Quantifying the Economic Development Dynamics of a Country Based on the Lorenz Curve

55 1, XXIV, 2021 Economics DOI: 10.15240/ ul/001/2021-1-004 QUANTIFYING THE ECONOMIC DEVELOPMENT DYNAMICS OF A COUNTRY BASED ON THE LORENZ CURVE Romualdas Gine ičius1, Joanicjusz Naza ko2, Daino a Ged ilai ė3, Zdzisława Dacko-Pikiewicz4 1 Vilnius Gediminas Technical Uni e si y, Facul y o Business Managemen , Ins i u e o Dynamic Managemen , Li huania, ORCID: 0000-0003-2067-4398, [email p o ec ed]; 2 Bialys ok Uni e si y o Technology, Facul y o Enginee ing Managemen , Poland, ORCID: 0000-0002-0236-2334, [email p o ec ed]; 3 Vilniaus Kolegija/Uni e si y o Applied Sciences, Facul y o Economics, Depa men o Finance, Li huania, ORCID: 000-0001-5813-0607, [email p o ec ed]; 4 WSB Uni e si y, Facul y o Applied Sciences, Poland, ORCID: 0000-0003-4542-5574, [email p o ec ed]. Abs ac : The wel a e o a coun y depends on i s economic de elopmen . In o de o ha e he impac on i , we should ha e a possibili y o quan i a i ely assess i s si ua ion a he desi ed poin in ime. Economic de elopmen , as a mul i ace ed and complex phenomenon, is e lec ed in wo dimensions – in ensi y and uni o mi y. These men ioned abo e can be iewed as pa ial indica o s o dynamics. Two main app oaches o measu ing de elopmen uni o mi y can be dis inguished. In one o he cases, i is measu ed on he basis o an index ha includes he main esul s o he coun y’s economic de elopmen . In he o he case, he alues o he indica o s e lec ing all he essen ial de elopmen ac ions a e combined in one app op ia e way. F om a scien i ic poin o iew, he second app oach is mo e accu a e as i allows o a be e assessmen o he complex na u e o a coun y’s economic de elopmen . On he o he hand, i s applica ion oday is s ill p oblema ic due o he ac ha he models o his di e in e ms o bo h he numbe and composi ion o indica o s. Fo his eason, i is no possible o compa e coun ies. The e o e, in in e na ional p ac ice, he economic de elopmen o coun ies is measu ed by g oss domes ic p oduc pe capi a (GDP). Based on GDP indica o , he me hod o he measu emen o uni o mi y is p oposed and he essence o which is he a io o he leng h o he ideal ajec o y o he de elopmen du ing he pe iod unde e iew o he leng h o he ac ual ajec o y. Wi hou uling ou he app op ia eness o such an app oach o assessing de elopmen uni o mi y, i makes sense o look o al e na i e me hods. In his sense, me hods ha allow assessmen o he ex en o luc ua ions o he phenomenon unde conside a ion as an essen ial ea u e o de elopmen dynamics a e sui able. These include he Gini coe icien , which is de e mined om he Lo enz cu e. Keywo ds: Coun y economic de elopmen , quan i ica ion o dynamics o economic de elopmen , Gini coe icien , Lo enz cu e. JEL Classi ica ion: O1, O11. APA S yle Ci a ion: Gine ičius, R., Naza ko, J., Ged ilai ė, D., & Dacko-Pikiewicz, Z. (2020). Quan i ying he Economic De elopmen Dynamics o a Coun y Based on he Lo enz Cu e. E&M Economics and Managemen , 24(1), 55–65. h ps://doi.o g/10.15240/ ul/001/2021-1-004 In oduc ion Today ma ke playe s a all le els, om business ope a o s o coun ies, s i e o be compe i i e. This aspi a ion is no passi e, and is no only abou main aining cu en posi ions. As a esul o he global economic de elopmen o he wo ld, he g ow h o global ma ke s o ces pa icula coun ies o inc ease he economic scale o he economic g ow h, o he wise hey will lose hei posi ions. The pu sui o 56 2021, XXIV, 1 Economics an inc easing sha e o in e na ional ma ke s becomes he basis o a coun y’s compe i i e capaci y. Only by keeping pace wi h he g ow h o he single ma ke wa an y ha hey emain compe i i e. The e o e, de elopmen becomes a hallma k o compe i i eness. In his con ex , i is impo an o bo h science and p ac ice o ully analyse he phenomenon o economic de elopmen . The de elopmen o any p ocess can be cha ac e ized by wo cha ac e is ics – i s in ensi y and i s uni o mi y (Gine ičius e al., 2018). In ensi y o de elopmen is he a e o de elopmen g ow h o e he pe iod conside ed, exp essed, o example, in yea s. S eady de elopmen eads as luc ua ions in he ex en o de elopmen o e he ime pe iods conside ed. These wo dimensions can be seen as sub-indica o s o he o e all de elopmen p ocess. The i s indica o e lec s upon he quan i a i e side o he de elopmen p ocess, and he second indica o s e lec s upon he quali a i e side. The de elopmen p ocess as a whole is e lec ed by i s dynamics, which combines bo h o he abo e men ioned indica o s. I shows he ex en and ype o de elopmen changes ha ha e aken place o e he pe iod unde e iew. The essence o dynamics as a phenomenon is exp essed by he ollowing synonyms o his e m in in e na ional dic iona ies: sus ainable, s eady, esilien , s able, immo able, solid, immu able, du able, pe manen , se led, long-las ing, e en, e c. This abundance o unde s anding o dynamics is in eg a ed by he wo dimensions men ioned abo e – de elopmen in ensi y and de elopmen con inui y. In he scien i ic li e a u e a emp s o quan i y his phenomenon can be me (Gine ičius e al., 2018). Based on he me hodology p esen ed in his s udy, he dynamics o economic de elopmen in some EU coun ies we e de e mined. This me hodology, which is e e ed o as he MDD me hod, p o ides o he in eg a ion o uni o mi y indica o o he de elopmen wi h i s in ensi y indica o . Uni o mi y is de ined as he a io o he alue o he pe iod unde conside a ion o he o al leng h o he ac ual de elopmen ajec o y: (1) whe e DT is he indica o o economic de elopmen T o e he pe iod unde conside a ion, N is he du a ion o he pe iod unde conside a ion e.g. yea s; pi is he change in de elopmen o e he ime pe iod i (yea ) o he ime span unde e iew; n is he numbe o ime pe iods (i = 1, n) o he pe iod unde conside a ion T. The in ensi y o he de elopmen shall be de e mined as ollows: (2) whe e Kp T is he in ensi y indica o o he coun y’s economic de elopmen o e he pe iod T unde conside a ion; Q T is he signi icance o economic de elopmen a he end o pe iod T, Qb T is he signi icance o economic de elopmen a beginning o pe iod T. The p ocess o economic de elopmen o socio-economic sys ems (SES) is a he mul i- ace ed, complex and ambiguous, and i makes sense o look o o he ways o quan i y i s dynamics. 1. Possibili ies o Quan i ying Sus ainabili yo Coun y’s EconomicDe elopmen The challenge posed – o quan i y he dynamics o he coun y’s economic de elopmen – equi es wo ques ions o be answe ed. Fi s , which p incipled models a e sui able o quan i ying he in ensi y and con inui y o he SES de elopmen p ocess; secondly, wha indica o o indica o s can be used o measu e hese sub-indica o s. The measu e o he in ensi y o economic de elopmen o a coun y can be aken as he alue exp essed by o mula (2). The de elopmen consis ency indica o can be o mula ed wi h he ollowing equi emen s: i mus be easy o unde s and, he in o ma ion needed o he calcula ions mus be easily accessible, and, mos impo an ly, i mus allow compa isons be ween en i ies a any le el: economy o coun ies, egions, coun ies as a whole, g oup o coun ies, e c. The economic de elopmen o he coun ies will be used o es he adequacy o he homogenei y indica o p oposed in his s udy. The analysis o li e a u e sou ces ha examine, measu e and compa e his phenomenon highligh s wo p incipal possibili ies. In one 57 1, XXIV, 2021 Economics case i e e s o GDP pe capi a in a e i o ial uni . I is conside ed o be a eliable indica o o success, e lec ing upon he le el o economic de elopmen achie ed in he coun y (Cha san, 2013; Čiegis e al., 2010; Bolcá o á & Kološ a, 2015; Babu & Da a, 2015). O he wise, he economic de elopmen o he analyzed objec s, usually coun ies, o hei egions, is e alua ed elying upon one agg ega e alue combining a la ge numbe o pa ial indica o s, which in he au ho s’ opinion e lec upon he essen ial aspec s o economic de elopmen . Recen ly, hese me hods ha e been inc easingly used o quan i y phenomena o all kinds. Impo ance o indica o s a ailable on an equal basis o de e mined by pee e iew (Song e al., 2017; Tu skis, 2018; Tu skis e al., 2017; Boggia & Co ina, 2010; P asce ic & P asce ic, 2017). We may conside ha mul i-c i e ia assessmen o economic de elopmen is mo e accu a e compa ed o GDP pe capi a, because enla gemen i sel is a complex p ocess ha mani es s i sel in many aspec s. Fo malizing hem and exp essing hem as indica o s allows a mo e complex e alua ion o he phenomenon unde conside a ion. On he o he hand, he possibili ies o applying his p omising me hod, o example o compa ing coun ies, a e limi ed by he a ie y o indica o s ha a e included in he e alua ion model and hei composi ion. The numbe o such indica o s a ies om se e al o se e al dozen in indi idual cases (Gine ičius e al., 2018; Čiegis e al., 2010). E en when a model is composed o a small numbe o indica o s, hei composi ion is usually di e en . This depends on a numbe o ci cums ances: wha aspec s o he phenomenon in ques ion a e dis inguished by he au ho s; o om access o in o ma ion needed o calcula e alues o an indica o , e c. These ci cums ances make i di icul o use he esul s o he mul i-c i e ia assessmen o economic de elopmen o compa ing coun ies. Meanwhile, in e na ional da abases and s a is ical yea books o coun ies p o ide all he necessa y in o ma ion on hei economic de elopmen on he basis o pe capi a GDP. The e o e, his s udy will be based on his indica o ( u he – GDP). Two di e en coun ies, Swi ze land and I aly, ha e been selec ed o illus a e he p oposed me hodology. Swi ze land has expe ienced a s eady g ow h o GDP pe capi a o e he pe iod unde e iew. On he o he hand, his p ocess is accompanied by qui e no iceable luc ua ions in indi idual ime pe iods (yea s) o he pe iod unde conside a ion. In I aly, du ing he pe iod unde e iew, he a e o economic de elopmen has ha dly inc eased, bu he e is no ma ked luc ua ion ei he (Tab. 1, Fig. 1). To quan i y he con inui y o he SES de elopmen p ocess me hods based on dynamic analysis o p ocesses can be used, which means ha hey can assess he magni ude o he luc ua ion o he phenomenon unde conside a ion, he essen ial a ibu e o dynamics, and ha allow o be in e p e ed. To he me hods o his kind we may asc ibe coe icien s used o analyze he con inui y o economic and social p ocesses. Fi s and o emos , hese would be he me hods o assessmen o inequali ies in income and economy (Amin, 2006; A kinson e al., 2002; Čiule ičienė e al., 2006a, b; Čiule ičius & Čiule ičienė, 2008; Ib agimo e al., 2018; Kawachi & Kennedy, 1999; Kawachi e al., 1999; Ku owska-Pysz e al., 2018). Alongside he s uc u al coe icien s, some special indica o s a e needed o assess he economic and social inequali y o he popula ion (Čiule ičienė, 2006a; Lazu ka, 2002). The mos commonly used is he Gini coe icien (index). The a io a ies om 0 o 1 o om 0 o 100 pe cen . The la ge i is, he g ea e is he inequali y. This indica o is widely used in in e na ional compa isons. The Gini coe icien is de e mined om he Lo enz cu e (Dagum, 1980; G usky, 2001; Rudzkienė, 2005; Coun y Yea s 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 I aly 27.6 26.4 26.8 27.3 26.7 26.5 26.7 27.2 27.9 28.5 Swi ze land 49.3 50.2 56.1 63.7 65.0 64.1 65.3 74.0 72.4 72.6 Sou ce: www.eu os a .com Tab. 1: G oss domes ic p oduc (GDP) pe capi a in EUR 58 2021, XXIV, 1 Economics B a čiko ienė & De eiky ė, 2006; Jann, 2016). The idea o his cu e is ha , i i is possible o de e mine he o al inequali y o he indica o unde conside a ion, he e comes he oppo uni y o analyze he na u e o i s dis ibu ion be ween he indi idual ime spans o he pe iod unde conside a ion. Fo example, o depic g aphically he dis ibu ion o households by income, hey a e a anged in ascending o de on he axis X o he o dina e sys em, indica ing he pe cen age o he popula ion (households); meanwhile depic ing he de e ed pe cen age o hei income in axis Y (Fig. 2). The na u e o he Lo enz cu e and he Fig. 1: GDP pe capi a o he coun ies conce ned Sou ce: own based on www.eu os a .com Fig. 2: Lo enz cu e Sou ce: own based on www.eu os a .com 59 1, XXIV, 2021 Economics o de in which i is cons uc ed allow i o be applied o assess he homogenei y o he coun y’s economic de elopmen . I s o de would be as ollows. Fi s , le us d aw a squa e wi h sides 100×100 and i s diagonal. The cumula i e alues o he economic de elopmen du ing he ime spans o he pe iod unde e iew, exp essed as a pe cen age, a e plo ed on he abscissa axis, and he pe cen age o he ac ual de elopmen o he ime pe iods a e plo ed on he o dina e axis. The in e sec ion o each o hese deciles will gi e a pa icula poin . Connec ing he poin s in a s aigh line gi es a Lo enz cu e. I e lec s upon he ac ual cou se o he p ocess o economic de elopmen o e he pe iod unde conside a ion, and he diagonal o he squa e ep esen s i s ideal de elopmen . The Lo enz cu e is e y widely applied in ma hema ics, especially in economic s a is ics. I is sui able o examining he inequali ies o a wide a ie y o phenomena ep esen ed by in e al lines. I s deg ee is ep esen ed by he con exi y o he cu e, e.g. he dis ance om he diagonal o he squa e; he s eepe he magni ude cu e is, he lesse he dis ance om he cu e i shows; he less i is dis an om he diagonal, he lesse he di e si ica ion o he dis ibu ion is, and ice e sa, as he cu e mo es away om he diagonal, he dis ibu ion i egula i y inc eases. The Gini coe icien (Dagum, 1980; Gu sky, 2001; Rudzkienė, 2005) is used o es ima e quan i a i e dis ibu ion compa isons based on Lo enz cu e. I is de e mined as ollows (Fig. 2): (3) The smalle he dis ibu ion i egula i y is, which means he close he cu e is o he diagonal o he squa e, he lowe he alue o he ac o G we see. I we equa e he a ea S1 + S2 o S, hen om Fig. 2. ollows ha S1 = S – S2. Then (4) In ou case, when he case o quan i ying he dynamics o SES economic de elopmen is unde e iew, he smalle he a ia ion in de elopmen and he close he Lo enz cu e app oaches he squa e o he squa e, he mo e e en he expansion is, so he Gini coe icien mus be ans o med in his way. (5) He e TG is he coe icien desc ibing he con inui y o SES economic de elopmen . Fig. 1 and o mulas (4) and (5) show ha in ideal case o de elopmen , S1 = 0, and TG = 1.0. Quan i a i e assessmen o he economic de elopmen dynamics o he coun ies conce ned was ca ied ou on he basis o he abo e me hodology. 2. Quan i yingEconomic De elopmen Dynamics in Coun ies As s a ed abo e, we quan i y he dynamics o he coun y’s economic de elopmen on he basis o pe capi a GDP. I s luc ua ions in he pa icula ime spans o he pe iod unde conside a ion may be e y une en (Tab. 1, Fig. 1). The same ep esen a i e coun ies – I aly and Swi ze land – a e aken o he calcula ions. F om Fig. 1 i is seen ha Swi ze land is unde going in ense de elopmen , whe eas I aly is expe iencing s agna ion in i s de elopmen . On he o he hand, in I aly, de elopmen is s able, wi h no majo luc ua ions, while in Swi ze land, luc ua ions a e signi ican ly highe . The e o e, i can be assumed ha he e is a ela ionship be ween de elopmen in ensi y and sus ainabili y, which means ha he in ensi y in luences he uni o mi y. F om a me hodological poin o iew, i would be ad an ageous o elimina e he in luence o in ensi y om he indica o o sus ainable de elopmen and o e alua e i la e , when a complex sus ainable de elopmen indica o is c ea ed. O he wise, he low le el o de elopmen may be o se by i s high in ensi y and esul in an inadequa e pic u e. The di e en economic de elopmen si ua ions o he coun ies in Fig. 1 need o be quan i ied. To ha end, i is i s o all necessa y o de e mine he de elopmen si ua ion in ela ion o which he ac ual si ua ion will be assessed. In o he wo ds, we need o ha e a benchma k o de elopmen con inui y o an ideal de elopmen case. This can be said o be he case when he 60 2021, XXIV, 1 Economics SES de elopmen inc emen o e he same pe iod o ime, such as he yea , is he same. In his case, he de elopmen ajec o y will coincide wi h he diagonal o he squa e (Fig. 1), and he de elopmen i sel will look like his (Fig. 3). F om Fig. 3 i can be seen ha he Fig. 3: Ideal case o SES dynamics o de elopmen Sou ce: own Fig. 4: Changes in de elopmen o e ime span i; i, i + 1 o he pe iod unde e iew Sou ce: own based on Gine ičius e al., 2018 61 1, XXIV, 2021 Economics uni o mi y o SES de elopmen uns ideally ∆qi = ∆qi + 1 (whe e ∆qi is he inc ease in de elopmen o he ime pe iod i). In eal li e we usually see a si ua ion whe e ∆qi≠∆qi + 1, which means we see g ea e o lesse luc ua ions in de elopmen o e pa icula ime pe iods o he pe iod unde e iew. In his case, he uni o mi y o de elopmen can be quan i ied based on he de elopmen al di e ences o hese pe iods ∆∆q=qi – qi + 1 (Fig. 4). We exp ess he a ia ions in he economic de elopmen o he coun ies shown in Fig. 1 by he Lo enz cu e. Fo his pu pose, we will use Tab. 1 o calcula e he absolu e magni udes o de elopmen di e ences be ween adjacen ime pe iods (Tab. 2). We will p esen he di e ences in Tab. 2 in ascending o de . Such a p ocedu e is possible because i will no a ec he a ea S2 o he Lo enz cu e S2, and he a ea S1 (Tab. 3). Based on Tab. 3, we de e mine he ela i e weigh o he di e ences as a pe cen age (Tab. 4). Coun y Yea s 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 I aly 0.2 1.2 0.4 0.5 0.6 0.2 0.2 0.5 0.7 0.6 Swi ze land 3.1 0.9 5.9 7.6 1.3 0.9 1.2 8.7 1.6 0.2 Sou ce: own Coun y Yea s To al 12345678910 I aly 0.2 0.2 0.2 0.4 0.5 0.5 0.6 0.6 0.7 1.2 5.1 Swi ze land 0.2 0.9 0.9 1.2 1.3 1.6 3.1 5.9 7.6 8.7 31.4 Sou ce: own Coun y Yea s To al 12345678910 I aly 3.9 3.9 3.9 7.8 9.8 9.8 11.8 11.8 13.8 23.5 100 Swi ze land 0.6 2.9 2.9 3.8 4.1 5.1 9.9 18.8 24.2 27.7 100 Sou ce: own Coun y Yea s 12345678910 I aly 3.9 7.8 11.7 19.5 29.3 39.1 50.9 62.7 76.5 100 Swi ze land 0.6 3.5 6.4 10.2 14.3 19.4 29.3 48.1 72.3 100 Sou ce: own Tab. 2: Di e ences in economic de elopmen o he coun ies conce ned o e he pe iods conside ed Tab. 3: Ascending o de o economic de elopmen di e ences be ween coun ies o he pe iod unde e iew Tab. 4: Compa a i e weigh s o di e ences in economic de elopmen o he coun ies conce ned o e he pe iod o ime in pe cen Tab. 5: Cumula i e alues o compa a i e weigh s o di e ences in economic de elopmen o he coun ies unde e iew o he conside ed pe iod 62 2021, XXIV, 1 Economics Based on Tab. 4, we de e mine he cumula i e alues o he weigh s. Based on Tab. 5, we can d aw he Lo enz cu es o he economic de elopmen o he coun ies unde conside a ion (Fig. 5–6). The ques ion is how o assess he s a e o SES de elopmen con inui y based on hese esul s. The li e a u e p o ides he ollowing Gini coe icien a ing scale (Lando e al., 2018; Lyon e al., 2016) (Tab. 7). Based on Tab. 7 and o mula (2), i is possible o p o ide he ollowing scale o assessing he sus ainabili y o economic de elopmen in a coun y (Tab. 8). Tab. 8 shows ha I aly has a mode a e deg ee o economic de elopmen and Swi ze land a low deg ee o sus ainabili y. The TG ac o o coun ies’ economic de elopmen unde es ima es i s in ensi y. Meanwhile, om Fig. 1. i can be judged o Fig. 5: Lo enz cu e o I alian economic de elopmen Sou ce: own Fig. 6: Lo enz cu e o Swiss economic de elopmen Sou ce: own 63 1, XXIV, 2021 Economics in luence uni o mi y. The in eg a i e size o hese wo aspec s o de elopmen will gi e a snapsho . I can be se up as ollows: (6) whe e is he index o economic de elopmen dynamics o coun y i; Kpi is he a e o economic de elopmen in ensi y o coun y i; and TGi is he coe icien o homogeneous o economic de elopmen o coun y. I is ound ha I aly equals 1.03 and Swi ze land 1.47. On his basis, an in eg al index o hei economic de elopmen dynamics can be calcula ed. I is 0.85 in I aly and 0.87 in Swi ze land. Such esul s o economic de elopmen dynamics o he coun ies a e ecei ed by conside ing ha he uni o mi y and in ensi y o de elopmen a e equally signi ican in e ms o dynamics. The si ua ion would change subs an ially i we conside he impo ance o he pa ial indica o s TG and Kp. I can be assumed ha sho - e m luc ua ions in economic de elopmen o e indi idual ime pe iods (yea s) o he pe iod unde e iew ha e a signi ican ly lesse impac on he s a e o social de elopmen o he coun y compa ed o he in ensi y o de elopmen co e ing he whole pe iod unde e iew. Expe s es ima ed he impo ance o de elopmen in ensi y o i s dynamics a 70 pe cen ou o 100, and luc ua ions in uni o mi y a 30 pe cen . In his case, a gene alized indica o o he dynamics o a coun y’s economic de elopmen can be de e mined by a mul i-c i e ia e alua ion, o example, by he SAW me hod, which is exp essed as ollows (Hwang & Yoon, 1981): (7) he e Di is an index o coun y’s i dynamics o economic g ow h; wi is an impo ance o coun yʼs index o dynamics o economic g ow h Coun y Coe icien G TG I aly 0.30 0.70 Swi ze land 0.49 0.51 Sou ce: own Gini coe icien alue G Conclusion G < 0.25 Ve y low le el 0.25 ≤ G ≤ 0.35 A e age le el G > 0.35 High le el Sou ce: own Value o coe icien TG Conclusion TG > 0.75 Ve y high deg ee o dynamics o de elopmen 0.75 > TG > 0.65 A e age deg ee o dynamics o de elopmen TG < 0.65 Low deg ee o dynamics o de elopmen Sou ce: own Tab. 6: Resul s o he calcula ion o de elopmen dynamics o he analyzed coun ies o 2008–2012 Tab. 7: G ading o Gini coe icien acco ding o uni o mi y o da a dis ibu ion Tab. 8: Coe icien TG g ada ion by homogenei y