3.2.3. Mediating Variable

In order to test whether farmland transfer (farmland transfer-out or farmland transferin) affects the income of rural households under different livelihoods, and then affects the consumption structure of rural households. In the questionnaire, we set the question "What is the annual income of your family in 2020 by choosing the corresponding livelihood mode through the transfer of farmland (farmland transfer-out or farmland transfer-in)?" to identify this. In addition, the logarithm of per capita household income in 2020 was used to indicate the income of rural households under different livelihood options.

#### 3.2.4. Control Variables

To mitigate the omission of variables that lead to biased estimation results, this paper also includes variables at the level of household head characteristics [1], family characteristics [19] and village characteristics [21] that affect rural household consumption as control variables. Among them, household head characteristics include the gender of the household head, age of the household head and marriage of the household head; family characteristics include the number of family members, age per capita of the family and assets per capita of the family (logarithmicized); and village characteristics include whether there is non-agricultural economy in the village, the availability of public transportation in the village, the topographical condition of the village, and the distance from the village to the county. In addition, the unit of consumption and asset-related variables is RMB yuan, and there is no unit in the value assignment of variables after logarithmic processing. The specific relevant variable settings and statistical descriptions are shown in Table 1.


**Table 1.** Variable definitions and descriptive statistics.

#### *3.3. Model Selection*

Because this paper mainly explores the impact of farmland transfer on rural household consumption, it is appropriate to use an OLS model for estimation. To this end, a relevant benchmark model is constructed by drawing on the research practices of Dong and Huang [48] and Hu and Ding [22], which has the following basic form:

$$CS\_i = \beta\_0 + \beta\_1 X\_i + \beta\_2 D\_i + \varepsilon\_{i1} \tag{1}$$

In Equation (1), *CSi* denotes the total consumption of rural households, food consumption and non-food consumption. *Xi* denotes farmland transfer-out and farmland transfer-in. *Di* denotes a matrix of control variables, including household head characteristics, family characteristics and village characteristics. *β*<sup>0</sup> is a constant term, *β*<sup>1</sup> and *β*<sup>2</sup> are coefficients to be estimated and *εi*<sup>1</sup> denotes an error term and is assumed to satisfy a standard normal distribution.

To test whether farmland transfer (farmland transfer-out or farmland transfer-in) acts on rural households' consumption and consumption structure through the path of influencing rural households' income under different livelihoods. Then, this paper draws on the study of Wen and Ye [49] and further constructs an intermediary effect model based on model (1) with rural households' income under different livelihoods as the mediating variable as follows:

$$FI\_i = \delta\_0 + \delta\_1 X\_i + \delta\_2 D\_i + \varepsilon\_{i2} \tag{2}$$

$$CS\_{\dot{i}} = \phi\_0 + \phi\_1 X\_{\dot{i}} + \phi\_2 F I\_{\dot{i}} + \phi\_3 D\_{\dot{i}} + \varepsilon\_{\dot{i}3} \tag{3}$$

In the above model, *FIi* is the mediating variable, representing rural households' income under different livelihoods; *δ*<sup>0</sup> and *φ*<sup>0</sup> are constant terms, *δ*1, *δ*2, *φ*1, *φ*<sup>2</sup> and *φ*<sup>3</sup> are coefficients to be estimated, *εi*<sup>2</sup> and *εi*<sup>3</sup> denote error terms and are assumed to satisfy standard normal distribution; other variables and coefficients are defined in the same way as Equation (1).

#### **4. Results and Analysis**

#### *4.1. Multicollinearity Test*

Since the introduction of more variables at the level of household head characteristics, family characteristics and village characteristics in this paper may pose the problem of multicollinearity, variance inflation factor (VIF) is used for multicollinearity diagnosis. In Table 2, the results show that the variance inflation factor (VIF) values are all less than 10, and we can judge that there is no more serious multicollinearity problem basically.


**Table 2.** Multicollinearity test.
