The vertical network organization as a specific governance structure: what are the challenges for incomplete contracts theories and what are the theoretical implications for the boundaries of the (hub-) firm?

Departing from the seminal question that Coase raised in his 1937 work, this article discusses and assesses incomplete contracts theories’ analyses of the firm’s boundaries—notably transaction cost theory and the modern theory of property rights—by investigating the case of the vertical network organization (VNO). We perform a theoretical characterization and analysis of the functioning rules of the VNO to shed light on intra-network incentive provisions and coordination mechanisms. Our findings cast doubt on the role that hold-up considerations on the firm’s boundaries play and allow us to question forms of power within the VNO. Finally, we focus on the theoretical implications of the emergence of the VNO. The legal nature of the firm does not match the economic definition of the VNO, which tends to treat the firm as a specific governance structure.     

Slope heuristics: overview and implementation

Model selection is a general paradigm which includes many statistical problems. One of the most fruitful and popular approaches to carry it out is the minimization of a penalized criterion. Birgé and Massart (Probab. Theory Relat. Fields 138:33–73, 2006) have proposed a promising data-driven method to calibrate such criteria whose penalties are known up to a multiplicative factor: the “slope heuristics”. Theoretical works validate this heuristic method in some situations and several papers report a promising practical behavior in various frameworks. The purpose of this work is twofold. First, an introduction to the slope heuristics and an overview of the theoretical and practical results about it are presented. Second, we focus on the practical difficulties occurring for applying the slope heuristics. A new practical approach is carried out and compared to the standard dimension jump method. All the practical solutions discussed in this paper in different frameworks are implemented and brought together in a Matlab graphical user interface called capushe. Supplemental Materials containing further information and an additional application, the capushe package and the datasets presented in this paper, are available on the journal Web site.