Economic and Environmental Decomposition of Luenberger-Hicks-Moorsteen Total Factor Productivity Indicator: Empirical Analysis of Chinese Textile Firms With a Focus on Reporting Infeasibilities and Questioning Convexity

We discuss an environmental Luenberger–Hicks–Moorsteen (LHM) total factor productivity (TFP) indicator and its decomposition that incorporates a negative externality into the measurement of economic performance. Special cases of a generalized environmental directional distance function are involved in the definition of this LHM indicator and its proposed decomposition. We also seek to test whether changes in the convexity assumption provoke differences in the TFP measures. We apply two specifications of the by-production nonparametric environmental technology to implement this LHM TFP. This LHM TFP indicator decomposes into three terms representing technical change, technical inefficiency change, and scale inefficiency change. The changes in the environmental TFP for China's textile industry is then estimated for the period from 2001 to 2010. We report infeasibilities and we show the differences of the proposed framework for the decomposition of the LHM indicator depending on the convexity assumption. The results suggest there has been an increase in the TFP of China's textile industry: the amount depends on the convexity or not of the technology. The environmental performance is poorer than the economic one. Moreover, contradictions between convex and nonconvex LHM indicators for individual observations appear for a substantial part of the sample.