Difference analysis of regional population ageing from temporal and spatial perspectives: a case study in China

ABSTRACT The ageing coefficient is selected as the index to evaluate population ageing, and some methods are proposed for analyzing differences in regional population ageing from temporal and spatial perspectives. China is used as the case study over the period 1998–2014. The concentration degree of the elderly varies regionally, but fluctuations in regional population ageing remain relatively stable. The coefficient of variation of population ageing fluctuates with an overall decreasing tendency. Population ageing in China exhibits a ladder-like distribution different from the distribution corresponding to economic strength. Spatial autocorrelation in population ageing is observed, with a comparatively steady spatial pattern.


INTRODUCTION
As of 2015, the global population of people aged 60 years or over had increased by 48% from the year 2000, reaching 901 million worldwide; this number is projected to grow to 1.4 billion by 2030 and 2.1 billion by 2050, accounting for 16% and 22% of the total population respectively.This phenomenon is often referred to as population ageing, also known as the 'silver tsunami'.Although declining fertility and increasing longevity are the key drivers of global population ageing, ageing trends are not identical in all countries.Available statistics indicate that older adults living in developing regions account for 66.7% of the world's aged population, with a growth rate far exceeding that of the corresponding demographic in developed regions (United Nations, 2015).China, as a developing country, has a total population of more than 1.37 billion as of 2015, of which those aged 60 years and over account for 16.1% (222 million) and those aged 65 years and over account for 10.5% (144 million) (National Bureau of Statistics of China, 2016).These figures indicate that China is already a greying society, and older persons are projected to comprise at least 30% of the population by 2050 (United Nations, 2015).Furthermore, with a wealth of land and considerable regional economic disparity, China is also characterized by regional differences with respect to such demographic measures as the rate of population development, distribution of elderly people and the degree of population ageing.These long-standing and increasingly pronounced differences influence the population structure of the entire country, and also hinder effective resource distribution.Within this context, difference analysis of population ageing among regions is significant and essential in order to aid understanding of the current state of population ageing and to provide a reference point for policy-making seeking to mitigate regional demographic differences.
From the existing body of research, three major avenues of study of population ageing can be identified: . Time oriented: Goodman (1987) uses Lorenz curves and Gini coefficients (GC) to measure population ageing in urban areas based on 1980 census data, but this is done from a static perspective and not taking into account temporal changes in urban elderly distributions.Several studies have sought to compare population ageing in various regions during the same period (Chatterji et al., 2008;Chomik, McDonald, & Piggott, 2016;Shrestha, 2000).However, these horizontal and temporal comparisons have been limited to higher-level comparisons between countries or continents, overlooking variations in population ageing among the regions within a given country.Dufek and Minařík (2009) choose two main factors out of 12 indicators related to demographic indicators using factor analysis and explore the development of population ageing in particular Czech regions during the period 1998-2007.Chen and Hao (2014) select two indicators based upon which to measure population ageing in China for the period 1995-2011 and examine the overall differences of population ageing, as well as the differences among three primary regions, using the Theil index. .Space oriented: the spatial distribution of population ageing has been analyzed in Poland by means of spatial clustering by Kurek (2003).In that study, several age groups, including seniors, are divided in order to assess the age structure and characterize the distribution of each group's proportion of the entire population.Yuan, Wu, and Wu (2007) compare spatial changes in population ageing among rural regions of China for 1990 and 2000 and cluster these regions into four quantiles accordingly. .Time and space oriented: Lai (1999) uses simple T-statistics to measure the temporal changes of China's population ageing among provinces and applies D-statistics to assess its spatial autocorrelation for the period 1953-94.Kcerov, Ondackov, and Mldek (2014)  In spite of the efforts made in existing studies, gaps in the body of knowledge still exist in this area.The current methods focus primarily on a single feature of population ageing (e.g., spatial autocorrelation) from either the spatial or the temporal perspective; thus, the research tends to be one-dimensional in nature.Furthermore, few studies have explored the differences in population ageing among the regions within a given country, integrating the temporal and spatial perspectives.To address the above issues, the present research proposes a comprehensive and systematic methodology for difference analysis of regional population ageing.Specifically, two multidimensional research frameworks for population ageing are presentedtemporal difference analysis and spatial difference analysisusing the corresponding methods.For the temporal perspective, features of population ageing such as ageing trends, regional variations and the concentration degree of population ageing are of significant interest, while the spatial clusters and spatial autocorrelation form the primary features of population ageing from the spatial perspective.In addition to the overall and regional differences of population ageing analyzed in a country, differences of population ageing in some aggregated regions of a country (e.g., classified based on economic strength) are explored from both the temporal and spatial perspectives.
The novel contributions of this study include: (1) integrating the temporal and spatial analysis of population ageing from multiple dimensions in terms of regional difference, thus achieving theoretical innovation in regional population ageing research; (2) exploring these ageing features in different regions (e.g., both the country and aggregated regions) in a manner that takes into account both holistic and individual aspects in order to refine the difference analysis; and (3) considering the effects of geographical location on population ageing, resulting in improvement measures that correspond more closely with reality.In practice, the presented research methodology can be applied to other countries where regional differences in population ageing exist.It can also help policy-makers to understand change trends and regional differences in population ageing and to provide the basis for regional population strategies in order to balance regional development and address the economic, social and public health challenges associated with population ageing.

METHODOLOGY
This paper explores differences in regional population ageing from both temporal and spatial perspectives.The temporal perspective entails analyzing the features of population ageing in a given region(s) during an observed periodthat is, time-based differences of population ageing.The spatial perspective takes geographical properties (e.g., the location of a region and its neighbouring regions) into account, and examines the spatial features in population ageing among regions.To achieve the above objectives, a comprehensive and systematic methodology is proposed and illustrated in Figure 1.It consists of three key components: (1) the measurement of regional population ageing by means of the ageing coefficient; (2) the temporal analysis of population distribution, population ageing trends, regional variations and the concentration degree using stacked column graphs, mean analysis, coefficient of variation (CV), Lorenz curves and GC; and (3) the spatial analysis of population ageing clusters, global and local autocorrelation, using spatial clustering, global Moran's I and a Moran scatterplot.A detailed introduction to these research methods will be presented in the following subsections.Figure 1 depicts the relationship between the research methods (rounded rectangles) and research objectives (rectangles), and facilitates an understanding of the potential application of the research methodology to areas of interest for measuring and comparing regional population ageing.
Based on the above three components, the innovativeness of the proposed methodology is highlighted as follows: . A systematic process for population ageing analysis is developed that embraces population ageing measurement and regional difference analysis.Furthermore, this process simultaneously considers features of population ageing from the perspectives of time and space. .The research is multidimensional since multiple features of population ageing are involved from either the temporal or the spatial perspective.As such, compared with previous studies, this research provides a relatively comprehensive profile of regional population ageing in terms of temporal and spatial differences. .The whole country, aggregated regions and their component parts (e.g., provinces) are selected as research units, since the regional diversity underscores not only the imbalance in population ageing across the country but also the differences among and within the regions.

Measurements of population ageing
The conventional indicators to measure population ageing encompass the following: . Proportion of elderly persons (typically defined as those aged 65 years and over)this indicator directly reflects the absolute degree of ageing, which is most frequently used as an index of demographic ageing (Cowgill, 1974;Lutz, Sanderson, & Scherbov, 2008;Ricciardi, Xia, & Currie, 2015), and has also been applied in studies of population ageing in China (Chen & Hao, 2014; Zhang & Chen, 2014).
. Median age of the population, which is an arbitrary metric, since it simply represents the age of persons who happen to be at the 50th percentile of the data set containing the ages of all individuals sorted in ascending (or descending) order (Shryock, Siegel, & Larmon, 1975). .Ratio of the elderly (typically defined as those aged 65 years and over) to the young (typically those aged 15 years and under), where the latter is a relative index, the value of which is influenced by the proportion changes of two groups.However, there is some deficiency in using this ratio as the index of population ageing since it uses only the proportion of elderly people in a population (Kii, 1982). .Dependency coefficients calculated based on three different age groups: youth (aged 0-14 years), productive (aged 15-64 years) and seniors (aged 65 years and over) (Dufek & Minařík, 2009).Based on this classification, the youth (and senior) dependency ratios are the number of individuals aged 0-14 years (and aged 65 years and over) per 100 persons whose age lies within the range of 15-64 years.The sum of these ratios is known as the overall dependency coefficient.Since the variations in the whole age distribution of a population are not considered, the degree of ageing in a specific year will be exaggerated when fertility declines steeply (Kii, 1982).
In this paper, preference is given to the first indictor (i.e., the proportion of elderly people) as the ageing coefficient in order to measure regional population ageing.The Difference analysis of regional population ageing from temporal and spatial perspectives in China reasons are two-fold: (1) considering the definitions and disadvantages of each of the above indicators, the proportion of elderly persons directly reflects the proportion of older adults in the total population with an extensive application; and (2) the selected ageing coefficientwhich only involves two population groups, that is, the elderly and the total populationis better suited to serve as the foundation on which the other methods in the proposed methodology (Figure 1) could be used synergistically to analyze other features of population ageing.

Methods for temporal analysis Lorenz curve and Gini coefficients
The Lorenz curve can be employed to quantify precisely the concentration degree of population ageing, that is, the variations in the distribution of the elderly in the total population.By sorting region-level observations of elderly populations in ascending order, the cumulative percentage of elderly people is represented as the vertical axis and the cumulative percentage of the total population as the horizontal axis (Goodman, 1987).If population ageing in each region is nearly identicalthat is, if all the regions share uniform proportions of the elderly segment of the populationthen the Lorenz curve is a diagonal line with equal distribution.Otherwise, the Lorenz curve is under the diagonal.A curve further from the diagonal indicates a more uneven distribution of population ageing, i.e., a higher concentration degree.
In reality, the GC is regarded as a relative index based on the Lorenz curve.Considering a Lorenz curve in which the cumulative percentage of the total population is plotted against the cumulative percentage of elderly people, the GC can be expressed by: where S refers to the area between the diagonal (signifying equal distribution) and the Lorenz curve; and P denotes the entire area under the diagonal.If G = 0, then the distribution of population ageing is regionally equal; if G = 1, then population ageing represents complete inequity; if 0 , G , 1 and closer to 1, this is indicative of more pronounced differences in regional population ageing; and if 0 , G , 1 and closer to 0, then the regional population ageing tends to be uniform.

Coefficient of variation
The CV metric is defined as the standard deviation of an indicator divided by its mean; it is the most widely used to measure differences in terms of regional development and imbalanced development (Wang, Chen, Liu, Shen, & Sun, 2013).The CV is thus used to analyze fluctuations in population ageing in different regions over an observed period.
where CV denotes the coefficient of variation; n indicates the number of regions; AC i is the value of the ageing coefficient in region i; m and s represent the mean and the standard deviation of ageing coefficients respectively; and, accordingly, where CV is larger, the larger is the difference in regional population ageing.

Spatial clustering
Clustering analysis is conducted on the basis of distance, and Euclidean distance (e.g., including location distance and attribute distance) is widely applied to traditional clustering analysis.The location distance reveals the degree of proximity between two objects, while the attribute distance reflects the similarity of attribute features between two objects (Wang et al., 2013).In consideration of similar objects with the above two features, spatial clustering is effective in solving the feature combination.If the location distance and the attribute distance are regarded equally, then spatial distance is expressed as: 3) where (x i , y i ) and (x j , y j ) are two-plane Cartesian coordinates of points or regions' centres P i and P j respectively; and a ik and a jk (k = 1, 2, . . ., n) are their corresponding attribute vectors.
If the location distance and attribute distance are weighted, then the spatial distance, D s , can be expressed in either of two ways: or where v l , v x or v y is the weight of the location distance; v a or v k is the weight of the attribute distance; and

Global spatial autocorrelation
It should be noted that CV is unrelated to the geographical location and only refers to the dispersion degree of data (Rey & Montouri, 1999).A global Moran's I is used to indicate the global autocorrelation and difference degree of the observed values in spatial neighbouring regions (Moran, 1948).Therefore, global Moran's I is applied here in order to measure the regional imbalance of population ageing and its global spatial autocorrelation.
where I t is the global Moran's I of the tth year; x ti is the 852 Yuan Chen et al.

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ageing coefficient of region i in the tth year; x t = 1\n n i=1 x ti and ) 2 are the mean and variance of the ageing coefficients of all the regions in the tth year respectively; and w ij represents the elements of the spatial weighting matrix W n×n determined by the spatial adjacency and spatial distance.The spatial adjacency method is selected for the present research based on the Rook rule: if region i adjoins region j, then w ij = 1; otherwise w ij = 0, and no adjacency relationship exists between region i and itself, that is, w ii = 0.
The range of global Moran's I-values is [-1, 1].I t .0 expresses a positive spatial autocorrelation, that is, the regions of relative high or low population ageing tend to be significantly spatially conglomerated; I t , 0 denotes a negative spatial autocorrelation, that is, there exist differences in population ageing between region i and its surrounding regions; and I t = 0 denotes no spatial autocorrelation, that is, the regional population ageing has a random spatial distribution.
Normally, the z-test is used to verify whether the calculated global Moran's I meets the significance level (Cliff, Ord, & Cliff, 1981):

Local spatial autocorrelation
To measure further the local spatial autocorrelation between a given region and its surrounding regions, the spatial degree of difference and the spatial pattern in terms of population ageing, a Moran scatterplot is used.A Moran scatterplot is two-dimensional and describes the correlation between a vector of observed ageing coefficients (y) and a weighted average of the neighbouring values, or spatial lag, Wy (Anselin, 1996): where N is the number of observed ageing coefficients; S 0 is the sum of all elements in the spatial weight matrix (S 0 = i j w ij ); y is the observed ageing coefficients in deviation from the mean; and Wy is the associated spatial lag, which is a weighted average of the neighbouring values.A Moran scatterplot divides the whole region into four types of spatial areas.The first quadrant (HH) and the third quadrant (LL) indicate the degree of population ageing in region i and its surrounding regions are high or low; the second quadrant (HL) denotes that degree of population ageing in region i is high, while its surrounding regions has a low degree; and the fourth quadrant (LH) indicates that the degree of population ageing in region i is low, while its surrounding regions have a high degree.The elements in HH and LL present a positive autocorrelation, while the elements in HL and LH present a negative autocorrelation.

Data description
This paper uses China as a case study and take its 31 provinces as the observed jurisdictions.Considering the differences in economic strength with respect to geographical location, the provinces are divided into three primary regions: eastern, central and western.A ladder-like distribution of economic strength is exhibited in China following the high to low principle.China's regional total and aged population data are selected in order to evaluate population ageing (National Bureau of Statistics, 1999Statistics, -2015)).The analysis is restricted to the period 1998-2014 (excluding 2001) based on data availability (see Table A1 in Appendix A in the supplemental data online).

Basic profile of total and aged population
The basic demography of total and elderly populations distributed in the three primary regions is presented in Figure A1 in Appendix A in the supplemental data online.The stacked columns A and B for each year show the total and aged populations respectively.The upper-most sections of the columns depict population ageing in the western region, while the middle and lower segments represent the central and eastern regions.
Overall, it can be observed that the population in the eastern region accounts for the largest proportion (about 40%), followed by the central (about 32%) and western regions (about 28%) over the whole period, even though the western region has the greatest number of provinces.This indicates that the regions in China with higher levels of economic development tend to have larger populations.In fact, numerous studies have demonstrated that economic development plays a significant role in population growth (Cincotta & Engelman, 1997;Firmino Costa da Silva, Elhorst, & Silveira Neto, 2017;Ogilvy, 1982).Compared with 1998, the percentage of the total population is observed to be increasing (by 11.1%) in the eastern region by the end of the studied period, while it is decreasing by 7.0% and 5.9% in the central and western regions respectively.In terms of aged population, there is a slight fluctuation during the observed period, and sorting based on percentage is congruent to that of the total population.The most notable difference is that the standard deviations of the total population percentage in the eastern and central regions (0.0130 and 0.0075 respectively) are larger than those of aged population percentage (0.0079 and 0.0042 respectively).Conversely, the variation of aged population percentage (0.0064) in the western region is slightly larger.In general, the proportional distribution of the total and aged populations remain relatively stable in each region during the observed period.
The average degree of population ageing is calculated for the entire country and the three primary regions Difference analysis of regional population ageing from temporal and spatial perspectives in China 853

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annually, and their change trends over the period are plotted in Figure 2.
In terms of the overall perspective, the average degree of population ageing gradually fluctuates with an increasing trend across the entire country and for each of the three primary regions during the 17-year period.This underscores the fact that population ageing in each region increases, while the maximum values do not exceed 11%.Moreover, the change trends of the four curves are similar, except that the eastern region experiences a higher fluctuation of population ageing during the period, and its differences before 2010, when compared with the other regions, are relatively clear.Also, the average degree of the eastern region typically exceeds the values of the other three regions, being followed by the entire country, then the central and western regions.To be specific, the fluctuations in population ageing for all regions are found to be small for the period of study before 2000, with the maximum in 1999 (0.092) and the minimum in 2000 (0.058).From 2000 to 2009, a surge in population ageing occurs in all regions in the first two years, while it transitions to more constant growth in the western and central regions and a large fluctuation in the eastern region over the period that follows.Moreover, regional population ageing sees a rapid decline in 2010 and then increases slightly over the remainder of the studied period.

Concentration degree of population ageing
For each year, the cumulative percentages of the elderly are calculated after first ranking the populations of the 31 provinces in ascending order, and the corresponding cumulative percentages of the total population are then obtained.Lorenz curves for population ageing in each year can be created based on the above principle.In the interest of clarity and simplicity given the large data set, Figure A2 in Appendix A in the supplemental data online presents four selected years to illustrate the concentration degree of population ageing by means of Lorenz curves.
All the Lorenz curves are under the diagonal, which indicates that the percentages of the aged in the various regions are not identical, that is, the concentration degree of the elderly varies regionally.However, the degree of deviation from the diagonal is not obvious and a small degree of fluctuation exists in regional population ageing over this period.This indicates that the distribution of population ageing is not concentrated among the provinces with the highest degrees of ageing.This result also verifies the finding represented in Figure A1 in Appendix A in the supplemental data onlinethat is, that the sorting of aged populations based on the percentage among three primary regions is the same as that of the total population.To capture more clearly the concentration degree of population ageing in China during these years, equation ( 1) is used to obtain the GCs presented in Table 1.
Overall, the degree of fluctuation of population ageing GC is found to be relatively stable.The values of GC lie in the interval (0, 1), indicating a difference in distributions of the elderly among the provinces, and that the entire situation is not complete inequity.Moreover, the values are much closer to zero, meaning that the distribution of population ageing tends to be regionally uniform.

Regional differences of population ageing
The regional diversity underscores not only the imbalance in population across the country but also the differences among the three primary regions and among the provinces within each region.According to equation (2), trends in the CV of population ageing in each region are measured and the mutual influences among them are analyzed.
As can be observed in Figure 3, the CV of population ageing is decreasingly variable across the entire country during the 17-year period, which reflects the fact that the gaps in population ageing between regions are declining overall.This point also verifies the result that the concentration degree of population ageing is not obvious, which is reflected by the Lorenz curve trends and the GC values.Yuan Chen et al.

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In terms of trends and degree of fluctuation, the CV of population ageing for the entire country has a similar tendency as that of the eastern region, while the values are clearly larger (mean ¼ 0.210 for the whole country versus a mean ¼ 0.170 in the eastern region).Conversely, the CVs of population ageing in both the central and western regions see an overall increase during this period.Population ageing has its greatest variation in the western region (mean ¼ 0.214) during the observed period, while the central region has the lowest fluctuation (mean ¼ 0.109) in the four curves.The change trends of CV in the three primary regions are consistent with the trend results over the period 1998-2011 using the Theil index (Chen & Hao, 2014).
Based on the mean CV for the entire country and the deviations among the three regions, it can be observed that the overall population ageing trend is primarily influenced by ageing fluctuations from the central and western regions.
A comparison of the CV in the four curves also reveals changes to the distribution of elderly people in each region.Before 2005, the CVs for the entire country are generally larger than those for any of the three primary regions, despite significant fluctuations among the three regions.By 2014, population ageing in the western region dominates the level of change with rapid growth.The CV of population ageing in the eastern region fluctuates continuously, while the CV in the central region exhibits an overall decreasing tendency.Although the level of economic development is lowest in the west, its comfortable living condition accounts for the marked change in the intraregion distribution of elderly people.Population health outcomes are shaped by complex interactions between individuals and the diverse physical, social and political conditions in which they live (Clarke & Nieuwenhuijsen, 2009).Older adults tend to be more impacted by barriers in their surrounding social and physical environment due to declining health and functional status, financial strain, and social isolation (Oswald et al., 2007;Wahl & Lang, 2003).This may become a factor to promote the migration of elderly people from other regions, indirectly resulting in variation of population ageing in the western region.
When comparing the results shown in Figures 2 and 3, it can be seen that there is a large difference between the two figures.The former only describes the average degree of regional population ageing, while it cannot quantify the degree of dispersion of population ageing among all provinces in each region.Hence, the latter is better used to display imbalanced development of population ageing.

Spatial differences of population ageing Spatial clustering of population ageing
To analyze further spatial differences in regional population ageing in China, based on the average ageing coefficients and spatial clustering theory, GeoDA095i software is employed to determine the three categories of population ageing.Detailed guidelines on the use of this software can be obtained from Anselin (2004).
The first category (i.e., high degree of population ageing) includes the following 10 provinces: Sichuan, Chongqing, Hunan, Beijing, Tianjin, Liaoning, Shanghai, Jiangsu, Table 1.Gini coefficients (GC) of population ageing in China, 1998China, -2014China, . 1998  Difference analysis of regional population ageing from temporal and spatial perspectives in China 855

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Zhejiang and Shandong.The first three are in the central and western regions; most of the others are in the eastern region.This also verifies the result in Figure 2 that the average degree of population ageing in the east remains the largest among all regions during the studied period.The provinces in the eastern region enjoy a significant level of economic development due to industrial development and political/economic status (e.g., Beijing and Shanghai).These provinces provide active employment markets with more opportunities for young adults and their families (National Bureau of Statistics, 1999-2015).As for the regions with relatively slow economic development, living conditions and lifestyle may figure as primary factors influencing elderly people in their decision about whether to reside in the area, since social and physical conditions strongly influence the health of seniors (Clarke & Nieuwenhuijsen, 2009;Oswald et al., 2007;Wahl & Lang, 2003).
The second category includes the following 11 provinces: Hebei, Fujian, Jilin, Anhui, Jiangxi, Henan, Hubei, Guangxi, Hainan, Guizhou and Shaanxi.These are mainly located in the central and western regions, which suggests a strong market potential for population ageing in these provinces.
The remaining 11 provinces form the third category comprising the group of low ageing degree.Nearly all these provinces are located in the western region.The components of the two categories also correspond to the results of the average degree of population ageingthat is, the western region tends to have the lowest degree of ageing.Based on the above findings, China's population ageing for all regions exhibits a ladder-like distribution different from the categorization based on regional economic strength.Moreover, the high degree of population ageing is not confined to a certain region; conversely, it spans all three regions despite their differing levels of economic development.

Spatial autocorrelation of population ageing
Global autocorrelation.According to the annual ageing coefficient data, the statistical inference based on 999 permutations is referenced (Anselin, 1996), and then Geo-DA095i is used to calculate global Moran's I for the regional population ageing of China, as presented in Table 2.The expectation of global Moran's I during the period is -0.033, obtained using the equation: where n is the number of observed units.
As indicated in Table 2, the global Moran's I-values are all found to be > 0, and all values pass the significance test (under a 0.05 significance level).This shows that population ageing in the various provinces is not mutually independent, but clearly exhibits the feature of spatial agglomeration.To be specific, there is a polarization between the high level of population ageing (in most of the eastern region) and the low level of population ageing (in most of the western region).Furthermore, the global Moran's I-values are decreasing overall.This indicates that the conglomerated area of relatively high or low population ageing in the geographical space is decreasing, which could explain why the distribution of population ageing tends to be regionally uniform (refer to the GC results).It also reflects that there are adjacent effects among the regions, meaning that population ageing in a given region is influenced by the ageing situation in neighbouring regions.
Local autocorrelation.To determine the type of local autocorrelation pertaining to regional population ageing and its spatial distribution, the annual Moran scatterplots of the 31 provinces in China are exported based on the ageing coefficients.By gathering the quadrant change (i.e., the local autocorrelation change) of each province during the period, the evolutionary process of regional population ageing can be summarized, as presented in Table A2 in Appendix A in the supplemental data online.
At the provincial level, local autocorrelation of population ageing in most of the provinces remains relatively stable during the 17 years.Fujian varies from HH to LH Figure 3. in the coefficient of variation (CV) of regional population ageing.

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in 2000, to HL in 2006, and remains in LL for the last five years of data.The local autocorrelation between this province and neighbouring provinces fluctuates continuously, while population ageing in this province is moderate.It can be observed that the ageing situation in Fujian is closely related to its neighbouring ageing change.As for Jilin, its population ageing exhibits a low level before 2007, similar to its neighbouring provinces.Then, from 2007 to 2010, Jilin falls within LH, then shifts positions among HH, HL and LL over the course of the following four years.This result indicates that population ageing in Jilin is generally low and that the fluctuations in neighbouring provinces are significant.In contrast to Jilin, in Shaanxi population ageing is representative of a trend of local autocorrelation.The key difference is that Shaanxi is in LH for the period 2007-10, which signifies a trend of increasing population ageing in neighbouring provinces compared with the situation at the beginning of the period of study.At the regional the provinces in the HH quadrant account for the largest percentage of all the provinces in the eastern region, followed by those in the LH and HL quadrants.Among these, Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang and Shandong exhibit a similar population ageing development trend.This not only demonstrates the existence of a cooperation mechanism in population ageing to some degree but also improves the level of population ageing for the whole region.The distributions of the central provinces in HH and LL tend to be relatively uniform, followed by LH with a small gap.This spatial pattern points to a moderate level of population ageing in the central region.In the western region, the provinces in LL reveal a clear dominance in population ageing, resulting in a low level of population ageing for the whole region.Furthermore, spatial autocorrelation of population ageing in these provinces and their neighbours, such as Hainan, Tibet, Qinghai, Xinjiang and Inner Mongolia, is relatively stable, indicating that, regardless of the province, the degree of population ageing is very low.The development of population ageing in Sichuan is also steady (HL), which confirms that this province belongs to the first clustering category of population ageing.
The number of provinces counted in each quadrant experiences a small fluctuation during this period.This situation can be regarded as a relatively stable spatial pattern.Of the quadrants, LL accounts for the largest percentage, followed by HH, LH and HL sequentially.Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang and Shandong fall within HH, which indicates that the high level of population ageing is mainly concentrated in the eastern region.Hainan, Yunnan, Tibet, Gansu, Qinghai, Ningxia, Xinjiang and Inner Mongolia are in LL, which indicates that the low level of population ageing is primarily concentrated in the western region.This verifies that China's population ageing exhibits bipolar agglomeration in the space.In the quadrants of negative autocorrelation (HL and LH), Liaoning is undergoing rapid economic development and features a high level of population ageing, but its neighbouring provinces, including Jilin, Hebei and Inner Mongolia, have a low level of population ageing.The situation is  Difference analysis of regional population ageing from temporal and spatial perspectives in China 857 similar in Sichuan and Guangxi for some portions of the period under study.

Suggestions and policy implications
Based on the above temporal and spatial analyses of regional differences in population ageing, some suggestions and policy implications are proposed: . Adjust starting age structures: either the entire country or the three primary regions have experienced an increase of ageing degree during the observed period.
Compared with other regions, in the east population ageing is relatively pronounced, which is reflected in both the change trends of population ageing and provincial distribution in the three spatial clusters.The Chinese government introduced a two-child policy in 2016 in order to boost the country's birth rate and further mitigate population ageing in future.As such, the government to strengthen the promotion of this new policy in three primary regions, especially directing its efforts toward those provinces in the east with a higher degree of population ageing, such as Beijing, Tianjin, Liaoning, Shanghai, Jiangsu, Zhejiang and Shandong. .According to spatial clusters and local spatial autocorrelation, the degree of population ageing in each province has been presented.Accordingly, policy-makers could establish and optimize a pension service system, reinforce social and welfare services for the elderly, and implement measures to prevent a mismatch between the established service system and the degree of local population ageing, such as over-or under-service.In this regard, it should also be mentioned that it is preferable to implement these measures beginning with the provinces where the degree of population ageing is much higher. .Necessary resources, such as medicine and healthcare, should be judiciously and evenly allocated to guarantee that the basic needs of the elderly are met.As for the central and western regions, the level of economic development still lags behind, while the average degree of population ageing in the two regions has an increasing trend.Meanwhile, differences in population ageing are found to exist within each of the two regions.Some provinces with low economic strength belong to the clusters with a higher degree of population ageing.As for these provinces, the government should consider providing more effort and focus on economic development and necessary resource allocation. .Although the concentration degree of population ageing is not obvious, differences in regional population ageing are diverse.The CVs of the country as a whole are found to be larger than those in the three primary regions for the period before 2006, while the CVs of the east represent the greatest contribution to the entire difference during the following period.Meanwhile, the degrees of fluctuation reflect diversity among these regions.Thus, an improvement plan for regional population ageing should consider differences within and among regions from temporal and spatial perspectives, and then provide the corresponding remedies to balance regional development. .Strengthen regional communication and collaboration: the ageing degree of the entire country is influenced by those of the three primary regions, indicated by ageing trends and CV.This regional effect also exists in global autocorrelation and local autocorrelation.In other words, change in a province (individual) will affect the neighbouring provinces (groups) and, in turn, the whole country (system).As for the provinces with similar degrees of population ageing (such as provinces in the first clustering category or the provinces in the HH quadrant), regional communication and collaboration are beneficial for promoting mutual learning and problem solving. .Implement a new pension mode: 'ageing in place', an emerging paradigm in ageing policy, aims to help older people to continue living at home, and fundamentally and positively contributes to an increase in wellbeing, independence, social participation and healthy ageing (Sixsmith & Sixsmith, 2008).It not only benefits the older person in terms of their quality of life but also presents a cost-effective solution to the problems caused by an expanding population of older adults (Tinker et al., 1999).Since the eastern region with better economic strength dominates the degree of population ageing, there is potential to deploy this new pension mode in some of the provinces in this region (e.g., Beijing, Shanghai, Jiangsu and Zhejiang) as a pilot project in order to implement this pension mode in other provinces if it performs well.

CONCLUSIONS
This paper proposes a systematic methodology for difference analysis of regional population ageing from temporal and spatial perspectives, and applies these methods to a case study of China over the period 1998-2014.As for the temporal analysis, regional population ageing trends, the concentration degree and regional differences are explored using stacked column graphs, a Lorenz curve, GC and CV.The results indicate that the average degree of population ageing fluctuates with an increasing trend in all the regions during the period, while the largest ageing degree does not exceed 11%.The change trends within the entire country and within the three primary regions are similar, but population ageing in the eastern region has a higher fluctuation, and is clearly different than in other regions in the period before 2010.The concentration degree of the elderly is low and varies regionally; there is a small degree of fluctuation in regional population ageing GC over the studied period; and the overall situation is not complete inequity due to the GCs located in the interval (0, 1).The CV of population ageing fluctuates with a decreasing tendency for the entire country during the period of study; this trend is similar to that in the eastern region, but opposite to those in the western region, with greatest variation, and the central region, with the lowest fluctuation; the CV trend for the whole country is mainly influenced by ageing fluctuation from the central and western regions.
As for the spatial analysis, spatial clusters, spatial autocorrelation and evolution of population ageing among regions are analyzed by means of spatial clustering, global Moran's I and Moran scatterplot.The results indicate that China's regional population ageing exhibits a ladder-like distribution different from the distributions pertaining to economic strength among the eastern, central and western regions; the highest degree of population ageing is not confined to a certain region, but has penetrated the three primary regions.Population ageing is not mutually independent among all the provinces but reveals a clear feature of spatial agglomeration; the spatial convergence effect is weakened overall during the period since the values of global Moran's I are found to be decreasing.There is also local spatial autocorrelation in China's population ageing, which forms a relatively stable spatial pattern.Specifically, the provinces in the HH quadrant account for the largest percentage of all the provinces in the eastern region; the number of provinces in each quadrant fluctuate constantly with slight variation.
Based on the achieved research results, some suggestions and policy implications are provided for population ageing involving several aspects: age structure adjustment, pension service system establishment, sound social and welfare services, reasonable resource distribution, diversity of regional management plan, regional communication and collaboration, and ageing in place.Simply put, the research methods proposed in this study can achieve theoretical innovation in the research area of regional population ageing from multiple dimensions, and can also be applied to other countries where regional differences in population ageing exist.Moreover, it can provide a reference point for policy-making pertaining to regional ageing gap reduction and balanced development.However, this study only explores population ageing in terms of regional differences from a descriptive analysis perspective.Future studies are needed to analyze the influencing factors of population ageing and the formation mechanism of regional differences from a spatial perspective.

Figure 2 .
Figure2.Trends in the average degree of regional population ageing. 854 National Bureau of Statistics only collected the total population of each province in 2001, but it lacks the data for different age groups including the elderly population in the same year.Owing to data availability, the case study did not include 2001 as the observed period.
National Bureau of Statistics only collected the total population of each province in 2001, but it lacks the data for different age groups including the elderly population in the same year.Owing to data availability, the case study did not include 2001 as the observed period.