Descriptive statistical result
During the 1992–2015 period, the overall ageing rate in mainland China maintained a sustained rise. The percentage of the population aged 65 and above was 6.08% in 1992 and grew to 10.47% in 2015, with an average annual growth rate of 2.29%. The extent of ageing has been increasing year by year (Fig. 1). The entire process can be divided into three sub-processes: 1992–1999, 2000–2010 and 2010–2015. The increasing tendency of the mean of three stages increased stage by stage, and the high quartile and low quartile also had some degree of increase.
At the same time, the ageing area showed a significant expansion trend. According to the lower limit of the Ageing Social Standard of the United Nation (7.0%) [23], the following five provinces (municipalities) became ageing areas as early as 1992:Shanghai (11.%), Beijing (8.0%), Zhejiang (7.5%), Tianjin (7.4%) and Jiangsu (7.4%). Thirty provinces, excepting Tibet, became ageing areas in 2015. Of these, Chongqing had the highest rate of ageing (13.3%). Figure 2 shows the evolution process of the spatial distribution of the ageing rate of 31 provinces (including some municipalities or autonomous regions; for brevity, the following text only uses the 31 provinces) in China during the study period, illustrating a clear expansion from southeast to northwest, which is consistent with the conclusions of Wang et al. [10]
We use Moran’s I [24] to measure the spatial difference of the ageing rate; the larger the Moran’s I is, the larger the spatial difference is. Figure 3 shows the trend of the spatial variation coefficient of the ageing rate in 31 provinces in mainland China from 1992 to 2015. It can be observed that the differences in ageing demonstrate a general decreasing trend. The difference in degree of ageing among provinces was quite large during 1992–2004, and decreased during 2004–2015, which is contrary to the conclusions of Xiu-Li and Wang. [8] In recent years, as can be seen in Fig. 1, the degree of ageing in each province has been aggravating. All regions attained a high ageing rate, so a smaller spatial difference resulted.
Bayesian statistical result
In order to explain the spatio-temporal evolution of the ageing rate in mainland China more thoroughly, this paper divides the research period into three stages (1992–1999, 2000–2010 and 2010–2015) based on the above descriptive statistical analysis, and then, using the extended nonlinearity BSTHM, estimates the common spatial pattern, the distribution of local first-order change (speed) and second-order change (acceleration) in the three sub-phases of the ageing rate in China.
The common spatial pattern
Based on this paper’s improved nonlinearity BSTHM, the posterior median estimation of the steady-state spatial relative magnitude of 31 Chinese provinces, exp(Si), in three sub-periods can be obtained; this value measures the relative magnitude of the provinces’ ageing levels relative to the overall national level, exp(α). If exp(Si) > 1.0, it indicates that the degree of population ageing in a province is exp(Si) times the overall level, and vice versa. Figure 4 shows the common spatial pattern in the three periods of 1992–1999, 2000–2010 and 2010–2015.
Overall, in the eastern provinces, especially in the six regions of mainland China of Beijing, Tianjin, Shandong, Jiangsu, Shanghai and Zhejiang, the degree of ageing is much higher than the overall level during the three periods. In the northwestern provinces, especially Xinjiang, Qinghai, Gansu, Inner Mongolia, Heilongjiang and Ningxia, the degree of ageing is lower than national level during the three periods. This is basically consistent with the conclusions of Wang et al. [10]、Xiu-Li and Wang [11]. and Ruyu et al. [12]
Specifically, certain provinces have unique characteristics during the three stages. Guangdong province, as the most populous province in mainland China (1.04 billion, 2010 population census), had its ageing level show a sequential decrease in three stages: during 1992–1999, the ageing degree was 1.139 times the national overall level, while during 2000–2009 and 2010–2015, the ageing level was at and below the national overall level, respectively, and the spatial relative magnitude of ageing was reduced to 1.012 and 0.920, respectively. Shandong province, as the second-most populous province (95.79 million, 2010 census) maintained a relatively high level of ageing over the three phases, with a spatial relative magnitude of 1.147, 1.143 and 1.129, respectively. Although Sichuan and Chongqing are located in the underdeveloped southwestern region, their population ageing problems were more serious than in the other southwestern provinces, which may be related to population movements. According to previous related studies, in these two regions a large number of young and middle-aged laborers have left in recent years [25], leading to a continuous ageing of the population. However, the ageing in Sichuan and Chongqing had different staged characteristics; the ageing in Sichuan was still on an average level (with a spatial relative degree of 1.015) during 1992–1999, and significantly higher than that of mainland China after 2000. Chongqing’s ageing level was higher than that in Sichuan in all three stages, as its ageing spatial relative magnitude was consistently above 1.10 and reached a peak value of 1.187 in 2010–2015. It should be pointed out that, in the three municipalities of Beijing, Tianjin and Shanghai, the ageing of the population was at a high level during the first two sub-periods, but overtaken by Chongqing, Jiangsu and Shandong during the last sub-period. In addition, the level of ageing in Jiangsu Province was higher than the average over the entire study period, while in Zhejiang province it was somewhat lower during the third stage. Ageing in the western and northwestern regions and Yunnan province was always lower than the average during the entire study period. An interesting phenomenon is that following the most recent 24 years of evolution, the high-level ageing areas of mainland China have spatially located in the two central provinces, connecting to seven eastern provinces and five southwestern provinces, as shown in Fig. 4. Although Wang et al. [10], Xiu-Li and Wang [11]. and Ruyu et al. [12] also pointed out that differences existed in inter-provincial ageing, they did not systematically and thoroughly study the relative ageing levels of provinces in various stages. This paper argues that, in the context of ageing rising across all regions, it is more scientific to study the matter from a relative perspective.
Local evolution trend
Based on the improved BSTHM, the paper achieves a more detailed estimation of the local evolution trend, including the first and second order trend. The former, denoted by b1i in equation (10), is equivalent to the growth rate in physics, whereas the latter, denoted by b2i in equation (10), is equivalent to acceleration and measuring the change of the former. b1i > 0 (b1i < 0) indicates that the province i belongs to the area with strong (weak) ageing growth rate, with the ageing growth rate being stronger (weaker) than the national general growth rate. Different combinations of b1i and b2i mean different local evolutionary characteristics: b1i > 0 and b2i > 0 means that province i’s ageing has a strong increase trend and the strong increase will become stronger; b1i > 0 and b2i < 0 indicates that province i’s ageing has a strong increase trend but the strong increase will become not strong; b1i < 0 and b2i > 0 means that the ageing in province i was weak, but the weak increase will transform into strong growth; b1i < 0 and b2i < 0 mean that the ageing in province i has a weak growth trend and the weak growth will become weaker.
Based on the comprehensive consideration of the common spatial effect, overall time effect and the time-space interaction effect, this paper estimates the local evolution trend of ageing in 31 Chinese provinces in three stages, and for the first time estimates the change in aging growth within each province, thereby providing a detailed description of the spatial and temporal evolution of ageing in mainland China. Figure 5 is a graphical representation of the local evolution characteristics of ageing in 31 provinces in mainland China in the three phases of 1992–1999, 2000–2009 and 2010–2015.
From 1992 to 1999, the areas of vigorous increasing ageing in mainland China were mainly distributed in the eastern and southern regions. Among them, six provinces (the middle-eastern coastal areas including Shandong, Jiangsu and Fujian and the southwestern provinces including Chongqing, Yunnan and Guangxi) had ageing that showed a tendency to surpass the overall growth rate, while the growth rate of ageing in 7 provinces (Guizhou, Hunan, Guangdong, Jiangxi, Anhui, Zhejiang and Shanghai) was higher than the overall average, although the growth rate was diminishing and approaching the overall trend. Both central and western provinces belong to the weak growth areas, especially in central China, including Hebei, Shanxi, Henan and Hubei, but also in western regions such as Xinjiang and Tibet. In these regions, not only was the ageing growth rate below the overall average, but also the gap was widening.
From 2000 to 2009, the areas of strongest increased ageing shifted from the eastern and southern regions to the central and western regions, with 14 strong growth provinces emerging. Among them, nine provinces, including Sichuan, Hubei and Henan, among others, experienced accelerated ageing growth rates, In five provinces (Beijing, Tianjin, Jiangxi, Guizhou and Xinjiang) the ageing growth rate demonstrated a slowing trend. The strong growth of ageing in the eastern region expanded from Heilongjiang to Jilin, with both located within to the accelerated growth area. The eastern and southern provinces, with the exceptions of Beijing and Tianjin, were all transformed from strong growth of ageing areas to weak growth of ageing areas. With the, exceptions of Jiangsu and Fujian, all five provinces experienced acceleration toward the overall trend in ageing growth rate.
Compared with the previous two phases, from 2010 to 2015 the number of ageing strong growth provinces increased significantly, reaching 16, which exceeded 50% of the total number of provinces in mainland China. With the exception of Hebei, Shandong, Beijing and Tianjin, which are located in the eastern region, most of the strong growth provinces are located in the central and western regions. Simultaneously, the provinces with accelerated ageing growth rates were Hebei, Inner Mongolia, Shanxi, Gansu, Ningxia and Jiangxi, numbering six in total, fewer than the second stage. According to the common spatial pattern of ageing as shown in Fig. 4, the eastern provinces, with high degrees of ageing, are among the weak ageing growth provinces.
Prediction of ageing in mainland China in 2030
Before prediction, the reliability of the model must be tested. In this paper, cross-validation is used for this purpose. Specifically, the data on the ageing rates of the three five-year periods (1995–1999, 2002–2006 and 2010–2014) are extracted separately and used as test truth data only, not in the calculation process. The remaining 19 years of data are used to estimate the rate of ageing of the test year. Then, we calculate the root mean square error (RMSE) between the estimated and observed values. In this paper, the RMSE of the prediction of the ageing rate during three periods is 0.71%, 0.53% and 0.62%, respectively, all less than 1%, so the model prediction error is within a reasonable range.
Under the premise of maintaining the “one child” policy unchanged, based on 1992–2015 population data, the population ageing rate in 2030 \( {p}_{2030}^{aging} \)
is projected to be 14.76% (95%CI: 12.02%, 20.13%). In the context of the comprehensive “two-child” policy, the total population in 2030 is projected to be 1.45 billion by the National Population Development Plan (2016–2030). According to Zhai et al. [26], the estimated value of the total population increase is 94 million. Therefore, without implementation of the comprehensive “two-child” policy, the predicted total population in 2030 is 1.36 billion. According to the above formula (10), considering the context of the comprehensive “two-child” policy, the prediction value of the ageing rate in 2030 in mainland China is 13.80% (95% CI: 11.24%, 18.83% is). This result means that the rate of ageing in China decreased by 0.96% (95% CI: 0.78%, 1.30%) in 2030 after the implementation of the comprehensive “two-child” policy.