Spatio-Temporal Differentiation and Impediments to Agricultural and Rural Modernization Under Regional Coordination: Based on Three Major Economic Circles in Shandong Province (区域协调下农业农村现代化的时空分异与障碍因素:基于山东省三大经济圈)

1. Introduction

Modernizing agriculture and rural areas is central to the broader advancement and quality of Chinese modernization. As the principal aim of the rural revitalization strategy, its development trajectory has long shown pronounced spatial non-equilibrium characteristics [1]. In response, the central “No. 1 Document” of 2026 proposed to “promote rural revitalization in an orderly and zoned manner by category”, providing top-level design and strategic planning for the coordinated regional development of agricultural and rural modernization. Existing research indicates that, since the implementation of China’s regional development strategy, regional disparities in agricultural and rural modernization have narrowed; however, regional development remains unbalanced and inadequate [2]. Under the regional coordinated development strategy, promoting synchronized regional advancement in agricultural and rural modernization—and shifting from isolated, point-like initiatives to zonal, integrated planning—is crucial for steadily advancing comprehensive rural revitalization [3,4]. The “Comprehensive Rural Revitalization Plan (2024–2027)” issued by the Central Committee of the Communist Party of China and the State Council in 2025 calls for coordinating different regions and defining phased key tasks and their implementation sequence. Promoting coordinated regional development of agricultural and rural modernization is therefore essential: it improves resource allocation efficiency, addresses shortfalls in agricultural and rural sectors, and is the only viable path to steady, comprehensive rural revitalization.

Constructing a scientific evaluation index system is a prerequisite for accurately measuring and comprehensively analyzing the development level of regional agricultural and rural modernization. Existing studies typically treat agricultural and rural modernization as an integrated whole, in which agricultural modernization and rural modernization are coupled, coexist and interact in a coordinated manner [5,6]. Some researchers, however, classified agricultural modernization as an industrial category and constructed its indicator system around goals such as ensuring the effective supply of key agricultural products and promoting the upgrading and sustainable development of the agricultural industrial structure [7]. By contrast, rural modernization is framed at the regional level and assessed through dimensions such as rural economic development, cultural construction, living environment, infrastructure and governance capacity [8]. Agricultural modernization primarily addressed rural productive forces, whereas rural modernization concerned rural production relations. The dialectic between these forces and relations therefore implied that agricultural modernization was the foundation and prerequisite for rural modernization, while rural modernization provided support and backing for agricultural modernization [9]. As the literature has deepened, some scholars have added a third dimension—farmers’ modernization—to indicator systems, incorporating measures of farmers’ income, consumption and urban–rural disparities [10,11].

Clarifying regional development disparities and identifying their driving factors are key to reducing imbalances in the regional modernization of agriculture and rural areas. Most existing studies of regional differences began at the national level or focused on a single province. They divided areas with similar geographical characteristics and then used spatial models such as SAR, SEM, and SDM to examine the spatial spillover effects of agricultural and rural modernization in each region [12,13,14]. Some studies have shown that areas with advanced agricultural and rural modernization and those with high economic development are spatially coupled to some extent. Moreover, coordinated regional development has been able to raise the modernization level of agriculture and rural areas in less-developed regions [15,16]. However, economic connectivity and governance coordination, the two pillars of regional coordinated development [17], struggle to fulfill their roles because of constraints imposed by administrative divisions and geographical boundaries. Research into the factors influencing agricultural and rural modernization has principally been conducted along two lines of enquiry: internal constraints and external drivers. Concerning internal constraints, scholars have predominantly employed the obstacle degree model; by measuring indices such as factor contribution, index deviation and obstacle degree, they have identified the primary barriers to agricultural and rural modernization across different regions [18,19,20]. Concerning external drivers, studies have concentrated on three domains—fiscal input, human capital and digital technology—and have used bidirectional fixed-effects and mediating-effect models to elucidate how these drivers have acted on the modernization of agriculture and rural areas [21,22].

Existing research has laid a solid theoretical foundation for this paper. However, most of the current studies on the modernization development level of agriculture and rural areas in Shandong have focused on the provincial scale or a single city [23,24]. In 2020, Shandong explicitly proposed implementing a regional development strategy centered on three major economic circles of the Provincial Capital, Jiaodong, and Lunan, which is an important institutional measure to promote coordinated development across the province. As a new spatial form of urbanization, the economic circle has been proven to promote regional coordinated development and urban–rural integration [25]. Its collaborative principle of dismantling administrative barriers and integrating regional resources plays a vital supporting role in the coordinated development of agricultural and rural modernization in Shandong, and provides a crucial spatial scale for regions to assess their development positioning. However, most studies of agricultural and rural modernization analyzed development levels and spatio-temporal evolution at the national or provincial scale. Few examined horizontal comparisons of regional spatial correlations, the sources of structural differences, or the hindering factors. To fill this gap, this paper selected the three major economic circles in Shandong Province as the spatial unit and adopted a horizontal perspective. We applied the GMI and LMI statistics, the Dagum coefficient, and an obstacle degree model to conduct multidimensional comparative analyses of spatial correlation effects, the structure of regional differences, and obstacle factors. The study aimed to provide theoretical support and policy guidance for promoting coordinated agricultural and rural modernization across Shandong’s three economic circles.

2. Methodology and Index Selection

2.1. Model Construction

2.1.1. Multi-Index Comprehensive Measurement

This study adopted the Critic weight analysis method to assign weights to the indicators, quantifying the contribution of the indicators to the evaluation system and avoiding the bias of subjective weighting. The scores of the modernization development levels of agriculture and rural areas in Shandong, the three major economic circles and 16 prefecture-level cities were obtained by using the multiple linear weighting method.

The formula for calculating the score of the STH element is:

$$
Q_{s} = \sum_{j = 1}^{m} X_{ij}^{'} \times w_{j}
$$

(1)

In this specification,

$X_{ij}^{'}$
denotes the value of the original data after standardization by the extreme value method,

$w_{j}$
is the weight of the corresponding indicator,

$Q_{s}$
is the comprehensive score of the STH element, and m is the total number of indicators covered by this element. The formula for the total score (G) of the modernization level of agriculture and rural areas is:

$$
G = \sum_{s = 1}^{3} Q_{s}
$$

(2)

2.1.2. GMI and LMI

To analyze the spatial dependence or differences in the modernization levels of agriculture and rural areas among neighboring cities, this study calculated the global and local autocorrelation degrees through the GMI and the LMI.

To reveal the local spatial agglomeration pattern, the distribution of abnormal states, and their significance, this study further combined the Moran scatter plot with the LISA value. The calculation formulas for GMI and LMI are respectively:

$$
G M I = \frac{\sum_{i = 1}^{n} \sum_{j \neq 1}^{n} \left[W_{i j} \left(X_{i} - \bar{X}\right) \left(X_{i} - \bar{X}\right)\right]}{S^{2} \times \sum_{i = 1}^{n} \sum_{j \neq 1}^{n} W_{i j}}
$$

(3)

$$
L M I = \frac{X_{i} - \bar{X}}{S^{2}} \sum_{j = 1}^{n} \left[W_{i j} \left(W_{i j} - \bar{X}\right)\right]
$$

(4)

In the above formula, n represents the total number of spatial units,

$X_{i}$
and

$X_{j}$
are respectively the comprehensive evaluation values of the modernization development level of agriculture and rural areas of units,

$\bar{X}$
is the average evaluation value of all units,

$S^{2}$
is their variance, and

$W_{i j}$
is the spatial weight. When calculating GMI and LMI, the Queen adjacency weight is adopted as the spatial weight to give the significance level. When GMI is positive and approaches 1, the degree of agglomeration is higher. LMI > 0 indicates high-level or low-level city agglomeration, which is represented in the first quadrant (HH) and the third quadrant (LL) in the Moran scatter plot. When GMI is negative and approaches −1, the global variance is higher. LMI < 0 indicates that high levels are surrounded by low-level cities or low levels are surrounded by high-level cities, which are respectively in the 4th quadrant (HL) and the 2nd quadrant (LH) in the Moran scatter plot. If GMI = 0, it indicates that there is no spatial correlation; that is, there is no regular distribution.

This study conducted tests using standardized Z-values to determine a certain significant level of GMI. The calculation formula is as follows:

$$
Z = \left[I - E \left(I\right)\right] / V a r \left(I\right)
$$

(5)

In the above formula, I represents GMI, E(I) and Var(I) respectively represent its mathematical expectation and variance. A significant Z value indicates the occurrence of significant clustering, while a negative Z value indicates the absence of significant clustering.

2.1.3. Dagum Coefficient

Most existing studies used the Theil index, Herfindahl index and Dagum coefficient to explore regional differences. However, the first two cannot reflect the overlapping parts of differences between and within groups. Therefore, this paper used the Dagum coefficient to measure and decompose the differences in the modernization development levels of agriculture and rural areas within and between the three major economic circles in order to explore the sources of the differences. The overall difference was decomposed into three parts: intra-circle difference, inter-circle difference and hypervariable density. The measurement formula of the overall coefficient is:

$$
G = \frac{1}{2 n^{2} u} \sum_{j = 1}^{k} \sum_{h = 1}^{k} \sum_{i = 1}^{n_{j}} \sum_{r = 1}^{n_{k}} \left|y_{i j} - y_{h r}\right|
$$

(6)

In the formula above, k denotes the quantity of regional groups, specifically the three primary economic circles; n signifies the total spatial units;

$n_{j}$
and

$n_{h}$
denote the spatial unit quantities in the JTH and HTH economic circles correspondingly.

$y_{i j}$
and

$y_{h r}$
respectively stand for the overall scores of the agricultural and rural modernization level of the i-th prefecture-level city in the JTH economic circle and the RTH prefecture-level city in the h-th economic circle. u represents the mean comprehensive score of the agricultural and rural modernization level across all prefecture-level cities.

2.1.4. The Obstacle Degree Model

The obstacle degree model calculates the obstacle degree for each evaluation index, identifying and analyzing the primary obstacle factors. The model is structured as follows:

$$
O_{i j} = \frac{\left(1 - x_{i j}\right) w_{j}}{\sum_{j}^{n} \left(1 - x_{i j}\right) w_{j}}
$$

(7)

$$
O_{i r} = \sum_{j = 1}^{q} O_{i r}
$$

(8)

where q denotes the number of indicators;

$1 - X_{i j}$
represents the indicator deviation, signifying the variance between the standardized value

$X_{i j}$
derived from the extreme value method for each indicator and its optimal goal.

$w_{j}$
signifies the indicator’s contribution degree.

$O_{i r}$
represents the final obstacle degree of the RTH element layer or criterion layer of the i-th evaluation object.

2.2. Index Selection

Drawing on existing studies [26,27] and aligned with the central objectives set out in the 2026 Central Document No. 1 to enhance agricultural production, raise farmers’ incomes and improve rural living standards, this study developed a framework with three core dimensions: agricultural modernization, rural modernization and farmers’ welfare. The assessment framework for agricultural and rural modernization comprised eight components and twenty-four specific indicators, detailed in Table 1, with indicators and their rationales given at each level.

Table 1. Indicator system for evaluating the level of agricultural and rural modernization.

To align with green agricultural production and water-saving irrigation goals, the evaluation indicators included fertilizer and pesticide application intensity, water consumption per 10,000 yuan of GDP, and the effective irrigation rate. To promote rural industrial integration, the indicators covered agricultural socialized services, the degree of agricultural product industrialization, geographical indication agricultural products, and adjustments to the rural industrial structure. For rural governance and urban–rural integration, the indicators comprised the level of urbanization, rural community governance, social security, and the equalization of urban–rural health and public services. To support harmonious villages and control soil erosion, the indicators included per capita park green space and a comprehensive soil erosion governance index. Finally, to optimize rural cultural services in line with the Rural Comprehensive Revitalization Plan (2024–2027), the indicators measured cultural and entertainment provision by cultural stations per 10,000 people.

2.3. Data Sources

Data were compiled from official sources, including statistical yearbooks, bulletins, and government websites for Shandong Province and its 16 prefecture-level cities. Because Laiwu City merged into Jinan City in 2019, Laiwu data for 2014–2018 were merged into Jinan’s records. Minor discrepancies and missing values were resolved by interpolation to maintain dataset continuity and reliability. The calculations reported in Table 2, Table 3 and Table 4 used the official statistical data cited above. To ensure scientific rigor and reliability, we standardized the original data. We applied the extreme-value method to resolve inconsistencies in dimensions, units, scales, and positive–negative attributes, thereby ensuring comparability within a unified framework. We conducted spatial analysis and mapping with ArcGIS 10.8 and decomposed regional differences using the Dagum coefficient method.

Table 2. Level of agricultural and rural modernization development in various cities of Shandong Province (2014–2023).

Table 3. Overall Moran index for the development level of agricultural and rural modernization in Shandong Province (2014–2023).

Table 4. Dagum coefficient and decomposition in Shandong Province (2014–2023).

3. Empirical Results

3.1. Spatio-Temporal Evolution Characteristics

After quantifying the contribution degree of indicators based on the Critic weight analysis method, the entropy method was used to test the robustness of the conclusions. The results are presented in Table 1. As shown in Table 2, agricultural and rural modernization in Shandong Province—spanning three major economic circles and 16 cities—from 2014 to 2023 has increased markedly. Indicator-weighted analysis showed an average annual growth rate of 18.50 co%. This rise reflected the strategic emphasis of the Rural Revitalization Strategy, whose coordinated implementation has driven sustained improvements and optimizations across multiple dimensions of modernization in Shandong Province.

As shown in Figure 1, the years 2014, 2017, 2020, and 2023 were selected as the observation years, and the natural breaks method in ArcGIS software was used to map the spatial distribution. The spatial distribution followed a clear southeast-to-northwest decline in development levels. High values clustered in Jiaodong and extended into the Lunan. Jiaodong recorded the highest level, 0.423, while Lunan registered 0.403. By contrast, Provincial Capital had the lowest level, 0.341.

Figure 1. Spatial distribution of agricultural and rural modernization levels in Shandong Province. Note: The natural breaks method in ArcGIS software was used to map the spatial distribution.

In terms of the change trend, the Provincial Capital circle recorded the highest average annual growth rate at 5.60%, followed by Lunan at 5.45% and Jiaodong at 4.34%. All three circles therefore displayed significant and persistent disparities in urba