2.1 Data

To analyze the efficiency level of large urban centers, this study uses information obtained from the dataset on the Safe Cities Index (ICS) generated by the Intelligence Unit of The Economist (URL: https://safecities.economist.com) (^{The Economist, 2022}).

The Safe Cities Index is the result of extensive research and in-depth interviews with a panel of experts in different fields: Hans Jayatissa (Chief Technology Officer at KMD); Esteban Léon (head of the City Resilience Global Program of UN-Habitat); and Nicola Tollin (professor of urban resilience at the University of Southern Denmark) (^{The Economist, 2022}).

The final sample includes information for a total of 60 large urban centers for the year 2021. The analyzed cities are located in North America (seven cities: 11.67%), Latin America (eight cities: 13.33%), Europe (15 cities: 25.00%), Africa (four cities: 6.67%), Asia (23 cities: 38.33%), and Oceania (three cities: 5.00%). This final data includes cities with marked differences in terms of size, geographic location, environmental and weather conditions, and income levels (Figure 1).

Figure 1: Geographic distribution of the analyzed cities 

Keep in mind that, in its evaluation of large urban centers worldwide, The Economist Intelligence Unit regularly revises and updates the safe city index. Thus, significant changes were observed in the different editions of the index since 2015. The modifications in the safe city index include updating the different sub-indicators with the aim of reflecting more broadly emerging problems in urban safety over the years, and improve the scoring methodology and data sources seeking to better capture the different dimensions of urban safety (e.g., in the latest edition published in 2021, a new dimension or pillar called 'Environmental Safety' that refers to the importance of sustainable development was added to the safe city index). As the safe city index has evolved over time, the different editions of the index do not show internal consistency, in terms of the composition of the sub-indicators of the index. This lack of internal consistency makes it impossible to analyze cities' efficiency from a longitudinal perspective.

2.2 Variable definition

The Safe City Index includes 76 variables that are grouped into five indicators (y): (1) digital security (y1), (2) health security (y2), (3) infrastructure security (y3), (4) personal security (y4), and 5) environmental security (y5) (^{The Economist, 2022}).

The Safe Cities Index includes both quantitative and qualitative indicators. Concretely, 31 out of the 76 variables (40.79%) are based on quantitative data (e.g., the number of secure internet servers, and life expectancy at birth). On the other hand, 45 of the 76 variables (59.21%) are qualitative assessments based on a methodology decided and established by The Economist's Intelligence Unit (e.g., privacy policies and prevalence of petty crime) (^{The Economist, 2022}).

To generate comparable data points as well as construct aggregate scores for each city, The Economist's Intelligence Unit follows a min-max approach was followed to normalize the quantitative indicators on a scale of 0 to 100. Qualitative indicators were normalized in a similar way, but for these indicators the scale ranges from 0 to 4 (^{The Economist, 2022}).

Descriptive statistics for the five indicators of the Safe City Index are presented in Table 1, while Table A1 in the Appendix shows the full list of variables included in the index.

Following the description in ^{The Economist (2022)}, the indicators included in the 'Digital security' output (y1) account for different digital capabilities and threats of cities, for example: the quality and dependence on digital infrastructures, existing technologies and teams dedicated to cybersecurity, the number of secure internet servers and the risk of online attacks, among others. 'Health security' (y2) refers to the quality level of cities' health services, where the Covid-19 pandemic highlighted the need to consider a more holistic approach to health security and its closer integration into urban resilience planning. The variables included in this indicator are related, among others, to the access and quality of healthcare services, the level of preparedness against pandemics, citizens' life expectancy, infant mortality, and lifestyle-related diseases. 'Infrastructure security' (y3) addresses the city's infrastructure, measuring its availability and its vulnerability to natural and man-made disasters. This indicator considers the quality of local infrastructures, the application of transport safety, the death toll resulting from traffic accidents, natural disasters and the percentage of the homeless population as a result of the combined effect of migration to urban areas and increased birth rates.

'Personal security' (y4) considers individual safety (i.e., theft, violence, economic vulnerabilities, or other man-made threats). This indicator includes factors related to police interventions, the use of data-driven crime prevention plans, the country's general political stability, women's safety, economic security, the prevalence of violent crime and drug abuse, perceived safety among citizens, corruption, and the effectiveness of the criminal justice system. Finally, 'Environmental security' (y5) considers the implementation of sustainability and green policies. This indicator includes variables linked to, among others, policy proposals aimed at improving the health of the natural and physical environment, the city's sustainability master plan, the incentives for the production of renewable energy, urban forest cover, the cities' water consumption, and waste management policies.

2.3 Method

A key point of our paper is to provide a composite indicator (CI) analysis that is suitable for tailor-made policy recommendations. Thus, we aggregate the five pillars of the safe city index into a CI to assess the relative efficiency of the 60 cities included in the analysis.

Because the weight assigned to variables is decisive to generate meaningful policy actions, we employ the 'Benefit of the Doubt' (BOD) weighting approach (^{Cherchye et al., 2007}, ²⁰⁰⁸) to compute endogenous (city-specific) weights for the five pillars of the safe city index that permit us to identify priorities that may become targets for policies aimed at promoting urban development.

The BOD approach is rooted in the non-parametric Data Envelopment Analysis (DEA) model (^{Charnes et al., 1978}; ^{Cooper et al., 2011}; ^{Grifell-Tatjé & Lovell, 2015}; ^{Ray, 2004}).

DEA is a benchmarking method that employs linear programming to evaluate the relative efficiency of a set of units, in our case cities, by estimating their distance to the efficiency frontier. DEA models a technology with multiple inputs and outputs without imposing any assumption on the distribution function (^{Grifell-Tatjé & Lovell, 2015}). A free function is ideal in models like ours where the core of the analysis is the identification of the specific weights assigned to each output. The primary technological assumption of DEA models is that cities (i) employ a set of inputs (x) to produce a set of outputs (y), and that these sets form the technology (T): T={( x , y ): x can produce y }.

The BOD weighting is a special case of the input-oriented DEA model with one constant input (^{Cherchye et al., 2007}; ^{Liu et al., 2011}; ^{Alonso & Leiva, 2019}; ^{Araya-Solano, 2019}; ^{Lafuente et al., 2022a}; ^{Lafuente et al., 2022b}). The BOD method exploits the observed data to generate the weight of the outputs so that, for any given city, a relatively good performing indicator points to the relevance of this policy dimension for the focal city. In words, output dimensions assigned with lower weights would reveal their weak relevance relative to the rest of cities in the data. Thus, the optimal weighting configuration can be empirically generated for each city by identifying the relative strengths and weaknesses of the output set (y). Without information about the exact weights of the five outputs (y), the BOD model assigns to each city the best possible weight configuration, relative to the rest of cities in the sample.

The following linear program computes, for each city (i), the BOD model used to generate the endogenous set of optimal weights for the five outputs (^{Cherchye et al., 2007}; ²⁰⁰⁸):

(1)

Equation (1) computes for each city a vector of endogenous weights for the five SCI pillars (w _j =w ₁,…,w₅) that maximizes the proposed city development index (CDI ^BOD ). The CDI ^BOD values are bounded (CDI ^BOD ≤1), where CDI ^BOD =1 for efficient cities (on the production frontier) while for inefficient cities CDI ^BOD <1 (1-CDI ^BOD is the estimated relative inefficiency). By computing non-negative (w _ij ≥0) endogenous weights to the SCI pillars the BOD approach assumes that cities have their own policy priorities and, consequently, optimal policy should be city specific.

We thus add to the CDI ^BOD model in equation (1) a 'pie share' restriction (^{Cherchye et al., 2007}): This restriction is especially attractive because pie shares (w _ij y _ij ) reveal the contribution of each output to the CDI ^BOD , while allowing for weight heterogeneity within and between cities. Similar to ^{Cherchye et al. (2008)}, ^{Lafuente et al. (2022a)} and ^{Acs et al. (2022)} , L _j and U _j are the lower (1/5 × 0.25) and upper (1/5 × 1.25) bound of 'pie shares'. That is, cities can freely choose their output weights conditional on the two weight constraints in equation (1) (i.e., non-negativity and bounded 'pie shares'). The 'pie share' constraint in equation (1) allows for a more realistic modeling of cities' efficiency and contributes to our objective: to identify city-specific policies that permit us to know what aspects of the CDI ^BOD should be prioritized in order to produce significant improvements in key city performance dimensions.

3.1 Baseline results

This section presents the results of the BOD model. Summary statistics of the proposed BOD model (CDI ^BOD ) are presented in Table 2, while figures 2 and 3 show the visual representation of the efficiency frontier and the frequency distribution of the efficiency scores, respectively. Also, Table A2 in the Appendix shows the full list of scores and endogenous weights for the analyzed cities.

Overall, the findings show a mean competitive efficiency level of 81.64%, which means that, on average, the analyzed cities can expand their outputs by 18.36% to become efficient and reach the efficiency frontier. Also, the model identifies three efficient cities, that is, Copenhagen, Singapore and Toronto; whereas the worst performing cities, in terms of the CDI ^BOD , are Caracas, Yangon and Karachi.

At the continent level, we observe that cities from Oceania present the highest efficiency level (mean inefficiency: 2.67%), while African cities report the poorest efficiency results (mean inefficiency: 39.41%). From Figure 3 it can be noted that efficiency scores for cities located in North America and Oceania present the lowest dispersion. On contrary, the efficiency scores of Asian cities show the highest dispersion.

At the city level, from Figure 2 and Table A2 in the Appendix it can be seen that the top performing cities (third quartile) are report an average inefficiency level of 4.90%, and they are located in Europe (Copenhagen, Amsterdam, Stockholm, Barcelona, Frankfurt), Oceania (Sidney, Melbourne, Wellington), USA (New York, San Francisco, Washington DC), Asia (Singapore, Tokyo, and Jong Kong), and Canada (Toronto). The second group of cities shows a mid-level efficiency scores (mean inefficiency level: 15.79%). Cities in this group are mostly located in Europe (10 cities), Asia (10 cities), Latin America (7 cities) and North America (3 cities).

Finally, the third group includes poor performing cities. This group of 15 cities reports an average inefficiency level of 28.20%. Cities in this group are mostly located in Asia (Dhaka, Jakarta, New Delhi, Karachi, Kuwait, Manila, Mumbai, Riyadh, and Yangon) and Africa (Cairo, Casablanca, Johannesburg, Lagos). Also, one European city (Baku) and one Latin American city (Caracas) are included in this group.

Figure 2: BOD results: Efficiency frontier 

Figure 3: BOD results: Frequency distribution of efficiency scores 

3.2 Cities' strategic priorities

This section focuses on the identification of the outputs (pillars) prioritized by the studied cities by analyzing the results of the weights computed via the BOD model. Results at continent level are presented in Table 3.

Results show that North American cities prioritize three sub-indicators: digital security, health security, and infrastructure security. New York and San Francisco are notable examples of cities prioritizing these pillars. On contrary, the environmental safety and personal safety sub-indicators are the least important sub-indicators among these cities, being Los Angeles and Chicago cases showing this strategic pattern (Table A2 in the Appendix).

Like North American cities, the cities from Oceania prioritize the sub-indicators related to digital security and infrastructure security, whereas environmental safety is the least important sub-indicator. However, keep in mind that Sydney and Melbourne prioritize actions plan that affect the health security while Wellington dedicates more resources to environmental policies (environmental security).

In the case of European cities we observe that the strategic priorities are linked to health security, infrastructure security and personal security. Five cities follow this prioritization strategy (Table A2 in the Appendix): Barcelona, Frankfurt, Madrid, Paris and Brussels. It should be mentioned that, similar to the case of Asian and Latin American cities, digital security is not yet a high priority among European cities; however, Copenhagen and Amsterdam move away from this approach and they give greater importance to policies related to these two pillars.

Regarding Asian cities, it was found that they mostly prioritize the health security and infrastructure security sub-indicators. Although Asian cities on average do not prioritize policies that affect digital security, we observed that various cities are implementing digital-oriented plans (i.e., Singapore, Tokyo and Hong Kong), while Shanghai is an example of a city that prioritizes environmental policies (Table A2 in the Appendix).

Among Latin American cities the most relevant sub-indicators are health security and environmental security. Buenos Aires, Sao Paulo and Mexico City are cases of cities following this strategic path. Finally, African cities prioritize the sub-indicators related to digital security, health security and personal security (e.g., Cairo and Casablanca), while the least important sub-indicator for these cities is infrastructure safety (e.g., Johannesburg and Lagos).

4.1 Concluding remarks and policy implications

At territorial level, social planners are increasingly turning their attention to the design of urban policies that contribute to enhance cities' welfare. In this sense, digitalization and environmental policies are gaining weight in the policy agenda.

By identifying cities' strategic priorities through a 'benefit of the doubt' (BOD) model, this study has produced evidence that helps to better grasp the potentially optimal design of policies aimed at improving the level of welfare of large urban centers around the world.

Overall, the results of this study show that the strategic priorities that promote urban well-being are heterogeneous among the analyzed cities.

The results reveal clear differences in the performance of the analyzed cities. Large urban centers located in North America, Europe and Oceania show higher levels of efficiency. On contrary, cities located in Africa report the poorest efficiency results. Additionally, the findings suggest that cities follow different strategic paths when it comes to prioritize welfare-enhancing policies. Whereas cities in North America and Oceania pay more attention to digital security, health policies are more relevant for Asian and African cities and Latin American cities prioritize environmental policies.

The findings of this study have relevant policy implications. The main policy recommendation that can be drawn from the results is clear: an informed, tailor-made policy that takes into account the multidimensional nature of the urban well-being construct is more appropriate, relative to homogeneous actions based on policy isomorphism.

In this sense, the proposed 'benefit of the doubt' (BOD) model has the potential to reduce social planners' ambiguity and discretionary decision making by allowing to identify specific components of urban well-being that must be prioritized if improvements in cities' standards of living is the desired objective. Logically, the results produced by a composite indicator analysis would turn unfruitful if the information on policy priorities does not reach policy makers in charge of developing and implementing interventions. In this sense, a greater connection between academics and policy makers is highly recommended for the generation of better informed and potentially effective support actions to materialize (^{Cherchye et al., 2008}; ^{Lafuente et al., 2022b}).

The new realities and concerns of the 21st century have led many policy makers to address these challenges from a holistic perspective and turn their attention towards the design of policies linked to the environment the society's digitalization. Among others, Copenhagen, Toronto, Amsterdam, Wellington, and Washington DC are notable examples of cities actively adopting digital and environmental policies.

In summary, in light of the relatively poor attention paid to digital and environmental plans, the introduction of public policies based on more informed models offer valuable guidance to cities' policy makers on how to use their (scarce) resources to maximize urban well-being and, consequently, promote a more organized and sustainable development of their urban centers.

4.2 Future research lines

Like any study, the results of this research are open to verification. First, the lack of consistency in the construction of the ICS by the Intelligence Unit of The Economist in its different editions is an important limitation that limits any comparative analysis using longitudinal data. It would be desirable that future studies access information to carry out longitudinal studies that allow to analyze the evolution of cities' efficiency using total factor productivity models based on the multidimensional definition of urban well-being used in this work.

Second, future research should consider the possibility to take into account budgetary information in order to scrutinize whether investments that cities make in certain areas (for example, environmental policy) are conducive to enhanced social welfare. Also, because support policies unquestionably have different costs, analyses including economic figures would help quantifying specific interventions, and offer a clearer picture of policy-related decision making, thus contributing to understand the cost-benefit of support actions designed to generate greater social outcomes. Third, in a related manner, future work would benefit from the comparison between models that compute strictly endogenous weights and models that use a 'budget allocation' approach in which experts (ideally, policy makers) are asked to prioritize the different variables included in the studied composite indicator (e.g., ^{Karagiannis & Karagiannis, 2020}; ^{Lafuente et al., 2022a}). This way, the role of experts (e.g., policy makers and other stakeholders) and their prioritization strategies can be put to the test which, in turn, increases the flow of information and knowledge transfer between scholars designing tools to evaluate territories' performance and policy makers leading the development and implementation of specific interventions.

Finally, future research should consider the possibility to gather information for a greater number of indicators in order to integrate more comprehensively into potential analyses the economic, social and environmental components of urban development.