To analyze how digital agriculture influences carbon emissions in agriculture, we construct the following baseline econometric model: C O 2 i t = α 0 + α 1 D i g i t a l _ a g r i i t + α 2 X i t + μ i + λ t + ε i t (1)

In Equation 1, i and t denote province and year, respectively. The explained variable CO 2 it represents agricultural carbon emissions in province i in year t; the primary explanatory variable, Digital _ agri it , measures the extent of digital agriculture advancement in province i during year t. X i t represents the set of control variables including industrial structure, agricultural mechanization, and rural energy consumption. The term ε i t represents the random error, μ i denotes province-specific fixed effects, and λ t refers to time-specific fixed effects.

Existing studies demonstrate that agricultural carbon emissions exhibit clear spatial dependence (Tian and Yin, 2022). Many scholars highlight that ignoring spatial interactions among economic indicators can lead to biased conclusions. Therefore, this study employs spatial econometric techniques to account for spatial correlations between variables and to investigate the impact of digital agriculture on agricultural carbon emissions. The specific spatial econometric model is as follows: C O 2 i t = ρ W C O 2 i t + θ 1 D i g i t a l _ a g r i i t + β X i t + θ 2 W D i g i t a l _ a g r i i t + δ W X i t + μ i + λ t + ε i t (2) ε i t = ρ W C O 2 i t + τ i t (3)

In Equations 2, 3, ρ denotes the spatial autocorrelation parameter, W represents the spatial weighting matrix, and X it includes various control variables that affect agricultural carbon emissions over time. The coefficients to be estimated include θ 1 , θ 2 , β and δ .

Spatial weighting matrices commonly include adjacency and geographic-distance matrices, representing geographic interactions. This research uses the adjacency matrix as the primary spatial weight structure, supplemented by the geographic-distance matrix for robustness testing. Specifically, the adjacency matrix considers first-order neighborhood relationships: if two provinces share a common boundary, the value is set to 1; otherwise, it is 0, as represented in Equations 4, 5: Adjacency Matrix : : W 1 = 1 , i f   p r o v i n c e s   i   a n d   j   a r e   n e i g h b o r s 0 , i f   p r o v i n c e s   i   a n d   j   a r e   n o t   n e i g h b o r s (4) Geographic Distance Matrix : W 2 = 1 d 2 , i ≠ j 0 , i = j (5)

To examine the channels through which digital agriculture influences carbon emissions in agriculture, we establish a mediation analysis framework, using environmental regulation and green technological innovation as intermediary variables. Initially, we investigate how digital agriculture impacts environmental regulation and green innovation by specifying the mediation models as follows: M e d i t = λ 0 + λ 1 D i g i t a l _ a g r i i t + λ 2 X i t + μ i + λ i + ε i t (6) C O 2 i t = η 0 + η 1 D i g i t a l _ a g r i i t + η 2 M e d i t + η 3 X i t + μ i + λ i + ε i t (7)

Equation 6 investigates the effect of digital agriculture on the mediators, whereas Equation 7 analyzes the combined influence of digital agriculture and the mediators on agricultural carbon emissions.

In this research, the dependent variable is defined as the carbon emission intensity from agriculture. Following Li et al. (2021), agricultural carbon emissions are estimated using IPCC-recommended coefficients. Six emission sources relevant to agricultural production are selected: fertilizers, pesticides, agricultural films, diesel consumption, irrigation, and tillage. Agricultural carbon emissions are computed using the corresponding emission factors, as shown below: E = ∑ E i = ∑ T i * δ i (8)

In Equation 8, E denotes total agricultural carbon emissions, Ti indicates the quantity of the i-th emission source, and δ i represents the emission coefficient associated with that source.

In agricultural production, various inputs contribute to carbon emissions, with their emission coefficients sourced from reputable references. Fertilizers have a carbon emission coefficient of 0.8956 kg C·kg^-1, based on data from Oak Ridge National Laboratory in the United States. Pesticides, another crucial agricultural input, exhibit a carbon emission coefficient of 4.9341 kg C·kg^-1, also from Oak Ridge National Laboratory. The carbon emission coefficient of agricultural films is reported as 5.1800 kg C·kg^-1 by the Institute of Agricultural Resources and Ecological Environment at Nanjing Agricultural University. Diesel fuel, commonly used in agricultural machinery, has an emission coefficient of 0.5927 kg C·kg^-1, according to the Intergovernmental Panel on Climate Change (IPCC). Tillage activities are associated with a significant emission coefficient of 312.60 kg C·hm^-2, as documented by the College of Biology and Technology at China Agricultural University. Additionally, irrigation contributes an emission coefficient of 266.48 kg C·hm^-2, according to Dubey and Lal (2009).

Using coefficient data and provincial statistical yearbooks, we calculated agricultural carbon emissions at the provincial level. ARCGIS 10.2 software was then employed to create spatial maps depicting provincial agricultural carbon emissions for the years 2013 and 2020 (Figure 1). The comparative analysis uncovered two primary trends: First, agricultural emissions demonstrated a declining pattern, decreasing from 81.9 million tons in 2013 to 74.67 million tons in 2020. This decline can likely be attributed to China’s recent promotion of green technologies, the push for zero growth in agricultural fertilizers and pesticides, and efforts aimed at mitigating agricultural non-point source pollution (Guo and Zhang, 2023). Secondly, significant spatial discrepancies in agricultural carbon emissions were identified. Provinces such as Shandong, Henan, Hebei, Jiangsu, Anhui, Heilongjiang, and Xinjiang reported higher emission levels, while provinces like Fujian, Jiangxi, Hainan, Ningxia, Shanxi, and Guizhou exhibited lower emissions. These variations may stem from differences in crop structures and the intensity of land use across provinces.

The main explanatory variable is the comprehensive development level of digital agriculture. Following the framework established by Jiang et al. (2022), digital agriculture is assessed across three key dimensions: digital infrastructure (Digital_infr), digital industrialization (Digital_indu), and farmers’ digital literacy (Digital_enti). The digital infrastructure dimension is quantified by the level of internet accessibility in rural areas, represented by the ratio of rural broadband subscribers to the rural population. The digital industrialization aspect is captured by the quantity of “Taobao Villages.” According to the Alibaba Research Institute (ARI), a “Taobao Village” is defined as a rural area where online businesses actively represent at least 10% of local households, and annual e-commerce transactions exceeding 10 million yuan (ARI, 2021). Farmers’ digital literacy is gauged by comparing the average communication expenditure per capita in rural areas to the average per capita consumption expenditure.

To integrate these metrics into a single comprehensive measure of digital agriculture, we applied the entropy weighting method. This data-driven technique assigns weights to indicators based on their intrinsic characteristics, offering greater objectivity, accuracy, and reliability compared to subjective weighting methods. The comprehensive digital agriculture development was evaluated using the entropy weighting approach in four steps:

1 Standardize the data using the formula: x i j ′ = x i j − x min x max − x min (9) In Equation 9, x ij represents the measurement of the j indicator in year i; x min and x max denote the lowest and highest values of the j indicator, respectively.

The results indicate that over the study period, the dimension of digital agriculture industrialization received the highest weight, averaging 0.5454. This was followed by digital agriculture infrastructure, with an average weight of 0.2958, while farmers’ digital literacy ranked third with an average weight of 0.1562.

Finally, the formula for calculating the overall level of digital agriculture is provided in Equation 14. Digital _ agri = w 1 ∗ Digital _ infr + w 2 ∗ Digital _ indu + w 3 ∗ Digital _ enti (14)

Using Equation 13 and data from provincial statistical yearbooks, the comprehensive digital agriculture level for each province was determined. By selecting 2013 and 2020 as reference years, spatial patterns of provincial digital agriculture development were visualized using ARCGIS 10.2 software (Figure 2). A comparative analysis of these years revealed two key trends: First, there was a general upward trend in the overall digital agriculture development level. Second, significant regional differences in digital agricultural practices were observed. In 2013, eastern coastal provinces, including Zhejiang, Shanghai, and Guangdong, demonstrated higher development levels, while provinces in the central and western regions were relatively less advanced. Notably, Alibaba, China’s largest e-commerce company, headquartered in Hangzhou, Zhejiang, has played a critical role in promoting digital agriculture in surrounding cities. By 2020, policies and financial support from the central government boosted digital agriculture in major agricultural regions of central and western China, leading to significant growth.

Following the methodologies of Guo and Zhang (2023) and Yan et al. (2023), this study includes the following control variables: Industrial Structure (stru): This is represented by the proportion of agricultural output value in GDP. A higher proportion suggests greater agricultural activity, potentially increasing resource consumption and agricultural carbon emissions. Agricultural Mechanization Level (lnmachine): Defined as the natural logarithm of the total power of agricultural machinery, reflecting the degree of mechanization in rural production. Resource Consumption (lnelect): Defined as the natural logarithm of rural electricity consumption, capturing the intensity of agricultural energy use.

Agricultural Green Technology Innovation (GTI): Following Wang H. et al. (2021), green total factor productivity (TFP) in agriculture is used as the proxy indicator. We apply the Malmquist productivity approach, utilizing a non-radial, non-angular SBM directional distance model, which addresses issues of negative data values and angle biases in efficiency analysis. Inputs include agricultural fixed capital, labor, and energy, with the desired output being total agricultural production (in constant 2000 prices) and the undesirable output being agricultural carbon dioxide emissions. Agricultural fixed capital using the perpetual inventory approach, while labor is represented by the average number of employees in agriculture. Energy usage is measured in 10,000 tons of standard coal. This study calculates agricultural green TFP for each province from 2013 to 2020, using data from the China Rural Statistical Yearbook and the China Energy Statistical Yearbook.

Environmental Regulation (ER): Measured by a comprehensive environmental regulatory index. Following Hu et al. (2022), data on industrial wastewater discharge, industrial SO2, and dust emissions across provinces between 2013 and 2020 were collected. The entropy weighting approach was used to develop the index.

The Global Moran’s Index is shown in Equation 15, where n represents the total provinces selected (in this study, n = 31), and X i , X j represent agricultural carbon emissions and digital agriculture levels for provinces i and j, respectively. x ¯ denotes the average value of the sample, and w ij represents the adjacency-based spatial weighting matrix, where the value equals 0 if provinces i and j do not share a boundary and equals 1 if they do. Moran’s I ranges between −1 and 1, with positive values suggesting positive spatial autocorrelation, negative values suggesting negative spatial autocorrelation, and a zero value indicating no spatial autocorrelation. Since Moran’s I is designed to evaluate spatial autocorrelation for cross-sectional data, the test was conducted separately for each year, and the result showed that the Moran’s I values from 2013 to 2020 are consistently greater than zero and statistically significant, indicating the presence of spatial autocorrelation in each year. M o r a n ’ s   I = n ∑ i = 1 n ∑ j = 1 n w i j + x i − x −   + x j − x −   ∑ i = 1 n ∑ j = 1 n w i j ∑ j = 1 n x i − x −   2 (15)

Before performing the spatial econometric analysis, multiple statistical procedures were applied to determine the appropriate model specification. Using the spatial adjacency weight matrix, we conducted LM, Wald, LR, Hausman, and fixed-effect tests. The significant LM test results suggested the use of a spatial econometric approach. Additionally, Wald and LR tests rejected the null hypothesis that the SDM could be simplified into either the Spatial Autoregressive Model (SAR) or Spatial Error Model (SEM), validating the suitability of the Spatial Durbin Model (SDM) model. The Hausman test indicated a preference for the fixed-effects approach over random-effects, confirming that the fixed-effects Spatial Durbin Model (SDM) using the spatial adjacency matrix is appropriate. Therefore, this study adopted the Spatial Durbin Model (SDM), incorporating bidirectional fixed effects. The choice of the Spatial Durbin Model (SDM) over the Spatial Autoregressive Model (SAR) and Spatial Error Model (SEM) is justified based on the results of the Wald and LR tests, which rejected the restrictions needed to simplify SDM into SAR or SEM. Moreover, SDM can capture both direct and indirect (spillover) effects, aligning with the study’s aim to investigate spatial externalities associated with digital agriculture. Therefore, SDM provides a more comprehensive framework for analyzing spatial dependencies.

The spatial spillover effects were further separated into direct and indirect components. The direct effect represents how digital agriculture affects local agricultural carbon emissions, while the indirect effect measures its spillover to neighboring regions. Table 3 summarizes the direct, indirect, and total effects of digital agriculture on agricultural carbon emissions using the spatial adjacency weight matrix. All coefficients are negative and statistically significant at the 1% level, confirming that digital agriculture effectively reduces agricultural carbon emissions both locally and in adjacent regions (Ma et al., 2022). The spatial autocorrelation parameter (ρ) is positive and significant at the 5% level, supporting Hypothesis 2. Additionally, the indirect (spillover) effects of digital agriculture on carbon emissions surpass the direct effects, highlighting the growing significance of spatial spillovers.

To address potential endogeneity, two instrumental variables were introduced, following Shen et al. (2022): the number of post offices per million people in 1984 (post) and the spherical distance from provincial capitals to Hangzhou (dis). Historically, post offices were vital for information transmission, which correlates with digital agriculture without directly influencing agricultural carbon emissions, satisfying the exclusivity requirement. Additionally, since Hangzhou leads digital agricultural development, provinces closer to it are likely to have higher digital agriculture levels. The spherical distance from Hangzhou does not affect agricultural carbon emissions, fulfilling both the relevance and exclusivity requirements.

Columns (1) and (2) in Table 4 present the estimation results using two instrumental variables: post and dis. The instrumental relevance was verified through the first-stage F-statistic, which exceeded the conventional threshold of 10, indicating the absence of weak instruments. The Sargan overidentification test also confirmed the validity of the instruments. The first-stage coefficient is significantly positive, with an F-statistic value of 28.54, which exceeds the threshold of 10, indicating that weak instrumental variables are not an issue. Additionally, the Sargan statistic of 21.46 is significant at the 1% level, suggesting no over-identification problems. The findings from column (2) demonstrate that digital agriculture significantly reduces agricultural carbon emissions, remaining statistically significant at the 1% level even after addressing potential endogeneity issues related to omitted variables.

Exclusion of specific samples: Due to the unique administrative characteristics of Chinese municipalities, this study excludes municipalities from the sample. The regression outcomes following this exclusion are presented in Table 5. The coefficient magnitude, direction, and significance of digital agriculture remain consistent with the baseline estimations, confirming the robustness of the results.

Alternative spatial weighting matrices: This research replaces the adjacency matrix with a geographic distance-based matrix. The resulting regression outcomes are presented in columns (4), (5), and (6) of Table 3. The estimated coefficient magnitude, direction, and significance levels of digital agriculture remain stable, further validating the robustness of the findings.

The adaptability of digital agricultural solutions to local conditions, including climate, crop types, and farming practices, is crucial for achieving optimal carbon reduction effects across diverse regions. In 2003, the China Ministry of Finance (CMF, 2003) designated 13 provinces as major grain-producing regions. In these areas, grain farming constitutes a larger share of agricultural activities, while non-major grain-producing regions focus more on other types of cultivation. Separate regression analyses were conducted for each group, with results shown in columns (1) and (2). Column (1) presents results for provinces primarily engaged in grain production, whereas column (2) displays findings for areas with lower grain production levels. The empirical results suggest that digital agriculture has a more substantial carbon emission reduction effect in regions predominantly focused on grain production. This is likely due to the specialized agricultural structures and larger-scale farming practices typical of grain-producing areas, which enhance resource use efficiency—particularly in water and fertilizer application—thereby reducing carbon emission intensity and bolstering carbon sequestration capacity (Zhu et al. 2022).

Economic development disparities between coastal and inland provinces in China result in variations in the adoption of digital agriculture and its associated carbon reduction impacts. Separate regression analyses were performed for these two regional groups, with results provided in columns (3) and (4) of Table 7. The findings show that digital agriculture’s effect on carbon emission reduction is more significant in inland provinces. This may be attributed to the comparatively lower level of agricultural infrastructure development in inland regions, where carbon emission intensity is usually higher. Thus, the benefits of digital agriculture in emission reduction are more pronounced in these areas, reflecting a “latecomer advantage” when compared to coastal areas.