Regional Differences, Dynamic Evolution, and Convergence of Global Agricultural Energy Efficiency

Abstract

Understanding the regional disparities, dynamic evolution, and convergence–divergence characteristics of global agricultural energy efficiency is crucial for enhancing agricultural energy efficiency, ensuring food security, and responding to global green development trends. This paper utilizes 2002–2021 panel data from 144 countries globally, employing the epsilon-based measure–global Malmquist–Luenberger (EBM-GML) model to estimate agricultural energy efficiency, considering unexpected output. The Dagum Gini coefficient, kernel density estimation, spatial Markov matrix, and spatial convergence model are employed to explain the spatial patterns and evolving trends of global and regional agricultural energy efficiency at three levels: regional disparities, dynamic evolution, and convergence. The results indicate significant spatial heterogeneity in global agricultural energy efficiency, with Europe exhibiting the highest efficiency, followed by Asia and the Americas, while Oceania and Africa demonstrate the lowest efficiency. Agricultural energy efficiency globally and in each region continues to improve, with increasing regional disparities, and difficulties in grade transitions in agricultural energy efficiency across regions. Each region exhibits β-convergence characteristics, but the convergence rates vary, and various factors influence growth rates of agricultural energy efficiency differently across regions. Therefore, countries should tailor their strategies based on local conditions, considering their own resource endowments and developmental stages, and strengthen international exchanges and cooperation.

1. Introduction

Agricultural carbon emissions already contribute to one-third of global carbon emissions [1]. Behind the issue of agricultural carbon emissions lies the substantial energy consumption in agricultural production. The modernization process of agriculture, characterized by the use of fertilizer, mechanization, and scale, has greatly increased agricultural production efficiency since the 20th century [2]. However, it has resulted in a swift surge in the consumption of agricultural energy. Global agricultural energy use has grown from 2.58 EJ in 1970 to 9.21 EJ in 2021, growing at a rate of 2.53% per year [3]. One of the pathways to address the massive energy consumption in agriculture is to enhance agricultural energy use efficiency. Studying the regional differences, dynamic evolution, and convergence of global agricultural energy efficiency aids countries in understanding regional differences in agricultural energy efficiency, fostering global sustainability through enhanced international cooperation.

As agricultural energy use gains attention, many researchers are now studying ways to improve its efficiency. Energy efficiency involves achieving comparable service or useful output with reduced energy consumption [4]. Regarding the calculation of energy efficiency, it is typically categorized into single-factor calculation and total-factor calculation [5]. Single-factor energy efficiency mainly uses energy intensity and energy productivity, where the former refers to the ratio of energy input to economic output [6], and the latter refers to the ratio of economic output to energy consumption [7,8]. As research on energy efficiency deepens, scholars realize that focusing only on one factor in energy efficiency does not consider the possible replacement and complementary effects that other inputs may bring to production. Therefore, in gauging energy efficiency, it could overstate the role of energy in economic contributions [7]. Considering the limitations of single-factor energy efficiency measurement, academia tends to favor the adoption of total-factor energy efficiency. Commonly used methods include data envelope analysis (DEA) [9,10] and stochastic frontier method (SFA) [11,12]. Compared with the SFA model, the DEA model does not have strict requirements on the form of the production function and is more suitable for the multi-input–multi-output model [13].

Various studies have assessed agricultural energy efficiency across different regions and crops. Aydın and Aktürk [14] found higher energy efficiency in well-regulated peach and cherry enterprises in Turkey. Pishgar-Komleh, et al. [15] observed increased energy efficiency in larger potato farms in Iran. Singh, et al. [16] reported that over 80% of wheat production energy in Punjab, India, was attributed to irrigation, electricity, and fertilizers. Mohseni, et al. [17] suggested energy optimization in grape production in Iran could reduce consumption by 10.90%. Paramesh, et al. [18] identified potential for efficiency improvements in betel nut production in Goa, India. Studies have also focused on regional variations, particularly in China [19,20] and the EU [21], with no comprehensive international comparative research identified.

According to scholarly research, various factors influence agricultural energy efficiency. These include income levels, energy prices, trade dynamics, human capital, and urbanization rate. For instance, [22] noted that per capita income is a significant factor, potentially leading to more energy-intensive lifestyles and an increase in energy intensity. This is exemplified by the fact that rising income enables more farmers to invest in agricultural machinery, as discussed by Han and Wu [23]. Moreover, an upsurge in income, indicative of economic development, often enhances environmental consciousness, as observed by Wu [24]. This heightened awareness could prompt rural residents to adopt newer, more efficient energy sources and technologies, replacing traditional ones, thereby boosting energy efficiency, as discussed by Van der Kroon, et al. [25]. Increase in energy prices encourages practicing energy-saving behaviors, thereby enhancing energy efficiency [26]. However, Mulder et al. [27] verified the limited role of energy prices in explaining changes in energy intensity using data from 18 Organization for Economic Co-operation and Development countries and 23 service sectors between 1980 and 2005.

Foreign trade openness plays a critical role in determining energy efficiency. Domestic development of energy-saving technologies reduces costs and enhances efficiency [28]. But the impact of foreign technological spillover, influenced by trade openness and foreign direct investment (FDI), is also significant. FDI, by introducing advanced technology and expertise, affects energy usage. Trade not only facilitates technology diffusion but also stimulates the uptake of energy-efficient technologies, particularly through exports and green trade barriers [23]. The import of capital goods, by facilitating access to new technologies and capital formation at lower costs, plays a crucial role in increasing energy efficiency and expanding production in developing countries [29,30]. Industrial structure significantly impacts energy efficiency, with the secondary industry consuming a greater amount of energy compared to the primary and tertiary industries [31,32]. Human capital is crucial in enhancing energy efficiency and innovation, with its role in knowledge absorption also highlighted [33,34]. Urbanization influences energy use in multifaceted ways, including structural economic changes and opportunities for economies of scale. Moreover, other factors like institutional quality spillovers, economic agglomeration, environmental policies, and fiscal systems also play important roles in determining energy efficiency [35].

An important question has emerged: What are the spatiotemporal trends in agricultural energy efficiency globally and across continents, and is there a convergence trend in agricultural energy efficiency? Do spatial factors and import and export trade affect the convergence of agricultural energy efficiency? This issue is worth in-depth exploration by scholars. Based on this, this study uses the epsilon-based data envelopment analysis (EBM-GML) model to calculate and evaluate the agricultural energy efficiency of 144 countries from 2002 to 2021, examining regional differences, dynamic progress, and convergence. The marginal contributions of this paper are mainly reflected in the following three aspects: First, from a global perspective, it comprehensively measures global agricultural energy efficiency, analyzing its temporal evolution trends and spatial distribution characteristics, which complement the understanding of global agricultural production characteristics. Second, it empirically analyzes the convergence of global agricultural energy efficiency, revealing the convergence trends of agricultural energy efficiency globally and across continents. Third, it incorporates geographical spatial factors and import-export trade into the β-convergence analysis to explore the spatial effects of global agricultural energy efficiency and the impact of import–export trade on convergence. This study provides practical and feasible guidance for formulating global trade policies and promoting sustainable global agricultural development, offering important insights for achieving global food security.

2. Research Methods, Indicator Selection, and Data Sources

The EBM-GML model is selected for the assessment of agricultural energy efficiency indicators, employing unexpected output as the measurement method. Dynamic changes are evaluated using kernel density and Markov chain analyses, while σ-convergence and β-convergence are utilized to assess convergence and divergence. Subsequently, the data sources are introduced.

2.1. Research Methods

2.1.1. Calculation of Agricultural Energy Efficiency: EBM-GML Model Based on Non-Expected Output

The DEA model is widely used due to its ability to study multiple inputs and outputs without the need to specify the production function [36]. The traditional radial DEA model requires all inputs and outputs to be reduced or expanded in the same proportion, making it unable to calculate slack variables. The slack-based measure (SBM) model, which is founded on non-radical measurement and takes into account slack variables that are not radial in nature [37], also cannot effectively handle the input–output relationships between “non-radial” factor inputs and “radial” non-expected outputs. However, the epsilon-based measure (EBM) model is capable of overcoming this constraint [38]. Given the transitivity of the global Malmquist–Luenberger (GML) index, this paper employs the EBM-GML model to assess agricultural energy efficiency. The specific model is as follows:

$$\begin{gathered} \theta =min{\displaystyle \frac{\xi -{\omega }_x{\sum }_{i=1}^m\frac{{\varpi }_i^{-}{s}_i^{-}}{x_{ih}}}{\phi +{\omega }_y\sum _{j=1}^n\frac{{{\varpi }_j^{+}s}_j^{+}}{y_{jh}}+{\omega }_b\sum _{z=1}^l\frac{{\varpi }_z^{-}{s}_z^{-}}{b_{zh}}}} \\ s.t\xi x_h=X\mathsf{\delta }+s_i^{-},i=1,2\dots m \\ \begin{array}{c}\phi y_h=Y\mathsf{\delta }-s_j^{+},j=1,2\dots n\end{array} \\ \phi b_h=B\mathsf{\delta }+s_z^{-},z=1,2\dots l \\ \mathsf{\delta },s_i^{-},s_j^{+},s_z^{-}\ge 0 \end{gathered}$$

(1)

where $X$, $Y$, and $B$ represent m types of inputs, n types of expected outputs, and l types of non-expected outputs, respectively. H is the number of decision-making units. θ (0 ≤ θ ≤ 1) is the optimal efficiency value. ${\varpi }_i^{-}$, ${\varpi }_j^{+}$, and ${\varpi }_z^{-}$, and $s_i^{-}$, $s_j^{+}$, and $s_z^{-}$, respectively, denote the weights and slack variables for the i-th input, j-th output, and z-th non-expected output. ω (0 ≤ ω ≤ 1) is a crucial parameter for the comprehensive radial efficiency value ξ and non-radial slack weights. $x_{ih}$, $y_{jh}$, and $b_{zh}$ represent the i-th input, j-th output, and z-th undesirable output of the h-th decision-making unit, respectively.

Combining the optimal efficiency θ, the GML index is constructed as follows:

$${GML}^{t,t+1}\left(x^t,y^t,b^t,x^{t+1},y^{t+1},b^{t+1}\right)={\displaystyle \frac{{\theta }^{G,t+1}\left(x^{t+1},y^{t+1},b^{t+1}\right)}{{\theta }^{G,t}\left(x^t,y^t,b^t\right)}}$$

(2)

${\theta }^{G,t+1}$ and ${\theta }^{G,t}$ represent the global efficiency values for periods t + 1 and t, respectively. This paper uses the GML index, accumulated by multiplying it over periods, with the base year set as 2001, to construct agricultural energy efficiency [39].

2.1.2. Measurement of Regional Relative Differences: Dagum Gini Coefficient and Its Decomposition

This paper employs the Dagum Gini coefficient [40] to assess the overall differences and their sources in agricultural energy efficiency. The calculation formula is as follows:

$$G={\displaystyle \frac{\sum _{j=1}^k\sum _{h=1}^k\sum _{i=1}^{n_j}\sum _{r=1}^{n_h}\left|y_{ji}-y_{hr}\right|}{2n^2\overline{y}}}$$

(3)

Here, G represents the overall Gini coefficient; k denotes the number of regional divisions; n is the number of countries; $y_{ji}\left(y_{hr}\right)$ denotes the agricultural energy efficiency of country i(r)within group j(h). $\overline{y}$ represents the mean value of agricultural energy efficiency for countries be studied. A larger G indicates a greater imbalance in agricultural energy efficiency.

The Dagum Gini coefficient can be decomposed into intra-regional difference $G_{\omega }$, inter-regional difference $G_{nb}$, and over-density $G_t$ with the calculation formulas as follows:

$$G_{jj}={\displaystyle \frac{\sum _{i=1}^{n_j}\sum _{r=1}^{n_j}|y_{ji}-y_{hr}|}{2{n_j}^2\overline{y}}}$$

(4)

$$G_{\omega }=\sum _{j=1}^k{G}_{jj}{p}_j{s}_j$$

(5)

$$G_{jh}={\displaystyle \frac{\sum _{i=1}^{n_j}\sum _{r=1}^{n_h}\left|y_{ji}-y_{hr}\right|}{n_j{n}_h(\overline{y_j}-{\overline{y}}_n)}}$$

(6)

$$G_{nb}=\sum _{j=2}^k\sum _{h=1}^{j-1}{G}_{jh}\left(p_j{s}_h+p_h{s}_j\right)D_{jh}$$

(7)

$$G_t=\sum _{j=2}^k\sum _{h=1}^{j-1}{G}_{jh}\left(p_j{s}_h+p_h{s}_j\right){(1-D}_{jh})$$

(8)

Here, $p_j$ represents the proportion of the number of samples in area j in the total number of samples; $s_j=n_j\overline{y_j}/n{\overline{y}}_n$ represents the proportion of agricultural energy efficiency in group j compared with the overall agricultural energy efficiency for all countries in the sample; $G_{jh}$ is the Gini coefficient between groups j and h; $D_{jh}$ refers to the mutual influence of agricultural energy efficiency between groups j and h, with the calculation formula given in Equation (9). $d_{jh}$ Signifies the overall impact between groups j and h; $p_{jh}$ represents the super-variation first moment between groups j and h, with the calculation formulas given in Equations (10) and (11). It is important to note that before the calculation, the numbering of the two groups needs to be adjusted so that $\overline{y_j}\ge {\overline{y}}_h$, $F_j(•)$, and $F_h(•)$, respectively, represent the cumulative distribution functions of adjusted agricultural energy efficiency for groups j and h.

$$D_{jh}={\displaystyle \frac{d_{jh}-p_{jh}}{d_{jh}+p_{jh}}}$$

(9)

$$d_{jh}={\int }_0^{\infty }d{F}_j\left(y\right){\int }_0^y\left(y-x\right)d{F}_h\left(x\right)$$

(10)

$$p_{jh}={\int }_0^{\infty }d{F}_h\left(y\right){\int }_0^y\left(y-x\right)d{F}_j\left(x\right)$$

(11)

In terms of the super-variation density $G_t$, it seems logical that the overall Gini coeffiencient could be diminished by reducing regional disparities by decreasing the average level in regions with relatively high agricultural energy efficiency while simultaneously increasing the efficiency in regions with lower agricultural energy efficiency. This is not, nevertheless, always the case. In the event that cross-overlap among various sub-samples suggests that certain countries exhibit higher agricultural efficiency in regions characterized by low efficiency compared to countries with high efficiency in high-efficiency regions, then enhancing the agricultural efficiency of countries with high efficiency in low-efficiency regions and diminishing it in countries with low efficiency in high-efficiency regions could potentially result in a regional increase in agricultural efficiency. The inter-group super-variation density, which represents the portion of the Gini coefficient attributed to inter-group overlap, takes on the value 0 in the absence of any overlap between groups.

2.1.3. Dynamic Evolution of Absolute Differences: Kernel Density Estimation and Markov Chain

Kernel Density Estimation

In economics, the kernel density estimation model, a non-parametric method, is employed for identifying the distribution of data. Kernel density estimation can intuitively reveal the evolving trends of agricultural energy efficiency. Using globally measured agricultural energy efficiency values for these countries, this study uses the Gaussian kernel function and focuses on explaining the evolving dynamics of global agricultural energy efficiency, including the distribution location, main peak shape, distribution spread, and the number of peaks. The kernel density function of agricultural energy efficiency is shown in Equation (12).

$$f\left(x\right)={\displaystyle \frac{1}{nh}}\sum _{i=1}^{n}K\left[{\displaystyle \frac{x_i-x_0}{h}}\right]$$

(12)

where $x_i$ represents the observed values, following the assumption of independent and identically distributed; $x_0$ represents the sample mean; $n$ is the number of observed values; K(•) is the kernel function, with this context choosing the Gaussian kernel function; $h$ is the bandwidth, and this study follows the method of optimal bandwidth selection.

Markov Chain

The Markov chain segments the continuous numerical magnitude of regional phenomena, categorizing the regional phenomena into k discrete types of states. It illustrates the probability of the attribute values of the research object evolving from type I to type J over time. Within the traditional Markov matrix, the element $p_{ij}=n_{ij}/n_i$ signifies the likelihood of transitioning from type j at time t to type j at time $t+1$. Here, $n_{ij}$ stands for the total number of transitions in spatial units where agricultural energy efficiency shifts from state i at time t to state j at time $t+1$ during the study period.

Existing research has often found significant spatial dependence and correlation in regional economic development in geographical space [41]. Given the regional connections in economic development, Rey [42], considering the spatial impact of traditional Markov chains, introduced the concept of “spatial lag”. Following this, it is also divided into k types, decomposing the k × k transition probability matrix to obtain k sets of k × k conditional transition probability matrices. For example, $P_{12|1}$ is the probability that the agricultural energy efficiency of a region is type 2 at time t and changes to type 1 at time t + 1, under the condition that the agricultural energy efficiency type of the neighborhood is 1.The spatial lag values determine the spatial unit’s attribution to the spatial lag type, with the specific formula as follows:

$$Lag=\sum _{m=1}^n{y}_m{W}_{mn}$$

(13)

Lag is the spatial lag value; n represents the total number of spatial units; $y_m$ represents the measured value of spatial unit m; $W_{mn}$ represents the spatial relationship between spatial units m and n. In this study, spatial relationships are defined using an adjacency matrix. For countries that do not share a border with other countries, this study defines the nearest country as an adjacent country.

2.1.4. Convergence Models: σ-Convergence and β-Convergence

σ-Convergence

The σ-convergence test, grounded in the stock perspective, examines the convergence traits of agricultural energy efficiency. It examines whether the degree of dispersion of agricultural energy efficiency among different countries shows a decreasing trend over time and is generally examined using the coefficient of variation. The computation expression is as follows:

$$\sigma ={\displaystyle \frac{\sqrt{\sum _{i=1}^{N_j}\frac{{\left({EER}_{ij}-\overline{{EER}_{ij}}\right)}^2}{N_j}}}{\overline{{EER}_{ij}}}}$$

(14)

where EER_ij represents the agricultural energy efficiency of country i within region j, $\overline{{EER}_{ij}}$ represents the mean agricultural energy efficiency within region j, and $N_j$ represents the number of countries within region j.

β-Convergence

A β-convergence test is based on an incremental perspective to analyze the convergence characteristics in agricultural energy efficiency. It focuses on whether nations starting with lower levels of agricultural energy efficiency have faster growth rates, and if there is a tendency for the disparity in agricultural energy efficiency among countries to narrow. It divided into absolute β-convergence and conditional β-convergence.

Absolute β-convergence assumes that countries have consistent levels of urbanization rate, regional economic development, institutional quality, and other factors. It suggests a trend of convergence in agricultural energy efficiency between countries. The ordinary panel regression model, spatial lag model, and spatial Durbin model for absolute β-convergence are represented by Equations (15) and (16), respectively.

$$\ln \left({\displaystyle \frac{{EER}_{i,t+1}}{{EER}_{i,t}}}\right)=\alpha +\beta \ln \left({EER}_{i,t}\right)+U_i+V_t+{\epsilon }_{i,t}$$

(15)

$$\ln \left({\displaystyle \frac{{EER}_{i,t+1}}{{EER}_{i,t}}}\right)=\alpha +\beta \ln \left({EER}_{i,t}\right)+\rho W\ln \left({\displaystyle \frac{{EER}_{i,t+1}}{{EER}_{i,t}}}\right)+U_i+V_t+{\epsilon }_{i,t}$$

(16)

where i represents the country; t represents time; ${EER}_{i,t}$ represents the agricultural energy efficiency of country i at time t; $\ln \left({\displaystyle \frac{{EER}_{i,t+1}}{{EER}_{i,t}}}\right)$ represents the rate of increase in agricultural energy efficiency for country i at time t + 1; β is the convergence coefficient, with β < 0 indicating a convergent trend in regional agricultural energy efficiency, otherwise a divergent pattern; and the convergence rate $v=-{\displaystyle \frac{\mathrm{l}\mathrm{n}(1+\beta )}{T}}$. U_i and V_t represent fixed effects for regions and years, respectively; ${\epsilon }_{i,t}$ is the random error term. ρ is the spatial lag coefficient, reflecting the effect of the growth rate of neighboring countries’ agricultural energy efficiency on the country itself; $\rho$ is the coefficient of the spatial lag of the independent variable, representing the influence of neighboring countries’ agricultural energy efficiency. W is the spatial weight, and in this study, the spatial weight matrix is constructed by taking the reciprocal of the square of geographical distance [43], expressed specifically as follows:

$$W_{ij}=\left\{\begin{array}{cc}{\displaystyle \frac{1}{{d_{ij}}^2}},& i\ne j\\ 0,& i=j\end{array}\right.$$

(17)

The conditional β-convergence model builds on the absolute β-convergence model by adding a set of control variables to see if agricultural energy efficiency shows a convergence coefficient when certain conditions are present that have a big effect on it. The ordinary panel regression model and spatial Durbin model for conditional β-convergence are shown in Equations (18) and (19), respectively, where $X_{i,t}$ represents a series of control variables.

$$\ln \left({\displaystyle \frac{{EER}_{i,t+1}}{{EER}_{i,t}}}\right)=\alpha +\beta \ln \left({EER}_{i,t}\right)+\sigma X_{i,t}+U_i+V_t+{\epsilon }_{i,t}$$

(18)

$$\begin{gathered} \ln \left({\displaystyle \frac{{EER}_{i,t+1}}{{EER}_{i,t}}}\right)=\alpha +\beta \mathit{ln}\left({EER}_{i,t}\right)+\rho W\ln \left({\displaystyle \frac{{EER}_{i,t+1}}{{EER}_{i,t}}}\right) \\ +\gamma W\mathit{ln}\left({EER}_{i,t}\right)+\sigma X_{i,t}+U_i+V_t+{\epsilon }_{i,t} \end{gathered}$$

(19)

2.2. Indicator Selection and Data Source

2.2.1. Agricultural Energy Efficiency

In a broader context, agriculture encompasses forestry and fisheries, while in a narrower sense, it refers specifically to cultivation. This study adopts the wider definition to assess agricultural energy efficiency. This efficiency aims to optimize the output of agriculture while minimizing resource input and nature burden, representing a synergistic balance between agricultural economy, resource deployment, and ecological stewardship. The selection of indicators for calculating agricultural energy efficiency in this study is based on research results of Li H et al. [44]. Given data availability and statistical consistency, input indicators for agricultural energy efficiency include labor, land, capital, and energy. The desired output indicator is agricultural value-added, and agricultural carbon emissions serve as the non-desired output indicator.

The agricultural capital input is determined by employing the perpetual inventory method [45] to calculate the inventory of agricultural capital. The yearly rate of capital depreciation is derived from the research of Hall and Jones [46] and Li et al. [47], and is 5.42%. The initial capital stock borrowed from [48] is computed by dividing the fixed capital formation total in the base year of 2001 by 10%. The indicator system for calculating agricultural energy efficiency is presented in

Table 1. Agricultural energy efficiency measurement indicator system.

Indicator Categories	Variable	Variable Declaration	Data Sources
Input indicators	Labor input	Agriculture industry/thousand people	Food and Agricultural Organization of the United Nations(FAO)
	Land input	Agricultural land/1000 hectares
	Capital	Agricultural capital stock/million US dollars unchanged in 2015
	Energy input	Total agricultural energy/megajoules
Output indicators	Agricultural output	Agricultural Value Added/Million USD 2015 Constant Price
	Carbon emission	Carbon dioxide equivalent/thousand tons in the early and late stages of agricultural production

.

2.2.2. Control Variables

The urbanization rate (URBA) is calculated by determining the percentage of the population residing in urban areas. Urbanization facilitates the mobility of agricultural workers, hence establishing advantageous circumstances for the establishment of industrialized operations and the attainment of large-scale agricultural output [49]. Nonetheless, the literature also contains divergent perspectives [50,51].

Regional economic level (PGDP) is assessed through per capita GDP. The increase in per capita GDP levels has the potential to foster greater awareness regarding energy conservation and facilitate the advancement and implementation of innovative technologies [52]. Additionally, some certain scholars contend that per capita GDP and energy efficiency exhibit a U-shaped correlation [53].

Institutional quality (ROL): In existing studies [54,55], the widely adopted measure is the Worldwide Governance Indicators (WGI) system, constructed by scholars such as Kaufmann [56]. This system includes six sub-indicators that comprehensively reflect a country’s governance and institutional quality. Drawing inspiration from other investigations [55], this study used the sub-indicator of legal quality to assess the quality of institutions. Efficient institutional frameworks facilitate technological progress [55,57]. Given the substantial variations in policies, regulations, institutional systems, and cultures across nations, institutional quality can be regarded as an all-encompassing indicator of those factors and more. Improving institutional quality can enhance energy efficiency [58]. Additionally, countries with higher institutional quality place greater emphasis on sustainable economic development [59].

Industrial Structure (IND) = 1 − Agricultural Value Added/ Gross Domestic Product (GDP): Industrial structure is a crucial carrier of economic activities, influencing resource allocation efficiency and energy efficiency [32]. Specifically, the advancement of manufacturing and service sectors could potentially deplete social resources allocated to agriculture, despite concurrently fostering agricultural progress via technology spillover effects [44].

Human capital (HUM), measured by higher education enrollment rate [60]: Education accelerates farmers’ adoption of new technologies [12].

Government Expenditure (ARCF) = Government Agricultural Expenditure/Total Fiscal Expenditure: The level of fiscal assistance allocated to agriculture can influence the labor input employed in the agricultural production process [61,62].

Agricultural imports (IMs) are calculated as the volume of import trade for agricultural products divided by the value added to agriculture. Through spill-over effects and diffusion effects, import trade can promote the use of novel technologies within the manufacturing procedures [30].

Agricultural Exports (EX) = Agricultural Product Export Trade Volume/Agricultural Value Added: Export trade can drive the adoption of energy-saving technologies through export competition effects [23].

Energy price (POIL), denoted by Brent crude oil prices [63]: an increase in energy prices helps strengthen energy-saving awareness, reduce energy waste [26], and provides support for improving energy efficiency [26].

Average maximum temperature: The rise in temperature provides more heat for grain production, prolongs the growth period of crops, promotes the northward migration of planting systems, and increases yield per unit. Farmers improve irrigation and fertilizer utilization efficiency and alleviate labor shortages by breeding stress-resistant varieties, constructing water conservancy facilities, using plastic film and straw mulching, and adjusting their work methods to adapt to temperature changes. Overall, rising temperatures contribute to increasing food production and improving input efficiency [64].

Average precipitation. Increased rainfall can easily lead to the decomposition and volatilization of pesticide active ingredients, thereby reducing their effectiveness. Farmers will increase the frequency and dosage of pesticide use to protect crops. In order to mitigate the losses caused by extreme weather, they will also increase investment, improve infrastructure, and implement measures such as diversified production to reduce risks [65].

Table 2. Definitions and data sources for control variables.

Variable	Variable	Definition	Unit	Data Sources
Urbanization rate	URBA	Urban population/total population	%	FAO
Regional economic level	PGDP	Per capita GDP	USD unchanged in 2015	World Bank
Institutional quality	ROL			World Bank
Industrial structure	IND	1-Agricultural value added/GDP	%	FAO
Human capital	HUM	Higher education enrollment rate	%	World Bank
Government investment	ARCF	Agricultural expenditure/total fiscal expenditure	%	FAO
Agricultural imports	IM	Import trade volume of agricultural products/added value of agriculture	%	World Trade Organization (WTO)
Agricultural exports	EX	Export trade volume of agricultural products/agricultural value added	%	WTO
Energy prices	POIL	Oil price	Domestic currency unchanged in 2015/barrel	BP Statistical Yearbook
Average precipitation	PRE		mm	Worldclim
Average maximum temperature	TMX		°C	Worldclim

presents the definitions and data sources of the control variables.

2.3. Data Source and Descriptive Statistics of Variables

Based on data availability and research needs, this article selects 144 countries as the research sample and categorizes them geographically into Asia (36 countries), Europe (36 countries), Africa (41 countries), the Americas (26 countries), and Oceania (5 countries). The time span covers the years 2002 to 2021. Due to the lack of permanent population, this study does not consider agricultural energy efficiency in Antarctica. The detailed sample scope is provided in

Table 3. Sample range.

Geographical Area	Country
Asia (36 countries)	Azerbaijan, Bahrain, Bangladesh, Armenia, Bhutan, Cambodia, Sri Lanka, China, Cyprus, Georgia, India, Indonesia, Iran, Israel, Japan, Kazakhstan, Jordan, South Korea, Kuwait, Kyrgyzstan, Laos, Lebanon, Malaysia, Maldives, Mongolia, Oman, Nepal, Pakistan, Philippines, Saudi Arabia, Singapore, Vietnam, Thailand, United Arab Emirates, Turkey, Yemen.
Europe (36 countries)	Albania, Austria, Belgium, Bulgaria, Belarus, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Moldova, Netherlands, Norway, Poland, Portugal, Romania, Russian Federation, Slovakia, Slovenia, Spain, Sweden, Switzerland, Ukraine, North Macedonia, United Kingdom.
Africa (41 countries)	Algeria, Angola, Botswana, Burundi, Cameroon, Cape Verde, Central African Republic, Comoros, Congo (Brazzaville), Benin, Ethiopia, Gabon, The Gambia, Ghana, Guinea, Ivory Coast, Kenya, Lesotho, Madagascar, Malawi, Mali, Mauritania, Mauritius, Morocco, Mozambique, Namibia, Niger, Nigeria, Rwanda, Sao Tome and Principe, Senegal, South Africa, Zimbabwe, Eswatini, Togo, Tunisia, Uganda, Egypt, Tanzania, Burkina Faso, Zambia.
Americas (26 countries)	Argentina, Barbados, Brazil, Belize, Canada, Chile, Colombia, Costa Rica, Dominican Republic, Ecuador, El Salvador, Guatemala, Guyana, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Saint Lucia, Saint Vincent and the Grenadines, Suriname, Trinidad and Tobago, United States, Uruguay.
Oceania (5 countries)	Australia, Solomon Islands, Fiji, New Zealand, Tonga.

. To avoid the influence of inflation, all price-related indicators are adjusted to the year 2015. To address minor data gaps, interpolation is employed for imputation. Additionally,

Table 4. Descriptive statistics of agricultural energy efficiency and control variables.

Variable	Variable	Mean	Standard Deviation	Min	Max	Observations
Agricultural Energy Efficiency	EER	1.166	0.504	0.190	7.360	2880
Urbanization rate	URBA	56.886	22.955	1.883	100	2736
Regional economic level	PGDP	14,452.343	20,103.773	111.796	132,058.438	2736
Institutional quality	ROL	51.062	27.089	0.469	100	2736
Industrial structure	IND	89.455	10.075	46.499	99.969	2736
Human capital	HUM	38.005	28.652	0.1	150.202	2736
Government investment	ARCF	2.861	2.74	0.02	24.71	2736
Agricultural imports	IM	192.209	876.239	0.019	14,045.630	2736
Agricultural exports	EX	244.865	1073.123	2.382	16,105.260	2736
Energy prices	POIL	87.397	49.618	0.576	589.102	2736
Average precipitation	PRE	1086.236	799.666	1.156	5333.594	2736
Average minimum temperature	TMX	23.891	9.122	−6.156	37.214	2736

provides descriptive statistics pertaining to agricultural energy efficiency and control variables.

3. Empirical Testing and Results Analysis

This section presents the data results, including regional differences, dynamic evolution, and convergence of agricultural energy efficiency in different regions. It is found that different regions have different convergence rates, and the impact of import and export trade and other factors on agricultural energy efficiency varies.

3.1. Spatiotemporal Development of Average Agricultural Energy Efficiency on Various Continents

3.1.1. Temporal Evolution

The annual findings obtained by employing the aforementioned techniques to determine the average agricultural energy efficiency on a continental and global scale are presented in Figure 1. In general, there is a modest but consistent upward trajectory observed in the global average agricultural energy efficiency, which surges from 1.011 in 2002 to 1.324 in 2021, expanding at an average yearly rate of 1.43 percent. This exemplifies the recent advancements in agriculture production efficiency and the transition towards low-carbon production practices.

Regarding the comparative analysis of agricultural energy efficiency across various regions, it is observed that Africa and Oceania manifest the least efficiency levels, exhibiting sample mean values of 1.013 and 0.968, respectively. In contrast, Asia’s mean agricultural energy efficiency approximately aligns with the global mean, registering at 1.161, which is slightly inferior to the Americas’ efficiency mean of 1.214. Notably, Europe stands at the forefront in this aspect, having a prevailing average of 1.337. The agricultural energy efficiency has a general regional pattern characterized by a “lower in the south and greater in the north” tendency.

A temporal analysis of agricultural energy efficiency across different geographical areas reveals that, with the exception of Oceania, all regions under consideration witnessed a surge in energy efficiency to different extents throughout the sample period, with a discernible trajectory indicating an upward trajectory. Since 2007, efficiency in Africa has increased, whereas in Oceania, it has varied considerably before beginning a trend of improvement in 2019. Overall, there is a rising trend in the disparities of average agricultural energy efficiency disparities between regions, with no discernible signs of convergence. Nonetheless, the disparities between Asia and the Americas regarding the average energy efficiency of agriculture are diminishing.

During the sample period, the yearly growth rates for Europe, Asia, and the Americas are 2.33 percent, 1.66 percent, and 1.32 percent, respectively, which are much greater than the 0.46 percent and 0.04 percent for Africa and Oceania, respectively, with high energy efficiency experiencing notably greater expansion compared to low energy efficiency. It is possible that agricultural production does not converge to a single steady state across regions due to the substantial variation in natural geographical circumstances between areas and the substantial influence that such conditions have on agricultural production. Conversely, the trajectory towards enhancing energy efficiency might lack replicability, making it impractical to adopt in regions with low energy efficiency. More precise measurements of the magnitudes of the disparities in agricultural energy efficiency across regions and an examination of their respective origins are required in order to delve into the underlying causes of regional variations in global agricultural energy efficiency.

3.1.2. Spatial Evolution

The spatial distribution patterns of agricultural energy efficiency data for the years 2002 and 2021 were analyzed through visualization using the Jenks natural breaks classification method. The findings from this analysis are illustrated Figure 2. Overall, agricultural energy efficiency gradually transitioned from a “discrete scattered” to a “continuous distribution” spatial pattern from 2002 to 2021. Agricultural energy efficiency in Europe and Asia showed a gradual but consistent pattern of distribution. Despite some progress in enhancing agricultural energy efficiency in Africa, the prevailing trend remained largely unchanged, and spatial stickiness persisted.

Agricultural energy efficiency values in North America and Oceania experienced a decrease in the global context. The spatial pattern of agricultural energy efficiency in Central and South America and the Caribbean region also did not undergo significant variations. Additionally, agricultural energy efficiency and the economic landscape across countries are spatially misaligned, suggesting that attaining a high level of economic development does not invariably entail abandoning a development paradigm characterized by high energy consumption. Simply increasing economic output is not a sufficient condition for achieving improvements in green economic efficiency.

3.2. Spatial Differences and Source Decomposition of Agricultural Energy Efficiency in Global Continents

3.2.1. Internal Differences in Agricultural Energy Efficiency within Each Region

The Dagum Gini coefficient was employed to measure the intra-group disparity levels of agricultural energy efficiency in 144 countries globally and within each region. The year-wise results of the measurements are presented in Figure 3.

From a global perspective, world’s overall Gini coefficient of agricultural energy efficiency stands at 0.183 on average throughout the sample period. Except for slight declines in 2010 and 2016, it consistently showed an increasing trend, indicating a cyclical growth pattern. This indicates that the agricultural energy efficiency disparity on a worldwide scale has deteriorated over time.

When comparing different regions, most regions exhibit intra-group Gini coefficients below the global average, indicating relatively low internal disparities. The overall differences in sample data primarily stem from variations between regions. In the later period of the sample, except for Oceania, the intra-group Gini coefficients of other continents are lower than the global average. This implies relatively smaller internal differences within regions, possibly due to similar natural environmental conditions within each region. In North America and Africa, internal disparities fluctuate significantly. In North America, internal differences have been widening since 2014, while in Africa, a trend of narrowing internal differences has been observed since 2016.

3.2.2. Differences in Agricultural Energy Efficiency among Various Regions

The Dagum between-group Gini coefficient was utilized to quantify the degree of variation in energy efficiency of agriculture across different locations of the world. The outcomes for specific pivotal years are illustrated in Figure 4.

The progressive expansion of the shaded area in Figure 4 signifies a discernible pattern of variation in agricultural energy efficiency across different parts of the world. This trend is evident between any two groups, signifying an exacerbated imbalance in agricultural development across regions. Upon analyzing the magnitude of changes in each period, it was seen that the region-specific disparities grew most pronounced during the initial half of the sample period. During the latter portion of the observed time frame, while the shaded area continues to expand, it also exhibits a tendency to contract, indicating a reduction in inter-group differences in agricultural energy efficiency for some regions.

Regarding the magnitude of numerical disparities, the differences between the Americas and Africa are comparatively modest, with a sample mean of 0.140. Asia and the Americas have the most substantial disparity, as seen by the sample mean of 0.195. Additionally, the sample means of the Gini coefficients between Asia and Africa, Europe, and Oceania are 0.194, 0.182, and 0.183, respectively, suggesting that Asia exhibits the greatest difference compared to other continents. The sample means of the Gini coefficients between Oceania and Europe, the Americas, and Africa are 0.182, 0.184, and 0.173, respectively, indicating significant differences between Oceania and other continents. The sample means of the Gini coefficients between Europe and the Americas, and Africa are 0.173 and 0.160, respectively, indicating that the disparities between Africa and Europe and the Americas are quite minor.

In relation to the temporal progression of regional disparities, Oceania exhibits the most substantial expansion, as evidenced by the average yearly escalation of 9.23 percent in inter-group Gini coefficients between Oceania and Europe, and 9.19 percent between Oceania and Asia. Asia has the second-highest growth rate of regional disparities, with an average yearly increase of 7.93 percent between Asia and Africa and 8.25 percent between Asia and Europe. The Americas exhibit the smallest growth in differences, with an average annual increase of 5.73% between the Americas and Africa, indicating an overall lag in agricultural energy efficiency improvement in the Americas compared to other continents.

3.2.3. Overall Differences and Decomposition of Agricultural Energy Efficiency

Using the methods mentioned earlier, the overall differences in sample data are divided into intra-group differences, inter-group net differences, and inter-group excess kurtosis density. The absolute values and proportional shares of each part are reported in Figure 5.

The intra-group Gini coefficient of global agricultural energy efficiency was 0.014 at the onset of the sample, rising steadily to 0.058 by the end of the sample period. However, its contribution to the overall difference remained around 23.5%.

Initially, the inter-group net difference stood at 0.016, indicating a gradual decrease from 2009 to 2012. In other years, it generally maintained an increasing trend, reaching 0.087 at the end of the sample. Its contribution to the overall difference exhibited a distinct “N”-shaped curve, slowly rising from 18.66% in 2003 to 39.22% in 2008. Following 2012, it showed a pattern of initial decline followed by subsequent increase, reaching 34.05% at the sample endpoint. During the sample period, the contribution rate averaged 31.714%.

The between-group excess variation density was 0.030 at the beginning of the sample period and exhibited a fluctuating upward trend during the sample period, reaching 0.111 as the sample period concludes. However, due to the faster overall increase in sample data differences, the fluctuation in its impact on the overall difference ranged from 49.71% at the beginning of the sample period to 43.29% at the end. The between-group excess variation density indicates the extent to which overlapping regions contribute to the total difference. In this study, the larger contribution rate implies that agricultural energy efficiency across continents is more heavily influenced by overlapping intervals.

3.3. Dynamic Evolution of Agricultural Energy Efficiency in Global Continents

3.3.1. Kernel Density Estimation

This study, based on the Dagum Gini coefficient, reveals the extent of the overall differences in global agricultural energy efficiency and their specific sources. It also identifies the changing trajectories of relative differences between regions. However, it cannot provide an in-depth description of the temporal evolution process of absolute differences in agricultural energy efficiency among regions. Therefore, to portray the distribution features of sample data in each region, the kernel density estimation method is utilized, with a focus on aspects like peak shape, spread, and the number of peaks. The dynamic evolution characteristics are reported in

Table 5. Dynamic evolution of agricultural energy efficiency.

Area Name	Distribution Location	Main Peak Distribution Pattern	Distribution Extensibility	Number of Peaks
Global	Right shift	Height decreases and width increases	Right trailing, extended convergence	Unimodal
Africa	Right shift	Height decreases and width increases	Right trailing, extended convergence	Unimodal
Asia	Right shift	Height decreases and width increases	Right trailing, extended convergence	Unimodal
Europe	Right shift	Height decreases and width increases	Right trailing, extended convergence	Unimodal
America	Right shift	Height decreases and width increases	Right trailing, extended convergence	Unimodal
Oceania	Right shift	Height increases, width increases	No convergence trend	Multimodal

, and specific kernel density plots are presented in Figure 6.

Distribution Position

As illustrated in Figure 6a, the kernel density curve of agricultural energy efficiency exhibits an overall rightward shift on a global scale, signifying that the energy efficiency of most countries are progressing upwards. The rightward shift in distribution curves across all continents indicates substantial progress in fostering low-carbon development and enhancing agricultural production efficiency in these areas. It is worth mentioning that the curve representing the Asian region exhibited a leftward shift in the midst of the sample period, as depicted in Figure 6c. Similarly, Africa witnessed a leftward shift during the late sample period, as illustrated in Figure 6b, which suggests a reduction in agricultural energy efficiency throughout these time periods.

Main Peak Distribution Form

At the global level, the kernel density curve illustrates a decrease in the height of the primary peak and an expansion in width, suggesting an upward trend in the dispersion of agricultural energy efficiency among countries in the sample, as illustrated in Figure 6a. This is because different countries have significantly different natural geographical environments and agricultural foundations, leading to considerable variations in the choice of paths and difficulty levels for improving agricultural energy efficiency. The kernel density curves for Africa (Figure 6b), Asia (Figure 6c), Europe (Figure 6d), and Americas (Figure 6e) exhibit similar patterns to the global level. In Oceania, the main peak’s height increases, as illustrated in Figure 6f, indicating an increased concentration of agricultural energy efficiency in the regional context.

Distribution Extensibility

The distribution curves for the global (Figure 6a), Africa (Figure 6b), Asia (Figure 6c), Europe (Figure 6d), and Americas (Figure 6e) regions all exhibit significant right tails, meaning that some countries within each region have significantly higher agricultural energy efficiency than others in the same region. For example, despite Africa having lower overall agricultural energy efficiency, countries such as Angola, Gabon, and Guinea on the west coast, and Egypt and Ethiopia in North Africa show higher efficiency.

Number of Peaks

Africa (Figure 6b), Asia (Figure 6c), Europe (Figure 6d), and Americas (Figure 6e) are unimodal during the sample period, indicating a high concentration of agricultural energy efficiency among countries within each region and no clear trend of polarization. Oceania exhibits a multimodal distribution, as illustrated in Figure 6f, indicating a high degree of differentiation in agricultural energy efficiency within the region.

3.3.2. Spatial Markov Chain Analysis

The transition of agricultural energy efficiency grades is not independent in space. Therefore, incorporating spatial factors is essential. The results of the spatial Markov transition probability matrices are reported in

Table 6. Spatial Markov transfer probability matrix of global agricultural energy efficiency from 2002 to 2021.

Lag Type	T/T + 1	I	II	III	IV	Observations
I	I	0.870	0.119	0.005	0.005	185
	II	0.235	0.597	0.168	0.000	119
	III	0.010	0.124	0.781	0.086	105
	IV	0.000	0.000	0.123	0.877	57
II	I	0.840	0.143	0.012	0.004	244
	II	0.144	0.656	0.179	0.021	285
	III	0.024	0.154	0.675	0.148	169
	IV	0.008	0.017	0.092	0.883	120
III	I	0.806	0.165	0.029	0.000	170
	II	0.143	0.603	0.232	0.021	237
	III	0.008	0.147	0.721	0.124	258
	IV	0.005	0.016	0.092	0.886	185
IV	I	0.864	0.080	0.045	0.011	88
	II	0.125	0.571	0.286	0.018	56
	III	0.025	0.127	0.614	0.234	158
	IV	0.000	0.003	0.067	0.930	300

. Firstly, under different spatial lag types, the four transition probability matrices are distinct, indicating that when there exist disparities in agricultural energy efficiency among neighboring countries, the probability of transitions in the domestic agricultural energy efficiency also varies. Secondly, under various spatial lag types, the diagonal elements of the transition probability matrix consistently exceed the off-diagonal elements. This implies that under spatial spillover effects, the probability of “locking” agricultural energy efficiency grades still exists. This trend is more pronounced under Type I lag conditions. Additionally, different lag types have different impacts on the same grade, and under Type IV lag conditions, the probability of transition from Grade II to Grade I is 12.5%, significantly lower than the probability of transition from Grade II to Grade I under Type I lag conditions, which is 23.5%. Finally, the influence of the same lag type on different grade transitions is also varied. Under Type IV lag conditions, the probabilities of Grades I, II, and III moving up one level after one year are 8.0%, 28.6%, and 3.4%, respectively, indicating that transition probabilities are simultaneously influenced by lag types and the initial grade of agricultural energy efficiency.

3.4. Convergence Study of Agricultural Energy Efficiency in Global Regions

3.4.1. σ-Convergence Test and Results Analysis

The σ-convergence results for agricultural energy efficiency in 144 countries globally and across various continents are illustrated in Figure 7. The coefficient of variation for global agricultural energy efficiency demonstrates a rising trend in volatility. The trends of the coefficient of variation for agricultural energy efficiency in each region are similar to the global trend. After 2014, the growth rate of the global and regional coefficients of variation slowed down, with a decline observed after 2018. Overall, agricultural energy efficiency in various regions is on the rise, and there is generally no σ-convergence, indicating an increasing regional disparity in horizontal agricultural energy efficiency.

3.4.2. β-Convergence Test and Results Analysis

Spatial Model Selection

A significant spatial correlation exists in agricultural energy efficiency, as per the first law of geography, which asserts that all elements in space are interconnected are interconnected, and this interconnection decreases with increasing distance [19]. Therefore, this study further tests global agricultural energy efficiency using the global Moran’s I index calculated using the inverse distance weight matrix. The findings are detailed in

Table 7. Spatial autocorrelation test results.

Year	Moran’s I	Z-Value	p-Value
2003	0.003	0.229	0.819
2004	0.066	1.745	0.081
2005	0.051	1.382	0.167
2006	0.072	1.910	0.056
2007	0.125	3.169	0.002
2008	0.139	3.540	0.000
2009	0.136	3.425	0.001
2010	0.100	2.562	0.010
2011	0.165	4.106	0.000
2012	0.110	2.784	0.005
2013	0.153	3.806	0.000
2014	0.142	3.567	0.000
2015	0.141	3.540	0.000
2016	0.165	4.109	0.000
2017	0.141	3.534	0.000
2018	0.130	3.270	0.001
2019	0.141	3.520	0.000
2020	0.138	3.465	0.001
2021	0.137	3.428	0.001

. For most years from 2003 to 2021, the global Moran’s I index for agricultural energy efficiency is significantly positive, indicating a substantial positive spatial correlation among the agricultural energy efficiency of different countries.

The above analysis of the Moran’s I index indicates a substantia spatial correlation in global agricultural energy efficiency. Thus, it becomes imperative to take into account the correlation of its geographical spatial distribution in the β-convergence analysis. Based on considering the spatial effects of agricultural energy efficiency, Lagrange multiplier test (LM), likelihood ratio test (LR), and Wald tests are used to select the spatial model, and the test results are reported in

Table 8. Practical testing of spatial panel models.

Variable	Absolute β-Convergence	p Value	Condition β-Convergence	p Value
Lm lag	42.930	0.000	43.062	0.000
Robust lm lag	1.724	0.189	0.908	0.341
Lm error	51.464	0.000	48.817	0.000
Robust lm error	10.257	0.001	6.663	0.010
Lr_spatial_lag	2.430	0.119	20.810	0.053
Lr_spatial_error	0.110	0.743	23.000	0.028
Wald_spatial_lag	2.440	0.118	20.000	0.029
Wald_spatial_error	0.100	0.747	22.200	0.014
Hausman test	74.950	0.000	114.370	0.000

. LM lag and LM error are tested at a significance level of 1%. If the LM test results show that either the spatial error model or the spatial autoregressive (SAR) model is effective, or both are effective, further estimation using the spatial Durbin model is required [66]. Therefore, this study continues to use the LR test and Wald test to check whether the spatial Durbin model can be simplified into a spatial lag model or a spatial error model under the absolute β-convergence situation. The LM test is not significant, and the ordinary least squares (OLS) model is selected. Under the conditional β-convergence situation, the LR statistic and Wald statistic for both spatial lag and spatial error significantly reject the null hypothesis, indicating that the spatial Durbin model cannot be simplified into a spatial lag model or a spatial error model. Therefore, this study sets OLS model and spatial Durbin model to examine the spatial convergence mechanism of spatial energy efficiency under absolute β-convergence and conditional β-convergence, respectively. In addition, the Hausman test shows that the fixed-effects model is superior to the random effects model. The spatial model selection process for β-convergence analysis in each region is the same as the spatial model selection process for global β-convergence analysis and is not repeated here.

Absolute β-Convergence Analysis

Table 9. Absolute β-convergence of global agricultural energy efficiency.

Region	Global	Europe	Africa	Asia	Central America, South America, and the Caribbean Region	North America and Oceania
Model type	OLS	SAR	OLS	OLS	OLS	OLS
Β	−0.163 ***	−0.268 ***	−0.139 ***	−0.132 ***	−0.219 ***	−0.440 ***
	(−14.646)	(−9.522)	(−7.801)	(−6.706)	(−6.599)	(−5.693)
Ρ		0.266 ***
		(4.070)
Convergence speed	0.009	0.016	0.008	0.007	0.013	0.031
Time effect	YES	YES	YES	YES	YES	YES
Individual effect	YES	YES	YES	YES	YES	YES
N	2736	684	779	684	456	133
R2	0.076	0.073	0.076	0.065	0.092	0.206

*** Represent 1% significance.

displays the results of the absolute β-convergence test for global and continental agricultural energy efficiency. Following Dyson’s research, North America and Oceania are combined into one region for analysis [67]. The results indicate the following:

Firstly, the convergence coefficient β for global and continental agricultural energy efficiency exhibits significant negativity at the 1% confidence level, indicating absolute β-convergence. This suggests that, over the long term, agricultural energy efficiency levels in countries and regions will tend to stabilize, absent various socioeconomic factors. Secondly, there is variation in the convergence speeds of global and continental agricultural energy efficiency. The global convergence speed is recorded as 0.009, while regions excluding Africa and Asia surpass the average convergence speed. This is particularly evident in the Americas, where, despite a higher variability coefficient, internal countries can sustain a relatively swift convergence pace through the reciprocal influence of spatial effects.

Thirdly, different spatial effects are observed globally and in various regions. The ρ for Europe is notably positive at the 1% level, indicating that changes in domestic agricultural energy efficiency rates positively influence the rates of change in agricultural energy efficiency in other regions within Europe. Global, Africa, Asia, Central America, South America, and the Caribbean, as well as North America and Oceania, are analyzed using a common panel model for absolute β-convergence analysis, and no spatial effects are found. It is worth noting that in the absolute β-convergence analysis for global and regional levels, assumptions are made about factors such as urbanization rate, institutional quality, industrial structure, human capital, government expenditure, agricultural imports, agricultural exports, and energy prices being similar. However, the actual situation is evidently not so, necessitating conditional β-convergence analysis.

Conditional β-Convergence Analysis

Table 10. Global agricultural energy efficiency exhibits conditional β-convergence.

Region	Global	Europe	Africa	Asia	Central America, South America, and the Caribbean Region	North America and Oceania
Model type	SDM	SDM	SDM	OLS	OLS	OLS
β	−0.190 ***	−0.259 ***	−0.151 ***	−0.135 ***	−0.227 ***	−0.551 ***
	(−14.145)	(−6.595)	(−6.988)	(−6.174)	(−5.337)	(−5.565)
ρ	0.164 ***	0.154 **	0.104 *
	−4.667	−2.153	−1.711
γ	−0.011	−0.193
	(−0.291)	(−1.602)
lnEX	0.003	0.033	−0.028 *	0.01	0.008	−0.149 ***
	−0.222	−0.6	(−1.846)	−0.478	−0.216	(−2.677)
lnIM	0.012 *	0.001	0.008	0.001	0.038	0.067 **
	−1.916	−0.037	−1.051	−0.064	−1.554	−2.353
lnURBA	0.020 *	0.046	0.015	0.002	−0.012	−0.027
	−1.795	−1.578	−0.838	−0.17	(−0.656)	(−1.393)
lnPGDP	0.004	−0.093	−0.026	0.032	−0.055	0.125
	−0.204	(−1.314)	(−0.777)	−1.525	(−1.500)	−1.484
lnROL	0.000	−0.004	0.004	−0.057 **	0.062 **	−0.067
	(−0.044)	(−0.059)	−0.366	(−2.538)	−2.341	(−1.416)
lnIND	−0.116	0.973	−0.067	−0.165	1.751 ***	0.433
	(−1.179)	−0.992	(−0.627)	(−0.677)	−3.36	−0.761
lnHUM	−0.011	−0.002	−0.005	−0.016	0.086 **	0.009
	(−1.370)	(−0.034)	(−0.451)	(−1.285)	−2.387	−0.248
lnARCF	−0.006	−0.016	−0.024 **	0.004	0.022	−0.043
	(−0.972)	(−0.859)	(−2.480)	−0.386	−1.422	(−1.432)
lnPOIL	−0.042	−0.061	−0.114 ***	−0.009	0.005	−0.009
	(−1.559)	(−0.633)	(−2.883)	(−0.608)	−0.257	(−0.369)
lnPRE	−0.003	−0.003	−0.026	0.023	0.075 **	−0.015
	(−0.252)	(−0.070)	(−1.243)	−1.069	−2.256	(−0.534)
lnTMX	0.064	0.01	0.286	0.366	0.625	−0.021
	−0.717	−0.064	−0.566	−1.594	−1.033	(−0.216)
Convergence speed	0.011	0.016	0.009	0.008	0.014	0.042
Time effect	YES	YES	YES	YES	YES	YES
Individual effect	YES	YES	YES	YES	YES	YES
N	2736	684	779	684	456	133
R2	0.030	0.031	0.017	0.086	0.166	0.302

Note: *, ** and *** represent 10%, 5% and 1% significance, respectively.

presents the results of the conditional β-convergence test for global and continental agricultural energy efficiency. The results indicate the following:

Firstly, the β-convergence for global and continental agricultural energy efficiency is significantly negative at the 1% confidence level, indicating conditional β-convergence. This means that, considering a series of socioeconomic factors such as urbanization rate, regional economic levels, institutional quality, industrial structure, human capital, government expenditure, agricultural imports, agricultural exports, and energy prices, the agricultural energy efficiency of countries and regions will still converge towards their unique steady-state levels in the long term. Secondly, compared to absolute β-convergence, the global speeds of conditional β-convergence have increased. The convergence speed for North America and Oceania showed a larger increase of 0.01, indicating the scientific validity of the selected control variables.

Thirdly, different spatial effects are observed globally and in various regions, with changes in spatial effects in individual regions compared to the absolute β-convergence analysis. The convergence model forms for both global and Africa transitioned from an OLS to a spatial Durbin model (SDM), with positive spatial autoregressive coefficients, indicating that changes in domestic agricultural energy efficiency rates within a region positively impact the rates of change in agricultural energy efficiency in other regions. Asia, Central America, South America, and the Caribbean, as well as North America and Oceania, are analyzed using a common panel model for absolute β-convergence analysis, and no spatial effects are found, consistent with the absolute β-convergence analysis.

From an economic perspective, there are significant differences in the impact of various factors on global and regional agricultural energy efficiency growth rates. In Africa, North America, and Oceania, there is an unpredictable negative relationship between agricultural exports and the rate of change in agricultural energy efficiency. This suggests that agricultural exports do not support improvements in the rate of change in agricultural energy efficiency in the region. The negative correlation may stem from the fact that, under the temptation of foreign trade gains, producers focus more on low-cost production to meet market demand and lack investment in technological innovation. This situation has resulted in relatively low added value of export products and insufficient investment in technological innovation, reducing the motivation for independent innovation.

There is a significant positive correlation between agricultural imports and the change rate of agricultural energy efficiency in regions such as the world, North America, and Oceania. This shows that imports of agricultural products help increase the rate of change in agricultural energy efficiency in these regions. This phenomenon may be attributed to the fact that imports can stimulate competition and demonstration effects in the host country’s internal industries, prompting local competitors to imitate technology [68], and international competition is a catalyst for innovation in the agricultural sector [69].

The significant positive correlation between global urbanization level and agricultural energy efficiency can be attributed to urbanization fostering the movement of workforce from rural regions to urban areas, thereby promoting the rationalization of distribution [70]. Financial support for agriculture and petroleum prices, on the other hand, demonstrate a significant negative correlation with change rate of agricultural energy efficiency in Africa. This may be attributed to the effective role of government subsidies in increasing grain production, while potentially leading to the misuse of fertilizers and energy resources [71]. Here is a case about policy agricultural subsidies: Tanzania’s National Agricultural Input Voucher Scheme (NAIVS) implemented from 2008 to 2014, aiming to assist poor small farmers, especially those with limited resources and technology. After 2011, the target was expanded to medium-sized farmers, and vouchers were used to subsidize the cost of seeds and fertilizers. However, many problems were exposed in the implementation of the policy: wealthy farmers became the main beneficiaries in the early stage due to lack of awareness and limited financial capabilities of small farmers; frequent problems such as delayed voucher issuance, corruption, politicized distribution, and collusion between leaders and dealers. There is a significant gap between the data and the actual amount received by farmers, showing that a large number of vouchers are “missing” and may be illegally misappropriated or resold, exacerbating social conflicts. In the end, the subsidy benefits failed to fully benefit the target group and were instead captured by a small number of powerful people [72].The increase in energy prices has stimulated energy-saving measures and the reduction of energy wastage [26]. The improvement in institutional quality in the Africa region does not contribute to improving the rate of change in agricultural energy efficiency. This may be attributed, on a global scale, to the significant disparities in institutional quality among countries. The improvement in institutional quality does not always align with the specific needs and realities of the agricultural sector. However, institutional quality exhibits a positive relationship with the change rate of agricultural energy efficiency in Central America, South America, and the Caribbean. This may reflect that in regions with lower institutional quality, improvements in institutional quality can effectively promote the change rate of agricultural energy efficiency [73]. Human capital is negatively but not significantly correlated with the global change rate of agricultural energy efficiency. This may reflect that as the level of education increases, the rate of loss of agricultural labor becomes more pronounced [12]. However, human capital positively influences the change rate of agricultural energy efficiency in Central America, South America, and the Caribbean. This could be attributed to the lower human capital levels in this region, and the current enhancements may not have prompted a substantial shift towards other industries. The development of the secondary and tertiary sectors is negatively but not significantly correlated with the global change rate of agricultural energy efficiency. This may indicate a certain degree of competition between the rapid growth of industry and services and the enhancement in agricultural energy efficiency. However, in Central America, South America, and the Caribbean, this relationship shows a positive correlation. This may reflect the industrial structure and economic development level in these regions, suggesting that even with an increase in the development of the secondary and tertiary sectors, it may not necessarily hinder the improvement in agricultural energy efficiency. Other factors, such as employment structure and resource allocation, may interact to promote an increase in the change rate of agricultural energy efficiency. Average precipitation is positively correlated with the rate of change of agricultural energy efficiency in Central America, South America, and the Caribbean, which may be because increased precipitation can improve soil moisture and fertility, provide better growing conditions for crops, and thus increase crop yield and quality. This means that more output can be obtained per unit of energy input, improving agricultural energy efficiency. The impact of maximum temperature on the rate of change of agricultural energy efficiency is not significant.

4. Discussion

As mentioned above, most existing studies on energy efficiency focus on the industrial sector, and there are not many studies on agriculture. When studying agricultural energy efficiency, most of them focus on a certain region [19,20,74] or a certain industry [14,15], and there is almost no research on agricultural energy efficiency from a global perspective. In addition, most studies on agricultural energy efficiency are based on a closed economic environment, with less consideration of foreign trade, and even fewer studies that divide foreign trade into import trade and export trade to see the difference in their impact on agricultural energy efficiency. Therefore, the main contribution of our work is to analyze agricultural energy efficiency from a global perspective and pay attention to the impact of import and export trade on it.

First, since the focus is on the global total, the individual is a region or country, and it is unrealistic to collect information from farmers or farms through questionnaires [75], so we use the EBM model to measure the total factor agricultural energy efficiency, which is more comprehensive than the single factor indicator [8]. We found that global agricultural energy efficiency showed a fluctuating upward trend, with the lowest agricultural energy efficiency in Oceania and Africa. There was no σ-convergence feature in the world and in each region, but there were absolute and conditional β-convergence features in the country and in each region. In the field of agricultural productivity, some studies have found the same trend [76,77,78]. Globally, agricultural productivity has increased, but Africa has grown the slowest. At the same time, countries with low productivity have grown faster, and there is obvious convergence. Some studies focusing on regions have found different trends. Some scholars [79] found that European agricultural technology declined slightly between 2004 and 2013, but there was a convergence trend, which was mainly due to the effective imitation of the technology and policies of advanced countries by countries with low agricultural technology levels; some scholars [80] found that India’s agricultural energy utilization efficiency was declining. The main reason for the difference in trends is the difference in indicators and research areas.

These results are related to various reasons. To deeply analyze the influencing factors of the change rate of agricultural energy efficiency, empirical tests were conducted. There is spatial correlation in the change rate of agricultural energy efficiency and a positive spatial spillover effect, which is consistent with other studies [19]. Among economic factors, import and export trade has different effects on agricultural energy efficiency. In Africa, North America, and Oceania, there is an unpredictable negative correlation between agricultural product exports and the change rate of agricultural energy efficiency. There is a significant positive correlation between agricultural imports and the change rate of agricultural energy efficiency in regions such as the world, North America, and Oceania. This is similar to other studies [81]. Exports are significantly detrimental to the improvement of total factor productivity in Africa, while imports are positively correlated with it but not significantly. The foreign R&D spillover effect generated by trade imports can promote the growth of agricultural total factor productivity [12]. There are also opposite conclusions [82]. Export trade increases agricultural productivity in many ways, including taking advantage of comparative advantages, economies of scale, technological progress brought about by international competitive pressures, providing foreign exchange to support modern inputs and capital formation, and increasing government revenue through export taxes to finance productive public investment. Among natural factors, average precipitation in Central America, South America, and the Caribbean is positively correlated with the rate of change of agricultural energy efficiency, and the maximum temperature has no significant impact on it. This result is consistent with some studies [83]. There is inequality in agricultural production in Latin America, and the main cultivated land is concentrated in tropical regions such as Brazil. The increase in precipitation brought about by climate change will help increase crop yields. Also different from some research results, in poor countries, weather and total factor productivity are negatively correlated, but the impact is not significant in developed countries [84]; climate change inhibits the growth of agricultural total factor productivity, and this impact is much more serious in warmer regions such as Africa, Latin America, and the Caribbean [85]. The main reason for the difference is that agriculture is greatly affected by climatic conditions, and the climate resources in different places are extremely different. For example, most of Africa is in the tropics and suffers from drought all year round, so changes in precipitation have a significant impact on its agricultural production. In Central Asia, due to low precipitation and frequent droughts, climate change has the greatest impact on it. These regions can turn to animal husbandry to adapt to changes in rain-fed agriculture [83].

5. Conclusions and Insights

This study utilized panel data from 2002 to 2021 for 144 countries globally, employing the EBM-GML model that considers unexpected output to assess agricultural energy efficiency. This study used the Dagum Gini coefficient, kernel density estimation, spatial Markov matrix, and spatial convergence model to investigate how agricultural energy efficiency changes over time and across regions, as well as how it converges and differs in different areas. Additionally, it distinguishes between import and export trade to assess their impact on the convergence of agricultural energy efficiency. The main conclusions are as follows:

In terms of regional disparities, global agricultural energy efficiency exhibits a significant spatial imbalance. Europe has the highest agricultural energy efficiency, with Asia and the Americas following closely behind, while Oceania and Africa have the lowest agricultural energy efficiency. Simultaneously, energy efficiency is expanding at a considerably faster rate in Europe, Asia, and the Americas than it is in Africa and Oceania, regions with lower energy efficiency. Globally, the regional distribution of agricultural energy efficiency stays comparatively consistent. Hyper-variation density is the primary spatial source of global differences in agricultural energy efficiency, followed by regional disparities. Regions with lower agricultural energy efficiency also include countries with higher efficiency, such as Angola, Gabon, and Guinea on the west coast of Africa, and Egypt and Ethiopia in North Africa. The internal differences within regions should not be overlooked.

From a dynamic perspective, the global and regional agricultural energy efficiency kernel density curves show a clear rightward shift trend. The peak height decreases, and the width increases, indicating a continuous improvement in global and regional agricultural energy efficiency, while regional disparities are also widening. Moreover, the analysis results of the Markov transition probability matrix show that there is considerable difficulty in the transition of agricultural energy efficiency levels, and it is influenced by the initial level and the energy efficiency of neighboring countries.

Regarding convergence characteristics, there is no evidence of σ-convergence globally or in various regions. However, absolute β-convergence and conditional β-convergence characteristics exist globally and in different regions, with the convergence speeds from fast to slow as follows: North America and Oceania; Europe, Central America, and South America; and the Caribbean, Africa, and Asia. The convergence speeds of Africa and Asia are relatively close to the global convergence speed.

Based on an understanding of the status of global agricultural energy efficiency, several insights are proposed:

(1) Countries should clearly recognize the objective fact of global spatial imbalance in agricultural energy efficiency. Due to differing developmental stages and natural geographical conditions, significant disparities exist in agricultural energy efficiency among regions and countries within regions. Countries with lower agricultural energy efficiency need to progressively enhance their efficiency. (2) The focus should be on reducing internal differences within regions and subsequently minimizing disparities between regions. Encouraging collaboration among countries is essential to collectively improve agricultural energy efficiency and achieve positive spatial clustering. (3) Agricultural energy efficiency is intertwined with essential human survival resources on one end and, conversely, agricultural carbon emissions. The influence of improving agricultural energy efficiency extends beyond any specific region, emphasizing its vital importance for global development. Countries worldwide should actively engage in collaborative efforts to enhance agricultural energy efficiency, ushering in a new era of mutually beneficial improvement in agricultural energy efficiency within the framework of international organizations such as the Food and Agriculture Organization (FAO), contributing to sustainable global agricultural development.

The limitations of this study are that the undesired output indicators only consider air pollution (carbon emissions), not soil pollution (agricultural non-point source pollution), and lack data from more emerging countries. To assess the robustness of the conclusions, future improvements in the study include focusing on specific regions and considering agricultural non-point source pollution.