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Article

Factors Influencing the Health of Cities: Panel Data from 22 Cities in Taiwan

College of General Education, Chihlee University of Technology, Taiwan No. 313, Sec. 1, Wenhua Rd., Banqiao Dist., New Taipei City 220305, Taiwan
Sustainability 2024, 16(16), 7056; https://doi.org/10.3390/su16167056
Submission received: 23 July 2024 / Revised: 14 August 2024 / Accepted: 15 August 2024 / Published: 16 August 2024
(This article belongs to the Section Sustainable Urban and Rural Development)

Abstract

:
There is an increasing emphasis on creating healthier living spaces and improving quality of life, making the planning and establishment of healthy cities a pivotal policy and a developmental goal worldwide. This study adopted WHO-recommended indicators for healthy cities and employed stochastic frontier analysis to estimate the correlation between influencing factors and efficiency in developing healthy cities across 22 counties and cities in Taiwan from 2001 to 2022. This study yielded several key findings: (1) there was significant room for improvement in the development of healthy cities in Taiwan; (2) western metropolitan areas demonstrated higher efficiency compared to eastern counties, cities, and outlying islands; and (3) key indicators of a healthy city included nursing manpower, air quality, employment rates, income levels, and the availability of kindergartens. Developing healthy cities requires integrating various factors including policy, environmental conditions, societal aspects, and economic considerations. Collaboration between the public and private sectors is essential for fostering sustainable, healthy cities.

1. Introduction

In recent years, healthy cities have emerged as a crucial direction and goal for fostering sustainable urban and societal development. The global population, which stood at approximately 2.5 billion in 1950, surged to 8 billion by November 2022, with projections indicating it will reach 9.7 billion by 2050 [1]. The proportion of the world’s population residing in urban areas has risen from 33% in 1960 to 54% in 2016, with expectations that urban dwellers will comprise around 70% of the global population by 2050 [2,3,4]. The urbanisation of rural areas, often accompanied by the rapid migration of rural populations to cities, has emerged as one of the significant trends affecting global societal change and development [4,5]. Consequently, there has been increasing attention on planning and establishing healthy cities, with primary concerns including air pollution exacerbated by industrialisation, followed by the growing demand for healthier living spaces and quality [4,6]. In addition, there is growing attention on urban spatial planning and development, with efforts to leverage innovative technologies that will enhance a safe and healthy environment, improve quality of life, and progress towards more sustainable and smarter cities [7].
In 1986, the World Health Organisation (WHO) introduced the Ottawa Charter for Health Promotion. European nations were early adopters, forming the ‘WHO European Healthy Cities Network’ to implement this concept. Over time, it became evident that many health challenges stem from environmental factors, such as poverty, poor living conditions, nutritional imbalance, limited educational opportunities, and environmental disasters [4,8,9]. In 1996, the WHO established 10 standards for healthy cities and initially set 53 indicators. Subsequently, unsuitable and unreliable indicators were removed, resulting in a refined set of 32 evaluation indicators across four categories: health (9 indicators), health services (8 indicators), environment (8 indicators), and economic conditions (7 indicators). Numerous studies have proposed frameworks for sustainable urban development, ecological cities, and low-carbon cities based on the WHO’s healthy city indicators, aiming to establish indicators for measuring urban sustainability and ecological livability [3,4,10,11,12,13]. However, these efforts have predominantly focused on sustainable development capabilities and ecological environments, often overlooking the aspect of developing healthy cities [4]. Nonetheless, as interest in healthy cities grows, scholars have begun to study healthy cities with a focus on conceptual definitions, developmental practices, and impacts [14].
With the rise of challenges such as exacerbated environmental pollution and climate change, the planning and development of healthy cities has become a national policy priority globally. Many countries and regions have embarked on explorations and implementations of healthy city initiatives [14]. In Europe, several studies have employed implementation policies and measures outlined in the WHO’s Phase V of the European Healthy Cities Network to assess both the supply and demand aspects of healthy city planning. These studies address governance policies and equity issues in urban development and spatial planning [14,15,16]. The alliance for healthy cities and communities has been established in the United States and other nations [14,17]. Countries like South Korea have initiated plans for establishing healthy cities and communities [14,18]. China’s efforts to improve public health began in the 1950s, initially focusing on improving sanitation and controlling infectious diseases. In the 1990s, China collaborated with the WHO to pioneer healthy city pilot projects. In 2018, China developed an evaluation system based on the WHO’s healthy cities framework, assessing city health across six dimensions: healthy environment, healthy society, health services, healthy people, healthy economy, and healthy culture [4,19].
In Taiwan, the concept of healthy cities began to take shape around 2000, coinciding with the WHO’s promotion of healthy city initiatives, which garnered increasing attention from various Taiwanese government agencies toward the development of healthy cities. In 2003, the ‘Taiwan Healthy City Promotion Association’ was established to develop healthy city indicators covering aspects such as the environment, behaviour, social support, and health policies, aimed at enhancing the health and quality of life for urban residents. By 2008, the ‘Taiwan Healthy Cities Alliance’ was formed, focusing on creating elderly-friendly environments, fostering social engagement, improving outdoor spaces and infrastructure, and enhancing community support and health services. In 2018, 25 counties, cities, and administrative units in Taiwan joined the Alliance for Healthy Cities, an international organisation dedicated to safeguarding and promoting urban residents’ health. Through this alliance, members collaborate on knowledge exchange, experience sharing, research and development, and capacity-building projects, fostering innovation in healthy city approaches [20,21].
Through a review of relevant literature, it is evident that numerous studies have focused on evaluating the performance and effectiveness of healthy city planning, healthcare systems, and medical capacities. However, there is a notable scarcity of research measuring the influencing factors and efficiency of the indicators for healthy city development. This gap may stem from differences in research perspectives and directions, as well as challenges associated with data acquisition. The innovations of this study include: (1) employing stochastic frontier analysis (SFA) to construct the Cobb–Douglas function; (2) quantifying healthy city indicators for empirical analysis; (3) exploring and analysing factors influencing healthy city development; (4) measuring the efficiency of each county and city in developing healthy cities; and (5) proposing recommendations and strategies based on research findings, offering insights and guidance for relevant stakeholders to enhance the formulation and implementation of policies and strategies that promote healthy city development. The goal of this research is to inform policy adjustments and resource allocation by analysing the influencing factors and efficiency of healthy city development. By optimising healthy city development indicators, the study aims to contribute to the broader development of healthy cities globally. The comprehensive objectives include establishing a continuous monitoring and evaluation mechanism, setting specific development goals for future healthy city initiatives, improving the quality of life for urban residents, promoting sustainable economic and environmental development, strengthening social equity, advancing healthy city infrastructure, and fostering international exchanges and collaboration.
This article is divided into five main sections. Section 1 provides an introduction, covering an overview of healthy city development and indicators, the content and background of past research, and the innovative aspects and goals of this study. Section 2 details the research methods, variables, and empirical model. Section 3 presents the research results, while Section 4 offers an analysis, discussion, and the study’s limitations. Section 5 contains the study’s conclusions and recommendations.

2. Methodology

2.1. SFA Method

Efficiency evaluation measures the operational performance of a decision-making unit (DMU) and identifies potential areas for improvement within the operational space of the DMU. A DMU can be a private manufacturer, a public institution, or even a country. Efficiency involves evaluating the optimal relationship between inputs and outputs with the goal of maximising output or minimising costs [22,23]. The concept of stochastic frontier, introduced by Aigner et al. [24] and Meeusen and van den Broeck [25], establishes a production efficiency frontier that connects the most efficient input–output combinations achievable by the DMU under evaluation. Not all DMUs evaluated are efficient; only those at the frontier are considered technically efficient. In this study, we employed the Cobb–Douglas stochastic frontier production function proposed by Battese and Coelli [26] for analysing continuous intertemporal data. The Cobb–Douglas stochastic frontier model takes the form [27]:
l n Y i t = β 0 + j β j l n X i t + v i t u i t ,   i = 1 , N ,   t = 1 , T
u i t = δ 0 + j δ j l n Z i t + + ε i t
where ln denotes logarithms; Yit represents the appropriate type of output of the i-th manufacturer at time t; Xit represents the i-th vendor input at time t; β represents the individual input coefficient of the production function; Zit is the exogenous variable; and vit represents the symmetric interference term of random variation of the production function. Here, vit ∼ iddN(0, σ2v) and uit are independent of each other. And uit is the inefficiency factor of manufacturer i at phase t. It represents the degree of production technology inefficiency and is the only nonnegative random variable. Finally, δ0 is the intercept term, and εit is a random error and a nonnegative truncated normal distribution [27].

2.2. Samples and Data Sources

This study referenced WHO-recommended healthy city indicators and gathered data from key statistical indicator websites maintained by Taiwan National Statistics [28]. These data were compiled by Taiwan’s Local Statistics Promotion Center under the Directorate-General of Budget, Accounting, and Statistics, Executive Yuan, aggregating statistical information from various county and city governments. They were uniformly published and made freely accessible for data retrieval across all sectors. In this study, panel data on healthy city indicators spanning 22 years (2001–2022) across 22 counties and cities in Taiwan were compiled for analysis from Taiwan National Statistics [28].

2.3. Variables and Empirical Model

This study investigated the influencing factors and efficiency of establishing healthy cities across various counties and cities in Taiwan from 2001 to 2022, for a total of 22 years. A review of the literature revealed that most existing research focused on planning healthy cities and their indicators, as well as on developing carbon reduction cities and achieving sustainable development goals. However, few studies have explored the relationship between influencing factors and the efficiency of healthy cities. This study aimed to address this gap by analysing the real-world impact of healthy city indicators through the evaluation of the influencing factors and the efficiency of healthy city development across 22 counties and cities in Taiwan. The findings are expected to contribute to a more comprehensive understanding and efficient planning of appropriate healthy city indicators, guiding the right direction and strategy for the development and implementation of healthy city planning initiatives.
This study selected input and output factors aligned with the concept of healthy cities from the key statistical indicators of counties and cities available on the website maintained by Taiwan National Statistics [28]. It referenced WHO’s recommendations of 32 quantifiable healthy city indicators categorised into four major groups. Using the Cobb–Douglas stochastic frontier model, the study assessed the inefficiency relationship between factors influencing the establishment of healthy cities and the number of deaths per 10,000 people across 22 counties and cities in Taiwan. The estimated inefficiency value for the number of deaths per 10,000 people ranges from 0 to 1: values closer to 1 indicate lower efficiency in implementing healthy city indicators for a given year, whereas values closer to 0 suggest higher overall efficiency in achieving the goals of healthy cities within the region for that year.
This study adjusted the variables for output and input items to adhere to the consistency requirements of SFA, which differ slightly from the quantitative units recommended by WHO for healthy city indicators. The study adopted the mortality rate from WHO’s health indicators as the output item, but employed ‘deaths per 10,000 people (Y)’ as the undesirable output to maintain consistency within the study’s equations. The three input variables included: (1) number of nursing personnel per 10,000 people (X1); (2) percentage of days with good air quality per year (X2); and (3) leisure and green space area per 10,000 people (X3). By substituting these undesirable output and input items into Equation (1), Equation (3) was derived.
Additionally, this study integrated socio-economic indicators based on WHO’s healthy city indicators and introduced three exogenous variables: employment rate (Z1), percentage of population not classified as low-income (Z2), and number of kindergartens available per 1000 children (Z3). Table 1 presents the descriptive statistics of these variables.
Substituting the exogenous variables into Equation (2) resulted in Equation (4). The Frontier Version 4.1 software, provided free of charge by Coelli [29], was used to estimate Equations (3) and (4).
ln Y i t = β 0 + β 1 ln ( X 1 i t ) + β 2 l n X 2 i t + β 3 ln X 3 i t + v i t u i t
u i t = δ 0 + δ 1 l n Z 1 j t + δ 2 l n Z 2 j t + δ 3 l n Z 3 j t + + ε i t

3. Results

Table 2 reveals that the annual average inefficiency value of factors influencing the establishment of healthy cities across Taiwan’s counties and cities from 2001 to 2022 was 0.829. The top five most efficient regions (with their inefficiency values) were Taoyuan City (0.702), Taichung City (0.705), Hsinchu City (0.720), Chiayi City (0.729), and New Taipei City (0.761). Conversely, the least efficient were Taitung County (0.975), Lienchiang County (0.949), Hualien County (0.944), Penghu County (0.927), and Pingtung County (0.926). These findings underscore Taiwan’s substantial room for improvement—82.9%—in promoting the planning and development of healthy cities. The study also revealed that metropolitan areas performed better, albeit with room for improvement of up to 70%. Furthermore, Table 2 and Figure 1 indicate that efficiency in western metropolitan cities surpassed that in eastern counties, cities, and outlying islands, which face challenges such as poor transportation infrastructure, delayed development, and economic limitations, with an average efficiency gap of approximately 22%. This underscores the need for both policy adjustments and efforts to address equity in resource allocation across Taiwan’s urban and rural areas during the planning and development of healthy cities.
The SFA analysis conducted in this study utilised maximum likelihood estimation for estimation. The results in Table 3, covering the period from 2001 to 2022, reveal several significant correlations. The number of nursing personnel per 10,000 people (estimate = 0.2416) showed a strong positive correlation with the efficiency of deaths per 10,000 people, suggesting that adequate nursing personnel can effectively lower mortality rates and contribute to the sustainable development of healthy cities. Conversely, good air quality (estimate = −0.4233) demonstrated a highly significant negative correlation with efficiency of deaths per 10,000 people. While air quality is a crucial factor for healthy cities, counties and cities in Taiwan experience poor air quality affecting health on less than 4.5% of days annually, indicating approximately 350 days of good air quality. The area of leisure and green space (estimate = 0.0014) did not show statistical significance as a contributing factor to healthy cities, possibly due to Taiwan’s low ratio of leisure and green space at 4.4 square meters per person. In contrast, developed countries typically offer 20–50 square meters of leisure and green space per capita. For instance, the average amount of green space per person in the UK is about 30 square meters, excluding leisure spaces [30].
Furthermore, the employment rate as an exogenous variable (estimate = −6.7434) showed a highly significant negative correlation with the inefficiencies of deaths per 10,000 people, indicating that a stable employment rate is a fundamental socio-economic indicator in healthy cities. Conversely, the percentage of the population not classified as low-income (Estimate = 8.2409) exhibited a highly significant positive correlation with the inefficiencies of deaths per 10,000 people, emphasising that a higher income and economic capacity contribute to life essentials and are crucial socio-economic indicators for healthy cities. The number of kindergartens available per 1000 children (estimate = −0.0250) also displayed a highly significant negative correlation with the inefficiencies of deaths per 10,000 people. Although the average number of young children per county or city was about 16,500 per year, the impact of this estimate on the efficiency of healthy cities was modest. Nevertheless, the result was highly statistically significant, emphasising the crucial role that adequate kindergarten provision plays in fostering healthy cities. Moreover, adequate and quality preschool education is linked to children’s long-term physical and mental well-being as well as behaviour, positively impacting families and society. Quality preschool care can reduce child mortality, offering lasting benefits for children, families, and society.

4. Discussion

The results of this study showed that factors affecting a healthy city include the number of nursing personnel, air quality, employment rate, income, and number of kindergartens. Taiwan’s average crude death rate per 1000 people during the 22 years (2001–2022) was 6.71‰, which was lower than the global average and ranked in the upper half of countries and regions. According to World Bank Group [31] statistics, during the same period, the crude death rates per 1000 people in various countries were 6.59‰ in Australia, 7.38‰ in Canada, 10.84‰ in Germany, 6.94‰ in China, 9.36‰ in the United Kingdom, 9.77‰ in Japan, 8.55‰ in the United States, and 4.74‰ in Singapore, and the global average was about 8.15‰.
In developed countries with well-established national health insurance, the quantity and caliber of nursing personnel (including nurses and nurse assistants) are typically higher, an important indicator of the strength of their healthcare systems. An adequate number of skilled nursing staff, coupled with a higher percentage of nursing care hours, can significantly reduce patient falls, medication errors, wound infections, and urinary tract infections, while also ensuring improved overall inpatient care and attention [32,33]. Clearly, ensuring sufficient and professional nursing personnel is a crucial factor in fostering a healthy city. According to World Bank Group [34] statistics, the number of nursing personnel per 1000 people in various countries during the same period was 12.15‰ in Australia, 10‰ in Canada, 10.39‰ in Germany, 1.80‰ in China, 8.88‰ in the United Kingdom, 10.5‰ in Japan, 5.26‰ in Singapore, and 12.98‰ in the United States. Over the 22-year span, Taiwan averaged 5.58‰ nursing personnel per 1000 people, significantly lower than many developed nations with robust health insurance systems. The shortage of nursing personnel is a global challenge exacerbated in recent years by factors such as the COVID-19 pandemic, aging populations, rising demands for chronic and multiple-disease care, high job stress, inadequate compensation, burnout, and poor working conditions [35,36]. Health authorities must prioritise increasing nursing staff to alleviate workloads and enhance salaries and benefits. Additionally, optimising medical work environments, increasing the provision of essential medical equipment and resources, and establishing psychological consultation and support mechanisms are crucial for helping nursing personnel cope with work stress and emotional challenges, thereby promoting a better work–life balance for nursing staff [36]. Comprehensive healthcare and adequate nursing personnel are among the paramount indicators for the development of healthy cities.
Since the industrial revolution, the extensive use of fossil fuels has steadily increased greenhouse gas concentrations, exacerbating air quality deterioration. Air pollution primarily stems from fossil fuel combustion, industrial operations, and natural particulates [37,38,39]. Research has indicated that reduced oxygen levels in densely populated cities can compromise immunity, heighten the susceptibility to allergens, and lead to conditions such as anxiety, neurasthenia, hypertension, heart diseases, and asthma [4,40]. Air pollution stands as the foremost environmental risk factor threatening healthy cities, with approximately one in eight deaths attributed to it, primarily from non-communicable diseases [4,6]. The estimates obtained in this study indicate that air quality has the highest coefficient, aligning with previous research and underscoring its critical role as a pivotal factor influencing healthy cities.
In this study, the employment rate and income (percentage of the population not classified as low-income) are recognised as interrelated factors influencing healthy cities. Establishing employment opportunities that meet residents’ needs is crucial for equity and serves as a social determinant of health and well-being. Employment and livability are among the key indicators of a healthy urban environment [41]. Employment and economic policies (impacting income and social status) and housing policies (influencing affordability, overcrowding, poor living conditions, and energy scarcity), along with a significant low-income population, can contribute to inadequate health conditions and environmental quality issues. These aspects are essential elements in the planning and policymaking for healthy cities [42,43].
The average annual number of infants in Taiwan is approximately 16,500 (2001–2022), a relatively small figure that corresponds to the modest estimated values derived from the equations in this study. However, the number of available kindergartens reflects different countries’ investments in early childhood education and care. Governments worldwide prioritise early childhood education by allocating resources to meet families’ needs with ample kindergartens. Ensuring safe and high-quality kindergartens allows parents to pursue employment with peace of mind, delivering long-term benefits for children, families, and society. Therefore, kindergartens designed for healthy cities should integrate aspects like aesthetic and barrier-free green spaces, as well as social and physical connections, to foster a diverse and secure preschool learning environment [44].
The per capita area of leisure and green space in various counties and cities in Taiwan is only about 4.4 square meters. This low proportion per capita may explain why the estimated results of this study were not significant in this aspect. Research has indicated that urban recreational spaces and green areas are often referred to as the lungs of cities. Higher proportions of green spaces in a region are associated with improved public health outcomes, such as reduced stress; mitigation of air pollution, noise, and heat exposure; the prevention of adverse mental health and cardiovascular diseases; and lower mortality rates [45,46,47,48].
The efficiency of Taiwan’s healthy cities notably lags behind in eastern counties, cities, and outlying islands compared to their western metropolitan counterparts. This disparity reflects the longstanding uneven development across Taiwan in terms of the economy, infrastructure, employment opportunities, and public services, with a concentrated focus on western cities. Addressing this imbalance in healthy city policies and planning requires careful attention to urban–rural disparities and resource allocation. Tailored strategies, additional subsidies, and support for different counties and cities are essential for bridging these gaps. Moreover, establishing a healthy city is a multifaceted, ongoing endeavor that requires cross-departmental collaboration and the integration of policies, environmental considerations, societal aspects, and economic factors through systematic planning and implementation. This effort also necessitates a high degree of cooperation among political entities, policymakers, public–private partnerships, and community groups. The goal is to continually enhance residents’ health, economy, and quality of life, aiming to provide sustainable and quality environmental, social, and economic benefits [49,50,51].

Limitations

This study had several limitations. Firstly, obtaining and quantifying data for studying healthy city indicators proved challenging. The study focused on 32 indicators recommended by the WHO for healthy cities but examined only 7 indicators (1 output, 3 inputs, and 3 exogenous variables). Future research could explore further by adding or removing variables considered in the analysis. Secondly, healthy city indicators extend beyond the WHO’s recommended 32 indicators. Other influential factors, such as political factors, gross domestic product, population dynamics, local climate conditions (e.g., temperature, heat waves, and humidity variations), and climate change, warrant exploration. Thirdly, using SFA required assuming the functional form before estimation and restricted analysis to a single output item. Finally, the current research methods may have introduced statistical biases. Future studies could employ more robust research methodologies to replicate and validate these findings.

5. Conclusions

This study referenced the WHO’s recommended indicators for healthy cities to identify specific and quantifiable metrics. A Cobb–Douglas stochastic frontier model was constructed to assess the relationship between influencing factors and the efficiency of planning and developing healthy cities across 22 counties and cities in Taiwan from 2001 to 2022. The findings indicated substantial room for improvement in Taiwan’s efforts to promote the planning and development of healthy cities. Moreover, disparities in urban and rural resource allocation have led to western metropolitan cities achieving an average efficiency that is 22% higher than that of eastern counties and cities and outlying islands. Estimated values of input items and exogenous variables revealed key factors influencing healthy city development, including the number of nursing personnel, air quality, employment rate, income level (percentage of the population not classified as low-income), and number of kindergartens.
The planning and development of healthy cities is a multifaceted and ongoing endeavor that requires the integration of political strategies and policies through systematic planning and implementation. Furthermore, it relies on collaboration among the public and private sectors, regional entities, and community groups to promote and establish sustainable, healthy cities. The findings of this study are anticipated to serve as a valuable reference for planning and implementing units in various countries, aiding in the formulation of policies and strategies for the sustainable development of healthy cities.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable. Institutional Review Board approval was not required because no interventions nor procedures were performed.

Informed Consent Statement

Not applicable.

Data Availability Statement

This data can be found here: [28].

Acknowledgments

The free software “Frontier Version 4.1” can be used to estimate the equations, which was kindly provided by Professor Coelli [29].

Conflicts of Interest

The author declares no conflicts of interest.

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Figure 1. Distribution map of the annual average scale inefficiency in various counties and cities in Taiwan.
Figure 1. Distribution map of the annual average scale inefficiency in various counties and cities in Taiwan.
Sustainability 16 07056 g001
Table 1. Descriptive statistics of variables.
Table 1. Descriptive statistics of variables.
ItemsVariablesWHO Recommended Health Indicators of Healthy CitiesSamplesMeanStd.Min.Max.Median
Output itemY = Number of deaths per 10,000 people (person).Health indicators48474.0518.7334.48132.8371.77
Input itemX1 = Number of nursing personnel per 10,000 people (person).Health service indicators48455.8324.2416.58144.4052.19
X2 = Percentage of days with good air quality per year (%), that is, the percentage of days where Air Quality Index (AQI) > 100.Environmental indicators48497.822.5088.66100.0098.77
X3 = Area of leisure and green space per 10,000 people (hectares), that is, the area of parks, green spaces, children’s playgrounds, sports venues, and squares per 10,000 people (hectares).Environmental indicators4846.135.070.8223.893.84
Exogenous variableZ1 = Employment rate (%), that is, (1—unemployment rate).Socio-economic indicators48496.031.0494.0099.9096.00
Z2 = Percentage of population not classified as low-income (%), that is, (1—low-income percentage).Socio-economic indicators48498.630.9893.7199.7398.92
Z3 = Number of kindergartens available per 1,000 children.Socio-economic indicators48416.656.108.4449.5114.97
Table 2. Estimation of the annual average inefficiency of health cities indicators in various counties and cities in Taiwan.
Table 2. Estimation of the annual average inefficiency of health cities indicators in various counties and cities in Taiwan.
ItemCounties or Cities (DMUs)Mean InefficiencyRankItemCounties or Cities (DMUs)Mean InefficiencyRank
1New Taipei City0.761512Yunlin County0.83613
2Taipei City0.776813Chiayi County0.88716
3Taoyuan City0.702114Pingtung County0.92618
4Taichung City0.705215Taitung County0.97522
5Tainan City0.771716Hualien County0.94420
6Kaohsiung City0.763617Penghu County0.92719
7Yilan County0.8121018Keelung City0.82912
8Hsinchu County0.8171119Hsinchu City0.7203
9Miaoli County0.8581520Chiayi City0.7294
10Changhua County0.793921Kinmen County0.84714
11Nantou County0.9121722Lienchiang County0.94921
mean inefficiency =0.829
Table 3. Estimates of the stochastic frontier function.
Table 3. Estimates of the stochastic frontier function.
Variable DescriptionCoefficientEstimateStandard Errort-Ratio
Constantβ05.4496 *0.73017.4637 *
lnX1itβ10.2416 *0.03087.8505 *
lnX2itβ2−0.4233 *0.1570−2.6964 *
lnX3jtβ30.00140.01680.0823
Constantδ0−6.5020 *2.0820−3.1230 *
lnZ1jtδ1−6.7434 *1.6503−4.0863 *
lnZ2jtδ28.2409 *1.99464.1315 *
lnZ3jtδ3−0.0250 *0.0049−5.0567 *
σ s 2 = σ u 2 + σ v 2 σ s 2 0.04890.00558.9024
r = σ u 2 / σ s 2 r0.19470.15431.2615
log likelihood function = 62.927652
Note: 1. * represents significance at the 1% levels, respectively. 2. σ u 2 and σ v 2 represent the inefficiency error variance and random error variance, respectively; σ s 2 is the total variance; and r is the proportion of inefficiency error variance ( σ u 2 ) to total variance ( σ s 2 ).
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Wu, J.-S. Factors Influencing the Health of Cities: Panel Data from 22 Cities in Taiwan. Sustainability 2024, 16, 7056. https://doi.org/10.3390/su16167056

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Wu J-S. Factors Influencing the Health of Cities: Panel Data from 22 Cities in Taiwan. Sustainability. 2024; 16(16):7056. https://doi.org/10.3390/su16167056

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Wu, Jih-Shong. 2024. "Factors Influencing the Health of Cities: Panel Data from 22 Cities in Taiwan" Sustainability 16, no. 16: 7056. https://doi.org/10.3390/su16167056

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Wu, J.-S. (2024). Factors Influencing the Health of Cities: Panel Data from 22 Cities in Taiwan. Sustainability, 16(16), 7056. https://doi.org/10.3390/su16167056

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