Energy Efficiency Convergence in China: Catch-Up, Lock-In and Regulatory Uniformity

Abstract

This paper examines alternative hypotheses of beta convergence for different measures of energy efficiency. We collect a novel set of prefecture-level data that substantially extend the breadth of the datasets ever used in this literature. GMM estimators are then used to empirically test the national and club convergence of energy efficiency among these prefectures. We find strong evidence for prefecture-level national and club convergence in energy efficiency. In particular, the listed key environmental protection (KEP) prefectures, prefectures in central and western regions and prefectures not listed as resource-based (RB) converge faster than the non-KEP prefectures, prefectures in eastern region and RB prefectures. Sensitivity analyses suggest that these results are robust to alternative measures of energy efficiency and GMM specifications.

Appendix: SBM and EBM

1.1 Input-Oriented Meta-Frontier Slack-Based Super Energy Efficiency

Assuming that there are a total of N DMUs, H technology-heterogeneous groups and $N_h$ DMUs in Group h, we have $\mathop \sum \nolimits _{h=1}^H N_h =N$. Each DMU uses inputs: ${\varvec{x}}=\left[ {x_1 ,x_2 ,\ldots ,x_M } \right] \in R_+^M$ to produce desirable (good) outputs: ${\varvec{y}}=\left[ {y_1 ,y_2 ,\ldots ,y_R } \right] \in R_+^R$ and undesirable (bad) outputs: ${\varvec{b}}=\left[ {b_1 ,b_2 ,\ldots ,b_J } \right] \in R_+^J$. The frontier production technology of Group h can be expressed as follows:

$$\begin{aligned} P^{h}= & {} \left\{ \left( {{\varvec{x}}^{h},{\varvec{y}}^{h},{\varvec{b}}^{h}} \right) :\mathop \sum \limits _{n=1}^{N_h } {\varvec{\lambda }}_n^h {\varvec{x}}_n^h \le {\varvec{x}}^{h};\mathop \sum \limits _{n=1}^{N_h } {\varvec{\lambda }}_n^h {\varvec{y}}_n^h \ge {\varvec{y}}^{h};\mathop \sum \limits _{n=1}^{N_h } {\varvec{\lambda }}_n^h {\varvec{b}}_n^h \le {\varvec{b}}^{h};\right. \nonumber \\&\left. n=1,2,\ldots N_h \right\} \end{aligned}$$

(6)

where ${\varvec{\lambda }}_n^h({\ge 0})$ is a weighting vector of nth DMU in Group h with reference to the corresponding group frontier. By enveloping all group frontier technologies (Battese et al. 2004), we can also express the meta-frontier production technology as follows:

$$\begin{aligned} P^{meta}= & {} \left\{ \left( {{\varvec{x}},{\varvec{y}},{\varvec{b}}} \right) :\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{n=1}^{N_h } {\varvec{\xi }}_n^h {\varvec{x}}_n^h \le {\varvec{x}}^{h};\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{n=1}^{N_h } {\varvec{\xi }}_n^h {\varvec{y}}_n^h \ge {\varvec{y}}^{h};\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{n=1}^{N_h } {\varvec{\xi }}_n^h {\varvec{b}}_n^h \le {\varvec{b}}^{h};\right. \nonumber \\&\left. n=1,2,\ldots N_h ;h=1,2,\ldots ,H\right\} \end{aligned}$$

(7)

where $P^{meta}=\left\{ {P^{1}\cup P^{2}\cup \cdots \cup P^{H}} \right\}$ and ${\varvec{\xi }}_n^h \left( {\ge 0} \right)$ is a weighting vector of nth DMU in Group h with reference to the meta-frontier. With group frontier and meta-frontier defined, we can now define input-oriented super efficiency SBMs for both frontiers. Assuming constant returns to scale (CRS), the optimal objective value for the oth DMU in Group ) with reference to the group frontier is estimated as:

$$\begin{aligned} \rho _{ko}^{group*}= & {} \hbox {min}\left( 1+\frac{1}{M}\mathop \sum \limits _{m=1}^M \frac{s_{mko}^x }{x_{mko} }\right) \nonumber \\&{\textit{s.t. }}x_{mko} -\mathop \sum \limits _{n=1,\ne o}^{N_k } \lambda _n^k x_{mkn} +s_{mko}^x \ge 0;\nonumber \\&\mathop \sum \limits _{n=1,\ne o}^{N_k } \lambda _n^k y_{rkn} -y_{rko} \ge 0;\nonumber \\&b_{jko} -\mathop \sum \limits _{n=1,\ne o }^{N_k } \lambda _n^k b_{jkn} \ge 0;\lambda _n^k \ge 0;\nonumber \\&m=1,2,\ldots ,M;r=1,2,\ldots ,R;j=1,2,\ldots , J \end{aligned}$$

(8)

and the same for the oth DMU in Group with reference to the meta-frontier is estimated as:

$$\begin{aligned} \rho _{ko}^{meta*}= & {} \hbox {min}\left( 1+\frac{1}{M}\mathop \sum \limits _{m=1}^M \frac{s_{mko}^x }{x_{mko} }\right) \nonumber \\&s.t.x_{mko} -\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{\begin{array}{c} n=1,\ne o \\ {\textit{if h}}=k \end{array}}^{N_k } \xi _n^h x_{mhn} +s_{mko}^x \ge 0;\nonumber \\&\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{\begin{array}{c} n=1,\ne o \\ {\textit{if h}}=k \end{array}}^{N_k } \xi _n^h y_{rhn} -y_{rko} \ge 0;\nonumber \\&b_{jko}-\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{\begin{array}{c} n=1,\ne o\\ {\textit{if h}}=k \end{array}}^{N_k } \xi _n^h b_{jhn} \ge 0;\xi _n^h \ge 0;\nonumber \\&m=1,2,\ldots ,M;r=1,2,\ldots ,R;j=1,2,\ldots ,J \end{aligned}$$

(9)

where $\lambda$ in Model 8 and $\xi$ in Model 9 are nonnegative weights, and $s_{mko}^x$ represents the input slacks. The difference between the super efficiency model and the standard model is that $\hbox {DMU}_{\mathrm{ko}}$ in the reference set in the super efficiency model is excluded (Andersen and Petersen 1993), which is denoted by $n\ne o$. Adding the constraints $\mathop \sum \nolimits _{n=1,\ne o}^{N_k } \lambda _n^k =1$ to 8 and $\mathop \sum \nolimits _{h=1}^H \mathop \sum \nolimits _{n=1,\ne {\textit{o if h}}=k}^{N_k } \xi _n^k =1$ to 9 will impose the variable returns to scale (VRS) assumption.

The optimal object values estimated in Model 8 and 9 are sometimes taken as the measure of energy efficiency. However, these values relate to the averages of the slacks of all inputs and maximize the average improvements of all relevant factors for the evaluated DMU to reach the corresponding frontier. One should focus on the slack of energy instead of the average slack of all inputs when measuring energy efficiency (Zhang et al. 2015). Suppose the actual energy input is $x_e$, and the energy slacks corresponding to the meta-frontier by solving the Model 9 is $S_e^{meta}$, then the meta-frontier energy efficiency can be calculated by

$$\begin{aligned} EE^{Meta}=\left( {x_e -S_e^{meta} } \right) /x_e \end{aligned}$$

(10)

Equation 10 defines our SBM based energy efficiency measure for the convergence analysis.

1.2 Input-Oriented Meta-Frontier Epsilon-Based Super Energy efficiency

Although the SBM has been widely used in the literature, it omits the radial characteristics of inputs and/or outputs. Tone (2004) and Cooper et al. (2007) advocate a mixture of SBM and radial model which takes into account the diversity of input/output data and their relative importance. Tone and Tsutsui (2010) proposed the epsilon-based measure (EBM) by introducing two parameters which connect radial and non-radial models. The inputs–outputs efficiency of oth DMU based on a standard input-oriented EBM model is derived by solving the following:

$$\begin{aligned} \rho _o^*= & {} \min \left( {\theta -\varepsilon \mathop \sum \limits _{m=1}^M \frac{\omega _m^- s_m^- }{x_{mo} }/\mathop \sum \limits _{m=1}^M \omega _m^- } \right) \nonumber \\&{\textit{s.t. }}{\varvec{x\lambda }} -\theta {\varvec{x_o}} +{\varvec{s}}^{-}=\mathbf{0};\nonumber \\&{\varvec{y\lambda }} \ge {\varvec{y_o}} ;{\varvec{\lambda }} \ge \mathbf{0};{\varvec{s}}^{-}\ge \mathbf{0} \end{aligned}$$

(11)

where ${\varvec{x}}$ and ${\varvec{y}}$ are the input and output vectors. ${\varvec{\lambda }}$ is a nonnegative weighting vector and ${\varvec{s}}^{-}$ is the slack vector of inputs. There are $m+1$ parameters: $\varepsilon$ and $\omega _m^-$ ($m=1,2,\ldots ,M)$. $\varepsilon$ combines the radial $\theta$ and the non-radial slacks terms, and takes a value between 0 and 1. The model has the radial model and the SBM model as special cases when $\varepsilon$ takes the value of 0 and 1 respectively. Tone and Tsutsui (2010) proposed an affinity index approach to the parameters; however, Cheng (2014) pointed out that the affinity index approach may be biased in extreme cases and proposed an approach based on the adjusted Pearson correlation coefficient. Similarly, we can define input-oriented super efficiency EBMs for both frontiers and estimate the CRS optimal objective values for the oth DMU in Group ) with reference to the group frontier and the meta-frontier as:

$$\begin{aligned} \rho _{ko}^{group*}= & {} \min \left( {\theta +\varepsilon \mathop \sum \limits _{m=1}^M \frac{\omega _{mko}^- s_{mko}^x }{x_{mko} }/\mathop \sum \limits _{m=1}^M \omega _{mko}^- } \right) \nonumber \\&{\textit{s.t. }}\theta x_{mko} -\mathop \sum \limits _{n=1,\ne o }^{N_k } \lambda _n^k x_{mkn} +s_{mko}^x \ge 0;\mathop \sum \limits _{n=1,\ne o }^{N_k } \lambda _n^k y_{rkn} -y_{rko} \ge 0;\nonumber \\&b_{jko} -\mathop \sum \limits _{n=1,\ne o }^{N_k } \lambda _n^k b_{jkn} \ge 0;\lambda _n^k ,s_{mko}^x \ge 0;\theta \le 1\nonumber \\&m=1,2,\ldots ,M;r=1,2,\ldots ,R;j=1,2,\ldots ,J \end{aligned}$$

(12)

and

$$\begin{aligned} \rho _{ko}^{meta*}= & {} \min \left( {\theta +\varepsilon \mathop \sum \limits _{m=1}^M \frac{\omega _{mko}^- s_{mko}^x }{x_{mko} }/\mathop \sum \limits _{m=1}^M \omega _{mko}^- } \right) \nonumber \\&s.t.\theta x_{mko} -\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{{\begin{array}{l} {n=1,\ne o } \\ {{\textit{if h}}=k} \\ \end{array} }}^{N_k } \xi _n^h x_{mhn} +s_{mko}^x \ge 0;\nonumber \\&\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{\begin{array}{c} n=1,\ne o \\ {\textit{if h}}=k \end{array}}^{N_k } \xi _n^h y_{rhn} -y_{rko} \ge 0;\nonumber \\&b_{jko} -\mathop \sum \limits _{h=1}^H \mathop \sum \limits _{\begin{array}{c} n=1,\ne o \\ {\textit{if h}}=k \end{array}}^{N_k } \xi _n^h b_{jhn} \ge 0;\xi _n^h ,s_{mko}^x \ge 0;\theta \le 1\nonumber \\&m=1,2,\ldots ,M;r=1,2,\ldots ,R;j=1,2,\ldots ,J \end{aligned}$$

(13)

Adding the constraints $\mathop \sum \nolimits _{n=1,\ne o }^{N_k } \lambda _n^k =1$ to 12 and $\mathop \sum \nolimits _{h=1}^H \mathop \sum \nolimits _{n=1,\ne {\textit{o if h}}=k}^{N_k } \xi _n^k =1$ to 13 will impose the variable returns to scale (VRS) assumption.

There may be counter-intuitive cases where energy efficiency estimated with reference to the meta-frontier is greater than that estimated with reference to group frontier. To address this issue, we perform the following three steps: First, we solve 11 without considering technological heterogeneity based the adjusted Pearson correlation coefficient and get $\varepsilon$ and $\omega _m^-$. Second, using those parameters as priors, we then solve 12 and 13, and get energy slacks. Lastly, we calculate the meta-frontier energy efficiency using 10, which defines our EBM based energy efficiency measure for the convergence analysis.

1.3 Entropy-Weighted Approach to Environmental Pollution Index

A potentially unfortunate consequence of the conventional DEA is that extreme values of inputs or outputs results in extreme weights such that some DMUs become “efficient by default” (Asmild and Zhu 2015). A widely applied approach to addressing this issue is to generate an entropy-weighted index of multiple factors (Bian and Yang 2010; Ludovisi 2014). Here we generate follow this approach to generate a composite environmental pollution index of four pollutants: carbon dioxide, sulfur dioxide, soot-dust and waste water, which helps to alleviate the influence of extreme values of individual factors. The calculation process involves four steps.

Let $\hbox {V}_{imt}$ denote the emission volume of pollutant m ($m=1, 2, 3, {\ldots }, M)$ at region $i (i=1, 2, 3, {\ldots }, K)$ in year $t (t=1, 2, 3, {\ldots }, T)$. This is first normalized over entire sample:

$$\begin{aligned} P_{imt} =\frac{V_{imt} }{\mathop \sum \nolimits _{i=1}^K \mathop \sum \nolimits _{t=1}^T V_{imt} } \end{aligned}$$

(14)

The entropy of pollutant m at region i is defined as:

$$\begin{aligned} e_{imt} =-\frac{1}{LN\left( {K\times T} \right) }\mathop \sum \limits _{t=1}^T \left( {P_{imt} \times LN(P_{imt} } \right) ) \end{aligned}$$

(15)

Next, we calculate the weight of pollutant m at region i as:

$$\begin{aligned} \hbox {w}_{imt} =\frac{1-\hbox {e}_{imt} }{\mathop \sum \nolimits _{m=1}^M (1-\hbox {e}_{imt)} } \end{aligned}$$

(16)

The composite pollution index (PI) covering four pollutants of region i in year t is given by:

$$\begin{aligned} \hbox {PI}_{it} =\mathop \sum \nolimits _{m=1}^M \left( {\hbox {P}_{imt} \times \hbox {w}_{imt} } \right) \end{aligned}$$

(17)

Higher PI indicates higher level of environmental pollution.