METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’.
METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’.
and 6 outputs described above separately. The multidimensional frontier constructed using the DEA (in our case, with 5 input dimensions and 6 output dimensions) will be formed by the efficient regions, i.e. those that maximised their outputs, given their inputs. Since the DEA optimises the efficiency of each region (min - imising the distance necessary to project on the efficiency frontier), a region will always be compared with the efficient subset of regions with a productive structure (both inputs and outputs) similar to its own. Inefficient regions will be those with lower out - puts than those on the frontier, at equal inputs (i.e. technical efficiency below 1). In contrast, efficient regions will be those on the produc - tion possibility frontier, since there is no other region capable of more outputs, at equal inputs (i.e. technical efficiency equal to 1). This will allow us to include substitution relationships between inputs and outputs in the efficiency analysis of each European region, and also to study specifically which outputs and inputs are responsible for inefficiency.
FIGURE 11 The best practice frontier based on RIS sub-indices
Synthetic index by groups of variables. The efficiency of European regions is measured as the distance to the best practice frontier (in pink) Source: Drafted in-house based on European Union (2021b)
EUROPEAN REGIONS SPANISH REGIONS BEST PRACTICE FRONTIER
INPUTS
0
0,1
0,2
0,3
0,4
0,6
0,7
0,8
0,9
1
0,5
1
0,9
0,8
0,7
0,6
VALENCIA REGION
0,5
BASQUE COUNTRY
0,4
0,3
0,2
0,1
0
56
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