3.2.1. DEA Two-Stage Method and Tobit Model

The DEA two-stage method is an advanced model derived to further explore the influencing factors and their degree of influence on efficiency values. In the first stage, the efficiency value of each DMU is calculated using the DEA method; in the second stage, the efficiency value calculated in the first stage is used as the dependent variable, and the factors influencing efficiency are used as the independent variables for regression analysis. The efficiency values measured by the DEA model are between 0 and 1, and the direct use of ordinary least squares (OLS) would cause bias and inconsistency problems. Therefore, the Tobit model is used in this paper and the maximum likelihood estimation method is applied for regression analysis [43].

**Table 1.** Results of input-output indicator selection and descriptive statistics.


The sample data used for the analysis are obtained from the China Forestry Statistical Yearbook and the provincial Statistical Yearbooks from 2008–2021.

The Tobit model is suitable for regressions where the dependent variable is restricted. The standard form of Tobit model is:

$$Y\_i = \begin{cases} \beta\_0 + \sum\_{t=1}^n \beta\_t \mathbf{x}\_t + \mu\_t, \text{ if } \beta\_0 + \sum\_{t=1}^n \beta\_t \mathbf{x}\_t + \mu\_t > 0\\ 0, \text{ if } \beta\_0 + \sum\_{t=1}^n \beta\_t \mathbf{x}\_t + \mu\_t \le 0 \end{cases},\tag{9}$$

where *Yi* denotes the actual dependent variable, i.e., the efficiency value of the ith DMU; *xt* denotes the independent variable; *β*<sup>0</sup> denotes the constant term; *β<sup>t</sup>* denotes the regression coefficient of the independent variable; *μ<sup>t</sup>* denotes the independent error disturbance term and obeys a normal distribution of N 0, *σ*<sup>2</sup> .
