Multi-sector environmental efficiency and productivity: A general Leontief optimization method

For efficiency evaluation purposes, a multi-sector economy is always regarded as a "black box" in which the linkages among sectors are not considered. This leads to biased efficiency evaluation and failure to identify the sources of inefficiency. To solve these problems, this paper proposes a general Leontief optimization method for environmental performance estimation. The proposed method can assess the environmental benefits that result from the adjustment of input coefficients and environmental factor intensities. Moreover, this study proposes two models under different elasticity of input substitution assumptions. The difference in environmental efficiency between the two assumptions is defined here as the substitution efficiency. Further, a new Luenberger environmental productivity indicator is constructed that contains a new element reflecting the effect of input substitution. To demonstrate the new method, a numerical example is used to compare the estimation results between the general Leontief optimization method and the traditional data envelopment analysis method. Then, the environmental performance associated with CO2 emissions and energy consumption in China is studied over two years, i.e., 2012 and 2017. By fully opening the "black box" of how to improve environmental efficiency, this study provides a reference with regard to cost-effective specific measures for policymakers in China.