A Modified Malmquist-Luenberger Productivity Index: Assessing Environmental Productivity Performance in China

Juan Du, Yao Chen, Ying Huang

European Journal of Operational Research 269(2018)

Recommended reason

Assessing the environmental performance has become one of the major concerns of sustainability research. Building on the DEA-based Malmquist-Luenberger index, this study contributes to the field by developing a modified M-L index that solves the infeasibility problem, thus providing a reliable method for the as-assessment of economic and environmental performance.

About the author

Juan Du: School of Economics and Management, professor.


Automobile manufacturer, Data envelopment analysis (DEA), Environmental productivity, Malmquist-Luenberger (M-L) productivity, index, Total factor productivity (TFP)

Brief introduction

The Malmquist-Luenberger (M-L) index is particularly useful when measuring productivity and environmental performance associated with undesirable outputs. The M-L index is a special form of the Malmquist index, in that it measures productivity change but in a specific context of producing undesirable outputs. The distance function of the M-L index is characterized by the directional distance function or DDF, and it seeks for the largest feasible increase in desirable outputs that are compatible with the largest feasible reduction in undesirable outputs.

Although widely-adopted, the M-L productivity index has long suffered from the infeasibility issue when calculating the cross-period DDFs, which limits its usefulness in the assessment of environmental performance. Up to now, only the global benchmark technology has been proposed to tackle the problem, but this approach fails to directly depict the technical change. The major contributions of this study lie in an in-depth discussion of infeasibility and the development of the modified M-L index that can fully addresses infeasibility with the contemporaneous benchmark technology. By selecting an appropriate directional reference bundle for the DDF, the modified M-L index is proved to be consistently feasible under either CRS or VRS, thus guaranteeing non-negative reference targets for all performance metrics.

Under the modified M-L index, the application fields of the productivity index can be greatly expanded. In this study, we illustrate the robustness of the modified M-L index in two applications. At the macro-level, we evaluated the environmental productivity or TFP growth in mainland China over the period of 1999-2012. The results indicate that technical change was the primary source of most TFP growth. The comparison of the average annual TFP changes supports the status quo in China in that economic development and environmental performance has been unbalanced be- tween the east and the west, and between the coastal and inland areas. At the micro-level, we used the modified M-L index to measure and compare the ecological performance of China’s auto manufacturers from 2005 to 2012. The results also suggest that Chinese automakers enjoyed a noticeable TFP improvement, and that technical change was the main contributor of the most growth during that period.

In both applications, this newly proposed modified M-L index constantly shows a strong differentiating capability that is superior to the GML index, which clearly demonstrates its robustness. Under this new evaluation mechanism, we suggest that provincial and municipal governments as well as manufacturers in China analyze work on reducing air emissions and other pollutants while boosting GDP in order to enhance environmental productivity and achieve sustainable performance.