Decomposing Malmquist Productivity Indexes into Explanatory Factors

Caves, Christensen, Diewert introduced Malmquist output, input and productivity indexes into production theory in a systematic way. These indexes use distance functions to represent the technology. In recent years, there have been many attempts to decompose Malmquist productivity indexes into explanatory components. This paper revisits this debate of how to decompose a Malmquist productivity index into explanatory factors, with a focus on extracting technical progress, technical efficiency change, and returns to scale components. In order to define these components, a reference technology is required. The paper does not make any convexity assumptions on the reference technology but instead follows the example of Tulkens and his coauthors in assuming that the reference technology satisfies free disposability assumptions.