Research on Coupling Coordination of Agricultural Carbon Emission Efficiency and Food Security in Hebei Province, China

Abstract

The delineation and measurement of carbon emissions in agricultural production systems constitute a complex issue involving multiple factors. Previous research in this area has been limited in terms of comprehensive carbon emission assessment throughout the agricultural production process and systematic measurement. This study focuses on both dynamic and static aspects, systematically analyzing the agricultural carbon emissions and emission efficiency in Hebei Province from 2000 to 2020. It comprehensively explores the influencing factors of carbon emissions and delves into the relationship between agricultural carbon emission efficiency and food security. The experimental results revealed the following: (1) From 2000 to 2020, the agricultural carbon emissions in Hebei Province exhibited a fluctuating downward trend, with a spatial distribution pattern where they were high in the south and low in the north. And the carbon emissions caused by chemical fertilizers and plowed land accounted for 42.6% of the total. (2) The efficiency of agricultural carbon emissions in the static dimension fluctuated at a rate of 0.0265, whereas the ML index fluctuated less in the dynamic dimension, and the agricultural industrial structure had the most significant impact. (3) The coupling coordination degree of food security and agricultural carbon emission efficiency increases with time, and “coordination” gradually dominates in spatial change. The conclusions of this study are of great significance in stabilizing grain production and achieving low-carbon production in the Hebei Province.

1. Introduction

With the rapid development of the social economy, global climate change has attracted considerable attention from many countries. The global average temperature increased by 1.09 °C from 2011 to 2020 [1,2,3]. Compared to other greenhouse gases and air pollutants, carbon dioxide (CO₂) remains the primary driver of climate change [4]. Global climate change caused by carbon emissions has significantly impacted food security [5,6]. With the acceleration of agricultural modernization, large amounts of chemical fertilizers and pesticides, electric fuel, and agricultural machinery have been used for agricultural activities, and agriculture has developed rapidly. However, at the same time, a large number of greenhouse gases have been released that affect the climate [7]. According to reported statistics, agricultural carbon emissions from China account for 17% of the total emissions [8] and have become one of the important sources of carbon emissions globally.

In recent years, domestic and foreign research examining agricultural carbon emission measurements, carbon emission efficiency, and food security has increased. For the calculation of agricultural carbon emissions, certain scholars begin from the source of carbon emissions and determine the source of agricultural carbon emissions by investigating and calculating the agricultural activities throughout the entire life cycle of production [9,10,11]. Other scholars have used different approaches to directly or indirectly measure carbon emissions such as the direct measurement of planting and agricultural carbon emissions to improve and optimize regional agricultural planting structures [12,13,14]. Related research examining carbon emission efficiency has primarily focused on the definition of carbon emission efficiency and the calculation of carbon emission efficiency. The former is primarily measured using a single factor index and a total factor index [15,16]. However, in practice, defining carbon emission efficiency is a complex problem that requires the consideration of multiple factors. Therefore, analysis of the total factor index is more reasonable than that of the single factor index. The calculation of carbon emission efficiency is primarily based on the method of calculating total factor energy efficiency, including data envelopment analysis (DEA) and stochastic frontier analysis (SFA) [17,18]. In terms of food security, more attention has been paid to the relationships between food supply and demand, climate and food security, agricultural innovation and technology, and other influencing factors [19,20,21,22]. In the face of global problems such as the intensification of the greenhouse effect and deterioration of the ecological environment, a number of scholars have begun to study the relationship between carbon and grain and also the relationship between carbon emission efficiency and food security [23,24]. For example, it is of interest to determine how carbon emission reduction per unit of grain production can be achieved by improving resource utilization, energy consumption, and greenhouse gas emissions to improve the efficiency and sustainability of grain production [25].

However, previous studies still have certain limitations: (1) Calculation of agricultural carbon emissions and emission efficiency: There is a lack of calculation of the carbon emissions from all production activities in agricultural regions, and the main sources of carbon emissions in agricultural activities are not clear enough. Most studies approach this from a static perspective, overlooking the dynamic changes in carbon emission efficiency over time. (2) Coupling between agricultural carbon emissions and food security: There are relatively few relevant studies, and most of them focus on large scales such as national levels, which may overlook local or micro-level correlations due to differences in agricultural management practices across regions.

To address the lack of systematic research outcomes for specific regions and the incompleteness of research indicators in existing studies, this study aims to analyze the static and dynamic evolution characteristics of agricultural carbon emission efficiency in Hebei Province using the Slacks-based Measure (SBM) model and the Malmquist–Luenberger (ML) index. Furthermore, it investigates the coordinated relationship between carbon emission efficiency and food security through the coupling coordination degree model. The technical route is shown in Figure 1. The conclusions drawn in this study can provide references for carbon emission accounting and the coordinated development of carbon and food in small regions, which is of significant importance for achieving low-carbon development in agriculture.

2. Study Area and Datasets

2.1. Study Area

Hebei Province is located in the North China Plain and possesses complex and diverse landforms and a vast territory. It is a major agricultural province and a grain- and vegetable-producing area in China. Grain production in this region accounts for 6% of the grain production of the entire country [26], and this province plays an important role in the development of the national agricultural economy. The proportion of cultivated land in Hebei Province is as high as 31.99% and is primarily distributed in the plain area and the Bashang Plateau (Figure 2a). Since 2021, the total grain output in Hebei Province has remained above 110 billion kilograms for three consecutive years, with an annual net grain transfer of over 10 billion kilograms, making outstanding contributions such as the “rice bag” for Beijing and Tianjin and ensuring the grain security of the Beijing–Tianjin–Hebei region. With the transformation of farming methods in agricultural production and life, large amounts of pesticides, agricultural films, machinery, and other large-scale use parameters have been utilized for promoting the increase in grain production in Hebei Province and have increased rural economic development; however, they have also led to increased agricultural carbon emissions yearly and have significantly damaged the agricultural ecological environment. Therefore, while ensuring a solid increase in agricultural production and promoting the green development of the rural economy in the future, effectively promoting agricultural carbon emission reduction, improving the agricultural ecological environment, and achieving low-carbon development of agriculture are important tasks.

2.2. Datasets

The research content of this paper primarily includes the calculation of agricultural carbon emissions, agricultural carbon emission efficiency, and their influencing factors and studying the relationship between agricultural carbon emission efficiency and food security. Agricultural carbon emissions primarily include those from pesticides, agricultural films, diesel oil, fertilizers, tilling, irrigation, pigs, cattle, and sheep. Agricultural fertilizers are primarily expressed by the amount of fertilizer applied in the year. The breeding amount of livestock such as pigs, cattle, and sheep is primarily adjusted according to the number of stocks and slaughters. These indicators are obtained from the Rural Statistical Yearbook of Hebei Province and the website of the National Bureau of Statistics. Relevant data focused on prefecture-level cities in Hebei Province were acquired from the Hebei Rural Statistical Yearbook. The efficiency of agricultural carbon emissions and its influencing factors were calculated based on previous calculations of agricultural carbon emissions using relevant methods. The data for the total output values of agriculture, forestry, animal husbandry, and fisheries were derived from the Statistical Yearbook of Hebei Province and were converted according to the constant price of the representative year. For the relationship between agricultural carbon emission efficiency and food security, the data acquisition and use of relevant indicators such as grain self-sufficiency rate, per capita grain possession, grain yield per unit area, per capita cultivated land, and grain production fluctuation coefficient were derived from the Hebei Province Rural Statistical Yearbook and the Hebei Province Statistical Yearbook (

Table 1. Data and sources.

Index Types	Select Data	Sources
Carbon emissions from agricultural production	Agricultural fertilizers	Oak Ridge National Laboratory
	Pesticide
	Agricultural film	Institute of Resoure, Ecosystem and Environment of Agriculture
	Diesel oil	Intergovernmental Panel on Climate Change
	Tilling	Wset TO [27], Cui et al. [28].
	Irrigation	College of Biological Sciences
Carbon emissions from animal husbandry	Gastrointestinal fermentation and fecal management of pigs, cattle, and sheep	Intergovernmental Panel on Climate Change
	The number of pigs, cattle, and sheep and their slaughter	Hebei Statistical Yearbook Hebei Rural Statistical Yearbook National Bureau of Statistics
Input indicators of agricultural production activities	Primary industry practitioners
	Fertilizer application rate
	Total power of agricultural machinery
	Sown area of crops
Output indicators of agricultural production activities	Investment in fixed assets of agriculture, forestry, animal husbandry, and fishery
	Total output value of farming, forestry, stock raising, and fishery
	Afforestation area
Other social indicators	The number of labor force participants at the end of the year
	Total population

).

3. Theory

3.1. Agricultural Carbon Emission Calculation Model

The carbon emissions from agricultural sources and their corresponding emission factors represent the carbon emissions of that particular type of carbon emission source (

Table 2. Table of corresponding carbon emission factors for agricultural carbon emission sources.

Carbon Emissions Source	Carbon Emission Factor
Agricultural fertilizers	0.8956 kg CE·kg−1
Pesticide	4.9341 kg CE·kg−1
Agricultural film	5.18 kg CE·kg−1
Diesel oil	0.5927 kg CE·kg−1
Tilling	266.48 kg CE·hm−1
Irrigation	312.6 kg CE·km−1

). And the sum of the carbon emissions of each carbon emission source is the total amount of agricultural carbon emissions to be measured. The estimation model was as follows:

$$C=\sum C_i=A_i{\delta }_i$$

(1)

In the formula, C is the total amount of agricultural carbon emissions, $C_i$ is the carbon emissions of the i-th type of agricultural carbon source, $A_i$ is the consumption of the selected carbon emission source, ${\delta }_i$ is the emission factor corresponding to the i-th carbon emission source.

To better understand the degree of agricultural carbon emissions, they were primarily characterized by the intensity of agricultural carbon emissions. The formula is as follows:

$$C_j=\raisebox{1ex}{$C$}\!\left/ \!\raisebox{-1ex}{${GDP}_i$}\right.$$

(2)

In the formula, C_j is the agricultural carbon emission intensity, and GDP_i refers to the total output value of agriculture and animal husbandry in the total agricultural output value of the region.

Carbon emissions from animal husbandry. This study primarily selected three types of animals (pigs, cattle, and sheep) that account for the primary position in the number to achieve estimates. Based on the results of the IPCC guidelines (2006) [4] and a previous publication by Zhang [29], the corresponding carbon emission coefficients of different livestock species were appropriately adjusted. The emission coefficients for intestinal fermentation and fecal management of the major animals are presented in

Table 3. Corresponding carbon emission factor values for major animals *.

	Emission Factor	Pigs	Cattle	Sheep
Gastrointestinal fermentation	CH4	1.00	0.50	2727
Adjusted carbon emission coefficient after conversion (kg CE/head/a−1)		6.82	370.53	68.2
Manure management	CH4	3.00	5.33	0.32
	N2O	0.53	1.24	0.66
Adjusted carbon emission coefficient after conversion (kg CE/head/a−1)		20.46	36.35	2.18
		3.61	8.46	4.5

* This study primarily refers to the research results of Hu [30], as the primary greenhouse gases emitted by animal gastrointestinal fermentation and fecal management are CH₄ and N₂O; to facilitate subsequent calculations of the carbon emission coefficient corresponding to these two, they were converted to the carbon emission coefficient corresponding to carbon (C). The primary conversion relationships are as follows: 1 t CH₄ = 6.8182 tC and 1 t N₂O = 81.2727 tC.

.

3.2. Agricultural Carbon Emission Calculation Model

3.2.1. Construction of the Agricultural Carbon Emission Efficiency Evaluation Index System

This article divides agricultural inputs into human, material, and financial inputs, while outputs are categorized into expected and unexpected outputs. Finally, five input indicators and three output indicators were selected to construct the evaluation system for agricultural carbon emission efficiency. The specific indicators are listed in

Table 4. Agricultural carbon emission efficiency evaluation index system.

Type	Criterion Layer	Index of Selection
Input	Manpower	Primary industry practitioners/ten thousand people
		Fertilizer application rate/million t
	Material resources	Total power of agricultural machinery/10 MW
		Crop sown area/10 km2
	Financial resources	Investment in fixed assets of agriculture, forestry, animal husbandry, and fishery/CNY 10,000
Output	Desirable output	Gross output value of agriculture, forestry, animal husbandry, and fishery/CNY 100 million
		Afforestation area/10 km2
	Undesirable output	Agricultural carbon emissions/million t

.

3.2.2. SBM Model

The SBM is a super-efficiency DEA model proposed by Tone [31] in 2001 on the basis of the existence of slack variables among the selected variables. Therefore, the proposed model not only compensates for the traditional radial DEA model by ignoring the influence of slack variables and putting slack variables directly into the objective function but also eliminates the influence of slack variables on efficiency evaluation. This has become an important evaluation method for the system evaluation of undesired output indicators.

Suppose there are n decision-making units, and each decision-making unit includes three parts that include input m, desirable output $r_1$, and undesirable output, $r_2$. The vectors can be expressed as an $xϵR^m,y^gϵR^{r_1},y^bϵR^{r_2}$, $X,Y^g,Y^b$ table matrix and are greater than or equal to 0, $X=\left[x_1,x_2\cdots x_n\right]ϵR^{m\times n}$, $Y^g=[y_1^g,y_2^g\cdots y_n^g]ϵR^{r_1\times n}$, $Y^b=[y_1^b,y_2^b\cdots y_n^b]ϵR^{r_2\times n}$, and based on this, the SBM model constructed in this paper is as follows:

$$p_{min}=\frac{1-\frac{{\sum }_{i=1}^m\frac{s_i^{-}}{x_{ik}}}{m}}{1+\frac{1}{\left(r_1+r_2\right)}\times \left({\sum }_{s=1}^{r_1}\frac{s_p^g}{y_{pk}^g}+{\sum }_{q=1}^{r_2}\frac{s_q^b}{y_{qk}^b}\right)}\left\{\begin{array}{c}{x}_{ik}=X{\lambda }_j+S_i^{-},i=\mathrm{1,2},\dots ,m\\ y_{pk}^g=Y^g{\lambda }_j+S_p^g,s=\mathrm{1,2},\dots ,r_1\\ y_{qk}^b=Y^b{\lambda }_j+S_q^b,q=\mathrm{1,2},\dots ,r_2\\ {\lambda }_j\ge 0,j=\mathrm{1,2},\dots ,n,j\ne 0\\ s_p^g\ge 0,p=\mathrm{1,2},\dots ,r_1\\ s_q^b\ge 0,q=\mathrm{1,2},\dots ,r_2\end{array}\right.$$

(3)

where $p$ is the agricultural carbon emission efficiency value, $S^{-}$, $S^g$, and $S^b$ are the relaxation vectors of input, expected output, and undesired output, respectively. When $S^{-}$ and $S^b$ > 0, the input in the production process of Mingye is excessive, the expected output is insufficient, and the undesired output increases. When $S^g$ > 0, the expected output is insufficient. $\lambda$ is the table weight vector. When $p$ is the objective function, at $p$ = 1, the decision-making unit is feasible and effective, and agricultural carbon emissions are the highest. When $p$ < 1, the decision-making unit may incur some loss and is invalid. At this time, it is necessary to adjust the input and output to achieve the optimal state of the decision-making unit and improve the efficiency of agricultural carbon emissions.

3.2.3. Malmquist–Luenberger Index

The ML index not only considers the impact of undesired output on the overall production efficiency but also makes a reasonable analysis of the efficiency changes and influencing factors of the evaluated units [32,33]. The change in the ML index from t to t + 1 can be expressed as follows:

$${ML}_t^{t+1}={\left[\frac{1+\overrightarrow{D_0^t}\left(x^t,y_g^t,y_b^t;g^t\right)}{1+\overrightarrow{D_0^t}\left(x^{t+1},y_g^{t+1},y_b^{t+1};g^{t+1}\right)}\times \frac{1+\overrightarrow{D_0^{t+1}}\left(x^t,y_g^t,y_b^t;g^t\right)}{1+\overrightarrow{D_0^{t+1}}\left(x^{t+1},y_g^{t+1},y_b^{t+1};g^{t+1}\right)}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(4)

$${ML}_t^{t+1}={Tech}_t^{t+1}\times {Effch}_t^{t+1}$$

(5)

In this formula, the ML index from t to t + 1 is the geometric mean of the ML index at the two moments. When Tech > 1, the continuous progress and development of technical conditions can promote the improvement of comprehensive efficiency. When Effch > 1, the improvement of production efficiency can also promote the improvement of comprehensive efficiency, and this is not conducive to the improvement of comprehensive efficiency.

3.2.4. Tobit Model

The Tobit model [34] was first proposed by James Tobin. It is used to handle situations where the dependent variable is truncated, meaning that certain values cannot be observed because they fall below or above a certain threshold. For the calculation of agricultural carbon emission efficiency, if the OLS method is used, the integrity of the data will be compromised as not all data points can be fully observed, leading to biased estimation results. Therefore, building upon existing research, this study selects key factors influencing agricultural carbon emission efficiency in Hebei Province and conducts a driver factor analysis using the Tobit model. The model calculation formula is as follows:

$$y_i={\beta }^T{x}_i+{\epsilon }_i,i=1,2,\dots n$$

(6)

$$\left\{\begin{array}{c}{y}^{*}\ge 0,y_i=y^{*}\\ y^{*}\le 0,y_i=0\end{array}\right.$$

(7)

In the formula, $y_i$ is the independent variable vector, $x_i$ is the independent variable vector, ${\beta }^T$ is the regression parameter vector, $x_i$ is the independent variable vector, and ${\epsilon }_i$ is the random error of the equation and obeys the normal distribution, $\mathsf{\epsilon }$~N (0, ${\sigma }^2$). When the independent variable vector $x_i$ is the actual value, the truncated dependent variable vector is valued in a restricted manner. Specifically, when y* is greater than or equal to 0, $y_i$ is the actual value, and when $y^{*}$ is less than or equal to 0, $y_i$ is 0.

3.3. Comprehensive Evaluation Method of Food Security

Based on the current situation and characteristics of agricultural development in Hebei Province and referring to the research results of Lv [35] and Yang [36], indicators that can objectively reflect the current situation of food security in Hebei Province were selected, including grain yield per unit area, grain self-sufficiency rate, per capita arable land area, per capita grain possession, and grain production fluctuation coefficient. Through the evaluation method of the grain safety factor, the food security of the study area is comprehensively evaluated, and the food security evaluation criteria are divided into four levels where a safety factor score above 0.7 is “security”, [0.6, 0.7] is “basic security”, [0.5, 0.6] is “critical security”, and below 0.5 is “insecurity”. The formula for a comprehensive evaluation of regional food security is as follows:

$$F=K_1\times Z+K_2\times L+K_3\times D+K_4\times G+K_5\times B$$

(8)

where K₁–K₅ are the index weight values of the five indices of the grain self-sufficiency rate, per capita grain possession, grain yield per unit area, per capita arable land area, and grain production fluctuation coefficient, respectively, and Z, L, D, G, and B represent the scores of the grain self-sufficiency rate, per capita grain possession, grain yield level, per capita cultivated land area, and grain production fluctuation coefficient, respectively. B reflects the fluctuation range of grain production over one year. The calculation formula is as follows:

$$B=(Y_i-Y_{1i})/Y_{1i}$$

(9)

where $Y_i$ is the actual grain yield of i year, and $Y_{1i}$ is the average actual grain yield that is obtained by the 3-year moving average method. A greater fluctuation coefficient of grain production indicates a lower level of food security.

3.4. Coupling Coordination Evaluation Method

The degree of coupling is typically used to characterize the interaction and coordination between two or more systems or elements. To a certain extent, it reflects the degree of dependence and restrictions between systems. The coordination between systems or elements is reflected in the degree of coordination. The degree of coordination is used to evaluate the degree of benign coupling development under the coupling effect between systems or elements. Based on existing research results, a coupling model of agricultural carbon emission efficiency and food security was constructed. The formula for the model is as follows:

$$C=\frac{f\left(x\right)g\left(y\right)}{{\left[{\left(f\left(x\right)+g\left(y\right)/2\right)}^2\right]}^i}$$

(10)

where C is the degree of coupling between systems. The closer C is to 1, the better the coupling, and C values can range between (0 and 1). $f\left(x\right)$ and $g\left(y\right)$ represent the scale indices of agricultural carbon emission efficiency and the scale index of food security, respectively. $i$ is the adjustment coefficient and is typically between [−2, 5].

To better explore the coupling coordination development state and degree of coordination between agricultural carbon emission efficiency and food security, the coupling coordination model was introduced. The model is expressed as follows:

$$D=\sqrt{C\times P},P=af\left(x\right)+bg\left(y\right)$$

(11)

where D represents the coupling coordination degree between agricultural carbon emission efficiency and food security, the D value is between [0, 1], and p represents the comprehensive coordination index of agricultural carbon emission efficiency and food security. a and b are the specific coefficients of the two systems, and a + b = 1. The authors believe that agricultural carbon emission efficiency and food security are equally important, and thus, a = b = 0.5.

In view of the knowledge that the coupling and coordination level between agricultural carbon emission efficiency and food security has not formed a unified division standard, to more intuitively analyze the degree of coupling and coordination development between the two, this paper draws on the research results of Wang et al. [37] and divides the D value into 10 grades. The specific classifications are listed in

Table 5. Classification of the coupling coordination degree between agricultural carbon emission efficiency and food security.

D Value	Coordination Level	Coupling Coordination Degree	f(x) > g(y)	f(x) < g(y)
(0, 0.1]	1	Extreme incoordination	Food security lags behind	Agricultural carbon emission efficiency lags behind
(0.1, 0.2]	2	Severe incoordination
(0.2, 0.3]	3	Moderate incoordination
(0.3, 0.4]	4	Mild incoordination
(0.4, 0.5]	5	Basic incoordination
(0.5, 0.6]	6	Barely coordination
(0.6, 0.7]	7	Primary coordination
(0.7, 0.8]	8	Intermediate coordination
(0.8, 0.9]	9	Quality coordination
(0.9, 1]	10	High coordination

.

4. Results and Analyses

4.1. Accounting and Analysis of Agricultural Carbon Emissions

4.1.1. Temporal Evolution Characteristics of Agricultural Carbon Emissions

(1)

Total carbon emissions and carbon emissions structures

The total agricultural carbon emissions in Hebei Province first increased and then decreased (Figure 3). They fell from 12.14 million t in 2000 to 10.80 million t in 2020 with an average annual growth rate of −0.52%, and they were in a fluctuating downward trend after 2005. Zhang et al. also confirm these results [38]. Among all carbon emissions, the carbon emissions generated by agricultural films, diesel oil, fertilizers, and pigs in breeding animals exhibited different degrees of growth with average annual growth rates of 2.83%, 0.52%, 0.30%, and 0.59%, respectively. The carbon emissions from carbon emission sources such as pesticides, plowing, cattle, and sheep exhibited a negative growth trend with average annual growth rates of −1.29%, −0.53%, −1.89%, −1.53%, and −0.52%, respectively. Irrigation carbon emissions remained stable at 1.19 million t in 2000 and 2020 with no significant changes. Changes in agricultural carbon emissions were divided into three primary stages that included rapid growth, fluctuating decline, and continuous decline. In the first stage (the rapid growth period) (2000–2005), agricultural carbon emissions exhibited an increasing trend. This was due to agriculture being in a traditional extensive development stage, with relatively low emphasis on addressing pollution caused by agricultural carbon emissions. The second stage was a period of fluctuating decline (2006–2015). During this stage, agricultural carbon emissions experienced a decrease starting from 2011 as a turning point, followed by an increase, with the decrease being greater than the increase of 294,700 t in 2011–2015. This was primarily due to the accelerated modernization of agriculture, which improved agricultural production efficiency and led to a reduction in carbon emissions. However, the emphasis on industrial development in Hebei Province resulted in pollution emissions that, to some extent, impacted agricultural development. In the third stage, known as the continuous decline period (2016–2020), agricultural carbon emissions continued to decrease with a total decline of 1.55 million t. This reduction was mainly due to the widespread implementation of actions to reduce agricultural emissions and enhance carbon sequestration following the introduction of low agriculture carbon emission initiatives.

According to the dynamic change trend of the growth rate of carbon emissions, the growth rate of agricultural carbon emissions in Hebei Province decreased significantly with a large change before 2009, and the largest increase occurred during 2003–2004 (11.23%). The largest decline occurred during 2004–2006 (13.65%). From 2007 to 2008, the growth rate was negative (−0.70% to −5.73%), and this was at the lowest reduction stage. At this time, agricultural carbon emissions decreased from 14.01 million t to 13.21 million t, thus reducing agricultural carbon emissions by nearly 1 million t. Since then, the year-on-year growth rate has been in a fluctuating downward trend, and particularly after 2017, a downward trend has continued to appear. This indicates that Hebei Province is promoting the development of the agricultural economy on the one hand, and conversely, it also pays attention to the protection of the agricultural ecological environment and the long-term sustainable development of agriculture.

From 2000 to 2020, the agricultural carbon emission intensity in Hebei Province decreased at a rate of −0.76% with an average annual agricultural carbon emission intensity of 0.067 t/CNY 10,000. The maximum value appeared in 2000 at 0.162 t/CNY 10,000, and the minimum value was 0.022 t/CNY 10,000 in 2020. In the study period, the agricultural carbon emission intensity increased only in 2003–2004 with an increase of 11.23%. The most prominent downward trend was in 2005–2006 from 0.139 t/CNY 10,000 to 0.06 t/CNY 10,000, and this represented a decline of 53.92%. The changing trend of agricultural carbon emission intensity indicates that from 2000 to 2020 under the guidance of policies and measures, agricultural carbon emissions in Hebei Province decreased with improvement in the economic development level.

From the perspective of agricultural carbon emission structure, among the selected agricultural carbon emission sources, agricultural fertilizer and plowing land carbon emissions are at a high level, and these are the most important agricultural carbon emission sources in Hebei Province and account for 22% and 21% of agricultural emissions, respectively. Over the years, carbon emissions have been above 2 million t. Due to the strong dependence of agriculture on chemical fertilizers, the use of chemical fertilizers in Hebei Province has been increasing while promoting agricultural development; however, the utilization efficiency is low. By the end of 2020, the nitrogen fertilizer utilization rate of major crops in Hebei Province reached 40.58%, and this undoubtedly added difficulty to the prevention and control of agricultural non-point source pollution. Pesticides produced the lowest carbon emissions with an average annual production of 383,100 t. All agricultural carbon emission sources were bounded by 2015–2016. Before that, the increasing trend was significant, and it exhibited a downward trend year by year. Primarily due to the formulation of relevant policies on pollution reduction, carbon reduction, green expansion, growth synergy, and other related policies in Hebei Province, it has actively responded to the realization of the “carbon peaking and carbon neutrality” goal proposed by the country and achieved remarkable results.

(2)

Carbon emissions and intensity of each city

The average annual agricultural carbon emissions of each city in Hebei Province are provided (Figure 4). The agricultural carbon emissions of each city exhibited a fluctuating downward trend, and the evolution trend changed in the same direction. As the capital of Hebei Province, Shijiazhuang is an important city in the Beijing–Tianjin–Hebei region. Its average annual agricultural carbon emissions were 1.998 million t and accounted for 14.34% of the province. These were significantly higher than those in other cities before 2010. In 2015, the agricultural carbon emissions of Shijiazhuang and Handan were equivalent at 1.72 million t and 1.71 million t, respectively. In 2020, the agricultural carbon emissions from Handan exceeded those of Shijiazhuang by 420,800 t. The agricultural carbon emissions from Langfang are low, and this is closely related to its own area. In recent years, it has attached importance to the solution of “three-dimensional rural issues” and the implementation of food security. Qinhuangdao exhibited the lowest annual agricultural carbon emissions at only 547,300 t and accounted for only 3.93% of the province. It was expected to reach its lowest value in 2020 at 420,800 t. This is primarily due to the small land area of Qinhuangdao that possesses fewer primary industry practitioners than other cities. Compared to the emissions in other years, the agricultural carbon emissions of all prefecture–level cities in 2020 were low, thus indicating that all prefecture-level cities achieved initial results in regard to promoting green agricultural development and reducing the level of agricultural carbon emissions.

From the perspective of the time evolution characteristics of agricultural carbon emission intensity in Hebei Province, the agricultural carbon emission intensity of each city exhibited a cascade decline that was the largest during 2000–2005. In 2000, Zhangjiakou, Chengde, and Cangzhou were larger at 2.27 t/CNY 10,000, 2.44 t/CNY 10,000, and 2.66 t/CNY 10,000, respectively, and this was primarily due to the low total output value of agriculture and animal husbandry in the three cities. In 2005, Cangzhou and Hengshui exhibited the largest agricultural carbon emission intensities at 0.89 t/CNY 10,000 and 0.86 t/CNY 10,000, respectively. In 2010, 2015, and 2020, the intensity of agricultural carbon emissions in each city did not change significantly, and the overall performance exhibited a slight decline. In 2010, the agricultural carbon emission intensity of Xingtai and Hengshui was equivalent, where both were 0.44 t/CNY 10,000. Shijiazhuang was the lowest at only 0.24 t/CNY 10,000. In 2015, Hengshui was still the highest, but it was 0.1 t/CNY 10,000 lower than it was in 2010. In 2020, the agricultural carbon emissions of all cities were at a low level (all below 0.3 t/CNY 10,000). In short, from 2000 to 2020, the agricultural carbon emission intensity of each prefecture–level city decreased significantly, thus indicating that while developing the economy, the agricultural carbon emissions of each city gradually decreased, and this likely contributed to the reduction in agricultural carbon emissions in Hebei Province.

4.1.2. Spatial Evolution Characteristics of Agricultural Carbon Emissions

The spatial distribution of agricultural carbon emissions in Hebei Province was high in the south and low in the north (Figure 5(I)). From 2015 to 2020, the agricultural carbon emissions of each city exhibited different degrees of decline with an obvious downward trend. The agricultural carbon emissions from Shijiazhuang were reduced the greatest at 476,400 t. Overall, regional changes in agricultural carbon emissions in Hebei Province from 2000 to 2020 were not obvious, but the total amount exhibited a fluctuating decline, thus indicating that under the influence of carbon emission reduction policies, all prefecture-level cities in Hebei Province took corresponding measures to restrict agricultural carbon emissions and were working towards green agricultural development.

The agricultural carbon emission intensity of each city in Hebei Province (Figure 5(II)) exhibited significant spatial differentiation at different stages and a decreasing trend. The intensity of agricultural carbon emissions reflected the relationship between economic development and carbon emissions. As the intensity of agricultural carbon emissions decreases gradually, cities begin to control agricultural carbon emissions and economic progress. During 2000–2005, the carbon emission intensity of each city decreased, and in 2005, with the exception of Tangshan, the other provinces and cities were between 0.52 and 0.89 t/CNY 10,000. From 2005 to 2010, the low-value area changed from Tangshan to Shijiazhuang at 0.24 t/CNY 10,000. From 2010 to 2015, the carbon emission intensity of eight cities continued to decline, ultimately falling to the lowest level (0.14–0.24 t/CNY 10,000). In 2015, the carbon emission intensities of Shijiazhuang, Hengshui, and Cangzhou were higher than those of other cities, but they were reduced by 0.04 t/CNY 10,000, 0.07 t/CNY 10,000, and 0.08 t/CNY 10,000, respectively, compared to levels in 2000. In 2020, the agricultural carbon emission intensity of each city reached the lowest value observed in the study period, and the difference between cities was small and ranged from 0.14 to 0.28 t/CNY 10,000.

The above calculations and analyses were conducted on the total agricultural carbon emissions, carbon emission intensity, and their respective rates of change in Hebei Province. This has clarified the developmental trends of agricultural carbon emissions in the province and provided a data foundation for subsequent studies on carbon emission efficiency and its coupling coordination with food security. In the following sections, we will further analyze the evolution characteristics of carbon emission efficiency using the SBM model and ML index, and subsequently assess the degree of coupling coordination between carbon emission efficiency and food security using coupling coordination models.

4.2. Evaluation of Agricultural Carbon Emission Efficiency in Hebei Province

4.2.1. The Time Evolution Characteristics of Agricultural Carbon Emission Efficiency in Hebei Province

The efficiency level of agricultural carbon emissions in Hebei Province was calculated based on the super-efficiency SBM model, and the results are presented in Figure 6. From 2000 to 2020, the agricultural carbon emission efficiency in Hebei Province exhibited a fluctuating increase with an annual average of 0.765. In 2000, the agricultural carbon emission efficiency in Hebei Province was approximately 0.454, and by 2019, the agricultural carbon emission efficiency was 1.00. In 2002–2003, the efficiency of agricultural carbon emissions increased significantly, and the areas of crop planting and grain yield also increased significantly. Additionally, a reduction in livestock breeding inhibited agricultural carbon emissions, and the efficiency of agricultural carbon emissions significantly increased under the dual effects of increased carbon sinks and reduced carbon emissions. From 2003 to 2004, the carbon emission efficiency decreased significantly, and this was primarily due to the large increase in the number of pigs, cattle, and sheep. In particular, pigs increased by 10.57% compared to levels in the previous year, and the increase in agricultural resource input increased agricultural carbon emissions by 11.23%.

Regarding the level of agricultural carbon emission efficiency in various prefecture-level cities in Hebei Province, the carbon emission efficiency of Tangshan, Qinhuangdao, Zhangjiakou, and Chengde in 2000–2020 was 1, thus indicating that the level of agricultural carbon emission efficiency in these cities was high and the level of agricultural low-carbon production was high. From 2000 to 2020, lower average annual agricultural carbon emission efficiencies appeared in Xingtai, Baoding, and Hengshui (0.245, 0.286, and 0.278, respectively), thus indicating that there was an uncoordinated allocation of agricultural resources, insufficient expected output, or excessive undesired output in the development of agricultural production in these cities.

To elaborate on the dynamic changes in agricultural production efficiency in Hebei Province and to consider the impact of technical efficiency, the ML index was used to decompose the agricultural production efficiency of Hebei Province from 2000 to 2020. From Figure 7, it can be observed that the ML index of Hebei Province in 2000–2020 changed smoothly and the fluctuation was small. During 2003–2006, 2008–2010, and 2017–2018, the ML values were less than 1, and the ML values in the remaining years were greater than 1. According to the decomposition results for Hebei Province over many years, the technological progress index typically exhibited a fluctuating downward trend, but the average level was above 1. The maximum value appeared in 2010–2011 (1.768), and the minimum value was 0.607 in 2004–2005. The technical efficiency index exhibits a fluctuating upward trend where the minimum value was 0.454 in 2000–2001, and the maximum value was 1.067 in 2005–2006. The current technical efficiency change and technological progress index of Hebei Province indicate that technological progress has promoted comprehensive scale efficiency.

The results of the total factor production efficiency data for each prefecture-level city in Hebei Province are presented in

Table 6. Malmquist–Luenberger index in Hebei Province in various cities from 2000 to 2020 *.

Time	SJZ	TS	QHD	HD	XT	BD	ZJK	CD	CZ	LF	HS
2000–2001	0.37	0.22	0.40	0.28	0.42	0.50	0.47	0.57	0.03	0.17	0.04
2001–2002	1.17	1.02	1.01	1.43	0.88	0.77	1.42	1.31	1.43	1.93	7.73
2002–2003	2.76	2.47	2.10	3.75	3.76	3.13	1.63	1.13	35.27	3.59	4.08
2003–2004	1.19	1.06	1.34	2.12	0.81	1.13	0.92	0.93	1.61	1.24	1.35
2004–2005	1.23	1.36	1.25	1.31	0.90	0.59	0.92	0.10	1.10	1.14	1.20
2005–2006	1.07	1.50	1.51	0.96	1.02	0.96	0.94	0.98	0.38	1.23	0.32
2006–2007	1.65	1.38	1.36	1.36	1.61	1.48	1.00	0.95	1.69	1.43	1.36
2007–2008	1.13	1.69	1.36	1.17	1.12	1.22	1.30	1.13	2.29	1.21	0.92
2008–2009	1.18	1.50	1.13	0.69	0.87	1.15	0.94	0.97	1.51	1.77	0.80
2009–2010	1.01	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
2010–2011	1.63	1.04	1.41	1.94	0.90	1.25	1.19	0.95	1.32	1.32	2.57
2011–2012	1.47	1.27	1.23	1.33	1.91	1.02	1.01	1.01	1.01	1.68	1.32
2012–2013	1.23	1.20	0.99	1.17	1.11	0.96	1.03	1.10	1.09	1.04	1.67
2013–2014	1.42	1.00	1.09	1.02	0.10	1.12	0.97	1.01	1.90	3.10	1.36
2014–2015	1.00	0.98	1.13	1.08	0.75	1.02	0.95	1.02	2.15	0.91	0.81
2015–2016	0.98	1.05	1.07	0.10	1.39	0.89	1.17	1.07	0.60	0.86	1.49
2016–2017	0.28	0.69	1.07	0.80	0.77	0.85	1.07	0.84	0.76	0.64	0.74
2017–2018	1.03	1.01	1.01	0.91	0.81	1.27	0.98	1.01	0.54	1.27	0.88
2018–2019	1.23	1.14	1.02	1.27	1.37	1.40	0.71	1.24	1.12	1.26	1.10
2019–2020	0.76	1.03	0.97	0.95	1.01	0.85	0.76	0.91	0.94	0.60	0.89

* SJZ, TS, QHD, HD, XT, BD, ZJK, CD, CZ, LF, and HS represent Shijiazhuang, Tangshan, Qinhuangdao, Handan, Xingtai, Baoding, Zhangjiakou, Chende, Cangzhou, Langfang, and Hengshui, respectively.

. The ML index of each city in Hebei Province exhibited significant regional differences, and each prefecture-level city also exhibited a certain range of changes. From 2000 to 2001, the ML index of the 11 prefecture–level cities in Hebei Province was less than 1, thus indicating that the technological impact was negative during this period and that the input and application of technological factors were not as rapid as the development of agricultural production. The years with an ML index of greater than one were primarily 2002–2003, 2006–2007, 2011–2012, and 2018–2019, thus indicating that the technical production factors in these periods played a positive role in promoting the improvement of agricultural production efficiency. Particularly in 2002–2003, the change in the ML index in Cangzhou was the most significant, and this was primarily due to the significant increase in the afforestation area in Cangzhou at this stage, which increased by 33,700 hm² compared to the previous year. Although the ML index was greater than 1 in 2018–2019, it exhibited different degrees of decline in 2019–2020, thus indicating that the level of agricultural low-carbon production efficiency in Hebei Province exhibited a downward trend and the development of agricultural low-carbon production stagnated slightly. In summary, the ML index of each city in Hebei Province fluctuated greatly, and this may have been due to the lack of input data, technology, and implementation of various policies in Hebei Province, which is in the transition period of agricultural development exploration. Agricultural production exhibits a state of greater than 1 and a continuous fluctuation below 1.

4.2.2. Spatial Evolution Characteristics of Agricultural Carbon Emission Efficiency in Hebei Province

The spatial variation in agricultural carbon emission efficiency in Hebei Province is presented in Figure 8. During the study period, the efficiency of agricultural carbon emissions in Hebei Province differed significantly, and the overall spatial distribution was uneven. High-value areas were primarily concentrated in the northern portion of the Hebei Province, whereas low-value areas were primarily distributed in local cities in the south.

From 2000 to 2005, the efficiency of agricultural carbon emissions in Handan changed the most, increasing by 0.45. Baoding decreased the most, but the downward trend was not obvious (from 0.14 to 0.12). In 2010, the overall agricultural carbon emission efficiency in southern Hebei Province was low, and the agricultural carbon emission efficiency in Hengshui was the lowest (0.07%). The agricultural carbon emission efficiency of Handan fluctuated greatly from the high-value area to the low-value area, thus indicating that the amounts of livestock breeding and the input of agricultural resources in Handan were reduced, agricultural carbon emissions were reduced, and agricultural carbon emission efficiency also changed in the same direction. In 2015, the agricultural carbon emission efficiency of seven prefecture-level cities reached 1, and the agricultural carbon emission efficiency of Shijiazhuang and Cangzhou increased by a large margin, thus indicating that with the gradual optimization of the agricultural production structure, the input of technical factors, and the support of relevant agricultural policies, the agricultural productivity of Hebei Province improved and that the agricultural carbon emission efficiency was higher. In 2020, the agricultural carbon emission efficiencies of Shijiazhuang, Cangzhou, and Langfang decreased to varying degrees with the former two decreasing by greater than 0.6.

4.3. Spatial and Temporal Changes in Food Security

4.3.1. Temporal Evolution

From Figure 9, it can be observed that the grain safety factor score of Hebei Province from 2000–2020 was above 0.7 (a safe level) and maintained an overall steady growth rate of 0.58%. Prior to 2005, the overall grain safety factor exhibited a fluctuating growth trend. In 2001, there was a slight decline (0.03) compared to the grain safety factor score in 2000, and this did not affect the grain safety level in Hebei Province. Fluctuations were relatively large in 2005 and 2016. In 2005, the grain safety coefficient reached its lowest value of 0.725, and this was 0.07 lower than that of the previous year with the largest decrease. This is primarily due to the higher level of agricultural disaster risk in Hebei Province in 2005. The affected area was as high as 6.87 × 10⁴ hm², the area of cultivated land at the end of the year decreased by 0.71% compared to the previous year, the population increased by 0.62% compared to the previous year, and in the early stage, the irrigation and water conservancy facilities were relatively backward and the grain production fluctuated. From 2006 to 2015, the grain safety factor value basically maintained a steady growth trend, the grain safety factor value remained above 0.8, and the safety level was high. In 2016, there was a significant decrease that was second only to that observed in 2005. In this year, the agricultural disaster area increased by approximately 4.1 × 10⁴ hm², and the grain yield decreased by approximately 15.77%. However, compared to 2005, the decline was lower, and this was primarily due to the improvement of farmland water conservation facilities and the promotion of agricultural production technology that played a positive role in grain production. After 2016, the fluctuation in the grain safety factor value did not change significantly, and this was primarily due to the improvement in cultivated land quality by high-standard farmland construction.

The time evolution characteristics of the grain safety factor values for each prefecture-level city in Hebei Province are presented (Figure 9). In 2000, the grain security of most cities in Hebei Province was at a safe level. The grain safety factor values of Chengde and Zhangjiakou were 0.535 and 0.6, respectively, and these were at the critical and basic safety levels. This may be related to imperfect policies related to early agricultural production and imperfect guarantee mechanisms related to food security. In 2005, the grain safety factor value in Zhangjiakou improved but was still at the basic safety level, whereas other municipal food safety levels were at the safety level. In 2010 and 2015, the fluctuation in the grain security level in each city was small and existed at the security level, thus indicating that all cities actively implemented the farmland protection system based on grain production and improved food security. In 2020, with the exception of food safety factors in Qinhuangdao and Langfang existing within the range of 0.4–0.5 (an unsafe level), other cities were within the safe level, and the fluctuation changes were relatively small.

4.3.2. Spatial Evolution

This section explores the food security level of Hebei Province from a spatial dimension and selects the years 2000, 2005, 2010, 2015, and 2020 for analysis (Figure 10). The spatial characteristics of food security levels in Hebei Province were significantly different. From 2000 to 2020, they experienced a “rise–fall” change process. In 2000, the southeastern portion of Hebei Province was at the security level, and only Chengde and Zhangjiakou in the north were below the security level. In 2005, the food security level in Cangzhou declined primarily due to the occurrence of numerous meteorological disasters in Cangzhou that year that posed a threat to food production. The safety levels of Zhangjiakou and Chengde were upgraded to basic safety levels. In 2010, Handan and Xingtai in the south and Cangzhou in the east were all upgraded to safety levels, and the safety factor for Cangzhou was the highest at 0.865. In 2015, the food security level in all regions of Hebei Province was generally high, and all were within the security level. In 2020, Qinhuangdao and Langfang were reduced to unsafe levels, and the overall security level in Hebei Province declined.

4.4. Analysis of Coupling Coordination Degree between Agricultural Carbon Emission Efficiency and Food Security

4.4.1. Temporal Evolution

From the perspective of the time-change dimension (Figure 11), the coupling coordination degree D value of agricultural carbon emission efficiency and food security in Hebei Province from 2000 to 2020 changed from 0.486 to 0.866, and the overall coupling coordination degree of the two exhibited a transition from non-coordination to quality coordination. During 2000–2013, the degree of coupling and coordination between the two was generally based on basic incoordination, minimal coordination, primary coordination, and intermediate coordination, and the degree of coupling and coordination was low. Particularly in 2000, 2001, and 2003, this value was on the verge of imbalance, and the degree of coupling coordination was the lowest. The D values were 0.486, 0.491, and 0.496, respectively, and f(x) > g(x) was indicative of the lagging development model of food security. From 2014 to 2020, good coordination was observed, the coordination level was 9, and the D value was between 0.8 and 0.9. At this stage, f(x) < g(x) was indicative of the lagging development mode of agricultural carbon emission efficiency. With the introduction and implementation of national and regional policies on low-carbon agricultural development in recent years and the continuous innovation and development of low-carbon technologies, the original traditional high-carbon emission production model has been innovated, and agricultural production has focused more on the principle of the unification of rapid economic development and ecological environment optimization. At this stage, the growth rate of agricultural carbon emissions has been effectively controlled, and agricultural carbon emission efficiency and food security have continued to develop in a quality-coordinated direction.

4.4.2. Spatial Evolution

Spatial dimensions are presented (Figure 12). The degree of coupling coordination of agricultural carbon emission efficiency and food security in Hebei Province was significantly different, and the trend of coordination gradually dominated over time. In 2000, four cities were in a state of non-coordination (Baoding, Xingtai, Cangzhou, and Hengshui), and this was primarily due to the large amount of agricultural carbon emissions in these cities and the unstable situation regarding grain production, purchase, and sale. Among them, the coupling coordination degree of agricultural carbon emission efficiency and food security in Baoding and Xingtai was the lowest, thus indicating a moderately imbalanced state, and the D value was between 0.2 and 0.3. Cangzhou and Hengshui exhibit mild and basic coordination, respectively. In 2005, most areas of the province were in basic non-coordination, and a few areas were barely coordinated. Between 2000 and 2005, cities in a state of imbalance gradually changed to barely coordinated. In 2010, the number of cities in coordination was greater than the number of cities in coordination, thus indicating that the efficiency of agricultural carbon emissions in these cities was better matched with food security in 2010. From 2005 to 2010, the northern portion of Hebei Province exhibited a coordinated development trend, whereas the southern part exhibited a spatial distribution pattern of non-coordination and coordination interactions. In 2015, the D value of each city in Hebei Province changed by values of between 0.4 and 0.7. The cities in the primary coordination state were Shijiazhuang, Tangshan, and Cangzhou with a coordination level of 7, and agricultural carbon emission efficiency and food security were well matched. The spatial variation in the degree of coupling coordination in the Hebei Province from 2010 to 2015 was small. In 2020, all prefecture-level cities in the Hebei Province were in a coordinated state, thus indicating that the efficiency of agricultural carbon emissions and food security were highly matched. From 2015 to 2020, the degree of coupling and coordination in the southern portion of the Hebei Province changed significantly, and a trend from non-coordination to coordination was evident.

5. Discussion

5.1. Analysis Examining the Influencing Factors of Agricultural Carbon Emission Efficiency in Hebei Province

Based on a regression analysis of the factors influencing agricultural carbon emission efficiency in Hebei Province, the degree of influence of each influencing factor on agricultural carbon emission efficiency is discussed.

Table 7. Residual number and rejection rate of points after the application of different filters.

Parameter	Coefficient	Std. Error	Test Value (T)	p > |T|
X1	0.0031224 **	0.0011750	2.66	0.019
X2	1.0001544 ***	0. 4640236	3.32	0.005
X3	−0.9258342	0.5070315	−1.83	0.925
X4	0.0225762 *	0.2350907	0.10	0.089
X5	−0.0065838	0.0044284	−1.49	0.159
X6	−0.0004024	0.0002714	−1.48	0.160
X7	−3.4441160 **	1.7890170	−1.93	0.075

* Significant correlation at the level of 0.1; ** significant correlation at the level of 0.05; *** significant correlation at the level of 0.01.

indicates that factors such as labor force scale, economic development level, agricultural mechanization level, and livestock manure treatment passed the significance test, thus indicating that these factors exerted a significant impact on agricultural carbon emission efficiency.

Labor scale (X1) and economic development level (X2) were significantly positively correlated with agricultural carbon emissions efficiency at the levels of 5% and 1%, respectively. This indicates that the labor force, as the primary body of agricultural development, requires more human resources to be put into production with the acceleration of agricultural modernization to strengthen the learning and application of new technologies and improve the efficiency of agricultural production. The degree of crop disasters (X3) and agricultural industrial structure (X7) were negatively correlated with agricultural carbon emission efficiency, and the agricultural industrial structure was significant at the level of 5%. The degree of crop damage is primarily due to the harm caused by natural disasters to agriculture, and this affects the agricultural output. Specifically, when other conditions remain unchanged, a higher degree of crop damage results in a lower efficiency of agricultural carbon emissions. Fertilizer use (X5) and livestock manure treatment (X6) in agricultural resource input were negatively correlated with agricultural carbon emission efficiency. Due to the use of chemical fertilizers being avoided in the process of agricultural development, farmers have wasted resources, caused environmental pollution, and emitted a large amount of carbon while pursuing high yields. Mechanization level (X4) exhibited a significant positive correlation with agricultural carbon emission efficiency at the level of 1%. The change in mechanization level is primarily reflected in the improvement in agricultural production efficiency. The improvement in agricultural production efficiency indicates that the utilization efficiency of resources used in agricultural production activities is improved simultaneously, and this exerts a positive effect on agricultural carbon emission efficiency. Specifically, when other conditions remain unchanged, improvements in agricultural mechanization levels can promote improvements in agricultural carbon emission efficiency.

5.2. Suggestions for Carbon Emission Reduction in Agricultural Development

The countermeasures and suggestions proposed in this section are primarily based on the calculation of agricultural carbon emissions in Hebei Province, a comprehensive evaluation of carbon emission efficiency, influencing factors of carbon emission efficiency, and the relationship between agricultural carbon emission efficiency and food security (

Table 8. Policy recommendations.

Measures	Percentage	Index I	Index II	Measures
Conservation tillage	42.63% Framing			Accelerate technological innovation
Returning crop straw to the field
				Promote energy-saving machinery
Application of organic fertilizer
Adjusting the nutritional structure of animal feed	26.93% Animal husbandry
				Establish a carbon emission compensation mechanism for food production
Utilization of livestock and poultry manure resources

). The rational use of agricultural means of production and optimization of the agricultural industrial layout can significantly reduce the increase in agricultural carbon emissions [39,40]. In the process of agricultural production, planting and animal husbandry accounted for 42.63% and 26.93% of agricultural carbon emissions in Hebei Province, respectively. Therefore, the following actions are necessary: First, starting from the planting industry, formulate a strict land tillage system and the rational use of agricultural fertilizers, and effectively implement source pollution control measures to fundamentally alleviate agricultural carbon emissions. Additionally, focusing on agricultural carbon sinks, measures such as organic fertilizers, intercropping, and crop rotation can be employed to improve soil structure and enhance carbon sequestration capacity. Secondly, it is necessary to strengthen the rational treatment of feces during the process of livestock breeding, formulate policies on carbon emissions reduction, and actively implement these policies [41]. Thirdly, promoting ecological agriculture is crucial, employing principles such as water resource management, soil conservation, and crop diversity to minimize the adverse impact of agricultural activities on ecosystems.

Intervention through human economic production activities was the primary factor affecting the efficiency of agricultural carbon emissions. Among them, the scale of the labor force, the level of economic development, and the level of mechanization that play a positive role must continue to maintain a good momentum in regard to development, strengthening the learning and application of new technologies. The improvement in science and technology levels and agricultural production efficiency is inseparable from the support of the economic foundation, and the economic output value will continue to be invested in technological research, development, and application, thus forming a productive cycle [42]. Modernization of the mechanization level needs to promote the adaptation of agricultural machinery and agronomy, mechanization and informatization, mechanized production, and farmland construction, and it must also promote the upgrading of the agricultural mechanization level to comprehensive and high-quality development. Considering the negative effects of crop damage, agricultural industrial structure, fertilizer use, and livestock manure treatment, it is necessary to strengthen the response to and management of natural disasters, adjust the agricultural industrial structure according to the actual situation of low-carbon agricultural production in Hebei Province, and encourage farmers to use clean green materials to achieve green and high-quality agricultural production.

Agricultural production produces a certain amount of carbon emissions and is an important component of grain production. Previous research has demonstrated that the coupled relationship between carbon emission efficiency and food security in the cities of Hebei Province is gradually coordinated. Therefore, it is necessary to integrate “low-carbon” practices into the entire life cycle of carbon emissions from grain production to maintain and improve the degree of coupling between the two. Before and during grain production, we should promote the efficient use of pesticides and fertilizers, strengthen the efficient cooperation mechanism of agricultural water use, water-saving irrigation, and water–fertilizer integration, promote the use of energy-saving machinery, improve grain production efficiency, and strive to achieve the green transformation of agricultural machinery. After grain production, we built a grain carbon emission compensation mechanism to compensate farmers who achieved low-carbon production.

6. Conclusions

Based on the current status of agricultural development in Hebei Province, this study constructs a comprehensive evaluation system for carbon emission efficiency, encompassing seven indicators and seven agricultural activity processes, from both dynamic and static perspectives. It conducts a comprehensive assessment of carbon emission efficiency and its influencing factors in Hebei Province from 2000 to 2020. Additionally, starting from the perspective of food security, the present study explores the degree of coupling between food security and carbon emission efficiency. The primary conclusions are as follows:

(1)

The change in agricultural carbon emissions in Hebei Province was primarily divided into three stages that included a rapid growth period (2000–2005), a fluctuating decline period (2006–2015), and a continuous decline period (2016–2020). In terms of time, the total amount of agricultural carbon emissions in Hebei Province increased first and then fluctuated and decreased at a rate of 6.99% from 2000 to 2020 from 12.14 million t in 2000 to 10.80 million t in 2020. Agricultural carbon emission intensity decreased at a rate of 0.76%. In the carbon emission structure, agricultural fertilizer and plowed land accounted for 22% and 21% of agricultural emissions, and these are the two most important carbon sources. Spatially, agricultural carbon emissions in Hebei Province generally exhibit a distribution pattern that is high in the south and low in the north.

(2)

From a static perspective, the level of agricultural carbon emissions in Hebei Province from 2000 to 2020 was above average, and the carbon emission efficiency fluctuated at a rate of 0.0265 with an annual average of 0.765. From a dynamic perspective, the ML index of Hebei Province during 2000–2020 changed smoothly, and the fluctuation was small. The technological progress index generally exhibits a trend of fluctuating decline, and the average level is above 1. The technical efficiency index exhibits a fluctuating upward trend with an overall range of 0.45–1.07.

(3)

In regard to time, the D value of agricultural carbon emission efficiency and food security in Hebei Province changed from 0.486 to 0.866 from 2000 to 2020, and the overall coupling coordination degree exhibited a transition from non-coordination to quality coordination. The coupling coordination degrees are significantly different in space. In 2020, the agricultural carbon emission efficiency and food security in Hebei Province were highly matched, and all prefecture-level cities were in a coordinated state.