2. Introduction to the BCC-DEA model

The CCR-DEA model based on the premise of constant returns to scale is slightly different from reality; the returns to scale are not constant in actual economic production activities, so Banker et al. [39] proposed an extension of the DEA analysis with the variable returns to scale model, namely the BBC-DEA model analysis method.

The assumptions in the BBC-DEA model are variable payoffs of scale, and also a decomposition of technical efficiency into two components. The BBC-DEA model incorporates convexity constraints, and its input-oriented model is:

$$\begin{cases} \max \left( \boldsymbol{\mu}^T \boldsymbol{y}\_0 + \mu\_0 \right) \\ \text{s.t.} \boldsymbol{\omega}^T \boldsymbol{x}\_i - \boldsymbol{\mu}^T \boldsymbol{y}\_i \ge 0 \\ \boldsymbol{\omega}^T \boldsymbol{x}\_0 = 0 \\ \boldsymbol{\omega} \ge 0, \boldsymbol{\mu} \ge 0, i = 1, 2, \dots, n \end{cases} \tag{7}$$

where *μ*<sup>0</sup> denotes the payoff of scale; ω is the portfolio ratio of effective decision units

3. Introduction of the super-efficient DEA analysis method

In the analysis results of the traditional DEA model, there will be multiple effective decision units at the same time, i.e., there are multiple efficiency values of 1, and thus the individual decision units cannot be ranked according to their high efficiency values. For this situation, then some scholars proposed Super-efficient DEA [40,41]. The Super-Efficiency DEA analysis method allows the simultaneous efficient decision units to be further analyzed and all DMUs reordered. With variable payoffs to scale, the super-efficient DEA is as follows: ⎧

$$\begin{cases} \min \left[ \theta - \varepsilon (\boldsymbol{\ell}^T \boldsymbol{S}^- + \boldsymbol{e}^T \boldsymbol{S}^+) \right] \\ \text{s.t.} \sum\_{i=1}^n \lambda\_i \mathbf{x}\_i + \boldsymbol{S}^- = \theta \mathbf{x}\_0 \\ \quad \sum\_{i=1}^n \lambda\_i \mathbf{y}\_i + \boldsymbol{S}^+ = \boldsymbol{y}\_0 \\ \boldsymbol{S}^- \ge 0, \boldsymbol{S}^+ \ge 0, \lambda\_i \ge 0, i = 1, 2, \dots, n \end{cases} \tag{8}$$

where *λ* represents the slack variable, and the next step introduces the slack variable *S*<sup>+</sup> and the residual variable *S*−; *θ* is the efficiency value required in the paper.

#### 3.1.2. Variable Selection and Data Sources

#### 1. Input variables

One of the most critical aspects of the super-efficient DEA evaluation model is the selection of input-output indicators and samples because they have a great impact on the final evaluation results. According to Pedraja—Chaparro and Salinas-Jimenez [42], for ensuring the credibility of the model's results, the inputs and outputs must be highly correlated. Forestry inputs should be the various factors of production that are invested to promote forestry development. In this paper, we study the ecological efficiency of forestry, therefore, the eco-forestry input and output index system should not only include the resource consumption factor component, but also the environmental pollution factor.

Forestry labor input: Labor input is the first influencing factor. As in other means of production, human capital is also a of means of production and plays an important role in production activities. In his study of economics, Quaker pointed out that people are the primary factor in the process of wealth creation. Labor input affects technical efficiency through both quantity and quality. In this paper, labor input refers only to the quantity of labor input, using the year-end number of forestry system employees to measure forestry labor input.

Forestry capital input: This paper uses the amount of forestry fixed asset investment in the current year as the capital input variable. Investment in forestry fixed assets refers to the monetary sum of man-hours or costs required for the construction and acquisition of forestry fixed assets in forestry production. Technical efficiency improvement of forestry production by forestry fixed assets is continuous and long-term and has an important role in forestry production. The impact of forestry fixed investment on eco-efficiency is not only expressed in the scale of investment, but also in the stability and continuity of the sources of forestry investment which will also improve FECO. For this reason, forestry fixed asset investment can well reflect funds and the smoothness of funding channels impact on FECO.

Forestry ecological input: It is expressed by the forestry ecological construction input. Forestry livelihood inputs: It is expressed by the forestry infrastructure inputs.

#### 2. Output variables

Desired output: This is the total output value of the forestry industry in each province, converted to constant prices in 2008 according to the CPI index, in order to exclude the influence of price changes

Non-desired output: Considering that it is difficult to characterize the environmental pressure by a single indicator, this paper uses "three waste" emissions from each region to represent pollution emissions: wastewater emissions from the secondary forestry industry in each province for wastewater, gas emissions from the secondary forestry industry in each province for gas emissions, and solid waste emissions from the secondary forestry industry in each province for solid waste. Specific variables and descriptive statistics are shown as follows in Table 1.
