Innovation efficiency in the Spanish service sectors, and open innovation

This paper analyzes the relationship between efficiency and innovation activity in Spanish industrial and service sectors by introducing a new methodology framework. A new model combining principal component analysis (PCA) and data envelopment analysis (DEA) is applied in order to obtain an efficiency score. To achieve a more comprehensive evaluation, a large dataset is included, but a large number of variables compared with the number of decision-making units (DMUs) may diminish the discriminatory power of DEA. To avoid this effect, we first apply PCA to separately obtain the input and output main factors. We then apply DEA to the new variables. The PCA-DEA model allows us to identify 5 efficient sectors out of 42. If only DEA were applied, 16 sectors would turn out to be efficient. This shows that the model improves the discriminatory capability of DEA. Methodologically, this work contributes to the literature by proposing an efficiency measurement using a large number of inputs and outputs that could be applied in different fields. Likewise, this analysis allows for the evaluation and interpretation of innovation activity in the different sectors, which can be taken into account in the management and allocation of resources by institutions.