African Growth, Non-linearities and Strong Dependence: An Empirical Study

Transcription

1 Economics and Finance Working Paper Series Deparmen of Economics and Finance Working Paper No Bora Balparda, Guglielmo Maria Caporale, and Luis A. Gil-Alana African Growh, Non-lineariies and Srong Dependence: An Empirical Sudy March 2015 hp://

2 AFRICAN GROWH, NON-LINEARIIES AND SRONG DEPENDENCE: AN EMPIRICAL SUDY Bora Balparda Universiy of Navarra, Faculy of Economics, Pamplona, Spain Guglielmo Maria Caporale Brunel Universiy London, CESIfo and DIW Berlin and Luis A. Gil-Alana Universiy of Navarra, Faculy of Economics, Pamplona, Spain March 2015 Absrac his paper applies a fracional inegraion approach incorporaing Chebyshev polynomials in ime o allow for possible non-lineariies in GDP growh. his is paricularly appropriae in he case of African counries, where growh has been affeced by various conflics. he resuls for a sample of 28 counries confirm he exisence of non-lineariies in mos cases, he only excepions being he Cenral African Republic, Niger, Sierra Leone and Somalia. Furher, here is heerogeneiy across counries in erms of he degree of persisence, he GDP series being characerised in differen cases by mean reversion, uni roo behaviour, and orders of inegraion significanly higher han 1 respecively. Keywords: GDP growh, African counries, non-lineariies, fracional inegraion, Chebyshev polynomials JEL Classificaion: C22, C50 Corresponding auhor: Professor Guglielmo Maria Caporale, Deparmen of Economics and Finance, Brunel Universiy London, UB8 3PH, UK. el.: Fax: Guglielmo.Maria.Caporale@brunel.ac.uk 1

3 1. Inroducion his paper examines he saisical properies of he growh raes of several African counries using saisical echniques based on he conceps of fracional inegraion and long-range dependence. I is normally assumed ha GDP and/or is log ransformaion is a non-saionary, inegraed of order 1 or I1, series and is firs difference, i.e. he growh rae, a saionary I0 one Nelson and Plosser, However, his is a raher resricive assumpion: he possibiliy of fracional degrees of inegraion has more recenly been aken ino accoun in several sudies on GDP growh Michelacci and Zaffaroni, 2000; Silverberg and Verspagen, 2000; Gil-Alana, 2003, 2008; Mayoral, 2006; Caporale and Gil-Alana, 2013; ec.. For insance, Michelacci and Zaffaroni 2000 provided evidence of long memory and mean-revering behaviour in US per capia oupu. heir paper, however, was criicised by Silverberg and Verspagen 2000, who quesioned is mehodology and repored I1 nonsaionary behaviour in US oupu. Mayoral 2006 examined annual real GNP and GNP per capia in he US for he ime period , using several parameric and semiparameric fracional inegraion mehods. Her resuls, hough slighly differen depending on he echnique used, suggesed ha he orders of inegraion lie in he inerval [0.5, 1, which implies nonsaionariy, high persisence and mean-revering behaviour. Caporale and Gil-Alana 2013 showed ha he behaviour of US per capia real oupu is capured well by a linear rend model wih saionary long-memory behaviour and breaks, and ha mean reversion occurs. I is well known ha fracional inegraion, non-lineariies and srucural breaks are inimaely relaed issues Cheung, 1993; Diebold and Inoue, 2001; Giraiis e al., 2001; Kapeanios and Shin, 2003; Mikosch and Sarica, 2004; Granger and Hyung, 2004; ec.. In paricular, fracional inegraion can be an arifac generaed by he 2

4 presence of breaks ha are no aken ino accoun. Furher, changes can occur smoohly raher han suddenly as implied by srucural breaks; Ouliaris e al herefore proposed regular polynomials o approximae deerminisic componens in he daa generaion process DGP. However, as laer poined ou by Bierens 1997, Chebyshev polynomials migh be a beer mahemaical approximaion of he ime funcions, since hey are bounded and orhogonal; being cosine funcions of ime, hey are a very flexible ool o approximae deerminisic rends. In he specific case of he African counries, growh raes migh be no only persisen, bu also subec o non-lineariies resuling from civil wars, ehnic conflics ec. herefore he presen sudy adops a GDP growh model incorporaing boh feaures non-lineariies and persisence in a single framework. he remainder of he paper is srucured as follows. Secion 2 briefly reviews he previous lieraure on economic growh in Africa. Secion 3 oulines he mehodology. Secion 4 describes he daa and discusses he empirical resuls. Secion 5 concludes he paper. 2. Lieraure review Relaively few sudies have focused on economic growh in Africa. In he paper by Fosu 1992a, who used daa from 1956 o 1985 for 31 sub-saharan counries, he counryspecific analysis is complemened by an invesigaion of he exen o which growh differenials beween counries can be explained by differences in producion oupu. Poliical insabiliy and corrupion are found o have adverse effecs on growh and o have played a maor role in he economic sagnaion of sub-saharan Africa, accouning for a subsanial reducion in he region s overall GDP growh over he period

5 Fosu 1992b invesigaed he effec of expor insabiliy on GDP growh in Africa, and found ha hese are paricularly significan in he case of sub-saharan Africa. Karikari 1995 examined he role of he governmen in he growh of a developing naion, using daa for Ghana from 1963 o He concluded ha he impac of governmen on economic growh was negaive. Savvides 1995 invesigaed he facors ha explain he differences in per capia growh across Africa, and concluded ha hese are: iniial condiions, invesmen, economic growh, rade orienaion, inflaion, financial developmen and he growh of he governmen secor. Easerly and Levice 1997 showed ha ehnic diversiy helps explain cross-counry differences in public policies and oher economic indicaors. Sub-Saharan economic growh is associaed wih low schooling, poliical insabiliy, an underdeveloped financial sysem, disored foreign exchange markes, high governmen deficis and insufficien infrasrucures. Guillaumon e al showed, using a cross-secion including a sample of African and non-african counries, ha insabiliy lowered African growh in he sevenies and eighies. hey concluded ha Africa has a higher level of primary insabiliy climaic, erms of rade and poliical insabiliy which lowers growh. Brempong and raynor 1999 also found an inverse relaionship beween poliical insabiliy and economic growh as well as oin endogeneiy of hese wo variables, and an indirec effec of poliical insabiliy on economic growh hrough lower long-run capial accumulaion. Gomanee e al found a posiive relaionship beween foreign aid and growh in a sample of 25 sub-saharan counries: on average, a percenage poin increase in he foreign aid/gnp raio conribues one-quarer of a percenage poin o he growh rae. Aghion e al showed ha mark-ups are higher in Souh Africa manufacuring indusries han in corresponding indusries 4

6 worldwide, which has a large negaive effec on produciviy growh in he Souh African manufacuring indusry. 3. Mehodology As a firs sep, we carry ou sandard uni roo ess, specifically he Augmened Dickey- Fuller ADF es Dickey and Fuller, 1979, as well as is generalizaion, i.e. he GLS specificaion Ellio el al., ERS, 1996, and he Kwiakowski e al. KPSS, 1992 es for he null of saionariy agains he alernaive of a uni roo. We hen consider he following non-linear model: m y i Pi x, 1, 2,..., 1 i 0 wih m indicaing he order of he Chebyshev polynomial, and x following an Id process of he form d 1 L x u, 0, 1,..., 2 wih x = 0 for 0, and d > 0, where L is he lag-operaor Lx x 1 and he Chebyshev polynomials P i, in equaion 1 are defined as: u is 0 I. P 0, 1, P i i 0.5 /, 1, 2,..., ; i 1, 2,..., 2 cos. 3 see Hamming 1973 and Smyh 1998 for a deailed descripion of hese polynomials. Bierens 1997 uses hem in he conex of uni roo esing. According o Bierens 1997 and omasevic and Sanivuk 2009, i is possible o approximae highly non-linear rends wih raher low degree polynomials. If m = 0 he model conains an inercep, if m = 1 i also includes a linear rend, and if m > 1 i becomes non-linear - he higher m is he less linear he approximaed deerminisic componen becomes. 5

7 An issue ha immediaely arises here is how o deermine he opimal value of m. As argued in Cuesas and Gil-Alana 2012, if one combines 1 and 2 in a single equaion, sandard -saisics will remain valid wih he error erm being I0 by definiion. he choice of m will hen depend on he significance of he Chebyshev coefficiens. Noe ha he model combining 1 and 2 becomes linear and d can be esimaed paramerically or esed as in Robinson 1994, Demerescu, Kuzin and Hassler 2008 and ohers see Cuesas and Gil-Alana, he mehod proposed here is a sligh modificaion of Robinson s He considers he same se-up as in 1 and 2 wih he firs componen in he righ hand side in 1 replaced by θ z, and esing he null hypohesis: H : d d, o 4 o for any real vecor value d o. Under H o 4, he model in Robinson 1994 becomes: ' y z u, 1, 2,..., 5 do do where y 1 L y, z 1 L z, and he symbol indicaing ransposiion. hen, given he linear srucure of he above relaionship and he I0 naure of he error erm u, he coefficiens in 5 can be esimaed by sandard ordinary leas square/generalized leas square OLS/GLS mehods. 1 he same applies in our case, wih 1 conaining he Chebyshev polynomials: despie he non-linear srucure, he relaionship is linear in he parameers. hus, combining equaions 1 and 2 we obain y m ' P P u, 1, 2,..., 6 i 0 i i where P i L; d o P i, 1 Alhough Robinson 1994 focuses exclusively on he linear case, he argues p ha undoubedly a non-linear regression will also leave our limi disribuions unchanged, under sandard regulariy condiions.. hese condiions can be found in Robinson

8 7 which can also be expressed as in Robinson 1994 z P, and hen, using OLS/GLS mehods, under he null hypohesis 4, he residuals are ; 0 P y u m i i i wih, ' y P P P and P as he mx1 vecor of ransformed Chebyshev polynomials. Using he above residuals û, we esimae he variance,, / 2 ; ; I g u 7 where u I is he periodogram of û ; g is a funcion relaed o he specral densiy of u i.e., s.d.f.u = σ 2 /2πgλ ;τ; and he nuisance parameer τ is esimaed, for example, by, arg min 2 where is a suiable subse of he R q Euclidean space. 2 he es saisic based on Robinson 1994 for esing H o 4 in 1 and 2 uses he Lagrange Muliplier LM principle, and is given by, 1 ' 4 a A a R 8 where is he sample size, and, ; 2 1 u I g a ' ' ' ' 2 A 2 Alernaive mehods for esimaing he variance, e.g., non-parameric ones, could also be used. Here we ake he same approach as in Robinson 1994.

9 wih i Re log ; e d, and d logg ;, and he sum over above refers o all he bounded discree frequencies in he specrum. Under very mild regulariy condiions, 3 i can be shown ha, as in Robinson R d as, 9 and, based on Gaussianiy of u, one can also show he Piman efficiency of he es agains local deparures from he null. In oher words, if one considers local alernaives of he form: Ha : d do where δ is a non-null parameer vecor, R 2 d as, indicaing a non-cenral 1/ 2, 1 chi-squared disribuion wih a non-cenraliy parameer which is opimal under Gaussianiy of u. Noe ha his mehod is a esing procedure and herefore we do no direcly esimae he fracional differencing parameer vecor bu simply presen confidence inervals based on he non-reecions for a given se of values. However, we display esimaes of d, based on he values minimizing he absolue value of he es saisic. Mone Carlo evidence suggess ha his approach performs well see Cuesas and Gil-Alana, Empirical resuls We use daa on real GDP per capia in 28 African counries a 2005 consan prices. he source is he Penn World able. [Inser able 1 abou here] 3 hese condiions only include momens up o a second order. 8

10 able 1 provides a lis of he counries wih he corresponding sample periods, he longes being hose saring in 1950 for he Congo Democraic Republic, Ehiopia, Morocco, Nigeria, Souh Africa and Uganda. he sar dae is 1954 for Zimbabwe, 1955 for Zambia and Ghana, 1960 for Algeria, Boswana, Burundi, Cenral African Rep., Chad, Congo Republic, Cape Verde, Equaorial Guinea, Gambia, Guinea Bissau, Mali, Mauriania, Mozambique, Namibia and Niger, 1961 for Sierra Leone and unisia, 1970 for Angola and Somalia. he end dae is 2010 in all cases. [Inser ables 2 and 3 abou here] he uni roo es resuls ADF, KPSS and ERS repored in ables 2 in levels and 3 in firs differences sugges ha he level series are I1, whils he GDP growh raes are I0 in all cases. However, i is well known ha such ess have very low power if he DGP is characerised by fracionally inegraion see, Diebold and Rudebusch, 1991; Hassler and Wolers, 1994; Lee and Schmid, 1996; and more recenly Ben Nasr e al., 2014; on he oher hand, fracional inegraion may be a spurious phenomenon caused by he presence of non-lineariies and srucural breaks in he daa ha have no been aken ino accoun. 4 For hese reasons, nex we allow for non-linear rends in he conex of fracional inegraion, and consider he following model, y m i 0 d P x, 1 L x u, 10 i i assuming ha u is a whie noise process. Allowing for auoregressive behaviour in he error erm u in 10 produced coefficiens close o 0 in all cases. We also performed a LR es ha srongly suppors he whie noise specificaion for all he series examined. Firs we assume ha m = 3 o allow for a high degree of non-linear behaviour. able 4 displays in he second column he esimaes of d along wih heir corresponding 4 his poin has been made by several auhors including Bhaacharya e al. 1983, everovsky and aqqu 1997, Smih 2005, Ohanissian e al. 2008, Perron and Qu 2010, ec. 9

11 95% confidence bands showing he values of d for which he null hypohesis 4 canno be reeced. he remaining columns display he esimaed coefficiens along wih heir corresponding -values. [Inser able 4 abou here] For he Cenral African Republic, Niger, Sierra Leone and Somalia here is no evidence of non-lineariies, since he wo coefficiens on he non-linear erms i.e., θ 2 and θ 3 are saisically insignifican. Furher, he order of inegraion varies considerably across hese counries: for he Cenral African Republic and Somalia, he esimaed value of d is significanly smaller han and 0.49 respecively, which implies in boh cases mean-revering behaviour; for Niger he esimae of d is below 1, bu he uni roo null hypohesis canno be reeced; and for Sierra Leone he esimaed value of d is 1.32 and he hypohesis of d = 1 is decisively reeced in favour of d > 1. he counries exhibiing a large degree of non-lineariy are hose for which all four coefficiens are saisically significan, namely Cabo Verde, Equaorial Guinea, Gambia, Mauriania, Mozambique and Uganda. In four of hem Cabo Verde, Equaorial Guinea, Mozambique and Uganda he uni roo null i.e., d = 1 canno be reeced, while for he remaining wo Gambia and Mauriania he null of mean reversion i.e., d < 1 canno be reeced. In beween, here are some cases wih a leas one of he wo non-linear coefficiens being saisically significan. Specifically, a significan θ 3 is found for Algeria, Ehiopia, Gambia, Morocco, Nigeria, Namibia, Souh Africa, unisia and Zambia, and a significan θ 2 -coefficien for Boswana, Burundi, Chad, Congo Democraic Republic, Congo Republic, Guinea Bissau and Mali. For his group of counries, mean reversion d < 1 is found in Algeria, Boswana, Guinea Bissau, Malia, Namibia and unisia, whils he uni roo null canno be reeced in Angola, Burundi, 10

12 Chad, Congo Democraic Republic, Congo, Ehiopia, Ghana, Morocco, Nigeria, Souh Africa, Zambia and Zimbabwe. herefore, we can conclude by saying ha here is some evidence of non-lineariy in all excep he above menioned four counries Cenral African Republic, Niger, Sierra Leone and Somalia. [Inser ables 5 and 6 abou here] ables 5 and 6 display he resuls for m = 2 and m = 1 respecively. hey are compleely in line wih hose repored above for he case of m = 3. able 7 repors he seleced model for each counry. In foureen counries he specificaion wih m = 3 is found o be he mos appropriae - hese are Algeria, Cabo Verde, Equaorial Guinea, Ehiopia, Gambia, Ghana, Mauriania, Mozambique, Namibia, Nigeria, Souh Africa, unisia, Uganda and Zambia. For anoher group of counries, including Angola, Boswana, Burundi, Chad, Congo Democraic Republic, Congo Republic. Guinea Bissau, Mali, Morocco and Zimbabwe, he bes model is he one wih m = 2; for Somalia, he specificaion includes a linear ime rend, and finally, for Cenral African, Niger and Sierra Leone i only includes an inercep. Mean reversion is only found for he following counries: Cenral African Republic, Gambia, Mali, Mauriania and Somalia, and orders of inegraion significanly above 1 are esimaed only for Angola and Sierra Leone. For he remaining counries, he uni roo null canno be reeced. 5. Conclusions his paper applies a fracional inegraion approach incorporaing Chebyshev polynomials o allow for possible non-lineariies in GDP per capia. his is paricularly appropriae in he case of African counries, where growh has been affeced by various conflics. he resuls for a sample of 28 counries confirm he exisence of nonlineariies in mos cases, he only excepions being he Cenral African Republic, Niger, 11

13 Sierra Leone and Somalia. For he remaining counries srong evidence of nonlineariies is obained for Cabo Verde, Equaorial Guinea, Gambia, Mauriania, Mozambique and Uganda, followed by Algeria, Ehiopia, Gambia, Morocco, Nigeria, Namibia, Souh Africa, unisia and Zambia where θ 3 is saisically significan, and for Boswana, Burundi, Chad, Congo Democraic Republic, Congo Republic, Guinea Bissau and Mali wih a significan θ 2 -coefficien. Heerogeneiy across counries is anoher feaure of our resuls, mean-reversion, uni roo behaviour and orders of inegraion significanly higher han 1 being found in differen cases. Overall, he evidence presened in his sudy confirms he imporance of aking ino accoun non-lineariies when modelling GDP per capia in counries such as he African ones where various ypes of conflics have disruped economic growh a differen sages. 12

14 References Aghion P., M. Braun and J. Fedderke 2008, Compeiion and produciviy growh in Souh Africa, Economics of ransiion 16, 4 Ben Nasr, A., Ami, A.N., & Gupa, R. 2014, Modeling he volailiy of he Dow Jones Islamic marke world index using a fracionally inegraed ime varying GARCH FIVGARCH model, Applied Financial Economics, 24, Bhaacharya, R.N. and V.K. Gupa and E. Waymire 1983 he Hurs effec under rends, Journal of Applied Probabiliy 20, Bierens, H.J esing he uni roo wih drif hypohesis agains nonlinear rend saionariy wih an applicaion o he US price level and ineres rae, Journal of Economerics 81, Brempong K. G. and. L. raynor 1999, Poliical insabiliy, invesmen and economic growh in Sub-Saharan Africa, Journal of African Economies 8, 1, Caporale, G.M. and L.A. Gil-Alana, L.A., 2013, Long memory in US real oupu per capia, Empirical Economics 44, 2, Cheung, Y.W., 1993 ess for fracional inegraion. A Mone Carlo invesigaion. Journal of ime Series Analysis 14: Cuesas, J.C. and L.A. Gil-Alana, 2012.A Non-Linear Approach wih Long Range Dependence Based on Chebyshev Polynomials, Working Papers , he Universiy of Sheffield, Deparmen of Economics. Demerescu, M., V. Kuzin, and U. Hassler, 2008, Long Memory esing in he ime Domain. Economeric heory, Cambridge Universiy Press, vol. 2401, pages , February. Dickey, D. and W.A. Fuller, 1979, Disribuions of he esimaors for auoregressive ime series wih a uni roo, Journal of he American Saisical Associaion 74, Diebold, F.X. and A. Inoue, 2001, Long memory and regime swiching, Journal of Economerics 105: Diebold, F.X. and Rudebusch G.D On he power of Dickey-Fuller es agains fracional alernaives. Economics Leers 35, Easerly W and R. Levice 1997, Africa s growh ragedy: Policies and ehnics divisions, he Quarerly Journal of Economics 112, 4, Ellio, G.,.J. Rohenberg, and J.H. Sock 1996, Efficien ess for an Auoregressive Uni Roo, Economerica 64,

15 Fosu A. W. 1992a, Effec of expor insabiliy on economic growh in Africa, he Journal of Developing Areas 26, 3, Fosu A. K. 1992b, Poliical insabiliy and Economic Growh: Evidence from Subsaharan African, Economic Developmen and Culural Change 40, 4, Gil-Alana, L.A. 2003, Long memory in he Spanish GDP using fracional inegraion wih Bloomfield disurbances, Applied Economics Leers 10, 1, Gil-Alana, L.A. 2008, Real GDP growh raes across counries: long memory and mean shifs, Applied Economics Leers 15, 6, Giraiis, L., P. Kokoszka P and R. Leipus, 2001 esing for long memory in he presence of a general rend. Journal of Applied Probabiliy 38, Gomanee K., S. Girma and O. Morrissey 2005, Aid and growh in Sub-Saharan Africa: accouning for ransmission mechanisms, Journal of Inernaional Developmens 17, 8. Granger, C.W.J. and N. Hyung, 2004 Occasional srucural breaks and long memory wih an applicaion o he S&P 500 absolue sock reurns, Journal of Empirical Finance 11: Guillaumon P., S. Guillaumon and J. F. Brun 1999, How insabiliu lowers African growh, Journal of African Economies 8, 1, Hamming, R. W., 1973, Numerical Mehods for Scieniss and Engineers, Dover Hasslers, U. and Wolers J On he power of uni roo ess agains fracional alernaives, Economics Leers 45, 1-5. Kapeanios, G. and Y. Shin 2003, esing for Nonsaionary Long Memory agains Nonlinear Ergodic Models, Queen Mary Universiy of London, School of Economics and Finance in is series Working Papers wih number 500. Karikari, J.A., Governmen and economic growh in a developing naion; he case of Ghana, Journal of Economic Developmen, 20, 2. Kwiakowski, D., P. C. B. Phillips, P. Schmid, and Y. Shin, 1992, esing he null hypohesis of saionariy agains he alernaive of a uni roo, Journal of Economerics 54, Lee, D., and Schmid, P On he power of he KPSS es of saionariy agains fracionally inegraed alernaives. Journal of Economerics 73, Mayoral, L., 2006, Furher Evidence on he Saisical Properies of Real GNP, Oxford Bullein of Economics and Saisics 68, Michelacci, C. and P. Zaffaroni 2000, Fracional Bea convergence, Journal of Moneary Economics, 45,

16 Mikosch and C. Sarica, 2004 Nonsaionariies in financial ime series, he long range dependence and he IGARCH effecs. Review of Economics and Saisics 86, Nelson, C. R., & Plosser, C. I rends and random walks in macroeconomic ime series. Journal of Moneary Economics, 10, Ohanissian, A., J.R. Russell and R.S. say 2008 rue or spurious long memory? A new es, Journal of Business Economics and Saisics 26, Ouliaris, S., J. Y. Park and P. C. B. Phillips 1989 esing for a uni roo in he presence of a mainained rend. In Ray, B. Ed. Advances in Economerics and Modelling. Kluwer, Dordrech, Perron, P. and Z. Qu 2010, Long-memory and level shifs in he volailiy of sock marke reurn indices, Journal of Business and Economic Saisics 28, Robinson, P.M Efficien ess of nonsaionary hypoheses. Journal of he American Saisical Associaion 89, Savvides, A. 1995, Economic Growh in Africa, World Developmen, vol. 23 3, pp Silverberg, G. and Verspagen, B., 2000, A noe on Michelacci and Zaffaroni long memory and ime series of economic growh, ECIS Working Paper Eindhoven Cenre for Innovaion Sudies, Eindhoven Universiy of echnology. Smih, A. 2005, Level shifs and he illusion of long memory in economic ime series, Journal of Business and Economic Saisics 23, Smyh, G.K., 1998, Polynomial Aproximaion, John Wiley & Sons, Ld, Chicheser, everovski, V. and M.S. aqqu 1997 esing for long range dependence in he presence of shifing means or a slow declining rend using a variance-ype esimaor, Journal of ime Series Analysis 18, omasevic, N.M. and. Sanivuk 2009, Regression Analysis and aproximaion by means of Chebyshev Polynomial, Informaologia 42, 2009., 3,

17 able 1: Lis of counries and sample size Counry Saring dae Ending dae No. of observaions Algeria Angola Boswana Burundi Cape Verde Cenral African Rep Chad Congo Dem. Rep Congo Rep Equaorial Guinea Ehiopia Gambia Ghana Guinea Bissau Mali Mauriania Morocco Mozambique Namibia Niger Nigeria Souh Africa Sierra Leone Somalia unisia Uganda Zambia Zimbabwe

18 able 2: Uni roo es resuls levels Counry ADF KPSS ERS Inercep. rend Inercep. rend Inercep. rend Algeria Angola Boswana Burundi Cape Verde Cenral African Rep Chad Congo Dem. Rep Congo Rep Equaorial Guinea Ehiopia Gambia Ghana Guinea Bissau Mali Mauriania Morocco Mozambique Namibia Niger Nigeria Souh Africa Sierra Leone Somalia unisia Uganda Zambia Zimbabwe Reecion al he 10%; Reecion a he 5%; Reecion a he 1% 17

19 able 3: Uni roo es resuls firs differences Counry ADF KPSS ERS Inercep. rend Inercep. rend Inercep. rend Algeria Angola Boswana Burundi Cape Verde Cenral African Rep Chad Congo Dem. Rep Congo Rep Equaorial Guinea Ehiopia Gambia Ghana Guinea Bissau Mali Mauriania Morocco Mozambique Namibia Niger Nigeria Souh Africa Sierra Leone Somalia unisia Uganda Zambia Zimbabwe Reecion al he 10%; Reecion a he 5%; Reecion a he 1% 18

20 able 4: Esimaed coefficiens in a model wih m = 3 Counry d 95 inerval θ 0 θ 1 θ 2 θ 3 Angola , Algeria , Boswana , Burundi , Cenral African Rep , Chad , Congo Dem. Rep , Congo Rep , Cabo Verde , Equaorial Guinea , Ehiopia , Gambia , Ghana , Guinea Bissau , Mali , Mauriania , Morocco , Mozambique , Namibia , Niger , Nigeria , Souh Africa , Sierra Leone , Somalia ,

21 unisia , Uganda , Zambia , Zimbabwe , In bold, significan coefficiens according o he -values a he 5% level

22 able 5: Esimaed coefficiens in a model wih m = 2 Counry d 95% inerval θ 0 θ 1 θ 2 Angola , Algeria , Boswana , Burundi , Cenral African Rep , Chad , Congo Dem. Rep , Congo Rep , Cabo Verde , Equaorial Guinea , Ehiopia , Gambia , Ghana , Guinea Bissau , Mali , Mauriania , Morocco , Mozambique , Namibia , Niger , Nigeria , Souh Africa , Sierra Leone , Somalia ,

23 unisia , Uganda , Zambia , Zimbabwe , In bold, significan coefficiens according o he -values a he 5% level

24 able 6: Esimaed coefficiens in a model wih m = 1 Counry d 95% inerval θ 0 θ 1 Angola , Algeria , Boswana , Burundi , Cenral African Rep , Chad , Congo Dem. Rep , Congo Rep , Cabo Verde , Equaorial Guinea , Ehiopia , Gambia , Ghana , Guinea Bissau Mali , Mauriania , Morocco , Mozambique , Namibia , Niger , Nigeria , Souh Africa , Sierra Leone , Somalia , unisia , Uganda , Zambia , Zimbabwe , In bold, significan coefficiens according o he -values a he 5% level. 23

25 able 7: Order of inegraion of each series according o he seleced models Counry m = 0 m = 1 m = 2 m = 3 Angola , 1.49 xxx , 1.44 xxx Algeria xxx , 1.03 xxx , 0.93 Boswana xxx xxx , 1.02 xxx Burundi , , 1.25 xxx Cenral African , 0.73 xxx xxx xxx Rep. Chad , 1.42 xxx , 1.40 xxx Congo Dem. Rep. xxx xxx , 1.19 xxx Congo Rep , 1.49 xxx , 1.43 xxx Cabo Verde xxx xxx xxx , 1.39 Equaorial Guinea xxx xxx xxx , 1.34 Ehiopia , 1.24 xxx xxx , 1.17 Gambia xxx xxx xxx , 0.98 Ghana , 1.29 xxx xxx , 1.21 Guinea Bissau , 1.04 xxx , 0.97 xxx Mali xxx xxx , 0.99 xxx Mauriania xxx xxx xxx , 0.82 Morocco xxx xxx , 1.15 xxx Mozambique xxx xxx xxx , 1.28 Namibia , 1.14 xxx xxx , 0.90 Niger , 1.13 xxx xxx Xxx Nigeria , 1.44 xxx xxx , 1.50 Souh Africa , 1.54 xxx xxx , 1.40 Sierra Leone , 1.50 xxx xxx xxx Somalia xxx , 0.92 xxx xxx unisia xxx , 1.19 xxx , 0.95 Uganda xxx xxx Xxx , 1.31 Zambia , 1.38 xxx xxx , 1.23 Zimbabwe xxx xxx , 1.22 xxx 24