We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.
Bibliographical noteFunding Information:
Juan Aparicio and José L. Zofío thank the grant PID2019-105952 GB-I00 funded by Ministerio de Ciencia e Innovación / Agencia Estatal de Investigación / 10.13039/501100011033 . Additionally, Prof. José L. Zofío acknowledges financial support from Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación /10.13039/501100011033 under grant EIN2020-112260 and from the Comunidad de Madrid Government, under grant H2019/HUM-5761 (INNJOBMAD-CM). Finally, Prof. Juan Aparicio thanks the grant PROMETEO/2021/063 funded by the Valencian Community (Spain).
© 2023 The Authors