The International Energy Agency (IEA, 2013) believes that energy efficiency should be taken as the first fuel rather than a hidden fuel and regards it as “a key tool for boosting economic and social development. From an economic perspective, efficiency is defined as the full and most efficient use of limited and scarce resources to satisfy people’s wants and needs given the technology, that is, produce more with less. If there is no way to make someone better off and nobody worse off, then the situation is Pareto efficient. Extending this concept to production economics, a 100% Pareto–Koopmans efficiency is achieved if and only if no inputs or outputs of any decision-making unit (DMU) can be improved without worsening the other inputs or outputs. However, in most management and social science applications, the theoretically possible Pareto efficiency is unknown. Therefore, it is replaced by relative efficiency [38], which is fully efficient if and only if other DMUs cannot improve inputs or outputs without worsening some of its other inputs or outputs on the basis of empirically available evidence. In this case, measuring production efficiency is actually evaluating whether there is waste of input by comparing the minimum input with the actual input while the output is unchanged or evaluating whether there is an output shortage by comparing the actual output with the maximum output with the input unchanged.
1. Defining Energy Efficiency and Carbon Emissions Efficiency
1.1. The Origin of Energy Efficiency and Carbon Emissions Efficiency
From an economic perspective, efficiency is defined as the full and most efficient use of limited and scarce resources to satisfy people’s wants and needs given the technology [
36], that is, produce more with less. If there is no way to make someone better off and nobody worse off, then the situation is Pareto efficient [
37]. Extending this concept to production economics, a 100% Pareto–Koopmans efficiency is achieved if and only if no inputs or outputs of any decision-making unit (DMU) can be improved without worsening the other inputs or outputs. However, in most management and social science applications, the theoretically possible Pareto efficiency is unknown. Therefore, it is replaced by relative efficiency [
38], which is fully efficient if and only if other DMUs cannot improve inputs or outputs without worsening some of its other inputs or outputs on the basis of empirically available evidence. In this case, measuring production efficiency is actually evaluating whether there is waste of input by comparing the minimum input with the actual input while the output is unchanged or evaluating whether there is an output shortage by comparing the actual output with the maximum output with the input unchanged.
1.2. Single-Factor Indicator of Energy Efficiency and Carbon Emissions Efficiency
1.2.1. Energy Intensity
Energy efficiency was first recorded in 1888 [
39] and is known as the thermal economy of a machine [
40]. Patterson [
41] was the first to elaborate on energy efficiency in economic terms. He defined energy efficiency as the ratio of GDP to energy consumption, commonly referred to as energy productivity. Energy intensity, as the reciprocal of energy productivity, is widely used to measure energy efficiency [
42], and is used by many international organizations and countries as a strictly binding target for carbon reduction [
43,
44].
1.2.2. Carbon Intensity
Actual production and energy consumption will inevitably produce environmental pollution as a by-product of economic growth, of which CO
2 emissions have the greatest impact on climate deterioration. Like energy intensity, carbon intensity, measured as CO
2 emissions per unit of output, is also widely used as a performance indicator of carbon emissions [
45,
46]. Goldemberg suggested using energy intensity to analyze national trends in energy consumption and carbon intensity to analyze climate change [
47,
48]. With the increasing severity of climate change, in addition to energy intensity, the International Energy Agency [
49] has also incorporated CO
2 intensity into its statistics to assess carbon emissions and sustainability targets.
1.2.3. Inadequacy of Single-Factor Indicator
Since only a single-input factor is considered in addition to one output, energy intensity and carbon intensity are often referred to as single-factor indicators [
50,
51]. Although these indicators are easy to understand and convenient to measure [
34,
52], they do have some shortcomings. On the one hand, the measurement of intensity does not conform to the definition of efficiency in economics. Intensity has no comparison between the optimal and actual energy consumption or carbon emissions. Blindly reducing the intensity may cause economic development to deviate from the optimal state. On the other hand, intensity only focuses on the goal of realizing energy saving, carbon emissions reduction, and output growth but pays little attention to other factors, such as capital and labor and structural changes in production [
53,
54]. It also fails to reflect the change in technical efficiency [
55]. Energy intensity may decrease due to labor substitution or organizational structure improvements rather than technological advancement in energy efficiency [
56], and it reflects energy consumption rather than energy efficiency [
57]. Carbon intensity separates the intrinsic connections between CO
2 emissions, energy consumption, and economic growth [
58,
59], making it a measure of decarburization and an assessment of energy policies at a national level rather than carbon efficiency [
60]. Improving energy efficiency is the most effective way to reduce the resource reallocation cost of energy saving and emission reduction.
1.3. Total-Factor Indicator of Energy Efficiency and Carbon Emissions Efficiency
Through the previous analysis, it is not difficult to find that the definition of single-factor is inconsistent with economic theory, which is divorced from reality and not in line with the production process. In view of the deficiencies of single-factor indicators, total-factor indicators are more convincing in measuring energy saving and carbon emissions reductions.
In measuring the efficiency of DMUs with multiple inputs and multiple outputs, Farrell extends the Pareto–Koopmans property to inputs and outputs, avoiding the necessity of resource prices or other weight assumptions and formal relations between inputs and outputs. This makes it possible to determine relative efficiency by taking the performance of other DMUs to evaluate the overall behavior of each DMU. The obtained result is known as Farrell efficiency [
61], which can estimate the amount of input that can be saved or the amount of output that can be increased without worsening any input and output. With the assumption of equal access to inputs by all DMUs, Farrell efficiency is restricted to expressing technical efficiency. However, Farrell’s empirical work was limited to cases of a single output and failed to take into account other non-zero slack, which is an important source for mix inefficiencies in both inputs and outputs.
1.3.1. Total-Factor Energy Efficiency
On the basis of Farrell efficiency, Charnes, Cooper, and Rhodes [
62] further formalized the relative efficiency, made up for the shortcomings of Farrell’s work, and developed a dual pair of linear programming model data envelopment analysis (DEA) to identify the best-practice frontier and estimate relative efficiency. The production function is generally regarded as the basis for economics. By constructing the frontier with the possibility of multiple production functions, DEA closely relates to the theory of production economics. Compared with other methods for measuring relative efficiencies, DEA does not need to set a specific function form and strict assumptions and has less data constraints [
63,
64]. Therefore, since the initial study of Charnes, Cooper, and Rhodes, DEA has become widely accepted and rapidly applied in a number of fields, including the nonprofit, public, and private sectors. It is often used to estimate production efficiency and to examine the overall performance of operations and management.
With more and more extensive application, in addition to deeper development of methodologies, DEA is also used to measure various efficiency values. As the catastrophic problems caused by man-made greenhouse gas emissions become more and more serious, reducing global energy consumption and CO
2 emissions has attracted great interest and become a primary focus of international attention. Ramanathan [
65] was the first to introduce DEA in carbon reduction and to measure the amount of carbon emissions that each country can reduce, but he did not measure specific carbon efficiency. Considering that the prominent driving factor of CO
2 emissions lies in huge energy consumption, Hu and Wang [
27] further proposed the concept of total-factor energy efficiency (TFEE) by employing a DEA model. This has been widely applied since it was proposed and has vigorously supporting research on energy efficiency and carbon emissions reduction.
Taking into account the role of capital, labor, and energy consumption in the production process and their contribution to GDP, TFEE is defined and measured as:
1.3.2. Total-Factor Carbon Emissions Efficiency
2. Efficiency Measurement Model Based on DEA
The concept and idea of data envelopment analysis (DEA) was first proposed by Farrell [61] and is a commonly used benchmark tool to measure the production efficiency of decision-making units (DMUs) and to reflect their performance. DEA is a method that is easy to operate. It does not need to make any restrictive assumptions about relevant functions and can deal with multiple input and output variables of different units.
2.1. Radial Model
2.1.1. CCR
In 1978, Charnes, Cooper, and Rhode [62] first proposed an input-oriented data envelopment analysis, which is based on Constant Return to Scale (CRS) in the intersection of mathematics, operational research, mathematical economics, and management science. Subsequently, this method has attracted widespread attention and application. An input-oriented CRS-DEA model can be expounded as follows:
According to Figure 6, SS’ is a piece-wise linear isoquant determined by all the DMUs in the sample, where the radial contraction of the input vector is (Xλ, Qλ), the radial adjustment is AA’, and the constraints in Equation (1) ensure that the projected point cannot lie outside the feasible set. There are four firms, A, B, C, and D, where firms using input combinations C and D are the two efficient firms that define the frontier, and firms A and B are inefficient firms. Based on the measure of technical efficiency, the efficiency of A and B can be represented as OA′/OA and OB′/OB, respectively. However, it is not certain if A′ is an efficient point because when the use of input x2 is reduced (that is, CA’), it still produces the same output. For firm B, it is effective when B moves to B′, as its input combinations change, i.e., efficiency equals one.
Figure 6. Input-oriented CRS-DEA model.
2.1.2. BCC
Figure 7. Output-oriented VRS-DEA model.
2.2. Non-Radial Model
2.2.1. Traditional Slacks-Based Measure (SBM) Model
In the traditional CRS/VRS-DEA model, the inefficient decision-making unit achieves the effective state by reducing all inputs or expanding all outputs in the same proportion. Therefore, the traditional DEA model is also referred to as a radial model. When the DMU is inefficient, there is a certain distance between the current state and the optimal target. In the radial model, this distance is equal to the sum of the radial improvement and the slack improvement, but the latter is not reflected in the efficiency measurement of the radial model.
In this context, Tone (2001) [
86] proposed a non-radial and non-angular Slacks-Based Measure model, which directly introduced the slack variable into the objective function. The SBM model can find the target energy input more effectively, avoid the influence and error caused by radial and angle differences, better reflect the essence of efficiency measurement, and improve the reliability and accuracy of efficiency measurement.
2.2.2. Slacks-Based Measure (SBM) Model with Undesirable Output
Tone (2004) [
87] constructed the SBM model by taking undesirable outputs into account. Therefore, compared with other DEA models, the SBM model with undesirable output can better reflect the essence of efficiency evaluation.
3. Input-Output Variables for Efficiency Measurement
The seemingly straightforward measurements have their underlying theoretical and empirical assumptions [
93]. Efficiency can be defined and measured in various forms, and the results obtained can affect socio-economic development in different ways, such as placing an unfair burden of carbon reduction on consumers and isolating humans from the natural world. In efficiency measurement, social scientists call for more observation of complex social contexts and practices and the dissecting of efficiency from conceptual foundations, practical applications, and sociology [
20,
94,
95]. This is mainly reflected in the selection of input and output variables of efficiency measurement.
3.1. Production Possibility Set
3.2. Input-Output Variables Selection
As an improvement of single-factor energy efficiency, total-factor energy efficiency overcomes the one-sidedness of single-factor energy efficiency to a certain extent and takes into account the coordination and substitution of factors. However, in the existing literature, the selected input-output variables are repeated or omitted, and this does not conform to the theory of production economics and the actual production situation.
In the current research on TFEE, the most commonly selected variables are capital, labor, and energy as input variables and value added as output variable [
50,
53,
100]. Some scholars also chose the value of output as an output variable [
101]. On this basis, some scholars consider the impact of the environment and add undesirable outputs into the output variable [
102]. Some scholars have also considered other intermediate inputs [
84]. However, these studies have a certain degree of repetition or omission in the selection of variables.
The input-output variables of total-factor energy efficiency (TFEE) are also applicable to the measurement of total-factor carbon emissions efficiency (TFCE). Pang (2015) chose employment, capital stock, and energy use as inputs; GDP as desirable output; and CO2 emissions as undesirable output, analyzing the impact of clean energy utilization on TFEE and TFCE, respectively. Based on the measurement of TFEE, Li and Lin (2017) also added CO2 emissions as an undesirable output and measured the TFCE.
Based on a comprehensive review of previous studies, this paper indicates an improved measurement method for total-factor efficiency and proposes a more accurate and complete measurement input-output variables of energy efficiency, which provides a scientific method for measuring energy efficiency and carbon emissions efficiency. In order to ensure the accuracy and reliability of results for energy efficiency measurement, it is necessary to select the most appropriate input-output variables. Input-output variables must be consistent with and reflect the production process as close to reality as possible.
This entry is adapted from the peer-reviewed paper 10.3390/en15030962
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