4.1.1. Model for Green Total Factor Efficiency Measurement
Green development means that economic development must be balanced with a guarantee of energy conservation and emission reduction. Most the traditional indicators for measuring green development, such as energy intensity or carbon emission intensity, are single-factor indicators that only reflect one aspect of green development. We use green total factor efficiency (GTFE) to evaluate the green development of Shaoxing’s industrial sector. It is a total factor indicator that incorporates energy utility and carbon dioxide emissions into performance measurement.
The GTFE is calculated based on the super-efficiency Slack-based-measure data envelopment analysis model (super-SBM-DEA). The model is proposed by Tone [
38,
39,
40]. With this method, using the input and output data of the sample observations, we can draw the efficient frontier consisting of all effective points which could be approximately regarded as the minimum inputs and undesirable outputs under a given desirable output or the maximum desirable outputs under a given input and undesirable outputs. The efficiency of any DMU can subsequently be measured by the distance from its actual production point to the reference efficient point located on the efficiency frontier.
We choose this method based on the following two reasons. Firstly, DEA models regard the proportion of inputs (outputs) that can be reduced (expanded) as the degree of inefficiency. The traditional radial DEA model requires inputs (outputs) to change proportionally. However, Super-SBM-DEA allows different inputs and outputs to be reduced or expanded in different proportions. This is more suitable to reality. Secondly, when multiple decision-making units (DMUs) are effective at the same time under traditional DEA models, further comparison among the efficiency of different DMU is impossible. The super-SBM-DEA model overcomes the problem through two-step processing.
The super-SBM-DEA model is a combination of the standard SBM-DEA model and the super SBM-DEA model. Under the super-SBM-DEA model, we need to evaluate the green performance of different DMUs with a standard SBM-DEA model first. The standard SBM-DEA model under constant returns-to-scale assumption is as follows.
Suppose there are n DMUs. Each DMU has m inputs, s desirable outputs and r undesirable outputs. We denote the vectors of inputs, desirable outputs and undesirable outputs for by , and , respectively. We define input, desirable output and undesirable output matrices X, Y and Z by X = , Y = and Z = .
Let
P(
X) be the production feasible set which contains all possible production points. It can be expressed as follows.
We assume X, Y and Z are all greater than zero and satisfy the axiom: if (Y, Z) ∈ P(X) and Y’ ≤ Y, Z’ ≥ Z or X’ ≥ X, then there is (Y’, Z) ∈ P(X), (Y, Z’) ∈ P(X), (Y’, Z’) ∈ P(X) or P(X’) ∈ P(X). The axiom implies that production could be carried out in an ineffective way. It is very much in tune with reality. Evidently, the efficiency frontier is the envelope curve of the P(X).
According to Tong [
38,
39,
40] and Cheng [
41], evaluating the efficiency of
(
) can be transformed into solving the following nonlinear program.
where:
j is the
jth DMU;
i is the
ith input;
k is the kth desirable output;
l is
lth undesirable output;
λ represents the vector of weight coefficients;
sx and
sz are called input and undesirable output slacks which represent the potential for reducing inputs and undesirable outputs;
sy is called desirable output slack which can be seen as the potential for expanding desirable outputs;
(0 ≤
≤ 1), which is strictly monotonically decreasing with respect to
sx,
sz and
sy, represents the efficiency value of
.
The process above is repeated n times for
o = (1, …, n). After collecting the data of the input and output variables in
Section 4.2.1, the optimal solution of
can be obtained by solving the nonlinear programs with the help of MATLAB. The objective function in the program can, on the one hand, find the efficient frontier by maximizing the slacks of inputs and outputs, and on the other hand, obtain the value of GTFE based on the fraction and the optimal solution.
As can be seen from Equation (1), is a weighted efficiency performance that reflects the average space for the reduction of inputs and undesirable outputs and the expansion of desirable outputs. If and only if equals to 1 (i.e., sx = 0, sz = 0 and sy = 0), there is no room for efficiency improvement. , therefore, is called SBM-efficient. When is smaller than 1, production is carried out in an ineffective way. is called SBM-inefficient.
In the first step, multiple DMUs may be found to be SBM-efficient. These DMUs cannot be compared with each other because their efficiency coefficient () equals to one. In order to rank these SBM-efficient DMUs, we move to the next step, that is, reevaluating the efficiency of SBM-efficient DMUs with the help of the super SBM-DEA model.
Suppose
is an SBM-efficient DMU found in the last step, according to Cheng [
41], the efficiency of
can be reevaluated with the help of the super SBM-DEA model. The super SBM-DEA model under constant returns-to-scale assumption is as follows.
All symbols in the super SBM-DEA model above have the same meaning as in the standard SBM-DEA model. The efficiency of can be recalculated by δ.
As can be seen from the mathematical expression of Equation (2), the efficiency of SBM-efficient DMUs is similarly measured by the distance from their production point to the point closest to the efficient frontier. However, different from in the standard SBM-DEA model, the efficient frontier in the super SBM-DEA model is constructed with the input and output data of all DMUs, excluding that of the target SBM-efficient DMU. It means that the efficient frontiers used in the efficiency measurement of different SBM-efficient DMUs are different. These differences reflect the technical gap between the SBM-efficient DMUs and form the basis for further ranking.
In addition, the traditional DEA models adopt the current period method to construct the efficient frontier, i.e., the current efficient frontier is constructed based on current observations. This causes some issues. On the one hand, the current period method is susceptible to exogenous factors such as economic fluctuations, and spurious technical regressions may occur in dynamic analysis; on the other hand, the efficiency performance of the same DMU in different periods cannot be compared with each other due to the different frontiers. In this regard, we take reference from Pastor and Lovell (2005) [
42], and adopt a global criterion function, i.e., assuming that the production techniques are fixed during the sample period and performing efficient frontier construction based on all observations.
4.1.2. Model for Effect Assessment of “Dual-Control” Regulations
The Differences-in-Differences model (DID) is used to analyze the Effects of the “Dual-Control” regulations.
In recent years, the DID model has been widely used in the field of policy effectiveness evaluation. The basic idea of DID is to identify the causal relationship between policy and dependent variables by comparing the differential effects of a Natural Experiment or a Quasi-experiment on the Treatment Group (the combination of samples affected by the experiment) and the Control Group (the combination of samples not affected by the experiment). Compared to traditional policy evaluation methods, DID can eliminate bias due to differences between treatment and control groups, and acquire more accurate and reliable results of policy effects [
43].
Referring to Feng et al. (2021) [
44], we build a DID model as follows.
where:
i (
i = 1, …, N) represents the ith industrial sector;
j (
j = 1, …, M) is the jth control variable number;
t stands for time;
y represents the dependent variable;
post is the policy dummy variable, taking 0 before the policy is implemented and 1 after the policy is implemented;
treat is the group dummy variable, taking 0 for the control group and 1 for the treatment group;
x is the control variable;
α is the coefficient to be estimated;
μ and
λ represent the individual fixed effect and the time fixed effect;
ε is the residual item, which represents all other factors that may affect the dependent variable but are not considered as control variables.
We focus on the coefficient α3, which reflects the net effect of the policy. A significant non-zero α3 indicates that policy has a significant effect on the explained variables.
The design of experimental and control groups is a key issue in DID model building. The “Dual-Control” regulations are applied to all industries, which means all regions and industries in Shaoxing are affected by the regulations. This makes it difficult to find experimental groups and control groups. Vig (2013) encountered a similar problem in his study of the effects of the Enhanced Mortgage Debt Protection Act, where theoretically there is no treatment or control group [
45]. His solution was that, given that tangible assets such as land and plants are more likely to act as collateral than intangible assets, the Act would have a greater impact on firms with a higher proportion of tangible assets, so treatment and control groups could be constructed based on the proportion of tangible assets in the firm. This gives us an inspiration: energy-intensive industries are the focus of various government regulations and often have greater room for energy saving, the “Dual-Control” regulations thereby will have a greater impact on energy-intensive industries. In line with Vig (2013) [
45], we construct the experimental group and control group based on the energy intensity performance of industrial sectors.