The knowledge complexity of the European metropolitan areas: Selecting and clustering their hidden features

Cities are key places of economic activity, as they produce an enormous amount of wealth compared to the land they cover. Their study is, therefore, of primary importance in understanding the success of nations. Given the many interactions among people that happen within them, cities are well described as complex evolving systems, and a thorough analysis of their economy should be able to deal with this complexity. A likely candidate to grasp the reality of complex evolving systems, such the economy of cities, is the Economic Complexity framework (Hidalgo and Hausmann, 2009), given its capacity to synthesize a large amount of informa- tion into a single index. We use patent data to compute the knowledge complexity index (KCI) of European metropolitan areas and describe their economy in terms of their innovative potential. Interpreted as a dimensionality-reduction algorithm, as proposed by Mealy et al. (2019), KCI helps to filter out the background noise from the abundant information produced by the interactions that happen within cities. By extending the work by van Dam et al. (2021), we highlight the relevance of going beyond the first leading eigenvector, to the analysis of which the rest of the literature is limited. We define clusters of similar cities, based on the additional dimensions obtained through this dimensionality-reduction procedure. The introduction of clusters dramatically increases the predicting power of KCI. Under this lens, the Economic Complexity framework is more than a single index: it is a powerful methodology to reveal the organized complexity hidden behind the large amount of chaotic information produced by out-of-equilibrium economic systems such as cities.