Impact of Agricultural Industrial Agglomeration on Agricultural Environmental Efficiency in China: A Spatial Econometric Analysis

Abstract

In recent years, China has made remarkable progress in increasing yield at the expense of resource depletion, excessive consumption, and overexploitation. Improving agricultural environmental efficiency (AEE) is crucial to achieve agricultural modernization and facilitate a green transformation. Agricultural industrial agglomeration (AIA), as a main policy in industrial space organization, is an effective way to promote resource allocation optimization. This paper selects panel data of 31 provinces in China from 2000 to 2020 and employs the fixed-effects stochastic frontier analysis with hyperbolic distance function to measure AEE. Based on this, an empirical analysis is conducted to investigate the impact of AIA on AEE. The study finds that the average value of AEE is 0.909, which needs to be further improved. Meanwhile, AEE demonstrates obvious agglomeration characteristics and positive correlations with space. AIA exerts an inverted U-shaped effect on AEE in local and neighboring regions. Therefore, this paper believes that to improve AEE, it is essential to carry out dynamic and differentiated strategies of industrial agglomeration, ensuring the level of AIA remains within a reasonable range and effectively eliminates the congestion effect.

1. Introduction

Between 1978 and 2020, China’s agricultural output witnessed tremendous increases, ending the period at CNY 13.8 trillion in 2020, with a year-on-year growth rate of 11.6 percent. Although past developments in agriculture have significantly increased productivity, agricultural production still relies heavily on the intensive usage of natural resources and chemical inputs. It is estimated that agriculture contributes significantly to greenhouse gas emissions, accounting for approximately 21 percent to 37 percent of the total emissions (IPCC, 2019 [1]). Therefore, transforming the agricultural development pattern and accelerating the promotion of low-carbon technologies are core supports for achieving the carbon peak and carbon neutrality strategy. Agricultural environmental efficiency (AEE) aims to integrate agricultural resource endowments and environmental constraints into the productivity accounting framework, and improving AEE is of great significance for green agricultural transformation in China. Moreover, agricultural industrial agglomeration (AIA) is a compact spatial economic behavior, which manifests as the cluster phenomenon of enterprises seeking economies of scale and scope. AIA can help agricultural producers expand their existing production scale and raise profitability to a certain extent (Cohen and Paul, 2005 [2]).

It is worth noting that AIA and AEE are important strategies and objectives for future China, and the inherent nexus between them should not be overlooked. The empirical study of the impact of industrial agglomeration on the environment is a hot topic of academic interest. Nevertheless, no consensus has yet been reached. The general views mainly focus on the promotion or inhibition impact of industrial agglomeration on the environment (Han et al., 2018 [3]; Zheng and Kahn, 2013 [4]; Wang et al., 2015 [5]), as well as the nonlinear effect (Shen and Peng, 2021 [6]; Zhang et al., 2021 [7]).

Many studies have employed a single undesirable output to characterize environmental pollution, such as carbon emissions and haze pollution (Wu et al., 2021 [8]; Li et al., 2021 [9]). However, the primary shortcoming of the use of a single factor is that it only reflects the undesirable output but ignores other factors that may impact environmental performance, including agricultural resource endowments, technological advancement, and other forms of environmental pollution. In addition, industrial agglomeration in adjacent areas can exert a demonstration effect and radiation effect on environmental efficiency in the province (Xu et al., 2023 [10]). Despite this, existing research has disregarded the spatial spillover effect in analyzing the nonlinear relationship between AIA and AEE. Moreover, most studies on the environmental effects of industrial agglomeration have focused on industrial energy enterprises, and there have been relatively few studies on the agricultural production sector. Hence, this paper aims to investigate the relationship between AIA and AEE while taking into account the spatial spillover effect. Clarifying the relationship between these two variables can provide insights for developing relevant policies to promote a sustainable and environmentally friendly agricultural system.

Relative to the existing study, this paper makes three contributions. First, the inverted U-shaped curve relationship between AIA and AEE is explained theoretically and empirically, which sheds light on the nonlinear nexus between them. Second, this paper constructs spatial lag, spatial error, and spatial Dubin models to investigate the spatial spillover effect of AIA on AEE, which captures the spatial dependence due to the connection between regions and fills the research gap. Third, we provide a more accurate estimate of AEE using a fixed-effects stochastic frontier model, by addressing various issues in existing models, including the neglect of endogenous problems caused by individual heterogeneity and the assumption that technical efficiency is time-invariant. The results of this study enrich the previous literature and provide new insights on agriculture-enhancing carbon sequestration capacity as well as the rational formulation of sustainable development policies.

The rest of this paper is organized as follows. Section 2 provides the literature review and the relevant research hypotheses. In Section 3, we introduce the methodology and data employed in this study. The empirical results are presented in Section 4, followed by a summary of the research findings and policy recommendations in Section 5.

2. Literature Review and Research Hypothesis

2.1. Methods for Measuring AEE

In the sustainable development of agriculture, agricultural economic growth no longer pursues high output at the cost of resource consumption, but pays equal attention to the sustainable development of both quantity and quality (Odum and Odum, 2000 [11]; Amigues and Moreaux, 2019 [12]). Traditional assessments of agricultural technology efficiency only considered desirable outputs and failed to take environmental costs into account, while environmental efficiency is defined as economic efficiency considering the consumption of resources and the environment (Song et al., 2012 [13]). It involves treating carbon emissions in the agricultural production process as undesirable outputs, while the desirable output is expressed by the agricultural economic output value. The performance of agricultural environmental productivity is defined by increasing desirable output while reducing undesirable output.

There are two main methods to measure AEE. One is the nonparametric method, which utilizes data envelopment analysis (DEA) based on linear programming and dual theory. The other is stochastic frontier analysis (SFA), an econometric method used to estimate function parameters. For the measurement of environmental efficiency including bad output, most scholars have incorporated the directional distance function into a DEA model framework (Chen and Jia, 2017 [14]; Vlontzos et al., 2014 [15]; Li et al., 2013 [16]; Yuan et al., 2020 [17]; Shang et al., 2022 [18]). However, DEA neither sets a specific functional relationship between output and input, nor can it control for the error terms (Headey et al., 2010 [19]; Honma and Hu, 2014 [20]). Compared with DEA, the SFA approach allows for random shocks and measurement error (Cullinan et al., 2006 [21]), which obtains a more reasonable calculation result. However, there is limited literature on the application of parametric methods as they only considered a single output in the early stage until the hyperbolic distance function was applied (Cuesta et al., 2009 [22]). Similar to the directional distance function, the hyperbolic distance function also takes into account the negative externality of undesired outputs. Generally speaking, DEA is less stable in comparison with SFA as it does not account for sample randomness. For example, Reinhard et al., 2000 [23] used DEA and SFA to estimate environmental efficiency and verified that statistical noise accounts for nearly 30% of the regression residuals in SFA. Additionally, in terms of applicability, the directional distance function is more suitable for the secondary production function, while the hyperbolic distance function can be applied to a more flexible translog specification due to its almost homogeneous property (Cuesta et al., 2009 [22]).

The panel data contains two dimensions, cross-section data and time series data, which can provide more accurate estimation results. The panel stochastic frontier model has evolved from a model whose efficiency does not change over time to models with time-varying inefficiency. Time-varying models of efficiency usually assume that the technical inefficiency term is a specific functional form of time t (Kumbhakar, 1990 [24]; Battese and Coelli, 1992 [25]; Lee and Schmidt, 1993 [26]), but early studies regarded the individual unobserved heterogeneity as a part of the inefficiency term, which might produce biased estimates. Greene, 2005 [27], tried to overcome this problem, and thus he proposed a true fixed-effects panel stochastic frontier model that differentiates the inefficiency term from individual unobserved heterogeneity. This method considers both time-invariant individual effects and time-varying inefficiency terms. To estimate this formulation, he proposed a ‘brute force’ approach by creating N dummy variables. However, as panel units tend towards infinity, the problem of incidental parameters (Neyman and Scott, 1948 [28]) can easily lead to inconsistent parameter estimates. Chen et al., 2014 [29], found that the transformed model within the group has a closed likelihood function and eliminates the individual effect, which could avoid the problem of incidental parameters. Furthermore, Belotti and Ilardi, 2018 [30], proposed two alternative consistent estimators by producing maximum likelihood consistent estimators, which would prevent this problem. However, the most recent literature has calculated environmental efficiency based on Battese and Coelli, 1992 [25] (Li et al., 2018 [31]; Zhang, 2021 [32], Zou et al., 2013 [33]), ignoring biased efficiency estimates caused by the unobservable time-invariant heterogeneity of individuals. To address this problem, this paper applies the method of Chen et al., 2014 [29], to calculate AEE.

2.2. Relationship between AIA and AEE

The impact of AIA on AEE mainly originates from three aspects: the input–output intermediate connection, knowledge and technology spillover, as well as labor market pooling (Yuan et al., 2020 [17]). Theoretically speaking, the role of industrial agglomeration in environmental efficiency will be reflected in two aspects: positive externality and negative externality. Furthermore, the effect of AIA on AEE ultimately depends on which externality dominates (Li et al., 2019 [34]).

On the one hand, this study explains the positive externality mechanism of AIA on AEE from the above three aspects. (1) The benefits of the scale economy effect. During the early stage of AIA, a large number of agricultural industries will form a joint force to achieve large-scale operations, thus promoting the expansion and intensification of agricultural production and lowering the overall cost of production (Wang et al., 2023 [35]). Furthermore, the centralization of agricultural resources will be conducive to effectively improving the efficiency of resource utilization in agriculture, thereby facilitating the development of an agricultural circular economy (Kevane, 1996 [36]; Du et al., 2020 [37]). (2) The knowledge–technology spillover effect. Industrial agglomeration can promote the spread and diffusion of knowledge and technology, enhancing the exchange of the innovation capacity of green technologies (Dong et al., 2012 [38]). This will lead to a sustainable increase in productivity while ensuring ecological well-being. (3) Labor market pooling. The concentration of the labor force serves as a labor ’reservoir’, which will help to improve labor productivity and accelerate the upgrading of agricultural industrial structures (Hanson, 2001 [39]). These factors will collectively contribute to increasing environmental efficiency.

On the other hand, when the degree of industrial agglomeration is too high, negative externality originating from crowding effects will be reflected (Andersson and Lööf, 2011 [40]). Industrial agglomeration brings population concentration, which will further exceed the maximum carrying capacity of urban public infrastructure (Henderson, 1986 [41]). Meanwhile, excessive competition will lead to wasteful and inefficient use of resources, thereby exerting a detrimental impact on the environment. Therefore, we hypothesize the following.

Hypothesis 1.

During the early period and rapid development stage of AIA, it can promote AEE. However, when AIA reaches a certain level, it starts to have a restraining effect on AEE. Therefore, the relationship between AIA and AEE is theoretically an inverted U-shape.

Furthermore, AEE in different areas is highly spatially connected and dependent, and AIA is an effective way to strengthen economic relations and intensify the frequent flow of materials and resources (Zhang et al., 2018 [42]). Moreover, with the gradual boom of the internet, logistics infrastructure, and transportation, the overflow of agricultural resource endowments between neighboring cities is becoming more frequent, which will result in increasingly close agricultural production ties (Wang et al., 2023 [43]). Therefore, it will further promote the spatial spillover of AIA on AEE. Thus, we hypothesize the following.

Hypothesis 2.

AIA has obvious spatial spillover effects on AEE.

3. Methodology and Data

This study is aimed at quantitatively analyzing the impact of AIA on AEE, and providing reliable data support for the formulation and implementation of government policies. Specifically, in the first step, employing the parametric hyperbolic distance function and fixed-effects stochastic frontier analysis, we estimate AEE in provincial areas in China from 2000 to 2020. In the second step, the effect of AIA on AEE is examined using the method of spatial econometrics. Then the direct and indirect effects of AIA are decomposed to further reveal the heterogeneous spillover impact.

3.1. Estimation of AEE

3.1.1. Traditional Stochastic Frontier Model

Considering the framework of an agricultural production function, taking agricultural resource endowments, including labor (LAB), land (LAND), fertilizer (FERT), and machinery (MAC) as input factors, desirable output (GVAO) and undesirable output (${\mathrm{CO}}_2$) as outputs, the environmental technology set can be defined as:

$$T=\left\{\left(X,GVAO,C{O}_2\right):X\mathrm{can}\mathrm{produce}GVAO,C{O}_2\right\},$$

(1)

where $X=(LAB,LAND,FERT,MAC)$ is a $1\times 4$ vector of input variables.

Based on Equation (1), the definition of the hyperbolic environmental technology distance function (Cuesta et al., 2009 [22]) can be defined as:

$$D_H\left(X,GVAO,C{O}_2\right)=inf\left\{\theta >0:\left(X,GVAO/\theta ,C{O}_2\theta \right)\in T\right\}.$$

(2)

The hyperbolic environmental technology distance function provides a friendly characterization of the environmental technology (Cuesta et al., 2009 [22]). The range of the hyperbolic environmental technology distance function is $0<D_H\le 1$, and the larger the value is, the higher the AEE score. Furthermore, the hyperbolic environmental technology distance function almost satisfies homogeneity given by

$$D_H\left(X,\lambda GVAO,{\lambda }^{-1}C{O}_2\right)=\lambda D_H\left(X,GVAO,C{O}_2\right),\lambda >0.$$

(3)

This equation indicates that holding inputs constant, if desirable output GVAO is increased by a given proportion, undesirable output ${\mathrm{CO}}_2$ is reduced by the same proportion and the distance function will increase by that same proportion.

We use the stochastic frontier production function model to estimate AEE, which is independently proposed by Aigner et al., 1977 [44], and Meeusen and van den Broeck, 1977 [45]. A stochastic frontier production function for the cross-sectional model is specified in the form:

$$\begin{array}{ccc}\hfill & \hfill & \hfill y_i={\beta }^{\prime }{x}_i+v_i-u_i,i=1,\dots ,N,\end{array}$$

(4)

where $y_i$ and $x_i$ are the corresponding output and input vectors in logarithms of unit i, respectively, ${\beta }_i$ is a vector of unknown parameters, $v_i$ is the disturbance term that follows a normal distribution, $v_i\sim N(0,{\sigma }_v^2)$, and $u_i$ is a non-negative random variable standing for technical inefficiency. Generally, $u_i$ is assumed to be independent identically and distributed with one of several distributions: half-normal distribution, $u_i\sim N^{+}(0,{\sigma }_u^2)$ (Aigner et al., 1977) [44], truncated normal distribution, $u_i\sim N^{+}(\mu ,{\sigma }_u^2)$ (Stevenson, 1980 [46]), and gamma distribution, $u_i\sim G(\theta ,P)$ (Greene, 1990 [47]). On this basis, it is further assumed that $u_i$ and $v_i$ are independent of each other. Thus, the standard stochastic frontier production, defined by Equation (4), can be estimated using the method of maximum likelihood (ML). By definition, the output-oriented measure of the technical efficiency of ith unit is defined by

$$T{E}_i=\frac{exp\left(y_i\right)}{exp\left({\beta }^{\prime }{x}_i+v_i\right)}=exp\left(-u_i\right),$$

(5)

where $T{E}_i$ is technical efficiency, $exp\left(y_i\right)$ is observed output, $exp({\beta }^{\prime }{x}_i+v_i)$ is the corresponding stochastic frontier output.

3.1.2. Fixed-Effects Stochastic Frontier Model

With panel data, we consider a fixed-effects frontier model of the form:

$$y_{it}={\alpha }_i+{\beta }^{\prime }{x}_{it}+v_{it}-u_{it},i=1,\dots ,N,t=1,\dots ,T,$$

(6)

which was first proposed by Schimidt and Sickles, 1984 [48]. This formulation differs from the cross-sectional model in Equation (4) in that it involves an individual item, which controls for time-invariant factors that affect an individual’s output but are not regarded as inefficiency. Furthermore, the inefficiency term $u_i$ is set as time-varying. Simultaneously, assume $v_i\sim N(0,{\sigma }_v^2)$, $u_i\sim N^{+}(0,{\sigma }_u^2)$, and $x, u, v$ are mutually independent.

We follow the method of (Chen et al., 2014) [29] to estimate $T{E}_i$ in the fixed-effects SFA model. Similar to the panel fixed-effects model, we apply first the within transformation to Equation (6) to obtain

$${\tilde{y}}_{it}={\beta }^{\prime }{\tilde{x}}_{it}+{\tilde{v}}_{it}-{\tilde{u}}_{it}.$$

(7)

Then the density of the composed error $\epsilon =v-u$ (suppressing subscripts for observations) is given by (Aigner et al., 1977) [45]

$$f\left(\epsilon \right)=\frac{2}{\sigma }\varphi \left(\frac{\epsilon }{\sigma }\right)\Phi \left(-\frac{\lambda \epsilon }{\sigma }\right),$$

(8)

where ${\sigma }^2={\sigma }_u^2+{\sigma }_v^2$ and $\lambda =\frac{{\sigma }_u}{{\sigma }_v}$ is the skewness parameter.

Furthermore, the composed error $\epsilon$ follows a closed skew normal (CSN) distribution with parameters ${\sigma }^2$ and $\lambda$ (González-Farías et al., 2004 [49]); that is

$${\epsilon }_{it}\sim CS{N}_{1,1}\left(0,{\sigma }^2,-\frac{\lambda }{\sigma },0,1\right).$$

(9)

Compared with normal distribution, CSN family has the analogous property that the joint distribution of independent CSN random vectors is still CSN distributed, then the joint distribution of ${\epsilon }_i={({\epsilon }_{i1},\dots ,{\epsilon }_{it})}^{\prime }$ is

$${\epsilon }_i\sim CS{N}_{T,T}\left(0_T,{\sigma }^2{I}_T,-\frac{\lambda }{\sigma }{I}_T,0_T,I_T\right).$$

(10)

Then decompose the vector ${\epsilon }_i$ into its mean ${\overline{\epsilon }}_i$ =$\frac{1}{T}{\sum }_{i=1}^T{\epsilon }_{it}$ and its first $T-1$ deviations ${\tilde{\epsilon }}_i^{*}=({\tilde{\epsilon }}_{i1}^{*},\dots ,{\tilde{\epsilon }}_{i,T-1}^{*})$.

MLE proposed in this paper is based only on the joint density of the first $T-1$ deviations from means ${\tilde{\epsilon }}_i^{*}$, and the parameters to be estimated are $\beta ,\lambda ,$ and ${\sigma }^2$. That is, the individual effects are removed by the within transformation, and then MLE applied. Therefore, this method is free from the incidental parameters problem. Furthermore, we can obtain one estimate of ${\alpha }_i$, which is labeled by the mean-adjusted estimate as:

$${\widehat{\alpha }}_i^M={\overline{y}}_i-{\overline{X}}_i\widehat{\beta }+\sqrt{\frac{2}{\pi }}{\widehat{\sigma }}_u,$$

(11)

where $\widehat{\beta }$ and ${\widehat{\sigma }}_u$ are the WMLE estimates.

Before building a stochastic frontier panel data model based on a hyperbolic distance function, it is necessary to set a specific form of the production function. We use the translog functional form, which is a more flexible variable elastic production function. The specific translog functional form of the parametric distance function can be set as:

$$\begin{array}{cc}\hfill ln{D}_{it}=& {\alpha }_0+\sum _j{\alpha }_{j}ln{X}_{jit}+\frac{1}{2}\sum _j\sum _k{\alpha }_{jk}ln{X}_{jit}ln{X}_{kit}+{\alpha }_{t}T+\sum _j{\alpha }_{jt}ln{X}_{jit}T\hfill \\ & +\frac{1}{2}{\alpha }_{it}{T}^2+{\beta }_{C{O}_2}lnC{O}_{2,it}+{\beta }_{GVAO}lnGVA{O}_{it}+\frac{1}{2}{\beta }_{C{O}_2^2}{\left(lnC{O}_{2,it}\right)}^2\hfill \\ & +\frac{1}{2}{\beta }_{GVA{O}^2}{\left(lnGVA{O}_{it}\right)}^2+{\beta }_{C{O}_2\times GVAO}lnC{O}_{2,it}lnGVA{O}_{it}\hfill \\ & +\sum _j{\gamma }_{j\times GVAO}ln{X}_{jit}lnGVA{O}_{it}+{\gamma }_{t\times GVAO}lnGVA{O}_{it}T+\sum _j{\delta }_{j\times C{O}_2}ln{X}_{jit}lnC{O}_{2,it}\hfill \\ & +{\delta }_{t\times C{O}_2}lnC{O}_{2,it}T+{\alpha }_i+v_{it},i=1,\dots ,N,t=1,\dots ,T,\hfill \end{array}$$

(12)

where $D_{it}$ is the distance function for province i in time t, ${\alpha }_i$ represents provincial dimensional heterogeneity.

Based on Equation (3), we have

$$D_{H,it}(X_{jit},GVA{O}_{it}/GVA{O}_{it},C{O}_{2,it}\times GVA{O}_{it})=D_{H,it}(X_{jit},GVA{O}_{it},C{O}_{2,it})/GVA{O}_{it}.$$

(13)

Taking the logarithmic form of both sides and combining it with Equation (12), we can obtain

$$\begin{array}{cc}\hfill -lnGVA{O}_{it}=& {\alpha }_0+\sum _j{\alpha }_{j}ln{X}_{jit}+\frac{1}{2}\sum _j\sum _k{\alpha }_{jk}ln{X}_{jit}ln{X}_{kit}+{\alpha }_{t}T\hfill \\ & +\sum _j{\alpha }_{jt}ln{X}_{jit}T+\frac{1}{2}{\alpha }_{tt}{T}^2+{\beta }_{C{O}_2^{*}}lnC{O}_{2,it}^{*}+\frac{1}{2}{\beta }_{C{O}_2^{*2}}{\left(lnC{O}_{2,it}^{*}\right)}^2\hfill \\ & +\sum _j{\delta }_{j\times C{O}_2^{*}}ln{X}_{jit}lnC{O}_{2,it}^{*}+{\delta }_{t\times C{O}_2^{*}}lnC{O}_{2,it}^{*}T\hfill \\ & +{\alpha }_i+v_{it}-ln{D}_{H,it},i=1,\dots ,N,t=1,\dots ,T,\hfill \end{array}$$

(14)

where $C{O}_{2,it}^{*}=C{O}_{2,it}\times GVA{O}_{it}$. In Equation (14), all terms involving GVAO are null.

Furthermore, by defining $u_{it}=-ln{D}_{H,it}$ as an inefficiency term, then we can calculate AEE based on the fixed-effects stochastic frontier model.

3.2. Empirical Models

3.2.1. Spatial Autocorrelation Test

Before using spatial econometric methods to analyze the spatial spillover effect of AIA on AEE, it is necessary to verify whether there exists a spatial correlation among AEE across different provinces. Therefore, we conduct Moran’s I test as follows:

$$I=\frac{n{\sum }_{i=1}^n{\sum }_{j=1}^n{w}_{ij}(AE{E}_i-\overline{AEE})(AE{E}_j-\overline{AEE})}{{\sum }_{i=1}^n{(AE{E}_i-\overline{AEE})}^2{\sum }_{i=1}^n{\sum }_{j=1}^n{w}_{ij}},$$

(15)

where $w_{ij}$ represents the element of the ith row and the jth column of the spatial weight matrix. The value of Moran’s I is generally between $(-1,1)$. If Moran’s I > 0, there is a positive clustering trend among provinces. Conversely, when Moran’s I < 0, there is a negative dispersion trend, while Moran’s I = 0 means no correlation.

3.2.2. Spatial Econometric Models

The traditional panel model only considers the impact of AIA on local AEE, ignoring the spatial spillover effect generated by the flow of agricultural resources and technology. As a result, endogeneity issues arise. Therefore, spatial econometric models are used to capture the spatial interaction between AIA and AEE. Additionally, individual fixed effects at the provincial level and time fixed effects are added to control for individual heterogeneity and time effects. Finally, based on the hypothesis, it is believed that AIA has a nonlinear inverted U-shaped effect on AEE, so AIA and its quadratic term are introduced.

To discuss the spatial spillover effect, we construct three types of models, including spatial lag model (SAR) (specified in Equation (16)), spatial error model (SEM) (specified in Equation (17)), and spatial Dubin model (SDM) (specified in Equation (18)). The final models are formulated as follows:

$$AE{E}_{it}={\rho }_0\sum _{j=1,j\ne i}^N{w}_{ij}AE{E}_{jt}+{\gamma }_{1}AI{A}_{it}+{\gamma }_{2}AI{A}_{it}^2+{\varphi }_1{Z}_{it}+{\mu }_i+{\eta }_t+{\epsilon }_{it},$$

(16)

$$AE{E}_{it}={\gamma }_{1}AI{A}_{it}+{\gamma }_{2}AI{A}_{it}^2+{\varphi }_1{Z}_{it}+{\mu }_i+{\eta }_t+{\epsilon }_{it}+\lambda \sum _{j=1,j\ne i}^N{w}_{ij}{v}_{jt},$$

(17)

$$\begin{array}{cc}\hfill AE{E}_{it}=& {\rho }_0\sum _{j=1,j\ne i}^N{w}_{ij}AE{E}_{jt}+{\gamma }_{1}AI{A}_{it}+{\gamma }_{2}AI{A}_{it}^2+{\rho }_1\sum _{j=1,j\ne i}^N{w}_{ij}AI{A}_{jt}\hfill \\ & +{\rho }_2\sum _{j=1,j\ne i}^N{w}_{ij}AI{A}_{jt}^2+{\varphi }_1{Z}_{it}+{\varphi }_2\sum _{j=1,j\ne i}^N{w}_{ij}{Z}_{jt}+{\mu }_i+{\eta }_t+{\epsilon }_{it},\hfill \end{array}$$

(18)

where i and t stand for province and year, respectively, $w_{ij}$ is the element of the spatial weight matrix, $AE{E}_{it}$ denotes the agricultural environmental efficiency of province i in year t, $AI{A}_{it}$ is the main explanatory variable representing the level of agricultural industrial agglomeration, $Z_{it}$ represents the matrix of control variables, including INC, IND, EDU, lnRGDP, lnTRANS, ENV, ${\mu }_i$ is the unobserved provincial fixed effects, ${\eta }_t$ denotes the time fixed effects. In Equation (16), $w_{ij}$ interacts with the spatially lagged explained variable, $AE{E}_{jt}$. In Equation (17), $w_{ij}$ interacts with the spatially random term, $v_{jt}$. Furthermore, in Equation (18), $w_{ij}$ interacts with the spatially lagged explained variable, $AE{E}_{jt}$, and spatially lagged explanatory variables, including $AI{A}_{jt}$, $AI{A}_{jt}^2$, and $Z_{jt}$.

3.2.3. Spatial Weight Matrix

To verify the robustness of the spatial weight matrix, this paper employs two different forms. The first method is to construct a 0–1 adjacent weight matrix ($W_1$). In $W_1$, when two provinces border on an administrative boundary, the corresponding element in the geographic adjacency matrix is 1, otherwise set to 0. The second approach utilizes the geographic distance matrix ($W_2$), where the elements in the matrix are the reciprocals of the distance between the corresponding two cities. The specific calculation formulas are as follows.

$$W_1=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}i\mathrm{and}j\mathrm{are}\mathrm{adjacent}\hfill \\ 0,\hfill & \mathrm{otherwise}\hfill \end{array}\right.,$$

(19)

$$W_2=\left\{\begin{array}{cc}\frac{1}{d_{ij}},\hfill & i\ne j\hfill \\ 0,\hfill & i=j\hfill \end{array}\right..$$

(20)

3.3. Variables and Data

3.3.1. Data Source

We collected a panel dataset of 31 provinces in China during the 2000–2020 period (Hongkong, Taiwan, and Macao are excluded due to lack of data). The data in this article were collected from China Statistical Yearbook [50], China Rural Statistical Yearbook [51], and China Agricultural Yearbook [52]. Missing data were replaced with the mean value of adjacent years.

3.3.2. Explained Variable: AEE

Based on the research objects of this paper and the basic requirements of stochastic frontier analysis for input–output indicators, the following variables are selected. We consider the gross value of agricultural output (GVAO) as desirable output, which is measured as the sum of production value from farming, forestry, animal husbandry, and fisheries. Furthermore, undesirable output is represented by agricultural carbon emissions (${\mathrm{CO}}_2$). Then we specifically measure the carbon emissions generated by fertilizers, pesticides, agricultural plastic sheeting, agricultural sheeting, agricultural diesel, agricultural ploughing, and agricultural irrigation, respectively. The calculation formula is defined as:

$$C=\sum C_r=\sum T_r·{\delta }_r,$$

(21)

where C is the total agricultural carbon emissions, $C_r$ represents the carbon emissions from each agricultural carbon source, $T_r$ refers to the number of agricultural carbon sources, and ${\delta }_r$ represents the coefficient of agricultural carbon sources. The coefficient of each agricultural carbon source is set according to Li et al., 2011 [53], which is shown in

Table 1. Agricultural carbon emission source, coefficient, and reference.

Carbon Source	Carbon Emission Coefficient	Reference
Fertilizer	0.8956 kg·kg${}^{-1}$	Oak Ridge National Laboratory, ORNL
Pesticides	4.9341 kg·kg${}^{-1}$	Oak Ridge National Laboratory, ORNL
Agricultural plastic sheeting	5.18 kg·kg${}^{-1}$	Nanjing Agricultural University
Agricultural diesel	0.5927 kg·kg${}^{-1}$	IPCC
Agricultural ploughing	312.6 kg·km${}^{-2}$	Institute of Agriculture and Biotechnology of China
Agricultural irrigation	20.476 kg/hm${}^2$	Dubey

.

In addition, following Gong, 2018 [54], and Liu et al., 2015 [55], we select LAB, LAND, FERT, and MAC as agricultural resource endowments and measure them with the number of employees in the primary industry, sown area, the total weight of nitrogen, phosphate, potash, and complex fertilizers, as well as the overall power of agricultural machinery, respectively.

3.3.3. Explanatory Variable: AIA

The explanatory variable is the level of agricultural industrial agglomeration, denoted by AIA. The position entropy method is used to measure AIA. Based on the work by (Zhang and Tu, 2022 [56]), the calculation formula of the position entropy method is as follows:

$$AI{A}_{it}=\frac{X_{it}/{\sum }_i{X}_{it}}{Y_{it}/{\sum }_i{Y}_{it}},$$

(22)

where $AI{A}_{it}$ represents the position entropy of province i in year t, $X_{it}$ represents the number of primary industry employees of province i in year t, ${\sum }_i{X}_{it}$ refers to the total number of employees in the primary industry in all provinces in year t. $Y_{it}$ represents the total number of employees industry-wide of province i in year t, ${\sum }_i{Y}_{it}$ is the total number of employees industry-wide in all provinces in year t.

3.3.4. Control Variables

The main control variables are urban–rural income gap, industrialization process, average schooling year, economic development, transportation infrastructure, and environmental regulation. (1) Urban–rural income gap (INC) is represented by the ratio of disposable income of urban residents to rural residents. (2) Industrialization process (IND) is measured as the ratio of the added value of the secondary industry to GDP. (3) Average schooling year (EDU) refers to the average number of years of education. (4) The level of economic development (lnRGDP) is estimated by per capita GDP in logarithmic form. (5) Transportation infrastructure (lnTRANS) is characterized by highway mileage in logarithmic form. (6) Environmental regulation (ENV) is measured as the ratio of investment industrial pollution treatment to industrial value-added.

The descriptive statistics of variables are shown in

Table 2. Descriptive statistics of variables.

Variable Type	Variables	Unit	Obs	Mean	Std. Dev.	Min	Max
Output variables	GVAO	billion CNY	651	2366.430	2168.945	51.220	10,190.600
	${\mathrm{CO}}_2$	million tons	651	301.299	227.189	7.282	995.753
Input variables	LAB	million people	651	893.618	698.079	27.000	3558.550
	LAND	million hectares	651	5168.415	3675.812	88.600	14,910.100
	FERT	million tons	651	169.616	138.495	2.500	716.090
	MAC	million kilowatts	651	2763.119	2687.327	94.000	13,353.000
Explanatory variable	AIA	%	651	1.015	0.406	0.083	2.123
Control variables	INC	%	651	2.857	0.595	1.845	5.525
	IND	%	651	0.422	0.083	0.160	0.619
	EDU	year	651	8.466	1.291	2.998	12.782
	lnRGDP	yuan	651	9.161	0.522	7.887	10.760
	lnTRANS	kilometer	651	11.347	0.904	8.372	12.885
	ENV	%	651	0.005	0.004	0.000	0.309

.

4. Empirical Results

4.1. Estimation of AEE

Before estimating the parameters of the hyperbolic distance function, in order to avoid the situation of nonconvergence of the model, all input and output variables are standardized. The maximum likelihood estimates are presented in

Table 3. Estimated parameters for the distance function.

Parameter	Coefficient	t-Value	Parameter	Coefficient	t-Value
${\alpha }_{\mathrm{LAB}}$	0.043	0.889	${\alpha }_{\mathrm{MAC}\times \mathrm{FERT}}$	−0.179 ***	−2.760
${\alpha }_{\mathrm{LAND}}$	−0.281 ***	−3.200	${\alpha }_{\mathrm{T}\times \mathrm{LAB}}$	−0.019 ***	−3.860
${\alpha }_{\mathrm{MAC}}$	−0.108 ***	−3.200	${\alpha }_{\mathrm{T}\times \mathrm{LAND}}$	−0.003	−0.628
${\alpha }_{\mathrm{FERT}}$	−0.295 ***	−5.050	${\alpha }_{\mathrm{T}\times \mathrm{MAC}}$	0.011 ***	3.230
${\alpha }_{\mathrm{T}}$	−0.055 ***	−22.900	${\alpha }_{\mathrm{T}\times \mathrm{FERT}}$	0.017 ***	3.760
${\alpha }_{{\mathrm{LAB}}^2}$	−0.136	−1.260	${\beta }_{{\mathrm{CO}}_2^{*}}$	−0.387 ***	−14.100
${\alpha }_{{\mathrm{LAND}}^2}$	0.016	0.132	${\beta }_{{{\mathrm{CO}}_2^{*}}^2}$	0.150 ***	7.620
${\alpha }_{{\mathrm{MAC}}^2}$	−0.096	−1.520	${\delta }_{\mathrm{LAB}\times {\mathrm{CO}}_2^{*}}$	0.098 ***	3.090
${\alpha }_{{\mathrm{FERT}}^2}$	−0.164 *	−1.750	${\delta }_{\mathrm{LAND}\times {\mathrm{CO}}_2^{*}}$	−0.089 ***	−2.620
${\alpha }_{{\mathrm{T}}^2}$	0.002 ***	4.560	${\delta }_{\mathrm{MAC}\times {\mathrm{CO}}_2^{*}}$	−0.011	−0.521
${\alpha }_{\mathrm{LAB}\times \mathrm{LAND}}$	−0.224 **	−2.560	${\delta }_{\mathrm{FERT}\times {\mathrm{CO}}_2^{*}}$	−0.074 **	−2.060
${\alpha }_{\mathrm{LAB}\times \mathrm{MAC}}$	0.155 ***	2.640	${\delta }_{\mathrm{T}\times {\mathrm{CO}}_2^{*}}$	−0.007 ***	−3.790
${\alpha }_{\mathrm{LAB}\times \mathrm{FERT}}$	0.115	1.580	$ln\left({{\sigma }_v}^2\right)$	6.164 ***	14.300
${\alpha }_{\mathrm{LAND}\times \mathrm{MAC}}$	0.093	1.350	$ln\left({{\sigma }_u}^2\right)$	4.486 ***	15.900
${\alpha }_{\mathrm{LAND}\times \mathrm{FERT}}$	0.217 ***	2.840
log-likelihood			759.027

Note: *** $p\le 0.01$, ** $p\le 0.05$, * $p\le 0.10$.

. The econometric test shows that the parameter estimation of the fixed-effects panel stochastic frontier model exhibits favorable statistical properties. Subsequently, we calculate the average value of China’s AEE as 0.909, indicating that the overall environmental efficiency is relatively high but there remains potential for improvement.

Based on the parameter estimates of Table 3, we then calculate the AEE of 31 provinces in China during 2000–2020. We find that the average value of China’s AEE is 0.909, indicating that Figure 1 describes the regional distribution characteristics of AEE in years 2000, 2007, 2014, and 2020. Among the 31 provinces, the top three in AEE are Liaoning (0.939), Hunan (0.937), and Sichuan (0.935), which are the main grain-producing areas in China. This indicates that these areas have achieved outstanding results in increasing yield and efficiently using resources while improving farmland carbon sequestrations. In comparison, Inner Mongolia (0.852), Tibet (0.861), and Qinghai (0.872) are the three provinces with relatively low AEE. The primary reasons for this are the limited availability of agricultural resources and the harsh natural environment, which have led to these regions relying heavily on the overuse and exploitation of resources. As a result, they face difficulties and challenges in turning carbon sources into carbon sinks and increasing pressure on the ecological environment. Since AEE not only examines agricultural output and carbon emissions, but also considers a variety of input factors, the reasons for the differences between provinces are complex. However, in general, AEE is mainly affected by factors such as agricultural resource endowment, regional advantage, and economic development level. It is worth noting that the AEE of all provinces and cities has not reached the frontier border, which needs to be further improved.

4.2. Spatial Autocorrelation of AEE

Based on spatial weight matrices, Moran’s I of the AEE from 2000 to 2020 in China is calculated. The results are shown in

Table 4. Results of global Moran’s I.

Year	${\mathit{W}}_1$		${\mathit{W}}_2$		Year	${\mathit{W}}_1$		${\mathit{W}}_2$
	Moran’s I	Z Value	Moran’s I	Z Value		Moran’s I	Z Value	Moran’s I	Z Value
2000	0.436 ***	3.942	0.240 ***	7.498	2011	0.541 ***	4.830	0.288 ***	8.588
2001	0.441 ***	3.988	0.239 ***	7.481	2012	0.539 ***	4.808	0.293 ***	8.709
2002	0.473 ***	4.252	0.227 ***	7.138	2013	0.543 ***	4.842	0.303 ***	8.964
2003	0.469 ***	4.229	0.245 ***	7.556	2014	0.544 ***	4.852	0.309 ***	9.114
2004	0.512 ***	4.589	0.263 ***	8.097	2015	0.544 ***	4.851	0.306 ***	9.042
2005	0.526 ***	4.706	0.269 ***	8.231	2016	0.522 ***	4.665	0.295 ***	8.698
2006	0.542 ***	4.842	0.274 ***	8.318	2017	0.516 ***	4.612	0.290 ***	8.569
2007	0.551 ***	4.915	0.283 ***	8.533	2018	0.519 ***	4.640	0.294 ***	8.661
2008	0.549 ***	4.894	0.285 ***	8.558	2019	0.536 ***	4.786	0.301 ***	8.835
2009	0.535 ***	4.777	0.283 ***	8.497	2020	0.582 ***	5.167	0.317 ***	9.218
2010	0.544 ***	4.850	0.288 ***	8.609

Note: *** $p\le 0.01$.

. It can be seen that the global Moran’s I statistics of AEE pass the significance test of the 1% level and show a gradual upward trend, indicating that AEE has obvious agglomeration characteristics and positive correlations with space. Therefore, it is suggested that the choice of a spatial econometric model is suitable for further analysis.

4.3. Estimation Results of Spatial Panel Data Model

To examine the spatial effect, various spatial models are presented. The Hausman test indicates that the fixed effects should be selected. Additionally, we use the LR test and Wald test to verify whether the SDM model could degenerate into SAR and SEM models. For the comparison, the estimated results of the regular OLS model with fixed effects, and the SAR and SDM models under two spatial weight matrices are presented. The results are shown in

Table 5. Results of regression using OLS and spatial panel models.

Variables	OLS with Fixed Effects	SAR		SDM
		${\mathit{W}}_{\mathbf{1}}$	${\mathit{W}}_{\mathbf{2}}$	${\mathit{W}}_{\mathbf{1}}$	${\mathit{W}}_{\mathbf{2}}$
AIA	0.246 *** (3.931)	0.190 *** (3.156)	0.226 *** (3.774)	0.128 ** (2.051)	0.219 *** (3.774)
${\mathrm{AIA}}^2$	−0.056 ** (−2.254)	−0.042 * (−1.779)	−0.053 ** (−2.637)	−0.020 (−0.818)	−0.060 *** (−2.637)
INC	−0.027 *** (−3.242)	−0.031 *** (−3.011)	−0.035 *** (−3.461)	−0.038 *** (−3.162)	−0.036 *** (−3.420)
IND	0.235 *** (4.141)	0.141 ** (2.060)	0.126 * (1.842)	0.152 ** (2.325)	0.209 *** (3.098)
EDU	−0.006 (−0.812)	−0.004 (−0.353)	−0.005 (−0.477)	−0.001 (−0.108)	−0.003 (−0.270)
lnRGDP	0.080 *** (3.142)	0.025 (0.945)	0.027 (1.016)	0.064 ** (2.323)	0.022 (0.808)
lnTRANS	−0.020 * (−1.960)	−0.018 (−1.234)	−0.017 (−1.165)	−0.012 (−0.734)	−0.013 (−0.955)
ENV	0.671 (0.861)	0.235 (0.294)	0.286 (0.356)	0.634 (0.836)	1.544 ** (1.988)
$\mathrm{W}\times \mathrm{AIA}$				0.319 *** (3.074)	1.888 *** (4.922)
$\mathrm{W}\times {\mathrm{AIA}}^2$				−0.083 * (−1.951)	−0.688 *** (−4.614)
$\mathrm{W}\times \mathrm{INC}$				0.023 (0.993)	−0.195 ** (−2.552)
$\mathrm{W}\times \mathrm{IND}$				−0.264 * (−1.849)	0.315 (0.719)
$\mathrm{W}\times \mathrm{EDU}$				0.015 (0.663)	−0.183 ** (−2.359)
$\mathrm{W}\times \mathrm{lnRGDP}$				−0.014 (−0.292)	0.005 (0.033)
$\mathrm{W}\times \mathrm{lnTRANS}$				−0.04 (−1.077)	−0.422 *** (−3.486)
$\mathrm{W}\times \mathrm{ENV}$				4.241 ** (2.473)	24.617 *** (4.306)
$\rho$		1.139 *** (2.723)	0.079 (0.708)	0.002 (0.036)	−0.412 *** (−2.865)
Regional control effect		Yes	Yes	Yes	Yes
Time control effect		Yes	Yes	Yes	Yes
R-squared	0.103	0.37	0.365	0.403	0.43
log-likelihood		1020.556	1020.404	1038.715	1051.049
LM test no spatial lag				5.204 **	3.166 *
LM test no spatial error				3.785 *	4.188 **
Wald_spatial_lag				14.159 *	31.424 ***
Wald_spatial_error				14.704 *	30.920 ***

Note: *** $p\le 0.01$, ** $p\le 0.05$, * $p\le 0.10$.

.

According to the regression results, it can be observed that choosing different spatial weight matrices leads to different regression results, but the direction of influence tends to be consistent. As is shown in Table 5, the $R^2$ value of the regular OLS model used in the analysis is relatively low. Furthermore, both the LR test and Wald test reject the null hypothesis, which means that the SDM model constructed in this study is more appropriate for our study.

From the regression results of the SDM model, the coefficients of AIA and ${\mathrm{AIA}}^2$ are positive and negative, respectively. This suggests that the relationship between AIA and AEE conforms to an inverted U-shaped curve. Hypothesis 1 is confirmed. Under $W_2$, the turning point value of AIA is calculated to be 1.825. It reveals that when the degree of AIA is below 1.825, AEE gradually increases due to the significant scale economy effect. In contrast, after AIA exceeds 1.825, environmental efficiency begins to decline. In 2020, only Shanxi and Guizhou provinces had an AIA level exceeding 1.825, indicating that most provinces are still on the left side of the inverted U-shaped curve. This indicates that these provinces can continue to leverage economies of scale to improve the environmental efficiency of agricultural production.

During the process of industrial agglomeration, environmental efficiency initially increases and then decreases. This paper explains the reasons for the tendency as follows. At different development stages of industrial agglomeration, the game results of positive externality and negative externality lead to the inverted U-shaped path of AIA and AEE. Specifically, in the early phase of AIA, the expansion of the scale of agriculture increases the carbon sink capacity of farmland and reduces greenhouse gas emissions. At the same time, the spatial layout and combination optimization of various agricultural natural resources are promoted, which makes them more centralized by exerting scale effects. Moreover, AIA induces a competition effect, forcing relevant agricultural industries to improve their green technologies to enhance differentiated competitive advantages, thereby improving AEE. However, when the degree of AIA is excessively high, the further expansion of industrial agglomeration inevitably improves the intensity of agricultural production and the extensive use of agricultural materials such as fertilizers. This could result in concentrated emissions of greenhouse gases. In addition, the congestion effect in the process of industrial agglomeration gradually becomes prominent and exceeds the optimal carrying capacity of the city, resulting in a less-than-optimal allocation of agricultural resources. These factors are not conducive to the sustainable development of agriculture. Hence, the relationship between AIA and AEE is an inverted U-shaped correlation.

In regard to the effect of control variables, the result shows that the coefficient of urban–rural income gap (INC) is significantly negative at the 1% level, denoting that the urbanization pattern that widens the gap between urban and rural development has been an important factor restraining AEE. The coefficient of industrialization process (IND) is significantly positive at the 5% level, which illustrates that industrialization might improve the production capacity of green agriculture. The impact of environmental regulation (ENV) is actually positive, which supports the “Porter hypothesis”.

Based on Elhorst, 2014 [57], the effect of AIA on AEE is divided into direct and indirect effects for further study. The direct, indirect, and total effects under two types of spatial weight matrix are shown in

Table 6. Decomposition of spatial effects.

Variables	${\mathit{W}}_1$			${\mathit{W}}_2$
	Direct	Indirect	Total	Direct	Indirect	Total
AIA	0.129 ** (2.054)	0.319 *** (3.175)	0.448 *** (4.540)	0.189 *** (3.147)	1.328 *** (4.207)	1.517 *** (4.923)
${\mathrm{AIA}}^2$	−0.020 (−0.833)	−0.083 ** (−2.003)	−0.103 ** (−2.492)	−0.049 ** (−2.118)	−0.489 *** (−3.993)	−0.538 *** (−4.436)
INC	−0.038 *** (−3.153)	0.022 (0.971)	−0.016 (−0.761)	−0.033 *** (−3.002)	−0.136 ** (−2.260)	−0.169 *** (−2.899)
IND	0.148 ** (2.204)	−0.270 * (−1.842)	−0.121 (−0.728)	0.206 *** (3.110)	0.163 (0.514)	0.368 (1.107)
EDU	−0.001 (−0.098)	0.015 ** (0.663)	0.014 (0.551)	−0.001 (−0.047)	−0.136 ** (−2.358)	−0.137 ** (−2.319)
lnRGDP	0.063 ** (2.287)	−0.013 (−0.275)	0.050 (1.072)	0.020 (0.716)	0.003 (0.031)	0.023 (0.237)
lnTRANS	−0.011 (−0.660)	−0.039 (−1.036)	−0.050 (−1.523)	−0.007 (−0.507)	−0.305 *** (−3.169)	−0.313 *** (−3.352)
ENV	0.633 (0.817)	4.200 *** (2.456)	4.834 ** (2.566)	1.178 (1.554)	17.481 *** (3.897)	18.659 *** (4.028)

Note: *** $p\le 0.01$, ** $p\le 0.05$, * $p\le 0.10$.

. Both direct and indirect effects of AIA are significant at the 5% level, indicating that it has significant spillover effects on AEE. Therefore, Hypothesis 2 is confirmed. Under $W_2$, in terms of the direct effect, the coefficients of AIA and ${\mathrm{AIA}}^2$ are significantly positive and negative at the 5% level, respectively, indicating that the direct impact of AIA on AEE presents an inverted U-shaped relationship. Improving industrial agglomeration to a certain extent is conducive to environmental efficiency, but the impact is characterized by diminishing marginal effects. When industrial agglomeration rises to a certain extent, it will decrease AEE, which reveals the “crowding out effect”. Furthermore, the result is consistent with the estimation results of the SDM model. Furthermore, from the perspective of the indirect effect, levels of AIA and ${\mathrm{AIA}}^2$ show significant spillover effects, and there is still an inverted U-shaped relationship between AIA and AEE. When AIA goes beyond a certain level, it will have a blocking effect on the AEE of geographically neighboring cities. Beyond that, it is worth noting that compared to the direct effect, the absolute value of AIA and its quadratic term in the indirect effect is generally larger. Thus, AIA has strong spatial spillover effects.

In regard to the indirect effect, the inverted U-shape between AIA and AEE can be explained as follows. In the short term, agricultural resource endowments radiate to underdeveloped areas via the economic chain. Through knowledge spillover, the demonstration and extension of green technologies improve the organizational efficiency of agricultural production. This effectively provides a cumulative effect and diffusion effect on the agricultural green economy between regions. However, in the long run, certain agricultural resources, such as capital, labor, and technology, gathered to the surrounding regions, subsequently lead to the weakening of AEE in the core regions. Due to the spatial correlation of AEE, local industrial policies targeted at a certain region may not be able to achieve the purpose of agricultural system resilience and emissions reduction, and only by the deep integration of industries as well as technology demonstration and extension can the green transformation of agriculture be realized.

4.4. Robust Analysis

In this paper, the robustness of the model is tested by replacing the calculation of AIA and the spatial model. The results of the robustness test are shown in

Table 7. The results of robustness test.

Variables	SDM		SEM
	${\mathit{W}}_{\mathbf{1}}$	${\mathit{W}}_{\mathbf{2}}$	${\mathit{W}}_{\mathbf{1}}$	${\mathit{W}}_{\mathbf{2}}$
AIA	0.280 (1.579)	0.038 ** (2.324)	0.198 *** (3.245)	0.245 *** (4.118)
${\mathrm{AIA}}^2$	−0.002 * (1.834)	−0.003 *** (−2.742)	−0.044 * (−1.835)	−0.060 *** (−2.565)
INC	−0.020 * (−1.704)	−0.027 *** (−2.606)	−0.035 *** (−3.381)	−0.037 *** (−3.635)
IND	0.065 0.915)	0.164 ** (2.267)	0.142 ** (2.083)	0.121 * (1.750)
EDU	−0.000 (−0.027)	−0.002 (−0.177)	−0.004 (−0.389)	−0.007 (−0.624)
lnRGDP	0.065 ** (2.281)	0.042 (1.473)	0.027 (1.001)	0.029 (1.112)
lnTRANS	−0.008 (−0.504)	−0.001 (−0.067)	−0.164 (−1.072)	−0.020 (−1.367)
ENV	0.573 (0.751)	1.267 (1.644)	0.152 (0.190)	0.435 (0.539)
$\mathrm{W}\times \mathrm{AIA}$	0.267 *** (7.250)	0.694 *** (6.473)
$\mathrm{W}\times {\mathrm{AIA}}^2$	−0.018 *** (−7.112)	−0.050 *** (−7.068)
$\mathrm{W}\times \mathrm{INC}$	0.007 (0.291)	−0.108 (−1.473)
$\mathrm{W}\times \mathrm{IND}$	−0.013 (−0.086)	0.834 * (1.757)
$\mathrm{W}\times \mathrm{EDU}$	0.016 (0.691)	−0.225 *** (−2.865)
$\mathrm{W}\times \mathrm{lnRGDP}$	0.082 (1.560)	0.331 ** (2.191)
$\mathrm{W}\times \mathrm{lnTRANS}$	−0.029 (−0.775)	−0.518 *** (−4.193)
$\mathrm{W}\times \mathrm{ENV}$	4.717 *** (2.698)	23.225 *** (4.066)
$\rho$/$\lambda$	0.117 ** (2.261)	−0.356 ** (−2.536)	0.130 ** (2.482)	−0.027 (−0.217)
Regional control effect	Yes	Yes	Yes	Yes
Time control effect	Yes	Yes	Yes	Yes
R-squared	0.396	0.415	0.403	0.366
log-likelihood	1033.993	1043.418	1038.715	1021.538

Note: *** $p\le 0.01$, ** $p\le 0.05$, * $p\le 0.10$.

.

Columns (1–3) are the estimated results of replacing the core explanatory variable. The level of AIA in a province is expressed as the ratio of the total primary industry output value of the province to the national total primary industry output value divided by the ratio of the GDP of that province to the national GDP. Columns (4–5) show the estimated results of the replacement of the spatial model. The SEM model is conducted as a robustness test.

In Table 7, it can be seen that the, main variables are consistent with the aforementioned benchmark regression results. There is an inverted U-shaped relationship between AIA and AEE, which is basically consistent with the previous ones. That is, the impact of changing the calculation method of AIA and replacing the spatial model is not obvious, suggesting the robustness of the regression results.

5. Discussion and Conclusions

5.1. Conclusions

Agricultural GHG emissions’ reduction potential is huge. Furthermore, agriculture plays a key role in balancing food security while also contributing to the achievement of the carbon peak and carbon neutrality strategy. Meanwhile, AIA, as a key factor acting on the spatial distribution pattern of natural resource allocation, is an inevitable trend in the process of urbanization. In this paper, industrial agglomeration and environmental efficiency are incorporated into the theoretical framework, then we estimate AEE in China using the panel stochastic frontier analysis of the hyperbolic distance function. On this basis, we use the spatial econometric model to empirically verify the impact of AIA on AEE and its spatial spillover effect.

The main conclusions drawn from the paper are as follows. First, the average value of AEE in China is 0.909, which indicates that China has great potential in agricultural carbon sequestration and emission reduction. In addition, AEE varies between provinces; Liaoning, Hunan, and Sichuan show the best environmental efficiency performance, whereas Inner Mongolia, Tibet, and Qinghai are in the bottom three. The overall distribution presents higher AEE in major grain-producing areas and lower in non-major food-producing areas. Second, AEE presents a significant and positive spatial correlation, and there is a trend of further strengthening over time. Model regression results show that the impact of AIA on local AEE indicate an inverted U-shaped relationship. Most provinces in China are at the stage where AIA can promote AEE. Third, by calculating the average direct effect and average indirect effect of industrial agglomeration, we find that AIA has a significant spillover effect on AEE due to the effects of external economies of scale and scope, with an inverted U-shaped effect on neighboring areas.

In conclusion, AIA has a nonlinear effect on AEE, i.e., an inverted U-shaped correlation. Industrial agglomeration as a spatial organization form has its own “life cycle” (Wang et al., 2023 [35]). In the initial stage, expanding the scale of AIA is conducive to labor specialization, cooperation among enterprises, and economies of scale. However, with the further expansion of industrial agglomeration, excessive competition and congestion impact do not contribute to the sustainable development of agriculture. The results are consistent with some scholars’ studies, such as Zhang et al., 2022 [58], and Luo et al., 2023 [59], who all found that there exists an inverted U-shaped relationship between agricultural industrial agglomeration and sustainable agricultural development. However, they ignored the possible spatial spillover effects of AEE in the geographic area. In this study, we emphasize that agricultural green development is spatially connected and dependent. Our findings indicate that AEE has spatial agglomeration characteristics and there exists spatial spillover effects of AIA on AEE. This is a new finding compared to previous studies. The research results have practical significance. Reasonably adjusting the level of industrial agglomeration can help promote the sustainable development of agriculture and maximize the benefits of industrial agglomeration. In addition, the spatial spillover effect of AIA on AEE is thought-provoking. The results of this paper enrich the research on the externality of industrial agglomeration to a certain extent.

5.2. Policy Recommendations

On the basis of the findings, the following policy implications are proposed.

First, it is necessary to promote green technologies in order to establish an environmentally sustainable and resilient agricultural system. Innovative and green technologies play a key role in sustainably increasing resource utilization while reducing greenhouse gas emissions and ensuring food security. Measures should be taken to minimize agricultural chemical inputs and establish standardized systems for their sustainable and circular management. Additionally, the utilization of alternative fuels such as biomass, wind, biogas, and solar power should be encouraged to reduce carbon intensity and slow down environmental deterioration.

Second, under the framework of agricultural sustainable development, the government should accurately grasp the process of industrial agglomeration. For areas whose AIA is relatively low, the government should incentivize the integration of agricultural resources and strategic industrial distribution planning in order to achieve economies of scale in agricultural management. For areas with relatively high levels of AIA, they should not only pursue large-scale concentration, but also pay attention to the specialized division of labor and collaborative agglomeration, facilitate the extension of sustainable and inclusive value chains, and promote the diversification and integration of agricultural systems. At the same time, the government should actively promote the spatial transfer of agricultural industries with high industrial agglomeration, and improve the basic conditions of industrial agglomeration by improving transportation and other infrastructure to enhance the regional environmental carrying capacity.

Third, the results of this study demonstrate that the spatial spillover effect of AIA on AEE is significant. This finding highlights the importance of enhancing inter-regional connectivity to mitigate the negative impacts of AIA on AEE. Therefore, it is crucial for all levels of government to foster regional cooperation and coordination, in order to advance sustainable agricultural practices across different regions. In terms of their local agroecological conditions and advantages, each region should carefully design the layout of the agricultural industry and define a clear pathway for the sustainable utilization of natural resources and emissions’ reduction. Furthermore, in order to strengthen inter-regional linkages and promote sustainable agricultural practices, policymakers should implement policies that develop inter-regional networks, collaborative policy frameworks, and knowledge-sharing platforms.

5.3. Limitations and Prospects of the Study

Despite these important findings and policy implications, this paper still has several limitations. Owing to the availability of data, our results show that industrial agglomeration has an inverted U-shaped effect on agricultural environmental efficiency at the provincial level, but the effect at the municipal level remains to be further investigated. Furthermore, this study focuses on the negative impact of carbon emissions resulting from agricultural production. Future research could consider incorporating both agricultural carbon emissions and nonpoint source pollution into the evaluation of the negative outputs of agricultural production.