Re-Evaluating Agricultural Carbon Efficiency Across Functional Grain Zones: From Spatial Analysis

Abstract

Regional reassessments of agricultural carbon emission efficiency are essential for improving the sustainability of food production systems under climate constraints. This study evaluates agricultural carbon emission efficiency (ACEE) across China’s major grain-producing zone (GPZ), major grain-consuming zone (GSZ), and grain production–consumption balanced zone (GBZ) during 2003–2022, excluding Hong Kong, Macao, Taiwan, and Tibet due to data limitations. A super-efficient EBM–GML model incorporating both desirable and undesirable outputs is employed to measure ACEE at the provincial level, with comparisons conducted within each functional zone and nationally unified efficiency values used as a benchmark. Spatial dependence is examined using Moran’s I, and a spatial Durbin model is applied to identify driving factors and spatial spillover effects. The results indicate that the average efficiency levels differ systematically across functional grain zones, following the order GBZ > GPZ > GSZ, while several provinces experience notable changes in their relative rankings. Carbon emissions increase in the earlier period and decline in later years, whereas efficiency exhibits an opposite temporal pattern, reflecting a gradual transition of grain production systems from extensive input-driven growth toward more sustainability-oriented practices. Substantial regional disparities in ACEE are also observed. Rational industrial organization and efficient allocation of production resources contribute to positive spillover effects on neighboring regions, whereas natural disasters and inefficient resource distribution tend to weaken such effects. These findings suggest that functional grain zones provide an effective framework for capturing intra-regional heterogeneity and should be adopted as the basic unit for efficiency assessment and the formulation of differentiated governance strategies.

1. Introduction

With increasing climate pressures, improving agricultural carbon emission efficiency is essential to balance food security and emissions reduction. The United Nations Environment Program’s Emissions Gap Report 2023 indicates that global anthropogenic greenhouse gas emissions reached 57.4 Gt carbon dioxide equivalent (CO₂e) between 2021 and 2022, representing a 1.2 percent increase [1]. The main reason behind increasing temperatures is the continuous release of carbon dioxide (CO₂), methane (CH₄), and nitrous oxide (N₂O) [2,3,4]. Therefore, it is essential to control emissions in order to have a chance of achieving the goal of limiting global warming to no more than 1.5 °C [5,6]. Agriculture contributes substantially to greenhouse gas emissions [7]. Compared with sectors such as thermal power generation and cement production, where emissions are concentrated in a few large point sources, agricultural carbon emissions are highly dispersed and therefore much harder to regulate [8,9]. Moreover, due to differences in agricultural production management across regions, carbon emission efficiency varies significantly [10,11,12]. If scientific management of agricultural activities enables simultaneous emission reduction and efficiency gains, it can not only lower global greenhouse gas emissions but also enhance the overall environmental performance of food production systems [13,14,15]. In this study, agricultural carbon emission efficiency (ACEE) refers to the efficiency of agricultural production under carbon emission constraints. It indicates whether a region can obtain higher agricultural output with lower carbon emissions at a given level of input. ACEE therefore captures the joint performance of production and emission control, rather than emission reduction alone. In agricultural production, higher ACEE does not mean eliminating emissions altogether; rather, it means producing more output with lower emissions for a given level of resource input. This can be achieved by reducing inefficient input use, improving production technologies, and adjusting the composition of agricultural production. For example, excessive use of fertilizers, diesel, irrigation water, and plastic films may raise emissions without corresponding gains in output, whereas more efficient production practices can improve the input–output relationship while lowering emission intensity. Therefore, examining grain production under carbon emission constraints helps identify a more balanced pathway between agricultural sustainability and environmental impact mitigation [16,17,18].

In recent years, various research methods have been used to measure agricultural carbon emission efficiency and applied in different fields. Methods for the static estimation of carbon efficiency levels include Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) [19,20]. Many studies have also adopted the super-efficiency SBM model and the SBM-Undesirable model, which incorporate the negative effects of pollutants while assessing carbon efficiency [21,22]. The Malmquist index under the DEA framework is the method most commonly used for the dynamic estimation of carbon efficiency levels [23,24,25]. Some studies focus on specific agricultural activities, such as rice cultivation [26,27,28], livestock and poultry farming [29,30,31], as well as agricultural inputs and land use [21,32,33], to examine how different emission sources, mitigation technologies, and policy measures affect improvements in agricultural carbon efficiency. In addition, several studies further apply the LMDI approach to decompose and quantify the drivers behind changes in carbon emission efficiency [34]. Although existing studies vary in measurement methods and research focus, most evaluate provincial carbon efficiency within a meta frontier framework and undertake regional or functional comparisons on this basis. However, this approach often neglects differences in the functional roles of regions within the national food security system, despite pronounced disparities in economic development, resource endowments, agricultural structure, and stages of development [35]. Therefore, in cross-regional comparisons, these structural differences may be misinterpreted as efficiency gaps, thereby affecting the accurate assessment of the low-carbon performance of food production systems. Moreover, changes in carbon efficiency in one region are not confined to the local area, as their effects may also extend to neighboring regions through policy transmission or technological diffusion [36,37]. Existing empirical evidence shows that agricultural carbon efficiency exhibits spatial spillover effects [38]. In highly interconnected food production–consumption systems, spatial linkages give rise to cross-regional spillovers in agricultural carbon efficiency.

To address these limitations, we argue that both regional functional differences and efficiency heterogeneity should be taken into account when measuring agricultural carbon emission efficiency [39,40]. Therefore, this study adopts a zonal measurement approach to estimate agricultural carbon emission efficiency separately across different grain functional zones. This approach helps distinguish regional heterogeneity from efficiency differences under a unified benchmark. Firstly, the super-efficiency EBM-GML model is used to estimate the agricultural carbon emission efficiency of the major grain-producing zone (GPZ), major grain-consuming zone (GSZ), and grain production–consumption balanced zone (GBZ) from 2003 to 2022. This model is appropriate for agricultural carbon emission efficiency analysis because it considers both desirable outputs and undesirable emissions, captures changes in efficiency over time, and allows provinces on the efficiency frontier to be further ranked. Using the results under a unified frontier as a reference, this study compares efficiency rankings under different measurement approaches to identify regions where efficiency may be overestimated or underestimated. In addition, the GML index is used to trace changes in agricultural carbon emission efficiency over time and to decompose them into efficiency change (EC) and technological change (TC), so as to compare the roles of these two components across functional zones. Secondly, global and local Moran’s I are used to test whether agricultural carbon emission efficiency exhibits spatial autocorrelation, that is, whether provinces with similar efficiency levels tend to cluster in space. Finally, the spatial Durbin model (SDM) is employed to identify the main factors influencing efficiency levels and to analyze spatial spillover effects.

The main contributions of this study are as follows. (1) By adopting grain functional zones as the analytical unit, this study relates the measurement of agricultural carbon emission efficiency more closely to the differentiated roles of regions in the national grain security system, rather than relying only on cross-regional comparisons under a unified framework. (2) By comparing zonal and unified frontier results, this study shows that alternative measurement frameworks may lead to different efficiency rankings and may therefore affect the interpretation of regional carbon efficiency performance. (3) The zonal measurement results can also reveal the spatial spillover effects of agricultural carbon emission efficiency, helping to clarify inter-regional interactions within grain production systems. (4) The zonal identification results can provide a more targeted basis for formulating low-carbon governance strategies for grain production systems.

2. Methods and Data

2.1. Study Area

This study examines 30 provinces in mainland China from 2003 to 2022. Hong Kong and Macao are not included due to data limitations, and Tibet is excluded due to missing data. Taiwan is not included in the sample. With reference to the State Council’s Guiding Opinions on Establishing Functional Zones for Grain Production and Protection Zones for Important Agricultural Products, and considering indicators such as grain output, per capita grain possession and grain self-sufficiency, this paper divides the whole country into the GPZ, GSZ and GBZ according to functional zones (see Figure 1).

2.2. Method for Measuring ACEE

2.2.1. Indicator System and Carbon Emissions Estimation

The indicators used in this study include inputs, a desirable output, and undesirable outputs (

Table 1. Inputs and outputs with descriptive statistics.

Variables	Indicator Specification (with Unit)	Obs.	Mean	Std.	Min	Max
Crop sown area	103 ha	600	5371.044	3759.939	88.55	15,209.41
Total agricultural machinery power	104 kW	600	3070.915	2795.458	93.97	13,353
Effective irrigated area	103 ha	600	2081.439	1590.545	109.24	6666.39
Pesticide use	ton	600	52,450.87	41,415.66	1000	173,461
Rural labor	104 persons	600	1782.258	1286.11	147.94	4914.67
Grain output	104 tons	600	1970.685	1681.887	28.76	7867.72
CO2	104 tons	600	320.0776	226.4324	14.3546	995.7526
CH4 (CO2e)	104 tons	600	526.6576	637.4659	0	2660.641
N2O (CO2e)	104 tons	600	559.6604	412.7101	1.7554	1493.199

; Figure 2). The input variables include crop sown area, total agricultural machinery power, effective irrigated area, pesticide use, and rural labor. Grain output is used as the desirable output because this study focuses on carbon emission efficiency in grain production within the planting sector. To maintain consistency between output measurement and emission accounting, both the desirable output and the associated carbon emissions are defined within the same grain production boundary. Grain output is used as the desirable output because this study focuses on carbon emission efficiency in grain production within the planting sector. To ensure consistency, inputs, outputs, and related emissions are defined within the same grain production boundary. This reduces the influence of non-grain agricultural activities across regions and improves the comparability of the results. The undesirable outputs include CO₂ emissions and the CO₂-equivalent forms of CH₄ and N₂O emissions from grain production-related activities. Following the 100-year global warming potential reported in the IPCC Fourth Assessment Report, CH₄ and N₂O are converted into CO₂-equivalent terms using factors of 25 and 298, respectively. CO₂ emissions are primarily associated with inputs such as chemical fertilizers, pesticides, agricultural film, irrigation, tillage, and diesel use, while CH₄ emissions are mainly linked to rice cultivation. N₂O emissions are mainly associated with fertilizer use and upland grain production, including wheat and maize. Emission coefficients are obtained from established references for each carbon source. An emission coefficient of 0.59 kg/kg is used for diesel, based on the IPCC (2013) [41]. The coefficients for chemical fertilizers and pesticides are 0.89 kg/kg and 4.93 kg/kg, respectively. The coefficients for irrigation and tillage are 266.48 kg/hm² and 312.60 kg/hm², respectively. The coefficient for agricultural film is 5.18 kg/kg. The coefficients for irrigation and tillage are 266.48 kg/hm² and 312.60 kg/hm², respectively. These coefficients follow commonly used estimation approaches in research on agricultural carbon emissions in China [42], and are consistent with recent studies based on emission factor methods [43].

The formula for total agricultural carbon emissions is as follows:

$$C={\displaystyle \sum _i{T}_i}\times {\alpha }_i\times GW{P}_i$$

(1)

where C denotes the total agricultural carbon emissions, T_i represents the activity level of carbon source i, α_i denotes the corresponding emission factor, and GWP_i denotes the global warming potential of greenhouse gas i. All greenhouse gases are converted into CO₂-equivalent terms using their respective GWP values.

2.2.2. Super-Efficiency EBM-GML Model

To examine the dynamic evolution of agricultural carbon emission efficiency, this paper uses the super-efficiency EBM model to estimate the efficiency scores of each province. Then, the GML index is applied to track changes in efficiency over time, and these changes are decomposed into EC and TC. Based on these results, this paper examines the temporal evolution and regional differences in agricultural carbon emission efficiency. Furthermore, Moran’s I index and the spatial Durbin model are used to analyze spatial patterns and their determinants.

To measure the change in agricultural carbon emission efficiency over time, this study combines an empirically based model (EBM) with the global Malmquist–Leuenberger (GML) index. This approach is well-suited for agricultural carbon efficiency analysis because it simultaneously considers both expected and undesired emissions, captures changes in efficiency over time, and decomposes these changes into EC and TC. Furthermore, the over-efficiency specification allows for further differentiation of regions at the efficiency frontier. The specific model specifications are as follows:

$$\begin{array}{l}\psi =\min {\displaystyle \frac{\xi -{\omega }_x{\displaystyle \sum _{u=1}^m\frac{{\overline{\omega }}_u^{-}{s}_u^{-}}{x_{uh}}}}{\phi +{\omega }_{yG}{\displaystyle \sum _{j=1}^n\frac{{\overline{\omega }}_j^{+}{s}_j^{+}}{y_{Gjh}}+{\omega }_{yB}{\displaystyle \sum _{z=1}^l\frac{{\overline{\omega }}_z^{-}{s}_z^{-}}{y_{Bzh}}}}}}s.t.\\ s.t.\left\{\begin{array}{l}x\delta +s_u^{-}=\xi x_h,u=1,2,\dots ,m\\ y_G\delta -s_j^{+}=\phi y_{Gh},j=1,2,\dots ,n\\ y_B\delta +s_z^{+}=\phi y_{Bh},z=1,2,\dots ,w\\ \delta \ge 0,s_u^{-},s_j^{+},s_z^{-}\ge 0\end{array}\right.\end{array}$$

(2)

In Equation (2), x, y_G and y_B represent the input, desirable output, and undesirable output vectors respectively; m, n and w represent the number of inputs or outputs respectively; h denotes the number of decision units; $\phi (0\le \phi \le 1)$ denotes the optimum efficiency value, while ${\overline{\omega }}_u^{-},{\overline{\omega }}_j^{-},{\overline{\omega }}_z^{-}$ and $s_u^{-},s_j^{-},s_z^{-}$ represent the weights and slack variables for the u-th input, j-th desirable output, and z-th undesirable output, respectively. $\omega (0\le \omega \le 1)$ is a key parameter for the composite radial efficiency value $\xi$ and the non-radial relaxation variable. The efficiency score indicates how each province performs relative to the production frontier. A higher value suggests that, under a given level of inputs, the province can generate more desirable outputs and/or fewer undesirable outputs. In the super-efficiency setting, values may exceed one for provinces on the frontier, while values below one indicate that the province remains inefficient and has room for improvement. CO₂, CH₄, and N₂O emissions are considered undesirable outputs and should be reduced. Their inclusion affects how the frontier is defined, as performance is evaluated not only by the level of agricultural output but also by the emissions associated with that output. Consequently, a province with high output but relatively high emissions may still be considered inefficient. The GML index constructed in conjunction with EBM efficiency is given by Formula (3):

$$G^{t,t+1}(x^t,y^t,b^t,x^{t+1},y^{t+1},b^{t+1})={\displaystyle \frac{{\psi }^{G,t+1}(x^{t+1},y^{t+1},b^{t+1})}{{\psi }^{G,t}(x^t,y^t,b^t)}}$$

(3)

In Equation (3), x, y, and b denote the input, desirable output, and undesirable output vectors respectively; t and t + 1 represent the observation periods; G represents the ACEE index, while ${\psi }^{G,t},{\psi }^{G,t+1}$ denote the global efficiency values for periods t and t + 1 respectively.

2.3. Spatiotemporal Analysis Methods for ACEE

2.3.1. Kernel Density Estimation

This paper employs non-parametric kernel density estimation to analyze the distribution of agricultural carbon emission efficiency (ACEE). The specific formula is as follows:

$$f(x)={\displaystyle \frac{1}{nh}}{\displaystyle \sum _{i=1}^{n}k}\left({\displaystyle \frac{x_i-\overline{x}}{h}}\right)$$

(4)

In Equation (4), f(x) denotes the density function, $k\left({\displaystyle \frac{x_i-\overline{x}}{h}}\right)$ represents the kernel function (a Gaussian kernel is used in this study), h is the bandwidth parameter, n is the number of observed samples, x_i is the i-th observed value, and $\overline{x}$ is the mean.

2.3.2. Global and Local Spatial Autocorrelation

(1)

Global Spatial Autocorrelation

This study employs the global Moran’s I to examine whether ACEE exhibits spatial interactions between neighboring regions. A significantly positive Moran’s I indicates positive spatial autocorrelation, reflected in the clustering of areas with similar values, including high–high and low–low patterns. A significantly negative Moran’s I indicates spatial dispersion, with high values located next to low values. A value close to zero suggests a random spatial pattern. The calculation of the Moran’s I relies on a spatial weight matrix, which defines the spatial relationships between regions. The weight matrix specifies which regions are considered neighboring regions and assigns weights to these relationships, thus determining how the values of neighboring regions participate in the calculation of spatial autocorrelation. Its expression is as follows:

$$I={\displaystyle \frac{n{\displaystyle {\sum }_{n=1}^n{\displaystyle {\sum }_{j=1}^n{W}_{ij}(Y_i-\overline{Y})(Y_j-\overline{Y})}}}{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^n{W}_{ij}{\displaystyle {\sum }_{i=1}^n{(Y_i-\overline{Y})}^2}}}}}$$

(5)

In Equation (5), I denotes the global Moran’s I value, n, and W_ij, the spatial weighting of the province i and province j, Y_i and Y_j are the effective values of the carbon emission of agriculture in the provinces i and j, and $\overline{Y}$ denotes the overall mean.

(2)

Local Spatial Autocorrelation

Based on the identified global spatial autocorrelation, this paper further uses local indicators of spatial association (LISA) to analyze the clustering patterns of each province. In this way, it identifies the efficiency clustering of different regions in each year. The calculation formula is as follows:

$$L{I}_i={\displaystyle \frac{n(x_i-\overline{x}){\displaystyle {\sum }_{t=1,t\ne i}^n{W}_{it}(x_t-\overline{x})}}{{\displaystyle {\sum }_{i=1}^n{(x_i-\overline{x})}^2}}}$$

(6)

In Formula (6), LI_i denotes the local Moran’s I value for the i-th province in a given year. If LI_i > 0, it indicates spatial clustering of either higher or lower performance between the region and its neighbors; if LI_i < 0, it reflects divergence in performance between the region and its surroundings; if statistical tests yield insignificant results, it suggests no discernible spatial trends in agricultural carbon efficiency like neighboring areas. The principal analysis employs an adjacency matrix, an inverse distance spatial weight matrix and an inverse squared distance spatial weight matrix used for robustness testing to ensure consistency with spatial regression model specifications.

2.3.3. SDM

ACEE depends not only on local resource allocation and government administrative capacity, but also on policies, technologies, capital, labor and other factors in neighboring regions. This paper employs a spatial Durbin model to identify spatial spillovers in terms of direct, indirect and total effects. The fundamental formula is as follows:

$$Y=\rho WY+\beta X+\theta WX+\alpha +\epsilon$$

(7)

In the model, Y denotes the ACEE, X represents explanatory variables, W denotes the spatial weighting matrix, ρ denotes the spatial lag coefficient of the dependent variable, β and θ denote local effects and spatial spillover effects respectively, α denotes the constant term, and ε denotes the random disturbance term. To identify the appropriate spatial specification, we conducted Hausman, LM, Robust LM, Wald, and LR tests. The Hausman test (χ² = 13.50, p = 0.0608) supports the use of a fixed-effects model. The LM and Robust LM tests are both significant, indicating the presence of spatial dependence. Furthermore, the Wald and LR tests reject the restrictions of the spatial lag model (SLM) and spatial error model (SEM) at the 1% significance level, suggesting that the spatial Durbin model (SDM) is more appropriate. Therefore, a two-way fixed-effects SDM is employed in the empirical analysis. Furthermore, the SDM includes spatial lags for both the dependent and explanatory variables, providing a more comprehensive reflection of spatial correlations and spillover effects. Compared to the SLM and SEM, the SDM is more general and robust in its specification. The selection of explanatory variables comprehensively considered agricultural natural conditions, input patterns, and environmental governance aspects. Variable definitions and descriptive statistics are detailed in

Table 2. Variable descriptions data sources and summary metrics.

Variables	Definition (Unit)	Obs.	Mean	Std.	Min	Max
Agricultural Industrial Structure (AIS)	Agricultural industrial structure (dimensionless)	600	0.5200	0.0849	0.3388	0.7396
Environmental Regulation Intensity (ERI)	Investment in environmental pollution control/regional gross domestic product (dimensionless)	600	1.2234	0.7454	0.2017	4.6252
Industrial Agglomeration (IA)	(Industrial added value of each province/total industrial added value)/(regional GDP/total GDP) (dimensionless)	600	1.2259	0.7020	0.0423	4.2328
Urbanization Rate (UR)	Urban permanent population/total permanent population (dimensionless)	600	0.5459	0.1507	0.1489	0.8958
Agricultural Fixed Asset Investment (AFAI)	Annual agricultural fixed asset investment (billion CNY)	600	7.3889	6.7805	0	51.27
Grain Crop Sown Area (GSA)	Sown area of grain crops (million hectares)	600	3.7415	3.022	0.4652	14.6823
Disaster-Affected Area (DAA)	Area affected by natural disasters (105 hectares)	600	10.1461	9.9488	0	73.937

.

The efficiency scores are estimated from a DEA framework and then used in the regression. They are treated as performance indicators, and the results are interpreted as associations rather than causal effects. Multicollinearity is not a concern. The mean VIF is 1.7.

2.4. Data Sources and Processing

Data utilized for agricultural carbon emissions calculations are sourced from the China Energy Statistical Yearbook, China Agricultural Statistical Yearbook, China Financial Yearbook, China Water Resources Statistical Yearbook, and China Population Statistical Yearbook spanning 2003 to 2022. Carbon emission factors reference the IPCC’s Fourth Assessment Report and are converted into CO₂ equivalents. All monetary variables were converted to constant prices to ensure inter-period comparability. Missing values were imputed using linear interpolation because the number of missing observations was small and the affected variables are annual statistical indicators that typically change smoothly rather than abruptly. This treatment preserves the continuity of the panel and is unlikely to materially affect the overall estimation results. Agricultural carbon efficiency calculations were performed using the MAXDEA 9.0 Ultra platform. Spatial econometric analysis was conducted with Stata 17 and MATLAB R2021b, while spatial visualization outputs were generated using Python 3.12 and ArcMap 10.8. The dataset used in this study is available in the Supplementary Materials.

3. Results

3.1. Dynamic Evolution of Agricultural Carbon Efficiency from a Zonal Perspective

From a time evolution perspective, the national ACEE declined for a period after 2003 and began to recover gradually after 2010. Overall, this pattern contrasts with the trajectory of agricultural carbon emissions. Emissions rose steadily after 2003, plateaued around 2015, and then declined slightly. Figure 3 illustrates variations in efficiency levels across the three major functional zones. The average agricultural carbon efficiency in the GPZ is 0.7041. Overall, the level is relatively stable, but efficiency still varies across regions within the zone. Other provinces like Jilin (0.9610), Heilongjiang (0.9600), Inner Mongolia (0.9298) and Shandong (0.8423) are always close to the efficiency frontier. Hebei (0.7553), Henan (0.7831), Liaoning (0.6853) and Sichuan (0.6437) are of the middle-efficiency range and vary greatly on the efficiency levels. Their performance is inconsistent, as they perform above the regional average in some years and below it in others. The low-efficiency group includes Jiangsu (0.5844), Jiangxi (0.5697), Anhui (0.4991), Hubei (0.4678), and Hunan (0.4717), with efficiency values in most years being significantly lower than the intra-zonal average.

The GSZ has an average efficiency of (0.6729), which is significantly smaller than the GPZ, with most of the provinces in the zone recorded to be constantly below 1, implying that it is a non-frontier. Beijing (0.994), Tianjin (0.981) and Shanghai (0.9508) have been at high levels of efficiency over the long run and thus they belong to a high-efficiency group. The average efficiency of Hainan is 0.6312. While the province reached the efficiency frontier (efficiency > 1) in 2003–2004, its efficiency has declined steadily since then, falling to 0.454 by 2022. Its efficiency values have been below the regional average most of the time, meaning that agricultural carbon efficiency has decreased considerably in recent years. In comparison, Zhejiang (0.3645), Fujian (0.4019), and Guangdong (0.3864) have long remained in the low-efficiency group.

The GBZ had the greatest average efficiency (0.7383), but substantial intra-regional differences were recorded. Qinghai (0.9818), Ningxia (0.9538) and Shanxi (0.9355) consistently demonstrated efficiency levels above the regional average over the long term. Shaanxi (0.724), Gansu (0.7875) and Chongqing (0.7359) fall within the medium-efficiency group, with most years showing efficiency levels close to or slightly above the regional average, albeit with fluctuations. Yunnan (0.4592), Guizhou (0.7228) and Guangxi (0.3747) consistently underperform the regional average, placing them in the low-efficiency group, where efficiency improvements have been slow.

In summary, from a regional perspective, the GBZ has a relatively high efficiency level within its own efficiency frontier, followed by the GPZ, while the GSZ has a relatively low efficiency. These differences reflect relative performance within each region, rather than absolute efficiency levels between regions. Significant differences still exist between different provinces within each region.

The existing literature, under a unified frontier estimation approach, ranks inter-regional efficiency as GSZ > GBZ > GPZ. Beijing, Shanghai, Jiangsu, and Hainan are categorized within the high-efficiency group [12,44], whilst Heilongjiang, Jiangxi, Hubei, and Yunnan are classified within the low-efficiency group. Following the partition calculation, the ranking has been adjusted to GBZ > GPZ > GSZ. Notably, the GPZ does not exhibit a pronounced disadvantage overall; Heilongjiang has long remained near the frontier within this zone, while Jiangxi is not the least efficient province. Hainan is average in terms of GSZ performance and Jiangsu has been low in terms of GPZ efficiency. These results suggest that the method of uniformly measuring efficiency across the country may have exaggerated the advantages of the GSZ, and thus zoned measurement can better reflect the true efficiency.

3.2. GML-Based Productivity Change

In this section, we decompose the GML index into the TC and changes in EC; in finer detail, we examine how the change in agricultural carbon efficiency is changing with time and the influences behind these changes. Figure 4 presents the annual mean GML index and its decomposition results for the GPZ, GSZ, and GBZ from 2003 to 2022.

The GML index is defined as the product of EC and TC. The values reported in this section are the averages of GML, EC, and TC calculated separately based on province–year observations. Therefore, the average GML value is not equal to the product of the average EC value and the average TC value.

The GML index shows that the mean GML of three functional zones ranks as follows: GPZ (1.0171) > GSZ (1.0124) > GBZ (1.0055). The GPZ realized a GML value of above 1 during 57 percent of the statistical years. The GPZ had a better efficiency improvement experience than other regions, with the long-term improvement duration taking an average of 4.4 years. This is quite high compared to the GSZ (42%, 3.6 years) and the GBZ (41.7%, 3.3 years). Figure 4 further shows that the annual mean GML values of the three zones fluctuated over time, but the GPZ maintained a relatively stronger improvement pattern overall. At the provincial level, substantial heterogeneity remained within each zone. In the case of regional gaps, provinces under the GPZ, like Hebei, Henan, and Shandong, were more efficient with significant inroads. In the GSZ, there were more fluctuations in places such as Hainan and Guangdong. The internal differences within the GBZ are relatively obvious. The productivity improvement in Gansu, Xinjiang and other places is relatively stable, while that in Guangxi and other places is slow. The above differences indicate that efficiency rankings vary markedly across different evaluation frameworks.

The EC results show that the mean EC scores of all three functional zones were above 1, which is an indication that there was a by-and-large increase in the level of efficiency of the various functional zones as the study period progressed. Nonetheless, major differences were found between the intensity, occurrence, and permanence of these gains. The average increase in the agricultural technical efficiency of the GPZ (1.0085) and GSZ (1.0064) was found to be the highest and slightly lower, respectively. Knowing that the total was 43 percent of the years with EC > 1 is evidence of the variability in the efficiency improvement process in the GSZ. EC perceived significant growth within a certain period. The average duration of the continuous improvement period was 3.71 years, which was more than the consecutive periods in both the GPZ and GBZ. Overall, the GBZ lagged behind the other two zones in both the magnitude and persistence of efficiency improvement. The province-level results also reveal considerable heterogeneity. In the GPZ, Henan and Anhui had the highest agricultural carbon efficiencies. The average EC value of Heilongjiang is close to 1, and the magnitude of efficiency change is relatively limited. Beijing (1.0403), Shanghai (1.0363), and Tianjin (1.0303) recorded the highest and continued growth of agricultural carbon efficiency in the GSZ. Guangxi (0.9844) underwent a general decrease in efficiency. Over the study period, efficiency increased in less than 30% of the years, indicating relatively weak persistence in efficiency improvement.

The TC rankings are as follows. GSZ (1.0151) > GPZ (1.0131) > GBZ (1.0095). The mean TC values of all three zones were above 1. TC > 1 per annum in the GSZ and GPZ is 61.7% and 61.5%, respectively, much greater as compared to 53.7% in the GBZ. The duration of consecutive development of technologies was shown to be the longest in the GPZ (4.38 years) and GBZ (4.00 years), higher than the indicator in the GSZ (3.86 years). On a provincial level, the provinces of Inner Mongolia (1.0348), Hebei (1.0282) and Shandong (1.027) topped the list in the GPZ, with the TC of the Shandong province having grown in the previous eight years. In the GSZ, stability is relatively high in Beijing (1.0328) and Tianjin (1.0325), but closely followed by Zhejiang (1.0163), Hainan (1.0144), and Fujian (1.0095); Shanghai (0.992) has been shown to be lower than that of the region. There are strong inequalities in the provinces within the GBZ in the improvements in ACEE. Shaanxi (1.0184) achieved seven consecutive years of technological progress, while Xinjiang (1.0207) recorded four. Conversely, Guizhou (0.9943) demonstrated a slight regression in technological progress for ACEE, though its TC remained above 1 for six years.

The GML index is defined as the product of EC and TC. The reported values in this section are averages computed separately for GML, EC, and TC based on province–year observations. Therefore, the mean GML does not equal the product of the mean EC and mean TC.

3.3. Dynamic Evolution of ACEE

This study employs kernel density methods to examine the distribution patterns and temporal evolution of agricultural carbon efficiency in China and its three major grain-producing functional zones over 2003–2022 (Figure 5). The figure illustrates changes in distribution shape, dispersion, and polarization over time.

At the national level (Figure 5a), the peak of the kernel density distribution shifts rightward over time, with the modal value moving from approximately 0.65 to around 0.96. This indicates a substantial overall improvement in agricultural carbon efficiency across all provinces nationwide. Over the same period, the interquartile range (IQR) expanded from 0.29 to 0.45, and a pronounced bimodal pattern emerged in the later years, indicating increasingly divergent performance across provinces. The disparity in agricultural carbon efficiency within the GPZ has been narrowing, with the main peak of the kernel density distribution gradually shifting upward to around 0.95, indicating improvements in efficiency levels across most provinces. Although the IQR has expanded slightly, the magnitude of change remains limited. Efficiency levels across provinces are still relatively concentrated, and no clear bimodal pattern is observed, suggesting that overall efficiency differences among provinces within the region are relatively small. In the GSZ, high-efficiency and low-efficiency provinces have coexisted over a long duration. The IQR remains consistently high, indicating pronounced disparities across provinces. The distribution also suggests that lower-efficiency provinces continue to occupy a noticeable share, and the shift in the distribution is less evident in these areas. There is not a great deal of variation in the overall level of carbon efficiency in the GBZ, with maximally high efficiency remaining at approximately 0.7. The fluctuation range of the IQR is relatively small, indicating that the overall gap in agricultural carbon efficiency among provinces remains stable.

Overall, although agricultural carbon efficiency in China has continued to improve, substantial disparities across regions remain evident. The trends may be described as convergence in the GPZ, polarization of the GSZ, and relative stability in the GBZ.

3.4. Global Spatial Autocorrelation Analysis

The study uses the Moran’s I, based on spatial adjacency relationships, to evaluate the spatial autocorrelation of ACEE within provinces and its association with neighboring regions. It tests the presence of spatial clustering in agricultural carbon efficiency in the country (

Table 3. Results of the global Moran’s I for 2003–2022.

Year	I	Z	p-Value *	Year	I	Z	p-Value *
2003	0.2573 **	2.3250	0.0201	2013	0.5620 ***	4.7575	0.0000
2004	0.2466 **	2.2362	0.0253	2014	0.4827 ***	4.1246	0.0000
2005	0.3213 ***	2.8371	0.0046	2015	0.5450 ***	4.6240	0.0000
2006	0.1066	1.1277	0.2594	2016	0.5568 ***	4.7129	0.0000
2007	0.3286 ***	2.9048	0.0037	2017	0.5719 ***	4.8304	0.0000
2008	0.4012 ***	3.4923	0.0005	2018	0.5464 ***	4.6256	0.0000
2009	0.3658 ***	3.2115	0.0013	2019	0.5662 ***	4.7841	0.0000
2010	0.4722 ***	4.0472	0.0001	2020	0.5592 ***	4.7292	0.0000
2011	0.5692 ***	4.8085	0.0000	2021	0.5955 ***	5.0179	0.0000
2012	0.5494 ***	4.6571	0.0000	2022	0.6209 ***	5.2234	0.0000

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

).

Moran’s I is statistically significant at the 1% or 5% level, and it was positive in all years but 2006. Agricultural carbon efficiency displays long-term positive spatial autocorrelation, and the clustering patterns are of high–high or low–low. The results for 2006 are not statistically significant (I = 0.1066, p = 0.2594), indicating that spatial correlation was not evident in that year.

This study selects four representative years (2003, 2009, 2015, and 2022) to compare the spatial variation in agricultural carbon efficiency across provinces. In 2003, provinces exhibited a significant positive spatial correlation, though the degree of clustering was relatively weak. Since 2009, an increasing number of provinces have shown patterns of high–high and low–low clustering. Since 2015, the provincial gap in agricultural carbon efficiency has further widened, with high-efficiency areas primarily concentrated in East China and several provinces within the GSZ. Low-efficiency provinces are mainly located in the central and western regions, as well as in the GBZ. By 2022, high–high and low–low patterns in agricultural carbon efficiency had become more stable.

Overall, China’s agricultural carbon efficiency has undergone a transition from localized to pronounced agglomeration, with spatial correlations steadily intensifying. Disparities in agricultural carbon efficiency across regions have persisted and exhibited a trend of continuous widening.

3.5. Local Spatial Structure Characteristics

While the global Moran’s I index provides a general measure of overall spatial autocorrelation, it fails to reveal the specific location of such patterns. Therefore, this study further employs the Local Spatial Association Index (LISA) to identify the location and type of spatial clustering. The LISA distinguishes different local spatial association patterns. Specifically, high–high clustering denotes contiguous areas with high values, while low–low clustering denotes contiguous areas with low values. These patterns reflect local spatial clustering rather than absolute efficiency levels. This study selects four representative years (2003, 2009, 2015, and 2022) to present the LISA clustering patterns (Figure 6). The maps show the geographic evolution of high- and low-efficiency areas under the zonal measurement framework.

The findings show strong local spatial correlation in ACEE across China. However, the spatial correlation patterns are not consistent across neighboring provinces across different functional zones, indicating significant regional differences. In 2003, the high–high cluster was primarily distributed across the GPZ of Northeast and North China. In contrast, the GSZ exhibited low–low clustering, with relatively low efficiency levels. From 2009 to 2015, the high–high pattern expanded from the eastern region and appeared in parts of central and western provinces. Meanwhile, agricultural carbon efficiency in some provinces within the GBZ showed upward movement, and provinces with previously large efficiency gaps moved closer to intermediate levels. By 2022, regional patterns remained relatively stable in areas with high–high clustering. Concurrently, within the GSZ, low–low clusters in the south-eastern coastal areas persisted, with relatively limited changes in efficiency levels.

From the perspective of spatial distribution dynamics, the GPZ occupies a relatively important position within the high–high clustering pattern. In the GBZ, the efficiency gap showed signs of narrowing during certain periods. In contrast, the GSZ showed relatively limited changes in efficiency, with modest overall variation.

3.6. Spatial Regression Estimation Results of Influencing Factors

Based on the model specification and test results above, this paper uses the spatial Durbin model (SDM) with two-way fixed effects for estimation.

The main model constructs spatial weights using a contiguity matrix, while the inverse distance matrix and the inverse squared distance matrix are used for robustness testing.

Table 4. SDM estimates for ACEE under alternative spatial weights.

Variables	SDM (Contiguity Matrix)		SDM (Inverse Distance Matrix)		SDM (Inverse Squared Distance Matrix)
	Coefficient	z-Value	Coefficient	z-Value	Coefficient	z-Value
AIS	0.315 **	2.77	0.397 ***	3.50	0.414 ***	3.54
ERI	0.0061	1.09	0.0066	1.16	0.0053	0.93
IA	−0.0819 ***	−5.63	−0.0812 ***	−5.47	−0.0870 ***	−5.90
UR	0.241 **	3.04	0.399 ***	4.94	0.234 **	2.92
AFAI	−0.0019 *	−2.54	−0.0025 ***	−3.31	−0.0018 *	−2.37
GSA	0.0530 ***	6.27	0.0683 ***	9.13	0.0677 ***	8.70
DAA	−0.0022 ***	−4.35	−0.0024 ***	−4.98	−0.0026 ***	−5.15
W×AIS	−0.0343	−0.15	−1.051	−1.44	−0.4580	−1.62
W×ERI	−0.0033	−0.34	−0.0068	−0.18	−0.0022	−0.14
W×IA	−0.0855 **	−2.81	−0.307 ***	−3.54	−0.0739 *	−2.05
W×UR	0.172	1.33	1.854 ***	3.61	0.336	1.85
W×AFAI	0.0001	0.03	−0.0315 ***	−5.01	−0.0127 ***	−5.04
W×GSA	0.0590 ***	3.85	0.332 ***	6.92	0.0655 **	3.21
W×DAA	0.0001	0.14	0.0014	0.50	0.0021	1.76
ρ	0.365 ***	7.28	0.281 *	2.34	0.367 ***	5.86
R2	0.0788		0.0543		0.0385
observations	600		600		600

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. Note: AIS denotes Agricultural Industrial Structure; ERI denotes Environmental Regulation Intensity; IA denotes Industrial Agglomeration; UR denotes Urbanization Rate; AFAI denotes agricultural fixed asset investment; GSA denotes grain crop sown area; DAA denotes Disaster-Affected Area.

presents the regression results under the three types of spatial weight matrices. In all models, the spatial lag term (ρ) is positive and statistically significant at the 1% or 5% level, indicating that agricultural carbon emission efficiency exhibits a significant positive spatial association. The decomposition of the effects yields Table 4 to support once again that the key variables present similar directions of influences among the direct, indirect, and total effects, but with varying magnitudes.

The estimation results show that the AIS and UR both exhibit significant positive effects under different model settings. In contrast, the coefficients of AFAI and IA are significantly negative. The negative value of AFAI indicates that an increase in agricultural fixed asset investment does not necessarily translate into higher carbon efficiency, especially when investment expansion is mismatched with improvements in resource utilization efficiency. The negative coefficient of IA may reflect factor competition and crowding-out effects under industrial concentration, which weaken agricultural carbon efficiency. Regarding natural factors, the coefficient of the GSA is significantly positive, while the coefficient of the DAA is significantly negative. Furthermore, the spatial lag terms of several explanatory variables are statistically significant, indicating that agricultural carbon efficiency and its determinants exhibit spatial dependence.

3.7. Spatial Effect Decomposition of Influencing Factors

This section conducts an effect decomposition of the SDM results, with the results shown in

Table 5. SDM effect decomposition for ACEE.

Variables	Direct Effects		Indirect Effects		Total Effects
	Coefficient	z-Value	Coefficient	z-Value	Coefficient	z-Value
AIS	0.320 ***	2.69	0.0693	0.22	0.390	1.05
ERI	0.0054	1.10	−0.0020	−0.14	0.0035	0.22
IA	−0.0924 ***	−6.05	−0.167 ***	−3.14	−0.259 ***	−4.27
UR	0.275 ***	3.11	0.405 *	1.91	0.680 ***	2.69
AFAI	−0.0021 **	−2.31	−0.0011	−0.42	−0.0032	−1.06
GSA	0.0613 ***	7.72	0.114 ***	6.53	0.176 ***	9.82
DAA	−0.0023 ***	−4.68	−0.0009	−0.80	−0.0031 ***	−2.62

Notes: *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels.

.

The direct effects show that the AIS, UR, and GSA have significant positive impacts on local agricultural carbon efficiency, whereas the AFAI, IA, and DAA have negative effects. Regarding the indirect effects, the GSA exhibits a significant positive spillover effect, while IA has a significant negative impact on neighboring regions; the remaining variables are not significant in the spatial dimension. In terms of total effects, the UR and GSA have significant positive influences on national agricultural carbon emission efficiency, whereas the total effects of IA and the DAA are negative.

4. Conclusions

This study applies the super-efficiency EBM–GML model to measure agricultural carbon emission efficiency and its dynamic changes across 30 provincial-level regions in China from 2003 to 2022. Hong Kong, Macao, Taiwan, and Tibet are excluded due to data limitations. The article analyzes the spatial–temporal changing patterns of agricultural carbon efficiency, the regional imbalance, and the spillover impacts by combining both the global Moran’s I and the SDM. Key discoveries include:

Firstly, agricultural carbon efficiency change was strongly confined to policy transitions. Agricultural development during 2003–2009 was accompanied by a decline in efficiency. After 2010, efficiency gradually recovered, alongside broader changes in agricultural and environmental policy.

Secondly, the provincial agricultural carbon efficiencies within individual functional zones vary greatly and have not been decreasing with time. Heilongjiang and Jilin have been doing well in the GPZ continuously, whereas Jiangxi and Hunan have remained relatively lagging. The same trends are observed in the GSZ and GBZ.

Thirdly, agricultural carbon efficiency has a high degree of spatial clustering. The global Moran’s I reveals that the high–high and the low–low clusters have been stable over time. This indicates that there is a lack of sufficient green technologies and environmental governance in low-efficiency regions.

Fourthly, there are considerable regional variations in the determinants and geographical spread of agricultural carbon efficiency. The GSA and UR augment nearby and regional carbon efficiency, whereas the AFAI, IA and DAA diminish it.

Overall, the combined effect of resources, technology and policies has promoted the improvement in agricultural carbon efficiency. Since the policy objectives, resource endowments, and governance capabilities differ among functional zones, assessment of agricultural carbon efficiency by functional zone is fairer and more accurate. The empirical results of this study suggest focused governance and differentiated management.

5. Discussion

During the study period, ACEE did not follow a linear upward trend. After 2003, it declined for several years and began to recover only after 2010. Over the same period, total agricultural carbon emissions continued to rise until they stabilized around 2015. This mismatch shows that early yield growth was not matched by a comparable improvement in carbon efficiency. A likely reason is that agricultural production still relied heavily on input expansion. Greater use of fertilizers, energy, and irrigation increased emissions, while gains in output efficiency remained limited. Under such conditions, higher yields did not lead to higher ACEE. The recovery after 2010 is better understood as a gradual improvement in the input–output–emission relationship, rather than a simple reduction in total emissions.

The decomposition results show that the sources of ACEE improvement differ across functional zones. In the GPZ, agricultural carbon efficiency rose with contributions from both efficiency change and technical change, whereas in the GSZ, the improvement was mainly linked to technical change. In the GBZ, both EC and TC contributed, but the overall increase was smaller and less sustained. This pattern is broadly consistent with the kernel density results. The GPZ tends to converge, the GSZ remains polarized, and the GBZ changes less over time. The differences across functional zones therefore lie not only in the pace of improvement, but also in the forces behind them.

The spatial regression results show that ACEE is shaped by more than local conditions alone. The positive and significant spatial lag coefficient points to a clear spatial association across provinces. Changes in one region are linked to those in neighboring regions, rather than remaining confined within administrative boundaries. The explanatory variables show different patterns across local and spatial dimensions. Locally, the AIS, UR, and GSA are positively associated with ACEE, whereas the AFAI, IA, and DAA show negative effects. The negative effect of AFAI suggests that greater fixed asset investment in agriculture does not always lead to higher carbon efficiency. In some regions, investment expansion may outpace improvements in resource use and low-carbon production, so additional capital input does not translate into better ACEE. The negative coefficient of IA may reflect stronger competition for land, labor, capital, and energy under industrial concentration, which can crowd out agricultural production and weaken input efficiency. In the spatial dimension, only a few variables display significant spillovers. The GSA has a positive spillover effect, while IA has a negative one. This suggests that improvements in ACEE depend on both within-region adjustment and inter-regional linkage.

Some limitations remain. Firstly, data constraints prevent the inclusion of non-point source pollution, soil carbon sequestration, and agricultural carbon storage in the measurement framework. This may lead to an underestimation of the carbon-related effects on agriculture. In addition, the reported efficiency scores should be interpreted as grain-oriented agricultural carbon emission efficiency rather than a comprehensive measure of environmental efficiency for the entire agricultural sector. Secondly, the empirical analysis focused on temporal variations, regional differences, and spatial effects, but did not delve into causal relationship identification or mechanism testing. These limitations also point to directions for future research. More refined data, including updated remote sensing information, could improve the monitoring of agricultural activities and support more detailed regional assessments. Future research could examine how institutional changes differ across functional zones. It should also consider whether policy effects vary over time, as well as across regions.