Data were obtained from the China Civil Affairs Statistical Yearbook, a national survey compiled by the Statistical Annual Report of the Social Service Industry, and the reports of relevant departments, which are related to social services in each year among all LTCFs in the 31 provinces of China from 2013 to 2020. The data content includes the input and output indicators of LTCFs, where the input indicators include human resources indicators and non-human resources indicators.

There is no consensus conclusion on the standard of input-output variables for the evaluation of the efficiency of LTCFs (46, 47). Based on the theory of production factors in economics, the principles of representativeness, independence, and operability should be included in the evaluation index selection. To be more specific, input factors can be divided into capital, labor, and material inputs, and output factors include economic and social benefits (48).

Considering the operability of decisions, input indicators should include the items that decision makers can control over and modify (49). As LTCFs were labor-intensive industries, fixed assets and institutional staff were commonly used separately as capital input human input index (50, 51). The actual number of beds could be easily controlled by managers, which belongs to material input. A number of studies also considered the number of beds, the number of institutions, and the original price of fixed assets as indicators of material resources (27, 52, 53). In addition, as the pension industry functions as a labor-intensive industry, there is less possibility for the capital of the labor substitution. Hence, human capital is an appropriate input index for efficiency comparison including the number of social workers and the number of employees, which are the main care resources in LTCFs (54). Therefore, the input indicators established in this study include the number of institutions, the number of employees at the end of the year, the original price of fixed assets, the number of social workers, and the number of beds at the end of the year (Table 1).

Output indicators are considered to be the most important factors in evaluating the quality and quantity of long-term care services (55). However, most studies only considered the output of operating revenue and profit, and the number of patients and beds, rarely considering the importance of service quality in evaluating the efficiency of LTCFs (56, 57). The quality of service directly affects the final effect of eldercare and the development prospects of LTCFs. For example, the health condition of older people is very important for the improvement and development of LTCFs, and it has a direct impact on the final performance evaluation results of the service such as the number of rehabilitation and medical outpatients. The quality of service is based on the fall rates of older adults, health conditions, the rate of complaint handling, and the annual incidence of major accidents (58). Furthermore, the number of older people with different care needs can reflect their social effects, and thus older population was classified into disabled, partially disabled, and completely independent in LTCFs, which were measured by the Barthel index including six basic activities of daily living, namely, eating, toileting, bathing, dressing, getting in and out of bed, and mobility (30). Therefore, the output indexes should include operating income, the number of disabled, the number of partially disabled, the number of independents in residential cares at the end of the year, and the number of rehabilitation and medical outpatients (Supplementary Table S1).

According to the summary statistics of input-output variables presented, the mean number of institutions reached the highest in 2014. All the input indexes have a significant correlation with output indexes, which indicates that the index selected is reasonable (Supplementary Tables S2, S3).

Data envelopment analysis is a linear programming technique proposed by Charnes et al. to deal with evaluation problems containing multiple input and output indicators (59), which are categorized into input- and output-oriented. Considering the input controllability of the pension industry and the limited eldercare resources in China, it is of great practical significance to increase the output with the given input to make more reasonable use of resources. Therefore, input-oriented variable scale DEA models, i.e., the generalized Charnes-Cooper-Rhodes (CCR) and Banker-Charnes Cooper (BCC) models, were used to analyze the comprehensive efficiency of LTCFs. The provincial domain is set as a decision unit in combination with the actual, i.e., a total of 31 decision units, which are presented by DMU (i = 1, 2, ……, n) (25). The calculation was adopted by the MaxDEA software.

The Tobit model is suitable for the research of the regression equation with a limited value of the dependent variable and is conducive to accurately measuring the influence of the independent variable on the dependent variable (70). As the operating efficiency of LTCFs measured by the DEA model is between 0 and 1, the least square method (OLS) may cause deviation in the results, so the panel Tobit model with limited dependent variables is adopted for analysis, which can better solve the regression problem with limited dependent variables (71). In addition, the efficiency of LTCFs is affected by not only the five input factor variables but also other exogenous variables (72). According to the availability of relevant literature and data, it mainly discusses three aspects, namely, service subjects, human resources, and non-human resources. Among them, service subjects include the type of object of service (self-paid, extreme poverty, and entitled groups) and the total number of subjects in LTCFs. Human resources include the influence of gender, educational background (junior college, college graduate, and above), age (35 years old or below, 36–45, 46–55, or above 56 years old), the number of assistant social workers, the number of volunteer service personnel, volunteer service time, and other factors on the efficiency. Non-human resources include construction space. To avoid the possible heteroscedasticity of the data and improve the convergence rate of the model, the values of the total number of variables were normalized before regression analysis (73). Taking comprehensive efficiency as a dependent variable, a panel data Tobit regression analysis was carried out to find out the factors affecting operation efficiency (74). The model is as follows:

where Y^* is the restricted dependent variable, X is the vector of independent variables, α is the vector of intercept terms, β is the vector of regression parameters, μ is the random error term, and μ~N(0, σ²).

All statistical analyses were performed using MATLAB, Stata 16.0, DEA solver 5.0, and GeoDa software.

The results of the DEA-BCC-CCR method showed that the number of LTCFs that achieved the optimal efficiency in TE, PTE, and SE presented a composite W-shape trend of change from 2013 to 2020. The number of institutions that have reached the optimal efficiency values in TE, PTE, and SE reached the lowest level in 2015 and 2019 and reached the highest level in 2016 (Figure 1).

In 2020, the overall efficiency value of LTCFs in 16 provinces (51.61%) was 1, which was in constant returns to scale, and the LTCFs in 6 provinces (19.35%) were in the stage of decreasing returns to scale. The super-SBM efficiency of LTCFs in Tibet ranked the highest, followed by Shanghai. The ranking of LTCFs in Guangxi Province is the lowest, followed by Shanxi Province (Table 1).

Combined with the radar map of the service efficiency distribution of LTCFs in all provinces in 2020 (Figure 2), it showed that the efficiency of various LTCFs varies significantly among all the units.

Malmquist intertemporal analysis demonstrated that the decrease in total factor productivity in LTCFs in 24 provinces is mainly caused by the decrease in technology. At the same time, the decrease in TE of LTCFs in six provinces is caused by a decrease in SE, in another four provinces by a decrease in PTE, and in three provinces by a decrease in both PTE and SE (Table 2; Supplementary Table S4).

The test statistics used are Pearson χ² statistics (q) and likelihood ratio statistics (LR) for the time heterogeneity test. The results show that both statistics reject the assumption of smooth transition probability at a significance level of 0.01. Therefore, the following will be divided into two periods, i.e., 2013–2017 and 2018–2020 (Supplementary Table S5).

According to the quantile rule [within 25% is low level (L), 26–50% is medium and low level (ML), 51–75% is medium and high level (MH), and >75% is high level (H)], the service efficiency of provincial LTCFs is divided into four categories, and the changes in transition probability are compared between two periods, i.e., 2013–2017 and 2018–2020. The results of the traditional Markov transition probability matrix showed that the diagonal probability of the super-SBM value is significantly higher than that of other positions, indicating that in the medium or short term, the efficiency development of LTCFs in China is relatively stable. This implies that it is difficult for provinces to realize the transition by relying on their own development without external causes. However, adjacent level types reached a large transfer probability, which might be the reason that industrial accumulation is the main development process in the current situation. Comparing the efficiency of human resources with that of non-human resources in LTCFs, the diagonal and other positions of human resources were more different in the 2013–2017 period with worse liquidity. However, in the 2018–2020 period, the liquidity was significantly higher than that of non-human resources, and there was a greater probability of cross-level development (Table 3).

After adding the spatial correlation matrix, the results of the service efficiency of national LTCFs also showed a stable transition probability, including the human resource efficiency and non-human resource efficiency of LTCFs. For example, when the overall efficiency is in an L, ML, or H adjacent area, the diagonal transition probability is higher than that of other locations. Only when the adjacent area is MH, provinces with MH have a high probability of transferring to the adjacent horizontal section, ML or H. In human resource efficiency, when the adjacent area is L, the provinces that are L and MH have a higher probability of transferring to ML and L, respectively; when the adjacent area is ML, the provinces that are ML will have a greater probability of transferring to L; when the adjacent area is H, the provinces with L have a greater probability of transferring to ML; and when the adjacent area is MH, the diagonal transfer probability is higher than that of other locations. In terms of non-human resource efficiency, when the adjacent area is ML, the provinces with MH are more likely to transfer to ML; when the adjacent area is MH, the provinces that are MH themselves are more likely to transfer to L and H; and when the adjacent area is H, the provinces with MH themselves have a greater probability of transferring to H. The diagonal probability values of other adjacent space transfer matrices are much greater than those of other positions, which reflects the convergence of mechanism efficiency space. This is consistent with the results of spatial autocorrelation, which showed that LTCFs continue to form industrial clusters in their own regions in the process of development with high homogeneity (Table 4).

To explore the interactive effect of the development of LTCFs among provinces, Moran's I was used to reflect the spatial relationship among regions. According to Table 5, the non-human resource efficiency in different provinces had a weak spatial correlation in 2013–2015; the human resource efficiency had a weak spatial correlation only in 2017; and the overall efficiency of LTCFs failed to pass the test in 2013–2020. As for non-human resource efficiency, in the early stage of development, the LTCFs were not developed in all regions, and there was a certain linkage between the resource efficiency of various provinces. However, with the continuous development and integration of the local pension industry, provinces began to accumulate pension resources within their own province, causing the inter-provincial spatial connection to weaken. As for human resource efficiency, there is no spatial correlation between provinces. There was a negative spatial relationship that passed the 0.1 test in 2017, but Moran's I in the other years failed to pass the test. There existed a negative exponential phenomenon, which resulted in an obvious polarization phenomenon and failed to form area linkage to develop efficiency.

Supplementary Figures S1A–H shows that during the period 2013–2020, when the test level is at p ≤ 0.05, there is a significant positive spatial correlation (+ +) between one province and its adjacent provinces or regions, which can be identified as diffusion effect that shows a relatively rapid development model, and there is a significant positive spatial correlation (– –) between eight provinces and their neighboring provinces or regions. The efficiency growth rate of these provinces is relatively slow, showing a typical lagging development model; there is a significant negative spatial correlation (+ –) between one city and its adjacent cities, which can be identified as the polarization effect or reflux effect; and there is a significant negative spatial correlation (– +) between four provinces and their neighboring provinces, which can be identified as the centrifugal effect.

Based on the Tobit model constructed in the previous section, the results showed that female workers aged between 35 and 45 years can positively affect the efficiency of LTCFs at a significant level of 1% and 5%. In addition, the type of service subjects has a positive impact on the efficiency of LTCFs. A possible reason for this is that those groups are generally in poorer health or able to receive more government subsidies from long-term care insurance, thus this income increases the efficiency of LTCFs.

However, the construction space of the LTCFs might negatively affect the efficiency of LTCFs at a 5% significant level. Table 6 shows that the comprehensive efficiency of LTCFs decreases by 0.210 for each square increase in construction space variation.

The number of LTCFs, which achieve optimal efficiency in TE, PTE, and SE, presented a composite W-shape changing trend from 2013 to 2020. During 2013–2015, the number of LTCFs with optimized service efficiency showed a downward trend in volatility. After reaching the peak in 2016, the number gradually decreased, reached the “trough” in 2019, and showed an upward trend in 2020. Taking 2016 as a reference, the front and back fluctuations show a symmetrical distribution, that is, the quantitative changes in the optimization of service efficiency of LTCFs form a circular rotation phenomenon in different years. The number of LTCFs with optimized efficiency reached a peak in 2016 and 2020, respectively, which might be due to the policy support of the three-year action plan for eldercare services (2014–2016) issued by the Ministry of Civil Affairs (75). In 2017, the State Council issued the “13th Five-Year Plan for the Development of the National Cause for Aging and the Construction of the Eldercare System”, which highlighted that the eldercare service system based on home, supported by communities, supplemented by institutions, and combined with medical care will be more complete (76). Subsequently, the policy and economic supports mainly focus on the development of home-based community eldercare services. This has led to a downward trend in the service efficiency of LTCFs since 2017. Specific phenomena include the decline in bed utilization rate and low service quality in LTCFs (77). However, the Ministry of Civil Affairs' Implementation Opinions on Further Expanding the Supply and Promoting the consumption of eldercare services in 2019 proposed that LTCFs and community eldercare service institutions should jointly provide support for home care (78). This further expands the market service demand of LTCFs and improves the efficiency of institutions. Taking 2020 as an example, the overall efficiency of institutions in all provinces in China is evaluated. The results show that the TE of LTCFs in 16 provinces (51.61%) is 1, the SE remains unchanged, and the TE of LTCFs in the other 15 provinces is lower. The reasons for low efficiency include the decline of scale efficiency and pure technical efficiency. SE refers to the impact of industrial structure on output efficiency through continuous optimization and improvement of its own allocation; PTE reflects the internal management and personnel management level of LTCFs. Due to the regional distribution and functional diversity of natural resources in China, provinces with high SE are mainly distributed in Northwestern regions with wide geographical areas and rich land resources (19) such as Henan, Tibet, and Xinjiang (79). Hence, the comprehensive efficiency of LTCFs in Northwestern regions is less likely to be affected by SE. The southeastern regions, such as Jiangsu, Shandong, Guangdong, and Chongqing, have a lower SE due to the characteristics of land supply scarcity. As their PTE is high, the reduction in the comprehensive efficiency of the above regions is mainly due to their low-scale efficiency (80). The Malmquist cross-period (2013–2020) analysis results also show that the decline of total factor productivity of LTCFs in the provinces of Northwestern regions is mainly caused by the decline of technical level (13), which is in accordance with the opinion from Torabipour that technical levels played a major role in total productivity changes (81).

The output and input efficiency indicators of LTCFs were divided into human and non-human resources, and the situation of the two periods 2013–2017 and 2018–2020 was analyzed separately. The results showed that the development of service efficiency of LTCFs in China is relatively stable and sustainable in the short-term period. This indicated that the convergence trend of the efficiency of LTCFs is increasing, with a gradual decrease in liquidity as time periods were extended (82). However, the transfer probability changed slowly between adjacent levels, which is similar to the test result of spatial autocorrelation, indicating a lower probability of achieving short-term cross-stage development (83). The regions are difficult to realize the transition by relying on their own development without any external causes. The reason for this might be LTCFs focused on the industrial accumulation in the early stage, forming a high homogeneity, and strong substitutability, with insufficient coordinated development, weakening the inter-provincial spatial connection, and poor liquidity (84, 85). Sufficient human resource embeddedness can not only promote the technical development of the eldercare service industry in the region but also play a greater role in regional diffusion than agglomeration; that is, it has a positive impact on the development of the pension industry in neighboring provinces (86–88). In human resource efficiency, our results showed that there was significant spatial polarization without spatial correlation among regions, making it difficult to develop area linkages. The reason for this might be that the staff have relatively stable regional characteristics, weakening the inter-provincial spatial connection. We found that female workers aged between 35 and 45 years can positively affect the efficiency of LTCFs. The efficiency growth is highly dependent on those workers with proficient skills (89). Those staff, at this age range, can stay with high workloads in order to refine and improve their existing skills in performing tasks efficiently, and in the process, complete their work with passion. They are expected to have more patience and dedication to eldercare so that they can obtain better service quality and then improve the efficiency of LTCFs in the process (30). However, younger staff aged < 35 years do not have any sense of longevity with their jobs due to their lack of sufficient skills or have more determinants of intention to leave jobs than older staff in LTCFs (90). Moreover, older staff aged more than 45 years stay focused and are less likely to improve their existing skills. They perform highly repetitive care tasks in a timely manner and complete their assignments within a tight work schedule (91). With restricted personal resources, they can only work in a highly regulated environment and tend to be job burnout and exhausted (90). So, increasing female workers aged between 35 and 45 years can enhance the growth of service quality and personnel stability of LTCFs, in turn, improving the service quality and the overall efficiency of LTCFs. In addition, the type of service subjects has a positive impact on the efficiency of LTCFs. A possible reason for this is that those groups are generally in poorer health or able to receive more government support and subsidies from long-term care insurance, so this income increases the efficiency of LTCFs. Therefore, strengthening policy support to encourage inter-regional initiatives, particularly highlighting the development of human resources interaction and common development, is urgent.

Non-human resources like construction space can also affect the temporal and spatial changes of the efficiency in LTCFs (92). More specifically, non-human resource efficiency presented a “cluster” distribution mode, demonstrating a certain linkage among various provinces, indicating a great probability to achieve cross-stage development, particularly in the later period. Economic development and land resource gaps might be the main reasons for regional disparities. Non-human resources, like economic development level, environmental regulation, education level, and resource endowment indicators, are all important prerequisites and guarantees for the development of the ability of the eldercare industry (93), but they have little impact on the development of technological innovation ability in surrounding provinces and do not have an obvious spatial spillover effect. Tobit regression analysis results also showed that the comprehensive efficiency of LTCFs decreases by 0.210 for every square increase in construction space variation. The appropriate scale for technical support is an important factor in improving the quality of the facilities (33). Excessive scales will increase care service consumption and cause problems such as deficits. Lower scales will affect comprehensive efficiency and reduce the ability of LTCFs to attract older adults in need of care and improve care technology and quality. Our results demonstrate that there is an urgent trade-off between resource reduction, construction excessive, and substantial regional variation in efficiency. Therefore, it is necessary to avoid excessive construction space changes and improve technology and service quality changes to further improve the efficiency of LTCFs.

According to the Pareto optimal theory, we selected the input-output indicators for the efficiency evaluation of LTCFs from the aspects of human and non-human resources to get a more refined basis for the development of LTCFs. The spatial Markov matrix was used to conduct continuous dynamic research on the efficiency of the services by considering areas and time heterogeneity. To make a scientific and accurate conclusion, we analyze the local spatial autocorrelation aggregation analysis of the service efficiency of LTCFs between adjacent provinces and their transfer condition. In a long-term period, we could find out the continuous and real changes in human resources and non-human resources efficiency of LTCFs in the development process, and explore the influencing factors leading to temporal and spatial changes.

In this study, the longitudinal data was used to analyze the temporal and spatial pattern of service efficiency in China's LTCFs, and further comprehensive and municipal data still need to be included in the future. More measurement design should be considered to further explore the potential influencing mechanisms of spatial differences in LTCFs. The efficiency changes of both human and non-human resources calculated in this study are compared, but they cannot represent the changes in all the efficiency characteristics of LTCFs. The index data of eldercare service efficiency classification must be mined from multiple dimensions.