1 Introduction

Public safety is a newly emerged topic in the trajectory of urban development (Yu and Fang 2017), and it is an important prerequisite for ensuring economic and social health as well as sustainable development of different regions. Scholars (Lin 2003; Lu et al. 2016; Proag and Proag 2014) suggest that cities with well-performed public safety are strongly resilient to natural disasters and social emergencies, and they maintain a dynamic equilibrium and coordinated development in ensuring environmental, social, and human safety. Therefore, public safety is one basic government function to prevent and control various accidents, disasters, and emergencies, and to maintain the safety of the lives and property of their people (Kożuch and Sienkiewicz-Małyjurek 2014; Liu et al. 2005).

The increasing number of incidents reveals that regions in China are exposed to risks that can threaten the stability and bring catastrophic consequences. According to the data from National Bureau of Statistics of China (National Bureau of Statistics 2019), public safety incidents have occurred more frequently and the number of deaths per million productions has remained high in recent years, which highlights the serious problems in regional public safety in China. Provincial governments strive to guarantee safety inputs, but they are unable to guarantee safety outputs because of the low public safety input awareness, insufficient and imbalanced allocation of safety inputs, and the inability of making reasonable and scientific safety-input decisions (Kong and Li 2006). These constraints cause randomly assigned safety inputs and inefficient utilization of the limited public safety resources. In addition, governments’ poor safety-input decisions lead to ineffectiveness of such input and consequent safety resources waste. Thus, a better understanding of efficiency of regional public safety is much needed.

Efficiency is a useful managerial control measure to assess how inputs and outputs act, aiming to obtain the desired results with the smallest possible amount of inputs or the ability to obtain the maximum possible amount of output from the available resources (Golany and Roll 1989). The use of available resources is generally measured by their efficient utilization. The inputs allocated for public safety are expected to result in safety improvements (Luo 2004). Thus, to enhance the efficient usage and management of safety inputs, the efficiency of these resources in improving public safety must be comprehensively evaluated (Zhang and Li 2004).

Public safety is the result of actions taken by all stakeholders of socioeconomic development (Kożuch and Sienkiewicz-Małyjurek 2014), which is associated with various input and output criteria. However, the criteria for safety input and output are subjectively determined by stakeholders (Cui and Li 2015; Fung et al. 2010; Kong and Li 2006); in previous studies, the weights of safety inputs and outputs are also subjectively evaluated (Aminbakhsh et al. 2013; Chang 2013; Feng et al. 2014; Gurcanli et al. 2015; Hu et al. 2009), which hinders the accurate or objective assessment of safety efficiency. Thus, to fill this research gaps, Data Envelopment Analysis (DEA) is used to comprehensively assess the efficient utilization of regional public safety. DEA measures the efficiency of decision-making units (DMUs) based on the input to DMU, which is often the resources used or consumed in the operation; whereas the output of DMU refers to the product or service offered by the system (Nahangi et al. 2019). DEA does not rely on the subjective assessments of an evaluator, and it reflects the efficient utilization of funds, other input resources, and safety management.

The previous literature primarily focuses on one specific area of public safety efficiency but largely ignores the public safety efficiency in wider regions and long-term observation. At the same time, public safety emergency usually influences the whole nation. For instance, due to the interpersonal transmission characteristics of the new coronavirus pneumonia (COVID-19), every region needs to participant and a systemic measurement is essential to stop the spread of COVID-19. Therefore, to fill the above-mentioned research gaps, this study uses the DEA to evaluate the public safety efficiency of 31 regions in China between 2014 and 2018 from the perspective of public safety inputs–outputs. The dynamic evolutions of the public safety efficiency of all regions are examined accordingly, with the aim to improve the public safety management in China. In other words, this study attempts to analyze the public safety efficiency by building a comprehensive model that includes the inputs and outputs index of public safety, and to measure and analyze the public safety efficiency of 31 province-level administrative divisions (regions) in China.

2 Literature review

2.1 The perspectives and contents of public safety assessment

Regional public safety is closely related to personal and property safety, but in the broad sense, it refers to the satisfaction of the safety and security needs of important systems, such as cities and its citizens, properties, and urban lifelines (Liao and Hou 2009). This concept is also described as the lawful social, economic, and cultural activities of cities and their production of the necessary goods for ensuring internal and external order (Frey 2015). Based on the general definition of safety, Lin (2003) suggests that public safety should represent the measures for the physical and mental health of residents. Regional public safety is influenced by complex and diverse factors and is constantly pursued by government and residents.

Regarding regional public safety assessments, previous research has focused on risk perspectives. From the perspective of risk, public safety assessment mainly focuses on single capability, simple vulnerability, and comprehensive vulnerability–capability. First, single capability assessment mainly evaluates the co** ability of public safety, which may include infrastructure, institutions, knowledge, skills, and integrated soft power, such as social relations, leadership, and management capabilities (Hu et al. 2009; Li et al. 2013). Second, simple vulnerability assessments, i.e., the vulnerability of regional public safety, can be assessed in two ways: (1) based on the types of accidents (e.g., natural and human accident indicators), and (2) by dividing its elements into indicators of exposure, sensitivity, and vulnerability (Schmidt-Thomé 2006; Luo et al. 2005; Zhao 2006). Vulnerability assessment indicators mainly include traffic accident casualties, traffic accident losses, fire-related casualties, direct economic losses, fire incidents, environmental pollution accidents, inundated area of flood disasters and droughts, and unemployment (Zhu and Lv 2010; Saunders et al. 2017). Identifying the efficiency of provincial public safety is a challenge that must be addressed while assessing and evaluating performance criteria. This study employs the existing public safety evaluation systems in selecting representative output indicators. Three indicators of vulnerability—unemployment rate, traffic accident casualties, and direct economic losses resulting from natural disasters—are taken as the unexpected safety output indicators of regional public safety efficiency (Zhao 2006; Zhu et al. 2011; Zhu and Lv 2011). Unemployment rate refers to China’s unique unemployment statistical indicators. The indicators include the ratio of the number of registered unemployed in cities and towns to the number of registered unemployed in urban units (after deducting the employed rural labor force, employed retired personnel, Hong Kong, Macao, Taiwan, and foreign personnel), non-working employees in urban units, urban private owners, individual heads of households, urban private enterprises, and the ratio of self-employed persons and urban registered unemployed persons. The number of casualties of traffic accidents refers to the number of casualties caused after a traffic accident occurs. The direct economic losses caused by natural disasters refer to the sum of the economic losses caused by natural disasters, including primary disasters and secondary disasters. Unemployment rate is closely related to the stability of the social environment; traffic accident casualties reflect the traffic safety; and direct economic losses resulting from natural disasters represent the extent of damage left by natural disasters.

When the input is certain, the expected output decreases while the level of regional public safety increases (Zhao 2006; Zhu et al. 2011; Zhu and Lv 2011). In addition, the sewage treatment capacity, GDP per capita, and number of beds in medical and health institutions are used as the expected outputs of public safety inputs. Sewage daily capacity refers to the design capacity of a sewage treatment plant to treat the amount of sewage each day and night. Regional GDP per capita, the total value of social final products, and labor services produced by a region in a certain period (usually one year) are calculated on the average of the population. The number of beds in medical and health institutions refers to the number of beds in medical and health institutions provided in a region. Specifically, the comprehensive utilization rate of industrial solid waste represents the regional ecological environment quality; GDP per capita reflects the regional risk resistance, and the number of beds in medical and health institutions demonstrates the regional capacity to respond to emergency situations. When the input is certain, the expected output, ecological environment quality, risk resistance, and regional emergency response capacity all increase.

3.2 Models

3.2.1 DEA-BC2 model

DEA-BC2 model is based on the variable returns to scale model (Azadeh et al. 2017), which measures the TE of DMUs and its TE can be further decomposed into PTE and SE. TE refers to the optimal configuration between input and output factors and shows the comprehensive ability of public safety resource utilization. TE reflects that the public safety resources have been fully utilized, the input factors have reached the optimal combination, and the maximum output effect has been achieved. The TE of a DMU is a comparative measure regarding how well it actually processes inputs to achieve its outputs, as compared to its maximum potential for doing so, as represented by its production possibility frontier (Barros and Mascarenhas 2005). Thus, TE of public safety is the ability to transform multiple safety input resources into multiple safety capability. A region is entitled as technically inefficient in public safety if it operates below the frontier. PTE reflects the allocation and utilization levels of public safety resources. It is a measure of TE without SE and purely reflects the managerial performance to organize the inputs in the production process. The PTE measure is obtained by estimating the efficient frontier under the assumption of variable returns to scale (Al-Muharrami 2008). Thus, PTE measure has been used as an index to capture safety managerial performance.

SE expresses whether a region is operating at its “optimal size” (Al-Muharrami 2008). The measure of SE allows the management to choose the optimum amount of public safety resources, i.e., to decide on the regional public safety input and to choose the scale of safety input that will attain the expected safety output level. Inappropriate amount of a public safety input (too large or too small) may sometimes be a cause of technical inefficiency (Muharrami 2008; Banker 1984). A region is scale efficient if public safety output increases by the same proportional change as all public safety inputs change (known as CRS) (Banker 1984). If it is scale inefficiency, further comparisons of decreasing returns to scale (DRS) and increasing returns to scale (IRS) should be applied (Banker 1984). Decreasing returns to scale (also known as diseconomies of scale) implies that public safety output increases by less than that proportional change in all public safety inputs (Banker 1984). In contrast, if public safety output increases by more than the proportional change in all public safety inputs, increasing returns-to-scale (also known as economies of scale) is achieved (Muharrami 2008, Banker 1984).

DEA has an input- and output-oriented model, where the former explores how to minimize the input when the output is certain, while the latter explores how to maximize the output when the input is certain. With regard to the regional public safety efficiency, the input factors of production are easier to control than the output factors. Therefore, this study adopts the BC2 model to analyze the efficiency of public safety inputs, to further understand PTE and SE and to improve the existing scales and technologies.

3.2.2 Malmquist index

The Malmquist index is mainly used to analyze the trend of changes in dynamic efficiency (Caves et al. 1984). This study uses the Malmquist index to analyze the inter-temporal regional public safety efficiency. According to Färe et al. (1992), the Malmquist index can be decomposed into the technical efficiency change index (TEC) and technical progress change (TPC). Under the premise of variable scale compensation, if the change in efficiency is calculated based on the geometric mean of the Malmquist index, then TEC can be decomposed into pure technical efficiency change (PTEC) and scale efficiency change (SEC).

TPC is considered a true measure of future improvements in public safety efficiency and reflects the degree of variation in safety production technology. PTEC reflects the usage efficiency of inputs and denotes whether a region can use safety technologies effectively to maximize the outputs, SEC reflects whether the proportion of inputs and outputs is appropriate, and Malmquist index reflects the degree of variation of the total factors productivity of regional public safety. TPC, PTEC, and SEC > 1,  =  1, and < 1 indicate an increase, no change, and a decrease in the regional public safety efficiency, respectively. If the Malmquist index is larger than 1 (M > 1), this index is identified as the main driver of technical improvement; otherwise, this index is identified as the main cause of technical loss. M > 1, M = 1, and M < 1 indicate an increase, no change, and a decrease in the level of total factor productivity compared with the previous period, respectively.

3.3 Data source and processing

The raw data of comprehensive utilization rate of industrial solid waste were from the China Statistical Yearbooks for the years 2014 to 2018, while the raw data for all other indicators were retrieved from the official website of the National Bureau of Statistics of China. The advanced search function of the website was used to obtain regional, sub-provincial, and provincial data. Other data taken from the website included the registered urban unemployment rate (%), number of deaths from traffic accidents (persons), direct economic losses resulting from natural disasters (100 million Yuan), percentage of general sewage treatment capacity used in production (%), GDP per capita (Yuan/person), and number of beds in medical and health institutions (millions). The inputs for local environmental protection inputs, local public safety, local social safety and employment, and local health were obtained by using data for local fiscal environmental protection expenditures (100 million Yuan), local fiscal health expenditures (100 million Yuan), local fiscal social safety and employment expenditures (100 million Yuan), and local fiscal public safety expenditures (100 million Yuan).

Some regions in China had missing values for direct economic loss resulting from natural disasters. Based on the fluctuation law of specific values, this study used the middle year to denote the mean value for the preceding and succeeding years. Meanwhile, given the possible annual variations in prices and to eliminate the price impact, this study used 2014 as the base year and processes the data for direct economic losses resulting from natural disasters, GDP per capita, and local fiscal expenditures for environmental protection, health, social safety and employment, and safety from 2014 to 2018 at constant prices through consumer price index (CPI) for comparison. An inverse relationship exists between the input variables and the three output indicators for unemployment rate, traffic accident casualties, and direct economic losses resulting from natural disasters. Therefore, to maintain a consistent input–output direction, this study used the inverse algorithm to deal with three undesired output indicators (Lewis and Sexton 2004).

4 Evaluation of the regional public safety efficiency

4.1 Measured values and spatial characteristics of regional public safety efficiency

The DEAP2.1 was used to calculate the TE, PTE, and SE of 31 regions in China from 2014 to 2018. The results for the three indicators of public safety efficiency are shown in Table 1. To clearly demonstrate the evolution of these efficiencies and the impact of PTE and SE across all phases, this study applied ArcMap to select all of the 31 regions in China for the years of 2014, 2016, and 2018. The results for the three indicators of spatial visualization are shown in Figs. 1, 2 and 3.

Table 1 TE, PTE, and SE of public safety of all 31 regions in China (2014–2018)
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Fig. 1
figure 1figure 1

Spatial characteristics of TE of public security in China

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Fig. 2
figure 2figure 2

Spatial characteristics of the PTE of public security in China

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Fig. 3
figure 3figure 3

Spatial characteristics of the SE of public security in China

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4.1.1 Measured values and spatial characteristics of TE

Table 1 indicates that the average public safety TE of all 31 regions in China increased every year from 2014 to 2018 but decreased in 2015. Specifically, the average public safety TE of these regions from 2014 to 2018 was 0.956, 0.945, 0.950, 0.948, and 0.957, respectively. The result indicates that despite a relatively high public safety TE, the efforts in guaranteeing public safety were rather ineffective. In 2014, all regions in China had an average public safety TE of 0.956, indicating that the TE of public safety in China was far from ideal and can still be improved by 4.4%. Similarly, the public safety TE from 2014 to 2018 needs further improvement.

From 2014 to 2018, there were 19 (2014), 20 (2015), 19 (2016), 17 (2017), and 20 (2018) regions in China that demonstrated an effective proportion of public safety efficiency (Table 1), indicating that the safety inputs of these regions reached their optimal levels in the corresponding year. In other words, under certain conditions, the safety inputs of these regions were minimal.

According to the technical efficiency measurement results of various regions from 2014 to 2018, although Bei**g’s unemployment rate, traffic accident casualties, and direct economic losses from natural disasters were relatively low, and the per capita regional GDP was relatively high, its public safety input was relatively large, and the number of beds in health facilities and the daily treatment capacity of daily sewage in the output were low, which led to a low level of public safety efficiency from 2014 to 2015. For Inner Mongolia, the public safety input was relatively low in 2016–2018, and its expected daily sewage treatment capacity and number of beds in health facilities were relatively low, and the registered unemployment rate and natural disasters in undesirable output were direct. Thus, the relatively high economic losses have led to the lowest technical efficiency.

The spatial characteristics of 2014, 2016, and 2018 TE of public safety in China are formulated in Fig. 1. The TEs of 19, 19, and 20 regions were effective in the years of 2014, 2016, and 2018, respectively. In addition, the TE of public safety efficiency in Tian**, Liaoning, Heilongjiang, Jiangsu, Anhui, Fujian, Shandong, Henan, Hunan, Guangxi, Hainan, Guizhou, Tibet, and Ningxia 14 regions has been reached their effective levels for five consecutive years since 2014. From the TE analysis of these 14 areas, the findings are as following:

  1. 1.

    From the perspective of safety input: Public safety input in 14 regions where the technical efficiency reaches the effective value was polarized. The regions with low input were Tibet, Ningxia, and Hainan, while the regions with higher input levels were Henan, Shandong, and Jiangsu.

  2. 2.

    According to the expected output data, in terms of daily sewage treatment capacity, Liaoning, Shandong, and Jiangsu had relatively strong sewage treatment capacity, while Tibet, Ningxia, and Hainan had relatively weak sewage treatment capacity. The GDP per capita was relatively high in Tian**, Fujian, and Jiangsu, and relatively low in Heilongjiang, Guangxi, Guizhou, and Tibet. For the number of beds in medical and health institutions, Shandong and Henan were relatively high, while Tian**, Hainan, Ningxia, and Tibet were relatively low.

  3. 3.

    From the unexpected output data, the registered unemployment rate in urban units was lower in Hainan, Guangxi, Tibet, and Anhui, while those in Hunan, Fujian, Ningxia, Liaoning, and Heilongjiang were relatively high. The number of casualties in traffic accidents was relatively low in Tibet, Ningxia, and Hainan, and Guizhou, Guangxi, and Henan were relatively high. For direct economic losses of natural disasters, Tian**, Hainan, Ningxia, Tibet, and Guangxi were lower, while Shandong was higher.

4.1.2 Measured values and spatial characteristics of PTE and SE

  1. (1)

    Spatial characteristics of PTE

PTE and TE demonstrated similar trend in 31 regions in China, which means a yearly decrease in their average PTE from 2014 to 2018 (Table 1). Specifically, the average PTE of these regions was 0.977(2014), 0.970 (2015), 0.968(2016), 0.965 (2017), and 0.973 (2018), respectively. The mean PTE of these regions was less than 1, suggesting that the PTE of these regions still needs to be improved along with their allocation and utilization of public safety resources. The PTEs of 21(2014), 22(2015), 23(2016), 21(2017), and 24(2018) regions reached their effective levels, and only 19 of these regions achieved effective PTE levels for five consecutive years.

Accordingly, several characteristics can be extracted as follows (Fig. 2). First, in 2014, 21 regions reached the effective levels of PTE, among which 19 regions reached the effective levels of TE in the same year. In 2016, 23 regions achieved the effective levels of PTE, among which 19 regions achieved the effective levels of TE in the same year. In 2018, 24 regions achieved the effective levels of PTE, among which 20 regions achieved the effective levels of TE. Other regions did not achieve an effective level of TE because of their SE. The above-mentioned regions also showed diminishing returns to scale in the corresponding years, suggesting that their public safety investment mix should be readjusted. Second, the PTE of public safety in Hebei, Chongqing, Sichuan, and **njiang changed from ineffective to effective, while Gansu changed from effective to ineffective, and Shanxi, Inner Mongolia, Jilin, Jiangxi, Yunnan, and Shaanxi had been continually ineffective since 2014.

Overall, the evolving spatial of the PTE of public safety in 31 regions changed, with more rapid change in Sichuan than in Hebei, Chongqing, and **njiang. Hebei, Chongqing and **njiang’s PTE achieved the effective level due to the three-folded reasons: the unexpected safety output indicators, unemployment rate, traffic accident casualties and direct economic losses of natural disasters continued to decline; the expected safety output indicators, sewage treatment capacity, GDP per capita, and the number of beds in health and medical institutions continued to rise; meanwhile, the investment in safety continued to increase, indicating that the performance of regional safety management was continuously improving. However, Gansu’s unexpected safety output indicators continued to rise, and PTE was in an ineffective level, indicating that the performance of regional public safety management needs to be improved. The public security performance levels of Shanxi, Inner Mongolia, Jilin, Jiangxi, Yunnan, and Shaanxi were low, because of high non-expected safety output, low expected safety output, and relatively low public safety input.

  1. (2)

    Spatial characteristics of SE

Table 1 shows that from 2014 to 2018, the public safety SEs of all regions were all less than 1, indicating that these regions had an invalid SE, and that the actual public safety of these regions was still far from its optimal level. Specifically, the average SE of public safety of these regions was 0.978, 0.973, 0.981, 0.982, and 0.984 from 2014 to 2018, respectively. The average SE of these regions in each year was relatively stable and showed a gradual increase. A total of 19 (2014), 20 (2015), 19 (2016), 17 (2017), and 20 (2018) regions achieved an effective level of SE, suggesting that the economies of scale of these regions in the corresponding years were optimal and had CRS. Therefore, these regions must maintain their current scales of production. 14 regions achieved optimal returns to scale for five consecutive years from 2014 to 2018. Meanwhile, 10 (2014), 8 (2015), 11 (2016), 10 (2017), and 7 (2018) regions showed a DRS, indicating that having an excessive amount of inputs may drive regions to expand beyond their capacity. Five regions (Bei**g, Hebei, Inner Mongolia, Chongqing, and Shaanxi) showed a DRS for five consecutive years, suggesting that these regions should strengthen and adjust their input elements to avoid unnecessary waste. Meanwhile, 2(Yunnan and ** a risk assessment model for construction safety. Int J Proj Manag 28(6):593–600" href="/article/10.1007/s00168-020-01025-y#ref-CR16" id="ref-link-section-d20465382e5542">2010; Saunders et al. 2017), this study constructed four safety input indicators (i.e., local environmental protection investments, public safety investments, financial healthcare investments, and social safety and employment investments), three unexpected output indicators (i.e., unemployment rate, traffic accident casualties, and direct economic losses resulting from natural disasters), and three expected output indicators (i.e., sewage treatment capacity, GDP per capita, and number of beds in medical and health institutions). These indicators represent four aspects of regional natural disasters, public health, accidents, and social security, which are correlated and have validity (Liao and Hou 2009; Liu et al. 2005; Zhu and Lv

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Acknowledgements

The author would like to thank Dr. Fang Meng, Associate Professor at the University of South Carolina, for her valuable help on the manuscript revising and editing.

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Authors and Affiliations

  1. College of Tourism Management, Huaqiao University, Quanzhou, 362021, People’s Republic of China

    Yongguang Zou

  2. Center of Tourism Safety and Security Research of China Tourism Academy, Quanzhou, 362021, People’s Republic of China

    Yongguang Zou

  3. College of History Cultrue and Tourism, Yulin Normal University, No. 299, Education Middle Road, Yuzhou District, Yulin City, Guangxi, People’s Republic of China

    Yuemei He

  4. Anxi College of Tea Science, Fujian Agriculture and Forestry University, Anxi, 362400, People’s Republic of China

    Weiling Lin

  5. Faculty of International Tourism and Management, City University of Macau, Avenida Padre Tomás Pereira, Taipa, Macau

    Sha Fang

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  1. Yongguang Zou
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  2. Yuemei He
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  3. Weiling Lin
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  4. Sha Fang
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Correspondence to Yongguang Zou.

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Zou, Y., He, Y., Lin, W. et al. China’s regional public safety efficiency: a data envelopment analysis approach. Ann Reg Sci 66, 409–438 (2021). https://doi.org/10.1007/s00168-020-01025-y

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  • DOI: https://doi.org/10.1007/s00168-020-01025-y

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