Introduction

Japan’s population aging is the most advanced in the world today. The elderly population proportion (i.e., the proportion of the population aged 65 and over) in 2021 was 28.9%, which is higher than any other country in the world (Cabinet Office & Government of Japan, 2022). The rate is forecasted to reach approximately 38.4% in 2065 (National Institute of Population and Social Security Research (IPSS), 2017). This study considers Japan’s population aging primarily from a demographic or geographical viewpoint, which is also the focus of the studies reviewed below.

Various demographic factors led to the nationwide population aging in Japan after World War II: (1) a sharp drop in fertility after the first baby boom from 1947–1949, (2) a below-replacement-level fertility decline after the second baby boom from 1971–1974, (3) a long-term common mortality decrease in developed countries, and (4) a relatively low level of immigration (Feeney, 1990; Fernandes et al., 2023; Goldman & Takahashi, 1996; Harper, 2016; Horlacher, 2001; Inoue et al., 2021; Ishikawa, 2015; Kojima, 1995; Kono, 1992; Kuroda, 1987; Retherford et al., 1996; Yashiro, 1997). The former two factors occurred uniquely or earlier, and the latter two occurred more strongly than in other developed countries, making Japan’s elderly population proportion the highest in the world (Horlacher, 2001; Inoue et al., 2021). Many studies on regional population aging have focused on metropolitan areas, non-metropolitan areas, or the inequalities between them. Inoue and Watanabe (2014) analyzed the results of the population census and the population projections by the IPSS (2013) and found the following: before around 2000, the elderly population proportion increased more rapidly in non-metropolitan areas than in metropolitan areas; by contrast, around 2000–15, it increased more rapidly in metropolitan areas than in non-metropolitan areas. Before around 2000, a sharp rise in the elderly population proportion and significant depopulation occurred simultaneously in non-metropolitan areas, especially rural or mountainous areas, primarily because of the massive out-migration of youth to metropolitan areas (Esaki, 2016; Inoue & Liaw, 2004; Ishikawa, 2020; Koike, 2014; Maruyama, 2018; Morikawa, 2018; Yamauchi, 2015). Such out-migration was maximized during the high economic growth period in the 1960s and early 1970s because, at that time, the first baby boomers born in 1947–49 and living in non-metropolitan areas reached their late teens and early twenties and actively left their birthplaces (Esaki, 2016; Ishikawa, 2020; Maruyama, 2018). The period around 2000–15 was characterized by a rapid increase in the elderly population proportion in metropolitan areas, particularly in their suburbs. The average elderly population proportions in countries of the Organization for Economic Cooperation and Development (OECD) in 2011 were 14.5 and 15.6% respectively in the core and hinterland (i.e., the suburbs) of metropolitan areas, and the hinterland reached nearly 25% only in Japan (OECD, 2015). This reason is that the first baby boomers moving into metropolitan areas entered the elderly population and the cohort distribution is strongly biased in favor of the suburbs (Inoue & Watanabe, 2014). Feng (2015) discussed population aging in four major cities in non-metropolitan areas from a spatial perspective, using the 2000 and 2010 small area census data. He found valuable findings that aging progresses independently and in waves in each city’s core and suburban areas. However, these findings are not a universal model of the aging process in developed countries because the model is limited to urban areas of the above four major cities in Japan and does not use the forecasted population. Several studies have discussed Japan’s population aging after 2015 using data from regional population projections and forecasted that the regional differences in various demographics would expand (e.g., Esaki & Nishioka, 2020; Koike, 2021; Yamauchi et al., 2017).

In general, small areasFootnote 1 are more homogeneous than larger ones, i.e., municipalities, prefectures, or nations. Therefore, when we analyze population aging by focusing on the geographical or demographic homogeneity of target areas, handling small areas has an advantage over handling municipalities, prefectures, or nations. Nevertheless, most of the studies have been conducted at the municipal, prefectural, or national scale, and no demographic or geographical study has analyzed Japan’s population aging nationwide using populations projected on a per-small area basis. This is because such projection data was unavailable for Japan before the 2016 launch of the website ‘The Web System of Small Area Population Projections for the Whole Japan’ (SAPP for Japan) (Inoue, 2018). SAPP for Japan opened the small-area (cho–cho and azasFootnote 2) and long-term (45 years) projected population of Japan for the first time on the World Wide Web. A new method was proposed by Inoue (2017a) for smoothing small area demographics to develop SAPP for Japan.

The purpose of this study is to quantitatively analyze the future aging processFootnote 3 using data from the latest version (ver. 3.0) of SAPP for Japan and, based on this analysis, attempt to present the standard aging process that developed countries will experience after the demographic transition, taking advantage of the fact that Japan has the most aged population in the world. A non-hierarchical cluster analysis is performed using two statistics on aging: the elderly population proportion and the elderly population change index (EPCI). The EPCI represents the ratio (%) of the elderly population in each year to that in 2015. Non-hierarchical cluster analysis has been widely utilized in studies on spatial clustering (e.g., de Souza & Taconeli, 2022; Murray & Grubesic, 2012), and can classify many small areas into some homogeneous clusters. This study examines the demographic and geographical features of such homogeneous clusters, introduces a new concept of the stage in the population aging process, and analyzes the relationship between the features of homogenous clusters and the stages.

The Outline of SAPP for Japan

This section outlines the SAPP for Japan (ver. 3.0) released byInoue (2019a),Footnote 4 which has opened the small-area (approximately 219,000 cho-cho and azas) and long-term (for a period of 45 years from 2020 to 2065)Footnote 5 projected population of Japan on the World Wide Web. This system projects the population based on the cohort change ratio method formulated by Hamilton and Perry (1962), which is a representative method for population projections (Smith et al., 2013), and its efficacy has been proven in several empirical studies (e.g., Baker et al., 2021; Swanson et al., 2010; Tayman et al., 2021; Wilson & Grossman, 2022). However, merely applying this method to small area populations leads to unstable results that frequently maximize the projected population. This system smoothed two demographics, the cohort change ratio (CCR) and the child-woman ratio (CWR), which are indispensable for the cohort change ratio method, prior to applying the Hamilton-Perry method. Various methods for estimating small area demographics have been developed or considered (e.g., Anselin et al., 2006; Clayton & Kaldor, 1987; Datta & Ghosh, 2012; Farrell et al., 1997; Fay & Herriot, 1979; Gonzalez & Hoza, 1978; Holt et al., 1979; Laake, 1979; Tango, 1988; Tsutakawa et al., 1985). These methods essentially perform data smoothing using population statistics from neighboring or adjoining small areas, some of which are based on empirical Bayes smoothers (Anselin et al., 2006). However, according to Inoue (2017a), empirical Bayes smoothers have disadvantages when applied to population projections. Consequently, this system used a new method by Inoue (2017a), which has a limited advantage over previous methods, and smooths the two demographics of CCR and the CWR. The new method was suggested on the analogy of the concept of population potential by Stewart (1947). The population potential, one of the major measures in population geography, has been discussed in many geographical studies (e.g., Mfungahema & Kitamura, 1997; Pueyo et al., 2013; Rich, 1980; Tocalis, 1978; Warntz, 1964). Comparative studies on methods for forecasting small area populations have also been performed (e.g., Tayman & Swanson, 2017; Wilson et al., 2022). Tayman and Swanson (2017) focused on the CCR and CWR of the Hamilton-Perry method and compared several methods that forecast by modifying these two demographics. As a result, they found that the method of modifying the CCR and CWR using these demographics’ change rates for larger areas reduced errors. Wilson et al. (2022) thoroughly reviewed and evaluated several existing methods, including those not based on smoothing. He placed the new method by Inoue (2017a), used in the development of SAPP for Japan, together with methods by Swanson et al. (2010) and Baker et al. (2014), as extensions of the Hamilton-Perry model.

The following procedure was used for calculating the data provided by the SAPP for Japan: First, we downloaded the 2010 and 2015 small area census population data by sex and 5-year age group from the website ‘Portal Site of the Official Statistics of Japan.’ Second, CCR and CWR were calculated and smoothed. The CCR was given by the ratio of the 2015 population of a certain cohort to the 2010 population of the same cohort, and the CWR was given by the ratio of the 2015 population aged 0–5 to the 2015 female population aged 20–39. We smoothed these two demographics for a small area using the prefectural CCR and CWR. The numerical formulasFootnote 6 are similar to the empirical Bayes estimator (EBE) or Stein-type shrinkage estimator (SE) (Datta & Ghosh, 2012; Efron & Morris, 1973, 1975; Shinozaki, 1991), although they are different from the EBE and SE in that the weight is changeable. Third, the population projected by small area was calculated from the smoothed CCR and CWR using the Hamilton-Perry method. We obtained the 2020 projected population by applying smoothed CCR and CWR to the 2015 census population and obtained the 2025–65 projected population by iterating the above procedure. Finally, the projected population derived was adjusted to match that of the IPSS (2017, 2018) at the prefectural or national level.

In addition, Inoue (2017b, 2019b, 2022) constructed the SAPP for the state of Washington (WA) in 2017, for Taiwan in 2019, and for the US in 2022, referred to as the SAPP series. SAPP for WA and SAPP for the US adopted ‘a two-step smoothing method’ formulated by applying Inoue’s method twice. The first and second steps smooth the demographics respectively at the county level using those at the state level and at the small area level using those at the county level. The effectiveness of this method has been examined by Marquez et al. (2024).

Cluster Analysis Method

A non-hierarchical cluster analysis was performed in this study where the classification of small areas was done into a few clusters in the first part, and the location quotient (LQ) was calculated in the second part, which is significant for discussion on a cluster's geographical features.

Performance of a Non-hierarchical Cluster Analysis

A non-hierarchical cluster analysis was performed using the elderly population proportion at 11-time points (2015, 20, ..., 65) and the EPCI at 10-time points (2020, 25, ..., 65). The EPCI is defined as the ratio (%) of the size of the elderly population each year to that in 2015. The next section discusses the elderly population proportion, EPCI, and the population change index (PCI), defined as the ratio (%) of the size of the total population each year to that in 2015. However, the PCI was not used to perform the cluster analysis because the elderly population proportion and EPCI can lead to the PCI as follows:

Let the elderly population proportion, EPCI, and PCI at time t be a(t), EPCI(t), and PCI(t), respectively, PCI(t) can be expressed as follows:

$$PCI\left( t \right)\, = \,EPCI\left( t \right) \cdot a\left( {2015} \right)/a\left( t \right)$$

This formula basically means that only the elderly population proportion and EPCI were sufficient inputs for cluster analysis.Footnote 7

Cluster analysis is largely divided into hierarchical and non-hierarchical clustering, and these two analysis methods have been compared in earlier studies (e.g., Everitt, 1993; Hartigan, 1975; Kaufman & Rousseuw, 2005). In general, hierarchical clustering can be utilized for data with a sample size of up to 100 because the amount of calculation involved accelerates with the expanding sample size. Thus, a non-hierarchical cluster analysis was utilized for grouping the small areas. Prior to cluster analysis, this study extracted approximately 204,000 small areas that satisfied the following condition from the SAPP data for Japan: both the total and elderly populations were nonzero at all time points, otherwise, the elderly population proportion and EPCI from the data cannot be calculated.

This study employed the k-means method, which provides the most basic clustering algorithm, to perform non-hierarchical cluster analysis. Nevertheless, this method has two main problems. One is that the results can vary greatly depending on how the initial values of the cluster centers of gravity are given, and the other is that the number of clusters must be determined in advance, which can easily lead to arbitrariness. For the former problem, although the k-means ++ has been proposed to avoid it by Arthur and Vassilvitskii (2007), the degree of dependence on initial values can be ascertained by conducting multiple trials. Hence, we determined that it was not necessary to adopt this method. For the latter problem, although the GAP statistic is known as a method for determining the optimal number of clusters (Tibshirani et al., 2001), this statistic was not an option because of its large computational load when the number of data is large.Footnote 8 As a method to solve the latter problem, x-means, an advanced algorithm of the k-means method, has also been proposed by Pelleg and Moore (2000). However, this method also requires more computation than the k-means method, and Ishioka (2000) has pointed out that there is room for improvement, so it was not adopted as an analysis method. With the above considerations, we decided to perform 10 trials of clustering for each of the cases with 5 to 30 clusters, for a total of 260 (= 10 \(\times\) 26) trials of clustering, and to calculate the sum of squared errors (SSE) for all of these 260 trials. The reason for calculating the SSE for 260 trials is to compare the SSE for each number of clusters to verify the stability of the results, and to plot the change in SSE with the number of clusters to determine the optimal number of clusters using the elbow method.

First, we calculated the relative range (= ratio of the range to the average)Footnote 9 of the SSE for each number of clusters to verify its stability. The results showed that the relative range was less than 5.0%, indicating a certain stability within the same number of clusters. In addition, cases where the value exceeded 0.5% were excluded from the candidates for analysis. This excluded cases where the number of clusters ranged from 22 to 30. Next, we calculated the average SSE of 10 trials for the number of clusters from 5 to 30 and plotted these values (Fig. 1). Figure 1 shows that the average value of SSE decreases rapidly until the number of clusters is around 10, and then decreases slowly after the number of clusters is 14. Nevertheless, it was difficult to detect a so-called elbow point, at which little or no change begins to occur, after the number of clusters is 14. For this reason, the cases with a relative range under 0.5% and a concave point,Footnote 10 i.e., the cases of 14, 15, 16, 18, and 20 clusters, were candidates for the elbow point. Finally, the study used a non-standard but certain rational method to determine the appropriate number of clusters, using the distribution of the number of small areas in the above five cases of 14, 15, 16, 18, and 20 clusters. Table 1 lists clusters for each of the five cases in descending order of the number of small areas belonging to them. This table indicates that for any number of clusters, several of the lower-ranked clusters have a share of the number of areas below 0.5%. These clusters were omitted from this study because they had little impact on the overall structure of the aging process and were difficult to interpret geodemographically. The largest gap between these omitted clusters and the clusters to be studied was seen between the 7th and 8th clusters in the case of 20 clusters, and the smallest gap within the cluster to be studied was seen in the same case. This implies that extracting the seven highest-ranked clusters in the 20 clusters case was an appropriate choice of clusters that make sense. This method of extracting the major clusters is based on the analogy of a principal component analysis in which the major ones are chosen from several components and is considered to have a certain rationale. Therefore, we determined the optimal number of clusters to be 20, of which the seven highest-ranked clusters were actually analyzed. For the seven clusters, the total and elderly populations of the small areas were summed up. Consequently, approximately 200,500 small areas were classified into seven clusters that covered more than 98% of Japan’s total population, which was approximately 127 million people in 2015.

Fig. 1
figure 1

The change of the average of SSE with the number of clusters

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Table 1 The distribution of the number of areas in the five cases of 14, 15, 16, 18, and 20 clusters
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Calculation of the Location Quotient

To understand the geographical features of the seven clusters, all the 1719 municipalities, as of 2015, were categorized into 18 areas according to their location and population size, and location quotients by cluster were calculated for each categorized area. The location quotient (LQ) is a common indicator, often used in geography and in some disciplines dealing with regionalities, such as regional economics and regional demography.Footnote 11 The LQ is used, for example, to express how much an area is specialized in an industry. Let LQij denote LQ for industry j in area i, then LQij is expressed by the following equation:

$$LQ_{ij} = \frac{{r_{ij} }}{{r_{j} }}$$

where rij is the proportion of workers in industry j in area i and rj is the proportion of workers in industry j nationwide. In general, if one wants to know the major industries in an area, one can simply calculate the proportion of workers in each industry, and if one wants to know which industries are specialized, the LQ is used. In this study, the LQ by cluster was decided to be calculated for each area because we wanted to know which cluster the population specializes in rather than which cluster most of the population belongs to.

First, the whole of Japan was divided into the Tokyo, Nagoya, and Osaka metropolitan areas and non-metropolitan areas. These four areas consist respectively of Saitama, Chiba, Tokyo, and Kanagawa Prefectures; Aichi, Gifu, and Mie Prefectures; Osaka, Kyoto, Hyogo, and Nara Prefectures; and 36 other prefectures. Figure 2 depicts the locations of those three metropolitan areas and non-metropolitan areas. In those four areas, cities of various sizes (metropolitan core, large, medium, and small cities) are located. This study refers to the places where these cities are located as urban areas and other places as rural areas. Figure 2 shows that many Japanese cities concentrate on the surroundings of three metropolitan core cities. If the population in 2015 is given by p(2015), these urban and rural areas are distinguished as below.

Fig. 2
figure 2

The locations of the three major metropolitan areas, non-metropolitan areas, and cities of various sizes

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Metropolitan core city: Tokyo special wards,Footnote 12 Nagoya City, or Osaka City;

Large city: municipality with 700,000 ≤ p (2015), responding to an ordinance-designated city;

Medium city: municipality with 200,000 ≤ p (2015) < 700,000;

Small city: municipality with 50,000 ≤ p (2015) < 200,000;

Rural area: municipality with p (2015) < 50,000.

This area categorization was based on the Statistics Bureau, Ministry of Internal Affairs and Communications, Japan (2008). However, to balance the population among large, medium, and small cities, the threshold between medium and small cities was changed from 150,000 to 200,000. Table 2 represents the numbers of municipalities and small areas by categorized area.

Table 2 The numbers of municipalities and small areas by categorized area
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Second, for categorized areas k and Cluster l, we calculated the location quotient LQkl as follows: Let the number of small areas included by territory A be n (A):

$$LQ_{kl} = \frac{{n\left( {{\text{categorized area}}\, k \cap {\text{Cluster}}\, l} \right)/n\left( {{\text{categorized area}}\, k} \right)}}{{n\left( {{\text{Cluster}}\, l} \right)/n\left( {\text{all Clusters}} \right)}}$$

As is evident, LQkl indicates how strictly Cluster l specializes in categorized area k.

Results

First, this section examines the demographic features of clusters focusing on the elderly population proportion, EPCI, and PCI. Second, the geographical features of clusters are examined based on the LQ. Third, the clusters’ stage shift in population aging is discussed.

The Demographic Features of Clusters

This study discusses the seven major clusters covering more than 98% of Japan’s population. Table 3 presents basic statistics such as the elderly population proportion, EPCI, and PCI. Clusters 1–7 are shown in ascending order of the elderly population proportion in 2015 (Table 3). The share of Clusters 4–5 is nearly 60% of the total population, and the share of Clusters 6–7 is over 70% with regard to the area size. Comparing the population density of clusters with that of the whole of Japan (approximately 341 persons/km2 as of 2015), it is understood that Clusters 1–4 are largely located in urban areas, and Clusters 6–7 are mostly located in rural or mountainous areas. Cluster 5 has the largest population among the clusters, and its population density is relatively near to the nationwide value.

Table 3 Basic statistics by cluster
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The elderly population proportion tends to increase from 2015 to 2065, except for Clusters 6–7, and its order is maintained from 2015 to 2065 in Clusters 1–7. In contrast, the orders of the EPCI and PCI in 2065 are reversed to those of the elderly population proportion in 2015. These interesting trends in the elderly population proportion, EPCI, and PCI are elaborated in the third part.

Figure 3 shows the changing patterns of the elderly population proportion, EPCI, and PCI from 2015 to 2065. The most remarkable change is that of EPCI in Clusters 1–4, especially Cluster 1. The EPCI begins to rapidly increase around 2030, peaks around 2050, and decreases until 2065. This changing trend is strongly suggested to be caused by the second baby boomers born in 1971–74. This is because the baby boomers enter the elderly population group in 2036–39 and probably begin to leave the group from around 2050. This consideration leads to the conjecture of the cohort’s distribution being biased toward Clusters 1–4 and a stronger bias in the order of Clusters 4, 3, 2, and 1. The change in Cluster 5 is the most similar to the whole country, and this is consistent with the fact that, as discussed below, Cluster 5 is distributed throughout Japan. The distinct decreasing trend in the elderly population proportion observed in Cluster 7 is discussed in the third part.

Fig. 3
figure 3

The change patterns of the elderly population proportion, the EPCI, and the PCI, 2015–65

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The Geographical Features of Clusters

Table 4 lists the LQs of the categorized areas and clusters that indicate how strictly the corresponding cluster specializes in the corresponding categorized area. Figure 4 illustrates the distribution of those LQs by cluster. According to Table 4 and Fig. 4, Clusters 1–4 are directed toward urban areas, and in contrast, Clusters 6–7 are oriented toward rural areas regardless of whether these are metropolitan or non-metropolitan areas. This fact matches the discussion on the population density of clusters in the first part.

Table 4 Location quotients by categorized area and cluster
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Fig. 4
figure 4

The distribution of the location quotients by cluster

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Clusters 1–4 show that the metropolitan core cities mostly provide the highest LQ in each metropolitan area. However, Clusters 1–2 depict that large cities give the highest LQ in the Tokyo metropolitan area (TMA). These large cities, which consist of five cities such as Yokohama City, are in the suburbs of the TMA (Fig. 4). Therefore, Clusters 1–2 are characterized by an inclination towards the suburbs of the TMA. This inclination is stronger for Cluster 1 because the LQ of the large cities is far higher than that of the core city, i.e., Tokyo’s special wards. Meanwhile, Clusters 3–4 indicate that the LQ of the core city of the TMA is much higher than that of the core cities of the other two metropolitan areas. Therefore, Clusters 3–4 are characterized by their inclination towards the core of the TMA. Figure 4 shows that Cluster 5 is widely distributed in medium and small cities throughout Japan. The linkage with rural areas is stronger for Cluster 7 than Cluster 6.

The Clusters’ Stage Shift in Population Aging

To summarize, this study introduced a new concept of the stage in the population aging process, with a focus on the increase/decrease in three variables: the total population, the elderly population, and its proportion. Of these three variables, obviously, the increase/decrease in the total and elderly populations is linked to the PCI and EPCI, respectively. This concept is quite different from the aging process that distinguishes personal changes in the body and mind according to aging. Furthermore, this is also different from the long-term process of worldwide population aging introduced by Fernandes et al. (2023), who determined the stage shift by focusing on the rejuvenating effect of births and deaths and by confirming an increase or decrease in mean age.

The procedure for formulating the stage defined in this study is as follows: First, for an arbitrary period and area, if any one of the above three variables increases, the position is written as the plus sign “ + ,” and if any one of them decreases, the position is written as the minus sign “ − .” Thus, the following eight combinations are derived from the increase/decrease of the total population, the elderly population, and its proportion: (+ , + , +), (+ , + , −), (+ , − , +), (+ , − , −), (− , + , +), (− , + , −), (− , − , +), and (− , − , −). For example, combination (− , + , +) depicts the following phase: the total population decreases, the elderly population increases, and its proportion increases.

However, among these combinations, (+ , − , +) and (− , + , −) are theoretically impossible. Furthermore, (+ , + , −) and (+ , − , −) are unlikely to occur in developed countries after the demographic transition because, due to low fertility rates in these countries, the growth rate of the non-elderly population is generally lower than that of the elderly population. Consequently, the discussion is confined to the combinations (+ , + , +), (− , + , +), (− , − , +), and (− , − , −). In fact, only these four combinations emerged for all seven clusters and all the 10 time periods (2015–20, 2020–25, ..., 2060–65). This suggests that the future process of Japan’s population aging will be the norm in many developed countries after the demographic transition.

Second, Stages 1, 2, 3, and 4 were assigned to combinations (+ , + , +), (− , + , +), (− , − , +), and (− , − , −), respectively. The relationship between the four stages and the increase/decrease in the three variables is depicted in Table 5. Third, we analyzed the stages for seven clusters and ten time periods and indicated the pattern of stage shifts in Table 6. There are two interesting trends in this pattern. One is that if 1 ≤ s < t ≤ 4, Stage s appears first before Stage t appears first in each cluster. In other words, for each cluster, after the total population begins to decline (Stage 1 to Stage 2), the elderly population begins to decrease (Stage 2 to Stage 3), and then the elderly population proportion begins to decrease (Stage 3 to Stage 4). Accordingly, Japan’s population aging proceeds completely in order from Stages 1 to 4. The other is that if 1 ≤ l < m ≤ 7, stages shift in Cluster l later than in Cluster m except for two periods of 2055–60 and 2060–65. This means that clusters with a higher elderly population proportion in 2015 cause earlier stage shifts because Clusters 1–7 were put in ascending order of elderly population proportion in 2015.

Table 5 The relationship between the four stages and the increase/decrease of three variables
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Table 6 The pattern of clusters’ stage shifts
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The population aging process is explained as follows. The shift from Stage 1 to Stage 2 is caused by the following mechanism: since the size of younger cohorts reduces owing to fertility decline, the total population begins to decline although the elderly population and its proportion continue to increase. Esaki and Nishioka (2020) demonstrated that the aging of previous in-migrants was likely to bring Stage 2 in the TMA. The shift from Stage 2 to Stage 3 is caused by the following mechanism: since the size of cohorts newly entering the elderly population begins to decrease due to long-term fertility decline, the elderly population also begins to decrease although the elderly population proportion continues to increase because of the relatively rapid decline in the total population. According to Hirai (2014), Stage 3 has already emerged in some rural municipalities. Hence, clusters with a higher elderly population proportion in 2015 reduce both the total and elderly populations earlier, and this fact explains why the PCI and EPCI of these clusters become lower in 2065 than those of clusters with a lower elderly population proportion in 2015.

The shift from Stage 3 to Stage 4 indicates the period when the elderly population proportion begins to decrease. The cause of this shift for Clusters 1–2 is different from Clusters 6–7. In Clusters 1–2, the shift is brought about by the second baby boomers’ withdrawal from the elderly population with their death and is characterized by their inclination to the suburbs of the TMA. Therefore, the shift is influenced by the second baby boomers living in the suburbs of the TMA. This is consistent with findings by Inoue & Watanabe (2014), such that the second baby boomers’ distribution is biased toward the suburbs of the TMA. This is because they were born as children of the first baby boomers, whose distribution is biased in favor of the suburbs of the TMA. Since some of the second baby boomers moved into the core of the TMA, their distribution is biased also toward that core. Alternatively, for Clusters 6–7, the above shift occurs long before the second baby boomers begin to withdraw from the elderly population, and therefore, the baby boomers should not primarily affect the shift. Meanwhile, in rural or mountainous areas, a rapid reduction in the size of cohorts newly entering the elderly population should be brought about not only by long-term fertility decline but also by long-term permanent out-migration of the youth population (Esaki, 2016; Ishikawa, 2020; Maruyama, 2018), and consequently, the above shift occurs. Hence, a distinct decreasing trend in the elderly population proportion is observed in Cluster 7 and it is the only cluster where the elderly population proportion exceeds 50%. According to Inoue and Inoue (2019), an elderly population proportion over 50% is the most influential risk factor for becoming uninhabited. This discussion enables us to assume that the decline in elderly population proportions might be an inevitable step toward becoming uninhabited.

Discussion

Through the analysis of the future aging process in Japan, this study has developed a hypothesis regarding the stage theory of the aging process in developed countries after the demographic transition. Since this hypothesis is the most important argument of this study, it is discussed here from the following three perspectives:

  1. (1)

    Why was the combination of small area population data and cluster analysis necessary and significant for this stage theory?

  2. (2)

    Why did we use data from the small area population, especially from the small area population projections?

  3. (3)

    How does the proposed stage theory position within previous studies or link to them?

First, let us discuss 1 above. The combination of small area population data and cluster analysis was one of the unique features of this study. The smallest area unit that aging studies address is often the municipality. In the case of Japan, it is the prefecture or basic municipality (e.g., Esaki & Nishioka, 2020; Inoue & Watanabe, 2014; Koike, 2021; Yamauchi et al., 2017). However, a typical municipality may have a mixture of urban and rural areas, high-density and low-density areas, and aging and non-aging areas within the same area, and even if these areas are classified by cluster analysis, the differences between the clusters may not be strongly expressed. In contrast, by dividing municipalities into many small areas and then reintegrating them through cluster analysis, it is possible to form clusters that are demographically very homogeneous (i.e., areas with different demographic characteristics are not mixed together), and differences between clusters become more apparent. In other words, the combination of small area population data and cluster analysis allows us to analyze the future aging process very precisely by comparing clusters with each other. This is the answer to query 1 above.

Second, let us discuss 2 above. This study aimed to identify hidden trends in the future aging process that could not be found in previous national or municipality-based analyses by setting up demographically homogeneous areas. To this end, this study used a unique method that combines small area population data with cluster analysis. However, it is obviously more advantageous to use the projected population data by small area to extract such trends than to use the past small area population data for single or multiple years. The study by Feng (2015) is one of the few studies to analyze the aging process in Japan using small area population data and made some reference to the process in Japan's large cities. However, since the data used in the study were census data from two previous time points (2000 and 2010), there was no discussion of the long-term aging process in the future. In contrast, since the projected population data by small area, such as the SAPP series, have been developed relatively recently, there have been very few studies on future aging using such data, and furthermore, to the best of our knowledge, none of them have used cluster analysis, with the exception of this study. These are the answers to question 2 above.

Third, let us discuss 3 above. As mentioned above, the combination of small area population data and cluster analysis allowed for a very precise analysis of the future aging process. This enabled us to derive a hypothesis of aging stage theory using three indicators. The stage theory using three indicators is much more advantageous than those with one or two indicators because it describes aging from three dimensions and thus can explain more complex processes. A well-known stage classification using a single indicator is the one defined by the World Health Organization (WHO) (Permanent Mission of Japan to the United Nations, 2016). This definition is not a stage theory but merely a stage classification based on the elderly population proportion, as follows: an aging society if the elderly population proportion exceeds 7%, an aged society if it exceeds 14%, and a super-aged society if it exceeds 21%. There have been many discussions using this definition, for example, some have calculated the number of doubling years, i.e., the number of years required from the time the elderly population proportion exceeds 7% to the time it doubles to 14% and made international comparisons of these years (Ministry of Health, Labour & Welfare, 2016). However, most of them have not gone into the aging stage theory. Regarding the stage theory using two indicators, Masuda (2015) is well-known in Japan, using the elderly population and the non-elderly population (i.e., the sum of the working age and child populations). Masuda (2015) defined the first stage as a period when the elderly population increases and the non-elderly population decreases, the second stage as a period when the elderly population maintains or slightly decreases and the non-elderly population decreases, and the third stage as a period when both populations decrease. Although Masuda’s theory shares some similarities with the stage theory presented in this study, it was not derived from a rigorous demographic analysis and did not mention the aging process, placing it in the demographic decline stage theory rather than the aging stage theory. In terms of stage theory using 3 or more indicators, the study by Fernandes et al. (2023), mentioned in the introduction, is noteworthy. Fernandes et al. (2023) determined the stage shift of aging using the mean age, its derivative, and the rejuvenating effect of births and deaths as follows: Stage 1 if the mean age is decreasing, its derivative is negative, and the rejuvenating effect > 1; Stage 2 if the mean age is increasing, its derivative is positive, and the rejuvenating effect < 1; Stage 3 if the mean age is increasing, its derivative is maximum, and the rejuvenating effect < 1; Stage 4 if it returns to a state similar to Stage 2; and Stage 5 if it returns to a state similar to Stage 1. In general, the mean age and the elderly population proportion are linked, so there is some overlap between this theory and the theory of this study. Nevertheless, the target of this stage theory is the world subregions from 1950 to 2100. In other words, not only are the indicators used different from those of the stage theory in this study, but the two are also very different in terms of both time and regional scales. Based on the above discussion, it can be concluded that the stage theory of the aging process presented in this study is quite unique and distinct from existing stage theories, both in terms of indicators used and in terms of the approach to aging. This is the answer to query 3 above.

Conclusion

This study aimed to quantitatively analyze the future aging process using data from the SAPP for Japan and, based on this analysis, to attempt to present the standard aging process that developed countries would experience after the demographic transition, taking advantage of the fact that Japan has the most aged population in the world. A non-hierarchical cluster analysis was performed using the two statistics on aging, i.e., the elderly population proportion and EPCI. Consequently, we extracted the seven major clusters, covering more than 98% of Japan’s total population in 2015.

This study examined the demographic and geographical features of these seven clusters, introduced a concept of the stage, and analyzed the relationship between the features and the stages. These discussions led to the following findings on the future process of Japan’s population aging:

  1. (1)

    In each area of Japan, first, the total population begins to decline (Stage 1 to Stage 2), second, the elderly population begins to decrease (Stage 2 to Stage 3), and finally, the elderly population proportion begins to decrease (Stage 3 to Stage 4).

  2. (2)

    The above stage shifts generally proceed earlier in areas with a higher elderly population proportion.

  3. (3)

    The above stage shifts are attributed to the reduced size of younger cohorts owing to long-term fertility decline.

  4. (4)

    The shift to Stage 4 occurs earlier in the two contrasting areas (i.e., suburbs of the TMA and rural or mountainous areas) than in other areas.

  5. (5)

    For the suburbs of the TMA, the reason for the above stage shift is the second baby boomers’ withdrawal from the elderly population, and for rural or mountainous areas, the reason is a rapid reduction in the size of cohorts newly entering the elderly population, which is brought about not only by long-term fertility decline but also by long-term permanent out-migration of the youth population.

Finally, we discuss the generalization of these findings to other developed countries/areas after the demographic transition to derive a hypothesis. Although Japan experienced a few unique demographic events, such as short-term baby booms, sharp fertility drops, and rapid longevity extensions, quite a few countries will follow Japan regarding population aging. This is because the fertility decline has been proceeding in many developed countries after the demographic transition, especially in East Asian countries/areas such as Korea, Taiwan, and Hong Kong, at a faster pace than in Japan. Therefore, at least the major findings 1–3 should occur in many developed countries/areas and will occur in Korea, Taiwan, and Hong Kong, and these could be generalized as a hypothesis. Findings 1–3 would be the norm in many developed countries after the demographic transition.