Natural resources and the underground economy: A cross-country study in ASEAN using Bayesian approach

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 3 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 42024, olume 27, issue 2, pp. 1–15, DOI: 10.15240/ ul/001/2024-2-001 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, Economics 5 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)