$\Lambda$-Returns to Scale and Individual Minimum Extrapolation Principle

TL;DR

This paper introduces a novel approach to estimating returns-to-scale at the individual firm level using $\\Lambda$-returns to scale, and constructs the global technology as an intersection of individual technologies, supported by an empirical analysis of US industries.

Contribution

It proposes a new axiomatic framework for $\\Lambda$-returns to scale and a non-parametric method to assess individual returns-to-scale, extending existing models.

Findings

The $\\Lambda$-returns to scale encompass traditional models as special cases.

Empirical analysis of 63 US industries demonstrates the applicability of the method.

The approach provides a detailed characterization of production technology over time.

Abstract

This paper proposes to estimate the returns-to-scale of production sets by considering the individual return of each observed firm 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 upon 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 upon a dataset involving 63 industries constituting the whole American economy over the period 1987-2018.