GDP PER CAPITA IN EUROPE: TIME TRENDS AND PERSISTENCE

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Economics and Finance Working Paper Series Deparmen of Economics and Finance Working Paper No. 17-18 Guglielmo Maria Caporale and Luis A. Gil-Alana GDP PER CAPITA IN EUROPE: TIME TRENDS AND PERSISTENCE Ocober 217 hp://www.brunel.ac.uk/economics

GDP PER CAPITA IN EUROPE: TIME TRENDS AND PERSISTENCE Guglielmo Maria Caporale Brunel Universiy London and Luis A. Gil-Alana Universiy of Navarra Ocober 217 Absrac This noe uses fracional inegraion echniques o show he exisence of a negaive correlaion beween he level of GDP per capia and is degree of persisence in a number of European counries. Weaker insiuions and shock absorbers (financial markes o diversify risk and sabilizaion policies o couner shocks) migh be he reason why counries wih lower GDP per capia are characerized by a less effecive managemen of he economy in response o shocks. Keywords: GDP per capia; Europe; ime rends; persisence JEL Classificaion: C22 Corresponding auhor: Professor Guglielmo Maria Caporale, Deparmen of Economics and Finance, Brunel Universiy London, UB8 3PH, UK. Tel.: +44 ()1895 266713. Fax: +44 ()1895 26977. Email: Guglielmo-Maria.Caporale@brunel.ac.uk The second named auhor graefully acknowledges financial suppor from he Miniserio de Economía y Compeiividad (ECO214-55236). 1

1. Inroducion This noe examines he long-run behaviour of GDP per capia in a number of European counries over he las fify-odd years. Specifically, i esimaes is degree of persisence using fracional inegraion echniques. The adoped framework sheds ligh on wheher or no he series of ineres exhibi ime rends and also on wheher he effecs of shocks are ransiory or permanen. 2. Time rends and persisence We analyse GDP per capia in various European counries using a fracional inegraion approach such ha he differencing parameer for making a series saionary I() is no necessarily an ineger (usually 1) and can ake insead any real value, including fracional ones. The model also includes a ime rend o capure echnological progress and is specified as follows: y 1, x (1) d ( 1 L) x u,, 1,..., (2) where y sands for GPD per capia; β and β 1 are unknown coefficiens on an inercep and a linear ime rend respecively, and he de-rended process x is assumed o be I(d), where d is o be esimaed. This specificaion is more general han he classical one based on he I()/I(1) dichoomy, i produces more accurae esimaes of he ime rend coefficiens and allows for much richer dynamics, including he case of non-saionary processes ha are neverheless mean-revering (i.e.,.5 d < 1). 2

3. Daa and Empirical Resuls We analyse annual daa on GDP per capia (curren US dollars), from 196 o 216, obained from he World Developmen Indicaors for he following counries: Ausria, Belgium, Denmark, Finland, France, Greece, Ireland, Ialy, Luxembourg, Neherlands, Porugal, Spain, Sweden and he UK. Naural logs are aken before carrying ou he saisical analysis. We sar by considering he model given by equaions (1) and (2), i.e. y 1 x, (1 L) d x u, 1, 2,..., (3) under he assumpion ha u in (3) is a whie noise process. We examine he hree sandard cases of i) no deerminisic erms (i.e., β = β 1 = in (3)), ii) an inercep (β 1 =), and iii) an inercep wih a linear ime rend, and repor in Table 1 along wih he esimaed values of d he 95% confidence bands of he non-rejecion values of d, using Robinson s (1994) LM ess, which are valid even in nonsaionary conexs. Tha is, we es he null hypohesis: H o : d d o, (4) in (3), where d o can be any real value. We choose d o =,.1,.2,, (.1),, 1.99 and 2; he non-rejecion values of d o in (4) a he 5% level are repored in brackes. [Inser Tables 1 and 2 abou here] The ime rend coefficien is found o be saisically significan in all counries excep Belgium, Greece and he UK, where he inercep is he only significan deerminisic erm. Noe ha his selecion is based on he -values on he d o -differenced series, i.e., d ~ ~ ( 1 L) o y 1 1 u, 1, 2,..., (5) ~ d where 1 o (1 L) 1 ~ d and (1 ) o L, and, since u is I() by consrucion, sandard -ess are valid. Table 2 displays he esimaed coefficiens in (3) for each 3

series; he highes ime rend coefficiens are found for Spain (.8446), Ireland (.7844) and Porugal (.698), i.e. some of he peripheral EU counries. [Inser Tables 3 and 4 abou here] The resuls based on he assumpion of auocorrelaed errors (as in he exponenial specral model of Bloomfield, 1973) are repored in Tables 3 and 4. Here he ime rends coefficien is significan in all cases, he esimaes ranging from.6 (France and Sweden) o.76 (Spain) and.82 (Ireland). As for he orders of inegraion, he I(1) hypohesis canno be rejeced in any case, wih he values of d now ranging from.591 (Luxembourg),.72 (Sweden and he UK) and.731 (Finland) o 1.41 in Greece. Given he differences in he resuls depending on he specificaion of he error erm, nex we esimae d using a semi-parameric mehod, no funcional form being imposed on he error erm in his case. In paricular, we use a local While esimae, iniially proposed by Robinson (1995) and developed laer by Velasco (1999), Shimosu and Phillips (25) and Abadir e al. (27) among ohers. [Inser Table 5 abou here] The resuls produced by his semi-parameric mehod, for a seleced group of bandwidh parameers, m = 5, 6,..., 9 and 1, are displayed in Table 5. Mos of he esimaes are wihin he I(1) inerval, he main excepions being Ausria (wih m = 6 and 1), Greece (m = 8, 9 and 1), he Neherlands (m = 9 and 1) and he UK (m = 5). In all hese cases, he esimaed value of d is significanly higher han 1. [Inser Tables 6 and 7 here] Table 6 displays he ranking for he ime rend coefficiens, while Table 7 orders he counries according o heir degree of persisence. 4

I is clear ha here is a negaive correlaion beween he level of GDP per capia and is degree of persisence, i.e. higher orders of inegraion are found for counries wih lower GDP per capia. In he case of developing economies insiuional weakness is ofen hough of as a possible explanaion for heir lower abiliy o respond effecively o shocks and he higher persisence of heir effecs (see Fukuyama, 214); in addiion, higher macroeconomic volailiy is also observed since he usual shock absorbers (financial markes o diversify risk and sabilizaion policies o couner shocks) are weaker (see Loayza e al., 27). For European counries i is less obvious ha he same reasons should apply. However, our evidence suggess ha even in heir case here sill exis insiuional, financial and policy differences leading o a less effecive managemen of he economy in response o shocks in hose wih lower GDP per capia. 4. Conclusions This noe applies fracional inegraion echniques o analyse he sochasic behaviour of GDP per capia in various European counries. The empirical evidence poins o a sylized fac, namely he exisence of a negaive correlaion beween he level of GDP per capia and is degree of persisence. This had already been observed in he case of developing counries and aribued o insiuional weakness, a lower degree of financial developmen and less effecive macro policies (see Loayza e al., 27). Our analysis suggess ha similar issues arise in he case of developed, European counries and ha some of hem are less capable of responding o shocks affecing he economy, and herefore are affeced by hem for a much longer period of ime. References Abadir, K.M., W. Disaso and L. Giraiis, (27) Nonsaionariy-exended local While esimaion, Journal of Economerics 141, 1353-1384. 5

Bloomfield, P. (1973) An exponenial model in he specrum of a scalar ime series, Biomerika 6, 217-226. Fukuyama, F. (214), Poliical Order and Poliical Decay: From he Indusrial Revoluion o he Globalisaion of Democracy, London: Profile Books Loayza, N.V., Ranciere, R., Serven, L., Venura, J. (27), Macroeconomic volailiy and welfare in developing counries: An inroducion, The World Bank Economic Review, 21, 3, 343-357. Robinson, P.M. (1994), Efficien ess of nonsaionary hypoheses. Journal of he American Saisical Associaion 89, 142-1437. Robinson, P.M. (1995), Gaussian Semiparameric Esimaion of Long Range Dependence, Annals of Saisics 23, 163-1661. Shimosu, K. and P.C.B. Phillips, 25, Exac local While esimaes of fracional inegraion, Annals of Saisics 33, 189-1933. Velasco, C. (1999): Gaussian semiparameric esimaion of non-saionary ime series, Journal of Time Series Analysis, 2(1), 87-127. 6

Table 1: Esimaes of d and 95% confidence bands wih uncorrelaed errors Counry No erms An inercep A linear rend AUSTRIA.912 (.731, 1.162) 1.324 (1.131, 1.618) 1.286 (1.15, 1.578) BELGIUM.916 (.739, 1.162) 1.395 (1.173, 1.722) 1.362 (1.145, 1.693) DENMARK.921 (.745, 1.165) 1.32 (1.98, 1.61) 1.255 (1.72, 1.546) FINLAND.919 (.739, 1.169) 1.318 (1.75, 1.714) 1.281 (1.58, 1.675) FRANCE.919 (.744, 1.163) 1.265 (1.64, 1.555) 1.228 (1.46, 1.512) GREECE.914 (.731, 1.166) 1.444 (1.251, 1.733) 1.41 (1.216, 1.675) IRELAND.914 (.725, 1.164) 1.229 (.999, 1.538) 1.189 (.986, 1.51) ITALY.917 (.737, 1.166) 1.273 (1.84, 1.562) 1.231 (1.63, 1.54) LUXEMBOURG.899 (.718, 1.147) 1.291 (1.56, 1.624) 1.269 (1.35, 1.612) NETHERLANDS.918 (.743, 1.162) 1.341 (1.149, 1.625) 1.295 (1.117, 1.576) PORTUGAL.93 (.714, 1.157) 1.365 (1.148, 1.684) 1.325 (1.119, 1.648) SPAIN.929 (.746, 1.178) 1.423 (1.186, 1.767) 1.366 (1.151, 1.7) SWEDEN.923 (.751, 1.166) 1.198 (.965, 1.535) 1.164 (.965, 1.494) UK.91 (.719, 1.146) 1.359 (1.97, 1.78) 1.339 (1.75, 1.785) In bold, he significan deerminisic erms. 7

Table 2: Esimaed coefficiens wihou auocorrelaion Counry d Inercep Time rend AUSTRIA 1.286 (1.15, 1.578) 6.76436 (73.69).6795 (1.96) BELGIUM 1.395 (1.173, 1.722) 7.11737 (81.84) --- DENMARK 1.255 (1.72, 1.546) 7.13912 (79.95).6631 (2.19) FINLAND 1.281 (1.58, 1.675) 6.99322 (69.1).6491 (1.72) FRANCE 1.228 (1.46, 1.512) 7.1356 (76.99).5894 (2.7) GREECE 1.444 (1.251, 1.733) 6.22933 (79.6 --- IRELAND 1.189 (.986, 1.51) 6.45112 (74.87).7844 (3.42) ITALY 1.231 (1.63, 1.54) 6.6114 (7.14).653 (2.22) LUXEMBOURG 1.269 (1.35, 1.612) 7.66736 (76.47).6143 (1.72) NETHERLANDS 1.295 (1.117, 1.576) 6.89833 (76.27).6781 (1.92) PORTUGAL 1.325 (1.119, 1.648) 5.81776 (62.67).698 (2.22) SPAIN 1.366 (1.151, 1.7) 5.87746 (59.18).8446 (1.72) SWEDEN 1.164 (.965, 1.494) 7.52621 (73.97).5788 (2.34) UK 1.281 (1.58, 1.675) 7.2381 (83.63) --- The values in parenhesis in he second column are he 95% confidence bands, while hose in columns 3 and 4 are -values for he deerminisic erms. 8

Table 3: Esimaes of d and 95% confidence bands wih auocorrelaed errors Counry No erms An inercep A linear rend AUSTRIA.725 (.397, 1.164).938 (.751, 1.336).891 (.625, 1.275) BELGIUM.749 (.388, 1.173).892 (.69, 1.374).841 (.541, 1.293) DENMARK.752 (.374, 1.182).893 (.71, 1.324).862 (.62, 1.239) FINLAND.734 (.332, 1.27).815 (.681, 1.119).731 (.482, 1.58) FRANCE.742 (.329, 1.184).93 (.72 1.374).889 (.622, 1.282) GREECE.684 (.384, 1.172) 1.97 (.812, 1.592) 1.41 (.74, 1.492) IRELAND.734 (.349, 1.194).879 (.722, 1.396).853 (.516, 1.31) ITALY.736 (.356, 1.184).965 (.764, 1.38).938 (.71, 1.264) LUXEMBOURG.729 (.362, 1.184).822 (.686, 1.24).591 (.191, 1.143) NETHERLANDS.764 (.334, 1.179).957 (.721, 1.46).927 (.655, 1.335) PORTUGAL.691 (.417, 1.153).924 (.744, 1.376).858 (.541, 1.282) SPAIN.76 (.384, 1.22).899 (.671, 1.412).891 (.623, 1.296) SWEDEN.754 (.343, 1.26).764 (.613, 1.127).727 (.479, 1.9) UK.722 (.369, 1.179).823 (.696, 1.142).729 (.474, 1.113) In bold, he significan deerminisic erms. 9

Table 4: Esimaed coefficiens wih auocorrelaion (Bloomfield, 1973) Counry d Inercep Time rend AUSTRIA.891 (.625, 1.275) 6.7823 (72.19).742 (8.32) BELGIUM.841 (.541, 1.293) 7.1222 (75.99).6411 (8.99) DENMARK.862 (.62, 1.239) 7.175 (78.43).678 (8.97) FINLAND.731 (.482, 1.58) 7.647 (63.49).6776 (11.18) FRANCE.889 (.622, 1.282) 7.15324 (76.2).651 (7.2) GREECE 1.41 (.74, 1.492) 6.21265 (71.39).6242 (4.66) IRELAND.853 (.516, 1.31) 6.45216 (72.36).828 (11.6) ITALY.938 (.71, 1.264) 6.53343 (69.17).6574 (6.46) LUXEMBOURG.591 (.191, 1.143) 7.63715 (52.32).7453 (13.1) NETHERLANDS.927 (.655, 1.335) 6.91527 (74.49).6773 (7.15) PORTUGAL.858 (.541, 1.282) 5.8447 (6.87).7388 (9.57) SPAIN.891 (.623, 1.296) 5.93138 (57.66).7622 (8.22) SWEDEN.727 (.479, 1.9) 7.58813 (7.7).671 (1.49) UK.729 (.474, 1.113) 7.17555 (78.96).6471 (13.13) The values in parenhesis in he second column are he 95% confidence band, while hose in columns 3 and 4 are -values for he deerminisic erms. 1

Table 5: Esimaes of d based on a semiparameric mehod Counry 5 6 7 8 9 1 AVG AUSTRIA 1.192 1.342 1.137 1.27 1.273 1.32 1.242 BELGIUM.925 1.67.974 1.73 1.167 1.27 1.68 DENMARK 1.34 1.122 1.12 1.18 1.24 1.237 1.119 FINLAND 1.41 1.143.876.936 1.29 1.58 1.13 FRANCE 1.38 1.177.994 1.77 1.124 1.12 1.85 GREECE.996 1.22 1.141 1.313 1.428 1.37 1.241 IRELAND 1.114.959.821.883.96 1.19.959 ITALY 1.258 1.253 1.44 1.151 1.194 1.1 1.166 LUXEMBOURG.95 1.11.952.997 1.15 1.131 1.33 NETHERLANDS 1.13 1.294 1.138 1.211 1.319 1.332 1.237 PORTUGAL 1.95 1.29 1.1 1.156 1.173 1.122 1.156 SPAIN.84 1.8.938 1.59 1.136 1.14 1.14 SWEDEN.941 1.31.839.957 1.39 1.27.972 U. K. 1.373 1.115.81.861.928.977 1.1 Lower 95%.632.664.689.79.725.739 --- Upper 95% 1.367 1.335 1.31 1.29 1.274 1.26 --- In bold, evidence of I(d) behaviour wih d > 1. 11

Table 6: Ranking of he ime rend coefficiens No auocorrelaion (whie noise) Auocorrelaion (Bloomfield) SPAIN (.8446) IRELAND (.828) IRELAND (.7844) SPAIN (.7622) PORTUGAL (.698) LUXEMBOURG (.7453) AUSTRIA (.6795) PORTUGAL (.7388) NETHERLANDS (.6781) AUSTRIA (.742) DENMARK (.6631) FINLAND (.6776) ITALY (.653) NETHERLANDS (.6773) FINLAND (.6491) DENMARK (.678) LUXEMBOURG (.6143) ITALY (.6574) FRANCE (.5894) UK (.6471) SWEDEN (.5788) BELGIUM (.6411) BELGIUM ( --- ) GREECE (.6242) UK (---) SWEDEN (.671) GREECE (---) FRANCE (.651) 12

Table 7: Ranking of he esimaes of d (degree of persisence) Parameric esimaion Semiparameric esimaion No auocorrelaion Auocorrelaion GREECE (1.444) GREECE (Bloomfield) (1.41) AUSTRIA (1.242) BELGIUM (1.395) ITALY (.938) GREECE (1.241) SPAIN (1.366) NETHERLANDS (.927) NETHERLANDS PORTUGAL (1.325) AUSTRIA (.891) (1.237) ITALY (1.166) NETHERLANDS (1.295) SPAIN (.891) PORTUGAL (1.156) AUSTRIA (1.286) FRANCE (.889) DENMARK (1.119) FINLAND (1.281) DENMARK (.862) FRANCE (1.85) UK (1.281) PORTUGAL (.858) BELGIUM (1.68) LUXEMBOURG (1.269) IRELAND (.853) LUXEMBOURG (1.33) DENMARK (1.255) BELGIUM (.841) SPAIN (1.14) ITALY (1.231) FINLAND (.731) FINLAND (1.13) FRANCE (1.228) UK SWEDEN (.729) UK (1.1) IRELAND (1.189) SWEDEN SWEDEN (.727) SWEDEN (.972) SWEDEN (1.164) LUXEMBOURG (.591) IRELAND (.959) 13

Figure 1: Correlaion beween he ime rend coefficiens and GDP per capia i) Correlaions using GDP per capia in 196 a) No auocorrelaion b) Auocorrelaion 25 2 15 1 5,5,55,6,65,7,75,8,85,9 25 2 15 1 5,6,65,7,75,8,85 ii) Correlaions using GDP per capia in 216 a) No auocorrelaion b) Auocorrelaion 12 1 8 6 4 2,55,6,65,7,75,8,85,9 12 1 8 6 4 2,6,65,7,75,8,85 14

Figure 2: Correlaion beween he orders of inegraion and GDP per capia i) Correlaions using GDP per capia in 196 a) Whie noise errors b) Auocorrelaed errors c) Semiparameric mehod 25 2 15 1 5 1,1 1,15 1,2 1,25 1,3 1,35 1,4 1,45 1,5 25 2 15 1 5,5,6,7,8,9 1 1,1 25 2 15 1 5,9,95 1 1,5 1,1 1,15 1,2 1,25 1,3 ii) Correlaions using GDP per capia in 216 a) Whie noise errors b) Auocorrelaed errors c) Semiparameric mehod 12 1 8 6 4 2 1,1 1,15 1,2 1,25 1,3 1,35 1,4 1,45 1,5 12 1 8 6 4 2,5,6,7,8,9 1 1,1 12 1 8 6 4 2,9,95 1 1,5 1,1 1,15 1,2 1,25 1,3 15

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