Economics
1
2024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
Na u al esou ces
and he unde g ound economy:
A c oss-coun y s udy in ASEAN
using Bayesian app oach
Thach Ngoc Nguyen1, My Ha Tien Duong2, Diep Van Nguyen3
1 Ho Chi Minh Uni e si y o Banking, Asian Jou nal o Economics and Banking, Vie nam, ORCID: 0000-0001-8822-2633,
[email p o ec ed];
2 Ho Chi Minh Ci y Open Uni e si y, Facul y o Economics and Public Managemen , Vie nam, ORCID: 0000-0001-
8796-4934, my[email p o ec ed];
3 Ho Chi Minh Ci y Open Uni e si y, Facul y o Finance and Banking, Vie nam, ORCID: 0000-0002-5222-2516,
[email p o ec ed] (co esponding au ho ).
Abs ac : The de elopmen o he unde g ound economy can signi ican ly a ec a coun y’s
economic indica o s. Al hough he e ha e been di e en s udies on his phenomenon, many
aspec s o unde g ound ac i i ies emain incomple ely de ined. The e o e, he cu en esea ch
aims o supplemen he exis ing li e a u e by analyzing he link be ween abundan na u al esou ces
and he scope o he unde g ound economy. To accomplish his objec i e, we collec ed panel da a
om en Associa ion o Sou heas Asian Na ions (ASEAN) coun ies du ing he pe iod 1991–2018.
We hen employed he Bayesian eg ession es ima o o look in o he in luence o na u al esou ces
weal h on he scope o he unde g ound sec o . We ound ha he o me can nega i ely and
s ongly a ec he la e in ASEAN coun ies. Tha is, na u al esou ces migh be a blessing a he
han a cu se o economic g ow h and de elopmen in hese coun ies. O he a iables we e ound
o ha e a s ong posi i e ela ionship wi h he unde g ound economy, like ade openness, ax
bu den, size o go e nmen , co up ion, and he global inancial c isis. Meanwhile, GDP g ow h,
u baniza ion, and poli ical s abili y had a s ong nega i e e ec on he size o he unde g ound
economy. These indings p o ide some implica ions o he go e nmen s o ASEAN coun ies
o pe o m app op ia e measu es o con ol he unde g ound economy.
Keywo ds: Na u al esou ces, unde g ound economy, Bayesian app oach, ASEAN.
JEL Classi ica ion: C11, E26, O13.
APA S yle Ci a ion: Nguyen, T. N., Duong, M. H. T., & Nguyen, D. V. (2024). Na u al esou ces
and he unde g ound economy: A c oss-coun y s udy in ASEAN using Bayesian app oach.
E&M Economics and Managemen , 27(2), 1–15. h ps://doi.o g/10.15240/ ul/001/2024-2-001
In oduc ion
The unde g ound economy is a sec ion
o he economy ha is no subjec o ax
decla a ion, and usually in ol es he ade
o goods and se ices paid in cash. The ise
o he unde g ound economy can dis o in-
es men s, inc ease income inequali y, c ea e
un ai compe i ion o o mal en e p ises, educe
he quali y o li e, and ul ima ely hinde eco-
nomic g ow h (A ezzo, 2014; Baklou i & Boujel-
bene, 2020; Ki eenko & Ne zo o a, 2015;
Nguyen & Duong, 2021). Due o he p e alence
and impac o he unde g ound economy, a i-
ous economis s ha e ied o measu e he size
Economics
22024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
and iden i y he de e minan s o his economy
sec o . Un o una ely, many aspec s o he un-
de g ound economy emain incomple ely de-
ined. Capasso and Jappelli (2013) a gue ha
i is di icul o p o ide comple e and a ional
explana ions o why en e p ises and indi idu-
als e ade axes o engage in illegal economic
ac i i ies. One po en ial eason is men ioned
in Alm e al. (2006). No ably, he au ho s s a e
ha axpaye s choose no o comply wi h
i hey belie e hey could bene i om ax e a-
sion. The ob ained bene i s depend on he ine
amoun hey a e subjec o pay i disco -
e ed and he p obabili y o being disco e ed.
The lowe he expec ed penal y (measu ed
in ines) and he p obabili y o being disco e ed
a e, he highe he ax shunning is.
Ne e heless, ax a es may no be
he only sou ce o unde g ound ac i i ies
in ASEAN coun ies. The e a e ample easons
o expec ha he unde g ound economy sec-
o and na u al esou ces dependence a e
ela ed. Fo ins ance, Le Billon (2011, p. 1)
sugges s ha “Coun ies highly dependen
on na u al esou ces a e among he mos se-
e ely a ec ed by he p oblem o illici inancial
lows.” Indeed, Blan on and Peksen (2023)
disco e ha esou ce wind alls can enhance
unde g ound economy ac i i ies. Blan on and
Peksen’s (2023) esul could ekindle he long-
s anding deba e abou whe he abundan
na u al esou ces a e a cu se o a blessing o
a na ion’s economic g ow h and de elopmen .
In e es ingly, So acool (2010) claims ha
Sou heas Asia can a oid he esou ce cu se
hanks o ce ain cha ac e is ics, while o he
economis s belie e ha na u al esou ces a e
one o he mos impo an economic asse s
and hei p esence will help coun ies achie e
a sus ainable g ow h ajec o y (Ba bie ,
2019). I na u al esou ces posi i ely in luence
sus ainable economic g ow h, o i he e icien
exploi a ion o hese esou ces helps p omo e
employmen in he o mal sec o , hey migh
mo i a e indi iduals o pa icipa e in he o -
icial economy, he eby educing he scope
o he unde g ound economy.
Despi e he impo an ole o his economic
sec o and na u al esou ces, he e is e y li le
li e a u e on he e ec o he weal h o na u al
esou ces on he in o mal economy. Blan on
and Peksen (2023) explo e he impac o na u al
esou ces on he unde g ound economy in nu-
me ous coun ies, bu hey do no speci ically
add ess he case o ASEAN, which ep esen s
an impo an economic egion in he wo ld.
In ha con ex , we aim o supplemen he exis -
ing esea ch by in es iga ing he link be ween
he weal h o na u al esou ces and he scope
o he unde g ound economy in ASEAN coun-
ies o e he 1991–2018 pe iod.
Ou pape a emp s o imp o e he unde -
g ound economy li e a u e in h ee ways. Fi s ,
o he bes o ou knowledge, ou pape is among
he i s s udies o empi ically in es iga e he im-
pac o na u al esou ces on he unde g ound
economy in ASEAN coun ies. Acco ding o El-
gin e al. (2021), he unde g ound economy
scope o 10 selec ed Sou heas Asian coun ies
be ween 1991–2018 a ies widely, anging
om less han 13% o g oss domes ic p od-
uc (GDP) in Singapo e up o mo e han 50%
in Thailand and Myanma . He e comes a ques-
ion ha needs o be esol ed: Wha makes
coun ies in he same geog aphical egion ha e
such ma ked di e ences in he unde g ound
economy scope? Second, his pape applies
new es ima es o he in o mal economy p o-
duced by Elgin e al. (2021), gi en un il 2018,
in con as o p e ious s udies. Many an e io
s udies use da a on he unde g ound sec o
de eloped by Medina and Schneide (2019).
In he analysis, we employ bo h es ima es
ypes o Elgin e al. (2021), namely he dynamic
gene al equilib ium (DGE) and he mul iple
indica o s mul iple causes (MIMIC) models,
o es whe he he esul s a e obus . Thi d, his
is he i s pape using he Bayesian app oach,
which has many ad an ages o e he e-
quency app oach, o explo e he link be ween
abundan na u al esou ces and he in o mal
economy. The indings o he s udy can con-
ibu e o he design o mo e e ec i e policies
o con ol unde g ound economic ac i i ies.
The esul s e eal ha na u al esou ces a e
one o he impo an ac o s o he unde g ound
economy in ASEAN. In e es ingly, we ind ha
abundan na u al esou ces educe he scope
o he in o mal economy. Such a inding sug-
ges s ha na u al esou ces migh be a bless-
ing a he han a cu se o ASEAN coun ies.
The es o his pape is gi en as ollows.
Sec ion 1 p esen s a quick li e a u e e iew.
Consequen ly, in sec ion 2, he da ase , mod-
els, and es ima ion s a egies a e p esen ed.
Sec ion 3 depic s and analyzes he esul s.
Finally, sec ion 4 concludes and sugges s some
policy ecommenda ions.
Economics
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2024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
1. Theo e ical backg ound
1.1 Na u al esou ces and
he unde g ound economy
Besides he unde g ound economy, mul-
iple o i s synonyms e ms a e equen ly used
in he ela ed documen s, consis ing o “da k”, “hid-
den”, “uno icial”, “black”, “in o mal”, o “shadow”
economy/a ea. The subsis ence o many e ms
hin s ha i is indeed a ague concep . In ou
s udy, he e ms a e subs i u able and de ined
as an economic ac i i y concealed om public
au ho i ies o mone a y, legal, o ins i u ional mo-
i es (Schneide e al., 2010). Mone a y mo i es
consis o a oiding axes and social secu i y
con ibu ions, legal mo i es consis o dodging
go e nmen bu eauc acy o egula o y bu -
dens, and ins i u ional mo i es consis o high
co up ion, which is o en ela ed o poo quali y
o ins i u ions (Schneide e al., 2010).
S udies on he unde g ound economy
o ked in o h ee undamen al g oups. The i s
g oup ocuses on calcula ing he scope o he
unde g ound economy (Elgin e al., 2021; Me-
dina & Schneide , 2019). The second g oup an-
alyzes he impac o he unde g ound economy
on economic indica o s such as economic
de elopmen and sus ainable de elopmen
(Gha leghi & Jahanshahi, 2020; Nguyen & Du-
ong, 2021). The hi d g oup explo es he ac-
o s ha a ec he scope o he unde g ound
economy (Lyulyo e al., 2021; My e al., 2022).
Na u al esou ces in ol e na u al p oduc s
ha people acqui e om na u e o sa is y hei
needs and he ou comes o human ac i i ies im-
pac ing hem (Wang e al., 2021). Al hough he e
is much esea ch on he a ini y be ween abun-
dan na u al esou ces and economic g ow h o
de elopmen , he linkage be ween he abundan
na u al esou ces and he scope o he unde -
g ound economy is a ely men ioned.
Blan on and Peksen (2023) use na u al
esou ces en s as a subs i u e o na u al
esou ces e enue and ind ha he mo e
abundan he na u al esou ces o a coun y
a e, he la ge he scope o he unde g ound
economy is. This is because e enues om
na u al esou ces alloca e skewed p oduc ion
capi al ac oss sec o s o he economy (Eb-
eke e al., 2015). Simul aneously, inc eased
in es men in na u al esou ces will cause
damage o he poo , and coun ies ha in es
less in human esou ces o labo -in ensi e in-
dus ies a e mo e inclined o employ common
labo (Gyl ason, 2001). Mo eo e , he absence
o anspa ency ega ding esou ce en s and
he poo accoun abili y in he way hese esou c-
es a e managed (Vadlamanna i & De Soysa,
2016) can acili a e he c ea ion o illegal en -
seeking. Inc eased e enues om esou ces
end o aise he scope o he in o mal economy
because hey ha e he e ec o “pushing”
labo ou o he o ice a ea and c ea ing mo e
en -seeking apa om he o icial sec o . Wi h
hese a gumen s, we sugges a posi i e e ec
o na u al esou ces on he scope o he unde -
g ound economy in ASEAN coun ies. The e-
o e, we cons uc he hypo hesis below:
H1: The abundan na u al esou ces posi-
i ely a ec he scope o he unde g ound eco-
nomy in ASEAN.
1.2 O he a iables and
he unde g ound economy
Focusing on he in luence o he ule o law and
economic g ow h on he shadow economy, Lu-
ong e al. (2020) explo e he impac o econom-
ic g ow h on he size o he shadow economy
in 18 ansi ion coun ies using he gene alized
me hod o momen s (GMM) echnique. The au-
ho s es ablish ha economic g ow h dec eases
he ac i i ies o shadow economies. In Sou h-
eas Asia, My e al. (2024) assess he nexus
be ween he inclusion o LGBT people and
he shadow economy h ough he lens o Bayes-
ian es ima ion echniques. The conclusion
om he s udy sugges s ha economic g ow h
educes he size o he shadow economy. Fu -
he mo e, Blan on and Peksen (2023) es ablish
a nega i e ela ionship be ween GDP pe cap-
i a and he shadow economy, hus sugges ing
ha economic g ow h lessens he ac i i ies
o he shadow economy. Simila ly, Blan on and
Peksen (2021) conclude ha an inc ease in GDP
will s op he expansion o he shadow economy
in 120 coun ies o he pe iod 1985–2012. Many
s udies also con i m he nega i e ela ionship be-
ween economic g ow h and he size o he da k
economy (Lyulyo e al., 2021; My e al., 2022;
Sahnoun & Abdennadhe , 2019; Siddik e al.,
2022; Thach e al., 2022).
Lyulyo e al. (2021) examine he d i -
e s o shadow economies wi hin ansi ion
economies. Findings om he s udy show
ha an inc ease in ax le el by 10% inc eases
he shadow economy by 1%. Duong e al.
(2021) also submi ha he ax bu den con ib-
u ed o inc easing he scale o unde g ound
economic ac i i ies in BRICS coun ies du ing
Economics
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1995 and 2014. Using Bayesian eg ession,
My e al. (2022) in es iga e he in luence
o ou ism and o he a iables on he shadow
economy in ASEAN coun ies. The s udy’s
ou come sugges s ha ou ism and ax bu -
den a iables inc ease he shadow economy.
Simila ly, A sić e al. (2015) and Sahnoun and
Abdennadhe (2019) conclude ha he size
o he ax bu den is one o he undamen al
ac o s de e mining ax e asion as well as pa -
icipa ion in he unde g ound economy.
Focusing on 18 Cen al Eas e n Eu opean
and o me So ie Union coun ies, Ghosh and
Paul (2008) documen ha u baniza ion in-
c eases he scale o he unde g ound economy.
Meanwhile, Acos a-González e al. (2014) es-
ablish a nega i e ela ionship be ween he u -
ban popula ion and he unde g ound economy,
hus sugges ing ha u baniza ion lessens
ac i i ies in he unde g ound economy.
Sahnoun and Abdennadhe (2019) ex-
amine he link be ween poli ical s abili y and
he unde g ound economy in 38 de eloping and
40 de eloped coun ies o e he 2000–2015 pe-
iod. Findings om he s udy show ha a nega-
i e ela ionship exis s be ween poli ical s abili y
and he unde g ound economy. Siddik e al.
(2022) submi ha poli ical s abili y con ibu ed
o educing he size o he shadow economy
in he Bay o Bengal Ini ia i e o Mul i-Sec o al
Technical and Economic Coope a ion Coun ies
(BIMSTEC) du ing 1998 and 2015. Simila ly,
Razmi and Jamalmanesh (2014) conclude ha
he mo e poli ically s able coun ies will ha e
a smalle shadow economy.
Fo go e nmen size, Ghosh and Paul
(2008) documen ha go e nmen size, mea-
su ed by gene al go e nmen inal consump ion
expendi u e, inc eases he shadow economy
in 18 Cen al and Eas e n Eu opean and o -
me So ie Union coun ies. My e al. (2022)
conclude ha go e nmen size and shadow
economy we e complemen a y in ASEAN
coun ies om 1999 o 2017. Sahnoun and
Abdennadhe (2019) ound a posi i e e ec
o he size o go e nmen spending on he un-
de g ound economy in de eloped coun ies.
Howe e , Siddik e al. (2022), using ixed-e ec
o andom-e ec in es iga ions o a sample
pe iod o 1998–2015, sugges ha go e nmen
spending has signi ican nega i e e ec s on
he shadow economy. Simila ly, My e al. (2024)
ound ha go e nmen spending weakens ac-
i i ies in he unde g ound economy.
In ASEAN na ions, My e al. (2022) as-
sess he nexus be ween in e na ional ade
and he shadow economy using Bayesian
es ima ion echniques. The conclusion om
he s udy sugges s ha ade openness de-
c eases he scale o he unde g ound economy.
Simila ly, Blan on and Peksen (2021), Duong
e al. (2021), and Siddik e al. (2022) es ablish
a nega i e ela ionship be ween in e na ional
ade and he unde g ound economy, hus sug-
ges ing ha in e na ional ade lessens he size
o he shadow economy. Con a y o he conclu-
sion abo e, Ghosh and Paul (2008) conclude
ha in e na ional ade by measu e o pe cen
o ade o e GDP s eng hens he shadow
economy in 18 Cen al Eas e n Eu opean
and o me So ie Union coun ies. Simila ly,
Blan on and Peksen (2023) conclude ha ade
openness has a posi i e ela ionship wi h
shadow economic ac i i ies.
Razmi and Jamalmanesh (2014) conside
he in luence o poli ical indica o s on he un-
de g ound economies o 34 coun ies using
da a o 8 yea s om 2000–2007. The wo
au ho s’ submission e eals ha be e go e n-
men con ol o co up ion dec eases he size
o he unde g ound economy. Simila ly, My
e al. (2022) conclude ha high co up ion will
encou age indi iduals and businesses o en-
gage in illegal ac i i ies in ASEAN coun ies.
Focusing on BRICS coun ies, Duong e al.
(2021) documen ha con ol o co up ion
aba es he unde g ound economy. Nume -
ous s udies (Acos a-González e al., 2014;
Blan on & Peksen, 2021, 2023; Luong e al.,
2020; Sahnoun & Abdennadhe , 2019; Thach
e al., 2022) ha e con i med he nega i e
ela ionship be ween co up ion con ol and
he unde g ound economy.
Finally, we examine he impac o he global
inancial c isis (GFC) on he size o he shadow
economy. Using andom e ec s, ixed e ec s,
and GMM o a sample pe iod o 1970–2011,
Blan on and Peksen (2021) sugges ha c ises
s eng hen he size o he shadow economy
in 143 coun ies. Simila ly, Siddik e al. (2022)
ound ha GFC s eng hens he shadow eco-
nomy in BIMSTEC coun ies.
2. Resea ch me hodology
2.1 Da ase
In his s udy, we explo e he e ec o na u al
esou ces on he unde g ound economy. Using
a seconda y da ase a ailable om 1991 o 2018,
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2024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
we co e en Sou heas Asian coun ies, includ-
ing B unei, Cambodia, Indonesia, Laos, Malay-
sia, Myanma , Philippines, Singapo e, Thailand,
and Vie nam, o a ain he s udy objec i es.
The dependen a iable is he scope
o he unde g ound economy. The a iable is
exp essed as a pe cen age o g oss domes ic
p oduc (GDP), showing he expansion o he un-
de g ound economy compa ed o he o mal
economy. I is de i ed om he wo k o Elgin
e al. (2021), in which hey used an es ima ion
me hod based on a DGE model as well as
an es ima e based on a MIMIC model o e alu-
a e he scope o he unde g ound ac i i ies.
The e o e, he scope o he unde g ound
economy will be measu ed by wo me hods, in-
cluding he scope o he unde g ound economy
es ima ed based on he dynamic gene al
equilib ium (DGE) model (undecon_DGE) and
he scope o he unde g ound economy es i-
ma ed based on he mul iple indica o s mul iple
causes (MIMIC) model (undecon_MIMIC).
Na u al esou ces (ln_na u es), ou main
a iable, a e conside ed an independen a i-
able since we aim o explo e he ela ionship
be ween na u al esou ces and he scope
o he unde g ound economy. We employ da a
on na u al esou ces en s om he Wo ld Go -
e nance Indica o s (WDI) da ase o he Wo ld
Bank. The da a comp ises oil, coal (ha d and
so ), na u al gas, o es , and mine al en s.
Following Blan on and Peksen (2023), we use
he na u al log o he na u al esou ces en s
o adjus he skewness o he da a.
Th ee ypes o con ol a iables a e used
o sepa a e he e ec o he main a iable
Va iables Legend Measu emen Sou ce
Dependen a iable
Unde g ound
economy 1 undecon_DGE DGE es ima es o unde g ound ou pu
(% o o icial GDP) Elgin e al. (2021)
Unde g ound
economy 2 undecon_MIMIC MIMIC es ima es o unde g ound ou pu
(% o o icial GDP) Elgin e al. (2021)
In e es a iable
Na u al
esou ces ln_na u es Whole na u al esou ces en s
(% o o icial GDP) WDI da abase
Con ol a iable
GDP g ow h GDPg GDP g ow h a e (annual %) WDI da abase
Tax bu den ax To al ax bu den (% o o icial GDP) He i age
Founda ion
U baniza ion u ban U baniza ion le el (u ban popula ion/
o al popula ion) WDI da abase
Poli ical s abili y polis ab Ranges om −2.5 (leas s abili y) o 2.5
(mos s abili y) WGI da abase
Size
o go e nmen go Gene al go e nmen inal consump ion
expendi u e (% o o icial GDP) WDI da abase
T ade
openness ln_open Volume o impo s plus expo s
(% o o icial GDP) WDI da abase
Co up ion co up Rescaled CPI om 0 (leas co up ) o 100
(mos co up )
T anspa ency
In e na ional
Global inancial
c isis GFC GFC is 1 o he global inancial c isis, and
0 o he wise
Blan on and
Peksen (2021),
Siddik e al. (2022)
Sou ce: own
Tab. 1: De ini ions and sou ces o a iables

Economics
62024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
(ln_na u es). The i s ype includes mac o-
economic a iables, such as he GDP an-
nual g ow h a e (GDPg ), ax bu den ( ax), and
he global inancial c isis (GFC). The second
in ol es ins i u ional ac o s, such as poli ical
s abili y (polis ab), co up ion (co up), and
he size o he go e nmen (go ). The hi d
ype ocuses on a iables such as comme cial
openness (ln_open), and u baniza ion (u ban).
GDPg , ln_open, go , and u ban a e collec ed
om he WDI da abase. The polis ab da a is
collec ed om he Wo ld Go e nance Indica o s
(WGI) da ase o he Wo ld Bank. The co up-
ion pe cep ions index (CPI) p o ided by T ans-
pa ency In e na ional will be used o measu e
co up ion (co up). Fo consis ency be ween
he da a, he da a om 1995 o 2011 is mul i-
plied by en so ha hey can equa e o he ange
cu en ly used by T anspa ency In e na ional
om 0 o 100. The eby, o simplici y and ease
o p esen a ion, he CPI is con e ed o a scale
om 0 (leas co up ) o 100 (mos co up ). Tax
bu den ( ax) da a is ob ained om he He i age
Founda ion. Finally, he GFC is a dummy a i-
able whose alue is 1 i i deno es he inancial
c isis o 2007–2008, and 0 o he wise.
De ailed in o ma ion abou he a iables
is p esen ed in Tab. 1. Whole a iables a e
ea ed in pe cen ages. The excep ions a e
ln_na u es and ln_open, which appea in hei
na u al loga i hm o m, and polis ab and co up,
exp essed as an index.
2.2 The models
Because he aim o his s udy is o del e in o
whe he abundan na u al esou ces impac
he scope o he uno icial economy in ASEAN,
by using he s udy conduc ed by Blan on
and Peksen (2023), we assign a base model
as ollows:
undeconi = β0 + βi ln_na u es +
+ βi Xi + εi (1)
whe e: he dependen a iable is he scope
o he unde g ound economy (undecon); in e -
es a iable is na u al esou ces (ln_na u es);
β is he co esponding coe icien o measu e i s
in luence on he scope o he unde g ound eco-
nomy; X is he ma ix o eigh con ol a iables,
ha is, he GDP annual pe cen age g ow h
a e (GDPg ), ax bu den ( ax), global inancial
c isis (GFC), size o go e nmen (go ), poli ical
s abili y (polis ab), co up ion (co up), ade
openness (ln_open), u baniza ion (u ban); and
ε is he e o e m.
Con ol a iables we e chosen based
on p e ious s udies by Acos a-González e al.
(2014), A sić e al. (2015), Blan on and Peksen
(2021, 2023), Duong e al. (2021), Ghosh
and Paul (2008), Luong e al. (2020), Lyulyo
e al. (2021), My e al. (2022), My e al. (2024),
Razmi and Jamalmanesh (2014), Sahnoun and
Abdennadhe (2019), Siddik e al. (2022), and
Thach e al. (2022). In his esea ch, we use
S a a e sion 17.0 o pe o m Bayesian eg es-
sion es ima es and ela ed analyses.
2.3 Es ima ion s a egies
Unlike p e ious s udies ha used equen-
is app oach, his s udy applies he Bayes-
ian app oach. Bayesian s a is ics has many
ad an ages o e he equency app oach.
The i s bene i o Bayesian s a is ics is ha
e idence can be con inuously compu ed and
upda ed as da a becomes a ailable (Oanh
e al., 2023; Van De Schoo & Depaoli, 2014;
Wagenmake s e al., 2017). This p ocess is
possible because all in e ences in Bayesian
s a is ics a e based on ac ual obse ed da a.
This is a majo ad an age o Bayesian o e e-
quen is me hods because in e ence does no
depend on da a ha has ne e been obse ed.
Second, Wagenmake s e al. (2017) no e ha
in con as o equen is s a is ics, Bayesian
in e ence is logically cohe en and in e nally
consis en . Speci ically, he Bayesian app oach
enables es e s o explici ly epo he p obabil-
i y o a sys em ob aining he desi ed ou come
by using pos e io p obabili y. This in e p e abili y
is in di ec con as o he equen is iew which
esul s in indi ec measu es o sys em pe o -
mance wi h mo e eso e ic de ini ions, such as
p- alues o con idence in e als. Thi d, Bayesian
eg ession demons a es supe io pe o mance
compa ed o equency school eg ession
models in scena ios wi h limi ed sample sizes
(K uschke e al., 2012, Oanh e al., 2023). This
app oach o e s accu a e and e idence-based
condi ional conclusions ha a e no in luenced
by asymp o ic app oxima ions. The p ocess
o small sample in e ence ollows a simila p o-
cedu e as ha o la ge sample in e ence. The e-
o e, he a ailabili y o us wo hy p io s enables
he a ainmen o meaning ul Bayesian es ima es
(Mioče ić e al., 2017). Mo eo e , Van De Schoo
and Depaoli (2014) s a e ha ano he impo an
ad an age o Bayesian s a is ics is ha hey
Economics
7
2024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
gi e a p obabili y dis ibu ion o he hypo h-
eses. Bayesian in e ence le s you igu e ou
whole p obabili y dis ibu ions o e a ange
o pa ame e alues. This is done by using
Bayes’ heo em o se p io dis ibu ions o e
he pa ame e s and hen changing hem based
on new da a. This esul s in pos e io dis ibu-
ions ha mi o he upda ed belie s abou
he pa ame e s gi en he da a. These pos e io
dis ibu ions can hen be used o in e ence,
p edic ion, and unce ain quan i ica ion. Las ly,
s anda d s a is ics models canno be used
o p edic some complex models (K uschke
e al., 2012). When models a e p e y compli-
ca ed, nume ical in eg a ion is o en needed
o ge numbe s based on maximum likelihood
es ima ion. This me hod is impossible o use
because i equi es es ima ing he maximum
likelihood o e a lo o dimensions. The e o e,
al e na i e es ima ion ools a e needed. Bayes-
ian es ima ion can also handle some commonly
encoun e ed p oblems in o hodox s a is ics.
Bayesian analysis is based on he Bayes
ule (Bayes, 1991), which unde pins Bayesian
s a is ical in e ences:
p(θ│X) = p(X│θ)p(θ)⁄p(X) (2)
whe e: p(θ│X) is desi ed pos e io dis ibu ion;
p(X│θ) is likelihood; p(θ) is p io in o ma ion;
and p(X) is no maliza ion cons an .
The Bayesian linea eg ession model
o he unde g ound economy (y) is gi en
in he ollowing o m:
yi ~ N(μi ,τ) (3)
whe e: μi = Xi
' β (i = 1, …, n) and τ = 1⁄σ2.
The p io dis ibu ion is de e mined as
ollows:
(4)
whe e: βj ~ N(μβj , Cj
2) and τ ~ gamma(a, b);
yi is he unde g ound economy; Xi
' ep esen s
he ec o o explana o y a iables; β deno es
he coe icien o he pa ame e es ima es;
μi is he mean o he es ima ed eg ession coe -
icien s, and 1/σ2 is he p ecision (𝜏).
Using a no mal dis ibu ion wi h subs an-
ial a iance, we apply a non-in o ma i e
p io o each unknown pa ame e in he
model (Koshele a e al., 2021). The p io
mean o 𝜏 is 1, and he a iance is 100,
so a = b = 0.01.
Fo he likelihood unc ions o he coe -
icien s, we assume ha he pa ame e s ha e
pa ame e s o no mal dis ibu ions de i ed
om Equa ion (1). Finally, we apply he Ma -
ko Chain Mon e Ca lo (MCMC) echnique
and Gibbs sampling algo i hm o app oach
he co esponding pos e io dis ibu ions o he
pa ame e s.
Fo he simula ed scena ios, we used wo
chains wi h an adap phase o 12,500 i e a ions,
ollowed by a bu n-in pe iod o 2,500 i e a ions,
and inally, he pos e io dis ibu ion was d awn
om he nex 10,000 i e a ions.
In Bayesian analysis, he con e gence
o MCMC is one o he mos impo an s eps.
Unde ce ain condi ions, MCMC algo i hms will
ake a sample om he desi ed pos e io dis ibu-
ion a e i has con e ged o he balanced s a e.
Tha is, a an equilib ium s a e, he dis ibu ion
o samples om he chains mus be he same
ega dless o he ini ial alue o he chain.
To es he con e gence o MCMC, we calcu-
la e he Rc alue o Gelman and Rubin (1992);
i he diagnos ic Rc alue is g ea e han 1.2 o
any model pa ame e , no con e gence is eco d-
ed. Besides, e ec i e sample size (ESS) is also
conside ed when de e mining whe he MCMC
con e ges o no . ESS measu es he deg ee
o au oco ela ion in samples ha inc ease un-
ce ain y compa ed o an independen sample.
K uschke (2015) a gues ha he close he sam-
pling e iciency is o 1, he be e i is.
3. Resul s and discussion
3.1 Desc ip i e s a is ics
The s a is ical summa y is p esen ed in Tab. 2,
while Tab. 3 summa izes desc ip i e s a is ics
o whole a iables o en na ions in he sample.
Fo he dependen a iable (undecon), he mean
o he unde g ound economy scope is 31.91
(undecon_DGE) o 33.06 (undecon_MIMIC), in-
dica ing ha ASEAN coun ies ha e a signi ican
scope o he unde g ound economy. Besides,
he s anda d de ia ion is 13.77 (undecon_DGE)
o 13.73 (undecon_MIMIC), which explains
a huge di e ence in he scope o he unde g ound
economy be ween hese Sou heas Asian coun-
ies. Singapo e has he lowes scope o he un-
de g ound economy o 12.46 (undecon_DGE)
o 12.62 (undecon_MIMIC); he coun y wi h
he highes scope o he unde g ound economy
Economics
82024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
is Thailand (undecon_DGE is 48.70) o Myan-
ma (undecon_MIMIC is 50.74). Fo he main
independen a iable o in e es , we ind ha
na u al esou ces (ln_na u es) ha e an a e -
age o 7.25 by s anda d de ia ions o 7.08,
which alludes o a la ge di e ence in na u al
esou ces in en coun ies in he s udy sample.
B unei has he mos abundan na u al esou c-
es (23.14) in ASEAN coun ies, while Singapo e
has almos no na u al esou ces, mos o which
ha e o be impo ed. We obse e an a e age
annual GDP g ow h o 5.49 by s anda d de-
ia ions o 4.29. Myanma anks i s in e ms
o he a e age annual GDP g ow h a e (8.73),
while B unei achie es he lowes a e age alue
o 1.25. Fo he ax bu den ( ax), Cambodia
has he highes le el o he ax bu den (91.12),
and Vie nam has he lowes ax bu den (67.14).
Singapo e is a coun y wi h a apid u baniza ion
a e, while Cambodia has he lowes u baniza-
ion a e in he egion (19.41). Fo go e nmen
size (go ), we ind a mean o 11.53, by s anda d
Va iable Obs. Mean S d. de . Min Max
Undecon_DGE 278 31.91 13.77 11.29 65.75
Undecon_MIMIC 260 33.06 13.73 11.89 53.78
Ln_na u es 269 7.25 7.08 0.00 35.27
GDPg 277 5.49 4.29 −34.81 14.53
Tax 217 79.20 10.58 32.20 91.70
U ban 280 46.70 24.72 15.78 100.00
Go 248 11.53 5.57 3.46 29.87
Polis ab 200 −0.17 0.94 −2.09 1.62
Ln_open 267 125.31 90.89 0.17 437.33
Co up 194 61.17 22.04 6.00 87.00
Sou ce: own
Coun ies Undecon_
DGE
Undecon_
MIMIC Ln_na u es GDPg Tax U ban Go Polis ab Ln_open Co up
B unei 30.70 31.04 23.14 1.25 87.08 72.65 23.76 1.18 102.71 42.49
Cambodia 47.17 48.58 3.49 6.01 91.12 19.41 5.34 −0.37 110.80 79.28
Indonesia 18.37 19.31 6.72 4.86 80.17 44.80 8.36 −1.08 54.79 73.69
Laos 30.20 30.16 8.22 6.87 68.88 25.56 10.60 −0.05 73.33 74.56
Malaysia 30.52 31.45 11.09 5.73 81.67 65.14 12.24 0.22 173.71 50.49
Myanma 46.49 50.74 9.06 8.73 82.29 27.89 17.14 −1.15 19.68 80.88
Philippines 38.35 41.09 1.07 4.58 76.77 46.12 10.66 −1.24 80.89 70.48
Singapo e 12.46 12.62 0.00 5.87 87.49 100.00 9.74 1.24 354.19 10.13
Thailand 48.70 50.41 1.84 4.22 76.29 37.98 13.87 −0.71 114.52 65.85
Vie nam 16.06 15.18 8.14 6.84 67.14 27.43 6.58 0.25 129.80 71.98
To al 31.91 33.06 7.25 5.49 79.20 46.70 11.53 −0.17 125.31 61.17
Sou ce: own
Tab. 2: Desc ip i e s a is ics b ie
Tab. 3: Na ion a e age alue o a iables in he model
Economics
9
2024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001
de ia ions o 5.57. B unei has he highes a e -
age alue o go e nmen size, while Cambodia
has he lowes median alue o 5.34. Singapo e
has he highes a e age poli ical s abili y, while
he Philippines has he lowes .
Fu he mo e, we obse e ha he mean
o ade openness (ln_open) is 125.31 wi h a s an-
da d de ia ion o 90.89, which shows a huge
di e ence in he ade openness o ASEAN
coun ies. Singapo e achie es he highes alue,
while Myanma achie es he lowes . In gene al,
ASEAN coun ies ha e a ela i ely high le el
o co up ion (61.17), Singapo e has he lowes
le el o co up ion (10.13), and Myanma has
he highes le el o co up ion among hese
Sou heas Asia na ions (80.88).
3.2 Baseline es ima ions
To epo p elimina y es ima es, we exhibi
he pos e io mean o he pa ame e s and
a 95%-c edible in e al, which con ains he pa-
ame e o in e es wi h a ce ain p obabili y,
in Tab. 4. I a pa icula pa ame e has a posi i e
(nega i e) pos e io mean and he p obabili y
o i s posi i e (nega i e) e ec in he 95%-c edi-
ble in e al is g ea e han 50%, i is a ed o cause
a s ongly posi i e (s ongly nega i e) impac .
Fi s o all, we e alua e he deg ee o con-
e gence o MCMCs when pe o ming Bayesian
eg ession. The deg ee o con e gence is con-
side ed h ough Rc and ESS alues. In Tab. 4,
ou esul s e eal ha he maximum Rc alue
o Gelman-Rubin diagnos ics is 1.00034, less
Independen
a iables Pos e io mean P obabili y
o mean (%) ESS min Rc max
Ln_na u es −0.75050 95.9 1.00000 1.00002
[−1.59378; 0.09589]
GDPg −0.31934 91.9 1.00000 0.99998
[−0.78962; 0.15264]
Ln_open 1.36011 96.6 0.96000 1.00006
[−0.08979; 2.80957]
Tax 0.22749 98.4 0.99360 1.00000
[0.02453; 0.43009]
U ban −0.27644 100.0 0.97690 1.00009
[−0.41846; −0.13434]
Go 1.17990 100.0 1.00000 1.00007
[0.77755; 1.58590]
Polis ab −1.77860 98.5 0.96570 1.00005
[−3.37112; −0.19537]
Co up 0.09457 86.8 0.98260 0.99999
[−0.07544; 0.26606]
GFC 0.40241 66.6 0.98770 0.99998
[−1.41455; 2.24339]
Cons an 0.01638 50.8 0.99670 1.00002
[−1.95807; 1.96093]
Va iance 94.27232 – 0.85710 1.00034
[74.7164; 118.8254]
No e: 95% c edible in e al in b acke s; ESS o e ec i e sample size and Rc is Gelman-Rubin s a is ic.
Sou ce: own
Tab. 4: Bayesian es ima ion o na u al esou ces on he unde g ound economy
(dependen a iable: undecon_DGE)