Simultaneous marginal homogeneity versus directional alternatives for multivariate binary data with application to circular economy assessments

Commodity price volatility is a major source of instability in those countries that are primarily commodity-dependent and has a negative impact, especially on economic growth. With this premise, commodities represent an effective financial exchange tool that nowadays finds relevance in being involved in the processes inherent to environmental sustainability. This work focus on raw materials and their demand, connected with the need for a transition towards the Circular Economy, as part of a strategy to address commodity supply disruptions. It presupposes changes in the mentality and behavior of companies in the various economic sectors. A crucial issue debated in the literature concerns whether or not the size of the companies favors their attitude towards Circular Economy. We propose a nonparametric method to test the effect of firm size on their propensity to undertake Circular Economy activities. Considering of such activities, this propensity is a multidimensional concept and it can be represented by a -dimensional vector of proportions. Each element of the vector represents the share of companies of the population under study that implement a specific Circular Economy activity. The main difficulty of such a multivariate testing problem, together with the multidimensional nature of the dichotomous response, is the one-sided type alternative, which is a stochastic dominance for multidimensional binary variables. A Monte Carlo simulation study proves the good power behavior of the proposed solution, based on a nonparametric approach. Case studies related to Italian small and medium enterprises in some strategic sectors are also addressed.