Characterization of production sets through individual returns-to-scale: A non parametric specification and an illustration with the U.S industries

This paper proposes to estimate the returns-to-scale of production sets by considering the individual return of each observation, considered as a decision-making unit through the notion of $\Lambda$-returns to scale assumption. Along this line, the global technology is then constructed as the intersection of all the individual technologies. Hence, an axiomatic foundation is proposed to present the notion of $\Lambda$-returns to scale. This new characterization of the returns-to-scale encompasses the definition of $\alpha$-returns to scale, as a special case as well as the standard non-increasing and non-decreasing returns-to-scale models. A non-parametric procedure based on the goodness of fit approach is proposed to assess these individual returns-to-scale. To illustrate this notion of $\Lambda$-returns to scale assumption, an empirical illustration is provided based on a dataset involving 63 industries constituting the whole American economy over the period 1987-2018.