Modelling Efficiency in Regional Innovation Systems: A Two-Stage Data Envelopment Analysis Problem with Shared Outputs within Groups of Decision-Making Units

Regional Innovation Systems (RISs) literature usually focuses on the comparative performance of different regions and analyzes how each region is utilizing its own dedicated resources. The available resources can be shared by many firms which are grouped by industry, just as universities collaborate with many firms in many industries. This paper studies a region in Mexico and the firms within that region with the aim being to identify which of those firms are using the available resources in the best way. We use Data Envelopment Analysis (DEA) as a methodology for evaluating the relative efficiencies of the firms, based on their multiple inputs and outputs, and considering their processes as being divided into two stages. An important problem in this setting is that the two-stage process exhibits the characteristic of having outputs being shared among the firms in each industry; this makes it more challenging to determine independent efficiency scores for each firm in each industry, where we need to cater for this phenomenon. To address this, the current article presents a methodology for measuring efficiency in situations where Decision Making Units (DMUs) share outputs with other units within the same group. By solving this problem, we can identify the best-performers and their strategies regarding how they use the available resources in the region.