A Non-Linear Exploration of the Digital Economy’s Impact on Agricultural Carbon Emission Efficiency in China

Abstract

As the global climate crisis intensifies, improving agricultural carbon emission efficiency has become crucial for achieving the sustainable development goals (SDGs). This study investigates the complex, non-linear relationship between China’s digital economy and agricultural carbon emission efficiency, utilizing panel data from Chinese provinces spanning 2012–2022. We employ a multi-method approach, including the Super-SBM model for efficiency measurement, two-way fixed effects models, quantile regression, and Generalized Additive Models (GAMs) for empirical analysis. Our findings reveal: (1) The digital economy significantly enhances agricultural carbon emission efficiency, but with distinct non-linear characteristics across different dimensions. (2) The impact varies among digital economy aspects: the digital economy foundation shows the most substantial influence, followed by the rural digital industry level, while rural digital infrastructure has a relatively minor effect. (3) A threshold effect is observed, with the digital economy’s impact more pronounced in regions with higher agricultural carbon emission efficiency. (4) GAM analysis unveils complex non-linear patterns: the rural digital industry’s impact initially decreases before increasing, the digital economy foundation shows an overall increasing trend with plateaus, and rural digital infrastructure exhibits a near-linear relationship. (5) Sensitivity analysis indicates that agricultural carbon emission efficiency is most responsive to changes in the digital economy foundation, followed by the rural digital industry level. These findings provide nuanced insights into the digital economy’s role in enhancing agricultural sustainability. We propose targeted policy recommendations, including accelerating rural digital infrastructure development, optimizing the rural digital industry structure, and implementing context-specific digital facility construction. These strategies aim to fully leverage the digital economy’s potential in improving agricultural carbon emission efficiency, contributing to China’s “dual carbon” goals and sustainable agricultural development.

1. Introduction

In recent years, the escalating global climate crisis has brought agricultural carbon emissions into sharp focus. As a significant contributor to greenhouse gas emissions, agriculture accounts for approximately 22% of global anthropogenic emissions [1]. Improving agricultural carbon emission efficiency has emerged as a key strategy in pursuing the sustainable development goals (SDGs) and mitigating climate change, particularly for countries like China that have set ambitious “dual carbon” goals [2]. Agricultural carbon emission efficiency is defined as the ratio between theoretically achievable carbon emissions and actual emissions [3]. This metric serves as an effective tool for achieving sustainable development goals. It accurately reflects the environmental impact of agricultural production activities [4] and provides crucial evidence for policymakers’ decision-making processes [5]. Consequently, it is considered a crucial metric for sustainable agricultural development. Concurrently, the rapid development of the digital economy has begun to reshape traditional agricultural practices, offering new pathways for enhancing productivity and sustainability. In China, the digital economy’s penetration rate in agriculture reached 11.2% in 2023, signaling its growing influence on the sector [6]. This study aims to unravel the complex, non-linear relationships between China’s digital economy and agricultural carbon emission efficiency, viewing it as an intricate tapestry where various digital dimensions interweave with agricultural practices. By employing advanced analytical methods, including GAMs [7], we seek to provide a nuanced understanding of how different aspects of the digital economy—its foundation, rural digital industry level, and rural digital infrastructure—impact agricultural carbon emission efficiency. This exploration is crucial not only for academic discourse but also for informing targeted policies that can effectively leverage digital technologies to achieve sustainable agricultural development and contribute to global climate goals.

Concurrently, the digital economy has rapidly developed in China and globally. According to the China Digital Economy Development Research Report (2024) released by the China Academy of Information and Communications Technology (CAICT), China’s digital economy reached 53.9 trillion yuan in 2023. The growth of the digital economy contributed to 66.45% of GDP growth, effectively supporting stable economic growth. In agriculture specifically, the digital economy has become a crucial production factor. The digital economy, with its intelligent and ecological development characteristics, is profoundly influencing traditional agricultural production methods. It plays a vital role in promoting agricultural carbon reduction, enhancing agricultural production efficiency, and driving sustainable agricultural development [8]. Digital technologies, such as precision agriculture and smart farming practices, have the potential to optimize resource use and reduce greenhouse gas emissions in the agricultural sector [9]. Furthermore, the development of rural digital platforms can help farmers better anticipate and address production risks, potentially leading to more efficient and sustainable farming practices [10]. However, the relationship between digital economic development and agricultural carbon emission efficiency is complex and potentially non-linear [6]. Wang et al. demonstrate that digital economy development contributes to carbon emission reduction and exhibits significant spatial effects with close inter-city spatial connections [11]. However, their study does not reveal the non-linear relationship between these variables. Using a new spatial panel smooth transition threshold model, Bai et al. discover an inverted U-shaped relationship between the digital economy and carbon emissions [12]. This study focuses on whether and how digital economic development can empower the improvement of agricultural carbon emission efficiency. By disaggregating specific dimensions of the digital economy, such as its foundation, rural digital industry level, and rural digital infrastructure, we aim to provide a more nuanced understanding of their differentiated impacts on agricultural carbon emission efficiency. This research has significant theoretical value and practical implications for leveraging digital economic development to enhance agricultural carbon emission efficiency and contribute to China’s “dual carbon” goals.

The remainder of this paper is organized as follows: Section 2 reviews the relevant literature on the digital economy and agricultural carbon emissions and proposes our contribution. Section 3 describes the data and methodology, including the Super-SBM model for efficiency measurement, panel regression models, and GAMs. Section 4 presents our empirical findings that discuss the non-linear relationships between different dimensions of the digital economy and agricultural carbon emission efficiency, along with sensitivity analysis results. Section 5 concludes with a summary of key findings and provides targeted policy recommendations for leveraging the digital economy to enhance agricultural carbon emission efficiency and achieve sustainable development goals.

2. Literature Review

Agricultural carbon emission efficiency serves as a bridge between agricultural economic output and carbon emissions. It is a comprehensive indicator that considers economic growth, resource consumption, and greenhouse gas emissions, reflecting the relationship between input and output in agricultural production. Agricultural carbon emission efficiency serves as a bridge between agricultural economic output and carbon emissions. It is a comprehensive indicator that considers economic growth, resource consumption, and greenhouse gas emissions, reflecting the relationship between input and output in agricultural production. Current academic research on agricultural carbon emission efficiency primarily focuses on the selection of agricultural carbon sources and differences in calculation methods. Scholars recognize that factors leading to agricultural carbon emissions are complex and diverse, resulting in variations in calculation methods. Regarding carbon sources, some scholars identify the main greenhouse gasses in agricultural production as CO₂ from agricultural films, machinery, and irrigation [13]; N₂O from fertilizer application and soil release [14]; and CH₄ from rice paddies and animal manure [15]. Others consider the primary sources to be agricultural production inputs [16,17], crop varieties [18], planting methods, and waste [19,20]. Yun et al. further found that soil was one of the major sources of agricultural carbon emissions [21]. Methodologically, scholars have employed diverse approaches to measure agricultural carbon emission efficiency and analyze spatial differences. These methods include the DEA model and DEA-Malmquist index decomposition [22] and the SBM-Undesirable model [23]. Additionally, researchers have utilized the GB-US-SBM model for these analyses [24,25].

The digital economy, as a new driver empowering high-quality economic development, represents the future direction of economic growth. Its environmental effects have garnered significant scholarly attention. Existing literature primarily focuses on two aspects: the carbon reduction effects and mechanisms of the digital economy. Regarding the carbon reduction effects, three main viewpoints emerge. The first posits that digital economic development increases carbon emissions. Some scholars argue that the rapid growth of the digital economy, accompanied by energy-intensive information and communication technologies [26,27], increases demand for electricity and other energy sources [28]. Particularly, the operation of digital centers [29] and the use of artificial intelligence [30,31] directly lead to higher carbon emissions [32,33], potentially causing significant environmental burdens [34]. Belkhir and Elmeligi [35] demonstrated that, without proper control, the information and communication industry’s greenhouse gas contribution could exceed 14% of global levels. The second viewpoint suggests that the digital economy facilitates carbon reduction. It promotes the integration and allocation of digital technologies with traditional economic resources in most countries, thereby reducing energy consumption levels [36,37]. Additionally, it accelerates digital information technology innovation, effectively promotes the integration of the digital economy with traditional manufacturing, and aids in the forming of green, low-carbon business models [38]. It also expedites cross-border innovation and sharing of carbon reduction technologies [39,40] and improves energy structures to reduce carbon emissions [41,42]. The third perspective proposes that the digital economy’s impact on carbon emissions follows an inverted U-shaped trend [43] with spatial spillover effects [44]. In China, agricultural carbon emissions have shown a stepped increase since 2000, but with a slow overall pace [45]. Agricultural carbon emission efficiency initially decreased and then increased, with notable provincial differences [46]. Regarding carbon reduction mechanisms and pathways, micro-level analyses focus on the substitution effects of digital factors on old energy-consuming technologies and products [47,48], technological changes [49,50], and improvements in production and energy utilization efficiency [51,52]. Macro-level analyses examine the impact pathways of digital economic development on carbon reduction through energy consumption behavior [53], carbon tax policies [54], and international trade [55]. Liu first introduced the study of the digital economy’s carbon emission effects in agricultural production [56]. Digital agriculture reduces greenhouse gas emissions through intelligent and refined operations [8], digital finance supporting agricultural development [57], and the application of Climate-Smart Agriculture (CSA) technologies [9]. Some scholars suggest that governments can help farmers anticipate and effectively address agricultural production risks through rural digital platforms [10]. Furthermore, research indicates that as China’s digital economy develops to a higher level, the carbon reduction effects will become more pronounced [58].

Existing research on the relationship between the digital economy and agricultural carbon emission efficiency has employed various econometric methods. Some studies have utilized linear models, such as fixed-effects and random-effects models [59]. Others have employed mediation effect models to explore influence mechanisms [60,61]. These models assume a constant impact of the digital economy on agricultural carbon emission efficiency, overlooking potential non-linear relationships. To address this limitation, scholars have introduced non-linear models. For instance, Wang et al. used threshold regression models, revealing threshold effects in the digital economy’s impact on carbon emissions [62]. Tan et al. applied quantile regression to study the influence of digital financial inclusion on regional agricultural carbon emissions in China. Their findings revealed that the negative coefficients of the digital financial inclusion index and its three-dimensional indices decreased with increasing quantiles [63]. However, these non-linear models still have limitations. Threshold regression models assume linear relationships within different intervals, potentially failing to capture more complex non-linear relationships. While quantile regression can reflect heterogeneous impacts, it struggles to intuitively display overall non-linear trends. Moreover, these models often require pre-assumed specific functional forms, which may lead to model specification bias. GAMs can flexibly capture non-linear relationships between variables without pre-assuming specific functional forms [7]. Recent years have witnessed the widespread application of GAM in natural sciences, particularly in ecology [64], environmental science [65,66], and computer science [67]. This statistical approach overcomes the limitations of conventional models while offering visual representations of complex relationships. GAM demonstrates robust performance in handling non-normal distributions and heteroscedasticity issues. Despite its widespread applications in natural sciences, the adoption of GAM in economic research remains limited.

While existing literature has extensively researched the relationship between the digital economy and carbon emissions, providing an important foundation for understanding the environmental impact of the digital economy, several gaps remain in the study of the digital economy and agricultural carbon emissions: (1) Current research focuses more on the impact of the digital economy on total agricultural carbon emissions, with relatively little attention to agricultural carbon emission efficiency. (2) Studies on the impact of the digital economy on agricultural carbon emissions predominantly use linear models. Although some research has explored non-linear relationships such as inverted U-shapes or threshold effects, these methods struggle to comprehensively reflect the complex, gradual non-linear relationships that may exist. (3) Most studies use comprehensive digital economy development indices to represent the level of digital economic development. While this approach can reflect overall trends, it lacks specific economic implications, making it difficult to identify the differentiated impacts of specific dimensions of the digital economy on agricultural carbon emissions. Given these limitations, this study focuses on the impact of the digital economy on agricultural carbon emission efficiency, employing more flexible non-linear models and disaggregating specific dimensions of the digital economy. This approach aims to provide new perspectives and empirical evidence for deepening the understanding of the relationship between the digital economy and sustainable agricultural development.

This study contributes to the existing literature in several ways: (1) It focuses on the impact of the digital economy on agricultural carbon emission efficiency, rather than just total emissions, offering a new perspective on agricultural sustainability from an efficiency standpoint. (2) Currently, the application of GAMs in the field of economics is rare. This study employs GAMs to address this research gap and facilitates a better understanding of the non-linear relationship between the digital economy and agricultural carbon emission efficiency. (3) The study disaggregates specific dimensions of the digital economy (such as digital economy foundation, rural digital industry level, and rural digital infrastructure construction), analyzing the differentiated impacts of each dimension on agricultural carbon emission efficiency. This provides empirical evidence for formulating targeted policies. (4) By examining the sensitivity of agricultural carbon emission efficiency to various dimensions of the digital economy, this research offers important references for optimizing the structure of the digital economy to enhance agricultural carbon emission efficiency. These contributions not only fill gaps in existing research but also provide new empirical evidence and policy implications for deepening the understanding of the relationship between the digital economy and sustainable agricultural development.

3. Data and Methodology

3.1. Explained Variable

The traditional DEA model, developed by Charnes and Cooper [68], has been widely applied in measuring agricultural carbon emission efficiency. However, this model overlooks the impact of slack variables and undesirable outputs, leading to imprecise measurements of agricultural carbon emission efficiency. To address these limitations, Tone refined the traditional DEA model, introducing the Super-SBM model [69]. This study employs the Super-SBM model, which incorporates undesirable outputs, to assess agricultural carbon emission efficiency across Chinese provinces. Building upon the research of Han et al. [70], we have constructed an evaluation index system for agricultural carbon emission efficiency. The specific indicators are presented in

Table 1. Evaluation index system of agricultural carbon emission efficiency.

Primary Indicators	Secondary Indicators	Unit
Input Indicators	Crop Sown Area	h${\mathrm{m}}^2$
	Agricultural Machinery Input	MW·h
	Primary Industry Employment	persons
	Chemical Fertilizer Usage	Tons
	Pesticide Usage	Tons
	Agricultural Film Usage	Tons
	Agricultural Fixed Capital Stock	Yuan
Output Indicators	Total Agricultural Output Value (Desirable Output)	Yuan
	Agricultural Carbon Emissions (Undesirable Output)	Tons

.

The calculation of agricultural carbon emissions in this study employs the IPCC methodology, which is widely recognized for quantifying greenhouse gas emissions [71]. This approach involves multiplying the activity level data of agricultural carbon emission sources by their respective emission factors. The resulting emissions from various greenhouse gasses in the agricultural sector are then aggregated to determine the total carbon emissions. The calculation formula is presented in Equation (1):

$${\mathrm{C}\mathrm{E}=\sum {\mathrm{T}}_{\mathrm{n}}\ast \sigma }_{\mathrm{n}}$$

(1)

In this equation, CE represents the total agricultural carbon emissions, ${\mathrm{T}}_{\mathrm{n}}$ denotes the activity level of the nth carbon emission source, and EFn is the emission factor for the nth source. Our study considers carbon sources including agricultural energy consumption, agricultural input materials, livestock farming, and crop growth. The emission factors are derived from IPCC guidelines, ORNL, IREEA, and studies by Tian et al. [72] and Min et al. [73]. It is important to note that different greenhouse gasses have varying global warming potentials. To ensure consistency in our results, we have converted all greenhouse gasses to standard carbon dioxide equivalents. Based on the IPCC Fourth Assessment Report, the conversion factors for carbon, methane, and nitrous oxide are 44/12, 25, and 298, respectively.

3.2. Explaining Variables

Drawing from the research of Guo et al. [74] and Ma et al. [8], this study categorizes the agricultural and rural digital economy into three dimensions: rural digital infrastructure construction, rural digital industry, and digital economy foundation. Rural radio and television network coverage (radio) serves as a proxy for rural digital infrastructure construction, represented by the household penetration rate of rural cable radio and television. Rural digital industry is represented by the scale of rural network payments (inclusion), using the digital financial inclusion index as a proxy. The digital economy foundation is indicated by the rural smartphone penetration rate (phone), measured by the average number of mobile phones owned per 100 rural households annually.

To ensure accurate and reliable results and avoid omitted variable bias, this study, following Tian et al. [75], incorporates the following control variables:

Agricultural economic development level (ADL): Represented by per capita value-added in agriculture, forestry, animal husbandry, and fishery, calculated based on primary industry employees. To eliminate price fluctuations, the value-added is deflated using 2011 as the base year.

Fiscal expenditure on agriculture (expenditure): Indicated by provincial agricultural fiscal expenditure.

Agricultural internal industry structure (AIS): Represented by the ratio of the sum of animal husbandry and crop cultivation output values to the total output value of agriculture, forestry, animal husbandry, and fishery.

Agricultural mechanization input level (machinery): Proxied by per capita agricultural machinery power, calculated based on primary industry employees. Due to data instability, this variable is logarithmically transformed.

Environmental regulation (ER): Represented by the ratio of regional pollution control project investment to regional GDP.

Urbanization rate (UR): Indicated by the ratio of urban population to total population.

3.3. Data Source

This study examines 30 Chinese provinces (excluding Tibet, Hong Kong, Macau, and Taiwan) over the period from 2012 to 2022. The scale of rural network payments is represented by the digital financial inclusion index sourced from the Peking University Digital Financial Inclusion Index. Data for the remaining variables are derived from annual editions of the China Rural Statistical Yearbook, China Statistical Yearbook, and provincial statistical yearbooks. Interpolation methods were employed to address occasional missing data points.

Table 2. Results of the descriptive statistics of the main variables.

	Variables	Variable Symbol	Mean	Max	Min	S.D.	VIF
Explained variable	Agricultural carbon emission efficiency	Efficiency	0.568	1.187	0.228	0.198
Explaining variable	Radio and television network coverage	Radio	33.050	127.210	0.500	23.900	1.939
	Scale of rural online payments	Inclusion	246.040	487.420	18.330	109.244	3.817
	Rural smartphone penetration	Phone	237.440	319.800	141.870	35.680	2.021
Control variables	Agricultural economic development level	ADL	12.210	121.923	−27.769	14.680	1.028
	Fiscal expenditures for agriculture	Expenditure	575.720	1359.300	91.780	283.810	3.280
	Agricultural internal industrial structure	AIS	0.814	1.066	0.538	0.113	1.685
	Agricultural mechanization input level	Machinery	3441.030	13,353.000	94.000	2931.610	3.502
	Environmental regulation	ER	0.001	0.010	0.000	0.001	1.347
	Urbanization rate	UR	60.120	89.600	35.030	12.072	3.394

presents the descriptive statistics for all variables used in this study.

3.4. Methodology

This study employed a multi-method approach to investigate the impact of the digital economy on agricultural carbon emission efficiency. This study began with a panel data regression model using double fixed effects to estimate the overall influence. To address potential biases from linear assumptions, we utilized quantile regression to examine variations in this impact across different percentiles of agricultural carbon emission efficiency. Additionally, we incorporated GAMs to capture complex non-linear relationships. This comprehensive strategy not only provides robust empirical results but also deepens our understanding of the relationship between the digital economy and agricultural carbon emission efficiency from multiple perspectives. The following sections detail the theoretical foundations, model specifications, and applications of these methods in our research.

(1)

Panel Data Regression Model with Double Fixed Effects

Panel data combines the advantages of cross-sectional and time-series data, allowing researchers to simultaneously examine individual heterogeneity and temporal dynamics. This approach offers a more comprehensive and in-depth analytical perspective. The basic form of the panel data model can be expressed as:

$$y_{it}={\mathrm{x}}_{it}^{\prime }\mathrm{\beta }+{\lambda }_t+u_i+{\epsilon }_{it}$$

(2)

where $y_{it}$ is the explained variable, ${\mathrm{x}}_{it}^{\prime }$ represents the explaining variables, ${\lambda }_t$ denotes time fixed effects, $u_i$ represents individual fixed effects, and ${\epsilon }_{it}$ is the random error term. Among these variables, logarithmic transformations were applied to efficiency, phone, and machinery.

(2)

Quantile Regression Model

Quantile regression offers significant advantages in economic research. It captures the effects of independent variables at different points of the dependent variable’s distribution, revealing heterogeneous impacts that traditional mean regression cannot detect. This model is robust to outliers, enhancing the reliability of estimates. It performs well with non-normal distributions and heteroscedastic data. Moreover, it requires fewer assumptions about error terms, increasing its applicability. To more accurately describe the impact of explanatory variables on the range and conditional distribution shape of the dependent variable, this paper followed Koenker et al. [76] and constructed the following model:

$${\mathrm{Q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}}_{\tau }\left(\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\mid {\mathrm{X}}_{\mathrm{i}\mathrm{t}}\right)={{\beta }_{\tau }^{\prime }\mathrm{X}}_{\mathrm{i}\mathrm{t}}$$

(3)

where ${\mathrm{X}}_{\mathrm{i}\mathrm{t}}$ represents the selected explanatory variables: broadcast and television network coverage, rural network payment scale, and rural smartphone penetration rate. ${\beta }_{\tau }^{\prime }$ is the coefficient vector. ${\mathrm{Q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}}_{\tau }\left(\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\mid {\mathrm{X}}_{\mathrm{i}\mathrm{t}}\right)$ denotes the conditional quantile of the dependent variable Efficiency corresponding to the quantile θ (0 < θ < 1), given the explanatory variables. This paper selected five representative quantiles: 10%, 25%, 50%, 75%, and 90%, to comprehensively cover the distribution.

(3)

Generalized Additive Models

GAMs, threshold models, and quantile regression models each have distinct strengths in statistical modeling. Threshold models are particularly useful for identifying regime changes or structural breaks in relationships, such as abrupt changes in economic systems or environmental dynamics [77]. Quantile regression models, on the other hand, excel at analyzing the conditional distribution of outcomes across different quantiles, making them powerful tools for examining heterogeneity and tail effects in economic and financial data [78]. However, both methods face challenges in capturing smooth, non-linear relationships without adding complexity. GAMs overcome these limitations by allowing non-parametric smoothers to model continuous, non-linear relationships, enabling the identification of intricate patterns and trends in data. This advantage makes GAMs particularly effective for applications requiring nuanced interpretations of variable interactions, such as environmental processes or economic systems [79]. Additionally, GAMs offer interpretability and flexibility in integrating parametric and non-parametric components, making them a versatile choice for analyzing complex systems. These features give GAMs an edge over threshold models and quantile regression in reflecting the non-linear dynamics between variables.

Generalized Linear Models (GLM), introduced by Nelder et al. [80], extend general linear regression models. GLMs allow the dependent variable to follow an exponential family distribution and link the linear predictor to the expected value of the dependent variable through a link function. Compared to quantile regression, GLMs can estimate the entire conditional distribution, not just specific quantiles, providing more comprehensive statistical inference. Our model is constructed as follows:

$$\begin{array}{ll}\mathrm{g}\left(\mathrm{E}\right(\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\left)\right)& ={\beta }_0+{\beta }_1\mathrm{R}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{o}+{\beta }_2\mathrm{I}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+{\beta }_3\mathrm{P}\mathrm{h}\mathrm{o}\mathrm{n}\mathrm{e}+\\ & \sum _{i=1}^n{\beta }_{i}covariates+\epsilon \end{array}$$

(4)

where $\mathrm{g}\left(\mathrm{E}\right(\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\left)\right)$ is the link function, ${\beta }_0$ is the intercept, ε is the truncated error, and $covariates$ represents six control variables.

Hastie et al. [7] expanded the application of additive models, proposing GAMs. GAMs offer great flexibility in handling complex non-linear relationships. They construct models by adding multiple univariate smoothing functions, each capturing the non-linear effect of a predictor on the response variable. This approach maintains the interpretability of additive models while overcoming limitations of linear models, allowing better fit to actual data. When dealing with panel data, GAMs can be combined with fixed and random effects models, forming more flexible and powerful analytical tools. Fixed-effects GAMs allow each cross-sectional unit to have a unique intercept, controlling for time-invariant heterogeneity between individuals and effectively eliminating bias due to inherent differences between provinces. Random-effects GAMs assume individual effects are random and uncorrelated with explanatory variables. This method is more effective in handling inter-group variation, particularly suitable when samples are randomly drawn from a larger population. The specific models can be expressed as:

$$\begin{array}{ll}\mathrm{g}\left(\mathrm{E}\right(\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\left)\right)& ={\beta }_0+s\left(Radio\right)+s\left(Inclusion\right)+s\left(Phone\right)+\\ & \sum _{i=1}^{n}s\left(covariates\right)+{\alpha }_i+\epsilon \end{array}$$

(5)

$$\begin{array}{ll}\mathrm{g}\left(\mathrm{E}\right(\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\left)\right)& ={\beta }_0+s\left(Radio\right)+s\left(Inclusion\right)+s\left(Phone\right)+\\ & \sum _{i=1}^{n}s\left(covariates\right)+u_i+\epsilon \end{array}$$

(6)

where s(.) denotes non-parametric smoothing functions, ${\alpha }_i$ and $u_i$ represent fixed and random effects terms, respectively, and $covariates$ represents six control variables introduced in the GAM.

The model is evaluated using Restricted Maximum Likelihood (REML). This method provides unbiased variance component estimates for GAMs, effectively assessing model goodness. REML excels in estimating smoothing parameters, helping prevent overfitting. For this paper’s data, REML proves more stable than maximum likelihood.

Severe multicollinearity can significantly affect the goodness of fit in GAM and increase the variance of parameter estimates. Variables should be removed from the model when their Pearson correlation coefficient exceeds 0.7 or their Variance Inflation Factor (VIF) exceeds 10 [81,82]. Therefore, this study initially calculated both the Pearson correlation coefficients and VIFs. As shown in Figure 1 and Table 2, all absolute correlation coefficients are below 0.7, and all VIF values are less than 4. These results indicate that no multicollinearity exists among the variables used in this study, making them suitable for regression analysis.

4. Empirical Results

4.1. Unit Root Test

To avoid spurious regression due to unit roots, panel unit root tests were conducted on all variables. As shown in

Table 3. Panel unit root test results.

Variables	LLC	p-Value	ADF	p-Value	PP	p-Value
Efficiency	−9.097 ***	<0.000	175.091 ***	<0.000	177.913 ***	<0.000
Radio	−9.690 ***	<0.000	112.51 ***	<0.000	123.331 ***	<0.000
Inclusion	−32.062 ***	<0.000	342.905 ***	<0.000	523.877 ***	<0.000
Phone	−10.676 ***	<0.000	99.149 ***	0.001	166.152 ***	<0.000
ADL	−14.392 ***	<0.000	195.305 ***	<0.000	265.763 ***	<0.000
Expenditure	−12.501 ***	<0.000	129.978 ***	<0.000	250.057 ***	<0.000
AIS	−12.476 ***	<0.000	135.430 ***	<0.000	120.463 ***	<0.000
Machinery	−15.300 ***	<0.000	108.934 ***	<0.000	141.390 ***	<0.000
ER	−12.777 ***	<0.000	127.000 ***	<0.000	133.190 ***	<0.000
UR	−15.038 ***	<0.000	113.779 ***	<0.000	139.978 ***	<0.000

Note: *** indicates significance at the 1% level.

, all variables passed the zero-order unit root test at a 99% confidence level.

4.2. Benchmark Regression Model Results

This study employs a two-way fixed effects model using RStudio 2024.04.2+764, with results presented in

Table 4. Benchmark regression model results.

Variable	Model 1	Model 2	Model 3	Model 4	GMM
Constant	−0.6737 *** (0.0193)	−0.9340 *** (0.1486)	−3.0826 *** (0.7247)	−2.6298 *** (0.6680)	−3.5779 *** (0.9182)
Radio	0.1519 *** (0.0585)	0.1617 *** (0.0545)	0.1598 *** (0.0549)	0.1023 ** (0.0510)	0.2086 *** (0.0709)
Inclusion		0.0010 * (0.0006)	0.0011 * (0.0006)	0.0017 *** (0.0006)	0.0019 ** (0.0009)
Phone			0.3912 *** (0.1290)	0.2091 ** (0.0988)	0.3472 * (0.1867)
ADL				−0.0001 (0.0005)	−0.0002 (0.0005)
Expenditure				0.0148 (0.0743)	−0.0031 (0.0602)
AIS				−0.2907 (0.2836)	−0.2755 (0.1901)
Machinery				−0.0548 * (0.0302)	−0.0202 (0.0522)
ER				−31.6359 *** (10.9238)	−26.8951 *** (9.8577)
UR				0.0167 *** (0.0046)	0.0151 ** (0.0061)
Individual effects	Yes	Yes	Yes	Yes	Yes
Time effects	Yes	Yes	Yes	Yes	Yes
Pesaran CD test	−1.181(0.069)	−1.963(0.050)	−1.967(0.049)	−1.905(0.0568)
Adj. $R^2$	0.8859	0.8868	0.8912	0.8991	0.9040
AIC	−1.3436	−1.3499	−1.3849	−1.446

Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. The values in () represent robust standard errors.

. Models 1–4 represent regression models with progressively added explanatory and control variables. The adjusted $R^2$ increases with the addition of variables, indicating improved model explanatory power. According to model selection criteria, Model 4 has the lowest AIC value, suggesting the best fit. Model 4 results show that, after including all control variables, the three variables reflecting digital economy levels have positive coefficients, indicating positive impacts. Specifically, a 1% change in radio leads to a 0.1023% increase in agricultural carbon emission efficiency. A one-unit change in inclusion results in a 0.17% increase, while a 1% change in phone corresponds to a 0.2091% increase. These findings suggest that the digital economy significantly promotes agricultural carbon emission efficiency. Among control variables, machinery, ER, and UR pass significance tests. A 1% change in machinery leads to a 0.0548% decrease in carbon emission efficiency. A one-unit change in ER results in a 31.6359% decrease. UR shows a positive impact, with a 1% change leading to a 0.0167% increase in efficiency. The negative impact of agricultural mechanization on carbon emission efficiency may be attributed to increased fossil fuel consumption. The decrease in efficiency due to environmental regulations could be related to high short-term adaptation costs, misalignment between regulatory focus and carbon emissions, and technology substitution effects. Urbanization’s positive impact on agricultural carbon emission efficiency can be explained by several factors. As urbanization progresses, agricultural production tends towards scale and intensification, facilitating the adoption of advanced low-carbon technologies and management methods. Technological advancements associated with urbanization promote precision agriculture, optimizing input structures and reducing excessive use of fertilizers and pesticides. Additionally, integrated urban-rural development encourages the resourceful utilization of agricultural waste, further reducing carbon emission intensity. These factors collectively contribute to improved agricultural carbon emission efficiency.

To further verify the robustness of results and address potential endogeneity issues, this study employed the System Generalized Method of Moments (System GMM). The GMM effectively handles endogeneity in dynamic panel data, particularly issues arising from omitted variables, reverse causality, or measurement errors, providing more reliable and consistent estimates. As shown in Table 4, the GMM model results largely align with Model 4, further validating the regression findings.

4.3. Quantile Regression Results

The quantile regression results in

Table 5. Quantile regression model estimation results.

Variables	10%	25%	50%	75%	90%
Constant	−0.9363 (1.2654)	−1.1565 (1.1629)	−3.5968 *** (0.7576)	−4.4633 *** (0.7268)	−3.6947 *** (0.9315)
Radio	0.01586 (0.1610)	0.0680 (0.1559)	0.1029 (0.1241)	0.2829 *** (0.0934)	0.2442 *** (0.0886)
Inclusion	0.0004 (0.0005)	0.0010 * (0.0005)	0.0005 (0.0004)	0.0005 (0.0003)	0.0009 *** (0.0002)
Phone	0.0182 (0.2121)	0.1255 (0.1778)	0.7355 *** (0.1297)	0.8694 *** (0.1274)	0.7477 *** (0.1552)
ADL	0.0011 (0.0015)	0.0024 (0.0016)	0.0003 (0.0017)	0.0014 (0.0010)	−0.0003 (0.0009)
Expenditure	0.1170 (0.0856)	0.0821 (0.0705)	0.0274 (0.0576)	−0.0342 (0.0529)	−0.1711 *** (0.0599)
AIS	−0.6643 (0.4359)	−0.5506 * (0.2963)	−0.6466 *** (0.2477)	−0.3589 * (0.1842)	−0.0977 (0.1454)
Machinery	−0.0615 * (0.0350)	−0.0622 ** (0.0252)	−0.0678 *** (0.0224)	−0.0313 (0.0325)	0.0408 (0.0305)
ER	−114.2676 *** (31.9020)	−130.6813 *** (31.9773)	−120.5122 *** (24.9972)	−99.6866 *** (18.9416)	−111.6636 *** (15.9970)
UR	0.0028 (0.0031)	−0.0014 (0.0035)	−0.0034 (0.0030)	−0.0019 (0.0025)	−0.0009 (0.0029)
Adj. $R^2$	0.3138	0.2910	0.3117	0.3168	0.3573
Quasi-LR statistic	135.4180	172.7674	199.7979	186.3762	185.6886
Probability	<0.0001	<0.0001	<0.0001	<0.0001	<0.0001

Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. The values in () represent robust standard errors.

reveal that rural digital infrastructure (radio), rural digital industry (inclusion), and digital economy foundation (phone) generally have positive effects on agricultural carbon emission efficiency. However, the magnitude and significance of these effects vary notably across different quantiles.

In lower and middle quantiles, the impact of these three variables is insignificant. This may indicate that in regions or periods with lower agricultural carbon emission efficiency, digital economic development has not reached a critical threshold. These areas likely face challenges such as inadequate digital infrastructure, underdeveloped digital industry ecosystems, and insufficient digital technology application capabilities. Consequently, the potential contributions of the digital economy to agricultural production efficiency and carbon reduction may not be fully realized. Conversely, in higher quantiles, the influence of these variables significantly strengthens. This suggests that in regions or periods with higher agricultural carbon emission efficiency, the enabling role of the digital economy becomes more prominent. Such areas may have established more comprehensive digital infrastructure, formed mature digital industry ecosystems, and developed stronger digital technology application capabilities. These factors enable more effective optimization of agricultural production processes and improved resource utilization efficiency through digital technologies, thereby enhancing agricultural carbon emission efficiency.

Notably, rural digital infrastructure (radio) and digital economy foundation (phone) exhibit threshold effects in higher quantiles, with their impact on agricultural carbon emission efficiency showing an initial increase followed by a decline. This phenomenon may reflect diminishing marginal returns on digital technology applications in the agricultural sector. Once digital infrastructure and smart device penetration reach certain levels, further improvements in agricultural carbon emission efficiency through hardware investments alone may become challenging. This observation suggests that in regions with more mature digital economic development, emphasis should be placed on the deep application and innovation of digital technologies, as well as the profound integration of digitalization with agricultural production. Such focus is crucial for overcoming technological application bottlenecks and continuously improving agricultural carbon emission efficiency.

4.4. Generalized Additive Model Regression Results

Table 6. Generalized Additive Model regression results.

Variable	GAM1	GAM2	GAM3	GAM4	GAM5
C	−2.4580 *** (0.6888)	−0.6234 *** (0.0460)	−0.7954 * (0.4628)	−0.9060 *** (0.1438)	−0.5009 (0.5880)
Radio	0.1023 ** (0.0483)
Inclusion	0.0017 *** (0.0005)
Phone	0.2091 * (0.1214)
ADL	−0.0001 (0.0005)		0.0005 (0.0004)		−0.0000 (0.0004)
Expenditure	0.0148 (0.0588)		−0.0645 (0.0494)		−0.0452 (0.0565)
AIS	−0.2907 (0.1839)		−0.4917 *** (0.1669)		−0.4566 *** (0.1752)
Machinery	−0.0548 (0.0465)		0.0350 (0.0338)		−0.0966 ** (0.0448)
ER	−31.6400 *** (9.6960)		28.3700 *** (9.0660)		−29.8300 *** (8.9900)
UR	0.0167 *** (0.0005)		0.0121 *** (0.0032)		0.0215 *** (0.0052)
The values in () represent robust standard errors.
Estimated degrees of freedom
s(Inclusion)		6.2070 *** (28.9980)	6.0680 *** (18.5540)	4.5970 ** (2.7680)	5.3790 *** (5.1340)
s(Phone)		6.5330*** (6.5760)	6.5530*** (5.3150)	6.9590 *** (5.7520)	6.7790 *** (5.1310)
s(Radio)		1.2720 *** (0.0056)	1.0820 * (3.4640)	1.7790 ** (3.1520)	1.5340 (0.9960)
s(Individual)		28.3600 *** (<0.0001)	27.3500 *** (44.7680)
s(Time)		<0.0001 *** (0.0004)	<0.0001 ** (<0.0001)
Individual effects	Yes	Yes	Yes	Yes	Yes
Time effects	Yes	Yes	Yes	Yes	Yes
Adj. $R^2$	0.8990	0.8920	0.9030	0.9070	0.9170
Deviance explained	0.9130	0.9050	0.9160	0.9200	0.9310
REML	−177.1500	−182.9100	−187.7200	−187.6700	−195.9500
AIC	−517.2007	−491.3811	−526.1832	−535.1550	−573.4804
The values in () represent F-statistic values.

Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

summarizes the regression results of the GAMs. GAM1 represents the generalized linear model, GAM2 and GAM3 are random effects models without and with control variables, respectively, while GAM4 and GAM5 are fixed effects models without and with control variables, respectively. The adjusted ${\mathrm{R}}^2$ values range from 89.9% to 91.7%, significantly higher than those of the baseline and quantile regressions. Based on model selection criteria, GAM5 exhibits the lowest REML and AIC values, indicating the best fit. Subsequent analyses and visualizations are therefore based on GAM5.

Figure 2, derived from the GAM analysis, reveals complex non-linear relationships between agricultural carbon emission efficiency and various dimensions of the digital economy. The impact of rural digital industry (inclusion) on agricultural carbon emission efficiency shows an initial slow decrease followed by an increase. This pattern may reflect initial adaptation costs in the early stages of digital industry development, with benefits gradually emerging as the industry matures. This phenomenon aligns with technology diffusion theory, where new technologies may face initial application barriers and learning costs before their benefits become apparent over time. The digital economy foundation (phone) generally shows an increasing relationship with agricultural carbon emission efficiency, indicating that the proliferation of smart devices can continuously enhance agricultural production efficiency and resource utilization. However, the effect plateaus within a specific range (5.2–5.6), possibly suggesting a threshold beyond which the marginal benefits of digital infrastructure may diminish. This non-linear relationship reflects the complexity of digital technology applications in agriculture, potentially involving factors such as technology saturation and adaptation bottlenecks. In contrast, rural digital infrastructure construction (radio) has a limited impact on agricultural carbon emission efficiency, with the fitted curve appearing nearly horizontal and smoothed fitted values approaching zero. This result suggests that traditional broadcast and television network coverage may no longer be a key factor in improving agricultural carbon emission efficiency, possibly being superseded by more advanced digital technologies. This phenomenon reflects the trend of digital technology evolution, where emerging technologies gradually replace traditional media in information dissemination and production efficiency enhancement.

The significant differences in how these three digital economy dimensions affect agricultural carbon emission efficiency may stem from their distinct mechanisms of action in agricultural production. Rural digital industry might influence carbon emission efficiency by optimizing production processes and improving resource allocation efficiency. The digital economy foundation could act by providing information access channels and promoting precision agriculture practices. Meanwhile, traditional digital infrastructure construction may have a relatively limited direct impact on agricultural production in the current technological environment. These differentiated impacts highlight the need to consider the characteristics and potential of various digital economy dimensions when formulating agricultural digitalization strategies, aiming to optimize resource allocation and maximize benefits.

To comprehensively evaluate the model’s predictive performance, this study extended the data range to 2012–2021 and utilized the Predict function to forecast agricultural carbon emission efficiency for Chinese provinces in 2022. Figure 3 visually presents a comparison between the predicted results and actual data. Red dots represent the actual values of agricultural carbon emission efficiency for each province in 2022 (based on available data), while the blue solid line indicates predicted values, and the black solid line represents the confidence interval. The figure demonstrates that predicted values for the vast majority of provinces fall within the confidence interval. This outcome suggests that the prediction function exhibits good accuracy and reliability.

Figure 4 illustrates the comparative analysis of agricultural carbon emission efficiency across provinces in 2022. The blue curve represents the fitted values for each province. Green, red, and purple solid lines indicate predicted efficiency values after a 10% increase in inclusion, phone, and radio, respectively. The orange solid line shows predicted values when all variables are simultaneously increased by 10%.

The analysis reveals that agricultural carbon emission efficiency is most sensitive to the digital economy foundation (phone), followed by rural digital industry (inclusion), while rural digital infrastructure construction (radio) has a relatively minor impact. This finding underscores the differentiated effects of various digital economy dimensions on agricultural carbon emission efficiency. The significant influence of the digital economy foundation may stem from smartphones serving as crucial tools for accessing agricultural information and supporting decision-making, directly enhancing agricultural production efficiency and resource utilization. The development of the rural digital industry, particularly digital inclusive finance, provides farmers with more accessible financial services, contributing to the optimization of agricultural production input structures. In contrast, rural digital infrastructure construction, while providing a basis for information dissemination, has a relatively limited direct impact on agricultural production efficiency. Consequently, the purple line overlaps with and obscures the blue line, making it invisible in Figure 4.

Notably, the impact of the digital economy on agricultural carbon emission efficiency exhibits significant regional variations. In provinces such as Guangdong, Guangxi, and Hunan, the digital economy demonstrates a more pronounced effect on improving agricultural carbon emission efficiency. Conversely, in regions like Tianjin and Shanxi, the promotional effect of the digital economy is less significant. This disparity is partly attributable to regional industrial structures; for instance, Tianjin’s relatively small primary industry sector limits the impact on agricultural carbon emission efficiency. Additionally, these variations indicate that some regions face challenges or structural barriers in their digital transformation processes.

4.5. Discussion

This study makes significant contributions to understanding the complex relationship between the digital economy and agricultural carbon emission efficiency. The findings corroborate Wang et al.’s conclusions, further confirming the significant promotional effect of the digital economy on carbon emission reduction [11]. However, this study transcends existing literature limitations by empirically revealing significant heterogeneous characteristics across different development stages and efficiency levels. Methodologically, this research innovatively employs the Generalized Additive Model (GAM) to capture continuous variations in non-linear relationships, advancing beyond the discrete threshold points identified by Wang et al.’s threshold regression model [62]. This methodological innovation effectively addresses the limitations of traditional inverted U-curve analysis methods [12]. While Anser et al. empirically verified the crucial role of green ICT infrastructure in sustainable agricultural production using data from 26 European countries, their research was limited to a single dimension of the digital economy [83]. In contrast, this study establishes a multi-dimensional evaluation system for digital economy, systematically revealing the differentiated impacts of various digital economy dimensions on agricultural carbon efficiency. Furthermore, it elaborates on the necessity of adopting diversified, locally adapted policy approaches for improving agricultural carbon efficiency. Notably, the significant threshold effects discovered in high-efficiency regions emphasize the importance of considering regional development stage differences when formulating digital transformation strategies. These findings, corroborating Haryanti et al.’s research, provide valuable guidance for policy implementation [84]. The results underscore the necessity of tailoring digital transformation strategies to regional development stages, offering significant implications for policy practices.

5. Conclusions and Policy Implications

5.1. Conclusions

This study thoroughly examined the impact of the digital economy on agricultural carbon emission efficiency. Through the construction of double fixed effects and quantile regression models, a significant positive influence of the digital economy on agricultural carbon emission efficiency was identified. Specifically, three dimensions—rural digital infrastructure construction (represented by radio), rural digital industry level (inclusion), and digital economy foundation (phone)—were found to promote agricultural carbon emission efficiency. However, this influence exhibits non-linear characteristics. In regions or periods with lower agricultural carbon emission efficiency, the impact of the digital economy is insignificant, while in areas or times of higher efficiency, its promotional effect becomes more pronounced. Notably, in high quantile regressions, rural digital infrastructure construction and digital economy foundation display threshold effects, with their impact on agricultural carbon emission efficiency showing an initial increase followed by a decline, possibly due to the saturation of existing technology applications.

Analysis based on the Generalized Additive Model (GAM) further revealed the non-linear characteristics of the digital economy’s influence on agricultural carbon emission efficiency. The results indicate that the rural digital industry level (inclusion) has a non-linear relationship with agricultural carbon emission efficiency, initially showing a slow decrease followed by an increase. The digital economy foundation (phone) demonstrates an overall increasing non-linear relationship with agricultural carbon emission efficiency, albeit with minimal variation within a certain range. In contrast, rural digital infrastructure construction (radio) exhibits an approximately linear relationship with agricultural carbon emission efficiency. Prediction results further indicate that agricultural carbon emission efficiency is most sensitive to the digital economy foundation, followed by the rural digital industry level, with rural digital infrastructure construction having a relatively minor impact. These findings not only reveal the differentiated effects of various digital economy dimensions on agricultural carbon emission efficiency but also provide crucial references for optimizing digital economy development strategies and enhancing agricultural carbon emission efficiency. These findings underscore the critical role of government policies in maximizing the digital economy’s potential for agricultural carbon emission efficiency. Government intervention is particularly crucial in addressing regional disparities and technological barriers that may hinder the effective implementation of digital solutions. Strategic policy support can help overcome initial adaptation challenges and ensure the sustainable development of digital agriculture while contributing to national carbon reduction goals.

5.2. Policy Implications

The empirical results of this study reveal that the digital economy has a significant positive impact on agricultural carbon emission efficiency, albeit with non-linear characteristics and regional disparities. To fully harness the potential of the digital economy in enhancing agricultural carbon emission efficiency while addressing the challenges identified in the research, targeted policy measures are necessary. These policy recommendations aim to optimize the digital economy structure, promote deep integration of digital technologies with agricultural production, and address regional development imbalances, thereby achieving sustainable agricultural development and “dual carbon” goals. Based on these findings, the following policy recommendations are proposed:

(1)

Accelerate the development of rural digital economy infrastructure, focusing on enhancing the digital economy foundation. Empirical results indicate that the digital economy foundation (phone) has the most significant impact on agricultural carbon emission efficiency. Governments should increase investment in digital infrastructure such as rural communication networks and smart devices, improving network coverage and smart terminal penetration in rural areas to lay the groundwork for the digital transformation of agricultural production.

(2)

Optimize the rural digital industry structure and promote deep integration of digital technologies with traditional agriculture. The research reveals a non-linear relationship between rural digital industry level (inclusion) and agricultural carbon emission efficiency. Governments should encourage the development of smart agriculture and precision farming models, promoting the application of IoT, big data, and AI technologies in agricultural production to improve resource utilization efficiency and reduce carbon emissions.

(3)

Implement rural digital infrastructure construction tailored to local conditions, avoiding blind investment. Empirical results show that rural digital infrastructure construction (radio) has a relatively small and linear impact on agricultural carbon emission efficiency. Governments should plan rural digital infrastructure construction rationally based on local conditions and needs, avoiding redundant construction and resource waste to improve investment efficiency.

(4)

Strengthen policy support and technical assistance for regions with lower agricultural carbon emission efficiency. Quantile regression results indicate that the digital economy’s impact is insignificant in areas with lower agricultural carbon emission efficiency. Governments should develop targeted support policies for these regions, enhancing technical training and guidance to help improve digital technology application capabilities and narrow the digital divide between regions.

(5)

Establish long-term mechanisms to continuously optimize the digital economy structure for improving agricultural carbon emission efficiency. The study finds non-linear characteristics and threshold effects in the digital economy’s impact on agricultural carbon emission efficiency. Governments should establish dynamic assessment and adjustment mechanisms to timely identify bottlenecks in digital economy development and continuously optimize its structure to enhance its promotional effect on agricultural carbon emission efficiency.

While this study explores the non-linear impact of the digital economy on agricultural carbon emission efficiency, it has limitations. Firstly, the research focuses primarily on the macro level, lacking in-depth analysis of micro-mechanisms. Secondly, it does not fully consider the moderating effect of regional heterogeneity on how the digital economy influences agricultural carbon emission efficiency. Future research could explore the following aspects: investigating the specific micro-mechanisms through which the digital economy affects agricultural carbon emission efficiency; analyzing regional differences in the digital economy’s impact on agricultural carbon emission efficiency, considering factors such as economic development levels and industrial structures in different regions; and studying how to optimize the digital economy structure at different development stages to more effectively enhance agricultural carbon emission efficiency and achieve sustainable agricultural development. In addition, future research could consider spatial correlation and spillover effects through spatial econometric models, which would help reveal the heterogeneous impacts of the digital economy across different regions.