ANALYSIS USING TIME SERIES: THE MEDITERRANEAN ARC

In this section, the sample is divided into the Mediterranean regions of Spain, France and Italy, although inland regions are also included. The objective is to examine in a more focused way how convergence has evolved through convergence clubs. This is a better way to find convergence, mainly because the fact of the entire sample converging to the mean of the whole group is a too strict course. Therefore, it can be observed that regions have not converged to the mean of the whole group, but they have converged to the mean of another subgroup, thus forming the Mediterranean area.

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DBalearic Islands -0,65 0,2128 -4,488***

DAndalusia -0,89 -1,867 -1,15

Note: The asterisks (*),(**) and (***) denote rejection of the hypothesis of unit root at 10, 5 and 1% respectively.

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Note: The asterisks (*), (**) and (***) denote rejection of the hypothesis of unit root at 10, 5 and 1% respectively.

Following the similar structure to the ADF analysis for the whole group, we proceed to the identification of the regions which have converged according to whether we include constant, constant and trend or neither.

Function with constant + trend

-1 Rejection at 10% * these are: Sicily, Aosta Valley.

2- Rejection at 5%** these are: Navarra, Vasque Country.

3- Rejection at 1% *** these are: Friuli-Venezia Giulia, Balearic Islands.

Function with constant

-1 Rejection at 10% * these are: neither

2- Rejection at 5%** these are: Province of Bolzano-Bozen.

3- Rejection at 1% *** these are: Aosta Valley.

Function without constant or trend

-1 Rejection at 10% * these are: Corsica, Marche, Emilia-Romagna,

2- Rejection at 5%** these are: Veneto, Province of Trento, Lombardy, Piedmont.

3- Rejection at 1% *** these are: neither

44 After ordering the test results for ADF identifying which regions have converged to the mean of this segment, it has been obtained that 14 regions have converged from the total group of 38, i.e. 37% of the regions have converged. It is also noteworthy that many of the convergent regions are Italian, concretely, 10, 1 French and 3 Spanish. It can be seen that the vast majority of the regions were Italian. Moreover, it is also observed that some of them have converged in the negative sense, i.e., they were located above the mean, but they have reduced distance, as is the case of the Province of Trento, Piedmont or Emilia Romagna, as it is shown in the following graphs.

45 KPSS TEST

We apply the KPSS test for the Mediterranean segment with constant and without constant, moreover 2 lags²³ are included.

The next page shows the results from KPSS test:

23 The test has been proved by using 3 lags but the outcomes have not changed.

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DProvince of Bolzano-Bozen 0,391* 0,177**

DProvince of Trento 0,609** 0,125*

DVeneto 0,644** 0,089

D Provence-Alpes-Côte d'Azur 0,542** 0,138*

DCorsica 0,569** 0,150**

Note: Asterisks * and ** denote rejection of stationarity at 10% and 5% respectively.

47 Test with trend

1 cannot be rejected at 10%: Auvergne, Limousin, Marche, Lazio, Midi-Pyrénées, Veneto, Friuli-Venezia Giulia, Emilia–Romagna, Tuscany, Sicily, Apulia, Molise, Piedmont, La Rioja, Aragon, Castile-La Mancha, Vasque Country.

2 cannot be rejected at 10% but is rejected at 5%: Provence-Alpes-Côte d'Azur, Umbria, Province of Trento, Sardinia, Calabria, Campania, Basilicata, Abruzzo, Lombardy, Liguria, Navarra, Andalucia.

Test without trend

1 cannot be rejected at 10%: Rhône-Alpes, Auvergne, Sardinia, Liguria, Valencia.

2 cannot be rejected at 10% but is rejected at 5%: Languedoc-Roussillon, Limousin, Lazio, Province of Bolzano-Bozen, Calabria, Aosta Valley, Balearic Islands.

In both cases, as in the case of the entire sample, we take as stationary those series which cannot reject stationarity (convergence) at 5%. Then, if this series is rejected at 5% it will be understood as non-stationary and therefore, there will be no convergence.

To sum up, observing the results, in the case of the KPSS with trend was obtained that 29 of the 38 regions of the Mediterranean arc have shown convergence (in percentage, the 76%). KPSS without trend showed that 13 from 38 have converged, that is, 34%

from the total. Note that most regions that are exhibiting convergence are Italian. The Spanish regions, on the other hand, do not show a strong relationship of convergence towards the mean; for example, in the case of KPSS without trend, convergence cannot reject to Valencia and Balearic Islands. However, when KPSS is performed with trend, there are more convergent regions, in this case, 6 regions whose convergence cannot be rejected. There is a similar analysis for the French regions. By performing KPSS with or without trend, it is showed that 4 regions have converged.

48 5.3 ANALYSIS USING TIME SERIES: THE CORE EUROPEAN REGIONS

In this section, the objective is to observe how convergence has evolved in those regions which have the highest per capita GDP. In the sample, characteristically, these regions are located in the centre of the European map. Moreover, it is interesting to observe if any region which was not initially located in this group has converged into these groups²⁴. Regarding the choice of the lags, as it was done before, they are selected by maximizing the Akaike criterion.

ADF TEST

The next page shows the results from ADF for the core European regions.

24 Basque Country and Madrid have been included to assess if they have converged into the group of the most advanced regions

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DNorth Netherlands 0,373 -0,740 -1,73

DWest Netherlands 0,428 -3,844*** -1,588

DBrussels Capital Region -1,739* 0,600 -0,089

DUpper Austria -1,733* 0,574 -2,442

DSalzburg -0,809 -0,179 -2,510

DTyrol -2,669** -0,691 -1,063

DVorarlberg -1,00 0,408 -5,910***

DVienna -0,778 -2,336 0,906

D North Rhine-Westphalia -0,411 -1,133 -0,137

DBaden-Württemberg 0,293 -1,782 0,794

DBavaria -0,600 -1,27 0,688

DHamburg -0,658 -0,980 -2,053

DHesse -0,571 -1,29 -2,182

DBremen -0,744 -0,333 -1,176

DHelsinki-Uusimaa -0,143 -2,587 -1,513

DStockholm 0,534 -1,688 -3,202*

Note: The asterisks (*), (**) and (***) denote rejection of the hypothesis of unit root at 10, 5 and 1% respectively.

50 Function with constant + trend

-1 Rejection at 10% * these are: Stockholm, Aosta Valley.

-2 Rejection at 5%** these are: neither -3 Rejection at 1% *** these are: Vorarlberg

Function with constant

-1 Rejection at 10% * these are: Aosta Valley, Greater London, South Netherlands.

-2 Rejection at 5%** these are: Province of Bolzano-Bozen, Luxembourg.

-3 Rejection at 1% *** these are: West Netherlands.

Function without constant or trend

1 Rejection at 10% * these are: Upper Austria, Province of Bolzano-Bozen, Brussels Capital Region.

-2 Rejection at 5%** these are: Tyrol, Basque Country.

-3 Rejection at 1% *** these are: neither.

Therefore, the regions, which have converged, have been: Stockholm, Aosta Valley, Vorarlberg, Greater London, South Netherlands, Province of Bolzano-Bozen, Luxembourg, Netherlands West, Upper Austria, Brussels Capital Region, Tyrol, Basque Country.

Presented the results of the ADF test it shows that, regardless of the specification of the function (it can reject the unit root for 12 of 26 regions), 46% of the regions in this segment have converged towards the mean of this segment. Also, an objective was to assess if any Spanish region had converged into the most advanced groups. In this case, we see that unit root can be rejected for Basque Country in the specification without constant or trend.

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DWest Netherlands 0,172 0,097

DSouth Netherlands 0,278 0,085

DGreater London 0,634** 0,171**

DIle de France 0,189 0,116

DAosta Valley 0,598** 0,113

DLombardy 0,656** 0,073

D Province of Bolzano-Bozen 0,615** 0,164**

D Emilia–Romagna 0,641** 0,168**

DBrussels Capital Region 0,619** 0,173**

DUpper Austria 0,621** 0,164**

DSalzburg 0,329 0,171**

DTyrol 0,540** 0,091

DVorarlberg 0,546** 0,141*

DVienna 0,650** 0,169**

D North Rhine-Westphalia 0,294 0,181**

DBaden-Württemberg 0,399* 0,164**

Note: Asterisks * and ** denote rejection of stationarity, 10% and 5% respectively.

52 Test with trend

1 cannot be rejected at 10%: Stockholm, Bremen, Hesse, Tyrol, Lombardy, Aosta Valley, Ille de France, West Netherlands, South Netherlands.

2 cannot be rejected at 10% but is rejected at 5%: Helsinki-Uusimaa, Hamburg, Vorarlberg.

Test without trend

1 cannot be rejected at 10%: Hamburg, Bavaria, North Rhine-Westphalia, Salzburg, Ille de France, North Netherlands, West Netherlands, South Netherlands, Madrid

2 cannot be rejected at 10% but is rejected at 5%:Stockholm, Bremen, Baden-Württemberg.

In both cases, as in the case of the entire sample, we take as stationary those series in which stationarity cannot be rejected at 5%. However, if the series is rejected at 5%, it will be understood as non-stationary and therefore, non-convergent.

In the case of test with trend, we cannot reject stationarity for 12 of 26, as with ADF test 46% of the regions exhibit convergence, whereas the test without constant shows that 11 regions have converged, in others words, 42% of regions have converged.

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