Green Total Factor Energy Efficiency in China and Its Influencing Factors

This paper measures the GTFEE in China through the DEA. Since its birth, this popular nonparametric method has been constantly improved. The earliest DEA models are Chames-Cooper-Rhodes (CCR) model and Banker-Chames-Cooper (BCC) model. The two models have been widely applied to efficiency evaluation of economy, ecology, energy, and many other fields. However, neither of them can effectively handle the undesirable output.

Traditionally, the undesirable output is converted into desirable output for efficiency evaluation. This practice clearly goes against the reality, and brings large errors in the evaluation results. To solve the problem, Tone [15] put forward the SBM model in 2001. Besides handling undesirable output, the SBM model can calculate the slack values of input and output indices, turning inefficiency to efficiency [16]. In general, the GTFEE measured by SBM model falls within [0, 1]. The principle of the SBM model is as follows:

Suppose there is a production system consisting of $n$ complete production flow. The production system can convert $m$ units of production input into $s_{1}$ units of desirable output and $s_{2}$ units of undesirable output. More intuitively, the input, desirable output, and undesirable output are expressed as vectors $X=\left(x_{1}, x_{2} \ldots, x_{n}\right) \in R_{+}^{m x n}, Y^{g}=\left(y_{1}^{g}, y_{2}^{g}, \ldots, y_{n}^{g}\right) \in R_{+}^{s_{1} \times n},$ and $Y^{b}=\left(y_{1}^{b}, y_{2}^{b}, \ldots, y_{n}^{b}\right) \in R_{+}^{s_{2} \times n},$ respectively. Let $D M U_{0}=$ $\left(x_{0}, y_{0}^{g}, y_{0}^{b}\right)$ be each DMU. Then, the SBM model with undesirable output can be expressed as:

$\begin{array}{l}

\min \rho=\frac{1-\frac{1}{m} \sum_{i=1}^{m} s_{i}^{x-} / x_{i o}}{1+\frac{1}{s_{d}+s_{u}}\left(\sum_{d=1}^{d} \frac{s_{d}^{y}}{y_{d o}}+\sum_{u=1}^{u} \frac{s_{u}^{b}}{b_{u o}}\right)} \\

\text { s.t. } x_{0}=\sum_{j=1}^{n} \lambda_{j} x_{i j}+s_{i}^{x-}, i=1,2, \ldots, m \\

y_{0}=\sum_{j=1}^{n} \lambda_{j} y_{d j}-s_{d}^{y+}, d=1,2, \ldots, d \\

b_{0}=\sum_{j=1}^{n} \lambda_{j} b_{u j}+s_{u}^{b-}, u=1,2, \ldots, u \\

\lambda \geq 0, s_{i}^{x-} \geq 0, s_{d}^{y+} \geq 0, s_{u}^{b-} \geq 0

\end{array}$       (1)

where $, s^{x-} \in R^{m}, s^{y+} \in R^{d},$ and $s^{b-} \in R^{u}$ are the slack terms of input, desirable output, and undesirable outputs (if $s^{x-}, s^{y+}$ or $s^{b-}$ is nonzero, then the input is excessive, the desirable output is insufficient, and the undesirable output is excessive, respectively; $0<\rho \leq 1$ is the ratio of inefficiency input (fewer input is needed to improve the efficiency) to inefficient output (more desirable output and fewer undesirable output are needed to improve the efficiency).

If $\rho=1,$ the $D M U_{0}$ has an efficiency of $1 .$ In this case, the $D M U_{0}$ is in the optimal state, without needing to improve the input and output variables; if $\rho<1,$ the entire $D M U_{0}$ is inefficient. In this case, the slack terms of input and outputs must be eliminated, making the inefficient DMU efficient.

Formula (1) shows that the basic form of our SBM model is a linear programming model. It can be seen that the SBM model has some important features, namely, the null jointless and joint weakly disposability of desirable and undesirable outputs [17].

2.2 GTFEE evaluation index system

As the evaluation target, the GTFEE is a concept involving multiple factors, including labor, capital, and energy. It can be understood as the economic efficiency of energy under the constraints of environmental variables.

Referring to the findings of Hao et al. [18], this paper defines the GTFEE as the ratio of the maximum desirable output to the minimum undesirable output at the minimal inputs of labor, capital, and energy. Mathematically, the GTFEE is described as the ratio of the target energy input (i.e. the minimal energy input) to the actual energy input. Hence, the GTFEE of region i at time t can be expressed as:

$G T F E E_{i t}=\frac{\text {target energy input}}{\text {actual energy input}}$      (2)

Formula (2) shows that the GTFEE falls within the value range of [0,1]. The result of formula (2) is positively correlated with the GTFEE. By the above definition, a GTFEE evaluation index system was set up based on the input-output relationship and the results of Zhang et al. [19] and Li and Hu [20]. As shown in Table 1, the evaluation indices in the system cover three input indices, a desirable output index, and an undesirable output index.

(1) Labor input: Labor input is indispensable to the evaluation index system. Labor is the key element of economic growth. Without labor input, the production equipment in enterprises cannot operate, making it impossible to tap the value of energy.

(2) Capital input: Capital is another essential input index of the evaluation index system. Labor alone cannot support the economic growth of the entire region, unless backed up by sufficient capital. The production activities of enterprises, the basic production units in national economy, determine the economic competitiveness of a region. In the absence of sufficient capital, an enterprise will not be able to purchase advanced production equipment or hire more workers, not to mention expanded reproduction. In this case, the energy cannot be utilized efficiently, and the economy will lose an important growth engine.

(3) Energy input: Energy input is the core input index of the evaluation index system, for our research aims to evaluate China’s GTFEE.

(4) Gross domestic product (GDP) (desirable output): Desirable output is the good output of energy utilization. GDP has long been recognized as the best indicator of regional economy [21].

(5) SO₂ (undesirable output): Undesirable output is the bad output of energy utilization. The utilization of energy often produces various pollutants, posing a serious threat to the eco-environment. Since China has made SO₂ the main target of pollutant control, SO₂ was taken as the undesirable output of the evaluation index system.

Table 1. The evaluation index system of GTFEE

2.3 Tobit model

In addition to GTFEE evaluation, this research attempts to identify and analyze the factors affecting the GTFEE in China, laying the basis for preparing energy policies that fit the situation of China. For this purpose, it is necessary to select a suitable metering model.

Since the GTFEE measured by the SBM model falls in [0, 1], the GTFEE as the explained variable in the metering model must be controlled between 0 and 1. If the model is regressed by the traditional ordinary least squares (OLS) method, the model result will skew to zero rather than reflect the actual situation [22]. In other words, the OLS method is not a desirable metering model for our research.

The above problem can be solved by the Tobit model, which was proposed by Tobit in 1958. Also known as the censored regression model, the Tobit model limits the explained variable between the upper bound of 1 and lower bound of 0 before regression analysis. Thus, the Tobit model adapts well to the empirical analysis of our research.

Drawing on the relevant literature Copeland and Talyer [23] and Xie et al. [24], this paper decides to discuss the influencing factors of the GTFEE from the aspects of economy, resource, institution, and technology. The effect mechanism of each influencing factor is summarized below:

(1) Economic growth (EG): The economic growth of a region is closely related to the intensity of energy consumption. On the one hand, the continuous growth of regional economy intensifies energy consumption, and pushes up pollutant emissions. On the other hand, economic growth promotes industrial upgrading and the awareness of environmental protection, and thereby suppresses the intensity of energy consumption and reduces pollutant emissions [25]. It is very meaningful to explore the exact impact of economic growth of the GTFEE.

(2) Industrial structure (IS): The industrial sector can be divided into primary, secondary, and tertiary industries. The secondary industry, which is mainly composed of manufacturing, consumes more energy, and produces more pollutants (SO₂) than the other two industries [26]. Still a developing country, China is being quickly industrialized. The secondary industry occupies a large portion of the national economy. This is obviously detrimental to the GTFEE.

(3) Property right structure (PS): The production activities of enterprises with different property rights are incentivized under different mechanisms. In general, the production activities of state-owned or state-controlled enterprises are affected by national policies. These enterprises tend to have a low production efficiency, and pay little attention to energy conservation. Meanwhile, most profit-seeking small and medium-sized enterprises focus on reducing costs (e.g. energy cost), and improve production efficiency. Their property right structure is conducive to the improvement of GTFEE.

(4) Technological progress (TP): Technological progress is an important driver for regional energy conservation and emission reduction. Normally, technological progress promotes enterprises to upgrade equipment, reduce input of factors (e.g. energy), and improve the energy efficiency. Moreover, technological progress also motivates enterprises to purchase advanced emission reduction equipment, reducing the level of pollutant emissions. These two mechanisms work together to promote the GTFEE.

(5) Opening-up (OU): China has been sticking to the opening-up policy. The degree of opening-up is mirrored by foreign direct investment (FDI). Over the past four decades, China has actively encouraged foreign investment. The influx of foreign capital provides the funds needed for regional economic development, speeding up economic growth. Furthermore, the FDI is accompanied by the entry of advanced production technologies, management experience, and environmental standards from foreign countries. All of these helps reduce regional energy intensity and slash pollutant emissions [27].

(6) Energy structure (ES): Energy is the core variable in the evaluation of the GTFEE. Thus, the energy structure can have a direct impact on GTFEE. Due to energy endowments, China has an energy system dominated by traditional fossil energies. Unlike bioenergy, wind power, and biomass energy, coal and other fossil energies are unclean. The utilization of unclean energies will produce a huge amount of SO₂. Till now, China remains as large producer and consumer of coal. The coal-dominated energy structure suppresses the GTFEE.

(7) Environmental regulation (ER): Studies have shown that environmental regulation could force enterprises to reduce emissions or cause the green paradox [28]. If a region has a high level of environmental regulation, e.g. the government imposes severe administrative penalties and charge pollution fees, the enterprises will be forced to optimize their energy structure and improve energy efficiency. If a region has a low level of environmental regulation, e.g. the government does not generously subsidize the use of clean energy, the enterprises will choose the profitable high-pollution production model over the attractiveness of the clean energy subsidy, resulting in the green paradox. The exact effect of environmental regulation on the GTFEE remains to be unveiled.

Based on the above effect mechanism, a Tobit model was constructed with GTFEE as the explained variable, and EG, IS, PS, TP, OU, ES and ER as the explanatory variables:

$\begin{array}{c}

G T F E E_{i t}^{*}=\alpha+\beta_{1} E G_{i t}+\beta_{2} I S_{i t}+\beta_{3} P S_{i t}+ \\

\beta_{4} T P_{i t}+\beta_{5} O U_{i t}+\beta_{6} E S_{i t}+\beta_{7} E R_{i t}+\varepsilon \\

\left\{\begin{array}{c}

G T F E E_{i t}=G T F E E_{i t}^{*} \\

G T F E E_{i t}=1

\end{array} \quad \begin{array}{c}

\left(i f G T F E E_{i t}^{*}<1\right) \\

\left(\text { if } G T F E E_{i t}^{*} \geq 1\right)

\end{array}\right.

\end{array}$       (3)

where, GTFEE$_{i t}^{*}$ is the GTFEE, the explained variable of the model; $E G_{i t}$ is economic growth measured by per-capita GDP (to eliminate the effect of collinearity, the natural logarithm of per-capita GDP is used in the model); $I S_{i t}$ is the industry structure measured by the output of secondary industry as a proportion of GDP; $P S_{i t}$ is the property right structure measured by the industrial output of state-owned or statecontrolled enterprises as a proportion of the total industrial output; $T P_{i t}$ is technical progress measured by the research and development (R\&D) expenditure as a proportion of GDP; $O U_{i t}$ is opening-up measured by the actual FDI as a proportion of $\mathrm{GDP}$ ( the USD is converted into $\mathrm{RMB}$ at the mean exchange rate); $E S_{\mathrm{it}}$ is energy structure measured by the coal consumption as a proportion of total energy consumption; $E R_{\mathrm{it}}$ is environmental regulation measured by the industrial pollution investment as a proportion of the total industrial output.

2.4 Data sources

Considering the data availability and completeness of all variables in the SBM model and the Tobit model, the panel data (2000-2017) of 30 Chinese provinces were selected for our research. Tibet, Hong Kong, Macao, and Taiwan were excluded, for the incompleteness of their data. The data on GDP, per-capita GDP, output of secondary industry, year-end number of employees, total energy consumption, coal consumption, fixed asset formation, SO₂, FDI, and R&D expenditure were extracted from China Statistical Yearbooks, China Energy Statistical Yearbooks, China Statistical Yearbooks on Environment, China Science and Technology Statistical Yearbooks, China Industry Statistical Yearbooks, local statistical yearbooks, and the website of the National Bureau of Statistics of China. The few missing items in the panel data were supplemented by moving average method.