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

The Malmquist-Luenberger (M-L) index has been used to assess environmental productivity growth with undesirable outputs, through applying directional distance function (DDF) to standard Malmquist productivity measurement. However, when calculating the cross-period DDFs, the M-L index has the same infeasibility problem as the Malmquist index does. To address this infeasibility problem, this paper discusses when infeasibility may happen and develops a modified M-L index that is based on a new DDF. We propose that the modified M-L index can be applied to assessing environmental performance at both macro- and micro-levels. At a macro-level, we evaluate China's growth in total factor productivity (TFP) from 1999 to 2012, accounting for undesirable impacts. The results show that technical change is the main driver of most TFP growth. The TFP changes support the status quo of a distinct gap in economic development among different regions. At a micro-level, we assess Chinese auto manufacturers’ environmental performance from 2005 to 2012. The results suggest that Chinese automakers have enjoyed a noticeable TFP improvement, and that technical change is the major contributor as well. Taking together, reducing air emissions and other pollutants is an effective way of improving environmental productivity. As demonstrated, the proposed modified M-L index has proved to be consistently feasible and guarantees non-negative reference targets for all metrics. As a result, we recommend the modified M-L index as a robust tool for solving the infeasibility problem that is typical in conventional index and for assessing productivity under environmental impacts.