Measuring energy efficiency incorporating regional heterogeneities: A meta-frontier method with log-linear technology

doi:10.3969/j.issn.0253-2778.2020.03.001

Abstract

Abstract: China’s provinces vary greatly in the economic development, resource endowments, and science and technology levels, which leads the heterogeneity of production technology. A data envelopment analysis model is proposed based on the log-linear energy technology and meta-frontier method, which considers the heterogeneity of production technology. Energy performances of China’s 30 provinces during the 2006-2015 period were measured and causes of energy inefficiency were analyzed with the model. Empirical results indicate that, most of the provinces in China have great potential for energy efficiency improvement. It is also shown that the eastern region has the highest average annual energy efficiency while that of the western region is the lowest, with the central region somewhere in between. It is suggested to enhance management capabilities for the eastern provinces should be enhanced, improve both technology and management efficiency for central and western provinces, to improve their energy performances.

Key words: Energy efficiency, Data envelopment analysis, Meta-frontier, Log-linear technology

CLC Number:

F224

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Appendix

Following Refs.[40,47-48], we introduce the directional-distance meta-frontier method to compare with our log-linear method. The production possibility sets under group frontier and meta-frontier are shown as Eqs.(15) and (16), respectively.
T=k,l,e,y,u:∑Njn=1λnkn≤k,∑Njn=1λnln≤l,∑Njn=1λnen≤e,∑Njn=1λnyn≥1+βjyy,∑Njn=1λnun≤(1-βju)u,λn≥0,n=1,…,Nj

Tmeta=k,l,e,y,u:∑Jj=1∑Njn=1λnkn≤k,∑Jj=1∑Njn=1λnln≤l,∑Jj=1∑Njn=1λnen≤e,∑Jj=1∑Njn=1λnyn≥(1+βy)y,∑Jj=1∑Njn=1λnun≤(1-βu)u,λn≥0,n=1,…,Nj（16）

Based on the production possibility sets, the directional DEA models under group frontier and meta-frontier are shown as models (17) and (18), respectively.

s.t. Dj=k,l,e,y,u;g=Maxωyβjy+ωuβju∑Njn=1λnkn≤k,∑Njn=1λnln≤l,∑Njn=1λnen≤e,∑Njn=1λnyn≥(1+βjy)y,∑Njn=1λnun≤(1-βju)u,λj≥0,βjy≥0,0≤βju<1（17）

s.t. Dj=k,l,e,y,u;g=Maxωyβy+ωuβu∑Jj=1∑Njn=1λnkn≤k,∑Jj=1∑Njn=1λnln≤l,∑Jj=1∑Njn=1λnen≤e,∑Jj=1∑Njn=1λnyn≥(1+βy)y,∑Jj=1∑Njn=1λnun≤(1-βu)u,λj≥0,βy≥0,0≤βu<1,（18）

Through models (17) and (18), the energy efficiency under group frontier as GEE and meta-frontier as MEE are computed as follows.

GEE=1-βju1+βjy（19）
MEE=1-βu1+βy（20）

()
()

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