Introduction

The global phenomenon of population aging, driven by increased life expectancy and declining birth rates (Sen and Nagaram 2024), represents one of the most significant social transformations of the 21st century (Jakovljevic et al. 2021; Magnus 2012). By 2050, the proportion of people aged 65 and older is expected to rise from 10% in 2022 to 16% (DESA 2022; Wang et al. 2020a, 2020b). This expanding elderly population has sharply escalated the demand for pensions, healthcare, and long-term care services (Norton 2016; Schulz et al. 2004), placing substantial strain on social, economic, and public health systems worldwide (Busse et al. 2011; Han et al. 2020; Li et al. 2024; Rechel et al. 2009). Aging not only impacts the labor market (Li et al. 2024) and alters family structures (Waite 2009) but also challenges social welfare systems (Kim 2003; Thang 2011) and highlights the urgent need for adaptability and innovation in public policies and social service systems (Beard and Bloom 2015). This challenge is particularly acute in developing countries, where there are limited capacities to meet the care needs of older people (Haldane et al. 2021; Rudnicka et al. 2020). Therefore, it necessitates a concerted effort by the international community to explore innovative policies and cooperative mechanisms to effectively address the challenges of aging.

As the world’s most populous developing country, China is experiencing a particularly rapid and multifaceted aging process. The demographic changes, including the increasing elderly dependency ratio (Han and Cheng 2020; Sang et al. 2024), and the uneven distribution of the older population between urban and rural regions (Qin et al. 2020), present distinct challenges to the country’s socio-economic development. These changes not only impact economic growth potential (Peng 2008) but also pose significant tests to public resource allocation and the social security system (Wang et al. 2010; Zhu and Walker 2019). Shifts in the population structure have heightened the need for eldercare services, leading both public and private sectors to seek more efficient and sustainable service models (Xu and Chow 2011). With social progress and changes in family structures, traditional familial eldercare models are being challenged, and there is increasing reliance on community services and professional institutions to meet the care needs of older people (Fang et al. 2020; Mao et al. 2020). Therefore, establishing an effective eldercare service system requires the collective effort of the government, society, and the market, with policy support, financial investment, and service innovation to meet the growing eldercare demands.

Currently, many scholars use different methods to explore medical and nursing resources. Du et al. (2021) used DEA to assess resources in over 30 eldercare institutions in China, noting that resource allocation still needs further optimization. Li et al. (2023) examined the spatiotemporal differences and adaptive development of resources in Chinese rural eldercare institutions from 2012 to 2021, pointing out that increasing government investment in resource allocation and optimizing these resources are key to improving the coverage and quality of eldercare services. Although the increase in the number of eldercare institutions has partially alleviated the demands of an aging society, the quality and standards of eldercare services vary significantly between institutions. There is currently a lack of a unified assessment system and service standards (Du et al. 2021), and further strengthening of policy and regulatory support is needed (Feng et al. 2020). These factors collectively impact the effectiveness and development of elderly care services (Fang et al. 2020; Feng et al. 2020; Li et al. 2023). Alternatively, challenges in eldercare institution resources include insufficient numbers of beds and facilities (Du et al. 2021; Feng et al. 2020), low levels of care (Feng et al. 2020), and funding shortages (Fang et al. 2020). Going forward, improving the coverage and quality of eldercare services, especially in resource-poor rural and economically underdeveloped areas, will be key. Fang et al. (2020) reported that public health financial protection for elderly in rural regions is particularly inadequate, and the issue of inequality in elderly public health remains a significant challenge. These disparities are primarily manifested in the speed of aging, the quality of life of older people, and the accessibility and quality of eldercare services (Dai et al. 2021; Gandy et al. 2023; Li et al. 2022). Meanwhile, urban areas generally have better facilities and higher-quality medical services (Liu et al. 2018), including specialized medical care, rehabilitation, and daily care (Shi et al. 2020). Rural areas, limited by economics, infrastructure, and professional talent, face shortages of resources and homogeneous services (Li et al. 2023). The spatiotemporal patterns of the coupling and coordination of eldercare service resources across China’s 31 provinces reveal notable disparities (Zhang et al. 2017), with significant inequality in the distribution of long-term care resources and access to medical services (Yang et al. 2023). For instance, Li et al. (2020) and Guo et al. (2020) revealed the uneven allocation of resources and unstable service quality in grassroots medical institutions, suggesting that policy support, financial investment, and talent development are needed to improve the quality of grassroots medical care and narrow the urban–rural gap. This unequal distribution of resources exacerbates the socio-economic disparities between urban and rural areas, severely affecting the welfare and quality of life of rural elderly, especially those living in remote and impoverished areas.

Discussing the inequality in elderly care resource allocation between urban and rural areas is crucial for Chinese public policy, especially in the context of elderly welfare and equitable resource distribution. Although existing research has analyzed the differences and resource allocations between urban and rural eldercare institutions to some extent, dynamic comparative studies are still lacking. This study delves into these inequalities and proposes mitigation strategies, aimed at helping policymakers improve elderly care services and quality of life. Different care models such as institutional care, community care, and home care show unique characteristics and needs in resource allocation, stemming from their respective social, economic, and policy environments. Currently, most research focuses on assessing the overall situation of eldercare resources, with less exploration from the perspective of institutional care. This study systematically combs through institutional eldercare resources, revealing the effectiveness and limitations of current configurations, providing key evidence for market regulation and policy-making for China’s silver economy.

This study focuses on the following key issues: (1) What are the specific patterns and trends in aging disparities between urban, rural, and different regions across China? (2) What inequalities exist in the resource allocation of eldercare institutions between urban and rural areas and different regions, and how have these issues evolved over time? (3) In response to the current inequalities in resource allocation and aging differences, how should public policy adjust to effectively mitigate these issues? For this purpose, the study collected resource data of urban and rural ECI from 2008 to 2021 and employed methods such as projection pursuit models, kernel density estimation, spatial autocorrelation, and Dagum Gini coefficient decomposition to conduct an in-depth comparative analysis of eldercare institution resources across China’s 31 provinces. By comparing the differences in eldercare resource distribution between different regions and urban and rural areas, this study reveals the imbalances in resource distribution and their changing patterns, assessing the potential impacts of these disparities on the welfare of older people, with the aim of providing a scientific basis for formulating more effective public policies.

Materials and methods

Data source

This research uses provincial panel data from China to evaluate the allocation of resources across urban and rural elderly care institutions (ECIs). Although China’s provinces are vast, this study opts for a provincial scale for analysis based primarily on the following considerations: first, data at the provincial administrative level are more complete and accessible, ensuring systematic continuity of the research; second, policy-making and resource allocation at the provincial level have significant influence in China’s practical operations, thus, research at this level can provide more practically valuable policy recommendations. Due to the partial absence of key data prior to 2008, there might be limitations in the comprehensiveness and depth of the research. Therefore, this study selects the period from 2008 to 2021 to ensure a comprehensive and systematic analysis. The aging data and elderly care resource allocation data utilized in this study are sourced from the “China Statistical Yearbook,” “China Civil Affairs Statistical Yearbook,” “China Rural Statistical Yearbook,” and “China Population and Employment Statistical Yearbook” for the years 2009–2022. Considering that “township” level units serve as a transition between rural and urban areas in China’s administrative divisions, this study does not categorize “township” data as either rural or urban to ensure scientific accuracy. The research includes not only data on ECI resources but also covers population (based on census data) and geographical area information. The analysis encompasses the seven main regions of mainland China and does not cover Hong Kong, Macau, and Taiwan, as shown in Fig. 1.

Fig. 1
figure 1

Geographic distribution map of China.

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Methodology

This study examines ECIs in urban and rural areas across 31 provinces of China from 2008 to 2021, employing methods such as projection pursuit models, kernel density estimation, spatial autocorrelation, and Dagum Gini coefficient decomposition to analyze the spatial equity of elderly care resources. In this context, “equity” refers to the fair distribution of resources across different regions and between urban and rural areas, while “inequality” highlights the imbalances and significant disparities in resource allocation.

  1. (1)

    The projection pursuit model is a statistical method for analyzing multidimensional data, which identifies the projection direction that best reveals the intrinsic structure of the data to evaluate and compare objects or situations within the dataset. This method is particularly suited for uncovering nonlinear relationships and complex patterns in data, effectively reducing the dimensionality of high-dimensional data for easier visualization and further analysis. Given its excellent performance in handling complex, nonlinear relationships, this model is especially suitable for revealing similar issues in the allocation of eldercare resources. In this study, the projection pursuit model is used in conjunction with an accelerated genetic algorithm to determine the weights of the resource allocation indicator system, thereby assessing the effectiveness of resource allocation in urban and rural eldercare institutions. This combined approach not only leverages the advantages of projection pursuit but also optimizes the weight determination process through the accelerated genetic algorithm, aiming for more precise assessment results.

  2. (2)

    Kernel density estimation, as an important non-parametric method, has become a popular method for studying uneven distributions. This method is primarily used for estimating the probability density of a random variable, describing the distribution shape of the random variable with a continuous density curve. Through this non-parametric approach, the shape of resource distribution can be more precisely depicted, thus identifying the concentrated or dispersed patterns of resource allocation in space, which aids in assessing the equitability of resource distribution. Suppose the random variable \(X\) has a probability density function \(f(x)\). The probability density at a given point \(x\) can be estimated using Eq. (1). In this equation, \(N\) represents the total number of observations, \(h\) is the bandwidth parameter, \(K(x)\) is the kernel function that serves as a weighting or smoothing function, \({X}_{i}\) are independent and identically distributed observations, and \(x\) denotes the mean value.

    $$f\left(x\right)=\frac{1}{Nh}\mathop{\sum}\limits_{i=1}^{N}K\left(\frac{{X}_{i}-x}{h}\right)$$
    (1)
    $$K\left(x\right)=\frac{1}{\sqrt{2\varPi }}\exp \left(-\frac{{x}^{2}}{2}\right)$$
    (2)
  3. (3)

    The Dagum Gini coefficient decomposition offers improvements over the traditional Gini coefficient. In this study, the decomposition of the Dagum Gini coefficient was used to analyze the overall disparities in ECI resources between urban and rural areas across seven major geographical regions of China. This includes examining intra- and inter-regional differences, transvariation density, and the contribution rate of each factor. By decomposing the total inequality into differences within regions, differences between regions, and transvariation density, we can gain a deeper understanding of the structure and sources of resource inequality, thereby providing a basis for formulating more equitable resource distribution policies.

    The Dagum Gini coefficient decomposition consists of three main parts: intra-regional differences \(({G}_{w})\), inter-regional differences \(({G}_{b})\), and transvariation density \(({G}_{t})\).

    Intra-regional differences \(({G}_{w})\) calculate the inequality of ECI resource allocation within each geographical region and quantify its contribution to the total inequality. The calculation formula is as follows:

    $${G}_{w}={\sum }_{i=1}^{n}\left(\frac{{Y}_{i}}{Y}\right){G}_{D,i}$$
    (3)

    Here, \(n\) represents the number of regions, \({Y}_{i}\) denotes the total resources in the \(i{\rm{th}}\) region, \(Y\) is the total nationwide resources, and \({G}_{D,i}\) refers to the Dagum Gini coefficient for the \(i{\rm{th}}\) region.

    Inter-regional differences \(({G}_{b})\) are based on the inequality of average resource allocation levels across regions, calculating their contribution to the total inequality. The formula is as follows:

    $${{{G}}}_{{{b}}}={\sum }_{i=1}^{n}\left(\frac{{Y}_{i}}{Y}\right)\left(\frac{{\bar{y}}_{i}}{\mu }-\frac{F\left({Y}_{i}\right)}{F\left(1\right)}\right)$$
    (4)

    where, \({\bar{y}}_{i}\) is the average resource level of the ith region, and F(Yi) is the cumulative distribution function up to the ith region.

    Transvariation density \(({G}_{t})\) reflects the contribution of extreme values to total inequality. This part is difficult to calculate separately directly from the Gini coefficient decomposition. It can be approached by excluding the effects of \({G}_{w}\) and \({G}_{b}\), and considering the remaining part as the impact of transvariation density.

    Therefore, the total decomposition of the Dagum Gini coefficient is represented as:

    $${G}_{D}={G}_{w}+{G}_{b}+{G}_{t}$$
    (5)
  4. (4)

    Global spatial autocorrelation analysis commonly relies on the Global Moran’s I index to evaluate the overall spatial relationship of observations within a geographic area. The Global Moran’s I index is used to quantify the degree of similarity between neighboring or spatially adjacent units, identifying patterns of clustering or dispersion in resource allocation across different regions. This method enables a detailed spatial analysis of inter-regional disparities in resource distribution. In this study, the index is applied to examine the spatial correlations and aggregation patterns of elderly care resources in urban and rural areas of China. Moran’s I index ranges from −1 to 1: positive values indicate spatial clustering, negative values reflect spatial dispersion, and a value of 0 suggests a random distribution. While global clustering analysis shows overall spatial correlation, it cannot precisely locate clustered areas. Even if the global results show no significant correlation, local areas may still be significantly correlated. Thus, combining global and local autocorrelation analyses can study spatial patterns more finely, often through hotspot analysis and Moran scatter plots.

  5. (5)

    The spatial Markov chain method integrates the concept of “spatial lag” into traditional Markov chain analysis, providing a more detailed understanding of how a region’s geographic context influences the evolution of resource allocation. By incorporating spatial lag into the Markov transition matrix, this study constructs a spatial Markov chain to more accurately predict changes in resource allocation within a spatial framework and to assess the dynamic evolution of resources in urban and rural ECIs. The statistical significance of the spatial lag effect is evaluated using the following formula:

$${Q}_{b}=-2\log \left\{\mathop{\prod}\limits_{l=1}^{k}\mathop{\prod}\limits_{i=1}^{k}\mathop{\prod}\limits_{j=1}^{k}{\left[\frac{{m}_{\text{ij}}}{{m}_{\text{ij}}\left(S\right)}\right]}^{{n}_{\text{ij}}\left(S\right)}\right\}$$
(6)

In this formula, \(k\) (set to 5) represents the number of resource allocation status types; \({m}_{\text{ij}}\) is the traditional Markov transition probability, while \({m}_{\text{ij}}\left(S\right)\) and \({n}_{\text{ij}}\left(S\right)\) denote the spatial Markov transition probability and the number of provinces, respectively, for regional background type \(S\). \({Q}_{b}\) follows a Chi-squared distribution with k(k − 1)2 degrees of freedom.

Index system

This study develops an evaluation framework for assessing the resource allocation and service capabilities of urban and rural ECIs, grounded in the Structure-Process-Outcome (SPO) theory (Ji and Jiang 2022; Li et al. 2022). According to the SPO theory, the evaluation system should comprehensively cover three key dimensions: the structural foundation of resources, the process of service execution, and the outcomes of service effectiveness, ensuring thorough and in-depth analysis.

Structural indicators such as the number of institutions, available beds, building area, and fixed assets represent the resource foundation of the institutions, highlighting the service capacity, spatial availability, and facility investment levels. These indicators are foundational in assessing the availability of elderly care services and the investment in infrastructure.

Process indicators include the total number of staff, the number of professional (assistant) social workers, and the proportion of staff with at least a junior college education. These indicators measure the quality and professionalism of human resources in service delivery, directly affecting the quality and efficiency of services.

Outcome indicators focus on assessing the effectiveness of services, including the number of extremely poor individuals, the number of self-paying individuals, and the number of entitled individuals such as veterans. These indicators demonstrate the scope of service coverage, economic accessibility, and social inclusiveness, reflecting the social impact and breadth of services.

By clearly aligning these indicators with the structural, process, and outcome dimensions, this evaluation system comprehensively reflects the performance of ECIs in resource allocation, service provision, and their effectiveness. This systematic evaluation framework not only enhances the scientific nature of the study but also provides a solid theoretical support and data foundation for formulating targeted policies.

Based on this, the study employs the Projection Pursuit Model to calculate weights, constructing a resource indicator system for urban and rural ECIs that encompasses 3 system levels, 6 element levels, and 10 indicators (Peng et al. 2024). This indicator system provides a precise quantitative framework for the study, enabling detailed analysis of the spatiotemporal evolution and regional differences in resource allocation of ECIs, ensuring the scientific reliability of the results. The specific calculation process is referenced from existing literature (Peng et al. 2024)\(.\)

Based on the calculation results of maximizing the projection objective function, compute the optimal projection direction, that is, where the objective function is maximized, with the specific constraint condition formula:

$$\mathop{\sum}\limits_{j=1}^{q}{n}^{2}\left(j=1\right)$$
(7)

The optimization of the projection function is essentially a nonlinear optimization problem with variables (n(j)|j = 1, 2, …, q), using an accelerated genetic algorithm to optimize and solve for its maximum value. Referencing existing research (Cheng et al. 2019; Yang 2014), the parameter settings are: initial size 400, crossover probability 0.80, acceleration times 20. The evaluation index system is constructed based on the average value of the optimal projection direction (i.e., weights) \({n}^{* }\) for the allocation of resources in urban and rural ECIs, as shown in Table 1.

Table 1 Evaluation system of urban and rural ECIs.
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Research analysis and results

Spatial-temporal evolution characteristics of urban and rural ECIs

According to international standards, a country or region is considered to have entered an aging society when individuals aged 65 and over account for 7% or more of the total population. An aging degree between 7% and 14% indicates a mild stage of aging, 14%–20% indicates a moderate stage, and over 20% indicates severe aging (DESA 1956). Figure 2 clearly shows the spatial distribution differences of urban and rural aging in China’s provinces from 2012 to 2021. During this period, the aging situation in urban areas was generally at a mild stage, while the degree of aging in rural areas progressed from mild to severe, displaying an obvious spatial characteristic of “high in the east, low in the west.”

Fig. 2
figure 2

Aging degree of urban and rural areas in 2008, 2015, and 2021.

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Figure 3, employing the kernel density estimation method, provides a detailed analysis of the distribution, status, and expansion of ECI resources in 2008, 2011, 2015, 2018, and 2021, uncovering the spatial patterns and dynamic changes in resource allocation between urban and rural ECIs.

Fig. 3
figure 3

Kernel density estimation of urban and rural elderly care institution resources.

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For further analysis, this study, taking the years 2008, 2015, and 2021 as key nodes, uses the natural breaks method in ArcGIS to conduct a mapping analysis of the distribution level of urban and rural ECI resources. Based on the assessment scores of elderly care resources in different regions, the resource levels are divided into five categories: low level (0–0.049), relatively low level (0.050–0.125), medium level (0.126–0.232), relatively high level (0.233–0.349), and high level (0.350–0.815). Figure 4 shows that, compared to urban areas, the fluctuations in the allocation of resources in rural ECIs are more intense and concentrated, reflecting the instability of elderly care resource allocation levels in rural areas. “Instability” refers to the significant fluctuations in rural elderly care resource levels at different time points, characterized by rapid changes or large swings in resource allocation. This phenomenon is often caused by insufficient economic support, frequent policy changes, or uneven regional development. Meanwhile, the center of the kernel density estimate for urban elderly care resource allocation continues to shift to the right, indicating a continuous improvement in the level of urban elderly care resources.

Fig. 4
figure 4

Resource allocation levels of urban and rural elderly care institutions.

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The comparative analysis of Figs. 3 and 4 reveals that fluctuations in resource allocation are greater in rural areas than in urban ones, and are also more concentrated. This suggests that the distribution of ECI resources across provinces is relatively more balanced in rural regions. Over time, the kernel density estimate for rural elderly care resource allocation shows a pattern of initial increase, followed by a decline, and then a gradual rise again, indicating fluctuations in rural elderly care resource levels. In contrast, the kernel density estimate for urban elderly care resources consistently shifts to the right, illustrating a steady improvement in the allocation of urban elderly care resources. Further analysis reveals that the allocation of elderly care resources in rural China follows a distinct pattern, with an initial rise in concentration followed by a subsequent decline. This suggests that the distribution of rural elderly care resources first becomes more centralized before later dispersing again. In contrast, the main peak of urban elderly care resource allocation exhibits a downward trend, suggesting a growing dispersion in urban resource allocation. From 2008 to 2021, the overall level of resource allocation in urban ECIs improved significantly. However, an analysis of the kernel density curve’s spread reveals that the absolute distance between the two ends of the curve has generally increased, suggesting that the gap between urban areas with high and low resource allocation levels has widened over time. This indicates that despite the overall improvement in urban elderly care resources, certain regions remain underdeveloped. Notably, urban elderly care resource allocation in Tibet is significantly below the national average, even as other urban areas have advanced.

The decomposition of space difference of urban and rural ECIs

To gain a deeper insight into the inequality in the distribution of resources in urban and rural ECIs in China and how it has evolved, a detailed analysis of the Dagum Gini coefficient decomposition is essential. This analysis will help identify the main drivers of inequality in resource allocation and offer strategies to reduce both urban–rural and regional disparities.

The decomposition of the overall difference of urban and rural ECIs

The analysis indicates that before 2015, the distribution of rural elderly care resources was relatively equitable, with a Gini coefficient lower than that of urban areas. However, starting from 2015, this trend reversed, with the Gini coefficient of rural ECIs surpassing that of urban areas, indicating a decline in the equity of rural resource distribution and significant improvements in cities. This change reflects the dynamic variation in the difference in resource allocation between urban and rural ECIs, pointing to a regression in resource distribution equity in rural areas and improvements in urban areas.

The disparities in resource allocation between urban and rural ECIs can be divided into three main components: intra-group contribution, inter-group net contribution, and inter-group transvariation density. Figure 5 displays the absolute values and relative proportions of these components. Notably, the figure highlights that inter-regional disparities are the dominant factor driving the observed differences.

Fig. 5
figure 5

The decomposition of the overall difference.

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The low share of inter-group transvariation density indicates that overlaps among samples contribute minimally to the differences, showing that the regional division effectively distinguishes between types of cities with strong rationality. The values show that initially, the transvariation density in urban areas was generally higher than in rural areas, but in later periods, it was lower than in rural areas.

Intra-regional differences of urban and rural ECIs

Next, calculate the Dagum Gini coefficient for each geographical region to reflect the degree of internal inequality. Figure 6a represents the values of differences within rural areas, Fig. 6b shows the values of differences within urban areas, and Fig. 6c displays the differences between rural and urban values along with the annual trends in change.

Fig. 6: Intra-regional differences of urban and rural elderly care institutions.
figure 6

a Values of differences within rural areas. b Values of differences within urban areas. c Differences between rural and urban values along with the annual trends in change.

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Further analysis reveals the trends in Gini coefficients for rural and urban ECIs. Figure 6a, b shows that inequality in rural ECIs exhibits an upward fluctuation, while in urban areas, the inequality fluctuates downward, suggesting a more equitable distribution of resources in cities. In the northwest region, the Gini coefficients for ECIs reach as high as 0.31 and 0.27, respectively, reflecting the highest levels of inequality across all regions, affecting both rural and urban areas. Long-term observation from 2008 to 2021 indicates a decrease in inequality in the eastern and central regions, while rural ECIs in North China, Northeast, South China, and Northwest regions experience an overall increase in inequality. Conversely, inequality in urban areas shows a decreasing trend, highlighting the widening resource gap between urban and rural areas (Table 2).

Table 2 Total differences of urban and rural ECIs.
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The trend of the difference in Gini coefficients between urban and rural areas, as shown in Fig. 6c, further clarifies this viewpoint. The curve is in a horizontal “S” shape, with the period between 2014 and 2015 acting as a symmetrical dividing point. Before 2014, the difference in the distribution of elderly care resources between urban and rural areas across the seven major regions was small, with the difference in Gini coefficients usually being less than zero. From 2015 onwards, the difference turned positive and reached a peak in 2017 before stabilizing. This trend change highlights the changes in the degree of inequality in the distribution of elderly care resources between urban and rural areas over the past few years, especially the significant widening of the gap between 2014 and 2015.

Inter-regional differences of urban and rural ECIs

The inter-regional Dagum Gini coefficient reflects the level of inequality in ECI resources across different regions. Figure 7a presents the variations in Gini coefficients between regions in China, while Fig. 7b highlights the disparities between rural and urban areas.

Fig. 7: Inter-regional differences of urban and rural elderly care institutions.
figure 7

a Variations in Gini coefficients between regions in China. b Disparities between rural and urban areas.

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In rural areas, the inter-regional Gini coefficient fluctuated from 0.15–0.44 to 0.12–0.68, indicating an increase in inequality of ECI resources. In contrast, the inter-regional Gini coefficient in urban areas decreased from 0.30–0.76 to 0.09–0.27, indicating a reduction in resource disparity.

From a geographical distribution perspective, the Qinling–Huaihe Line serves as a boundary, presenting different characteristics in resource disparity between the northern and southern regions. The southern regions, particularly the eastern, central, and southern areas, exhibit relatively smaller differences in ECI resources, while the northern regions, especially between the north, northwest, and northeast, show more significant disparities. In terms of temporal trends, data from 2008 to 2021 indicate that the inter-regional Gini coefficient differences between urban and rural ECIs show an overall increasing trend. Particularly during the period from 2014 to 2015, the intersection of the change curve and the coordinate axis suggests that the differences are increasing, implying that the disparity in ECI resources between urban and rural areas may further widen in the future.

Spatial correlation analysis of urban and rural ECIs

This study intends to further explore the spatial characteristics and clustering effects of different regions using spatial cluster analysis, that is, the spatial layout of ECI resource allocation across provincial areas.

Global autocorrelation of urban and rural ECIs

Table 3 presents the global Moran’s I index for the spatial compatibility between ECI resources and aging in both urban and rural areas from 2008 to 2021. As shown in the table, the global Moran’s I index is positive and significant for rural areas in the years 2008, 2009, 2013, 2014, 2015, 2020, and 2021, and for urban areas in 2011, 2012, 2016, 2017, and 2020. When the index for urban–rural areas is negative, the results are not significant. In several years, Z values exceed 1.96 and P values fall below 0.1, indicating that the results pass significance testing. These findings suggest that in recent years, the spatial compatibility of neighboring regions shows significant spatial autocorrelation, with a general clustering trend.

Table 3 Global Moran’s I index of rural and urban institutional elder care in 2012–2021.
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Local autocorrelation of urban and rural ECIs

Hotspot analysis was employed to detect the evolution of local hotspot areas and assess the contribution of different spatial units to global autocorrelation, as illustrated in Fig. 8. From 2008 to 2021, the hotspot areas for rural ECI resources transitioned from North China to the Tibetan Plateau, while cold spot areas moved from South China to North China. The hotspot areas for urban ECI resources initially shifted from the Southwest to North China, then to the Yellow River Basin. Meanwhile, starting from 2015, the cold spot areas centered around South China for urban elderly care resources gradually disappeared.

Fig. 8
figure 8

Hot and cold spots of urban and rural elderly care institutions.

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Moran’s scatter plot analysis is a two-dimensional visual representation of the correlation between variable z and Wz, with all variable observations’ standard deviations (Z) on the horizontal axis and all values of the spatial lag vector (Wz) on the vertical axis, with (z, Wz) as the coordinate points. As depicted in Fig. 9, the rural Moran’s scatter plot shows that the provinces within each quadrant are fairly dispersed. In the urban Moran’s scatter plot, the points of the provinces in 2008 are mainly concentrated in the third quadrant (L-L), and in 2021, the points of the provinces are mainly concentrated in the first quadrant (H-H). Over time, surrounding provinces such as Shanxi, Inner Mongolia, Heilongjiang, and Henan transitioned from the third quadrant to the first quadrant, indicating that the allocation of resources in urban ECIs in surrounding provinces is becoming more concentrated and developed. The radiation effect of high-level urban areas on the surrounding areas is evident, driving the joint improvement of urban elderly care resources. Comparing the Moran’s scatter plots of urban and rural ECIs in 2021, provinces like Hebei, Jilin, Tibet, and Shanghai correspond along the diagonal. This suggests a certain siphoning effect of resources such as labor, capital, infrastructure, etc., between urban and rural ECIs within the province.

Fig. 9
figure 9

Moran scatter scatter plot of urban and rural elderly care institutions.

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Markov chain of urban and rural ECIs

Based on the principles of Markov chains, the annual changes in resource allocation levels for urban and rural ECIs from 2008 to 2021 were tracked and analyzed. By applying the previous classifications of “high,” “relatively high,” “medium,” “relatively low,” and “low” based on the natural breaks method, a traditional Markov transition probability matrix was generated. The probabilities shown on the diagonal represent the likelihood of a province maintaining its current level of resource allocation, while the probabilities outside the diagonal represent the likelihood of transitioning to the corresponding level.

As shown in Table 4, the stability of resource allocation levels in ECIs across China is relatively weak, with generally low probabilities of maintaining the current state in the Markov transition probability matrix. Notably, in the matrix for urban elderly care resource allocation, the probabilities at the high end of the diagonal are significantly greater than those below the diagonal, except for the diagonal probabilities themselves, which are lower than those below the diagonal. Additionally, the probabilities at the extremes of the diagonal are generally higher than those in the middle, indicating the potential for a “club effect.” Furthermore, rural hotspot areas exhibit higher stability compared to urban areas.

Table 4 Traditional Markov chain matrix.
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From the perspective of transition paths, the initial level of resource allocation in provinces plays a significant role in guiding future development paths. In rural ECIs, provinces with lower levels of resource allocation are least affected by path dependency effects. Moreover, these states are most prone to transformation, with probabilities of transitioning upwards (to higher levels of allocation) and downwards (to lower levels of allocation) being 16% and 38%, respectively. Provinces with a medium level of allocation have a 22% probability of transitioning upwards and a 22% probability of transitioning downwards. Provinces with higher levels of allocation have a 27% probability of transitioning upwards and an 18% probability of transitioning downwards. Provinces with lower levels of allocation have a 37% probability of transitioning downwards. Provinces with high levels of allocation have a transition probability of 44%. In urban ECIs, provinces with lower levels of allocation are least affected by path dependency effects, thus are most likely to transition, with upward and downward transition probabilities of 16% and 53%, respectively. Provinces with a medium level of allocation have a 10% probability of transitioning upwards and a 53% probability of transitioning downwards. Provinces with higher levels of allocation have a 27% probability of transitioning upwards and a 38% probability of transitioning downwards. Provinces with low levels of allocation have a 60% probability of transitioning downwards. Provinces with high levels of allocation have a transition probability of 7%. This indicates that the possibility of transitioning downwards is higher in urban ECIs than in rural areas. Furthermore, in the Markov transition probability matrix, provinces with lower levels of ECI resources are least affected by path dependency effects and are more likely to improve.

This study used the formula to verify whether the spatial lag effect has statistical significance. The results show that the transition types of resource allocation in urban and rural ECIs in China have spatial independence (\({Q}_{b}\) (rural) = 101.29, P value (rural) = 0.054, df (rural) = 80; \({Q}_{b}\)(urban) = 102.37, P value (urban) = 0.047, df (rural) = 80 (Wang et al. 2020a, 2020b).

Therefore, we opted for a spatial Markov transition probability matrix with spatial lag conditions to further explore the impact of spatial relationships on spatial effect characteristics. Table 5 is a spatial Markov transition probability matrix with regional background as the spatial lag condition, fully considering local autocorrelation factors.

Table 5 Spatial Markov chain matrix.
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In rural areas, the high–high clustering of resource allocation indicates that resources tend to remain at a higher level or further improve, especially with a probability of 0.63 for resource allocation to shift to a higher level, reflecting a positive cycle of resource optimization and development. Conversely, high–low and low–high clusters show that resource allocation may undergo significant changes, highlighting the direct impact of neighboring area development on resource allocation. Urban areas also show this trend, with a probability of 0.92 for resource allocation in high–high clusters to shift to a higher level, reflecting the clustering effect and optimization potential of resource allocation in urbanization. Moreover, the evolution of resource allocation shows a spatial spillover effect, where the resource changes in one area may be influenced by changes in neighboring areas. The differences in transition probabilities between different areas underscore the uneven development between regions and the potential for cross-grade changes in resource allocation in the short term.

Discussion

Result discussion

This study utilized a range of spatial analysis techniques to investigate the evolution of resource allocation in urban and rural ECIs in China between 2008 and 2021. The following in-depth analyses were derived from this exploration:

  1. (1)

    From 2008 to 2021, the degree of aging in urban and rural China has significantly intensified, with notable spatial differences. Overall, the aging characteristics of China’s population show that the eastern regions are older than the western ones, and rural areas significantly surpass urban areas in terms of aging. Rural aging is particularly severe in Sichuan, Chongqing, and the Huadong region, which is directly related to the migration of young people to more developed cities from these areas. Meanwhile, the significance of urban aging in the Northeast is closely related to the economic slowdown and the outflow of the young population in that area. The geographical mobility of the workforce not only changes the population structure but also exacerbates the imbalance in socio-economic development and the demand for elderly care resources across different regions. In reallocating elderly care resources, the government must consider regional disparities in population aging alongside evolving patterns of labor mobility. Addressing the challenges of an aging population requires enhancing the elderly care service system, increasing investment in rural elderly care resources, and optimizing social welfare policies for older adults. These measures can help promote a more balanced distribution of elderly care resources between urban and rural areas as well as across different regions.

  2. (2)

    The resource allocation index of urban ECIs in China has increased year by year. Although initially not as high as rural ECIs, it has since surpassed them. This reflects the national emphasis on improving the urban elderly care service system and the natural result of resource concentration in the urbanization process. Considering the aging population, the inequality in resource allocation between urban and rural ECIs has become more pronounced. Further analysis indicates that relative to the growth in demand, the capital and human resources in urban ECIs have grown significantly, notably improving faster than the demand. The rapid improvement in the service capacity of urban ECIs is due to policy and financial support and the economies of scale brought by urban population density and economic concentration. In contrast, rural ECIs have seen slow growth in resource allocation since 2013, especially in terms of capital and service provision, highlighting the challenges in accessing resources, building infrastructure, and attracting professionals in rural areas. This gap is not limited to economic capital but also includes differences in social capital and the capacity for service innovation, resulting in rural elderly care services being unable to effectively meet the needs and expectations of the older population. The urban–rural inequality in elderly care resource allocation directly affects the willingness of older people to choose care institutions. Urban elderly have more service options and high-quality services, while rural elderly face a shortage of services and limited choices. This inequality stems from differences in urban and rural development, particularly in economic development levels, public service system construction, and social welfare distribution mechanisms.

  3. (3)

    The level of resource allocation in rural ECIs first increased, then decreased, and later slowly rose again. At the same time, the degree of dispersion first decreased and then increased. This suggests that the spatial distribution of resources in rural ECIs remains unstable, with considerable variation among provinces due to differences in rural economies, elderly care policies, and the development of the elderly care market. Although government support and investment in rural elderly care services have increased in recent years, the pace of resource allocation improvement in rural ECIs continues to lag behind that of urban areas, particularly in terms of financial resources and service provision. In contrast, resource allocation in urban ECIs has shown continuous improvement, with an increasing degree of dispersion, indicating a more comprehensive enhancement of resource distribution across urban areas. Overall, the level of resource allocation in urban ECIs is higher than in rural areas. However, the absolute differences in resource allocation between provinces are more pronounced in urban ECIs than in rural ones. This uneven distribution of resources between urban and rural ECIs has a significant impact on older adults’ willingness to choose institutional care. While the general improvement in resource allocation in urban ECIs reflects the continuous optimization of the urban elderly care system, it also widens the disparities in resource distribution between urban and rural areas, as well as among different regions within cities. These inequalities may further limit the options available to older adults, particularly in rural areas, where access to high-quality elderly care services remains a challenge. To address this, increased government and societal support and investment are necessary to strengthen the rural elderly care system, optimize resource allocation, and narrow the urban–rural and regional gaps. Additionally, private and nonprofit organizations should be encouraged and supported to participate in the elderly care market. Through policy guidance and incentive mechanisms, these sectors can help enhance the quality and efficiency of elderly care services, ensuring that all older adults have access to equitable and sustainable care.

  4. (4)

    The Dagum Gini coefficient is used to measure the overall degree of difference in ECI resources between urban and rural areas. According to the decomposition results, the main differences stem from inter-regional disparities. From the perspective of numerical levels of inter-regional differences, the differences in the southern regions, divided by the Qinling–Huaihe line, are relatively smaller, while the differences in the northern regions are relatively larger. The reason behind this is the vast territory in the north with relatively lower levels of economic development, which exacerbates the differences in resource allocation. The intra-regional Gini coefficients for rural and urban ECIs in the northwest region reach as high as 0.31 and 0.27, respectively. Limited by poor natural conditions and the impact of an aging population, these factors together make the difference in resource allocation for urban and rural ECIs significant in the northwest. Harsh natural conditions and an aging population exacerbate the supply–demand contradiction in elderly care services, especially in rural areas where resource scarcity and service inadequacy are more severe. Moreover, the development pace of the northwest region is uncoordinated and imbalanced compared to other regions, reflecting the economic gap within the region and with the developed eastern regions, further intensifying the inequality in elderly care resource allocation.

  5. (5)

    The positive and significant global Moran’s I index for urban and rural areas indicates the presence of spatial autocorrelation, generally showing a clustering trend. Hotspot analysis results reveal a clear geographical shift in the spatial clustering center of elderly care resource allocation. The shift of the rural elderly care resource allocation center from North China to the Tibetan Plateau, and the urban elderly care resource allocation center from the Southwest to North China and then to the Yellow River Basin, reflects the change in policy focus and economic development’s geographical center over time. This change could be related to the government’s adjustment of development strategies for specific regions at different times, or it might reflect the impact of economic growth, urbanization, and aging population trends on the demand and allocation of elderly care resources. In the urban Moran scatter plots, the points of the provinces in 2008 are mainly concentrated in the third quadrant (L-L), and in 2021, the points of the provinces are mainly concentrated in the first quadrant (H-H). Over time, surrounding provinces such as Shanxi, Inner Mongolia, Heilongjiang, and Henan transition from the third quadrant to the first quadrant, indicating a concentrated development trend in the resource allocation of urban ECIs in surrounding provinces. The significant impact of high-level urban areas on surrounding regions drives progress in urban elderly care resources. Comparing the Moran scatter plots of urban and rural ECIs in 2021, provinces like Hebei, Jilin, Tibet, and Shanghai correspond along the diagonal. This suggests a certain siphoning effect of resources such as labor, capital, infrastructure, etc., between urban and rural ECIs within the province. Policy recommendations should focus on optimizing the development environment in provinces with high levels of resource allocation, using policy support and resource guidance to make them engines for enhancing elderly care resource allocation in surrounding areas. At the same time, efforts should be made to avoid excessive siphoning of rural elderly care resources by cities, through cross-regional cooperation, financial support, and technical exchanges, to strengthen the construction of rural elderly care service facilities, improve the quality of rural elderly care services, achieve balanced and equitable allocation of elderly care resources between urban and rural areas, and ensure that all elderly have access to suitable, high-quality care services.

  6. (6)

    From the traditional Markov chain, it is evident that the likelihood of downward transition in resource allocation for rural ECIs is greater than that for urban areas. This reveals that rural areas face a higher risk of decline in elderly care resource allocation. This trend may be related to factors such as relatively lagging economic development in rural areas, severe aging of the population, and the migration of young labor forces out of these areas. According to the spatial Markov chain, under a “low–high” clustering background, the development trend of ECI resource allocation in provincial urban and rural areas tends toward an upward direction. The upward trend in resource allocation indicates that the economic development of specific areas has influenced the improvement of elderly care resource allocation in neighboring areas. This means that even in areas with lower levels of resource allocation, interaction and influence with neighboring areas that have higher levels of economic development can potentially promote an overall improvement in elderly care resource allocation. This upward trend reflects the positive impact of regional economic development levels on enhancing elderly care resource allocation, especially between economically developed areas and their surrounding regions, where economic connections and resource flows can drive improvements in elderly care resource allocation in neighboring areas.

Policy implications

In light of the inequality and instability in ECI resource allocation between urban and rural areas revealed by this study, the following policy recommendations are proposed to improve the current system and promote sustainable development of the elderly care service network:

  1. (1)

    Enhanced financial and policy support for rural ECIs: in light of the findings that rural areas experience unstable resource allocation and relatively lower service levels, it is recommended to increase financial input and policy support to improve rural elderly care infrastructure and enhance service quality.

  2. (2)

    Promotion of information technology in elderly care: the study shows that while urban elderly care resources have improved annually, rural areas lag behind, especially in sparsely populated or inaccessible areas. Therefore, it is crucial for governments and relevant authorities to promote the widespread adoption of telemedicine and remote health monitoring technologies to improve the accessibility and quality of elderly care services in rural areas, thereby narrowing the urban–rural service gap.

  3. (3)

    Development of region-specific policies: policies should be tailored according to the differences in elderly care resource allocation and needs across regions. For areas where resource allocation is relatively underdeveloped, policies should focus more on improving equity and accessibility.

  4. (4)

    Strengthened integration of urban–rural resources: given the tendency for urban areas to draw resources away from rural regions, it is essential to establish mechanisms for integrating resources and incentivizing balanced development of elderly care services between urban and rural areas.

Conclusion

This study explored the evolution patterns of resource allocation in urban and rural ECIs in China, with a particular focus on the issue of uneven resource distribution. It revealed the differences in resource allocation between urban and rural areas as well as among different regions, clarifying the trends in spatial distribution of resources. The study found significant spatial differences and inequalities in elderly care resource allocation between urban and rural China. Particularly, rural areas face more pronounced issues in elderly care resource allocation, with a noticeable insufficiency in resource allocation and service provision compared to urban areas. The main reasons include the geographic mobility of labor, uneven economic development levels, and differences in social welfare policies. These factors lead to imbalances in elderly care resource allocation not only between urban and rural areas but also among regions.

Furthermore, the study revealed trends and characteristics of urban and rural elderly care resource allocation, including the instability of resource allocation in rural ECIs, the overall improvement in urban elderly care resource levels, and the phenomenon of spatial clustering of elderly care resources. Through the analysis of indicators such as the Dagum Gini coefficient, global Moran’s I index, and spatial Markov chains, this study not only revealed the overall degree of difference in elderly care resource allocation between urban and rural areas but also showcased the specific manifestations and influencing factors of regional differences.

The primary contribution of this study is that it systematically reveals, for the first time, the instability and dynamic evolution trends of urban and rural elderly care resource allocation in China. It provides empirical evidence on how to improve the inequality in resource distribution between urban and rural areas through policy intervention and resource optimization. These new findings enrich the existing literature and offer new perspectives for future research. In future research, it is recommended to prioritize an in-depth analysis of the underlying causes of the uneven distribution of elder care resources between urban and rural areas, explore the innovation and diversification of elder care service models. Additionally, a detailed assessment of the effectiveness of elder care policies, and an examination of the state and outcomes of smart technology applications in current elder care institutions should also become focal points of study. Furthermore, future research can delve deeper into the municipal level. Analysis at the municipal level can reveal more detailed resource allocation situations and provide more precise policy recommendations for local governments. Municipal data can help better understand the distribution differences within urban and rural areas and optimize resource allocation plans.