Nonparametric analysis of firm size and innovation intensity in Circular Economy adoption

The concept of Circular Economy (CE) is nowadays a much-discussed topic because the idea that a linear production system is no longer sustainable from an environmental point of view is taking hold. Some empirical studies have been published on the topic but there is a lack of literature about valid statistical approaches for testing complex hypotheses about CE. One of such interesting but complex hypotheses concerns the effect of companies’ size on the intensity of innovation for CE. The intensity of innovation is measured by the number of innovations adopted to implement CE practices. The main difficulties of such a problem, usually ignored by the empirical literature on CE, are the discrete multivariate nature of the response variable, the need to control for company’s age and business sector, the small sample sizes and the non-monotonic relationship ("inverted U-shaped" or "inverted V-shaped") between firm size and intensity of innovation for CE. These difficulties can be overcome with the use of a nonparametric approach based on a combined permutation test. The scientific innovation of the paper consists of the application of this advanced method to prove that the innovation intensity is a non-monotonic function of the firm’s size. Furthermore, such a result depends on the firm’s age and on the economic sector.