Selecting the appropriate spatial weight matrix is fundamental for performing spatial autocorrelation tests and spatial econometric model regression. Since certain cities in the Yellow River Basin are not adjacent, this study opts for the utilization of the economic geography nested matrix and geographic distance weight matrix for analysis (Gong et al., 2022).

Geographical distance weight matrix (W1):

In the formula, d_ij represents the distance between region i and j.

The economic distance weight matrix (W2):

In the formula, $\overline{{{y}_{i}}}$, $\overline{{{y}_{j}}}$ represent the per capita GDP of region i and j.

Economic geographical nested matrix (W3):

In the formula, $\varphi $ ranging from 0 to 1, represents the proportional weight of the geographical distance matrix, and for simplicity of analysis, $\varphi $ is taken as 0.5 (Hou et al., 2023).

The Global Moran’s Index is utilized in this study for spatial autocorrelation to test the spatial autocorrelation of different indicators. The objective is to look into the degree of spatial association of agricultural carbon emissions between cities and their neighboring cities. The formula for the Global Moran’s I Index is as follows:

In this formula, n represents the number of spatial locations, ${{w}_{ij}}$ is the spatial weight matrix, representing the spatial relationship between units i and j; ${{r}_{i}}$ and ${{r}_{j}}$ represent the agricultural carbon emissions of each city, and $\bar{r}$ is the mean value.

The Global Moran’s I index ranges from [-1, 1]. When I=0, it indicates that agricultural carbon emissions are spatially unrelated and randomly distributed in space. When I<0, it signifies the presence of negative spatial correlation, showing a dispersed pattern. When I>0, it represents positive spatial correlation, indicating a clustered characteristic.

This study empirically tests the spatial spillover effects of agricultural mechanization on agricultural carbon emissions using the Spatial Econometric Model. The formula is as follows：

In this formula,$\ln c{{e}_{it}}$ represents agricultural carbon emissions, $l{{m}_{it}}$ represents agricultural mechanization,$\rho $ is the spatial correlation coefficient, W represents the spatial weight matrix,${{X}_{it}}$ represents control variables，subscript i indicates the i city, and t indicates the t year. ${{\alpha }_{0}}$ is a constant term,${{\beta }_{1}}$,${{\beta }_{2}}$ ${{\gamma }_{1}}$, ${{\gamma }_{2}}$ are coefficients to be estimated, ${{\mu }_{i}}$ and ${{\eta }_{t}}$ respectively represent individual and time effects,${{\varepsilon }_{it}}$ it is the random disturbance term.

After opting for spatial econometric models for empirical research, the selection of the appropriate model is determined through LM, Wald, and LR tests (Table 1). The LM test results show significance at the 1% level for both the Spatial Error Model (SEM) and the Spatial Autoregressive Model (SAR), suggesting that the Spatial Durbin Model (SDM) outperforms both. Subsequent LR and Wald tests also show significant results, indicating that the SDM model does not degenerate into the SAR or SEM models. The Hausman test is passed, suggesting that choosing a fixed-effects model is preferable to a random-effects model. In conclusion, the fixed-effects SDM model is chosen to explore the impact of agricultural mechanization on agricultural carbon emissions, with the regression results mainly analyzed using an economic geography nested matrix.

Agricultural carbon emissions (ce). This study integrates different carbon sources in agricultural carbon emissions to establish a measurement index system. It includes five dimensions in both planting and breeding industries: agricultural product input, agricultural energy utilization, crop planting and growth, livestock enteric fermentation, and livestock manure management. The details are shown in Table 2.

Using the carbon emissions factors provided by the Intergovernmental Panel on Climate Change (IPCC), we construct an agricultural carbon emissions measurement index system. This is done by calculating the product of the emissions volume for each carbon source and its corresponding emissions factor, yielding the volume of greenhouse gas emissions. Following this, the emissions are converted into carbon-equivalent emissions utilizing the Global Warming Potential (GWP) values for different gases. This process results in the total carbon emissions. The formula used to achieve this is as follows:

In the formula, ${{E}_{i}}$ represents the emission volume of agricultural greenhouse gases; ${{T}_{i}}$ is the volume of each carbon source; ${{\delta }_{i}}$ is the greenhouse gas coefficient caused by each carbon source; E is the total carbon emission volume; and ${{\mu }_{i}}$ is the Global Warming Potential value of

each greenhouse gas. According to the latest IPCC report, the Global Warming Potential values of methane and nitrous oxide are respectively 28-36 and 265-298 (with carbon dioxide’s value being 1), and this study uses their respective average values of 32 and 281.5. The original unit for carbon elements is multiplied by 44/12 to standardize it as carbon dioxide. The specific values of other coefficients are as detailed in Table 3 and Table 4.

Agricultural mechanization (lm). This study uses the total power of agricultural machinery relative to the total sown area of crops to measure the level of agricultural mechanization (Yang et al., 2022a).

To eliminate the influence of other factors on the measurement results, this paper, referencing existing studies (Hu et al., 2022; Li et al., 2023; Wei et al., 2023b), incorporates the following control variables into the analysis for more comprehensive results. 1) Government support (gov): This variable is calculated as the ratio of forestry, agriculture, and water conservancy expenditures to the total output value of agriculture, forestry, animal husbandry, and fishery. 2) Urban-rural coordination (urban): The ratio of per capita living expenses of rural residents to urban residents is used as the standard of measurement. 3) Economic development level (pegdp): Represented by the actual per capita gross domestic product. 4) Rural industrial structure (industry): Calculated as the ratio of the total agricultural output value to the total output value of agriculture, forestry, animal husbandry, and fishery. 5) Urbanization rate (ur): Represented by the proportion of urban population to the total population.

As shown in Figure 1, the Yellow River Basin holds significant ecological, economic, and cultural status in China. It does not only serve as a critical base for agricultural and energy production but also sports a unique geographical and climatic profile. With its boundaries stretching from 96°E to 119°E and 32°N to 42°N, the river flows from the west to the east, traversing nine provinces (and autonomous regions), which include Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shanxi, Shaanxi, Henan, and Shandong, before making its way into the Bohai Sea.

The Yellow River Basin’s topographical complexity presents a fascinating landscape with a considerable elevation gradient. It features the west as the highest point with an average elevation surpassing 4000 m above sea level. The central region rests at an approximate altitude of 1000 to 2000 m, while the east comprises primarily of the Yellow River alluvial plain.

The climate mirrors the geographic diversity, featuring variations that notably influence the local agriculture— predominantly dryland farming. Interestingly, carbon emissions from these dryland soils share a close connection with global warming ^②

② https://baike.baidu.com.

. Besides, the region’s delicate natural environment is particularly susceptible to irreversible ecological degradation (Xiong et al., 2016).

All these factors underscore the urgent need and relevance for a precise analysis of the agricultural carbon emis-sions and their associated influencers in the Yellow River Basin. Doing so offers valuable insights for realizing low- carbon agricultural development and enforcing effective ecological safeguards—both of which contribute meaningfully towards a sustainable future.

This study utilizes the panel data from 99 cities located in the nine provinces of the Yellow River Basin, comprising data spanning from 2001 to 2020. The principal sources of this city-based data include publications such as the “China City Statistical Yearbook” (2000-2021), the “China Rural Statistical Yearbook” (2000-2021), and information drawn from the EPS database, among others.

Any gaps present in the data were addressed through the use of linear interpolation methods. Moreover, all price- related indicators were adjusted to align with the constant prices of the year 2001 to maintain the uniformity of data.

For a detailed descriptive statistical analysis of the variables, please refer to Table 5.

Figure 2 shows the trend of total agricultural carbon emissions in the Yellow River Basin from 2001 to 2020. Overall, the total carbon emissions from agriculture in the Yellow River Basin present an “M” shape, which can roughly be seen as four different stages: ‘fluctuating rise-fluctuating fall-slow rise-continuous fall.’ This indicates that agriculture is gradually moving towards low-carbon development. Specifically, from 2001 to 2004, agricultural carbon emissions showed an upward trend, followed by a significant decline after 2005. This may be due to China’s implementation of agricultural tax reduction and exemption policies from 2003, which, along with the development of agricultural cooperatives, promoted the scale of agricultural production, leading to an accelerated decline in agricultural carbon emissions from 2005 to 2007 (Cheng et al., 2023). After 2007, agricultural carbon emissions showed a slow upward trend. The reason might be that with the development of the social economy and the advancement of agricultural technology (Guo and Zhang, 2023), agricultural production efficiency was improved (Yin et al., 2017), which suppressed agricultural carbon emissions, but external economies had not yet formed. In 2015, a plan for zero growth in fertilizers and pesticides was introduced ^③

③ https://www.moa.gov.cn/xw/zwdt/201503/t20150318_4443677.htm.

, and the ‘National Agricultural Modernization Plan (2016-2020)’ in 2016 explicitly proposed to fully implement the five development concepts, raise awareness of environmental protection, actively develop efficient green agriculture, and achieve agricultural modernization ^④

④ https://www.gov.cn/zhengce/content/2016-10/20/content_5122217.htm.

. Farmers began to shift from traditional agricultural production methods to green, low-carbon methods, engaging in low-carbon production or adopting low-carbon agricultural technologies, followed by a further decline in agricultural carbon emissions (Hu et al., 2022). Secondly, from the perspective of the regions shown in the figure, the carbon emissions from agriculture in the downstream area are far higher than those in the middle and upper reaches.

Figure 3 shows the spatial distribution of total agricultural carbon emissions in 2001, 2007, 2013, and 2020. Overall, the agricultural carbon emissions in the Yellow River Basin exhibit a pattern of “highest in the downstream, followed by the midstream, and lowest in the upstream,” with significant regional differences. From a spatial perspective: 1) The upstream area of the Yellow River Basin has lower agricultural carbon emissions. This may be due to the fact that the upstream area includes provinces such as Qinghai, Gansu, and Ningxia, which have harsh natural conditions and terrain consisting mostly of plateaus, deserts, and grasslands, unfavorable for large-scale agricultural production (Zhang et al., 2018). Additionally, the agricultural structure in these areas is predominantly livestock-based (Tian et al., 2021), which has lower carbon emissions compared to crop farming. 2) The midstream area of the Yellow River Basin includes Shanxi and Shaanxi provinces. Their agricultural carbon emissions are also relatively low. This may be due to these areas still relying on traditional agriculture with limited crop diversity. The development of livestock farming is relatively restricted, thus leading to lower carbon emissions. Shaanxi Province, in particular, exhibits a reverse “N” trend in agricultural carbon emissions. 3) The downstream area of the Yellow River Basin includes Henan and Shandong, two major grain-producing areas. Higher grain production means more agricultural carbon emissions. Additionally, the downstream area of the Yellow River Basin consists of more economically developed regions. The shift towards modern agriculture, along with extensive use of pesticides, fertilizers, and energy, also increases agricultural carbon emissions (Klasen et al., 2016). Currently, the downstream area of the Yellow River Basin remains a high agricultural carbon emission region.

In summary, although the agricultural carbon emissions in the Yellow River Basin have shown a declining and fluctuating trend during the study period, there are still individual cities where agricultural carbon emissions have increased, with clear regional differences. Therefore, developing low- carbon agriculture will be a major measure for future agricultural carbon emission reduction in the Yellow River Basin (Chen et al., 2019).

The global Moran’s Index calculated according to the formula, as shown in Table 6, indicates that the Moran’s Index from 2001 to 2020 passed the significance test. This suggests that there is a certain degree of spatial dependency and spatial spillover effect in the agricultural carbon emissions in the Yellow River Basin. Moran’s I ranges from 0.149 to 0.208, showing little fluctuation, which indicates a stable spatial clustering effect in the agricultural carbon emissions of the Yellow River Basin. Furthermore, as can be seen from Table 6, the spatial correlation of agricultural carbon emissions has gradually weakened since 2008. This weakening may be due to the recent adjustments in industrial structure, with a significant increase in the proportions of the secondary and tertiary industries (Su et al., 2023). Additionally, the transformation in agricultural operation models is another factor. Modern agricultural operation models place more emphasis on sustainable development. Lastly, the government’s support for agriculture has been continuously increasing, with the introduction of a series of policies and measures encouraging farmers to adopt low-carbon and environmentally friendly production methods, such as promoting energy-saving and emission-reduction technologies (Yang et al., 2022b).

The Local Moran’s I scatter plot can be used to reveal the local evolutionary characteristics and differences in agricultural carbon emissions in the Yellow River Basin. Within this study, Moran’s scatter plots are created for the years 2001, 2007, 2013, and 2020, as shown in Figure 4. The Moran scatter plot categorizes cities into four quadrants based on their agricultural carbon emissions and their neighbors’ emissions: “High-High,” “Low-High,” “Low-Low,” and “High-Low”. These represent spatial relationships among cities. The “High-High” and “Low-Low” clusters indicate cities with similar high or low emissions surrounded by cities with the same trend, respectively. Conversely, “Low- High” and “High-Low” clusters show cities with emissions contrasting their neighbors’. Placement within the first and third quadrants signifies a high positive spatial correlation, indicating spatial uniformity, whereas placement within the second and fourth quadrants indicates a negative spatial correlation, signifying spatial heterogeneity. Across the selected years of 2001, 2007, 2013, and 2020, the distribution pattern of agricultural carbon emissions appears generally consistent. Most cities tend to fall into the first and third quadrants, thus forming either a “High-High” or “Low- Low” clustering trend, which suggests a positive spatial autocorrelation. Consequently, it can be deduced that there exists a stable spatial clustering effect in agricultural carbon emissions among the majority of cities within the Yellow River Basin.

The regression results of the spatial Durbin model are shown in Table 7. Table 7 presents the econometric results using an economic geographic distance-nested matrix. The results indicate that the direct effect of agricultural mechanization on agricultural carbon emissions is significantly negative at the 1% statistical level. Agricultural mechanization significantly reduces local agricultural carbon emissions, exhibiting a clear direct carbon reduction effect. The spatial spillover effect of agricultural mechanization on agricultural carbon emissions is also significantly negative at the 1% statistical level. A one-unit increase in the level of agricultural mechanization leads to a 7.566 unit decrease in agricultural carbon emissions in neighboring regions, demonstrating a significant spatial carbon reduction effect. The analysis suggests that considering the spatial spillover effect of agricultural mechanization, its carbon reduction impact will be even greater.

From Table 7, it can be seen that among the control variables, policy support has a significant direct effect on agricultural carbon emissions at the 1% statistical level, and its spatial spillover effect and total effect on agricultural carbon emissions are significant at the 5% statistical level. Urban-rural coordination has a significantly negative direct effect, spatial spillover effect, and total effect on agricultural carbon emissions at the 1% statistical level. The rural industrial structure has a significantly negative direct effect on agricultural carbon emissions at the 1% statistical level, but its spatial spillover effect and total effect on agricultural carbon emissions are not significant. The level of economic development has a significantly positive direct effect, spatial spillover effect, and total effect on agricultural carbon emissions at the 1% statistical level. The level of urbanization has a significantly negative direct effect, spatial spillover effect, and total effect on agricultural carbon emissions at the 1% statistical level.