METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’.
METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’.
4.2
FIGURE 8 RIS distribution for alternative weights
The significance of RIS differences between regions according to the relative weights of the variables in the RIS
The distributions represent frequency in the RIS calculation with random weights for each variable. Source: Drafted in-house based on European Union (2021b)
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As indicated in Chapter 2, one of the most dif- ficult points in estimating synthetic indicators is choosing the relative weights of each of the variables. As choosing these weights is an ar - bitrary decision, it is reasonable to ask whether their implications (especially the rankings) are stable with respect to these weights. This prob - lem is particularly important in the case of the RIS since, as commented above, transforming and normalising their indicators is a source of instability in the ranking it induces, especially in middle positions (see section 4.1).
To clarify these questions, we will study the stability of the RIS and its ranking in the event of marginal changes in the weights of the vari- ables. One initial approach is the debate around the relevance of the variables included in the RIS. In this first analysis, we will assume that they are all, to some extent, relevant in meas- uring the capacity of the regional innovation system. Although we cannot choose a specific weighting, it will be assumed to be around the weighting chosen by the European Commis- sion (European Union, 2021b). To implement this assumption, we will turn the weights of the RIS indicators into a random variable whose expected value is the weight assigned by the Commission 6 . Using the bootstrap technique, we will calculate ten thousand times the RIS of all European regions with random values of the weights vector. This will allow us to “broad - en” the index, giving us a measurement of the proximity between regions in terms of their po- sition in the ranking induced by the RIS. Figure 8 shows this possibility in graphic terms using three Spanish Regions as a whole: Andalusia, Galicia and the Basque Country. The figure represents the frequency a specific RIS value would be observed at in each of the regions represented, depending on the combination of weights assigned.
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if we accept that the 21 RIS indicators are relevant to explain the performance of region- al innovation systems, the fact that Galicia is above Andalusia in the final RIS ranking could be attributed to this decision. This is due to the fact that there are relative weights around the weighting used by the Commission (i.e. all variables have the same relative weights for all European regions), meaning the difference between the two regions disappears. In con - trast, this is not the case for the differences between Andalusia and the Basque Country. In this regard, we can say that the differences between Andalusia and the Basque Country are robust with respect to the weights assigned to the indicators in the RIS computation. Although the possibility of an intersection be- tween the histograms in Figure 8 gives a graph- ical idea of the “closeness” of two regions, our
differences between their observed indices are due to the choice of weights assigned to each indicator (i.e. there is a weights vector for which the indices of these two regions would be equal). In contrast, the absence of an inter - section tells us that the observed indices are different, regardless of the weights used. In the example, we can see that the Basque Country has a significantly higher index than Galicia and Andalusia. However, the differences be - tween the latter two are less significant, since there are a large number of relative weights for which their rankings would be very similar. (FIGURE 8) This exercise allows us to obtain a likelihood distribution for the RIS of each European region, attributing differences in the positions of the regions in the European ranking accord- ing to the allocation of weights. For example,
We study the sta- bility of the RIS and its ranking in the event of mar- ginal changes in the weights of the variables
The fact that there is an intersection between the functions of two regions tells us that the
6 More formally, we will assume that the weights are a random vector that is uniformly distributed over a simplex whose centroid is the weight assigned by the European Commission. Annex I shows a detailed explanation of this procedure.
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