Local Spatial Autocorrelation

The lessons arising from the Moran's I statistic have a global scope, and do not allow us to understand the structure of local interactions among the geographical entities concerned. To analyze the configuration of these local interactions identifying the units that contribute most to the overall spatial autocorrelation or, in the absence of autocorrelation, those that are atypical locations or pockets of non - local-stationarity must be done. The diagram of Moran is the standard tool for the analysis of local spatial autocorrelation. It proposes to show the scatter of geographical entities in the plane formed by the intersection of income per capita y (horizontal axis) and the variableWy that represents the average per capita income neighbours (vertical axis). The plan then consists of four quadrants associated with the four possibilities of local spatial association between an entity and its neighbours: HH is a unit that displays high GDP per capita and is surrounded by units characterized by high GDP per head; LL is a unit characterized by a low GDP per capita but its environs comprise of units with low GDP per capita; in the third quadrant (HL), a unit has a high per capita income but is surrounded by units with low income per capita; and, in the fourth quadrant (LH), a unit with a low income per head has units with high per capita incomes around it. In terms of interpretation, the HH and LL quadrants associated with clusters of similar values represent a situation of positive autocorrelation. Conversely, the LH and HL quadrants which comprise dissimilar values show a negative autocorrelation.

The diagrams on three data sets of GDP per capita are constructed to take into account the dynamics of each country and their neighbours: those concerning countries in the initial date (1977), the final date (2006) and those giving the average growth rate over the „whole period 1977-2006. Figures 8 through 10 show the results of the three weighted matrices. When these graphs are examined and compared a number of observations can be seen:

- At the initial period, the distribution of countries in the four areas of the diagram is as follows: 2 (11.7%) and 5 (29.4%) in quadrant HH and BB, respectively, while 4 (23.6%) and 6 (35.3%) were in quadrants HB and BH. Also, the majority of Caribbean countries exhibited an unusual combination of income per capita; only a percentage (41.2%) of countries characterized by a geographical relation of similar values of their GDP per capita can be seen. - The configuration of the final year shows a distribution with little differences from the year of 1977: 2 (11.7%) and 5 (29.4%) countries are classified in quadrant HH and BB respectively and, 5 are associated with HB and 4 in quadrant BH.

- In both 1977 and 2006, it should be noted that there is a group of countries from Haiti, Cuba, Dominican Republic, Puerto Rico and Jamaica that corresponds to countries with low GDP per head and surrounded by other countries with low GDP per head. This group of 5 countries form a spatial concentration that persists over time.

- In the beginning and end of the study period, the overall pattern of spatial association is that of a negative autocorrelation. Around this global trend, it is noteworthy that there is a marked deviation made by three countries: St. Lucia, Dominica and Martinique. Also, it appears that St. Lucia and Dominica are countries with low GDP per head whose environs are composed of countries with higher GDP per capita. Barbados, Martinique, and the Bahamas are found to be associated with the HB type, that is to say, high-income countries are surrounded by countries with low per capita income.

- It is important to note that the map of the Caribbean (see Figure 8) confirms the consistency between the positions of countries and geographical classification given by the diagram of Moran.

1977 and 2006 in the spatial pattern of standard of living of the countries, whether considered separately or by neighbouring subgroups. As illustrated in the colour game legend on both maps, there are stable "images of clusters of neighbours". Thus, within the arc of the Lesser Antilles, Martinique and Barbados a combination of HB type exists, but the neighbours, St. Lucia, Dominica, Grenada, and Saint Vincent and the Grenadines have not benefited from the diffusion process of growth.

The stability of spatial patterns of association highlighted with the diagrams of Moran in the years 1977 and 2006 reflects a strong presumption of the persistence of spatial disparities in development levels within the Caribbean basin, from the Greater Antilles to Lesser Antilles. To go further in exploring the local schema of the statistical pattern of local spatial association, it is interesting to examine the dynamics of spatial association by considering the same information as those used for Figure 2. Also, the diagram of Moran for growth rate of GDP per capita over the period 1977-2006 can be compared to the diagram of Moran's GDP per capita in 1977.

The main findings arising from the above can now be stated: - Haiti and the Dominican Republic that were located in quadrant BB of Moran 1977 diagram also remain positioned in the same quadrant when considering their average growth rate over the period 1977-2006. This result shows once more the poor performance of these two countries;

- The Bahamas, which belonged to the HL group in 1977 was in the BB group when its average growth rate is considered over the same period, these positions are consistent with a phenomenon of the growth slowdown of the Bahamas;

- Barbados and Trinidad and Tobago, which were attached to the HL and HH quadrants diagram of Moran in the early period, respectively, belong to type the LH grouping when considering their growth. These two countries should also be interpreted as countries that experienced lower growth;

- Martinique who was in the HL group during the initial part, is however in the HH quadrant diagram of the growth rate. Guadeloupe situated in the HH quadrant of the diagram of the initial period is found in the HL quadrant of the diagram of the growth rate; it appears that in the French islands, strong growth is unrelated to the performance of their immediate neighbours but is rather dependent on external factors like the importance of public transfers allocated by France and the European Commission in the training of their income populations;

- St. Lucia, Dominica, Antigua and Barbuda, Saint Vincent and the Grenadines, Grenada, Saint Kitts and Nevis are located in the quadrant HH diagram of growth as they formed groups of space or type LL and LH in 1977, this result provides further illustration of the phenomenon of convergence of the OECS countries mentioned above.

Figure 9. Maps of the per-capita GDP in 1977 and in 2006 Map of the per-capita GDP in 1977