Annex B. New polarisation coefficient as an indicator of territorial disparities

A polarisation coefficient has been developed to highlight the specificity of the Bulgarian context. It identifies: i) when one region or a small group of regions stands out from the majority of regions; and ii) when the disparities among the majority of regions are relatively low. This coefficient measures the difference in distance between the maximum and the median, and the minimum and the median, as a share of the total distance between the maximum and the minimum; it ranges from -1 to 1.

This coefficient can identify extreme polarisation, with one region performing significantly better (or worse) than the other, such as for Countries A and G in Figure A B.1 but it cannot identify if only one region, or a small group of regions, perform significantly better (or worse) that the large group of homogeneous regions. Indeed, Countries E and F have the same polarisation coefficient while the performance of the second worst region is significantly different between these two countries. This has been addressed in this publication by analysing each region within Bulgaria to identify the territorial profile, if it is case for Countries E or F.

This polarisation coefficient can also identify cases of low polarisation, as for Countries C and D. If one region (or a small group) performs significantly better (worse) but the majority of regions do not have homogeneous performances, then the polarisation coefficient will remain relatively low, as is the case for Country B.

This coefficient ensures that if the Bulgarian polarisation coefficient is higher than 60% of the country coefficients, Bulgarian territorial disparities are at least larger than in 60% of the countries studied. This results from the fact that this coefficient better captures low polarisation rather than high polarisation. In other words, a country with a low polarisation coefficient will have a low polarisation among its regions but a country with a high polarisation coefficient might not have high polarisation among its regions, especially if it has many regions. Imagine that Bulgaria is Country E, its polarisation coefficient is higher than three countries out of eight and is equal to Countries F and Z. However, polarisation is higher among Country E regions than Country F regions. Polarisation is also higher in Country E than in Country Z, which has 11 regions instead of 6. Hence, polarisation in Country E is at least higher than three countries out of eight.

Note that the polarisation coefficient cannot capture if there are two groups of regions at each extremity or if there are two small groups at each extremity and the majority of regions close to the median.

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