Does Improving Comprehensive Elderly Care Capacity Contribute to Achieving Carbon Neutrality Goals? Analysis Based on the Spatial Durbin Model and Mediation Model

Abstract

This study uses panel data from 30 provinces in China between 2014 and 2022 to investigate the relationship between comprehensive elderly care capacity and carbon neutrality goals. The research finds that there is a positive relationship between comprehensive elderly care capacity and the achievement of carbon neutrality, with a coefficient of 0.061 that is significant at the 5% significance level. However, there exists a negative spatial spillover effect, with a coefficient of −0.119 that is significant at the 1% significance level. The unemployment rate plays a mediating role between the two; the improvement in elderly care capacity can reduce the unemployment rate, with a coefficient of −0.457, while there is also a negative relationship between the unemployment rate and carbon neutrality goals, with a coefficient of −0.015. Therefore, enhancing the elderly care capacity can lower the unemployment rate, which, in turn, can promote the achievement of carbon neutrality goals.

1. Introduction

Climate change is a significant global challenge that has far-reaching impacts on various aspects of society and ecosystems. Greenhouse gas emissions, particularly carbon emissions, are the primary drivers of climate change. To address this challenge, countries have set carbon reduction targets and taken measures to achieve carbon neutrality (Zhao et al., 2022) [1]. As one of the largest emitters, China plays a critical role in combating climate change and has incorporated carbon neutrality into its national development strategy. However, in implementing climate response measures, the impact of demographic changes, especially population aging, must also be considered. As the most populous country, China faces severe challenges due to declining birth rates and a growing elderly population (Huang et al., 2021; Yi et al., 2023) [2,3]. The increasing demand for elderly care services, healthcare, and long-term care places significant pressure on the social security system. This rising demand, coupled with labor market pressures, could lead to declining productivity and slowed economic growth. Therefore, enhancing comprehensive elderly care capacity has become a crucial solution to address this issue.

Comprehensive elderly care capacity refers to the collective ability of society, the economy, and government to meet the needs of an aging population, including the provision of elderly care services, the establishment of social security systems, and the promotion of the elderly care industry (Fang et al., 2020) [4]. Improving this capacity is not only vital for enhancing the welfare of the elderly but also essential for ensuring social stability and promoting sustainable development. Specifically, improving the sustainability of healthcare facilities plays a critical role in achieving carbon neutrality goals. As the elderly population increases, the demand for care services rises, which not only adds additional pressure to the social security system but can also exacerbate energy consumption and carbon emissions. Traditional elderly care facilities often rely on high-energy-consuming resources (such as electricity and natural gas), resulting in significant carbon emissions. However, by adopting energy-efficient technologies, green building standards, and renewable energy sources, energy consumption and greenhouse gas emissions can be effectively reduced. For instance, elderly care facilities can transition to environmentally friendly heating technologies, such as geothermal energy or air source heat pumps, which not only meet the elderly’s need for a comfortable environment but also significantly reduce their carbon footprint.

Additionally, the reliance of the elderly on transportation services also contributes to carbon emissions (Liu et al., 2017) [5]. Promoting low-carbon transportation options, such as electric vehicles and public transport, as well as designing convenient low-carbon travel facilities, can help mitigate the environmental impact of travel. The energy usage and consumption habits of nursing homes also require attention; promoting green consumption concepts and energy-efficient appliances can lower household carbon emissions. In this process, government policies are crucial, as measures like establishing green certification systems and providing financial subsidies can promote the green transformation of elderly services and encourage the application of low-carbon technologies. Although some elderly care institutions have begun to explore green transformation, the integration of elderly services and carbon neutrality is still in the exploratory stage (Kurramovich et al., 2022) [6].

Many institutions have yet to fully consider energy efficiency and carbon emission control. Therefore, future research should focus on how to promote the implementation of green elderly services through technological innovation, policy support, and industrial development, thereby contributing to global carbon neutrality goals while addressing the challenges of population aging. By clarifying the connection between improving healthcare facilities and environmental sustainability, it is possible to better understand the interplay between enhancing elderly care capacity and carbon reduction targets.

Additionally, the unemployment rate has profound effects on elderly people’s employment opportunities and the social security system. A lower unemployment rate usually means more elderly people can continue working to earn income, alleviating the pressure on public elderly care resources and enhancing the elderly’s ability to care for themselves. A reduced unemployment rate also assists the government in implementing more effective social security policies, which can enhance the quality of life for the elderly and further strengthen comprehensive elderly care capabilities. Moreover, fluctuations in the unemployment rate significantly affect social stability. A lower unemployment rate often signals a robust economy and stable incomes for residents, boosting public confidence and creating a conducive environment for the execution of long-term sustainable development strategies (Zhao et al., 2021) [7]. Consequently, the unemployment rate is pivotal in enhancing the comprehensive elderly care capacity and advancing progress toward carbon neutrality objectives. Policymakers need to thoroughly consider its impact to ensure the harmonious development of the economy, society, and environment, ultimately achieving multiple sustainability targets. In this regard, the unemployment rate serves not only as an economic indicator but also as a crucial factor in promoting green transformation, improving the elderly care system, and lowering carbon emissions.

This study offers several potential contributions. Firstly, regarding the development of indicators, researchers like Yu et al. (2023) [8] and Shi et al. (2023) [9] have mainly concentrated on specific areas such as carbon emissions, carbon sequestration, carbon policies, and carbon trading in their examinations of carbon neutrality. However, they have not constructed a comprehensive indicator system that systematically considers carbon neutrality from multiple dimensions. Similarly, studies conducted by Van et al. (2019) [10] and Engelen et al. (2022) [11] in the area of comprehensive elderly care capacity have primarily addressed aspects like pension funds and social security while overlooking the significance of infrastructure development. In contrast, this research builds a comprehensive elderly care capacity framework to offer a more detailed assessment of the elderly care capabilities across various Chinese provinces. Furthermore, from a research perspective, although scholars such as Zhang et al. (2021) [12] have examined the link between population aging and carbon emissions, they have not specifically addressed the connection between comprehensive elderly care capacity and carbon emissions.

Furthermore, they did not approach the elderly care capacity and carbon neutrality as separate systems to investigate their interconnection. This study employs methods like OLS and spatial econometrics to analyze both the direct relationship and the spatial spillover effects between these two systems across different provinces. It also evaluates the coupling coordination degree between them, providing a deeper analysis of their correlation and development trends in various provinces. Lastly, in the context of path analysis, previous research by Wang et al. (2021) [13] primarily examined the link between changes in the population structure and unemployment rates or the connection between population structure changes and carbon emissions. In contrast, this study highlights the mediating role of the unemployment rate as a mediating variable, thereby addressing a research gap in this field.

2. Literature Review

2.1. Analyzing the Impact of Digitalization on Sustainability over a Longer Time Horizon

As the global population ages rapidly, the demand for elderly care services is increasing, and the study of comprehensive elderly care capacity has gradually become an important topic in the social sciences. Comprehensive elderly care capacity refers to a society’s overall ability to meet the needs of the elderly, encompassing a range of services such as healthcare, nursing, social security, and psychological support. It emphasizes the collaborative role of diversified services in enhancing the quality of life and well-being of older adults.

The factors influencing comprehensive elderly care capacity primarily include social, economic, and policy factors. Social culture significantly impacts perceptions of elderly care; traditional cultures that respect the elderly encourage families to provide care. However, urbanization and changes in family structures have diminished the capacity for family care, necessitating support from social service systems. The level of economic development directly affects the supply capacity of elderly care services (Zhang et al., 2023) [14]. Developed countries have advantages in funding, professional training, and the construction of service facilities, while the aging population’s impact on the economy also indirectly influences the construction of the comprehensive elderly care capacity.

Moreover, government policies play a crucial role in enhancing comprehensive elderly care capacity. By increasing financial investment and establishing sound social security systems, the overall level of elderly care services can be improved. Enhancing the comprehensive elderly care capacity directly improves the quality of life for older adults, reduces levels of depression and anxiety, and increases life satisfaction (Shapira et al., 2007) [15]. Additionally, adequate elderly care services can alleviate pressure on families and communities, promoting social harmony. The development of the elderly care industry not only meets the needs of older adults but also creates numerous job opportunities, promoting economic growth and industrial diversification. By improving the health and quality of life of older adults, enhancing the comprehensive elderly care capacity can effectively reduce medical expenses and social security expenditures, thereby alleviating the economic burden on the state.

Therefore, the enhancement of comprehensive elderly care capacity has multifaceted impacts on society and the economy. Future research should continue to explore innovative models of elderly care services and their interactions with policies and economic development, aiming to provide effective solutions to the challenges of global aging. Comprehensive elderly care capacity is not only related to the well-being of older adults but also constitutes an important component of sustainable social development.

2.2. Integrating New Explanatory Variables, Such as the Role of Local Environmental Policies

Carbon neutrality refers to achieving a balance between the amount of carbon dioxide emitted and the amount absorbed, thereby realizing “net zero emissions” of greenhouse gases through the reduction of greenhouse gas emissions and the increase of carbon sinks. To achieve this goal, academics and policymakers have begun to focus on the pathways and methods for carbon neutrality, as well as relevant econometric models, to analyze and predict the dynamic changes and influencing factors of carbon emissions. Researchers have explored the impacts of various emission reduction technologies (such as renewable energy, carbon capture and storage technologies, etc.) and their policy frameworks on carbon neutrality (Fang et al., 2020) [4]. These studies emphasize the important role of technological innovation and policy intervention in achieving carbon neutrality goals. The realization of carbon neutrality has profound impacts on economic growth, employment, and industrial structure transformation. Research indicates that, while short-term negative effects may occur in certain industries, in the long run, the development of a green economy will create new job opportunities and promote economic transformation. Public acceptance and participation in carbon neutrality policies are crucial factors for achieving these goals. Studies point out that raising public awareness and engagement is vital for the successful implementation of carbon neutrality policies.

Econometric models play an important role in analyzing carbon emissions and their influencing factors. Various econometric methods have been employed in the relevant literature, including (1) the use of time series models to analyze carbon emission data, exploring the trends of carbon emissions and their relationships with variables such as economic growth, and energy consumption; (2) the comparison of carbon emission situations in different regions through panel data models, analyzing their influencing factors and policy effects. This method can simultaneously consider time and individual differences, enhancing the explanatory power of the models (Kurramovich et al., 2022) [6]; and (3) structural equation modeling used to explore the complex relationships between carbon emissions and socioeconomic factors, allowing for the simultaneous analysis of multiple variable interactions (Zhao et al., 2022) [1]. The research on carbon neutrality and the application of econometric models are increasingly gaining attention. Future studies can further explore the challenges and opportunities faced by different countries and regions in the process of achieving carbon neutrality, as well as the applicability and limitations of various econometric models. By establishing more precise econometric models, policymakers can obtain scientific evidence to effectively promote the realization of carbon neutrality goals, contributing to global sustainable development.

2.3. Developing More Advanced Simulation Models to Test Different Intervention Policies

Digital transformation is regarded as an important means to promote the enhancement of comprehensive elderly care capacity and the achievement of carbon neutrality goals. By optimizing resource allocation and improving service efficiency, it aims to realize the dual objectives of enhancing the well-being of the elderly and ensuring environmental sustainability. The success of digital transformation often depends on the indicator system it employs, making research on the monitoring of these indicators particularly important.

Digital transformation refers to the application of information technology to drive changes in organizational structure, business processes, and cultural concepts, thereby enhancing the efficiency and innovation capability. In the field of elderly care services, digital transformation helps improve the quality of life for the elderly by providing more personalized services through technologies such as smart homes and telemedicine. At the same time, digital transformation also offers new pathways for achieving carbon neutrality. For example, intelligent energy management systems can enhance energy use efficiency, thus reducing carbon emissions.

Research indicates that the application of digital technology in elderly care services is closely related to the comprehensive elderly care index. The comprehensive elderly care index typically includes multiple dimensions such as healthcare, nursing, social security, and psychological support. Digital transformation can effectively enhance the performance of each dimension by improving the accessibility and quality of services. For instance, digital health monitoring can timely identify health issues among the elderly, thereby improving the responsiveness and effectiveness of medical services. Additionally, digital platforms can promote social activities among the elderly, enhancing their mental health and social support.

The role of digital transformation in promoting carbon neutrality is equally significant. Studies have shown that intelligent urban management and energy use systems can significantly reduce greenhouse gas emissions (Fang et al., 2020) [4]. For example, optimizing traffic management through big data analysis can reduce transportation-related carbon emissions while improving the quality of life in urban areas. In the realm of elderly care, digital transformation not only improves the living conditions of the elderly but also promotes sustainable development and carbon neutrality through the application of green technologies.

Therefore, digital transformation has an important synergistic effect on enhancing the comprehensive elderly care index and achieving carbon neutrality goals. Future research should pay more attention to the monitoring indicator system for digital transformation to assess its actual effects on elderly care services and environmental protection. This will provide policymakers with scientific evidence to more effectively promote sustainable social development.

3. Hypothesis Formulation

3.1. Comprehensive Elderly Care Capacity and Carbon Neutrality

Research exploring the relationship between elderly care capacity and carbon neutrality is relatively scarce. Consequently, future studies could delve deeper into how improving the elderly care capacity affects the challenges of population aging. This could be followed by an analysis of how a robust elderly care system impacts carbon neutrality and the progress toward achieving related goals. The majority of researchers assert that population aging contributes to increased carbon emissions, impeding efforts to reach carbon neutrality. This is due to the rising demand for housing, healthcare, transportation, and other essential services by the elderly, which, in turn, drives up energy consumption and emissions. For instance, Feng et al. (2023) [16] demonstrated that the elderly’s need for medical services generates carbon emissions from the production, transport, and use of medical equipment and pharmaceuticals, as well as from energy consumption in healthcare facilities.

However, as the comprehensive elderly care capacity improves, these negative impacts may be mitigated to some extent. The impact of enhancing the comprehensive elderly care capacity on an aging society can be understood through resource allocation theory. According to resource allocation theory, during the process of enhancing the elderly care capacity, optimizing resource allocation can improve elderly people’s labor participation, fully utilize their human resources, promote economic development, and ultimately achieve carbon neutrality goals. Some researchers suggest that boosting the elderly care capacity not only enhances the quality of life and well-being of older adults but also empowers them to engage more actively in social and economic activities (Van et al., 2019; Engelen et al., 2022; Wierucki et al., 2022) [10,11,17]. The resulting increase in the labor participation of the elderly fosters economic growth. Additionally, through advancements in technology and enhanced energy efficiency, it leads to better resource utilization, reduced waste and emissions, and supports progress toward carbon neutrality goals.

Furthermore, as the elderly care capacity increases, shifts in the demand patterns of the elderly influence the adjustment of socioeconomic needs, thereby driving the optimization of the industrial structure and the advancement of low-carbon industries (Wang et al., 2022) [18]. Technological innovation is pivotal in fostering the growth of elderly care services and industries as care capacity expands. By integrating new technologies and smart devices, the quality and efficiency of elderly care services can be enhanced, giving rise to sustainable, intelligent, and eco-friendly care models that aid in reaching carbon neutrality (Budzianowski et al., 2017) [19]. Lastly, based on public policy theory, the government can adopt various strategies to guide the economy towards low-carbon development while enhancing the elderly care capacity and pursuing carbon neutrality goals. These strategies might involve supporting the growth of green industries, offering technological assistance, and implementing environmental protection regulations. Additionally, as environmental awareness among the elderly increases, they are more inclined to endorse and engage in low-carbon lifestyles and sustainable development, furthering the social consensus that accelerates the achievement of carbon neutrality goals.

Building on the aforementioned analysis, this study puts forward the following hypotheses:

Hypothesis 1:

The enhancement of the elderly care capacity can promote carbon neutrality.

3.2. Comprehensive Elderly Care Capacity and Unemployment Rate

When exploring the impact of expanding the elderly care capacity on unemployment rates, it is essential to initially grasp the connection between population aging and employment trends. Various studies have examined the effect of aging populations on employment, and their results suggest that it intensifies employment issues in China, leading to an increase in unemployment rates (He et al., 2018; Cui et al., 2023) [20,21]. These scholars suggest that as the elderly population rises, older workers gradually withdraw from the workforce, thereby reducing the overall labor supply. When this decline in available workers occurs amidst stable or growing labor demand, it can lead to labor shortages, which, in turn, drive up unemployment levels (Mindell et al., 2022) [22]. Additionally, population aging may shift the skill requirements in the labor market. The rise of emerging industries and technologies often necessitates new skills and knowledge that older workers may struggle to adapt to, potentially leading to skill mismatches and making it harder for them to find suitable employment, further increasing the unemployment rate. Yang et al. (2022) [23] found that aging populations increase elderly care expenditures, placing more strain on government resources. As governments must provide additional pensions, healthcare, and welfare services to meet the needs of older adults, fiscal pressure may limit funding for employment programs, reducing support for job creation and increasing unemployment. Moreover, as the elderly population grows, consumption patterns change. Older adults tend to be more conservative with spending, leading to a reduced demand for certain products and services. This decreased consumption can negatively affect related industries, reduce employment opportunities, and raise the unemployment rate.

However, enhancing the comprehensive elderly care capacity can effectively address the issue of rising unemployment caused by population aging (Cui et al., 2024) [24]. Scholars have generally focused on two key areas in their research. According to human capital theory, an individual’s education, training, and skill level are crucial factors for employment and wage prospects. By improving the elderly care capacity, older adults can receive better training and skill development, thereby enhancing their human capital and increasing their competitiveness in the labor market, which can help reduce the unemployment rate. On the one hand, an increased demand for elderly care-related industries can create more jobs. On the other hand, enhancing the elderly care capacity directly increases employment opportunities for older adults, enabling them to delay retirement or engage in part-time work, entrepreneurship, and other flexible employment options.

From an industrial development perspective, some scholars argue that enhancing the elderly care capacity increases employment opportunities. This improvement typically involves building nursing homes, training elderly care professionals, and related activities that generate a significant number of jobs. These job opportunities can help reduce the unemployment rate (Nakatani et al., 2019) [25]. Furthermore, as the demand for elderly care services expands, it stimulates the growth of related industries, such as healthcare, wellness products, and rehabilitation equipment, which, in turn, creates additional employment opportunities, thus helping to reduce unemployment. Moreover, the improvement of the elderly care capacity enhances the physical and mental well-being of older adults, allowing them to extend their working lives or remain in the workforce for longer. This increase in the labor supply can alleviate labor shortages and reduce unemployment (Madhusanka et al., 2021; Dhakal et al., 2022) [26,27].

According to flexible employment theory, flexible employment arrangements, such as part-time work and freelancing, offer more employment options and can reduce unemployment rates. Enhancing the elderly care capacity can support flexible employment for older adults, enabling them to better align their work with their lifestyle needs. With an aging population, many older adults may prefer flexible work arrangements to better balance their work and personal lives. By fostering the development of flexible employment and part-time job opportunities, enhancing the elderly care capacity provides older adults with more employment choices, helping to reduce the unemployment rate.

Drawing from the preceding analysis, the study presents the following hypotheses:

Hypothesis 2:

The enhancement of the comprehensive elderly care capacity can reduce the unemployment rate.

3.3. Carbon Neutrality and Unemployment Rate

The unemployment rate is intricately linked to a country’s economic landscape, and during the process of advancing towards carbon neutrality, fluctuations in the unemployment rate play a pivotal role. While direct research exploring the correlation between unemployment rates and carbon neutrality remains limited, a significant body of work has examined the relationship between unemployment and carbon emission reduction. A common perspective among researchers is that lowering unemployment can help reduce carbon dioxide emissions. Cui et al. (2022) [28] explored the mediating role of unemployment, green finance, and carbon emissions, finding that a decline in the unemployment rate tends to accompany more robust economic activity and more job opportunities. This can drive a transformation in the economic structure, moving away from traditional high-carbon industries toward low-carbon options. The expansion of sectors like renewable energy, clean technology, and environmental services directly helps to lower carbon emissions. For example, increasing the adoption of renewable energy lessens the reliance on fossil fuels, thus reducing carbon emissions. The economic theory of technological innovation further supports this dynamic; growing economic activity is often accompanied by innovation, including the development of green technologies. These technological advancements are critical for reducing emissions and promoting carbon neutrality.

Fan et al. (2021) [29] examined corporate pollution governance and found that increased economic activity leads businesses to prioritize energy efficiency. During economic recovery, when unemployment decreases, companies are more likely to invest in energy-efficient technologies and production equipment, which reduces both energy consumption and emissions. Moreover, a reduction in unemployment encourages governments to adopt stronger green policies and incentives that promote carbon emission reduction (Liu et al., 2022) [30]. Fiscal support and tax incentives from the government can drive both businesses and individuals to take action toward a low-carbon economy. Economic recovery also stimulates innovation and technological advancement, including in green technologies, which contribute to emissions reduction.

Building on this research, we can explore the connection between a declining unemployment rate and carbon neutrality. First, a decrease in unemployment expands the labor market, increasing the human resources available for the growth of green industries and clean technologies (Dong et al., 2023) [31]. Carbon neutrality requires significant investments in areas such as clean energy, sustainable transportation, and environmental protection, which, in turn, create jobs and push the economy toward a low-carbon future. Second, a lower unemployment rate can facilitate energy transition and emission reduction efforts. The stability that comes with lower unemployment enhances the feasibility of policies targeting energy transformation and emission reduction. In such a scenario, the social and economic stability created by lower unemployment fosters active participation and investment from both governments and businesses in energy transition projects.

Finally, decreasing the unemployment rate can help reduce social inequality, fostering greater social inclusivity and fairness (Tri et al., 2022; Cicchiello et al., 2021) [32,33]. Widespread support for carbon neutrality is essential, and high unemployment often exacerbates social tensions. Lower unemployment alleviates these pressures, promotes social harmony, and provides a stronger social foundation for the pursuit of carbon neutrality.

Based on the above analysis, the following hypotheses are proposed in this study:

Hypothesis 3:

The reduction in the unemployment rate can facilitate the development of carbon neutrality.

4. Methodology and Data

4.1. Variable Description and Data Source

4.1.1. Explained Variable

The concept of “carbon neutrality” pertains to the net sum of carbon dioxide emissions, whether direct or indirect, produced by a country, company, product, activity, or individual over a given period. Achieving carbon neutrality can be accomplished by offsetting CO₂ emissions through strategies like reforestation, energy efficiency, and emission reductions. In this article, carbon neutrality indicators are developed using the entropy method. A higher index value indicates a greater capability to manage carbon emissions and reach carbon neutrality targets in a given region.

Carbon neutrality and carbon emission reductions are deeply intertwined in the pursuit of global climate objectives. In general terms, carbon neutrality entails the balance between a country or region’s total carbon emissions and the amount that is absorbed or offset over a specified timeframe. On the other hand, carbon emission reduction involves directly decreasing emissions through innovations in technology, policy advancements, industrial restructuring, and other methods. From this standpoint, lowering carbon emissions is a fundamental precursor to achieving carbon neutrality goals. Firstly, reducing emissions represents a direct route to carbon neutrality (Huang et al., 2022) [34]. Significantly cutting down on fossil fuel consumption, enhancing energy efficiency, and transitioning to renewable energy sources enable countries or regions to effectively decrease their carbon output. This mitigates the accumulation of greenhouse gases by limiting or reducing emissions at their origin, which, in turn, curbs the progression of global warming (Chen et al., 2024) [35]. For instance, decreasing emissions in sectors like electricity generation, transportation, and industry is crucial for advancing toward carbon neutrality. Without actual reductions, achieving climate targets through measures such as afforestation or carbon capture alone would be insufficient.

Secondly, reducing carbon emissions not only directly contributes to meeting carbon neutrality objectives but also establishes the groundwork for transitioning to a sustainable economic model (Chen et al., 2022) [36]. By markedly decreasing greenhouse gas emissions, a country can progressively eliminate high-polluting and high-carbon industries and practices while fostering the growth of green technologies and low-carbon industries, thereby facilitating the transformation toward a green economy. This transformation not only helps achieve carbon neutrality goals but also enhances the overall environmental carrying capacity of society, improves the human living environment, and promotes sustainable social development (Xu et al., 2022) [37]. Finally, achieving carbon emission reduction and carbon neutrality goals are not two completely independent objectives (Salvia et al., 2021) [38]. Under the global climate policy framework, reducing carbon emissions is a fundamental step towards gradually achieving carbon neutrality goals, and the two complement and promote each other. With the continuous advancement of emission reduction policies and technologies, the reduction of carbon emissions provides essential conditions for achieving carbon neutrality. Countries and regions that actively implement carbon emission reduction policies globally are usually able to achieve carbon neutrality earlier and occupy a favorable position in international climate negotiations. Hence, carbon neutrality and carbon emission reductions are closely interconnected, as they represent two key components in the pursuit of global climate objectives and tackling climate change. Attaining carbon neutrality by means of lowering carbon emissions is a prolonged and sustainable endeavor.

When constructing the carbon neutrality index, it is essential to include six critical aspects: government commitment, infrastructure foundation, natural resources, industry composition, energy usage, and economic and technological capacities. These dimensions collectively capture the essential resources and capacities required to achieve carbon neutrality. Government ambition plays a pivotal role, as a strong political will and the effective implementation of policies provide significant momentum for the green transition. The infrastructure foundation plays a critical role in accelerating the development of green infrastructure, especially in areas like renewable energy, low-emission transportation, and sustainable buildings. Natural resources, including aspects such as geography and climate, have a direct impact on the feasibility of renewable energy development and the efficiency of energy systems. The industrial sector emphasizes the need for transformation in key industries, where the adoption of green technologies can significantly cut carbon emissions. Patterns and structures of energy consumption are also essential, as moving away from fossil fuels and increasing the use of clean energy are key to achieving carbon neutrality. Finally, economic and technological capabilities are crucial, as they determine a country’s capacity to innovate and expand low-carbon technologies. Collectively, these six elements form a comprehensive framework for assessing progress toward carbon neutrality, as detailed in

Table 1. Carbon neutral development index system.

Level 1 Indicators	Level 2 Indicators	Level 3 Indicators	Code	Symbol
Carbon neutral development index	Government ambition	Ecological Attention	$X_1$	+
		Green development attention	$X_2$	+
		Digital attention	$X_3$	+
		Pilot policy of carbon exchange	$X_4$	+
		Low carbon policy pilot	$X_5$	+
	Infrastructure Details	Heating area	$X_6$	-
		Urban road lighting	$X_7$	-
		Number of bus and trolley bus operations	$X_8$	+
		Taxi	$X_9$	+
		Private car ownership	$X_{10}$	-
		Civil automobile ownership	$X_{11}$	-
		Urban green area	$X_{12}$	+
		Park green area	$X_{13}$	+
		Area of urban construction land	$X_{14}$	-
	Natural endowment	Forest coverage	$X_{15}$	+
		Forest land area	$X_{16}$	+
		Plantation area	$X_{17}$	+
		Number of reservoirs	$X_{18}$	+
		Total reservoir capacity	$X_{19}$	+
		Permanent population at the end of the year	$X_{20}$	-
	Industrial dimension	Proportion of secondary industry	$X_{21}$	-
		Proportion of tertiary industry	$X_{22}$	+
		Total agricultural output value	$X_{23}$	+
		Total output value of forestry	$X_{24}$	+
		Total output value of animal husbandry	$X_{25}$	-
	Energy consumption	Coal consumption	$X_{26}$	-
		Coke consumption	$X_{27}$	-
		Crude oil consumption	$X_{28}$	-
		Gasoline consumption	$X_{29}$	-
		Kerosene consumption	$X_{30}$	-
		Diesel consumption	$X_{31}$	-
		Fuel oil consumption	$X_{32}$	-
		Natural gas consumption	$X_{33}$	-
		Power consumption	$X_{34}$	-
	Economy and technology	Carbon decoupling index	$X_{35}$	+
		Green finance	$X_{36}$	+
		Digital economy	$X_{37}$	+
		Number of green patent applications	$X_{38}$	+

Note: “+” in the column of “Symbol” represents positive indicators, and “-” represents negative indicators.

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4.1.2. Core Explanatory Variable

This study draws on the methods used by Cao et al. (2022) [39] to construct a rural elderly care capacity index and applies the entropy method to develop a comprehensive elderly care capacity index. In building this index, key factors such as population demographics, medical resources, elderly care services, economic capacity, and government support are all taken into account. These elements are essential in determining the effectiveness and sustainability of elderly care systems in responding to the challenges of an aging society. First, demographic factors, especially the increasing elderly population, directly affect the demand for elderly care services. As the aging population grows, the need for such services intensifies, making it important to consider the changing population structure when planning and allocating resources. Secondly, medical resources are highly connected to elderly care services, given that older adults tend to face more frequent health issues. Sufficient healthcare provisions and specialized services are essential for preserving a high quality of life for seniors. As population aging speeds up, the expansion of elderly care facilities and support systems must be accompanied by robust medical security and healthcare infrastructure. Economic capability is also vital, as it determines whether a region has the resources to tackle the challenges associated with an aging population. Only a strong economic foundation can support comprehensive elderly care services, social security, and a sustainable elderly care industry. Government involvement is crucial in guaranteeing the effectiveness of elderly care systems. Through policy support, financial investment, and strategic guidance, the government contributes to the development of care facilities, enhancements in healthcare systems, and the long-term advancement of services for older adults. By creating an elderly care capacity index that incorporates these five factors, this study offers a comprehensive framework to evaluate and enhance a region’s capacity to address the needs of its aging population, ensuring that seniors receive the care and protection they require. The detailed classification is presented in

Table 2. Index system of the inter-provincial comprehensive elderly care ability, and partial calculation results of the entropy method.

Level 1 Indicators	Level 2 Indicators	Level 3 Indicators	Code	Symbol
Comprehensive elderly care capacity	Demographic factors	Proportion of older people over 65 years old	$X_1$	-
		Elderly dependency ratio	$X_2$	-
		Average household size	$X_3$	-
		Natural growth rate of population	$X_4$	-
	Medical resources	Number of medical institutions	$X_5$	+
		Per capita health expenses	$X_6$	+
		Number of medical beds per thousand population	$X_7$	+
	Endowment resources	Number of pension institutions	$X_8$	+
		Number of employees in pension institutions	$X_9$	+
		Number of beds in pension institutions.	$X_{10}$	+
		Elderly activity station/center/room	$X_{11}$	+
		Number of elderly participants	$X_{12}$	+
		Number of elderly subsidies	$X_{13}$	+
	Economic capability	Per capita disposable income	$X_{14}$	+
		Per capita consumption expenditure	$X_{15}$	+
	Support from government	General budget revenue	$X_{16}$	+
		General financial budget expenditure	$X_{17}$	+

Note: “+” in the column of “Symbol” represents positive indicators, and “-” represents negative indicators.

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4.1.3. Mediating Variable

The unemployment rate refers to the percentage of individuals within the labor force who are actively looking for work but are currently unemployed. This metric serves as a crucial economic indicator, offering valuable insights for governments, businesses, and investors alike. Shifts in the overall elderly care capacity could influence economic activity. In this context, the unemployment rate, acting as an intermediary variable that reflects economic conditions, can help illuminate how comprehensive elderly care capacity influences the path towards carbon neutrality. Improvements in comprehensive elderly care capacity may create more job opportunities, thereby reducing the unemployment rate. By selecting the unemployment rate as an intermediate variable, researchers can gain insight into whether the impact of comprehensive elderly care capacity on carbon neutrality is achieved through changes in employment opportunities.

4.1.4. Control Variable

(1) Environmental regulation ($eri$): The environmental regulation index functions as a framework for regulatory agencies to guide companies in lowering pollutant discharges while balancing economic growth and ecological preservation. In this study, recent data on wastewater, sulfur dioxide, and residue emissions are utilized to calculate overall regional environmental indicators (Cao et al., 2022) [40]. When examining the influence of comprehensive elderly care capacity on carbon neutrality, environmental regulations can act as a significant external factor that impacts carbon neutrality either directly or indirectly. By including environmental regulations as a control variable, the study can neutralize their impact, enabling a more precise evaluation of how comprehensive elderly care capacity affects carbon neutrality. Additionally, as an important control variable, environmental regulations can help researchers better control potential biases in the research design. By controlling for environmental regulations, the errors in the research results can be reduced, thereby enhancing the reliability and interpretability of the findings.

(2) Green total factor productivity ($gtfp$): This concept varies from traditional total factor productivity (TFP) by not only emphasizing the input–output efficiency of production factors like capital and labor but also integrating environmental factors, especially the impact of pollution emissions and resource consumption on economic activities. In this paper, we employ the SBM-GML model to assess green total factor productivity. Suppose there are k decision-making units; each unit has inputs, desired outputs, and undesirable outputs denoted by m, s₁, and s₂, respectively, with corresponding vectors x, y, and z. Under the assumption of constant returns to scale, the SBM model that accounts for undesirable outputs is presented in Equation (1). Here, λ represents the weight vector, S is the slack variable, and the objective function ρ signifies the efficiency of the decision-making unit, where 0 ≤ ρ ≤ 1. A value of ρ < 1 suggests inefficiency within the decision-making unit, while ρ = 1 indicates that the unit is fully efficient ($\rho =min{\displaystyle \frac{1+\frac{1}{m}\sum _{i=1}^m\frac{s_i^x}{x_{i0}}}{1-\frac{1}{s_1+s_2}\left(\sum _{k=1}^{s_1}\frac{s_k^y}{y_{k0}}+\sum _{i=1}^{s_2}\frac{s_i^z}{z_{i0}}\right)}}$).

$$s.t.\left\{\begin{array}{c}{x}_{i0}\ge \sum _{j=1,x\ne 0}^n{\lambda }_j{x}_j-s_i^{*},\forall i;\\ y_{k0}\le \sum _{j=1,x\ne 0}^n{\lambda }_j{y}_j+s_k^{*},\forall k;\\ z_{j0}\ge \sum _{j=1,x\ne 0}^n{\lambda }_j{z}_j-s_i^{*},\forall l;\\ 1-{\displaystyle \frac{1}{s_1+s_2}}\left(\sum _{k=1}^{s_1}{\displaystyle \frac{s_k^{*}}{y_{k0}}}+\sum _{l=1}^{s_2}{\displaystyle \frac{s_i^{*}}{z_{i0}}}\right)>0\\ s_i^x\ge 0,s_k^x\ge 0,s_i^x\ge 0,{\lambda }_j\ge 0,\forall i,j,k,l\end{array}\right.$$

(1)

The GML index model is shown in Equation (2), where the subscript C indicates that the return to scale remains unchanged. If ${GML}_t^{t+1}$ > 1, it indicates an increase in green total factor productivity. On the contrary, it also indicates a decrease.

$$GM{L}_t^{t+1}={\displaystyle \frac{S_C^G(x^t,y^t,z^t)}{S_C^G(x^{t+1},y^{t+1},z^{t+1})}}={\displaystyle \frac{S_C^t(x^t,y^t,z^t)}{S_C^{t+1}(x^{t+1},y^{t+1},z^{t+1})}}\left[{\displaystyle \frac{S_C^{t+1}(x^{t+1},y^{t+1},z^{t+1})}{S_C^G(x^{t+1},y^{t+1},z^{t+1})}}\times {\displaystyle \frac{S_C^G(x^t,y^t,z^t)}{S_C^t(x^t,y^t,z^t)}}\right]$$

(2)

The input indicators of this article are selected as employment, fixed capital stock, and total energy consumption. The output indicators are based on actual added value as the expected output, while wastewater discharge, sulfur dioxide emissions, and solid waste are considered as unexpected output indicators.

(3) Natural birth rate ($lnpop$): The natality rate of the natural population may serve as an indicator of a country’s population growth (Cao et al., 2023) [41]. The improvement of comprehensive elderly care capacity may have an impact on population structure, such as extending lifespans and improving healthcare. By selecting the natural population birth rate as a control variable, researchers can control for changes in the population structure and more accurately assess the impact of comprehensive elderly care capacity on carbon neutrality. Additionally, as the natural population birth rate declines, the degree of population aging may increase, leading to an increased demand for elderly care services, healthcare, and other resources. By including the natural population birth rate as a control variable, researchers can gain a clearer understanding of whether the effect of comprehensive elderly care capacity on carbon neutrality is affected by fluctuations in resource demand.

(4) Upgrading of industrial structure ($industrial$): The industrial structure represents the relative significance of different sectors within a country’s or region’s economy. These sectors vary in their resource demands and usage patterns. An enhancement in comprehensive elderly care capacity might influence the industrial structure, potentially raising the demand for sectors such as healthcare and elderly care services. By incorporating the industrial structure as a control variable, researchers can account for variations in resource utilization methods, enabling a more precise assessment of how comprehensive elderly care capacity affects carbon neutrality. Including this control variable helps manage the impact of carbon emissions, facilitating a clearer understanding of the direct effect of elderly care capacity on carbon neutrality. By doing so, the influence of industrial carbon emissions on the research outcomes can be mitigated, leading to a more accurate analysis of the relationship between elderly care capacity and carbon neutrality.

4.2. Methodology

4.2.1. OLS Panel Regression Model Construction

The ordinary least squares (OLS) model is among the most widely utilized regression techniques in the fields of statistics and econometrics. Its primary goal is to assess the linear association between the independent variable (or explanatory variable) and the dependent variable (or outcome variable) by minimizing the sum of squared differences between observed data and the corresponding predicted values. When standard assumptions are met, including the errors being independently and identically distributed and the absence of autocorrelation, the OLS estimator is regarded as the best linear unbiased estimator (BLUE). Due to its straightforward computation, clear interpretation, and strong reliability across various applications, the OLS model has emerged as a key analytical tool in disciplines such as economics, sociology, and environmental science. In this article, we constructed an OLS regression model aimed at exploring the relationship between comprehensive elderly care capacity and carbon neutrality. By introducing multiple control variables, the OLS model can accurately estimate the independent contribution of elderly care capacity to carbon neutrality, thereby providing an effective decision-making basis for policymakers.

In recent years, there has been a growing focus among researchers on the connection between elderly care and environmental sustainability. The OLS model is widely applied within the social sciences for various analyses. Lorek (2014) [42] examined how an aging society influences sustainable development, suggesting that the elderly’s lifestyle, consumption patterns, and demand for healthcare resources significantly affect carbon emissions. Gupta et al. (2018) [43] highlighted that, as the elderly care sector expands, it becomes crucial to reconcile the objectives of elderly care and green development through policy interventions. Furthermore, Xiong and Xu (2021) [44] utilized the OLS model to investigate the link between economic growth and environmental degradation, enhancing model precision by incorporating control variables, thereby offering insights for refining environmental policies.

The OLS model is capable of efficiently uncovering the linear connection between independent and dependent variables. In this article, we assume that comprehensive elderly care capacity has a direct linear impact on carbon neutrality, and the OLS model is precisely applicable to this assumption. Through regression analysis, the relationship between elderly care capacity (such as elderly care services, living conditions for the elderly, etc.) and carbon neutrality goals (such as carbon emissions, green development policies, etc.) can be estimated. In this research, we incorporated several control variables that could influence the relationship between elderly care capacity and carbon neutrality. The OLS model can accurately evaluate the independent contribution of elderly care capacity to carbon neutrality by controlling for these exogenous factors. Due to its ability to handle multiple explanatory variables, the OLS model can help us comprehensively understand the degree and direction of influence of various factors.

The coefficients of the OLS model are highly interpretable, with the magnitude and sign of the coefficients in the regression results directly indicating the direction and strength of the impact that each variable has on the dependent variable. For this study, the OLS model provides a concise and intuitive way to answer the specific contribution of elderly care capacity to carbon neutrality, while its interpretability also enables policymakers to quickly understand and apply research conclusions.

Through the OLS regression model, this article can deeply analyze how comprehensive elderly care capacity affects the achievement of carbon neutrality goals. Compared to other complex models such as panel data models or structural equation models, the advantage of the OLS model in this study lies in its simplicity and clear disclosure of causal relationships. The results of the model help clarify policy priorities and provide specific directions for improving carbon neutrality goals. The OLS model has high controllability, and researchers can flexibly add control variables according to specific needs. By introducing various factors such as economy and society, the model can comprehensively consider multiple aspects that affect elderly care services and carbon neutrality, making the research results more accurate and practical.

The OLS regression analysis in this article not only demonstrates the quantitative relationship between elderly care capacity and carbon neutrality but also provides practical theoretical basis for policymaking. By analyzing the results, policymakers can better understand how to achieve carbon neutrality goals by adjusting elderly care industry policies and promoting green development. The constructed model is as follows:

$${socre1}_{it}=a_0+{\beta }_1{old1}_{it}+{\beta }_2{eri}_{it}+{\beta }_3{tfp}_{it}+{\beta }_4{lnpop}_{it}+{\beta }_5{industrial}_{it}+{\mathrm{ℇ}}_{it}$$

(3)

$${ socre1}_{it}=a_0+{\beta }_1{old1}_{it}+{{\beta }_2{old12}_{it}+\beta }_3{eri}_{it}+{\beta }_4{tfp}_{it}+{\beta }_5{lnpop}_{it}+{\beta }_6{industrial}_{it}+{\mathrm{ℇ}}_{it}$$

(4)

In Formulas (3) and (4), $i$ represents the region, and $t$ represents the year; ${old1}_{it}$ refers to the independent variable, representing the overall elderly care capacity level. ${old12}_{it}$ represents the square term of the overall elderly care capability level. ${score1}_{it}$ is the dependent variable, representing the level of carbon neutrality; ${eri}_{it}$ indicates the intensity of environmental regulation; ${tfp}_{it}$ represents the total factor productivity; ${lnpop}_{it}$ denotes the natural population growth rate; ${industrial}_{it}$ represents an upgrading of the industrial structure; ${\beta }_1~{\beta }_6$ represents variable coefficients; $a_0$ represents the constant term; $\epsilon$ is the random error term.

4.2.2. Construction of the Spatial Durbin Model

The Spatial Durbin Model (SDM) is an econometric framework developed to address spatial correlations and falls within the wider range of spatial econometric models. In contrast to classical regression models, spatial econometric models account for spatial dependence, recognizing that variables in one area can be affected by corresponding variables in nearby regions. Building upon both the Spatial Lag Model (SLM) and the Spatial Error Model (SEM), the Spatial Durbin Model has found extensive application in disciplines like regional economics, geography, and urban economics. By incorporating spatial lag effects for both the dependent and independent variables, the SDM effectively captures spatial interdependence, making it particularly well suited for analyzing data exhibiting spatial correlations.

In the context of comprehensive elderly care capacity and carbon neutrality, there may be a significant mutual influence in a geographic space. For example, the level of elderly care services in a region may be influenced by policies and practices in neighboring areas, while carbon emissions may spread across different regions due to natural factors such as air flow (Stewart et al., 2015) [45]. The Spatial Durbin Model (SDM) is well suited for capturing these spatial interactions and spillover effects, delivering more comprehensive and precise analysis outcomes. By integrating spatial dependency, the SDM not only examines the direct connections between independent and dependent variables but also explores how variables in one area influence those in adjacent areas. When compared to conventional spatial error models (SEMs) and spatial lag models (SLMs), the SDM emerges as a more flexible and inclusive tool, capable of more effectively illustrating complex spatial relationships. Additionally, the Spatial Durbin Model successfully addresses the issue of spatial autocorrelation, offering more accurate and reliable estimation results.

In this study, the objective is to examine the spatial impacts of comprehensive elderly care capacity and carbon neutrality. The Spatial Durbin Model is an appropriate selection for several reasons. Firstly, it is able to model both direct and spillover effects across regions, which is crucial when studying phenomena that may have widespread impacts on neighboring areas. Secondly, the model is capable of handling spatial autocorrelation issues, which are common features in environmental and policy outcome data, such as carbon emissions and elderly care, typically influenced by neighboring regions. Finally, SDM allows for the simultaneous consideration of spatial dependencies of both independent and dependent variables, providing us with a more detailed understanding of spatial dynamics.

Current models, especially spatial lag models (SLMs) and spatial error models (SEMs), offer significant insights into the spatial connections within economic and environmental studies. However, they have limitations in dealing with complex interactions where both independent and dependent variables have spatial dependencies. In contrast, SDM provides a more comprehensive framework for understanding these interactions. Mainali (2015) [46] discovered that the Spatial Durbin Model (SDM) not only increases the model’s flexibility in capturing spatial relationships but also strengthens the reliability of the estimation results, particularly when spatial spillover effects are present. In this research, the SDM successfully captured the spatial lag effects of both dependent and independent variables, offering a more precise and trustworthy view to understand the interaction between elderly care capacity and carbon emissions across different regions. This provides strong support for policy analysis, as it can take into account local and external factors that affect outcomes, providing valuable insights for designing more effective and regional carbon reduction and elderly care policies.

To explore the spatial impact of comprehensive elderly care capacity on carbon neutral development, this paper constructs a Spatial Durbin Model (SDM), as shown in Equation (5):

$${score1}_{it}=\rho {\sum }_{j=1}^n{W}_{ij}{score1}_{it}+{{\beta }_{1}old1}_{it}+{\theta }_1{\sum }_{j=1}^n{W}_{ij}{old1}_{it}+\lambda X_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(5)

In Equation (5), $i$ represents area,$j$ represents the area adjacent to $i;$ $t$ denotes year; $W$ is a $n\times n$ order geographical distance spatial weight matrix; $\rho$ refers to the spatial autocorrelation coefficient of the explained variable to measure the possible spatial correlation of the explained variable between regions; $\beta$ indicates the regression coefficient of the explanatory variables, which measures the influence of explanatory variables on explained variables in the region; $\theta$ is the spatial regression coefficient of explanatory variables to measure the spatial spillover effect of explanatory variables; $X_{it}$ denotes control variables, including ${eri}_{it},{tfp}_{it},{lnpop}_{it}, \mathrm{a}\mathrm{n}\mathrm{d} {industrial}_{it}$; ${\mu }_i$ is the spatial fixed effect; ${\lambda }_t$ is the time fixed effect; ${\epsilon }_{it}$ is the random error term.

4.2.3. Construction of a Mediating Effect Model

The Mediation Effect Model is employed to examine whether the effect of an independent variable (X) on a dependent variable (Y) is transmitted through a mediator variable (M), essentially exploring if X influences Y indirectly by affecting M. This model helps uncover the indirect relationships between variables and provides deeper insights into complex influence mechanisms. Typically, the analysis involves three steps: (1) confirming whether the total effect of X on Y is significant; (2) verifying whether X significantly affects the mediator variable (M); and (3) assessing whether, controlling for X, M significantly influences Y, thereby confirming the indirect effect of X on Y through M. The mediation model is particularly useful for revealing the indirect influence mechanisms and aiding in the understanding of complex causal relationships, offering a systematic method to analyze the role of mediator variables and enriching theories and practical applications.

When examining the role of the unemployment rate as a mediator in the relationship between comprehensive pension capacity and the development of carbon neutrality, the mediation model becomes essential for understanding the complex interactions among these variables. The capacity for comprehensive pension provision indirectly influences the labor market, specifically the unemployment rate, by reducing family responsibilities and enhancing the quality of life for older adults. Enhanced pension services enable middle-aged workers to enter and stabilize the job market, thereby reducing the unemployment rate, which, in turn, influences carbon neutrality development. A lower unemployment rate generally promotes stable economic activities, fostering the adoption of green technologies and low-carbon policies.

The mediation model effectively demonstrates the unemployment rate’s role as a mediator, showing how improvements in comprehensive pension capacity affect carbon neutrality through changes in the unemployment rate. For example, a decrease in the unemployment rate can boost economic activity, leading to greater investment in renewable energy and eco-friendly technologies, which, in turn, helps reduce carbon emissions. Conversely, a high unemployment rate may dampen economic vitality and hinder carbon reduction efforts. By applying the mediation model, researchers can quantify the specific impact of the unemployment rate in this process, accurately assessing the extent to which comprehensive pension capacity influences carbon neutrality via the labor market. This analytical framework not only elucidates the complex interactions among comprehensive pension capacity, unemployment rate, and carbon neutrality but also provides empirical support for more effective policy design, facilitating the achievement of multiple social goals. To investigate the role of the unemployment rate (${ur1}_{it}$) in mediating the impact of carbon neutral development on high-quality economic development, this paper constructs a mediation model as follows:

$${socre1}_{it}=a_0+{\beta }_1{old1}_{it}+{\beta }_2{eri}_{it}+{\beta }_3{tfp}_{it}+{\beta }_4{lnpop}_{it}+{\beta }_5{industrial}_{it}+{\mathrm{ℇ}}_{it}$$

(6)

$${ur1}_{it}=a_0+{\beta }_1{old1}_{it}+{\beta }_2{eri}_{it}+{\beta }_3{tfp}_{it}+{\beta }_4{lnpop}_{it}+{\beta }_5{industrial}_{it}+{\mathrm{ℇ}}_{it}$$

(7)

$${socre1}_{it}=a_0+{\beta }_1{\mathrm{u}\mathrm{r}1}_{it}+{\beta }_2{old1}_{it}+{\beta }_3{eri}_{it}+{\beta }_4{tfp}_{it}+{\beta }_5{lnpop}_{it}+{\beta }_6{industrial}_{it}+{ℇ}_{it}$$

(8)

In Formulas (6)–(8), $i$ represents the region, and $t$ represents the year; ${old1}_{it}$ represents the dependent variable, representing the overall elderly care capacity level. ${score1}_{it}$ is the independent variable, representing the level of carbon neutrality; ${ur1}_{it}$ is the mediating variable, representing the unemployment rate; the control variables include ${eri}_{it},{tfp}_{it},{lnpop}_{it}, \mathrm{a}\mathrm{n}\mathrm{d} {industrial}_{it}$; ${\beta }_1~{\beta }_6$ represents variable coefficients; $a_0$ denotes the constant term; $\epsilon$ is the random error term.

4.2.4. Entropy Method Calculation Model

The entropy weight method is an objective approach that relies on the calculation of information entropy to assign weights to indicators. This method helps to effectively minimize subjective bias that may arise from human influences. When constructing the comprehensive capacity for elderly care and carbon neutrality index, multiple complex social, economic, and environmental indicators are involved, and the entropy weight method can handle these multidimensional data. It measures the information content and dispersion of each indicator, assigning higher weights to indicators with larger information content, thereby ensuring the objectivity, impartiality, and scientificity of the evaluation results. Especially in comprehensive evaluation systems involving multiple factors, the entropy weight method helps to improve the reliability and rationality of analysis results.

To neutralize the effect of varying measurement units, a dimensionless treatment of the indicators is performed. This method involves using the maximum and minimum values as reference points for linear transformation. After this transformation, the values of the indicators fall within the range of 0 to 1. Indicators are classified as either positive or negative. Positive indicators contribute to higher scores, while negative indicators lead to lower scores. The calculations are detailed in Formulas (9) and (10):

$$Y_{ij}={\displaystyle \frac{X_{ij}-X_{min}}{X_{max}-X_{min}}}$$

(9)

$$Y_{ij}={\displaystyle \frac{X_{max}-X_{ij}}{X_{max}-X_{min}}}$$

(10)

where $X_{max}$ and $X_{min}$ represent the maximum and minimum values of an index, $Y_{ij}$ and $X_{ij}$ are a dimensionless index.

Third, calculate the information entropy. This metric measures the level of disorder within the system. Although the absolute values of the system and information entropy are identical, their signs are opposite. A higher information entropy indicates greater disorder and lower utility value, while the converse is true for lower entropy. The exact formula is provided in Formula (11):

$$e_{ij}=-k{\sum }_{i=1}^n{Y}_{ij}ln{Y}_{ij},k>0$$

(11)

$Y_{ij}={\displaystyle \frac{r_{ij}}{\sum _{i=1}^n{r}_{ij}}}$ represents the proportion of index value of the $i$ region under the $j$ index.

Fourth, calculate the difference coefficient $d_j$. See Formula (12) for details.

$$d_j=1-e_j$$

(12)

Fifth, the weight of each indicator is obtained by normalizing the difference coefficient. The specific algorithm is shown in Formula (13):

$$W_j={\displaystyle \frac{d_j}{\sum _{i=1}^n{d}_j}}$$

(13)

Sixth, calculate the green finance index indicators of each region. The specific algorithm is shown in Formula (14):

$$Y_{ij}={\sum }_{j=1}^n{W}_j{e}_{ij}$$

(14)

4.3. Descriptive Statistics

This article performs descriptive statistics on the variables of the relevant model using Stata (https://www.stata.com/), with the results presented in

Table 3. Descriptive statistics.

Variable	Obs	Mean	SD	Min	Max
score1	270	0.501	0.054	0.322	0.594
old1	270	0.291	0.114	−0.032	0.651
eri	270	0.570	0.713	−1.200	3.920
gtfp	270	1.337	0.520	0.606	4.491
lnpop	270	5.504	1.277	2.098	8.261
industrial	270	52.080	10.078	29.100	91.060
financeim	270	3.471	1.174	1.181	7.901
ur1	270	3.008	0.785	0.050	4.820

. The original data for these variables are obtained from various sources, including the China Statistical Yearbook, China Financial Yearbook, China Environmental Statistical Yearbook, China Industrial Statistical Yearbook, China Insurance Yearbook, and China Provincial Statistical Yearbook, as well as the CSMAR database and Wind database.

The reasons for selecting the data time are as follows: Firstly, after 2014, China began to pay more attention to sustainable development and carbon neutrality goals, and relevant policies and measures were gradually implemented. The data during this period can reflect the actual impact of policy implementation on elderly care services and carbon neutrality. Secondly, during this period, the aging problem in Chinese society has become increasingly prominent, and the improvement of comprehensive elderly care capabilities and the relationship with carbon neutrality have become more important. Therefore, selecting data for this time period is more in line with the research topic, and between 2014 and 2022, relevant statistical data were relatively easy to obtain, and various indicators usually maintained consistency within this time range, which is helpful for data comparison and analysis. When conducting regression analysis or other model analysis, the robustness of the results can be tested through in-sample and out-of-sample validation. Selecting data from 2014 to 2022 can provide a basis for cross-validation of the results of different models.

5. Results and Discussion

5.1. Data Stability Test

Prior to performing the regression analysis, this paper carries out a data stationarity test, which includes a unit root test. The results are presented in

Table 4. Unit root tests.

Unit Root Test		score1	old1	eri	gtfp
FISHER	Inverse chi-squared	121.837 ***	458.020 ***	159.935 ***	114.575 ***
	Inverse normal	2.320	−6.934 ***	0.549	1.176
	Inverse logit t	0.249	−18.815 ***	−1.036 **	−0.069
	Modified inv. chi-squared	5.645 ***	36.334 ***	9.123 ***	4.982 ***
LLC	Adjusted t	−110 ***	−21.864 ***	−30.052 ***	−7.180 ***
IPS	W-t-bar	−280 ***	−5.715 ***	−5.037 ***	2.922
HADRI	z	9.090 ***	8.652 ***	8.852 ***	9.852 ***
Unit Root Test		lmpop	industrial	financeim	ur1
	Inverse chi-squared	510.925 ***	167.022 ***	349.628 ***	422.285 ***
FISHER	Inverse normal	−8.672 ***	0.391	−6.421 ***	−6.142 ***
	Inverse logit t	−22.340 ***	−3.497 ***	−14.469 ***	−17.003 ***
	Modified inv. chi-squared	41.164 ***	9.770 ***	26.439 ***	33.072 ***
LLC	Adjusted t	−7.630 ***	−17.576 ***	−160 ***	−20.841 ***
IPS	W-t-bar	0.918	−69.352 ***	−30.952 ***	−9.926 ***
HADRI	z	9.176 ***	9.314 ***	8.363 ***	9.172 ***

Standard errors in parentheses; ** p < 0.05, and *** p < 0.01.

.

(1) Each variable has successfully passed at least two of the FISHER, LLC, IPS, and HADRI unit root tests, confirming the validity of the selected variables, as shown in Table 4.

(2) The panel data successfully passed both the Pedroni and Westerlund cointegration tests, which verifies the stability of the regression residuals and indicates a long-term equilibrium relationship among the variables. Consequently, the regression results are more trustworthy, allowing the original equation to be directly estimated based on these results, as shown in

Table 5. Panel cointegration tests.

Panel Cointegration Tests		Statistic	p-Value
Pedroni	Modified Phillips–Perron t	9.285	0.000
Pedroni	Phillips–Perron t	−18.375	0.000
Pedroni	Augmented Dickey–Fuller t	−25.853	0.000
Westerlund	Variance ratio	717.046	0.000

.

5.2. OLS Regression

This study employed feasible generalized least squares (FGLS) and panel-corrected standard errors (PCSEs) regression. The results presented in

Table 6. Results of the FGLS test, PCSE test, and OLS.

	OLS	PCSE	FGLS
old1	0.061 **	0.061 *	0.061 **
	(0.029)	(0.032)	(0.029)
eri	−0.050 ***	−0.050 ***	−0.050 ***
	(0.004)	(0.009)	(0.004)
lnpop	0.002	0.002	0.002
	(0.002)	(0.002)	(0.002)
industrial	−0.0002	−0.0002	−0.0002
	(0.0003)	(0.0003)	(0.0003)
gtfp	0.008	0.008	0.008
	(0.005)	(0.006)	(0.005)
_cons	0.502 ***	0.502 ***	0.502 ***
	(0.016)	(0.010)	(0.016)
R2	0.372	-	-
Id	Yes	Yes	Yes
Year	Yes	Yes	Yes
Obs	270	270	270
Province	30	30	30

Standard errors in parentheses; * p < 0.1, ** p < 0.05, and *** p < 0.01.

align with those obtained from ordinary least squares (OLS) regression, bolstering the reliability of the research findings. Additionally, a stepwise methodology is utilized to introduce control variables and reduce the impact of confounding factors.

The OLS results show that the coefficient of 0.061 suggests an improvement in comprehensive elderly care capacity and contributes to carbon neutrality, with statistical significance at the 5% level. This indicates that enhancing elderly care capabilities can effectively support carbon neutrality efforts and aid in reaching carbon neutrality objectives. Thus, Hypothesis 1 is validated. This perspective is straightforward, as enhancing the overall pension capacity is directly linked to pension funds. Such funds can be invested in green financial instruments like green bonds and sustainable development funds. These investments, in turn, can finance environmentally friendly projects and businesses, helping to advance carbon neutrality.

5.3. Spatial Durbin Regression

5.3.1. Moran Index Test

Prior to developing the spatial model, the Moran’s index was computed for both the carbon neutrality index and the comprehensive elderly care capacity index, utilizing a spatial weight matrix based on geographic distances. The significance test of the Moran’s index assists in assessing whether there is notable spatial autocorrelation in the geographical data. If the significance test reveals substantial spatial autocorrelation, indicating that the Moran’s index significantly differs from a random distribution, we can infer that the spatial distribution of the data is not random and thus justify the use of a spatial model. As illustrated in

Table 7. Moran’s I test results.

Year	score1	old1
2014	0.136 *	0.119 *
	(0.095)	(0.095)
2015	0.124 **	0.030
	(0.094)	(0.096)
2016	0.153 **	0.176 **
	(0.093)	(0.096)
2017	0.173 **	0.129 *
	(0.093)	(0.096)
2018	0.180 **	0.219 ***
	(0.093)	(0.096)
2019	0.181 **	0.152 *
	(0.093)	(0.097)
2020	0.179 **	0.066
	(0.093)	(0.097)
2021	0.173 **	−0.005 *
	(0.093)	(0.096)
2022	0.167 **	−0.054 *
	(0.094)	(0.096)

Standard errors in parentheses; * p < 0.1, ** p < 0.05, and *** p < 0.01.

, the Moran’s index for the carbon neutrality index is significant from 2014 to 2021, and for the comprehensive elderly care capacity index, it is significant in most years. Hence, it is reasonable to proceed with building a spatial model.

5.3.2. Spatial Durbin Regression

To examine the spatial relationship between the two variables, this study employs the Spatial Durbin Model (SDM) regression to analyze their spatial effects. Prior to running the SDM regression, a series of preliminary tests was carried out, and the findings are presented in Model (2) of

Table 8. Results of the OLS panel regression and spatial regression.

	Model (1a) OLS	Model (2a) (Main)	Model (2b) (Wx)
old1	0.061 **	0.032 **	−0.119 ***
	(0.029)	(0.014)	(0.034)
eri	−0.050 ***	−0.004 **	0.016 **
	(0.004)	(0.002)	(0.007)
lnpop	0.002	0.097 ***	−0.152 ***
	(0.002)	(0.031)	(0.052)
industrial	−0.0002	0.0004 ***	0.0002
	(0.0003)	(0.0002)	(0.0003)
gtfp	0.008	−0.0008	−0.004
	(0.005)	(0.003)	(0.005)
_cons	0.502 ***	0.538 ***	-
	(0.016)	(0.174)	-
		Log-likelihood	−0.155 ***
		lrtest both ind	44.91 ***
		lrtest both time	746.60 ***
		Wald_lag	42.30 ***
		Wald_error	26.32 ***
		LR_lag	40.66 ***
		LR_error	35.69 ***
		rho	0.588 ***
			(0.077)
		sigma2_e	0.0001 ***
			(0.00001)
Obs	270
Province	30

Standard errors in parentheses; ** p < 0.05, and *** p < 0.01.

. Based on these results, the Spatial Durbin Model adopted in this paper is deemed scientifically appropriate and justified.

As illustrated in Model (2) of Table 8, the direct effect (Main) of the Spatial Durbin Model is consistent with the findings from the OLS regression. It indicates a positive and statistically significant correlation between the enhancement of the comprehensive elderly care capacity and carbon neutrality, with a coefficient of 0.032, significant at the 5% level. This suggests that enhancing the elderly care capacity contributes to advancing carbon neutrality. However, the spatial spillover effects tell a different story: the local improvement in elderly care capacity appears to negatively affect neighboring regions’ carbon neutrality, warranting further investigation into the underlying causes. In Model (2b) (Mx), the spatial spillover effect is markedly negative, with a coefficient of −0.119, significant at the 1% level. This suggests that, although improvements in local elderly care contribute to regional carbon neutrality, they have a detrimental impact on carbon neutrality efforts in nearby areas. This leads to an important question: Why do the direct effect and the spatial spillover effect show contrasting outcomes? Firstly, the improvement of comprehensive elderly care capacity may imply economic development and social progress in the local area, which can lead to more resources and technologies being invested in the field of carbon neutrality, thus driving carbon neutrality. Secondly, the improvement of comprehensive elderly care capacity may bring about population stability and a sense of social security, contributing to the creation of a stable social environment and providing the basic conditions for carbon neutrality. Furthermore, enhancing the comprehensive elderly care capacity may also encourage increased social engagement and awareness, leading individuals and organizations to place greater emphasis on environmental protection and carbon reduction, thus supporting carbon neutrality. However, when the local area’s elderly care capacity improves, it may have a certain inhibitory effect on the carbon neutrality of neighboring areas. This could be due to competition for resources and investment, as the local area may attract more resources and investment after the improvement of the elderly care capacity, resulting in limitations on the carbon neutrality of neighboring areas. Furthermore, the improvement of the elderly care capacity may lead to population and resource flows, thereby affecting the carbon neutrality of neighboring areas.

5.4. Regression Results and Analysis of the Mediating Effect Model

This study employed a mediation regression model to explore the mediating effect of the unemployment rate on the link between comprehensive elderly care capacity and carbon neutrality. As illustrated in

Table 9. Results of the mediating effect regression analysis.

	Path (1)	Path (2)	Path (3)
Variable	score1	ur1	score1
ur1	-	-	−0.015 ***
			(0.004)
old1	0.061 **	−0.457 *	0.055 *
	(0.029)	(0.489)	(0.028)
eri	−0.050 ***	−0.119	−0.052 ***
	(0.004)	(0.093)	(0.004)
gtfp	0.002	−0.091	0.007
	(0.002)	(0.090)	(0.005)
lnpop	−0.0002	0.150 ***	−0.004 *
	(0.0003)	(0.042)	(0.002)
industrial	0.008	−0.034 ***	−0.001 **
	(0.005)	(0.005)	(0.0003)
_cons	0.502 ***	4.285 ***	0.564 ***
	(0.020)	(0.268)	(0.022)
Id	Yes	Yes	Yes
Year	Yes	Yes	Yes
obs	270
province	30

Standard errors in parentheses; * p < 0.1, ** p < 0.05, and *** p < 0.01.

, Path (1) denotes the direct impact of elderly care capacity on carbon neutrality, whereas Path (2) and Path (3) reflect the indirect effects. The regression analysis indicates that enhancing the comprehensive elderly care capacity tends to lower the unemployment rate, with a statistically significant reduction at the 10% significance level (coefficient of −0.457). Additionally, there is a negative relationship between the unemployment rate and carbon neutrality, suggesting that a decline in the unemployment rate supports carbon neutrality, significant at the 1% level with a coefficient of −0.015. These regression results demonstrate that the enhancement of the comprehensive elderly care capacity effectively reduces the unemployment rate, thereby achieving carbon neutrality and validating Hypotheses 2 and 3. This channel can be easily understood. Firstly, the improvement in comprehensive elderly care capacity will facilitate the development of modern elderly care services, including specialized nursing homes, digital caregiving agencies, and health management. This will create more green employment opportunities, absorb unemployed individuals into the workforce, and reduce the unemployment rate. Simultaneously, these green and intelligent industries will drive carbon neutrality, contributing to the achievement of carbon neutrality goals. Secondly, the enhancement of the comprehensive elderly care capacity requires support from green technologies and green industries. Investment and development in the green economy will generate more job positions in renewable energy, clean transportation, environmental protection, and other fields. This will stimulate economic growth and reduce the unemployment rate. In conclusion, the improvement in comprehensive elderly care capacity effectively reduces the unemployment rate, while a decrease in the unemployment rate contributes to carbon neutrality. By creating job opportunities, promoting the development of the green economy, enhancing labor force skills, stimulating consumer demand, and providing policy support, a virtuous cycle between comprehensive elderly care capacity and carbon neutrality can be achieved.

5.5. Discussion on the Robustness Test Result

Robustness Test of the OLS

To evaluate the robustness of the regression outcomes, this study employed principal component analysis (PCA) to develop alternative composite indices for comprehensive elderly care capacity. These newly created indices were then used in a subsequent regression analysis. As presented in column (1) of

Table 10. Robustness test of the OLS.

(1)		(2)
old2	0.051 *	old1	0.055 *
	(0.027)		(0.029)
eri	−0.050 ***	eri	−0.051 ***
	(0.004)		(0.004)
gtfp	0.008	gtfp	0.006
	(0.005)		(0.005)
lnpop	0.003	lnpop	0.002
	(0.002)		(0.002)
industrial	−0.0002	industrial	0.0002
	(0.0003)		(0.0004)
-	-	financeim	−0.005
	-		(0.003)
_cons	0.497 ***	_cons	0.501 ***
	(0.016)		(0.016)
Id	Yes	Id	Yes
Year	Yes	Year	Yes
Obs	270	Obs	270
province	30	province	30

Standard errors in parentheses; * p < 0.1, and *** p < 0.01.

, the results suggest that enhancements in elderly care capacity lead to advancements in carbon neutrality, consistent with the results from the OLS regression, further confirming the model’s robustness. Furthermore, an additional regression analysis was carried out, this time including control variables. The findings, illustrated in column (2) of

Table 11. Endogeneity test.

(1)		(2)		(3)
	-	-	-	score1 (L1)	0.413 ***
	-	-	-		(0.059)
old11	0.088 **	old1	0.109 ***	old1	0.483 ***
	(0.039)		(0.033)		(0.125)
eri	−0.060 ***	eri1	−0.071 ***	eri1	−0.012 ***
	(0.005)		(0.006)		(0.003)
gtfp	0.017 **	gtfp1	0.025 ***	gtfp1	−0.0002
	(0.007)		(0.009)		(0.0004)
lnpop	0.001	lnpop1	−0.0001	lnpop1	0.035
	(0.003)		(0.003)		(0.044)
industrial	−0.0004	industrial1	−0.0004	industrial1	0.001 *
	(0.0003)		(0.0004)		(0.0007)
_cons	0.506 ***	_cons	0.500 ***	AR(2)	2.22 **
	(0.019)		(0.019)	Sargan	34.74 ***
Id	Yes	ID	Yes	ID	Yes
Year	Yes	Year	Yes	Year	Yes
province	30	province	30	province	30

Standard errors in parentheses; * p < 0.1, ** p < 0.05, and *** p < 0.01.

, largely correspond with the OLS results, underscoring the model’s stability.

Endogeneity refers to the potential correlation between explanatory variables and error terms, which can result in biased estimates in regression models. To address this issue, we can introduce a time lag to the explanatory or control variables by one period. This allows for a comparison between the current values of these variables and their earlier values, thereby helping to reduce endogeneity concerns. If, after incorporating lagged variables, the coefficient estimates of the regression model continue to be statistically significant and in line with the anticipated direction, it can be inferred that the endogeneity problem has been mitigated. In this study, the explanatory variable “old1” and associated control variables were lagged by one period, and a regression analysis was performed. The results presented in columns (1) and (2) of Table 11 align with those of the OLS regression. Furthermore, the Generalized Method of Moments (GMMs) Model was employed to test for endogeneity, with the results shown in Table 11 (3) also corroborating the baseline regression findings.

6. Conclusions and Policy Implications

This study investigates the relationship between carbon neutrality and comprehensive elderly care capabilities by developing relevant indicators, making significant innovative contributions to the field. Compared to the existing literature, our research not only expands the theoretical framework but also introduces new perspectives in empirical analysis. Utilizing panel data from 30 provinces (cities) in China from 2014 to 2022, we employ baseline regression models, spatial effect models, and multidimensional coupling coordination analysis to systematically explore the relationship between enhanced elderly care capabilities and carbon neutrality.

(1)

Innovative Contributions

Firstly, this study is the first to quantitatively analyze the relationship between comprehensive elderly care capabilities and carbon neutrality goals by constructing a clear indicator system, thereby filling a gap in this area of research. Our findings emphasize the positive role of enhancing elderly care capabilities in achieving carbon neutrality, revealing a direct relationship between the two, which contrasts sharply with previous studies that mainly focused on single-factor analyses. Secondly, this research specifically addresses the issue of spatial spillover effects, discovering a negative spatial spillover effect, which indicates that improvements in elderly care capabilities in one region may hinder carbon neutrality in neighboring areas. This finding expands the existing understanding of inter-regional interactions, highlighting the need for policymakers to consider regional coordination when promoting the development of elderly services to avoid resource and policy imbalances.

(2)

Differences from Existing Research

Differing from previous studies, this research delves into the role of unemployment rates as a significant mediating variable connecting elderly care capabilities and carbon neutrality. Prior literature has often overlooked the impact of employment factors on elderly services and environmental sustainability. Our research indicates that enhancing elderly care capabilities not only directly promotes carbon neutrality but also indirectly advances the achievement of carbon neutrality goals by lowering unemployment rates. This perspective offers new insights into understanding the complex relationships between elderly services, economic development, and environmental protection. Additionally, this study explores the potential impact of digitalization in elderly services on enhancing care capabilities and achieving carbon neutrality, emphasizing the importance of digital transformation in promoting sustainable development. This direction of research is relatively scarce in the existing literature, making this exploration significant from both academic and practical standpoints.

In summary, this study not only presents new perspectives and contributions theoretically but also deeply investigates the complex relationship between elderly care, digitalization, and environmental sustainability in empirical analysis, providing scientific evidence for the formulation and implementation of related policies.

Based on these conclusions, the study offers the following recommendations:

(1)

Analyzing the Impact of Digitalization on Long-Term Sustainability

In the process of enhancing elderly care capabilities, the application of digital technologies can significantly improve service efficiency and quality. By introducing intelligent management systems and data analysis tools, elderly care institutions can better monitor the needs of the elderly, optimize resource allocation, and reduce operational costs. At the same time, digitalization can promote remote care and health monitoring, allowing elderly individuals to receive better care at home, thereby reducing reliance on physical care facilities and promoting sustainable development. Therefore, analyzing the impact of digitalization on elderly care and carbon neutrality over a longer timespan helps to understand its potential in improving efficiency, reducing carbon emissions, and enhancing the quality of life for the elderly.

(2)

The Role of Local Environmental Policies

In addressing the U-shaped relationship between the improvement of elderly care capabilities and carbon neutrality, local environmental policies play a crucial role. Local governments can encourage elderly care institutions to adopt low-carbon technologies and renewable energy through the formulation and implementation of green policies. Such policies not only help reduce carbon emissions but also promote the sustainable development of elderly services. For example, establishing green building standards for elderly care facilities can push for the use of environmentally friendly materials and energy-efficient equipment, achieving a win–win in both economic and environmental aspects. Integrating the role of local environmental policies helps to delve deeper into how they influence the enhancement of elderly care capabilities and the achievement of carbon neutrality goals.

(3)

Developing Advanced Simulation Models to Test Intervention Policies

In managing the negative spatial spillover effects of improving elderly care capabilities and carbon neutrality, developing more advanced simulation models will aid in assessing the effects of different policy interventions. By constructing dynamic system models, it is possible to simulate the flow of elderly service resources, their spatial distribution, and the impact of policy interventions on the supply of elderly services and carbon emissions. These models can provide policymakers with more scientific evidence, helping them formulate more precise resource allocation plans and regional cooperation mechanisms. Additionally, simulation models can evaluate the effects of various intervention policies under different scenarios, guiding the comprehensive advancement of elderly capability enhancement and carbon neutrality goals.

(4)

Exploring the Role of Human Factors in Sustainability

When promoting the comprehensive progress of elderly capabilities and carbon neutrality, the role of human factors cannot be overlooked. Training for elderly care professionals, public awareness of elderly services, and societal support for carbon neutrality all have significant impacts on sustainable development. Therefore, exploring how to enhance societal awareness of both elderly care and environmental protection through education and outreach can foster coordinated development of the two. For instance, community-based campaigns promoting green care and sustainable consumption can raise residents’ awareness. Additionally, policies should strengthen professional support and career development planning for those in the elderly care sector to motivate more individuals to engage in this field, contributing to the achievement of carbon neutrality objectives.