Abstract
This paper presents a continuous version of the model of distribution dynamics to analyse the transition dynamics and implied long-run behaviour of the EU-27 NUTS-2 regions over the period 1995–2003. It departs from previous research in two respects: first, by introducing kernel estimation and three-dimensional stacked conditional density plots as well as highest density regions plots for the visualisation of the transition function, based on Hyndman et al. (J Comput Graph Stat 5(4):315–336, 1996), and second, by combining Getis’ spatial filtering view with kernel estimation to explicitly account for the spatial dimension of the growth process. The results of the analysis indicate a very slow catching-up of the poorest regions with the richer ones, a process of shifting away of a small group of very rich regions, and highlight the importance of geography in understanding regional income distribution dynamics.
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Notes
Recent surveys of the new growth literature in general and the convergence literature in particular can be found in Durlauf and Quah (1999), Temple (1999) and Islam (2003), while Fingleton (2003), Abreu et al. (2004), and Magrini (2004) survey the regional convergence literature, with region denoting a subnational unit.
On the basis of the mean integrated square error criterion, Silverman (1986) has shown that there is very little to choose between alternatives. In contrast, the choice of the bandwidths plays a crucial role.
It is well known that the selection of the bandwidth parameters rather than the choice between various kernels is of crucial importance in density estimation.
The rule is to assume that the underlying density is normal and to find the bandwidth which could minimise the integrated mean square error function.
For a given h z and a given value z, finding \(\hat{g}\,(z\vert y)\) is viewed here as a standard non-parametric problem of regressing \(h_z^{-1} \,K(h_z^{-1} \vert z-Z_i \vert \,)\,\,\hbox{on}\;Y_i.\)
The controverse is not necessarily true (Ord and Getis 1995). Nevertheless, tests for spatial autocorrelation are typically viewed as appropriate assessments of spatial dependence. Moran’s I and Geary’s c statistics are typical testing tools.
Griffith’s eigenfunction decomposition approach that uses an eigenfunction decomposition based on the geographic connectivity matrix used to compute a Moran’s I statistic provides an alternative way (Griffith 2006).
In this study distances are measured in terms of geodesic distances between regional centres.
Getis and Ord (1992) and Ord and Getis (1995) show that the statistic G i (δ) is asymptotically normally distributed as δ increases. When the underlying distribution of the variable in question is skewed, appropriate normality of the statistic can be guaranteed when the number of j neighbours is large.
Combining stochastic kernel estimation with the conditioning scheme suggested by Quah (1996b, 1997a) is an alternative way to evaluate the role of spatial interactions among neighbouring regions. Conditioning means here normalising each region’s observations by the (population weighted) average income of its neighbours. This approach removes substantive, but not nuisance spatial dependence effects.
In order to deal with the widely known problem measuring Groningen’s GRP figure we replaced its energy specific gross value added component by the average of the neighbouring regions (Drenthe and Friesland).
Figures given in PPPs are derived from figures expressed in national currency by using PPPs as conversion factors. These parities are obtained as a weighted average of relative price ratios in respect to a homogeneous basket of goods and services, both comparable and representative for each individual country. The use of national purchasing power parities is based on the assumption that there are no—or negligible—purchasing power disparities between the regions within individual countries. This assumption may not appear to be entirely realistic, but it is inevitable in view of the data available.
Note that the use of administratively defined regions, such as NUTS-2 regions, can lead to misleading inferences due to the presence of significant nuisance spatial dependence. In the case of Hamburg, for example, the NUTS-2 boundary is very narrowly drawn with respect to the corresponding functional region so that residential areas extend well beyond the boundary and substantial in-commuting takes place. This implies that per capita GRP is overestimated, while in the surrounding NUTS-2 regions underestimated.
We exclude the Spanish North African territories of Ceuta y Melilla, the Portuguese non-continental territories Azores and Madeira, and the French Départements d’Outre-Mer Guadeloupe, Martinique, French Guayana and Réunion.
This normalisation makes it possible to separate the global (European) effects on the cross-section distribution of European forces from the effects from regional-specific effects.
A mode is defined as a point at which the gradient changes from positive to negative.
The bandwidths for the estimator were chosen according to Bashtannyk and Hyndman’s three-step-strategy. See Sect. 2.2 for more details.
An HDR boxplot replaces the box bounded by the interquartile range with the 50% HDR, the region bounded by the upper and lower adjacent values is replaced by the 99% HDR that roughly reflects the probability coverage of the adjacent values on a standard boxplot for a normal distribution. In keeping with the emphasis on highest density, the mode rather than the median is marked.
It is well known that the shape of the estimated ergodic density is sensitive to the bandwidths chosen in computing the underlying estimated joint density functions. Wider bandwidths tend to obscure detail in the shapes while narrower bandwidths tend to increase it but possibly spuriously so. It is important to note that smaller equiproportionate decreases and increases in bandwidths do not remove the tendency to bimodality in the ergodic density.
The upper peak, however, is imprecisely estimated. Only few observations were actually made there, and the precision of the estimate is low.
Using Moran’s I, the spatial autocorrelation latent in each of the income variables ranges from z(MI) = 8.86 for the 1995 income variable to z(MI) = 8.06 for the 2003 income variable where z(MI) denotes the z-score value of Moran’s I. From this, it is clear that there is a strong spatial autocorrelation, and hence the assumption of spatial independence does not hold.
Rather than use an individual δ for each observation, the modal value for δ was chosen for each income variable as recommended by Getis and Griffith (2002).
See Rey and Dev (2006) for appropriate inference methods of σ-convergence in the presence of spatial effects.
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Acknowledgments
The authors gratefully acknowledge the grant no. P19025-G11 provided by the Austrian Science Fund (FWF). They also thank two anonymous referees for their comments which improved the quality of the paper. The calculations were done using a combination of the R package HDRCDE, provided by Rob Hyndman, and the PPA package, provided by Arthur Getis. Special thanks to Roberto Basile for providing the original stimulus to carry out this study.
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Appendix
Appendix
NUTS is an acronym of the French for the “nomenclature of territorial units for statistics”, which is a hierarchical system of regions used by the statistical office of the European Community for the production of regional statistics. At the top of the hierarchy are NUTS-0 regions (countries) below which are NUTS-1 regions and then NUTS-2 regions. The sample is composed of 257 NUTS-2 regions located in 27 EU member states (NUTS revision 1999, except for Finland NUTS revision 2003). We exclude the Spanish North African territories of Ceuta and Melilla, and the French Départements d’Outre-Mer Guadeloupe, Martinique, French Guayana and Réunion, the Spanish North African territories of Ceuta y Mellila, and the Portuguese non-continental territories Azores and Madeira. Thus, we include the NUTS 2 regions listed in the table.
Country | ID code | Region |
|---|---|---|
Austria | AT11 | Burgenland |
AT12 | Niederösterreich | |
AT13 | Wien | |
AT21 | Kärnten | |
AT22 | Steiermark | |
AT31 | Oberösterreich | |
AT32 | Salzburg | |
AT33 | Tirol | |
AT34 | Vorarlberg | |
Belgium | BE10 | Région de Bruxelles-Capitale |
BE21 | Prov. Antwerpen | |
BE22 | Prov. Limburg (B) | |
BE23 | Prov. Oost-Vlaanderen | |
BE24 | Prov. Vlaams Brabant | |
BE25 | Prov. West-Vlaanderen | |
BE31 | Prov. Brabant Wallon | |
BE32 | Prov. Hainaut | |
BE33 | Prov. Liège | |
BE34 | Prov. Luxembourg (B) | |
BE35 | Prov. Namur | |
Bulgaria | BG11 | Severozapaden |
BG12 | Severen tsentralen | |
BG13 | Severoiztochen | |
BG21 | Yugozapaden | |
BG22 | Yuzhen tsentralen | |
BG23 | Yugoiztochen | |
Cyprus | CY00 | Kypros / Kibris |
Czech Republic | CZ01 | Praha |
CZ02 | Strední Cechy | |
CZ03 | Jihozápad | |
CZ04 | Severozápad | |
CZ05 | Severovýchod | |
CZ06 | Jihovýchod | |
CZ07 | Strední Morava | |
CZ08 | Moravskoslezko | |
Denmark | DK00 | Danmark |
Estonia | EE00 | Eesti |
Finland | FI13 | Itä-Suomi |
FI18 | Etelä-Suomi | |
FI19 | Länsi-Suomi | |
FI1A | Pohjois-Suomi | |
FI20 | Åland | |
France | FR10 | Île de France |
FR21 | Champagne-Ardenne | |
FR22 | Picardie | |
FR23 | Haute-Normandie | |
FR24 | Centre | |
FR25 | Basse-Normandie | |
FR26 | Bourgogne | |
FR30 | Nord-Pas-de-Calais | |
FR41 | Lorraine | |
FR42 | Alsace | |
FR43 | Franche-Comté | |
FR51 | Pays de la Loire | |
FR52 | Bretagne | |
FR53 | Poitou-Charentes | |
FR61 | Aquitaine | |
FR62 | Midi-Pyrénées | |
FR63 | Limousin | |
FR71 | Rhône-Alpes | |
FR72 | Auvergne | |
FR81 | Languedoc-Roussillon | |
FR82 | Provence-Alpes-Côte d’Azur | |
FR83 | Corse | |
Germany | DE11 | Stuttgart |
DE12 | Karlsruhe | |
DE13 | Freiburg | |
DE14 | Tübingen | |
DE21 | Oberbayern | |
DE22 | Niederbayern | |
DE23 | Oberpfalz | |
DE24 | Oberfranken | |
DE25 | Mittelfranken | |
DE26 | Unterfranken | |
DE27 | Schwaben | |
DE30 | Berlin | |
DE40 | Brandenburg (Südwest and Nordost) | |
DE50 | Bremen | |
DE60 | Hamburg | |
DE71 | Darmstadt | |
DE72 | Gießen | |
DE73 | Kassel | |
DE80 | Mecklenburg-Vorpommern | |
DE91 | Braunschweig | |
DE92 | Hannover | |
DE93 | Lüneburg | |
DE94 | Weser-Ems | |
DEA1 | Düsseldorf | |
DEA2 | Köln | |
DEA3 | Münster | |
DEA4 | Detmold | |
DEA5 | Arnsberg | |
DEB1 | Koblenz | |
DEB2 | Trier | |
DEB3 | Rheinhessen-Pfalz | |
DEC0 | Saarland | |
DED1 | Chemnitz | |
DED2 | Dresden | |
DED3 | Leipzig | |
DEE1 | Dessau | |
DEE2 | Halle | |
DEE3 | Magdeburg | |
DEF0 | Schleswig-Holstein | |
DEG0 | Thüringen | |
Greece | GR11 | Anatoliki Makedonia, Thraki |
GR12 | Kentriki Makedonia | |
GR13 | Dytiki Makedonia | |
GR14 | Thessalia | |
GR21 | Ipeiros | |
GR22 | Ionia Nisia | |
GR23 | Dytiki Ellada | |
GR24 | Sterea Ellada | |
GR25 | Peloponnisos | |
GR30 | Attiki | |
GR41 | Voreio Aigaio | |
GR42 | Notio Aigaio | |
GR43 | Kriti | |
Hungary | HU10 | Közép-Magyarország |
HU21 | Közép-Dunántúl | |
HU22 | Nyugat-Dunántúl | |
HU23 | Dél-Dunántúl | |
HU31 | Észak-Magyarország | |
HU32 | Észak-Alföld | |
HU33 | Dél-Alföld | |
Ireland | IE01 | Border, Midlands and Western |
IE02 | Southern and Eastern | |
Italy | IT31 | Bolzano-Bozen e Trento |
ITC1 | Piemonte | |
ITC2 | Valle d’Aosta/Vallée d’Aoste | |
ITC3 | Liguria | |
ITC4 | Lombardia | |
ITD3 | Veneto | |
ITD4 | Friuli-Venezia Giulia | |
ITD5 | Emilia-Romagna | |
ITE1 | Toscana | |
ITE2 | Umbria | |
ITE3 | Marche | |
ITE4 | Lazio | |
ITF1 | Abruzzo | |
ITF2 | Molise | |
ITF3 | Campania | |
ITF4 | Puglia | |
ITF5 | Basilicata | |
ITF6 | Calabria | |
ITG1 | Sicilia | |
ITG2 | Sardegna | |
Lithuania | LT00 | Lietuva |
Luxembourg | LU00 | Luxembourg (Grand-Duché) |
Latvia | LV00 | Latvija |
Malta | MT00 | Malta |
Netherlands | NL11 | Groningen |
NL12 | Friesland | |
NL13 | Drenthe | |
NL21 | Overijssel | |
NL22 | Gelderland | |
NL23 | Flevoland | |
NL31 | Utrecht | |
NL32 | Noord-Holland | |
NL33 | Zuid-Holland | |
NL34 | Zeeland | |
NL41 | Noord-Brabant | |
NL42 | Limburg (NL) | |
Poland | PL11 | Lódzkie |
PL12 | Mazowieckie | |
PL21 | Malopolskie | |
PL22 | Slaskie | |
PL31 | Lubelskie | |
PL32 | Podkarpackie | |
PL33 | Swietokrzyskie | |
PL34 | Podlaskie | |
PL41 | Wielkopolskie | |
PL42 | Zachodniopomorskie | |
PL43 | Lubuskie | |
PL51 | Dolnoslaskie | |
PL52 | Opolskie | |
PL61 | Kujawsko-Pomorskie | |
PL62 | Warminsko-Mazurskie | |
PL63 | Pomorskie | |
Portugal | PT11 | Norte |
PT15 | Algarve | |
PT16 | Centro (P) | |
PT17 | Lisboa | |
PT18 | Alentejo | |
Romania | RO01 | Nord-Est |
RO02 | Sud-Est | |
RO03 | Sud | |
RO04 | Sud-Vest | |
RO05 | Vest | |
RO06 | Nord-Vest | |
RO07 | Centru | |
RO08 | Bucuresti | |
Slovakia | SK01 | Bratislavský kraj |
SK02 | Západné Slovensko | |
SK03 | Stredné Slovensko | |
SK04 | Východné Slovensko | |
Slovenia | SI00 | Slovenija |
Spain | ES11 | Galicia |
ES12 | Principado de Asturias | |
ES13 | Cantabria | |
ES21 | País Vasco | |
ES22 | Comunidad Foral de Navarra | |
ES23 | La Rioja | |
ES24 | Aragón | |
ES30 | Comunidad de Madrid | |
ES41 | Castilla y León | |
ES42 | Castilla-La Mancha | |
ES43 | Extremadura | |
ES51 | Cataluña | |
ES52 | Comunidad Valenciana | |
ES53 | Illes Balears | |
ES61 | Andalucía | |
ES62 | Región de Murcia | |
Sweden | SE01 | Stockholm |
SE02 | Östra Mellansverige | |
SE04 | Sydsverige | |
SE06 | Norra Mellansverige | |
SE07 | Mellersta Norrland | |
SE08 | Övre Norrland | |
SE09 | Småland med öarna | |
SE0A | Västsverige | |
United Kingdom | UKC1 | Tees Valley and Durham |
UKC2 | Northumberland, Tyne and Wear | |
UKD1 | Cumbria | |
UKD2 | Cheshire | |
UKD3 | Greater Manchester | |
UKD4 | Lancashire | |
UKD5 | Merseyside | |
UKE1 | East Riding and North Lincolnshire | |
UKE2 | North Yorkshire | |
UKE3 | South Yorkshire | |
UKE4 | West Yorkshire | |
UKF1 | Derbyshire and Nottinghamshire | |
UKF2 | Leicestershire, Rutland and Northants | |
UKF3 | Lincolnshire | |
UKG1 | Herefordshire, Worcestershire and Warks | |
UKG2 | Shropshire and Staffordshire | |
UKG3 | West Midlands | |
UKH1 | East Anglia | |
UKH2 | Bedfordshire, Hertfordshire | |
UKH3 | Essex | |
UKI1 | Inner London | |
UKI2 | Outer London | |
UKJ1 | Berkshire, Bucks and Oxfordshire | |
UKJ2 | Surrey, East and West Sussex | |
UKJ3 | Hampshire and Isle of Wight | |
UKJ4 | Kent | |
UKK1 | Gloucestershire, Wiltshire and North Somerset | |
UKK2 | Dorset and Somerset | |
UKK3 | Cornwall and Isles of Scilly | |
UKK4 | Devon | |
UKL1 | West Wales and The Valleys | |
UKL2 | East Wales | |
UKM1 | North Eastern Scotland | |
UKM2 | Eastern Scotland | |
UKM3 | South Western Scotland | |
UKM4 | Highlands and Islands | |
UKN0 | Northern Ireland |
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Fischer, M.M., Stumpner, P. Income distribution dynamics and cross-region convergence in Europe. J Geograph Syst 10, 109–139 (2008). https://doi.org/10.1007/s10109-008-0060-x
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DOI: https://doi.org/10.1007/s10109-008-0060-x