion and i s s ong ela ion o VAT, he common VAT sys em wi hou su icien con ol
mechanisms has been a majo weakness in he whole VAT sys em.
The au ho s o he pape decided o s a e and s a is ically analyse he esea ch hypo hesis ha
special measu es in oduced o comba ax e asion may ha e had a signi ican e ec on he o eign ade
epo ing in he Czech Republic and Slo akia. Mo e speci ically, hey may ha e caused a s eep decline
in coppe expo om he Czech Republic o Slo akia. The au ho s delibe a ely use he e m “s a is ical
epo ing” he e because in many cases he e is no eal c oss-bo de supply o goods. The goods a e
me ely eloca ed be ween he Membe S a es and, whe e app op ia e, hi d coun ies, o he pu pose
o VAT auds, and hei mo emen can e en c ea e he so-called ca ousel ( o mo e explana ion o
his e m, see Figu e 1). Ano he possibili y is ha he goods physically do no mo e a all, and he e
is only ic i ious in oicing and epo ing. Fo his analysis, coppe commodi y and i s expo om
he Czech Republic o Slo akia we e selec ed because hese ades we e accompanied by auds in
he pas , and he wo coun ies pa icipa ed in adop ing ools agains VAT e asion. The esea ch
speci ically conce ned he commodi y Re ined coppe and coppe alloys, unw ough (Ha monized
sys em code 7403). The Czech Republic decided o use he RCM on a wide ange o commodi ies
and se ices, while Slo akia was one o he i s coun ies o in oduce he VAT con ol s a emen .
The o iginali y o his pape lies in he ac ha , unlike o he s udies o be e e enced in he nex sec ion,
his analysis is based on mo e ad anced eg ession models, and also akes in o accoun undamen al
Sus ainabili y 2020,12, 4925 3 o 25
economic ac o s ha may ha e a ec ed he o eign ade, as well. The esea ch, compa ed o o he
s udies, is also applied o a di e en commodi y and conside s he in oduc ion o ye ano he measu e,
he VAT con ol s a emen , in addi ion o he RCM.
The ollowing sec ion desc ibes he p inciples go e ning ypical VAT auds, and ca ousel auds
in pa icula , and p esen s some esul s o ela ed s udies in his a ea om o he au ho s.
2. Theo e ical F amewo k and Li e a u e Re iew
Fi s , i is easonable o dis inguish ax a oidance om ax e asion. The main di e ence is be ween
he legali y o he o me , when he beha iou o a axpaye is no agains he law, and he illegali y o
he la e [
11
,
12
]. Tax a oidance o en esul s om shi s in comme cial ac i i y ela ed o in e na ional
income ax s uc u e. Fo example, Clausing [
13
] in he s udy ound ou a s a is ically signi ican ela ion
be ween ax a oidance incen i es and Ame ican in e na ional ade. Simila ly, o he au ho s, such as
Bue ne and Ru [
14
], con i med a signi ican e ec o ax condi ions on he loca ion o subsidia ies o
Ge man mul ina ional companies. Ne e heless, he undecla ed wo k is o en associa ed wi h bo h
ax a oidance and e asion when i comes o pe sonal income ax and social insu ance con ibu ions.
Fo mo e in o ma ion, see he empi ical esea ch done by K umply e and Samule icius [
15
] in Li huania.
K ajˇn
á
k [
16
] also deals wi h selec ed aspec s o pe sonal income ax in he Czech Republic in his espec .
Wha usually leads o ax e asion is he axpaye ’s a ge ed VAT liabili y educ ion. Unlike
income ax, he e is a possibili y o ecei e an excessi e ax deduc ion, which is why VAT is e y popula
o he pu pose o ax e asion. The VAT e asion can be ca ied ou only by VAT- egis e ed companies o
sole p op ie o s [
17
]. I mus be men ioned, howe e , ha en ep eneu s and company managemen s
a e only people whose s a egic decisions abou commi ing a c ime, especially ax e asion, a e no
always in acco dance wi h he s anda d neoclassical economic model o human beha iou [
18
,
19
]. Mo e
abou he heo y o i ms’ ax e asion can be ound in Sandmo [
20
], o ins ance, and he heo y o isk
a e sion in connec ion wi h ax e asion is co e ed in Allingham and Sandmo [21] o Be nasconi [22].
Slem od [
23
] in his s udy poin s ou ha he main ac o in ax-e asion decisions is he chance o being
de ec ed. Olsen, Kaspe , Kogle , Muehlbache and Ki chle [
24
] did an empi ical esea ch among
sel -employed axpaye s om Aus ia and Ge many. This esea ch was ocused on men al accoun ing
o income ax and VAT. Men al accoun ing is a p ocess o o ganizing inancial ope a ions, especially
he en ep eneu s’ ax obliga ions. The esul s showed ha he inancially s apped, who a e less
ca e ul and impulsi e, a e mo e willing o e ade axes. Age, sex and coun y o o igin do no play
any ole.
Wo h men ioning in his con ex is Po ugal which ies o igh VAT e asion in an o iginal
way— h ough a ax lo e y. I s ci izens a e encou aged o mo i a ed o eques sales in oices wi h hei
pe sonal ax iden i ica ion numbe so as o pa icipa e in a ax lo e y. Wilks, C uz and Sousa [
25
] claim
ha hese iscal bene i s helped dec ease he VAT gap om 16% in 2013 o 12% in 2014, when he lo e y
was in oduced. Simila ly, B azil and China in oduced a ax lo e y wi h he aim o encou age VAT
compliance [26,27].
Ano he way how o educe VAT a oidance and e asion is o dec ease he VAT a es, acco ding o
Kalliampakos and Ko zamani [
28
]. Thei s udy conce ning G eece sugges s a educ ion in he s anda d
VAT a e om 24% o 20% and an es ablishmen o one, educed VAT a e o 10% applied only o
selec ed goods and se ices wi h a socio-economic impac . The esul s o he s udy poin o a VAT
e enue imp o emen . Taxes a e iewed om o he pe spec i es, as well. Fo ins ance, he e a e
also a ious opinions and sugges ions on ax e o ms and hei impac om bo h he mic oeconomic
and mac oeconomic poin o iew. McClellan [
29
], o ins ance, unde ook esea ch, using i m-le el
da a on ax e asion and en o cemen and mac oeconomic da a om se en y-nine coun ies, o ind
he e ec o ax en o cemen measu es and ax e enue dec ease on economic g ow h. On he one
hand, dec ease in ax e enues causes mo e unds o co po a e in es men s, bu , on he o he hand,
a dec ease in unds o public goods and se ices, as well. I means ha economic g ow h can be a ec ed
by an inc ease in ax e enues as well as by ax en o cemen measu es. McClellan he e o e sugges s
Sus ainabili y 2020,12, 4925 4 o 25
e o ms o inc ease ax e enues wi hou in oducing s ic ax en o cemen measu es. Howe e , a e y
impo an aspec , sus ainabili y, also comes in o play. Timme mans and Ach en [
30
], o example,
examined a po en ial con e sion o VAT o sales ax o damage and alue added ax (DaVAT). Based on
he esul s o he esea ch, hey ecommend his shi as a consump ion ax e o m om he pe spec i e
o sus ainable g ow h. The DaVAT is an en i onmen al-cha ac e sugges ion made by De Cammilis
and Go alczyk [
31
], and i is buil on a di e en ia ion o ax a es acco ding o he li e cycle o a p oduc
Tax e asion is he mos signi ican cause o he VAT gap, which is essen ially he di e ence
be ween expec ed and ac ual VAT e enues [
32
]. The e a e se e al commonly used me hods o he gap
es ima ion [
33
]. Ne udo
á
and Dob anschi [
34
] b ough a new app oach in his ega d, he so-called
s ochas ic ax on ie model. A compa ison o esul s ob ained wi h a ious me hods designed o
he case o he Czech Republic was made by Mo a ec, Hinke and Kaˇnka [
35
]. An ex eme gap came
ou o he s udy by Cuceu and Vaidean [
36
] who emphasized ha Romania’s VAT gap, exp essed as
a sha e o he VAT To al Tax Liabili y (VTTL), was 42% in 2011, he highes among he EU coun ies.
Sus ainabili y 2020, 12, x FOR PEER REVIEW 5 o 25
Figu e 1. The p inciple o he basic ca ousel aud. Adop ed om [35], own p ocessing.
Čejko á and Zídko á [45] made ano he esea ch ocused gene ally on he impac ha he
in oduc ion o he RCM o was e and sc ap had had on he ax e enues in he Czech Republic.
They disco e ed ha a e he implemen a ion o he measu e agains he VAT ca ousel auds, he
ade be ween he Czech Republic and o he EU coun ies had dec eased, especially he
in acommuni y supplies. Acco ding o hei calcula ions, he p esumed olume o ca ousel auds
in he Czech Republic, ela ed o was e o sc ap, eached abou 56 million eu os/yea p io o RCM.
A posi i e e ec o he RCM on aud educ ion was also con i med by S ille and Heinemann
[46]. Thei esea ch was based on o eign ade da a, as well, his ime be ween Ge many and
Aus ia. To men ion a non-Eu opean esea ch ini ia i e in his a ea o expe ise, a poll un by Yoon
[47] among Sou h Ko ean small and medium-sized deale s in coppe , gold and s eel sc ap indica ed
a posi i e e ec o RCM on ade anspa ency and ai ness.
Simila esea ch and poll esul s sugges ed ha he RCM migh be he kind o ins umen he
socie y needs in i s ba le agains VAT e asions. As ou lined ea lie , he au ho s o he pape le
hemsel es be inspi ed by hese hin s and decided o subjec his ma e o a mo e igo ous s a is ical
analysis, using da a on coppe expo om he Czech Republic o Slo akia and aking also in o
accoun majo economic ac o s ha may in luence his kind o ade. Thei analysis is elabo a ed in
he ollowing sec ions.
3. Ma e ials and Me hods
The Czech Republic and Slo akia ank among he coun ies ha ac i ely s i e o inhibi ax
e asion by adop ing di e se legisla i e measu es. In he ime pe iod 2006–2018 he coun ies
in oduced he alue added ax con ol s a emen and e e se cha ge mechanism in his ega d. No
long be o e doing so, he epo ed amoun o expo o coppe om he Czech Republic o Slo akia,
iewed as a ime se ies, mani es ed a sudden and p onounced decline ha would la e u n ou o be
pe manen . This is an in e es ing coincidence ha p o ides an oppo uni y o con i m, o ejec , ha
he measu es we e co ec ly designed, a e unc ioning and should be used in p ac ice. The
con i ma ion can be made p o ided ha he decline is p o ed o be he esul o a signi ican change
in he o e all cha ac e o he ime se ies, no jus a na u al luc ua ion mos ime se ies a e subjec o,
and he change was no induced by o he , mo e na u al ac o s, which would include he usual and
majo economic o ces ha no mally a ec such ades. The au ho s decided o analyse bo h whe he
he se ies did indeed expe ience a signi ican change in i s de elopmen , and i so, whe he such a
u ning poin can be pu down o he legisla i e measu es and no economic o comme cial easons.
This is done in he analy ical pa o he pape ha ollows.
To e i y he possibili y o an unexpec ed change in he de elopmen o he se ies, he au ho s
exploi ed he heo y o in e en ion models, a pa o he gene al ime se ies heo y [48,49]. These
models assume ha he modelled se ies p og essed in ime in a ce ain way be o e a speci ic ime
poin when i may ha e been suddenly and ei he empo a ily o pe manen ly shi ed by an
in e en ion o ano he le el. I he shi is p esen , he de elopmen o he se ies is hen go e ned by
Figu e 1. The p inciple o he basic ca ousel aud. Adop ed om [35], own p ocessing.
Ca ousel auds in lic losses on bo h he public budge o a pa icula Membe S a e and he budge
o he EU as a whole. Fo his eason, his is a p oblem ha has been unde spo ligh o qui e some ime.
In his con ex , se e alsubs an ial e o ms o heVAT sys emwe e p oposed, al hough hei e ec i eness
is o en ques ionable. One o he s udies, made by Gebaue , Nam and Pa sche [
37
] and ocused
on he po en ial impac o h ee di e en VAT sys ems in Ge many, showed, o ins ance, ha hei
implemen a ion would by con as gi e ise o o he possibili ies o ax a oidance and an inc eased
adminis a i e bu den. The nega i e impac o adminis a i e bu den on small and medium-sized
en e p ises is also s essed in Mikušo á[38].
Ca ousel aud o Missing T ade In a-Communi y (MTIC) aud ep esen s a mo e sophis ica ed
VAT decep ion [
39
]. I s p inciple is ou lined in Figu e 1. Suppose ha all ade pa icipan s a e
VAT- egis e ed in hei coun ies. Ini ially, a Company A, he “condui ” company [
40
], which is
VAT- egis e ed in Membe S a e 1, supplies goods o he goods a e supplied only ic i ely ( he so-called
“absence o ac ual supply”) o Membe S a e 2, while his ansac ion is VAT-exemp ed o he Company
A (ze o- a ed). The cus ome , a Company B om Membe S a e 2, has he du y o cha ge he ou pu
ax om he in acommuni y acquisi ion acco ding o he des ina ion p inciple, and a he same ime is
allowed o claim he inpu ax. This means ha he acquisi ion om Membe S a e 1 is ax-neu al
o he Company B. The goods should be axed by he VAT a e ha is applicable in he s a e o
des ina ion, depending on he ype o goods. In he nex s ep, he Company B esells he commodi y o
a Company C, he so-called “bu e ”, on i s domes ic ma ke . A his ins an , he Company B should
cha ge he ou pu ax om his domes ic supply. Howe e , in he case o aud, he Company B
does no submi he ax e u n and disappea s ( he e o e he company B is called he missing ade ),
o submi s he ax e u n wi hou paying he ax liabili y o he ax adminis a ion. The loss in lic ed
on he public unds will deepen when he Company C claims he igh o he inpu ax deduc ion
om he in oice issued by he Company B. The e can also be a g ea numbe o VAT axpaye s in
he posi ion o he bu e ha may no e en be awa e o being pa o a ca ousel aud. These companies
Sus ainabili y 2020,12, 4925 5 o 25
make he de ec ion o he aud mo e di icul . In he nex s ep, ano he domes ic ansac ion akes
place when he Company C supplies he obse ed commodi y o a Company D, which is ye ano he
audulen company ha is called he “b oke “. In he end, he Company D supplies he goods om
Membe S a e 2 o he Company A om Membe S a e 1 and he ci cle is closed. This in acommuni y
supply is VAT-exemp ed o he Company D. The same goods some imes ci cle only ic i ely among
he same VAT axpaye s se e al imes [41,42].
Figu e 1is only illus a i e, as in eali y many mo e companies a e in ol ed in he aud.
Fo example, in 2016 he Financial Adminis a ion o he Czech Republic de ec ed a aud in ol ing
171 domes ic VAT axpaye s [43].
The Con ede a ion o Indus y o he Czech Republic [
44
] encou aged in his ega d an applica ion
o he domes ic RCM o me als, poin ing o he decline in ade in he ein o ced s eel be ween he Czech
Republic and Poland a e he in oduc ion o he RCM o his commodi y in Poland. I es ima ed
he ax losses a wo billion Czech c owns.
ˇ
Cejko
á
and Z
í
dko
á
[
45
] made ano he esea ch ocused gene ally on he impac ha
he in oduc ion o he RCM o was e and sc ap had had on he ax e enues in he Czech Republic.
They disco e ed ha a e he implemen a ion o he measu e agains he VAT ca ousel auds, he ade
be ween he Czech Republic and o he EU coun ies had dec eased, especially he in acommuni y
supplies. Acco ding o hei calcula ions, hep esumed olumeo ca ousel audsin heCzech Republic,
ela ed o was e o sc ap, eached abou 56 million eu os/yea p io o RCM.
A posi i e e ec o he RCM on aud educ ion was also con i med by S ille and Heinemann [
46
].
Thei esea ch was based on o eign ade da a, as well, his ime be ween Ge many and Aus ia.
To men ion a non-Eu opean esea ch ini ia i e in his a ea o expe ise, a poll un by Yoon [
47
] among
Sou h Ko ean small and medium-sized deale s in coppe , gold and s eel sc ap indica ed a posi i e
e ec o RCM on ade anspa ency and ai ness.
Simila esea ch and poll esul s sugges ed ha he RCM migh be he kind o ins umen
he socie y needs in i s ba le agains VAT e asions. As ou lined ea lie , he au ho s o he pape le
hemsel es be inspi ed by hese hin s and decided o subjec his ma e o a mo e igo ous s a is ical
analysis, using da a on coppe expo om he Czech Republic o Slo akia and aking also in o
accoun majo economic ac o s ha may in luence his kind o ade. Thei analysis is elabo a ed in
he ollowing sec ions.
3. Ma e ials and Me hods
The Czech Republic and Slo akia ank among he coun ies ha ac i ely s i e o inhibi ax
e asion by adop ing di e se legisla i e measu es. In he ime pe iod 2006–2018 he coun ies in oduced
he alue added ax con ol s a emen and e e se cha ge mechanism in his ega d. No long be o e
doing so, he epo ed amoun o expo o coppe om he Czech Republic o Slo akia, iewed as
a ime se ies, mani es ed a sudden and p onounced decline ha would la e u n ou o be pe manen .
This is an in e es ing coincidence ha p o ides an oppo uni y o con i m, o ejec , ha he measu es
we e co ec ly designed, a e unc ioning and should be used in p ac ice. The con i ma ion can be made
p o ided ha he decline is p o ed o be he esul o a signi ican change in he o e all cha ac e o
he ime se ies, no jus a na u al luc ua ion mos ime se ies a e subjec o, and he change was no
induced by o he , mo e na u al ac o s, which would include he usual and majo economic o ces
ha no mally a ec such ades. The au ho s decided o analyse bo h whe he he se ies did indeed
expe ience a signi ican change in i s de elopmen , and i so, whe he such a u ning poin can be pu
down o he legisla i e measu es and no economic o comme cial easons. This is done in he analy ical
pa o he pape ha ollows.
To e i y he possibili y o an unexpec ed change in he de elopmen o he se ies, he au ho s
exploi ed he heo yo in e en ionmodels, apa o hegene al imese ies heo y[
48
,
49
]. Thesemodels
assume ha he modelled se ies p og essed in ime in a ce ain way be o e a speci ic ime poin when i
may ha e been suddenly and ei he empo a ily o pe manen ly shi ed by an in e en ion o ano he

Sus ainabili y 2020,12, 4925 6 o 25
le el. I he shi is p esen , he de elopmen o he se ies is hen go e ned by bo h he p e-in e en ion
pa e n and he in e en ion. I he in e en ion akes place only a one poin in ime, i e en ually
ades away and he se ies e u ns o i s p e-in e en ion p og ess. I , howe e , he in e en ion ac s
pe manen ly, he se ies s ill ollows i s p e-in e en ion and na u al pa e n, bu e en ually on ano he
le el. The la e case is he subjec o he analysis p esen ed he e, gi en how he expo o coppe
his o ically de eloped. The e ec o he in e en ion is cap u ed in he model by a dummy a iable,
which akes on alue ze o be o e he momen o he in e en ion and one a e he in e en ion.
Since he ime se ies models used a e usually ecu si e in he sense ha he alue o he ime se ies
is modelled as a unc ion o i s pas alues, he inclusion o he dummy a iable will cause ha
he modelled alue o he se ies is pushed e en ually o ano he le el. To be mo e p ecise, his is
he case when he model pa ame e e lec ing he e ec o he dummy a iable is nonze o. I i is ze o,
he modelled se ies will no mo e pe manen ly o ano he le el.
A e y gene al model ha desc ibes he de elopmen o a ime se ies z is o he o m [50]
z =c+Xp
i=1ϕiz −i+Xq
j=1θja −j+a , (1)
a =e
σ ε ,e
σ2
=d+X
i=1γia2
−i+Xs
j=1βje
σ2
−j, (2)
ε ∼N(0,1),ε0
s a e independen . (3)
Equa ion (1) desc ibes he ime dynamics o he se ies. The se ies depends on i s pas alues and an
addi ional noise
a
, which has he p ope ies o he s anda d whi e noise excep o i s condi ional
a iance
e
σ2
, equal o he condi ional expec a ion o
a2
, which e lec s he noise ola ili y as a unc ion
o he ealiza ion o he s ochas ic p ocess up o ime . This ola ili y is no cons an in ime, as in
he case o he s anda d whi e noise, bu de elops dynamically in ime, as well, a ea u e ypical o
economic ime se ies. The dynamics o he ola ili y is cap u ed by (2).
The pa ame e s
c
,
ϕ1
,
. . .
,
ϕp
,
θ1
,
. . .
,
θq
,
d
,
γ1
,
. . .
,
γ
,
β1
,
. . .
,
βs
o his ARMA(p,q)-GARCH(s, )
model a e es ima ed using he so-called likelihood unc ion, which is a unc ion o he pa ame e s,
LT(unknown pa ame e s, ε1,. . . ,εT)=YT
=12πe
σ2
−1
2exp(−ε2
/2e
σ2
). (4)
The es ima es o he unknown pa ame e s a e de ined as he alues o he pa ame e s ha
maximize
LT
[
50
]. Fo hem o be ob ained, ini ial alues o
a
and
e
σ2
a e chosen sui ably, so ha
he ecu sions (1) and (2) can be used o calcula e he alue o
LT
o a gi en se o pa ame e s in
he op imiza ion.
In p ac ice, log
LT
is maximized ins ead almos always, since his p ocedu e is simple , albei s ill
complica ed as a nonlinea op imiza ion p oblem, while p o iding he same solu ion. The solu ion is
consis en and asymp o ically no mally dis ibu ed unde gene al condi ions, which include he alidi y
o (1)–(3). This esul allows he use o he model o pe o m s a is ical in e ence, i.e., hypo hesis
es ing ela ed o he unknown pa ame e s and cons uc ion o con idence in e als o he pa ame e s.
The p ocedu e is known as he maximum likelihood es ima ion. I is also used in he case when (1)–(3)
is alid wi hou he no mali y assump ion, hough, in which case i is called he quasi-maximum
likelihood es ima ion. The condi ions a e gene al enough o p o ide he es ima es wi h he desi ed
s a is ical p ope ies e en o his no-no mali y case. Since nonlinea op imiza ion is ex emely complex
an issue, gene ally speaking, he p ocedu e mus be done by a so wa e.
The es ima ion and i s p ope ies ely on (1)–(3), wi h o wi hou no mali y, and he gene al
condi ions. While i is ha dly e e possible o examine he gene al condi ions in p ac ice, (3) is
checked a e he model is es ima ed, using he subsequen es ima es o
ε
. I he p ope ies o hese
es ima es a e in line wi h he assump ion (3), o i s gene alized o m wi hou no mali y, i is concluded
ha (1)–(3) may easonably ep esen he mechanisms ha gene a ed he se ies. This well-known
s a is ical s a egy elies on he idea ha (1)–(3), wi h o wi hou no mali y, is gene al enough o
Sus ainabili y 2020,12, 4925 7 o 25
cap u e he mechanisms behind he se ies, in which case he p ope model should yield es ima es
o
ε
whose p ope ies mimick he p ope ies o
ε
because es ima es o
ε
a e simila o
ε
in la ge
da a samples unde he gene al condi ions and he p ope ly selec ed model. I such es ima es a e no
ound, hen ei he he selec ed model is inapp op ia e, o he mechanisms gene a ing he se ies a e so
o e ly complex ha no e en he cons uc (1)–(3) su ices o hei desc ip ion. Such a pessimis ic
conclusion, howe e , is made only a e many a emp s o ind he model ailed.
The same logic is also applied o he ARMA-GARCH models en iched wi h exogenous a iables
on hei igh -hand side, which esul s in he so-called ARMAX-GARCH models. A ep esen a i e
o his class o models shall be used in he pape , since a dummy a iable, e lec ing he po en ial
in e en ion, will be inse ed in he model on i s igh -hand side. We e e o [
51
] o a discussion o
he po en ial hese models ha e. The model will be subjec o he checks in he pape .
Using s anda d s a is ical p ocedu es, he app op ia e models will show ha he se ies on coppe
expo unde wen a his o ical p og ess ha can be be e mimicked wi h he dummy a iable han
wi hou i . Thissugges s ha hemechanisms de ining he beha iou o hese iesbe o e hein e en ion
do no su ice o he p ope desc ip ion o i s pos -in e en ion de elopmen [52].
The conclusion ha some hing signi ican happened in he his o ical e ol emen o he se ies leads
subsequen ly o an analysis o wha may ha e caused he shi . The analysis is ca ied ou by going
h ough a ious economic and o he ac o s ha we e a wo k a ound he ime o he in e en ion.
The analysis is da a—d i en. The da a sou ces used in ol e mainly in o ma ion om he Czech
S a is ical O ice on c oss-bo de mo emen o goods, which includes coppe expo s om he Czech
Republic o Slo akia, in o ma ion on coppe p ope ies and demand om he Coppe De elopmen
Associa ion and he In e na ional Coppe Associa ion, da a om he se e MINING.com on he global
coppe ma ke , da a om Mac o ends on coppe p ices, da a om T ading Economics on he Slo ak
and he EU’s g oss domes ic p oduc his o y, annual epo s o he Czech Na ional Bank, which keep
ack o he bank’s o eign exchange in e en ions, he eal- ime in o ma ion on exchange a es
main ained by he se e Ku zy.cz and da a om Agence F ance-P esse on he Slo ak ca p oduc ion.
4. Resul s
The au ho s o he pape a e conce ned wi h he possibili y ha he e may ha e been a ac o a
wo k in he o m o an in e en ion ha occu ed in a sho pe iod o ime, bu had had a las ing e ec ,
gi en how he se ies on coppe expo om he Czech Republic o Slo akia de eloped. This may
conce n speci ically he in e en ion induced by he measu e ha was in oduced in Slo akia in 2014
in he o m o he VAT con ol s a emen . This ype o epo ing allows a c oss-check o supplie s’
and cus ome s’ in oices o disclose he so-called missing ade aud, o he ela ed ca ousel aud, o
he supply chain aud. Fo mo e in o ma ion abou his ool, see [
53
]. The in e en ion e ec may ha e
also been co-p oduced by he RCM applied o coppe in he Czech Republic since 1 Ap il 2015. Tha his
migh ha e been he case is sugges ed by he ac ha such illegal ading had aken place in he Czech
Republic. F audulen ades in coppe occu ed in 2012 and he Czech e i o y played he ole o
a geog aphic go-be ween in hem. The ades pu po ing o be based on impo and immedia e
expo o coppe p oduc s ne e happened and we e epo ed on ade accoun s o a pu pose ully
c ea ed comme cial chain in o de o p o i om he exis ing VAT mechanisms. This illegal ac i i y
was disclosed by he Czech special eam Tax Cob a in coope a ion wi h Slo ak au ho i ies h ough
he ope a ion called “Cup al” [
54
]. Tax Cob a is ep esen ed by he Financial Adminis a ion o
he Czech Republic, he Cus oms Adminis a ion o he Czech Republic and he Uni o Comba ing
Co up ion and Financial C ime. The eam de ec s, iden i ies and comba s selec ed ax e asion cases
on bo h he ax and c iminal side. And he e we e mo e o hese cases. Fo mo e in o ma ion, see [
55
].
I mus be said ha al hough he Slo ak measu e was in oduced in 2014, he coun y’s plans o do so
we e publicly known in ad ance, and so he ade s in ol ed in he auds had enough ime o cease
hei c iminal ac i i ies be o e he measu e was ully pu in o ope a ion. Ob iously, doing so on he day
he measu es came in o e ec o a e ha would ha e exposed hem easily o jus ice. Thus, one migh
Sus ainabili y 2020,12, 4925 8 o 25
expec ha he plans o es ic such ading p ac ices could ha e esona ed in ad ance on he coppe
ma ke a he ime p io o he d op in he expo s. To e i y his possibili y, he a o emen ioned heo y
o in e en ion models was used, i s o de ec whe he he sha p u n in he ime se ies could a all be
a ibu ed o a new egime in i s de elopmen , and i so, whe he such a change could be explained by
he legisla i e measu es.
The me hodology o in e en ion models is desc ibed in [
49
,
52
]. The co esponding analysis was
ca ied ou in he s a is ical so wa e S a a. The en i e se ies con aining he da a on coppe expo om
he Czech Republic o Slo akia consis ed o 149 obse a ions [
56
]. I is shown in Figu e 2. The se ies,
y 149
=1, is no s a iona y, as is o en he case in economic applica ions.
Sus ainabili y 2020, 12, x FOR PEER REVIEW 8 o 25
o de ec whe he he sha p u n in he ime se ies could a all be a ibu ed o a new egime in i s
de elopmen , and i so, whe he such a change could be explained by he legisla i e measu es.
The me hodology o in e en ion models is desc ibed in [49,52]. The co esponding analysis was
ca ied ou in he s a is ical so wa e S a a. The en i e se ies con aining he da a on coppe expo
om he Czech Republic o Slo akia consis ed o 149 obse a ions [56]. I is shown in Figu e 2. The
se ies, 󰇝󰇞
, is no s a iona y, as is o en he case in economic applica ions.
Figu e 2. Coppe expo om he Czech Republic o Slo akia in 3/2006–7/2018. Adop ed om [56],
own p ocessing.
The poin o in e en ion is usually unknown in in e en ion analyses, i is no pa o he da a.
One way o p oceed in such cases is o make assump ions abou i s loca ion, using o he in o ma ion
ou side he ime se ies da a, such as he economic undamen al ac o s and hei de elopmen . I was
p ima ily his de elopmen ha led o he au ho s’ opinion ha i he e was an in e en ion, he 85 h
da a poin in he se ies migh ha e been he momen , when he s a e measu es kicked in, as i was
hen ha he se ies had emba ked on i s e e se p og ess, e en ually accele a ing i s decline o he
poin o nea disappea ance, as compa ed o i s p e-in e en ion le els.
To ca y ou he in e en ion analysis, s anda d p ocedu es we e ollowed. Fi s , he p e-
in e en ion pa o he se ies, 󰇝󰇞
 , was desc ibed by an ARMA o mo e complex s a iona y model
applied o a p ope ans o ma ion ∆() o he da a. Once such a model was ound, i was
en iched wi h an in e en ion, bina y a iable  ha ook on alue ze o be o e he in e en ion and
one a e wa ds. The model wi h  basically says ha p io o he in e en ion he se ies an as
desc ibed by he p e-in e en ion analysis and hen, a e he in e en ion ha emained in e ec
om ha momen onwa d, he se ies s ill ollowed he p e-in e en ion mechanism, bu was o ced
by  o slide o a new le el whe e i emained, being s ill go e ned by he p e-in e en ion
mechanism. This is a e all sugges ed by Figu e 2.
Al hough he p e-in e en ion model should be checked o i s app op ia eness, i is no
impe a i e ha he check be ho ough a his s age o he analysis, because he model se es only as
a hin as o which model could po en ially be used o he en i e se ies. The model o he whole se ies
mus hen be checked ho oughly, howe e . The e o e, in he p e-in e en ion analysis, he au ho s
used only some o he ools o show wha led hem subsequen ly o i s models wi h  o he
se ies.
Rega ding he p e-in e en ion p ocedu e, a ans o ma ion o he co esponding se ies,
∆(), which would make he se ies s a iona y in he mean and a iance, was sea ched o in he
i s s ep. To do so, d was se o 1 and ans o ma ions o he o m ()=

, ∈
󰇝-1, -0.9, -0.8,…, 0.8, 0.9, 1󰇞, we e analysed. T was o s abilize he luc ua ions in he se ies, he e o e a
was selec ed so ha max
|∆
|/min
|∆
| was minimized. The esul was =0.6 wi h max
|∆
|/
min
|∆
|= 65.76. The se ies ∆
. is shown in Figu e 3.
0
100
200
300
400
500
600
1 21416181101121141
Millions o c owns
Da a uni
Coppe expo om Czechia do Slo akia
Figu e 2.
Coppe expo om he Czech Republic o Slo akia in 3/2006–7/2018. Adop ed om [
56
],
own p ocessing.
The poin o in e en ion is usually unknown in in e en ion analyses, i is no pa o he da a.
One way o p oceed in such cases is o make assump ions abou i s loca ion, using o he in o ma ion
ou side he ime se ies da a, such as he economic undamen al ac o s and hei de elopmen . I was
p ima ily his de elopmen ha led o he au ho s’ opinion ha i he e was an in e en ion, he 85 h
da a poin in he se ies migh ha e been he momen , when he s a e measu es kicked in, as i was hen
ha he se ies had emba ked on i s e e se p og ess, e en ually accele a ing i s decline o he poin o
nea disappea ance, as compa ed o i s p e-in e en ion le els.
To ca y ou he in e en ion analysis, s anda d p ocedu es we e ollowed. Fi s , he p e-in e en ion
pa o hese ies,
y 84
=1
, was desc ibed by anARMA o mo e complex s a iona y modelapplied oa p ope
ans o ma ion
∆dT(y )
o he da a. Once such a model was ound, i was en iched wi h an in e en ion,
bina y a iable
S
ha ook on alue ze o be o e he in e en ion and one a e wa ds. The model wi h
S
basically says ha p io o he in e en ion he se ies an as desc ibed by he p e-in e en ion analysis
and hen, a e he in e en ion ha emained in e ec om ha momen onwa d, he se ies s ill ollowed
he p e-in e en ion mechanism, bu was o ced by
S
o slide o a new le el whe e i emained, being s ill
go e ned by he p e-in e en ion mechanism. This is a e all sugges ed by Figu e 2.
Al hough he p e-in e en ion model should be checked o i s app op ia eness, i is no impe a i e
ha he check be ho ough a his s age o he analysis, because he model se es only as a hin as o
which model could po en ially be used o he en i e se ies. The model o he whole se ies mus hen
be checked ho oughly, howe e . The e o e, in he p e-in e en ion analysis, he au ho s used only
some o he ools o show wha led hem subsequen ly o i s models wi h S o he se ies.
Rega ding he p e-in e en ion p ocedu e, a ans o ma ion o he co esponding se ies,
∆dT(y )
,
which would make he se ies s a iona y in he mean and a iance, was sea ched o in he i s s ep.
To do so, dwas se o 1 and ans o ma ions o he o m
T(y )=ya
,
a∈{−1, −0.9, −0.8,. . . , 0.8, 0.9, 1}
,
we e analysed. Twas o s abilize he luc ua ions in he se ies, he e o e awas selec ed so
ha
max
a∆ya
/min
a∆ya

was minimized. The esul was
a=
0.6 wi h
max
a∆ya
/min
a∆ya
=
65.76.
The se ies ∆y0.6
is shown in Figu e 3.
Sus ainabili y 2020,12, 4925 9 o 25
Sus ainabili y 2020, 12, x FOR PEER REVIEW 9 o 25
Figu e 3. T ans o ma ion ∆
.,  = 1, … , 84, o he o iginal se ies. Own p ocessing.
The augmen ed Dickey-Fulle es wi hou de e minis ic end and wi h maximum lag o i e,
p o ided by S a a, e u ned he alue −3.757 o he es s a is ic and he c i ical alues −3.542,
−2.908, and −2.589 a one, i e and en pe cen signi icance le els, espec i ely. Thus, assuming a
his ea ly s age ha he ans o med da a a e a ealiza ion o a s a iona y p ocess, au oco ela ions
(ACF) and pa ial au oco ela ions (PACF) we e calcula ed o he ans o med se ies (Figu es 4 and
5).
Figu e 4. Au oco ela ions (ACF) o he se ies ∆
.,  = 1, … , 84. Own p ocessing.
Figu e 5. Pa ial au oco ela ions (PACF) o he se ies ∆
.,  = 1, … , 84. Own p ocessing.
Using 99% bands, he ACF and PACF u ned ou o be signi ican only a lag one. In heo y,
MA(1) p ocesses ha e a signi ican ACF spike a lag one only ( his case), while he PACF con e ges
o ze o only e en ually, and mono onically on he nega i e side i he ue MA(1) model coe icien
is nega i e. Howe e , a ue MA(1) p ocess o leng h less han one hund ed alues wi h a nega i e
coe icien can easily be gene a ed, whe e he PACF spike a lag one is signi ican , whe eas he o he
PACF spikes a e insigni ican and appea on bo h sides o he x-axis ( he case he e again). A simila
-1000
-500
0
500
1000
1 1121314151617181
Di e enced, powe ed se ies
Da a uni
T ans o med coppe expo
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 6 11 16 21
Au oco ela ions in he se ies
Time lag
ACF o he p e-in e en ion se ies
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 6 11 16 21
Pa ial co ela ions in he se ies
Time lag
PACF o he p e-in e en ion se ies
Figu e 3. T ans o ma ion ∆y0.6
, =1,..., 84, o he o iginal se ies. Own p ocessing.
The augmen ed Dickey-Fulle es wi hou de e minis ic end and wi h maximum lag o i e,
p o ided by S a a, e u ned he alue
−
3.757 o he es s a is ic and he c i ical alues
−
3.542,
−
2.908,
and
−
2.589 a one, i e and en pe cen signi icance le els, espec i ely. Thus, assuming a his
ea ly s age ha he ans o med da a a e a ealiza ion o a s a iona y p ocess, au oco ela ions (ACF)
and pa ial au oco ela ions (PACF) we e calcula ed o he ans o med se ies (Figu es 4and 5).
Sus ainabili y 2020, 12, x FOR PEER REVIEW 9 o 25
Figu e 3. T ans o ma ion ∆
.,  = 1, … , 84, o he o iginal se ies. Own p ocessing.
The augmen ed Dickey-Fulle es wi hou de e minis ic end and wi h maximum lag o i e,
p o ided by S a a, e u ned he alue −3.757 o he es s a is ic and he c i ical alues −3.542,
−2.908, and −2.589 a one, i e and en pe cen signi icance le els, espec i ely. Thus, assuming a
his ea ly s age ha he ans o med da a a e a ealiza ion o a s a iona y p ocess, au oco ela ions
(ACF) and pa ial au oco ela ions (PACF) we e calcula ed o he ans o med se ies (Figu es 4 and
5).
Figu e 4. Au oco ela ions (ACF) o he se ies ∆
.,  = 1, … , 84. Own p ocessing.
Figu e 5. Pa ial au oco ela ions (PACF) o he se ies ∆
.,  = 1, … , 84. Own p ocessing.
Using 99% bands, he ACF and PACF u ned ou o be signi ican only a lag one. In heo y,
MA(1) p ocesses ha e a signi ican ACF spike a lag one only ( his case), while he PACF con e ges
o ze o only e en ually, and mono onically on he nega i e side i he ue MA(1) model coe icien
is nega i e. Howe e , a ue MA(1) p ocess o leng h less han one hund ed alues wi h a nega i e
coe icien can easily be gene a ed, whe e he PACF spike a lag one is signi ican , whe eas he o he
PACF spikes a e insigni ican and appea on bo h sides o he x-axis ( he case he e again). A simila
-1000
-500
0
500
1000
1 1121314151617181
Di e enced, powe ed se ies
Da a uni
T ans o med coppe expo
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 6 11 16 21
Au oco ela ions in he se ies
Time lag
ACF o he p e-in e en ion se ies
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 6 11 16 21
Pa ial co ela ions in he se ies
Time lag
PACF o he p e-in e en ion se ies
Figu e 4. Au oco ela ions (ACF) o he se ies ∆y0.6
, =1,..., 84. Own p ocessing.
Sus ainabili y 2020, 12, x FOR PEER REVIEW 9 o 25
Figu e 3. T ans o ma ion ∆
.,  = 1, … , 84, o he o iginal se ies. Own p ocessing.
The augmen ed Dickey-Fulle es wi hou de e minis ic end and wi h maximum lag o i e,
p o ided by S a a, e u ned he alue −3.757 o he es s a is ic and he c i ical alues −3.542,
−2.908, and −2.589 a one, i e and en pe cen signi icance le els, espec i ely. Thus, assuming a
his ea ly s age ha he ans o med da a a e a ealiza ion o a s a iona y p ocess, au oco ela ions
(ACF) and pa ial au oco ela ions (PACF) we e calcula ed o he ans o med se ies (Figu es 4 and
5).
Figu e 4. Au oco ela ions (ACF) o he se ies ∆
.,  = 1, … , 84. Own p ocessing.
Figu e 5. Pa ial au oco ela ions (PACF) o he se ies ∆
.,  = 1, … , 84. Own p ocessing.
Using 99% bands, he ACF and PACF u ned ou o be signi ican only a lag one. In heo y,
MA(1) p ocesses ha e a signi ican ACF spike a lag one only ( his case), while he PACF con e ges
o ze o only e en ually, and mono onically on he nega i e side i he ue MA(1) model coe icien
is nega i e. Howe e , a ue MA(1) p ocess o leng h less han one hund ed alues wi h a nega i e
coe icien can easily be gene a ed, whe e he PACF spike a lag one is signi ican , whe eas he o he
PACF spikes a e insigni ican and appea on bo h sides o he x-axis ( he case he e again). A simila
-1000
-500
0
500
1000
1 1121314151617181
Di e enced, powe ed se ies
Da a uni
T ans o med coppe expo
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 6 11 16 21
Au oco ela ions in he se ies
Time lag
ACF o he p e-in e en ion se ies
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 6 11 16 21
Pa ial co ela ions in he se ies
Time lag
PACF o he p e-in e en ion se ies
Figu e 5. Pa ial au oco ela ions (PACF) o he se ies ∆y0.6
, =1,..., 84. Own p ocessing.
Using 99% bands, he ACF and PACF u ned ou o be signi ican only a lag one. In heo y,
MA(1) p ocesses ha e a signi ican ACF spike a lag one only ( his case), while he PACF con e ges
o ze o only e en ually, and mono onically on he nega i e side i he ue MA(1) model coe icien
is nega i e. Howe e , a ue MA(1) p ocess o leng h less han one hund ed alues wi h a nega i e
Sus ainabili y 2020,12, 4925 16 o 25
o hei ad an age. Fo he explana ion o he e m “missing ade ”, see Sec ion 2and Figu e 1.
Such indings we e also made by ˇ
Cejko
á
and Z
í
dko
á
[
45
]. This may also be he explana ion why
in 2013, he o al coppe impo o Slo akia was smalle han ha om he Czech Republic. Based on
hese da a, he e is a good chance ha no a small amoun o he coppe impo s o Slo akia om
he Czech Republic ep esen ed aud, and undamen al economic ac o s a e o no impo ance o
such ades.
Table 6.
Coppe impo o Slo akia om he wo ld (line 1) and he Czech Republic (lines 2—CZSO,
3—SOSR). Adap ed om [56,73], own p ocessing.
Yea s 2011 2012 2013 2014 2015 2016 2017
To al impo o SK 89,178 182,729 80,083
127,579
74,526 86,501 82,051
Impo o SK om CR 59,313 139,229 170,596 76,603 3204 699 1198
Impo o SK om CR 19,503 17,020 12,847 50,112 2555 3908 3115
Las bu no leas , acco ding o he CZSO [
56
], he coppe expo did no seem o shi om
he Czech Republic o o he coun ies ei he , as a subs i u e o Slo akia, because ha expo d opped,
as well, see Table 7. In e es ingly enough, he e e se cha ge mechanism on his commodi y was
in oduced also in o he neighbou ing s a es, such as Aus ia and Poland.
Table 7.
Coppe expo om he Czech Republic (in hs. o EUR). Adap ed om [
56
], own p ocessing.
Yea 2011 2012 2013 2014 2015 2016 2017
Expo o SK
59,313
139,229 170,596
76,603 3204 699 1198
To al expo
82,525
195,788 306,130 149,445
25,956 9999 10,172
To sum up, i is di icul o ind a single majo economic o comme cial ac o ha would explain
sa is ac o ily why he coppe expo s om he Czech Republic o i s neighbou ook a sha p u n a
he beginning o 2013 and hen sh ank pe manen ly.
The only majo ex e nal mechanism concei able a ha ime we e he wo measu es planned by
he Czech Republic and Slo akia in hei igh agains VAT auds.
5. Upcoming and P oposed Changes in he VAT Rules wi hin he Eu opean Union
As we ha e seen he e is a good chance ha he special ools such as VAT con ol s a emen
and RCM make sense in he ba le wi h ax auds e s. This sec ion co e s o he s eps aken o p oposed
by he EU bodies, and commen s on hei s eng hs and weaknesses. A e all, he s udies p esen ed
in his pape , as well as he Eu opean Commission’s ac ions, showed ha VAT e asion is a p essing
p oblem ha canno be o e come by a simple solu ion. I needs a numbe o sys ema ic measu es.
Following he esul s o he public consul a ion “The G een Pape on he Fu u e o VAT” [
74
],
he Eu opean Commission p epa ed “The Ac ion Plan on VAT” [
75
]. The plan con ains p oposals
ha aim o imp o e ax collec ion, in oduce addi ional ins umen s o comba ax e asion,
educe adminis a i e bu den on SMEs in B2C ansac ions, imp o e e iciency o ax adminis a ion
and mode nize VAT a es. A e he adop ion o he plan, he Eu opean Commission app o ed se e al
di ec i es and p epa ed a numbe o o he p oposals in his ield.
Fi s , in line wi h he opic o his pape , i is necessa y o men ion he p oposal o a de ini i e
VAT sys em o in acommuni y B2B ansac ions. This sys em, which could come in o e ec in 2022,
means ha goods would be axed in he Membe S a e ha is i s inal des ina ion. In ela ion o
he sys em, he ins i u e o ce i ied axable pe son (CTP) would be es ablished. The adop ion o
he sys em would no b ing any changes o he cu en p ocedu e o CTPs whose pa ne s a e CTPs
om o he Membe S a es. The cus ome would s ill be liable o collec VAT on he e e se cha ge
basis. Howe e , his ins i u e would be g an ed only o VAT axpaye s who mee ela i ely s ic

Sus ainabili y 2020,12, 4925 17 o 25
condi ions. Fo mo e in o ma ion on hem, see [
76
]. I is ob ious ha his change may nega i ely a ec
SMEs. The eason is ha unlike CTPs, VAT axpaye s wi hou he ce i ica ion would ha e o pay
he ax in he des ina ion s a e a he a e applicable in ha coun y h ough he “One S op Shop”. On
he one hand, he “One S op Shop” sys em is a acili a ion because he supplie pays he ax liabili y
o all s a es wi h one paymen in his home s a e. On he o he hand, he supplie mus always check
he VAT a e, which is applicable in he coun y o des ina ion, o each deli e ed commodi y. A
he same ime, he ecapi ula i e s a emen would be cancelled, which would complica e he wo k
o ax au ho i ies because hey would lose in o ma ion abou indi idual in acommuni y supplies.
This si ua ion may a ou VAT e asion on a di e en basis.
A e y impo an aspec is he ex ension o he possibili y o applying he a o emen ioned
ins umen in he igh agains ax e asion, he RCM. Applica ion o his measu e is p olonged un il
June 2022, and is go e ned by Council Di ec i e (EU) 2018/1695 o 6 No embe 2018, amending
Di ec i e 2006/112/EC on he common sys em o alue added ax as ega ds he pe iod o applica ion
o he op ional e e se cha ge mechanism in ela ion o supplies o ce ain goods and se ices
suscep ible o aud and o he Quick Reac ion Mechanism agains VAT aud [
77
]. The p e ious
RCM di ec i es, especially Council Di ec i es 2013/42/EU [
78
] and 2013/43/EU [
79
], we e e ec i e un il
31 Decembe 2018.
Mo eo e , due o he magni ude o ca ousel auds, some Membe S a es including
he Czech Republic and Slo akia called o a solu ion ha would no limi he scope o commodi ies
and se ices o he RCM and would he e o e simpli y he applica ion o VAT in domes ic supplies.
This is why he Eu opean Commission app o ed Council Di ec i e (EU) 2018/2057 o 20 Decembe 2018,
amending Di ec i e 2006/112/EC on he common sys em o alue added ax as ega ds he empo a y
applica ion o a gene alised e e se cha ge mechanism in ela ion o supplies o goods and se ices
abo e a ce ain h eshold [
80
]. Howe e , each Membe S a e has o mee se e al c i e ia acco ding
o he A icle 199c o he VAT Di ec i e in o de o apply o he implemen a ion o he gene alized
RCM (GRCM). The mechanism will be applied o domes ic supplies o goods and se ices abo e
he h eshold o 17,500 eu os pe ansac ion. O cou se, in ela ion o his limi , he Membe S a es
should p e en he po en ial ci cum en ion o he GRCM by a i icially spli ing he axable amoun o
he axpaye s’ ansac ions. Fo una ely, he Czech Republic and Slo akia a e among he coun ies ha
a e able o moni o his po en ial new way o VAT aud ia he VAT con ol s a emen s. In any case,
implemen a ion o his measu e can lead o mig a ion o ca ousel auds o o he Membe S a es ha
canno implemen he GRCM and can gene a e a nega i e impac on he in e nal ma ke . The e o e,
he neighbou ing coun ies will be able o apply his sys em e en i hey do no mee he c i e ia based
on he Di ec i e 2018/2057, as i is clea ha he auds would mo e o hei a ea. The Czech Republic
has al eady ob ained a pe mission o applica ion o he GRCM om he Eu opean Commission and an
app o al o he Eu opean Council. Un o una ely, he measu e can be applied only o a sho ime
pe iod, om 1 July 2020 o 30 June 2022. Fo his eason, he Czech Republic has no inco po a ed his
ool in i s legisla ion and decided o seek i s p olonga ion [81].
On he one hand, he GRCM seems o be a sui able ool o ackle VAT e asion. On he o he hand,
i is s ill ob ious ha i could b ing complica ions o companies, whose business pa ne s a e bo h VAT
and non-VAT paye s. I could inc ease adminis a ion cos s and scope o mis akes caused by imp ope
case-speci ic applica ion o his sys em. In addi ion, i can cause p oblems in business ac i i ies ha
a e VAT-exemp ed, such as ce ain inancial o insu ance se ices.
Also, he RCM has no been p o ed o be qui e e ec i e in comba ing VAT aud in Poland,
o ins ance. Fo his eason, he measu e was eplaced in he coun y by he manda o y spli -paymen
mechanism, e ec i e om 1 No embe 2019. This mechanism is applied o selec ed se ices
and commodi ies, such as cons uc ion se ices, s eel p oduc s and non- e ous me als including coppe .
In ol ed a e B2B ansac ions exceeding he limi PLN 15,000. The p inciple o he mechanism lies in
spli ing he paymen o a ansac ion in o a ax base and he ax. The ax base is paid o he accoun
o he supplie ha is commonly used o business and he VAT is deposi ed in o a sepa a e VAT
Sus ainabili y 2020,12, 4925 18 o 25
accoun . This special accoun is used only o he paymen o VAT liabili y o he ax adminis a ion [
82
].
Ne e heless, his sys em has been olun a y since 1 July 2018 in Poland and since 1 Ap il 2011 in
he Czech Republic [
83
]. The main disad an age o his sys em is an inc ease in compliance cos s.
In addi ion, he conclusions o a s udy made by S oicea and Io ga [
84
] show a nega i e impac on
insol en ag icul u al companies due o hei educed chance o eco e y. In Romania, he sys em has
been manda o y o s a e companies and companies in insol ency since Janua y 2018. Poland also
in oduced ano he measu e in i s igh agains ca ousel auds, he STIR-In o ma ion Sys em o
he Reconcilia ion Chambe , in e ec since 1 Janua y 2018. I is a so wa e ha enables us o de ec
he isk o iscal- aud occu ence. The sys em equi es inancial ins i u ions o p o ide da a o analysis
o he Polish ax adminis a ion. Fo mo e in o ma ion abou he ool, see, e.g., [83].
The so-called “quick ixies” is also wo h men ioning in his con ex . These a e measu es o
imp o e he VAT sys em o in acommuni y supplies o goods. Changes in he sys em a e egula ed
by Council Di ec i e 2018/1910 o 4 Decembe 2018, amending Di ec i e 2006/112/EC as ega ds
he ha monisa ion and simpli ica ion o ce ain ules in he alue added ax sys em o he axa ion o
ade be ween Membe S a es [
85
]. The Di ec i e egula es in acommuni y supplies unde call-o
s ock a angemen s and supplies o goods in he chain. The EU Membe S a es shall apply hose
p o isions om 1 Janua y 2020.
In any case, alking abou he de elopmen o VAT ules, he EU canno be isola ed om he es
o he wo ld. This app oach could cause double axa ion o no axa ion, especially in he case o
c oss-bo de supply o se ices and in angibles. The e o e, se e al chap e s o “The In e na ional
VAT/GST Guidelines” we e adop ed in mo e han 100 coun ies [86].
6. Discussion
Based on he esul s o he s a is ical analysis p esen ed in his pape and o he Eu opean
Commissions’ planned s eps, he au ho s’ a ou he iew ha one o he mo e app op ia e op ions in
he igh agains ax e asion is he in oduc ion o he GRCM ha Membe S a es will be allowed o apply
om 1 Janua y 2020. I seems ha he Czech Republic will be one o he pionee s o ully implemen
his sys em. Howe e , such measu es should be implemen ed in he Membe S a es simul aneously,
ega ding bo h he ime ame and he ange o commodi ies and se ices. Mo eo e , di e ences exis
in he limi s o applying he scheme in indi idual Membe S a es. This means ha ax e ade s ha e
endency o a i icially di ide hei supplies so ha hey ge unde he inancial limi , and he egime
does no apply o hem. They can hen use he classical inpu -ou pu VAT egime. The misma ch
speci ically a ises when one o he s a es se s a limi o he applica ion o he scheme and a neighbou ing
s a e applies ha scheme wi hou a billing h eshold (e.g., he Czech Republic and he neighbou ing
Slo akia). Gene ally, di e ences in he implemen a ion o he egime in indi idual coun ies help
mo e hese auds o s a es whe e he egime has no been pu in o p ac ice.
The esul s o he analysis imply ha he common VAT sys em, cu en ly applied in he EU,
is no sus ainable and equi es e o ms. I is necessa y o emphasize, howe e , ha all coun ies
should p epa e signi ican legisla i e changes in acco dance wi h he Uni ed Na ions’ 2030 Agenda o
Sus ainable De elopmen . The Czech Republic included equi ed sus ainable-de elopmen goals in i s
documen S a egic F amewo k Czech Republic 2030. The documen , among o he hings, con ains
a SWOT analysis which men ions a simple, anspa en and p edic able ax sys em as one o i s
oppo uni ies and gene ally high adminis a i e bu den as one o he weaknesses [87].
No wi hs anding, acco ding o heau ho s, he newsys em p oposedby heEu opeanCommission,
he in oduc ion o he CTP including a de-ha moniza ion o VAT a es, could lead o he opposi e
si ua ion. I could lead o unce ain y ega ding applica ion o co ec VAT ules, which could dis o
he in e nal ma ke , inc ease he adminis a i e bu den on businesses and cause di icul y in iden i ying
and e i ying in o ma ion on ading pa ne s ha a e o en no up o da e. Implemen a ion o hese
p inciples would ha e a nega i e impac on he small and medium-sized en e p ises ha do no ha e
su icien inancial and ime esou ces o e i y such in o ma ion.
Sus ainabili y 2020,12, 4925 19 o 25
Also, i should no be o go en ha despi e he ac ha many o he esea ch s udies men ioned
in he heo e ical pa o he pape con i med a posi i e e ec o he RCM, Poland, ano he neighbou
o he Czech Republic, happened o ind ou ha i migh no be so s ong a mechanism by i sel
as was expec ed, which is why he coun y es ablished he spli -paymen mechanism. This means
ha he paymen is spli in o a ax base and VAT. The VAT is sen o a special accoun and hen
passed on o he ax adminis a ion. The obliga ion is alid bo h o he companies esiding in
Poland and he companies esiding in ano he coun y, bu egis e ed o VAT in Poland. The sys em
is applied in Poland only o selec ed goods and se ices. In he au ho s’ opinion, his should be
applied gene ally. This migh also be a good way o igh ax e asion. The e is a possibili y o use
he spli -paymen sys em on a olun a y basis in he Czech Republic oo. Howe e , his mechanism
is used e y seldom, only in he cases when he cus ome has a easonable ea ha he supplie
will no pay he VAT o he ax adminis a ion. I mus be no ed ha he supplie has o ag ee wi h
he applica ion o he mechanism. The adminis a i e bu den and ela ed compliance cos s a e also
e y high. Ano he disad an age o he spli -paymen sys em is ha he sys em can b ing liquidi y
p oblems o businesses whose inpu s a e axed wi h a s anda d VAT a e, while hei ou pu s a e subjec
o a educed o supe - educed VAT a e. In he Czech Republic, his is he case o he cons uc ion
indus y, especially social housing. Las bu no leas , due o he impo an impac on cash low,
he sys em could ha e nega i e e ec on insol en en i ies.
Ano he ool ha could inspi e he Czech go e nmen o o he Membe S a es is he Poland’s IT
sys em STIR. STIR is able o analyse da a on money ans e s among bank accoun s used by businesses
and de ec o ganized c iminal ac i i ies on he iscal basis. E en i he sys em wo ks ela i ely
au oma ically, he e is some h ea , hough, ha inancial ins i u ions will compensa e he inc ease in
compliance cos s by aising hei own ees.
Based on he esul s o his s udy, he au ho s ecommend an in oduc ion o se e al measu es
agains ax e asion a he same ime, o in a sho ime ame, in o de o mul iply hei e ec i eness.
The u h is ha he ac ual e ec i eness o he measu es can only be assessed e ospec i ely, which is
in ac wha keeps pushing he VAT sys em ou o i s s eady s a e.
Mo eo e , i is ob ious ha COVID-19 will ha e a e y nega i e impac on he economy and will
deepen s a e budge de ici s. Nowadays, ax e ade s ha e mo e oppo uni ies o auds, as ac i i ies
o Tax Adminis a ions ela ed o con ol mechanisms a e limi ed. The EU should uni e and ag ee on
ools in i s igh agains ax e asion ha could help dec ease he all in ax e enues and encou age
sus ainabili y o public budge s.
The u u e esea ch o he au ho s could be ocused on he e ec o COVID-19 on ax e enues
and occu ence o he VAT e asion wi hin he EU.
7. Conclusions
Since public adminis a ion sys ems can unc ion p ope ly only i hey a e capable o collec ing
axes, i is o pa amoun in e es o ha e mechanisms in place ha will e ec i ely es ain oom o ax
aud. This speci ically conce ns he alue added ax, which is by na u e a e y popula ins umen
among law o ende s. Coun ies ha ha e expe ience wi h his kind o law iola ion a e o ced o
adjus hei legisla ion in o de o cu ail such exploi a ion o he legal sys em, al hough he ex en o
unc ionali y o he changes is no easy o iden i y in ad ance, o e en gua an ee, gi en he slyness o
hose who pa icipa e in he shadow economy. The legal adjus men s should he e o e be subjec o
analysis, no only be o e, bu also a e being pu in o use, o see i hey uly ac as a de e en .
This pape seized he oppo uni y o do so in he case o he Czech Republic and Slo akia because
coppe expo om one coun y o ano he is known o ha e been abused by ax c iminals in he pas ,
and also because hose ades showed a sudden and s eep d op in hei his o ical de elopmen ,
coinciden ally a ound he ime when he coun ies we e eadying o launch new legisla i e measu es
o igh ax e asion. This is mainly he eason why he analysis was pe o med in he pape , since i is
e y emp ing o link unad isedly an ab up change in a ime se ies de elopmen o a newly appea ing
Sus ainabili y 2020,12, 4925 20 o 25
ac o —a legisla i e measu e, which a e in his case he VAT con ol s a emen and e e se cha ge
mechanism. The e a e wo p oblems when such a link is has ily es ablished. Fi s ly, i canno be uled
ou ha he ime se ies de elopmen , co e ing he ime pe iod bo h be o e and a e he d op, emained
na u al because o he cha ac e o all he economic ac o s ha no mally a ec i . These ac o s would
no ha e included he legisla i e measu es, and hey would no ha e changed undamen ally hei own
beha iou . Simply pu , i could su ice o u ilize he economic ac o s alone and hei na u al cha ac e ,
adically unchanged, o explain he de elopmen o he coppe ades no ma e how d ama ic i
seemed o be. Secondly, e en i he e is a suspicion ha ci cums ances changed adically, i is no
immedia ely ob ious and gua an eed ha i mus ha e been he legisla i e o go e nmen measu e
ha caused he s eep decline in he coppe ades. I could ha e been one o he economic ac o s.
These a e wo s ong easons why he phenomenon should be analysed in g ea e de ail.
The pape analysed he p oblem, using he heo y o in e en ion ime se ies models
and a b eakdown o undamen al ac o s ha ha e he po en ial o change adically he his o ical
de elopmen o ading habi s. An in e en ion model conside s he idea ha he obse ed se ies
migh ha e ollowed a pa e n o a ce ain poin in ime, which aises suspicion because i is a poin
o ab up change in he se ies, and hen s a ed o shi , e en ually ending up ollowing he same
pa e n on ano he le el. In o de o he model o be mo e able o copy such shi s, a special a iable is
inse ed in i s equa ion. Subsequen ly, he signi icance o he coe icien belonging o he a iable is
es ed s a is ically, i.e., i is es ed whe he he coe icien is ze o o no . I i u ns ou o be ze o, i is
concluded ha he se ies had con inued o ollow he same pa e n a e he ime poin in ques ion.
Since no change in i s cha ac e ook place, i is assumed ha no in e en ion was p esen , as he special
a iable ac s as a swi ch ha e lec s in e e ence. In o de o his heo y o wo k, he model desc ibing
he en i e his o y o he se ies, and con aining he special a iable, mus pass se e al checks in he i s
place. These checks es ablish i s c edibili y. Once he c edibili y is es ablished, i is assumed ha
he model desc ibes well enough he mechanisms go e ning he de elopmen o he se ies. Wha hen
emains is o check, as men ioned, whe he he special a iable is also necessa y o such desc ip ion.
In his ega d, mo e han a hund ed ime se ies models we e ied in he analysis. Th ee o he models
passed he checks s ongly, while wo o hem also did no allow he special a iable o be emo ed.
One model was inconclusi e in his ega d. This is a sound sugges ion ha an ab up change in
he cha ac e o he se ies migh ha e aken place.
Since he esul s o he s a is ical analysis we e clea ly mo e inclined owa ds he conclusion ha
some hing ab up did happen in he beha iou al cha ac e o he se ies, he au ho s ook up he ask
o de ec ing wha had caused his change. We analysed an en i e g oup o ac o s in ol ing majo
economic o ces, da a on coppe expo om o he coun ies and he legisla i e measu es adop ed by
he wo coun ies o de e c iminals om ading in coppe , i he e we e any. Looking a he o icial
da a om s a is ical o ices and in e na ionally ecognized agencies, he e is no meaning in linking
he undamen al economic ac o s, such as coppe p ices, coppe p oduc ion, g oss na ional p oduc s
o exchange a es, o he all ha he coppe expo om he Czech Republic o Slo akia suddenly
and pe manen ly expe ienced a he beginning o 2013. No is i possible o say, based on he da a,
ha o he coun ies ac ed as a eplacemen o he Czech Republic, when i comes o expo ing coppe
o Slo akia, o ha he Czech coppe expo changed di ec ion.
The au ho s conclude ha he only a ional explana ion behind he sudden and p onounced
d op in he coppe expo s can be ound in he wo coun ies’ igh agains ax e asion and hei
co esponding legisla i e measu es. The da a no only sugges ha hese measu es seem o be
unc ioning, bu also e eal ha he coppe ading be ween he wo s a es was p obably no mean o
be eal o a g ea ex en . Al hough he esul s may no seem oo su p ising o some, hey a e da a-d i en
a mo e han simila s udies.
Since he analysed legisla i e measu es ha e he po en ial o be o alue, i is also wo h discussing
how much and in wha o m he Eu opean Union bene i s om hem. The au ho s p o ided ha
discussion in he la e pa s o he ex , poin ing ou ha he cu en ax sys em is no se up in
Sus ainabili y 2020,12, 4925 21 o 25
such a way so as o u ilize he measu es su icien ly, and needs o be imp o ed. We also men ioned
he ad an ages and disad an ages o o he measu es in oduced in o he Membe S a es, in pa icula
he p oposed de ini i e VAT sys em o in acommuni y B2B ansac ions.
Au ho Con ibu ions:
Concep ualiza ion, K.K.; me hodology, F.T.; so wa e, F.T.; alida ion, K.K and F.T.; o mal
analysis, F.T.; in es iga ion, K.K.; esou ces, K.K.; da a cu a ion, F.T.; w i ing—o iginal d a p epa a ion, K.K.
and F.T.; w i ing— e iew and edi ing, K.K. and F.T.; isualiza ion, K.K. and F.T.; supe ision, K.K. and F.T.; p ojec
adminis a ion, K.K. and F.T.; unding acquisi ion, K.K. and F.T. All au ho s ha e ead and ag eed o he published
e sion o he manusc ip .
Funding:
This esea ch was unded by VSB—Technical Uni e si y o Os a a, g an numbe SGS SP2020/10
and SP2020/51.
Con lic s o In e es :
The au ho s decla e no con lic o in e es . The unde s had no ole in he design o he s udy;
in he collec ion, analyses, o in e p e a ion o da a; in he w i ing o he manusc ip , o in he decision o publish
he esul s.
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