The effects of the local and regional conditions and inequalities on urban shrinkage: a multilevel analysis focusing on local population decline

ABSTRACT

Urban shrinkage is becoming a worldwide issue. However, empirical investigation still lacks an understanding of the spatial extent of the factors that drive local population decline, a prevalent aspect of urban shrinkage. Empirical evidence on multilevel factors relating to population decline is particularly scarce. We investigated the influences by analyzing economic, social, physical, and policy conditions at the local and regional levels. Regional conditions, as well as local conditions, are also related to the decline of the local population. The effect goes beyond economic and demographic conditions; conditions such as the local infrastructure level and development policy also significantly influence.

KEYWORDS:

• Urban shrinkage
• population decline
• multilevel factors
• regional inequalities
• hierarchical linear modeling

1. Introduction

If urbanization is analogous to growth, urban shrinkage becomes an anomaly rather than a general urban phenomenon (see Oswalt 2006). However, urban shrinkage is becoming a common global problem (Galster 2017). More than a quarter of the world’s largest cities are already experiencing urban shrinkage (Xie et al. 2018). The research suggests various causes (Hartt 2019), but population decline is the most common and significant feature of urban shrinkage (Delken 2008; Haase et al. 2016; Hollander and Németh 2011). Due to regional gaps that cause competitive population migrations, countries with stagnant or declining populations, such as the United States, Europe, Japan, South Korea, and countries with fast population expansion, such as China and India, can expect urban shrinkage.

In line with stagnating worldwide population growth, urban shrinkage will likely increase even further. If general population stagnation or decline continues, urban shrinkage due to interregional urban competition (Coppola 2019) and selective migration (Nelle 2015) will become increasingly common, requiring policies to address urban shrinkage (Eraydin and Özatağan 2021). Traditional planning methods, such as regional zoning and building permits, do not perform well in these areas with decentralized features, limiting policy responses (Galster 2017).

Responding to the urban shrinkage problem requires an intimate understanding of the various conditions affecting it. However, despite ongoing theoretical discussions and a consensus that multilevel effects (Bernt 2016; Hartt and Hackworth 2018; Haase et al. 2014) and regional disparities (Fol 2012; Xie et al. 2018) have a significant correlate with urban shrinkage, empirical investigations verifying these effects remain very scarce (Bernt 2016; Haase et al. 2014; Döringer et al. 2020).

This study aims to confirm the poorly understood relationship between urban shrinkage of various multilevel conditions and their interactions. Hierarchical linear modeling (HLM) can examine the relationship between multilevel factors and dependent variables. Therefore, the study used public data from central governments, performing HLM on data for the local and regional areas of South Korea where nationwide population decline and regional inequalities occur. Research proceeded as follows. First, we determined which conditions correlate with population decline. Second, we investigated the extent to which various levels of those conditions and their interaction relate population decline. Third, we explored how the unequal distribution of multiple conditions correlates with population decline. This study broadens the empirical discussion on urban shrinkage and defines the correct policy-enforcement entity and scope for local population decline response strategies.

2. Literature review

This section reviews various conditions that qualify as factors of urban shrinkage and examines the possibility of their multilevel effect. Urban shrinkage has the characteristics of complex, context-specific, diverse processes (Hartt 2019), which limits defining it as a single process. Despite various suggestions about the causes of urban shrinkage, its traditional primary causes are globalization (Martinez‐fernandez et al. 2012), deindustrialization (Rieniets 2009), suburbanization (Fishman 2005), a declining fertility rate, and an aging population (Wiechmann and Pallagst 2012). Traditional explanations of urban shrinkage in a particular country primarily focus on economic issues as macro and long-term influencing factors.

In recent discussions, circular causality occurs in processes in shrinking cities (Hartt and Hackworth 2018; Haase et al. 2014). A complex phenomenon, changes in the external environment, urban development effects, and governance activities interact in complex way (Ma, Li, and Zhang 2020) and lead to understanding it as a multidimensional phenomenon (Martinez‐fernandez et al. 2012). Such urban-change processes occur on multiple scales, suggesting that studying and governing shrinkage require a multilevel approach (Weaver and Holtkamp 2015). For instance, Haase et al. (2014) suggest an urban-shrinkage concept that leads to population decline, as global and regional drivers of shrinkage and local level direct or indirect consequences for urban development affect urban development on a local scale. Hartt and Hackworth (2018) also explains urban shrinkage as a phenomenon in which local factors and external (regional, national, and global) contexts and trends work together to act.

Understanding multilevel impacts are particularly important in the discussion of the city regions (Scott 2019) and the multilevel governance (Tang, Luo, and Ying 2022), which has recently been attracting attention as an alternative to urban problems. Establishing city regions and coordinating multilevel governance requires understanding the local and regional level impact and their interaction (Tang, Luo, and Ying 2022). The right-sizing, which is attracting attention as an alternative to urban shrinkage, is also related to the spatial extent of policy influence. For the implementation of the right-sizing (Coppola 2019) or smart decline (Hollander and Németh 2011), a comprehensive, multidimensional understanding is needed rather than a discussion in a single city (Coppola 2019). In other words, an empirical understanding of the multilevel impact is essential to develop feasible alternatives to reduced cities through these agendas.

On the other hand, there are too few studies on such multilevel interrelations (Bernt 2016). Most studies on this topic are theoretical debates or case studies (e.g., Bernt 2016; Hartt and Hackworth 2018; Haase et al. 2014; Joo and Seo 2018; Zhou, Koutský, and Hollander 2021), while empirical studies on the multilevel influence on the urban decline are rare.

Among the few multilevel studies, Jun (2013) finds that neighborhood change occurs through the interaction of factors on various scales, such as the demographic and physical characteristics of the neighborhood, the demographic and economic aspects of municipalities, and the economic features of metropolitan areas. Furthermore, the study also confirms that all three levels affect neighborhood change. However, this study did not deal with the interactions between levels, only adding the condition variables of each level to the model.

By using the hierarchical linear model in Northeast China, Tong et al. (2021) empirically found that the economic and demographic conditions at the town level and the economic, demographic, and physical conditions at the county level affect urban shrinkage. At the town level, a small population and low-level administrative units amplified the shrinking phenomena. The study examined county-level conditions for a significant cross-level effect on shrinking towns.

However, Tong et al. (2021) and Jun (2013) conducted studies defining variables at both levels differently and supposed using different measures/indicators for the same concept. In such a case, determining whether a significant variable is due to different levels, different measurement indicators, or both effects is difficult (Gim 2018b).

Multilevel theories aim to explain whether a theoretical relationship of A-B holds at multiple levels (Lacey and Fiss 2009). Chen, Bliese, and Mathieu (2005) suggested using identical variable relationship between levels as a method for cross-level generalization in multilevel theory. If various conditions to explain population decline are consistently configured, the effect of each level on population decline can be analyzed without bias according to variable settings. On the topic of urban shrinkage, no research exists on this effect. Still, in a related field, research exists on the influence of identical variables measured at multiple levels, to examine the impact of a range of variables on a given occurrence. For example, Greenwald and Boarnet (2001) apply the identical variable to different levels (census-block group and zip-code levels). They confirm that each variable exerts different influences at each level. Curtis, Voss, and Long (2012) examine the poverty-generating process, using identical variables at different aggregate levels and discussing their variations.

The literature also suggests that regional inequalities, such as differences between regions, uneven development, urban inequality, spatial disparity, residential segregation, and gentrification, also influence the dynamics of shrinking cities. Xie et al. (2018) reveal that regional and socio-regional inequality on various scales inevitably intertwines with urban shrinkage and is its leading cause, according to empirical research on Metropolitan Detroit. However, this study focuses on how uneven the conditions look at each regional level when compared to the average, limiting assessments of whether spatial disparities of various conditions affect urban shrinkage.

Li, Kong, and Zhu (2020) also use the Theil index to derive urban factors, showing relative inequalities that affect population change and the expansion of developed areas. Their study focuses on regional inequality by indicating the unequal placement of each regional condition. Still, measuring only the inequality of per capita urban construction land area, to determine the effect of unequal placement of various regional conditions on urban shrinkage, has its limit.

Studying the spatial extent and interaction of urban shrinkage causes, as well as the administrative level and the practical scope of implementing urban shrinkage policies, is also necessary (Haase et al. 2014). In fact, urban studies lack research on the policy itself, compared to reflections on cities’ physical and demographic characteristics (Gim 2018a). Responding to urban shrinkage requires comprehending the complex urban-governance process that occurs at the regional level as well as the local level (Hospers 2014), then establishing an urban-shrinkage suppression strategy appropriate to each regional context (Li, Kong, and Zhu 2020). Closely analyzing the policy effect on urban shrinkage in a specific region calls for considering the hierarchical impact of each regional unit on urban shrinkage and the policy hierarchy as multilevel planning (Pallagst et al. 2021).

However, most research on the hierarchical effect or interrelation of urban-shrinkage policies has used case studies (e.g., Camarda, Rotondo, and Selicato 2015; Joo and Seo 2018), and only a few are empirical studies. An exception by Hu et al. (2020) empirically examines the effect of development policies on urban shrinkage and proves the effect of urban-shrinkage suppression in development policies. However, its drawback is using a dummy variable to assess briefly whether each location had been classified as a development zone.

This study aims to elucidate the relationship, scope, and interaction of influences by analyzing the consistent variables at the local and regional levels. As discussed, studies on the relationship between multilevel factors and urban shrinkage did not do empirical tests on the actual scope of action. Instead of studying the effects of conditions in data-aggregation units, studies on spatial disparities set limited conditions. Furthermore, there is little empirical research on policy consequences. Therefore, this study groups the factors that earlier studies show influencing urban shrinkage as economic, social, and physical factors. Furthermore, we added policy factors to the model to evaluate policy consequences.

3. Data and methods

3.1. Study area

In Korea, despite continuous economic growth, the population is stagnant, and urban shrinkage is occurring extensively in non-urban areas. Urban shrinkage in Korea, the subject of this study, is increasingly deepening due to the complex consequences of fast industrialization, industrial transformation, rapid urbanization, lifestyle changes, and a continually dropping birth rate (Joo and Seo 2018). The population has been stagnant since the 2000s, and only then did discussions on curbing population decline through regional policies begin in earnest (Kim 2018). The net population has declined since 2021, and the nationwide population decline is likely to continue. In this process, the competition for attracting population across regions may further reduce less competitive areas, creating a vicious cycle of urban shrinkage. In fact, population declines from 2012 to 2019 are evident in many areas, except the metropolitan area. Moreover, they are gradually worsening in areas with a decreasing population (see Figure 1).

Figure 1. Population changes in the study area.

Korea has an administrative system composed of three levels (regional level, local level, and neighborhood level). Among them, we analyzed the regional level province units (teuk-byeol si, gwang-yeok si, and do) and local level district units (si, gun, and gu), which have the status of autonomous administrative organizations. The regional government is supervised and financially supported by the central government. The local government is supervised and financially supported by the regional government. Local governments at regional and local levels in Korea have autonomy in the execution of budgets in some sectors.

3.2. Variables

The population change rate of each area was a dependent variable to measure urban shrinkage. Although population decline and urban shrinkage are often interchangeable, they are not strictly the same concept. However, most studies on urban shrinkage focus on population decline, the most critical change that urban shrinkage causes (Bernt 2016; Haase et al. 2014; Hummel 2015). Since population decline represents the primary aspect of urban shrinkage (Hartt 2019), most empirical studies (e.g., Haase et al. 2012; Hu, Wang, and Deng 2021; Tong et al. 2021; Wolff and Wiechmann 2017), including this study, use the population change rate as a proxy for urban shrinkage. While factors such as the built-up area or local economic level have relatively dynamically nonlinear and asymmetrically scalable characteristics (Galster 2017), the population is an aspect of urban shrinkage that can respond more immediately to changes in local and regional conditions (Duranton and Puga 2013). Even though it does not include all the different aspects of urban dynamics, population decline has advantages when developing an empirical model and is widely used since it accounts for a significant portion of urban shrinkage (Bernt 2016).

To control for the average population changes in each year, according to the national influencing factors or trends, the local population change rate is standardized by subtracting the national population change rate for the current year (i.e., the national population for the current year minus the national population for the previous year, divided by the national population for the current year). The population change rate consists of natural change and interregional migration. And interregional migration may respond more sensitively to local and regional conditions (Hoekveld 2014; Wolff and Wiechmann 2017). However, when only population changes caused by social factors are considered, it is challenging to represent local and regional shrinkage caused by the sum of natural change and interregional migration (see Hoekstra et al. 2020; Lauf, Haase, and Kleinschmit 2016). Therefore, the population change rate, including natural change and interregional migration, was used in this study. And the model was constructed by controlling demographic characteristics that could affect the increase or decrease of the natural population change (Hoekveld 2014).

Previous studies theoretically reveal that population decline is related to economic, social, physical, and policy conditions at each local and regional level (Hartt and Hackworth 2018; Haase et al. 2014; Hollander et al., 2017). However, despite theoretical discussions, the relationship between these conditions and population decline has not been sufficiently verified empirically. We selected variables for each factor correlated with population decline considering previous empirical research results, knowledge in related fields, the relationship between variables, and data availability.

We used independent variables representing economic conditions, including the paid worker ratio, relating to the region’s employment status and industrial structure, and the service worker ratio, representing workers in the tertiary industry. In many studies (e.g., Firmino Costa da Silva, Elhorst, and Silveira Neto 2016; Tong et al. 2021; Xie et al. 2018), the paid worker ratio has been regarded as a variable that affects demographic change as an employment characteristic that determines the attractiveness of a region for migration. Additionally, we added the service worker ratio, reflecting the selective migration by occupation due to urban shrinkage that Galster (2017) assumes.

As public expenditure variables, we used the proportion of the welfare budget in the total regional budget and fiscal independence, which indicates the balance of revenues to expenditures within the region. Many shrinking cities are experiencing a fiscal crisis, with more expenses than revenues and deteriorating services (Hummel 2015). The welfare regime is a significant driver of population decline (Hoekveld 2014; Hoekstra et al. 2020). In Korea, the central government compensates for insufficient revenue compared to local expenditure through transfer expenditure, and the revenue capacity/expenditure needs are used as a proxy for fiscal independence (Joo and Seo 2018).

We used as variables representative social conditions, specifically the elderly population ratio (e.g., Wolff and Wiechmann 2017) and the average persons per household (e.g., Hartt and Hackworth 2018), to control demographic characteristics in urban shrinkage studies. When the elderly population ratio is high, the population of reproductive age is relatively low, negatively affecting the natural growth rate of the population and incurring additional social welfare and support costs (Wolff and Wiechmann 2017), thus affecting the regional characteristics. The average persons per household can change due to outmigration and internal household restructuring, according to the social movement of the population (Hartt and Hackworth 2018). These can affect regional characteristics, expressed in household units rather than individual units, such as local housing demand and its characteristics and administrative service demand. Therefore, we controlled the elderly population ratio and the average persons per household.

For physical conditions, we used population density indicating the level of physical density (Duranton and Puga 2013; Tong et al. 2021), and road density as an indicator of the overall level of infrastructure in the region (Wang, Yang, and Qian 2020). These variables represent each area’s population and infrastructure agglomeration level and relate to the region’s economy, amenities, and accessibility (Firmino Costa da Silva, Elhorst, and Silveira Neto 2016; Yao et al. 2022). Yao et al. (2022) suggest that these densities may act differently depending on local characteristics and contexts. Nevertheless, physical density was used as a variable because it is crucial to the growth or decline of the population through combination with other conditions.

As policy conditions, we used the new building-permit area ratio (Ma, Li, and Zhang 2020) and the development-budget ratio to represent changes in the built environment. As a traditional planning tool, the building permit plays an essential role in shaping the local physical structure and creating a place for residence and business (Galster 2017). development budget ratio to each region’s total budget was set as a variable that could represent local development policy (see Carbonaro et al. 2018). Specifically, among local fiscal statistics, the size of expenditure corresponding to the ‘local and regional development budget’ became a proxy for local development policy. The absolute quantity of the regional development budget does not indicate regional development inclination because the size of the local population or regional features heavily influences per capita public spending (Baba and Asami 2022). Instead, we used the development-budget ratio as a variable to reflect local development policy. The higher the regional development budget ratio is, the higher the priority on regional development.

The Gini coefficient, the Atkinson index, and the generalized entropy index were reviewed as alternatives to measuring regional inequalities. The Gini coefficient is based on the Lorenz curve. Since this study deals with various condition variables, we could not assume the same curve function for each variable, limiting the measurement of regional inequality. The Atkinson index is based on social welfare, but the limited comprehension of social welfare in the numerous variables in this study makes it challenging to use. Therefore, as a special case of the generalized entropy index, we used the Theil-T index ($T=\frac{1}{n}\sum _{i=1}^n\frac{x_i}{\mu }ln\left(\frac{x_i}{\mu }\right)$), widely used in the planning field (e.g., Hoekstra et al. 2020; Li, Kong, and Zhu 2020). The Theil-T index is an index that can intuitively grasp the degree of unequal arrangement of conditions and has the strength to use continuous variables as they occur (Hoekstra et al. 2020). The index has a value between 0 (perfect equilibrium) and ∞ (perfect inequality), depending on the level of inequality.

3.3. Data

The analysis unit at the local level was operationalized as the district, and the analysis unit at the regional level was operationalized as the province and the metropolitan area. We used as research data government-produced public data of 17 provinces and 261 districts (mean = 15.35 districts/provinces) from 2012 to 2019. Region-level data have long been accumulated. Still, local level data are gradually building, and using identical variables for regional and local levels consistently has limitations. Therefore, we set the research period from 2012, when we could simultaneously secure data at the local and regional levels, to 2019, when we could acquire the latest data.

We performed mean centering for each input variable, to smoothly interpret the variable value by converting it into a local or regional gap. Group mean centering occurred for local level condition variables, and grand mean centering for region-level condition and regional inequality variables. The correlation between the local level variable and the region level variable decreases when we apply the group mean at the local level, exposing more clearly the influence of the local level conditions and the effect of the regional level conditions (Enders and Tolfighi, 2007). Centralization defines local level variables as representing the relative conditions of the district, compared to the average conditions of the provinces to which they belong. Regional variables represent the close conditions of the province, compared to the national average conditions. The variables we used in the study appear in Table 1. Although the year dummy was initially introduced, it did not differ significantly from the model that did not consider the year dummy. The analysis results of the model considering the time dummy variables were posted online.

Table 1. Input variables.

		Variable	Formula	Data source	Mean	Std. Dev.	Max.	Min.
Dependent variable		Standardized population change rate	(Local population of the current year-local population of the previous year) /Local population of the previous year	Statistics Korea	−0.243	2.605	36.000	−9.970
Economic conditions	Private sector	Paid worker ratio	Number of paid workers/Local population	Statistics Korea	31.825	21.329	260.076	11.178
		Service worker ratio	Number of service workers/Local population	Ministry of Employment and Labor	22.511	19.317	241.856	8.166
	Public sector	Welfare budget ratio	Welfare budget/Total local budget	Statistics Korea	32.618	15.020	67.400	8.000
		Fiscal capacity ratio	Revenue capacity/ Expenditure needs	Statistics Korea	26.709	14.113	81.500	7.300
Social conditions		Elderly population ratio	Population aged 65 or older/ Local population	Statistics Korea	18.654	7.945	39.900	5.600
		The average persons per household	Local population/number of households	Statistics Korea	2.365	0.365	5.404	0.646
Physical conditions		Population density	Local population/Local area	Statistics Korea	4.060	6.402	28.769	0.019
		Road density	Road area/Local area	Statistics Korea	5.002	8.590	74.353	0.017
Policy conditions		Development budget ratio	Development budget/Total local budget	Ministry of Interior and Safety Local Finance	7.180	26.132	862.011	0.000
		New building-permit area ratio	Building-permit area/Local area	Ministry of Land, Infrastructure and Transport	13.527	6.460	53.020	1.590

The data sources and descriptive statistics for the study’s variables appear in Table 1. Most variables had a high standard deviation compared to the average, indicating that regional economic, social, physical, and policy conditions vary widely. In certain areas in large cities, the paid worker ratio and the service worker ratio surpass 100%. The new building permit area ratio exceeds 100% in certain areas undergoing urban renewal.

4. Methods

This study aims to confirm how the multilevel factors relating to urban shrinkage in the economic, demographic, physical, and policy sectors affect urban shrinkage, measured by population decline. Hierarchical linear modeling is a statistical technique for dealing with hierarchical data. In HLM, parameter estimates of the relationship between independent and dependent variables are fixed, and variances by individuals in cluster data are random effects. HLM can simultaneously handle within-group variation and between-group variation (Tong et al. 2021).

Kreft’s rule-of-thumb (Kreft 1996), based on 30 groups of 30 people each, is commonly recognized in the analysis of the multilevel model this study considers; therefore, around 900 examples are adequate. However, using the panel model reduces the sample size to 261, which is insufficient, so we pooled nine years of data and used that to provide an adequate sample. Empirical studies in planning (e.g., Ewing et al. 2015; Laurence and Bentley 2016) also use the pooled HLM, using pooled data to overcome data limitations. Despite socioeconomic and political transformations often producing delayed effects on demographic dynamics, pooled HLM cannot reflect them. Therefore, we focused on investigating the correlation between various conditions at local and regional levels and population changes rather than the causal relationship.

Therefore, adopting pooled HLM to control the random effect enabled us to confirm how local and regional conditions correlate with the local population. Also, we verified the influence of regional inequality of these conditions on population change. Following the review of previous studies (Haase et al. 2014; Jun 2013; Li, Kong, and Zhu 2020; Tong et al. 2021; Xie et al. 2018) in section 2, we grouped factors that may correlate with urban shrinkage into economic conditions (including private and public sectors), social conditions, physical conditions, and policy conditions. Moreover, we added variables that potentially affect each condition in section 3.1. For economic conditions, we used the paid worker ratio and the service worker ratio (Galster 2017; Tong et al. 2021; Xie et al. 2018), the welfare-budget ratio (Hoekveld 2014; Hoekstra et al. 2020) and the fiscal capacity ratio (Joo and Seo 2018). We used the elderly population ratio (Wolff and Wiechmann 2017) and the average persons per household (Hartt and Hackworth 2018) for social conditions. The population density (Tong et al. 2021) and road density (Wang, Yang, and Qian 2020) represented physical conditions. The new building-permit area ratio (Ma, Li, and Zhang 2020) and the development-budget ratio represented policy conditions. We also attempted to reduce errors that might occur, depending on the content range that the variable covered, and to evaluate the spatial-effect range of each variable by setting the variables representing local and regional conditions and regional inequalities to be equal.

Using the conditions of the district unit as the local level and those of the province unit as the regional level, we performed pooled HLM while managing the random effect according to the regional level to which it belonged. We conducted an additional analysis utilizing data from the local level as ‘level 1’ and the degree of regional inequality of each local level comprising the regional level as ‘level 2’ to better understand the influence of regional inequality on population decrease. Once we discovered the possibility of interaction between local and regional factors throughout the analytical process, we did an extra study.

5. Results

5.1. Effects by levels

We confirmed the preliminary analysis to determine whether to use the HLM, ICC (Intra-Class Coefficient), which indicates the extent to which group effects appear in the data, using the null model including only random effects. The random effect variance was 20.914, while the residual variance was 4.406, showing an ICC of .826 (82.6%). The ICC cut-off for considering the nesting effect is 5% (Sorra and Dyer 2010), establishing that the random effect at the second level happens to a significant degree. As a result, a statistical Type I error may arise when doing the analysis using Ordinary Least Squares. If the hierarchical relationship is not considered, a false-positive becomes possible, which appears to significantly affect regional conditions even though they do not significantly affect population change.

We conducted an analysis based on the preliminary study results, to assess the effect of multilevel conditions on urban shrinkage (see Table 2). At first, we analyzed only local level variables (Model I), and subsequently added regional variables (Model II). Last, we added the inequality level of each condition to Model II, to examine the effect of regional inequality on regional population change (Model III). As a result of the analysis, we confirmed that Model II, including both local and regional level conditions, is more fit than Model I which included only local level conditions. The Model III AIC was lower than that of Model II. Still, the BIC was higher, seemingly due to the BIC indicator’s preference for the parsimonious model as it penalizes the model with more variables. Model III had the lowest deviance (−2LL). The VIF (Variance Inflation Factors) test was performed for each model to examine the multicollinearity problem. The maximum VIF was 6.22, less than 10, which is a rule-of-thumb (O’Brien 2007), so the multicollinearity problem was not significant.

Table 2. Result of effects by levels.

			Model I				Model II				Model III
level		Variables	level 1 condition				level 1 and level 2 conditions				level 1 and level 2 conditions with level 2 regional inequalities
			Coeff.		Std. error	t value	Coeff.		Std. error	t value	Coeff.		Std. error	t value
Local level	Conditions	Paid worker ratio	0.0257***		0.0070	3.6580	0.0257***		0.0073	3.5360	0.0266***		0.0073	3.6490
		Service worker ratio	−0.0548***		0.0075	−7.3310	−0.0542***		0.0077	−7.0100	−0.0546***		0.0077	−7.0570
		Fiscal capacity ratio	0.0640***		0.0072	8.8590	0.0620***		0.0075	8.2970	0.0602***		0.0075	8.0370
		Welfare budget ratio	−0.0593***		0.0090	−6.5780	−0.0628***		0.0093	−6.7860	−0.0605***		0.0093	−6.5000
		Elderly population ratio	−0.0409**		0.0137	−2.9970	−0.0435**		0.0141	−3.0770	−0.0441**		0.0141	−3.1180
		The average persons per household	0.2352		0.1645	1.4300	0.2693		0.1696	1.5880	0.2387		0.1705	1.4010
		Population density	−0.0848***		0.0179	−4.7240	−0.0783***		0.0185	−4.2430	−0.0820***		0.0186	−4.4120
		Road density	0.0295***		0.0072	4.0880	0.0287***		0.0074	3.8800	0.0295***		0.0075	3.9530
		New building-permit area ratio	0.0041*		0.0018	2.3430	0.0043*		0.0018	2.3370	0.0042*		0.0018	2.3190
		Development budget ratio	0.0231*		0.0101	2.2820	0.0238*		0.0104	2.2810	0.0241*		0.0105	2.3080
Regional level	Conditions	Paid worker ratio	-		-	-	0.1201*		0.0553	2.1730	0.0807		0.0847	0.9530
		Service worker ratio	-		-	-	0.1101		0.0572	1.9240	0.0114		0.1065	0.1070
		Fiscal capacity ratio	-		-	-	0.0018		0.0256	0.0720	0.0192		0.0286	0.6710
		Welfare budget ratio	-		-	-	−0.1840***		0.0333	−5.5240	−0.1690**		0.0515	−3.2830
		Elderly population ratio	-		-	-	−0.0776		0.1167	−0.6650	0.1970		0.1984	0.9930
		The average persons per household	-		-	-	−1.5830		3.6120	−0.4380	2.3710		5.2530	0.4510
		Population density	-		-	-	−1.6220***		0.1527	−10.6230	−1.2970***		0.2409	−5.3860
		Road density	-		-	-	2.3660***		0.1777	13.3190	2.1910***		0.2153	10.1730
		New building-permit area ratio	-		-	-	0.0152		0.0083	1.8320	0.0200		0.0108	1.8570
		Development budget ratio	-		-	-	0.2831***		0.0507	5.5840	0.2879***		0.0581	4.9530
	Inequalities	Paid worker ratio	-		-	-	-		-	-	−14.0400		9.4660	−1.4840
		Service worker ratio	-		-	-	-		-	-	8.2240		7.0300	1.1700
		Fiscal capacity ratio	-		-	-	-		-	-	−10.1500		7.9930	−1.2700
		Welfare budget ratio	-		-	-	-		-	-	9.7850		11.3100	0.8650
		Elderly population ratio	-		-	-	-		-	-	−7.2080		10.1800	−0.7080
		The average persons per household	-		-	-	-		-	-	7.1710		5.6520	1.2690
		Population density	-		-	-	-		-	-	−0.8921		0.7917	−1.1270
		Road density	-		-	-	-		-	-	−0.8024		0.5418	−1.4810
		New building-permit area ratio	-		-	-	-		-	-	−0.3932		0.4631	−0.8490
		Development budget ratio	-		-	-	-		-	-	−10.1600*		4.5210	−2.2460
			−2LL = 7,902.1 AIC = 8,005.9 BIC = 8,082.9				−2LL = 7,685.3 AIC = 7,856.4 BIC = 7,988.5				−2LL = 7,654.8 AIC = 7,814.5 BIC = 8,001.7

* p < 0.05, ** p < 0.01, *** p < 0.001.

We first examined the model with only local level variables, to validate the influence of the conditions. The results showed that most of the conditions at the local level in the study’s economic, social, physical, and policy variables had significant correlates with population change. The paid worker ratio, which refers to employees in secondary and tertiary industries in the area, positively correlated with the local population. This is consistent with the theory of Martinez‐fernandez et al. (2012). Martinez‐fernandez et al. (2012) suggested two possibilities. First, a high paid worker ratio promotes population inflow. Second, the paid worker ratio might be caused by higher investors’ interest in the area due to its richer demographic resources. However, because this study targeted correlation rather than causation, there are limitations in revealing a causal relationship. On the other hand, the service worker ratio, representing the ratio of the employees in the tertiary industry, correlates with population decline. It may be a simple correlation between service workers (more mobile in relation to economic capabilities and urban service demand) and areas where the population declines (infrastructure is in development).

The economic conditions, especially the fiscal capacity ratio, which reflects the local income level, are positively correlated with population change. As Joo and Seo (2018) and Wang, Yang, and Qian (2020) point out, the higher the level of financial independence in the region, the more favorable it is for population growth. The welfare-budget ratio and the elderly population ratio negatively correlate with population change. Since the welfare and development budgets are local finance components in the model, if the welfare budget is larger than the development budget, it will be adversely associated with population change. (The opposite is also true. If the development budget is larger than the welfare budget, the result is an increase in the population.) Another possibility is that the size of the welfare budget depends on the proportion of minority groups in the area – that is, the population, social, and economic level of the area. Since it can be seen as a proxy variable for the degree of backwardness of a region, indicating how poor it is, population decline is noticeable in backward areas that require a relatively large welfare budget. As a result of work by Wiechmann and Pallagst (2012), the elderly population ratio closely correlates with population decline. The elderly population ratio is also related to natural changes in the local population, such as fertility or mortality rates. Furthermore, we confirmed that road density, referring to the aggregation of infrastructure, positively correlated with the local population, and both the new building-permit area ratio and the development-budget ratio, representing the development-oriented policy, positively associated with local population increase.

Regional conditions, as well as local conditions, are also related to the decline of the local population after adding regional level variables to Model I to validate the influence of regional conditions. The result means that the assumption that the relationship between A and B holds at multiple levels in multilevel theory (Lacey and Fiss 2009) is satisfied even using identical variable for each level (Chen, Bliese, and Mathieu 2005). As points to note, the service workers ratio, fiscal capacity ratio, and the elderly population ratio significantly affected the local level, insignificant at the regional level. In other words, the level of industrial advancement in the adjacent area, which the service worker ratio represents, can be present as meaningful only in the local level unit, a relatively narrow-space unit. Also, the elderly population ratio, which indirectly represents population reproductivity, is significant only at the local level where population reproduction is occurring.

We constructed and analyzed a model after adding regional inequality variables to Model II, including local and regional level variables. As a result, we first confirmed that the local level conditions had the same effect as the model (Model I). Only the local level conditions were input; in Model II, the local- and regional level conditions were input. Second, as Fol (2012) and Xie et al. (2018) conclude, we found that the higher the inequality, the more negatively it affects the population. Among the tested inequality variables, the more unequal the development-budget ratio is, the more negatively it affects the population. This might imply that in regional development, the total balance at both the regional and local levels calls for appropriate consideration.

5.2. Interactions between levels

It is natural to examine the interaction between significant predictors (Haybatollahi et al. 2015). It is also necessary to explore the interaction between variables at different levels, to better understand the multilevel interrelation of urban shrinkage (Bernt 2016). Other-level conditions can cause a synergistic effect (when the coefficients are the same) or an offset effect (when the coefficients are opposite). Therefore, we examined whether the interaction term between the local and regional variables has an effect.

We examined the interaction of local and regional level variables of all independent variables used in the study. Among them, an interaction term between population density and development budget ratio, which has a significant relationship with the standardized population change rate, was additionally constructed as a model. Model VI-1 added a population density interaction term between levels, and Model VI-2 added development-budget interaction between levels. Model VI-3 adds all the interaction terms of each variable input to Model VI-1 and Model VI-2 (see Table 3).

Table 3. Result of interactions between levels.

			Model Ⅵ-1				Model Ⅵ-2				Model Ⅵ-3
			Population density interaction				Development budget ratio interaction				Population density interaction and development budget ratio interaction
level		Variables	Coeff.		Std. error	t value	Coeff.		Std. error	t value	Coeff.		Std. error	t value
Local level	Conditions	Paid worker ratio	0.0250***		0.0073	3.4050	0.0227**		0.0071	3.2120	0.0221**		0.0072	3.0830
		Service worker ratio	−0.0483***		0.0079	−6.1060	−0.0498***		0.0075	−6.5980	−0.0454***		0.0077	−5.9090
		Fiscal capacity ratio	0.0647***		0.0075	8.6210	0.0600***		0.0073	8.2220	0.0649***		0.0074	8.7990
		Welfare budget ratio	−0.0524***		0.0096	−5.4820	−0.0556***		0.0094	−5.8870	−0.0497***		0.0096	−5.1780
		Elderly population ratio	−0.0364**		0.0140	−2.6070	−0.0427**		0.0137	−3.1220	−0.0359**		0.0137	−2.6170
		The average persons per household	0.2389		0.1660	1.4400	0.2680		0.1625	1.6490	0.2506		0.1622	1.5450
		Population density	−0.1401***		0.0314	−4.4590	−0.0728***		0.0180	−4.0500	−0.1200***		0.0244	−4.9250
		Road density	0.0310***		0.0075	4.1480	0.0271***		0.0071	3.8410	0.0312***		0.0072	4.3340
		New building-permit area ratio	0.0048**		0.0018	2.7150	0.0043*		0.0018	2.4600	0.0047**		0.0017	2.7150
		Development budget ratio	0.0194		0.0103	1.8940	0.0359*		0.0170	2.1170	0.0323*		0.0153	2.1060
Regional level	Conditions	Paid worker ratio	0.0823		0.0616	1.3380	0.1554*		0.0645	2.4090	0.1451*		0.0643	2.2560
		Service worker ratio	0.1970**		0.0597	3.3010	0.0388		0.0648	0.5990	0.0801		0.0645	1.2420
		Fiscal capacity ratio	0.0384		0.0254	1.5100	−0.0081		0.0276	−0.2950	0.0192		0.0267	0.7180
		Welfare budget ratio	−0.1938***		0.0352	−5.5120	−0.1670***		0.0380	−4.3880	−0.1587***		0.0373	−4.2560
		Elderly population ratio	0.0383		0.1293	0.2960	−0.1070		0.1292	−0.8280	−0.0254		0.1294	−0.1960
		The average persons per household	−0.2552		4.0060	−0.0640	−1.7260		4.1230	−0.4190	−2.0200		4.1270	−0.4900
		Population density	−1.7720***		0.1545	−11.4680	−1.4530***		0.1687	−8.6110	−1.5740***		0.1646	−9.5650
		Road density	2.3790***		0.1861	12.7860	2.2240***		0.2058	10.8050	2.2570***		0.2014	11.2060
		New building-permit area ratio	0.0217**		0.0064	3.3950	0.0205**		0.0073	2.8090	0.0212**		0.0065	3.2590
		Development budget ratio	0.2153***		0.0487	4.4230	0.3620***		0.0673	5.3760	0.3248***		0.0643	5.0520
Interaction term		Local population density * regional population density	0.0115*		0.0044	2.6320	-		-	-	0.0078*		0.0030	2.6120
		Local development budget ratio * regional development budget ratio	-		-	-	0.0124*		0.0051	2.4190	0.0101*		0.0049	2.0490
			−2LL = 7,657.3 AIC = 7,842.1 BIC = 7,990.7				−2LL = 7,656.6 AIC = 7,839.9 BIC = 7,988.5				−2LL = 7,636.9 AIC = 7,834.3 BIC = 8,008.9

* p < 0.05, ** p < 0.01, *** p < 0.001.

Model Ⅵ-2, with the development-budget interaction, was a better fit for Model Ⅵ-1 with the population-density interaction. Model Ⅵ-3 had a lower AIC than Model Ⅵ-2 but a higher BIC, considered attributable to the BIC indicator’s preference for the parsimonious model. In terms of deviance (−2LL), Model Ⅵ-3 was the fittest model.

As a result of the analysis, we confirmed that the interaction effect occurred in the population-density variable (Model VI-1) and the development-budget ratio (Model VI-2). The results were the same in Model Ⅵ-3, which included the interaction of both level conditions. On the other hand, there was no interaction effect in the paid worker ratio, welfare-budget ratio, and road density, which were significant at local and regional levels. The population density had a negative effect on population maintenance at the local and regional levels. Still, the interaction term showed an offset effect that was positive. In other words, if population density is high at the local level, the outflow is severe; however, if population density is similarly high at the regional level, the outflow is relatively minor. We discovered that the development-budget ratio had a beneficial effect on population growth at the local and regional levels. We also established a synergistic effect in their interaction terms that positively correlated with the population. Accordingly, investing more in development budgets at the local and regional levels amplifies the effect at the same time.

6. Discussion and conclusions

This study uses HLM to access the determinants of population decline, summarized through prior studies, to see what variables relate to population decline and the extent to which they have an effect. It differs from previous studies in that it looks simultaneously at various conditions at the local and regional levels, and reveals that they also interact. Theoretically, both local factors and regional factors can affect urban shrinkage (Haase et al. 2014; Hartt and Hackworth 2018), but while controlling for random effects that may occur between administrative levels, there have been few studies that empirically verified these multilevel effects at the same time (Bernt 2016; Döringer et al. 2020). Identifying the conditions that cause population decline at the district and province levels, which are administrative units, this study can support evidence-based urban shrinkage policy (Döringer et al. 2020). For example, the fact that several regional conditions are related to locals can be a reference for the implementation of city regions (Scott 2019) or right-sizing (Coppola 2019), whose effects have not yet been verified. Because both city regions and right-sizing are based on the discussion of the interaction between local and regional and their spatial extent.

The multilevel effect of conditions may also comprehend the spatial context problem (Hoekveld 2014), in which urban shrinkage patterns differ, even among locations with similar characteristics. In other words, even though the conditions at the local level are similar, the multilevel effect that happens between the local and regional levels might explain why urban shrinkage occurs in some local areas but not in others. In the case of variables representing the regional industrial structure and infrastructure level, we confirmed that both local and regional conditions affect population change, requiring a check of various conditions, such as local level industry and infrastructure and improvement. Furthermore, the service worker ratio works differently from the paid worker ratio, requiring investigating the impact of population decline based on more detailed demographic factors. In fact, Galster (2017) suggests the possibility of selective outflow in shrinking cities and points out that this phenomenon will further exacerbate urban shrinkage.

We confirmed that local and regional development policies could be related to population decline. Although the effect of curbing population decline due to regional development has been widely supported theoretically (Eraydin and Özatağan 2021), empirical proofs are rare, with the exceptions of Busso, Gregory, and Kline (2013) and Hu, Wang, and Deng (2021). Furthermore, synergy will occur if the active implementation of local and regional development policies occurs simultaneously, further alleviating population decline. The effect of alleviating population declines at local and regional levels and their interactions suggest that multilevel governance, whose effectiveness has not been verified (Tang, Luo, and Ying 2022), can be effective in development policies. Therefore, preparing an integrated development policy through collaboration between governments at various levels appears necessary. Furthermore, we note that the greater the inequality in development policies (development policy balance) between adjacent cities and counties, the smaller the local population. It means that unbalanced development policies at the regional level can have the effect of promoting the decline of the local population. However, these effects may vary depending on the quality of the local conditions, such as local expenditure per capita, or regional population size and demographic characteristics (Baba and Asami 2022), requiring further research on the mitigation of population decline policies, taking regional characteristics into account.

Due to data limitations, this study only employed local and regional conditions as variables. Nonetheless, these and the conditions at the neighborhood level, where inhabitants’ very life take place, will likely relate to local population decline (Hoekstra et al. 2020). Also, since the pooled HLM used to secure a sufficient sample in this study has a limitation in not accurately controlling the effect of time-varying, time-series data should be considered if data can be secured. Since conditions at the local and regional levels can affect population change with a time lag (Firmino Costa da Silva, Elhorst, and Silveira Neto 2016), it is necessary to examine their influence using a panel model. Due to these methodological limitations, this study analyzed the correlation between multilevel conditions and population decline, so some causal relationships need further investigation. Identifying the causal relationship between various conditions assumed in this study and population decline is paramount in establishing and implementing policies for urban shrinkage (Bernt 2016). Furthermore, the expenditure scale corresponding to the ‘local and regional development budget’ was used as a proxy for local development policy among local budgets. Still, this development budget can serve various purposes, including new city development, housing supply, urban reorganization, and regional regeneration (Carbonaro et al. 2018; Eraydin and Özatağan 2021). Evaluating the effects of development policies more accurately requires a more in-depth study, to discover whether policies have the effect of reducing actual population loss, by assessing the consequences of each expenditure for each purpose.

Acknowledgments

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2021S1A3A2A01087370)

Disclosure statement

No potential conflict of interest was reported by the authors.