Production Theory: Accounting for Firm Heterogeneity and Technical Change

The paper presents a new framework to assess firm level heterogeneity and to study the rate and direction of technical change. Building on the analysis of revealed short‐run production functions by Hildenbrand ( 1981 ), we propose the (normalized) volume of the zonotope composed by vectors‐firms as indicator of inter‐firm heterogeneity. Moreover, the angles that the zonotope's main diagonal form with the axes provide a measure of the rates and directions of productivity change. The proposed framework also accounts for n‐inputs and m‐outputs and, crucially, the measures of heterogeneity and technical change do not require many of the standard assumptions from production theory.