Quantitative performance assessment of Asian stellar cities by a DEA cascade system: a capability interpretation

Asia hosts several mega-cities with great economic power, which are often in a mutual competitive relationship. Despite smart specialisation and heterogeneity on national and global markets, they are often in pursuit of the highest possible socio-economic outcome so as to outperform their peers in this dynamic region. The present study seeks to present an operational comparative framework for judging the complex performance of several (12) large urban agglomerations in Asia. In the framework of this paper, these cities are called ‘stellar cities’. Two particular research challenges are addressed: (i) the development and application of a new Data Envelopment Analysis (DEA) approach, culminating—after a cascade of sequential analytical steps—in an Autoconfiguration Target Model which serves as a quantitative statistical tool for evaluating the (relative) multidimensional goal-oriented performance of the cities concerned; and (ii) a new functional interpretation of the DEA slack space for the possible improvement of inefficiently operating cities on the basis of Amartya Sen’s capability theory. In the paper, we use an extensive database on 12 Asian stellar cities, extracted from the annual Global Power City Index (GPCI) system which contains more than 60 urban performance indicators, which has been constructed by the Institute of Urban Strategies (Tokyo). We find that the performance ranking of these Asian mega-cities shows the ‘winners’, but also a high variability, with several positive and negative outliers. We conclude that there is clearly scope (‘capability’) for further improvement of the efficiency of most Asian cities in various specific policy domains, as shown by the DEA results.


3 Introduction: aims and scope
In a recently published book on 'Urban Empires', the authors (Glaeser et al. 2020) highlight the rise in the economic importance and political power of large cities worldwide. The massive growth of urban agglomerations all over the worldespecially in Asia, Africa and Latin America-marks a new epoch in the history of human and urban geography. Clearly, this new development has both sunny and shadow sides. The socio-economic benefits from agglomeration advantages manifest themselves in ever-rising urban achievements (economic, cultural, technological), but there are also many social costs involved, such as overcrowding, congestion, social stress, criminality, and individual and social alienation. It is a major challenge for contemporary large cities to cope with important 'headaches' in many domains of urban life, e.g. health care, pandemics, the labour market, the housing market, mobility, environmental quality, energy resources, cultural amenities and so forth (for a broad overview, see Kourtit et al. 2015). No wonder that modern urban planning has a great variety of new initiatives to cope with these challenges and to upscale urban performance, for instance, in the field of innovative mobility solutions (both high-speed solutions like rapid trains and low-speed solutions like the pedestrianisation or 'bicyclisation' of inner cities), favourable climate adaptation strategies for sustainable urban agglomerations (e.g. non-carbon energy transition), high-tech urban developments (in fields like robotics) or rigorous 'circular cities' initiatives (to drastically reduce the ecological footprint of cities). Such urban redevelopment programmes would ideally have to be developed in tandem with urban regeneration policies (see, for example, Bryson et al. 2018;Lehmann 2019).
There is no doubt that the current world is rapidly moving towards an 'urban century' (McDonald 2020), in which the position of large urban agglomerations is becoming more and more pivotal. Population dynamics, technological progress and rising welfare are critical in shaping this 'New Urban World' (Kourtit 2019). In this context, it is noteworthy that many countries are experiencing rapid population growth, whereas others (for instance, Japan) are showing clear signs of a structural population decline as a result of the ongoing ageing process (Stough et al. 2018). Other Asian countries like Korea, Thailand and China will probably also become depopulating nations in the near future. Despite a population decline in many countries, nevertheless most cities in our world are still continuing to grow, including those in Asian countries. As part of a general urbanisation trend, cities all over the world are likely to increase in both number and size in the decades to come. This unprecedented increase in the urban population, especially in many developed and emerging economies, is closely linked to the strong magnetism and economic attraction force of big cities: urban agglomerations and metropolitan areas have become the escalators of economic, technological, political and social power. Consequently, cities are not passive or static population concentrations in a dynamic and open world geography (Dziecielski et al. 2021). On the contrary, the fact is that major agglomerations-especially mega-cities (those metropolitan areas with more than 10 million inhabitants)-are becoming the new global 'control and command centres' of our world (Sassen 1991) or even 'urban empires' (Glaeser et al. 2020). Today, such large urban areas are advanced and influential powerhouses of economic activity, in combination with their creative, cognitive and innovative ability. Their historically centripetal and centrifugal impact is now extending worldwide from their traditional hinterlands in a globalising economy.
Over the last few decades, many Asian cities-including Chinese cities particular-have experienced an unprecedented high degree of economic, spatial and population growth (Brakman et al. 2018). It is noteworthy, however, that cities in the Asian region are very heterogeneous in terms of their economic performance, technological innovativeness, cultural profile and logistic interaction pattern. But all of them aim to become 'rising stars' in the 'urban century', and therefore, in our study we call these cities 'stellar cities'. Hence, it is pertinent to develop an evidencebased ranking of the multidimensional performance of these stellar cities in Asia, so as to identify and assess the position of these Asian mega-cities on a quantitative 'performance ladder'.
In the past decade, various studies have been carried out to create a classification of cities based on their multidimensional performance or success indicators (see, for example, Taylor et al. 2009;Grosveld 2002;Arribas-Bel et al. 2011;Kourtit et al. 2012;Wahlstrom et al. 2020). A main challenge in past and current empirical research is the development of a consistent and reliable multidimensional database that is suitable for a comparative, strategic urban benchmark analysis. In the existing literature on comparisons of cities, there is a great diversity in such evaluation approaches which are often based on quantitative scorecards. Generally, urban achievements have been empirically assessed from a broad perspective based on various quantitative models or statistical methods (Qui et al. 2015;Hao et al. 2015;Saaty and Sagir 2015;Guan and Rowe 2016;Manijeh 2016;. Our study provides a new performance measurement tool for cities, based on an extended Data Envelopment Analysis (DEA).
The measurement of urban efficiency achievement calls for an appropriate methodological approach, in which-in contrast to simple ranking methods-the smart use of resources in attaining a given output level (output-input ratio) of cities is translated into a quantitative success indicator of performance (in economics this is usually called 'efficiency' or 'productivity'). The assessment of urban output achievements and urban input efforts is, however, fraught with many operational data problems. In the present study, we offer a new approach for a data cascade methodology to cope with heterogeneous data sources. In the last few decades, a very effective instrument has been developed and employed, called Data Envelopment Analysis (DEA), which is able to confront a multidimensional set of outputs with a multidimensional set of inputs (for details, see Charnes et al. 1978;Cooper et al. 2006). This standard DEA technique named after its respective authors is usually called the CCR method. It has become a popular benchmarking tool in the management and industrial organisation literature.
DEA has also become an established quantitative assessment method in evaluation practice of corporate organisations and public institutions (see, for example, Seiford 2005). In recent years, in an urban planning context, several assessment studies have applied DEA models to measure economic efficiency among cities,which in the DEA jargon are usually called decision-making units (DMUs). An extensive technical overview can be found in ; in Sect. 2, we summarise some key contributions from the existing DEA literature. But first we will highlight the novel methodological contribution to DEA applied in the present paper.
The results of a conventional DEA approach are normally in the form of a numerical ranking of candidates or alternatives, based on multidimensional success (efficiency) scores. The optimal position of a DMU among several competitors is (theoretically) a place on the efficiency frontier, implying to a DEA score equal to 1. This case refers to a DMU with the highest efficiency, while all others have a sub-optimal (or inferior) performance, with a DEA score smaller than 1. The non-efficient DMUs have, of course, the potential to improve their efficiency up to the level of the 'winner' located on the production possibility frontier. Thus, the degree of efficiency gain of a non-efficient DMU depends on the distance from its actual position to the efficiency frontier. This slack space thus opens the opportunity to enhance the DMU's performance, for example, by removing or mitigating shortcomings or bottlenecks in the available resources. This 'opportunity space' for actors will be interpreted in the present study from the perspective of Amartya Sen's (1982) capability theory (see Sect. 6).
In the light of these considerations, the main aim of the present paper is to produce a DEA-based ranking of the integral efficiency performance of 12 large (stellar) cities in the Asian region, with a particular focus on three large Chinese mega-cities (Beijing, Hong Kong and Shanghai). The related DEA assessment methodology is based on a systematic extension of the conventional CCR approach in DEA, in which, inter alia, the super-efficiency concept (that provides an unambiguous ranking of DMUs) plays a critical role. This DEA modelling approach is then further refined by means of a stepwise cascade approach in which several limitations inherent in the conventional DEA methodology are removed or mitigated. This analysis comprises five successive steps and culminates in an Autoconfiguration Target Model for DEA assessment. This approach is then used for a comprehensive assessment of the 12 Asian stellar cities considered in our study.
The paper is organised as follows. Section 2 summarises our new comprehensive DEA methodology in a cascade with five steps, with a particular focus on the new Autoconfiguration Target Model as the end result of a DEA cascade system. Then Section 3 describes the GPCI database used in our empirical application. Next, Section 4 applies the DEA cascade model to assess the performance of 12 Asian stellar cities, and Section 5 presents the efficiency improvement projection results based on our new Autoconfiguration Target Model. Section 6 provides a new interpretation of the DEA findings by employing a capability interpretation inspired by Sen (1982). Finally, Sect. 7 draws some methodological and urban governance conclusions.

3
Quantitative performance assessment of Asian stellar cities… 2 A stepwise overview of the comprehensive DEA cascade methodology Cities in our world are multifaceted organisms that may be conceived of as active agents that operate in a complex environment and produce socio-economic outcomes with different degrees of efficiency. This differentiation in urban performance may concern, inter alia, (un)employment rates, human health outcomes, poverty rates, environmental quality, income growth, safety or happiness. Such welfare indicators are not nature-given, but are-at least partly-the result of a deliberate policy and of (business or individual) actors' choices in a city. A city is thus not a passive geographical entity, but has the potential to influence-through its stakeholders-its own welfare outcome. Consequently, cities may occupy different positions on a comparative welfare ladder and may thus be judged on the basis of their efficiency in realising such welfare outcomes.
As mentioned in Introduction, over the past few decades DEA has developed into a powerful analysis instrument for comparing and assessing the competitive performance of agents or decision-making units (DMUs) (e.g. business firms, corporate organisations and public institutions, like schools, hospitals or energy companies). DEA has demonstrated that it has a promising potential-as a decision-support technique-to offer a solid quantitative basis for a comparative and benchmark analysis in efficiency and productivity research and management. Over the past decades, DEA has acquired a respectable history in the quantitative approach to the evaluation of industrial organisations. It finds its roots in multi-objective linear programming (MOLP) theory which aims to identify optimal solutions for decisions characterised by multiple goals or objectives (Golany 1988;Thannassoulis and Dyson 1992;Joro et al. 1998;Frei et al. 1999;Halme et al. 1999;Korkonen and Siljamäki 2002;Korkonen et al. 2003;Lins et al. 2004;Silva et al. 2003;Washio et al. 2012;Yang and Morita 2013).
After the seminal work of Charnes et al. (1978)-often called the CCR approach-an avalanche of studies has been published, mainly of an applied nature. In the present study, we will employ as a start of our analysis the standard CCR model, which is based on constant returns to scale (CRS). In principle, we might have applied a variable returns to scale (VRS) model (see, for example, Banker et al. 1984), but this model tends to overvalue small and large DMUs, which may affect its discriminatory power. A wealth of introductions and expositions on DEA-including, in particular, applications to city efficiency rankings-can be found in Borger and Kerstens (1996), Dinc and Haynes (1999a, b), Worthington and Dollery (2000), Afonso and Fernandes (2006), Suzuki et al. (2008), Nijkamp and Suzuki (2009), Kourtit et al. (2013), Kourtit et al. (2017Kourtit et al. ( , 2020a, Suzuki and Nijkamp (2016, 2020 and . This large number of applied studies shows that an operational analysis of city efficiency in a competitive environment is an important, but also an ongoing research topic in the recent urban and regional science literature. Clearly, with several thousands of publications in the international literature on DEA methods and applications, it is impossible to provide a complete and systematic literature overview of all DEA developments. Here, we only present selected key contributions that are essential for our new comprehensive DEA. For more extensive details on DEA and its variants, we refer the reader to . In the present study, we pinpoint five weaknesses or limitations inherent in the use of a standard DEA. These are, in particular: (i) the presence of equal efficiency scores for all DMU's on the efficiency frontier (leading to the need to apply a Super-Efficiency model-SEM); (ii) the ambiguity in the distance projection method in DEA models (leading to the development of an adjusted Euclidean-based Distance Friction Minimisation model-DFM); (iii) undefined or fuzzy target achievements for inefficient DMUs (prompting the development of a quantitative Target-Oriented Model-TOM); (iv) lack of an objective and unambiguous policy target setting for a DMU (requiring the development of what is called an Autoconfiguration Target Model-ATM); and (v) finally-in specific cases-insufficient attention for 'lumpiness' (indivisibilities) in the input resources (requiring the use of a Fixed Factor Model-FFM). In our paper, we integrate these five elements as critical building blocks for a new comprehensive DEA model in the form of a new stepwise cascade approach and apply this new methodology to an efficiency analysis of the multifaceted achievements of the Asian and Chinese stellar cities in our study.
As argued above, the conventional DEA model suffers from several methodological and operational weaknesses. To cope with these shortcomings in DEA, we present here in a stepwise way five new amendments that are able to mitigate the abovementioned shortcomings in the standard DEA approach. This cascade structure is presented in Fig. 1 and is then discussed briefly.
Step 1 in Fig. 1 addresses the possible ambiguity in the score results of a traditional DEA approach (Charnes et al. 1978): all DMUs located on the efficiency frontier will, by definition, receive a DEA score equal to 1. The consequence is that it is impossible to discriminate among several efficient DMUs which have an identical score. To cope with this shortcoming, the concept of a super-efficiency model (SEM) was introduced in DEA, so as to arrive at a complete and unambiguous ranking of all DMUs (Andersen and Petersen 1993). The DEA score of a given DMU is then calculated by omitting the input and output data of this DMU in order to identify its relative effect. By repeating this for all successive efficiency DMUs, a complete ranking of all DMUs on the efficiency frontier can be obtained, with the necessary implication that the SEM DEA scores may be higher than 1, while of course the scores of all remaining (inefficient) DMUs are not altered and remain below the threshold value 1. More details on the SEM DEA model can be found in, among others, Andersen and Petersen (1993).
Step 2 in Fig. 1 addresses another anomaly in the initial DEA methodology; DEA models originated, as mentioned, from a MOLP approach using a piecewise linear production frontier and projecting the outcome of each DMU present in the sample of DMUs on the frontier concerned. If a DMU is positioned on the frontier, it is, by definition, efficient; otherwise, it is inefficient. Consequently, by adjusting its inputs or outputs (or both), an inefficient DMU might become more efficient. This slack space is what we call here the capability space (see Sect. 6). In the standard CCR DEA method this adjustment is achieved by means of a uniform reduction in 1 3 Quantitative performance assessment of Asian stellar cities… all inputs (or a uniform increase in all outputs), but this uniform adjustment is an unnecessary limitation. Several attempts have been made in the literature to improve this shortcoming. In particular, Suzuki et al. (2010) have developed a new projection approach, called the Distance Friction Minimisation (DFM) model, in which Euclidean distance is used to improve a DMU's efficiency through an appropriate movement towards the efficiency frontier surface, with optimal weights based on the input/output data features of the DMU concerned. More details and extensions of this DFM DEA model can be found in, inter alia, .
Step 3 in the adjusted DEA methodology serves to address the transformation costs of low-efficiency DMUs in reaching the 'ideal' DEA score of 1. To ensure a realistic and feasible improvement strategy for highly inefficient DMUs, Suzuki et al. (2015) designed an adjusted DEA approach, in which the advantages of the above DFM model were incorporated in a target setting approach (also incorporating the SEM DEA method), so as to identify a fit-for-purpose efficiency improving projection model. This target-oriented model (TOM) is more normative in nature and specifies the minimum output targets to be attained, as well as the target efficiency scores (TES) for inefficient DMUs. On the basis of these pre-specified TES values, a corresponding input reduction or output increase value can be calculated. For more details on this step, we refer again to .

Fig. 1 Cascade of incremental amendments in DEA
provide a more objective way of establishing the TES values, namely, through the statistical use of either appropriate input reduction or output increase values. In the ATM module, the average efficiency scores over all DMUs and the standard deviation of these scores play a key role. The ATM approach offers a solid approach to rational decision-making aiming at performance improvement, but is mathematicaly rather cumbersome. Its technical details are provided in a separate "Appendix A". Some details on this recent advance can also be found in Suzuki and Nijkamp (2020). The final and complementary Step 5 in our DEA amendment approach addresses a specific question that is related to the possible problematic nature of scarce input resources. In many cases, such inputs may be indivisible and hence cannot be adjusted in an incremental or smooth way; they are integers. Examples are infrastructure, airports, hospitals, cultural resources, universities, etc. Such situations of input 'lumpiness' call for an adjusted DEA approach, since a flexible (continuous) change in input factors is not possible under these circumstances. For example, half an airport is not a meaningful DEA strategy. This then calls-whenever needed-for the design of a fixed factor model (FFM) inside a DEA cascade approach (see Suzuki et al. 2011;Suzuki and Nijkamp 2016).
The mathematical technicalities of each stage of the DEA cascade systems have separately been well documented in the prevailing literature referred to in each step, with the exception of the Autoconfiguration Target Model (ATM). A detailed specification of this model and technicalities are given in "Appendix A".
The new and integrated DEA cascade methodology described above is able to cope with several weak elements in the standard DEA methodology and will be tested on its feesibility in our empirical application to the performance assessment of 12 Asian stellar cities. The present paper thus proposes a combined cascade system for a series of DEA approaches which culminate in an Autoconfiguration Target Model (ATM), containing the SEM and DFM steps and followed-when needed-by a complementary FFM application (see Fig. 1). The application of the stepwise DEA cascade system, as mapped out in Fig. 1, will allow us to perform a comprehensive ranking analysis of 12 large cities in the Asian region, also including three major Chinese cities (Beijing, Hong Kong, Shanghai). We note here that the focus on 12 Asian cities is not a necessary limitation. In principle, more cities might be considered, provided similar data would be available.
As mentioned earlier, all relevant input and output data are extracted from the GPCI database. This database contains detailed annual data from the year 2009 onward for about 40 world cities (including the 12 Asian cities under consideration in our research). For our comparative performance analysis, we use, in particular: economic performance, technological innovativeness, geographical interactions and cultural resources. In our empirical study, we regard the 'cultural resource' in a given city as a historically determined and fixed input or production factor whose size cannot be flexibly adjusted (upward or downward) in the short term; it is therefore conceived of as a 'fixed input factor' (i.e. an FFM module). More details on the database are provided in Sect. 3.

3
Quantitative performance assessment of Asian stellar cities…

Database and analytical framework
For a systematic operational comparison of the Asian cities' performance outcomes, our empirical approach uses a unique and extensive data set on appropriate measurable indicators for the cities under consideration, viz. the Global Power City Index (GPCI), produced by the Institute for Urban Strategies and managed by the Mori Memorial Foundation in Tokyo. Here we use urban data for the year 2016, which have a good potential for a comparative benchmark analysis for the 12 Asian stellar cities. The GPCI database will be used here as an analytical tool to evaluate and rank the comprehensive strategic power determinants of 12 stellar cities in this region, in terms of their strengths and weaknesses in performance. In principle, a multi-annual DEA could also have been applied, since the database covers a period of more than a decade.
The GPCI database contains numerical performance scores and related rankings of global cities based on six main assessment categories, namely: economy; research & development; cultural interaction; liveability; environment; and accessibility. Each of these main indicators classes is subdivided into a set of appropriate and measurable sub-indicators. Finally, a strictly consistent and carefully tested database on approx. 70 sub-indicators related to many world cities (40 in total) is created. The 70 indicators break down into 59 indicators based on statistics or numerical data and 11 indicators using original city questionnaires, some of which combine the scores from questionnaires with additional numerical data. This database contains both official statistical data and standardised survey data (see Institute of Urban Strategies 2017). The composition of the data is as follows: (1) Statistical sources (59 indicators) • Whenever possible, official statistics are used as main sources of numerical data. • Quantitative data that are not derived from official statistics are taken from reliable sources such as academic research papers or other types of publications which are clearly sourced.
(2) Original questionnaires (11 indicators) • Questionnaires for residents and workers aimed at those living and/ or working in a target city. • Questionnaires of experts, aimed at those with experience of living in and / or visiting multiple target cities.
This comprehensive database has been published annually since 2009. The 12 Asian cities used in our analysis are taken from this database. So, there was no possibility to choose other cities. All further details are available in the abovementioned annual GPCI reports. In our study, we employ the score by indicator data sets. These indicator data are converted into standardised indicator values, falling between 0 and 100, so that the data can be evaluated according to a uniform standard measurement scale. The highest performance of an indicator receives a score of 100 and the poorest a score of 0. The DMUs (in this case, cities) used in our comprehensive analysis are listed in Table 1.
For our comparative DEA efficiency analysis of the efficiency of the cities under consideration, we need to define the performance (output) criteria and the resource (input) criteria. Based on this viewpoint, we select and employ two appropriate output items and three appropriate input items as follows: Output ( Based on numerical information on three inputs and two outputs, our study seeks to assess the efficiency performance of 12 Asian stellar cities, as shown in the integral analysis framework depicted in Fig. 2. These data will be employed in our Autoconfiguration Target Model (ATM) in the DEA cascade system (Sects. 4 and 5).

Performance assessment of Asian stellar cities
The performance assessment results for the 12 Asian stellar cities based on the comprehensive DEA cascade system are now presented in a stepwise way, following the structure of Figs. 1 and 2. We first provide the empirical DEA results for an unambiguous ranking of the 12 Asian stellar cities, based on the super-efficiency criterion (Sect. 4.1), followed by a presentation of the optimal DEA weights (Sect. 4.2).

3
Quantitative performance assessment of Asian stellar cities…

SEM DEA results
In the first stage of our cascade analysis, we apply the SEM DEA model to our data on Asian cities. The results are given in Fig. 3. This figure displays quite some variability in the efficiency performance values of Asian cities. From this figure, it can be seen that Hong Kong, Kuala Lumpur, Bangkok, Tokyo and Singapore may be regarded as super-efficient cities in the Asian context. It also appears that-in a relative sense-Osaka, Shanghai, Beijing, Seoul, Fukuoka, Mumbai and Taipei may be interpreted as inefficient cities which definitely have much scope for enhancing their performance. If we focus on the three Chinese cites in our sample, it is clear that Hong Kong is a top-performing stellar city in the Asian region. On the other hand, Shanghai and Beijing are evaluated as underperforming cities, and hence, these two inefficient Chinese cities may need a rational, evidence-based efficiency enhancement strategy so as to improve their integral performance. And the same holds for Osaka, Seoul, Fukuoka, Mumbai and Taipei. The specific type of improvement strategy is presented analytically in Sect. 5.

Optimum weights for input and output items
As mentioned above, the Asian cities do not share many similar characteristics, so that urban policies tend to be differentiated. But, generally, for several cities there is much room an improvement in their efficiency state. The DFM approach leads-as explained above-to the identification of optimum weights for input factors and output variables. These weights represent the set of most favourable weights for each DMU, so as to determine the relative importance of each input or output indicator in improving the overall DMU performance. Thus, these values show not only which items are critical in contributing to the efficiency performance of a DMU, but also to what extent they do so. Thus, these weights provide the policy handles for urban improvement strategies. The optimum weights for all input and output items for each city are presented in Figs. 4 and 5. Figures 4 and 5 show that, for instance, Hong Kong obtains for Cultural Resources a weight of 1.000 in its inputs and for GDP a weight of 5.085 in its outputs. It can also be seen that Shanghai receives for R&D a weight of 0.879 and for Cultural Resources a weight of 0.121 in its inputs and for GDP a weight of 0.814 in its outputs, while Beijing receives for Number of Employees a weight of 0.274 and for R&D a weight of 0.726 in its inputs and for GDP a weight of 0.706 in its outputs. The values of these weights provide empirical guidelines for the type and intensity of adjustments in inputs or outputs so as to get closer to the efficiency frontiers.
From our findings, we also notice that Chinese cities reveal features similar to the optimum weights, especially since these cities have in common a high value for R&D in their input items and for GDP in their output items. Based on this fact, Quantitative performance assessment of Asian stellar cities… Chinese cities, and especially Hong Kong, have a feature that has an advantage in terms of a GDP orientation as an output item compared with other cities. Our findings are largely supported by the overall findings from the GPCI report for 2016.
After the presentation and discussion of the DEA results including an SEM module, we will now show the results of the ATM approach (Sect. 5).

Description
As mentioned, the ATM-FFM approach-as the culmination of the DEA cascade system-is rather complicated (for technical details, see "Appendix A"). The main goal in Sect. 5.1 is to identify a realistic value of the Autoconfiguration Target Efficiency Score (ATES) with a Fixed Factor module. The above-mentioned ATM-FFM DEA model will be used to envisage real-world policy circumstances and to determine the requirements for an operational adjustment strategy for a feasible efficiency improvement in inefficient cities in Asia. In this comparative analysis, we will consider 'cultural resources' in these cities as a production factor that cannot be flexibly adjusted (implying a FFM situation). In general, a TES (Target Efficiency Score) (see Step 3 in Fig. 1) may be set by a policy maker or decision-maker based on promised target achievements or actual problem situations. Clearly, our initial DFM model maintains its flexibility in target value setting under changing situations, but, if the TES approach requires a solid method to set the target values in a less arbitrary way, our new ATM-FFM model is more appropriate (see for details "Appendix A").

Fig. 5 Optimum weights for output items
Our DEA cascade approach now comprises the following numerical steps. The Autoconfiguration Target Efficiency Score (ATES), with a Fixed Factor input α for DMU k (hereafter ATES k FF−α ), is numerically determined as follows: we compute both the efficiency score θ* for DMU k and an average efficiency score for all DMU sets μ, as well as a standard deviation of the efficiency scores for all DMU sets σ.
Next, we adopt a super-efficiency approach; the standard SEM-DEA model usually computes an efficiency score higher than 1 for efficient DMUs (note: the original CCR model usually leads to an efficiency score just equal to 1 for efficient DMUs). This means that μ and σ depend on the specification of the model and hence on its outcomes. For the time being, the present paper assumes that all efficiency scores for all efficient DMUs just hold at the value of 1, in order to facilitate our mathematical experiments for the ATES (see "Appendix A").
These six cases can now be used to classify the set of seven inefficient cities (see Fig. 6 in Sect. 5.2). More technical details are given in "Appendix A". Quantitative performance assessment of Asian stellar cities…

Empirical illustration (Seoul)
Taking the ATM-FFM model as a new DEA foundation, we can compute the ATES FF values, as shown in Table 2 and Figs. 6. Of course, these values apply only to inefficient cities. This can be done for each individual city in our database. For example, Seoul has an efficiency score of 0.697 and hence belongs to Case 2 in Fig. 6.
We will now use Seoul as an illustrative case (Case 2) and point of reference and present an efficiency improvement projection result. As shown in Fig. 6, the efficiency score is 0.697 (see also Fig. 3). We now assume that the ATES FF−2 value is set for Case 2 at 0.708 ( ATES FF−2 k ). The resulting optimal input reduction values and output increase values for Seoul, based on the SEM module, the standard DFM and the ATM-FFM model, are presented in Fig. 7. As shown in Fig. 7, the results of the standard DFM model clearly show that a different-and likely more efficient-solution than the SEM projection is available for reaching the efficiency frontier. For instance, the SEM projection shows that, for cities to become efficient, reductions are required in their Number of Employees by 30.34%, R&D Expenditure by 52.91% and their Cultural Resources by 30.34%. On the other hand, the standard DFM results show that for cities to become efficient, reductions are required in their Number of Employees by 19.50% and their R&D Expenditure by 34.08%, together with an increase in their Nominal GDP of 21.60%. So, there is quite some variability.
However, if we introduce explicitly a realistic target setting strategy in our DEA approach, it appears that our new ATM-FFM model (including a DFM) is clearly able to provide a more feasible efficiency improvement plan, as compared with the results of the SEM model and the standard DFM model. For instance, the ATM-FFM results show that a reduction in the Number of Employees of 0.88% and an increase in the Nominal GDP of 1.06% are required to reach the ATES FF−2 k level of 0.708. The visual results in Fig. 7 are illustrative for the advantages of the ATM-FFM approach.

Empirical illustration (3 Chinese stellar cities)
The results of an efficiency improvement projection based on the application of a SEM-CCR model and on ATM-DFM-FFM model for the three Chinese cities concerned will now be presented in Figs. 8 and 9. We start with Beijing. Regarding Beijing, the efficiency score is 0.706 (see Fig. 6). We now assume that the ATES FF−2 value is set, for Case 2, at 0.708 ( ATES FF−2 k ). Applying now the above DEA we can infer from Fig. 8 that, if Beijing implements an efficiency improvement plan based on the SEM-DEA model, for it to become efficient requires significant reductions in its Number of Employees by 29.38%, its R&D Expenditure by 29.38% and its Cultural Resources by 58.34%, together with an increase in Volume of Interaction of 221.31%! Furthermore, the standard DFM results in Fig. 8 show that, to become efficient, Beijing should reduce its R&D Expenditure by 23.72% and its Cultural Resources by 30.25%, together with an increase in its Nominal GDP of 17.22% and its Volume of Interaction of 335.89%. On the other hand, on examination of the ATM-DFM-FFM results in Fig. 8 shows that a reduction in its R&D Expenditure of 0.22% and an increase in its Nominal GDP of 0.16% would be needed. From the above findings, we note that the ATM-DFM-FFM model is able to provide a more realistic and smooth efficiency improvement programme compared with the SEM model and the standard DFM model. Note also that here Cultural Resources is interpreted in our application as a fixed factor in the ATM-DFM-FFM model.
Regarding Shanghai, the efficiency score is 0.814 (see Fig. 6). We assume here that, for Case 4, the ATES FF−4 value is set at 0.851 ( ATES FF−4 k ). Figure 9 shows that, if Shanghai intends to implement an efficiency improvement plan based on the SEM model, this would require a reduction in its Number of Employees by 41.65%, its R&D Expenditure by 18.65% and its Cultural Resources by 18.65%\, together with an increase in its Volume of Interaction of 198.30%! Next, the standard DFM results in Fig. 9 show that to become efficient Shanghai should reduce its Number of Employees by 32.59%, its R&D Expenditure by 11.66% and its Cultural Resources by 0.21%, together with an increase in its Nominal GDP of 10.28% and in its Volume of Interaction of 240.47%. This is a rather drastic scenario. However, it turns out that, according to the ATM-DFM-FFM results in Fig. 9, a reduction in its R&D Expenditure of 2.40% and an increase in its Nominal GDP of 2.40% would be needed to be efficient. From the above findings, we also note that the ATM-DFM-FFM model is able to offer a much less dramatic efficiency improvement plan, compared with the SEM model and standard DFM model. Apparently, the introduction of realistic policy targets in a DEA model helps to generate more realistic policyrelevant outcomes.
From these facts, we may draw the conclusion that the ATM-DFM-FFM model is able to produce a more reasonable and realistic efficiency improvement projection than previous SEM models and standard DFM models. This is an important lesson, also for future applications.

Overall results
The aggregate results of an efficiency improvement projection based on the application of a SEM, a standard DFM and an ATM-DFM-FFM model for the remaining 5 inefficient Asian cities (Fukuoka, Mumbai, Osaka, Seoul, Taipei) are presented in Table 3 (θ** in Table 3 expresses the efficiency score after the improvement projection). Clearly, this efficiency improving projection can be computed only for inefficient DMUs. Thus, this approach is not applicable for Hong Kong, Kuala Lumpur, Bangkok, Tokyo and Singapore which are-according to Fig. 3-super-efficient cities. For those super-efficient cities a target setting is of course less meaningful.

A capability interpretation of DEA
DEA has undoubtedly become a powerful analytical instrument in comparative assessment research, even though it is still 'work in progress'. It is based on sound economic principles and a solid quantitative framework. Nevertheless, consultation of numerous DEA studies also brings to light an inherent shortcoming in the interpretation of the ranking results. Although the efficiency rank orders of DMUs are unambiguous, given the input and output data, the question concerning how to reach a more efficient position on the relative performance ladder of DMUs remains largely neglected. Clearly, the DEA results show which inputs need to be adjusted in order to achieve a higher-rank order. But, if other inefficient DMUs would also change their scarce inputs, it remains to be seen whether and how the relative position of the DMU concerned would shift. And, in addition, any additional input of resources by a given DMU carries with it extra costs, and it is not clear how and where these costs would affect the multidimensional outcomes or objectives of a DMU.
The main point is that the slack space (the distance between the actual position of a DMU and its theoretically attainable position on the efficiency frontier) only represents the possible improvement space compared with other DMUs. But such an improvement possibility depends on two critical factors, viz. the external context and the internal strength of the DMU. These will be briefly discussed.
The external context refers to fixed conditions which may limit a DMU's scope for manoevre: for instance, the physical-geographical location constrains or increases the market power of the most important competitors. Under such conditions, the amendment space for a DMU may be very limited, as any change may incur high transaction costs. The degree of a successful improvement strategy may then depend on its contextual adaptability, so that the evaluation of a DMU's achievements would have to take into consideration place-specific characteristics. This latter observation is in agreement with the emerging literature on 'contextspecific policy' (see, for example, Corvers 2019; Cooke and Morgan 1998;Martin and Trippl 2014;McCann and Ortega-Argiles 2015). An improvement in performance is not a mechanistic strategy, but reflects the capability to enhance a DMU's outcome.
Next, a DMU has its own internal drive to improve the DEA outcomes. But again, this is not an automatic strategy with guaranteed outcomes. To make the jump from an inferior or inefficient position towards a relatively optimal outcome calls for additional resources (financial, material, human power and innovativeness). Thus, a DMU's response to the challenging task to reach a desired location on the production possibility frontier calls for intelligent agility. This is where entrepreneurship or smart governance place a critical role. The current discussion on 'smart city' governance is highly relevant in this setting (see Kourtit et al. 2017Kourtit et al. , 2019, as it emphasises the potential ('capability') of a DMU to improve the socio-economic outcome of its organisation.
It is noteworthy that especially the determination of optimal weights-in the context of a DFM module in DEA-provides guidance for DMUs to improve their outcomes, since the weights allow, for both inputs and outputs, the best possible selection of trajectories for adjustments in input factors or output variables, including the extent to which an efficiency improvement is possible.
We may thus posit that DEA results highlight a spectrum for performance improvement, but by no means provide an automatic recipe for a higher position on the competitive performance ladder. Such results only suggest the capability to improve, but the outcome is particularly determined by contextual adaptability and intelligent agility. Capability is a concept that has gained quite some importance in the recent literature. It refers to the human ability to take action; it allows an agent to obtain the cognitive ability and competence to understand, and to act and to improve. This also holds for city governance, where contextual adaptability and intelligent agility belong to the core capabilities that are required to enhance urban achievements. Thus, capability in an urban context is a necessary though not sufficient condition for the improvement of urban outcomes. In a DEA framework, the slack (or improvement) space of a DMU defines the maximum span for improving efficient and effective performance.
This capability perspective on DEA results has been inspired by the capability theory developed by Sen (1982).
The urban capability approach originates essentially from the development studies and poverty analyses of Sen (1999Sen ( , 2008, who claims that a socio-economic system has many roles and functionings which-if employed in an appropriate manner-will contribute to the better socio-economic performance or happiness of a country, region or population group. Thus, the capability approach is essentially based on an enabling theory that pinpoints the conditions necessary for a rise in economic and social achievements (Comim et al. 2008). Later on, this capability approach was also adjusted for and applied to other fields, e.g. emancipation Quantitative performance assessment of Asian stellar cities… movements (see Nussbaum 2003), while recently it has also been applied to assess the potential achievements of cities (see Basta 2015).
In a recent article, Nijkamp (2016) argues that the roots of capability theory can essentially be traced back to the classical work of the French geographer Vidal de la Blache (1903) who introduced the principle of 'possibilism'. This principle claims that any agent in space (e.g. a city, a region) has essentially a portfolio of options from which a choice can be made by agents to enhance their socio-economic performance: '…. man as a master of the possibilities, is the judge of their use' (see Johnson et al. 2000, p. 609). In his contribution, Nijkamp (2016) provides a synthesis of these various strands of ideas through the notion of a 'resourceful region' or 'resourceful space', to highlight that-in contrast to spatial determinism-spatial agents (e.g. cities) can shape or influence their future by creating and choosing appropriate combinations of assets from a broad portfolio of choice possibilities or options. Thus, cities and regions may be seen as 'opportunity seekers' that are able to improve their socio-economic 'fortune' by a smart use of their capability space. From this perspective, DEA offers an 'optimal' development strategy in regional policy.

Discussion and conclusion
The present study aimed to provide a novel contribution to regional development theory and practice. It has taken for granted that-in a relative sense-regions or cities can improve their socio-economic achievement by changing in a smart way their ratio between productive input and resulting outputs. This approach takes us essentially back to Sen's capability theory, which argues that socio-economic improvement is possible as the result of explicit choices of actors. The extent to which efficiency can be enhanced and the necessary changes in output-input ratios to achieve an efficiency improvement can be calculated by an empirical DEA.
In this paper, we have designed a comprehensive DEA model as the basis for an empirical assessment framework to assess the efficiency of large Asian cities, which have a certain scope for socio-economic performance improvement. We find that Hong Kong is a prime stellar city in the Asian region. From our results, it is also clear that Hong Kong, Kuala Lumpur, Bangkok, Tokyo and Singapore may be regarded as super-efficient cities in the Asian context. It appears that Osaka, Shanghai, Beijing, Seoul, Fukuoka, Mumbai and Taipei are evaluated here as inefficient cities.
From a methodological perspective, we have designed a new comprehensive DEA methodology, the ATM-FFM model. Its feasibility for improving the efficiency of large Asian cities was tested using the global GPCI database containing many statistically verified indicators. From our findings, we note that the ATM-FFM model is able to provide a realistic efficiency improvement programme which incorporates a more objective way to set a target efficiency score including fixed factors. Our ATM-DFM model is able to programme a less extreme efficiency improving city development plan and may thus provide a meaningful contribution to balanced and robust planning for improving the efficiency of not only large cities in Asia, but also other cities in mature or emerging economies.
The present study has clearly demonstrated the great potential of DEA for comparative and decision-making purposes. In particular, the new DEA variants systematically put together in a decomposed DEA cascade system have clearly demonstrated the power of advanced DEA methods. It is also evident that the DEA methodology offers a new and innovative spectrum of models for further evidence-based comparative studies on the performance of cities and regions, while it also offers indications for the road to be chosen for enhancing their socio-economic performance.

Appendix A. Specification of the ATM DEA Model with DFM and FFM components
The ATM DEA model takes for granted-as indicated-a more normative perspective on the road to be taken by an efficient DMU on its way to the production possibility frontier. The cascade structure in Fig. 1 provides the analysis framework. First, we start from the standard CCR model and then incorporate the more appropriate DFM approach so as to obtain a more satisfying projection on the efficiency frontier. This procedure also allows us to identify-though the use of multiple objective quadratic programming-a set of optimal weights for the inputs, which indicate in relative terms how much a given input change may contribute to overall efficiency. This information thus provides quantitative guidance to a DMU on the relative input changes necessary to achieve an optimum. The same holds of course for the output. The next step is the calculation of the super-efficiency solution for all efficient DMUs. This procedure does not affect the previous DFM results, as the DEA scores for all inefficient DMUs are maintained. It only helps us to find an unambiguous ranking of efficient DMUs. Next, we have to address the target setting model. An introduction to Autoconfiguration Target Efficiency Scores (ATES), with a Fixed Factor of input α for DMU k (hereafter ATES k FF−α ) was already given in Sect. 5.1. The main question is of course the mathematical derivation of the ATES values in the ATM-DFM-FFM model. This derivation will now concisely be given.
The determination of the numerical value of ATES FF is done as follows (based on the logic of the DEA literatures (see : where x mk is the volume of input m (m = 1,…, M) for DMU k (k = 1, …, K); y sk is the output s (s = 1, …, S) of DMU k ; and v * m and u * s are the weights given to input m , Finally, the optimal solution for an inefficient DMU k can now be expressed by means of (10)-(13): The slacks s − * * , m ∈ ND and s + * * , s ∈ ND are not incorporated in (12) and (13), because these factors are 'fixed' or 'non-discretionary' inputs and outputs, in a way similar to the Banker and Morey (1986) model. A simple illustration of this model is given in the adjusted standard DEA Fig. 11. From Fig. 11, we also note that the ATM projection does not always reach the efficiency frontier; thus, it may be a meaningful improvement goal projection to reach an ATES FF value that is lower than 1. This is essentially a 'satisfying' approach in the sense of Simon (1955).