Unrestricted geometric distance functions and the Geometric Young productivity index: an analysis of Indian manufacturing

In this paper, we employ the less frequently used Geometric Young index to measure productivity change. We reformulate the Geometric Distance Function of Portela and Thanassoulis (J Product Anal 25:25–41, 2006) by removing the restrictions on the individual input scaling factors and the output scaling factors to obtain the benchmark input–output bundle on the frontier. In this reformulated model, the Geometric Young index is exhaustively decomposed into the technical efficiency change and technical change factors even under variable returns to scale. Further, between any two periods, the measured rate of technical change is identical across all units. In our empirical analysis, we use state-level data from the Annual Survey of Industries for the period 2010–2011 through 2016–2017 to measure total factor productivity growth in Indian manufacturing and provide its decomposition for the major manufacturing states in India. At the All-India level, the annual average Geometric Young productivity index shows a modest growth over the sample period. This resulted from an improvement in technical efficiency reinforced by a very modest increase in the Technical Change Index.