METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’.
METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’.
Annex I Methodology to obtain random weights
This paper uses the 21 normalised indicators in the Regional Innovation Scoreboard (RIS), as the European Commission does not make the orig- inal data public before normalisation. The steps leading to the calcula - tion of the normalised indicators are as follows: (1) eliminate outliers; (2) reduce data asymmetry; and (3) normalise the data using the min- max procedure (Hollanders and Es-Sadki, 2021). The first two steps are intended to make the indicators follow a distribution that approximates a normal function, while the third step compresses all indicators in the interval between zero and the unit. The RIS synthetic index is calculated as the simple average of these transformed indicators 9 . In other words, for the normalised indicators vector, (�, �, ... , �) , the RIS of a region is calculated as follows: 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝜃𝜃 ! 𝑧𝑧 !" ! ! ! ! , donde z !" es el valor de 𝑖𝑖 − ésimo indicador para la 𝑗𝑗 − ésima región , y 𝜃𝜃 ! = 1 𝑝𝑝 para todo 𝑖𝑖 = 1 , 2 , … , 𝑝𝑝 ( 1 ) We will assume that the vector of weights = (_1, ... ,_p) for each of the RIS indicators is distributed uniformly over the standard simplex : where is the number of indicators in the RIS synthetic index (=21 for the RIS 2021 edition). We will call this random variable � = (�� �,...,� ). 𝑆𝑆 = 𝜃𝜃 ! , 𝜃𝜃 ! , … , 𝜃𝜃 ! ∈ 𝑅𝑅 ! 𝜃𝜃 ! !
(1)
! ! ! = 1 𝑦𝑦 𝜃𝜃 ! ≥ 0 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑖𝑖 = 1 , 2 , … , 𝑝𝑝 ( 2 ) (2)
I
9 Since the RIS uses a different set of indicators to the European Innovation Scoreboard (EIS), the RIS synthetic index is multiplied by a country correction factor so the order induced by the RIS at country level matches the order generated by the EIS. We will not use these correction factors, since calculating them involves some of the assumptions we want to discuss in this paper, such as the use of arbitrary weights in the indicators in the RIS. Moreover, their effect on the ranking of regions induced by the RIS is marginal (and nil in the case of Spain’s regions).
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