1.1 Background

Shrinking cities pose significant urban planning issues [1]. These issues have been seen, for example, in former East Germany due to political changes [2] and in United States’ Rust Belt due to the economic decline [3]. In addition, during the COVID-19 pandemic, it was reported that city populations declined due to urban exodus [4]. Among the various types of population decline, this study focused on Japanese shrinking cities due to the low birthrates and aging populations [5]. The population decline is inevitable in Japan, where immigration is low. In 2021, the Japanese population aged over 65 comprised 36.21 million people, constituting 28.9% of the total population [6]. It was also reported that the national population will decrease to between 38 and 65 million people by 2100 [6]. Fig 1 shows the population change rate (PCR) in Japanese cities in 2010. In Fig 1, PCR is the percentage of change from population in 2005 (P₂₀₀₅) to population in 2010 (P₂₀₁₀), as calculated in Eq (1). Fig 1 indicates that most cities’ populations have been declining. Similar problems are likely to be faced in other East Asian countries such as China [7, 8]. In China, it was identified that 153 cities were shrinking between 1992 and 2019 [9]. Population decline driven by low birthrates and aging populations poses various problems, including overall economic and social decline [10]. For example, population decline correlates with various types of social problems, such as economic decline and increasing vacant houses [11]. However, there is a cascading and complex relationship between economic and social factors within the context of population decline, and researchers have yet to systematically elucidate the factors affecting population decline.

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Fig 1. Population change rate in Japanese cities in 2010.

In Fig 1, left side map indicates the location of Tokyo and Osaka in major East Asian cities, and right side indicates map focused on the Osaka Metropolitan area. Fig 1 shows the population change in graduated colors from red to blue. The gray color areas are other cities, such as merged cities. Republished from Fig 1 under a CC BY license, with permission from ESRI Japan, original copyright 2023.

https://doi.org/10.1371/journal.pone.0284134.g001

The research question of this study is: which economic, social, and educational factors affect population decline in Japanese shrinking cities? These economic, social, and educational factors might be strongly or weakly interrelated with the PCR; such relationships are complex, ranging from the micro to the macro level [12]. That means that the relationship would not reveal deductively using a fixed framework, but inductively using a large set of indicators. The relationships between these factors also do not occur through a simple linear mechanism, but through a non-linear and complex mechanism [13]. To understand these relationships, the logical framework to be utilized is an inductive statistical urban model using various indicators of shrinking cities [14]. The statistical urban models allow policymakers to monitor population decline [15]. For the analysis, this study developed an urban network model that interrelates economic, social, and educational indicators. By providing systematic insights into the issues emerging due to population decline, the model can deliver a planning support system for municipal leaders and urban planners.

1.2 Purpose

This study aims to clarify the indicators that affect the PCR by modeling shrinking cities. For the analysis, this study uses the case of Japanese cities. In Japan, there were 1,733 cities in 2010. Among these, this study analyzes 1,316 cities whose populations were declining as of 2010 (Fig 1). Japan is suitable for this study because it contains the largest number of shrinking cities due to low birthrates and aging populations worldwide. In Japan, the government has begun to develop urban plannings for shrinking cities [16]. Therefore, this study’s results from Japan may contribute by providing insights and a planning support system for shrinking cities worldwide facing similar problems.

Methodologically, this study employed Bayesian network analysis, a machine learning technique, to model shrinking cities using a dataset of economic, social, and educational indicators by cities. The Japanese Ministry of Education, Culture, Sports, Science, and Technology (MEXT) developed the dataset used in this study to promote research that contributes to policy formulation. The dataset comprises cross-sectional data of 259 indicators, including economic, social, and educational indicators [17]. The dataset covers most city-level government statistics that are available publicly. The Bayesian network constructed from this dataset is a stochastic model representing the quantitative causal relationship between individual indicators with conditional probability [18]. The probabilistic estimation of the network makes it possible to predict uncertain scenarios.

1.3 Literature review

The novelty of this study is to develop an urban statistical model of shrinking cities by Bayesian network analysis. Urban models of shrinking cities have been proposed in previous studies. In an early study, the researchers conceptualized an urban model consisting of economic and population decline and policy changes [19]. As research on shrinking cities progressed, particularly in Europe, researchers also conceptualized an urban model in which diverse forms of decline at the global and regional levels caused population declines [20]. These conceptual urban models indicated that population decline is related to economic and social decline. However, it was also found that the indicators associated with population decline are multifaceted and pertain to diverse perspectives [21]. Therefore, to investigate the complicated relationships among these indicators, researchers need to develop both an urban statistical model that strength conceptual models of shrinking cities. Accordingly, this study aimed to develop an urban statistical model of shrinking cities.

Previous studies have analyzed the statistical relationship between population decline and economic indicators in shrinking cities. Specifically, the positive correlation between population change and industrial diversity was clarified [22]. For example, it was investigated the case of Yubari City, a single-industry mining city in Japan, well-known for suffering from rapid population decline and financial collapse because of the mining industry decline [23]. From a different perspective, researchers demonstrated the positive correlation between investment network centralities and population change in shrinking cities [24]. In addition, it was explained that development zone policies have helped curb population decline in these shrinking cities [25]. Academicians also demonstrated that shrinking cities are influenced by socioeconomic development and social indicators, including expenditure on education [26]. In Japan, it was found that population decline in densely inhabited districts is caused by the outflow of residents and the formulation of suburban residential areas [27]. In addition, in the case of Yokohama city, Japan, it was clarified that urban shrinkage was correlated with the aging population, distance to the nearest parks, and proportion of private houses and flats [28]. Despite the important contributions of these past studies, they failed to elucidate the complex and cascading relationships of factors related to population decline. Accordingly, the originality of this study lies in its extension of these prior pieces of evidence by developing an urban statistical model of shrinking cities using a dataset comprising economic, social, and educational indicators, and in its aim to identify the factors influencing PCR. For the analytical methodology, this study refers to the study by Kato [29], wherein urban modeling developed by Bayesian network analysis was used to estimate future populations.

2.1 Economic, social, and educational indicators

As mentioned above, this study’s data come from a cross-sectional dataset of economic, social, and educational indicators by cities which MEXT collected to promote research contributing to the formulation of educational policies [17]. This study used this dataset because it covers most publicly available city-level government statistics in Japan. Specifically, it stems from sources such as the Japanese Census, the School Basic Survey, the National Survey of Academic Progress, the Social Education Survey, the Survey on Time Uses and Leisure Activities, the Housing and Land Survey of Japan, the Major Financial Indicators of Local Governments, the Economic Census, and the National Survey of Family Income and Expenditure [30]. While this dataset cannot be shared publicly because of governments’ confidentiality, the dataset is available from the Japanese MEXT Institutional data access for researchers who meet the criteria for access to confidential data. Since April 5, 2022, the author has received permission from MEXT to provide this data. All indicators are listed in S1 Table.

The indicators present in the dataset are used not only for policymaking but also for academic research [31, 32], and the dataset encompasses 259 indicators in total [33]. This study used all 259 indicators containing numerical and nominal scale data. The dataset covers the ten years from April 1, 2001, to April 1, 2011. This study used data as of April 2011. Although the dataset is 10 years old, no other datasets in Japan have such a comprehensive range of indicators. As population decline is a long-term urban phenomenon, the dataset is valuable and appropriate for this study.

2.2 Bayesian network analysis

Bayesian network analysis was used for urban modeling based on the economic, social, and educational indicators. Compared to similar statistical analysis methods, such as structural equation model analysis, neural network analysis, and decision tree analysis, Bayesian network analysis allows for the flexible analysis of nonlinear and non-normal relationships between indicators [29]. It also enables researchers to obtain robust models that avoid collinearity risk [34]. It is important for the current study that that the analytical process of choice can avoid collinearity risk because 259 indicators are under scrutiny. This study used BayesiaLab 10.2 as its Bayesian network construction algorithm [34].

This study adopted the maximum weight spanning tree (MWST) and taboo algorithms for the optimal local search for each child node; the MWST algorithm was deployed first, followed by the taboo algorithm. The MWST algorithm makes it possible to compute big data, which this study analyzed, faster than other algorithms [35]. The taboo algorithm is effective for refining networks built by updating another network learned on a different dataset, because it refers to structural learning by implementing the taboo search for Bayesian networks [36].

For the analysis, this study set the indicator of PCR as the target variable; Bayesian network analysis revealed the total effect (TE) and correlation of indicators on the PCR. TE was analyzed by standard target mean analysis (STMA), which uses the mean value evidence to go through the indicators’ variation domain and measure the impact of indicators on the target’s mean. That is, TE is the derivative of the total effects curve computed at the a priori mean of that variable, δ_x = 0 and δ_y = 0 [34]. The standardized total effect (STE) normalized the TE by taking into account the ratio between the standard deviations of the indicators (σ_x) and the target indicator (PCR) (σ_y) [34]. The STE was calculated using Eq (2), as follows: (2)

Correlation analysis was based on mutual information (MI), defined as the difference between the marginal entropy H(Y) of the target indicator (PCR) and its conditional entropy H(Y|X). The MI was calculated using Eq (3), which is equivalent to Eq (4); in the latter, p(x,y) is the joint probability function of X and Y, while p(x) and p(y) are the marginal probability functions of X and Y.

(3)

(4)

The binary mutual information (BMI) is the amount of information brought by each indicator to the knowledge of the state of the target indicator (PCR) compared to an unconnected network [34]. That means that BMI is amount of information brought by each variable to the knowledge of the state of the target indicator (PCR).