Impact mechanism and spatial spillover effect of the digital economy on the high-quality development of undertakings for the aged in China

Abstract

Background

Digitalization and population aging have had a profound impact on the development of undertakings for the aged, which brings challenges as well as opportunities for elder care system. This study examines the impact of the digital economy on the high-quality development (HQD) of undertakings for the aged in China.

Methods

Based on the panel data of 31 provinces in mainland China from 2013 to 2021, this study explores the influence mechanism of the HQD of undertakings for the aged driven by the digital economy and its spatial spillover effects. The benchmark regression model is used to investigate the impact of the development level of the digital economy on the HQD of undertakings for the aged. The mediation effect model is used to explore the indirect effects of the digital economy on the HQD of undertakings for the aged through the influence of the intermediary variable. The spatial panel model is then used to analyze the spatial spillover effect of the digital economy on the HQD of undertakings for the aged.

Results

The digital economy has a positive effect (coefficient = 0.1530, P-value < 0.01) on the local HQD of undertakings for the aged and a negative effect (coefficient = − 0.1012, P-value < 0.01) on the level of the HQD of undertakings for the aged in neighboring areas after controlling for other variables. The mediation effect of the proportion of the tertiary industry in GDP accounts for 6.6% of the total effect of the digital economy on the HQD of undertakings for the aged.

Conclusions

The digital economy can significantly promote the HQD of undertakings for the aged by transforming the development of the tertiary industry. The improvement in the digital economy has a significant spatial spillover effect. This research enriches the existing body of literature by suggesting effective ways to enhance the HQD of undertakings for the aged through the digital economy and the tertiary industry.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-024-20750-z.

Background

Population aging has challenged the Chinese government’s ability to deal with the increasing demand for elderly care services [1–3]. According to the China Statistical Yearbook, China had around 205 million older adults aged 65 years and over in 2021, accounting for 14.2% of the total population. Moreover, the dependency ratio of the older adults aged 65 and over was 20.8%, indicating that every 100 working-age people must undertake the task of caring for over 20 older adults. However, the development level of undertakings for the aged in China is relatively low [4], characterized by insufficient human capital for care services [1], a mismatch between the supply and needs of care facilities [1], and inadequate social old-age security for the older adults [3]. In response, the Chinese central government put forward to promote the high-quality development (HQD) of undertakings for the aged during the 14th five-year plan period (2021–2025) [5]. The HQD of undertakings for the aged means a more comprehensive social security system for the elderly, a high-quality elderly care system, a high-quality health support system for the elderly, and a high level of social participation of the elderly [4]. In view of the rich connotation of the HQD of undertakings for the aged, it is a noteworthy research proposition to explore the innovation impetus and path mechanism to promote the HQD of undertakings for the aged.

At present, the global digital economy is in a stage of rapid development. According to the Digital Economy Report 2024 released by the United Nations Trade and Development Organization, the digital sales of enterprises in 43 global economies accounted for 75% of the global GDP in 2022 [6]. In the United States, the application of digital technologies such as the Internet and big data in healthcare in the field of digital healthcare, online telemedicine services, and digital health interventions [7] have brought benefits to the older adults, including improving the quality of life [8] and helping them maintain their life independence [8]. In 2022, China’s digital sales reached $4.5 trillion, ranking third among the world’s 43 economies, only lower than the United States and the European Union [6]. According to data released by the Ministry of Industry and Information Technology, China’s digital economy in GDP rose from 32.9% in 2017 to 41.5% in 2022 [9]. From 2017 to 2021, the Chinese government continued to release the Action Plan for the Development of the Smart Health and Elderly Care Industry aimed to promote the integrated innovation and application of information technology in the health and elderly care fields, and improve the intelligent level of health and elder care products and services [10, 11]. The development of a new mode of intelligent elderly care that applies digital technologies to elderly care services is an essential part of them. In the context of aging and digital superposition, the digital economy is expected to revitalize the development of undertakings for the aged in China [4, 12, 13]. Thus, it is meaningful to explore the impact of the digital economy on the development of undertakings for the aged by taking China as the research object. This study can not only provide evidence from China for the study of the impact of digital economy on the HQD of undertakings for the aged, but also enrich the relevant literature on the driving force of the HQD of undertakings for the aged in China.

Much research has been done on the measurement and consequences of the digital economy [14, 15]. The digital economy is an economy based on a technological framework utilizing digital technology [16]. The European Commission maintains an index system of the digital economy and society index with four primary indicators: human capital, connectivity, integration of digital technology, and digital public service [14]. Moreover, the U.S. Bureau of Economic Analysis’ (BEA) digital economy statistics comprise three major categories of goods and services: infrastructure, e-commerce, and priced digital services [15]. According to the 2021 Statistical Classification of Digital Economy and its Core Industries, released by the National Bureau of Statistics of China, the digital economy is divided into five categories: digital product manufacturing, digital product service, digital technology application, digital factor-driven industry, and digital efficiency improvement industry. The core idea of these measurement methods is consistent. Most agree that the digital economy can be divided into two categories: digital industrialization and digitalization of industry.

In terms of the consequences of digital economy development in all around the world, the findings show that the digital economy is a powerful driving force of innovation and total factor productivity [17] in almost all fields of production, ranging from agriculture [18] and manufacturing [19] to the tertiary industry [20]. It can also enhance operational improvements and social and environmental sustainability [21]. Digital technology capital is making more contribution to labor productivity than traditional capital [22]. Based on the literature from the European and the United States, it is believed that the application of digital technologies such as digital medical platform [23], digital health equipment [24, 25], artificial intelligence [26] can provide more personalized services for the elderly [12] and improve the efficiency of medical services [27]. The application of digital technology has not only promoted the digitization of aging industries [28], but also created more jobs [29]. Digital technologies also play a significant role in the development of the undertakings for the aged [4] and work as a driving force of innovation in elderly care services [12, 13], health-care services [27, 30], and the social participation of the elderly [31].

Although some studies have theoretically proposed the view that the digital economy benefits the HQD of undertakings for the aged [32, 33], little research has investigated the relationship between the digital economy and the HQD of undertakings for the aged by using empirical research methods [4, 34]. For example, Peng et al. (2023) [4] studied the driving factors of the HQD of undertakings for the aged [4], and Ding et al. (2024) studied the impact of digital economy on the HQD of the healthcare industry [34]. Unlike the existing literature, this study aims to examine the impact of digital economy on the HQD of undertakings for the aged. Specifically, the influencing mechanism and spatial spillover effect of the digital economy on the HQD of undertakings for the aged in China were examined, the former is used to identify the path of digital economy affecting the HQD of undertakings for the aged, while the latter is used to capture the spatial dependence of HQD of undertakings for the aged in different regions and study the indirect impact of the development of local digital economy on the surrounding areas.

This study makes several key contributions. First, this study analyzes the theoretical mechanism of the direct and indirect impact of the digital economy on the HQD of undertakings for the aged. Second, this study proposes a transmission path of the influence of the digital economy on the HQD of the undertakings for the aged. The mediating role of the tertiary industry development is identified. Third, the spillover effect of the digital economy’s influence on the HQD of elderly care undertakings is examined, which helps us observe their correlation from a spatial perspective.

Theoretical analysis and research hypothesis

Theoretical analysis of digital economy influencing the HQD of the undertakings for the aged

The digital economy can affect the HQD of undertakings for the aged in three dimensions: elderly care services, elderly health services, and social participation of older adults [4]. First, the digital economy helps establish a more comprehensive elderly care service system that provides care services including daily life assistance, community engagement support services, and psychological comfort services [35]. Home-based and community-based elderly care services, including meal assistance, bathing and cleaning assistance, and daily living support, require the implementation of the Internet and the Internet of Things (IoT) [36]. These digital-assisted technologies may potentially improve the effectiveness and output of the elderly care service system [13].

Second, digital technology has transformed health-care delivery. Telemedicine and electronic health records enable elderly individuals to access medical services more conveniently [13, 27, 37], avoiding long waiting times and transportation issues [27]. Moreover, smart devices and sensors can monitor the health status of elderly individuals and provide real-time data to doctors and caregivers [27, 37]. These technologies improve the quality of life and health management for the older adults [38, 39].

Third, digital technology provides more social interaction opportunities through social media, video calls, and online communications [31]. Older adults can engage in remote communication and interaction with family members, friends, and other community members, which reduces their loneliness and facilitates participation in social activities. They can also enjoy the benefits of the digital economy through convenient payment, lower costs associated with searching for care, and more social interaction [40]. Based on the above analysis, the following hypothesis is put forward.

• Hypothesis 1: The digital economy has a positively direct impact on the HQD of undertakings for the aged.

Theoretical analysis of the tertiary industry development as a mediating role

Digital economy and tertiary industry development

The development of the digital economy has promoted the innovative development of the tertiary industry and driven the transformation and upgrading of the tertiary industry [41, 42]. In particular, if we focus on the development of the tertiary industry related to the older adults, the digital economy still plays an important role [43]. The application of digital technology promotes the development of smart elderly care services. For instance, smart home technology provides intelligent safety monitoring and intelligent home assistance facilities, improving the home safety and quality of life for older adults [37, 44]. Furthermore, health management apps and smart devices can monitor the health status of older adults in real time and provide personalized health guidance and preventive measures. Similarly, remote medical technology enables elderly people to interact with doctors through video consultation and remote monitoring, avoiding the inconvenience of long-distance medical treatment [45].

In addition, the development of the digital economy stimulates older adults’ consumer demand for digital products, such as smart phones, digital TV, and social media. For example, social media makes it more convenient for older adults to access external information [37], solving the problem of information silos for the older adults [46] and enhancing the connection between older adults and their family members and friends [47]. Moreover, meeting the consumer demand of the huge elderly population is expected to become an important growth point of the digital industry [13].

Tertiary industry development and the HQD of undertakings for the aged

It has been shown that the development of the tertiary industry has a positive impact on the HQD of undertakings for the aged [4]. A possible reason is that the development of the tertiary industry can provide more resources and opportunities for elderly care services, health care for older adults, and old-age social participation, which benefit the development of undertakings for the aged.

First, let us consider the development of the tertiary industry, accompanied by the improvement of the quantity and diversity of elderly care services. For example, the proportion of the tertiary industry in China’s GDP increased from 43.2% in 2010 to 54.5% in 2020, according to the Chinese Statistic Year Book. During the same period, the number of elderly care beds per 1,000 older adults increased from 17.6 to 31.1, and the number of elderly care institutions increased from 38,900 thousand to 329,000 in China. Elderly care services are also becoming more diversified, not only including daily life care and rehabilitation activities but also cultural and social services, indicating the progress of undertakings for the aged.

Second, the development of the tertiary industry has highlighted the demand for integrated medical and care services [48], which has led to more comprehensive, personalized services for older adults. Moreover, the development of the service industry provides a platform and technical support for the integration of medical and elderly care, making the integration of service provision possible. By integrating medical and elderly care services, medical professionals, geriatricians, and care providers can collaborate to develop care plans based on the needs of older adults and to improve the quality and efficiency of care delivery.

Third, the development of the tertiary industry provides more opportunities for older adults for social participation. The development of the tertiary industry provides a platform and support for elderly education institutions [20], such as university learning programs for older adults and community education projects for older adults. These educational programs have enriched older adults’ social participation, benefiting the HQD of undertakings for the aged. Moreover, the development of the tertiary industry has increased the demand for infrastructure, promoted the construction of infrastructure, provided greater convenience for the interpersonal communication of the older adults, and increased their willingness to participate in society [49]. The development of the tertiary industry has also promoted the development of online platforms through which older adults can better participate in social volunteer services, promoting the social participation of the older adults [50]. Based on the above analysis, the following hypothesis is put forward.

• Hypothesis 2: The development of the tertiary industry plays a mediating role between the relationship of the digital economy and the HQD of undertakings for the aged.

Theoretical analysis of the spatial spillover effect of the digital economy

Existing studies have found that there is a spatial autocorrelation in the development of both digital economy and HQD of undertakings for the aged [4, 34]. According to the cumulative causality of Myrdal [51], once the developed regions (growth poles) have the first mover advantage, they will constantly strengthen their own advantages, and hinder or adversely affect the surrounding backward areas, namely the “echo effect”; after reaching a certain level of development, the developed areas will also spread this advantage condition to drive the rapid development of the surrounding backward areas, that is, the “diffusion effect” [51]. In the initial stage of the development of digital economy, areas with high level of digital economy development will siphon the development resources of the surrounding areas [52, 53], resulting in the loss of human resources for the aged in the surrounding areas and inhibiting the HQD of undertakings for the aged in the surrounding areas. In the advanced stage of digital economy development, the areas with high level of digital economy development force the achievements of digital economy development to spread to the surrounding areas due to the increasing internal competition pressure [52]. On the one hand, digital technology has broken through the barriers of production factors and product information circulation caused by geographical distance restrictions [54]. The application and promotion of telemedicine, intelligent elderly care services can eliminate the adverse impact of insufficient elderly care resources on the development of undertakings for the aged [55]. On the other hand, digital technology has changed the service mode and management concept, and promoted the innovation of elderly care service concept and products [56]. The substitution of intelligent production mode to the traditional production mode makes the elderly manufacturing industry and service industry highly integrated, which further promotes the spillover of elderly care services and aging products in the developed digital economy to the surrounding areas [54–56]. Szerb et al. (2022) measures the development level of the digital economy, ranged from 0 to 100, of all countries in the world. Among them, the digital economy index of the United States is the highest at 85.5, while China’s digital economy index is only 28.1, ranking 58 [57]. Several literatures measured China’s digital economy development level have got the conclusion that the current development of China’s digital economy is not high [52, 58]. Therefore, this study believes that the current development of China’s digital economy is in the primary stage and put forward the following assumption.

• Hypothesis 3: There is an "echo effect" on the impact of digital economy on the HQD of undertakings for the aged.

Data and methods

Data sources and preprocessing

In consideration of the availability of data, this study uses the panel data of 31 provincial administrative regions in mainland China from 2013 to 2021. The data are derived from the datasets of the China Economic and Social Big Data Research Platform (https://data.cnki.net/), the Chinese Research Data Services Platform (https://www.cnrds.com/Home/Login), and the Center for Digital Financial Inclusion at Peking University [59]. The missing data account for less than 4% of the total sample size and are compensated for by using the nearest neighbor interpolation method. More specifically, the missing values are filled with the arithmetic mean of the previous and next data points if both of the data are available. Otherwise, one of the previous and next data points is used to replace it. Excel 2016 and Stata 17 are used to process and analyze the data. ArcGIS 10.2 is used for the generation of maps.

Measurement and calculation method

Referring to the digital economic index system issued by the Chinese National Bureau of Statistics and some empirical analysis literature [60, 61], the index system of the digital economy is constructed from the perspectives of both production factor inputs and outputs of the digital economy. Digital economy input factors include traditional factors of production such as capital, labor, and technology, and digital factors of production including the user base of digital technology, the hardware foundation, and the software foundation of digital technology. Digital economy output factors are used to measure the digitalization of industries and the industrialization of digital technologies. The digitalization of industries consists of the electronic and communication equipment manufacturing industry, telecommunication and internet industry, and software and information technology services industry. The industrialization of digital technologies consists of the digitalization of business transactions and the digitalization of finance. See Table S1 for the details of each indicator.

The index system of the HQD of undertakings for the aged is based on that presented by Peng et al. (2023) [4]. The measuring dimensions of the HQD of undertakings for the aged include old-age social security, elder care service, health care service, and elderly’s social participation. Unlike the index system of Peng et al. (2023) [4], our system excludes two indicators because their official data have not been released since 2019. See Table S2 for the details of each indicator.

The entropy-weight method is employed to calculate the comprehensive development index of the digital economy and the HQD of undertakings for the aged. The basic idea of the entropy-weight method is that the indicator with higher entropy is less informative and, therefore, should be given less weight [62]. The relative importance or weight is calculated based on the degree of uncertainty or entropy associated with each indicator [62]. The values both of digital economy index and HQD index of undertakings for the aged range between 0 and 1. A larger value of these indices indicates a higher level of development. The advantage of the entropy-weight method is that it is an objective evaluation method. It has been widely used to calculate the composite index in literature [4, 60]. The ArcGIS software is used to visualize the comprehensive index of the digital economy and the HQD of undertakings for the aged so that the spatial pattern can be revealed.

Model specification

Based on the theoretical analysis, the benchmark regression model is used to investigate the impact of the development level of the digital economy on the HQD of undertakings for the aged. The mediation effect model is used to explore the indirect effects of the digital economy on the HQD of undertakings for the aged through the influence of the intermediary variable. The spatial panel model is then used to analyze the spatial spillover effect of the digital economy on the HQD of undertakings for the aged.

Benchmark regression model

To investigate the direct effect of the digital economy on the HQD of undertakings for the aged, we establish the benchmark regression models as follows:

$${\mathrm{y}}_{\mathit{it}}={\alpha }_0+{\alpha }_1{\mathrm{X}}_{\mathit{it}}+{\alpha }_2{C}_{\mathit{i}\mathit{t}}+{\delta }_i+{\nu }_{\mathit{it}}+{\mu }_{\mathit{it}}$$ 1

where $y_{\mathit{it}}$ represents the comprehensive index of the HQD of the undertakings of the i^th province in year t, $X_{\mathit{it}}$ is the comprehensive index of the digital economy, and $C_{\mathit{it}}$ represents the control variables. With reference to Peng et al. (2023) [4], the control variables are as follows: the logarithm of per-capita GDP, measuring the local economic development; the level of per-capita social welfare expenditure, measuring the local social well-being; and the proportion of older adults aged 65+, reflecting the population aging level. Moreover, ${\alpha }_i$ is the coefficient, ${\delta }_i$ is the individual fixed effect, $v_t$ is the time fixed effect, and ${\mu }_{\mathit{it}}$ is the random disturbance term.

Before model estimation, we use Wald test and Wooldridge test to test the heteroscedastic and autocorrelation of the panel data, and adopt panel corrected standard error to overcome the above problems [63]. Since panel data usually have endogeneity issue, multiple ways were used to test model robustness. First, to avoid interference with the benchmark regression results by special observations, we conduct the robustness test in two ways. The one is to eliminate the maximum and minimum values by 1% of the variable of digital economy. The another is to exclude the data for 2021 considering to the major emergency of the COVID-19 pandemic. Second, to avoid the interference of the variable measure method to the regression results, we change the digital economic measure method, namely principal component analysis instead of entropy weight method. Third, to alleviate the endogeneity, we replace the digital economy with the first-order lag term of the digital economy to observe the stability of the parameter estimation results.

Mediation effect model

The mediation effect model is used to study the mechanisms of interaction between variables [64]. Given the relationship between the HQD of undertakings for the aged, the tertiary industry development, and the digital economy, a mediation model is established as follows:

$$Z_{\mathit{it}}={\beta }_0+{\beta }_1{X}_{\mathit{it}}+{\beta }_2{C}_{\mathit{it}}+{\delta }_i+{\nu }_t+{\mu }_{\mathit{it}}$$ 2

$$y_{\mathit{it}}={\gamma }_0+{\gamma }_1{X}_{\mathit{it}}+{\gamma }_2{Z}_{\mathit{it}}+{\gamma }_3{C}_{\mathit{it}}+{\delta }_i+{\nu }_t+{\mu }_{\mathit{it}}$$ 3

where $Z_{\mathit{it}}$ is the mediation variable referring to the proportion of the tertiary industry in GDP and ${\beta }_i\text{and}{\gamma }_i$ are coefficients. The meaning of other variables is the same as above. The statistical description of these variables is presented in Table 1. The Sobel test is used to confirm the existence of the mediation effect.

Table 1.

Descriptive statistics of the variables

Variables	Mean	Std.Dev.	Min	Max	Unit
The comprehensive index of the high-quality development of undertakings for the aged	0.1803	0.0706	0.0516	0.4609	-
The comprehensive index of the digital economy	0.1446	0.1274	0.0140	0.7939	-
The logarithm of per capita GDP	1.7235	0.4191	0.8416	2.9124	-
The per capita social welfare expenditure	0.7539	0.6462	0.1422	4.3491	Hundred Yuan
The proportion of older adults aged 65+	0.0818	0.0478	0.0006	0.1613	%
The proportion of tertiary industry in GDP	0.4939	0.0901	0.32	0.84	%

Spatial panel models

Spatial panel models are linear regression models of panel data with spatial lag variables, which are used to analyze data that have both spatial and temporal dimensions [65]. Spatial models are more suitable when the results of the spatial autocorrelation test show an autocorrelation in the error term [66]. The global Moran’s Index is used to test the spatial autocorrelation of the digital economy and the HQD of undertakings for the aged.

In this study, the three widely used spatial models, namely, the spatial autoregressive (SAR) model, the spatial error model (SEM), and the spatial Dubin model (SDM), are employed to examine the impact of the digital economy on the HQD of the undertakings for the aged. The expressions of the model are as follows:

$$y_{\mathit{it}}=\rho W{y}_{\mathit{it}}+X_{\mathit{it}}\beta +C_{\mathit{it}}\gamma +{\delta }_i+{\nu }_t+{\in }_{it}\left(\mathrm{SAR}\right)$$

$$y_{\mathit{it}}=X_{\mathit{it}}\beta +C_{\mathit{it}}\gamma +\lambda W{\mu }_{\mathit{it}}+{\delta }_i+{\nu }_t+{\in }_{\mathit{it}}\left(\mathrm{SEM}\right)$$

$$y_{\mathit{it}}=\rho W{y}_{\mathit{it}}+X_{\mathit{it}}\beta +C_{\mathit{it}}\gamma +W{X}_{\mathit{it}}\theta +{\delta }_i+{\nu }_t+{\in }_{\mathit{it}}\left(\mathrm{SDM}\right)$$

where ρ, λ, and $\theta$ are the spatial autoregressive coefficients; β is the coefficient of the variable; and W is the spatial weight matrix (SWM). $W{y}_{\mathit{it}}$ and $W{X}_{\mathit{it}}$ are spatially lagged variables. $W{\mu }_{\mathit{it}}$ is a spatially lagged error term. ${ϵ}_{\mathit{it}}$ is the random error term. The meaning of other variables is the same as mentioned above.

The binary adjacency matrix used is a basic SWM. The geographic distance matrix and economic distance matrix are used to test the robustness of the regression results. The LM test, LR test, and Wald test are conducted to select a suitable model among SAR, SEM, and SDM [67]. The Hausman’s test is used to determine the fixed effect or random effect of the spatial panel models.

Results

Spatial pattern of digital economy and the HQD of undertakings for the aged

Figure 1 shows that the development level of both the digital economy and the HQD of undertakings for the aged in all provinces (see Table S3 and Table S4 for the detailed values) improves from 2013 to 2021. The development level of the digital economy with the mean increases from 0.079 in 2013 to 0.205 in 2021, a growth rate of more than 150%. The development level of the HQD of undertakings for the aged increases from 0.145 in 2013 to 0.188 in 2021, a growth rate of 30%. Despite the obvious upward trend, in the period from 2013 to 2021, the average digital economy index was 0.144, and the average HQD index of undertakings for the aged was 0.177. It indicates that the development level of China’s digital economy and the HQD level of undertakings for the aged are not high, which is consistent with the findings of the literature [4, 58]. From the perspective of the regional comparison, the level of digital economic development shows a stepwise upward trend from west to east, with a development pattern of “low-medium-high.” It can be seen that provinces with high-level development are primarily concentrated in the eastern region, while provinces with low-level development are around the western region. Unlike the development pattern of the digital economy, the HQD level of undertakings for the aged in eastern and western China is higher than that in the central China.

Fig. 1.

Spatial characteristics of China’s digital economy development and the HQD of undertakings for the aged (2013–2021)

Benchmark regression model results

Table 2 shows that the p-value of Wald test and Wooldridge test are 0.0000, indicating that the panel data used in this study have heteroscedasticity and autocorrelation, and adopting panel corrected standard error is appropriate. Table 2 shows the estimated coefficients of the cross-sectional mix model, the individual fixed model, the time fixed model, the individual and time fixed model, and the random effect model, based on panel data from 2013 to 2021. It can be seen that in each model, the digital economy has a positive impact on the HQD of undertakings for the aged after controlling for the other variables. In addition, the Hausman test results (Chi2 = 50.90, P-value < 0.01) show that the time fixed model is more suitable than the others. Thus, the time fixed model is used in the following robustness test and mediation effect models.

Table 2.

Benchmark regression model results for the panel data

Variables	Mix	Individual fixed	Time fixed	Individual and time double fixed	Random effect
The comprehensive index of the digital economy	0.1068***	0.1300***	0.1576***	0.0824*	0.1506***
	(0.0401)	(0.0481)	(0.0251)	(0.0424)	(0.0240)
The logarithm of per capita GDP	0.0713***	0.0621***	0.0338***	0.0649***	0.0169
	(0.0136)	(0.0150)	(0.0128)	(0.0181)	(0.0112)
The per capita social welfare expenditure	0.0220***	0.0088***	0.0617***	0.0072**	0.0616***
	(0.0055)	(0.0031)	(0.0113)	(0.0029)	(0.0118)
The proportion of the older adults aged 65+	-0.5555***	0.1471**	-0.5101***	-0.5175***	0.1583**
	(0.1551)	(0.0676)	(0.1222)	(0.1729)	(0.0685)
Constants	0.0779***	0.0134	0.1116***	0.0696**	0.0700***
	(0.0224)	(0.0245)	(0.0110)	(0.0289)	(0.0124)
Ind	No	Yes	No	Yes	No
Year	Yes	No	Yes	Yes	No
N	279	279	279	279	279
Adj R2	0.3835	0.8476	0.6628	0.8714	0.6070
Wald test	0.0000
Wooldridge test	0.0000

^*, ^**, ^*** indicate significance at the level of 0.1, 0.05 and 0.01 respectively; Standard errors in parentheses

Table 3 shows the robustness test results of the benchmark regression model. It can be seen that the regression coefficient of the digital economy is always positive in the four models. This result indicates that the digital economy has a stable positive impact on the development of undertakings for the aged. Therefore, Hypothesis 1 is verified.

Table 3.

Robustness test results of benchmark regression model

Variables	Delete data for 2021	Removing extreme values	Replace index of the digital economy	Using the first-order lag term of digital economy
The comprehensive index of the digital economy	0.1902***	0.2213***	0.0946***	0.1738***
	(0.0220)	(0.0248)	(0.0027)	(0.0319)
The logarithm of per capita GDP	0.0289**	0.0240*	0.0120***	0.0295**
	(0.0129)	(0.0124)	(0.0035)	(0.0134)
The per capita social welfare expenditure	0.0649***	0.0611***	0.3288***	0.0618***
	(0.0132)	(0.0116)	(0.0794)	(0.0107)
The proportion of the older adults aged 65+	-0.5207***	-0.5187***	-0.0078***	-0.4432***
	(0.1323)	(0.1358)	(0.0026)	(0.1199)
Constants	0.1161***	0.1207***	0.1477***	0.1058***
	(0.0097)	(0.0101)	(0.0085)	(0.0122)
Ind	No	No	No	No
Year	Yes	Yes	Yes	Yes
N	248	275	279	248
Adj R2	0.6568	0.6859	0.9014	0.6593

^*, ^**, ^*** indicate significance at the level of 0.1, 0.05 and 0.01 respectively; Standard errors in parentheses; In the third column, the comprehensive index of digital economy lags by one period

Mediation effect model results

Table 4 shows that the development of digital economy has a significant positive impact on the HQD of undertakings for the aged (coefficient = 0.1472, P-value < 0.01) and the development of tertiary industry (coefficient = 0.0676, P-value < 0.01). The coefficient of the digital economy in Model 3 decreases by 0.0104 compared with Model 1, indicating that the impact of the development of digital economy on the HQD of undertakings for the aged is not only caused by the direct effect but also by the mediation effect of the proportion of tertiary industry. Further, the Sobel test results show that the indirect effect of the proportion of tertiary industry is significant (coefficient = 0.0104, P-value < 0.05). The mediation effect of the proportion of the tertiary sector accounts for 6.6% of the total effect of the digital economy on the HQD of undertakings for the aged. Therefore, Hypothesis 2 is verified.

Table 4.

The estimated results of mediation effect models

Variables	The HQD of undertakings for the aged (model 1)	The proportion of tertiary industry in GDP (model 2)	The HQD of undertakings for the aged (model 3)
The comprehensive index of the digital economy	0.1576***	0.0676***	0.1472***
	(0.0251)	(0.0193)	(0.0247)
The logarithm of per capita GDP	0.0338***	0.0539***	0.0255**
	(0.0128)	(0.0114)	(0.0101)
The per capita social welfare expenditure	0.0617***	0.0594***	0.0525***
	(0.0113)	(0.0152)	(0.0107)
The proportion of the older adults aged 65+	-0.5101***	-0.0902	-0.4963***
	(0.1222)	(0.1347)	(0.1069)
The proportion of tertiary industry in GDP			0.1539***
			(0.0512)
Constant	0.1116***	0.3239***	0.0617***
	(0.011)	(0.0077)	(0.0223)
Ind	No	No	No
Year	Yes	Yes	Yes
N	279	279	279
Adj R2	0.6628	0.5419	0.6804
Sobel test	Total effect	0.1576***
		(0.0251)
	Indirect effect	0.0104**
		(0.0046)
	Direct effect	0.1472***
		(0.0247)

^** and ^*** indicate significance at the level of 0.05 and 0.01 respectively; Standard errors in parentheses

Spatial panel model results

Table 5 presents the results of the spatial autocorrelation test. The Moran’s Index values of the digital economic development are significantly positive at the 0.1 level of significance, indicating a spatial positive autocorrelation. The Moran’s Index values of the HQD of undertakings for the aged are significantly positive at the 0.1 level of significance, except in 2013, 2016, 2017, and 2019. This result indicates a certain degree of spatial positive autocorrelation. Therefore, it is appropriate to use a spatial econometric model to empirically analyze the spatial effects.

Table 5.

Moran’s index of the spatial autocorrelation test

Variables	Year	Moran’I	Z-value	P-value
The comprehensive index of the digital economy	2013	0.141*	1.613	0.053
	2014	0.146**	1.644	0.050
	2015	0.147**	1.648	0.050
	2016	0.161**	1.779	0.038
	2017	0.152**	1.720	0.043
	2018	0.130*	1.547	0.061
	2019	0.128*	1.525	0.064
	2020	0.123*	1.478	0.070
	2021	0.149**	1.703	0.044
The comprehensive index of the HQD of undertakings for the aged	2013	0.067	0.913	0.181
	2014	0.127*	1.434	0.076
	2015	0.126*	1.414	0.079
	2016	0.088	1.089	0.138
	2017	0.067	0.895	0.185
	2018	0.116*	1.310	0.095
	2019	0.037	0.640	0.261
	2020	0.196**	2.085	0.019
	2021	0.211**	2.281	0.011

^*, ^** indicate significance at the level of 0.1 and 0.05 respectively

Table 6 shows the results of the LM, LR, Wald, and Hausman tests. It can be seen that LM-error and LM-lag tests are significant, indicating that both SAR and SEM are appropriate. The LR test and Wald tests reject the null hypothesis that the SDM can be simplified to SAR or SEM, which indicates that the SDM model is better than the SAR and SEM. The Hausman test results reject the null hypothesis of the random effect model at the 5% significance level and show that the time fixed model is the best among the three fixed models, indicating the selection of a time fixed-effect model.

Table 6.

The test results related to model selection

		Statistics	P-value
LM test	SEM	21.372***	0.000
	Robust SEM	17.245***	0.000
	SAR	4.339**	0.037
	Robust SAR	0.212	0.645
LR test	SDM can be simplified to SAR	24.29***	0.000
	SDM can be simplified to SEM	24.46***	0.000
Wald test	SDM can be simplified to SAR	25.29***	0.000
	SDM can be simplified to SEM	22.76***	0.000
Hausman test	SAR	10.37*	0.066
	SEM	10.23*	0.069
	SDM	20.12**	0.017

^*, ^**, ^*** indicate significance at the level of 0.1, 0.05 and 0.01 respectively

Table 7 shows the estimated coefficients of the spatial panel models. The spatial autoregressive coefficients in both SDM1 (− 0.2140) and SDM2 (− 0.6704) are significant at the level of 1%, indicating that the HQD of undertakings for the aged shows significant spatial dependence under the effect of digital economy and other explanatory variables. The improvement in the level of the HQD of the local undertakings for the aged has a significant negative impact on the HQD of undertakings for the aged of adjacent areas. The regression coefficients of the digital economy in all models are significantly positive, indicating that in consideration of the differences in economic development, social welfare, and population structure, the digital economy has a significant positive impact on the HQD of undertakings for the aged. However, because the estimated coefficients of SDM are biased and cannot be interpreted as a marginal effect [65], the regression results only provide a preliminary judgment on the action direction of each factor. Therefore, it is necessary to further deconstruct the total effect.

Table 7.

Estimated coefficients of the spatial panel models

Variables	SDM1	SDM2	SDM3	SAR	SEM
The comprehensive index of the digital economy	0.1468***	0.1150***	0.1314***	0.1499***	0.1428***
	(0.0260)	(0.0262)	(0.0267)	(0.0267)	(0.0277)
The logarithm of per capita GDP	0.0350***	0.0399***	0.0399***	0.0391***	0.0361***
	(0.0110)	(0.0108)	(0.0135)	(0.0103)	(0.0096)
The per capita social welfare expenditure	0.0613***	0.0633***	0.0606***	0.0627***	0.0633***
	(0.0051)	(0.0051)	(0.0051)	(0.0052)	(0.0051)
The proportion of the older adults aged 65+	-0.7049***	-0.5384***	-0.8545***	-0.5167***	-0.4834***
	(0.1672)	(0.1375)	(0.1606)	(0.1358)	(0.1302)
Spatial rho	-0.2140**	-0.6704**	-0.0211	-0.1149*
	(0.0942)	(0.2682)	(0.0676)	(0.0672)
lambda					-0.1719*
					(0.0973)
N	279	279	279	279	279
R2	0.5812	0.5772	0.6292	0.503	0.487
Log-likelihood	504.8794	511.3656	507.0877	497.1384	497.268
AIC	-989.7588	-1002.731	-994.1754	-982.2768	-982.5359
BIC	-953.4466	-966.4191	-957.8633	-960.4895	-960.7487

*, **, *** indicate significance at the level of 0.1, 0.05 and 0.01 respectively; Standard errors in parentheses. The SDM1 model is based on binary adjacency matrix, the SDM2 model is based on geographic distance matrix, the SDM3 is based on the economic distance matrix

Table 8 shows the results of the spatial effect decomposition of the SDM models. The direct effect refers to the impact of the digital economy on the HQD of undertakings for the aged of the region; the indirect effect refers to the impact of the digital economy on the HQD of undertakings for the aged of the surrounding areas (i.e., the spatial spillover effect); and the total effect refers to the sum of the two. It can be seen that both SDM models under the two weight matrices have consistent results, indicating that the results are consistent. Taking the SDM1 model as an example, we find that the direct effect of the digital economy on the HQD of undertakings for the aged is significantly positive (coefficient = 0.1530, P-value < 0.01), indicating that the local digital economy can promote the HQD of undertakings for the aged in the region. However, the coefficient of the spillover effect is 0.1012, which passes the 1% significance test, indicating that the impact of the development of the digital economy in neighboring regions on the local HQD of undertakings for the aged is significantly negative. Therefore, Hypothesis 3 is verified.

Table 8.

The results of the spatial effect decomposition of the SDM models

Variables	SDM1			SDM2			SDM3
	Direct effect	Indirect effect	Total effect	Direct effect	Indirect effect	Total effect	Direct effect	Indirect effect	Total effect
The comprehensive index of the digital economy	0.1530***	-0.1012***	0.0518	0.1345***	-0.4984***	-0.3638**	0.1333***	-0.1928***	-0.0595
	(0.0266)	(0.0362)	(0.0449)	(0.0261)	(0.1376)	(0.1434)	(0.0271)	(0.0515)	(0.0646)
The logarithm of per capita GDP	0.0335***	0.0171	0.0507***	0.0359***	0.0885**	0.1245***	0.0391***	0.0326*	0.0717***
	(0.0114)	(0.0180)	(0.0158)	(0.0112)	(0.0392)	(0.0357)	(0.0133)	(0.0182)	(0.0160)
The per capita social welfare expenditure	0.0603***	0.0191*	0.0794***	0.0621***	0.0357*	0.0977***	0.0606***	0.0112	0.0718***
	(0.0052)	(0.0104)	(0.0095)	(0.0050)	(0.0205)	(0.0209)	(0.0051)	(0.0078)	(0.0083)
The proportion of the older adults aged 65+	-0.7147***	0.5388	-0.1760	-0.5314***	0.2534	-0.2780	-0.8420***	0.7653***	−0.0767
	(0.1696)	(0.3281)	(0.2538)	(0.1455)	(0.8062)	(0.7406)	(0.1552)	(0.2318)	(0.2065)

*, **, *** indicate significance at the level of 0.1, 0.05 and 0.01 respectively; Standard errors in parentheses. The SDM1 model is based on binary adjacency matrix, the SDM2 model is based on geographic distance matrix, the SDM3 is based on the economic distance matrix

Discussion

This study has examined the impact of the digital economic development on the HQD of undertakings for the aged in China and explored the influencing mechanism by investigating the mediating role of tertiary industry development in the relationship between the digital economy and the HQD of undertakings for the aged. The findings of this study help us understand the importance of developing both the digital economy and the tertiary industry to promote the HQD of undertakings for the aged.

The direct effect of digital economy on the HQD of undertakings for the aged

The findings of the study reveal that the digital economy has a significantly positive impact on the HQD of undertakings for the aged, which verifies our theoretical analysis and our first research hypothesis. Various reasons exist for the positive impact of the digital economy on the HQD of undertakings for the aged. First, the digital economy makes a contribution to improving the elderly population’s economic structure and material affluence [40], which translates to broader access to the elderly care services. Second, digital and intelligent transformation of the elderly care institutions as well as community elderly and home-based elderly care services can improve the quality and quantity of elderly care services [27, 29, 30, 44]. Third, the digital economy is beneficial for improving the social participation of elder adults and enabling them to have a more active elderly life [31], which is necessary for achieving the HQD of undertakings for the aged.

The mediation effect of tertiary industry development between the digital economy and the HQD of undertakings for the aged

The findings of this study further reveal that the impact of the digital economy on the HQD of undertakings for the aged is not only caused by the direct effect but also by the mediation effect of tertiary industry development. The elderly care service industry is a part of the tertiary industry, and other components of the tertiary industry, such as education, medical care, and entertainment, are closely related to the aging industry. Therefore, the digital economy’s promotion of the development of the tertiary industry will have a positive impact on the HQD of undertakings for the aged. In addition, the development of digital economy is accompanied by the application of digital technology and digital platforms. Digital technology provides tools and methods for the development of the tertiary industry, and the application of digital platform is a carrier for the development of the tertiary industry. The combination of the two promotes the digital transformation of the tertiary industry [41, 42]. With the digital transformation of the tertiary industry, the health-care services and the elderly care services have also begun to transform digitally, which is conducive to a more comprehensive, personalized elderly care service system [47].

The spatial spillover effect of the digital economy

The findings of this study also prove the rationality and necessity of incorporating the spatial effect into the econometric model, that is, the development of the digital economy in this region can only promote the level of the HQD of undertakings for the aged in this region, but they inhibit the HQD of undertakings for the aged in adjacent cities. The possible reason may be that a siphon effect exists in the process of HQD of undertakings for the aged in Chinese provincial administration regions, due to the relatively low level of digital economy development (see Table S3). That is, a region with a high level of digital economy will use its own advantages to attract production factors that promote the development of local undertakings for the aged, but this will have a negative impact on the development of undertakings for the aged in adjacent cities. In China, there is a large gap in the social and economic development level of the geographically adjacent areas [17], coupled with the regional growth poles formed by some international metropolises and strong provincial capitals. As a result, the side near the growth pole in the region develops rapidly, and the side far away from the growth pole develops relatively slowly. Furthermore, the digital economy intensifies the agglomeration of resource elements to the growth pole, thus leading to the siphon effect of the HQD of undertakings for the aged at the regional level.

Policy implications for promoting the HQD of undertakings for the aged

Promote the application of digital technology in the HQD of undertakings for the aged

One of the main findings of this study is that the digital economy has a great positive impact on the HQD of undertakings for the aged. This finding can inspire us to vigorously develop the digital economy and, in turn, promote the HQD of undertakings for the aged. The following measures can be adopted to promote the application of digital technology in elderly care and elder health services.

First, it is suggested to carry out aging-suitable transformation based on digital technology. It is critical to create integrated care settings located in smart buildings supported by cyber-physical systems using IoT as an infrastructure with embedded ambient assisted living technologies, wireless sensor networks, big data, and machine learning. This approach has two benefits: one is that the life expectancy of older adults with declining community functioning can be extended [13]. Another is that older adults can stay independently in their community for a longer period of time [68], alleviating the problem of inadequate supply of care services in elderly care institutions.

Second, digital technology can be utilized to integrate the medical treatment and endowment into the elderly care service [27, 29, 30]. Health-care delivery and management, such as predictive and personalized health care combined with information and communication technologies, home-based care, and health prevention can improve health care for older adults. What is needed is to determine how to design these good practices and integrate them into a health-care system that addresses the multidimensional health care issues of older adults [69].

In addition, it is vital to bridge the digital divide for older adults to expand their ability to use digital products. Social media usage have had positive effects on older adults’ social participation [31]. However, the digital divide impacting older adults may prevent them from enjoying the dividends of the digital economy. The government can play a role in investing in resources such as educational programs for older adults to help them extract the benefits of the digital economy [31].

Promote the development of the tertiary industry

Another important finding of this study is that the development of the tertiary industry plays a significant mediating role between digital technology and the HQD of undertakings for the aged. Therefore, it is necessary to formulate policies to promote the tertiary sector of the economy, especially those related to elderly care service, health services, and elderly education, to improve the HQD of undertakings for the aged. First, China’s undertaking for the aged is a typical government-led mode; however, the government’s financial resources are limited [2]. Measures such as providing financing incentives, tax incentives, and land use incentives should be taken to direct more capital into the elderly care service industry. Second, the government should provide more opportunities for training and encourage more labor to enter the elderly care service industry [70]. This can improve the employment rate and increase the supply of care services [71]. Third, engage in digital transformation of the health-care system so that the health-care delivery capacity can be enhanced to meet the growing need of older people [30]. Finally, create an elder-friendly community and environment to expand older people’s social participation.

Promote the HQD of undertakings for the aged considering local conditions

This study found that there are large regional differences in the HQD level of undertakings for the aged in China. It is suggested that local government should identify the weaknesses in coping with the population aging from the perspective of the development of digital economy and the status of the elderly care resource, and formulate targeted strategies to promote the HQD of undertakings for the aged in accordance with local conditions. For areas with backward digital economy, the government should increase investment in digital infrastructure and promote the popularization of the Internet and digital technology. Regular digital skills training is provided for the community-dwelling older adults to help them master the skills of using digital health platforms and telemedicine services. In areas with high endowment of elderly care resource, it is suggested to strengthen the integration of medical care and elderly care resources, increase the capital and technology investment in the construction of smart pension, and actively develop the service mode of “Internet +” care. In areas with low endowment of elderly care resource, it is suggested to strengthen the construction of elderly care infrastructure, guide social funds to flow into the elderly care industry, promote the integration of digital technology and basic elderly care services, and improve the supply capacity of social elderly care services.

Promote the balanced development of digital infrastructure

This study shows that provinces with high level of digital economy development have “echo effect” on surrounding provinces. Thus, it is suggested to promote the balanced development of digital infrastructure construction, bring about the equal development of various digital infrastructure and resource elements in different regions, and reduce or prevent the “siphon effect”. First, it is vital to strengthen exchanges and cooperation between provinces with high level of development and neighboring provinces by establishing the cross-provincial long-term cooperation mechanism. Technology sharing and collaboration can help promote the construction of digital infrastructure in neighboring provinces. Second, certain policy preference should be given to regions with low level of digital economy development to encourage high-level regions to help low-level regions and promote the balanced development of digital economy. Third, it is necessary to encourage local universities to cultivate talents in line with the development needs of the local digital economy, which benefits the sustainable development of the regional digital economy. In addition, a regional digital service platform should be established to promote information sharing within the region, so that all regions can better integrate into the development of the regional digital economy and promote the coordinated development of the region.

Limitations

We recognize at least two limitations of this study. First, this study has only identified the mediation effect of the development of the tertiary industry, but the influence mechanism may not have been sufficiently identified. Further research can conduct a more detailed study of the influence mechanism based on the subdivision dimension of the digital economy and the HQD of undertakings for the aged, and exploring other possible influence pathways between the digital economy and the HQD of undertakings for the aged. Second, the time span of the panel data used in this study is not long enough, and the number of control variables in the model is limited owing to the difficulty and unavailability of data collection. In future studies, we will continue to collect more data to verify the relationship between digital economy and the HQD of undertakings for the aged.

Conclusion

This study demonstrates the theoretical mechanism of digital economy affecting the HQD of undertakings for the aged and uses several empirical models to analyze the impact of the digital economy on the HQD of undertakings for the aged in China. The main conclusions are as follows. First, the digital economy has a positive impact on the HQD of undertakings for the aged. Second, the development of the tertiary industry works as a mediator between the digital economy and the HQD of undertakings for the aged, and it also has a positive effect on the HQD of undertakings for the aged. Third, there is a significant negative spatial spillover effect of digital economy on the HQD of undertakings for the aged. Thus, it is suggested to formulate targeted strategies to promote the HQD of undertakings for the aged in accordance with local conditions. Strategies to accelerate the development of the tertiary industry and to balance the development of digital infrastructure should be formulated to promote the HQD of undertakings for the aged.

Authors’ contributions

R.P. designed the study and secured funding. R.P. and X.D. wrote the main manuscript text. M.H. analyzed data. Y.W. contributed to discussion. All authors reviewed the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (72074055) and the Innovation Team Project of Guangdong Provincial Department of Education (2020WCXTD014).

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.