Global and local technical changes: a new decomposition of the Malmquist productivity index using virtual units

Abstract

In estimating productivity change over time, technical change is frequently miscalculated as the geometric average of technological changes between two periods based on firm-specific information in the dataset. However, the frontier shift over time is a global phenomenon linked to relative technological progress or regress across the entire frontiers. In this paper, we fill this gap by determining the technical change using synthetic observations generated at random within a unit hypercube and calculating the distances between them and the two frontiers being evaluated. Accordingly, we propose a decomposition of the Malmquist index's traditional technical change into two components: average global technical change, which is shared by all production units, and local technical change, which captures how each firm experiences global technical change. In this way, our approach establishes a new research avenue in production economics based on using randomly generated virtual points to assess overall phenomena.