Method

The Intramax method is a hierarchical clustering algorithm that maximizes the proportion of the total interaction which takes place within the aggregation of basic data units (Masser & Brown, 1975). The intramax method is concerned with the relative strength of interactions as the effect of variation in the size of the row and column totals is removed.

The interaction table, as above, could be se as a contingency table, then the expected flow of each element are derived as the product of the column sum multiplied by the ratio of the row sum to total interaction (Mitchell & Watts, 2010). So, as example, the expected flow from Region 2 into Region 1 is given as:

`a^ *_(21)=sum_(i)a_(i1) (sum_(j)a_(2j))/(sum_(i)sum_(j)a_(ij))`

Assuming that, any difference between the observed and expected values for a given pair of places could be a measure of the relative strength of interactions between them. Two places will have a greater proximity as greater the difference between observed and expected values.

The first objective function suggested by Masser & al. was fully implemented by Masser and Brown (1975) to study movement data for London and Liverpool. That well-known method is the so-called Continuous Intramax Analysis developed by Masser and Scheurwater in 1977. The Intramax objective function aims to:

 `max I=(a_(ij)-a^*_(ij))+(a_(ji)-a^*_(ji)), i!=j`

 with: `a^*_(ij)=sum_(i=1)^n a_(ij)((sum_(j=1)^n a_(ij))/m),``a_(i*)=sum_(n)^n a_(ij),``a_(j*)=sum_(i=1)^n a_(ij) and m=sum_(i=1)^n sum_(j=1)^n a_(ij)`

The methodological process merges together the N units step-by-step by maximizing the proportion of the total interaction in a hierarchical joining clustering process.

Results

The division of the World based on inwards FDI flows reveals a complicated pattern which is not without link with the difficulty to obtain FDI data and build the database. Europe is splited into three main classes: an EU6 plus old colonies in blue with gather countries where FDI mainly come from EU6 countries except Italy, especially France and UK.; an Eastern and Balkanic Europe in orange where Germany, Scandinavian countries and Russia are the most important investors; and thirdly Iberian countries with are linked with South American ones. The green class is those centred on the USA as the most important investor in these countries. The red class is more difficult to understand cause it gathers countries for which USA and EU are equally important as investors as well as countries. But for some of Asian ones, the FDI come also from tax havens as well as USA and/or EU.

The divisions of the World based on Trade flows reveal a set of relations where contiguity and physical proximity seems to have a more important role than political and cultural proximity. Still European countries show again differential behaviours, still visible after the fall of Berlin wall. The Northern European cluster, the Central and Southern European cluster, connected to Africa, and the Eastern European cluster. At world level, is easy to identify the American cluster and the Asian, Oceania and East African cluster.

The divisions of the World based on OECD migration flows show, three strong clusters United States – Mexico; Japan- South Korea; and United Kingdom – Australia – New Zealand and Canada (joined in 2005), the Commonwealth cluster. The European countries, without United Kingdom, show a Scandinavian cluster, the German-Turkey cluster, and the Austrian position as hinge between West and East. This position is also assumed by Germany and the Scandinavian, revealed at other step of hierarchical aggregation.

Objective Europe according to Intramax

Intramax analyses allow giving a first answer to both questions. This method groups together countries which trade more between themselves than expected through a simple model which eliminates the size effect. Intramax analyses confirm the high level of integration of Europe: if the world is divided into 5 classes, there is only one Europe (except Serbia which remains isolated), which mean that European countries trade preferentially between themselves  This result is important because the situation was different in the recent past: in 1996, there was a north/south divide within Europe (Nordic countries vs. the rest of Europe; see also Poon, 2000 on the same question) and some Eastern countries were not yet included in the European space of trade; in 1968, the major divide lies at the level of the iron curtain. In 2007, these intra-European divides have not disappeared but one needs to keep more typological groups to confirm they are still alive.